diff --git a/.gitignore b/.gitignore index 5afc0b0..7d1a224 100644 --- a/.gitignore +++ b/.gitignore @@ -1,66 +1,77 @@ # git-ls-files --others --ignored # Lines that start with '#' are comments. +# Working files 2015 +# Need to clean up bin/ and build/ for git +bin/ +build/ +build-mar14/ +build-new/ +buildqt/ +buildvc/ +src/qhulltest/qhulltest-mini.pro +src/qhulltest/RoadTest.h.cpp + # Backup and data files eg/eg.* *~ *.bak *.off *.x x.* r x x? r? # patch results *.rej # Build products tmp/* build-cmake/* build/Debug/* build/moc/* build/qhulltest/* build/Release/* build/cmake_install.cmake build/CMakeCache.txt build/CMakeFiles build/install_manifest.txt build/Makefile* build/*/Makefile* build/*/object_script* build/*/Release/* build/*/Debug/* build/*/MinSizeRel/* build/*/RelWithDebInfo/* lib *.a *.dll *.idb *.lib *.exe *.o *.md5sum # Qt files *.pro.user # DevStudio files *.bsc *.ncb *.pdb *.suo *.user *.ilk # CVS files CVS/* */CVS/* */*/CVS/* */*/*/CVS/* *.cvsignore # Other files working/ diff --git a/eg/make-vcproj.sh b/eg/make-vcproj.sh index 90f3450..faee9eb 100644 --- a/eg/make-vcproj.sh +++ b/eg/make-vcproj.sh @@ -1,83 +1,84 @@ #!/bin/bash # # make-vcproj.sh -- Make sln and vcproj files from CMakeLists.txt and qhull-all.pro # # [jan'12] Additional changes made by hand for qhull 2012.1. This file updated but not tested. # # $Id: //main/2011/qhull/eg/make-vcproj.sh#5 $$Change: 1476 $ # $DateTime: 2012/01/28 09:37:56 $$Author: bbarber $ if [[ ! -f CMakeLists.txt || ! -f src/qhull-all.pro ]]; then echo "Excute eg/make-vcproj.sh from qhull directory with CMakeLists.txt and src/qhull-all.pro" exit fi echo "Set up build directories..." if [[ ! -d build-prev ]]; then echo "Backup previous build" cp -r build build-prev && rm -r build fi rm -r buildvc buildqt mkdir -p build mkdir -p buildvc mkdir -p buildqt echo "Create vcproj files with cmake and qmake..." cd buildvc && cmake -G "Visual Studio 8 2005" .. && cmake .. cd .. cd buildqt && qmake -tp vc -r ../src/qhull-all.pro cd .. if [[ ! -f CMakeLists.txt || ! -f buildvc/qhull.vcproj || ! -f buildqt/qhulltest/qhulltest.vcproj ]]; then echo "qmake and cmake did not build vcproj files in buildvc/ and buildqt" exit fi for f in buildvc/*.vcproj buildqt/qhulltest/*.vcproj; do echo $f if [[ ! ${f##*INSTALL*} || ! ${f##*ALL_BUILD*} || ! ${f##*ZERO_CHECK*} ]]; then continue fi dest=build/${f##*\/} sed -r -e 's|[cC]:\\bash\\local\\qhull|..|g' \ -e 's|[cC]:/bash/local/qhull|..|g' \ -e '\|CMake| d' \ -e 's/;CMAKE_INTDIR=..quot;[A-Za-z]*..quot;//' \ -e 's/LinkIncremental="2"/LinkIncremental="1"/' \ -e 's/RuntimeLibrary[=]/RuntimeTypeInfo="false" RuntimeLibrary=/' \ -e 's/.*RuntimeTypeInfo."TRUE".*//' \ -e 's/buildvc/build/g' \ -e 's/buildqt/build/g' \ -e 's/\.\.\\\.\./../g' \ -e 's|\.\./\.\.|..|g' \ -e 's/c:\\qt\\[0-9]\.[0-9]\.[0-9]/\$(QTDIR)/g' \ -e 's|..\\build\\[a-zA-Z]*[\\/]([_a-z0-9]*.pdb)|..\\bin\\\1|g' \ -e 's|..\\build\\[a-zA-Z]*[\\/]([_a-z0-9]*.exe)|..\\bin\\\1|g' \ -e 's|..\\build\\[a-zA-Z]*[\\/]([_a-z0-9]*.lib)|..\\lib\\\1|g' \ -e 's|..\\build\\[a-zA-Z]*[\\/]([_a-z0-9]*.dll)|..\\bin\\\1|g' \ -e 's| [a-zA-Z]*[\\/]([_a-z0-9]*.lib)| ..\\lib\\\1|g' \ -e 's/"([_a-z0-9]*.exe)/"..\\bin\\\1/g' \ $f > $dest done -echo -e '\nExcept for qhulltest.vcproj,\n*.vcproj: delete empty File in Files section near end of vcproj' -echo -e '\nExcept for qhulltest.vcproj,\n*.vcproj: rename debug targets to qhull_d.dll, etc.' +echo -e '\nExcept for qhulltest.vcproj,\n*.vcproj: [mar'14 none] delete empty File in Files section near end of vcproj' +echo -e '\nExcept for qhulltest.vcproj,\n*.vcproj: [mar'14 where?] rename debug targets to qhull_d.dll, etc.' # If need to rebuild sln sed -e '\|Project.*ALL_BUILD|,\|EndProject$| d' \ -e '\|Project.*INSTALL|,\|EndProject$| d' \ -e '\|Project.*ZERO_CHECK|,\|EndProject$| d' \ buildvc/qhull.sln >build/qhull.sln echo -echo 'qhull.sln: Remove first line of each GUID list -- postProject\n.* > postProject' -echo 'qhull.sln: Remove four empty project sections' -echo 'qhull.sln: Remove first part of Global section.' +echo 'qhull.sln: Identify the GUID on the first line of each list.' +echo 'qhull.sln: Remove first part of Global section down to this GUID' +echo 'qhull.sln: Remove this GUID from each GUID list -- postProject\n.* > postProject' +echo 'qhull.sln: Remove five empty project sections' echo 'qhull.sln: Save as PC' -echo '*.vcproj: Remove libqhullcpp from AdditionalIncludeDirectories except for cpp' +echo '\nExcept for libqhullcpp, libqhullpcpp, qhulltest, user_eg3\n*.vcproj: Remove "..\src\libqhullcpp;" from AdditionalIncludeDirectories' echo echo 'Open qhull.sln with DevStudio and add qhulltest.vcproj' echo 'Add dependencies on libqhull libqhull6_p and qhullcpp' echo 'Change Linker>OutputFile to qhulltest.exe' echo 'Remove qhulltest via Configuration Manager from Release, Debug, etc.' diff --git a/html/Changes.txt b/html/Changes.txt deleted file mode 100644 index 724c6a1..0000000 --- a/html/Changes.txt +++ /dev/null @@ -1,890 +0,0 @@ -$Id: //main/2005/thid/src/Changes.txt#124 $$Change: 1496 $$Date: 2012/02/23 $ - - ThError.THIDlastError 20107 - throw ThError(10527, ""); - - install qInstallMsgHandler - - Store thid_sha1 along with data - store thidid, sha1, blockid, date -- but already in thid-info. Allows re-creation. - can't reallocate a blockid in the same second? - sha1-out-of-date only needs to go up through in-date ones. - Recursive algorithm -- depth first search -- writes new blockids as a blockid? - blockids become invalid if any component changes - thid sha1 - tuples of blockids => tuples of sha1 - tuples? of group thids -> tuples of sha1 - other tuples as is - where are groups stored? as a block? grabbed from header? -- usually -- but its compressed - - Add an 'unknown' test, equivalent to NULL. But then need to make it a type -Need - Dump program -- serialized/wire format as sha1 blocks - need blockid to sha1 and sha1 to blockid - Minimal reuse of blockIds - Review low-level syntax - Is Print/Dump simply well known names? - Auto propagate - Editor - Data representation as tuples - - - why can I have two views open of the same DB? - setThid should change focus to thid's window - - recursive calls require an explicit reference -- assumes a termination proof - strict aliasing - pointers are smart unless otherwise marked - - Editor - No wrap - - Label ID.next needed for goto's - Label ID.title needed for programs - Label 0.title needed for unresolved programs - addArgument makes 0.title an operand, but it is not used - addOperand of 0.title gets the non-label version - Undo the 0.title operand? - Reset its name? OK if 0? - Problem of literal vs. local literal - Do I need a new arg type for label? - - A call in the same depot - - concept of local literals - Add line numbers to ThCode parse errrors - Add atomic primitive -- ==6-> - Need assigned-type for mispellings - Need formated print instead of printSpace == == - Need ThCode::printProgram - check for empty arguments in ThCode (addArgument, etc.) -- around split? - Scan for valid primitive, maybe primitive - ?.?= ? first equals after matching pattern - ?==? -> ? first equals, last -> - -> ? No -> in labels - ? -> ? Try... then - - why is non-const operator[] selected for - QStringList compare= RoadUtility::splitFirst(instruction, comparison); - QStringList gotoLabel= RoadUtility::splitLast(compare[1], QString("->")); - - static QStringList splitFirst(const QString &s, const QString &sep, int from= 0, Qt::CaseSensitivity cs= Qt::CaseSensitive); - Add VAX configuration (e.g., clips) into perforce - - want a list of thids. A ThidListSelector("xpath") e.g., qml or goes to a localId - - Goal of storing/editing notes/code and executing code - Get language encodings - On Thid::writeToDisk, also write its ThDepot - static function QApplication::focusWidget() - #ifndef Q_MOC_RUN - - Need ThDiskBlock for Thid - get language. Then work on structured text. - Reserve Depot: ... as name for depots. - want to check in VAX configuration - Not written to disk, no bootBlocks either - - execute a Thid - UI - - Need to specify how a lower version handles a higher version. Note MIME is frozen at 1.0 - -============================================ -== At home -============================================ - - Get copy of git - -unsigned access to byte array via uchar c= uchar(...) - -As a pointer or return a reference if modified? - -reassign F12 to a different key -RegisterHotKey -- The F12 key is reserved for use by the debugger at all times, so it should not be registered as a hot key. Even when you are not debugging an application, F12 is reserved in case a kernel-mode debugger or a just-in-time debugger is resident. - -Need better solution than cout<< - -Need doc links between QApplication and QMainWindow - -Where to trap errors in UI -- throws caught by QMetaObject::activate when invoking a signal, e.g., gotoNewFile - -QApplication: contradicts constructor doc - it is usually a good idea to create it before any interpretation or modification of argv is done in the application itself. - -How to hid item-ids in text -- should be a glyph How to work with QRegExp -QTextFormat::UserObject - -int QTextCursor::blockNumber () const -Returns the number of the block the cursor is in, or 0 if the cursor is invalid. -Note that this function only makes sense in documents without complex objects such as tables or frames. - -Need context menu and Tools->Bookmarks menu for 'add bookmark'. QtCreator only has an add bookmark button -Peter Abelard (1079-1142) diversity of authoratative opinion - -QTest -- ignore failures mode - -In debugger, shows as QObject instead of QTextDoument - QTextDocument *text= main_ui.content_view_a->document(); - - // QList displays as int in debugger - // Problem of readLine() w/o line terminator -- runs forever - // No equivalent to "has" for a QList (index within bounds - -Provide a template layout for .h with constructors, virtual methods, get/set, etc. - -Add SplitFirst and SplitLast to QString::SplitBehavior - ---------------- -programs.txt - -Fix spacing in snippets - -Get MIME standard and yaml standard - -Guidelines ----------- -fieldAt(const char *fieldStart, const char **fieldEnd/*= 0*/) const - -Support -------- - -QDir::remove() -- how to tell reason that a remove failed? - -Why is qrc code in QDir? -void Q_CLEANUP_RESOURCE ( name ) -Unloads the resources specified by the .qrc file with th - -List of filename substrings to ignore. Auto switch between files on alt-o - -QString::chop not referenced from remove() - -Create from Usage gets $SymbolName$ and $SymbolType$ reversed in snippet - -'foreach keyword' doesn't say how to create foreach for yourself. Not in index. - -foreach requires T::const_iterator, begin(), and end() - -Create implementation not defined for multiple lines - -How to use QStringBuilder over multiple assignments - -Refactor Rename is a modal dialog box. Should allow navigation to investigate hits. - -How to open a QFile for exclusive access - -Change Signature does not preserve internal spacing - bool tryCheckOwner(const ThDiskBlockId &b, const ThidHandle &owner, int howOwned); - -QByteArray documentation -If data is 0, a null byte array is constructed. -QByteArray::QByteArray(const char *data, int size) -{ - if (!data) { - d = &shared_null; - } else if (size <= 0) { - d = &shared_empty; - - -Comments can do name expansion on initial or internal cap - -QTestLib manual -Creating a Benchmark - -To create a benchmark, follow the instructions for crating a tes - -Need $SymbolClass$ (complements $SymbolName$ and $SymbolContext$ - -$end$ did not work (all selected) -- $SymbolContext$$end$ - -Refactor Selection, should run Create Implementation on each line in selection - -Snippets ---------- - -@token@ @1@ @xmlns:thi@ @RS_FIRST@ @AT_START@ @{\rtf@ @^\{\\rtf\d+ ?@ @RA_ATTRIBUTE@ @@ @AT_NEXT_WHERE@ @@ @pv@ -@pv@ @freepool@ @1@ @129@ @234232@ @pv@ - -@hd@ @thdisk@ @1@ @diskBlockId@ @hd@ -@pv@ @thdisk@ @1@ @0x32234221@ @pv@ - -#if defined(Q_CC_MSVC) // Disable warning for 0x80 as type 'char' -# pragma warning(disable: 4309) /* 'initializing' : truncation of constant value */ -#endif - - -ToDo ----- - need Statistics object using unique ids. - change to const char * - static const QString ThidHex128RE; //!< "-1234567890abcdef..." 32 hex digits, md5sum - - Change ThDiskBlock to QObject - Rename ThItem to ThBlock - use RoadError - convert ItemFlags to QFlag - Move flags to ThItem from ThAbstractItem - - ThSettings * ThSettings::s_thid_configuration= 0; - remove handleForThid -- using field instead - determineThidFromName -- convert string to char array - Rethink ThidInfo format -- how to name things - ThField.h is not standalone - Fixed moc by linking with the the 2009.05 version - qHash(Thesa::ThidIdentifier *t) { return qHash(static_cast(*t)) ^ qHash(t.second); }; - Bug in notes-dump.xml -- \n"par" - - need conventions for error reporting e.g. determineHandleForThid - - Rename determineHandle to assignHandle - -Test coverage - Read all routines in _test and *.h and make sure that they match - Check all error codes in _test and *.cpp - -============================================ -== History -============================================ - -.............This file lists all changes to thid..................... - -[Nov'11] - Can create a persistent thid and execute 'Hello World' - -[feb'11] - Can create thid/.. with boot blocks - -[jan'11] - Can create and read bootBlock for a ThDiskBlockPool - -[nov'10] - Can open an empty database and manipulate its configuration (first sector, etc) - Can find and allocate a previously freed block id - - get number of sectors needed - if fits, rewrite as free sector and remainders - get enough sectors, - if any not free, check if in freepool, add previous to freepool and repeat - if last fits, add previous to freepool and break - if out-of-sectors - allocate more sectors (i.e., advance size of remainders) - rewrite as free sector and remainders - next_sector is after allocated sector - - Write a block id - -[oct'10] - Can read and write ThDiskBlockHeader from ThDiskBlock - Need blockIds on disk > Need BlockPool and free blocks > Need files - -[aug'10] Want data on disk. - A pool file of everything - A free list is a list of blockids. duplicated on the disk - - -============================================ -== Notes on QAbstractModelIndex -============================================ - -Incomplete description "The underlying data model...". This is describing a tableView, not the item view. -Make parent clear. - -The root is a table of rows and columns. -Each cell of the table is a collection of role:value pairs, a set of flags, and an optional table (hasChildren) -Roles are numbers, 0..31 are reserved by Qt. The values are QVariant -The 'index' of a cell is its row, column, and parent in the model. -'sibling' is the same as index(row,column, index.parent()) -Document meaning of QModelIndex::operator< - -Common models - A list, column 0 - A table, no children - A tree, column 0 has chidren (c.f., parent()). Other columns can provide associated information. - -Model Subclassing reference - Read-only access - Editable access - No mention that QListView requires EditRole for data() - No mention that QDataWidgetMapper::populate invokes QItemDelegate::setEditorData which requires EditRole - void QDataWidgetMapperPrivate::populate(WidgetMapper &m) - ---- -Why enabled if invalid -addressbook example -Qt::ItemFlags TableModel::flags(const QModelIndex &index) const -{ - if (!index.isValid()) - return Qt::ItemIsEnabled; - - return QAbstractTableModel::flags(index) | Qt::ItemIsEditable; -} -//! [7] - ----- - -Methods alphabetical with [private] -Editor.gotoNextLocation -create... is same as new... but void return - -$(QTDIR)\include -$(QTDIR)\include\Qt -$(QTDIR)\include\QtCore -$(QTDIR)\include\QtGui -$(QTDIR)\include\QtHelp -$(QTDIR)\include\QtNetwork -$(QTDIR)\include\QtOpenGL -$(QTDIR)\include\QtScript -$(QTDIR)\include\QtSql -$(QTDIR)\include\QtSvg -$(QTDIR)\include\QtTest -$(QTDIR)\include\QtUiTools -$(QTDIR)\include\QtWebKit -$(QTDIR)\include\QtXml -$(QTDIR)\include\QtXmlPatterns -$(QTDIR)\src - -Source maintenance (jul'11) - Search for missing P4: \:[^a-zA-Z0-9]*\$ - Search for missing date: -2010 - -============================================ -== Notes on ThDisk -============================================ - -Problem of ThidIdentifier::thidHash32 (for ThidDepot::computeThidIdentifer) -and ThDiskThidPool::thidHash32 for hash bucket - - By default, hash of depot+label w/ depot is itemid - getunique find an item id in the same bucket by common bits - Sorted and Unsorted 4-byte hash + 8 byte block-id - QMultiHash for staging -- store compress -- 55K - Bits for Recent and New - Need split and merge buckets - write QMultiHash and buckets to two files - rebuild by streaming into large QMultiHash, and flushing to bucket - cally ygetidhash ;;get HashItemID, OtherHash for ItemID and BlockID, Different? - cally yaddidhash ;;.add HashItemID, OtherHash, BlockID to ItemTable and ItemCache - ynewitem creates ItemId for LabelFieldId, optional TitleId and precomputed size - called by createitem ;;create ItemId, BlockId, and Title for Syntax .label, TitleID, and DepotItemId with SyntaxTable - called by maybenew ;;maybe new ItemId and Title at TitleText and TitleID - - want ThItemId with a ThDiskBlockId containing title, owner itemid, depot itemid, and text - want title lookup to itemId and diskBlockId - - Change to BlockType enum - - set next_empty+sector at boot - next_empty_sector -- always valid - reset after emptied - search from end of file - sector header is zero, sector tail is zero - allow intermediate mode for sector rewrites - -A) Need a label hash -- same as Thesa for 24-bit IDs. Hash function by Depot's itemId size - ygetidhash -- Hash a 24-bit itemid and its blockid (i.e., Label) for shared itemid-label buckets - ylblhash -- 32-bit Hash of itemid label and DepotId (8-bit) - remidhash -- removes hash-itemid and its blockid from curcache. - -B) Need a multi-level hash for - LabelHash -> BlockId of corresponding ItemId - One hash of QVariants on separate hash for each? - Is LabelHash persistent. If so, can add a lot at once, like Xref, then parcel out to Buckets as needed. - e.g., when importing ids. Then problem of conflicts. - For now, a simple hash table. If sorted, it might compress better - -ThDisk::newItem -- tuple format for ItemId with aliases and various owned data - -Need to assign unique ItemId for Label in DepotId. By default use label hash (ylblhash). Unique in ThDisk. -Retry n times, then unique in Depot by fewest hits. - - delitem -- All parts of an item - itemblock -- diskblockid - tgaliasid -- TopItemId for this alias - tgaliases -- list of aliases for this itemId (moveitem fields to new TopItemId) - if alias, someoneelse will own any text blocks, etc. (tgowned) - remidcache -- In memory cache of itemid->diskBlockId - delsig -- signature or conversion for itemId - tgowned -- text, code, etc. with matchig howowned - _adddel -- text blocks held onto for a while - _addid -- resets xref itemid for text, xridcode, and xridtitle - remdatas -- remove celldata for itemid - item.-bucket -- Contains itemid's and label's to diskblockid by hashbucket - -ss:curcache - itemid->blockid -- includes hash of label as itemid - -delsig convert.-routines - ifconvert -- if Label is a typeid conversion from item - delptr (tsisptr) -- isPointer signature (only one of type?) - yupdstring(tsidlist) -- signature list - -block.sym - fifieldid -- disk data - tglabel -- type of disk data - -bkheld blocks -- in separete pool -- or separate list for each size as before - itemid blocks - text blocks - - m_unparsedTexts.insert(qMakePair(uri, encoding), result); - - -==================================== -== Notes -==================================== - -protocol buffers - wiretype 2, field 0, byte count for header - -==================================== -== Notes on git -==================================== - -Git - Where to put the special value use sha1 convention - how to check for all zero - - -Check gitmailing list for messages titled "A note from the maintainer", "What's in -git.git (stable)" and "What's cooking in git.git (topics)" and - -git verify-pack - sha1 sorted -> type, size, offset, delta-base - most are small! More than half are diffs. conpressed is larger for small diffs - git a --depth clone for ghull - -git update-index - --info-only is used to register files without placing them in the object database. This is useful for status-only repositories. - - git ls-files -s - 100644 6569cf607b18b84f39ebee613471f270e42cfbdc 0 string-list.h - 100644 3007f7d5a6279c14a7c29efdc752dbbc41218c76 0 submodule.c - 100644 4c0269d67933659da5ff81e53c21b5f25ca8cf9d 0 submodule.h - 100644 88601200114f857a57214a9bf0d02ffd39a83504 0 symlinks.c - 100644 1b97c5465b7d9e4404e11668b44c5c507a302d4a 0 t/.gitattributes - 100644 7dcbb232cd876cb7b976443cc586f60a94ab92bf 0 t/.gitignore - 100644 bd09390d3208d7eac362cd9cf45f7dde623c4ae6 0 t/Makefile - 100644 dcd3ebb5f2dcdbf15ca0e4a043b45cd2fc36cbb5 0 t/README - 100755 d5bab75d7da49ebb53e368d67f6b867f5417a125 0 t/aggregate-results.sh - 100644 396b9653a3ad80490cf360c86a910edff58862a2 0 t/annotate-tests.sh - - ----------- -gitrepository-layout.html -HowTo/maintain-git.txt -- what the branches mean -git-rev-list -- identify commits and objects log and pack -git-receive-pack -- works with git-send-pack and calls hooks sha1 sha2 - ------------- -technical/pack-protocol.txt -- details of git pack transfer protocol - -technical/pack-format.txt -- where the bytes are. idx and pack files - -technical/pack-heuristics.txt -- how to create a pack and thin packs - - What is a "thin" pack? - - Use of --objects-edge to rev-list as the upstream of - pack-objects. The pack transfer protocol negotiates that. - - - larger objects tend to be "more recent" (Linus' law: files grow) - - we actively try to generate deltas from a larger object to a - smaller one - - this means that the top-of-tree very seldom has deltas - (i.e. deltas in _practice_ are "backwards deltas") ----- -git-notes.sh -- store notes for commits as a directory with sha1 filenames /refs/notes/sha1 - -read-cache.c -- read and search the cache/index - Can create an alias to an entry - static struct cache_entry *create_alias_ce(struct cache_entry *ce, struct cache_entry *alias) - reads cache/index into memory. Builds hash structure - ---- -git/cache.h -- directory cache, comments - - file status, sha1, name - ... - TREE sha1 of corresponding tree object - sha1 of index - - gitlink -- a submodule - add_name_hash -- name index in cache - OBJ_COMMIT = 1, - OBJ_TREE = 2, - OBJ_BLOB = 3, - OBJ_TAG = 4, - /* 5 for future expansion */ - OBJ_OFS_DELTA = 6, - OBJ_REF_DELTA = 7, - - # Gitlink is a commit - S_ISGITLINK(mode) ? OBJ_COMMIT : - # Cache used in multiple environments? - #define GIT_NOTES_REF_ENVIRONMENT "GIT_NOTES_REF" -#define REFRESH_IGNORE_SUBMODULES 0x0010 /* ignore submodules */ -static inline int hashcmp(const unsigned char *sha1, const unsigned char *sha2) -struct ref { - struct ref *next; - unsigned char old_sha1[20]; - unsigned char new_sha1[20]; - char *symref; -extern struct ref **get_remote_heads(int in, struct ref **list, int nr_match, char **match, unsigned int flags, struct extra_have_objects *); - -git-apply a patch -git-remote - manage set of tracked repositories - -git-clone ---shared --s -When the repository to clone is on the local machine, instead of using hard links, automatically setup .git/objects/info/alternates to share the objects with the source repository. The resulting repository starts out without any object of its own. - -config() -core.gitProxy - -==================================== -== Thid Design, To Do, and Programming Style -==================================== - -[Feb 2008] - -does a Field know its type? It ought to, though can always look it up. The later avoids two type systems, conversion and consistency - -use QMetaType as the type system, it's just names, but ties into QVariant - -Want value semantics, owner semantics - -Should a field name be a thid? Can then call it what you will - -ItemReference.toName() - -Implemenetation ideas - Staircase Join (used for XQuery) - -QMap -Thid - context, number handle, rev desc - => flags, name, thidformat, handle - immutable, appendable, ordered, mutable, mastership - -QMap -ThField - context, name handle, date desc - => value handle, op, flags - Vesta op for singleton, set, merge - Similar to QObject dynamic properties, string name, QVariant value - -QMap -ThName - context (namespace) - string - => flags - includes absolute and relative dirpaths - immutable - QString name= ThString::stringForHandle(m_nameHandle); - -QMultiMap -ThNumber - int128 -- includes fingerprints - => flags - -ThList -QList - -ThHandleIndex -QMultiHash - -ThStringIndex -QMultiHash - -DeletedHandles -QSet - -All data is cached in memory - -On disk - ThidComponent stores ThField hierarchy down to thid values - Split into mutable and immutable pieces - Mutable is specific to a location, and may be replicated elsewhere - Immutable is specific to the thid revision and may be replicated - Appendable means Add only - Set means add, del, set - -1. Data in memory -2. Read all data from disk -3. Flush unused data -- fairly expensive, at the thid level - -Vesta has mutable attributes only if context is mutable - -not applicable - Not xref value=>handles -- containing handles instead of actual - -vesta - Vesta does attributes by shortid,name,value, add,del,datetime -- has advantage that handle never goes out of date, and easily merged. One advantage of handles is for hierarchical structure. can have a value and sub-values. - - VMemPool -- packed objects == thhandle - VestaSource -- base type == thid - VestaAttribs -- attributes of a VestaSource - Val.H -- any SDL value, including bindings (BindVC) - -th add sdfA3_2007.rtf -th get sadA* - -want to add a topic file with ids and titles -a biblio file with entries -memory-based id/file -memory-based id/titles -memory-based xref -disk-based id/file -disk-based xref -disk-based id/titles/owner -- a form of xref -network-based id/file -network-based id/titles -network-based xref -a depot indexes all of its content -all servers index all of their content - -change type tag to a char[4] -Need recent list -Work list editor, based on ListView -Work list and item list accelerators -Aliased items -Condensed view -Paragraph view -Line editor -Tree editor -Add all data to expanded view (e.g., thid ID) -Search by thid -Logging -- multi-level -Error handling -Gprof -Performance counters -Versioning -Remote access -Merging -Pointer machine -CppCastingHelper -- in xml/query/util -PlainSharedPtr -- never does a deref - -port logging model to Qt -index="" for topics in nodes-dump.xml -title= replaces element name -attributes are tool tip -TitleOf is all item-title elements of 'root' -ContentOf is contents of item-def -fix scroll of content - -==================================== -== thnode parser -==================================== - -Problems - -- Record bad files with sufficient state to analyze, then skip - -- unstructured text - -- \b in a .Title or a \i in a .J -- should be an error, need to continue - -- a blank indented line \li333 \ - -- illegal markup - ;;2343 ;;@asdfsf asdfsdf - - not closed properly, see nodes.xml - not formated properly, see nodes.xml - -==================================== -== C++ Style conventions for Thid -==================================== - - -Append '_' to distinguish parameter names from member names -Use all lower-case, abbreviated for local declarations and parameters declared at top. They act as pronoun references. -Use camel-case for class components. -Use initial caps for class names -Define all entities as const by default -All blocks defined by {...} -- if () x=1; is illegal -Use Stroustrop formatting -Set local variables instead of building a long expression - ThItemModel model = db.getModel(); - mainwin.setSourceModel(model); -vs. - mainwin.setSourceModel(db.getModel()); - - : modelSource(source), curThid(ThLocalID_null) - , thidList(db->listForModelSourcedb()) -"explicit" means a non-converting constructor with one argument -Place static strucs, fields, and methods last -On whether to use nsFoo aFoo (bFoo) or nsFoo aFoo = bFoo: everyone agrees, the form with "=" looks better - -From Cwalina, K., Abrams, B., Framework Design Guidelines, 2006 -Use camel casing for all parameters -Use PascalCase for all public IDs -Only capitalize two-letter acroynms (e.g., IOFile) -No public fields, use properties instead. -Use m_ and s_ for fields and static fields (J. Richter) -No underscores, hyphens, etc. -Enumerations -- use plural names for bit fields (e.g., ConsoleModifiers), otherwise use singular names. Do not use Enum, Flag, or Flags suffixes, do not give enums a common prefix -Try boolean predicates in an if statement, e.g., if(collection.Contains(item) vs. IsContained(item) -add... -- append, insert, or otherwise add something to a collection - -QObject (e.g., QScriptEngine) -QSharedData (e.g., QHash) -Q_DISABLE_COPY frequently used, e.g., QTokenizer -private d pointer to private data (e.g., QTestData) -q pointer back to public, e.g., QObject -public members in private data -class with private data using m_... -static data with s_.... - -class ThidInfo { - friend class ThidInfoPrivate; - - ThidInfoPrivate *d; - -//== class variables - -public: -//== constants - static const QString Separator; - enum ThidFormat : char { - NoFormat=0 - }; - -//== constructor, destructor -//== conversion -//== accessor -//== predicate -//== mutator -//== class function - -};//ThidInfo - -=============================== -== qHash for QHash -=============================== -Dropped jul'11 - -uint -qHash(Thesa::Thid *t) -{ - return qHash(t->thidIdentifier()); -};//qHash - - -=============================== -== #pragma message(Remind "abc" ) -=============================== -//! Add fixup error log -//! Windows Developer Journal, 197?) -//! Alan De Smet -- Microsoft Visual C++ Tips and Tricks - -#ifndef Q_MOC_RUN -#define Stringize( L ) #L -#define MakeString( M, L ) M(L) -#define MyLine MakeString( Stringize, __LINE__ ) -#define Fixup __FILE__ "(" MyLine ") : warning C1111: FIXUP " -#pragma message(Remind "abc" ) -#endif -// Can not define 'fixup' as #pragma - - - -void ThDiskBlock:: -setBlockOwner(const ThidIdentifier &depot, const ThidIdentifier &thid, HowId how) -{ - if(how!=NoHow && how!=HowInvalid){ - ThFlagsInt code= how&HowCodeMask; - if(code==0){ - throw ThError(10069, "ThDiskBlock: can not set howOwned to special code %u. Expecting NoHow(0) or HowInvalid(0x10000000)", 0,0,0.0, quint64(how)); - } - if(code!=HowItemBucket){ - if(how&~HowCodeMask){ - throw ThError(10070, "ThDiskBlock: extra bits (0xFFFFFF00) set for howOwned %u", 0,0,0.0, quint64(how)); - } - if((code>HowMaxSpecial && codeHowMaxOwned){ - throw ThError(10071, "ThDiskBlock: unknown code for setHowOwned %u. Expecting 0..9 or 0x60..62", 0,0,0.0, quint64(how)); - } - } - } - owner_depot= depot; - owner_thid= thid; - how_owned= how; -}//setBlockOwner - -============================================ -== DevStudio debugger -============================================ - -Alan De Smet's suggestions - Workspace Whiz - #pragma message(Reminder, "text") - Resource Leaks: Detecting, Locating, and Repairing your leaky GDI code - Watch window: @err or @err,hr for GetLastError and HRESULT - p,10 shows 10 elements at p - - Debugging: - __asm int 3; or __debugbreak (Common Expression Evaluator) - Watches - @clk ... @clk=0 Show and reset value of clock - QuickWatch window - Execute functions e.g., dumpT(p) which calls OutputDebugString or printf - SetThreadName - @tib+24 is the Thread ID (thread information block) - set "Microsoft C++ Exception" to Stop Always (Debug > Exceptions) - Breakpoints - on argument value (condition dw esp+0x8==3) where 0x8 is the arg offset - Avoid the very slow emulation mode -- no expressions - 4 hardware data breakpoints -- may be triggered by process swap requiring a reboot - Set breakpoint count to large value. Get actual count at crash. Break just before. - Use breakpoint by name to handle edits - Casts need exact type name (watch variable then look in properties) - For pObject local while CMyClass defined in foo.dll - {,,foo.dll}(CMyClass *){*}pObject - Disassembly - ^G EIP -- Goes to current location - - -Through the Interface: Advanced Visual Studio debugging... July 24, 2006 - Or HKEY_LOCAL/Software/MS/VS/8.0/Native/StepOver - autoexp.dat in devstudio/Common7/Packages/Debugger - [ExecutionControl] - CString::CString=NoStepInto # skips CString constructor - CString::CString::operator==NoStepInto # skips CString::operator= - CString::*=NoStepInto # skips all of CString - At most 256 characters - No multi-line output - Can develop an AddIn for more complex displays - $ADDIN -- Customizing the Visual Studio Debugger Display of Your Data (msdn aa730838 and 8fwk67y3) - Very Advanced Debugging Tips - Load debug symbols (see blogs.msdn/calvin_hsia/... 246382 - Register Window -- set Show Effecive Address) - Common Expression... - Add /MAP to LINK for full decorated names - - Writing custom visualizers for Visual Studio 2005 [blog.csdn.net/wilton] - Match templates with type. Template parameters are $T1, $T2 - Match multiple types with Foo|Bar - Preview must be one line. Use #(...) for a comma list of expressions using $c - Preview sizeof() does not work. - Avoid using colon, paren, brackets within strings and character literals - The children block shows a sorted list (+[*]), optionally named with name:expr - Names may have brackets - Add sub-blocks by referencing an object with a visualizer - Array expression [$c.start, 4c] - Show all fields [$c,!] without autoexpand or visualizers - #array with expr w/ $i, size, base w/o $e formating (offset), rank $r (multi-D). - Follow #array with value autoexpander #array(..):&$e where $e is *expr - Can be anything (except for #if) - #if () (...) #elif (..) #else (..) - #switch () #case 0x000 (...) #case ... #default (...) Do not use #array - #list ( head: $c.head, next: nextNode, skip:stop-here, size:max-count):display-expression with $e - #tree ( head: $c head, left: leftNode, right: rightNode, size: max-count, skip: stop-here ), - The stringview block displays a modal text, xml, or html visualizer. - No literal string in value expressions. Can't escape HTML - - Display code ,su is string in quotes. ,sub is string w/o quotes - - HKLM\SOFTWARE\Microsoft\Windows NT\CurrentVersion\AeDebug\UserDebuggerHotKey registry key. Modifying this you can set the keycode (scancode) that is registered as a global hotkey for the debugger. By default it's value is zero (0x0, F12), but you can set it to eg. 0x2F (VK_HELP) - - ----- -EOF - diff --git a/html/qh-code.htm b/html/qh-code.htm index 25ea608..4141718 100644 --- a/html/qh-code.htm +++ b/html/qh-code.htm @@ -1,954 +1,954 @@ Qhull code

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[4-d cube] Qhull code

This section discusses the code for Qhull.

Copyright © 1995-2012 C.B. Barber

»Qhull code: Table of Contents

»Performance of Qhull

Empirically, Qhull's performance is balanced in the sense that the average case happens on average. This may always be true if the precision of the input is limited to at most O(log n) bits. Empirically, the maximum number of vertices occurs at the end of constructing the hull.

Let n be the number of input points, v be the number of output vertices, and f_v be the maximum number of facets for a convex hull of v vertices. If both conditions hold, Qhull runs in O(n log v) in 2-d and 3-d and O(n f_v/v) otherwise. The function f_v increases rapidly with dimension. It is O(v^floor(d/2) / floor(d/2)!).

The time complexity for merging is unknown. Options 'C-0' and 'Qx' (defaults) handle precision problems due to floating-point arithmetic. They are optimized for simplicial outputs.

When running large data sets, you should monitor Qhull's performance with the 'TFn' option. The time per facet is approximately constant. In high-d with many merged facets, the size of the ridge sets grows rapidly. For example the product of 8-d simplices contains 18 facets and 500,000 ridges. This will increase the time needed per facet.

As dimension increases, the number of facets and ridges in a convex hull grows rapidly for the same number of vertices. For example, the convex hull of 300 cospherical points in 6-d has 30,000 facets.

If Qhull appears to stop processing facets, check the memory usage of Qhull. If more than 5-10% of Qhull is in virtual memory, its performance will degrade rapidly.

When building hulls in 20-d and higher, you can follow the progress of Qhull with option 'T1'. It reports each major event in processing a point.

To reduce memory requirements, recompile Qhull for single-precision reals (REALfloat in user.h). Single-precision does not work with joggle ('QJ'). Check qh_MEMalign in user.h and the match between free list sizes and data structure sizes (see the end of the statistics report from 'Ts'). If free list sizes do not match, you may be able to use a smaller qh_MEMalign. Setting qh_COMPUTEfurthest saves a small amount of memory, as does clearing qh_MAXoutside (both in user.h).

Shewchuk is working on a 3-d version of his triangle program. It is optimized for 3-d simplicial Delaunay triangulation and uses less memory than Qhull.

To reduce the size of the Qhull executable, consider qh_NOtrace and qh_KEEPstatistics 0 in user.h. By changing user.c you can also remove the input/output code in io.c. If you don't need facet merging, then version 1.01 of Qhull is much smaller. It contains some bugs that prevent Qhull from initializing in simple test cases. It is slower in high dimensions.

The precision options, 'Vn', 'Wn', 'Un'. 'A-n', 'C-n', 'An', 'Cn', and 'Qx', may have large effects on Qhull performance. You will need to experiment to find the best combination for your application.

The verify option ('Tv') checks every point after the hull is complete. If facet merging is used, it checks that every point is inside every facet. This can take a very long time if there are many points and many facets. You can interrupt the verify without losing your output. If facet merging is not used and there are many points and facets, Qhull uses a directed search instead of an exhaustive search. This should be fast enough for most point sets. Directed search is not used for facet merging because directed search was already used for updating the facets' outer planes.

The check-frequently option ('Tc') becomes expensive as the dimension increases. The verify option ('Tv') performs many of the same checks before outputting the results.

Options 'Q0' (no pre-merging), 'Q3' (no checks for redundant vertices), 'Q5' (no updates for outer planes), and 'Q8' (no near-interior points) increase Qhull's speed. The corresponding operations may not be needed in your application.

In 2-d and 3-d, a partial hull may be faster to produce. Option 'QgGn' only builds facets visible to point n. Option 'QgVn' only builds facets that contain point n. In higher-dimensions, this does not reduce the number of facets.

User.h includes a number of performance-related constants. Changes may improve Qhull performance on your data sets. To understand their effect on performance, you will need to read the corresponding code.

GNU gprof reports that the dominate cost for 3-d convex hull of cosperical points is qh_distplane(), mainly called from qh_findbestnew(). The dominate cost for 3-d Delaunay triangulation is creating new facets in qh_addpoint(), while qh_distplane() remains the most expensive function.

»Calling Qhull from C++ programs

Warning: The C++ interface to Qhull is new and incomplete. You will need to extend the interface for all but the simplest applications. You will need to understand the data structures and read the code. Most users will find it easier to call Qhull as a program.

Note: Please download the 'next' branch from git://gitorious.org/qhull/qhull.git

Qhull's C++ interface provides wrapper classes for Qhull and Rbox. It provides access to Qhull's data structures. Most of the classes derive from the corresponding qhull data structure. For example, QhullFacet is an instance of Qhull's facetT.

The main methods are
  • RboxPoints.appendRandomPoints -- append random points according to rbox options.
  • Qhull.runQhull -- construct the convex hull of the input points
  • Qhull.outputQhull -- write output according to Qhull options
The sample program, user_eg3.cpp, duplicates Qhull's facet dump (option 'f'). Example (c.f., user_eg3 eg-100) 
     RboxPoints rbox;
     rbox.appendRandomPoints("100");
     Qhull qhull;
     qhull.runQhull("", rbox);
     QhullFacetList facets(qhull);
     cout<< facets;

The C++ iterface for RboxPoints redefines the fprintf() calls in rboxlib.c. Instead of writing its output to stdout, RboxPoints appends the output to a std::vector. The same technique may be used for calling Qhull from C++.

  • Run Qhull with option 'Ta' to annotate the output with qh_fprintf() identifiers.
  • Redefine qh_fprintf() for these identifiers.
  • See RboxPoints.cpp for an example.

A more flexible approach extends Qhull's classes. For example, to access the vertices of a QhullFacet, define a constructor of QhullVertexSet that takes a QhullFacet as a parameter.

With care, you may create multiple Qhull instances, but only one thread may use qh_qh, qh_qhstat, and qhmem at a time (i.e., most of libqhull, the original C program). only one instance may be active at time. The global pointer qh_qh points to Qhull's data structure, QhullQh. The class UsingLibQhull checks that qh_qh is correct.

Qhull objects have the entire qhull data structure, so they can explore this data structure independent of libqhull. You can use any method that does not refer to UsingLibQhull, or invoke methods that refer to UsingLibQhull. You may also use any method in libqhull that does not reference qh_qh, qh_qhstat (i.e., does not include the macro 'qh', zinc_, etc) and does not allocate or deallocate memory via mem.c. In particular, you can call most of the qset macros and functions, allowing you to explore the data structure with 'foreachFacet_(), etc.' You can call all of the qset.h functions if you turn off Qhull's memory manager (qh_NOmem in mem.h)

»Cpp questions for Qhull

Developing C++ code requires many conventions, idioms, and technical details. The following questions have either mystified the author or do not have a clear answer. See also C++ and Perl Guidelines, C++ interface to Qhull. and FIXUP in the code. Please add notes to Gitorious wiki.
  • FIXUP QH11026 Should return reference, but get reference to temporary 
    iterator Coordinates::operator++() { return iterator(++i); }
  • size() as size_t, size_type, or int
  • Should all containers have a reserve()?
  • Qhull.feasiblePoint interface
  • How to avoid copy constructor while logging, maybeThrowQhullMessage()
  • How to configure Qhull output. Trace and results should go to stdout/stderr
  • Qhull and RboxPoints messaging. e.g., ~Qhull, hasQhullMessage(). Rename them as QhullErrorMessage?
  • How to add additional output to an error message, e.g., qh_setprint
  • Is idx the best name for an index? It's rather cryptic, but BSD strings.h defines index().
  • Qhull::feasiblePoint Qhull::useOutputStream as field or getter?
  • Define virtual functions for user customization of Qhull (e.g., qh_fprintf, qh_memfree,etc.)
  • Figure out RoadError::global_log. clearQhullMessage currently clearGlobalLog
  • Should the false QhullFacet be NULL or empty? e.g., QhullFacet::tricoplanarOwner() and QhullFacetSet::end()
  • Should output format for floats be predefined (qh_REAL_1, 2.2g, 10.7g) or as currently set for stream
  • Should cout << !point.defined() be blank or 'undefined'
  • Interface for UsingLibQhull::globalAngleEpsilon(), globalDistanceEpsilon, etc.
  • Interface for UsingLibQhull::globalDimension
  • Set up globals for thread-private storage (redefine macros qh, qhstat, etc)
  • Is Q_GLOBAL_STATIC non-threaded/threaded, needed for Qhull?
  • Infinite point as !defined()
  • qlist and qlinkedlist define pointer, reference, size_type, difference_type, const_pointer, const_reference for the class but not for iterator and const_iterator vector.h -- 
    reference operator[](difference_type _Off) const
  • When forwarding an implementation is base() an approriate name (e.g., Coordinates::iterator::base() as std::vector::iterator).
  • When forwarding an implementation, does not work "returning address of temporary"
  • Also --, +=, and -= 
    iterator       &operator++() { return iterator(i++); }
  • if vector inheritance is bad, is QhullVertexSet OK?
  • Should QhullPointSet define pointer and reference data types?
  • Allow UsingQhullLib to work with static allocation of qh_qh

»CoordinateIterator

A CoordinateIterator or ConstCoordinateIterator [RboxPoints.cpp] is a std::vector<realT>::iterator for Rbox and Qhull coordinates. It is the result type of RboxPoints.coordinates().

Qhull does not use CoordinateIterator for its data structures. A point in Qhull is an array of reals instead of a std::vector. See QhullPoint.

»Qhull

Qhull is the top-level class for running Qhull. It initializes Qhull, runs the computation, and records errors. It provides access to the global data structure QhullQh, Qhull's facets, and vertices.

»QhullError

QhullError is derived from std::exception. It reports errors from Qhull and captures the output to stderr.

If error handling is not set up, Qhull exits with a code from 1 to 5 [qh_ERR* in libqhull.h via qh_exit() in usermem.c]. The C++ interface does not report the captured output in QhullError. Call Qhull::setErrorStream to send output to cerr instead.

»QhullFacet

A QhullFacet is a facet of the convex hull, a region of the Delaunay triangulation, a vertex of a Voronoi diagram, or an intersection of the halfspace intersection about a point. A QhullFacet has a set of QhullVertex, a set of QhullRidge, and a set of neighboring QhullFacets.

»QhullFacetList

A QhullFacetList is a linked list of QhullFacet. The result of Qhull.runQhull is a QhullFacetList stored in QhullQh.

»QhullFacetSet

A QhullFacetSet is a QhullSet of QhullFacet. QhullFacetSet may be ordered or unordered. The neighboring facets of a QhullFacet is a QhullFacetSet. The neighbors of a QhullFacet is a QhullFacetSet. The neighbors are ordered for simplicial facets, matching the opposite vertex of the facet.

»QhullIterator

QhullIterator contains macros for defining Java-style iterator templates from a STL-style iterator template.

»QhullLinkedList

A QhullLinkedLIst is a template for linked lists with next and previous pointers. QhullFacetList and QhullVertexList are QhullLinkedLists.

»QhullPoint

A QhullPoint is an array of point coordinates, typically doubles. The length of the array is QhullQh.hull_dim. The identifier of a QhullPoint is its 0-based index from QhullQh.first_point followed by QhullQh.other_points.

»QhullPointSet

A QhullPointSet is a QhullSet of QhullPoint. The QhullPointSet of a QhullFacet is its coplanar points.

»QhullQh

QhullQh is the root of Qhull's data structure. It contains initialized constants, sets, buffers, and variables. It contains an array and a set of QhullPoint, a list of QhullFacet, and a list of QhullVertex. The points are the input to Qhull. The facets and vertices are the result of running Qhull.

Qhull's functions access QhullQh through the global variable, qh_qh. The global data structures, qh_stat and qh_mem, record statistics and manage memory respectively.

»QhullRidge

A QhullRidge represents the edge between two QhullFacet's. It is always simplicial with qh.hull_dim-1 QhullVertex)'s.

»QhullRidgeSet

A QhullRidgeSet is a QhullSet of QhullRidge. Each QhullFacet contains a QhullRidgeSet.

»QhullSet

A QhullSet is a set of pointers to objects. QhullSets may be ordered or unordered. They are the core data structure for Qhull.

»QhullVertex

A QhullVertex is a vertex of the convex hull. A simplicial QhullFacet has qh.hull_dim-1 vertices. A QhullVertex contains a QhullPoint. It may list its neighboring QhullFacet's.

»QhullVertexList

A QhullVertexList is a QhullLinkedList of QhullVertex. The global data structure, QhullQh contains a QhullVertexList of all the vertices.

»QhullVertexSet

A QhullVertexSet is a QhullSet of QhullVertex. The QhullVertexSet of a QhullFacet is the vertices of the facet. It is ordered for simplicial facets and unordered for non-simplicial facets.

»RboxPoints

RboxPoints is a std::vector of point coordinates (QhullPoint). It's iterator is CoordinateIterator.

RboxPoints.appendRandomPoints() appends points from a variety of distributions such as uniformly distributed within a cube and random points on a sphere. It can also append a cube's vertices or specific points.

»UsingLibQhull

UsingLibQhull checks that the current thread owns Qhull's global data structure, QhullQh. It is required while calling the Qhull library. Otherwise two threads may be updating and reading the same data structure.

»Calling Qhull from C programs

Warning: Qhull was not designed for calling from C programs. You may find the C++ interface easier to use. You will need to understand the data structures and read the code. Most users will find it easier to call Qhull as an external command.

For examples of calling Qhull, see GNU Octave's computational geometry code, and Qhull's user_eg.c, user_eg2.c, and user.c. To see how Qhull calls its library, read unix.c, qconvex.c, qdelaun.c, qhalf.c, and qvoronoi.c.

The BGL Boost Graph Library [aka GGCL] provides C++ classes for graph data structures and algorithms [Dr. Dobb's 9/00 p. 29-38; OOPSLA '99 p. 399-414]. It is modelled after the Standard Template Library. It would provide a good interface to Qhull. If you are interested in adapting BGL to Qhull, please contact bradb@shore.net.

See Qhull functions, macros, and data structures for internal documentation of Qhull. The documentation provides an overview and index. To use the library you will need to read and understand the code. For most users, it is better to write data to a file, call the qhull program, and read the results from the output file.

When you read the code, be aware of the macros "qh" and "qhstat", e.g., "qh hull_dim". They are defined in libqhull.h. They allow the global data structures to be pre-allocated (faster access) or dynamically allocated (allows multiple copies).

Qhull's Makefile produces a library, libqhull.a, for inclusion in your programs. First review libqhull.h. This defines the data structures used by Qhull and provides prototypes for the top-level functions. Most users will only need libqhull.h in their programs. For example, the Qhull program is defined with libqhull.h and unix.c. To access all functions, use qhull_a.h. Include the file -with "#include <qhull/qhull_a.h>". This +with "#include <libqhull/qhull_a.h>". This avoids potential name conflicts.

If you use the Qhull library, you are on your own as far as bugs go. Start with small examples for which you know the output. If you get a bug, try to duplicate it with the Qhull program. The 'Tc' option will catch many problems as they occur. When an error occurs, use 'T4 TPn' to trace from the last point added to the hull. Compare your trace with the trace output from the Qhull program.

Errors in the Qhull library are more likely than errors in the Qhull program. These are usually due to feature interactions that do not occur in the Qhull program. Please report all errors that you find in the Qhull library. Please include suggestions for improvement.

»sets and quick memory allocation

You can use mem.c and qset.c individually. Mem.c implements quick-fit memory allocation. It is faster than malloc/free in applications that allocate and deallocate lots of memory.

Qset.c implements sets and related collections. It's the inner loop of Qhull, so speed is more important than abstraction. Set iteration is particularly fast. qset.c just includes the functions needed for Qhull.

»Delaunay triangulations and point indices

Here some unchecked code to print the point indices of each Delaunay triangle. Use option 'QJ' if you want to avoid non-simplicial facets. Note that upper Delaunay regions are skipped. These facets correspond to the furthest-site Delaunay triangulation. 

   facetT *facet;
   vertexT *vertex, **vertexp;
 
   FORALLfacets {
     if (!facet->upperdelaunay) {
       printf ("%d", qh_setsize (facet->vertices);
       FOREACHvertex_(facet->vertices)
         printf (" %d", qh_pointid (vertex->point));
       printf ("\n");
     }
   }

»locate a facet with qh_findbestfacet()

The routine qh_findbestfacet in poly2.c is particularly useful. It uses a directed search to locate the facet that is furthest below a point. For Delaunay triangulations, this facet is the Delaunay triangle that contains the lifted point. For convex hulls, the distance of a point to the convex hull is either the distance to this facet or the distance to a subface of the facet.

Warning: If triangulated output ('Qt') and the best facet is triangulated, qh_findbestfacet() returns one of the corresponding 'tricoplanar' facets. The actual best facet may be a different tricoplanar facet.

See qh_nearvertex() in poly2.c for sample code to visit each tricoplanar facet. To identify the correct tricoplanar facet, see Devillers, et. al., ['01] and Mucke, et al ['96]. If you implement this test in general dimension, please notify qhull@qhull.org.

qh_findbestfacet performs an exhaustive search if its directed search returns a facet that is above the point. This occurs when the point is inside the hull or if the curvature of the convex hull is less than the curvature of a sphere centered at the point (e.g., a point near a lens-shaped convex hull). When the later occurs, the distance function is bimodal and a directed search may return a facet on the far side of the convex hull.

Algorithms that retain the previously constructed hulls usually avoid an exhaustive search for the best facet. You may use a hierarchical decomposition of the convex hull [Dobkin and Kirkpatrick '90].

To use qh_findbestfacet with Delaunay triangulations, lift the point to a paraboloid by summing the squares of its coordinates (see qh_setdelaunay in geom2.c). Do not scale the input with options 'Qbk', 'QBk', 'QbB' or 'Qbb'. See Mucke, et al ['96] for a good point location algorithm.

The intersection of a ray with the convex hull may be found by locating the facet closest to a distant point on the ray. Intersecting the ray with the facet's hyperplane gives a new point to test.

»on-line construction with qh_addpoint()

The Qhull library may be used for the on-line construction of convex hulls, Delaunay triangulations, and halfspace intersections about a point. It may be slower than implementations that retain intermediate convex hulls (e.g., Clarkson's hull program). These implementations always use a directed search. For the on-line construction of convex hulls and halfspace intersections, Qhull may use an exhaustive search (qh_findbestfacet).

You may use qh_findbestfacet and qh_addpoint (libqhull.c) to add a point to a convex hull. Do not modify the point's coordinates since qh_addpoint does not make a copy of the coordinates. For Delaunay triangulations, you need to lift the point to a paraboloid by summing the squares of the coordinates (see qh_setdelaunay in geom2.c). Do not scale the input with options 'Qbk', 'QBk', 'QbB' or 'Qbb'. Do not deallocate the point's coordinates. You need to provide a facet that is below the point (qh_findbestfacet).

You can not delete points. Another limitation is that Qhull uses the initial set of points to determine the maximum roundoff error (via the upper and lower bounds for each coordinate).

For many applications, it is better to rebuild the hull from scratch for each new point. This is especially true if the point set is small or if many points are added at a time.

Calling qh_addpoint from your program may be slower than recomputing the convex hull with qh_qhull. This is especially true if the added points are not appended to the qh first_point array. In this case, Qhull must search a set to determine a point's ID. [R. Weber]

See user_eg.c for examples of the on-line construction of convex hulls, Delaunay triangulations, and halfspace intersections. The outline is: 

 initialize qhull with an initial set of points
 qh_qhull();
 
 for each additional point p
    append p to the end of the point array or allocate p separately
    lift p to the paraboloid by calling qh_setdelaunay
    facet= qh_findbestfacet (p, !qh_ALL, &bestdist, &isoutside);
    if (isoutside)
       if (!qh_addpoint (point, facet, False))
          break;  /* user requested an early exit with 'TVn' or 'TCn' */
 
 call qh_check_maxout() to compute outer planes
 terminate qhull

»Constrained Delaunay triangulation

With a fair amount of work, Qhull is suitable for constrained Delaunay triangulation. See Shewchuk, ACM Symposium on Computational Geometry, Minneapolis 1998.

Here's a quick way to add a constraint to a Delaunay triangulation: subdivide the constraint into pieces shorter than the minimum feature separation. You will need an independent check of the constraint in the output since the minimum feature separation may be incorrect. [H. Geron]

»Tricoplanar facets and option 'Qt'

Option 'Qt' triangulates non-simplicial facets (e.g., a square facet in 3-d or a cubical facet in 4-d). All facets share the same apex (i.e., the first vertex in facet->vertices). For each triangulated facet, Qhull sets facet->tricoplanar true and copies facet->center, facet->normal, facet->offset, and facet->maxoutside. One of the facets owns facet->normal; its facet->keepcentrum is true. If facet->isarea is false, facet->triowner points to the owning facet.

Qhull sets facet->degenerate if the facet's vertices belong to the same ridge of the non-simplicial facet.

To visit each tricoplanar facet of a non-simplicial facet, either visit all neighbors of the apex or recursively visit all neighbors of a tricoplanar facet. The tricoplanar facets will have the same facet->center.

See qh_detvridge for an example of ignoring tricoplanar facets.

»Voronoi vertices of a region

The following code iterates over all Voronoi vertices for each Voronoi region. Qhull computes Voronoi vertices from the convex hull that corresponds to a Delaunay triangulation. An input site corresponds to a vertex of the convex hull and a Voronoi vertex corresponds to an adjacent facet. A facet is "upperdelaunay" if it corresponds to a Voronoi vertex "at-infinity". Qhull uses qh_printvoronoi in io.c for 'qvoronoi o' 

 /* please review this code for correctness */
 qh_setvoronoi_all();
 FORALLvertices {
    site_id = qh_pointid (vertex->point);
    if (qh hull_dim == 3)
       qh_order_vertexneighbors(vertex);
    infinity_seen = 0;
    FOREACHneighbor_(vertex) {
       if (neighbor->upperdelaunay) {
         if (!infinity_seen) {
           infinity_seen = 1;
           ... process a Voronoi vertex "at infinity" ...
         }
       }else {
         voronoi_vertex = neighbor->center;
         ... your code goes here ...
       }
    }
 }

»Voronoi vertices of a ridge

Qhull uses qh_printvdiagram() in io.c to print the ridges of a Voronoi diagram for option 'Fv'. The helper function qh_eachvoronoi() does the real work. It calls the callback 'printvridge' for each ridge of the Voronoi diagram.

You may call qh_printvdiagram2(), qh_eachvoronoi(), or qh_eachvoronoi_all() with your own function. If you do not need the total number of ridges, you can skip the first call to qh_printvdiagram2(). See qh_printvridge() and qh_printvnorm() in io.c for examples.

»vertex neighbors of a vertex

To visit all of the vertices that share an edge with a vertex:

  • Generate neighbors for each vertex with qh_vertexneighbors in poly2.c.
  • For simplicial facets, visit the vertices of each neighbor
  • For non-simplicial facets,
    • Generate ridges for neighbors with qh_makeridges in merge.c.
    • Generate ridges for a vertex with qh_vertexridges in merge.c.
    • Visit the vertices of these ridges.

For non-simplicial facets, the ridges form a simplicial decomposition of the (d-2)-faces between each pair of facets -- if you need 1-faces, you probably need to generate the full face graph of the convex hull.

»Enhancements to Qhull

There are many ways in which Qhull can be improved. 

 [Jan 2010] Suggestions
  - Generate vcproj from qtpro files
    cd qtpro && qmake -spec win32-msvc2005 -tp vc -recursive
    sed -i 's/C\:\/bash\/local\/qhull\/qtpro\///' qhull-all.sln
    Change qhullcpp to libqhull.dll
    Allow both builds on same host (keep /tmp separate)
  - Make distribution -- remove tmp, news, .git, leftovers from project, change CRLF
      search for 2010.1, Dates
      qhulltest --all added to output
      Add md5sum
      Add test of user_eg3, etc.
  - C++ class for access to statistics, accumulate vs. add
  - Add dialog box to RoadError-- a virtual function?
  - Option 'Gt' does not make visible all facets of the mesh example, rbox 32 M1,0,1 | qhull d Gt
  - Option to select bounded Voronoi regions [A. Uzunovic]
  - Merge small volume boundary cells into unbounded regions [Dominik Szczerba]
  - Postmerge with merge options
  - Add const to C code
  - Add modify operators and MutablePointCoordinateIterator to PointCoordinates
  - Add Qtest::toString() functions for QhullPoint and others.  QByteArray and qstrdup()
  - Fix option Qt for conformant triangulations of merged facets
  - Investigate flipped facet -- rbox 100 s D3 t1263080158 | qhull R1e-3 Tcv Qc
  - Add doc comments to c++ code
  - Measure performance of Qhull, seconds per point by dimension
  - Report potential wraparound of 64-bit ints -- e.g., a large set or points
 
 Documentation
 - Qhull::addPoint().  Problems with qh_findbestfacet and otherpoints see
    qh-code.htm#inc on-line construction with qh_addpoint()
 - How to handle 64-bit possible loss of data.  WARN64, ptr_intT, size_t/int
 - Show custom of qh_fprintf
 - grep 'qh_mem ' x | sort | awk '{ print $2; }' | uniq -c | grep -vE ' (2|4|6|8|10|12|14|16|20|64|162)[^0-9]'
 - qtpro/qhulltest contains .pro and Makefile.  Remove Makefiles by setting shadow directory to ../../tmp/projectname
 - Rules for use of qh_qh and multi processes
     UsingQhull
     errorIfAnotherUser
     ~QhullPoints() needs ownership of qh_qh
     Does !qh_pointer work?
     When is qh_qh required?  Minimize the time.
    qhmem, qhstat.ferr
    qhull_inuse==1 when qhull globals active [not useful?]
    rbox_inuse==1 when rbox globals active
    - Multithreaded -- call largest dimension for infinityPoint() and origin()
  - Better documentation for qhmem totshort, freesize, etc.
  - how to change .h, .c, and .cpp to text/html.  OK in Opera
  - QhullVertex.dimension() is not quite correct, epensive
  - Check globalAngleEpsilon
  - Deprecate save_qhull()
 
 [Dec 2003] Here is a partial list:
  - fix finddelaunay() in user_eg.c for tricoplanar facets
  - write a BGL, C++ interface to Qhull
      http://www.boost.org/libs/graph/doc/table_of_contents.html
  - change qh_save_qhull to swap the qhT structure instead of using pointers
  - change error handling and tracing to be independent of 'qh ferr'
  - determine the maximum width for a given set of parameters
  - prove that directed search locates all coplanar facets
  - in high-d merging, can a loop of facets become disconnected?
  - find a way to improve inner hulls in 5-d and higher
  - determine the best policy for facet visibility ('Vn')
  - determine the limitations of 'Qg'
 
 Precision improvements:
  - For 'Qt', resolve cross-linked, butterfly ridges.
      May allow retriangulation in qh_addpoint().
  - for Delaunay triangulations ('d' or 'v') under joggled input ('QJ'),
      remove vertical facets whose lowest vertex may be coplanar with convex hull
  - review use of 'Qbb' with 'd QJ'.  Is MAXabs_coord better than MAXwidth?
  - check Sugihara and Iri's better in-sphere test [Canadian
      Conf. on Comp. Geo., 1989; Univ. of Tokyo RMI 89-05]
  - replace centrum with center of mass and facet area
  - handle numeric overflow in qh_normalize and elsewhere
  - merge flipped facets into non-flipped neighbors.
      currently they merge into best neighbor (appears ok)
  - determine min norm for Cramer's rule (qh_sethyperplane_det).  It looks high.
  - improve facet width for very narrow distributions
 
 New features:
  - implement Matlab's tsearch() using Qhull
  - compute volume of Voronoi regions.  You need to determine the dual face
    graph in all dimensions [see Clarkson's hull program]
  - compute alpha shapes [see Clarkson's hull program]
  - implement deletion of Delaunay vertices
       see Devillers, ACM Symposium on Computational Geometry, Minneapolis 1999.
  - compute largest empty circle [see O'Rourke, chapter 5.5.3] [Hase]
  - list redundant (i.e., coincident) vertices [Spitz]
  - implement Mucke, et al, ['96] for point location in Delaunay triangulations
  - implement convex hull of moving points
  - implement constrained Delaunay diagrams
       see Shewchuk, ACM Symposium on Computational Geometry, Minneapolis 1998.
  - estimate outer volume of hull
  - automatically determine lower dimensional hulls
  - allow "color" data for input points
       need to insert a coordinate for Delaunay triangulations
 
 Input/output improvements:
  - Support the VTK Visualization Toolkit, http://www.kitware.com/vtk.html
  - generate output data array for Qhull library [Gautier]
  - need improved DOS window with screen fonts, scrollbar, cut/paste
  - generate Geomview output for Voronoi ridges and unbounded rays
  - generate Geomview output for halfspace intersection
  - generate Geomview display of furthest-site Voronoi diagram
  - use 'GDn' to view 5-d facets in 4-d
  - convert Geomview output for other 3-d viewers
  - add interactive output option to avoid recomputing a hull
  - orient vertex neighbors for 'Fv' in 3-d and 2-d
  - track total number of ridges for summary and logging
 
 Performance improvements:
  - optimize Qhull for 2-d Delaunay triangulations
  -   use O'Rourke's '94 vertex->duplicate_edge
  -   add bucketing
  -   better to specialize all of the code (ca. 2-3x faster w/o merging)
  - use updated LU decomposition to speed up hyperplane construction
  -        [Gill et al. 1974, Math. Comp. 28:505-35]
  - construct hyperplanes from the corresponding horizon/visible facets
  - for merging in high d, do not use vertex->neighbors

Please let us know about your applications and improvements.

Up: Home page for Qhull
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The Geometry Center Home Page

Comments to: qhull@qhull.org
Created: Sept. 25, 1995 --- Last modified: see changes.txt

diff --git a/html/qhalf.htm b/html/qhalf.htm index ec88291..ef8b15f 100644 --- a/html/qhalf.htm +++ b/html/qhalf.htm @@ -1,597 +1,598 @@ qhalf -- halfspace intersection about a point

Up: Home page for Qhull
Up: Qhull manual: Table of Contents
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To: synopsis • input • outputs • controls • graphics • notes • conventions • options

[halfspace]qhalf -- halfspace intersection about a point

The intersection of a set of halfspaces is a polytope. The polytope may be unbounded. See Preparata & Shamos ['85] for a discussion. In low dimensions, halfspace intersection may be used for linear programming.

Example: rbox c | qconvex FQ FV n | qhalf Fp
Print the intersection of the facets of a cube. rbox c generates the vertices of a cube. qconvex FV n returns of average of the cube's vertices (in this case, the origin) and the halfspaces that define the cube. qhalf Fp computes the intersection of the halfspaces about the origin. The intersection is the vertices of the original cube.

Example: rbox c d G0.55 | qconvex FQ FV n | qhalf Fp

Print the intersection of the facets of a cube and a diamond. There are 24 facets and 14 intersection points. Four facets define each diamond vertex. Six facets define each cube vertex.

Example: rbox c d G0.55 | qconvex FQ FV n | qhalf Fp Qt

Same as above except triangulate before computing the intersection points. Three facets define each intersection point. There are two duplicates of the diamond and four duplicates of the cube.

Qhull computes a halfspace intersection by the geometric duality between points and halfspaces. See halfspace examples, qhalf notes, and option 'p' of qhalf outputs.

By default, halfspace intersections may be defined by more than d halfspaces. See the previous cube and diamond example. This is the expected output for halfspace intersection.

You can try triangulated output and joggled input. It demonstrates that triangulated output is more accurate than joggled input.

If you use 'Qt' (triangulated output), all halfspace intersections are simplicial (e.g., three halfspaces per intersection in 3-d). In 3-d, if more than three halfspaces intersect at the same point, triangulated output will produce duplicate intersections, one for each additional halfspace. See the previous cube and diamond example.

If you use 'QJ' (joggled input), all halfspace intersections are simplicial. This may lead to nearly identical intersections. For example, replace 'Qt' with 'QJ' above and compare the duplicated intersections. See Merged facets or joggled input.

The 'qhalf' program is equivalent to 'qhull H' in 2-d to 4-d, and 'qhull H Qx' in 5-d and higher. It disables the following Qhull options: d n v Qbb QbB Qf Qg Qm Qr QR Qv Qx Qz TR E V Fa FA FC FD FS Ft FV Gt Q0,etc.

Copyright © 1995-2012 C.B. Barber

»qhalf synopsis

 qhalf- halfspace intersection about a point.
     input (stdin): [dim, 1, interior point]
                    dim+1, n
                    halfspace coefficients + offset
     comments start with a non-numeric character
 
 options (qhalf.htm):
     Hn,n - specify coordinates of interior point
     Qt   - triangulated output
     QJ   - joggle input instead of merging facets
     Tv   - verify result: structure, convexity, and redundancy
     .    - concise list of all options
     -    - one-line description of all options
 
 output options (subset):
     s    - summary of results (default)
     Fp   - intersection coordinates
     Fv   - non-redundant halfspaces incident to each intersection
     Fx   - non-redundant halfspaces
     o    - OFF file format (dual convex hull)
     G    - Geomview output (dual convex hull)
     m    - Mathematica output (dual convex hull)
     QVn  - print intersections for halfspace n, -n if not
     TO file - output results to file, may be enclosed in single quotes
 
 examples:
     rbox d | qconvex n | qhalf s H0,0,0 Fp
     rbox c | qconvex FV n | qhalf s i
     rbox c | qconvex FV n | qhalf s o

»qhalf input

The input data on stdin consists of:

  • [optional] interior point
    • dimension
    • 1
    • coordinates of interior point
  • dimension + 1
  • number of halfspaces
  • halfspace coefficients followed by offset

Use I/O redirection (e.g., qhalf < data.txt), a pipe (e.g., rbox c | qconvex FV n | qhalf), or the 'TI' option (e.g., qhalf TI data.txt).

Qhull needs an interior point to compute the halfspace -intersection. An interior point is inside all of the halfspaces Hx+b -<= 0. The interior point may be in the input. If not, option +intersection. An interior point is clearly inside all of the halfspaces. +The interior point may be in the input. If not, option 'Hn,n' defines the interior point as [n,n,0,...] where 0 is the default coordinate (e.g., 'H0' is the origin). Use linear programming if you do not know the interior point (see halfspace notes),

The input to qhalf is a set of halfspaces. Each halfspace is defined by d coefficients followed by a signed offset. This defines a linear inequality. The coefficients define a vector that is normal to the halfspace. The vector may have any length. If it has length one, the offset is the distance from the origin to the -halfspace's boundary.

+halfspace's boundary. The distance from the interior point to each +halfspace is negative.

-

This is the same format used for output options 'The halfspace format is the same as Qhull's output options 'n', 'Fo', and 'Fi'. Use option 'Fd' to use cdd format for the halfspaces.

For example, here is the input for computing the intersection of halfplanes that form a cube.

rbox c | qconvex FQ FV n TO data 

 RBOX c | QCONVEX FQ FV n
 3 1
      0      0      0
 4
 6
      0      0     -1   -0.5
      0     -1      0   -0.5
      1      0      0   -0.5
     -1      0      0   -0.5
      0      1      0   -0.5
      0      0      1   -0.5

qhalf s Fp < data 

 
 Halfspace intersection by the convex hull of 6 points in 3-d:
 
   Number of halfspaces: 6
   Number of non-redundant halfspaces: 6
   Number of intersection points: 8
 
 Statistics for: RBOX c | QCONVEX FQ FV n | QHALF s Fp
 
   Number of points processed: 6
   Number of hyperplanes created: 11
   Number of distance tests for qhull: 11
   Number of merged facets: 1
   Number of distance tests for merging: 45
   CPU seconds to compute hull (after input):  0
 
 3
 3
 8
   -0.5    0.5    0.5
    0.5    0.5    0.5
   -0.5    0.5   -0.5
    0.5    0.5   -0.5
    0.5   -0.5    0.5
   -0.5   -0.5    0.5
   -0.5   -0.5   -0.5
    0.5   -0.5   -0.5

»qhalf outputs

The following options control the output for halfspace intersection.

 
Intersections
FN
list intersection points for each non-redundant halfspace. The first line is the number of non-redundant halfspaces. Each remaining lines starts with the number of intersection points. For the cube example, each halfspace has four intersection points.
Fn
list neighboring intersections for each intersection point. The first line is the number of intersection points. Each remaining line starts with the number of neighboring intersections. For the cube example, each intersection point has three neighboring intersections. In 3-d, a non-simplicial intersection has more than three neighboring intersections. Use option 'QJ' to avoid non-simplicial intersections.
Fp
print intersection coordinates. The first line is the dimension and the second line is the number of intersection points. The following lines are the coordinates of each intersection.
FI
list intersection IDs. The first line is the number of intersections. The IDs follow, one per line.
 
 
Halfspaces
Fx
list non-redundant halfspaces. The first line is the number of non-redundant halfspaces. The other lines list one halfspace per line. A halfspace is non-redundant if it defines a facet of the intersection. Redundant halfspaces are ignored. For the cube example, all of the halfspaces are non-redundant.
Fv
list non-redundant halfspaces incident to each intersection point. The first line is the number of non-redundant halfspaces. Each remaining line starts with the number of non-redundant halfspaces. For the cube example, each intersection is incident to three halfspaces.
i
list non-redundant halfspaces incident to each intersection point. The first line is the number of intersection points. Each remaining line lists the incident, non-redundant halfspaces. For the cube example, each intersection is incident to three halfspaces.
Fc
list coplanar halfspaces for each intersection point. The first line is the number of intersection points. Each remaining line starts with the number of coplanar halfspaces. A coplanar halfspace is listed for one intersection point even though it is coplanar to multiple intersection points.
Qi Fc
list redundant halfspaces for each intersection point. The first line is the number of intersection points. Each remaining line starts with the number of redundant halfspaces. Use options 'Qc Qi Fc' to list coplanar and redundant halfspaces.
 
 
General
s
print summary for the halfspace intersection. Use 'Fs' if you need numeric data.
o
print vertices and facets of the dual convex hull. The first line is the dimension. The second line is the number of vertices, facets, and ridges. The vertex coordinates are next, followed by the facets, one per line.
p
print vertex coordinates of the dual convex hull. Each vertex corresponds to a non-redundant halfspace. Its coordinates are the negative of the hyperplane's coefficients divided by the offset plus the inner product of the coefficients and the interior point (-c/(b+a.p). Options 'p Qc' includes coplanar halfspaces. Options 'p Qi' includes redundant halfspaces.
m
Mathematica output for the dual convex hull in 2-d or 3-d.
FM
Maple output for the dual convex hull in 2-d or 3-d.
G
Geomview output for the dual convex hull in 2-d, 3-d, or 4-d.

»qhalf controls

These options provide additional control:

Qt
triangulated output. If a 3-d intersection is defined by more than three hyperplanes, Qhull produces duplicate intersections -- one for each extra hyperplane.
QJ
joggle the input instead of merging facets. In 3-d, this guarantees that each intersection is defined by three hyperplanes.
f
facet dump. Print the data structure for each intersection (i.e., facet)
TFn
report summary after constructing n intersections
QVn
select intersection points for halfspace n (marked 'good')
QGn
select intersection points that are visible to halfspace n (marked 'good'). Use -n for the remainder.
Qbk:0Bk:0
remove the k-th coordinate from the input. This computes the halfspace intersection in one lower dimension.
Tv
verify result
TI file
input data from file. The filename may not use spaces or quotes.
TO file
output results to file. Use single quotes if the filename contains spaces (e.g., TO 'file with spaces.txt'
Qs
search all points for the initial simplex. If Qhull can not construct an initial simplex, it reports a descriptive message. Usually, the point set is degenerate and one or more dimensions should be removed ('Qbk:0Bk:0'). If not, use option 'Qs'. It performs an exhaustive search for the best initial simplex. This is expensive is high dimensions.

»qhalf graphics

To view the results with Geomview, compute the convex hull of the intersection points ('qhull FQ H0 Fp | qhull G'). See Halfspace examples.

»qhalf notes

See halfspace intersection for precision issues related to qhalf.

If you do not know an interior point for the halfspaces, use linear programming to find one. Assume, n halfspaces defined by: aj*x1+bj*x2+cj*x3+dj>=0, j=1..n. Perform the following linear program:

max(x5) aj*x1+bj*x2+cj*x3+dj*x4-x5>=0, j=1..n

Then, if [x1,x2,x3,x4,x5] is an optimal solution with x4,x5>0 we get:

aj*(x1/x4)+bj*(x2/x4)+cj*(x3/x4)+dj>=(x5/x4)>0, j=1..n

and conclude that the point [x1/x4,x2/x4,x3/x4] is in the interior of all the halfspaces. Note that x5 is optimal, so this point is "way in" the interior (good for precision errors).

After finding an interior point, the rest of the intersection algorithm is from Preparata & Shamos ['85, p. 316, "A simple case ..."]. Translate the halfspaces so that the interior point is the origin. Calculate the dual polytope. The dual polytope is the convex hull of the vertices dual to the original faces in regard to the unit sphere (i.e., halfspaces at distance d from the origin are dual to vertices at distance 1/d). Then calculate the resulting polytope, which is the dual of the dual polytope, and translate the origin back to the interior point [S. Spitz and S. Teller].

»qhalf conventions

The following terminology is used for halfspace intersection in Qhull. This is the hardest structure to understand. The underlying structure is a convex hull with one vertex per non-redundant halfspace. See convex hull conventions and Qhull's data structures.

  • interior point - a point in the intersection of the halfspaces. Qhull needs an interior point to compute the intersection. See halfspace input.
  • halfspace - d coordinates for the normal and a signed offset. The distance to an interior point is negative.
  • non-redundant halfspace - a halfspace that defines an output facet
  • vertex - a dual vertex in the convex hull corresponding to a non-redundant halfspace
  • coplanar point - the dual point corresponding to a similar halfspace
  • interior point - the dual point corresponding to a redundant halfspace
  • intersection point- the intersection of d or more non-redundant halfspaces
  • facet - a dual facet in the convex hull corresponding to an intersection point
  • non-simplicial facet - more than d halfspaces intersect at a point
  • good facet - an intersection point that satisfies restriction 'QVn', etc.

»qhalf options

 qhalf- compute the intersection of halfspaces about a point
     http://www.qhull.org
 
 input (stdin):
     optional interior point: dimension, 1, coordinates
     first lines: dimension+1 and number of halfspaces
     other lines: halfspace coefficients followed by offset
     comments:    start with a non-numeric character
 
 options:
     Hn,n - specify coordinates of interior point
     Qt   - triangulated ouput
     QJ   - joggle input instead of merging facets
     Qc   - keep coplanar halfspaces
     Qi   - keep other redundant halfspaces
 
 Qhull control options:
     QJn  - randomly joggle input in range [-n,n]
     Qbk:0Bk:0 - remove k-th coordinate from input
     Qs   - search all halfspaces for the initial simplex
     QGn  - print intersection if redundant to halfspace n, -n for not
     QVn  - print intersections for halfspace n, -n if not
 
 Trace options:
     T4   - trace at level n, 4=all, 5=mem/gauss, -1= events
     Tc   - check frequently during execution
     Ts   - print statistics
     Tv   - verify result: structure, convexity, and redundancy
     Tz   - send all output to stdout
     TFn  - report summary when n or more facets created
     TI file - input data from file, no spaces or single quotes
     TO file - output results to file, may be enclosed in single quotes
     TPn  - turn on tracing when halfspace n added to intersection
     TMn  - turn on tracing at merge n
     TWn  - trace merge facets when width > n
     TVn  - stop qhull after adding halfspace n, -n for before (see TCn)
     TCn  - stop qhull after building cone for halfspace n (see TVn)
 
 Precision options:
     Cn   - radius of centrum (roundoff added).  Merge facets if non-convex
      An  - cosine of maximum angle.  Merge facets if cosine > n or non-convex
            C-0 roundoff, A-0.99/C-0.01 pre-merge, A0.99/C0.01 post-merge
     Rn   - randomly perturb computations by a factor of [1-n,1+n]
     Un   - max distance below plane for a new, coplanar halfspace
     Wn   - min facet width for outside halfspace (before roundoff)
 
 Output formats (may be combined; if none, produces a summary to stdout):
     f    - facet dump
     G    - Geomview output (dual convex hull)
     i    - non-redundant halfspaces incident to each intersection
     m    - Mathematica output (dual convex hull)
     o    - OFF format (dual convex hull: dimension, points, and facets)
     p    - vertex coordinates of dual convex hull (coplanars if 'Qc' or 'Qi')
     s    - summary (stderr)
 
 More formats:
     Fc   - count plus redundant halfspaces for each intersection
          -   Qc (default) for coplanar and Qi for other redundant
     Fd   - use cdd format for input (homogeneous with offset first)
     FF   - facet dump without ridges
     FI   - ID of each intersection
     Fm   - merge count for each intersection (511 max)
     FM   - Maple output (dual convex hull)
     Fn   - count plus neighboring intersections for each intersection
     FN   - count plus intersections for each non-redundant halfspace
     FO   - options and precision constants
     Fp   - dim, count, and intersection coordinates
     FP   - nearest halfspace and distance for each redundant halfspace
     FQ   - command used for qhalf
     Fs   - summary: #int (8), dim, #halfspaces, #non-redundant, #intersections
                       for output: #non-redundant, #intersections, #coplanar
                                   halfspaces, #non-simplicial intersections
                     #real (2), max outer plane, min vertex
     Fv   - count plus non-redundant halfspaces for each intersection
     Fx   - non-redundant halfspaces
 
 Geomview output (2-d, 3-d and 4-d; dual convex hull)
     Ga   - all points (i.e., transformed halfspaces) as dots
      Gp  -  coplanar points and vertices as radii
      Gv  -  vertices (i.e., non-redundant halfspaces) as spheres
     Gi   - inner planes (i.e., halfspace intersections) only
      Gn  -  no planes
      Go  -  outer planes only
     Gc   - centrums
     Gh   - hyperplane intersections
     Gr   - ridges
     GDn  - drop dimension n in 3-d and 4-d output
 
 Print options:
     PAn  - keep n largest facets (i.e., intersections) by area
     Pdk:n- drop facet if normal[k] <= n (default 0.0)
     PDk:n- drop facet if normal[k] >= n
     Pg   - print good facets (needs 'QGn' or 'QVn')
     PFn  - keep facets whose area is at least n
     PG   - print neighbors of good facets
     PMn  - keep n facets with most merges
     Po   - force output.  If error, output neighborhood of facet
     Pp   - do not report precision problems
 
     .    - list of all options
     -    - one line descriptions of all options

Up: Home page for Qhull
Up: Qhull manual: Table of Contents
To: Programs • Options • Output • Formats • Geomview • Print • Qhull • Precision • Trace
To: synopsis • input • outputs • controls • graphics • notes • conventions • options

The Geometry Center Home Page

Comments to: qhull@qhull.org
Created: Sept. 25, 1995 --- Last modified: see top

diff --git a/index.htm b/index.htm index 2053789..16fd51d 100644 --- a/index.htm +++ b/index.htm @@ -1,279 +1,280 @@ Qhull code for Convex Hull, Delaunay Triangulation, Voronoi Diagram, and Halfspace Intersection about a Point URL: http://www.qhull.org
To: News • Download • CiteSeer • Images • Manual • FAQ • Programs • Options

Qhull

[CONE] 		Qhull computes the convex hull, Delaunay triangulation, Voronoi diagram, halfspace intersection about a point, furthest-site Delaunay triangulation, and furthest-site Voronoi diagram. The source code runs in 2-d, 3-d, 4-d, and higher dimensions. Qhull implements the Quickhull algorithm for computing the convex hull. It handles roundoff errors from floating point arithmetic. It computes volumes, surface areas, and approximations to the convex hull.

Qhull does not support triangulation of non-convex surfaces, mesh generation of non-convex objects, medium-sized inputs in 9-D and higher, alpha shapes, weighted Voronoi diagrams, Voronoi volumes, or constrained Delaunay triangulations,

Qhull 2012.1 fixes qhull-go for Windows 64-bit. If you use Qhull 2003.1. please upgrade to 2012.1 or apply poly.c-qh_gethash.patch.

Introduction

  • Fukuda's introduction to convex hulls, Delaunay triangulations, Voronoi diagrams, and linear programming
  • Lambert's Java visualization of convex hull algorithms
  • LEDA Guide to geometry algorithms
  • MathWorld's Computational Geometry from Wolfram Research
  • Skiena's Computational Geometry from his Algorithm Design Manual.
  • Stony Brook Algorithm Repository, computational geometry

Qhull Documentation and Support

Related URLs

FAQs and Newsgroups

The program includes options for input transformations, randomization, tracing, multiple output formats, and execution statistics. The program can be called from within your application.

You can view the results in 2-d, 3-d and 4-d with Geomview. An alternative is VTK.

For an article about Qhull, download from ACM or CiteSeer:

Barber, C.B., Dobkin, D.P., and Huhdanpaa, H.T., "The Quickhull algorithm for convex hulls," ACM Trans. on Mathematical Software, 22(4):469-483, Dec 1996, http://www.qhull.org

Abstract:

The convex hull of a set of points is the smallest convex set that contains the points. This article presents a practical convex hull algorithm that combines the two-dimensional Quickhull Algorithm with the general dimension Beneath-Beyond Algorithm. It is similar to the randomized, incremental algorithms for convex hull and Delaunay triangulation. We provide empirical evidence that the algorithm runs faster when the input contains non-extreme points, and that it uses less memory.

Computational geometry algorithms have traditionally assumed that input sets are well behaved. When an algorithm is implemented with floating point arithmetic, this assumption can lead to serious errors. We briefly describe a solution to this problem when computing the convex hull in two, three, or four dimensions. The output is a set of "thick" facets that contain all possible exact convex hulls of the input. A variation is effective in five or more dimensions.

Up: Past Software Projects of the Geometry Center
URL: http://www.qhull.org
To: News • Download • CiteSeer • Images • Manual • FAQ • Programs • Options

[HOME] The Geometry Center Home Page

Comments to: qhull@qhull.org
Created: May 17 1995 --- diff --git a/src/Changes.txt b/src/Changes.txt index efa9e9c..52f9a1f 100644 --- a/src/Changes.txt +++ b/src/Changes.txt @@ -1,1674 +1,1912 @@ .............This file lists all changes to qhull and rbox..................... ------------ Need help - Qhull needs RPM and Debian builds (CMake's CPackRMP and CPackDeb). - Add an Autotools build for everything - Set up debian build [octave-maintainers] Please keep debian files in config/ - Qhull needs a mirror/archive site for old and new builds + - Constrained delaunay triangulation via Shewchuk's algorithm (ACM Symp. Comp. Geo., 1998) - The C++ interface needs work. Give it a try and make it better. http://gitorious.org/qhull/ - Document with Qt conventions using Doxygen (//! and //!<) - Produce conformant triangulations for merged facets using option 'Qt' To do + - Can allocate memory for QhullSet using Qhull.qhmem, Then default constructors for QhullVertexSet etc. - Review email for doc changes before jun'10 - Git: Create signed tags for Qhull versions - Wiki: Add FIXUP to QH11026 for known problems + - Review all FIXUP + - Update README for libqhullr etc. - Notes to compgeom on conformant triangulation and Voronoi volume - Set File Ver and Product Ver in dll - - For the C++ interface, make qh_qh a parameter instead of a global static - This replaces qh_QHpointer. It simplifies multithreading. - Compute the convex hull of each Voronoi or Delaunay region - Performance test of qset and qhull - + - Rescale output to match 'QbB' on input [J. Metz, 1/30/2014 12:21p] - qh-get.htm: List the Window OSs for Qhull [T. Winkler] + - Add publications that compare Qhull and CGAL. Review results - Reconsider Qhull version numbering (e.g., Traveler 4/5/12) + - Add interior point for automatic translation? + - Allow comma separated input? + - Allocate a new QhullPoint + - countT -1 used as a flag in Coordinates.mid(), QhullFacet->id() + Also QhullPoints indexOf and lastIndexOf + Also QhullPointSet indexOf and lastIndexOf + - Coordinates.indexOf assumes countT is signed (from end) + - Coordinates.lastIndexOf assumes countT is signed (from end) + - All error messages with countT are wrong, convert to int? + - Review all cpp code for 'int' + - Review all c code for 'int' + - RboxPoints.qh_fprintf_rbox, etc. message 9393 assumes countT but may be int, va_arg(args, countT); Need to split + - vertexT unsigned id:24; /* too small */ + - Why QhullFacetList.PrintFacetList and .PrintFacet? + - Remove s_qhull_output + - qset_r.h defines countT -- duplicates code in user_h.h -- need to add to qset.h/user.h + - rbox_errexit assumed to exit. Protect with a flag? + - checkAndFreeQhullMemory does not work since it does not free qhmem itself. + - Check base address for qhstatT, add Qhull initializers + - Review all classes + Check that assignment copies everything + Check alignment for Fields + Qhull& constructors before QhullQh* constructors, otherwise the same + operator= for all + check explicit + Remove print(), add << T if needed + Remove QhullFacet.print() -- Use << instead + - Reduce includes + - Document C++ + Designed for exploring the results of Qhull. + All objects contain a QhullQh reference, making them memory inefficient. + May also use libqhull (e.g., FOREACHfacet_(...)) + - Review default constructors (QhullPoint OK) + - QhullVertexSet uses QhullSetBase::referenceSetT() to free it's memory. Probably needed elsewhere + - Add defineAs to each object + - Add QList and vector instance of facetT*, etc. + - Generalize QhullPointSetIterator + - Review all tests + Add QhullStat_test + Add printIdentifiers to Set tests + Add QhullVertexSet_test + Add Qhull* to constructors + Test QhullQh* constructors + Test QhullFacetList.operator= + Test QhullLinkedList.operator= + Test QhullFacetSet.operator= + Test QhullFacetSet.print("message") + Test QhullPoints.operator= + Test QhullPointSet.operator= + Test QhullSet.operator= + Test qh_NOmem, etc. + - Reviewed + QhullPoint_test + - Update LASTerror for qhullpcpp.QhullError.h + - Check that QtCreator can load and build with CMakefile + - Incremental addition of input points to existing tesselation + - Add reference (compares to cgal, http://www.mcs.anl.gov/papers/P5154-0614.pdf, 4x more memory, cgal much faster) + Y. Liu and J. Snoeyink, “A Comparison of Five Implementations of 3D Delaunay Tessellation,” Combinatorial and Computational Geometry, vol. 52, pp. 439–458, 2005. + - Fix no-more facets error + - Fix interface to Qhull. Shouldn't do all the work in the constructor + void runQhull(const char *qhullCommand2); +------------ +Dec'14 notes + +make-vcproj.sh -- Renames build/ to build-prev. Creates build, build-vc and build-qt (needs editing) +Renamed build to build-new +Copied build-prev to build and renamed as build-mar14 +Devenv loaded build/qhullr.sln with qhullmini + build/qhulltest-mini/qhullmini.vcproj + build/libqhullcpp/libqhullcpp.vcproj + build/libqhullstaticr/libqhullstaticr.vcproj +Includes + build/libqhullr/libqhullr.vcproj + +Load Qt Creator (Oct'14) with src/qhull-all.pro -- The project is odd due to the include files +Successfully compiled and ran qhullmini with QhullPoint_test +Updated Perforce +Added user_eg3 + ------------ Qhull + - Fixed documentation for 'include' path in qh-code.htm. It should be include/libqhull [fe rew] + - Fixed documentation for 'i' in qconvex.htm. It triangulates in 4-d and higher [ + - Clarified qhalf space documentation for the interior point [J. Santos] - Rename debugging routines dfacet/dvertex to qh_dfacet/qh_dvertex - Rename rbox routines to qh_roundi/qh_out1/qh_out2n/qh_out3n - Rename dfacet and dvertex to qh_dfacet and qh_dvertex - Rename user_eg, user_eg2, and user_eg3 to user_eg7,etc. - Rewrote user_eg, user_eg2, and user_eg3 as reentrant code - Replace 'qhmem .zzz' with 'qhmem.zzz' - Removed spaces between function and parentheses - Rename 'enum statistics' to 'enum qh_statistics' - Rename 'qh_rand_seed' to 'qh_last_random'. Declare it as DATA - Declare rbox as DATA in qhull-exports.def and qhull_p-exports.def - In comments, use 'qh.zzz' to reference qhT fields - In qh_fprintf, use qhmem.ferr to report errors - qh_fprintf may be called for errors in qh_initstatistics and qh_meminit - After qh_meminit, qhmem.ferr is non-zero - Update qh_MEMalign in testqset.c to user.h (with realT and void*) - -qhullr + - Split rboxT into a header file + - Add rboxlib.h to libqhull_a.h + - Rename PI to qh_PI and extend to 30 digits + - Rename MAXdim to qh_MAXdim + - Change spacing for type annotations '*' and '&' in C++ header files + - Remove 'inline' annotation from explicit inline declarations + - Column 25 formatting for iterators, etc. + - Use '#//!\name' for section headers + - QhullFacet.cpp: zinc_(Zdistio); + - Set qhT.NOerrexit on initialization + - Clear qhT.ALLOWrestart in qh_errexit + - Replace longjmp with qh_errexit_rbox in qh_rboxpoints + - Add jmpExtra after rbox_errexit to protect against compiler errors + +qhullr (reentrant Qhull) + - Make the Qhull data structure (qh_qh) a parameter instead of a global static + It simplifies multithreading and the C++ user interface + All functions are reentrant (Qt: "A reentrant function can ... be called simultaneously from multiple threads, but only if each invocation uses its own data.") + This replaces qh_QHpointer. + New libraries + libqhullr -- Shared library with reentrant sources (e.g., poly_r.h and poly_r.c which replace libqhull's poly.h and poly.c) + libqhullstaticr -- Static library with the same sources as libqhullr + libqhullcpp -- The C++ interface using libqhullr (further notes below) + New executables + qhulltest -- Test the C++ interface using Qt + testqsetr -- Test qset_r.c (the reentrant version of qset.c + Renamed libraries and executables + libqhullpcpp -- The old C++ interface using qh_QHpointer and libqhullp (previously called libqhullcpp) + qhullptest -- The old test program for the C++ interface (previously called qhulltest) + + Source code changes for libqhullr - Remove qh_save_qhull(), qh_restore_qhull(), and qh.old_qhstat from global_r.c - Remove qh_freeqhull2() (global_r.c) - Remove qh_freestatistics() (stat_r.c) - Remove qh_compare_vertexpoint (qhT is not available, unused code) - Remove conditional code for __POWERPC__ from unix_r.c and rbox_r.c - Move qh_last_random into qh->last_random (random_r.c) - - Rename sources files with a '_r' suffix + - Rename sources files with a '_r' suffix. qhull_a.h becomes qhull_ra.h - Replace 'qh' macro with 'qh->' - Replace global qhT with parameter-0 - Add qhmemT to beginning of qhT. It may not be used standalone. - Add qhstatT to end of qhT - Remove qhull_inuse - Change qhmem.zzz to qh->qhmem.zzz - Replace qh_qhstat with qh->qhstat - Remove qh_freestatistics - Replace qh_last_random with qh->last_random - Replace rboxT with qh->rbox_errexit, rbox_isinteger, rbox_out_offset - Replace rbox.ferr/fout with qh->ferr/fout - No qh for qh_exit, qh_free, qh_malloc, qh_strtod, qh_strtol, qh_stddev - New qmake include files qhull-app-c_r.pri, qhull-app-shared_r.pri, qhull-libqhull-src_r.pri + - Replace 'int' with 'countT' and 'COUNTmax' for large counts and identifiers + - qhset converted to countT + - Removed vertexT.dim -- No longer needed by cpp + Removed MAX_vdim + - Guarantee that qh->run_id!=0. Old code assumed that qh_RANDOMint was 31 bits C++ interface - Reimplement C++ interface on reentrant libqhullr instead of libqhull - Renamed libqhullcpp to libqhullpcpp - Renamed qhulltest to qhullptest - Renamed qhull-app-cpp.pri to qhull-app-cpp_p.pri + - Added QhullVertexSet.h to libqhullcpp.pro and libqhullpcpp.pro + - Replaced UsingLibQhull with QhullQh and macro QH_TRY + Removed UsingLibQhull.currentAngleEpsilon and related routines + Replaced globalDistanceEpsilon with QhullQh.distanceEpsilon + Replaced globalAngleEpsilon with QhullQh.angleEpsilon + Replaced FACTORepsilon=10 with QhullQh.factor_epsilon=1.0 + - Fixed double free by QhullVertexSet's copy constructor if qhsettemp_defined + - Moved messaging from Qhull to QhullQh + - RboxPoints(rboxCommand).comment() includes the command with its + - Add check of RboxPoints* in qh_fprintf_rbox + - Renamed Qhull.initializeQhull to Qhull.allocateQhullQh + - Renamed UsingQhullLib.checkQhullMemoryEmpty to QhullQh.checkAndFreeQhullMemory + Added qh_freeqhull(!qh_ALL) as done by unix.c and other programs + - Moved QhullPoints.extraCoordinatesCount into QhullPoints.cpp + - Changed QhullPoint.operator== to sqrt(distanceEpsilon) + - Replaced section tags with '#//!\name ...' + - PointCoordinates.operator=: initialize QhullPoints, otherwise does not copy point_dimension + +C++ interface for most classes + - Remove qhRunId + - Add QhullQh *qh_qh to all types + Pointer comparisons of facetT,etc. do not test corresponding qh_qh + Added to end of type for debugging information, unless wasteful alignment + - Add QhullQh * to all constructors + - All constructors may use Qhull & instead of QhullQh * + - For inherited QhullQh types, change to 'protected' + - Renamed 'o' to 'other' except where used extensively in iterators + - Except for conditional code, merged the Conversion section into GetSet + - Removed empty(). Use isEmpty() instead + - Add operator= instead of keeping it private + - print_message=0 not allowed. Use "" instead. +C++ interface by class + - Coordinates + Removed empty(). Use isEmpty() instead + Reformated the iterators + Convert to countT + - PointCoordinates + Constructor requires Qhull or QhullQh* pointer + Renamed point_comment to describe_points + Convert to countT + - Qhull + Remove qhull_run_i + Remove qh_active + Replaced qhull_dimension with qh->input_dim //! Dimension of result (qh.hull_dim or one less for Delaunay/Voronoi) + Remove globals s_qhull_output= 0; + Renamed qhullQh() to qh() + Added check of base address to allocateQhullQh(), Was not needed for qhullpcpp + - QhullFacet + Constructor requires Qhull or QhullQh* pointer + Convert to countT + Dropped implicit conversion from facetT + Dropped runId + - QhullFacetList + Constructor requires Qhull or QhullQh* pointer + Convert to countT + Dropped runId + - QhullFacetSet + Removed empty(). Use isEmpty() instead + Constructor requires Qhull or QhullQh* pointer + Convert to countT + Dropped runId + Add operator= + Implement print("message") + - QhullHyperplane + Constructor requires Qhull or QhullQh* pointer + Reorganized + - QhullLinkedList + Add operator= + Removed empty(). Use isEmpty() instead + Convert to countT + - QhullPoint + Constructor requires Qhull or QhullQh* pointer + An empty QhullPoint sets point_dimension to hull_dim + Added checks for point_coordinates==0, i.e., QhullPoint(q) + Removed QhullPoint::id, use QhullPoint.id() instead + distance() throws an error if dimension doesn't agree or if a point is undefined + Convert to countT + Removed test of qh_qh from operator== + Use cout<

[R. Richter, S. Pasko] - Remove deprecated libqhull/qhull.h Use libqhull/libqhull.h instead. Avoids confusion with libqhullcpp/Qhull.h - Makefile: Add LIBDIR, INCDIR, and DESTDIR to install [L.H. de Mello] Separate MAN install from DOC install Create install directories Installs headers to include/libqhull, include/libqhullcpp, include/road - CMakeLists.txt: Add MAN_INSTALL_DIR for qhull.1 and rbox.1 man pages Add RoadTest.h to include/road for Qt users (road_HEADERS) - Renamed md5sum files to avoid two extensions - qh-get.htm: Add Readme links and 2009.1 note. - qh-optf.htm: Fix link - index.htm: Updated Google Scholar link - qhull-zip.sh: Improved error message. ------------ Qhull 2011.1 2011/04/17 6.2.0.1373 Changes to deliverables - qvoronoi: Deprecated 'Qt' and 'QJn'. Removed from documentation and prompts. These options produced duplicate Voronoi vertices for cospherical data. - Removed doskey from Qhull-go.bat. It is incompatible with Windows 7 - Added 'facets' argument to user_eg3.cpp - user_eg links with shared library - qhulltest.cpp: Add closing prompt. Changes to build system - Reorganized source directories - Moved executables to bin directory - Add CMake build for all targets (CMakeFiles.txt) [M. Moll assisted] - Add gcc build for all targets (Makefile) - Fixed location of qhull.man and rbox.man [M. Moll] - Add DevStudio builds for all targets (build/*.vcproj) - Added shared library (lib/qhull6.dll) Added qh_QHpointer_dllimport to work around problems with MSVC - Added static libraries with and without qh_QHpointer (lib/qhullstatic.lib) - Added eg/make-vcproj.sh to create vcproj/sln files from cmake and qmake - Document location of qh_QHpointer - Use shadow build directory - Made -fno-strict-aliasing conditional on gcc version - Added src/qhull-app-cpp.pri, src/qhull-app-c.pri, etc. for common settings - Add .gitignore with ignored files and directories. - Use .git/info/exclude for locally excluded files. - Fixed MBorland for new directory structure Changes to documentation - qvoronoi.htm: Remove quotes from qvoronoi example - qhull-cpp.xml: Add naming conventions - index.htm: Add Google Scholar references - qh-optf.htm: Add note about order of 'Fn' matching 'Fv' order [Q. Pan] - Add patch for old builds in qh-get.htm - Added C++ compiling instructions to README.txt - Add instructions for fixing the DOS window - Changed DOS window to command window - Fixed html links - qh-get.htm: Dropped the Spanish mirror site. It was disabled. Changes to C code - mem.h: Define ptr_intT as 'long long' for Microsoft Windows _win64 builds. On Linux and Mac, 'long' is 64-bits on a 64-bit host - Added qh_QHpointer_dllimport to work around MSVC problem - qconvex.c,etc.: Define prototype for _isatty - Define MSG_QHULL_ERROR in user.h - Move MSG_FIXUP to 11000 and updated FIXUP QH11... Changes to test code - Add note to q_test than R1e-3 may error (qh-code.htm, Enhancements) - Add test for executables to q_eg, etc. - Fixed Qhull-go.bat. QHULL-GO invokes it with command.com, Changes to C++ interface - QhullFacet: Added isSimplicial, isTopOrient, isTriCoplanar, isUpperDelaunay - Added Qhull::defineVertexFacetNeighbors() for facetNeighbors of vertices. Automatically called for facet merging and Voronoi diagrams Do not print QhullVertex::facetNeighbors is !facetNeighborsDefined() - Add Fixup identifiers - QhullError: Add copy constructor, assignment operator, and destructor - Add throw() specifiers to RoadError and QhullError - Renamed RoadError::defined() to RoadError::isDefined() - Add #error to Qhull.h if qh_QHpointer is not defined Changes to C++ code - Fixed bug reported by renangms. Vertex output throws error QH10034 and defineVertexNeighbors() does not exist. - Define QHULL_USES_QT for qt-qhull.cpp [renangms] - Reviewed all copy constructors and copy assignments. Updated comments. Defined Qhull copy constructor and copy assignment [G. Rivet-Sabourin] Disabled UsingQhullLib default constructor, copy construct, and copy assign - Merged changes from J. Obermayr in gitorious/jobermayrs-qhull:next - Fix strncat limit in rboxlib.c and global.c - Changes to CMakeLists.txt for openSUSE - Fixed additional uses of strncat - Fixed QhullFacet::PrintRidges to check hasNextRidge3d() - Removed gcc warnings for shadowing from code (src/qhull-warn.pri) - Removed semicolon after extern "C" {...} - Removed experimental QhullEvent/QhullLog - Use fabs() instead of abs() to avoid accidental conversions to int - Fixed type of vertex->neighbors in qh_printvoronoi [no effect on results] - Removed unnecessary if statement in qh_printvoronoi ------------ qhull 2010.1 2010/01/14 - Fixed quote for #include in qhull.h [U.Hergenhahn, K.Roland] - Add qt-qhull.cpp with Qt conditional code - Add libqhullp.proj - Add libqhull5 to Readme, Announce, download - Reviewed #pragma - Reviewed FIXUP and assigned QH tags - All projects compile with warnings enabled - Replaced 'up' glyphs with » - Moved cpp questions to qh-code.htm#questions-cpp - Moved suggestions to qh-code.htm#enhance - Moved documentation requests to qh-code.htm#enhance - Add md5sum file to distributions - Switched to DevStudio builds to avoid dependent libraries, 10% slower Removed user_eg3.exe and qhullcpp.dll from Windows build Fix qhull.sln and project files for qh_QHpointer - Add eg/qhull-zip.sh to build qhull distribution files ------------ qhull 2010.1 2010/01/10 - Test for NULL fp in qh_eachvoronoi [D. Szczerba] qhull 2010.1 2010/01/09 Changes to build and distribution - Use qh_QHpointer=0 for libqhull.a, qhull, rbox, etc. Use -Dqh_QHpointer for libqhullp.a, qhullcpp.dll, etc. qh_QHpointer [2010, gcc] 4% time 4% space, [2003, msvc] 8% time 2% space - Add config/ and project/debian/ for Autoconf build [R. Laboissiere] from debian branch in git and http://savannah.nongnu.org/cvs/?group=qhull - Add CMakeLists.txt [kwilliams] - Fix tabs in Makefile.txt [mschamschula] - Add -fno-strict-aliasing to Makefile for gcc 4.1, 4.2, and 4.3 qset segfault - Remove user_eg.exe and user_eg2.exe from Windows distribution - Order object files by frequency of execution for better locality. Changes to source - Remove ptr_intT from qh_matchvertices. It was int since the beginning. - user.h requires for CLOCKS_PER_SEC - Move ostream<

  ---------------------------------
 
    global.c
    initializes all the globals of the qhull application
 
    see README
 
    see libqhull.h for qh.globals and function prototypes
 
    see qhull_a.h for internal functions
 
    Copyright (c) 1993-2014 The Geometry Center.
-   $Id: //main/2011/qhull/src/libqhull/global.c#15 $$Change: 1490 $
-   $DateTime: 2012/02/19 20:27:01 $$Author: bbarber $
+   $Id: //main/2011/qhull/src/libqhull/global.c#17 $$Change: 1709 $
+   $DateTime: 2014/03/26 22:27:14 $$Author: bbarber $
  */
 
 #include "qhull_a.h"
 
 /*========= qh definition -- globals defined in libqhull.h =======================*/
 
 int qhull_inuse= 0; /* not used */
 
 #if qh_QHpointer
 qhT *qh_qh= NULL;       /* pointer to all global variables */
 #else
 qhT qh_qh;              /* all global variables.
                            Add "= {0}" if this causes a compiler error.
                            Also qh_qhstat in stat.c and qhmem in mem.c.  */
 #endif
 
 /*----------------------------------
 
   qh_version
     version string by year and date
 
     the revision increases on code changes only
 
   notes:
     change date:    Changes.txt, Announce.txt, index.htm, README.txt,
                     qhull-news.html, Eudora signatures, CMakeLists.txt
     change version: README.txt, qh-get.htm, File_id.diz, Makefile.txt
     change year:    Copying.txt
     check download size
     recompile user_eg.c, rbox.c, libqhull.c, qconvex.c, qdelaun.c qvoronoi.c, qhalf.c, testqset.c
 */
 
 const char *qh_version = "2012.1 2012/02/18";
 
 /*---------------------------------
 
   qh_appendprint( printFormat )
     append printFormat to qh.PRINTout unless already defined
 */
 void qh_appendprint(qh_PRINT format) {
   int i;
 
   for (i=0; i < qh_PRINTEND; i++) {
     if (qh PRINTout[i] == format && format != qh_PRINTqhull)
       break;
     if (!qh PRINTout[i]) {
       qh PRINTout[i]= format;
       break;
     }
   }
 } /* appendprint */
 
 /*---------------------------------
 
   qh_checkflags( commandStr, hiddenFlags )
     errors if commandStr contains hiddenFlags
     hiddenFlags starts and ends with a space and is space deliminated (checked)
 
   notes:
     ignores first word (e.g., "qconvex i")
     use qh_strtol/strtod since strtol/strtod may or may not skip trailing spaces
 
   see:
     qh_initflags() initializes Qhull according to commandStr
 */
 void qh_checkflags(char *command, char *hiddenflags) {
   char *s= command, *t, *chkerr; /* qh_skipfilename is non-const */
   char key, opt, prevopt;
   char chkkey[]= "   ";
   char chkopt[]=  "    ";
   char chkopt2[]= "     ";
   boolT waserr= False;
 
   if (*hiddenflags != ' ' || hiddenflags[strlen(hiddenflags)-1] != ' ') {
     qh_fprintf(qh ferr, 6026, "qhull error (qh_checkflags): hiddenflags must start and end with a space: \"%s\"", hiddenflags);
     qh_errexit(qh_ERRinput, NULL, NULL);
   }
   if (strpbrk(hiddenflags, ",\n\r\t")) {
     qh_fprintf(qh ferr, 6027, "qhull error (qh_checkflags): hiddenflags contains commas, newlines, or tabs: \"%s\"", hiddenflags);
     qh_errexit(qh_ERRinput, NULL, NULL);
   }
   while (*s && !isspace(*s))  /* skip program name */
     s++;
   while (*s) {
     while (*s && isspace(*s))
       s++;
     if (*s == '-')
       s++;
     if (!*s)
       break;
     key = *s++;
     chkerr = NULL;
     if (key == 'T' && (*s == 'I' || *s == 'O')) {  /* TI or TO 'file name' */
       s= qh_skipfilename(++s);
       continue;
     }
     chkkey[1]= key;
     if (strstr(hiddenflags, chkkey)) {
       chkerr= chkkey;
     }else if (isupper(key)) {
       opt= ' ';
       prevopt= ' ';
       chkopt[1]= key;
       chkopt2[1]= key;
       while (!chkerr && *s && !isspace(*s)) {
         opt= *s++;
         if (isalpha(opt)) {
           chkopt[2]= opt;
           if (strstr(hiddenflags, chkopt))
             chkerr= chkopt;
           if (prevopt != ' ') {
             chkopt2[2]= prevopt;
             chkopt2[3]= opt;
             if (strstr(hiddenflags, chkopt2))
               chkerr= chkopt2;
           }
         }else if (key == 'Q' && isdigit(opt) && prevopt != 'b'
               && (prevopt == ' ' || islower(prevopt))) {
             chkopt[2]= opt;
             if (strstr(hiddenflags, chkopt))
               chkerr= chkopt;
         }else {
           qh_strtod(s-1, &t);
           if (s < t)
             s= t;
         }
         prevopt= opt;
       }
     }
     if (chkerr) {
       *chkerr= '\'';
       chkerr[strlen(chkerr)-1]=  '\'';
       qh_fprintf(qh ferr, 6029, "qhull error: option %s is not used with this program.\n             It may be used with qhull.\n", chkerr);
       waserr= True;
     }
   }
   if (waserr)
     qh_errexit(qh_ERRinput, NULL, NULL);
 } /* checkflags */
 
 /*---------------------------------
 
   qh_clear_outputflags()
     Clear output flags for QhullPoints
 */
 void qh_clear_outputflags(void) {
   int i,k;
 
   qh ANNOTATEoutput= False;
   qh DOintersections= False;
   qh DROPdim= -1;
   qh FORCEoutput= False;
   qh GETarea= False;
   qh GOODpoint= 0;
   qh GOODpointp= NULL;
   qh GOODthreshold= False;
   qh GOODvertex= 0;
   qh GOODvertexp= NULL;
   qh IStracing= 0;
   qh KEEParea= False;
   qh KEEPmerge= False;
   qh KEEPminArea= REALmax;
   qh PRINTcentrums= False;
   qh PRINTcoplanar= False;
   qh PRINTdots= False;
   qh PRINTgood= False;
   qh PRINTinner= False;
   qh PRINTneighbors= False;
   qh PRINTnoplanes= False;
   qh PRINToptions1st= False;
   qh PRINTouter= False;
   qh PRINTprecision= True;
   qh PRINTridges= False;
   qh PRINTspheres= False;
   qh PRINTstatistics= False;
   qh PRINTsummary= False;
   qh PRINTtransparent= False;
   qh SPLITthresholds= False;
   qh TRACElevel= 0;
   qh TRInormals= False;
   qh USEstdout= False;
   qh VERIFYoutput= False;
   for (k=qh input_dim+1; k--; ) {  /* duplicated in qh_initqhull_buffers and qh_clear_ouputflags */
     qh lower_threshold[k]= -REALmax;
     qh upper_threshold[k]= REALmax;
     qh lower_bound[k]= -REALmax;
     qh upper_bound[k]= REALmax;
   }
 
   for (i=0; i < qh_PRINTEND; i++) {
     qh PRINTout[i]= qh_PRINTnone;
   }
 
   if (!qh qhull_commandsiz2)
       qh qhull_commandsiz2= (int)strlen(qh qhull_command); /* WARN64 */
   else {
       qh qhull_command[qh qhull_commandsiz2]= '\0';
   }
   if (!qh qhull_optionsiz2)
     qh qhull_optionsiz2= (int)strlen(qh qhull_options);  /* WARN64 */
   else {
     qh qhull_options[qh qhull_optionsiz2]= '\0';
     qh qhull_optionlen= qh_OPTIONline;  /* start a new line */
   }
 } /* clear_outputflags */
 
 /*---------------------------------
 
   qh_clock()
     return user CPU time in 100ths (qh_SECtick)
     only defined for qh_CLOCKtype == 2
 
   notes:
     use first value to determine time 0
     from Stevens '92 8.15
 */
 unsigned long qh_clock(void) {
 
 #if (qh_CLOCKtype == 2)
   struct tms time;
   static long clktck;  /* initialized first call */
   double ratio, cpu;
   unsigned long ticks;
 
   if (!clktck) {
     if ((clktck= sysconf(_SC_CLK_TCK)) < 0) {
       qh_fprintf(qh ferr, 6030, "qhull internal error (qh_clock): sysconf() failed.  Use qh_CLOCKtype 1 in user.h\n");
       qh_errexit(qh_ERRqhull, NULL, NULL);
     }
   }
   if (times(&time) == -1) {
     qh_fprintf(qh ferr, 6031, "qhull internal error (qh_clock): times() failed.  Use qh_CLOCKtype 1 in user.h\n");
     qh_errexit(qh_ERRqhull, NULL, NULL);
   }
   ratio= qh_SECticks / (double)clktck;
   ticks= time.tms_utime * ratio;
   return ticks;
 #else
   qh_fprintf(qh ferr, 6032, "qhull internal error (qh_clock): use qh_CLOCKtype 2 in user.h\n");
   qh_errexit(qh_ERRqhull, NULL, NULL); /* never returns */
   return 0;
 #endif
 } /* clock */
 
 /*---------------------------------
 
   qh_freebuffers()
     free up global memory buffers
 
   notes:
     must match qh_initbuffers()
 */
 void qh_freebuffers(void) {
 
   trace5((qh ferr, 5001, "qh_freebuffers: freeing up global memory buffers\n"));
   /* allocated by qh_initqhull_buffers */
   qh_memfree(qh NEARzero, qh hull_dim * sizeof(realT));
   qh_memfree(qh lower_threshold, (qh input_dim+1) * sizeof(realT));
   qh_memfree(qh upper_threshold, (qh input_dim+1) * sizeof(realT));
   qh_memfree(qh lower_bound, (qh input_dim+1) * sizeof(realT));
   qh_memfree(qh upper_bound, (qh input_dim+1) * sizeof(realT));
   qh_memfree(qh gm_matrix, (qh hull_dim+1) * qh hull_dim * sizeof(coordT));
   qh_memfree(qh gm_row, (qh hull_dim+1) * sizeof(coordT *));
   qh NEARzero= qh lower_threshold= qh upper_threshold= NULL;
   qh lower_bound= qh upper_bound= NULL;
   qh gm_matrix= NULL;
   qh gm_row= NULL;
   qh_setfree(&qh other_points);
   qh_setfree(&qh del_vertices);
   qh_setfree(&qh coplanarfacetset);
   if (qh line)                /* allocated by qh_readinput, freed if no error */
     qh_free(qh line);
   if (qh half_space)
     qh_free(qh half_space);
   if (qh temp_malloc)
     qh_free(qh temp_malloc);
   if (qh feasible_point)      /* allocated by qh_readfeasible */
     qh_free(qh feasible_point);
   if (qh feasible_string)     /* allocated by qh_initflags */
     qh_free(qh feasible_string);
   qh line= qh feasible_string= NULL;
   qh half_space= qh feasible_point= qh temp_malloc= NULL;
   /* usually allocated by qh_readinput */
   if (qh first_point && qh POINTSmalloc) {
     qh_free(qh first_point);
     qh first_point= NULL;
   }
   if (qh input_points && qh input_malloc) { /* set by qh_joggleinput */
     qh_free(qh input_points);
     qh input_points= NULL;
   }
   trace5((qh ferr, 5002, "qh_freebuffers: finished\n"));
 } /* freebuffers */
 
 
 /*---------------------------------
 
   qh_freebuild( allmem )
     free global memory used by qh_initbuild and qh_buildhull
     if !allmem,
       does not free short memory (e.g., facetT, freed by qh_memfreeshort)
 
   design:
     free centrums
     free each vertex
     mark unattached ridges
     for each facet
       free ridges
       free outside set, coplanar set, neighbor set, ridge set, vertex set
       free facet
     free hash table
     free interior point
     free merge set
     free temporary sets
 */
 void qh_freebuild(boolT allmem) {
   facetT *facet;
   vertexT *vertex;
   ridgeT *ridge, **ridgep;
   mergeT *merge, **mergep;
 
   trace1((qh ferr, 1005, "qh_freebuild: free memory from qh_inithull and qh_buildhull\n"));
   if (qh del_vertices)
     qh_settruncate(qh del_vertices, 0);
   if (allmem) {
     while ((vertex= qh vertex_list)) {
       if (vertex->next)
         qh_delvertex(vertex);
       else {
         qh_memfree(vertex, (int)sizeof(vertexT));
         qh newvertex_list= qh vertex_list= NULL;
       }
     }
   }else if (qh VERTEXneighbors) {
     FORALLvertices
       qh_setfreelong(&(vertex->neighbors));
   }
   qh VERTEXneighbors= False;
   qh GOODclosest= NULL;
   if (allmem) {
     FORALLfacets {
       FOREACHridge_(facet->ridges)
         ridge->seen= False;
     }
     FORALLfacets {
       if (facet->visible) {
         FOREACHridge_(facet->ridges) {
           if (!otherfacet_(ridge, facet)->visible)
             ridge->seen= True;  /* an unattached ridge */
         }
       }
     }
     while ((facet= qh facet_list)) {
       FOREACHridge_(facet->ridges) {
         if (ridge->seen) {
           qh_setfree(&(ridge->vertices));
           qh_memfree(ridge, (int)sizeof(ridgeT));
         }else
           ridge->seen= True;
       }
       qh_setfree(&(facet->outsideset));
       qh_setfree(&(facet->coplanarset));
       qh_setfree(&(facet->neighbors));
       qh_setfree(&(facet->ridges));
       qh_setfree(&(facet->vertices));
       if (facet->next)
         qh_delfacet(facet);
       else {
         qh_memfree(facet, (int)sizeof(facetT));
         qh visible_list= qh newfacet_list= qh facet_list= NULL;
       }
     }
   }else {
     FORALLfacets {
       qh_setfreelong(&(facet->outsideset));
       qh_setfreelong(&(facet->coplanarset));
       if (!facet->simplicial) {
         qh_setfreelong(&(facet->neighbors));
         qh_setfreelong(&(facet->ridges));
         qh_setfreelong(&(facet->vertices));
       }
     }
   }
   qh_setfree(&(qh hash_table));
   qh_memfree(qh interior_point, qh normal_size);
   qh interior_point= NULL;
   FOREACHmerge_(qh facet_mergeset)  /* usually empty */
     qh_memfree(merge, (int)sizeof(mergeT));
   qh facet_mergeset= NULL;  /* temp set */
   qh degen_mergeset= NULL;  /* temp set */
   qh_settempfree_all();
 } /* freebuild */
 
 /*---------------------------------
 
   qh_freeqhull( allmem )
     see qh_freeqhull2
     if qh_QHpointer, frees qh_qh
 */
 void qh_freeqhull(boolT allmem) {
     qh_freeqhull2(allmem);
 #if qh_QHpointer
     qh_free(qh_qh);
     qh_qh= NULL;
 #endif
 }
 
 /*---------------------------------
 
 qh_freeqhull2( allmem )
   free global memory
   if !allmem,
     does not free short memory (freed by qh_memfreeshort)
 
 notes:
   sets qh.NOerrexit in case caller forgets to
 
 see:
   see qh_initqhull_start2()
 
 design:
   free global and temporary memory from qh_initbuild and qh_buildhull
   free buffers
   free statistics
 */
 void qh_freeqhull2(boolT allmem) {
 
   trace1((qh ferr, 1006, "qh_freeqhull2: free global memory\n"));
   qh NOerrexit= True;  /* no more setjmp since called at exit and ~QhullQh */
   qh_freebuild(allmem);
   qh_freebuffers();
   qh_freestatistics();
 #if qh_QHpointer
   memset((char *)qh_qh, 0, sizeof(qhT));
   /* qh_qh freed by caller, qh_freeqhull() */
 #else
   memset((char *)&qh_qh, 0, sizeof(qhT));
 #endif
   qh NOerrexit= True;
 } /* freeqhull2 */
 
 /*---------------------------------
 
   qh_init_A( infile, outfile, errfile, argc, argv )
     initialize memory and stdio files
     convert input options to option string (qh.qhull_command)
 
   notes:
     infile may be NULL if qh_readpoints() is not called
 
     errfile should always be defined.  It is used for reporting
     errors.  outfile is used for output and format options.
 
     argc/argv may be 0/NULL
 
     called before error handling initialized
     qh_errexit() may not be used
 */
 void qh_init_A(FILE *infile, FILE *outfile, FILE *errfile, int argc, char *argv[]) {
   qh_meminit(errfile);
   qh_initqhull_start(infile, outfile, errfile);
   qh_init_qhull_command(argc, argv);
 } /* init_A */
 
 /*---------------------------------
 
   qh_init_B( points, numpoints, dim, ismalloc )
     initialize globals for points array
 
     points has numpoints dim-dimensional points
       points[0] is the first coordinate of the first point
       points[1] is the second coordinate of the first point
       points[dim] is the first coordinate of the second point
 
     ismalloc=True
       Qhull will call qh_free(points) on exit or input transformation
     ismalloc=False
       Qhull will allocate a new point array if needed for input transformation
 
     qh.qhull_command
       is the option string.
       It is defined by qh_init_B(), qh_qhull_command(), or qh_initflags
 
   returns:
     if qh.PROJECTinput or (qh.DELAUNAY and qh.PROJECTdelaunay)
       projects the input to a new point array
 
         if qh.DELAUNAY,
           qh.hull_dim is increased by one
         if qh.ATinfinity,
           qh_projectinput adds point-at-infinity for Delaunay tri.
 
     if qh.SCALEinput
       changes the upper and lower bounds of the input, see qh_scaleinput()
 
     if qh.ROTATEinput
       rotates the input by a random rotation, see qh_rotateinput()
       if qh.DELAUNAY
         rotates about the last coordinate
 
   notes:
     called after points are defined
     qh_errexit() may be used
 */
 void qh_init_B(coordT *points, int numpoints, int dim, boolT ismalloc) {
   qh_initqhull_globals(points, numpoints, dim, ismalloc);
   if (qhmem.LASTsize == 0)
     qh_initqhull_mem();
   /* mem.c and qset.c are initialized */
   qh_initqhull_buffers();
   qh_initthresholds(qh qhull_command);
   if (qh PROJECTinput || (qh DELAUNAY && qh PROJECTdelaunay))
     qh_projectinput();
   if (qh SCALEinput)
     qh_scaleinput();
   if (qh ROTATErandom >= 0) {
     qh_randommatrix(qh gm_matrix, qh hull_dim, qh gm_row);
     if (qh DELAUNAY) {
       int k, lastk= qh hull_dim-1;
       for (k=0; k < lastk; k++) {
         qh gm_row[k][lastk]= 0.0;
         qh gm_row[lastk][k]= 0.0;
       }
       qh gm_row[lastk][lastk]= 1.0;
     }
     qh_gram_schmidt(qh hull_dim, qh gm_row);
     qh_rotateinput(qh gm_row);
   }
 } /* init_B */
 
 /*---------------------------------
 
   qh_init_qhull_command( argc, argv )
     build qh.qhull_command from argc/argv
 
   returns:
     a space-delimited string of options (just as typed)
 
   notes:
     makes option string easy to input and output
 
     argc/argv may be 0/NULL
 */
 void qh_init_qhull_command(int argc, char *argv[]) {
 
   if (!qh_argv_to_command(argc, argv, qh qhull_command, (int)sizeof(qh qhull_command))){
     /* Assumes qh.ferr is defined. */
     qh_fprintf(qh ferr, 6033, "qhull input error: more than %d characters in command line\n",
           (int)sizeof(qh qhull_command));
     qh_exit(qh_ERRinput);  /* error reported, can not use qh_errexit */
   }
 } /* init_qhull_command */
 
 /*---------------------------------
 
   qh_initflags( commandStr )
     set flags and initialized constants from commandStr
 
   returns:
     sets qh.qhull_command to command if needed
 
   notes:
     ignores first word (e.g., "qhull d")
     use qh_strtol/strtod since strtol/strtod may or may not skip trailing spaces
 
   see:
     qh_initthresholds() continues processing of 'Pdn' and 'PDn'
     'prompt' in unix.c for documentation
 
   design:
     for each space-deliminated option group
       if top-level option
         check syntax
         append approriate option to option string
         set appropriate global variable or append printFormat to print options
       else
         for each sub-option
           check syntax
           append approriate option to option string
           set appropriate global variable or append printFormat to print options
 */
 void qh_initflags(char *command) {
   int k, i, lastproject;
   char *s= command, *t, *prev_s, *start, key;
   boolT isgeom= False, wasproject;
   realT r;
 
   if (command <= &qh qhull_command[0] || command > &qh qhull_command[0] + sizeof(qh qhull_command)) {
     if (command != &qh qhull_command[0]) {
       *qh qhull_command= '\0';
       strncat(qh qhull_command, command, sizeof(qh qhull_command)-strlen(qh qhull_command)-1);
     }
     while (*s && !isspace(*s))  /* skip program name */
       s++;
   }
   while (*s) {
     while (*s && isspace(*s))
       s++;
     if (*s == '-')
       s++;
     if (!*s)
       break;
     prev_s= s;
     switch (*s++) {
     case 'd':
       qh_option("delaunay", NULL, NULL);
       qh DELAUNAY= True;
       break;
     case 'f':
       qh_option("facets", NULL, NULL);
       qh_appendprint(qh_PRINTfacets);
       break;
     case 'i':
       qh_option("incidence", NULL, NULL);
       qh_appendprint(qh_PRINTincidences);
       break;
     case 'm':
       qh_option("mathematica", NULL, NULL);
       qh_appendprint(qh_PRINTmathematica);
       break;
     case 'n':
       qh_option("normals", NULL, NULL);
       qh_appendprint(qh_PRINTnormals);
       break;
     case 'o':
       qh_option("offFile", NULL, NULL);
       qh_appendprint(qh_PRINToff);
       break;
     case 'p':
       qh_option("points", NULL, NULL);
       qh_appendprint(qh_PRINTpoints);
       break;
     case 's':
       qh_option("summary", NULL, NULL);
       qh PRINTsummary= True;
       break;
     case 'v':
       qh_option("voronoi", NULL, NULL);
       qh VORONOI= True;
       qh DELAUNAY= True;
       break;
     case 'A':
       if (!isdigit(*s) && *s != '.' && *s != '-')
         qh_fprintf(qh ferr, 7002, "qhull warning: no maximum cosine angle given for option 'An'.  Ignored.\n");
       else {
         if (*s == '-') {
           qh premerge_cos= -qh_strtod(s, &s);
           qh_option("Angle-premerge-", NULL, &qh premerge_cos);
           qh PREmerge= True;
         }else {
           qh postmerge_cos= qh_strtod(s, &s);
           qh_option("Angle-postmerge", NULL, &qh postmerge_cos);
           qh POSTmerge= True;
         }
         qh MERGING= True;
       }
       break;
     case 'C':
       if (!isdigit(*s) && *s != '.' && *s != '-')
         qh_fprintf(qh ferr, 7003, "qhull warning: no centrum radius given for option 'Cn'.  Ignored.\n");
       else {
         if (*s == '-') {
           qh premerge_centrum= -qh_strtod(s, &s);
           qh_option("Centrum-premerge-", NULL, &qh premerge_centrum);
           qh PREmerge= True;
         }else {
           qh postmerge_centrum= qh_strtod(s, &s);
           qh_option("Centrum-postmerge", NULL, &qh postmerge_centrum);
           qh POSTmerge= True;
         }
         qh MERGING= True;
       }
       break;
     case 'E':
       if (*s == '-')
         qh_fprintf(qh ferr, 7004, "qhull warning: negative maximum roundoff given for option 'An'.  Ignored.\n");
       else if (!isdigit(*s))
         qh_fprintf(qh ferr, 7005, "qhull warning: no maximum roundoff given for option 'En'.  Ignored.\n");
       else {
         qh DISTround= qh_strtod(s, &s);
         qh_option("Distance-roundoff", NULL, &qh DISTround);
         qh SETroundoff= True;
       }
       break;
     case 'H':
       start= s;
       qh HALFspace= True;
       qh_strtod(s, &t);
       while (t > s)  {
         if (*t && !isspace(*t)) {
           if (*t == ',')
             t++;
           else
             qh_fprintf(qh ferr, 7006, "qhull warning: origin for Halfspace intersection should be 'Hn,n,n,...'\n");
         }
         s= t;
         qh_strtod(s, &t);
       }
       if (start < t) {
         if (!(qh feasible_string= (char*)calloc((size_t)(t-start+1), (size_t)1))) {
           qh_fprintf(qh ferr, 6034, "qhull error: insufficient memory for 'Hn,n,n'\n");
           qh_errexit(qh_ERRmem, NULL, NULL);
         }
         strncpy(qh feasible_string, start, (size_t)(t-start));
         qh_option("Halfspace-about", NULL, NULL);
         qh_option(qh feasible_string, NULL, NULL);
       }else
         qh_option("Halfspace", NULL, NULL);
       break;
     case 'R':
       if (!isdigit(*s))
         qh_fprintf(qh ferr, 7007, "qhull warning: missing random perturbation for option 'Rn'.  Ignored\n");
       else {
         qh RANDOMfactor= qh_strtod(s, &s);
         qh_option("Random_perturb", NULL, &qh RANDOMfactor);
         qh RANDOMdist= True;
       }
       break;
     case 'V':
       if (!isdigit(*s) && *s != '-')
         qh_fprintf(qh ferr, 7008, "qhull warning: missing visible distance for option 'Vn'.  Ignored\n");
       else {
         qh MINvisible= qh_strtod(s, &s);
         qh_option("Visible", NULL, &qh MINvisible);
       }
       break;
     case 'U':
       if (!isdigit(*s) && *s != '-')
         qh_fprintf(qh ferr, 7009, "qhull warning: missing coplanar distance for option 'Un'.  Ignored\n");
       else {
         qh MAXcoplanar= qh_strtod(s, &s);
         qh_option("U-coplanar", NULL, &qh MAXcoplanar);
       }
       break;
     case 'W':
       if (*s == '-')
         qh_fprintf(qh ferr, 7010, "qhull warning: negative outside width for option 'Wn'.  Ignored.\n");
       else if (!isdigit(*s))
         qh_fprintf(qh ferr, 7011, "qhull warning: missing outside width for option 'Wn'.  Ignored\n");
       else {
         qh MINoutside= qh_strtod(s, &s);
         qh_option("W-outside", NULL, &qh MINoutside);
         qh APPROXhull= True;
       }
       break;
     /************  sub menus ***************/
     case 'F':
       while (*s && !isspace(*s)) {
         switch (*s++) {
         case 'a':
           qh_option("Farea", NULL, NULL);
           qh_appendprint(qh_PRINTarea);
           qh GETarea= True;
           break;
         case 'A':
           qh_option("FArea-total", NULL, NULL);
           qh GETarea= True;
           break;
         case 'c':
           qh_option("Fcoplanars", NULL, NULL);
           qh_appendprint(qh_PRINTcoplanars);
           break;
         case 'C':
           qh_option("FCentrums", NULL, NULL);
           qh_appendprint(qh_PRINTcentrums);
           break;
         case 'd':
           qh_option("Fd-cdd-in", NULL, NULL);
           qh CDDinput= True;
           break;
         case 'D':
           qh_option("FD-cdd-out", NULL, NULL);
           qh CDDoutput= True;
           break;
         case 'F':
           qh_option("FFacets-xridge", NULL, NULL);
           qh_appendprint(qh_PRINTfacets_xridge);
           break;
         case 'i':
           qh_option("Finner", NULL, NULL);
           qh_appendprint(qh_PRINTinner);
           break;
         case 'I':
           qh_option("FIDs", NULL, NULL);
           qh_appendprint(qh_PRINTids);
           break;
         case 'm':
           qh_option("Fmerges", NULL, NULL);
           qh_appendprint(qh_PRINTmerges);
           break;
         case 'M':
           qh_option("FMaple", NULL, NULL);
           qh_appendprint(qh_PRINTmaple);
           break;
         case 'n':
           qh_option("Fneighbors", NULL, NULL);
           qh_appendprint(qh_PRINTneighbors);
           break;
         case 'N':
           qh_option("FNeighbors-vertex", NULL, NULL);
           qh_appendprint(qh_PRINTvneighbors);
           break;
         case 'o':
           qh_option("Fouter", NULL, NULL);
           qh_appendprint(qh_PRINTouter);
           break;
         case 'O':
           if (qh PRINToptions1st) {
             qh_option("FOptions", NULL, NULL);
             qh_appendprint(qh_PRINToptions);
           }else
             qh PRINToptions1st= True;
           break;
         case 'p':
           qh_option("Fpoint-intersect", NULL, NULL);
           qh_appendprint(qh_PRINTpointintersect);
           break;
         case 'P':
           qh_option("FPoint-nearest", NULL, NULL);
           qh_appendprint(qh_PRINTpointnearest);
           break;
         case 'Q':
           qh_option("FQhull", NULL, NULL);
           qh_appendprint(qh_PRINTqhull);
           break;
         case 's':
           qh_option("Fsummary", NULL, NULL);
           qh_appendprint(qh_PRINTsummary);
           break;
         case 'S':
           qh_option("FSize", NULL, NULL);
           qh_appendprint(qh_PRINTsize);
           qh GETarea= True;
           break;
         case 't':
           qh_option("Ftriangles", NULL, NULL);
           qh_appendprint(qh_PRINTtriangles);
           break;
         case 'v':
           /* option set in qh_initqhull_globals */
           qh_appendprint(qh_PRINTvertices);
           break;
         case 'V':
           qh_option("FVertex-average", NULL, NULL);
           qh_appendprint(qh_PRINTaverage);
           break;
         case 'x':
           qh_option("Fxtremes", NULL, NULL);
           qh_appendprint(qh_PRINTextremes);
           break;
         default:
           s--;
           qh_fprintf(qh ferr, 7012, "qhull warning: unknown 'F' output option %c, rest ignored\n", (int)s[0]);
           while (*++s && !isspace(*s));
           break;
         }
       }
       break;
     case 'G':
       isgeom= True;
       qh_appendprint(qh_PRINTgeom);
       while (*s && !isspace(*s)) {
         switch (*s++) {
         case 'a':
           qh_option("Gall-points", NULL, NULL);
           qh PRINTdots= True;
           break;
         case 'c':
           qh_option("Gcentrums", NULL, NULL);
           qh PRINTcentrums= True;
           break;
         case 'h':
           qh_option("Gintersections", NULL, NULL);
           qh DOintersections= True;
           break;
         case 'i':
           qh_option("Ginner", NULL, NULL);
           qh PRINTinner= True;
           break;
         case 'n':
           qh_option("Gno-planes", NULL, NULL);
           qh PRINTnoplanes= True;
           break;
         case 'o':
           qh_option("Gouter", NULL, NULL);
           qh PRINTouter= True;
           break;
         case 'p':
           qh_option("Gpoints", NULL, NULL);
           qh PRINTcoplanar= True;
           break;
         case 'r':
           qh_option("Gridges", NULL, NULL);
           qh PRINTridges= True;
           break;
         case 't':
           qh_option("Gtransparent", NULL, NULL);
           qh PRINTtransparent= True;
           break;
         case 'v':
           qh_option("Gvertices", NULL, NULL);
           qh PRINTspheres= True;
           break;
         case 'D':
           if (!isdigit(*s))
             qh_fprintf(qh ferr, 6035, "qhull input error: missing dimension for option 'GDn'\n");
           else {
             if (qh DROPdim >= 0)
               qh_fprintf(qh ferr, 7013, "qhull warning: can only drop one dimension.  Previous 'GD%d' ignored\n",
                    qh DROPdim);
             qh DROPdim= qh_strtol(s, &s);
             qh_option("GDrop-dim", &qh DROPdim, NULL);
           }
           break;
         default:
           s--;
           qh_fprintf(qh ferr, 7014, "qhull warning: unknown 'G' print option %c, rest ignored\n", (int)s[0]);
           while (*++s && !isspace(*s));
           break;
         }
       }
       break;
     case 'P':
       while (*s && !isspace(*s)) {
         switch (*s++) {
         case 'd': case 'D':  /* see qh_initthresholds() */
           key= s[-1];
           i= qh_strtol(s, &s);
           r= 0;
           if (*s == ':') {
             s++;
             r= qh_strtod(s, &s);
           }
           if (key == 'd')
             qh_option("Pdrop-facets-dim-less", &i, &r);
           else
             qh_option("PDrop-facets-dim-more", &i, &r);
           break;
         case 'g':
           qh_option("Pgood-facets", NULL, NULL);
           qh PRINTgood= True;
           break;
         case 'G':
           qh_option("PGood-facet-neighbors", NULL, NULL);
           qh PRINTneighbors= True;
           break;
         case 'o':
           qh_option("Poutput-forced", NULL, NULL);
           qh FORCEoutput= True;
           break;
         case 'p':
           qh_option("Pprecision-ignore", NULL, NULL);
           qh PRINTprecision= False;
           break;
         case 'A':
           if (!isdigit(*s))
             qh_fprintf(qh ferr, 6036, "qhull input error: missing facet count for keep area option 'PAn'\n");
           else {
             qh KEEParea= qh_strtol(s, &s);
             qh_option("PArea-keep", &qh KEEParea, NULL);
             qh GETarea= True;
           }
           break;
         case 'F':
           if (!isdigit(*s))
             qh_fprintf(qh ferr, 6037, "qhull input error: missing facet area for option 'PFn'\n");
           else {
             qh KEEPminArea= qh_strtod(s, &s);
             qh_option("PFacet-area-keep", NULL, &qh KEEPminArea);
             qh GETarea= True;
           }
           break;
         case 'M':
           if (!isdigit(*s))
             qh_fprintf(qh ferr, 6038, "qhull input error: missing merge count for option 'PMn'\n");
           else {
             qh KEEPmerge= qh_strtol(s, &s);
             qh_option("PMerge-keep", &qh KEEPmerge, NULL);
           }
           break;
         default:
           s--;
           qh_fprintf(qh ferr, 7015, "qhull warning: unknown 'P' print option %c, rest ignored\n", (int)s[0]);
           while (*++s && !isspace(*s));
           break;
         }
       }
       break;
     case 'Q':
       lastproject= -1;
       while (*s && !isspace(*s)) {
         switch (*s++) {
         case 'b': case 'B':  /* handled by qh_initthresholds */
           key= s[-1];
           if (key == 'b' && *s == 'B') {
             s++;
             r= qh_DEFAULTbox;
             qh SCALEinput= True;
             qh_option("QbBound-unit-box", NULL, &r);
             break;
           }
           if (key == 'b' && *s == 'b') {
             s++;
             qh SCALElast= True;
             qh_option("Qbbound-last", NULL, NULL);
             break;
           }
           k= qh_strtol(s, &s);
           r= 0.0;
           wasproject= False;
           if (*s == ':') {
             s++;
             if ((r= qh_strtod(s, &s)) == 0.0) {
               t= s;            /* need true dimension for memory allocation */
               while (*t && !isspace(*t)) {
                 if (toupper(*t++) == 'B'
                  && k == qh_strtol(t, &t)
                  && *t++ == ':'
                  && qh_strtod(t, &t) == 0.0) {
                   qh PROJECTinput++;
                   trace2((qh ferr, 2004, "qh_initflags: project dimension %d\n", k));
                   qh_option("Qb-project-dim", &k, NULL);
                   wasproject= True;
                   lastproject= k;
                   break;
                 }
               }
             }
           }
           if (!wasproject) {
             if (lastproject == k && r == 0.0)
               lastproject= -1;  /* doesn't catch all possible sequences */
             else if (key == 'b') {
               qh SCALEinput= True;
               if (r == 0.0)
                 r= -qh_DEFAULTbox;
               qh_option("Qbound-dim-low", &k, &r);
             }else {
               qh SCALEinput= True;
               if (r == 0.0)
                 r= qh_DEFAULTbox;
               qh_option("QBound-dim-high", &k, &r);
             }
           }
           break;
         case 'c':
           qh_option("Qcoplanar-keep", NULL, NULL);
           qh KEEPcoplanar= True;
           break;
         case 'f':
           qh_option("Qfurthest-outside", NULL, NULL);
           qh BESToutside= True;
           break;
         case 'g':
           qh_option("Qgood-facets-only", NULL, NULL);
           qh ONLYgood= True;
           break;
         case 'i':
           qh_option("Qinterior-keep", NULL, NULL);
           qh KEEPinside= True;
           break;
         case 'm':
           qh_option("Qmax-outside-only", NULL, NULL);
           qh ONLYmax= True;
           break;
         case 'r':
           qh_option("Qrandom-outside", NULL, NULL);
           qh RANDOMoutside= True;
           break;
         case 's':
           qh_option("Qsearch-initial-simplex", NULL, NULL);
           qh ALLpoints= True;
           break;
         case 't':
           qh_option("Qtriangulate", NULL, NULL);
           qh TRIangulate= True;
           break;
         case 'T':
           qh_option("QTestPoints", NULL, NULL);
           if (!isdigit(*s))
             qh_fprintf(qh ferr, 6039, "qhull input error: missing number of test points for option 'QTn'\n");
           else {
             qh TESTpoints= qh_strtol(s, &s);
             qh_option("QTestPoints", &qh TESTpoints, NULL);
           }
           break;
         case 'u':
           qh_option("QupperDelaunay", NULL, NULL);
           qh UPPERdelaunay= True;
           break;
         case 'v':
           qh_option("Qvertex-neighbors-convex", NULL, NULL);
           qh TESTvneighbors= True;
           break;
         case 'x':
           qh_option("Qxact-merge", NULL, NULL);
           qh MERGEexact= True;
           break;
         case 'z':
           qh_option("Qz-infinity-point", NULL, NULL);
           qh ATinfinity= True;
           break;
         case '0':
           qh_option("Q0-no-premerge", NULL, NULL);
           qh NOpremerge= True;
           break;
         case '1':
           if (!isdigit(*s)) {
             qh_option("Q1-no-angle-sort", NULL, NULL);
             qh ANGLEmerge= False;
             break;
           }
           switch (*s++) {
           case '0':
             qh_option("Q10-no-narrow", NULL, NULL);
             qh NOnarrow= True;
             break;
           case '1':
             qh_option("Q11-trinormals Qtriangulate", NULL, NULL);
             qh TRInormals= True;
             qh TRIangulate= True;
             break;
           default:
             s--;
             qh_fprintf(qh ferr, 7016, "qhull warning: unknown 'Q' qhull option 1%c, rest ignored\n", (int)s[0]);
             while (*++s && !isspace(*s));
             break;
           }
           break;
         case '2':
           qh_option("Q2-no-merge-independent", NULL, NULL);
           qh MERGEindependent= False;
           goto LABELcheckdigit;
           break; /* no warnings */
         case '3':
           qh_option("Q3-no-merge-vertices", NULL, NULL);
           qh MERGEvertices= False;
         LABELcheckdigit:
           if (isdigit(*s))
             qh_fprintf(qh ferr, 7017, "qhull warning: can not follow '1', '2', or '3' with a digit.  '%c' skipped.\n",
                      *s++);
           break;
         case '4':
           qh_option("Q4-avoid-old-into-new", NULL, NULL);
           qh AVOIDold= True;
           break;
         case '5':
           qh_option("Q5-no-check-outer", NULL, NULL);
           qh SKIPcheckmax= True;
           break;
         case '6':
           qh_option("Q6-no-concave-merge", NULL, NULL);
           qh SKIPconvex= True;
           break;
         case '7':
           qh_option("Q7-no-breadth-first", NULL, NULL);
           qh VIRTUALmemory= True;
           break;
         case '8':
           qh_option("Q8-no-near-inside", NULL, NULL);
           qh NOnearinside= True;
           break;
         case '9':
           qh_option("Q9-pick-furthest", NULL, NULL);
           qh PICKfurthest= True;
           break;
         case 'G':
           i= qh_strtol(s, &t);
           if (qh GOODpoint)
             qh_fprintf(qh ferr, 7018, "qhull warning: good point already defined for option 'QGn'.  Ignored\n");
           else if (s == t)
             qh_fprintf(qh ferr, 7019, "qhull warning: missing good point id for option 'QGn'.  Ignored\n");
           else if (i < 0 || *s == '-') {
             qh GOODpoint= i-1;
             qh_option("QGood-if-dont-see-point", &i, NULL);
           }else {
             qh GOODpoint= i+1;
             qh_option("QGood-if-see-point", &i, NULL);
           }
           s= t;
           break;
         case 'J':
           if (!isdigit(*s) && *s != '-')
             qh JOGGLEmax= 0.0;
           else {
             qh JOGGLEmax= (realT) qh_strtod(s, &s);
             qh_option("QJoggle", NULL, &qh JOGGLEmax);
           }
           break;
         case 'R':
           if (!isdigit(*s) && *s != '-')
             qh_fprintf(qh ferr, 7020, "qhull warning: missing random seed for option 'QRn'.  Ignored\n");
           else {
             qh ROTATErandom= i= qh_strtol(s, &s);
             if (i > 0)
               qh_option("QRotate-id", &i, NULL );
             else if (i < -1)
               qh_option("QRandom-seed", &i, NULL );
           }
           break;
         case 'V':
           i= qh_strtol(s, &t);
           if (qh GOODvertex)
             qh_fprintf(qh ferr, 7021, "qhull warning: good vertex already defined for option 'QVn'.  Ignored\n");
           else if (s == t)
             qh_fprintf(qh ferr, 7022, "qhull warning: no good point id given for option 'QVn'.  Ignored\n");
           else if (i < 0) {
             qh GOODvertex= i - 1;
             qh_option("QV-good-facets-not-point", &i, NULL);
           }else {
             qh_option("QV-good-facets-point", &i, NULL);
             qh GOODvertex= i + 1;
           }
           s= t;
           break;
         default:
           s--;
           qh_fprintf(qh ferr, 7023, "qhull warning: unknown 'Q' qhull option %c, rest ignored\n", (int)s[0]);
           while (*++s && !isspace(*s));
           break;
         }
       }
       break;
     case 'T':
       while (*s && !isspace(*s)) {
         if (isdigit(*s) || *s == '-')
           qh IStracing= qh_strtol(s, &s);
         else switch (*s++) {
         case 'a':
           qh_option("Tannotate-output", NULL, NULL);
           qh ANNOTATEoutput= True;
           break;
         case 'c':
           qh_option("Tcheck-frequently", NULL, NULL);
           qh CHECKfrequently= True;
           break;
         case 's':
           qh_option("Tstatistics", NULL, NULL);
           qh PRINTstatistics= True;
           break;
         case 'v':
           qh_option("Tverify", NULL, NULL);
           qh VERIFYoutput= True;
           break;
         case 'z':
           if (qh ferr == qh_FILEstderr) {
             /* The C++ interface captures the output in qh_fprint_qhull() */
             qh_option("Tz-stdout", NULL, NULL);
             qh USEstdout= True;
           }else if (!qh fout)
             qh_fprintf(qh ferr, 7024, "qhull warning: output file undefined(stdout).  Option 'Tz' ignored.\n");
           else {
             qh_option("Tz-stdout", NULL, NULL);
             qh USEstdout= True;
             qh ferr= qh fout;
             qhmem.ferr= qh fout;
           }
           break;
         case 'C':
           if (!isdigit(*s))
             qh_fprintf(qh ferr, 7025, "qhull warning: missing point id for cone for trace option 'TCn'.  Ignored\n");
           else {
             i= qh_strtol(s, &s);
             qh_option("TCone-stop", &i, NULL);
             qh STOPcone= i + 1;
           }
           break;
         case 'F':
           if (!isdigit(*s))
             qh_fprintf(qh ferr, 7026, "qhull warning: missing frequency count for trace option 'TFn'.  Ignored\n");
           else {
             qh REPORTfreq= qh_strtol(s, &s);
             qh_option("TFacet-log", &qh REPORTfreq, NULL);
             qh REPORTfreq2= qh REPORTfreq/2;  /* for tracemerging() */
           }
           break;
         case 'I':
           if (!isspace(*s))
             qh_fprintf(qh ferr, 7027, "qhull warning: missing space between 'TI' and filename, %s\n", s);
           while (isspace(*s))
             s++;
           t= qh_skipfilename(s);
           {
             char filename[qh_FILENAMElen];
 
             qh_copyfilename(filename, (int)sizeof(filename), s, (int)(t-s));   /* WARN64 */
             s= t;
             if (!freopen(filename, "r", stdin)) {
               qh_fprintf(qh ferr, 6041, "qhull error: could not open file \"%s\".", filename);
               qh_errexit(qh_ERRinput, NULL, NULL);
             }else {
               qh_option("TInput-file", NULL, NULL);
               qh_option(filename, NULL, NULL);
             }
           }
           break;
         case 'O':
             if (!isspace(*s))
                 qh_fprintf(qh ferr, 7028, "qhull warning: missing space between 'TO' and filename, %s\n", s);
             while (isspace(*s))
                 s++;
             t= qh_skipfilename(s);
             {
               char filename[qh_FILENAMElen];
 
               qh_copyfilename(filename, (int)sizeof(filename), s, (int)(t-s));  /* WARN64 */
               s= t;
               if (!freopen(filename, "w", stdout)) {
                 qh_fprintf(qh ferr, 6044, "qhull error: could not open file \"%s\".", filename);
                 qh_errexit(qh_ERRinput, NULL, NULL);
               }else {
                 qh_option("TOutput-file", NULL, NULL);
               qh_option(filename, NULL, NULL);
             }
           }
           break;
         case 'P':
           if (!isdigit(*s))
             qh_fprintf(qh ferr, 7029, "qhull warning: missing point id for trace option 'TPn'.  Ignored\n");
           else {
             qh TRACEpoint= qh_strtol(s, &s);
             qh_option("Trace-point", &qh TRACEpoint, NULL);
           }
           break;
         case 'M':
           if (!isdigit(*s))
             qh_fprintf(qh ferr, 7030, "qhull warning: missing merge id for trace option 'TMn'.  Ignored\n");
           else {
             qh TRACEmerge= qh_strtol(s, &s);
             qh_option("Trace-merge", &qh TRACEmerge, NULL);
           }
           break;
         case 'R':
           if (!isdigit(*s))
             qh_fprintf(qh ferr, 7031, "qhull warning: missing rerun count for trace option 'TRn'.  Ignored\n");
           else {
             qh RERUN= qh_strtol(s, &s);
             qh_option("TRerun", &qh RERUN, NULL);
           }
           break;
         case 'V':
           i= qh_strtol(s, &t);
           if (s == t)
             qh_fprintf(qh ferr, 7032, "qhull warning: missing furthest point id for trace option 'TVn'.  Ignored\n");
           else if (i < 0) {
             qh STOPpoint= i - 1;
             qh_option("TV-stop-before-point", &i, NULL);
           }else {
             qh STOPpoint= i + 1;
             qh_option("TV-stop-after-point", &i, NULL);
           }
           s= t;
           break;
         case 'W':
           if (!isdigit(*s))
             qh_fprintf(qh ferr, 7033, "qhull warning: missing max width for trace option 'TWn'.  Ignored\n");
           else {
             qh TRACEdist= (realT) qh_strtod(s, &s);
             qh_option("TWide-trace", NULL, &qh TRACEdist);
           }
           break;
         default:
           s--;
           qh_fprintf(qh ferr, 7034, "qhull warning: unknown 'T' trace option %c, rest ignored\n", (int)s[0]);
           while (*++s && !isspace(*s));
           break;
         }
       }
       break;
     default:
       qh_fprintf(qh ferr, 7035, "qhull warning: unknown flag %c(%x)\n", (int)s[-1],
                (int)s[-1]);
       break;
     }
     if (s-1 == prev_s && *s && !isspace(*s)) {
       qh_fprintf(qh ferr, 7036, "qhull warning: missing space after flag %c(%x); reserved for menu. Skipped.\n",
                (int)*prev_s, (int)*prev_s);
       while (*s && !isspace(*s))
         s++;
     }
   }
   if (qh STOPcone && qh JOGGLEmax < REALmax/2)
     qh_fprintf(qh ferr, 7078, "qhull warning: 'TCn' (stopCone) ignored when used with 'QJn' (joggle)\n");
   if (isgeom && !qh FORCEoutput && qh PRINTout[1])
     qh_fprintf(qh ferr, 7037, "qhull warning: additional output formats are not compatible with Geomview\n");
   /* set derived values in qh_initqhull_globals */
 } /* initflags */
 
 
 /*---------------------------------
 
   qh_initqhull_buffers()
     initialize global memory buffers
 
   notes:
     must match qh_freebuffers()
 */
 void qh_initqhull_buffers(void) {
   int k;
 
   qh TEMPsize= (qhmem.LASTsize - sizeof(setT))/SETelemsize;
   if (qh TEMPsize <= 0 || qh TEMPsize > qhmem.LASTsize)
     qh TEMPsize= 8;  /* e.g., if qh_NOmem */
   qh other_points= qh_setnew(qh TEMPsize);
   qh del_vertices= qh_setnew(qh TEMPsize);
   qh coplanarfacetset= qh_setnew(qh TEMPsize);
   qh NEARzero= (realT *)qh_memalloc(qh hull_dim * sizeof(realT));
   qh lower_threshold= (realT *)qh_memalloc((qh input_dim+1) * sizeof(realT));
   qh upper_threshold= (realT *)qh_memalloc((qh input_dim+1) * sizeof(realT));
   qh lower_bound= (realT *)qh_memalloc((qh input_dim+1) * sizeof(realT));
   qh upper_bound= (realT *)qh_memalloc((qh input_dim+1) * sizeof(realT));
   for (k=qh input_dim+1; k--; ) {  /* duplicated in qh_initqhull_buffers and qh_clear_ouputflags */
     qh lower_threshold[k]= -REALmax;
     qh upper_threshold[k]= REALmax;
     qh lower_bound[k]= -REALmax;
     qh upper_bound[k]= REALmax;
   }
   qh gm_matrix= (coordT *)qh_memalloc((qh hull_dim+1) * qh hull_dim * sizeof(coordT));
   qh gm_row= (coordT **)qh_memalloc((qh hull_dim+1) * sizeof(coordT *));
 } /* initqhull_buffers */
 
 /*---------------------------------
 
   qh_initqhull_globals( points, numpoints, dim, ismalloc )
     initialize globals
     if ismalloc
       points were malloc'd and qhull should free at end
 
   returns:
     sets qh.first_point, num_points, input_dim, hull_dim and others
     seeds random number generator (seed=1 if tracing)
     modifies qh.hull_dim if ((qh.DELAUNAY and qh.PROJECTdelaunay) or qh.PROJECTinput)
     adjust user flags as needed
     also checks DIM3 dependencies and constants
 
   notes:
     do not use qh_point() since an input transformation may move them elsewhere
 
   see:
     qh_initqhull_start() sets default values for non-zero globals
 
   design:
     initialize points array from input arguments
     test for qh.ZEROcentrum
       (i.e., use opposite vertex instead of cetrum for convexity testing)
     initialize qh.CENTERtype, qh.normal_size,
       qh.center_size, qh.TRACEpoint/level,
     initialize and test random numbers
     qh_initqhull_outputflags() -- adjust and test output flags
 */
 void qh_initqhull_globals(coordT *points, int numpoints, int dim, boolT ismalloc) {
   int seed, pointsneeded, extra= 0, i, randi, k;
   realT randr;
   realT factorial;
 
   time_t timedata;
 
   trace0((qh ferr, 13, "qh_initqhull_globals: for %s | %s\n", qh rbox_command,
       qh qhull_command));
   qh POINTSmalloc= ismalloc;
   qh first_point= points;
   qh num_points= numpoints;
   qh hull_dim= qh input_dim= dim;
   if (!qh NOpremerge && !qh MERGEexact && !qh PREmerge && qh JOGGLEmax > REALmax/2) {
     qh MERGING= True;
     if (qh hull_dim <= 4) {
       qh PREmerge= True;
       qh_option("_pre-merge", NULL, NULL);
     }else {
       qh MERGEexact= True;
       qh_option("Qxact_merge", NULL, NULL);
     }
   }else if (qh MERGEexact)
     qh MERGING= True;
   if (!qh NOpremerge && qh JOGGLEmax > REALmax/2) {
 #ifdef qh_NOmerge
     qh JOGGLEmax= 0.0;
 #endif
   }
   if (qh TRIangulate && qh JOGGLEmax < REALmax/2 && qh PRINTprecision)
     qh_fprintf(qh ferr, 7038, "qhull warning: joggle('QJ') always produces simplicial output.  Triangulated output('Qt') does nothing.\n");
   if (qh JOGGLEmax < REALmax/2 && qh DELAUNAY && !qh SCALEinput && !qh SCALElast) {
     qh SCALElast= True;
     qh_option("Qbbound-last-qj", NULL, NULL);
   }
   if (qh MERGING && !qh POSTmerge && qh premerge_cos > REALmax/2
   && qh premerge_centrum == 0) {
     qh ZEROcentrum= True;
     qh ZEROall_ok= True;
     qh_option("_zero-centrum", NULL, NULL);
   }
   if (qh JOGGLEmax < REALmax/2 && REALepsilon > 2e-8 && qh PRINTprecision)
     qh_fprintf(qh ferr, 7039, "qhull warning: real epsilon, %2.2g, is probably too large for joggle('QJn')\nRecompile with double precision reals(see user.h).\n",
           REALepsilon);
 #ifdef qh_NOmerge
   if (qh MERGING) {
     qh_fprintf(qh ferr, 6045, "qhull input error: merging not installed(qh_NOmerge + 'Qx', 'Cn' or 'An')\n");
     qh_errexit(qh_ERRinput, NULL, NULL);
   }
 #endif
   if (qh DELAUNAY && qh KEEPcoplanar && !qh KEEPinside) {
     qh KEEPinside= True;
     qh_option("Qinterior-keep", NULL, NULL);
   }
   if (qh DELAUNAY && qh HALFspace) {
     qh_fprintf(qh ferr, 6046, "qhull input error: can not use Delaunay('d') or Voronoi('v') with halfspace intersection('H')\n");
     qh_errexit(qh_ERRinput, NULL, NULL);
   }
   if (!qh DELAUNAY && (qh UPPERdelaunay || qh ATinfinity)) {
     qh_fprintf(qh ferr, 6047, "qhull input error: use upper-Delaunay('Qu') or infinity-point('Qz') with Delaunay('d') or Voronoi('v')\n");
     qh_errexit(qh_ERRinput, NULL, NULL);
   }
   if (qh UPPERdelaunay && qh ATinfinity) {
     qh_fprintf(qh ferr, 6048, "qhull input error: can not use infinity-point('Qz') with upper-Delaunay('Qu')\n");
     qh_errexit(qh_ERRinput, NULL, NULL);
   }
   if (qh SCALElast && !qh DELAUNAY && qh PRINTprecision)
     qh_fprintf(qh ferr, 7040, "qhull input warning: option 'Qbb' (scale-last-coordinate) is normally used with 'd' or 'v'\n");
   qh DOcheckmax= (!qh SKIPcheckmax && qh MERGING );
   qh KEEPnearinside= (qh DOcheckmax && !(qh KEEPinside && qh KEEPcoplanar)
                           && !qh NOnearinside);
   if (qh MERGING)
     qh CENTERtype= qh_AScentrum;
   else if (qh VORONOI)
     qh CENTERtype= qh_ASvoronoi;
   if (qh TESTvneighbors && !qh MERGING) {
     qh_fprintf(qh ferr, 6049, "qhull input error: test vertex neighbors('Qv') needs a merge option\n");
     qh_errexit(qh_ERRinput, NULL ,NULL);
   }
   if (qh PROJECTinput || (qh DELAUNAY && qh PROJECTdelaunay)) {
     qh hull_dim -= qh PROJECTinput;
     if (qh DELAUNAY) {
       qh hull_dim++;
       if (qh ATinfinity)
         extra= 1;
     }
   }
   if (qh hull_dim <= 1) {
     qh_fprintf(qh ferr, 6050, "qhull error: dimension %d must be > 1\n", qh hull_dim);
     qh_errexit(qh_ERRinput, NULL, NULL);
   }
   for (k=2, factorial=1.0; k < qh hull_dim; k++)
     factorial *= k;
   qh AREAfactor= 1.0 / factorial;
   trace2((qh ferr, 2005, "qh_initqhull_globals: initialize globals.  dim %d numpoints %d malloc? %d projected %d to hull_dim %d\n",
         dim, numpoints, ismalloc, qh PROJECTinput, qh hull_dim));
   qh normal_size= qh hull_dim * sizeof(coordT);
   qh center_size= qh normal_size - sizeof(coordT);
   pointsneeded= qh hull_dim+1;
   if (qh hull_dim > qh_DIMmergeVertex) {
     qh MERGEvertices= False;
     qh_option("Q3-no-merge-vertices-dim-high", NULL, NULL);
   }
   if (qh GOODpoint)
     pointsneeded++;
 #ifdef qh_NOtrace
   if (qh IStracing) {
     qh_fprintf(qh ferr, 6051, "qhull input error: tracing is not installed(qh_NOtrace in user.h)");
     qh_errexit(qh_ERRqhull, NULL, NULL);
   }
 #endif
   if (qh RERUN > 1) {
     qh TRACElastrun= qh IStracing; /* qh_build_withrestart duplicates next conditional */
     if (qh IStracing != -1)
       qh IStracing= 0;
   }else if (qh TRACEpoint != -1 || qh TRACEdist < REALmax/2 || qh TRACEmerge) {
     qh TRACElevel= (qh IStracing? qh IStracing : 3);
     qh IStracing= 0;
   }
   if (qh ROTATErandom == 0 || qh ROTATErandom == -1) {
     seed= (int)time(&timedata);
     if (qh ROTATErandom  == -1) {
       seed= -seed;
       qh_option("QRandom-seed", &seed, NULL );
     }else
       qh_option("QRotate-random", &seed, NULL);
     qh ROTATErandom= seed;
   }
   seed= qh ROTATErandom;
   if (seed == INT_MIN)    /* default value */
     seed= 1;
   else if (seed < 0)
     seed= -seed;
   qh_RANDOMseed_(seed);
   randr= 0.0;
   for (i=1000; i--; ) {
     randi= qh_RANDOMint;
     randr += randi;
     if (randi > qh_RANDOMmax) {
       qh_fprintf(qh ferr, 8036, "\
 qhull configuration error (qh_RANDOMmax in user.h):\n\
    random integer %d > qh_RANDOMmax(%.8g)\n",
                randi, qh_RANDOMmax);
       qh_errexit(qh_ERRinput, NULL, NULL);
     }
   }
   qh_RANDOMseed_(seed);
   randr = randr/1000;
   if (randr < qh_RANDOMmax * 0.1
   || randr > qh_RANDOMmax * 0.9)
     qh_fprintf(qh ferr, 8037, "\
 qhull configuration warning (qh_RANDOMmax in user.h):\n\
    average of 1000 random integers (%.2g) is much different than expected (%.2g).\n\
    Is qh_RANDOMmax (%.2g) wrong?\n",
              randr, qh_RANDOMmax * 0.5, qh_RANDOMmax);
   qh RANDOMa= 2.0 * qh RANDOMfactor/qh_RANDOMmax;
   qh RANDOMb= 1.0 - qh RANDOMfactor;
   if (qh_HASHfactor < 1.1) {
     qh_fprintf(qh ferr, 6052, "qhull internal error (qh_initqhull_globals): qh_HASHfactor %d must be at least 1.1.  Qhull uses linear hash probing\n",
       qh_HASHfactor);
     qh_errexit(qh_ERRqhull, NULL, NULL);
   }
   if (numpoints+extra < pointsneeded) {
     qh_fprintf(qh ferr, 6214, "qhull input error: not enough points(%d) to construct initial simplex (need %d)\n",
             numpoints, pointsneeded);
     qh_errexit(qh_ERRinput, NULL, NULL);
   }
   qh_initqhull_outputflags();
 } /* initqhull_globals */
 
 /*---------------------------------
 
   qh_initqhull_mem(  )
     initialize mem.c for qhull
     qh.hull_dim and qh.normal_size determine some of the allocation sizes
     if qh.MERGING,
       includes ridgeT
     calls qh_user_memsizes() to add up to 10 additional sizes for quick allocation
       (see numsizes below)
 
   returns:
     mem.c already for qh_memalloc/qh_memfree (errors if called beforehand)
 
   notes:
     qh_produceoutput() prints memsizes
 
 */
 void qh_initqhull_mem(void) {
   int numsizes;
   int i;
 
   numsizes= 8+10;
   qh_meminitbuffers(qh IStracing, qh_MEMalign, numsizes,
                      qh_MEMbufsize,qh_MEMinitbuf);
   qh_memsize((int)sizeof(vertexT));
   if (qh MERGING) {
     qh_memsize((int)sizeof(ridgeT));
     qh_memsize((int)sizeof(mergeT));
   }
   qh_memsize((int)sizeof(facetT));
   i= sizeof(setT) + (qh hull_dim - 1) * SETelemsize;  /* ridge.vertices */
   qh_memsize(i);
   qh_memsize(qh normal_size);        /* normal */
   i += SETelemsize;                 /* facet.vertices, .ridges, .neighbors */
   qh_memsize(i);
   qh_user_memsizes();
   qh_memsetup();
 } /* initqhull_mem */
 
 /*---------------------------------
 
   qh_initqhull_outputflags
     initialize flags concerned with output
 
   returns:
     adjust user flags as needed
 
   see:
     qh_clear_outputflags() resets the flags
 
   design:
     test for qh.PRINTgood (i.e., only print 'good' facets)
     check for conflicting print output options
 */
 void qh_initqhull_outputflags(void) {
   boolT printgeom= False, printmath= False, printcoplanar= False;
   int i;
 
   trace3((qh ferr, 3024, "qh_initqhull_outputflags: %s\n", qh qhull_command));
   if (!(qh PRINTgood || qh PRINTneighbors)) {
     if (qh KEEParea || qh KEEPminArea < REALmax/2 || qh KEEPmerge || qh DELAUNAY
         || (!qh ONLYgood && (qh GOODvertex || qh GOODpoint))) {
       qh PRINTgood= True;
       qh_option("Pgood", NULL, NULL);
     }
   }
   if (qh PRINTtransparent) {
     if (qh hull_dim != 4 || !qh DELAUNAY || qh VORONOI || qh DROPdim >= 0) {
       qh_fprintf(qh ferr, 6215, "qhull input error: transparent Delaunay('Gt') needs 3-d Delaunay('d') w/o 'GDn'\n");
       qh_errexit(qh_ERRinput, NULL, NULL);
     }
     qh DROPdim = 3;
     qh PRINTridges = True;
   }
   for (i=qh_PRINTEND; i--; ) {
     if (qh PRINTout[i] == qh_PRINTgeom)
       printgeom= True;
     else if (qh PRINTout[i] == qh_PRINTmathematica || qh PRINTout[i] == qh_PRINTmaple)
       printmath= True;
     else if (qh PRINTout[i] == qh_PRINTcoplanars)
       printcoplanar= True;
     else if (qh PRINTout[i] == qh_PRINTpointnearest)
       printcoplanar= True;
     else if (qh PRINTout[i] == qh_PRINTpointintersect && !qh HALFspace) {
       qh_fprintf(qh ferr, 6053, "qhull input error: option 'Fp' is only used for \nhalfspace intersection('Hn,n,n').\n");
       qh_errexit(qh_ERRinput, NULL, NULL);
     }else if (qh PRINTout[i] == qh_PRINTtriangles && (qh HALFspace || qh VORONOI)) {
       qh_fprintf(qh ferr, 6054, "qhull input error: option 'Ft' is not available for Voronoi vertices or halfspace intersection\n");
       qh_errexit(qh_ERRinput, NULL, NULL);
     }else if (qh PRINTout[i] == qh_PRINTcentrums && qh VORONOI) {
       qh_fprintf(qh ferr, 6055, "qhull input error: option 'FC' is not available for Voronoi vertices('v')\n");
       qh_errexit(qh_ERRinput, NULL, NULL);
     }else if (qh PRINTout[i] == qh_PRINTvertices) {
       if (qh VORONOI)
         qh_option("Fvoronoi", NULL, NULL);
       else
         qh_option("Fvertices", NULL, NULL);
     }
   }
   if (printcoplanar && qh DELAUNAY && qh JOGGLEmax < REALmax/2) {
     if (qh PRINTprecision)
       qh_fprintf(qh ferr, 7041, "qhull input warning: 'QJ' (joggle) will usually prevent coincident input sites for options 'Fc' and 'FP'\n");
   }
   if (printmath && (qh hull_dim > 3 || qh VORONOI)) {
     qh_fprintf(qh ferr, 6056, "qhull input error: Mathematica and Maple output is only available for 2-d and 3-d convex hulls and 2-d Delaunay triangulations\n");
     qh_errexit(qh_ERRinput, NULL, NULL);
   }
   if (printgeom) {
     if (qh hull_dim > 4) {
       qh_fprintf(qh ferr, 6057, "qhull input error: Geomview output is only available for 2-d, 3-d and 4-d\n");
       qh_errexit(qh_ERRinput, NULL, NULL);
     }
     if (qh PRINTnoplanes && !(qh PRINTcoplanar + qh PRINTcentrums
      + qh PRINTdots + qh PRINTspheres + qh DOintersections + qh PRINTridges)) {
       qh_fprintf(qh ferr, 6058, "qhull input error: no output specified for Geomview\n");
       qh_errexit(qh_ERRinput, NULL, NULL);
     }
     if (qh VORONOI && (qh hull_dim > 3 || qh DROPdim >= 0)) {
       qh_fprintf(qh ferr, 6059, "qhull input error: Geomview output for Voronoi diagrams only for 2-d\n");
       qh_errexit(qh_ERRinput, NULL, NULL);
     }
     /* can not warn about furthest-site Geomview output: no lower_threshold */
     if (qh hull_dim == 4 && qh DROPdim == -1 &&
         (qh PRINTcoplanar || qh PRINTspheres || qh PRINTcentrums)) {
       qh_fprintf(qh ferr, 7042, "qhull input warning: coplanars, vertices, and centrums output not\n\
 available for 4-d output(ignored).  Could use 'GDn' instead.\n");
       qh PRINTcoplanar= qh PRINTspheres= qh PRINTcentrums= False;
     }
   }
   if (!qh KEEPcoplanar && !qh KEEPinside && !qh ONLYgood) {
     if ((qh PRINTcoplanar && qh PRINTspheres) || printcoplanar) {
       if (qh QHULLfinished) {
         qh_fprintf(qh ferr, 7072, "qhull output warning: ignoring coplanar points, option 'Qc' was not set for the first run of qhull.\n");
       }else {
         qh KEEPcoplanar = True;
         qh_option("Qcoplanar", NULL, NULL);
       }
     }
   }
   qh PRINTdim= qh hull_dim;
   if (qh DROPdim >=0) {    /* after Geomview checks */
     if (qh DROPdim < qh hull_dim) {
       qh PRINTdim--;
       if (!printgeom || qh hull_dim < 3)
         qh_fprintf(qh ferr, 7043, "qhull input warning: drop dimension 'GD%d' is only available for 3-d/4-d Geomview\n", qh DROPdim);
     }else
       qh DROPdim= -1;
   }else if (qh VORONOI) {
     qh DROPdim= qh hull_dim-1;
     qh PRINTdim= qh hull_dim-1;
   }
 } /* qh_initqhull_outputflags */
 
 /*---------------------------------
 
   qh_initqhull_start( infile, outfile, errfile )
     allocate memory if needed and call qh_initqhull_start2()
 */
 void qh_initqhull_start(FILE *infile, FILE *outfile, FILE *errfile) {
 
 #if qh_QHpointer
   if (qh_qh) {
     qh_fprintf(errfile, 6205, "qhull error (qh_initqhull_start): qh_qh already defined.  Call qh_save_qhull() first\n");
     qh_exit(qh_ERRqhull);  /* no error handler */
   }
   if (!(qh_qh= (qhT *)qh_malloc(sizeof(qhT)))) {
     qh_fprintf(errfile, 6060, "qhull error (qh_initqhull_start): insufficient memory\n");
     qh_exit(qh_ERRmem);  /* no error handler */
   }
 #endif
   qh_initstatistics();
   qh_initqhull_start2(infile, outfile, errfile);
 } /* initqhull_start */
 
 /*---------------------------------
 
   qh_initqhull_start2( infile, outfile, errfile )
     start initialization of qhull
     initialize statistics, stdio, default values for global variables
     assumes qh_qh is defined
   notes:
     report errors elsewhere, error handling and g_qhull_output [Qhull.cpp, QhullQh()] not in initialized
   see:
     qh_maxmin() determines the precision constants
     qh_freeqhull2()
 */
 void qh_initqhull_start2(FILE *infile, FILE *outfile, FILE *errfile) {
   time_t timedata;
   int seed;
 
   qh_CPUclock; /* start the clock(for qh_clock).  One-shot. */
 #if qh_QHpointer
   memset((char *)qh_qh, 0, sizeof(qhT));   /* every field is 0, FALSE, NULL */
 #else
   memset((char *)&qh_qh, 0, sizeof(qhT));
 #endif
   qh ANGLEmerge= True;
   qh DROPdim= -1;
   qh ferr= errfile;
   qh fin= infile;
   qh fout= outfile;
   qh furthest_id= -1;
   qh JOGGLEmax= REALmax;
   qh KEEPminArea = REALmax;
   qh last_low= REALmax;
   qh last_high= REALmax;
   qh last_newhigh= REALmax;
   qh max_outside= 0.0;
   qh max_vertex= 0.0;
   qh MAXabs_coord= 0.0;
   qh MAXsumcoord= 0.0;
   qh MAXwidth= -REALmax;
   qh MERGEindependent= True;
   qh MINdenom_1= fmax_(1.0/REALmax, REALmin); /* used by qh_scalepoints */
   qh MINoutside= 0.0;
   qh MINvisible= REALmax;
   qh MAXcoplanar= REALmax;
   qh outside_err= REALmax;
   qh premerge_centrum= 0.0;
   qh premerge_cos= REALmax;
   qh PRINTprecision= True;
   qh PRINTradius= 0.0;
   qh postmerge_cos= REALmax;
   qh postmerge_centrum= 0.0;
   qh ROTATErandom= INT_MIN;
   qh MERGEvertices= True;
   qh totarea= 0.0;
   qh totvol= 0.0;
   qh TRACEdist= REALmax;
   qh TRACEpoint= -1; /* recompile or use 'TPn' */
   qh tracefacet_id= UINT_MAX;  /* recompile to trace a facet */
   qh tracevertex_id= UINT_MAX; /* recompile to trace a vertex */
   seed= (int)time(&timedata);
   qh_RANDOMseed_(seed);
-  qh run_id= qh_RANDOMint+1; /* disallow 0 [UsingLibQhull::NOqhRunId] */
+  qh->run_id= qh_RANDOMint;
+  if(!qh->run_id)
+      qh->run_id++;  /* guarantee non-zero */
   qh_option("run-id", &qh run_id, NULL);
   strcat(qh qhull, "qhull");
 } /* initqhull_start2 */
 
 /*---------------------------------
 
   qh_initthresholds( commandString )
     set thresholds for printing and scaling from commandString
 
   returns:
     sets qh.GOODthreshold or qh.SPLITthreshold if 'Pd0D1' used
 
   see:
     qh_initflags(), 'Qbk' 'QBk' 'Pdk' and 'PDk'
     qh_inthresholds()
 
   design:
     for each 'Pdn' or 'PDn' option
       check syntax
       set qh.lower_threshold or qh.upper_threshold
     set qh.GOODthreshold if an unbounded threshold is used
     set qh.SPLITthreshold if a bounded threshold is used
 */
 void qh_initthresholds(char *command) {
   realT value;
   int idx, maxdim, k;
   char *s= command; /* non-const due to strtol */
   char key;
 
   maxdim= qh input_dim;
   if (qh DELAUNAY && (qh PROJECTdelaunay || qh PROJECTinput))
     maxdim++;
   while (*s) {
     if (*s == '-')
       s++;
     if (*s == 'P') {
       s++;
       while (*s && !isspace(key= *s++)) {
         if (key == 'd' || key == 'D') {
           if (!isdigit(*s)) {
             qh_fprintf(qh ferr, 7044, "qhull warning: no dimension given for Print option '%c' at: %s.  Ignored\n",
                     key, s-1);
             continue;
           }
           idx= qh_strtol(s, &s);
           if (idx >= qh hull_dim) {
             qh_fprintf(qh ferr, 7045, "qhull warning: dimension %d for Print option '%c' is >= %d.  Ignored\n",
                 idx, key, qh hull_dim);
             continue;
           }
           if (*s == ':') {
             s++;
             value= qh_strtod(s, &s);
             if (fabs((double)value) > 1.0) {
               qh_fprintf(qh ferr, 7046, "qhull warning: value %2.4g for Print option %c is > +1 or < -1.  Ignored\n",
                       value, key);
               continue;
             }
           }else
             value= 0.0;
           if (key == 'd')
             qh lower_threshold[idx]= value;
           else
             qh upper_threshold[idx]= value;
         }
       }
     }else if (*s == 'Q') {
       s++;
       while (*s && !isspace(key= *s++)) {
         if (key == 'b' && *s == 'B') {
           s++;
           for (k=maxdim; k--; ) {
             qh lower_bound[k]= -qh_DEFAULTbox;
             qh upper_bound[k]= qh_DEFAULTbox;
           }
         }else if (key == 'b' && *s == 'b')
           s++;
         else if (key == 'b' || key == 'B') {
           if (!isdigit(*s)) {
             qh_fprintf(qh ferr, 7047, "qhull warning: no dimension given for Qhull option %c.  Ignored\n",
                     key);
             continue;
           }
           idx= qh_strtol(s, &s);
           if (idx >= maxdim) {
             qh_fprintf(qh ferr, 7048, "qhull warning: dimension %d for Qhull option %c is >= %d.  Ignored\n",
                 idx, key, maxdim);
             continue;
           }
           if (*s == ':') {
             s++;
             value= qh_strtod(s, &s);
           }else if (key == 'b')
             value= -qh_DEFAULTbox;
           else
             value= qh_DEFAULTbox;
           if (key == 'b')
             qh lower_bound[idx]= value;
           else
             qh upper_bound[idx]= value;
         }
       }
     }else {
       while (*s && !isspace(*s))
         s++;
     }
     while (isspace(*s))
       s++;
   }
   for (k=qh hull_dim; k--; ) {
     if (qh lower_threshold[k] > -REALmax/2) {
       qh GOODthreshold= True;
       if (qh upper_threshold[k] < REALmax/2) {
         qh SPLITthresholds= True;
         qh GOODthreshold= False;
         break;
       }
     }else if (qh upper_threshold[k] < REALmax/2)
       qh GOODthreshold= True;
   }
 } /* initthresholds */
 
 /*---------------------------------
 
   qh_option( option, intVal, realVal )
     add an option description to qh.qhull_options
 
   notes:
     NOerrors -- qh_option can not call qh_errexit() [qh_initqhull_start2]
     will be printed with statistics ('Ts') and errors
     strlen(option) < 40
 */
 void qh_option(const char *option, int *i, realT *r) {
   char buf[200];
   int len, maxlen;
 
   sprintf(buf, "  %s", option);
   if (i)
     sprintf(buf+strlen(buf), " %d", *i);
   if (r)
     sprintf(buf+strlen(buf), " %2.2g", *r);
   len= (int)strlen(buf);  /* WARN64 */
   qh qhull_optionlen += len;
   maxlen= sizeof(qh qhull_options) - len -1;
   maximize_(maxlen, 0);
   if (qh qhull_optionlen >= qh_OPTIONline && maxlen > 0) {
     qh qhull_optionlen= len;
     strncat(qh qhull_options, "\n", (size_t)(maxlen--));
   }
   strncat(qh qhull_options, buf, (size_t)maxlen);
 } /* option */
 
 #if qh_QHpointer
 /*---------------------------------
 
   qh_restore_qhull( oldqh )
     restores a previously saved qhull
     also restores qh_qhstat and qhmem.tempstack
     Sets *oldqh to NULL
   notes:
     errors if current qhull hasn't been saved or freed
     uses qhmem for error reporting
 
   NOTE 1998/5/11:
     Freeing memory after qh_save_qhull and qh_restore_qhull
     is complicated.  The procedures will be redesigned.
 
   see:
     qh_save_qhull(), UsingLibQhull
 */
 void qh_restore_qhull(qhT **oldqh) {
 
   if (*oldqh && strcmp((*oldqh)->qhull, "qhull")) {
     qh_fprintf(qhmem.ferr, 6061, "qhull internal error (qh_restore_qhull): %p is not a qhull data structure\n",
                   *oldqh);
     qh_errexit(qh_ERRqhull, NULL, NULL);
   }
   if (qh_qh) {
     qh_fprintf(qhmem.ferr, 6062, "qhull internal error (qh_restore_qhull): did not save or free existing qhull\n");
     qh_errexit(qh_ERRqhull, NULL, NULL);
   }
   if (!*oldqh || !(*oldqh)->old_qhstat) {
     qh_fprintf(qhmem.ferr, 6063, "qhull internal error (qh_restore_qhull): did not previously save qhull %p\n",
                   *oldqh);
     qh_errexit(qh_ERRqhull, NULL, NULL);
   }
   qh_qh= *oldqh;
   *oldqh= NULL;
   qh_qhstat= qh old_qhstat;
   qhmem.tempstack= qh old_tempstack;
   qh old_qhstat= 0;
   qh old_tempstack= 0;
   trace1((qh ferr, 1007, "qh_restore_qhull: restored qhull from %p\n", *oldqh));
 } /* restore_qhull */
 
 /*---------------------------------
 
   qh_save_qhull(  )
     saves qhull for a later qh_restore_qhull
     also saves qh_qhstat and qhmem.tempstack
 
   returns:
     qh_qh=NULL
 
   notes:
     need to initialize qhull or call qh_restore_qhull before continuing
 
   NOTE 1998/5/11:
     Freeing memory after qh_save_qhull and qh_restore_qhull
     is complicated.  The procedures will be redesigned.
 
   see:
     qh_restore_qhull()
 */
 qhT *qh_save_qhull(void) {
   qhT *oldqh;
 
   trace1((qhmem.ferr, 1045, "qh_save_qhull: save qhull %p\n", qh_qh));
   if (!qh_qh) {
     qh_fprintf(qhmem.ferr, 6064, "qhull internal error (qh_save_qhull): qhull not initialized\n");
     qh_errexit(qh_ERRqhull, NULL, NULL);
   }
   qh old_qhstat= qh_qhstat;
   qh_qhstat= NULL;
   qh old_tempstack= qhmem.tempstack;
   qhmem.tempstack= NULL;
   oldqh= qh_qh;
   qh_qh= NULL;
   return oldqh;
 } /* save_qhull */
 
 #endif
 
diff --git a/src/libqhull/libqhull.h b/src/libqhull/libqhull.h
index 1d05958..6762352 100644
--- a/src/libqhull/libqhull.h
+++ b/src/libqhull/libqhull.h
@@ -1,1100 +1,1101 @@
 /*
  ---------------------------------
 
    libqhull.h
    user-level header file for using qhull.a library
 
    see qh-qhull.htm, qhull_a.h
 
    Copyright (c) 1993-2014 The Geometry Center.
-   $Id: //main/2011/qhull/src/libqhull/libqhull.h#9 $$Change: 1651 $
-   $DateTime: 2014/01/17 08:13:57 $$Author: bbarber $
+   $Id: //main/2011/qhull/src/libqhull/libqhull.h#10 $$Change: 1708 $
+   $DateTime: 2014/03/26 19:13:56 $$Author: bbarber $
 
    NOTE: access to qh_qh is via the 'qh' macro.  This allows
    qh_qh to be either a pointer or a structure.  An example
    of using qh is "qh.DROPdim" which accesses the DROPdim
    field of qh_qh.  Similarly, access to qh_qhstat is via
    the 'qhstat' macro.
 
    includes function prototypes for libqhull.c, geom.c, global.c, io.c, user.c
 
    use mem.h for mem.c
    use qset.h for qset.c
 
    see unix.c for an example of using libqhull.h
 
    recompile qhull if you change this file
 */
 
 #ifndef qhDEFlibqhull
 #define qhDEFlibqhull 1
 
 /*=========================== -included files ==============*/
 
 #include "user.h"      /* user definable constants (e.g., qh_QHpointer) */
 
 #include 
 #include 
 #include 
 #include 
 
 #if __MWERKS__ && __POWERPC__
 #include  
 #include  
 #include        
 #endif
 
 #ifndef __STDC__
 #ifndef __cplusplus
 #if     !_MSC_VER
 #error  Neither __STDC__ nor __cplusplus is defined.  Please use strict ANSI C or C++ to compile
 #error  Qhull.  You may need to turn off compiler extensions in your project configuration.  If
 #error  your compiler is a standard C compiler, you can delete this warning from libqhull.h
 #endif
 #endif
 #endif
 
 /*============ constants and basic types ====================*/
 
 extern const char *qh_version; /* defined in global.c */
 
 /*----------------------------------
 
   coordT
     coordinates and coefficients are stored as realT (i.e., double)
 
   notes:
     Qhull works well if realT is 'float'.  If so joggle (QJ) is not effective.
 
     Could use 'float' for data and 'double' for calculations (realT vs. coordT)
       This requires many type casts, and adjusted error bounds.
       Also C compilers may do expressions in double anyway.
 */
 #define coordT realT
 
 /*----------------------------------
 
   pointT
     a point is an array of coordinates, usually qh.hull_dim
 */
 #define pointT coordT
 
 /*----------------------------------
 
   flagT
     Boolean flag as a bit
 */
 #define flagT unsigned int
 
 /*----------------------------------
 
   boolT
     boolean value, either True or False
 
   notes:
     needed for portability
     Use qh_False/qh_True as synonyms
 */
 #define boolT unsigned int
 #ifdef False
 #undef False
 #endif
 #ifdef True
 #undef True
 #endif
 #define False 0
 #define True 1
 #define qh_False 0
 #define qh_True 1
 
 /*----------------------------------
 
   qh_CENTER
     to distinguish facet->center
 */
 typedef enum
 {
     qh_ASnone = 0, qh_ASvoronoi, qh_AScentrum
 }
 qh_CENTER;
 
 /*----------------------------------
 
   qh_PRINT
     output formats for printing (qh.PRINTout).
     'Fa' 'FV' 'Fc' 'FC'
 
 
    notes:
    some of these names are similar to qhT names.  The similar names are only
    used in switch statements in qh_printbegin() etc.
 */
 typedef enum {qh_PRINTnone= 0,
   qh_PRINTarea, qh_PRINTaverage,           /* 'Fa' 'FV' 'Fc' 'FC' */
   qh_PRINTcoplanars, qh_PRINTcentrums,
   qh_PRINTfacets, qh_PRINTfacets_xridge,   /* 'f' 'FF' 'G' 'FI' 'Fi' 'Fn' */
   qh_PRINTgeom, qh_PRINTids, qh_PRINTinner, qh_PRINTneighbors,
   qh_PRINTnormals, qh_PRINTouter, qh_PRINTmaple, /* 'n' 'Fo' 'i' 'm' 'Fm' 'FM', 'o' */
   qh_PRINTincidences, qh_PRINTmathematica, qh_PRINTmerges, qh_PRINToff,
   qh_PRINToptions, qh_PRINTpointintersect, /* 'FO' 'Fp' 'FP' 'p' 'FQ' 'FS' */
   qh_PRINTpointnearest, qh_PRINTpoints, qh_PRINTqhull, qh_PRINTsize,
   qh_PRINTsummary, qh_PRINTtriangles,      /* 'Fs' 'Ft' 'Fv' 'FN' 'Fx' */
   qh_PRINTvertices, qh_PRINTvneighbors, qh_PRINTextremes,
   qh_PRINTEND} qh_PRINT;
 
 /*----------------------------------
 
   qh_ALL
     argument flag for selecting everything
 */
 #define qh_ALL      True
 #define qh_NOupper  True     /* argument for qh_findbest */
 #define qh_IScheckmax  True     /* argument for qh_findbesthorizon */
 #define qh_ISnewfacets  True     /* argument for qh_findbest */
 #define qh_RESETvisible  True     /* argument for qh_resetlists */
 
 /*----------------------------------
 
   qh_ERR
     Qhull exit codes, for indicating errors
     See: MSG_ERROR and MSG_WARNING [user.h]
 */
 #define qh_ERRnone  0    /* no error occurred during qhull */
 #define qh_ERRinput 1    /* input inconsistency */
 #define qh_ERRsingular 2 /* singular input data */
 #define qh_ERRprec  3    /* precision error */
 #define qh_ERRmem   4    /* insufficient memory, matches mem.h */
 #define qh_ERRqhull 5    /* internal error detected, matches mem.h */
 
 /*----------------------------------
 
 qh_FILEstderr
 Fake stderr to distinguish error output from normal output
 For C++ interface.  Must redefine qh_fprintf_qhull
 */
 #define qh_FILEstderr ((FILE*)1)
 
 /* ============ -structures- ====================
    each of the following structures is defined by a typedef
    all realT and coordT fields occur at the beginning of a structure
         (otherwise space may be wasted due to alignment)
    define all flags together and pack into 32-bit number
 */
 
 typedef struct vertexT vertexT;
 typedef struct ridgeT ridgeT;
 typedef struct facetT facetT;
 #ifndef DEFsetT
 #define DEFsetT 1
 typedef struct setT setT;          /* defined in qset.h */
 #endif
 
 #ifndef DEFqhstatT
 #define DEFqhstatT 1
 typedef struct qhstatT qhstatT;    /* defined in stat.h */
 #endif
 
 /*----------------------------------
 
   facetT
     defines a facet
 
   notes:
    qhull() generates the hull as a list of facets.
 
   topological information:
     f.previous,next     doubly-linked list of facets
     f.vertices          set of vertices
     f.ridges            set of ridges
     f.neighbors         set of neighbors
     f.toporient         True if facet has top-orientation (else bottom)
 
   geometric information:
     f.offset,normal     hyperplane equation
     f.maxoutside        offset to outer plane -- all points inside
     f.center            centrum for testing convexity
     f.simplicial        True if facet is simplicial
     f.flipped           True if facet does not include qh.interior_point
 
   for constructing hull:
     f.visible           True if facet on list of visible facets (will be deleted)
     f.newfacet          True if facet on list of newly created facets
     f.coplanarset       set of points coplanar with this facet
                         (includes near-inside points for later testing)
     f.outsideset        set of points outside of this facet
     f.furthestdist      distance to furthest point of outside set
     f.visitid           marks visited facets during a loop
     f.replace           replacement facet for to-be-deleted, visible facets
     f.samecycle,newcycle cycle of facets for merging into horizon facet
 
   see below for other flags and fields
 */
 struct facetT {
 #if !qh_COMPUTEfurthest
   coordT   furthestdist;/* distance to furthest point of outsideset */
 #endif
 #if qh_MAXoutside
   coordT   maxoutside;  /* max computed distance of point to facet
                         Before QHULLfinished this is an approximation
                         since maxdist not always set for mergefacet
                         Actual outer plane is +DISTround and
                         computed outer plane is +2*DISTround */
 #endif
   coordT   offset;      /* exact offset of hyperplane from origin */
   coordT  *normal;      /* normal of hyperplane, hull_dim coefficients */
                         /*   if tricoplanar, shared with a neighbor */
   union {               /* in order of testing */
    realT   area;        /* area of facet, only in io.c if  ->isarea */
    facetT *replace;     /*  replacement facet if ->visible and NEWfacets
                              is NULL only if qh_mergedegen_redundant or interior */
    facetT *samecycle;   /*  cycle of facets from the same visible/horizon intersection,
                              if ->newfacet */
    facetT *newcycle;    /*  in horizon facet, current samecycle of new facets */
    facetT *trivisible;  /* visible facet for ->tricoplanar facets during qh_triangulate() */
    facetT *triowner;    /* owner facet for ->tricoplanar, !isarea facets w/ ->keepcentrum */
   }f;
   coordT  *center;      /*  centrum for convexity, qh.CENTERtype == qh_AScentrum */
                         /*  Voronoi center, qh.CENTERtype == qh_ASvoronoi */
                         /*   if tricoplanar, shared with a neighbor */
   facetT  *previous;    /* previous facet in the facet_list */
   facetT  *next;        /* next facet in the facet_list */
   setT    *vertices;    /* vertices for this facet, inverse sorted by ID
                            if simplicial, 1st vertex was apex/furthest */
   setT    *ridges;      /* explicit ridges for nonsimplicial facets.
                            for simplicial facets, neighbors define the ridges */
   setT    *neighbors;   /* neighbors of the facet.  If simplicial, the kth
                            neighbor is opposite the kth vertex, and the first
                            neighbor is the horizon facet for the first vertex*/
   setT    *outsideset;  /* set of points outside this facet
                            if non-empty, last point is furthest
                            if NARROWhull, includes coplanars for partitioning*/
   setT    *coplanarset; /* set of points coplanar with this facet
                            > qh.min_vertex and <= facet->max_outside
                            a point is assigned to the furthest facet
                            if non-empty, last point is furthest away */
   unsigned visitid;     /* visit_id, for visiting all neighbors,
                            all uses are independent */
   unsigned id;          /* unique identifier from qh.facet_id */
   unsigned nummerge:9;  /* number of merges */
 #define qh_MAXnummerge 511 /*     2^9-1, 32 flags total, see "flags:" in io.c */
   flagT    tricoplanar:1; /* True if TRIangulate and simplicial and coplanar with a neighbor */
                           /*   all tricoplanars share the same ->center, ->normal, ->offset, ->maxoutside */
                           /*   all tricoplanars share the same apex */
                           /*   if ->degenerate, does not span facet (one logical ridge) */
                           /*   one tricoplanar has ->keepcentrum and ->coplanarset */
                           /*   during qh_triangulate, f.trivisible points to original facet */
   flagT    newfacet:1;  /* True if facet on qh.newfacet_list (new or merged) */
   flagT    visible:1;   /* True if visible facet (will be deleted) */
   flagT    toporient:1; /* True if created with top orientation
                            after merging, use ridge orientation */
   flagT    simplicial:1;/* True if simplicial facet, ->ridges may be implicit */
   flagT    seen:1;      /* used to perform operations only once, like visitid */
   flagT    seen2:1;     /* used to perform operations only once, like visitid */
   flagT    flipped:1;   /* True if facet is flipped */
   flagT    upperdelaunay:1; /* True if facet is upper envelope of Delaunay triangulation */
   flagT    notfurthest:1; /* True if last point of outsideset is not furthest*/
 
 /*-------- flags primarily for output ---------*/
   flagT    good:1;      /* True if a facet marked good for output */
   flagT    isarea:1;    /* True if facet->f.area is defined */
 
 /*-------- flags for merging ------------------*/
   flagT    dupridge:1;  /* True if duplicate ridge in facet */
   flagT    mergeridge:1; /* True if facet or neighbor contains a qh_MERGEridge
                             ->normal defined (also defined for mergeridge2) */
   flagT    mergeridge2:1; /* True if neighbor contains a qh_MERGEridge (mark_dupridges */
   flagT    coplanar:1;  /* True if horizon facet is coplanar at last use */
   flagT     mergehorizon:1; /* True if will merge into horizon (->coplanar) */
   flagT     cycledone:1;/* True if mergecycle_all already done */
   flagT    tested:1;    /* True if facet convexity has been tested (false after merge */
   flagT    keepcentrum:1; /* True if keep old centrum after a merge, or marks owner for ->tricoplanar */
   flagT    newmerge:1;  /* True if facet is newly merged for reducevertices */
   flagT    degenerate:1; /* True if facet is degenerate (degen_mergeset or ->tricoplanar) */
   flagT    redundant:1;  /* True if facet is redundant (degen_mergeset) */
 };
 
 
 /*----------------------------------
 
   ridgeT
     defines a ridge
 
   notes:
   a ridge is hull_dim-1 simplex between two neighboring facets.  If the
   facets are non-simplicial, there may be more than one ridge between
   two facets.  E.G. a 4-d hypercube has two triangles between each pair
   of neighboring facets.
 
   topological information:
     vertices            a set of vertices
     top,bottom          neighboring facets with orientation
 
   geometric information:
     tested              True if ridge is clearly convex
     nonconvex           True if ridge is non-convex
 */
 struct ridgeT {
   setT    *vertices;    /* vertices belonging to this ridge, inverse sorted by ID
                            NULL if a degen ridge (matchsame) */
   facetT  *top;         /* top facet this ridge is part of */
   facetT  *bottom;      /* bottom facet this ridge is part of */
   unsigned id:24;       /* unique identifier, =>room for 8 flags, bit field matches qh.ridge_id */
   flagT    seen:1;      /* used to perform operations only once */
   flagT    tested:1;    /* True when ridge is tested for convexity */
   flagT    nonconvex:1; /* True if getmergeset detected a non-convex neighbor
                            only one ridge between neighbors may have nonconvex */
 };
 
 /*----------------------------------
 
   vertexT
      defines a vertex
 
   topological information:
     next,previous       doubly-linked list of all vertices
     neighbors           set of adjacent facets (only if qh.VERTEXneighbors)
 
   geometric information:
     point               array of DIM3 coordinates
 */
 struct vertexT {
   vertexT *next;        /* next vertex in vertex_list */
   vertexT *previous;    /* previous vertex in vertex_list */
   pointT  *point;       /* hull_dim coordinates (coordT) */
   setT    *neighbors;   /* neighboring facets of vertex, qh_vertexneighbors()
                            inits in io.c or after first merge */
   unsigned visitid:31;  /* for use with qh.vertex_visit, size must match */
   flagT    seen2:1;     /* another seen flag */
   unsigned id:24;       /* unique identifier, bit field matches qh.vertex_id */
   unsigned dim:4;       /* dimension of point if non-zero, used by cpp */
                         /* =>room for 4 flags */
   flagT    seen:1;      /* used to perform operations only once */
   flagT    delridge:1;  /* vertex was part of a deleted ridge */
   flagT    deleted:1;   /* true if vertex on qh.del_vertices */
   flagT    newlist:1;   /* true if vertex on qh.newvertex_list */
 };
 
 #define MAX_vdim 15  /* Maximum size of vertex->dim */
 
 /*======= -global variables -qh ============================*/
 
 /*----------------------------------
 
   qh
    all global variables for qhull are in qh, qhmem, and qhstat
 
   notes:
    qhmem is defined in mem.h, qhstat is defined in stat.h, qhrbox is defined in rboxpoints.h
    Access to qh_qh is via the "qh" macro.  See qh_QHpointer in user.h
 
    All global variables for qhull are in qh, qhmem, and qhstat
    qh must be unique for each instance of qhull
    qhstat may be shared between qhull instances.
    qhmem may be shared across multiple instances of Qhull.
    Rbox uses global variables rbox_inuse and rbox, but does not persist data across calls.
 
    Qhull is not multithreaded.  Global state could be stored in thread-local storage.
 */
 
 extern int qhull_inuse;
 
 typedef struct qhT qhT;
 #if qh_QHpointer_dllimport
 #define qh qh_qh->
 __declspec(dllimport) extern qhT *qh_qh;     /* allocated in global.c */
 #elif qh_QHpointer
 #define qh qh_qh->
 extern qhT *qh_qh;     /* allocated in global.c */
 #elif qh_dllimport
 #define qh qh_qh.
 __declspec(dllimport) extern qhT qh_qh;      /* allocated in global.c */
 #else
 #define qh qh_qh.
 extern qhT qh_qh;
 #endif
 
 struct qhT {
 
 /*----------------------------------
 
   qh constants
     configuration flags and constants for Qhull
 
   notes:
     The user configures Qhull by defining flags.  They are
     copied into qh by qh_setflags().  qh-quick.htm#options defines the flags.
 */
   boolT ALLpoints;        /* true 'Qs' if search all points for initial simplex */
   boolT ANGLEmerge;       /* true 'Qa' if sort potential merges by angle */
   boolT APPROXhull;       /* true 'Wn' if MINoutside set */
   realT   MINoutside;     /*   'Wn' min. distance for an outside point */
   boolT ANNOTATEoutput;   /* true 'Ta' if annotate output with message codes */
   boolT ATinfinity;       /* true 'Qz' if point num_points-1 is "at-infinity"
                              for improving precision in Delaunay triangulations */
   boolT AVOIDold;         /* true 'Q4' if avoid old->new merges */
   boolT BESToutside;      /* true 'Qf' if partition points into best outsideset */
   boolT CDDinput;         /* true 'Pc' if input uses CDD format (1.0/offset first) */
   boolT CDDoutput;        /* true 'PC' if print normals in CDD format (offset first) */
   boolT CHECKfrequently;  /* true 'Tc' if checking frequently */
   realT premerge_cos;     /*   'A-n'   cos_max when pre merging */
   realT postmerge_cos;    /*   'An'    cos_max when post merging */
   boolT DELAUNAY;         /* true 'd' if computing DELAUNAY triangulation */
   boolT DOintersections;  /* true 'Gh' if print hyperplane intersections */
   int   DROPdim;          /* drops dim 'GDn' for 4-d -> 3-d output */
   boolT FORCEoutput;      /* true 'Po' if forcing output despite degeneracies */
   int   GOODpoint;        /* 1+n for 'QGn', good facet if visible/not(-) from point n*/
   pointT *GOODpointp;     /*   the actual point */
   boolT GOODthreshold;    /* true if qh.lower_threshold/upper_threshold defined
                              false if qh.SPLITthreshold */
   int   GOODvertex;       /* 1+n, good facet if vertex for point n */
   pointT *GOODvertexp;     /*   the actual point */
   boolT HALFspace;        /* true 'Hn,n,n' if halfspace intersection */
+  boolT ISqhullQh;        /* Set by Qhull.cpp on initialization */
   int   IStracing;        /* trace execution, 0=none, 1=least, 4=most, -1=events */
   int   KEEParea;         /* 'PAn' number of largest facets to keep */
   boolT KEEPcoplanar;     /* true 'Qc' if keeping nearest facet for coplanar points */
   boolT KEEPinside;       /* true 'Qi' if keeping nearest facet for inside points
                               set automatically if 'd Qc' */
   int   KEEPmerge;        /* 'PMn' number of facets to keep with most merges */
   realT KEEPminArea;      /* 'PFn' minimum facet area to keep */
   realT MAXcoplanar;      /* 'Un' max distance below a facet to be coplanar*/
   boolT MERGEexact;       /* true 'Qx' if exact merges (coplanar, degen, dupridge, flipped) */
   boolT MERGEindependent; /* true 'Q2' if merging independent sets */
   boolT MERGING;          /* true if exact-, pre- or post-merging, with angle and centrum tests */
   realT   premerge_centrum;  /*   'C-n' centrum_radius when pre merging.  Default is round-off */
   realT   postmerge_centrum; /*   'Cn' centrum_radius when post merging.  Default is round-off */
   boolT MERGEvertices;    /* true 'Q3' if merging redundant vertices */
   realT MINvisible;       /* 'Vn' min. distance for a facet to be visible */
   boolT NOnarrow;         /* true 'Q10' if no special processing for narrow distributions */
   boolT NOnearinside;     /* true 'Q8' if ignore near-inside points when partitioning */
   boolT NOpremerge;       /* true 'Q0' if no defaults for C-0 or Qx */
   boolT ONLYgood;         /* true 'Qg' if process points with good visible or horizon facets */
   boolT ONLYmax;          /* true 'Qm' if only process points that increase max_outside */
   boolT PICKfurthest;     /* true 'Q9' if process furthest of furthest points*/
   boolT POSTmerge;        /* true if merging after buildhull (Cn or An) */
   boolT PREmerge;         /* true if merging during buildhull (C-n or A-n) */
                         /* NOTE: some of these names are similar to qh_PRINT names */
   boolT PRINTcentrums;    /* true 'Gc' if printing centrums */
   boolT PRINTcoplanar;    /* true 'Gp' if printing coplanar points */
   int   PRINTdim;         /* print dimension for Geomview output */
   boolT PRINTdots;        /* true 'Ga' if printing all points as dots */
   boolT PRINTgood;        /* true 'Pg' if printing good facets */
   boolT PRINTinner;       /* true 'Gi' if printing inner planes */
   boolT PRINTneighbors;   /* true 'PG' if printing neighbors of good facets */
   boolT PRINTnoplanes;    /* true 'Gn' if printing no planes */
   boolT PRINToptions1st;  /* true 'FO' if printing options to stderr */
   boolT PRINTouter;       /* true 'Go' if printing outer planes */
   boolT PRINTprecision;   /* false 'Pp' if not reporting precision problems */
   qh_PRINT PRINTout[qh_PRINTEND]; /* list of output formats to print */
   boolT PRINTridges;      /* true 'Gr' if print ridges */
   boolT PRINTspheres;     /* true 'Gv' if print vertices as spheres */
   boolT PRINTstatistics;  /* true 'Ts' if printing statistics to stderr */
   boolT PRINTsummary;     /* true 's' if printing summary to stderr */
   boolT PRINTtransparent; /* true 'Gt' if print transparent outer ridges */
   boolT PROJECTdelaunay;  /* true if DELAUNAY, no readpoints() and
                              need projectinput() for Delaunay in qh_init_B */
   int   PROJECTinput;     /* number of projected dimensions 'bn:0Bn:0' */
   boolT QUICKhelp;        /* true if quick help message for degen input */
   boolT RANDOMdist;       /* true if randomly change distplane and setfacetplane */
   realT RANDOMfactor;     /*    maximum random perturbation */
   realT RANDOMa;          /*    qh_randomfactor is randr * RANDOMa + RANDOMb */
   realT RANDOMb;
   boolT RANDOMoutside;    /* true if select a random outside point */
   int   REPORTfreq;       /* buildtracing reports every n facets */
   int   REPORTfreq2;      /* tracemerging reports every REPORTfreq/2 facets */
   int   RERUN;            /* 'TRn' rerun qhull n times (qh.build_cnt) */
   int   ROTATErandom;     /* 'QRn' seed, 0 time, >= rotate input */
   boolT SCALEinput;       /* true 'Qbk' if scaling input */
   boolT SCALElast;        /* true 'Qbb' if scale last coord to max prev coord */
   boolT SETroundoff;      /* true 'E' if qh.DISTround is predefined */
   boolT SKIPcheckmax;     /* true 'Q5' if skip qh_check_maxout */
   boolT SKIPconvex;       /* true 'Q6' if skip convexity testing during pre-merge */
   boolT SPLITthresholds;  /* true if upper_/lower_threshold defines a region
                                used only for printing (!for qh.ONLYgood) */
   int   STOPcone;         /* 'TCn' 1+n for stopping after cone for point n */
                           /*       also used by qh_build_withresart for err exit*/
   int   STOPpoint;        /* 'TVn' 'TV-n' 1+n for stopping after/before(-)
                                         adding point n */
   int   TESTpoints;       /* 'QTn' num of test points after qh.num_points.  Test points always coplanar. */
   boolT TESTvneighbors;   /*  true 'Qv' if test vertex neighbors at end */
   int   TRACElevel;       /* 'Tn' conditional IStracing level */
   int   TRACElastrun;     /*  qh.TRACElevel applies to last qh.RERUN */
   int   TRACEpoint;       /* 'TPn' start tracing when point n is a vertex */
   realT TRACEdist;        /* 'TWn' start tracing when merge distance too big */
   int   TRACEmerge;       /* 'TMn' start tracing before this merge */
   boolT TRIangulate;      /* true 'Qt' if triangulate non-simplicial facets */
   boolT TRInormals;       /* true 'Q11' if triangulate duplicates normals (sets Qt) */
   boolT UPPERdelaunay;    /* true 'Qu' if computing furthest-site Delaunay */
   boolT USEstdout;        /* true 'Tz' if using stdout instead of stderr */
   boolT VERIFYoutput;     /* true 'Tv' if verify output at end of qhull */
   boolT VIRTUALmemory;    /* true 'Q7' if depth-first processing in buildhull */
   boolT VORONOI;          /* true 'v' if computing Voronoi diagram */
 
   /*--------input constants ---------*/
   realT AREAfactor;       /* 1/(hull_dim-1)! for converting det's to area */
   boolT DOcheckmax;       /* true if calling qh_check_maxout (qh_initqhull_globals) */
   char  *feasible_string;  /* feasible point 'Hn,n,n' for halfspace intersection */
   coordT *feasible_point;  /*    as coordinates, both malloc'd */
   boolT GETarea;          /* true 'Fa', 'FA', 'FS', 'PAn', 'PFn' if compute facet area/Voronoi volume in io.c */
   boolT KEEPnearinside;   /* true if near-inside points in coplanarset */
   int   hull_dim;         /* dimension of hull, set by initbuffers */
   int   input_dim;        /* dimension of input, set by initbuffers */
   int   num_points;       /* number of input points */
   pointT *first_point;    /* array of input points, see POINTSmalloc */
   boolT POINTSmalloc;     /*   true if qh.first_point/num_points allocated */
   pointT *input_points;   /* copy of original qh.first_point for input points for qh_joggleinput */
   boolT input_malloc;     /* true if qh.input_points malloc'd */
   char  qhull_command[256];/* command line that invoked this program */
   int   qhull_commandsiz2; /*    size of qhull_command at qh_clear_outputflags */
   char  rbox_command[256]; /* command line that produced the input points */
   char  qhull_options[512];/* descriptive list of options */
   int   qhull_optionlen;  /*    length of last line */
   int   qhull_optionsiz;  /*    size of qhull_options at qh_build_withrestart */
   int   qhull_optionsiz2; /*    size of qhull_options at qh_clear_outputflags */
   int   run_id;           /* non-zero, random identifier for this instance of qhull */
   boolT VERTEXneighbors;  /* true if maintaining vertex neighbors */
   boolT ZEROcentrum;      /* true if 'C-0' or 'C-0 Qx'.  sets ZEROall_ok */
   realT *upper_threshold; /* don't print if facet->normal[k]>=upper_threshold[k]
                              must set either GOODthreshold or SPLITthreshold
                              if Delaunay, default is 0.0 for upper envelope */
   realT *lower_threshold; /* don't print if facet->normal[k] <=lower_threshold[k] */
   realT *upper_bound;     /* scale point[k] to new upper bound */
   realT *lower_bound;     /* scale point[k] to new lower bound
                              project if both upper_ and lower_bound == 0 */
 
 /*----------------------------------
 
   qh precision constants
     precision constants for Qhull
 
   notes:
     qh_detroundoff() computes the maximum roundoff error for distance
     and other computations.  It also sets default values for the
     qh constants above.
 */
   realT ANGLEround;       /* max round off error for angles */
   realT centrum_radius;   /* max centrum radius for convexity (roundoff added) */
   realT cos_max;          /* max cosine for convexity (roundoff added) */
-  realT DISTround;        /* max round off error for distances, 'E' overrides */
+  realT DISTround;        /* max round off error for distances, 'E' overrides qh_distround() */
   realT MAXabs_coord;     /* max absolute coordinate */
   realT MAXlastcoord;     /* max last coordinate for qh_scalelast */
   realT MAXsumcoord;      /* max sum of coordinates */
   realT MAXwidth;         /* max rectilinear width of point coordinates */
   realT MINdenom_1;       /* min. abs. value for 1/x */
   realT MINdenom;         /*    use divzero if denominator < MINdenom */
   realT MINdenom_1_2;     /* min. abs. val for 1/x that allows normalization */
   realT MINdenom_2;       /*    use divzero if denominator < MINdenom_2 */
   realT MINlastcoord;     /* min. last coordinate for qh_scalelast */
   boolT NARROWhull;       /* set in qh_initialhull if angle < qh_MAXnarrow */
   realT *NEARzero;        /* hull_dim array for near zero in gausselim */
   realT NEARinside;       /* keep points for qh_check_maxout if close to facet */
   realT ONEmerge;         /* max distance for merging simplicial facets */
   realT outside_err;      /* application's epsilon for coplanar points
                              qh_check_bestdist() qh_check_points() reports error if point outside */
   realT WIDEfacet;        /* size of wide facet for skipping ridge in
                              area computation and locking centrum */
 
 /*----------------------------------
 
   qh internal constants
     internal constants for Qhull
 */
   char qhull[sizeof("qhull")]; /* "qhull" for checking ownership while debugging */
   jmp_buf errexit;        /* exit label for qh_errexit, defined by setjmp() */
   char jmpXtra[40];       /* extra bytes in case jmp_buf is defined wrong by compiler */
   jmp_buf restartexit;    /* restart label for qh_errexit, defined by setjmp() */
   char jmpXtra2[40];      /* extra bytes in case jmp_buf is defined wrong by compiler*/
   FILE *fin;              /* pointer to input file, init by qh_meminit */
   FILE *fout;             /* pointer to output file */
   FILE *ferr;             /* pointer to error file */
   pointT *interior_point; /* center point of the initial simplex*/
   int normal_size;     /* size in bytes for facet normals and point coords*/
   int center_size;     /* size in bytes for Voronoi centers */
   int   TEMPsize;         /* size for small, temporary sets (in quick mem) */
 
 /*----------------------------------
 
   qh facet and vertex lists
     defines lists of facets, new facets, visible facets, vertices, and
     new vertices.  Includes counts, next ids, and trace ids.
   see:
     qh_resetlists()
 */
   facetT *facet_list;     /* first facet */
   facetT  *facet_tail;     /* end of facet_list (dummy facet) */
   facetT *facet_next;     /* next facet for buildhull()
                              previous facets do not have outside sets
                              NARROWhull: previous facets may have coplanar outside sets for qh_outcoplanar */
   facetT *newfacet_list;  /* list of new facets to end of facet_list */
   facetT *visible_list;   /* list of visible facets preceeding newfacet_list,
                              facet->visible set */
   int       num_visible;  /* current number of visible facets */
   unsigned tracefacet_id;  /* set at init, then can print whenever */
   facetT *tracefacet;     /*   set in newfacet/mergefacet, undone in delfacet*/
   unsigned tracevertex_id;  /* set at buildtracing, can print whenever */
   vertexT *tracevertex;     /*   set in newvertex, undone in delvertex*/
   vertexT *vertex_list;     /* list of all vertices, to vertex_tail */
   vertexT  *vertex_tail;    /*      end of vertex_list (dummy vertex) */
   vertexT *newvertex_list; /* list of vertices in newfacet_list, to vertex_tail
                              all vertices have 'newlist' set */
   int   num_facets;       /* number of facets in facet_list
                              includes visble faces (num_visible) */
   int   num_vertices;     /* number of vertices in facet_list */
   int   num_outside;      /* number of points in outsidesets (for tracing and RANDOMoutside)
                                includes coplanar outsideset points for NARROWhull/qh_outcoplanar() */
   int   num_good;         /* number of good facets (after findgood_all) */
   unsigned facet_id;      /* ID of next, new facet from newfacet() */
   unsigned ridge_id:24;   /* ID of next, new ridge from newridge() */
   unsigned vertex_id:24;  /* ID of next, new vertex from newvertex() */
 
 /*----------------------------------
 
   qh global variables
     defines minimum and maximum distances, next visit ids, several flags,
     and other global variables.
     initialize in qh_initbuild or qh_maxmin if used in qh_buildhull
 */
   unsigned long hulltime; /* ignore time to set up input and randomize */
                           /*   use unsigned to avoid wrap-around errors */
   boolT ALLOWrestart;     /* true if qh_precision can use qh.restartexit */
   int   build_cnt;        /* number of calls to qh_initbuild */
   qh_CENTER CENTERtype;   /* current type of facet->center, qh_CENTER */
   int   furthest_id;      /* pointid of furthest point, for tracing */
   facetT *GOODclosest;    /* closest facet to GOODthreshold in qh_findgood */
   boolT hasAreaVolume;    /* true if totarea, totvol was defined by qh_getarea */
   boolT hasTriangulation; /* true if triangulation created by qh_triangulate */
   realT JOGGLEmax;        /* set 'QJn' if randomly joggle input */
   boolT maxoutdone;       /* set qh_check_maxout(), cleared by qh_addpoint() */
   realT max_outside;      /* maximum distance from a point to a facet,
                                before roundoff, not simplicial vertices
                                actual outer plane is +DISTround and
                                computed outer plane is +2*DISTround */
   realT max_vertex;       /* maximum distance (>0) from vertex to a facet,
                                before roundoff, due to a merge */
   realT min_vertex;       /* minimum distance (<0) from vertex to a facet,
                                before roundoff, due to a merge
                                if qh.JOGGLEmax, qh_makenewplanes sets it
                                recomputed if qh.DOcheckmax, default -qh.DISTround */
   boolT NEWfacets;        /* true while visible facets invalid due to new or merge
                               from makecone/attachnewfacets to deletevisible */
   boolT findbestnew;      /* true if partitioning calls qh_findbestnew */
   boolT findbest_notsharp; /* true if new facets are at least 90 degrees */
   boolT NOerrexit;        /* true if qh.errexit is not available */
   realT PRINTcradius;     /* radius for printing centrums */
   realT PRINTradius;      /* radius for printing vertex spheres and points */
   boolT POSTmerging;      /* true when post merging */
   int   printoutvar;      /* temporary variable for qh_printbegin, etc. */
   int   printoutnum;      /* number of facets printed */
   boolT QHULLfinished;    /* True after qhull() is finished */
   realT totarea;          /* 'FA': total facet area computed by qh_getarea, hasAreaVolume */
   realT totvol;           /* 'FA': total volume computed by qh_getarea, hasAreaVolume */
   unsigned int visit_id;  /* unique ID for searching neighborhoods, */
   unsigned int vertex_visit:31; /* unique ID for searching vertices, reset with qh_buildtracing */
   boolT ZEROall_ok;       /* True if qh_checkzero always succeeds */
   boolT WAScoplanar;      /* True if qh_partitioncoplanar (qh_check_maxout) */
 
 /*----------------------------------
 
   qh global sets
     defines sets for merging, initial simplex, hashing, extra input points,
     and deleted vertices
 */
   setT *facet_mergeset;   /* temporary set of merges to be done */
   setT *degen_mergeset;   /* temporary set of degenerate and redundant merges */
   setT *hash_table;       /* hash table for matching ridges in qh_matchfacets
                              size is setsize() */
   setT *other_points;     /* additional points */
   setT *del_vertices;     /* vertices to partition and delete with visible
                              facets.  Have deleted set for checkfacet */
 
 /*----------------------------------
 
   qh global buffers
     defines buffers for maxtrix operations, input, and error messages
 */
   coordT *gm_matrix;      /* (dim+1)Xdim matrix for geom.c */
   coordT **gm_row;        /* array of gm_matrix rows */
   char* line;             /* malloc'd input line of maxline+1 chars */
   int maxline;
   coordT *half_space;     /* malloc'd input array for halfspace (qh normal_size+coordT) */
   coordT *temp_malloc;    /* malloc'd input array for points */
 
 /*----------------------------------
 
   qh static variables
     defines static variables for individual functions
 
   notes:
     do not use 'static' within a function.  Multiple instances of qhull
     may exist.
 
     do not assume zero initialization, 'QPn' may cause a restart
 */
   boolT ERREXITcalled;    /* true during qh_errexit (prevents duplicate calls */
   boolT firstcentrum;     /* for qh_printcentrum */
   boolT old_randomdist;   /* save RANDOMdist flag during io, tracing, or statistics */
   setT *coplanarfacetset;  /* set of coplanar facets for searching qh_findbesthorizon() */
   realT last_low;         /* qh_scalelast parameters for qh_setdelaunay */
   realT last_high;
   realT last_newhigh;
   unsigned lastreport;    /* for qh_buildtracing */
   int mergereport;        /* for qh_tracemerging */
   qhstatT *old_qhstat;    /* for saving qh_qhstat in save_qhull() and UsingLibQhull.  Free with qh_free() */
   setT *old_tempstack;    /* for saving qhmem.tempstack in save_qhull */
   int   ridgeoutnum;      /* number of ridges for 4OFF output (qh_printbegin,etc) */
 };
 
 /*=========== -macros- =========================*/
 
 /*----------------------------------
 
   otherfacet_(ridge, facet)
     return neighboring facet for a ridge in facet
 */
 #define otherfacet_(ridge, facet) \
                         (((ridge)->top == (facet)) ? (ridge)->bottom : (ridge)->top)
 
 /*----------------------------------
 
   getid_(p)
     return int ID for facet, ridge, or vertex
     return -1 if NULL
 */
 #define getid_(p)       ((p) ? (int)((p)->id) : -1)
 
 /*============== FORALL macros ===================*/
 
 /*----------------------------------
 
   FORALLfacets { ... }
     assign 'facet' to each facet in qh.facet_list
 
   notes:
     uses 'facetT *facet;'
     assumes last facet is a sentinel
 
   see:
     FORALLfacet_( facetlist )
 */
 #define FORALLfacets for (facet=qh facet_list;facet && facet->next;facet=facet->next)
 
 /*----------------------------------
 
   FORALLpoints { ... }
     assign 'point' to each point in qh.first_point, qh.num_points
 
   declare:
     coordT *point, *pointtemp;
 */
 #define FORALLpoints FORALLpoint_(qh first_point, qh num_points)
 
 /*----------------------------------
 
   FORALLpoint_( points, num) { ... }
     assign 'point' to each point in points array of num points
 
   declare:
     coordT *point, *pointtemp;
 */
 #define FORALLpoint_(points, num) for (point= (points), \
       pointtemp= (points)+qh hull_dim*(num); point < pointtemp; point += qh hull_dim)
 
 /*----------------------------------
 
   FORALLvertices { ... }
     assign 'vertex' to each vertex in qh.vertex_list
 
   declare:
     vertexT *vertex;
 
   notes:
     assumes qh.vertex_list terminated with a sentinel
 */
 #define FORALLvertices for (vertex=qh vertex_list;vertex && vertex->next;vertex= vertex->next)
 
 /*----------------------------------
 
   FOREACHfacet_( facets ) { ... }
     assign 'facet' to each facet in facets
 
   declare:
     facetT *facet, **facetp;
 
   see:
     FOREACHsetelement_
 */
 #define FOREACHfacet_(facets)    FOREACHsetelement_(facetT, facets, facet)
 
 /*----------------------------------
 
   FOREACHneighbor_( facet ) { ... }
     assign 'neighbor' to each neighbor in facet->neighbors
 
   FOREACHneighbor_( vertex ) { ... }
     assign 'neighbor' to each neighbor in vertex->neighbors
 
   declare:
     facetT *neighbor, **neighborp;
 
   see:
     FOREACHsetelement_
 */
 #define FOREACHneighbor_(facet)  FOREACHsetelement_(facetT, facet->neighbors, neighbor)
 
 /*----------------------------------
 
   FOREACHpoint_( points ) { ... }
     assign 'point' to each point in points set
 
   declare:
     pointT *point, **pointp;
 
   see:
     FOREACHsetelement_
 */
 #define FOREACHpoint_(points)    FOREACHsetelement_(pointT, points, point)
 
 /*----------------------------------
 
   FOREACHridge_( ridges ) { ... }
     assign 'ridge' to each ridge in ridges set
 
   declare:
     ridgeT *ridge, **ridgep;
 
   see:
     FOREACHsetelement_
 */
 #define FOREACHridge_(ridges)    FOREACHsetelement_(ridgeT, ridges, ridge)
 
 /*----------------------------------
 
   FOREACHvertex_( vertices ) { ... }
     assign 'vertex' to each vertex in vertices set
 
   declare:
     vertexT *vertex, **vertexp;
 
   see:
     FOREACHsetelement_
 */
 #define FOREACHvertex_(vertices) FOREACHsetelement_(vertexT, vertices,vertex)
 
 /*----------------------------------
 
   FOREACHfacet_i_( facets ) { ... }
     assign 'facet' and 'facet_i' for each facet in facets set
 
   declare:
     facetT *facet;
     int     facet_n, facet_i;
 
   see:
     FOREACHsetelement_i_
 */
 #define FOREACHfacet_i_(facets)    FOREACHsetelement_i_(facetT, facets, facet)
 
 /*----------------------------------
 
   FOREACHneighbor_i_( facet ) { ... }
     assign 'neighbor' and 'neighbor_i' for each neighbor in facet->neighbors
 
   FOREACHneighbor_i_( vertex ) { ... }
     assign 'neighbor' and 'neighbor_i' for each neighbor in vertex->neighbors
 
   declare:
     facetT *neighbor;
     int     neighbor_n, neighbor_i;
 
   see:
     FOREACHsetelement_i_
 */
 #define FOREACHneighbor_i_(facet)  FOREACHsetelement_i_(facetT, facet->neighbors, neighbor)
 
 /*----------------------------------
 
   FOREACHpoint_i_( points ) { ... }
     assign 'point' and 'point_i' for each point in points set
 
   declare:
     pointT *point;
     int     point_n, point_i;
 
   see:
     FOREACHsetelement_i_
 */
 #define FOREACHpoint_i_(points)    FOREACHsetelement_i_(pointT, points, point)
 
 /*----------------------------------
 
   FOREACHridge_i_( ridges ) { ... }
     assign 'ridge' and 'ridge_i' for each ridge in ridges set
 
   declare:
     ridgeT *ridge;
     int     ridge_n, ridge_i;
 
   see:
     FOREACHsetelement_i_
 */
 #define FOREACHridge_i_(ridges)    FOREACHsetelement_i_(ridgeT, ridges, ridge)
 
 /*----------------------------------
 
   FOREACHvertex_i_( vertices ) { ... }
     assign 'vertex' and 'vertex_i' for each vertex in vertices set
 
   declare:
     vertexT *vertex;
     int     vertex_n, vertex_i;
 
   see:
     FOREACHsetelement_i_
 */
 #define FOREACHvertex_i_(vertices) FOREACHsetelement_i_(vertexT, vertices,vertex)
 
 /********* -libqhull.c prototypes (duplicated from qhull_a.h) **********************/
 
 void    qh_qhull(void);
 boolT   qh_addpoint(pointT *furthest, facetT *facet, boolT checkdist);
 void    qh_printsummary(FILE *fp);
 
 /********* -user.c prototypes (alphabetical) **********************/
 
 void    qh_errexit(int exitcode, facetT *facet, ridgeT *ridge);
 void    qh_errprint(const char* string, facetT *atfacet, facetT *otherfacet, ridgeT *atridge, vertexT *atvertex);
 int     qh_new_qhull(int dim, int numpoints, coordT *points, boolT ismalloc,
                 char *qhull_cmd, FILE *outfile, FILE *errfile);
 void    qh_printfacetlist(facetT *facetlist, setT *facets, boolT printall);
 void    qh_printhelp_degenerate(FILE *fp);
 void    qh_printhelp_narrowhull(FILE *fp, realT minangle);
 void    qh_printhelp_singular(FILE *fp);
 void    qh_user_memsizes(void);
 
 /********* -usermem.c prototypes (alphabetical) **********************/
 void    qh_exit(int exitcode);
 void    qh_free(void *mem);
 void   *qh_malloc(size_t size);
 
 /********* -userprintf.c and userprintf_rbox.c prototypes **********************/
 void    qh_fprintf(FILE *fp, int msgcode, const char *fmt, ... );
 void    qh_fprintf_rbox(FILE *fp, int msgcode, const char *fmt, ... );
 
 /***** -geom.c/geom2.c/random.c prototypes (duplicated from geom.h, random.h) ****************/
 
 facetT *qh_findbest(pointT *point, facetT *startfacet,
                      boolT bestoutside, boolT newfacets, boolT noupper,
                      realT *dist, boolT *isoutside, int *numpart);
 facetT *qh_findbestnew(pointT *point, facetT *startfacet,
                      realT *dist, boolT bestoutside, boolT *isoutside, int *numpart);
 boolT   qh_gram_schmidt(int dim, realT **rows);
 void    qh_outerinner(facetT *facet, realT *outerplane, realT *innerplane);
 void    qh_printsummary(FILE *fp);
 void    qh_projectinput(void);
 void    qh_randommatrix(realT *buffer, int dim, realT **row);
 void    qh_rotateinput(realT **rows);
 void    qh_scaleinput(void);
 void    qh_setdelaunay(int dim, int count, pointT *points);
 coordT  *qh_sethalfspace_all(int dim, int count, coordT *halfspaces, pointT *feasible);
 
 /***** -global.c prototypes (alphabetical) ***********************/
 
 unsigned long qh_clock(void);
 void    qh_checkflags(char *command, char *hiddenflags);
 void    qh_clear_outputflags(void);
 void    qh_freebuffers(void);
 void    qh_freeqhull(boolT allmem);
 void    qh_freeqhull2(boolT allmem);
 void    qh_init_A(FILE *infile, FILE *outfile, FILE *errfile, int argc, char *argv[]);
 void    qh_init_B(coordT *points, int numpoints, int dim, boolT ismalloc);
 void    qh_init_qhull_command(int argc, char *argv[]);
 void    qh_initbuffers(coordT *points, int numpoints, int dim, boolT ismalloc);
 void    qh_initflags(char *command);
 void    qh_initqhull_buffers(void);
 void    qh_initqhull_globals(coordT *points, int numpoints, int dim, boolT ismalloc);
 void    qh_initqhull_mem(void);
 void    qh_initqhull_outputflags(void);
 void    qh_initqhull_start(FILE *infile, FILE *outfile, FILE *errfile);
 void    qh_initqhull_start2(FILE *infile, FILE *outfile, FILE *errfile);
 void    qh_initthresholds(char *command);
 void    qh_option(const char *option, int *i, realT *r);
 #if qh_QHpointer
 void    qh_restore_qhull(qhT **oldqh);
 qhT    *qh_save_qhull(void);
 #endif
 
 /***** -io.c prototypes (duplicated from io.h) ***********************/
 
 void    qh_dfacet( unsigned id);
 void    qh_dvertex( unsigned id);
 void    qh_printneighborhood(FILE *fp, qh_PRINT format, facetT *facetA, facetT *facetB, boolT printall);
 void    qh_produce_output(void);
 coordT *qh_readpoints(int *numpoints, int *dimension, boolT *ismalloc);
 
 
 /********* -mem.c prototypes (duplicated from mem.h) **********************/
 
 void qh_meminit(FILE *ferr);
 void qh_memfreeshort(int *curlong, int *totlong);
 
 /********* -poly.c/poly2.c prototypes (duplicated from poly.h) **********************/
 
 void    qh_check_output(void);
 void    qh_check_points(void);
 setT   *qh_facetvertices(facetT *facetlist, setT *facets, boolT allfacets);
 facetT *qh_findbestfacet(pointT *point, boolT bestoutside,
            realT *bestdist, boolT *isoutside);
 vertexT *qh_nearvertex(facetT *facet, pointT *point, realT *bestdistp);
 pointT *qh_point(int id);
 setT   *qh_pointfacet(void /*qh.facet_list*/);
 int     qh_pointid(pointT *point);
 setT   *qh_pointvertex(void /*qh.facet_list*/);
 void    qh_setvoronoi_all(void);
 void    qh_triangulate(void /*qh.facet_list*/);
 
 /********* -rboxpoints.c prototypes **********************/
 int     qh_rboxpoints(FILE* fout, FILE* ferr, char* rbox_command);
 void    qh_errexit_rbox(int exitcode);
 
 /********* -stat.c prototypes (duplicated from stat.h) **********************/
 
 void    qh_collectstatistics(void);
 void    qh_printallstatistics(FILE *fp, const char *string);
 
 #endif /* qhDEFlibqhull */
diff --git a/src/libqhull/qh-user.htm b/src/libqhull/qh-user.htm
index a8afed4..b917920 100644
--- a/src/libqhull/qh-user.htm
+++ b/src/libqhull/qh-user.htm
@@ -1,263 +1,265 @@
 
 
 
 
 user.c -- user-definable operations
 
 
 
 
 
Up: Home page for Qhull

 Up: Qhull manual: Table of Contents 

 Up: Programs
 • Options
 • Output
 • Formats
 • Geomview
 • Print
 • Qhull
 • Precision
 • Trace

 Up: Qhull code: Table of Contents

 To: Qhull functions, macros, and data structures

 To: Geom • Global
 • Io • Mem
 • Merge • Poly
 • Qhull • Set
 • Stat • User
 

 

 
user.c -- user-definable operations

 

 
This section contains functions and constants that the
 user may want to change. 

 
 

 
Copyright © 1995-2012 C.B. Barber

 

 
» Geom
 • Global
 • Io • Mem
 • Merge • Poly
 • Qhull • Set
 • Stat • User
 

 
Index to user.c, usermem.c, userprintf.c, userprintf_rbox.c and
 user.h

 
 
 
»Qhull library constants

 
 
 
 
»user.h data
 types and configuration macros

 
 
 
»definition constants

 
    
 
  • qh_DEFAULTbox
 define default box size for rbox, 'Qbb', and 'QbB' (Geomview expects 0.5) 
    • 
 
  • qh_INFINITE on
 output, indicates Voronoi center at infinity 
    • 
 
  • qh_ORIENTclock
 define convention for orienting facets
    • 
 
  • qh_ZEROdelaunay
 define facets that are ignored in Delaunay triangulations
    • 
 

 
 
»joggle constants

 
 
 
»performance
 related constants

 
 
 
»memory constants

 
 
 
»conditional compilation

 
 
 
»merge
 constants

 
 
 
»user.c
 functions

 
 
 
»usermem.c
 functions

 
    
 
  • qh_exit exit program, same as exit().
    • 
 
  • qh_free free memory, same as free().
    • 
 
  • qh_malloc allocate memory, same as malloc()
    • 
 

 
 
»userprintf.c
  and userprintf_rbox,c functions

 
    
 
  • qh_fprintf print
 information from Qhull, sames as fprintf(). 
    • 
 
  • qh_fprintf_rbox print
 information from Rbox, sames as fprintf(). 
    • 
 

 
 
 

 

 
Up:
 Home page for
 Qhull 

 Up: Qhull manual: Table of Contents 

 Up: Programs
 • Options
 • Output
 • Formats
 • Geomview
 • Print
 • Qhull
 • Precision
 • Trace

 Up: Qhull code: Table of Contents 

 To: Qhull functions, macros, and data structures

 To: Geom •
 Global • Io
 • Mem • Merge
 • Poly • Qhull
 • Set • Stat
 • User

 

 
 

 

 
The
 Geometry Center Home Page 

 
Comments to: qhull@qhull.org
 

 Created: May 2, 1997 ---  Last modified: see top  

 
 
diff --git a/src/libqhull/rboxlib.c b/src/libqhull/rboxlib.c
index 8eecdd6..d6eea41 100644
--- a/src/libqhull/rboxlib.c
+++ b/src/libqhull/rboxlib.c
@@ -1,795 +1,799 @@
 /*
  ---------------------------------
 
    rboxlib.c
      Generate input points
 
    notes:
      For documentation, see prompt[] of rbox.c
      50 points generated for 'rbox D4'
 
    WARNING:
      incorrect range if qh_RANDOMmax is defined wrong (user.h)
 */
 
 #include "random.h"
 #include "libqhull.h"
 
 #include 
 #include 
 #include 
 #include 
 #include 
 #include 
 #include 
 #include 
 
 #ifdef _MSC_VER  /* Microsoft Visual C++ */
 #pragma warning( disable : 4706)  /* assignment within conditional expression. */
 #pragma warning( disable : 4996)  /* this function (strncat,sprintf,strcpy) or variable may be unsafe. */
 #endif
 
 #define MAXdim 200
 #define PI 3.1415926535897932384
 
 /* ------------------------------ prototypes ----------------*/
 int qh_roundi( double a);
 void qh_out1( double a);
 void qh_out2n( double a, double b);
 void qh_out3n( double a, double b, double c);
 
 void    qh_fprintf_rbox(FILE *fp, int msgcode, const char *fmt, ... );
 void    qh_free(void *mem);
 void   *qh_malloc(size_t size);
 int     qh_rand( void);
 void    qh_srand( int seed);
 
 
 /* ------------------------------ globals -------------------*/
 
 /* No state is carried between rbox requests */
 typedef struct rboxT rboxT;
 struct rboxT {
   FILE *fout;
   FILE *ferr;
   int isinteger;
   double out_offset;
   jmp_buf errexit;        /* exit label for rboxpoints, defined by setjmp(), called by qh_errexit_rbox() */
+  char  jmpXtra[40];      /* extra bytes in case jmp_buf is defined wrong by compiler */
 };
 
 
 int rbox_inuse= 0;
 rboxT rbox;
 
 /*---------------------------------
 
   qh_rboxpoints( fout, ferr, rbox_command )
     Generate points to fout according to rbox options
     Report errors on ferr
 
   returns:
     0 (qh_ERRnone) on success
     1 (qh_ERRinput) on input error
     4 (qh_ERRmem) on memory error
     5 (qh_ERRqhull) on internal error
 
   notes:
     To avoid stdio, redefine qh_malloc, qh_free, and qh_fprintf_rbox (user.c)
     Rbox is not multithreaded.
 
   design:
     Straight line code (consider defining a struct and functions):
 
     Parse arguments into variables
     Determine the number of points
     Generate the points
 */
 int qh_rboxpoints(FILE* fout, FILE* ferr, char* rbox_command) {
   int i,j,k;
   int gendim;
   int cubesize, diamondsize, seed=0, count, apex;
   int dim=3 , numpoints= 0, totpoints, addpoints=0;
   int issphere=0, isaxis=0,  iscdd= 0, islens= 0, isregular=0, iswidth=0, addcube=0;
   int isgap=0, isspiral=0, NOcommand= 0, adddiamond=0;
   int israndom=0, istime=0;
   int isbox=0, issimplex=0, issimplex2=0, ismesh=0;
   double width=0.0, gap=0.0, radius= 0.0;
   double coord[MAXdim], offset, meshm=3.0, meshn=4.0, meshr=5.0;
   double *simplex= NULL, *simplexp;
   int nthroot, mult[MAXdim];
   double norm, factor, randr, rangap, lensangle= 0, lensbase= 1;
   double anglediff, angle, x, y, cube= 0.0, diamond= 0.0;
   double box= qh_DEFAULTbox; /* scale all numbers before output */
   double randmax= qh_RANDOMmax;
   char command[200], seedbuf[200];
   char *s= command, *t, *first_point= NULL;
   time_t timedata;
   int exitcode;
 
   if (rbox_inuse) {
     qh_fprintf_rbox(rbox.ferr, 6188, "rbox error: rbox in use by another process.  Please lock calls to rbox.\n");
     return qh_ERRqhull;
   }
   rbox_inuse= True;
   rbox.ferr= ferr;
   rbox.fout= fout;
 
   exitcode= setjmp(rbox.errexit);
   if (exitcode) {
     /* same code for error exit and normal return */
     if (simplex)
         qh_free(simplex);
     rbox_inuse= False;
     return exitcode;
   }
 
   *command= '\0';
   strncat(command, rbox_command, sizeof(command)-strlen(command)-1);
 
   while (*s && !isspace(*s))  /* skip program name */
     s++;
   while (*s) {
     while (*s && isspace(*s))
       s++;
     if (*s == '-')
       s++;
     if (!*s)
       break;
     if (isdigit(*s)) {
       numpoints= qh_strtol(s, &s);
       continue;
     }
     /* ============= read flags =============== */
     switch (*s++) {
     case 'c':
       addcube= 1;
       t= s;
       while (isspace(*t))
         t++;
       if (*t == 'G')
         cube= qh_strtod(++t, &s);
       break;
     case 'd':
       adddiamond= 1;
       t= s;
       while (isspace(*t))
         t++;
       if (*t == 'G')
         diamond= qh_strtod(++t, &s);
       break;
     case 'h':
       iscdd= 1;
       break;
     case 'l':
       isspiral= 1;
       break;
     case 'n':
       NOcommand= 1;
       break;
     case 'r':
       isregular= 1;
       break;
     case 's':
       issphere= 1;
       break;
     case 't':
       istime= 1;
       if (isdigit(*s)) {
         seed= qh_strtol(s, &s);
         israndom= 0;
       }else
         israndom= 1;
       break;
     case 'x':
       issimplex= 1;
       break;
     case 'y':
       issimplex2= 1;
       break;
     case 'z':
       rbox.isinteger= 1;
       break;
     case 'B':
       box= qh_strtod(s, &s);
       isbox= 1;
       break;
     case 'D':
       dim= qh_strtol(s, &s);
       if (dim < 1
       || dim > MAXdim) {
         qh_fprintf_rbox(rbox.ferr, 6189, "rbox error: dimension, D%d, out of bounds (>=%d or <=0)", dim, MAXdim);
         qh_errexit_rbox(qh_ERRinput);
       }
       break;
     case 'G':
       if (isdigit(*s))
         gap= qh_strtod(s, &s);
       else
         gap= 0.5;
       isgap= 1;
       break;
     case 'L':
       if (isdigit(*s))
         radius= qh_strtod(s, &s);
       else
         radius= 10;
       islens= 1;
       break;
     case 'M':
       ismesh= 1;
       if (*s)
         meshn= qh_strtod(s, &s);
       if (*s == ',') {
         ++s;
         meshm= qh_strtod(s, &s);
       }else
         meshm= 0.0;
       if (*s == ',') {
         ++s;
         meshr= qh_strtod(s, &s);
       }else
         meshr= sqrt(meshn*meshn + meshm*meshm);
       if (*s && !isspace(*s)) {
         qh_fprintf_rbox(rbox.ferr, 7069, "rbox warning: assuming 'M3,4,5' since mesh args are not integers or reals\n");
         meshn= 3.0, meshm=4.0, meshr=5.0;
       }
       break;
     case 'O':
       rbox.out_offset= qh_strtod(s, &s);
       break;
     case 'P':
       if (!first_point)
         first_point= s-1;
       addpoints++;
       while (*s && !isspace(*s))   /* read points later */
         s++;
       break;
     case 'W':
       width= qh_strtod(s, &s);
       iswidth= 1;
       break;
     case 'Z':
       if (isdigit(*s))
         radius= qh_strtod(s, &s);
       else
         radius= 1.0;
       isaxis= 1;
       break;
     default:
       qh_fprintf_rbox(rbox.ferr, 7070, "rbox error: unknown flag at %s.\nExecute 'rbox' without arguments for documentation.\n", s);
       qh_errexit_rbox(qh_ERRinput);
     }
     if (*s && !isspace(*s)) {
       qh_fprintf_rbox(rbox.ferr, 7071, "rbox error: missing space between flags at %s.\n", s);
       qh_errexit_rbox(qh_ERRinput);
     }
   }
 
   /* ============= defaults, constants, and sizes =============== */
   if (rbox.isinteger && !isbox)
     box= qh_DEFAULTzbox;
   if (addcube) {
     cubesize= (int)floor(ldexp(1.0,dim)+0.5);
     if (cube == 0.0)
       cube= box;
   }else
     cubesize= 0;
   if (adddiamond) {
     diamondsize= 2*dim;
     if (diamond == 0.0)
       diamond= box;
   }else
     diamondsize= 0;
   if (islens) {
     if (isaxis) {
         qh_fprintf_rbox(rbox.ferr, 6190, "rbox error: can not combine 'Ln' with 'Zn'\n");
         qh_errexit_rbox(qh_ERRinput);
     }
     if (radius <= 1.0) {
         qh_fprintf_rbox(rbox.ferr, 6191, "rbox error: lens radius %.2g should be greater than 1.0\n",
                radius);
         qh_errexit_rbox(qh_ERRinput);
     }
     lensangle= asin(1.0/radius);
     lensbase= radius * cos(lensangle);
   }
 
   if (!numpoints) {
     if (issimplex2)
         ; /* ok */
     else if (isregular + issimplex + islens + issphere + isaxis + isspiral + iswidth + ismesh) {
         qh_fprintf_rbox(rbox.ferr, 6192, "rbox error: missing count\n");
         qh_errexit_rbox(qh_ERRinput);
     }else if (adddiamond + addcube + addpoints)
         ; /* ok */
     else {
         numpoints= 50;  /* ./rbox D4 is the test case */
         issphere= 1;
     }
   }
   if ((issimplex + islens + isspiral + ismesh > 1)
   || (issimplex + issphere + isspiral + ismesh > 1)) {
     qh_fprintf_rbox(rbox.ferr, 6193, "rbox error: can only specify one of 'l', 's', 'x', 'Ln', or 'Mn,m,r' ('Ln s' is ok).\n");
     qh_errexit_rbox(qh_ERRinput);
   }
 
   /* ============= print header with total points =============== */
   if (issimplex || ismesh)
     totpoints= numpoints;
   else if (issimplex2)
     totpoints= numpoints+dim+1;
   else if (isregular) {
     totpoints= numpoints;
     if (dim == 2) {
         if (islens)
           totpoints += numpoints - 2;
     }else if (dim == 3) {
         if (islens)
           totpoints += 2 * numpoints;
       else if (isgap)
         totpoints += 1 + numpoints;
       else
         totpoints += 2;
     }
   }else
     totpoints= numpoints + isaxis;
   totpoints += cubesize + diamondsize + addpoints;
 
   /* ============= seed randoms =============== */
   if (istime == 0) {
     for (s=command; *s; s++) {
       if (issimplex2 && *s == 'y') /* make 'y' same seed as 'x' */
         i= 'x';
       else
         i= *s;
       seed= 11*seed + i;
     }
   }else if (israndom) {
     seed= (int)time(&timedata);
     sprintf(seedbuf, " t%d", seed);  /* appends an extra t, not worth removing */
     strncat(command, seedbuf, sizeof(command)-strlen(command)-1);
     t= strstr(command, " t ");
     if (t)
       strcpy(t+1, t+3); /* remove " t " */
   } /* else, seed explicitly set to n */
   qh_RANDOMseed_(seed);
 
   /* ============= print header =============== */
 
   if (iscdd)
       qh_fprintf_rbox(rbox.fout, 9391, "%s\nbegin\n        %d %d %s\n",
       NOcommand ? "" : command,
       totpoints, dim+1,
       rbox.isinteger ? "integer" : "real");
   else if (NOcommand)
       qh_fprintf_rbox(rbox.fout, 9392, "%d\n%d\n", dim, totpoints);
   else
       qh_fprintf_rbox(rbox.fout, 9393, "%d %s\n%d\n", dim, command, totpoints);
 
   /* ============= explicit points =============== */
   if ((s= first_point)) {
     while (s && *s) { /* 'P' */
       count= 0;
       if (iscdd)
         qh_out1( 1.0);
       while (*++s) {
         qh_out1( qh_strtod(s, &s));
         count++;
         if (isspace(*s) || !*s)
           break;
         if (*s != ',') {
           qh_fprintf_rbox(rbox.ferr, 6194, "rbox error: missing comma after coordinate in %s\n\n", s);
           qh_errexit_rbox(qh_ERRinput);
         }
       }
       if (count < dim) {
         for (k=dim-count; k--; )
           qh_out1( 0.0);
       }else if (count > dim) {
         qh_fprintf_rbox(rbox.ferr, 6195, "rbox error: %d coordinates instead of %d coordinates in %s\n\n",
                   count, dim, s);
         qh_errexit_rbox(qh_ERRinput);
       }
       qh_fprintf_rbox(rbox.fout, 9394, "\n");
       while ((s= strchr(s, 'P'))) {
         if (isspace(s[-1]))
           break;
       }
     }
   }
 
   /* ============= simplex distribution =============== */
   if (issimplex+issimplex2) {
     if (!(simplex= (double*)qh_malloc( dim * (dim+1) * sizeof(double)))) {
       qh_fprintf_rbox(rbox.ferr, 6196, "rbox error: insufficient memory for simplex\n");
       qh_errexit_rbox(qh_ERRmem); /* qh_ERRmem */
     }
     simplexp= simplex;
     if (isregular) {
       for (i=0; i randmax/2)
           coord[dim-1]= -coord[dim-1];
       /* ============= project 'Wn' point toward boundary =============== */
       }else if (iswidth && !issphere) {
         j= qh_RANDOMint % gendim;
         if (coord[j] < 0)
           coord[j]= -1.0 - coord[j] * width;
         else
           coord[j]= 1.0 - coord[j] * width;
       }
       /* ============= write point =============== */
       if (iscdd)
         qh_out1( 1.0);
       for (k=0; k < dim; k++)
         qh_out1( coord[k] * box);
       qh_fprintf_rbox(rbox.fout, 9399, "\n");
     }
   }
 
   /* ============= write cube vertices =============== */
   if (addcube) {
     for (j=0; j=0; k--) {
         if (j & ( 1 << k))
           qh_out1( cube);
         else
           qh_out1( -cube);
       }
       qh_fprintf_rbox(rbox.fout, 9400, "\n");
     }
   }
 
   /* ============= write diamond vertices =============== */
   if (adddiamond) {
     for (j=0; j=0; k--) {
         if (j/2 != k)
           qh_out1( 0.0);
         else if (j & 0x1)
           qh_out1( diamond);
         else
           qh_out1( -diamond);
       }
       qh_fprintf_rbox(rbox.fout, 9401, "\n");
     }
   }
 
   if (iscdd)
     qh_fprintf_rbox(rbox.fout, 9402, "end\nhull\n");
 
   /* same code for error exit and normal return */
   if (simplex)
     qh_free(simplex);
   rbox_inuse= False;
   return qh_ERRnone;
 } /* rboxpoints */
 
 /*------------------------------------------------
 outxxx - output functions
 */
 int qh_roundi( double a) {
   if (a < 0.0) {
     if (a - 0.5 < INT_MIN) {
       qh_fprintf_rbox(rbox.ferr, 6200, "rbox input error: negative coordinate %2.2g is too large.  Reduce 'Bn'\n", a);
       qh_errexit_rbox(qh_ERRinput);
     }
     return (int)(a - 0.5);
   }else {
     if (a + 0.5 > INT_MAX) {
       qh_fprintf_rbox(rbox.ferr, 6201, "rbox input error: coordinate %2.2g is too large.  Reduce 'Bn'\n", a);
       qh_errexit_rbox(qh_ERRinput);
     }
     return (int)(a + 0.5);
   }
 } /* qh_roundi */
 
 void qh_out1(double a) {
 
   if (rbox.isinteger)
     qh_fprintf_rbox(rbox.fout, 9403, "%d ", qh_roundi( a+rbox.out_offset));
   else
     qh_fprintf_rbox(rbox.fout, 9404, qh_REAL_1, a+rbox.out_offset);
 } /* qh_out1 */
 
 void qh_out2n( double a, double b) {
 
   if (rbox.isinteger)
     qh_fprintf_rbox(rbox.fout, 9405, "%d %d\n", qh_roundi(a+rbox.out_offset), qh_roundi(b+rbox.out_offset));
   else
     qh_fprintf_rbox(rbox.fout, 9406, qh_REAL_2n, a+rbox.out_offset, b+rbox.out_offset);
 } /* qh_out2n */
 
 void qh_out3n( double a, double b, double c) {
 
   if (rbox.isinteger)
     qh_fprintf_rbox(rbox.fout, 9407, "%d %d %d\n", qh_roundi(a+rbox.out_offset), qh_roundi(b+rbox.out_offset), qh_roundi(c+rbox.out_offset));
   else
     qh_fprintf_rbox(rbox.fout, 9408, qh_REAL_3n, a+rbox.out_offset, b+rbox.out_offset, c+rbox.out_offset);
 } /* qh_out3n */
 
+/*------------------------------------------------
+   Only called from qh_rboxpoints or qh_fprintf_rbox (which is only called from qh_rboxpoints)
+*/
 void qh_errexit_rbox(int exitcode)
 {
     longjmp(rbox.errexit, exitcode);
 } /* rbox_errexit */
 
diff --git a/src/libqhull/user.c b/src/libqhull/user.c
index 653c5a4..7249843 100644
--- a/src/libqhull/user.c
+++ b/src/libqhull/user.c
@@ -1,527 +1,528 @@
 /*
  ---------------------------------
 
    user.c
    user redefinable functions
 
    see user2.c for qh_fprintf, qh_malloc, qh_free
 
    see README.txt  see COPYING.txt for copyright information.
 
    see libqhull.h for data structures, macros, and user-callable functions.
 
    see user_eg.c, unix.c, and qhull_interface.cpp for examples.
 
    see user.h for user-definable constants
 
       use qh_NOmem in mem.h to turn off memory management
       use qh_NOmerge in user.h to turn off facet merging
       set qh_KEEPstatistics in user.h to 0 to turn off statistics
 
    This is unsupported software.  You're welcome to make changes,
    but you're on your own if something goes wrong.  Use 'Tc' to
    check frequently.  Usually qhull will report an error if
    a data structure becomes inconsistent.  If so, it also reports
    the last point added to the hull, e.g., 102.  You can then trace
    the execution of qhull with "T4P102".
 
    Please report any errors that you fix to qhull@qhull.org
 
    call_qhull is a template for calling qhull from within your application
 
    if you recompile and load this module, then user.o will not be loaded
    from qhull.a
 
    you can add additional quick allocation sizes in qh_user_memsizes
 
    if the other functions here are redefined to not use qh_print...,
    then io.o will not be loaded from qhull.a.  See user_eg.c for an
    example.  We recommend keeping io.o for the extra debugging
    information it supplies.
 */
 
 #include "qhull_a.h"
 
 #include 
 
 /*---------------------------------
 
   qh_call_qhull( void )
     template for calling qhull from inside your program
     remove #if 0, #endif to compile
 
   returns:
     exit code(see qh_ERR... in libqhull.h)
     all memory freed
 
   notes:
     This can be called any number of times.
 
   see:
     qh_call_qhull_once()
 
 */
 #if 0
 {
   int dim;                  /* dimension of points */
   int numpoints;            /* number of points */
   coordT *points;           /* array of coordinates for each point */
   boolT ismalloc;           /* True if qhull should free points in qh_freeqhull() or reallocation */
   char flags[]= "qhull Tv"; /* option flags for qhull, see qh_opt.htm */
   FILE *outfile= stdout;    /* output from qh_produce_output()
                                use NULL to skip qh_produce_output() */
   FILE *errfile= stderr;    /* error messages from qhull code */
   int exitcode;             /* 0 if no error from qhull */
   facetT *facet;            /* set by FORALLfacets */
   int curlong, totlong;     /* memory remaining after qh_memfreeshort */
 
 #if qh_QHpointer  /* see user.h */
   if (qh_qh){
       printf ("QH6238: Qhull link error.  The global variable qh_qh was not initialized\n\
               to NULL by global.c.  Please compile this program with -Dqh_QHpointer_dllimport\n\
               as well as -Dqh_QHpointer, or use libqhullstatic, or use a different tool chain.\n\n");
       exit -1;
   }
 #endif
 
   /* initialize dim, numpoints, points[], ismalloc here */
   exitcode= qh_new_qhull(dim, numpoints, points, ismalloc,
                       flags, outfile, errfile);
   if (!exitcode) {                  /* if no error */
     /* 'qh facet_list' contains the convex hull */
     FORALLfacets {
        /* ... your code ... */
     }
   }
   qh_freeqhull(!qh_ALL);
   qh_memfreeshort(&curlong, &totlong);
   if (curlong || totlong)
     qh_fprintf(errfile, 7068, "qhull internal warning (main): did not free %d bytes of long memory(%d pieces)\n", totlong, curlong);
 }
 #endif
 
 /*---------------------------------
 
   qh_new_qhull( dim, numpoints, points, ismalloc, qhull_cmd, outfile, errfile )
     build new qhull data structure and return exitcode (0 if no errors)
 
   notes:
     do not modify points until finished with results.
       The qhull data structure contains pointers into the points array.
     do not call qhull functions before qh_new_qhull().
       The qhull data structure is not initialized until qh_new_qhull().
 
     outfile may be null
     qhull_cmd must start with "qhull "
     projects points to a new point array for Delaunay triangulations ('d' and 'v')
     transforms points into a new point array for halfspace intersection ('H')
 
 
   To allow multiple, concurrent calls to qhull()
     - set qh_QHpointer in user.h
     - use qh_save_qhull and qh_restore_qhull to swap the global data structure between calls.
     - use qh_freeqhull(qh_ALL) to free intermediate convex hulls
 
   see:
     user_eg.c for an example
 */
 int qh_new_qhull(int dim, int numpoints, coordT *points, boolT ismalloc,
                 char *qhull_cmd, FILE *outfile, FILE *errfile) {
   int exitcode, hulldim;
   boolT new_ismalloc;
   static boolT firstcall = True;
   coordT *new_points;
 
   if (firstcall) {
     qh_meminit(errfile);
     firstcall= False;
   }
   if (strncmp(qhull_cmd,"qhull ", (size_t)6)) {
     qh_fprintf(errfile, 6186, "qhull error (qh_new_qhull): start qhull_cmd argument with \"qhull \"\n");
     qh_exit(qh_ERRinput);
   }
   qh_initqhull_start(NULL, outfile, errfile);
   trace1((qh ferr, 1044, "qh_new_qhull: build new Qhull for %d %d-d points with %s\n", numpoints, dim, qhull_cmd));
   exitcode = setjmp(qh errexit);
   if (!exitcode)
   {
     qh NOerrexit = False;
     qh_initflags(qhull_cmd);
     if (qh DELAUNAY)
       qh PROJECTdelaunay= True;
     if (qh HALFspace) {
       /* points is an array of halfspaces,
          the last coordinate of each halfspace is its offset */
       hulldim= dim-1;
       qh_setfeasible(hulldim);
       new_points= qh_sethalfspace_all(dim, numpoints, points, qh feasible_point);
       new_ismalloc= True;
       if (ismalloc)
         qh_free(points);
     }else {
       hulldim= dim;
       new_points= points;
       new_ismalloc= ismalloc;
     }
     qh_init_B(new_points, numpoints, hulldim, new_ismalloc);
     qh_qhull();
     qh_check_output();
     if (outfile) {
       qh_produce_output();
     }else {
       qh_prepare_output();
     }
     if (qh VERIFYoutput && !qh STOPpoint && !qh STOPcone)
       qh_check_points();
   }
   qh NOerrexit = True;
   return exitcode;
 } /* new_qhull */
 
 /*---------------------------------
 
   qh_errexit( exitcode, facet, ridge )
     report and exit from an error
     report facet and ridge if non-NULL
     reports useful information such as last point processed
     set qh.FORCEoutput to print neighborhood of facet
 
   see:
     qh_errexit2() in libqhull.c for printing 2 facets
 
   design:
     check for error within error processing
     compute qh.hulltime
     print facet and ridge (if any)
     report commandString, options, qh.furthest_id
     print summary and statistics (including precision statistics)
     if qh_ERRsingular
       print help text for singular data set
     exit program via long jump (if defined) or exit()
 */
 void qh_errexit(int exitcode, facetT *facet, ridgeT *ridge) {
 
   if (qh ERREXITcalled) {
     qh_fprintf(qh ferr, 8126, "\nqhull error while processing previous error.  Exit program\n");
     qh_exit(qh_ERRqhull);
   }
   qh ERREXITcalled= True;
   if (!qh QHULLfinished)
     qh hulltime= qh_CPUclock - qh hulltime;
   qh_errprint("ERRONEOUS", facet, NULL, ridge, NULL);
   qh_fprintf(qh ferr, 8127, "\nWhile executing: %s | %s\n", qh rbox_command, qh qhull_command);
   qh_fprintf(qh ferr, 8128, "Options selected for Qhull %s:\n%s\n", qh_version, qh qhull_options);
   if (qh furthest_id >= 0) {
     qh_fprintf(qh ferr, 8129, "Last point added to hull was p%d.", qh furthest_id);
     if (zzval_(Ztotmerge))
       qh_fprintf(qh ferr, 8130, "  Last merge was #%d.", zzval_(Ztotmerge));
     if (qh QHULLfinished)
       qh_fprintf(qh ferr, 8131, "\nQhull has finished constructing the hull.");
     else if (qh POSTmerging)
       qh_fprintf(qh ferr, 8132, "\nQhull has started post-merging.");
     qh_fprintf(qh ferr, 8133, "\n");
   }
   if (qh FORCEoutput && (qh QHULLfinished || (!facet && !ridge)))
     qh_produce_output();
   else if (exitcode != qh_ERRinput) {
     if (exitcode != qh_ERRsingular && zzval_(Zsetplane) > qh hull_dim+1) {
       qh_fprintf(qh ferr, 8134, "\nAt error exit:\n");
       qh_printsummary(qh ferr);
       if (qh PRINTstatistics) {
         qh_collectstatistics();
         qh_printstatistics(qh ferr, "at error exit");
         qh_memstatistics(qh ferr);
       }
     }
     if (qh PRINTprecision)
       qh_printstats(qh ferr, qhstat precision, NULL);
   }
   if (!exitcode)
     exitcode= qh_ERRqhull;
   else if (exitcode == qh_ERRsingular)
     qh_printhelp_singular(qh ferr);
   else if (exitcode == qh_ERRprec && !qh PREmerge)
     qh_printhelp_degenerate(qh ferr);
   if (qh NOerrexit) {
     qh_fprintf(qh ferr, 6187, "qhull error while ending program.  Exit program\n");
     qh_exit(qh_ERRqhull);
   }
   qh ERREXITcalled= False;
   qh NOerrexit= True;
+  qh->ALLOWrestart= False;  /* longjmp will undo qh_build_withrestart */
   longjmp(qh errexit, exitcode);
 } /* errexit */
 
 
 /*---------------------------------
 
   qh_errprint( fp, string, atfacet, otherfacet, atridge, atvertex )
     prints out the information of facets and ridges to fp
     also prints neighbors and geomview output
 
   notes:
     except for string, any parameter may be NULL
 */
 void qh_errprint(const char *string, facetT *atfacet, facetT *otherfacet, ridgeT *atridge, vertexT *atvertex) {
   int i;
 
   if (atfacet) {
     qh_fprintf(qh ferr, 8135, "%s FACET:\n", string);
     qh_printfacet(qh ferr, atfacet);
   }
   if (otherfacet) {
     qh_fprintf(qh ferr, 8136, "%s OTHER FACET:\n", string);
     qh_printfacet(qh ferr, otherfacet);
   }
   if (atridge) {
     qh_fprintf(qh ferr, 8137, "%s RIDGE:\n", string);
     qh_printridge(qh ferr, atridge);
     if (atridge->top && atridge->top != atfacet && atridge->top != otherfacet)
       qh_printfacet(qh ferr, atridge->top);
     if (atridge->bottom
         && atridge->bottom != atfacet && atridge->bottom != otherfacet)
       qh_printfacet(qh ferr, atridge->bottom);
     if (!atfacet)
       atfacet= atridge->top;
     if (!otherfacet)
       otherfacet= otherfacet_(atridge, atfacet);
   }
   if (atvertex) {
     qh_fprintf(qh ferr, 8138, "%s VERTEX:\n", string);
     qh_printvertex(qh ferr, atvertex);
   }
   if (qh fout && qh FORCEoutput && atfacet && !qh QHULLfinished && !qh IStracing) {
     qh_fprintf(qh ferr, 8139, "ERRONEOUS and NEIGHBORING FACETS to output\n");
     for (i=0; i < qh_PRINTEND; i++)  /* use fout for geomview output */
       qh_printneighborhood(qh fout, qh PRINTout[i], atfacet, otherfacet,
                             !qh_ALL);
   }
 } /* errprint */
 
 
 /*---------------------------------
 
   qh_printfacetlist( fp, facetlist, facets, printall )
     print all fields for a facet list and/or set of facets to fp
     if !printall,
       only prints good facets
 
   notes:
     also prints all vertices
 */
 void qh_printfacetlist(facetT *facetlist, setT *facets, boolT printall) {
   facetT *facet, **facetp;
 
   qh_printbegin(qh ferr, qh_PRINTfacets, facetlist, facets, printall);
   FORALLfacet_(facetlist)
     qh_printafacet(qh ferr, qh_PRINTfacets, facet, printall);
   FOREACHfacet_(facets)
     qh_printafacet(qh ferr, qh_PRINTfacets, facet, printall);
   qh_printend(qh ferr, qh_PRINTfacets, facetlist, facets, printall);
 } /* printfacetlist */
 
 
 /*---------------------------------
 
   qh_printhelp_degenerate( fp )
     prints descriptive message for precision error
 
   notes:
     no message if qh_QUICKhelp
 */
 void qh_printhelp_degenerate(FILE *fp) {
 
   if (qh MERGEexact || qh PREmerge || qh JOGGLEmax < REALmax/2)
     qh_fprintf(fp, 9368, "\n\
 A Qhull error has occurred.  Qhull should have corrected the above\n\
 precision error.  Please send the input and all of the output to\n\
 qhull_bug@qhull.org\n");
   else if (!qh_QUICKhelp) {
     qh_fprintf(fp, 9369, "\n\
 Precision problems were detected during construction of the convex hull.\n\
 This occurs because convex hull algorithms assume that calculations are\n\
 exact, but floating-point arithmetic has roundoff errors.\n\
 \n\
 To correct for precision problems, do not use 'Q0'.  By default, Qhull\n\
 selects 'C-0' or 'Qx' and merges non-convex facets.  With option 'QJ',\n\
 Qhull joggles the input to prevent precision problems.  See \"Imprecision\n\
 in Qhull\" (qh-impre.htm).\n\
 \n\
 If you use 'Q0', the output may include\n\
 coplanar ridges, concave ridges, and flipped facets.  In 4-d and higher,\n\
 Qhull may produce a ridge with four neighbors or two facets with the same \n\
 vertices.  Qhull reports these events when they occur.  It stops when a\n\
 concave ridge, flipped facet, or duplicate facet occurs.\n");
 #if REALfloat
     qh_fprintf(fp, 9370, "\
 \n\
 Qhull is currently using single precision arithmetic.  The following\n\
 will probably remove the precision problems:\n\
   - recompile qhull for realT precision(#define REALfloat 0 in user.h).\n");
 #endif
     if (qh DELAUNAY && !qh SCALElast && qh MAXabs_coord > 1e4)
       qh_fprintf(fp, 9371, "\
 \n\
 When computing the Delaunay triangulation of coordinates > 1.0,\n\
   - use 'Qbb' to scale the last coordinate to [0,m] (max previous coordinate)\n");
     if (qh DELAUNAY && !qh ATinfinity)
       qh_fprintf(fp, 9372, "\
 When computing the Delaunay triangulation:\n\
   - use 'Qz' to add a point at-infinity.  This reduces precision problems.\n");
 
     qh_fprintf(fp, 9373, "\
 \n\
 If you need triangular output:\n\
   - use option 'Qt' to triangulate the output\n\
   - use option 'QJ' to joggle the input points and remove precision errors\n\
   - use option 'Ft'.  It triangulates non-simplicial facets with added points.\n\
 \n\
 If you must use 'Q0',\n\
 try one or more of the following options.  They can not guarantee an output.\n\
   - use 'QbB' to scale the input to a cube.\n\
   - use 'Po' to produce output and prevent partitioning for flipped facets\n\
   - use 'V0' to set min. distance to visible facet as 0 instead of roundoff\n\
   - use 'En' to specify a maximum roundoff error less than %2.2g.\n\
   - options 'Qf', 'Qbb', and 'QR0' may also help\n",
                qh DISTround);
     qh_fprintf(fp, 9374, "\
 \n\
 To guarantee simplicial output:\n\
   - use option 'Qt' to triangulate the output\n\
   - use option 'QJ' to joggle the input points and remove precision errors\n\
   - use option 'Ft' to triangulate the output by adding points\n\
   - use exact arithmetic (see \"Imprecision in Qhull\", qh-impre.htm)\n\
 ");
   }
 } /* printhelp_degenerate */
 
 
 /*---------------------------------
 
   qh_printhelp_narrowhull( minangle )
     Warn about a narrow hull
 
   notes:
     Alternatively, reduce qh_WARNnarrow in user.h
 
 */
 void qh_printhelp_narrowhull(FILE *fp, realT minangle) {
 
     qh_fprintf(fp, 9375, "qhull precision warning: \n\
 The initial hull is narrow (cosine of min. angle is %.16f).\n\
 Is the input lower dimensional (e.g., on a plane in 3-d)?  Qhull may\n\
 produce a wide facet.  Options 'QbB' (scale to unit box) or 'Qbb' (scale\n\
 last coordinate) may remove this warning.  Use 'Pp' to skip this warning.\n\
 See 'Limitations' in qh-impre.htm.\n",
           -minangle);   /* convert from angle between normals to angle between facets */
 } /* printhelp_narrowhull */
 
 /*---------------------------------
 
   qh_printhelp_singular( fp )
     prints descriptive message for singular input
 */
 void qh_printhelp_singular(FILE *fp) {
   facetT *facet;
   vertexT *vertex, **vertexp;
   realT min, max, *coord, dist;
   int i,k;
 
   qh_fprintf(fp, 9376, "\n\
 The input to qhull appears to be less than %d dimensional, or a\n\
 computation has overflowed.\n\n\
 Qhull could not construct a clearly convex simplex from points:\n",
            qh hull_dim);
   qh_printvertexlist(fp, "", qh facet_list, NULL, qh_ALL);
   if (!qh_QUICKhelp)
     qh_fprintf(fp, 9377, "\n\
 The center point is coplanar with a facet, or a vertex is coplanar\n\
 with a neighboring facet.  The maximum round off error for\n\
 computing distances is %2.2g.  The center point, facets and distances\n\
 to the center point are as follows:\n\n", qh DISTround);
   qh_printpointid(fp, "center point", qh hull_dim, qh interior_point, -1);
   qh_fprintf(fp, 9378, "\n");
   FORALLfacets {
     qh_fprintf(fp, 9379, "facet");
     FOREACHvertex_(facet->vertices)
       qh_fprintf(fp, 9380, " p%d", qh_pointid(vertex->point));
     zinc_(Zdistio);
     qh_distplane(qh interior_point, facet, &dist);
     qh_fprintf(fp, 9381, " distance= %4.2g\n", dist);
   }
   if (!qh_QUICKhelp) {
     if (qh HALFspace)
       qh_fprintf(fp, 9382, "\n\
 These points are the dual of the given halfspaces.  They indicate that\n\
 the intersection is degenerate.\n");
     qh_fprintf(fp, 9383,"\n\
 These points either have a maximum or minimum x-coordinate, or\n\
 they maximize the determinant for k coordinates.  Trial points\n\
 are first selected from points that maximize a coordinate.\n");
     if (qh hull_dim >= qh_INITIALmax)
       qh_fprintf(fp, 9384, "\n\
 Because of the high dimension, the min x-coordinate and max-coordinate\n\
 points are used if the determinant is non-zero.  Option 'Qs' will\n\
 do a better, though much slower, job.  Instead of 'Qs', you can change\n\
 the points by randomly rotating the input with 'QR0'.\n");
   }
   qh_fprintf(fp, 9385, "\nThe min and max coordinates for each dimension are:\n");
   for (k=0; k < qh hull_dim; k++) {
     min= REALmax;
     max= -REALmin;
     for (i=qh num_points, coord= qh first_point+k; i--; coord += qh hull_dim) {
       maximize_(max, *coord);
       minimize_(min, *coord);
     }
     qh_fprintf(fp, 9386, "  %d:  %8.4g  %8.4g  difference= %4.4g\n", k, min, max, max-min);
   }
   if (!qh_QUICKhelp) {
     qh_fprintf(fp, 9387, "\n\
 If the input should be full dimensional, you have several options that\n\
 may determine an initial simplex:\n\
   - use 'QJ'  to joggle the input and make it full dimensional\n\
   - use 'QbB' to scale the points to the unit cube\n\
   - use 'QR0' to randomly rotate the input for different maximum points\n\
   - use 'Qs'  to search all points for the initial simplex\n\
   - use 'En'  to specify a maximum roundoff error less than %2.2g.\n\
   - trace execution with 'T3' to see the determinant for each point.\n",
                      qh DISTround);
 #if REALfloat
     qh_fprintf(fp, 9388, "\
   - recompile qhull for realT precision(#define REALfloat 0 in libqhull.h).\n");
 #endif
     qh_fprintf(fp, 9389, "\n\
 If the input is lower dimensional:\n\
   - use 'QJ' to joggle the input and make it full dimensional\n\
   - use 'Qbk:0Bk:0' to delete coordinate k from the input.  You should\n\
     pick the coordinate with the least range.  The hull will have the\n\
     correct topology.\n\
   - determine the flat containing the points, rotate the points\n\
     into a coordinate plane, and delete the other coordinates.\n\
   - add one or more points to make the input full dimensional.\n\
 ");
   }
 } /* printhelp_singular */
 
 /*---------------------------------
 
   qh_user_memsizes()
     allocate up to 10 additional, quick allocation sizes
 
   notes:
     increase maximum number of allocations in qh_initqhull_mem()
 */
 void qh_user_memsizes(void) {
 
   /* qh_memsize(size); */
 } /* user_memsizes */
 
 
diff --git a/src/libqhull/user.h b/src/libqhull/user.h
index b0f57b1..0a162e2 100644
--- a/src/libqhull/user.h
+++ b/src/libqhull/user.h
@@ -1,858 +1,859 @@
 /*
  ---------------------------------
 
    user.h
    user redefinable constants
 
    see qh-user.htm.  see COPYING for copyright information.
 
    before reading any code, review libqhull.h for data structure definitions and
    the "qh" macro.
 
 Sections:
    ============= qhull library constants ======================
    ============= data types and configuration macros ==========
    ============= performance related constants ================
    ============= memory constants =============================
    ============= joggle constants =============================
    ============= conditional compilation ======================
    ============= -merge constants- ============================
 
 Code flags --
   NOerrors -- the code does not call qh_errexit()
   WARN64 -- the code may be incompatible with 64-bit pointers
 
 */
 
 #include 
 
 #ifndef qhDEFuser
 #define qhDEFuser 1
 
 /*============================================================*/
 /*============= qhull library constants ======================*/
 /*============================================================*/
 
 /*----------------------------------
 
   FILENAMElen -- max length for TI and TO filenames
 
 */
 
 #define qh_FILENAMElen 500
 
 /*----------------------------------
 
   msgcode -- Unique message codes for qh_fprintf
 
   If add new messages, assign these values and increment in user.h and user_r.h
+  See QhullError.h for 10000 errors.
 
   def counters =  [27, 1047, 2059, 3025, 4068, 5003,
      6243, 7079, 8143, 9410, 10000, 11026]
 
   See: qh_ERR* [libqhull.h]
 */
 
 #define MSG_TRACE0 0
 #define MSG_TRACE1 1000
 #define MSG_TRACE2 2000
 #define MSG_TRACE3 3000
 #define MSG_TRACE4 4000
 #define MSG_TRACE5 5000
 #define MSG_ERROR  6000   /* errors written to qh.ferr */
 #define MSG_WARNING 7000
 #define MSG_STDERR  8000  /* log messages Written to qh.ferr */
 #define MSG_OUTPUT  9000
-#define MSG_QHULL_ERROR 10000 /* errors thrown by QhullError [QhullError.h] */
+#define MSG_QHULL_ERROR 10000 /* errors thrown by QhullError.cpp */
 #define MSG_FIXUP  11000  /* FIXUP QH11... */
 #define MSG_MAXLEN  3000 /* qh_printhelp_degenerate() in user.c */
 
 
 /*----------------------------------
 
   qh_OPTIONline -- max length of an option line 'FO'
 */
 #define qh_OPTIONline 80
 
 /*============================================================*/
 /*============= data types and configuration macros ==========*/
 /*============================================================*/
 
 /*----------------------------------
 
   realT
     set the size of floating point numbers
 
   qh_REALdigits
     maximimum number of significant digits
 
   qh_REAL_1, qh_REAL_2n, qh_REAL_3n
     format strings for printf
 
   qh_REALmax, qh_REALmin
     maximum and minimum (near zero) values
 
   qh_REALepsilon
     machine roundoff.  Maximum roundoff error for addition and multiplication.
 
   notes:
    Select whether to store floating point numbers in single precision (float)
    or double precision (double).
 
    Use 'float' to save about 8% in time and 25% in space.  This is particularly
    helpful if high-d where convex hulls are space limited.  Using 'float' also
    reduces the printed size of Qhull's output since numbers have 8 digits of
    precision.
 
    Use 'double' when greater arithmetic precision is needed.  This is needed
    for Delaunay triangulations and Voronoi diagrams when you are not merging
    facets.
 
    If 'double' gives insufficient precision, your data probably includes
    degeneracies.  If so you should use facet merging (done by default)
    or exact arithmetic (see imprecision section of manual, qh-impre.htm).
    You may also use option 'Po' to force output despite precision errors.
 
    You may use 'long double', but many format statements need to be changed
    and you may need a 'long double' square root routine.  S. Grundmann
    (sg@eeiwzb.et.tu-dresden.de) has done this.  He reports that the code runs
    much slower with little gain in precision.
 
    WARNING: on some machines,    int f(){realT a= REALmax;return (a == REALmax);}
       returns False.  Use (a > REALmax/2) instead of (a == REALmax).
 
    REALfloat =   1      all numbers are 'float' type
              =   0      all numbers are 'double' type
 */
 #define REALfloat 0
 
 #if (REALfloat == 1)
 #define realT float
 #define REALmax FLT_MAX
 #define REALmin FLT_MIN
 #define REALepsilon FLT_EPSILON
 #define qh_REALdigits 8   /* maximum number of significant digits */
 #define qh_REAL_1 "%6.8g "
 #define qh_REAL_2n "%6.8g %6.8g\n"
 #define qh_REAL_3n "%6.8g %6.8g %6.8g\n"
 
 #elif (REALfloat == 0)
 #define realT double
 #define REALmax DBL_MAX
 #define REALmin DBL_MIN
 #define REALepsilon DBL_EPSILON
 #define qh_REALdigits 16    /* maximum number of significant digits */
 #define qh_REAL_1 "%6.16g "
 #define qh_REAL_2n "%6.16g %6.16g\n"
 #define qh_REAL_3n "%6.16g %6.16g %6.16g\n"
 
 #else
 #error unknown float option
 #endif
 
 /*----------------------------------
 
   qh_CPUclock
     define the clock() function for reporting the total time spent by Qhull
     returns CPU ticks as a 'long int'
     qh_CPUclock is only used for reporting the total time spent by Qhull
 
   qh_SECticks
     the number of clock ticks per second
 
   notes:
     looks for CLOCKS_PER_SEC, CLOCKS_PER_SECOND, or assumes microseconds
     to define a custom clock, set qh_CLOCKtype to 0
 
     if your system does not use clock() to return CPU ticks, replace
     qh_CPUclock with the corresponding function.  It is converted
     to 'unsigned long' to prevent wrap-around during long runs.  By default,
      defines clock_t as 'long'
 
    Set qh_CLOCKtype to
 
      1          for CLOCKS_PER_SEC, CLOCKS_PER_SECOND, or microsecond
                 Note:  may fail if more than 1 hour elapsed time
 
      2          use qh_clock() with POSIX times() (see global.c)
 */
 #define qh_CLOCKtype 1  /* change to the desired number */
 
 #if (qh_CLOCKtype == 1)
 
 #if defined(CLOCKS_PER_SECOND)
 #define qh_CPUclock    ((unsigned long)clock())  /* return CPU clock */
 #define qh_SECticks CLOCKS_PER_SECOND
 
 #elif defined(CLOCKS_PER_SEC)
 #define qh_CPUclock    ((unsigned long)clock())  /* return CPU clock */
 #define qh_SECticks CLOCKS_PER_SEC
 
 #elif defined(CLK_TCK)
 #define qh_CPUclock    ((unsigned long)clock())  /* return CPU clock */
 #define qh_SECticks CLK_TCK
 
 #else
 #define qh_CPUclock    ((unsigned long)clock())  /* return CPU clock */
 #define qh_SECticks 1E6
 #endif
 
 #elif (qh_CLOCKtype == 2)
 #define qh_CPUclock    qh_clock()  /* return CPU clock */
 #define qh_SECticks 100
 
 #else /* qh_CLOCKtype == ? */
 #error unknown clock option
 #endif
 
 /*----------------------------------
 
   qh_RANDOMtype, qh_RANDOMmax, qh_RANDOMseed
     define random number generator
 
     qh_RANDOMint generates a random integer between 0 and qh_RANDOMmax.
     qh_RANDOMseed sets the random number seed for qh_RANDOMint
 
   Set qh_RANDOMtype (default 5) to:
     1       for random() with 31 bits (UCB)
     2       for rand() with RAND_MAX or 15 bits (system 5)
     3       for rand() with 31 bits (Sun)
     4       for lrand48() with 31 bits (Solaris)
     5       for qh_rand() with 31 bits (included with Qhull)
 
   notes:
     Random numbers are used by rbox to generate point sets.  Random
     numbers are used by Qhull to rotate the input ('QRn' option),
     simulate a randomized algorithm ('Qr' option), and to simulate
     roundoff errors ('Rn' option).
 
     Random number generators differ between systems.  Most systems provide
     rand() but the period varies.  The period of rand() is not critical
     since qhull does not normally use random numbers.
 
     The default generator is Park & Miller's minimal standard random
     number generator [CACM 31:1195 '88].  It is included with Qhull.
 
     If qh_RANDOMmax is wrong, qhull will report a warning and Geomview
     output will likely be invisible.
 */
 #define qh_RANDOMtype 5   /* *** change to the desired number *** */
 
 #if (qh_RANDOMtype == 1)
 #define qh_RANDOMmax ((realT)0x7fffffffUL)  /* 31 bits, random()/MAX */
 #define qh_RANDOMint random()
 #define qh_RANDOMseed_(seed) srandom(seed);
 
 #elif (qh_RANDOMtype == 2)
 #ifdef RAND_MAX
 #define qh_RANDOMmax ((realT)RAND_MAX)
 #else
 #define qh_RANDOMmax ((realT)32767)   /* 15 bits (System 5) */
 #endif
 #define qh_RANDOMint  rand()
 #define qh_RANDOMseed_(seed) srand((unsigned)seed);
 
 #elif (qh_RANDOMtype == 3)
 #define qh_RANDOMmax ((realT)0x7fffffffUL)  /* 31 bits, Sun */
 #define qh_RANDOMint  rand()
 #define qh_RANDOMseed_(seed) srand((unsigned)seed);
 
 #elif (qh_RANDOMtype == 4)
 #define qh_RANDOMmax ((realT)0x7fffffffUL)  /* 31 bits, lrand38()/MAX */
 #define qh_RANDOMint lrand48()
 #define qh_RANDOMseed_(seed) srand48(seed);
 
 #elif (qh_RANDOMtype == 5)
 #define qh_RANDOMmax ((realT)2147483646UL)  /* 31 bits, qh_rand/MAX */
 #define qh_RANDOMint qh_rand()
 #define qh_RANDOMseed_(seed) qh_srand(seed);
 /* unlike rand(), never returns 0 */
 
 #else
 #error: unknown random option
 #endif
 
 /*----------------------------------
 
   qh_ORIENTclock
     0 for inward pointing normals by Geomview convention
 */
 #define qh_ORIENTclock 0
 
 
 /*============================================================*/
 /*============= joggle constants =============================*/
 /*============================================================*/
 
 /*----------------------------------
 
 qh_JOGGLEdefault
 default qh.JOGGLEmax is qh.DISTround * qh_JOGGLEdefault
 
 notes:
 rbox s r 100 | qhull QJ1e-15 QR0 generates 90% faults at distround 7e-16
 rbox s r 100 | qhull QJ1e-14 QR0 generates 70% faults
 rbox s r 100 | qhull QJ1e-13 QR0 generates 35% faults
 rbox s r 100 | qhull QJ1e-12 QR0 generates 8% faults
 rbox s r 100 | qhull QJ1e-11 QR0 generates 1% faults
 rbox s r 100 | qhull QJ1e-10 QR0 generates 0% faults
 rbox 1000 W0 | qhull QJ1e-12 QR0 generates 86% faults
 rbox 1000 W0 | qhull QJ1e-11 QR0 generates 20% faults
 rbox 1000 W0 | qhull QJ1e-10 QR0 generates 2% faults
 the later have about 20 points per facet, each of which may interfere
 
 pick a value large enough to avoid retries on most inputs
 */
 #define qh_JOGGLEdefault 30000.0
 
 /*----------------------------------
 
 qh_JOGGLEincrease
 factor to increase qh.JOGGLEmax on qh_JOGGLEretry or qh_JOGGLEagain
 */
 #define qh_JOGGLEincrease 10.0
 
 /*----------------------------------
 
 qh_JOGGLEretry
 if ZZretry = qh_JOGGLEretry, increase qh.JOGGLEmax
 
 notes:
 try twice at the original value in case of bad luck the first time
 */
 #define qh_JOGGLEretry 2
 
 /*----------------------------------
 
 qh_JOGGLEagain
 every following qh_JOGGLEagain, increase qh.JOGGLEmax
 
 notes:
 1 is OK since it's already failed qh_JOGGLEretry times
 */
 #define qh_JOGGLEagain 1
 
 /*----------------------------------
 
 qh_JOGGLEmaxincrease
 maximum qh.JOGGLEmax due to qh_JOGGLEincrease
 relative to qh.MAXwidth
 
 notes:
 qh.joggleinput will retry at this value until qh_JOGGLEmaxretry
 */
 #define qh_JOGGLEmaxincrease 1e-2
 
 /*----------------------------------
 
 qh_JOGGLEmaxretry
 stop after qh_JOGGLEmaxretry attempts
 */
 #define qh_JOGGLEmaxretry 100
 
 /*============================================================*/
 /*============= performance related constants ================*/
 /*============================================================*/
 
 /*----------------------------------
 
   qh_HASHfactor
     total hash slots / used hash slots.  Must be at least 1.1.
 
   notes:
     =2 for at worst 50% occupancy for qh hash_table and normally 25% occupancy
 */
 #define qh_HASHfactor 2
 
 /*----------------------------------
 
   qh_VERIFYdirect
     with 'Tv' verify all points against all facets if op count is smaller
 
   notes:
     if greater, calls qh_check_bestdist() instead
 */
 #define qh_VERIFYdirect 1000000
 
 /*----------------------------------
 
   qh_INITIALsearch
      if qh_INITIALmax, search points up to this dimension
 */
 #define qh_INITIALsearch 6
 
 /*----------------------------------
 
   qh_INITIALmax
     if dim >= qh_INITIALmax, use min/max coordinate points for initial simplex
 
   notes:
     from points with non-zero determinants
     use option 'Qs' to override (much slower)
 */
 #define qh_INITIALmax 8
 
 /*============================================================*/
 /*============= memory constants =============================*/
 /*============================================================*/
 
 /*----------------------------------
 
   qh_MEMalign
     memory alignment for qh_meminitbuffers() in global.c
 
   notes:
     to avoid bus errors, memory allocation must consider alignment requirements.
     malloc() automatically takes care of alignment.   Since mem.c manages
     its own memory, we need to explicitly specify alignment in
     qh_meminitbuffers().
 
     A safe choice is sizeof(double).  sizeof(float) may be used if doubles
     do not occur in data structures and pointers are the same size.  Be careful
     of machines (e.g., DEC Alpha) with large pointers.
 
     If using gcc, best alignment is  [fmax_() is defined in geom_r.h]
               #define qh_MEMalign fmax_(__alignof__(realT),__alignof__(void *))
 */
 #define qh_MEMalign ((int)(fmax_(sizeof(realT), sizeof(void *))))
 
 /*----------------------------------
 
   qh_MEMbufsize
     size of additional memory buffers
 
   notes:
     used for qh_meminitbuffers() in global.c
 */
 #define qh_MEMbufsize 0x10000       /* allocate 64K memory buffers */
 
 /*----------------------------------
 
   qh_MEMinitbuf
     size of initial memory buffer
 
   notes:
     use for qh_meminitbuffers() in global.c
 */
 #define qh_MEMinitbuf 0x20000      /* initially allocate 128K buffer */
 
 /*----------------------------------
 
   qh_INFINITE
     on output, indicates Voronoi center at infinity
 */
 #define qh_INFINITE  -10.101
 
 /*----------------------------------
 
   qh_DEFAULTbox
     default box size (Geomview expects 0.5)
 
   qh_DEFAULTbox
     default box size for integer coorindate (rbox only)
 */
 #define qh_DEFAULTbox 0.5
 #define qh_DEFAULTzbox 1e6
 
 /*============================================================*/
 /*============= conditional compilation ======================*/
 /*============================================================*/
 
 /*----------------------------------
 
   __cplusplus
     defined by C++ compilers
 
   __MSC_VER
     defined by Microsoft Visual C++
 
   __MWERKS__ && __POWERPC__
     defined by Metrowerks when compiling for the Power Macintosh
 
   __STDC__
     defined for strict ANSI C
 */
 
 /*----------------------------------
 
   qh_COMPUTEfurthest
     compute furthest distance to an outside point instead of storing it with the facet
     =1 to compute furthest
 
   notes:
     computing furthest saves memory but costs time
       about 40% more distance tests for partitioning
       removes facet->furthestdist
 */
 #define qh_COMPUTEfurthest 0
 
 /*----------------------------------
 
   qh_KEEPstatistics
     =0 removes most of statistic gathering and reporting
 
   notes:
     if 0, code size is reduced by about 4%.
 */
 #define qh_KEEPstatistics 1
 
 /*----------------------------------
 
   qh_MAXoutside
     record outer plane for each facet
     =1 to record facet->maxoutside
 
   notes:
     this takes a realT per facet and slightly slows down qhull
     it produces better outer planes for geomview output
 */
 #define qh_MAXoutside 1
 
 /*----------------------------------
 
   qh_NOmerge
     disables facet merging if defined
 
   notes:
     This saves about 10% space.
 
     Unless 'Q0'
       qh_NOmerge sets 'QJ' to avoid precision errors
 
     #define qh_NOmerge
 
   see:
     qh_NOmem in mem.c
 
     see user.c/user_eg.c for removing io.o
 */
 
 /*----------------------------------
 
   qh_NOtrace
     no tracing if defined
 
   notes:
     This saves about 5% space.
 
     #define qh_NOtrace
 */
 
 /*----------------------------------
 
   qh_QHpointer
     access global data with pointer or static structure
 
   qh_QHpointer  = 1     access globals via a pointer to allocated memory
                         enables qh_saveqhull() and qh_restoreqhull()
                         [2010, gcc] costs about 4% in time and 4% in space
                         [2003, msvc] costs about 8% in time and 2% in space
 
                 = 0     qh_qh and qh_qhstat are static data structures
                         only one instance of qhull() can be active at a time
                         default value
 
   qh_QHpointer_dllimport and qh_dllimport define qh_qh as __declspec(dllimport) [libqhull.h]
   It is required for msvc-2005.  It is not needed for gcc.
 
   notes:
     all global variables for qhull are in qh, qhmem, and qhstat
     qh is defined in libqhull.h
     qhmem is defined in mem.h
     qhstat is defined in stat.h
     C++ build defines qh_QHpointer [libqhullp.pro, libqhullcpp.pro]
 
   see:
     user_eg.c for an example
 */
 #ifdef qh_QHpointer
 #if qh_dllimport
 #error QH6207 Qhull error: Use qh_QHpointer_dllimport instead of qh_dllimport with qh_QHpointer
 #endif
 #else
 #define qh_QHpointer 0
 #if qh_QHpointer_dllimport
 #error QH6234 Qhull error: Use qh_dllimport instead of qh_QHpointer_dllimport when qh_QHpointer is not defined
 #endif
 #endif
 #if 0  /* sample code */
     qhT *oldqhA, *oldqhB;
 
     exitcode= qh_new_qhull(dim, numpoints, points, ismalloc,
                       flags, outfile, errfile);
     /* use results from first call to qh_new_qhull */
     oldqhA= qh_save_qhull();
     exitcode= qh_new_qhull(dimB, numpointsB, pointsB, ismalloc,
                       flags, outfile, errfile);
     /* use results from second call to qh_new_qhull */
     oldqhB= qh_save_qhull();
     qh_restore_qhull(&oldqhA);
     /* use results from first call to qh_new_qhull */
     qh_freeqhull(qh_ALL);  /* frees all memory used by first call */
     qh_restore_qhull(&oldqhB);
     /* use results from second call to qh_new_qhull */
     qh_freeqhull(!qh_ALL); /* frees long memory used by second call */
     qh_memfreeshort(&curlong, &totlong);  /* frees short memory and memory allocator */
 #endif
 
 /*----------------------------------
 
   qh_QUICKhelp
     =1 to use abbreviated help messages, e.g., for degenerate inputs
 */
 #define qh_QUICKhelp    0
 
 /*============================================================*/
 /*============= -merge constants- ============================*/
 /*============================================================*/
 /*
    These constants effect facet merging.  You probably will not need
    to modify them.  They effect the performance of facet merging.
 */
 
 /*----------------------------------
 
   qh_DIMmergeVertex
     max dimension for vertex merging (it is not effective in high-d)
 */
 #define qh_DIMmergeVertex 6
 
 /*----------------------------------
 
   qh_DIMreduceBuild
      max dimension for vertex reduction during build (slow in high-d)
 */
 #define qh_DIMreduceBuild 5
 
 /*----------------------------------
 
   qh_BESTcentrum
      if > 2*dim+n vertices, qh_findbestneighbor() tests centrums (faster)
      else, qh_findbestneighbor() tests all vertices (much better merges)
 
   qh_BESTcentrum2
      if qh_BESTcentrum2 * DIM3 + BESTcentrum < #vertices tests centrums
 */
 #define qh_BESTcentrum 20
 #define qh_BESTcentrum2 2
 
 /*----------------------------------
 
   qh_BESTnonconvex
     if > dim+n neighbors, qh_findbestneighbor() tests nonconvex ridges.
 
   notes:
     It is needed because qh_findbestneighbor is slow for large facets
 */
 #define qh_BESTnonconvex 15
 
 /*----------------------------------
 
   qh_MAXnewmerges
     if >n newmerges, qh_merge_nonconvex() calls qh_reducevertices_centrums.
 
   notes:
     It is needed because postmerge can merge many facets at once
 */
 #define qh_MAXnewmerges 2
 
 /*----------------------------------
 
   qh_MAXnewcentrum
     if <= dim+n vertices (n approximates the number of merges),
       reset the centrum in qh_updatetested() and qh_mergecycle_facets()
 
   notes:
     needed to reduce cost and because centrums may move too much if
     many vertices in high-d
 */
 #define qh_MAXnewcentrum 5
 
 /*----------------------------------
 
   qh_COPLANARratio
     for 3-d+ merging, qh.MINvisible is n*premerge_centrum
 
   notes:
     for non-merging, it's DISTround
 */
 #define qh_COPLANARratio 3
 
 /*----------------------------------
 
   qh_DISToutside
     When is a point clearly outside of a facet?
     Stops search in qh_findbestnew or qh_partitionall
     qh_findbest uses qh.MINoutside since since it is only called if no merges.
 
   notes:
     'Qf' always searches for best facet
     if !qh.MERGING, same as qh.MINoutside.
     if qh_USEfindbestnew, increase value since neighboring facets may be ill-behaved
       [Note: Zdelvertextot occurs normally with interior points]
             RBOX 1000 s Z1 G1e-13 t1001188774 | QHULL Tv
     When there is a sharp edge, need to move points to a
     clearly good facet; otherwise may be lost in another partitioning.
     if too big then O(n^2) behavior for partitioning in cone
     if very small then important points not processed
     Needed in qh_partitionall for
       RBOX 1000 s Z1 G1e-13 t1001032651 | QHULL Tv
     Needed in qh_findbestnew for many instances of
       RBOX 1000 s Z1 G1e-13 t | QHULL Tv
 
   See:
     qh_DISToutside -- when is a point clearly outside of a facet
     qh_SEARCHdist -- when is facet coplanar with the best facet?
     qh_USEfindbestnew -- when to use qh_findbestnew for qh_partitionpoint()
 */
 #define qh_DISToutside ((qh_USEfindbestnew ? 2 : 1) * \
      fmax_((qh MERGING ? 2 : 1)*qh MINoutside, qh max_outside))
 
 /*----------------------------------
 
   qh_RATIOnearinside
     ratio of qh.NEARinside to qh.ONEmerge for retaining inside points for
     qh_check_maxout().
 
   notes:
     This is overkill since do not know the correct value.
     It effects whether 'Qc' reports all coplanar points
     Not used for 'd' since non-extreme points are coplanar
 */
 #define qh_RATIOnearinside 5
 
 /*----------------------------------
 
   qh_SEARCHdist
     When is a facet coplanar with the best facet?
     qh_findbesthorizon: all coplanar facets of the best facet need to be searched.
 
   See:
     qh_DISToutside -- when is a point clearly outside of a facet
     qh_SEARCHdist -- when is facet coplanar with the best facet?
     qh_USEfindbestnew -- when to use qh_findbestnew for qh_partitionpoint()
 */
 #define qh_SEARCHdist ((qh_USEfindbestnew ? 2 : 1) * \
       (qh max_outside + 2 * qh DISTround + fmax_( qh MINvisible, qh MAXcoplanar)));
 
 /*----------------------------------
 
   qh_USEfindbestnew
      Always use qh_findbestnew for qh_partitionpoint, otherwise use
      qh_findbestnew if merged new facet or sharpnewfacets.
 
   See:
     qh_DISToutside -- when is a point clearly outside of a facet
     qh_SEARCHdist -- when is facet coplanar with the best facet?
     qh_USEfindbestnew -- when to use qh_findbestnew for qh_partitionpoint()
 */
 #define qh_USEfindbestnew (zzval_(Ztotmerge) > 50)
 
 /*----------------------------------
 
   qh_WIDEcoplanar
     n*MAXcoplanar or n*MINvisible for a WIDEfacet
 
     if vertex is further than qh.WIDEfacet from the hyperplane
     then its ridges are not counted in computing the area, and
     the facet's centrum is frozen.
 
   notes:
    qh.WIDEfacet= max(qh.MAXoutside,qh_WIDEcoplanar*qh.MAXcoplanar,
       qh_WIDEcoplanar * qh.MINvisible);
 */
 #define qh_WIDEcoplanar 6
 
 /*----------------------------------
 
   qh_MAXnarrow
     max. cosine in initial hull that sets qh.NARROWhull
 
   notes:
     If qh.NARROWhull, the initial partition does not make
     coplanar points.  If narrow, a coplanar point can be
     coplanar to two facets of opposite orientations and
     distant from the exact convex hull.
 
     Conservative estimate.  Don't actually see problems until it is -1.0
 */
 #define qh_MAXnarrow -0.99999999
 
 /*----------------------------------
 
   qh_WARNnarrow
     max. cosine in initial hull to warn about qh.NARROWhull
 
   notes:
     this is a conservative estimate.
     Don't actually see problems until it is -1.0.  See qh-impre.htm
 */
 #define qh_WARNnarrow -0.999999999999999
 
 /*----------------------------------
 
   qh_ZEROdelaunay
     a zero Delaunay facet occurs for input sites coplanar with their convex hull
     the last normal coefficient of a zero Delaunay facet is within
         qh_ZEROdelaunay * qh.ANGLEround of 0
 
   notes:
     qh_ZEROdelaunay does not allow for joggled input ('QJ').
 
     You can avoid zero Delaunay facets by surrounding the input with a box.
 
     Use option 'PDk:-n' to explicitly define zero Delaunay facets
       k= dimension of input sites (e.g., 3 for 3-d Delaunay triangulation)
       n= the cutoff for zero Delaunay facets (e.g., 'PD3:-1e-12')
 */
 #define qh_ZEROdelaunay 2
 
 #endif /* qh_DEFuser */
 
 
 
diff --git a/src/libqhull/usermem.c b/src/libqhull/usermem.c
index 2608c18..5794c91 100644
--- a/src/libqhull/usermem.c
+++ b/src/libqhull/usermem.c
@@ -1,64 +1,64 @@
 /*
  ---------------------------------
 
    usermem.c
    qh_exit(), qh_free(), and qh_malloc()
 
    See README.txt.
 
    If you redefine one of these functions you must redefine all of them.
    If you recompile and load this file, then usermem.o will not be loaded
    from qhull.a or qhull.lib
 
    See libqhull.h for data structures, macros, and user-callable functions.
    See user.c for qhull-related, redefinable functions
    see user.h for user-definable constants
-   See userprintf.c for qh_fprintf and userprintf_rbox,c for qh_fprintf_rbox
+   See userprintf.c for qh_fprintf and userprintf_rbox.c for qh_fprintf_rbox
 
    Please report any errors that you fix to qhull@qhull.org
 */
 
 #include "libqhull.h"
 
 #include 
 
 /*---------------------------------
 
   qh_exit( exitcode )
     exit program
 
   notes:
     same as exit()
 */
 void qh_exit(int exitcode) {
     exit(exitcode);
 } /* exit */
 
 /*---------------------------------
 
   qh_free( mem )
     free memory
 
   notes:
     same as free()
 */
 void qh_free(void *mem) {
     free(mem);
 } /* free */
 
 /*---------------------------------
 
     qh_malloc( mem )
       allocate memory
 
     notes:
       same as malloc()
 */
 void *qh_malloc(size_t size) {
     return malloc(size);
 } /* malloc */
 
 
diff --git a/src/libqhullcpp/Coordinates.cpp b/src/libqhullcpp/Coordinates.cpp
index fa38795..522b45c 100644
--- a/src/libqhullcpp/Coordinates.cpp
+++ b/src/libqhullcpp/Coordinates.cpp
@@ -1,184 +1,184 @@
 /****************************************************************************
 **
 ** Copyright (c) 2009-2014 C.B. Barber. All rights reserved.
-** $Id: //main/2011/qhull/src/libqhullcpp/Coordinates.cpp#5 $$Change: 1663 $
-** $DateTime: 2014/01/19 17:59:16 $$Author: bbarber $
+** $Id: //main/2011/qhull/src/libqhullcpp/Coordinates.cpp#7 $$Change: 1712 $
+** $DateTime: 2014/03/30 22:34:33 $$Author: bbarber $
 **
 ****************************************************************************/
 
 #include "functionObjects.h"
 #include "QhullError.h"
 #include "Coordinates.h"
 
 #include 
 #include 
 #include 
 
 #ifdef _MSC_VER  // Microsoft Visual C++ -- warning level 4
 #endif
 
 namespace orgQhull {
 
 #//! Coordinates -- vector of coordT (normally double)
 
 #//Element access
 
 // Inefficient without result-value-optimization or implicitly shared object
 Coordinates Coordinates::
-mid(int idx, int length) const
+mid(countT idx, countT length) const
 {
-    int newLength= length;
+    countT newLength= length;
     if(length<0 || idx+length > count()){
         newLength= count()-idx;
     }
     Coordinates result;
     if(newLength>0){
         std::copy(begin()+idx, begin()+(idx+newLength), std::back_inserter(result));
     }
     return result;
 }//mid
 
 coordT Coordinates::
-value(int idx, const coordT &defaultValue) const
+value(countT idx, const coordT &defaultValue) const
 {
     return ((idx < 0 || idx >= count()) ? defaultValue : (*this)[idx]);
 }//value
 
-#//Operator
+#//!\name GetSet
 
 Coordinates Coordinates::
 operator+(const Coordinates &other) const
 {
     Coordinates result(*this);
     std::copy(other.begin(), other.end(), std::back_inserter(result));
     return result;
 }//operator+
 
 Coordinates & Coordinates::
 operator+=(const Coordinates &other)
 {
     if(&other==this){
         Coordinates clone(other);
         std::copy(clone.begin(), clone.end(), std::back_inserter(*this));
     }else{
         std::copy(other.begin(), other.end(), std::back_inserter(*this));
     }
     return *this;
 }//operator+=
 
 #//Read-write
 
 coordT Coordinates::
-takeAt(int idx)
+takeAt(countT idx)
 {
     coordT c= at(idx);
     erase(begin()+idx);
     return c;
 }//takeAt
 
 coordT Coordinates::
 takeLast()
 {
     coordT c= last();
     removeLast();
     return c;
 }//takeLast
 
 void Coordinates::
-swap(int idx, int other)
+swap(countT idx, countT other)
 {
     coordT c= at(idx);
     at(idx)= at(other);
     at(other)= c;
 }//swap
 
 #//Search
 
 bool Coordinates::
 contains(const coordT &t) const
 {
     CoordinatesIterator i(*this);
     return i.findNext(t);
 }//contains
 
-int Coordinates::
+countT Coordinates::
 count(const coordT &t) const
 {
     CoordinatesIterator i(*this);
-    int result= 0;
+    countT result= 0;
     while(i.findNext(t)){
         ++result;
     }
     return result;
 }//count
 
-int Coordinates::
-indexOf(const coordT &t, int from) const
+countT Coordinates::
+indexOf(const coordT &t, countT from) const
 {
     if(from<0){
         from += count();
         if(from<0){
             from= 0;
         }
     }
     if(from(i-begin())); // WARN64 coordinate index
+                return (static_cast(i-begin())); // WARN64 coordinate index
             }
             ++i;
         }
     }
     return -1;
 }//indexOf
 
-int Coordinates::
-lastIndexOf(const coordT &t, int from) const
+countT Coordinates::
+lastIndexOf(const coordT &t, countT from) const
 {
     if(from<0){
         from += count();
     }else if(from>=count()){
         from= count()-1;
     }
     if(from>=0){
         const_iterator i= begin()+from+1;
         while(i-- != constBegin()){
             if(*i==t){
-                return (static_cast(i-begin())); // WARN64 coordinate index
+                return (static_cast(i-begin())); // WARN64 coordinate index
             }
         }
     }
     return -1;
 }//lastIndexOf
 
 void Coordinates::
 removeAll(const coordT &t)
 {
     MutableCoordinatesIterator i(*this);
     while(i.findNext(t)){
         i.remove();
     }
 }//removeAll
 
 }//namespace orgQhull
 
-#//Global functions
+#//!\name Global functions
 
 using std::endl;
 using std::istream;
 using std::ostream;
 using std::string;
 using std::ws;
 using orgQhull::Coordinates;
 
 ostream &
 operator<<(ostream &os, const Coordinates &cs)
 {
     Coordinates::const_iterator c= cs.begin();
-    for(int i=cs.count(); i--; ){
+    for(countT i=cs.count(); i--; ){
         os << *c++ << " ";
     }
     return os;
 }//operator<<
 
diff --git a/src/libqhullcpp/Coordinates.h b/src/libqhullcpp/Coordinates.h
index 042936b..b30183c 100644
--- a/src/libqhullcpp/Coordinates.h
+++ b/src/libqhullcpp/Coordinates.h
@@ -1,311 +1,305 @@
 /****************************************************************************
 **
-** Copyright (c) 2009-2012 C.B. Barber. All rights reserved.
-** $Id: //main/2011/qhull/src/libqhullcpp/Coordinates.h#6 $$Change: 1464 $
-** $DateTime: 2012/01/25 22:58:41 $$Author: bbarber $
+** Copyright (c) 2009-2014 C.B. Barber. All rights reserved.
+** $Id: //main/2011/qhull/src/libqhullcpp/Coordinates.h#10 $$Change: 1712 $
+** $DateTime: 2014/03/30 22:34:33 $$Author: bbarber $
 **
 ****************************************************************************/
 
 #ifndef QHCOORDINATES_H
 #define QHCOORDINATES_H
 
 #include "QhullError.h"
 #include "QhullIterator.h"
 extern "C" {
-    #include "libqhull/qhull_r.h"
+    #include "libqhullr/qhull_ra.h"
 }
 
 
 #include  // ptrdiff_t, size_t
 #include 
+// Requires STL vector class.  Can use with another vector class such as QList.
 #include 
 
 namespace orgQhull {
 
-#//Types
-    //! an allocated vector of point coordinates
-    //!  Used by PointCoordinates for RboxPoints
-    //!  A QhullPoint refers to previously allocated coordinates
-    class  Coordinates;
-    class  MutableCoordinatesIterator;
-
+#//!\name Defined here
+    //! An std::vector of point coordinates independent of dimension
+    //! Used by PointCoordinates for RboxPoints
+    //! A QhullPoint refers to previously allocated coordinates
+    class Coordinates;
+    class MutableCoordinatesIterator;
 
 class Coordinates {
 
 private:
-#//Fields
+#//!\name Fields
     std::vector coordinate_array;
 
 public:
-#//Subtypes
+#//!\name Subtypes
 
-    class                       const_iterator;
-    class                       iterator;
+    class const_iterator;
+    class iterator;
     typedef iterator Iterator;
     typedef const_iterator ConstIterator;
 
     typedef coordT              value_type;
     typedef const value_type   *const_pointer;
-    typedef const value_type   &const_reference;
-    typedef value_type         *pointer;
-    typedef value_type         &reference;
+    typedef const value_type &  const_reference;
+    typedef value_type *        pointer;
+    typedef value_type &        reference;
     typedef ptrdiff_t           difference_type;
-    typedef int                 size_type;
+    typedef countT              size_type;
 
-#//Construct
+#//!\name Construct
                         Coordinates() {};
     explicit            Coordinates(const std::vector &other) : coordinate_array(other) {}
                         Coordinates(const Coordinates &other) : coordinate_array(other.coordinate_array) {}
-    Coordinates        &operator=(const Coordinates &other) { coordinate_array= other.coordinate_array; return *this; }
-    Coordinates        &operator=(const std::vector &other) { coordinate_array= other; return *this; }
-                       ~Coordinates() {}
-
-#//Conversion
+    Coordinates &       operator=(const Coordinates &other) { coordinate_array= other.coordinate_array; return *this; }
+    Coordinates &       operator=(const std::vector &other) { coordinate_array= other; return *this; }
+                        ~Coordinates() {}
 
-    coordT             *data() { return isEmpty() ? 0 : &at(0); }
-    const coordT       *data() const { return const_cast(isEmpty() ? 0 : &at(0)); }
+#//!\name Conversion
 
 #ifndef QHULL_NO_STL
     std::vector toStdVector() const { return coordinate_array; }
 #endif //QHULL_NO_STL
 #ifdef QHULL_USES_QT
-    QList      toQList() const;
+    QList       toQList() const;
 #endif //QHULL_USES_QT
 
-#//GetSet
-    int                count() const { return static_cast(size()); }
-    bool               empty() const { return coordinate_array.empty(); }
-    bool               isEmpty() const { return empty(); }
-    bool               operator==(const Coordinates &other) const  { return coordinate_array==other.coordinate_array; }
-    bool               operator!=(const Coordinates &other) const  { return coordinate_array!=other.coordinate_array; }
-    size_t             size() const { return coordinate_array.size(); }
-
-#//Element access
-    coordT             &at(int idx) { return coordinate_array.at(idx); }
-    const coordT       &at(int idx) const { return coordinate_array.at(idx); }
-    coordT             &back() { return coordinate_array.back(); }
-    const coordT       &back() const { return coordinate_array.back(); }
-    coordT             &first() { return front(); }
-    const coordT       &first() const { return front(); }
-    coordT             &front() { return coordinate_array.front(); }
-    const coordT       &front() const { return coordinate_array.front(); }
-    coordT             &last() { return back(); }
-    const coordT       &last() const { return back(); }
-    Coordinates        mid(int idx, int length= -1) const;
-    coordT            &operator[](int idx) { return coordinate_array.operator[](idx); }
-    const coordT      &operator[](int idx) const { return coordinate_array.operator[](idx); }
-    coordT             value(int idx, const coordT &defaultValue) const;
-
-#//Iterator
+#//!\name GetSet
+    countT              count() const { return static_cast(size()); }
+    coordT *            data() { return isEmpty() ? 0 : &at(0); }
+    const coordT *      data() const { return const_cast(isEmpty() ? 0 : &at(0)); }
+    bool                isEmpty() const { return coordinate_array.empty(); }
+    bool                operator==(const Coordinates &other) const  { return coordinate_array==other.coordinate_array; }
+    bool                operator!=(const Coordinates &other) const  { return coordinate_array!=other.coordinate_array; }
+    size_t              size() const { return coordinate_array.size(); }
+
+#//!\name Element access
+    coordT &            at(countT idx) { return coordinate_array.at(idx); }
+    const coordT &      at(countT idx) const { return coordinate_array.at(idx); }
+    coordT &            back() { return coordinate_array.back(); }
+    const coordT &      back() const { return coordinate_array.back(); }
+    coordT &            first() { return front(); }
+    const coordT &      first() const { return front(); }
+    coordT &            front() { return coordinate_array.front(); }
+    const coordT &      front() const { return coordinate_array.front(); }
+    coordT &            last() { return back(); }
+    const coordT &      last() const { return back(); }
+    Coordinates         mid(countT idx, countT length= -1) const; //!<\todo countT -1 indicates 
+    coordT &            operator[](countT idx) { return coordinate_array.operator[](idx); }
+    const coordT &      operator[](countT idx) const { return coordinate_array.operator[](idx); }
+    coordT              value(countT idx, const coordT &defaultValue) const;
+
+#//!\name Iterator
     iterator            begin() { return iterator(coordinate_array.begin()); }
     const_iterator      begin() const { return const_iterator(coordinate_array.begin()); }
     const_iterator      constBegin() const { return begin(); }
     const_iterator      constEnd() const { return end(); }
     iterator            end() { return iterator(coordinate_array.end()); }
     const_iterator      end() const { return const_iterator(coordinate_array.end()); }
 
-#//Read-only
+#//!\name GetSet
     Coordinates         operator+(const Coordinates &other) const;
 
-#//Modify
+#//!\name Modify
     void                append(const coordT &c) { push_back(c); }
     void                clear() { coordinate_array.clear(); }
     iterator            erase(iterator idx) { return iterator(coordinate_array.erase(idx.base())); }
     iterator            erase(iterator beginIterator, iterator endIterator) { return iterator(coordinate_array.erase(beginIterator.base(), endIterator.base())); }
-    void                insert(int before, const coordT &c) { insert(begin()+before, c); }
+    void                insert(countT before, const coordT &c) { insert(begin()+before, c); }
     iterator            insert(iterator before, const coordT &c) { return iterator(coordinate_array.insert(before.base(), c)); }
-    void                move(int from, int to) { insert(to, takeAt(from)); }
-    Coordinates        &operator+=(const Coordinates &other);
-    Coordinates        &operator+=(const coordT &c) { append(c); return *this; }
-    Coordinates        &operator<<(const Coordinates &other) { return *this += other; }
-    Coordinates        &operator<<(const coordT &c) { return *this += c; }
+    void                move(countT from, countT to) { insert(to, takeAt(from)); }
+    Coordinates &       operator+=(const Coordinates &other);
+    Coordinates &       operator+=(const coordT &c) { append(c); return *this; }
+    Coordinates &       operator<<(const Coordinates &other) { return *this += other; }
+    Coordinates &       operator<<(const coordT &c) { return *this += c; }
     void                pop_back() { coordinate_array.pop_back(); }
     void                pop_front() { removeFirst(); }
     void                prepend(const coordT &c) { insert(begin(), c); }
     void                push_back(const coordT &c) { coordinate_array.push_back(c); }
     void                push_front(const coordT &c) { insert(begin(), c); }
                         //removeAll below
-    void                removeAt(int idx) { erase(begin()+idx); }
+    void                removeAt(countT idx) { erase(begin()+idx); }
     void                removeFirst() { erase(begin()); }
     void                removeLast() { erase(--end()); }
-    void                replace(int idx, const coordT &c) { (*this)[idx]= c; }
-    void                reserve(int i) { coordinate_array.reserve(i); }
-    void                swap(int idx, int other);
-    coordT              takeAt(int idx);
+    void                replace(countT idx, const coordT &c) { (*this)[idx]= c; }
+    void                reserve(countT i) { coordinate_array.reserve(i); }
+    void                swap(countT idx, countT other);
+    coordT              takeAt(countT idx);
     coordT              takeFirst() { return takeAt(0); }
     coordT              takeLast();
 
-#//Search
+#//!\name Search
     bool                contains(const coordT &t) const;
-    int                 count(const coordT &t) const;
-    int                 indexOf(const coordT &t, int from = 0) const;
-    int                 lastIndexOf(const coordT &t, int from = -1) const;
+    countT              count(const coordT &t) const;
+    countT              indexOf(const coordT &t, countT from = 0) const;
+    countT              lastIndexOf(const coordT &t, countT from = -1) const;
     void                removeAll(const coordT &t);
 
-#//Coordinates::iterator -- from QhullPoints, forwarding to coordinate_array
+#//!\name Coordinates::iterator -- from QhullPoints, forwarding to coordinate_array
     // before const_iterator for conversion with comparison operators
     class iterator {
 
     private:
         std::vector::iterator i;
-        friend class    const_iterator;
+        friend class const_iterator;
 
     public:
         typedef std::random_access_iterator_tag  iterator_category;
         typedef coordT      value_type;
         typedef value_type *pointer;
         typedef value_type &reference;
         typedef ptrdiff_t   difference_type;
 
                         iterator() {}
                         iterator(const iterator &other) { i= other.i; }
         explicit        iterator(const std::vector::iterator &vi) { i= vi; }
-        iterator       &operator=(const iterator &other) { i= other.i; return *this; }
+        iterator &      operator=(const iterator &other) { i= other.i; return *this; }
         std::vector::iterator &base() { return i; }
                         // No operator-> for base types
-        coordT         &operator*() const { return *i; }
-        coordT         &operator[](int idx) const { return i[idx]; }
+        coordT &        operator*() const { return *i; }
+        coordT &        operator[](countT idx) const { return i[idx]; }
 
         bool            operator==(const iterator &other) const { return i==other.i; }
         bool            operator!=(const iterator &other) const { return i!=other.i; }
         bool            operator<(const iterator &other) const { return i(const iterator &other) const { return i>other.i; }
         bool            operator>=(const iterator &other) const { return i>=other.i; }
               // reinterpret_cast to break circular dependency
         bool            operator==(const Coordinates::const_iterator &other) const { return *this==reinterpret_cast(other); }
         bool            operator!=(const Coordinates::const_iterator &other) const { return *this!=reinterpret_cast(other); }
         bool            operator<(const Coordinates::const_iterator &other) const { return *this(other); }
         bool            operator<=(const Coordinates::const_iterator &other) const { return *this<=reinterpret_cast(other); }
         bool            operator>(const Coordinates::const_iterator &other) const { return *this>reinterpret_cast(other); }
         bool            operator>=(const Coordinates::const_iterator &other) const { return *this>=reinterpret_cast(other); }
 
         iterator        operator++() { return iterator(++i); } //FIXUP QH11012 Should return reference, but get reference to temporary
         iterator        operator++(int) { return iterator(i++); }
         iterator        operator--() { return iterator(--i); }
         iterator        operator--(int) { return iterator(i--); }
-        iterator        operator+=(int idx) { return iterator(i += idx); }
-        iterator        operator-=(int idx) { return iterator(i -= idx); }
-        iterator        operator+(int idx) const { return iterator(i+idx); }
-        iterator        operator-(int idx) const { return iterator(i-idx); }
+        iterator        operator+=(countT idx) { return iterator(i += idx); }
+        iterator        operator-=(countT idx) { return iterator(i -= idx); }
+        iterator        operator+(countT idx) const { return iterator(i+idx); }
+        iterator        operator-(countT idx) const { return iterator(i-idx); }
         difference_type operator-(iterator other) const { return i-other.i; }
     };//Coordinates::iterator
 
-#//Coordinates::const_iterator
+#//!\name Coordinates::const_iterator
     class const_iterator {
 
     private:
         std::vector::const_iterator i;
 
     public:
         typedef std::random_access_iterator_tag  iterator_category;
         typedef coordT            value_type;
         typedef const value_type *pointer;
         typedef const value_type &reference;
         typedef ptrdiff_t         difference_type;
 
                         const_iterator() {}
                         const_iterator(const const_iterator &other) { i= other.i; }
                         const_iterator(iterator o) : i(o.i) {}
         explicit        const_iterator(const std::vector::const_iterator &vi) { i= vi; }
         const_iterator &operator=(const const_iterator &other) { i= other.i; return *this; }
                         // No operator-> for base types
                         // No reference to a base type for () and []
-        const coordT   &operator*() const { return *i; }
-        const coordT   &operator[](int idx) const { return i[idx]; }
+        const coordT &  operator*() const { return *i; }
+        const coordT &  operator[](countT idx) const { return i[idx]; }
 
         bool            operator==(const const_iterator &other) const { return i==other.i; }
         bool            operator!=(const const_iterator &other) const { return i!=other.i; }
         bool            operator<(const const_iterator &other) const { return i(const const_iterator &other) const { return i>other.i; }
         bool            operator>=(const const_iterator &other) const { return i>=other.i; }
 
         const_iterator  operator++() { return const_iterator(++i); } //FIXUP QH11014 -- too much copying
         const_iterator  operator++(int) { return const_iterator(i++); }
         const_iterator  operator--() { return const_iterator(--i); }
         const_iterator  operator--(int) { return const_iterator(i--); }
-        const_iterator  operator+=(int idx) { return const_iterator(i += idx); }
-        const_iterator  operator-=(int idx) { return const_iterator(i -= idx); }
-        const_iterator  operator+(int idx) const { return const_iterator(i+idx); }
-        const_iterator  operator-(int idx) const { return const_iterator(i-idx); }
+        const_iterator  operator+=(countT idx) { return const_iterator(i += idx); }
+        const_iterator  operator-=(countT idx) { return const_iterator(i -= idx); }
+        const_iterator  operator+(countT idx) const { return const_iterator(i+idx); }
+        const_iterator  operator-(countT idx) const { return const_iterator(i-idx); }
         difference_type operator-(const_iterator other) const { return i-other.i; }
     };//Coordinates::const_iterator
 
 };//Coordinates
 
 //class CoordinatesIterator
 //QHULL_DECLARE_SEQUENTIAL_ITERATOR(Coordinates, coordT)
 
 class CoordinatesIterator
 {
     typedef Coordinates::const_iterator const_iterator;
-    const Coordinates *c;
-    const_iterator i;
-    public:
-    inline CoordinatesIterator(const Coordinates &container)
-    : c(&container), i(c->constBegin()) {}
-    inline CoordinatesIterator &operator=(const Coordinates &container)
-    { c = &container; i = c->constBegin(); return *this; }
-    inline void toFront() { i = c->constBegin(); }
-    inline void toBack() { i = c->constEnd(); }
-    inline bool hasNext() const { return i != c->constEnd(); }
-    inline const coordT &next() { return *i++; }
-    inline const coordT &peekNext() const { return *i; }
-    inline bool hasPrevious() const { return i != c->constBegin(); }
-    inline const coordT &previous() { return *--i; }
-    inline const coordT &peekPrevious() const { const_iterator p = i; return *--p; }
-    inline bool findNext(const coordT &t)
-    { while (i != c->constEnd()) if (*i++ == t) return true; return false; }
-    inline bool findPrevious(const coordT &t)
-    { while (i != c->constBegin()) if (*(--i) == t) return true;
-    return false;  }
+
+private:
+    const Coordinates * c;
+    const_iterator      i;
+
+public:
+                        CoordinatesIterator(const Coordinates &container): c(&container), i(c->constBegin()) {}
+    CoordinatesIterator &operator=(const Coordinates &container) { c= &container; i= c->constBegin(); return *this; }
+                        ~CoordinatesIterator() {}
+
+    bool                findNext(const coordT &t) { while (i != c->constEnd()) if(*i++ == t){ return true;} return false; }
+    bool                findPrevious(const coordT &t) { while (i != c->constBegin())if (*(--i) == t){ return true;} return false;  }
+    bool                hasNext() const { return i != c->constEnd(); }
+    bool                hasPrevious() const { return i != c->constBegin(); }
+    const coordT &      next() { return *i++; }
+    const coordT &      previous() { return *--i; }
+    const coordT &      peekNext() const { return *i; }
+    const coordT &      peekPrevious() const { const_iterator p= i; return *--p; }
+    void                toFront() { i= c->constBegin(); }
+    void                toBack() { i= c->constEnd(); }
 };//CoordinatesIterator
 
 //class MutableCoordinatesIterator
 //QHULL_DECLARE_MUTABLE_SEQUENTIAL_ITERATOR(Coordinates, coordT)
 class MutableCoordinatesIterator
 {
     typedef Coordinates::iterator iterator;
     typedef Coordinates::const_iterator const_iterator;
-    Coordinates *c;
-    iterator i, n;
-    inline bool item_exists() const { return const_iterator(n) != c->constEnd(); }
-    public:
-    inline MutableCoordinatesIterator(Coordinates &container)
-    : c(&container)
-    { i = c->begin(); n = c->end(); }
-    inline ~MutableCoordinatesIterator()
-    {}
-    inline MutableCoordinatesIterator &operator=(Coordinates &container)
-    { c = &container;
-    i = c->begin(); n = c->end(); return *this; }
-    inline void toFront() { i = c->begin(); n = c->end(); }
-    inline void toBack() { i = c->end(); n = i; }
-    inline bool hasNext() const { return c->constEnd() != const_iterator(i); }
-    inline coordT &next() { n = i++; return *n; }
-    inline coordT &peekNext() const { return *i; }
-    inline bool hasPrevious() const { return c->constBegin() != const_iterator(i); }
-    inline coordT &previous() { n = --i; return *n; }
-    inline coordT &peekPrevious() const { iterator p = i; return *--p; }
-    inline void remove()
-    { if (c->constEnd() != const_iterator(n)) { i = c->erase(n); n = c->end(); } }
-    inline void setValue(const coordT &t) const { if (c->constEnd() != const_iterator(n)) *n = t; }
-    inline coordT &value() { QHULL_ASSERT(item_exists()); return *n; }
-    inline const coordT &value() const { QHULL_ASSERT(item_exists()); return *n; }
-    inline void insert(const coordT &t) { n = i = c->insert(i, t); ++i; }
-    inline bool findNext(const coordT &t)
-    { while (c->constEnd() != const_iterator(n = i)) if (*i++ == t) return true; return false; }
-    inline bool findPrevious(const coordT &t)
-    { while (c->constBegin() != const_iterator(i)) if (*(n = --i) == t) return true;
-    n = c->end(); return false;  }
+
+private:
+    Coordinates *       c;
+    iterator            i;
+    iterator            n;
+    bool                item_exists() const { return const_iterator(n) != c->constEnd(); }
+
+public:
+                        MutableCoordinatesIterator(Coordinates &container) : c(&container) { i= c->begin(); n= c->end(); }
+    MutableCoordinatesIterator &operator=(Coordinates &container) { c= &container; i= c->begin(); n= c->end(); return *this; }
+                        ~MutableCoordinatesIterator() {}
+
+    bool                findNext(const coordT &t) { while(c->constEnd()!=const_iterator(n= i)){ if(*i++==t){ return true;}} return false; }
+    bool                findPrevious(const coordT &t) { while(c->constBegin()!=const_iterator(i)){ if(*(n= --i)== t){ return true;}} n= c->end(); return false;  }
+    bool                hasNext() const { return (c->constEnd()!=const_iterator(i)); }
+    bool                hasPrevious() const { return (c->constBegin()!=const_iterator(i)); }
+    void                insert(const coordT &t) { n= i= c->insert(i, t); ++i; }
+    coordT &            next() { n= i++; return *n; }
+    coordT &            peekNext() const { return *i; }
+    coordT &            peekPrevious() const { iterator p= i; return *--p; }
+    coordT &            previous() { n= --i; return *n; }
+    void                remove() { if(c->constEnd()!=const_iterator(n)){ i= c->erase(n); n= c->end();} }
+    void                setValue(const coordT &t) const { if(c->constEnd()!=const_iterator(n)){ *n= t;} }
+    void                toFront() { i= c->begin(); n= c->end(); }
+    void                toBack() { i= c->end(); n= i; }
+    coordT &            value() { QHULL_ASSERT(item_exists()); return *n; }
+    const coordT &      value() const { QHULL_ASSERT(item_exists()); return *n; }
 };//MutableCoordinatesIterator
 
 
 }//namespace orgQhull
 
-#//Global functions
+#//!\name Global
 
 std::ostream &operator<<(std::ostream &os, const orgQhull::Coordinates &c);
 
 #endif // QHCOORDINATES_H
diff --git a/src/libqhullcpp/PointCoordinates.cpp b/src/libqhullcpp/PointCoordinates.cpp
index 9aaa09f..be57c60 100644
--- a/src/libqhullcpp/PointCoordinates.cpp
+++ b/src/libqhullcpp/PointCoordinates.cpp
@@ -1,294 +1,342 @@
 /****************************************************************************
 **
 ** Copyright (c) 2009-2014 C.B. Barber. All rights reserved.
-** $Id: //main/2011/qhull/src/libqhullcpp/PointCoordinates.cpp#6 $$Change: 1464 $
-** $DateTime: 2012/01/25 22:58:41 $$Author: bbarber $
+** $Id: //main/2011/qhull/src/libqhullcpp/PointCoordinates.cpp#11 $$Change: 1797 $
+** $DateTime: 2014/12/15 17:23:41 $$Author: bbarber $
 **
 ****************************************************************************/
 
 #include "QhullError.h"
 #include "QhullPoint.h"
 #include "PointCoordinates.h"
 
 #include 
 #include 
 
 using std::istream;
 using std::string;
 using std::ws;
 
 #ifdef _MSC_VER  // Microsoft Visual C++ -- warning level 4
 #pragma warning( disable : 4996)  // function was declared deprecated(strcpy, localtime, etc.)
 #endif
 
 namespace orgQhull {
 
 #//! PointCoordinates -- vector of PointCoordinates
 
-#//Construct
+#//!\name Constructors
+
+//! Qhull and QhullQh constructors are the same
 PointCoordinates::
-PointCoordinates()
-: QhullPoints()
+PointCoordinates(const Qhull &q)
+: QhullPoints(q)
 , point_coordinates()
-, point_comment()
+, describe_points()
 {
     makeValid();
 }
 
-#//Construct
 PointCoordinates::
-PointCoordinates(int pointDimension)
-: QhullPoints(pointDimension)
+PointCoordinates(const Qhull &q, int pointDimension)
+: QhullPoints(q, pointDimension)
 , point_coordinates()
-, point_comment()
+, describe_points()
 {
     makeValid();
 }
 
 PointCoordinates::
-PointCoordinates(const std::string &aComment)
-: QhullPoints()
+PointCoordinates(const Qhull &q, const std::string &aComment)
+: QhullPoints(q)
 , point_coordinates()
-, point_comment(aComment)
+, describe_points(aComment)
 {
     makeValid();
 }
 
 PointCoordinates::
-PointCoordinates(int pointDimension, const std::string &aComment)
-: QhullPoints(pointDimension)
+PointCoordinates(const Qhull &q, int pointDimension, const std::string &aComment)
+: QhullPoints(q, pointDimension)
 , point_coordinates()
-, point_comment(aComment)
+, describe_points(aComment)
 {
     makeValid();
 }
 
 PointCoordinates::
-PointCoordinates(int pointDimension, const std::string &aComment, int coordinatesCount, const coordT *c)
-: QhullPoints(pointDimension)
+PointCoordinates(const Qhull &q, int pointDimension, const std::string &aComment, countT coordinatesCount, const coordT *c)
+: QhullPoints(q, pointDimension)
 , point_coordinates()
-, point_comment(aComment)
+, describe_points(aComment)
+{
+    append(coordinatesCount, c);
+}
+
+PointCoordinates::
+PointCoordinates(QhullQh *qh)
+: QhullPoints(qh)
+, point_coordinates()
+, describe_points()
+{
+    makeValid();
+}
+
+PointCoordinates::
+PointCoordinates(QhullQh *qh, int pointDimension)
+: QhullPoints(qh, pointDimension)
+, point_coordinates()
+, describe_points()
+{
+    makeValid();
+}
+
+PointCoordinates::
+PointCoordinates(QhullQh *qh, const std::string &aComment)
+: QhullPoints(qh)
+, point_coordinates()
+, describe_points(aComment)
+{
+    makeValid();
+}
+
+PointCoordinates::
+PointCoordinates(QhullQh *qh, int pointDimension, const std::string &aComment)
+: QhullPoints(qh, pointDimension)
+, point_coordinates()
+, describe_points(aComment)
+{
+    makeValid();
+}
+
+PointCoordinates::
+PointCoordinates(QhullQh *qh, int pointDimension, const std::string &aComment, countT coordinatesCount, const coordT *c)
+: QhullPoints(qh, pointDimension)
+, point_coordinates()
+, describe_points(aComment)
 {
     append(coordinatesCount, c);
 }
 
 PointCoordinates::
 PointCoordinates(const PointCoordinates &other)
 : QhullPoints(other)
 , point_coordinates(other.point_coordinates)
-, point_comment(other.point_comment)
+, describe_points(other.describe_points)
 {
-    makeValid();
+    makeValid();  // Update point_first and point_end
 }
 
 PointCoordinates & PointCoordinates::
 operator=(const PointCoordinates &other)
 {
+    QhullPoints::operator=(other);
     point_coordinates= other.point_coordinates;
-    point_comment= other.point_comment;
-    makeValid();
+    describe_points= other.describe_points;
+    makeValid(); // Update point_first and point_end
     return *this;
 }//operator=
 
 PointCoordinates::
 ~PointCoordinates()
 { }
 
-#//GetSet
+#//!\name GetSet
 
 void PointCoordinates::
 checkValid() const
 {
     if(getCoordinates().data()!=data()
     || getCoordinates().count()!=coordinateCount()){
         throw QhullError(10060, "Qhull error: first point (%x) is not PointCoordinates.data() or count (%d) is not PointCoordinates.count (%d)", coordinateCount(), getCoordinates().count(), 0.0, data());
     }
 }//checkValid
 
 void PointCoordinates::
 setDimension(int i)
 {
     if(i<0){
         throw QhullError(10062, "Qhull error: can not set PointCoordinates dimension to %d", i);
     }
     int currentDimension=QhullPoints::dimension();
     if(currentDimension!=0 && i!=currentDimension){
         throw QhullError(10063, "Qhull error: can not change PointCoordinates dimension (from %d to %d)", currentDimension, i);
     }
     QhullPoints::setDimension(i);
 }//setDimension
 
-//#Foreach
+#//!\name Foreach
 
 Coordinates::ConstIterator PointCoordinates::
-beginCoordinates(int pointIndex) const
+beginCoordinates(countT pointIndex) const
 {
     return point_coordinates.begin()+indexOffset(pointIndex);
 }
 
 Coordinates::Iterator PointCoordinates::
-beginCoordinates(int pointIndex)
+beginCoordinates(countT pointIndex)
 {
     return point_coordinates.begin()+indexOffset(pointIndex);
 }
 
-#//Modify
+#//!\name Methods
 
 void PointCoordinates::
-append(int coordinatesCount, const coordT *c)
+append(countT coordinatesCount, const coordT *c)
 {
     if(coordinatesCount<=0){
         return;
     }
     if(includesCoordinates(c)){
         throw QhullError(10065, "Qhull error: can not append a subset of PointCoordinates to itself.  The coordinates for point %d may move.", indexOf(c, QhullError::NOthrow));
     }
     reserveCoordinates(coordinatesCount);
     std::copy(c, c+coordinatesCount, std::back_inserter(point_coordinates));
     makeValid();
 }//append coordT
 
 void PointCoordinates::
 append(const PointCoordinates &other)
 {
     setDimension(other.dimension());
     append(other.coordinateCount(), other.data());
 }//append PointCoordinates
 
 void PointCoordinates::
 append(const QhullPoint &p)
 {
     setDimension(p.dimension());
     append(p.dimension(), p.coordinates());
 }//append QhullPoint
 
 void PointCoordinates::
 appendComment(const std::string &s){
-    if(char c= s[0] && point_comment.empty()){
+    if(char c= s[0] && describe_points.empty()){
         if(c=='-' || isdigit(c)){
             throw QhullError(10028, "Qhull argument error: comments can not start with a number or minus, %s", 0, 0, 0.0, s.c_str());
         }
     }
-    point_comment += s;
+    describe_points += s;
 }//appendComment
 
 //! Read PointCoordinates from istream.  First two numbers are dimension and count.  A non-digit starts a rboxCommand.
-//! Overwrites point_comment.  See qh_readpoints [io.c]
+//! Overwrites describe_points.  See qh_readpoints [io.c]
 void PointCoordinates::
 appendPoints(istream &in)
 {
-    int inDimension, inCount;
+    int inDimension;
+    countT inCount;
     in >> ws >> inDimension >> ws;
     if(!in.good()){
         in.clear();
         string remainder;
         getline(in, remainder);
         throw QhullError(10005, "Qhull error: input did not start with dimension or count -- %s", 0, 0, 0, remainder.c_str());
     }
     char c= (char)in.peek();
     if(c!='-' && !isdigit(c)){         // Comments start with a non-digit
-        getline(in, point_comment);
+        getline(in, describe_points);
         in >> ws;
     }
     in >> inCount >> ws;
     if(!in.good()){
         in.clear();
         string remainder;
         getline(in, remainder);
         throw QhullError(10009, "Qhull error: input did not start with dimension and count -- %d %s", inDimension, 0, 0, remainder.c_str());
     }
     c= (char)in.peek();
     if(c!='-' && !isdigit(c)){         // Comments start with a non-digit
-        getline(in, point_comment);
+        getline(in, describe_points);
         in >> ws;
     }
     if(inCount> p >> ws;
         if(in.fail()){
             in.clear();
             string remainder;
             getline(in, remainder);
             throw QhullError(10008, "Qhull error: failed to read coordinate %d  of point %d\n   %s", coordinatesCount % inDimension, coordinatesCount/inDimension, 0, remainder.c_str());
         }else{
             point_coordinates.push_back(p);
             coordinatesCount++;
         }
     }
     if(coordinatesCount != inCount*inDimension){
         if(coordinatesCount%inDimension==0){
             throw QhullError(10006, "Qhull error: expected %d %d-d PointCoordinates but read %i PointCoordinates", int(inCount), inDimension, 0.0, int(coordinatesCount/inDimension));
         }else{
             throw QhullError(10012, "Qhull error: expected %d %d-d PointCoordinates but read %i PointCoordinates plus %f extra coordinates", inCount, inDimension, float(coordinatesCount%inDimension), coordinatesCount/inDimension);
         }
     }
     makeValid();
 }//appendPoints istream
 
 PointCoordinates PointCoordinates::
 operator+(const PointCoordinates &other) const
 {
     PointCoordinates pc= *this;
     pc << other;
     return pc;
 }//operator+
 
 void PointCoordinates::
-reserveCoordinates(int newCoordinates)
+reserveCoordinates(countT newCoordinates)
 {
     // vector::reserve is not const
-    point_coordinates.reserve((int)point_coordinates.size()+newCoordinates); // WARN64
+    point_coordinates.reserve((countT)point_coordinates.size()+newCoordinates); // WARN64
     makeValid();
 }//reserveCoordinates
 
 #//Helpers
 
-int PointCoordinates::
-indexOffset(int i) const {
-    int n= i*dimension();
-    int coordinatesCount= point_coordinates.count();
+countT PointCoordinates::
+indexOffset(countT i) const {
+    countT n= i*dimension();
+    countT coordinatesCount= point_coordinates.count();
     if(i<0 || n>coordinatesCount){
         throw QhullError(10061, "Qhull error: point_coordinates is too short (%d) for point %d", coordinatesCount, i);
     }
     return n;
 }
 
 }//namespace orgQhull
 
-#//Global functions
+#//!\name Global functions
 
 using std::endl;
 using std::ostream;
 
 using orgQhull::Coordinates;
 using orgQhull::PointCoordinates;
 
 ostream&
 operator<<(ostream &os, const PointCoordinates &p)
 {
     p.checkValid();
-    int count= p.count();
+    countT count= p.count();
     int dimension= p.dimension();
     string comment= p.comment();
     if(comment.empty()){
         os << dimension << endl;
     }else{
         os << dimension << " " << comment << endl;
     }
     os << count << endl;
     Coordinates::ConstIterator c= p.beginCoordinates();
-    for(int i=0; i
+#include 
+
+#ifndef QHULL_NO_STL
 #include 
+#endif
 
 namespace orgQhull {
 
-#//Types
-    //! Zero or more points with Coordinates, count, and dimension
+#//!\name Defined here
+    //! Zero or more QhullPoints with Coordinates and description
     class PointCoordinates;
 
 class PointCoordinates : public QhullPoints {
 
 private:
-#//Field
-    Coordinates         point_coordinates;      //! array of point coordinates
+#//!\name Fields
+    Coordinates         point_coordinates;      //! std::vector of point coordinates
                                                 //! may have extraCoordinates()
-    std::string         point_comment;          //! Comment describing PointCoordinates
+    std::string         describe_points;          //! Comment describing PointCoordinates
 
 public:
-#//Construct
-                        PointCoordinates();
-    explicit            PointCoordinates(int pointDimension);
-    explicit            PointCoordinates(const std::string &aComment);
-                        PointCoordinates(int pointDimension, const std::string &aComment);
-                        PointCoordinates(int pointDimension, const std::string &aComment, int coordinatesCount, const coordT *c); // may be invalid
+#//!\name Construct
+    explicit            PointCoordinates(const Qhull &q);
+                        PointCoordinates(const Qhull &q, int pointDimension);
+                        PointCoordinates(const Qhull &q, const std::string &aComment);
+                        PointCoordinates(const Qhull &q, int pointDimension, const std::string &aComment);
+                        PointCoordinates(const Qhull &q, int pointDimension, const std::string &aComment, countT coordinatesCount, const coordT *c); // may be invalid
+                        //! Use append() and appendPoints() for Coordinates and vector
+    explicit            PointCoordinates(QhullQh *qh);
+                        PointCoordinates(QhullQh *qh, int pointDimension);
+                        PointCoordinates(QhullQh *qh, const std::string &aComment);
+                        PointCoordinates(QhullQh *qh, int pointDimension, const std::string &aComment);
+                        PointCoordinates(QhullQh *qh, int pointDimension, const std::string &aComment, countT coordinatesCount, const coordT *c); // may be invalid
                         //! Use append() and appendPoints() for Coordinates and vector
                         PointCoordinates(const PointCoordinates &other);
-    PointCoordinates   &operator=(const PointCoordinates &other);
-    ~PointCoordinates();
+    PointCoordinates &  operator=(const PointCoordinates &other);
+                        ~PointCoordinates();
 
-#//Convert
+#//!\name Convert
     //! QhullPoints coordinates, constData, data, count, size
 #ifndef QHULL_NO_STL
     void                append(const std::vector &otherCoordinates) { if(!otherCoordinates.empty()){ append((int)otherCoordinates.size(), &otherCoordinates[0]); } }
     std::vector toStdVector() const { return point_coordinates.toStdVector(); }
 #endif //QHULL_NO_STL
 #ifdef QHULL_USES_QT
     void                append(const QList &pointCoordinates) { if(!pointCoordinates.isEmpty()){ append(pointCoordinates.count(), &pointCoordinates[0]); } }
     QList       toQList() const { return point_coordinates.toQList(); }
 #endif //QHULL_USES_QT
 
-#//GetSet
+#//!\name GetSet
     //! See QhullPoints for coordinates, coordinateCount, dimension, empty, isEmpty, ==, !=
     void                checkValid() const;
-    std::string         comment() const { return point_comment; }
+    std::string         comment() const { return describe_points; }
     void                makeValid() { defineAs(point_coordinates.count(), point_coordinates.data()); }
-    const Coordinates  &getCoordinates() const { return point_coordinates; }
-    void                setComment(const std::string &s) { point_comment= s; }
+    const Coordinates & getCoordinates() const { return point_coordinates; }
+    void                setComment(const std::string &s) { describe_points= s; }
     void                setDimension(int i);
 
 private:
-    void                defineAs(int coordinatesCount, coordT *c) { QhullPoints::defineAs(coordinatesCount, c); }
+    void                defineAs(countT coordinatesCount, coordT *c) { QhullPoints::defineAs(coordinatesCount, c); }
     //! defineAs() otherwise disabled
 public:
 
-#//ElementAccess
+#//!\name ElementAccess
     //! See QhullPoints for at, back, first, front, last, mid, [], value
 
-#//Foreach
+#//!\name Foreach
     //! See QhullPoints for begin, constBegin, end
     Coordinates::ConstIterator  beginCoordinates() const { return point_coordinates.begin(); }
     Coordinates::Iterator       beginCoordinates() { return point_coordinates.begin(); }
-    Coordinates::ConstIterator  beginCoordinates(int pointIndex) const;
-    Coordinates::Iterator       beginCoordinates(int pointIndex);
+    Coordinates::ConstIterator  beginCoordinates(countT pointIndex) const;
+    Coordinates::Iterator       beginCoordinates(countT pointIndex);
     Coordinates::ConstIterator  endCoordinates() const { return point_coordinates.end(); }
     Coordinates::Iterator       endCoordinates() { return point_coordinates.end(); }
 
-#//Search
+#//!\name Search
     //! See QhullPoints for contains, count, indexOf, lastIndexOf
 
-#//Read-only
+#//!\name GetSet
     PointCoordinates    operator+(const PointCoordinates &other) const;
 
-#//Modify
+#//!\name Modify
     //FIXUP QH11001: Add clear() and other modify operators from Coordinates.h.  Include QhullPoint::operator=()
-    void                append(int coordinatesCount, const coordT *c);  //! Dimension previously defined
+    void                append(countT coordinatesCount, const coordT *c);  //! Dimension previously defined
     void                append(const coordT &c) { append(1, &c); } //! Dimension previously defined
     void                append(const QhullPoint &p);
     //! See convert for std::vector and QList
     void                append(const Coordinates &c) { append(c.count(), c.data()); }
     void                append(const PointCoordinates &other);
     void                appendComment(const std::string &s);
     void                appendPoints(std::istream &in);
-    PointCoordinates   &operator+=(const PointCoordinates &other) { append(other); return *this; }
-    PointCoordinates   &operator+=(const coordT &c) { append(c); return *this; }
-    PointCoordinates   &operator+=(const QhullPoint &p) { append(p); return *this; }
-    PointCoordinates   &operator<<(const PointCoordinates &other) { return *this += other; }
-    PointCoordinates   &operator<<(const coordT &c) { return *this += c; }
-    PointCoordinates   &operator<<(const QhullPoint &p) { return *this += p; }
+    PointCoordinates &  operator+=(const PointCoordinates &other) { append(other); return *this; }
+    PointCoordinates &  operator+=(const coordT &c) { append(c); return *this; }
+    PointCoordinates &  operator+=(const QhullPoint &p) { append(p); return *this; }
+    PointCoordinates &  operator<<(const PointCoordinates &other) { return *this += other; }
+    PointCoordinates &  operator<<(const coordT &c) { return *this += c; }
+    PointCoordinates &  operator<<(const QhullPoint &p) { return *this += p; }
     // reserve() is non-const
-    void                reserveCoordinates(int newCoordinates);
+    void                reserveCoordinates(countT newCoordinates);
 
-#//Helpers
+#//!\name Helpers
 private:
     int                 indexOffset(int i) const;
 
 };//PointCoordinates
 
 // No references to QhullPoint.  Prevents use of QHULL_DECLARE_SEQUENTIAL_ITERATOR(PointCoordinates, QhullPoint)
 class PointCoordinatesIterator
 {
     typedef PointCoordinates::const_iterator const_iterator;
+
+private:
     const PointCoordinates *c;
-    const_iterator i;
-    public:
-    inline PointCoordinatesIterator(const PointCoordinates &container)
-    : c(&container), i(c->constBegin()) {}
-    inline PointCoordinatesIterator &operator=(const PointCoordinates &container)
-    { c = &container; i = c->constBegin(); return *this; }
-    inline void toFront() { i = c->constBegin(); }
-    inline void toBack() { i = c->constEnd(); }
-    inline bool hasNext() const { return i != c->constEnd(); }
-    inline const QhullPoint next() { return *i++; }
-    inline const QhullPoint peekNext() const { return *i; }
-    inline bool hasPrevious() const { return i != c->constBegin(); }
-    inline const QhullPoint previous() { return *--i; }
-    inline const QhullPoint peekPrevious() const { const_iterator p = i; return *--p; }
-    inline bool findNext(const QhullPoint &t)
-    { while (i != c->constEnd()) if (*i++ == t) return true; return false; }
-    inline bool findPrevious(const QhullPoint &t)
-    { while (i != c->constBegin()) if (*(--i) == t) return true;
-    return false;  }
+    const_iterator      i;
+
+public:
+                        PointCoordinatesIterator(const PointCoordinates &container) : c(&container), i(c->constBegin()) {}
+                        PointCoordinatesIterator &operator=(const PointCoordinates &container) { c = &container; i = c->constBegin(); return *this; }
+
+    void                toFront() { i = c->constBegin(); }
+    void                toBack() { i = c->constEnd(); }
+    bool                hasNext() const { return i != c->constEnd(); }
+    const QhullPoint    next() { return *i++; }
+    const QhullPoint    peekNext() const { return *i; }
+    bool                hasPrevious() const { return i != c->constBegin(); }
+    const QhullPoint    previous() { return *--i; }
+    const QhullPoint    peekPrevious() const { const_iterator p = i; return *--p; }
+    bool                findNext(const QhullPoint &t) { while(i != c->constEnd()){ if (*i++ == t) return true;} return false; }
+    bool                findPrevious(const QhullPoint &t) { while(i != c->constBegin()){ if (*(--i) == t) return true;} return false;  }
 };//CoordinatesIterator
 
 // FIXUP QH11002:  Add MutablePointCoordinatesIterator after adding modify operators
 \
 }//namespace orgQhull
 
-#//Global functions
+#//!\name Global
 
-std::ostream           &operator<<(std::ostream &os, const orgQhull::PointCoordinates &p);
+std::ostream &          operator<<(std::ostream &os, const orgQhull::PointCoordinates &p);
 
 #endif // QHPOINTCOORDINATES_H
diff --git a/src/libqhullcpp/Qhull.cpp b/src/libqhullcpp/Qhull.cpp
index a34cbcb..aaf2cbd 100644
--- a/src/libqhullcpp/Qhull.cpp
+++ b/src/libqhullcpp/Qhull.cpp
@@ -1,543 +1,313 @@
 /****************************************************************************
 **
 ** Copyright (c) 2008-2014 C.B. Barber. All rights reserved.
-** $Id: //main/2011/qhull/src/libqhullcpp/Qhull.cpp#7 $$Change: 1645 $
-** $DateTime: 2014/01/15 12:51:30 $$Author: bbarber $
+** $Id: //main/2011/qhull/src/libqhullcpp/Qhull.cpp#15 $$Change: 1799 $
+** $DateTime: 2014/12/17 16:17:40 $$Author: bbarber $
 **
 ****************************************************************************/
 
 #//! Qhull -- invoke qhull from C++
 #//! Compile libqhull and Qhull together due to use of setjmp/longjmp()
 
 #include "QhullError.h"
-#include "UsingLibQhull.h"
 #include "RboxPoints.h"
 #include "QhullQh.h"
 #include "QhullFacet.h"
 #include "QhullFacetList.h"
 #include "Qhull.h"
 extern "C" {
-    #include "libqhull/qhull_r.h"
+    #include "libqhullr/qhull_ra.h"
 }
 
 #include 
 
 using std::cerr;
 using std::string;
 using std::vector;
 using std::ostream;
 
 #ifdef _MSC_VER  // Microsoft Visual C++ -- warning level 4
 #pragma warning( disable : 4611)  // interaction between '_setjmp' and C++ object destruction is non-portable
 #pragma warning( disable : 4996)  // function was declared deprecated(strcpy, localtime, etc.)
 #endif
 
 namespace orgQhull {
 
 #//Global variables
 
-char s_unsupported_options[]=" Fd TI ";
-char s_not_output_options[]= " Fd TI A C d E H P Qb QbB Qbb Qc Qf Qg Qi Qm QJ Qr QR Qs Qt Qv Qx Qz Q0 Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10 Q11 R Tc TC TM TP TR Tv TV TW U v V W ";
+const char s_unsupported_options[]=" Fd TI ";
+const char s_not_output_options[]= " Fd TI A C d E H P Qb QbB Qbb Qc Qf Qg Qi Qm QJ Qr QR Qs Qt Qv Qx Qz Q0 Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10 Q11 R Tc TC TM TP TR Tv TV TW U v V W ";
 
 #//Constructor, destructor, etc.
 Qhull::
 Qhull()
-: qhull_qh(0)
-, qhull_run_id(UsingLibQhull::NOqhRunId)
+: qh_qh(0)
 , origin_point()
-, qhull_status(qh_ERRnone)
-, qhull_dimension(0)
 , run_called(false)
-, qh_active(false)
-, qhull_message()
-, error_stream(0)
-, output_stream(0)
 , feasiblePoint()
-, useOutputStream(false)
 {
-    initializeQhull();
+    allocateQhullQh();
 }//Qhull
 
+//! Invokes Qhull on rboxPoints 
+//! Same as runQhull()
+//! For rbox commands, see http://www.qhull.org/html/rbox.htm or html/rbox.htm
+//! For qhull commands, see http://www.qhull.org/html/qhull.htm or html/qhull.htm
 Qhull::
 Qhull(const RboxPoints &rboxPoints, const char *qhullCommand2)
-: qhull_qh(0)
-, qhull_run_id(UsingLibQhull::NOqhRunId)
+: qh_qh(0)
 , origin_point()
-, qhull_status(qh_ERRnone)
-, qhull_dimension(0)
 , run_called(false)
-, qh_active(false)
-, qhull_message()
-, error_stream(0)
-, output_stream(0)
 , feasiblePoint()
-, useOutputStream(false)
 {
-    initializeQhull();
+    allocateQhullQh();
     runQhull(rboxPoints, qhullCommand2);
 }//Qhull rbox
 
+//! Invokes Qhull on a set of input points
+//! Same as runQhull()
+//! For qhull commands, see http://www.qhull.org/html/qhull.htm or html/qhull.htm
 Qhull::
-Qhull(const char *rboxCommand2, int pointDimension, int pointCount, const realT *pointCoordinates, const char *qhullCommand2)
-: qhull_qh(0)
-, qhull_run_id(UsingLibQhull::NOqhRunId)
+Qhull(const char *inputComment, int pointDimension, int pointCount, const realT *pointCoordinates, const char *qhullCommand2)
+: qh_qh(0)
 , origin_point()
-, qhull_status(qh_ERRnone)
-, qhull_dimension(0)
 , run_called(false)
-, qh_active(false)
-, qhull_message()
-, error_stream(0)
-, output_stream(0)
 , feasiblePoint()
-, useOutputStream(false)
 {
-    initializeQhull();
-    runQhull(rboxCommand2, pointDimension, pointCount, pointCoordinates, qhullCommand2);
+    allocateQhullQh();
+    runQhull(inputComment, pointDimension, pointCount, pointCoordinates, qhullCommand2);
 }//Qhull points
 
-Qhull::
-Qhull(const Qhull &other)
-: qhull_qh(0)
-, qhull_run_id(UsingLibQhull::NOqhRunId)
-, origin_point()
-, qhull_status(qh_ERRnone)
-, qhull_dimension(0)
-, run_called(false)
-, qh_active(false)
-, qhull_message(other.qhull_message)
-, error_stream(other.error_stream)
-, output_stream(other.output_stream)
-, feasiblePoint(other.feasiblePoint)
-, useOutputStream(other.useOutputStream)
-{
-    if(other.initialized()){
-        throw QhullError(10069, "Qhull error: can not use Qhull copy constructor if initialized() is true");
-    }
-    initializeQhull();
-}//copy constructor
-
-Qhull & Qhull::
-operator=(const Qhull &other)
-{
-    if(other.initialized() || initialized()){
-        throw QhullError(10070, "Qhull error: can not use Qhull copy assignment if initialized() is true");
-    }
-    qhull_message= other.qhull_message;
-    error_stream= other.error_stream;
-    output_stream= other.output_stream;
-    feasiblePoint= other.feasiblePoint;
-    useOutputStream= other.useOutputStream;
-    return *this;
-}//copy constructor
-
 void Qhull::
-initializeQhull()
+allocateQhullQh()
 {
-    #if qh_QHpointer
-        qhull_qh= new QhullQh;
-        qhull_qh->old_qhstat= qh_qhstat;
-        qhull_qh->old_tempstack= qhmem.tempstack;
-        qh_qh= 0;
-        qh_qhstat= 0;
-    #else
-        qhull_qh= new (&qh_qh) QhullQh;
-        qhull_qh->old_qhstat= &qh_qhstat;
-        qhull_qh->old_tempstack= qhmem.tempstack;
-    #endif
-    qhmem.tempstack= 0;
-    qhull_run_id= qhull_qh->run_id;
-}//initializeQhull
+    qh_qh= new QhullQh;
+    if(qh_qh!=static_cast(qh_qh)){
+        throw QhullError(10074, "Qhull error: QhullQh at a different address than base type QhT (%d bytes).  Please report compiler to qhull.org", (int)(static_cast(qh_qh)-qh_qh));
+    }
+}//allocateQhullQh
 
 Qhull::
 ~Qhull() throw()
 {
-    //! UsingLibQhull is required by ~QhullQh
-    UsingLibQhull q(this, QhullError::NOthrow);
-    if(q.defined()){
-        int exitCode = setjmp(qh errexit);
-        if(!exitCode){ // no object creation -- destructors skipped on longjmp()
-#if qh_QHpointer
-            delete qhull_qh;
-            // clears qhull_qh and qh_qh
-            qh_qh= 0;
-#else
-            qhull_qh->~QhullQh();
-            qhull_qh= 0;
-#endif
-            qhull_run_id= UsingLibQhull::NOqhRunId;
-            // Except for cerr, does not throw errors
-            if(hasQhullMessage()){
-                cerr<< "\nQhull output at end\n"; //FIXUP QH11005: where should error and log messages go on ~Qhull?
-                cerr<hasQhullMessage()){
+        cerr<< "\nQhull output at end\n"; //FIXUP QH11005: where should error and log messages go on ~Qhull?
+        cerr<< qh_qh->qhullMessage();
+        qh_qh->clearQhullMessage();
     }
-    s_qhull_output= 0; // Set by UsingLibQhull
+    delete qh_qh;
+    qh_qh= 0;
 }//~Qhull
 
-#//Messaging
-
-void Qhull::
-appendQhullMessage(const string &s)
-{
-    if(output_stream && useOutputStream && qh USEstdout){   // threading errors caught elsewhere
-        *output_stream << s;
-    }else if(error_stream){
-        *error_stream << s;
-    }else{
-        qhull_message += s;
-    }
-}//appendQhullMessage
-
-//! clearQhullMessage does not throw errors (~Qhull)
-void Qhull::
-clearQhullMessage()
-{
-    qhull_status= qh_ERRnone;
-    qhull_message.clear();
-    RoadError::clearGlobalLog();
-}//clearQhullMessage
-
-//! hasQhullMessage does not throw errors (~Qhull)
-bool Qhull::
-hasQhullMessage() const
-{
-    return (!qhull_message.empty() || qhull_status!=qh_ERRnone);
-    //FIXUP QH11006 -- inconsistent usage with Rbox.  hasRboxMessage just tests rbox_status.  No appendRboxMessage()
-}
-
-//! qhullMessage does not throw errors (~Qhull)
-std::string Qhull::
-qhullMessage() const
-{
-    if(qhull_message.empty() && qhull_status!=qh_ERRnone){
-        return "qhull: no message for error.  Check cerr or error stream\n";
-    }else{
-        return qhull_message;
-    }
-}//qhullMessage
-
-int Qhull::
-qhullStatus() const
-{
-    return qhull_status;
-}//qhullStatus
-
-void Qhull::
-setErrorStream(ostream *os)
-{
-    error_stream= os;
-}//setErrorStream
-
-//! Updates useOutputStream
-void Qhull::
-setOutputStream(ostream *os)
-{
-    output_stream= os;
-    useOutputStream= (os!=0);
-}//setOutputStream
-
-#//GetSet
+#//!\name GetSet
 
 void Qhull::
 checkIfQhullInitialized()
 {
     if(!initialized()){ // qh_initqhull_buffers() not called
         throw QhullError(10023, "Qhull error: checkIfQhullInitialized failed.  Call runQhull() first.");
     }
 }//checkIfQhullInitialized
 
-//! Setup global state (qh_qh, qh_qhstat, qhmem.tempstack)
-int Qhull::
-runId()
-{
-    UsingLibQhull u(this);
-    QHULL_UNUSED(u);
-
-    return qhull_run_id;
-}//runId
-
-
 #//GetValue
 
 double Qhull::
 area(){
     checkIfQhullInitialized();
-    UsingLibQhull q(this);
-    if(!qh hasAreaVolume){
-        int exitCode = setjmp(qh errexit);
-        if(!exitCode){ // no object creation -- destructors skipped on longjmp()
-            qh_getarea(qh facet_list);
+    if(!qh_qh->hasAreaVolume){
+        QH_TRY_(qh_qh){ // no object creation -- destructors skipped on longjmp()
+            qh_getarea(qh_qh, qh_qh->facet_list);
         }
-        maybeThrowQhullMessage(exitCode);
+        qh_qh->maybeThrowQhullMessage(QH_TRY_status);
     }
-    return qh totarea;
+    return qh_qh->totarea;
 }//area
 
 double Qhull::
 volume(){
     checkIfQhullInitialized();
-    UsingLibQhull q(this);
-    if(!qh hasAreaVolume){
-        int exitCode = setjmp(qh errexit);
-        if(!exitCode){ // no object creation -- destructors skipped on longjmp()
-            qh_getarea(qh facet_list);
+    if(!qh_qh->hasAreaVolume){
+        QH_TRY_(qh_qh){ // no object creation -- destructors skipped on longjmp()
+            qh_getarea(qh_qh, qh_qh->facet_list);
         }
-        maybeThrowQhullMessage(exitCode);
+        qh_qh->maybeThrowQhullMessage(QH_TRY_status);
     }
-    return qh totvol;
+    return qh_qh->totvol;
 }//volume
 
-#//ForEach
+#//!\name Foreach
 
 //! Define QhullVertex::neighborFacets().
 //! Automatically called if merging facets or computing the Voronoi diagram.
 //! Noop if called multiple times.
 void Qhull::
 defineVertexNeighborFacets(){
     checkIfQhullInitialized();
-    UsingLibQhull q(this);
-    if(!qh hasAreaVolume){
-        int exitCode = setjmp(qh errexit);
-        if(!exitCode){ // no object creation -- destructors skipped on longjmp()
-            qh_vertexneighbors();
+    if(!qh_qh->hasAreaVolume){
+        QH_TRY_(qh_qh){ // no object creation -- destructors skipped on longjmp()
+            qh_vertexneighbors(qh_qh);
         }
-        maybeThrowQhullMessage(exitCode);
+        qh_qh->maybeThrowQhullMessage(QH_TRY_status);
     }
 }//defineVertexNeighborFacets
 
 QhullFacetList Qhull::
 facetList() const{
     return QhullFacetList(beginFacet(), endFacet());
 }//facetList
 
 QhullPoints Qhull::
 points() const
 {
-    return QhullPoints(hullDimension(), qhull_qh->num_points*hullDimension(), qhull_qh->first_point);
+    return QhullPoints(qh_qh, qh_qh->hull_dim, qh_qh->num_points*qh_qh->hull_dim, qh_qh->first_point);
 }//points
 
 QhullPointSet Qhull::
 otherPoints() const
 {
-    return QhullPointSet(hullDimension(), qhull_qh->other_points);
+    return QhullPointSet(qh_qh, qh_qh->other_points);
 }//otherPoints
 
 //! Return vertices of the convex hull.
 QhullVertexList Qhull::
 vertexList() const{
     return QhullVertexList(beginVertex(), endVertex());
 }//vertexList
 
-#//Modify
+#//!\name Methods
 
 void Qhull::
 outputQhull()
 {
     checkIfQhullInitialized();
-    UsingLibQhull q(this);
-    int exitCode = setjmp(qh errexit);
-    if(!exitCode){ // no object creation -- destructors skipped on longjmp()
-        qh_produce_output2();
+    QH_TRY_(qh_qh){ // no object creation -- destructors skipped on longjmp()
+        qh_produce_output2(qh_qh);
     }
-    maybeThrowQhullMessage(exitCode);
+    qh_qh->maybeThrowQhullMessage(QH_TRY_status);
 }//outputQhull
 
 void Qhull::
 outputQhull(const char *outputflags)
 {
     checkIfQhullInitialized();
-    UsingLibQhull q(this);
     string cmd(" "); // qh_checkflags skips first word
     cmd += outputflags;
     char *command= const_cast(cmd.c_str());
-    int exitCode = setjmp(qh errexit);
-    if(!exitCode){ // no object creation -- destructors skipped on longjmp()
-        qh_clear_outputflags();
-        char *s = qh qhull_command + strlen(qh qhull_command) + 1; //space
-        strncat(qh qhull_command, command, sizeof(qh qhull_command)-strlen(qh qhull_command)-1);
-        qh_checkflags(command, s_not_output_options);
-        qh_initflags(s);
-        qh_initqhull_outputflags();
-        if(qh KEEPminArea < REALmax/2
-           || (0 != qh KEEParea + qh KEEPmerge + qh GOODvertex
-                    + qh GOODthreshold + qh GOODpoint + qh SPLITthresholds)){
+    QH_TRY_(qh_qh){ // no object creation -- destructors skipped on longjmp()
+        qh_clear_outputflags(qh_qh);
+        char *s = qh_qh->qhull_command + strlen(qh_qh->qhull_command) + 1; //space
+        strncat(qh_qh->qhull_command, command, sizeof(qh_qh->qhull_command)-strlen(qh_qh->qhull_command)-1);
+        qh_checkflags(qh_qh, command, const_cast(s_not_output_options));
+        qh_initflags(qh_qh, s);
+        qh_initqhull_outputflags(qh_qh);
+        if(qh_qh->KEEPminArea < REALmax/2
+           || (0 != qh_qh->KEEParea + qh_qh->KEEPmerge + qh_qh->GOODvertex
+                    + qh_qh->GOODthreshold + qh_qh->GOODpoint + qh_qh->SPLITthresholds)){
             facetT *facet;
-            qh ONLYgood= False;
-            FORALLfacet_(qh facet_list) {
+            qh_qh->ONLYgood= False;
+            FORALLfacet_(qh_qh->facet_list) {
                 facet->good= True;
             }
-            qh_prepare_output();
+            qh_prepare_output(qh_qh);
         }
-        qh_produce_output2();
-        if(qh VERIFYoutput && !qh STOPpoint && !qh STOPcone){
-            qh_check_points();
+        qh_produce_output2(qh_qh);
+        if(qh_qh->VERIFYoutput && !qh_qh->STOPpoint && !qh_qh->STOPcone){
+            qh_check_points(qh_qh);
         }
     }
-    maybeThrowQhullMessage(exitCode);
+    qh_qh->maybeThrowQhullMessage(QH_TRY_status);
 }//outputQhull
 
+//! For qhull commands, see http://www.qhull.org/html/qhull.htm or html/qhull.htm
 void Qhull::
 runQhull(const RboxPoints &rboxPoints, const char *qhullCommand2)
 {
     runQhull(rboxPoints.comment().c_str(), rboxPoints.dimension(), rboxPoints.count(), &*rboxPoints.coordinates(), qhullCommand2);
 }//runQhull, RboxPoints
 
-//! points is a array of points, input sites ('d' or 'v'), or halfspaces with offset last ('H')
+//! pointCoordinates is a array of points, input sites ('d' or 'v'), or halfspaces with offset last ('H')
 //! Derived from qh_new_qhull [user.c]
+//! For rbox commands, see http://www.qhull.org/html/rbox.htm or html/rbox.htm
+//! For qhull commands, see http://www.qhull.org/html/qhull.htm or html/qhull.htm
 void Qhull::
-runQhull(const char *rboxCommand2, int pointDimension, int pointCount, const realT *rboxPoints, const char *qhullCommand2)
+runQhull(const char *inputComment, int pointDimension, int pointCount, const realT *pointCoordinates, const char *qhullCommand2)
 {
     if(run_called){
         throw QhullError(10027, "Qhull error: runQhull called twice.  Only one call allowed.");
     }
     run_called= true;
     string s("qhull ");
     s += qhullCommand2;
     char *command= const_cast(s.c_str());
-    UsingLibQhull q(this);
-    int exitCode = setjmp(qh errexit);
-    if(!exitCode){ // no object creation -- destructors skipped on longjmp()
-        qh_checkflags(command, s_unsupported_options);
-        qh_initflags(command);
-        *qh rbox_command= '\0';
-        strncat( qh rbox_command, rboxCommand2, sizeof(qh rbox_command)-1);
-        if(qh DELAUNAY){
-            qh PROJECTdelaunay= True;   // qh_init_B() calls qh_projectinput()
+    /* FIXUP
+    int QH_TRY_status; 
+    if(qh_qh->NOerrexit){ 
+        qh_qh->NOerrexit= False; 
+        QH_TRY_status= setjmp(qh_qh->errexit); 
+    }else{ 
+    QH_TRY_status= QH_TRY_ERROR; 
+    } 
+    if(!QH_TRY_status){ 
+*/
+    QH_TRY_(qh_qh){ // no object creation -- destructors are skipped on longjmp()
+        qh_checkflags(qh_qh, command, const_cast(s_unsupported_options));
+        qh_initflags(qh_qh, command);
+        *qh_qh->rbox_command= '\0';
+        strncat( qh_qh->rbox_command, inputComment, sizeof(qh_qh->rbox_command)-1);
+        if(qh_qh->DELAUNAY){
+            qh_qh->PROJECTdelaunay= True;   // qh_init_B() calls qh_projectinput()
         }
-        pointT *newPoints= const_cast(rboxPoints);
+        pointT *newPoints= const_cast(pointCoordinates);
         int newDimension= pointDimension;
         int newIsMalloc= False;
-        if(qh HALFspace){
+        if(qh_qh->HALFspace){
             --newDimension;
             initializeFeasiblePoint(newDimension);
-            newPoints= qh_sethalfspace_all(pointDimension, pointCount, newPoints, qh feasible_point);
+            newPoints= qh_sethalfspace_all(qh_qh, pointDimension, pointCount, newPoints, qh_qh->feasible_point);
             newIsMalloc= True;
         }
-        qh_init_B(newPoints, pointCount, newDimension, newIsMalloc);
-        qhull_dimension= (qh DELAUNAY ? qh hull_dim - 1 : qh hull_dim);
-        qh_qhull();
-        qh_check_output();
-        qh_prepare_output();
-        if(qh VERIFYoutput && !qh STOPpoint && !qh STOPcone){
-            qh_check_points();
+        qh_init_B(qh_qh, newPoints, pointCount, newDimension, newIsMalloc);
+        qh_qhull(qh_qh);
+        qh_check_output(qh_qh);
+        qh_prepare_output(qh_qh);
+        if(qh_qh->VERIFYoutput && !qh_qh->STOPpoint && !qh_qh->STOPcone){
+            qh_check_points(qh_qh);
         }
     }
-    for(int k= qhull_dimension; k--; ){  // Do not move up (may throw)
+    for(int k= qh_qh->hull_dim; k--; ){  // Do not move into QH_TRY block.  It may throw an error
         origin_point << 0.0;
     }
-    maybeThrowQhullMessage(exitCode);
+    qh_qh->maybeThrowQhullMessage(QH_TRY_status);
 }//runQhull
 
 #//Helpers -- be careful of allocating C++ objects due to setjmp/longjmp() error handling by qh_... routines
 
 void Qhull::
 initializeFeasiblePoint(int hulldim)
 {
-    if(qh feasible_string){
-        qh_setfeasible(hulldim);
+    if(qh_qh->feasible_string){
+        qh_setfeasible(qh_qh, hulldim);
     }else{
-        if(feasiblePoint.empty()){
-            qh_fprintf(qh ferr, 6209, "qhull error: missing feasible point for halfspace intersection.  Use option 'Hn,n' or set qh.feasiblePoint\n");
-            qh_errexit(qh_ERRmem, NULL, NULL);
+        if(feasiblePoint.isEmpty()){
+            qh_fprintf(qh_qh, qh_qh->ferr, 6209, "qhull error: missing feasible point for halfspace intersection.  Use option 'Hn,n' or set qh_qh.feasiblePoint\n");
+            qh_errexit(qh_qh, qh_ERRmem, NULL, NULL);
         }
         if(feasiblePoint.size()!=(size_t)hulldim){
-            qh_fprintf(qh ferr, 6210, "qhull error: dimension of feasiblePoint should be %d.  It is %u", hulldim, feasiblePoint.size());
-            qh_errexit(qh_ERRmem, NULL, NULL);
+            qh_fprintf(qh_qh, qh_qh->ferr, 6210, "qhull error: dimension of feasiblePoint should be %d.  It is %u", hulldim, feasiblePoint.size());
+            qh_errexit(qh_qh, qh_ERRmem, NULL, NULL);
         }
-        if (!(qh feasible_point= (coordT*)qh_malloc(hulldim * sizeof(coordT)))) {
-            qh_fprintf(qh ferr, 6202, "qhull error: insufficient memory for feasible point\n");
-            qh_errexit(qh_ERRmem, NULL, NULL);
+        if (!(qh_qh->feasible_point= (coordT*)qh_malloc(hulldim * sizeof(coordT)))) {
+            qh_fprintf(qh_qh, qh_qh->ferr, 6202, "qhull error: insufficient memory for feasible point\n");
+            qh_errexit(qh_qh, qh_ERRmem, NULL, NULL);
         }
-        coordT *t= qh feasible_point;
+        coordT *t= qh_qh->feasible_point;
         // No qh_... routines after here -- longjmp() ignores destructor
         for(Coordinates::ConstIterator p=feasiblePoint.begin(); p--------------------------------
-
-  qh_fprintf(fp, msgcode, format, list of args )
-    fp is ignored (replaces qh_fprintf() in userprintf.c)
-    s_qhull_output == Qhull
-
-notes:
-    only called from libqhull
-    same as fprintf() and RboxPoints::qh_fprintf_rbox()
-    fgets() is not trapped like fprintf()
-    Do not throw errors from here.  Use qh_errexit;
-*/
-extern "C"
-void qh_fprintf(FILE *fp, int msgcode, const char *fmt, ... ) {
-    va_list args;
-
-    using namespace orgQhull;
-
-    if(!s_qhull_output){
-        fprintf(stderr, "QH10025 Qhull error: UsingLibQhull not declared prior to calling qh_...().  s_qhull_output==NULL.\n");
-        qh_exit(10025);
-    }
-    Qhull *out= s_qhull_output;
-    va_start(args, fmt);
-    if(msgcode=MSG_ERROR && msgcodeqhull_statusqhull_status>=MSG_WARNING){
-                out->qhull_status= msgcode;
-            }
-        }
-        char newMessage[MSG_MAXLEN];
-        // RoadError will add the message tag
-        vsnprintf(newMessage, sizeof(newMessage), fmt, args);
-        out->appendQhullMessage(newMessage);
-        va_end(args);
-        return;
-    }
-    if(out->output_stream && out->useOutputStream){
-        char newMessage[MSG_MAXLEN];
-        vsnprintf(newMessage, sizeof(newMessage), fmt, args);
-        *out->output_stream << newMessage;
-        va_end(args);
-        return;
-    }
-    // FIXUP QH11008: how do users trap messages and handle input?  A callback?
-    char newMessage[MSG_MAXLEN];
-    vsnprintf(newMessage, sizeof(newMessage), fmt, args);
-    out->appendQhullMessage(newMessage);
-    va_end(args);
-} /* qh_fprintf */
-
diff --git a/src/libqhullcpp/Qhull.h b/src/libqhullcpp/Qhull.h
index c9eed9f..07f7559 100644
--- a/src/libqhullcpp/Qhull.h
+++ b/src/libqhullcpp/Qhull.h
@@ -1,147 +1,122 @@
 /****************************************************************************
 **
-** Copyright (c) 2008-2012 C.B. Barber. All rights reserved.
-** $Id: //main/2011/qhull/src/libqhullcpp/Qhull.h#4 $$Change: 1464 $
-** $DateTime: 2012/01/25 22:58:41 $$Author: bbarber $
+** Copyright (c) 2008-2014 C.B. Barber. All rights reserved.
+** $Id: //main/2011/qhull/src/libqhullcpp/Qhull.h#12 $$Change: 1799 $
+** $DateTime: 2014/12/17 16:17:40 $$Author: bbarber $
 **
 ****************************************************************************/
 
 #ifndef QHULLCPP_H
 #define QHULLCPP_H
 
-#include "QhullQh.h"
-#include "RboxPoints.h"
-#include "QhullLinkedList.h"
 #include "QhullPoint.h"
-#include "QhullPoints.h"
 #include "QhullVertex.h"
 #include "QhullFacet.h"
 
-#include 
-#include 
-#include 
-#include 
-#include 
-
-#if qh_QHpointer != 1
-#error  qh_QHpointer is not set.  Please set it in user.h or
-#error  compile Qhull with -Dqh_QHpointer.  The C++ classes
-#error  require dynamic allocation for Qhulls global data
-#error  structure qhT (QhullQh).
-#endif
-
 namespace orgQhull {
 
 /***
    Compile qhullcpp and libqhull with the same compiler.  setjmp() and longjmp() must be the same.
-*/
 
-#//Types
-    //! Qhull -- run Qhull from C++
-    class Qhull;
+   #define QHULL_NO_STL 
+      Do not supply conversions to STL
+      Coordinates.h requires .  It could be rewritten for another vector class such as QList
+   #define QHULL_USES_QT
+      Supply conversions to QT
+      qhulltest requires QT.  It is defined in RoadTest.h
 
-    //Defined elsewhere
+  #define QHULL_ASSERT
+      Defined by QhullError.h
+      It invokes assert()
+*/
+
+#//!\name Used here
     class QhullFacetList;
+    class QhullPoints;
+    class QhullQh;
     class RboxPoints;
 
+#//!\name Defined here
+    class Qhull;
+
+//! Interface to Qhull from C++
 class Qhull {
 
 private:
-#//Members and friends
-    QhullQh            *qhull_qh;       //! qh_qh for this instance
-    int                 qhull_run_id;    //! qh.run_id at initialization (catch multiple runs if !qh_QHpointer)
-    Coordinates         origin_point;   //! origin for qhull_dimension.  Set by runQhull()
-    int                 qhull_status;   //! qh_ERRnone if valid
-    int                 qhull_dimension; //! Dimension of result (qh.hull_dim or one less for Delaunay/Voronoi)
+#//!\name Members and friends
+    QhullQh *           qh_qh;          //! qhT for this instance
+    Coordinates         origin_point;   //! origin for qh_qh->hull_dim.  Set by runQhull()
     bool                run_called;     //! True at start of runQhull.  Errors if call again.
-    bool                qh_active;      //! True if global pointer qh_qh equals qhull_qh
-    std::string         qhull_message;
-    std::ostream       *error_stream;   //! overrides errorMessage, use appendQhullMessage()
-    std::ostream       *output_stream;  //! send output to stream
 
-    friend void       ::qh_fprintf(FILE *fp, int msgcode, const char *fmt, ... );
-    friend class        UsingLibQhull;
-
-#//Attribute
+#//!\name Attribute
 public:
     Coordinates         feasiblePoint;  //! feasible point for half-space intersection
-    bool                useOutputStream; //! Set if using outputStream
     // FIXUP QH11003 feasiblePoint useOutputStream as field or getter?
 
-#//constructor, assignment, destructor, invariant
-                        Qhull();      //! Qhull::runQhull() must be called next
+#//!\name Constructors
+                        Qhull();      //!< call Qhull::runQhull() next
                         Qhull(const RboxPoints &rboxPoints, const char *qhullCommand2);
-                        Qhull(const char *rboxCommand2, int pointDimension, int pointCount, const realT *pointCoordinates, const char *qhullCommand2);
-                        // Throws error if other.initialized().  Needed for return by value and parameter passing
-                        Qhull(const Qhull &other);
-                        // Throws error if initialized() or other.initialized().  Needed for vector
-    Qhull              &operator=(const Qhull &other);
-                       ~Qhull() throw();
+                        Qhull(const char *inputComment, int pointDimension, int pointCount, const realT *pointCoordinates, const char *qhullCommand2);
+                        ~Qhull() throw();
+private:                // Disable copy constructor and assignment.  Qhull owns QhullQh.
+                        Qhull(const Qhull &);
+    Qhull               &operator=(const Qhull &);
+
 private:
-    void                initializeQhull();
+    void                allocateQhullQh();
 
 public:
-#//virtual methods
-    //FIXUP QH11004 -- qh_memfree, etc. as virtual?
-
-#//Messaging
-    void                appendQhullMessage(const std::string &s);
-    void                clearQhullMessage();
-    std::string         qhullMessage() const;
-    bool                hasQhullMessage() const;
-    int                 qhullStatus() const;
-    void                setErrorStream(std::ostream *os);
-    void                setOutputStream(std::ostream *os);
-
-#//GetSet
-    void                checkIfQhullInitialized();
-    bool                initialized() const { return qhull_dimension>0; }
-    int                 dimension() const { return qhull_dimension; }
-    int                 hullDimension() const { return qhullQh()->hull_dim; }
-                        // non-const due to QhullPoint
-    QhullPoint          origin() { QHULL_ASSERT(initialized()); return QhullPoint(dimension(), origin_point.data()); }
-    QhullQh            *qhullQh() const { return qhull_qh; };
-    int                 runId(); // Modifies my_qhull
-
-#//GetQh -- access to qhT (Qhull's global data structure)
-    const char         *qhullCommand() const { return qhull_qh->qhull_command; }
-    const char         *rboxCommand() const { return qhull_qh->rbox_command; }
-    int                 facetCount() const { return qhull_qh->num_facets; }
-    int                 vertexCount() const { return qhull_qh->num_vertices; }
-
-#//GetValue
-    double              area();
-    double              volume();
 
-#//ForEach
-    QhullFacet          beginFacet() const { return QhullFacet(qhull_qh->facet_list); }
-    QhullVertex         beginVertex() const { return QhullVertex(qhull_qh->vertex_list); }
+#//!\name GetSet
+    void                checkIfQhullInitialized();
+    int                 dimension() const { return qh_qh->input_dim; } //!< Dimension of input and result
+    countT              facetCount() const { return qh_qh->num_facets; }
+    int                 hullDimension() const { return qh_qh->hull_dim; } //!< Dimension of the computed hull
+    bool                initialized() const { return (qh_qh->hull_dim>0); }
+    const char *        inputComment() const { return qh_qh->rbox_command; }
+    //! non-const due to QhullPoint
+    QhullPoint          origin() { QHULL_ASSERT(initialized()); return QhullPoint(qh_qh, origin_point.data()); }
+    QhullQh *           qh() const { return qh_qh; };
+    const char *        qhullCommand() const { return qh_qh->qhull_command; }
+    const char *        rboxCommand() const { return qh_qh->rbox_command; }
+    countT              vertexCount() const { return qh_qh->num_vertices; }
+
+#//!\name GetEpsilon
+    double              angleEpsilon() const { return qh_qh->angleEpsilon(); } //!< Epsilon for hyperplane angle equality
+    double              distanceEpsilon() const { return qh_qh->distanceEpsilon(); } //!< Epsilon for distance to hyperplane
+    double              factorEpsilon() const { return qh_qh->factorEpsilon(); }  //!< Factor for angleEpsilon and distanceEpsilon
+    void                setFactorEpsilon(double a) { qh_qh->setFactorEpsilon(a); }
+
+#//!\name ForEach
+    QhullFacet          beginFacet() const { return QhullFacet(qh_qh, qh_qh->facet_list); }
+    QhullVertex         beginVertex() const { return QhullVertex(qh_qh, qh_qh->vertex_list); }
     void                defineVertexNeighborFacets(); //!< Automatically called if merging facets or Voronoi diagram
-    QhullFacet          endFacet() const { return QhullFacet(qhull_qh->facet_tail); }
-    QhullVertex         endVertex() const { return QhullVertex(qhull_qh->vertex_tail); }
+    QhullFacet          endFacet() const { return QhullFacet(qh_qh, qh_qh->facet_tail); }
+    QhullVertex         endVertex() const { return QhullVertex(qh_qh, qh_qh->vertex_tail); }
     QhullFacetList      facetList() const;
     QhullFacet          firstFacet() const { return beginFacet(); }
     QhullVertex         firstVertex() const { return beginVertex(); }
     QhullPoints         points() const;
     QhullPointSet       otherPoints() const;
                         //! Same as points().coordinates()
-    coordT             *pointCoordinateBegin() const { return qhull_qh->first_point; }
-    coordT             *pointCoordinateEnd() const { return qhull_qh->first_point + qhull_qh->num_points*qhull_qh->hull_dim; }
+    coordT *            pointCoordinateBegin() const { return qh_qh->first_point; }
+    coordT *            pointCoordinateEnd() const { return qh_qh->first_point + qh_qh->num_points*qh_qh->hull_dim; }
     QhullVertexList     vertexList() const;
 
-#//Modify
+#//!\name Methods
+    double              area();
+    void                checkAndFreeQhullMemory() { qh_qh->checkAndFreeQhullMemory(); }
     void                outputQhull();
     void                outputQhull(const char * outputflags);
     void                runQhull(const RboxPoints &rboxPoints, const char *qhullCommand2);
-    void                runQhull(const char *rboxCommand2, int pointDimension, int pointCount, const realT *rboxPoints, const char *qhullCommand2);
+    void                runQhull(const char *inputComment, int pointDimension, int pointCount, const realT *pointCoordinates, const char *qhullCommand2);
+    double              volume();
 
+#//!\name Helpers
 private:
-#//Helpers
     void                initializeFeasiblePoint(int hulldim);
-    void                maybeThrowQhullMessage(int exitCode);
-    void                maybeThrowQhullMessage(int exitCode, int noThrow) throw();
 };//Qhull
 
 }//namespace orgQhull
 
 #endif // QHULLCPP_H
diff --git a/src/libqhullcpp/QhullError.h b/src/libqhullcpp/QhullError.h
index 861737b..da39d3a 100644
--- a/src/libqhullcpp/QhullError.h
+++ b/src/libqhullcpp/QhullError.h
@@ -1,64 +1,62 @@
 /****************************************************************************
 **
-** Copyright (c) 2008-2012 C.B. Barber. All rights reserved.
-** $Id: //main/2011/qhull/src/libqhullcpp/QhullError.h#5 $$Change: 1490 $
-** $DateTime: 2012/02/19 20:27:01 $$Author: bbarber $
+** Copyright (c) 2008-2014 C.B. Barber. All rights reserved.
+** $Id: //main/2011/qhull/src/libqhullcpp/QhullError.h#11 $$Change: 1799 $
+** $DateTime: 2014/12/17 16:17:40 $$Author: bbarber $
 **
 ****************************************************************************/
 
 #ifndef QHULLERROR_H
 #define QHULLERROR_H
 
 #include "RoadError.h"
+// No dependencies on libqhull
 
+#ifndef QHULL_ASSERT
+#define QHULL_ASSERT assert
 #include 
-#include 
-#include 
+#endif
 
 namespace orgQhull {
 
-#//Types
+#//!\name Defined here
     //! QhullError -- std::exception class for Qhull
     class QhullError;
 
 class QhullError : public RoadError {
 
 public:
-#//Constants
+#//!\name Constants
     enum {
         QHULLfirstError= 10000, //MSG_QHULL_ERROR in Qhull's user.h
-        QHULLlastError= 10070,
+        QHULLlastError= 10076,
         NOthrow= 1 //! For flag to UsingLibQhull()
     };
 
-#//Constructors
+#//!\name Constructors
     // default constructors
     QhullError() : RoadError() {};
     QhullError(const QhullError &other) : RoadError(other) {}
     QhullError(int code, const std::string &message) : RoadError(code, message) {};
     QhullError(int code, const char *fmt) : RoadError(code, fmt) {};
     QhullError(int code, const char *fmt, int d) : RoadError(code, fmt, d) {};
     QhullError(int code, const char *fmt, int d, int d2) : RoadError(code, fmt, d, d2) {};
     QhullError(int code, const char *fmt, int d, int d2, float f) : RoadError(code, fmt, d, d2, f) {};
     QhullError(int code, const char *fmt, int d, int d2, float f, const char *s) : RoadError(code, fmt, d, d2, f, s) {};
     QhullError(int code, const char *fmt, int d, int d2, float f, const void *x) : RoadError(code, fmt, d, d2, f, x) {};
     QhullError(int code, const char *fmt, int d, int d2, float f, int i) : RoadError(code, fmt, d, d2, f, i) {};
     QhullError(int code, const char *fmt, int d, int d2, float f, long long i) : RoadError(code, fmt, d, d2, f, i) {};
     QhullError(int code, const char *fmt, int d, int d2, float f, double e) : RoadError(code, fmt, d, d2, f, e) {};
     QhullError &operator=(const QhullError &other) { this->RoadError::operator=(other); return *this; }
     ~QhullError() throw() {}
 
 };//class QhullError
 
-#ifndef QHULL_1
-    #define QHULL_ASSERT assert
-
-#endif
 
 }//namespace orgQhull
 
-#//Global functions
+#//!\name Global
 
 inline std::ostream &operator<<(std::ostream &os, const orgQhull::QhullError &e) { return os << e.what(); }
 
 #endif // QHULLERROR_H
diff --git a/src/libqhullcpp/QhullFacet.cpp b/src/libqhullcpp/QhullFacet.cpp
index ca25d0e..ac5780d 100644
--- a/src/libqhullcpp/QhullFacet.cpp
+++ b/src/libqhullcpp/QhullFacet.cpp
@@ -1,524 +1,506 @@
 /****************************************************************************
 **
 ** Copyright (c) 2008-2014 C.B. Barber. All rights reserved.
-** $Id: //main/2011/qhull/src/libqhullcpp/QhullFacet.cpp#7 $$Change: 1464 $
-** $DateTime: 2012/01/25 22:58:41 $$Author: bbarber $
+** $Id: //main/2011/qhull/src/libqhullcpp/QhullFacet.cpp#13 $$Change: 1797 $
+** $DateTime: 2014/12/15 17:23:41 $$Author: bbarber $
 **
 ****************************************************************************/
 
 #//! QhullFacet -- Qhull's facet structure, facetT, as a C++ class
 
 #include "QhullError.h"
+#include "Qhull.h"
 #include "QhullSet.h"
 #include "QhullPoint.h"
 #include "QhullPointSet.h"
 #include "QhullRidge.h"
 #include "QhullFacet.h"
 #include "QhullFacetSet.h"
 #include "QhullVertex.h"
 
 #include 
 
 using std::endl;
-using std::string;
-using std::vector;
 using std::ostream;
 
 #ifdef _MSC_VER  // Microsoft Visual C++ -- warning level 4
 #pragma warning( disable : 4611)  // interaction between '_setjmp' and C++ object destruction is non-portable
 #pragma warning( disable : 4996)  // function was declared deprecated(strcpy, localtime, etc.)
 #endif
 
 namespace orgQhull {
 
-#//class statics
+#//!\name Class objects
 facetT QhullFacet::
-        s_empty_facet= {0,0,0,0,{0},
-                0,0,0,0,0,
-                0,0,0,0,0,
-                0,0,0,0,0,
-                0,0,0,0,0,
-                0,0,0,0,0,
-                0,0,0,0,0,
-                0,0,0,0};
-
-#//GetSet
-
-int QhullFacet::
-dimension() const
+s_empty_facet= {0,0,0,0,{0},
+        0,0,0,0,0,
+        0,0,0,0,0,
+        0,0,0,0,0,
+        0,0,0,0,0,
+        0,0,0,0,0,
+        0,0,0,0,0,
+        0,0,0,0};
+
+#//!\name Constructors
+
+QhullFacet::
+QhullFacet(const Qhull &q) 
+: qh_facet(&s_empty_facet)
+, qh_qh(q.qh())
 {
-    if(qh_facet->ridges){
-        setT *s= qh_facet->ridges;
-        ridgeT *r= reinterpret_cast(SETfirst_(s));
-        return r ? QhullSetBase::count(r->vertices)+1 : 0;
-    }else{
-        return QhullSetBase::count(qh_facet->vertices);
-    }
-}//dimension
+}
+
+QhullFacet::
+QhullFacet(const Qhull &q, facetT *f) 
+: qh_facet(f ? f : &s_empty_facet)
+, qh_qh(q.qh())
+{
+}
 
-//! Return voronoi center or facet centrum.  Derived from qh_printcenter [io.c]
+#//!\name GetSet
+
+//! Return voronoi center or facet centrum.  Derived from qh_printcenter [io_r.c]
 //! printFormat=qh_PRINTtriangles if return centrum of a Delaunay facet
 //! Sets center if needed
 //! Code duplicated for PrintCenter and getCenter
-//! .empty() if none or qh_INFINITE
+//! Returns QhullPoint() if none or qh_INFINITE
 QhullPoint QhullFacet::
-getCenter(int qhRunId, qh_PRINT printFormat)
+getCenter(qh_PRINT printFormat)
 {
-    UsingLibQhull q(qhRunId);
-
-    if(qh CENTERtype==qh_ASvoronoi){
-        if(!qh_facet->normal || !qh_facet->upperdelaunay || !qh ATinfinity){
+    if(qh_qh->CENTERtype==qh_ASvoronoi){
+        if(!qh_facet->normal || !qh_facet->upperdelaunay || !qh_qh->ATinfinity){
             if(!qh_facet->center){
-                int exitCode = setjmp(qh errexit);
-                if(!exitCode){ // no object creation -- destructors skipped on longjmp()
-                    qh_facet->center= qh_facetcenter(qh_facet->vertices);
+                QH_TRY_(qh_qh){ // no object creation -- destructors skipped on longjmp()
+                    qh_facet->center= qh_facetcenter(qh_qh, qh_facet->vertices);
                 }
-                q.maybeThrowQhullMessage(exitCode);
+                qh_qh->maybeThrowQhullMessage(QH_TRY_status);
             }
-            return QhullPoint(qh hull_dim-1, qh_facet->center);
+            return QhullPoint(qh_qh, qh_qh->hull_dim-1, qh_facet->center);
         }
-    }else if(qh CENTERtype==qh_AScentrum){
-        volatile int numCoords= qh hull_dim;
-        if(printFormat==qh_PRINTtriangles && qh DELAUNAY){
+    }else if(qh_qh->CENTERtype==qh_AScentrum){
+        volatile int numCoords= qh_qh->hull_dim;
+        if(printFormat==qh_PRINTtriangles && qh_qh->DELAUNAY){
             numCoords--;
         }
         if(!qh_facet->center){
-            int exitCode = setjmp(qh errexit);
-            if(!exitCode){ // no object creation -- destructors skipped on longjmp()
-                qh_facet->center= qh_getcentrum(getFacetT());
+            QH_TRY_(qh_qh){ // no object creation -- destructors skipped on longjmp()
+                qh_facet->center= qh_getcentrum(qh_qh, getFacetT());
             }
-            q.maybeThrowQhullMessage(exitCode);
+            qh_qh->maybeThrowQhullMessage(QH_TRY_status);
         }
-        return QhullPoint(numCoords, qh_facet->center);
+        return QhullPoint(qh_qh, numCoords, qh_facet->center);
     }
-    return QhullPoint();
+    return QhullPoint(qh_qh);
  }//getCenter
 
 //! Return innerplane clearly below the vertices
-//! from io.c[qh_PRINTinner]
+//! from io_r.c[qh_PRINTinner]
 QhullHyperplane QhullFacet::
-innerplane(int qhRunId) const{
-    UsingLibQhull q(qhRunId);
+innerplane() const{
     realT inner;
     // Does not error
-    qh_outerinner(const_cast(getFacetT()), NULL, &inner);
+    qh_outerinner(qh_qh, const_cast(getFacetT()), NULL, &inner);
     QhullHyperplane h= hyperplane();
     h.setOffset(h.offset()-inner); //inner is negative
     return h;
 }//innerplane
 
 //! Return outerplane clearly above all points
-//! from io.c[qh_PRINTouter]
+//! from io_r.c[qh_PRINTouter]
 QhullHyperplane QhullFacet::
-outerplane(int qhRunId) const{
-    UsingLibQhull q(qhRunId);
+outerplane() const{
     realT outer;
     // Does not error
-    qh_outerinner(const_cast(getFacetT()), &outer, NULL);
+    qh_outerinner(qh_qh, const_cast(getFacetT()), &outer, NULL);
     QhullHyperplane h= hyperplane();
     h.setOffset(h.offset()-outer); //outer is positive
     return h;
 }//outerplane
 
 //! Set by qh_triangulate for option 'Qt'.
 //! Errors if tricoplanar and facetArea() or qh_getarea() called first.
 QhullFacet QhullFacet::
 tricoplanarOwner() const
 {
     if(qh_facet->tricoplanar){
         if(qh_facet->isarea){
             throw QhullError(10018, "Qhull error: facetArea() or qh_getarea() previously called.  triCoplanarOwner() is not available.");
         }
-        return qh_facet->f.triowner;
+        return QhullFacet(qh_qh, qh_facet->f.triowner);
     }
-    return 0; // FIXUP QH11009 Should false be the NULL facet or empty facet
+    return QhullFacet(qh_qh); 
 }//tricoplanarOwner
 
 QhullPoint QhullFacet::
-voronoiVertex(int qhRunId)
+voronoiVertex()
 {
-    if(
-#if qh_QHpointer
-      !qh_qh ||
-#endif
-      qh CENTERtype!=qh_ASvoronoi){
+    if(qh_qh->CENTERtype!=qh_ASvoronoi){
           throw QhullError(10052, "Error: QhullFacet.voronoiVertex() requires option 'v' (qh_ASvoronoi)");
     }
-    return getCenter(qhRunId);
+    return getCenter();
 }//voronoiVertex
 
 #//Value
 
 //! Disables tricoplanarOwner()
 double QhullFacet::
-facetArea(int qhRunId)
+facetArea()
 {
     if(!qh_facet->isarea){
-        UsingLibQhull q(qhRunId);
-        int exitCode = setjmp(qh errexit);
-        if(!exitCode){ // no object creation -- destructors skipped on longjmp()
-            qh_facet->f.area= qh_facetarea(qh_facet);
+        QH_TRY_(qh_qh){ // no object creation -- destructors skipped on longjmp()
+            qh_facet->f.area= qh_facetarea(qh_qh, qh_facet);
             qh_facet->isarea= True;
         }
-        q.maybeThrowQhullMessage(exitCode);
+        qh_qh->maybeThrowQhullMessage(QH_TRY_status);
     }
     return qh_facet->f.area;
 }//facetArea
 
-#//Foreach
+#//!\name Foreach
 
 QhullPointSet QhullFacet::
 coplanarPoints() const
 {
-    return QhullPointSet(dimension(), qh_facet->coplanarset);
+    return QhullPointSet(qh_qh, qh_facet->coplanarset);
 }//coplanarPoints
 
 QhullFacetSet QhullFacet::
 neighborFacets() const
 {
-    return QhullFacetSet(qh_facet->neighbors);
+    return QhullFacetSet(qh_qh, qh_facet->neighbors);
 }//neighborFacets
 
 QhullPointSet QhullFacet::
 outsidePoints() const
 {
-    return QhullPointSet(dimension(), qh_facet->outsideset);
+    return QhullPointSet(qh_qh, qh_facet->outsideset);
 }//outsidePoints
 
 QhullRidgeSet QhullFacet::
 ridges() const
 {
-    return QhullRidgeSet(qh_facet->ridges);
+    return QhullRidgeSet(qh_qh, qh_facet->ridges);
 }//ridges
 
 QhullVertexSet QhullFacet::
 vertices() const
 {
-    return QhullVertexSet(qh_facet->vertices);
+    return QhullVertexSet(qh_qh, qh_facet->vertices);
 }//vertices
 
-
 }//namespace orgQhull
 
-#//operator<<
+#//!\name GetSet<<
 
 using std::ostream;
 
 using orgQhull::QhullFacet;
 using orgQhull::QhullFacetSet;
 using orgQhull::QhullPoint;
 using orgQhull::QhullPointSet;
 using orgQhull::QhullRidge;
 using orgQhull::QhullRidgeSet;
 using orgQhull::QhullSetBase;
 using orgQhull::QhullVertexSet;
-using orgQhull::UsingLibQhull;
 
 ostream &
 operator<<(ostream &os, const QhullFacet::PrintFacet &pr)
 {
     QhullFacet f= *pr.facet;
     if(f.getFacetT()==0){ // Special values from set iterator
         os << " NULLfacet" << endl;
         return os;
     }
     if(f.getFacetT()==qh_MERGEridge){
         os << " MERGEridge" << endl;
         return os;
     }
     if(f.getFacetT()==qh_DUPLICATEridge){
         os << " DUPLICATEridge" << endl;
         return os;
     }
-    os << f.printHeader(pr.run_id);
+    os << f.printHeader();
     if(!f.ridges().isEmpty()){
-        os << f.printRidges(pr.run_id);
+        os << f.printRidges();
     }
     return os;
 }//operator<< PrintFacet
 
-//! Print Voronoi center or facet centrum to stream.  Same as qh_printcenter [io.c]
+//! Print Voronoi center or facet centrum to stream.  Same as qh_printcenter [_r.]
 //! Code duplicated for PrintCenter and getCenter
 //! Sets center if needed
 ostream &
 operator<<(ostream &os, const QhullFacet::PrintCenter &pr)
 {
     facetT *f= pr.facet->getFacetT();
-    if(qh CENTERtype!=qh_ASvoronoi && qh CENTERtype!=qh_AScentrum){
+    if(pr.facet->qh()->CENTERtype!=qh_ASvoronoi && pr.facet->qh()->CENTERtype!=qh_AScentrum){
         return os;
     }
     if (pr.message){
         os << pr.message;
     }
     int numCoords;
-    if(qh CENTERtype==qh_ASvoronoi){
-        numCoords= qh hull_dim-1;
-        if(!f->normal || !f->upperdelaunay || !qh ATinfinity){
+    if(pr.facet->qh()->CENTERtype==qh_ASvoronoi){
+        numCoords= pr.facet->qh()->hull_dim-1;
+        if(!f->normal || !f->upperdelaunay || !pr.facet->qh()->ATinfinity){
             if(!f->center){
-                f->center= qh_facetcenter(f->vertices);
+                f->center= qh_facetcenter(pr.facet->qh(), f->vertices);
             }
             for(int k=0; kcenter[k] << " "; // FIXUP QH11010 qh_REAL_1
             }
         }else{
             for(int k=0; kqh()->hull_dim;
+        if(pr.print_format==qh_PRINTtriangles && pr.facet->qh()->DELAUNAY){
             numCoords--;
         }
         if(!f->center){
-            f->center= qh_getcentrum(f);
+            f->center= qh_getcentrum(pr.facet->qh(), f);
         }
         for(int k=0; kcenter[k] << " "; // FIXUP QH11010 qh_REAL_1
         }
     }
     if(pr.print_format==qh_PRINTgeom && numCoords==2){
         os << " 0";
     }
     os << endl;
     return os;
 }//operator<< PrintCenter
 
-//! Print flags for facet to stream.  Space prefix.  From qh_printfacetheader [io.c]
+//! Print flags for facet to stream.  Space prefix.  From qh_printfacetheader [io_r.c]
 ostream &
 operator<<(ostream &os, const QhullFacet::PrintFlags &p)
 {
     const facetT *f= p.facet->getFacetT();
     if(p.message){
         os << p.message;
     }
 
     os << (p.facet->isTopOrient() ? " top" : " bottom");
     if(p.facet->isSimplicial()){
         os << " simplicial";
     }
     if(p.facet->isTriCoplanar()){
         os << " tricoplanar";
     }
     if(p.facet->isUpperDelaunay()){
         os << " upperDelaunay";
     }
     if(f->visible){
         os << " visible";
     }
     if(f->newfacet){
         os << " new";
     }
     if(f->tested){
         os << " tested";
     }
     if(!f->good){
         os << " notG";
     }
     if(f->seen){
         os << " seen";
     }
     if(f->coplanar){
         os << " coplanar";
     }
     if(f->mergehorizon){
         os << " mergehorizon";
     }
     if(f->keepcentrum){
         os << " keepcentrum";
     }
     if(f->dupridge){
         os << " dupridge";
     }
     if(f->mergeridge && !f->mergeridge2){
         os << " mergeridge1";
     }
     if(f->mergeridge2){
         os << " mergeridge2";
     }
     if(f->newmerge){
         os << " newmerge";
     }
     if(f->flipped){
         os << " flipped";
     }
     if(f->notfurthest){
         os << " notfurthest";
     }
     if(f->degenerate){
         os << " degenerate";
     }
     if(f->redundant){
         os << " redundant";
     }
     os << endl;
     return os;
 }//operator<< PrintFlags
 
-//! Print header for facet to stream. Space prefix.  From qh_printfacetheader [io.c]
+//! Print header for facet to stream. Space prefix.  From qh_printfacetheader [io_r.c]
 ostream &
 operator<<(ostream &os, const QhullFacet::PrintHeader &pr)
 {
     QhullFacet facet= *pr.facet;
     facetT *f= facet.getFacetT();
     os << "- f" << facet.id() << endl;
     os << facet.printFlags("    - flags:");
     if(f->isarea){
         os << "    - area: " << f->f.area << endl; //FIXUP QH11010 2.2g
-    }else if(qh NEWfacets && f->visible && f->f.replace){
+    }else if(pr.facet->qh()->NEWfacets && f->visible && f->f.replace){
         os << "    - replacement: f" << f->f.replace->id << endl;
     }else if(f->newfacet){
         if(f->f.samecycle && f->f.samecycle != f){
             os << "    - shares same visible/horizon as f" << f->f.samecycle->id << endl;
         }
     }else if(f->tricoplanar /* !isarea */){
         if(f->f.triowner){
             os << "    - owner of normal & centrum is facet f" << f->f.triowner->id << endl;
         }
     }else if(f->f.newcycle){
         os << "    - was horizon to f" << f->f.newcycle->id << endl;
     }
     if(f->nummerge){
         os << "    - merges: " << f->nummerge << endl;
     }
     os << facet.hyperplane().print("    - normal: ", "\n    - offset: "); // FIXUP QH11010 %10.7g
-    if(qh CENTERtype==qh_ASvoronoi || f->center){
-        os << facet.printCenter(pr.run_id, qh_PRINTfacets, "    - center: ");
+    if(pr.facet->qh()->CENTERtype==qh_ASvoronoi || f->center){
+        os << facet.printCenter(qh_PRINTfacets, "    - center: ");
     }
 #if qh_MAXoutside
-    if(f->maxoutside > qh DISTround){
+    if(f->maxoutside > pr.facet->qh()->DISTround){
         os << "    - maxoutside: " << f->maxoutside << endl; //FIXUP QH11010 %10.7g
     }
 #endif
     QhullPointSet ps= facet.outsidePoints();
     if(!ps.isEmpty()){
         QhullPoint furthest= ps.last();
         if (ps.size() < 6) {
-            os << "    - outside set(furthest p" << furthest.id(pr.run_id) << "):" << endl;
+            os << "    - outside set(furthest p" << furthest.id() << "):" << endl;
             for(QhullPointSet::iterator i=ps.begin(); i!=ps.end(); ++i){
                 QhullPoint p= *i;
-                os << p.print(pr.run_id, "     ");
+                os << p.print("     ");
             }
         }else if(ps.size()<21){
-            os << ps.print(pr.run_id, "    - outside set:");
+            os << ps.print("    - outside set:");
         }else{
             os << "    - outside set:  " << ps.size() << " points.";
-            os << furthest.print(pr.run_id, "  Furthest");
+            os << furthest.print("  Furthest");
         }
 #if !qh_COMPUTEfurthest
         os << "    - furthest distance= " << f->furthestdist << endl; //FIXUP QH11010 %2.2g
 #endif
     }
     QhullPointSet cs= facet.coplanarPoints();
     if(!cs.isEmpty()){
         QhullPoint furthest= cs.last();
         if (cs.size() < 6) {
-            os << "    - coplanar set(furthest p" << furthest.id(pr.run_id) << "):" << endl;
+            os << "    - coplanar set(furthest p" << furthest.id() << "):" << endl;
             for(QhullPointSet::iterator i=cs.begin(); i!=cs.end(); ++i){
                 QhullPoint p= *i;
-                os << p.print(pr.run_id, "     ");
+                os << p.print("     ");
             }
         }else if(cs.size()<21){
-            os << cs.print(pr.run_id, "    - coplanar set:");
+            os << cs.print("    - coplanar set:");
         }else{
             os << "    - coplanar set:  " << cs.size() << " points.";
-            os << furthest.print(pr.run_id, "  Furthest");
+            os << furthest.print("  Furthest");
         }
-        zinc_(Zdistio);
+        // FIXUP zinc_(Zdistio);
         double d= facet.distance(furthest);
         os << "      furthest distance= " << d << endl; //FIXUP QH11010 %2.2g
     }
     QhullVertexSet vs= facet.vertices();
     if(!vs.isEmpty()){
-        os << vs.print(pr.run_id, "    - vertices:");
+        os << vs.print("    - vertices:");
     }
     QhullFacetSet fs= facet.neighborFacets();
     fs.selectAll();
     if(!fs.isEmpty()){
         os << fs.printIdentifiers("    - neighboring facets:");
     }
     return os;
 }//operator<< PrintHeader
 
 
-//! Print ridges of facet to stream.  Same as qh_printfacetridges [io.c]
-//! If qhRunId==UsingLibQhull::NOqhRunId, does not use qh
+//! Print ridges of facet to stream.  Same as qh_printfacetridges [io_r.c]
 ostream &
 operator<<(ostream &os, const QhullFacet::PrintRidges &pr)
 {
     const QhullFacet facet= *pr.facet;
     facetT *f= facet.getFacetT();
     QhullRidgeSet rs= facet.ridges();
     if(!rs.isEmpty()){
-        if(pr.run_id!=UsingLibQhull::NOqhRunId){
-            UsingLibQhull q(pr.run_id);
-            // No calls to libqhull
-            if(f->visible && qh NEWfacets){
-                os << "    - ridges(ids may be garbage):";
-                for(QhullRidgeSet::iterator i=rs.begin(); i!=rs.end(); ++i){
-                    QhullRidge r= *i;
-                    os << " r" << r.id();
-                }
-                os << endl;
-            }else{
-                os << "    - ridges:" << endl;
+        if(f->visible && pr.facet->qh()->NEWfacets){
+            os << "    - ridges(ids may be garbage):";
+            for(QhullRidgeSet::iterator i=rs.begin(); i!=rs.end(); ++i){
+                QhullRidge r= *i;
+                os << " r" << r.id();
             }
+            os << endl;
         }else{
             os << "    - ridges:" << endl;
         }
 
         // Keep track of printed ridges
         for(QhullRidgeSet::iterator i=rs.begin(); i!=rs.end(); ++i){
             QhullRidge r= *i;
             r.getRidgeT()->seen= false;
         }
         int ridgeCount= 0;
         if(facet.dimension()==3){
             for(QhullRidge r= rs.first(); !r.getRidgeT()->seen; r= r.nextRidge3d(facet)){
                 r.getRidgeT()->seen= true;
-                os << r.print(pr.run_id);
+                os << r.print("");
                 ++ridgeCount;
                 if(!r.hasNextRidge3d(facet)){
                     break;
                 }
             }
         }else {
             QhullFacetSet ns(facet.neighborFacets());
             for(QhullFacetSet::iterator i=ns.begin(); i!=ns.end(); ++i){
                 QhullFacet neighbor= *i;
                 QhullRidgeSet nrs(neighbor.ridges());
                 for(QhullRidgeSet::iterator j=nrs.begin(); j!=nrs.end(); ++j){
                     QhullRidge r= *j;
                     if(r.otherFacet(neighbor)==facet){
                         r.getRidgeT()->seen= true;
-                        os << r.print(pr.run_id);
+                        os << r.print("");
                         ridgeCount++;
                     }
                 }
             }
         }
         if(ridgeCount!=rs.count()){
             os << "     - all ridges:";
             for(QhullRidgeSet::iterator i=rs.begin(); i!=rs.end(); ++i){
                 QhullRidge r= *i;
                 os << " r" << r.id();
             }
             os << endl;
         }
         for(QhullRidgeSet::iterator i=rs.begin(); i!=rs.end(); ++i){
             QhullRidge r= *i;
             if(!r.getRidgeT()->seen){
-                os << r.print(pr.run_id);
+                os << r.print("");
             }
         }
     }
     return os;
 }//operator<< PrintRidges
 
 // "No conversion" error if defined inline
 ostream &
 operator<<(ostream &os, QhullFacet &f)
 {
-    os << f.print(UsingLibQhull::NOqhRunId);
+    os << f.print();
     return os;
 }//<< QhullFacet
diff --git a/src/libqhullcpp/QhullFacet.h b/src/libqhullcpp/QhullFacet.h
index 124c00d..7cd4b6c 100644
--- a/src/libqhullcpp/QhullFacet.h
+++ b/src/libqhullcpp/QhullFacet.h
@@ -1,155 +1,151 @@
 /****************************************************************************
 **
-** Copyright (c) 2008-2012 C.B. Barber. All rights reserved.
-** $Id: //main/2011/qhull/src/libqhullcpp/QhullFacet.h#7 $$Change: 1464 $
-** $DateTime: 2012/01/25 22:58:41 $$Author: bbarber $
+** Copyright (c) 2008-2014 C.B. Barber. All rights reserved.
+** $Id: //main/2011/qhull/src/libqhullcpp/QhullFacet.h#13 $$Change: 1800 $
+** $DateTime: 2014/12/17 21:46:45 $$Author: bbarber $
 **
 ****************************************************************************/
 
 #ifndef QHULLFACET_H
 #define QHULLFACET_H
 
-#include "Coordinates.h"
 #include "QhullHyperplane.h"
 #include "QhullPoint.h"
 #include "QhullSet.h"
 #include "QhullPointSet.h"
 extern "C" {
-    #include "libqhull/qhull_r.h"
+    #include "libqhullr/qhull_ra.h"
 }
 
-#include 
-#include 
 #include 
 
 namespace orgQhull {
 
-#//ClassRef
+#//!\name Used here
+    class Coordinates;
+    class Qhull;
     class QhullFacetSet;
     class QhullRidge;
-    typedef QhullSet  QhullRidgeSet;
     class QhullVertex;
     class QhullVertexSet;
 
-#//Types
-    //! QhullFacet -- Qhull's facet structure, facetT [libqhull.h], as a C++ class
+#//!\name Defined here
     class QhullFacet;
+    typedef QhullSet  QhullRidgeSet;
 
 //! A QhullFacet is the C++ equivalent to Qhull's facetT*
 class QhullFacet {
 
+#//!\name Defined here
+public:
+    typedef facetT *   base_type;  // for QhullVertexSet
+
 private:
-#//Fields -- no additions (QhullFacetSet of facetT*)
-    facetT             *qh_facet;  //! May be 0 (!isDefined) for corner cases (e.g., *facetSet.end()==0) and tricoplanarOwner()
+#//!\name Fields -- no additions (QhullFacetSet of facetT*)
+    facetT *            qh_facet;  //! May be 0 (!isDefined) for corner cases (e.g., *facetSet.end()==0) and tricoplanarOwner()
+    QhullQh *           qh_qh;     //! qhT
 
-#//Class objects
+#//!\name Class objects
     static facetT       s_empty_facet; // needed for shallow copy
 
 public:
-#//Constants
-
-#//Constructors
-                        QhullFacet() : qh_facet(&s_empty_facet) {}
+#//!\name Constructors
+    explicit            QhullFacet(const Qhull &q);
+                        QhullFacet(const Qhull &q, facetT *f);
+    explicit            QhullFacet(QhullQh *qh) : qh_facet(&s_empty_facet), qh_qh(qh) {}
+                        QhullFacet(QhullQh *qh, facetT *f) : qh_facet(f ? f : &s_empty_facet), qh_qh(qh) {}
                         // Creates an alias.  Does not copy QhullFacet.  Needed for return by value and parameter passing
-                        QhullFacet(const QhullFacet &o) : qh_facet(o.qh_facet ? o.qh_facet : &s_empty_facet) {}
+                        QhullFacet(const QhullFacet &other) : qh_facet(other.qh_facet ? other.qh_facet : &s_empty_facet), qh_qh(other.qh_qh) {}
                         // Creates an alias.  Does not copy QhullFacet.  Needed for vector
-    QhullFacet         &operator=(const QhullFacet &o) { qh_facet= o.qh_facet ? o.qh_facet : &s_empty_facet; return *this; }
-                       ~QhullFacet() {}
+    QhullFacet &        operator=(const QhullFacet &other) { qh_facet= other.qh_facet ? other.qh_facet : &s_empty_facet; qh_qh= other.qh_qh; return *this; }
+                        ~QhullFacet() {}
+
 
-#//Conversion
-                        //Implicit conversion from facetT
-                        QhullFacet(facetT *f) : qh_facet(f ? f : &s_empty_facet) {}
+#//!\name GetSet
+    int                 dimension() const { return qh_qh->hull_dim; }
+    QhullPoint          getCenter() { return getCenter(qh_PRINTpoints); }
+    QhullPoint          getCenter(qh_PRINT printFormat);
+    facetT *            getBaseT() const { return getFacetT(); } //!< For QhullSet
                         // Do not define facetT().  It conflicts with return type facetT*
-    facetT             *getFacetT() const { return qh_facet; }
-
-#//QhullSet
-    facetT             *getBaseT() const { return getFacetT(); }
-
-#//getSet
-    int                 dimension() const;
-    QhullPoint          getCenter(int qhRunId) { return getCenter(qhRunId, qh_PRINTpoints); }
-    QhullPoint          getCenter(int qhRunId, qh_PRINT printFormat);
-    QhullHyperplane     hyperplane() const { return QhullHyperplane(dimension(), qh_facet->normal, qh_facet->offset); }
-    int                 id() const { return qh_facet ? qh_facet->id : -1; }
-    QhullHyperplane     innerplane(int qhRunId) const;
+    facetT *            getFacetT() const { return qh_facet; }
+    QhullHyperplane     hyperplane() const { return QhullHyperplane(qh_qh, dimension(), qh_facet->normal, qh_facet->offset); }
+    countT              id() const { return (qh_facet ? qh_facet->id : -1); }
+    QhullHyperplane     innerplane() const;
     bool                isDefined() const { return qh_facet && qh_facet != &s_empty_facet; }
     bool                isGood() const { return qh_facet && qh_facet->good; }
-    bool                isSimplicial() const { return qh_facet->simplicial; }
-    bool                isTopOrient() const { return qh_facet->toporient; }
-    bool                isTriCoplanar() const { return qh_facet->tricoplanar; }
-    bool                isUpperDelaunay() const { return qh_facet->upperdelaunay; }
-    QhullFacet          next() const { return qh_facet->next; }
-    bool                operator==(const QhullFacet &o) const { return qh_facet==o.qh_facet; }
-    bool                operator!=(const QhullFacet &o) const { return !operator==(o); }
-    QhullHyperplane     outerplane(int qhRunId) const;
-    QhullFacet          previous() const { return qh_facet->previous; }
+    bool                isSimplicial() const { return qh_facet && qh_facet->simplicial; }
+    bool                isTopOrient() const { return qh_facet && qh_facet->toporient; }
+    bool                isTriCoplanar() const { return qh_facet && qh_facet->tricoplanar; }
+    bool                isUpperDelaunay() const { return qh_facet && qh_facet->upperdelaunay; }
+    QhullFacet          next() const { return QhullFacet(qh_qh, qh_facet->next); }
+    bool                operator==(const QhullFacet &other) const { return qh_facet==other.qh_facet; }
+    bool                operator!=(const QhullFacet &other) const { return !operator==(other); }
+    QhullHyperplane     outerplane() const;
+    QhullFacet          previous() const { return QhullFacet(qh_qh, qh_facet->previous); }
+    QhullQh *           qh() const { return qh_qh; }
     QhullFacet          tricoplanarOwner() const;
-    QhullPoint          voronoiVertex(int qhRunId);
+    QhullPoint          voronoiVertex();
 
-#//value
+#//!\name value
     //! Undefined if c.size() != dimension()
     double              distance(const Coordinates &c) const { return distance(c.data()); }
-    double              distance(const pointT *p) const { return distance(QhullPoint(dimension(), const_cast(p))); }
+    double              distance(const pointT *p) const { return distance(QhullPoint(qh_qh, const_cast(p))); }
     double              distance(const QhullPoint &p) const { return hyperplane().distance(p); }
-    double              facetArea(int qhRunId);
+    double              facetArea();
 
-#//foreach
+#//!\name foreach
     // Can not inline.  Otherwise circular reference
     QhullPointSet       coplanarPoints() const;
     QhullFacetSet       neighborFacets() const;
     QhullPointSet       outsidePoints() const;
     QhullRidgeSet       ridges() const;
     QhullVertexSet      vertices() const;
 
-#//IO
+#//!\name IO
     struct PrintCenter{
-        QhullFacet     *facet;  // non-const due to facet.center()
-        const char     *message;
-        int             run_id;
+        QhullFacet *    facet;  // non-const due to facet.center()
+        const char *    message;
         qh_PRINT        print_format;
-                        PrintCenter(int qhRunId, QhullFacet &f, qh_PRINT printFormat, const char * s) : facet(&f), message(s), run_id(qhRunId), print_format(printFormat){}
+                        PrintCenter(QhullFacet &f, qh_PRINT printFormat, const char * s) : facet(&f), message(s), print_format(printFormat){}
     };//PrintCenter
-    PrintCenter         printCenter(int qhRunId, qh_PRINT printFormat, const char *message) { return PrintCenter(qhRunId, *this, printFormat, message); }
+    PrintCenter         printCenter(qh_PRINT printFormat, const char *message) { return PrintCenter(*this, printFormat, message); }
 
     struct PrintFacet{
-        QhullFacet     *facet;  // non-const due to f->center()
-        int             run_id;
-                        PrintFacet(int qhRunId, QhullFacet &f) : facet(&f), run_id(qhRunId) {}
+        QhullFacet *    facet;  // non-const due to f->center()
+        explicit        PrintFacet(QhullFacet &f) : facet(&f) {}
     };//PrintFacet
-    PrintFacet          print(int qhRunId) { return PrintFacet(qhRunId, *this); }
+    PrintFacet          print() { return PrintFacet(*this); }
 
     struct PrintFlags{
         const QhullFacet *facet;
-        const char     *message;
+        const char *    message;
                         PrintFlags(const QhullFacet &f, const char *s) : facet(&f), message(s) {}
     };//PrintFlags
     PrintFlags          printFlags(const char *message) const { return PrintFlags(*this, message); }
 
     struct PrintHeader{
-        QhullFacet     *facet;  // non-const due to f->center()
-        int             run_id;
-                        PrintHeader(int qhRunId, QhullFacet &f) : facet(&f), run_id(qhRunId) {}
+        QhullFacet *    facet;  // non-const due to f->center()
+                        PrintHeader(QhullFacet &f) : facet(&f) {}
     };//PrintHeader
-    PrintHeader         printHeader(int qhRunId) { return PrintHeader(qhRunId, *this); }
+    PrintHeader         printHeader() { return PrintHeader(*this); }
 
     struct PrintRidges{
         const QhullFacet *facet;
-        int             run_id;
-                        PrintRidges(int qhRunId, QhullFacet &f) : facet(&f), run_id(qhRunId) {}
+                        PrintRidges(QhullFacet &f) : facet(&f) {}
     };//PrintRidges
-    PrintRidges         printRidges(int qhRunId) { return PrintRidges(qhRunId, *this); }
+    PrintRidges         printRidges() { return PrintRidges(*this); }
 
 };//class QhullFacet
 
 }//namespace orgQhull
 
-#//Global functions
+#//!\name Global
 
 std::ostream &operator<<(std::ostream &os, const orgQhull::QhullFacet::PrintCenter &pr);
 std::ostream &operator<<(std::ostream &os, const orgQhull::QhullFacet::PrintFlags &pr);
 std::ostream &operator<<(std::ostream &os, const orgQhull::QhullFacet::PrintHeader &pr);
 std::ostream &operator<<(std::ostream &os, const orgQhull::QhullFacet::PrintRidges &pr);
 std::ostream &operator<<(std::ostream &os, const orgQhull::QhullFacet::PrintFacet &pr);
 std::ostream &operator<<(std::ostream &os, orgQhull::QhullFacet &f); // non-const due to qh_getcenter()
 
 #endif // QHULLFACET_H
diff --git a/src/libqhullcpp/QhullFacetList.cpp b/src/libqhullcpp/QhullFacetList.cpp
index b518b1a..cbd3b64 100644
--- a/src/libqhullcpp/QhullFacetList.cpp
+++ b/src/libqhullcpp/QhullFacetList.cpp
@@ -1,164 +1,172 @@
 /****************************************************************************
 **
 ** Copyright (c) 2008-2014 C.B. Barber. All rights reserved.
-** $Id: //main/2011/qhull/src/libqhullcpp/QhullFacetList.cpp#3 $$Change: 1464 $
-** $DateTime: 2012/01/25 22:58:41 $$Author: bbarber $
+** $Id: //main/2011/qhull/src/libqhullcpp/QhullFacetList.cpp#7 $$Change: 1797 $
+** $DateTime: 2014/12/15 17:23:41 $$Author: bbarber $
 **
 ****************************************************************************/
 
 #//! QhullFacetList -- Qhull's linked facets, as a C++ class
 
 #include "QhullFacet.h"
 #include "QhullFacetList.h"
 #include "QhullPoint.h"
 #include "QhullRidge.h"
 #include "QhullVertex.h"
 
 using std::string;
 using std::vector;
 
 #ifdef _MSC_VER  // Microsoft Visual C++ -- warning level 4
 #pragma warning( disable : 4611)  // interaction between '_setjmp' and C++ object destruction is non-portable
 #pragma warning( disable : 4996)  // function was declared deprecated(strcpy, localtime, etc.)
 #endif
 
 namespace orgQhull {
 
-#//Conversion
+#//!\name Constructors
+
+QhullFacetList::
+QhullFacetList(const Qhull &q, facetT *b, facetT *e ) 
+: QhullLinkedList(QhullFacet(q, b), QhullFacet(q, e))
+, select_all(false)
+{
+}
+
+#//!\name Conversions
 
 // See qt_qhull.cpp for QList conversions
 
 #ifndef QHULL_NO_STL
 std::vector QhullFacetList::
 toStdVector() const
 {
     QhullLinkedListIterator i(*this);
     std::vector vs;
     while(i.hasNext()){
         QhullFacet f= i.next();
         if(isSelectAll() || f.isGood()){
             vs.push_back(f);
         }
     }
     return vs;
 }//toStdVector
 #endif //QHULL_NO_STL
 
 #ifndef QHULL_NO_STL
 //! Same as PrintVertices
 std::vector QhullFacetList::
-vertices_toStdVector(int qhRunId) const
+vertices_toStdVector() const
 {
     std::vector vs;
-    QhullVertexSet qvs(qhRunId, first().getFacetT(), NULL, isSelectAll());
+    QhullVertexSet qvs(qh(), first().getFacetT(), 0, isSelectAll());
 
     for(QhullVertexSet::iterator i=qvs.begin(); i!=qvs.end(); ++i){
         vs.push_back(*i);
     }
     return vs;
 }//vertices_toStdVector
 #endif //QHULL_NO_STL
 
-#//Read-only
+#//!\name GetSet
 
 bool QhullFacetList::
 contains(const QhullFacet &facet) const
 {
     if(isSelectAll()){
         return QhullLinkedList::contains(facet);
     }
     for(QhullFacetList::const_iterator i=begin(); i != end(); ++i){
         QhullFacet f= *i;
         if(f==facet && f.isGood()){
             return true;
         }
     }
     return false;
 }//contains
 
 int QhullFacetList::
 count() const
 {
     if(isSelectAll()){
         return QhullLinkedList::count();
     }
     int counter= 0;
     for(QhullFacetList::const_iterator i=begin(); i != end(); ++i){
         if((*i).isGood()){
             counter++;
         }
     }
     return counter;
 }//count
 
 int QhullFacetList::
 count(const QhullFacet &facet) const
 {
     if(isSelectAll()){
         return QhullLinkedList::count(facet);
     }
     int counter= 0;
     for(QhullFacetList::const_iterator i=begin(); i != end(); ++i){
         QhullFacet f= *i;
         if(f==facet && f.isGood()){
             counter++;
         }
     }
     return counter;
 }//count
 
 }//namespace orgQhull
 
-#//Global functions
+#//!\name Global functions
 
 using std::endl;
 using std::ostream;
 using orgQhull::QhullFacet;
 using orgQhull::QhullFacetList;
 using orgQhull::QhullVertex;
 using orgQhull::QhullVertexSet;
-using orgQhull::UsingLibQhull;
 
 ostream &
 operator<<(ostream &os, const QhullFacetList::PrintFacetList &pr)
 {
     QhullFacetList fs= *pr.facet_list;
     os << "Vertices for " << fs.count() << " facets" << endl;
-    os << fs.printVertices(pr.run_id);
-    os << fs.printFacets(pr.run_id);
+    os << fs.printVertices();
+    os << fs.printFacets();
     return os;
 }//operator<<
 
-//! Print facet list to stream.  From qh_printafacet [io.c]
+//! Print facet list to stream.  From qh_printafacet [io_r.c]
 ostream &
 operator<<(ostream &os, const QhullFacetList::PrintFacets &pr)
 {
     for(QhullFacetList::const_iterator i= pr.facet_list->begin(); i != pr.facet_list->end(); ++i){
         QhullFacet f= *i;
         if(pr.facet_list->isSelectAll() || f.isGood()){
-            os << f.print(pr.run_id);
+            os << f.print();
         }
     }
     return os;
 }//printFacets
 
-//! Print vertices of good faces in facet list to stream.  From qh_printvertexlist [io.c]
+//! Print vertices of good faces in facet list to stream.  From qh_printvertexlist [io_r.c]
 //! Same as vertices_toStdVector
 ostream &
 operator<<(ostream &os, const QhullFacetList::PrintVertices &pr)
 {
-    QhullVertexSet vs(pr.run_id, pr.facet_list->first().getFacetT(), NULL, pr.facet_list->isSelectAll());
+    QhullVertexSet vs(pr.facet_list->qh(), pr.facet_list->first().getFacetT(), NULL, pr.facet_list->isSelectAll());
     for(QhullVertexSet::iterator i=vs.begin(); i!=vs.end(); ++i){
         QhullVertex v= *i;
-        os << v.print(pr.run_id);
+        os << v.print("");
     }
     return os;
 }//printVertices
 
 std::ostream &
 operator<<(ostream &os, const QhullFacetList &fs)
 {
-    os << fs.printFacets(UsingLibQhull::NOqhRunId);
+    os << fs.printFacets();
     return os;
 }//QhullFacetList
 
diff --git a/src/libqhullcpp/QhullFacetList.h b/src/libqhullcpp/QhullFacetList.h
index 46664f3..4b6bb64 100644
--- a/src/libqhullcpp/QhullFacetList.h
+++ b/src/libqhullcpp/QhullFacetList.h
@@ -1,102 +1,104 @@
 /****************************************************************************
 **
-** Copyright (c) 2008-2012 C.B. Barber. All rights reserved.
-** $Id: //main/2011/qhull/src/libqhullcpp/QhullFacetList.h#3 $$Change: 1464 $
-** $DateTime: 2012/01/25 22:58:41 $$Author: bbarber $
+** Copyright (c) 2008-2014 C.B. Barber. All rights reserved.
+** $Id: //main/2011/qhull/src/libqhullcpp/QhullFacetList.h#9 $$Change: 1797 $
+** $DateTime: 2014/12/15 17:23:41 $$Author: bbarber $
 **
 ****************************************************************************/
 
 #ifndef QHULLFACETLIST_H
 #define QHULLFACETLIST_H
 
 #include "QhullLinkedList.h"
 #include "QhullFacet.h"
 
 #include 
 
+#ifndef QHULL_NO_STL
+#include 
+#endif
+
 namespace orgQhull {
 
-#//ClassRef
-    class               QhullFacet;
+#//!\name Used here
+    class Qhull;
+    class QhullFacet;
+    class QhullQh;
 
-#//Types
+#//!\name Defined here
     //! QhullFacetList -- List of Qhull facets, as a C++ class.  See QhullFacetSet.h
-    class               QhullFacetList;
+    class QhullFacetList;
     //! QhullFacetListIterator -- if(f.isGood()){ ... }
-    typedef QhullLinkedListIterator
-                        QhullFacetListIterator;
+    typedef QhullLinkedListIterator QhullFacetListIterator;
 
 class QhullFacetList : public QhullLinkedList {
 
-#// Fields
+#//!\name  Fields
 private:
     bool                select_all;   //! True if include bad facets.  Default is false.
 
-#//Constructors
+#//!\name Constructors
 public:
+                        QhullFacetList(const Qhull &q, facetT *b, facetT *e);
+                        QhullFacetList(QhullQh *qh, facetT *b, facetT *e);
                         QhullFacetList(QhullFacet b, QhullFacet e) : QhullLinkedList(b, e), select_all(false) {}
                         //Copy constructor copies pointer but not contents.  Needed for return by value and parameter passing.
-                        QhullFacetList(const QhullFacetList &o) : QhullLinkedList(*o.begin(), *o.end()), select_all(o.select_all) {}
-                       ~QhullFacetList() {}
+                        QhullFacetList(const QhullFacetList &other) : QhullLinkedList(*other.begin(), *other.end()), select_all(other.select_all) {}
+    QhullFacetList &    operator=(const QhullFacetList &other) { QhullLinkedList::operator =(other); select_all= other.select_all; }
+                        ~QhullFacetList() {}
 
-private:
-                        //!Disable default constructor and copy assignment.  See QhullLinkedList
+private:                //!Disable default constructor.  See QhullLinkedList
                         QhullFacetList();
-    QhullFacetList     &operator=(const QhullFacetList &);
 public:
 
-#//Conversion
+#//!\name Conversion
 #ifndef QHULL_NO_STL
     std::vector toStdVector() const;
-    std::vector vertices_toStdVector(int qhRunId) const;
+    std::vector vertices_toStdVector() const;
 #endif //QHULL_NO_STL
 #ifdef QHULL_USES_QT
     QList   toQList() const;
-    QList  vertices_toQList(int qhRunId) const;
+    QList  vertices_toQList() const;
 #endif //QHULL_USES_QT
 
-#//GetSet
+#//!\name GetSet
+                        //! Filtered by facet.isGood().  May be 0 when !isEmpty().
+    countT              count() const;
+    bool                contains(const QhullFacet &f) const;
+    countT              count(const QhullFacet &f) const;
     bool                isSelectAll() const { return select_all; }
+    QhullQh *           qh() const { return first().qh(); }
     void                selectAll() { select_all= true; }
     void                selectGood() { select_all= false; }
+                        //!< operator==() does not depend on isGood()
 
-#//Read-only
-                        //! Filtered by facet.isGood().  May be 0 when !isEmpty().
-    int                 count() const;
-    bool                contains(const QhullFacet &f) const;
-    int                 count(const QhullFacet &f) const;
-                        //! operator==() does not depend on isGood()
-
-#//IO
+#//!\name IO
     struct PrintFacetList{
         const QhullFacetList *facet_list;
-        int             run_id;
-                        PrintFacetList(int qhRunId, const QhullFacetList &fl) : facet_list(&fl), run_id(qhRunId) {}
+                        PrintFacetList(const QhullFacetList &fl) : facet_list(&fl) {}
     };//PrintFacetList
-    PrintFacetList     print(int qhRunId) const  { return PrintFacetList(qhRunId, *this); }
+    PrintFacetList      print() const  { return PrintFacetList(*this); }
 
     struct PrintFacets{
         const QhullFacetList *facet_list;
-        int             run_id;
-                        PrintFacets(int qhRunId, const QhullFacetList &fl) : facet_list(&fl), run_id(qhRunId) {}
+                        PrintFacets(const QhullFacetList &fl) : facet_list(&fl) {}
     };//PrintFacets
-    PrintFacets     printFacets(int qhRunId) const { return PrintFacets(qhRunId, *this); }
+    PrintFacets         printFacets() const { return PrintFacets(*this); }
 
     struct PrintVertices{
         const QhullFacetList *facet_list;
-        int             run_id;   //! Can not be NOrunId due to qh_facetvertices
-                        PrintVertices(int qhRunId, const QhullFacetList &fl) : facet_list(&fl), run_id(qhRunId) {}
+                        PrintVertices(const QhullFacetList &fl) : facet_list(&fl) {}
     };//PrintVertices
-    PrintVertices   printVertices(int qhRunId) const { return PrintVertices(qhRunId, *this); }
+    PrintVertices       printVertices() const { return PrintVertices(*this); }
 };//class QhullFacetList
 
 }//namespace orgQhull
 
-#//== Global namespace =========================================
+#//!\name == Global namespace =========================================
 
 std::ostream &operator<<(std::ostream &os, const orgQhull::QhullFacetList::PrintFacetList &p);
 std::ostream &operator<<(std::ostream &os, const orgQhull::QhullFacetList::PrintFacets &p);
 std::ostream &operator<<(std::ostream &os, const orgQhull::QhullFacetList::PrintVertices &p);
 std::ostream &operator<<(std::ostream &os, const orgQhull::QhullFacetList &fs);
 
 #endif // QHULLFACETLIST_H
diff --git a/src/libqhullcpp/QhullFacetSet.cpp b/src/libqhullcpp/QhullFacetSet.cpp
index 3bb80f7..411b730 100644
--- a/src/libqhullcpp/QhullFacetSet.cpp
+++ b/src/libqhullcpp/QhullFacetSet.cpp
@@ -1,145 +1,147 @@
 /****************************************************************************
 **
 ** Copyright (c) 2008-2014 C.B. Barber. All rights reserved.
-** $Id: //main/2011/qhull/src/libqhullcpp/QhullFacetSet.cpp#5 $$Change: 1464 $
-** $DateTime: 2012/01/25 22:58:41 $$Author: bbarber $
+** $Id: //main/2011/qhull/src/libqhullcpp/QhullFacetSet.cpp#10 $$Change: 1800 $
+** $DateTime: 2014/12/17 21:46:45 $$Author: bbarber $
 **
 ****************************************************************************/
 
 #//! QhullFacetSet -- Qhull's linked facets, as a C++ class
 
-#include "QhullFacet.h"
 #include "QhullFacetSet.h"
+
+#include "QhullFacet.h"   // Before QhullFacetSet for base_type
 #include "QhullPoint.h"
 #include "QhullRidge.h"
 #include "QhullVertex.h"
 
-using std::string;
+#ifndef QHULL_NO_STL
 using std::vector;
+#endif
 
 #ifdef _MSC_VER  // Microsoft Visual C++ -- warning level 4
 #pragma warning( disable : 4611)  // interaction between '_setjmp' and C++ object destruction is non-portable
 #pragma warning( disable : 4996)  // function was declared deprecated(strcpy, localtime, etc.)
 #endif
 
 namespace orgQhull {
 
-#//Conversion
+#//!\name Conversions
 
 // See qt-qhull.cpp for QList conversions
 
 #ifndef QHULL_NO_STL
 std::vector QhullFacetSet::
 toStdVector() const
 {
     QhullSetIterator i(*this);
     std::vector vs;
     while(i.hasNext()){
         QhullFacet f= i.next();
         if(isSelectAll() || f.isGood()){
             vs.push_back(f);
         }
     }
     return vs;
 }//toStdVector
 #endif //QHULL_NO_STL
 
-#//Read-only
+#//!\name GetSet
 
 bool QhullFacetSet::
 contains(const QhullFacet &facet) const
 {
     if(isSelectAll()){
         return QhullSet::contains(facet);
     }
     for(QhullFacetSet::const_iterator i=begin(); i != end(); ++i){
         QhullFacet f= *i;
         if(f==facet && f.isGood()){
             return true;
         }
     }
     return false;
 }//contains
 
 int QhullFacetSet::
 count() const
 {
     if(isSelectAll()){
         return QhullSet::count();
     }
     int counter= 0;
     for(QhullFacetSet::const_iterator i=begin(); i != end(); ++i){
         QhullFacet f= *i;
         if(f.isGood()){
             counter++;
         }
     }
     return counter;
 }//count
 
 int QhullFacetSet::
 count(const QhullFacet &facet) const
 {
     if(isSelectAll()){
         return QhullSet::count(facet);
     }
     int counter= 0;
     for(QhullFacetSet::const_iterator i=begin(); i != end(); ++i){
         QhullFacet f= *i;
         if(f==facet && f.isGood()){
             counter++;
         }
     }
     return counter;
 }//count
 
 }//namespace orgQhull
 
-#//Global functions
+#//!\name Global functions
 
 using std::endl;
 using std::ostream;
 using orgQhull::QhullFacet;
 using orgQhull::QhullFacetSet;
-using orgQhull::UsingLibQhull;
 
 ostream &
 operator<<(ostream &os, const QhullFacetSet &fs)
 {
-    os << fs.print(UsingLibQhull::NOqhRunId, "");
+    os << fs.print("");
     return os;
 }//<begin(); i!=p.facet_set->end(); ++i){
         const QhullFacet f= *i;
         if(f.getFacetT()==qh_MERGEridge){
             os << " MERGE";
         }else if(f.getFacetT()==qh_DUPLICATEridge){
             os << " DUP";
         }else if(p.facet_set->isSelectAll() || f.isGood()){
             os << " f" << f.id();
         }
     }
     os << endl;
     return os;
 }//<
 
 namespace orgQhull {
 
-#//ClassRef
-    class               QhullFacet;
+#//!\name Used here
+    class Qhull;
 
-#//Types
+#//!\name Defined here
     //! QhullFacetSet -- a set of Qhull facets, as a C++ class.  See QhullFacetList.h
-    class               QhullFacetSet;
-    typedef QhullSetIterator
-                        QhullFacetSetIterator;
+    class QhullFacetSet;
+    typedef QhullSetIterator QhullFacetSetIterator;
 
 class QhullFacetSet : public QhullSet {
 
+#//!\name Defined here
+public:
+    typedef facetT *   base_type;  // for QhullVertexSet
+
 private:
-#//Fields
+#//!\name Fields
     bool                select_all;   //! True if include bad facets.  Default is false.
 
 public:
-#//Constructor
+#//!\name Constructor
                         //Conversion from setT* is not type-safe.  Implicit conversion for void* to T
-   explicit             QhullFacetSet(setT *s) : QhullSet(s), select_all(false) {}
+                        QhullFacetSet(const Qhull &q, setT *s) : QhullSet(q, s), select_all(false) {}
+                        QhullFacetSet(QhullQh *qh, setT *s) : QhullSet(qh, s), select_all(false) {}
                         //Copy constructor copies pointer but not contents.  Needed for return by value and parameter passing.
-                        QhullFacetSet(const QhullFacetSet &o) : QhullSet(o), select_all(o.select_all) {}
+                        QhullFacetSet(const QhullFacetSet &other) : QhullSet(other), select_all(other.select_all) {}
+    QhullFacetSet &     operator=(const QhullFacetSet &other) { QhullSet::operator=(other); select_all= other.select_all; }
 
 private:
-                        //!Disable default constructor and copy assignment.  See QhullSetBase
+                        //!Disable default constructor.  See QhullSetBase
                         QhullFacetSet();
-    QhullFacetSet      &operator=(const QhullFacetSet &);
 public:
 
-#//Conversion
+#//!\name Conversion
 #ifndef QHULL_NO_STL
     std::vector toStdVector() const;
 #endif //QHULL_NO_STL
 #ifdef QHULL_USES_QT
     QList   toQList() const;
 #endif //QHULL_USES_QT
 
-#//GetSet
-    bool                isSelectAll() const { return select_all; }
-    void                selectAll() { select_all= true; }
-    void                selectGood() { select_all= false; }
-
-#//Read-only
+#//!\name GetSet
                         //! Filtered by facet.isGood().  May be 0 when !isEmpty().
-    int                 count() const;
+    countT              count() const;
     bool                contains(const QhullFacet &f) const;
-    int                 count(const QhullFacet &f) const;
+    countT              count(const QhullFacet &f) const;
+    bool                isSelectAll() const { return select_all; }
                         //! operator==() does not depend on isGood()
+    void                selectAll() { select_all= true; }
+    void                selectGood() { select_all= false; }
 
-#//IO
+#//!\name IO
     // Not same as QhullFacetList#IO.  A QhullFacetSet is a component of a QhullFacetList.
 
     struct PrintFacetSet{
         const QhullFacetSet *facet_set;
-        const char     *print_message;
-        int             run_id;
-                        PrintFacetSet(int qhRunId, const char *message, const QhullFacetSet *s) : facet_set(s), print_message(message), run_id(qhRunId) {}
+        const char *    print_message;
+                        PrintFacetSet(const char *message, const QhullFacetSet *s) : facet_set(s), print_message(message) {}
     };//PrintFacetSet
-    const PrintFacetSet       print(int qhRunId, const char *message) const { return PrintFacetSet(qhRunId, message, this); }
+    const PrintFacetSet print(const char *message) const { return PrintFacetSet(message, this); }
 
     struct PrintIdentifiers{
         const QhullFacetSet *facet_set;
-        const char     *print_message;
+        const char *    print_message;
                         PrintIdentifiers(const char *message, const QhullFacetSet *s) : facet_set(s), print_message(message) {}
     };//PrintIdentifiers
     PrintIdentifiers    printIdentifiers(const char *message) const { return PrintIdentifiers(message, this); }
 
 };//class QhullFacetSet
 
 }//namespace orgQhull
 
-#//== Global namespace =========================================
+#//!\name == Global namespace =========================================
 
 std::ostream &operator<<(std::ostream &os, const orgQhull::QhullFacetSet &fs);
 std::ostream &operator<<(std::ostream &os, const orgQhull::QhullFacetSet::PrintFacetSet &pr);
 std::ostream &operator<<(std::ostream &os, const orgQhull::QhullFacetSet::PrintIdentifiers &p);
 
 #endif // QHULLFACETSET_H
diff --git a/src/libqhullcpp/QhullHyperplane.cpp b/src/libqhullcpp/QhullHyperplane.cpp
index c1f0925..0a6f51f 100644
--- a/src/libqhullcpp/QhullHyperplane.cpp
+++ b/src/libqhullcpp/QhullHyperplane.cpp
@@ -1,166 +1,185 @@
 /****************************************************************************
 **
 ** Copyright (c) 2009-2014 C.B. Barber. All rights reserved.
-** $Id: //main/2011/qhull/src/libqhullcpp/QhullHyperplane.cpp#6 $$Change: 1464 $
-** $DateTime: 2012/01/25 22:58:41 $$Author: bbarber $
+** $Id: //main/2011/qhull/src/libqhullcpp/QhullHyperplane.cpp#10 $$Change: 1797 $
+** $DateTime: 2014/12/15 17:23:41 $$Author: bbarber $
 **
 ****************************************************************************/
 
 #include "QhullHyperplane.h"
+
+#include "Qhull.h"
 #include "QhullPoint.h"
 
 #include 
 
 
 #ifdef _MSC_VER  // Microsoft Visual C++ -- warning level 4
 #endif
 
 namespace orgQhull {
 
-#//Conversion
+#//!\name Constructors
+
+QhullHyperplane::
+QhullHyperplane(const Qhull &q) 
+: hyperplane_coordinates(0)
+, hyperplane_dimension(0)
+, hyperplane_offset(0.0)
+, qh_qh(q.qh())
+{
+}
+
+QhullHyperplane::
+QhullHyperplane(const Qhull &q, int hyperplaneDimension, coordT *c, coordT hyperplaneOffset) 
+: hyperplane_coordinates(c)
+, hyperplane_dimension(hyperplaneDimension)
+, hyperplane_offset(hyperplaneOffset)
+, qh_qh(q.qh())
+{
+}
+
+#//!\name Conversions
 
 // See qt-qhull.cpp for QList conversions
 
 #ifndef QHULL_NO_STL
 std::vector QhullHyperplane::
 toStdVector() const
 {
     QhullHyperplaneIterator i(*this);
     std::vector fs;
     while(i.hasNext()){
         fs.push_back(i.next());
     }
     fs.push_back(hyperplane_offset);
     return fs;
 }//toStdVector
 #endif //QHULL_NO_STL
 
-#//Value
+#//!\name GetSet
+
+bool QhullHyperplane::
+operator==(const QhullHyperplane &other) const
+{
+    if(hyperplane_dimension!=other.hyperplane_dimension){
+        return false;
+    }
+    double d= fabs(hyperplane_offset-other.hyperplane_offset);
+    if(d>qh_qh->distanceEpsilon()){
+        return false;
+    }
+    const coordT *c= hyperplane_coordinates;
+    const coordT *c2= other.hyperplane_coordinates;
+    if(c==c2){
+        return true;
+    }
+    double dist2= 0.0;
+    for(int k= hyperplane_dimension; k--; ){
+        double diff= *c++ - *c2++;
+        dist2 += diff*diff;
+    }
+    if(dist2 > qh_qh->angleEpsilon()){
+        return false;
+    }
+    return true;
+}//operator==
+
+#//!\name Methods
 
 //! Return distance from point to hyperplane.
 //!   If greater than zero, the point is above the facet (i.e., outside).
-// qh_distplane [geom.c], QhullFacet::distance, and QhullHyperplane::distance are copies
+// qh_distplane [geom_r.c], QhullFacet::distance, and QhullHyperplane::distance are copies
 //    Does not support RANDOMdist or logging
 double QhullHyperplane::
 distance(const QhullPoint &p) const
 {
     const coordT *point= p.coordinates();
     int dim= p.dimension();
     QHULL_ASSERT(dim==dimension());
     const coordT *normal= coordinates();
     double dist;
 
     switch (dim){
   case 2:
       dist= offset() + point[0] * normal[0] + point[1] * normal[1];
       break;
   case 3:
       dist= offset() + point[0] * normal[0] + point[1] * normal[1] + point[2] * normal[2];
       break;
   case 4:
       dist= offset()+point[0]*normal[0]+point[1]*normal[1]+point[2]*normal[2]+point[3]*normal[3];
       break;
   case 5:
       dist= offset()+point[0]*normal[0]+point[1]*normal[1]+point[2]*normal[2]+point[3]*normal[3]+point[4]*normal[4];
       break;
   case 6:
       dist= offset()+point[0]*normal[0]+point[1]*normal[1]+point[2]*normal[2]+point[3]*normal[3]+point[4]*normal[4]+point[5]*normal[5];
       break;
   case 7:
       dist= offset()+point[0]*normal[0]+point[1]*normal[1]+point[2]*normal[2]+point[3]*normal[3]+point[4]*normal[4]+point[5]*normal[5]+point[6]*normal[6];
       break;
   case 8:
       dist= offset()+point[0]*normal[0]+point[1]*normal[1]+point[2]*normal[2]+point[3]*normal[3]+point[4]*normal[4]+point[5]*normal[5]+point[6]*normal[6]+point[7]*normal[7];
       break;
   default:
       dist= offset();
       for (int k=dim; k--; )
           dist += *point++ * *normal++;
       break;
     }
     return dist;
 }//distance
 
 double QhullHyperplane::
 norm() const {
     double d= 0.0;
     const coordT *c= coordinates();
     for (int k=dimension(); k--; ){
         d += *c * *c;
         ++c;
     }
     return sqrt(d);
 }//norm
 
-#//Operator
-
-bool QhullHyperplane::
-operator==(const QhullHyperplane &other) const
-{
-    if(hyperplane_dimension!=other.hyperplane_dimension){
-        return false;
-    }
-    double d= fabs(hyperplane_offset-other.hyperplane_offset);
-    if(d>UsingLibQhull::globalDistanceEpsilon()){
-        return false;
-    }
-    const coordT *c= hyperplane_coordinates;
-    const coordT *c2= other.hyperplane_coordinates;
-    if(c==c2){
-        return true;
-    }
-    double dist2= 0.0;
-    for(int k= hyperplane_dimension; k--; ){
-        double diff= *c++ - *c2++;
-        dist2 += diff*diff;
-    }
-    if(dist2 > UsingLibQhull::globalAngleEpsilon()){
-        return false;
-    }
-    return true;
-}//operator==
-
-#//GetSet
-
 }//namespace orgQhull
 
-#//Global functions
+#//!\name Global functions
 
 using std::ostream;
 using orgQhull::QhullHyperplane;
-using orgQhull::UsingLibQhull;
 
-#//operator<<
+#//!\name GetSet<<
 
 ostream &
 operator<<(ostream &os, const QhullHyperplane &p)
 {
     os << p.print();
     return os;
 }
 
 ostream &
 operator<<(ostream &os, const QhullHyperplane::PrintHyperplane &pr)
 {
-    QhullHyperplane p= *pr.hyperplane;
     if(pr.print_message){
         os << pr.print_message;
     }
+    QhullHyperplane p= *pr.hyperplane;
     const realT *c= p.coordinates();
     for(int k=p.dimension(); k--; ){
         realT r= *c++;
         if(pr.print_message){
             os << " " << r; // FIXUP QH11010 %8.4g
         }else{
             os << " " << r; // FIXUP QH11010 qh_REAL_1
         }
     }
     if(pr.hyperplane_offset_message){
         os << pr.hyperplane_offset_message << " " << p.offset();
     }else{
         os << " " << p.offset();
     }
     os << std::endl;
     return os;
 }//PrintHyperplane
 
diff --git a/src/libqhullcpp/QhullHyperplane.h b/src/libqhullcpp/QhullHyperplane.h
index b2ee895..eaad842 100644
--- a/src/libqhullcpp/QhullHyperplane.h
+++ b/src/libqhullcpp/QhullHyperplane.h
@@ -1,122 +1,123 @@
 /****************************************************************************
 **
-** Copyright (c) 2009-2012 C.B. Barber. All rights reserved.
-** $Id: //main/2011/qhull/src/libqhullcpp/QhullHyperplane.h#6 $$Change: 1464 $
-** $DateTime: 2012/01/25 22:58:41 $$Author: bbarber $
+** Copyright (c) 2009-2014 C.B. Barber. All rights reserved.
+** $Id: //main/2011/qhull/src/libqhullcpp/QhullHyperplane.h#11 $$Change: 1797 $
+** $DateTime: 2014/12/15 17:23:41 $$Author: bbarber $
 **
 ****************************************************************************/
 
 #ifndef QHHYPERPLANE_H
 #define QHHYPERPLANE_H
 
 #include "QhullError.h"
 #include "QhullIterator.h"
-#include "UsingLibQhull.h"
+#include "QhullQh.h"
 extern "C" {
-    #include "libqhull/qhull_r.h"
+    #include "libqhullr/qhull_ra.h"
 }
 
 #include 
 
 namespace orgQhull {
-#//ClassRef
+
+#//!\name Used here
+    class Qhull;
     class QhullPoint;
 
-#//Types
+#//!\name Defined here
     //! QhullHyperplane as an offset, dimension, and pointer to coordinates
     class QhullHyperplane;
     //! Java-style iterator for QhullHyperplane coordinates
     class QhullHyperplaneIterator;
 
 class QhullHyperplane { // Similar to QhullPoint
-
-private:
-#//Fields
-    coordT             *hyperplane_coordinates;  // Keep pointers aligned
-    int                 hyperplane_dimension;
-    coordT              hyperplane_offset;
-
 public:
-#//Subtypes
+#//!\name Subtypes
     typedef const coordT *                  iterator;
     typedef const coordT *                  const_iterator;
     typedef QhullHyperplane::iterator       Iterator;
     typedef QhullHyperplane::const_iterator ConstIterator;
 
-#//Construct
-                        QhullHyperplane() : hyperplane_coordinates(0), hyperplane_dimension(0), hyperplane_offset(0.0) {};
-                        QhullHyperplane(int hyperplaneDimension, coordT *c, coordT hyperplaneOffset) : hyperplane_coordinates(c), hyperplane_dimension(hyperplaneDimension), hyperplane_offset(hyperplaneOffset) {}
+private:
+#//!\name Fields
+    coordT *            hyperplane_coordinates;  // Keep pointers aligned
+    int                 hyperplane_dimension;
+    coordT              hyperplane_offset;
+    QhullQh *           qh_qh;
+
+#//!\name Construct
+public:
+                        QhullHyperplane(const Qhull &q);
+                        QhullHyperplane(const Qhull &q, int hyperplaneDimension, coordT *c, coordT hyperplaneOffset);
+                        QhullHyperplane(QhullQh *qh) : hyperplane_coordinates(0), hyperplane_dimension(0), hyperplane_offset(0.0), qh_qh(qh) {}
+                        QhullHyperplane(QhullQh *qh, int hyperplaneDimension, coordT *c, coordT hyperplaneOffset) : hyperplane_coordinates(c), hyperplane_dimension(hyperplaneDimension), hyperplane_offset(hyperplaneOffset), qh_qh(qh) {}
                         // Creates an alias.  Does not copy the hyperplane's coordinates.  Needed for return by value and parameter passing.
-                        QhullHyperplane(const QhullHyperplane &other)  : hyperplane_coordinates(other.hyperplane_coordinates), hyperplane_dimension(other.hyperplane_dimension), hyperplane_offset(other.hyperplane_offset) {}
+                        QhullHyperplane(const QhullHyperplane &other)  : hyperplane_coordinates(other.hyperplane_coordinates), hyperplane_dimension(other.hyperplane_dimension), hyperplane_offset(other.hyperplane_offset), qh_qh(other.qh_qh) {}
                         // Creates an alias.  Does not copy the hyperplane's coordinates.  Needed for vector
-    QhullHyperplane    &operator=(const QhullHyperplane &other) { hyperplane_coordinates= other.hyperplane_coordinates; hyperplane_dimension= other.hyperplane_dimension; hyperplane_offset= other.hyperplane_offset; return *this; }
-                       ~QhullHyperplane() {}
+    QhullHyperplane &   operator=(const QhullHyperplane &other) { hyperplane_coordinates= other.hyperplane_coordinates; hyperplane_dimension= other.hyperplane_dimension; hyperplane_offset= other.hyperplane_offset; qh_qh= other.qh_qh; return *this; }
+                        ~QhullHyperplane() {}
 
-#//Conversions --
+#//!\name Conversions --
 //! Includes offset at end
 #ifndef QHULL_NO_STL
     std::vector toStdVector() const;
 #endif //QHULL_NO_STL
 #ifdef QHULL_USES_QT
     QList       toQList() const;
 #endif //QHULL_USES_QT
 
-#//Read-only
+#//!\name GetSet
 public:
-    const coordT       *coordinates() const { return hyperplane_coordinates; }
-    coordT             *coordinates() { return hyperplane_coordinates; }
+    const coordT *      coordinates() const { return hyperplane_coordinates; }
+    coordT *            coordinates() { return hyperplane_coordinates; }
+    void                defineAs(int hyperplaneDimension, coordT *c, coordT hyperplaneOffset) { QHULL_ASSERT(hyperplaneDimension>=0); hyperplane_coordinates= c; hyperplane_dimension= hyperplaneDimension; hyperplane_offset= hyperplaneOffset; }
+    //! Creates an alias to other using the same qh_qh
+    void                defineAs(QhullHyperplane &other) { hyperplane_coordinates= other.coordinates(); hyperplane_dimension= other.dimension();  hyperplane_offset= other.offset(); }
     int                 dimension() const { return hyperplane_dimension; }
     bool                isDefined() const { return hyperplane_coordinates!=0 && hyperplane_dimension>0; }
     coordT              offset() const { return hyperplane_offset; }
-
-#//Define
-    void                defineAs(int hyperplaneDimension, coordT *c, coordT hyperplaneOffset) { QHULL_ASSERT(hyperplaneDimension>=0); hyperplane_coordinates= c; hyperplane_dimension= hyperplaneDimension; hyperplane_offset= hyperplaneOffset; }
-    //! Creates an alias to other
-    void                defineAs(QhullHyperplane &other) { hyperplane_coordinates= other.coordinates(); hyperplane_dimension= other.dimension();  hyperplane_offset= other.offset(); }
+    bool                operator==(const QhullHyperplane &other) const;
+    bool                operator!=(const QhullHyperplane &other) const { return !operator==(other); }
+    const coordT &      operator[](int idx) const { QHULL_ASSERT(idx>=0 && idx=0 && idx=0 && idx=0 && idx
 #include 
 #include 
 //! Avoid dependence on 
 namespace std { struct bidirectional_iterator_tag; struct random_access_iterator_tag; }
 
 namespace orgQhull {
 
-#//Defined here
+#//!\name Defined here
     //! QHULL_DECLARE_SEQUENTIAL_ITERATOR(C) -- Declare a Java-style iterator
     //! QHULL_DECLARE_MUTABLE_SEQUENTIAL_ITERATOR(C) -- Declare a mutable Java-style iterator
     //! QHULL_DECLARE_SET_ITERATOR(C) -- Declare a set iterator
     //! QHULL_DECLARE_MUTABLE_SET_ITERATOR(C) -- Declare a mutable set iterator
-    //! Derived from Qt/core/tools/qiterator.h and qset.h/FOREACHsetelement_()
+    //! Derived from Qt/core/tools/qiterator.h and qset_r.h/FOREACHsetelement_()
 
 // Changed c to C* as in Mutable...  Assumes c does not go away.
 #define QHULL_DECLARE_SEQUENTIAL_ITERATOR(C, T) \
     \
     class C##Iterator \
     { \
         typedef C::const_iterator const_iterator; \
         const C *c; \
         const_iterator i; \
         public: \
         inline C##Iterator(const C &container) \
         : c(&container), i(c->constBegin()) {} \
         inline C##Iterator &operator=(const C &container) \
         { c = &container; i = c->constBegin(); return *this; } \
         inline void toFront() { i = c->constBegin(); } \
         inline void toBack() { i = c->constEnd(); } \
         inline bool hasNext() const { return i != c->constEnd(); } \
         inline const T &next() { return *i++; } \
         inline const T &peekNext() const { return *i; } \
         inline bool hasPrevious() const { return i != c->constBegin(); } \
         inline const T &previous() { return *--i; } \
         inline const T &peekPrevious() const { const_iterator p = i; return *--p; } \
         inline bool findNext(const T &t) \
         { while (i != c->constEnd()) if (*i++ == t) return true; return false; } \
         inline bool findPrevious(const T &t) \
         { while (i != c->constBegin()) if (*(--i) == t) return true; \
         return false;  } \
     };//C##Iterator
 
 // Remove setShareable() from Q_DECLARE_MUTABLE_SEQUENTIAL_ITERATOR
 // Uses QHULL_ASSERT (assert.h)
 // Duplicated in MutablePointIterator without insert or remove
 #define QHULL_DECLARE_MUTABLE_SEQUENTIAL_ITERATOR(C, T) \
     class Mutable##C##Iterator \
     { \
         typedef C::iterator iterator; \
         typedef C::const_iterator const_iterator; \
         C *c; \
         iterator i, n; \
         inline bool item_exists() const { return const_iterator(n) != c->constEnd(); } \
         public: \
         inline Mutable##C##Iterator(C &container) \
         : c(&container) \
         { i = c->begin(); n = c->end(); } \
         inline ~Mutable##C##Iterator() \
         {} \
         inline Mutable##C##Iterator &operator=(C &container) \
         { c = &container; \
         i = c->begin(); n = c->end(); return *this; } \
         inline void toFront() { i = c->begin(); n = c->end(); } \
         inline void toBack() { i = c->end(); n = i; } \
         inline bool hasNext() const { return c->constEnd() != const_iterator(i); } \
         inline T &next() { n = i++; return *n; } \
         inline T &peekNext() const { return *i; } \
         inline bool hasPrevious() const { return c->constBegin() != const_iterator(i); } \
         inline T &previous() { n = --i; return *n; } \
         inline T &peekPrevious() const { iterator p = i; return *--p; } \
         inline void remove() \
         { if (c->constEnd() != const_iterator(n)) { i = c->erase(n); n = c->end(); } } \
         inline void setValue(const T &t) const { if (c->constEnd() != const_iterator(n)) *n = t; } \
         inline T &value() { QHULL_ASSERT(item_exists()); return *n; } \
         inline const T &value() const { QHULL_ASSERT(item_exists()); return *n; } \
         inline void insert(const T &t) { n = i = c->insert(i, t); ++i; } \
         inline bool findNext(const T &t) \
         { while (c->constEnd() != const_iterator(n = i)) if (*i++ == t) return true; return false; } \
         inline bool findPrevious(const T &t) \
         { while (c->constBegin() != const_iterator(i)) if (*(n = --i) == t) return true; \
         n = c->end(); return false;  } \
     };//Mutable##C##Iterator
 
 #define QHULL_DECLARE_SET_ITERATOR(C) \
 \
     template  \
     class Qhull##C##Iterator \
     { \
         typedef typename Qhull##C::const_iterator const_iterator; \
         Qhull##C c; \
         const_iterator i; \
     public: \
         inline Qhull##C##Iterator(const Qhull##C &container) \
         : c(container), i(c.constBegin()) {} \
         inline Qhull##C##Iterator &operator=(const Qhull##C &container) \
         { c = container; i = c.constBegin(); return *this; } \
         inline void toFront() { i = c.constBegin(); } \
         inline void toBack() { i = c.constEnd(); } \
         inline bool hasNext() const { return i != c.constEnd(); } \
         inline const T &next() { return *i++; } \
         inline const T &peekNext() const { return *i; } \
         inline bool hasPrevious() const { return i != c.constBegin(); } \
         inline const T &previous() { return *--i; } \
         inline const T &peekPrevious() const { const_iterator p = i; return *--p; } \
         inline bool findNext(const T &t) \
         { while (i != c.constEnd()) if (*i++ == t) return true; return false; } \
         inline bool findPrevious(const T &t) \
         { while (i != c.constBegin()) if (*(--i) == t) return true; \
         return false;  } \
     };//Qhull##C##Iterator
 
 #define QHULL_DECLARE_MUTABLE_SET_ITERATOR(C) \
 \
 template  \
 class QhullMutable##C##Iterator \
 { \
     typedef typename Qhull##C::iterator iterator; \
     typedef typename Qhull##C::const_iterator const_iterator; \
     Qhull##C *c; \
     iterator i, n; \
     inline bool item_exists() const { return const_iterator(n) != c->constEnd(); } \
 public: \
     inline Mutable##C##Iterator(Qhull##C &container) \
         : c(&container) \
     { c->setSharable(false); i = c->begin(); n = c->end(); } \
     inline ~Mutable##C##Iterator() \
     { c->setSharable(true); } \
     inline Mutable##C##Iterator &operator=(Qhull##C &container) \
     { c->setSharable(true); c = &container; c->setSharable(false); \
       i = c->begin(); n = c->end(); return *this; } \
     inline void toFront() { i = c->begin(); n = c->end(); } \
     inline void toBack() { i = c->end(); n = i; } \
     inline bool hasNext() const { return c->constEnd() != const_iterator(i); } \
     inline T &next() { n = i++; return *n; } \
     inline T &peekNext() const { return *i; } \
     inline bool hasPrevious() const { return c->constBegin() != const_iterator(i); } \
     inline T &previous() { n = --i; return *n; } \
     inline T &peekPrevious() const { iterator p = i; return *--p; } \
     inline void remove() \
     { if (c->constEnd() != const_iterator(n)) { i = c->erase(n); n = c->end(); } } \
     inline void setValue(const T &t) const { if (c->constEnd() != const_iterator(n)) *n = t; } \
     inline T &value() { Q_ASSERT(item_exists()); return *n; } \
     inline const T &value() const { Q_ASSERT(item_exists()); return *n; } \
     inline void insert(const T &t) { n = i = c->insert(i, t); ++i; } \
     inline bool findNext(const T &t) \
     { while (c->constEnd() != const_iterator(n = i)) if (*i++ == t) return true; return false; } \
     inline bool findPrevious(const T &t) \
     { while (c->constBegin() != const_iterator(i)) if (*(n = --i) == t) return true; \
       n = c->end(); return false;  } \
 };//QhullMutable##C##Iterator
 
 }//namespace orgQhull
 
 #endif // QHULLITERATOR_H
 
diff --git a/src/libqhullcpp/QhullLinkedList.h b/src/libqhullcpp/QhullLinkedList.h
index 9f05dc9..74b0000 100644
--- a/src/libqhullcpp/QhullLinkedList.h
+++ b/src/libqhullcpp/QhullLinkedList.h
@@ -1,377 +1,380 @@
 /****************************************************************************
 **
-** Copyright (c) 2008-2012 C.B. Barber. All rights reserved.
-** $Id: //main/2011/qhull/src/libqhullcpp/QhullLinkedList.h#3 $$Change: 1464 $
-** $DateTime: 2012/01/25 22:58:41 $$Author: bbarber $
+** Copyright (c) 2008-2014 C.B. Barber. All rights reserved.
+** $Id: //main/2011/qhull/src/libqhullcpp/QhullLinkedList.h#9 $$Change: 1797 $
+** $DateTime: 2014/12/15 17:23:41 $$Author: bbarber $
 **
 ****************************************************************************/
 
 #ifndef QHULLLINKEDLIST_H
 #define QHULLLINKEDLIST_H
 
 namespace std { struct bidirectional_iterator_tag; struct random_access_iterator_tag; }
 
 #include "QhullError.h"
+extern "C" {
+    #include "libqhullr/qhull_ra.h"
+}
 
 #ifdef QHULL_USES_QT
 #include 
 #endif
 
 #ifndef QHULL_NO_STL
 #include 
 #endif
 
 namespace orgQhull {
 
-#//Type
+#//!\name Defined here
     //! QhullLinkedList -- A linked list modeled on QLinkedList.
     //!   T is an opaque type with T(B *b), b=t.getBaseT(), t=t.next(), and t=t.prev().  The end node is a sentinel.
     //!   libqhull owns the contents.
     //!   QhullLinkedList does not define erase(), clear(), removeFirst(), removeLast(), pop_back(), pop_front(), fromStdList()
-    //!   Derived from Qt/core/tools/qlinkedlist.h and libqhull.h/FORALLfacets_()
+    //!   Derived from Qt/core/tools/qlinkedlist.h and libqhull_r.h/FORALLfacets_()
     //! QhullLinkedList::const_iterator -- STL-style iterator
     //! QhullLinkedList::iterator -- STL-style iterator
     //! QhullLinkedListIterator -- Java-style iterator
     //!   Derived from Qt/core/tools/qiterator.h
     //!   Works with Qt's foreach keyword [Qt/src/corelib/global/qglobal.h]
 
 template 
 class QhullLinkedList
 {
-private:
-#//Fields
-    T                   begin_node;
-    T                   end_node;     //! Sentinel node at end of list
-
+#//!\name Defined here
 public:
-#//Subtypes and types
-    class               const_iterator;
-    class               iterator;
+    class const_iterator;
+    class iterator;
     typedef const_iterator  ConstIterator;
     typedef iterator    Iterator;
     typedef ptrdiff_t   difference_type;
-    typedef int         size_type;
+    typedef countT      size_type;
     typedef T           value_type;
     typedef const value_type *const_pointer;
     typedef const value_type &const_reference;
     typedef value_type *pointer;
     typedef value_type &reference;
 
-#//Constructors
+#//!\name Fields
+private:
+    T                   begin_node;
+    T                   end_node;     //! Sentinel node at end of list
+
+#//!\name Constructors
+public:
                         QhullLinkedList(T b, T e) : begin_node(b), end_node(e) {}
                         //Copy constructor copies pointer but not contents.  Needed for return by value and parameter passing.
-                        QhullLinkedList(const QhullLinkedList &o) : begin_node(o.begin_node), end_node(o.end_node) {}
-                       ~QhullLinkedList() {}
+                        QhullLinkedList(const QhullLinkedList &other) : begin_node(other.begin_node), end_node(other.end_node) {}
+                        QhullLinkedList & operator=(const QhullLinkedList &other) { begin_node= other.begin_node; end_node= other.end_node; }
+                        ~QhullLinkedList() {}
 
 private:
                         //!disabled since a sentinel must be allocated as the private type
                         QhullLinkedList() {}
                         //!disabled since qs= qs2 is ambiguous (pointer vs. contents)
-    QhullLinkedList &operator=(const QhullLinkedList &l) {}
 public:
 
-#//Conversions
+#//!\name Conversions
 #ifndef QHULL_NO_STL
     std::vector      toStdVector() const;
 #endif
 #ifdef QHULL_USES_QT
     QList            toQList() const;
 #endif
 
-#//Read-only
-    int                 count() const;
-                        //count(t) under #//Search
-    bool                empty() const { return isEmpty(); }
+#//!\name GetSet
+    countT              count() const;
+                        //count(t) under #//!\name Search
     bool                isEmpty() const { return (begin_node==end_node); }
     bool                operator==(const QhullLinkedList &o) const;
     bool                operator!=(const QhullLinkedList &o) const { return !operator==(o); }
     size_t              size() const { return count(); }
 
-#//Element access
+#//!\name Element access
     //! Return by value which contains a pointer (e.g., typedef vertexT * QhullVertex).  A reference does not make sense.
     T                   back() const { return last(); }
     T                   first() const { QHULL_ASSERT(!isEmpty()); return *begin(); }
     T                   front() const { return first(); }
     T                   last() const { QHULL_ASSERT(!isEmpty()); return *--end(); }
 
-#//Modify -- Allocation of opaque types not implemented.
+#//!\name Modify -- Allocation of opaque types not implemented.
 
-#//Search
+#//!\name Search
     bool                contains(const T &t) const;
-    int                 count(const T &t) const;
+    countT              count(const T &t) const;
 
-#//Iterator
+#//!\name Iterator
     iterator            begin() { return begin_node; }
     const_iterator      begin() const { return begin_node; }
     const_iterator      constBegin() const { return begin_node; }
     const_iterator      constEnd() const { return end_node; }
     iterator            end() { return end_node; }
     const_iterator      end() const { return end_node; }
 
     class iterator {
 
     private:
         T               i;
-        friend class    const_iterator;
+        friend class const_iterator;
 
     public:
         typedef std::bidirectional_iterator_tag  iterator_category;
         typedef T           value_type;
         typedef value_type *pointer;
         typedef value_type &reference;
         typedef ptrdiff_t   difference_type;
 
                         iterator() : i() {}
                         iterator(T t) : i(t) {}
                         iterator(const iterator &o) : i(o.i) {}
-        iterator       &operator=(const iterator &o) { i= o.i; return *this; }
+        iterator &      operator=(const iterator &o) { i= o.i; return *this; }
 
         T               operator*() const { return i; }
         T               operator->() const { return i; }
         bool            operator==(const iterator &o) const { return i == o.i; }
         bool            operator!=(const iterator &o) const { return !operator==(o); }
         bool            operator==(const const_iterator &o) const { return i==reinterpret_cast(o).i; }
         bool            operator!=(const const_iterator &o) const { return !operator==(o); }
-        iterator       &operator++() { i= i.next(); return *this; }
+        iterator &      operator++() { i= i.next(); return *this; }
         iterator        operator++(int) { iterator o= i; i= i.next(); return o; }
-        iterator       &operator--() { i= i.previous(); return *this; }
+        iterator &      operator--() { i= i.previous(); return *this; }
         iterator        operator--(int) { iterator o= i; i= i.previous(); return o; }
         iterator        operator+(int j) const;
         iterator        operator-(int j) const { return operator+(-j); }
-        iterator       &operator+=(int j) { return *this= *this + j; }
-        iterator       &operator-=(int j) { return *this= *this - j; }
+        iterator &      operator+=(int j) { return *this= *this + j; }
+        iterator &      operator-=(int j) { return *this= *this - j; }
     };//QhullLinkedList::iterator
 
     class const_iterator {
 
     private:
         T               i;
 
     public:
         typedef std::bidirectional_iterator_tag  iterator_category;
         typedef T                 value_type;
         typedef const value_type *pointer;
         typedef const value_type &reference;
         typedef ptrdiff_t         difference_type;
 
                         const_iterator() : i() {}
                         const_iterator(T t) : i(t) {}
                         const_iterator(const const_iterator &o) : i(o.i) {}
                         const_iterator(iterator o) : i(o.i) {}
         const_iterator &operator=(const const_iterator &o) { i= o.i; return *this; }
 
         T               operator*() const { return i; }
         T               operator->() const { return i; }
         bool            operator==(const const_iterator &o) const { return i == o.i; }
         bool            operator!=(const const_iterator &o) const { return !operator==(o); }
                         // No comparisons or iterator diff
         const_iterator &operator++() { i= i.next(); return *this; }
         const_iterator  operator++(int) { const_iterator o= i; i= i.next(); return o; }
         const_iterator &operator--() { i= i.previous(); return *this; }
         const_iterator  operator--(int) { const_iterator o= i; i= i.previous(); return o; }
         const_iterator  operator+(int j) const;
         const_iterator  operator-(int j) const { return operator+(-j); }
         const_iterator &operator+=(int j) { return *this= *this + j; }
         const_iterator &operator-=(int j) { return *this= *this - j; }
     };//QhullLinkedList::const_iterator
 
 };//QhullLinkedList
 
 template 
 class QhullLinkedListIterator // FIXUP QH11016 define QhullMutableLinkedListIterator
 {
     typedef typename QhullLinkedList::const_iterator const_iterator;
     const QhullLinkedList *c;
     const_iterator      i;
 
 public:
                         QhullLinkedListIterator(const QhullLinkedList &container) : c(&container), i(c->constBegin()) {}
                         QhullLinkedListIterator &operator=(const QhullLinkedList &container) { c= &container; i= c->constBegin(); return *this; }
     bool                findNext(const T &t);
     bool                findPrevious(const T &t);
     bool                hasNext() const { return i != c->constEnd(); }
     bool                hasPrevious() const { return i != c->constBegin(); }
     T                   next() { return *i++; }
     T                   peekNext() const { return *i; }
     T                   peekPrevious() const { const_iterator p= i; return *--p; }
     T                   previous() { return *--i; }
     void                toFront() { i= c->constBegin(); }
     void                toBack() { i= c->constEnd(); }
 };//QhullLinkedListIterator
 
-#//== Definitions =========================================
+#//!\name == Definitions =========================================
 
-#//Conversion
+#//!\name Conversion
 
 #ifndef QHULL_NO_STL
 template 
 std::vector QhullLinkedList::
 toStdVector() const
 {
     std::vector tmp;
     std::copy(constBegin(), constEnd(), std::back_inserter(tmp));
     return tmp;
 }//toStdVector
 #endif
 
 #ifdef QHULL_USES_QT
 template 
 QList  QhullLinkedList::
 toQList() const
 {
     QhullLinkedListIterator i(*this);
     QList ls;
     while(i.hasNext()){
         ls.append(i.next());
     }
     return ls;
 }//toQList
 #endif
 
-#//Read-only
+#//!\name GetSet
 
 template 
-int QhullLinkedList::
+countT QhullLinkedList::
 count() const
 {
     const_iterator i= begin_node;
-    int c= 0;
+    countT c= 0;
     while(i != end_node){
         c++;
         i++;
     }
     return c;
 }//count
 
-#//Search
+#//!\name Search
 
 template 
 bool QhullLinkedList::
 contains(const T &t) const
 {
     const_iterator i= begin_node;
     while(i != end_node){
         if(i==t){
             return true;
         }
         i++;
     }
     return false;
 }//contains
 
 template 
-int QhullLinkedList::
+countT QhullLinkedList::
 count(const T &t) const
 {
     const_iterator i= begin_node;
-    int c= 0;
+    countT c= 0;
     while(i != end_node){
         if(i==t){
             c++;
         }
         i++;
     }
     return c;
 }//count
 
 template 
 bool QhullLinkedList::
 operator==(const QhullLinkedList &l) const
 {
     if(begin_node==l.begin_node){
         return (end_node==l.end_node);
     }
     T i= begin_node;
     T il= l.begin_node;
     while(i != end_node){
         if(i != il){
             return false;
         }
         i= static_cast(i.next());
         il= static_cast(il.next());
     }
     if(il != l.end_node){
         return false;
     }
     return true;
 }//operator==
 
-#//Iterator
+#//!\name Iterator
 
 template 
 typename QhullLinkedList::iterator  QhullLinkedList::iterator::
 operator+(int j) const
 {
     T n= i;
     if(j>0){
         while(j--){
             n= n.next();
         }
     }else{
         while(j++){
             n= n.previous();
         }
     }
     return iterator(n);
 }//operator+
 
 template 
 typename QhullLinkedList::const_iterator  QhullLinkedList::const_iterator::
 operator+(int j) const
 {
     T n= i;
     if(j>0){
         while(j--){
             n= n.next();
         }
     }else{
         while(j++){
             n= n.previous();
         }
     }
     return const_iterator(n);
 }//operator+
 
-#//QhullLinkedListIterator
+#//!\name QhullLinkedListIterator
 
 template 
 bool QhullLinkedListIterator::
 findNext(const T &t)
 {
     while(i != c->constEnd()){
         if (*i++ == t){
             return true;
         }
     }
     return false;
 }//findNext
 
 template 
 bool QhullLinkedListIterator::
 findPrevious(const T &t)
 {
     while(i!=c->constBegin()){
         if(*(--i)==t){
             return true;
         }
     }
     return false;
 }//findNext
 
 }//namespace orgQhull
 
-#//Global functions
+#//!\name Global
 
 template 
 std::ostream &
 operator<<(std::ostream &os, const orgQhull::QhullLinkedList &qs)
 {
     typename orgQhull::QhullLinkedList::const_iterator i;
     for(i= qs.begin(); i != qs.end(); ++i){
         os << *i;
     }
     return os;
 }//operator<<
 
 #endif // QHULLLINKEDLIST_H
 
diff --git a/src/libqhullcpp/QhullPoint.cpp b/src/libqhullcpp/QhullPoint.cpp
index ca9eda2..2378ad7 100644
--- a/src/libqhullcpp/QhullPoint.cpp
+++ b/src/libqhullcpp/QhullPoint.cpp
@@ -1,177 +1,189 @@
 /****************************************************************************
 **
 ** Copyright (c) 2009-2014 C.B. Barber. All rights reserved.
-** $Id: //main/2011/qhull/src/libqhullcpp/QhullPoint.cpp#4 $$Change: 1464 $
-** $DateTime: 2012/01/25 22:58:41 $$Author: bbarber $
+** $Id: //main/2011/qhull/src/libqhullcpp/QhullPoint.cpp#12 $$Change: 1799 $
+** $DateTime: 2014/12/17 16:17:40 $$Author: bbarber $
 **
 ****************************************************************************/
 
-#include "UsingLibQhull.h"
 #include "QhullPoint.h"
+#include "QhullError.h"
+#include "Qhull.h"
 
 #include 
 #include 
 
 #ifdef _MSC_VER  // Microsoft Visual C++ -- warning level 4
 #endif
 
 namespace orgQhull {
 
-#//Class public variables and methods
+#//!\name Constructors
 
-//! If qhRundID undefined uses QhullPoint::s_points_begin and dimension
-int QhullPoint::
-id(int qhRunId, int dimension, const coordT *c)
+
+QhullPoint::
+QhullPoint(const Qhull &q) 
+: point_coordinates(0)
+, qh_qh(q.qh())
+, point_dimension(q.hullDimension())
 {
-    QHULL_UNUSED(dimension);
-
-    if(UsingLibQhull::hasPoints()){
-        if(qhRunId==UsingLibQhull::NOqhRunId){
-            const coordT *pointsEnd;
-            int dim;
-            const coordT *points= UsingLibQhull::globalPoints(&dim, &pointsEnd);
-            if(c>=points && c(c));
-        }
-    }
-    long long i=(long long)c;
-    return (int)i; // WARN64
-}//id
+}//QhullPoint
 
-#//Conversion
+QhullPoint::
+QhullPoint(const Qhull &q, coordT *c) 
+: point_coordinates(c)
+, qh_qh(q.qh())
+, point_dimension(q.hullDimension())
+{
+}//QhullPoint dim, coordT
+
+QhullPoint::
+QhullPoint(const Qhull &q, int pointDimension, coordT *c) 
+: point_coordinates(c)
+, qh_qh(q.qh())
+, point_dimension(pointDimension)
+{
+}//QhullPoint dim, coordT
+
+QhullPoint::
+QhullPoint(const Qhull &q, Coordinates &c) 
+: point_coordinates(c.data())
+, qh_qh(q.qh())
+, point_dimension(c.count())
+{
+}//QhullPoint Coordinates
+
+#//!\name Conversions
 
 // See qt-qhull.cpp for QList conversion
 
 #ifndef QHULL_NO_STL
 std::vector QhullPoint::
 toStdVector() const
 {
     QhullPointIterator i(*this);
     std::vector vs;
     while(i.hasNext()){
         vs.push_back(i.next());
     }
     return vs;
 }//toStdVector
 #endif //QHULL_NO_STL
 
-#//Operator
+#//!\name GetSet
 
+//! QhullPoint is equal if it has the same address and dimension, or if the distance between the points is less than sqrt(qh_qh->distanceEpsilon())
+//! Uses sqrt() since distanceEpsilon is the roundoff for distance to hyperplane, i.e., the inner product
 bool QhullPoint::
 operator==(const QhullPoint &other) const
 {
     if(point_dimension!=other.point_dimension){
         return false;
     }
     const coordT *c= point_coordinates;
     const coordT *c2= other.point_coordinates;
     if(c==c2){
         return true;
     }
+    if(!c || !c2 || !qh_qh){
+        return false;
+    }
     double dist2= 0.0;
     for(int k= point_dimension; k--; ){
         double diff= *c++ - *c2++;
         dist2 += diff*diff;
     }
-    double epsilon= UsingLibQhull::globalDistanceEpsilon();
-    // std::cout << "DEBUG dist2 " << dist2 << " epsilon^2 " << epsilon*epsilon << std::endl;
-    return (dist2<=(epsilon*epsilon));
+    return (dist2 < qh_qh->distanceEpsilon()); // dist2 is distance()^2
 }//operator==
 
+#//!\name Methods
 
-#//Value
-
-//! Return distance betweeen two points.
+//! Return distance between two points.
 double QhullPoint::
 distance(const QhullPoint &p) const
 {
-    const coordT *c= coordinates();
-    const coordT *c2= p.coordinates();
-    int dim= dimension();
-    QHULL_ASSERT(dim==p.dimension());
+    const coordT *c= point_coordinates;
+    const coordT *c2= p.point_coordinates;
+    int dim= point_dimension;
+    if(dim!=p.point_dimension){
+        throw QhullError(10075, "QhullPoint error: Expecting dimension %d for distance().  Got %d", dim, p.point_dimension);
+    }
+    if(!c || !c2){
+        throw QhullError(10076, "QhullPoint error: Cannot compute distance() for undefined point");
+    }
     double dist;
 
     switch(dim){
   case 2:
       dist= (c[0]-c2[0])*(c[0]-c2[0]) + (c[1]-c2[1])*(c[1]-c2[1]);
       break;
   case 3:
       dist= (c[0]-c2[0])*(c[0]-c2[0]) + (c[1]-c2[1])*(c[1]-c2[1]) + (c[2]-c2[2])*(c[2]-c2[2]);
       break;
   case 4:
       dist= (c[0]-c2[0])*(c[0]-c2[0]) + (c[1]-c2[1])*(c[1]-c2[1]) + (c[2]-c2[2])*(c[2]-c2[2]) + (c[3]-c2[3])*(c[3]-c2[3]);
       break;
   case 5:
       dist= (c[0]-c2[0])*(c[0]-c2[0]) + (c[1]-c2[1])*(c[1]-c2[1]) + (c[2]-c2[2])*(c[2]-c2[2]) + (c[3]-c2[3])*(c[3]-c2[3]) + (c[4]-c2[4])*(c[4]-c2[4]);
       break;
   case 6:
       dist= (c[0]-c2[0])*(c[0]-c2[0]) + (c[1]-c2[1])*(c[1]-c2[1]) + (c[2]-c2[2])*(c[2]-c2[2]) + (c[3]-c2[3])*(c[3]-c2[3]) + (c[4]-c2[4])*(c[4]-c2[4]) + (c[5]-c2[5])*(c[5]-c2[5]);
       break;
   case 7:
       dist= (c[0]-c2[0])*(c[0]-c2[0]) + (c[1]-c2[1])*(c[1]-c2[1]) + (c[2]-c2[2])*(c[2]-c2[2]) + (c[3]-c2[3])*(c[3]-c2[3]) + (c[4]-c2[4])*(c[4]-c2[4]) + (c[5]-c2[5])*(c[5]-c2[5]) + (c[6]-c2[6])*(c[6]-c2[6]);
       break;
   case 8:
       dist= (c[0]-c2[0])*(c[0]-c2[0]) + (c[1]-c2[1])*(c[1]-c2[1]) + (c[2]-c2[2])*(c[2]-c2[2]) + (c[3]-c2[3])*(c[3]-c2[3]) + (c[4]-c2[4])*(c[4]-c2[4]) + (c[5]-c2[5])*(c[5]-c2[5]) + (c[6]-c2[6])*(c[6]-c2[6]) + (c[7]-c2[7])*(c[7]-c2[7]);
       break;
   default:
       dist= 0.0;
       for(int k=dim; k--; ){
           dist += (*c - *c2) * (*c - *c2);
           ++c;
           ++c2;
       }
       break;
     }
     return sqrt(dist);
 }//distance
 
 }//namespace orgQhull
 
-#//Global functions
+#//!\name Global functions
 
 using std::ostream;
 using orgQhull::QhullPoint;
-using orgQhull::UsingLibQhull;
-
-#//operator<<
-
-ostream &
-operator<<(ostream &os, const QhullPoint &p)
-{
-    os << p.printWithIdentifier(UsingLibQhull::NOqhRunId, "");
-    return os;
-}
 
 //! Same as qh_printpointid [io.c]
 ostream &
 operator<<(ostream &os, const QhullPoint::PrintPoint &pr)
 {
     QhullPoint p= *pr.point; 
-    int i= p.id(pr.run_id);
+    countT i= p.id();
     if(pr.point_message){
         if(*pr.point_message){
             os << pr.point_message << " ";
         }
         if(pr.with_identifier && (i!=-1)){
             os << "p" << i << ": ";
         }
     }
     const realT *c= p.coordinates();
     for(int k=p.dimension(); k--; ){
         realT r= *c++;
         if(pr.point_message){
             os << " " << r; // FIXUP QH11010 %8.4g
         }else{
             os << " " << r; // FIXUP QH11010 qh_REAL_1
         }
     }
     os << std::endl;
     return os;
 }//printPoint
 
+ostream & 
+operator<<(ostream &os, const QhullPoint &p)
+{
+    os << p.print(""); 
+    return os;
+}//operator<<
diff --git a/src/libqhullcpp/QhullPoint.h b/src/libqhullcpp/QhullPoint.h
index b8b978d..5416d6f 100644
--- a/src/libqhullcpp/QhullPoint.h
+++ b/src/libqhullcpp/QhullPoint.h
@@ -1,130 +1,131 @@
 /****************************************************************************
 **
-** Copyright (c) 2009-2012 C.B. Barber. All rights reserved.
-** $Id: //main/2011/qhull/src/libqhullcpp/QhullPoint.h#6 $$Change: 1464 $
-** $DateTime: 2012/01/25 22:58:41 $$Author: bbarber $
+** Copyright (c) 2009-2014 C.B. Barber. All rights reserved.
+** $Id: //main/2011/qhull/src/libqhullcpp/QhullPoint.h#15 $$Change: 1800 $
+** $DateTime: 2014/12/17 21:46:45 $$Author: bbarber $
 **
 ****************************************************************************/
 
 #ifndef QHPOINT_H
 #define QHPOINT_H
 
 #include "QhullError.h"
 #include "QhullIterator.h"
-#include "UsingLibQhull.h"
+#include "QhullQh.h"
 #include "Coordinates.h"
 extern "C" {
-    #include "libqhull/qhull_r.h"
+    #include "libqhullr/qhull_ra.h"
 }
 
 #include 
 
 namespace orgQhull {
 
-#//Types
-    //! QhullPoint as a pointer and dimension to shared memory
-    class QhullPoint;
-    //! Java-style iterator for QhullPoint coordinates
-    class QhullPointIterator;
+#//!\name Defined here
+    class QhullPoint;  //!<  QhullPoint as a pointer and dimension to shared memory
+    class QhullPointIterator; //!< Java-style iterator for QhullPoint coordinates
 
-class QhullPoint {
-
-    //! A point is a pointer into an array of coordinates.
+#//!\name Used here
+    class Qhull;
 
-private:
-#//Fields
-    coordT             *point_coordinates;  // Keep pointers aligned
-    int                 point_dimension;
+//! A point in Qhull is an array of coordinates.
+class QhullPoint {
 
+#//!\name Iterators
 public:
-#//Subtypes
+    typedef coordT *                    base_type;  // for QhullPointSet
     typedef const coordT *              iterator;
     typedef const coordT *              const_iterator;
     typedef QhullPoint::iterator        Iterator;
     typedef QhullPoint::const_iterator  ConstIterator;
 
-#//Class methods -- Convert point to id w/o QhullQh data structure
-    static int          id(const coordT *c) { return QhullPoint::id(UsingLibQhull::NOqhRunId, 0, c); }
-    static int          id(int qhRunId, const coordT *c) { return QhullPoint::id(qhRunId, 0, c); }
-    static int          id(int qhRunId, int dimension, const coordT *c);
+#//!\name Fields
+protected: // For QhullPoints::iterator, QhullPoints::const_iterator
+    coordT *            point_coordinates;  //!< Pointer to first coordinate,   0 if undefined
+    QhullQh *           qh_qh;              //!< qhT for this instance of Qhull. 0 if undefined.  Used by id() and operator=()
+    int                 point_dimension;    //!< Default dimension is qh_qh->hull_dim
+public:
 
-#//Construct
-                        QhullPoint() : point_coordinates(0), point_dimension(0) {};
-                        QhullPoint(int pointDimension, coordT *c) : point_coordinates(c), point_dimension(pointDimension) {}
-    explicit            QhullPoint(Coordinates &c) : point_coordinates(c.data()), point_dimension(c.count()) {}
+#//!\name Constructors
+                        QhullPoint() : point_coordinates(0), qh_qh(0), point_dimension(0) {}
+    explicit            QhullPoint(const Qhull &q);
+                        QhullPoint(const Qhull &q, int pointDimension, coordT *c);
+                        QhullPoint(const Qhull &q, coordT *c);
+                        QhullPoint(const Qhull &q, Coordinates &c);
+    explicit            QhullPoint(QhullQh *qh) : point_coordinates(0), qh_qh(qh), point_dimension(qh->hull_dim) {}
+                        QhullPoint(QhullQh *qh, int pointDimension, coordT *c) : point_coordinates(c), qh_qh(qh), point_dimension(pointDimension) {}
+                        QhullPoint(QhullQh *qh, coordT *c) : point_coordinates(c), qh_qh(qh), point_dimension(qh->hull_dim) {}
+                        QhullPoint(QhullQh *qh, Coordinates &c) : point_coordinates(c.data()), qh_qh(qh), point_dimension(c.count()) {}
                         // Creates an alias.  Does not copy the point.  Needed for return by value and parameter passing.
-                        QhullPoint(const QhullPoint &other)  : point_coordinates(other.point_coordinates), point_dimension(other.point_dimension) {}
+                        QhullPoint(const QhullPoint &other) : point_coordinates(other.point_coordinates), point_dimension(other.point_dimension), qh_qh(other.qh_qh) {}
                         // Creates an alias.  Does not copy the point.  Needed for vector
-    QhullPoint         &operator=(const QhullPoint &other) { point_coordinates= other.point_coordinates; point_dimension= other.point_dimension; return *this; }
-                       ~QhullPoint() {}
+    QhullPoint &        operator=(const QhullPoint &other) { point_coordinates= other.point_coordinates; point_dimension= other.point_dimension; qh_qh= other.qh_qh; return *this; }
+                        ~QhullPoint() {}
+
+
+#//!\name Conversions
 
-#//Conversions
-    // see coordinates()
 #ifndef QHULL_NO_STL
     std::vector toStdVector() const;
 #endif //QHULL_NO_STL
 #ifdef QHULL_USES_QT
     QList       toQList() const;
 #endif //QHULL_USES_QT
 
-#//Read-only
+#//!\name GetSet
 public:
-    const coordT       *coordinates() const { return point_coordinates; }
-    coordT             *coordinates() { return point_coordinates; }
-    int                 dimension() const { return point_dimension; }
-    int                 id(int qhRunId) const { return id(qhRunId, dimension(), coordinates()); }
-    int                 id() const { return id(UsingLibQhull::NOqhRunId, dimension(), coordinates()); }
-    bool                isDefined() const { return point_coordinates!=0 && point_dimension>0; }
-
-#//Define
-    void                advancePoint(int idx) { point_coordinates += idx*point_dimension; }
+    const coordT *      coordinates() const { return point_coordinates; }  //!< 0 if undefined
+    coordT *            coordinates() { return point_coordinates; }        //!< 0 if undefined
     void                defineAs(int pointDimension, coordT *c) { QHULL_ASSERT(pointDimension>=0); point_coordinates= c; point_dimension= pointDimension; }
-    //! Creates an alias to other
-    void                defineAs(QhullPoint &other) { point_coordinates= other.coordinates(); point_dimension= other.dimension(); }
+    //! Creates an alias, but does not change qh()
+    void                defineAs(QhullPoint &other) { point_coordinates= other.point_coordinates; point_dimension= other.point_dimension; }
+    int                 dimension() const { return point_dimension; }
+    coordT *            getBaseT() const { return point_coordinates; } // for QhullSet
+    countT              id() const { return qh_pointid(qh_qh, point_coordinates); } // NOerrors
+    bool                isDefined() const { return (point_coordinates!=0 && point_dimension>0); };
+    bool                operator==(const QhullPoint &other) const;
+    bool                operator!=(const QhullPoint &other) const { return !operator==(other); }
+    const coordT &      operator[](int idx) const { QHULL_ASSERT(point_coordinates!=0 && idx>=0 && idx=0 && idx=0 && idx=0 && idx
 #include 
 
 #ifdef _MSC_VER  // Microsoft Visual C++ -- warning level 4
 #endif
 
 namespace orgQhull {
 
-#// Conversion
+#//!\name Conversions
 
+/************** FIXUP
 // See qt-qhull.cpp for QList conversion
 
 #ifndef QHULL_NO_STL
 std::vector QhullPointSet::
 toStdVector() const
 {
     QhullPointSetIterator i(*this);
     std::vector vs;
     while(i.hasNext()){
         vs.push_back(i.next());
     }
     return vs;
 }//toStdVector
 #endif //QHULL_NO_STL
 
-#//Element-access
+#//!\name GetSet
+
+bool QhullPointSet::
+operator==(const QhullPointSet &o) const
+{
+    if(dimension()!=o.dimension() || count()!=o.count()){
+        return false;
+    }
+    QhullPointSetIterator i(*this);
+    QhullPointSetIterator j(o);
+    while(i.hasNext()){
+        if(i.next()!=j.next()){
+            return false;
+        }
+    }
+    return true;
+}//operator==
+
 //! Derived from QhullSet::value
+//! Returns QhullPoint() on error
 QhullPoint QhullPointSet::
-value(int idx) const
+value(countT idx) const
 {
-    // Avoid call to qh_setsize() and assert in elementPointer()
+    // Avoid error in qh_setsize() and assert in elementPointer()
     //const T *n= reinterpret_cast(&SETelem_(getSetT(), idx));
     void **n= reinterpret_cast(&SETelem_(getSetT(), idx));
     coordT **n2= reinterpret_cast(n);
     if(idx>=0 && n(&SETelem_(getSetT(), idx));
     coordT **n2= reinterpret_cast(n);
     if(idx>=0 && nconstEnd()){
         if(*i++ == p){
             return true;
         }
     }
     return false;
 }//findNext
 
 bool QhullPointSetIterator::
 findPrevious(const QhullPoint &p)
 {
     while(i!=c->constBegin()){
         if(*(--i) == p){
             return true;
         }
     }
     return false;
 }//findPrevious
+*/
 
 }//namespace orgQhull
 
-#//Global functions
+#//!\name Global functions
 
 using std::endl;
 using std::ostream;
 using orgQhull::QhullPoint;
 using orgQhull::QhullPointSet;
-using orgQhull::UsingLibQhull;
-
-#//operator<<
-
-ostream &
-operator<<(ostream &os, const QhullPointSet &ps)
-{
-    os << ps.print(UsingLibQhull::NOqhRunId);
-    return os;
-}//<
 
 namespace orgQhull {
 
-#//Types
-    //! QhullPointSet -- a set of coordinate pointers with dimension
-    // with const_iterator and iterator
-    class               QhullPointSet;
-    //! Java-style iterator
-    class QhullPointsIterator;
+#//!\name Used here
+    class Qhull;
+    class QhullPoint;
 
-#//Classref
-    class               QhullPoint;
+#//!\name Defined here
+    //! QhullPointSet -- a set of coordinate pointers with input dimension
+    // with const_iterator and iterator
+    class QhullPointSet;
 
-class QhullPointSet : public QhullSet {
+class QhullPointSet : public QhullSet {
 
 private:
-#//Field
-    int                 point_dimension;
-
+#//!\name Fields
+    // no fields
 public:
-#//Subtypes and types
-    class               const_iterator;
-    class               iterator;
-    typedef QhullPointSet::const_iterator ConstIterator;
-    typedef QhullPointSet::iterator Iterator;
-
-    typedef QhullPoint  value_type;
-    typedef ptrdiff_t   difference_type;
-    typedef int         size_type;
-    //typedef const value_type *const_pointer;    // FIXUP QH11019: QhullPointSet does not define pointer or reference due to point_dimension
-    //typedef const value_type &const_reference;
-    //typedef value_type *pointer;
-    //typedef value_type &reference;
-
-#//Construct
+
+#//!\name Construct
+                        QhullPointSet(const Qhull &q, setT *s) : QhullSet(q, s) {}
                         //Conversion from setT* is not type-safe.  Implicit conversion for void* to T
-                        QhullPointSet(int pointDimension, setT *s) : QhullSet(s), point_dimension(pointDimension) {}
+                        QhullPointSet(QhullQh *qh, setT *s) : QhullSet(qh, s) {}
                         //Copy constructor copies pointer but not contents.  Needed for return by value and parameter passing.
-                        QhullPointSet(const QhullPointSet &o) : QhullSet(o), point_dimension(o.point_dimension) {}
-                       ~QhullPointSet() {}
+                        QhullPointSet(const QhullPointSet &other) : QhullSet(other) {}
+    QhullPointSet &     operator=(const QhullPointSet &other) { QhullSet::operator=(other); }
+                        ~QhullPointSet() {}
 
-//Default constructor and copy assignment disabled since p= p2 is ambiguous (coord* vs coord)
+                        //!Default constructor disabled.
 private:
                         QhullPointSet();
-    QhullPointSet      &operator=(const QhullPointSet &);
 public:
 
-#//Conversions
-    // inherited -- constData, data
-#ifndef QHULL_NO_STL
-    std::vector toStdVector() const;
-#endif
-#ifdef QHULL_USES_QT
-    QList   toQList() const;
-#endif
-
-#//Read-only
-    //inherits count, empty, isEmpty, size
-    using QhullSetBase::count;
-    int                 dimension() const { return point_dimension; }
-    bool                operator==(const QhullPointSet &o) const;
-    bool                operator!=(const QhullPointSet &o) const { return !operator==(o); }
-
-#//Element access -- can not return references since QhullPoint must be generated
-    QhullPoint          at(int idx) const { return operator[](idx); }
-    QhullPoint          back() const { return last(); }
-    //! end element is NULL
-    QhullPoint          first() const { QHULL_ASSERT(!isEmpty()); return *begin(); }
-    QhullPoint          front() const { return first(); }
-    QhullPoint          last() const { QHULL_ASSERT(!isEmpty()); return *(end()-1); }
-    // mid() not available.  No setT constructor
-    QhullPoint          operator[](int idx) const { return QhullPoint(dimension(), QhullSet::operator[](idx)); }
-    QhullPoint          second()  const { return operator[](1); }
-    QhullPoint          value(int idx) const;
-    // Non-const since copy is an alias
-    QhullPoint          value(int idx, QhullPoint &defaultValue) const;
-
-#//iterator
-    iterator            begin() { return iterator(dimension(), reinterpret_cast(beginPointer())); }
-    const_iterator      begin() const { return const_iterator(dimension(), reinterpret_cast(beginPointer())); }
-    const_iterator      constBegin() const { return const_iterator(dimension(), reinterpret_cast(beginPointer())); }
-    const_iterator      constEnd() const { return const_iterator(dimension(), reinterpret_cast(endPointer())); }
-    iterator            end() { return iterator(dimension(), reinterpret_cast(endPointer())); }
-    const_iterator      end() const { return const_iterator(dimension(), reinterpret_cast(endPointer())); }
-
-//Read-write -- Not available, no setT constructor
-
-#//Search
-    bool                contains(const QhullPoint &t) const;
-    int                 count(const QhullPoint &t) const;
-    int                 indexOf(const QhullPoint &t) const;
-    int                 lastIndexOf(const QhullPoint &t) const;
-
-    // before const_iterator for conversion with comparison operators
-    class iterator {
-        friend class    const_iterator;
-
-    private:
-        coordT        **i;
-        int             point_dimension;
-
-    public:
-        typedef ptrdiff_t   difference_type;
-        typedef std::bidirectional_iterator_tag  iterator_category;
-        typedef QhullPoint *pointer;
-        typedef QhullPoint &reference;
-        typedef QhullPoint  value_type;
-
-                        iterator() : i(0), point_dimension(0) {}
-                        iterator(int dimension, coordT **c) : i(c), point_dimension(dimension) {}
-                        iterator(const iterator &o) : i(o.i), point_dimension(o.point_dimension) {}
-        iterator       &operator=(const iterator &o) { i= o.i; point_dimension= o.point_dimension; return *this; }
-
-        QhullPoint      operator*() const { return QhullPoint(point_dimension, *i); }
-                      //operator->() n/a, value-type
-        QhullPoint      operator[](int idx) { return QhullPoint(point_dimension, *(i+idx)); }
-        bool            operator==(const iterator &o) const { return i == o.i && point_dimension == o.point_dimension; }
-        bool            operator!=(const iterator &o) const { return !operator==(o); }
-        bool            operator==(const const_iterator &o) const
-        { return i == reinterpret_cast(o).i && point_dimension == reinterpret_cast(o).point_dimension; }
-        bool            operator!=(const const_iterator &o) const { return !operator==(o); }
-
-        //! Assumes same point set
-        int             operator-(const iterator &o) { return (int)(i-o.i); } //WARN64
-        bool            operator>(const iterator &o) const { return i>o.i; }
-        bool            operator<=(const iterator &o) const { return !operator>(o); }
-        bool            operator<(const iterator &o) const { return i=(const iterator &o) const { return !operator<(o); }
-        bool            operator>(const const_iterator &o) const
-        { return i > reinterpret_cast(o).i; }
-        bool            operator<=(const const_iterator &o) const { return !operator>(o); }
-        bool            operator<(const const_iterator &o) const
-        { return i < reinterpret_cast(o).i; }
-        bool            operator>=(const const_iterator &o) const { return !operator<(o); }
-
-        iterator       &operator++() { ++i; return *this; }
-        iterator        operator++(int) { iterator o= *this; ++i; return o; }
-        iterator       &operator--() { --i; return *this; }
-        iterator        operator--(int) { iterator o= *this; --i; return o; }
-        iterator        operator+(int j) const { return iterator(point_dimension, i+j); }
-        iterator        operator-(int j) const { return operator+(-j); }
-        iterator       &operator+=(int j) { i += j; return *this; }
-        iterator       &operator-=(int j) { i -= j; return *this; }
-    };//QhullPointSet::iterator
-
-    class const_iterator {
-    private:
-        coordT        **i;
-        int             point_dimension;
-
-    public:
-        typedef std::random_access_iterator_tag  iterator_category;
-        typedef QhullPoint value_type;
-        typedef value_type *pointer;
-        typedef value_type &reference;
-        typedef ptrdiff_t  difference_type;
-
-                        const_iterator() : i(0), point_dimension(0) {}
-                        const_iterator(int dimension, coordT **c) : i(c), point_dimension(dimension) {}
-                        const_iterator(const const_iterator &o) : i(o.i), point_dimension(o.point_dimension) {}
-                        const_iterator(iterator o) : i(o.i), point_dimension(o.point_dimension) {}
-        const_iterator &operator=(const const_iterator &o) { i= o.i; point_dimension= o.point_dimension; return *this; }
-
-        QhullPoint      operator*() const { return QhullPoint(point_dimension, *i); }
-        QhullPoint      operator[](int idx) { return QhullPoint(point_dimension, *(i+idx)); }
-                      //operator->() n/a, value-type
-        bool            operator==(const const_iterator &o) const { return i == o.i && point_dimension == o.point_dimension; }
-        bool            operator!=(const const_iterator &o) const { return !operator==(o); }
-
-        //! Assumes same point set
-        int             operator-(const const_iterator &o) { return (int)(i-o.i); } //WARN64
-        bool            operator>(const const_iterator &o) const { return i>o.i; }
-        bool            operator<=(const const_iterator &o) const { return !operator>(o); }
-        bool            operator<(const const_iterator &o) const { return i=(const const_iterator &o) const { return !operator<(o); }
-
-        const_iterator &operator++() { ++i; return *this; }
-        const_iterator  operator++(int) { const_iterator o= *this; ++i; return o; }
-        const_iterator &operator--() { --i; return *this; }
-        const_iterator  operator--(int) { const_iterator o= *this; --i; return o; }
-        const_iterator  operator+(int j) const { return const_iterator(point_dimension, i+j); }
-        const_iterator  operator-(int j) const { return operator+(-j); }
-        const_iterator &operator+=(int j) { i += j; return *this; }
-        const_iterator &operator-=(int j) { i -= j; return *this; }
-    };//QhullPointSet::const_iterator
-
-#//IO
+#//!\name IO
     struct PrintIdentifiers{
         const QhullPointSet *point_set;
-        const char     *print_message;
-        int             run_id;
+        const char *    print_message;
         PrintIdentifiers(const char *message, const QhullPointSet *s) : point_set(s), print_message(message) {}
     };//PrintIdentifiers
     PrintIdentifiers printIdentifiers(const char *message) const { return PrintIdentifiers(message, this); }
 
     struct PrintPointSet{
         const QhullPointSet *point_set;
-        const char     *print_message;
-        int             run_id;
-        PrintPointSet(int qhRunId, const char *message, const QhullPointSet &s) : point_set(&s), print_message(message), run_id(qhRunId) {}
+        const char *    print_message;
+        PrintPointSet(const char *message, const QhullPointSet &s) : point_set(&s), print_message(message) {}
     };//PrintPointSet
-    PrintPointSet       print(int qhRunId) const { return PrintPointSet(qhRunId, 0, *this); }
-    PrintPointSet       print(int qhRunId, const char *message) const { return PrintPointSet(qhRunId, message, *this); }
+    PrintPointSet       print(const char *message) const { return PrintPointSet(message, *this); }
 
 };//QhullPointSet
 
-//derived from qiterator.h
-class QhullPointSetIterator { // FIXUP QH11020 define QhullMutablePointSetIterator
-    typedef QhullPointSet::const_iterator const_iterator;
-    const QhullPointSet *c;
-    const_iterator      i;
-
-public:
-                        QhullPointSetIterator(const QhullPointSet &container) : c(&container), i(c->constBegin()) {}
-    QhullPointSetIterator &operator=(const QhullPointSet &container) { c= &container; i= c->constBegin(); return *this; }
-    bool                findNext(const QhullPoint &p);
-    bool                findPrevious(const QhullPoint &p);
-    bool                hasNext() const { return i != c->constEnd(); }
-    bool                hasPrevious() const { return i != c->constBegin(); }
-    QhullPoint          next() { return *i++; }
-    QhullPoint          peekNext() const { return *i; }
-    QhullPoint          peekPrevious() const { const_iterator p= i; return *--p; }
-    QhullPoint          previous() { return *--i; }
-    void                toBack() { i= c->constEnd(); }
-    void                toFront() { i= c->constBegin(); }
-};//QhullPointSetIterator
+typedef QhullSetIterator  QhullPointSetIterator;
 
 }//namespace orgQhull
 
-#//Global functions
+#//!\name Global
 
-std::ostream &operator<<(std::ostream &os, const orgQhull::QhullPointSet &fs); // Not inline to avoid using statement
 std::ostream &operator<<(std::ostream &os, const orgQhull::QhullPointSet::PrintIdentifiers &pr);
 std::ostream &operator<<(std::ostream &os, const orgQhull::QhullPointSet::PrintPointSet &pr);
 
 #endif // QHULLPOINTSET_H
diff --git a/src/libqhullcpp/QhullPoints.cpp b/src/libqhullcpp/QhullPoints.cpp
index 1015b10..fe95c18 100644
--- a/src/libqhullcpp/QhullPoints.cpp
+++ b/src/libqhullcpp/QhullPoints.cpp
@@ -1,235 +1,303 @@
 /****************************************************************************
 **
 ** Copyright (c) 2009-2014 C.B. Barber. All rights reserved.
-** $Id: //main/2011/qhull/src/libqhullcpp/QhullPoints.cpp#4 $$Change: 1464 $
-** $DateTime: 2012/01/25 22:58:41 $$Author: bbarber $
+** $Id: //main/2011/qhull/src/libqhullcpp/QhullPoints.cpp#10 $$Change: 1712 $
+** $DateTime: 2014/03/30 22:34:33 $$Author: bbarber $
 **
 ****************************************************************************/
 
 #include "QhullPoints.h"
+#include "Qhull.h"
 
 #include 
-#include 
+
+#ifndef QHULL_NO_STL
+#include 
+#endif
 
 #ifdef _MSC_VER  // Microsoft Visual C++ -- warning level 4
 #endif
 
 namespace orgQhull {
 
-#//Conversion
+#//!\name Constructors
+
+QhullPoints::
+QhullPoints(const Qhull &q) 
+: point_first(0)
+, point_end(0)
+, qh_qh(q.qh())
+, point_dimension(q.hullDimension())
+{
+}//QhullPoints Qhull
+
+QhullPoints::
+QhullPoints(const Qhull &q, int pointDimension) 
+: point_first(0)
+, point_end(0)
+, qh_qh(q.qh())
+, point_dimension(pointDimension)
+{
+    QHULL_ASSERT(pointDimension>=0);
+}//QhullPoints Qhull dim
+
+QhullPoints::
+QhullPoints(const Qhull &q, int pointDimension, countT coordinateCount2, coordT *c) 
+: point_first(c)
+, point_end(c+coordinateCount2)
+, qh_qh(q.qh())
+, point_dimension(pointDimension)
+{
+    QHULL_ASSERT(pointDimension>=0);
+    QHULL_ASSERT(coordinateCount2>=0);
+}//QhullPoints Qhull dim coordT
+
+QhullPoints::
+QhullPoints(QhullQh *qh, int pointDimension, countT coordinateCount2, coordT *c) 
+: point_first(c)
+, point_end(c+coordinateCount2)
+, qh_qh(qh)
+, point_dimension(pointDimension)
+{
+    QHULL_ASSERT(pointDimension>=0);
+    QHULL_ASSERT(coordinateCount2>=0);
+}//QhullPoints QhullQh dim coordT
+
+#//!\name Conversions
 // See qt-qhull.cpp for QList conversion
 
 #ifndef QHULL_NO_STL
 std::vector QhullPoints::
 toStdVector() const
 {
     QhullPointsIterator i(*this);
     std::vector vs;
     while(i.hasNext()){
         vs.push_back(i.next());
     }
     return vs;
 }//toStdVector
 #endif //QHULL_NO_STL
 
-#//Read-only
+#//!\name GetSet
 
+countT QhullPoints::
+extraCoordinatesCount() const
+{
+    if(point_dimension>0){
+        return (countT)((point_end-point_first)%(size_t)point_dimension);
+    }
+    return 0;
+}//extraCoordinatesCount
+
+//! QhullPoints is equal if the same address, or if the coordinates are identical
+//! Use QhullPoint.operator==() for DISTround equality
 bool QhullPoints::
 operator==(const QhullPoints &other) const
 {
-    if(point_dimension!=other.point_dimension || (point_end-point_first) != (other.point_end-other.point_first)){
+    if((point_end-point_first) != (other.point_end-other.point_first)){
         return false;
     }
+    if(point_first==other.point_first){
+        return true;
+    }
     const coordT *c= point_first;
     const coordT *c2= other.point_first;
     while(c=n){
-        n= 0;
-    }else if(length<0 || idx+length>=n){
-        n -= idx;
-    }else{
-        n -= idx+length;
+    if(qh && qh_qh){
+        throw QhullError(10073, "Qhull error: QhullQh already set for QhullPoints");
     }
-    return QhullPoints(point_dimension, n*point_dimension, point_first+idx*point_dimension);
-}//mid
+    qh_qh= qh;
+}//setQhullQh
 
 QhullPoint QhullPoints::
-value(int idx) const
+value(countT idx) const
 {
-    QhullPoint p;
+    QhullPoint p(qh_qh);
     if(idx>=0 && idxhull_dim, point_first+idx*qh_qh->hull_dim);
     }
     return p;
 }//value
 
 QhullPoint QhullPoints::
-value(int idx, QhullPoint &defaultValue) const
+value(countT idx, QhullPoint &defaultValue) const
 {
-    QhullPoint p;
+    QhullPoint p(qh_qh);
     if(idx>=0 && idxhull_dim, point_first+idx*qh_qh->hull_dim);
     }else{
         p.defineAs(defaultValue);
     }
     return p;
 }//value
 
-#//Search
+#//! Methods
 
 bool QhullPoints::
 contains(const QhullPoint &t) const
 {
     const_iterator i= begin();
     while(i != end()){
         if(*i==t){
             return true;
         }
         i++;
     }
     return false;
 }//contains
 
-int QhullPoints::
+countT QhullPoints::
 count(const QhullPoint &t) const
 {
-    int n= 0;
+    countT n= 0;
     const_iterator i= begin();
     while(i != end()){
         if(*i==t){
             ++n;
         }
         i++;
     }
     return n;
 }//count
 
-int QhullPoints::
+countT QhullPoints::
 indexOf(const coordT *pointCoordinates) const
 {
-    if(!includesCoordinates(pointCoordinates) || dimension()==0){
+    if(!includesCoordinates(pointCoordinates) || point_dimension==0){
         return -1;
     }
     size_t offset= pointCoordinates-point_first;
-    int idx= (int)(offset/(size_t)dimension()); // int for error reporting
-    int extra= (int)(offset%(size_t)dimension());
+    countT idx= (countT)(offset/(size_t)point_dimension);
+    countT extra= (countT)(offset%(size_t)point_dimension);
     if(extra!=0){
         throw QhullError(10066, "Qhull error: coordinates %x are not at point boundary (extra %d at index %d)", extra, idx, 0.0, pointCoordinates);
     }
     return idx;
 }//indexOf coordT
 
-int QhullPoints::
+countT QhullPoints::
 indexOf(const coordT *pointCoordinates, int noThrow) const
 {
     size_t extra= 0;
     if(noThrow){
-        if(!includesCoordinates(pointCoordinates) || dimension()==0){
+        if(!includesCoordinates(pointCoordinates) || point_dimension==0){
             return -1;
         }
-        extra= (pointCoordinates-point_first)%(size_t)dimension();
+        extra= (pointCoordinates-point_first)%(size_t)point_dimension;
     }
     return indexOf(pointCoordinates-extra);
 }//indexOf coordT noThrow
 
-int QhullPoints::
+countT QhullPoints::
 indexOf(const QhullPoint &t) const
 {
-    int j=0;
+    countT j=0;
     const_iterator i= begin();
     while(i!=end()){
         if(*i==t){
             return j;
         }
         ++i;
         ++j;
     }
     return -1;
 }//indexOf
 
-int QhullPoints::
+countT QhullPoints::
 lastIndexOf(const QhullPoint &t) const
 {
-    int j=count();
+    countT j= count();
     const_iterator i= end();
     while(i != begin()){
         --i;
         --j;
         if(*i==t){
             return j;
         }
     }
     return -1;
 }//lastIndexOf
 
-#//QhullPointsIterator
+QhullPoints QhullPoints::
+mid(countT idx, countT length) const
+{
+    countT n= count();
+    if(idx<0 || idx>=n){
+        n= 0;
+    }else if(length<0 || idx+length>=n){
+        n -= idx;
+    }else{
+        n -= idx+length;
+    }
+    return QhullPoints(qh_qh, qh_qh->hull_dim, n*qh_qh->hull_dim, point_first+idx*qh_qh->hull_dim);
+}//mid
+
+#//!\name QhullPointsIterator
 
 bool QhullPointsIterator::
 findNext(const QhullPoint &p)
 {
     while(i!=ps->constEnd()){
         if(*i++ == p){
             return true;
         }
     }
     return false;
 }//findNext
 
 bool QhullPointsIterator::
 findPrevious(const QhullPoint &p)
 {
     while(i!=ps->constBegin()){
         if(*--i == p){
             return true;
         }
     }
     return false;
 }//findPrevious
 
 }//namespace orgQhull
 
-#//Global functions
+#//!\name Global functions
 
 using std::ostream;
 using orgQhull::QhullPoint;
 using orgQhull::QhullPoints;
 using orgQhull::QhullPointsIterator;
 
 ostream &
 operator<<(ostream &os, const QhullPoints &p)
 {
     QhullPointsIterator i(p);
     while(i.hasNext()){
         os << i.next();
     }
     return os;
 }//operator<
 
 namespace orgQhull {
 
-#//Types
-    //! coordinate pointer with dimension
-    // with const_iterator and iterator
-    class QhullPoints;
-    //! Java-style iterator
-    class QhullPointsIterator;
+#//!\name Defined here
+    class QhullPoints;          //!< One or more points Coordinate pointers with dimension and iterators
+    class QhullPointsIterator;  //!< Java-style iterator
 
 class QhullPoints {
 
-    // QhullPoints consists of pointers into an array of coordinates.
-
 private:
-#//Field
-    coordT             *point_first;
-    coordT             *point_end;  // end>=first.  Trailing coordinates ignored
-    int                 point_dimension;  // >= 0
+#//!\name Fields
+    coordT *            point_first; //!< First coordinate of an array of points of point_dimension
+    coordT *            point_end;   //!< End of point coordinates (end>=first).  Trailing coordinates ignored
+    QhullQh *           qh_qh;       //!< Maybe initialized NULL to allow ownership by RboxPoints
+    int                 point_dimension;  //!< Dimension, >=0
 
 public:
-#//Subtypes
-    class               const_iterator;
-    class               iterator;
+#//!\name Subtypes
+    class const_iterator;
+    class iterator;
     typedef QhullPoints::const_iterator ConstIterator;
-    typedef QhullPoints::iterator Iterator;
-
-#//Construct
-                        QhullPoints() : point_first(0), point_end(0), point_dimension(0) {};
-                        QhullPoints(int pointDimension) : point_first(0), point_end(0), point_dimension(pointDimension) { QHULL_ASSERT(pointDimension>=0); }
-                        QhullPoints(int pointDimension, int coordinateCount2, coordT *c) : point_first(c), point_end(c+coordinateCount2), point_dimension(pointDimension) { QHULL_ASSERT(pointDimension>=0 && coordinateCount2>=0 ); }
-                        //Copy constructor copies pointers but not contents.  Needed for return by value and parameter passing.
-                        QhullPoints(const QhullPoints &other)  : point_first(other.point_first), point_end(other.point_end), point_dimension(other.point_dimension) {}
-                       ~QhullPoints() {}
+    typedef QhullPoints::iterator       Iterator;
+
+#//!\name Construct
+    explicit            QhullPoints(const Qhull &q);
+                        QhullPoints(const Qhull &q, int pointDimension);
+                        QhullPoints(const Qhull &q, int pointDimension, countT coordinateCount2, coordT *c);
+    explicit            QhullPoints(QhullQh *qh) : point_first(0), point_end(0), qh_qh(qh), point_dimension(qh ? qh->hull_dim : 0) {}
+                        QhullPoints(QhullQh *qh, int pointDimension) : point_first(0), point_end(0), qh_qh(qh), point_dimension(pointDimension) { QHULL_ASSERT(pointDimension>=0); }
+                        QhullPoints(QhullQh *qh, int pointDimension, countT coordinateCount2, coordT *c);
+                        //! Copy constructor copies pointers but not contents.  Needed for return by value and parameter passing.
+                        QhullPoints(const QhullPoints &other)  : point_first(other.point_first), point_end(other.point_end), qh_qh(other.qh_qh), point_dimension(other.point_dimension) {}
+    QhullPoints &       operator=(const QhullPoints &other) { point_first= other.point_first; point_end= other.point_end; qh_qh= other.qh_qh; point_dimension= other.point_dimension; return *this; }
+                        ~QhullPoints() {}
 
-//disabled since p= p2 is ambiguous (coord* vs coord)
-private:
-    QhullPoints        &operator=(const QhullPoints &other) { point_first= other.point_first; point_end= other.point_end; point_dimension= other.point_dimension; return *this; }
 public:
 
-#//Conversion
-    const coordT       *constData() const { return coordinates(); }
-    // See coordinates()
-    coordT             *data() { return coordinates(); }
-    const coordT       *data() const { return coordinates(); }
+#//!\name Conversion
+
 #ifndef QHULL_NO_STL
     std::vector toStdVector() const;
 #endif //QHULL_NO_STL
 #ifdef QHULL_USES_QT
     QList   toQList() const;
 #endif //QHULL_USES_QT
 
-#//GetSet
-    coordT             *coordinates() const { return point_first; }
-    int                 coordinateCount() const { return (int)(point_end-point_first); } // WARN64
-    int                 count() const { return (int)size(); } // WARN64
-    void                defineAs(int pointDimension, int coordinatesCount, coordT *c) { QHULL_ASSERT(pointDimension>=0 && coordinatesCount>=0 && c!=0); point_first= c; point_end= c+coordinatesCount; point_dimension= pointDimension; }
-    void                defineAs(int coordinatesCount, coordT *c) { QHULL_ASSERT((coordinatesCount>=0 && c!=0) || (c==0 && coordinatesCount==0)); point_first= c; point_end= c+coordinatesCount; }
-    void                defineAs(const QhullPoints &other) { point_first= other.point_first; point_end= other.point_end; point_dimension= other.point_dimension; }
+#//!\name GetSet
+    QhullPoint          at(countT idx) const { /* point_first==0 caught by point_end assert */ coordT *p= point_first+idx*point_dimension; QHULL_ASSERT(p=0 && c!=0) || (c==0 && coordinatesCount==0)); point_first= c; point_end= c+coordinatesCount; }
+    void                defineAs(const QhullPoints &other) { point_first= other.point_first; point_end= other.point_end; qh_qh= other.qh_qh; point_dimension= other.point_dimension; }
     int                 dimension() const { return point_dimension; }
-    bool                empty() const { return point_end==point_first; }
-    coordT             *extraCoordinates() const { return extraCoordinatesCount() ? (point_end-extraCoordinatesCount()) : 0; }
-    int                 extraCoordinatesCount() const { return point_dimension>0 ? (int)((point_end-point_first)%(size_t)point_dimension) : 0; }  // WARN64
+    ConstIterator       end() const { return ConstIterator(qh_qh, point_end); }
+    Iterator            end() { return Iterator(qh_qh, point_end); }
+    coordT *            extraCoordinates() const { return extraCoordinatesCount() ? (point_end-extraCoordinatesCount()) : 0; }
+    countT              extraCoordinatesCount() const;  // WARN64
+    QhullPoint          first() const { return QhullPoint(qh_qh, point_dimension, point_first); }
+    QhullPoint          front() const { return first(); }
     bool                includesCoordinates(const coordT *c) const { return c>=point_first && c=0); point_dimension= pointDimension; }
-    size_t              size() const { return (point_dimension ? (point_end-point_first)/point_dimension : 0); }
-
-#//ElementAccess -- can not return references to QhullPoint
-    QhullPoint          at(int idx) const { coordT *p= point_first+idx*point_dimension; QHULL_ASSERT(p(other)); return *this; }
-        QhullPoint     *operator->() { return this; }
+        iterator &      operator=(const iterator &other) { defineAs( const_cast(other)); return *this; }
+ 
+        QhullPoint *    operator->() { return this; }
         // value instead of reference since advancePoint() modifies self
         QhullPoint      operator*() const { return *this; }
-        QhullPoint      operator[](int idx) const { QhullPoint n= *this; n.advancePoint(idx); return n; }
-        bool            operator==(const iterator &other) const { QHULL_ASSERT(dimension()==other.dimension()); return coordinates()==other.coordinates(); }
-        bool            operator!=(const iterator &other) const { return !operator==(other); }
-        bool            operator<(const iterator &other) const  { QHULL_ASSERT(dimension()==other.dimension()); return coordinates() < other.coordinates(); }
-        bool            operator<=(const iterator &other) const { QHULL_ASSERT(dimension()==other.dimension()); return coordinates() <= other.coordinates(); }
-        bool            operator>(const iterator &other) const  { QHULL_ASSERT(dimension()==other.dimension()); return coordinates() > other.coordinates(); }
-        bool            operator>=(const iterator &other) const { QHULL_ASSERT(dimension()==other.dimension()); return coordinates() >= other.coordinates(); }
+        QhullPoint      operator[](countT idx) const { QhullPoint n= *this; n.advancePoint(idx); return n; }
+        bool            operator==(const iterator &o) const { return point_coordinates==o.point_coordinates; }
+        bool            operator!=(const iterator &o) const { return !operator==(o); }
+        bool            operator<(const iterator &o) const  { return point_coordinates < o.point_coordinates; }
+        bool            operator<=(const iterator &o) const { return point_coordinates <= o.point_coordinates; }
+        bool            operator>(const iterator &o) const  { return point_coordinates > o.point_coordinates; }
+        bool            operator>=(const iterator &o) const { return point_coordinates >= o.point_coordinates; }
         // reinterpret_cast to break circular dependency
-        bool            operator==(const QhullPoints::const_iterator &other) const { QHULL_ASSERT(dimension()==reinterpret_cast(other).dimension()); return coordinates()==reinterpret_cast(other).coordinates(); }
-        bool            operator!=(const QhullPoints::const_iterator &other) const { return !operator==(reinterpret_cast(other)); }
-        bool            operator<(const QhullPoints::const_iterator &other) const  { QHULL_ASSERT(dimension()==reinterpret_cast(other).dimension()); return coordinates() < reinterpret_cast(other).coordinates(); }
-        bool            operator<=(const QhullPoints::const_iterator &other) const { QHULL_ASSERT(dimension()==reinterpret_cast(other).dimension()); return coordinates() <= reinterpret_cast(other).coordinates(); }
-        bool            operator>(const QhullPoints::const_iterator &other) const  { QHULL_ASSERT(dimension()==reinterpret_cast(other).dimension()); return coordinates() > reinterpret_cast(other).coordinates(); }
-        bool            operator>=(const QhullPoints::const_iterator &other) const { QHULL_ASSERT(dimension()==reinterpret_cast(other).dimension()); return coordinates() >= reinterpret_cast(other).coordinates(); }
-        iterator       &operator++() { advancePoint(1); return *this; }
+        bool            operator==(const QhullPoints::const_iterator &o) const { QHULL_ASSERT(qh_qh==reinterpret_cast(o).qh_qh); return point_coordinates==reinterpret_cast(o).point_coordinates; }
+        bool            operator!=(const QhullPoints::const_iterator &o) const { return !operator==(reinterpret_cast(o)); }
+        bool            operator<(const QhullPoints::const_iterator &o) const  { QHULL_ASSERT(qh_qh==reinterpret_cast(o).qh_qh); return point_coordinates < reinterpret_cast(o).point_coordinates; }
+        bool            operator<=(const QhullPoints::const_iterator &o) const { QHULL_ASSERT(qh_qh==reinterpret_cast(o).qh_qh); return point_coordinates <= reinterpret_cast(o).point_coordinates; }
+        bool            operator>(const QhullPoints::const_iterator &o) const  { QHULL_ASSERT(qh_qh==reinterpret_cast(o).qh_qh); return point_coordinates > reinterpret_cast(o).point_coordinates; }
+        bool            operator>=(const QhullPoints::const_iterator &o) const { QHULL_ASSERT(qh_qh==reinterpret_cast(o).qh_qh); return point_coordinates >= reinterpret_cast(o).point_coordinates; }
+        iterator &      operator++() { advancePoint(1); return *this; }
         iterator        operator++(int) { iterator n= *this; operator++(); return iterator(n); }
-        iterator       &operator--() { advancePoint(-1); return *this; }
+        iterator &      operator--() { advancePoint(-1); return *this; }
         iterator        operator--(int) { iterator n= *this; operator--(); return iterator(n); }
-        iterator       &operator+=(int idx) { advancePoint(idx); return *this; }
-        iterator       &operator-=(int idx) { advancePoint(-idx); return *this; }
-        iterator        operator+(int idx) const { iterator n= *this; n.advancePoint(idx); return n; }
-        iterator        operator-(int idx) const { iterator n= *this; n.advancePoint(-idx); return n; }
-        difference_type operator-(iterator other) const { QHULL_ASSERT(dimension()==other.dimension()); return (coordinates()-other.coordinates())/dimension(); }
+        iterator &      operator+=(countT idx) { advancePoint(idx); return *this; }
+        iterator &      operator-=(countT idx) { advancePoint(-idx); return *this; }
+        iterator        operator+(countT idx) const { iterator n= *this; n.advancePoint(idx); return n; }
+        iterator        operator-(countT idx) const { iterator n= *this; n.advancePoint(-idx); return n; }
+        difference_type operator-(iterator o) const { QHULL_ASSERT(qh_qh==o.qh_qh && point_dimension==o.point_dimension); return (point_dimension ? (point_coordinates-o.point_coordinates)/point_dimension : 0); }
     };//QhullPoints::iterator
 
-#//QhullPoints::const_iterator -- FIXUP QH11018 const_iterator same as iterator
+#//!\name QhullPoints::const_iterator
+    //!\todo FIXUP QH11018 const_iterator same as iterator
     class const_iterator : public QhullPoint {
 
     public:
         typedef std::random_access_iterator_tag  iterator_category;
         typedef QhullPoint          value_type;
-        typedef const value_type   *pointer;
-        typedef const value_type   &reference;
+        typedef const value_type *  pointer;
+        typedef const value_type &  reference;
         typedef ptrdiff_t           difference_type;
 
-                        const_iterator() : QhullPoint() {}
-                        const_iterator(const const_iterator &other) : QhullPoint(*other) {}
-                        const_iterator(const QhullPoints::iterator &other) : QhullPoint(*other) {}
-        explicit        const_iterator(const QhullPoints &ps) : QhullPoint(ps.dimension(), ps.coordinates()) {}
-        explicit        const_iterator(int pointDimension, coordT *c): QhullPoint(pointDimension, c) {}
-        const_iterator &operator=(const const_iterator &other) { defineAs(const_cast(other)); return *this; }
+                        const_iterator(const QhullPoints::iterator &o) : QhullPoint(*o) {}
+        explicit        const_iterator(const QhullPoints &ps) : QhullPoint(ps.qh(), ps.dimension(), ps.coordinates()) {}
+                        const_iterator(const Qhull &q, coordT *c): QhullPoint(q, c) {}
+                        const_iterator(const Qhull &q, int pointDimension, coordT *c): QhullPoint(q, pointDimension, c) {}
+                        const_iterator(QhullQh *qh, coordT *c): QhullPoint(qh, c) {}
+                        const_iterator(QhullQh *qh, int pointDimension, coordT *c): QhullPoint(qh, pointDimension, c) {}
+                        const_iterator(const const_iterator &o) : QhullPoint(*o) {}
+        const_iterator &operator=(const const_iterator &o) { defineAs(const_cast(o)); return *this; }
+
         // value/non-const since advancePoint(1), etc. modifies self
         QhullPoint      operator*() const { return *this; }
-        QhullPoint     *operator->() { return this; }
-        QhullPoint      operator[](int idx) const { QhullPoint n= *this; n.advancePoint(idx); return n; }
-        bool            operator==(const const_iterator &other) const { QHULL_ASSERT(dimension()==other.dimension()); return coordinates()==other.coordinates(); }
-        bool            operator!=(const const_iterator &other) const { return !operator==(other); }
-        bool            operator<(const const_iterator &other) const  { QHULL_ASSERT(dimension()==other.dimension()); return coordinates() < other.coordinates(); }
-        bool            operator<=(const const_iterator &other) const { QHULL_ASSERT(dimension()==other.dimension()); return coordinates() <= other.coordinates(); }
-        bool            operator>(const const_iterator &other) const  { QHULL_ASSERT(dimension()==other.dimension()); return coordinates() > other.coordinates(); }
-        bool            operator>=(const const_iterator &other) const { QHULL_ASSERT(dimension()==other.dimension()); return coordinates() >= other.coordinates(); }
+        QhullPoint *    operator->() { return this; }
+        QhullPoint      operator[](countT idx) const { QhullPoint n= *this; n.advancePoint(idx); return n; }
+        bool            operator==(const const_iterator &o) const { return point_coordinates==o.point_coordinates; }
+        bool            operator!=(const const_iterator &o) const { return !operator==(o); }
+        bool            operator<(const const_iterator &o) const  { return point_coordinates < o.point_coordinates; }
+        bool            operator<=(const const_iterator &o) const { return point_coordinates <= o.point_coordinates; }
+        bool            operator>(const const_iterator &o) const  { return point_coordinates > o.point_coordinates; }
+        bool            operator>=(const const_iterator &o) const { return point_coordinates >= o.point_coordinates; }
         const_iterator &operator++() { advancePoint(1); return *this; }
         const_iterator  operator++(int) { const_iterator n= *this; operator++(); return const_iterator(n); }
         const_iterator &operator--() { advancePoint(-1); return *this; }
         const_iterator  operator--(int) { const_iterator n= *this; operator--(); return const_iterator(n); }
-        const_iterator &operator+=(int idx) { advancePoint(idx); return *this; }
-        const_iterator &operator-=(int idx) { advancePoint(-idx); return *this; }
-        const_iterator  operator+(int idx) const { const_iterator n= *this; n.advancePoint(idx); return n; }
-        const_iterator  operator-(int idx) const { const_iterator n= *this; n.advancePoint(-idx); return n; }
-        difference_type operator-(const_iterator other) const { QHULL_ASSERT(dimension()==other.dimension()); return (coordinates()-other.coordinates())/dimension(); }
+        const_iterator &operator+=(countT idx) { advancePoint(idx); return *this; }
+        const_iterator &operator-=(countT idx) { advancePoint(-idx); return *this; }
+        const_iterator  operator+(countT idx) const { const_iterator n= *this; n.advancePoint(idx); return n; }
+        const_iterator  operator-(countT idx) const { const_iterator n= *this; n.advancePoint(-idx); return n; }
+        difference_type operator-(const_iterator o) const { QHULL_ASSERT(qh_qh==o.qh_qh && point_dimension==o.point_dimension); return (point_dimension ? (point_coordinates-o.point_coordinates)/point_dimension : 0); }
     };//QhullPoints::const_iterator
 
-#//IO
+#//!\name IO
     struct PrintPoints{
         const QhullPoints  *points;
-        const char     *point_message;
-        int             run_id;
+        const char *    point_message;
         bool            with_identifier;
-        PrintPoints(int qhRunId, const char *message, bool withIdentifier, const QhullPoints &ps) : points(&ps), point_message(message), run_id(qhRunId), with_identifier(withIdentifier) {}
+        PrintPoints(const char *message, bool withIdentifier, const QhullPoints &ps) : points(&ps), point_message(message), with_identifier(withIdentifier) {}
     };//PrintPoints
-    PrintPoints          print() const { return  PrintPoints(UsingLibQhull::NOqhRunId, "", false, *this); }
-    PrintPoints          print(int qhRunId) const { return PrintPoints(qhRunId, "", true, *this); }
-    PrintPoints          print(int qhRunId, const char *message) const { return PrintPoints(qhRunId, message, false, *this); }
-    PrintPoints          printWithIdentifier(int qhRunId, const char *message) const { return PrintPoints(qhRunId, message, true, *this); }
+    PrintPoints          print() const { return  PrintPoints("", false, *this); }
+    PrintPoints          print(const char *message) const { return PrintPoints(message, false, *this); }
+    PrintPoints          printWithIdentifier(const char *message) const { return PrintPoints(message, true, *this); }
     //FIXUP remove message for print()?
 };//QhullPoints
 
-// can't use QHULL_DECLARE_SEQUENTIAL_ITERATOR because next(),etc would return a reference to a temporary
+// Instead of QHULL_DECLARE_SEQUENTIAL_ITERATOR because next(),etc would return a reference to a temporary
 class QhullPointsIterator
 {
     typedef QhullPoints::const_iterator const_iterator;
 
+#//!\name Fields
 private:
-#//Fields
     const QhullPoints  *ps;
     const_iterator      i;
 
 public:
                         QhullPointsIterator(const QhullPoints &other) : ps(&other), i(ps->constBegin()) {}
     QhullPointsIterator &operator=(const QhullPoints &other) { ps = &other; i = ps->constBegin(); return *this; }
+
     bool                findNext(const QhullPoint &t);
     bool                findPrevious(const QhullPoint &t);
     bool                hasNext() const { return i != ps->constEnd(); }
     bool                hasPrevious() const { return i != ps->constBegin(); }
     QhullPoint          next() { return *i++; }
     QhullPoint          peekNext() const { return *i; }
     QhullPoint          peekPrevious() const { const_iterator p = i; return *--p; }
     QhullPoint          previous() { return *--i; }
     void                toBack() { i = ps->constEnd(); }
     void                toFront() { i = ps->constBegin(); }
 };//QhullPointsIterator
 
 }//namespace orgQhull
 
-#//Global functions
+#//!\name Global
 
-std::ostream           &operator<<(std::ostream &os, const orgQhull::QhullPoints &p);
-std::ostream           &operator<<(std::ostream &os, const orgQhull::QhullPoints::PrintPoints &pr);
+std::ostream &          operator<<(std::ostream &os, const orgQhull::QhullPoints &p);
+std::ostream &          operator<<(std::ostream &os, const orgQhull::QhullPoints::PrintPoints &pr);
 
 #endif // QHULLPOINTS_H
diff --git a/src/libqhullcpp/QhullQh.cpp b/src/libqhullcpp/QhullQh.cpp
index ed7fae9..3e03c81 100644
--- a/src/libqhullcpp/QhullQh.cpp
+++ b/src/libqhullcpp/QhullQh.cpp
@@ -1,104 +1,223 @@
 /****************************************************************************
 **
 ** Copyright (c) 2008-2014 C.B. Barber. All rights reserved.
-** $Id: //main/2011/qhull/src/libqhullcpp/QhullQh.cpp#3 $$Change: 1464 $
-** $DateTime: 2012/01/25 22:58:41 $$Author: bbarber $
+** $Id: //main/2011/qhull/src/libqhullcpp/QhullQh.cpp#8 $$Change: 1797 $
+** $DateTime: 2014/12/15 17:23:41 $$Author: bbarber $
 **
 ****************************************************************************/
 
 #//! QhullQh -- Qhull's global data structure, qhT, as a C++ class
 
 
 
 #include "QhullError.h"
 #include "QhullQh.h"
 #include "QhullStat.h"
+#include "Qhull.h"
 
 #include 
 #include 
 
+#include 
+
 using std::cerr;
 using std::string;
 using std::vector;
 using std::ostream;
 
 #ifdef _MSC_VER  // Microsoft Visual C++ -- warning level 4
 #pragma warning( disable : 4611)  // interaction between '_setjmp' and C++ object destruction is non-portable
 #pragma warning( disable : 4996)  // function was declared deprecated(strcpy, localtime, etc.)
 #endif
 
 namespace orgQhull {
 
 #//Global variables
+const double QhullQh::
+default_factor_epsilon= 1.0;
 
 #//Constructor, destructor, etc.
 
-//! If qh_QHpointer==0, invoke with placement new on qh_qh;
-//! Sets qh_qh and qh_qhstat.  Need to reset before UsingLibQhull.
 //! Derived from qh_new_qhull[user.c]
 QhullQh::
 QhullQh()
+: qhull_status(qh_ERRnone)
+, qhull_message()
+, error_stream(0)
+, output_stream(0)
+, factor_epsilon(QhullQh::default_factor_epsilon)
+, useOutputStream(false)
 {
-    static boolT firstcall = True;
-
-    if(firstcall){
-        if(qhmem.BUFinit!=0){
-            throw QhullError(10017, "Qhull error: qhmem already initialized by another class.");
-        }
-        qh_meminit(NULL);
-        firstcall= False;
-    }
-    // QhullQh() and UsingLibQhull() are the same
-#if qh_QHpointer
-    if(qh_qh){
-        if(qh old_qhstat){
-            throw QhullError(10041, "Qhull internal error: qh_qh.old_qhstat defined (%x) but qh_qh is active.  qh_qh not restored correctly.", 0, 0, 0.0, qh old_qhstat);
-        }
-        qh old_qhstat= qh_qhstat;
-        qh old_tempstack= qhmem.tempstack;
-        qh_qhstat= 0;
-        qhmem.tempstack= 0;
-    }
-    qh_qh= static_cast(this);
-#else
-    if(strncmp(qh qhull, "qhull", 5) == 0){
-        throw QhullError(10022, "Qhull error: Qhull already initialized as run %d", qh run_id);
-    }
-#endif
     // NOerrors -- Does not call qh_errexit()
-    qh_initstatistics();
+    qh_meminit(this, NULL);
+    this->ISqhullQh= True;
+    // NOerrors -- Does not call qh_errexit()
+    qh_initstatistics(this);
     // NOerrors -- Does not call qh_errexit()
-    qh_initqhull_start2(NULL, NULL, qh_FILEstderr);
+    qh_initqhull_start2(this, NULL, NULL, qh_FILEstderr);
 }//QhullQh
 
-//! UsingLibQhull must be declared along with QhullQh
 QhullQh::
 ~QhullQh()
 {
-#if qh_QHpointer
-    if(!qh_qh){
-        QhullError e(10042, "Qhull internal error: qh_qh undefined.  Was ~QhullQh() invoked independent of UsingLibQhull?", qh run_id, 0, 0, qh_qh);
-        e.logError();
-    }else if(!qh_qhstat){
-        QhullError e(10043, "Qhull internal error: qh_qhstat null.  Is another thread running?");
-        e.logError();
-    }else if(qh_qh!=this){
-        QhullError e(10044, "Qhull error: ~QhullQh() invoked independent of UsingLibQhull. qh_qh %x (runId %d) vs. QhullQh.runId %d.", qh run_id, run_id, 0.0, qh_qh);
-        e.logError();
+    qh_freeqhull(this, qh_ALL); // sets qh.NOerrexit. Clears struct *qh_qh including run_id
+}//~QhullQh
+
+#//!\name Methods
+
+void QhullQh::
+checkAndFreeQhullMemory()
+{
+#ifdef qh_NOmem
+    qh_freeqhull(this, qh_ALL);
+#else
+    qh_freeqhull(this, !qh_ALL);
+    countT curlong;
+    countT totlong;
+    qh_memfreeshort(this, &curlong, &totlong);
+    if (curlong || totlong)
+        throw QhullError(10026, "Qhull error: qhull did not free %d bytes of long memory (%d pieces).", totlong, curlong);
+#endif
+}//checkAndFreeQhullMemory
+
+#//Messaging
+
+void QhullQh::
+appendQhullMessage(const string &s)
+{
+    if(output_stream && useOutputStream && this->USEstdout){ 
+        *output_stream << s;
+    }else if(error_stream){
+        *error_stream << s;
     }else{
-        qh_freeqhull2(qh_ALL); // sets qh.NOerrexit.  Clears struct *qh_qh including run_id, but not qh_qh itself
+        qhull_message += s;
     }
-#else
-    if(&qh_qh!=this){
-        QhullError e(10045, "Qhull error: ~QhullQh() invoked independent of UsingLibQhull. qh_qh %x (runId %d) vs. QhullQh.runId %d.", qh run_id, run_id, 0.0, qh_qh);
+}//appendQhullMessage
+
+//! clearQhullMessage does not throw errors (~Qhull)
+void QhullQh::
+clearQhullMessage()
+{
+    qhull_status= qh_ERRnone;
+    qhull_message.clear();
+    RoadError::clearGlobalLog();
+}//clearQhullMessage
+
+//! hasQhullMessage does not throw errors (~Qhull)
+bool QhullQh::
+hasQhullMessage() const
+{
+    return (!qhull_message.empty() || qhull_status!=qh_ERRnone);
+    //FIXUP QH11006 -- inconsistent usage with Rbox.  hasRboxMessage just tests rbox_status.  No appendRboxMessage()
+}
+
+void QhullQh::
+maybeThrowQhullMessage(int exitCode)
+{
+    if(qhull_status==qh_ERRnone){
+        qhull_status= exitCode;
+    }
+    if(qhull_status!=qh_ERRnone){
+        QhullError e(qhull_status, qhull_message);
+        clearQhullMessage();
+        throw e; // FIXUP QH11007: copy constructor is expensive if logging
+    }
+}//maybeThrowQhullMessage
+
+void QhullQh::
+maybeThrowQhullMessage(int exitCode, int noThrow)  throw()
+{
+    QHULL_UNUSED(noThrow);
+
+    if(qhull_status==qh_ERRnone){
+        qhull_status= exitCode;
+    }
+    if(qhull_status!=qh_ERRnone){
+        QhullError e(qhull_status, qhull_message);
         e.logError();
+    }
+}//maybeThrowQhullMessage
+
+//! qhullMessage does not throw errors (~Qhull)
+std::string QhullQh::
+qhullMessage() const
+{
+    if(qhull_message.empty() && qhull_status!=qh_ERRnone){
+        return "qhull: no message for error.  Check cerr or error stream\n";
     }else{
-        qh_freeqhull2(qh_ALL); // sets qh.NOerrexit.  Clears struct *qh_qh including run_id, but not qh_qh itself
+        return qhull_message;
     }
-#endif
-}//~QhullQh
+}//qhullMessage
 
-#//Parallel Access
+int QhullQh::
+qhullStatus() const
+{
+    return qhull_status;
+}//qhullStatus
+
+void QhullQh::
+setErrorStream(ostream *os)
+{
+    error_stream= os;
+}//setErrorStream
+
+//! Updates useOutputStream
+void QhullQh::
+setOutputStream(ostream *os)
+{
+    output_stream= os;
+    useOutputStream= (os!=0);
+}//setOutputStream
 
 }//namespace orgQhull
 
+/*---------------------------------
+
+  qh_fprintf(qhT *qh, fp, msgcode, format, list of args )
+    FIXUP s_qhull_output vs. fp is ignored (replaces qh_fprintf() in userprintf_r.c)
+
+notes:
+    only called from libqhull
+    same as fprintf() and RboxPoints.qh_fprintf_rbox()
+    fgets() is not trapped like fprintf()
+    Do not throw errors from here.  Use qh_errexit;
+*/
+extern "C"
+void qh_fprintf(qhT *qh, FILE *fp, int msgcode, const char *fmt, ... ) {
+    va_list args;
+
+    using namespace orgQhull;
+
+    if(!qh->ISqhullQh){
+        fprintf(stderr, "QH10025 Qhull error: qh_fprintf called from a Qhull instance without QhullQh defined\n");
+        qh_exit(10025);
+    }
+    QhullQh *qhullQh= static_cast(qh);
+    va_start(args, fmt);
+    if(msgcode=MSG_ERROR && msgcodeqhull_statusqhull_status>=MSG_WARNING){
+                qhullQh->qhull_status= msgcode;
+            }
+        }
+        char newMessage[MSG_MAXLEN];
+        // RoadError will add the message tag
+        vsnprintf(newMessage, sizeof(newMessage), fmt, args);
+        qhullQh->appendQhullMessage(newMessage);
+        va_end(args);
+        return;
+    }
+    if(qhullQh->output_stream && qhullQh->useOutputStream){
+        char newMessage[MSG_MAXLEN];
+        vsnprintf(newMessage, sizeof(newMessage), fmt, args);
+        *qhullQh->output_stream << newMessage;
+        va_end(args);
+        return;
+    }
+    // FIXUP QH11008: how do users trap messages and handle input?  A callback?
+    char newMessage[MSG_MAXLEN];
+    vsnprintf(newMessage, sizeof(newMessage), fmt, args);
+    qhullQh->appendQhullMessage(newMessage);
+    va_end(args);
+} /* qh_fprintf */
diff --git a/src/libqhullcpp/QhullQh.h b/src/libqhullcpp/QhullQh.h
index 7675383..a375b80 100644
--- a/src/libqhullcpp/QhullQh.h
+++ b/src/libqhullcpp/QhullQh.h
@@ -1,51 +1,111 @@
 /****************************************************************************
 **
-** Copyright (c) 2008-2012 C.B. Barber. All rights reserved.
-** $Id: //main/2011/qhull/src/libqhullcpp/QhullQh.h#6 $$Change: 1464 $
-** $DateTime: 2012/01/25 22:58:41 $$Author: bbarber $
+** Copyright (c) 2008-2014 C.B. Barber. All rights reserved.
+** $Id: //main/2011/qhull/src/libqhullcpp/QhullQh.h#13 $$Change: 1712 $
+** $DateTime: 2014/03/30 22:34:33 $$Author: bbarber $
 **
 ****************************************************************************/
 
 #ifndef QHULLQH_H
 #define QHULLQH_H
 
 extern "C" {
-    #include "libqhull/qhull_r.h"
+    #include "libqhullr/qhull_ra.h"
 }
 
 #include 
-#include 
+
+#ifdef _MSC_VER  // Microsoft Visual C++ -- warning level 4
+#pragma warning( disable : 4611)  /* interaction between '_setjmp' and C++ object destruction is non-portable */
+/* setjmp should not be implemented with 'catch' */
+#endif
+
+//! QH_TRY_(qh_qh){ // no object creation -- destructors skipped on longjmp()
+//! }
+//! qh->maybeThrowQhullMessage(QH_TRY_status);
+
+#define QH_TRY_ERROR 10071
+
+#define QH_TRY_(qh) \
+    int QH_TRY_status; \
+    if(qh->NOerrexit){ \
+        qh->NOerrexit= False; \
+        QH_TRY_status= setjmp(qh->errexit); \
+    }else{ \
+        throw QhullError(QH_TRY_ERROR, "Already inside a QH_TRY_().  qh.NOerrexit is false"); \
+    } \
+    if(!QH_TRY_status) 
+
+#define QH_TRY_NO_THROW_(qh) \
+    int QH_TRY_status; \
+    if(qh->NOerrexit){ \
+        qh->NOerrexit= False; \
+        QH_TRY_status= setjmp(qh->errexit); \
+    }else{ \
+        QH_TRY_status= QH_TRY_ERROR; \
+    } \
+    if(!QH_TRY_status) 
 
 namespace orgQhull {
 
-#//defined here
+#//!\name Defined here
     //! QhullQh -- Qhull's global data structure, qhT, as a C++ class
-    //! See UsingLibQhull.h for C++/C interface to qhT
     class QhullQh;
 
+//! POD type equivalent to qhT.  No virtual members
 class QhullQh : public qhT {
 
-#//Constants
-    // Set ignored.  PointSet needs explicit dimension
-    // Facet from vertices or ridges.vertices.count
-    // Ridge from vertices.count
-    // Vertex stored in vertexT?  1->16?
-    // QhullPoint needs explicit dimension
+#//!\name Constants
+
+#//!\name Fields 
+private:
+    int                 qhull_status;   //! qh_ERRnone if valid
+    std::string         qhull_message;  //! Returned messages from libqhull_r
+    std::ostream *      error_stream;   //! overrides errorMessage, use appendQhullMessage()
+    std::ostream *      output_stream;  //! send output to stream
+    double              factor_epsilon; //!< Factor to increase ANGLEround and DISTround for hyperplane equality
 
-#//members (empty) -- POD type equivalent to qhT.  No data or virtual members
+    friend void         ::qh_fprintf(qhT *qh, FILE *fp, int msgcode, const char *fmt, ... );
+    
+    static const double default_factor_epsilon;  //!< Default factor_epsilon is 1.0
 
+#//!\name Attribute
 public:
-#//constructor, assignment, destructor, invariant
-    QhullQh();
-    ~QhullQh();
+    bool                useOutputStream; //! Set if using outputStream
+    // FIXUP QH11003 feasiblePoint useOutputStream as field or getter?
 
+#//!\name Constructors
+public:
+                        QhullQh();
+                        ~QhullQh();
 private:
-    //!disable copy constructor and assignment
+                        //!disable copy constructor and assignment
                         QhullQh(const QhullQh &);
-    QhullQh            &operator=(const QhullQh &);
+    QhullQh &           operator=(const QhullQh &);
+public:
+
+#//!\name GetSet
+    double              factorEpsilon() const { return factor_epsilon; }
+    void                setFactorEpsilon(double a) { factor_epsilon= a; }
+
+#//!\name Messaging
+    void                appendQhullMessage(const std::string &s);
+    void                clearQhullMessage();
+    std::string         qhullMessage() const;
+    bool                hasQhullMessage() const;
+    void                maybeThrowQhullMessage(int exitCode);
+    void                maybeThrowQhullMessage(int exitCode, int noThrow) throw();
+    int                 qhullStatus() const;
+    void                setErrorStream(std::ostream *os);
+    void                setOutputStream(std::ostream *os);
+
+#//!\name Methods
+    double              angleEpsilon() const { return this->ANGLEround*factor_epsilon; } //!< Epsilon for hyperplane angle equality
+    void                checkAndFreeQhullMemory();
+    double              distanceEpsilon() const { return this->DISTround*factor_epsilon; } //!< Epsilon for distance to hyperplane
 
 };//class QhullQh
 
 }//namespace orgQhull
 
 #endif // QHULLQH_H
diff --git a/src/libqhullcpp/QhullRidge.cpp b/src/libqhullcpp/QhullRidge.cpp
index b1f030e..610dd61 100644
--- a/src/libqhullcpp/QhullRidge.cpp
+++ b/src/libqhullcpp/QhullRidge.cpp
@@ -1,102 +1,110 @@
 /****************************************************************************
 **
 ** Copyright (c) 2008-2014 C.B. Barber. All rights reserved.
-** $Id: //main/2011/qhull/src/libqhullcpp/QhullRidge.cpp#4 $$Change: 1464 $
-** $DateTime: 2012/01/25 22:58:41 $$Author: bbarber $
+** $Id: //main/2011/qhull/src/libqhullcpp/QhullRidge.cpp#8 $$Change: 1797 $
+** $DateTime: 2014/12/15 17:23:41 $$Author: bbarber $
 **
 ****************************************************************************/
 
 #//! QhullRidge -- Qhull's ridge structure, ridgeT, as a C++ class
 
 #include "QhullSets.h"
 #include "QhullVertex.h"
 #include "QhullRidge.h"
+#include "Qhull.h"
 
 #ifdef _MSC_VER  // Microsoft Visual C++ -- warning level 4
 #pragma warning( disable : 4611)  // interaction between '_setjmp' and C++ object destruction is non-portable
 #pragma warning( disable : 4996)  // function was declared deprecated(strcpy, localtime, etc.)
 #endif
 
 namespace orgQhull {
 
-#//class statics
+#//!\name Class objects
 ridgeT QhullRidge::
 s_empty_ridge= {0,0,0,0,0,
                 0,0};
 
-#//Constructor, destructor, etc.
+#//!\name Constructors
 
-#//Accessors
+QhullRidge::QhullRidge(const Qhull &q)
+: qh_ridge(&s_empty_ridge)
+, qh_qh(q.qh())
+{
+}//Default
+
+QhullRidge::QhullRidge(const Qhull &q, ridgeT *r)
+: qh_ridge(r ? r : &s_empty_ridge)
+, qh_qh(q.qh())
+{
+}//ridgeT
+
+#//!\name foreach
 
 //! Return True if nextRidge3d
 //! Simplicial facets may have incomplete ridgeSets
-//! Does not use qh_qh or qh_errexit()
+//! Does not use qh_errexit()
 bool QhullRidge::
-hasNextRidge3d(const QhullFacet f) const
+hasNextRidge3d(const QhullFacet &f) const
 {
     vertexT *v= 0;
-    ridgeT *ridge= qh_nextridge3d(getRidgeT(), f.getFacetT(), &v);
+    ridgeT *ridge= qh_nextridge3d(qh_qh, getRidgeT(), f.getFacetT(), &v);
     return (ridge!=0);
 }//hasNextRidge3d
 
-
-
 //! Return next ridge and optional vertex for a 3d facet and ridge
-//! Does not use qh_qh or qh_errexit()
+//! Does not use qh_errexit()
 QhullRidge QhullRidge::
-nextRidge3d(const QhullFacet f, QhullVertex *nextVertex) const
+nextRidge3d(const QhullFacet &f, QhullVertex *nextVertex) const
 {
     vertexT *v= 0;
-    ridgeT *ridge= qh_nextridge3d(getRidgeT(), f.getFacetT(), &v);
+    ridgeT *ridge= qh_nextridge3d(qh_qh, getRidgeT(), f.getFacetT(), &v);
     if(!ridge){
         throw QhullError(10030, "Qhull error nextRidge3d:  missing next ridge for facet %d ridge %d.  Does facet contain ridge?", f.id(), id());
     }
     if(nextVertex!=0){
-        *nextVertex= QhullVertex(v);
+        *nextVertex= QhullVertex(qh_qh, v);
     }
-    return QhullRidge(ridge);
+    return QhullRidge(qh_qh, ridge);
 }//nextRidge3d
-
-
 }//namespace orgQhull
 
-#//Global functions
+#//!\name Global functions
 
 using std::endl;
 using std::ostream;
 using orgQhull::QhullRidge;
 using orgQhull::QhullVertex;
-using orgQhull::UsingLibQhull;
 
 ostream &
 operator<<(ostream &os, const QhullRidge &r)
 {
-    os << r.print(UsingLibQhull::NOqhRunId);
+    os << r.print("");
     return os;
 }//<< QhullRidge
 
-//! Duplicate of qh_printridge [io.c]
-//!  if pr.run_id==UsingLibQhull::NOqhRunId, no access to qh [needed for QhullVertex/QhullPoint]
+//! Duplicate of qh_printridge [io_r.c]
 ostream &
 operator<<(ostream &os, const QhullRidge::PrintRidge &pr)
 {
+    os << pr.print_message;
     QhullRidge r= *pr.ridge;
     os << "     - r" << r.id();
     if(r.getRidgeT()->tested){
         os << " tested";
     }
     if(r.getRidgeT()->nonconvex){
         os << " nonconvex";
     }
     os << endl;
-    os << r.vertices().print(pr.run_id, "           vertices:");
+    os << r.vertices().print("           vertices:");
     if(r.getRidgeT()->top && r.getRidgeT()->bottom){
         os << "           between f" << r.topFacet().id() << " and f" << r.bottomFacet().id() << endl;
     }else if(r.getRidgeT()->top){
         os << "           top f" << r.topFacet().id() << endl;
     }else if(r.getRidgeT()->bottom){
         os << "           bottom f" << r.bottomFacet().id() << endl;
     }
 
     return os;
 }//<< PrintRidge
diff --git a/src/libqhullcpp/QhullRidge.h b/src/libqhullcpp/QhullRidge.h
index 73ee9ad..d1fb3bd 100644
--- a/src/libqhullcpp/QhullRidge.h
+++ b/src/libqhullcpp/QhullRidge.h
@@ -1,110 +1,113 @@
 /****************************************************************************
 **
-** Copyright (c) 2008-2012 C.B. Barber. All rights reserved.
-** $Id: //main/2011/qhull/src/libqhullcpp/QhullRidge.h#6 $$Change: 1464 $
-** $DateTime: 2012/01/25 22:58:41 $$Author: bbarber $
+** Copyright (c) 2008-2014 C.B. Barber. All rights reserved.
+** $Id: //main/2011/qhull/src/libqhullcpp/QhullRidge.h#11 $$Change: 1800 $
+** $DateTime: 2014/12/17 21:46:45 $$Author: bbarber $
 **
 ****************************************************************************/
 
 #ifndef QHULLRIDGE_H
 #define QHULLRIDGE_H
 
 #include "QhullSet.h"
 #include "QhullVertex.h"
 #include "QhullVertexSet.h"
 #include "QhullFacet.h"
 extern "C" {
-    #include "libqhull/qhull_r.h"
+    #include "libqhullr/qhull_ra.h"
 }
 
 #include 
 
 namespace orgQhull {
 
-#//ClassRef
+#//!\name Used here
+    class Qhull;
     class QhullVertex;
     class QhullVertexSet;
     class QhullFacet;
 
-#//Types
+#//!\name Defined here
     //! QhullRidge -- Qhull's ridge structure, ridgeT [libqhull.h], as a C++ class
     class QhullRidge;
     typedef QhullSet  QhullRidgeSet;
     typedef QhullSetIterator  QhullRidgeSetIterator;
-
     // see QhullSets.h for QhullRidgeSet and QhullRidgeSetIterator -- avoids circular references
 
 /************************
 a ridge is hull_dim-1 simplex between two neighboring facets.  If the
 facets are non-simplicial, there may be more than one ridge between
 two facets.  E.G. a 4-d hypercube has two triangles between each pair
 of neighboring facets.
 
 topological information:
     vertices            a set of vertices
     top,bottom          neighboring facets with orientation
 
 geometric information:
     tested              True if ridge is clearly convex
     nonconvex           True if ridge is non-convex
 */
 
 class QhullRidge {
 
-#//Fields
-    ridgeT             *qh_ridge;
+#//!\name Defined here
+public:
+    typedef ridgeT *   base_type;  // for QhullRidgeSet
+
+#//!\name Fields
+private:
+    ridgeT *            qh_ridge;
+    QhullQh *           qh_qh;
 
-#//Class objects
+#//!\name Class objects
     static ridgeT       s_empty_ridge;
 
 public:
-#//Constants
+#//!\name Constants
 
-#//Constructors
-                        QhullRidge() : qh_ridge(&s_empty_ridge) {}
+#//!\name Constructors
+    explicit            QhullRidge(const Qhull &q);
+                        QhullRidge(const Qhull &q, ridgeT *r);
+    explicit            QhullRidge(QhullQh *qh) : qh_ridge(&s_empty_ridge), qh_qh(qh) {}
+                        QhullRidge(QhullQh *qh, ridgeT *r) : qh_ridge(r ? r : &s_empty_ridge), qh_qh(qh) {}
                         // Creates an alias.  Does not copy QhullRidge.  Needed for return by value and parameter passing
-                        QhullRidge(const QhullRidge &o) : qh_ridge(o.qh_ridge) {}
+                        QhullRidge(const QhullRidge &other) : qh_ridge(other.qh_ridge), qh_qh(other.qh_qh) {}
                         // Creates an alias.  Does not copy QhullRidge.  Needed for vector
-    QhullRidge         &operator=(const QhullRidge &o) { qh_ridge= o.qh_ridge; return *this; }
-                       ~QhullRidge() {}
-
-#//Conversion
-                        //Implicit conversion from ridgeT
-                        QhullRidge(ridgeT *r) : qh_ridge(r ? r : &s_empty_ridge) {}
-    ridgeT             *getRidgeT() const { return qh_ridge; }
-
-#//QhullSet
-    ridgeT             *getBaseT() const { return getRidgeT(); }
-
-#//getSet
-    QhullFacet          bottomFacet() const { return QhullFacet(qh_ridge->bottom); }
-    int                 dimension() const { return QhullSetBase::count(qh_ridge->vertices); }
-    int                 id() const { return qh_ridge->id; }
+    QhullRidge &        operator=(const QhullRidge &other) { qh_ridge= other.qh_ridge; qh_qh= other.qh_qh; return *this; }
+                        ~QhullRidge() {}
+
+#//!\name GetSet
+    QhullFacet          bottomFacet() const { return QhullFacet(qh_qh, qh_ridge->bottom); }
+    int                 dimension() const { return qh_qh->hull_dim; }
+    ridgeT *            getBaseT() const { return getRidgeT(); } //!< For QhullSet
+    ridgeT *            getRidgeT() const { return qh_ridge; }
+    countT              id() const { return qh_ridge->id; }
     bool                isDefined() const { return qh_ridge != &s_empty_ridge; }
-    bool                operator==(const QhullRidge &o) const { return qh_ridge==o.qh_ridge; }
-    bool                operator!=(const QhullRidge &o) const { return !operator==(o); }
-    QhullFacet          otherFacet(QhullFacet f) const { return QhullFacet(qh_ridge->top==f.getFacetT() ? qh_ridge->bottom : qh_ridge->top); }
-    QhullFacet          topFacet() const { return QhullFacet(qh_ridge->top); }
+    bool                operator==(const QhullRidge &other) const { return qh_ridge==other.qh_ridge; }
+    bool                operator!=(const QhullRidge &other) const { return !operator==(other); }
+    QhullFacet          otherFacet(const QhullFacet &f) const { return QhullFacet(qh_qh, (qh_ridge->top==f.getFacetT() ? qh_ridge->bottom : qh_ridge->top)); }
+    QhullFacet          topFacet() const { return QhullFacet(qh_qh, qh_ridge->top); }
 
-#//forEach
-    bool                hasNextRidge3d(const QhullFacet f) const;
-    QhullRidge          nextRidge3d(const QhullFacet f) const { return nextRidge3d(f, 0); }
-    QhullRidge          nextRidge3d(const QhullFacet f, QhullVertex *nextVertex) const;
-    QhullVertexSet      vertices() const { return QhullVertexSet(qh_ridge->vertices); }
+#//!\name foreach
+    bool                hasNextRidge3d(const QhullFacet &f) const;
+    QhullRidge          nextRidge3d(const QhullFacet &f) const { return nextRidge3d(f, 0); }
+    QhullRidge          nextRidge3d(const QhullFacet &f, QhullVertex *nextVertex) const;
+    QhullVertexSet      vertices() const { return QhullVertexSet(qh_qh, qh_ridge->vertices); }
 
-#//IO
+#//!\name IO
 
     struct PrintRidge{
         const QhullRidge *ridge;
-        int             run_id;
-                        PrintRidge(int qhRunId, const QhullRidge &r) : ridge(&r), run_id(qhRunId) {}
+        const char *    print_message;
+                        PrintRidge(const char *message, const QhullRidge &r) : ridge(&r), print_message(message) {}
     };//PrintRidge
-    PrintRidge          print(int qhRunId) const { return PrintRidge(qhRunId, *this); }
+    PrintRidge          print(const char* s) const { return PrintRidge(s, *this); }
 };//class QhullRidge
 
 }//namespace orgQhull
 
 std::ostream &operator<<(std::ostream &os, const orgQhull::QhullRidge &r); 
 std::ostream &operator<<(std::ostream &os, const orgQhull::QhullRidge::PrintRidge &pr);
 
 #endif // QHULLRIDGE_H
diff --git a/src/libqhullcpp/QhullSet.cpp b/src/libqhullcpp/QhullSet.cpp
index 29402a5..b664838 100644
--- a/src/libqhullcpp/QhullSet.cpp
+++ b/src/libqhullcpp/QhullSet.cpp
@@ -1,47 +1,61 @@
 /****************************************************************************
 **
 ** Copyright (c) 2008-2014 C.B. Barber. All rights reserved.
-** $Id: //main/2011/qhull/src/libqhullcpp/QhullSet.cpp#6 $$Change: 1663 $
-** $DateTime: 2014/01/19 17:59:16 $$Author: bbarber $
+** $Id: //main/2011/qhull/src/libqhullcpp/QhullSet.cpp#10 $$Change: 1799 $
+** $DateTime: 2014/12/17 16:17:40 $$Author: bbarber $
 **
 ****************************************************************************/
 
 #//! QhullSet -- Qhull's set structure, setT, as a C++ class
 
+#include "Qhull.h"
 #include "QhullError.h"
 #include "QhullSet.h"
 
 #ifdef _MSC_VER  // Microsoft Visual C++ -- warning level 4
 #endif
 
 namespace orgQhull {
 
-#//static members
+#//!\name Class objects
 
 setT QhullSetBase::
 s_empty_set;
 
-// Same code for qh_setsize [qset.c] and QhullSetBase::count
-int QhullSetBase::count(const setT *set)
+#//!\name Constructors
+
+QhullSetBase::
+QhullSetBase(const Qhull &q, setT *s) 
+: qh_set(s ? s : &s_empty_set)
+, qh_qh(q.qh())
 {
-    int size;
+}
+
+#//!\name Class methods
+
+// Same code for qh_setsize [qset_r.c] and QhullSetBase::count [static]
+countT QhullSetBase::
+count(const setT *set)
+{
+    countT size;
     const setelemT *sizep;
 
-    if (!set)
+    if (!set){
         return(0);
+    }
     sizep= SETsizeaddr_(set);
     if ((size= sizep->i)) {
         size--;
         if (size > set->maxsize) {
             // FIXUP QH11022 How to add additional output to a error? -- qh_setprint(qhmem.ferr, "set: ", set);
             throw QhullError(10032, "QhullSet internal error: current set size %d is greater than maximum size %d\n",
                 size, set->maxsize);
         }
-    }else
+    }else{
         size= set->maxsize;
+    }
     return size;
-}
-
+}//count
 
 }//namespace orgQhull
 
diff --git a/src/libqhullcpp/QhullSet.h b/src/libqhullcpp/QhullSet.h
index 7ef5d8b..e6cee15 100644
--- a/src/libqhullcpp/QhullSet.h
+++ b/src/libqhullcpp/QhullSet.h
@@ -1,360 +1,453 @@
 /****************************************************************************
 **
-** Copyright (c) 2008-2012 C.B. Barber. All rights reserved.
-** $Id: //main/2011/qhull/src/libqhullcpp/QhullSet.h#7 $$Change: 1464 $
-** $DateTime: 2012/01/25 22:58:41 $$Author: bbarber $
+** Copyright (c) 2008-2014 C.B. Barber. All rights reserved.
+** $Id: //main/2011/qhull/src/libqhullcpp/QhullSet.h#15 $$Change: 1801 $
+** $DateTime: 2014/12/17 22:37:12 $$Author: bbarber $
 **
 ****************************************************************************/
 
 #ifndef QhullSet_H
 #define QhullSet_H
 
 #include "QhullError.h"
+#include "QhullQh.h"
 extern "C" {
-    #include "libqhull/qhull_r.h"
+    #include "libqhullr/qhull_ra.h"
 }
 
 
 #ifndef QHULL_NO_STL
 #include 
 #endif
 
 #ifdef QHULL_USES_QT
  #include 
 #endif
 
 namespace orgQhull {
 
-#//Type
-    class QhullSetBase;  //! Base class for QhullSet
-    //! QhullSet -- A read-only wrapper to Qhull's collection class, setT.
-    //!  QhullSet is similar to STL's  and Qt's QVector.
-    //!  QhullSet is unrelated to STL and Qt's set and map types (e.g., QSet and QMap)
-    //!  For STL efficiency, QhullSet caches endPointer()
-    //!  T must be a pointer type
-    //!  A QhullSet does not own its contents -- erase(), clear(), removeFirst(), removeLast(), pop_back(), pop_front(), fromStdList() not defined
-    //!  Qhull's FOREACHelement_() [qset.h] is more efficient than QhullSet.  It uses a NULL terminator instead of an end pointer.  STL requires an end pointer.
-    //!  Derived from QhullLinkedList.h and Qt/core/tools/qvector.h
+#//!\name Used here
+    class Qhull;
 
+#//!\name Defined here
+    class QhullSetBase;  //! Base class for QhullSet
+    //! QhullSet defined below
     //! QhullSetIterator defined below
-    //See: QhullPointSet, QhullLinkedList
+    //! \see QhullPointSet, QhullLinkedList
 
+//! QhullSetBase is a wrapper for Qhull's setT of void* pointers 
+//! \see libqhullr/qset.h
 class QhullSetBase {
 
 private:
-#//Fields --
-    setT               *qh_set;
+#//!\name Fields --
+    setT *              qh_set;
+    QhullQh *           qh_qh;             //! Provides access to setT memory allocator
 
-#//Class objects
-    static setT         s_empty_set;  //! Workaround for no setT allocator.  Used if setT* is NULL
+#//!\name Class objects
+    static setT         s_empty_set;  //! Used if setT* is NULL
 
 public:
-#//Class methods
-    static int          count(const setT *set);
-    //s may be null
-    static bool         isEmpty(const setT *s) { return SETempty_(s); }
-
-
-#//Constructors
+#//!\name Constructors
+                        QhullSetBase(const Qhull &q, setT *s);
+                        QhullSetBase(QhullQh *qh, setT *s) : qh_set(s ? s : &s_empty_set), qh_qh(qh) {}
                         //! Copy constructor copies the pointer but not the set.  Needed for return by value and parameter passing.
-                        QhullSetBase(const QhullSetBase &o) : qh_set(o.qh_set) {}
-    explicit            QhullSetBase(setT *s) : qh_set(s ? s : &s_empty_set) {}
-                       ~QhullSetBase() {}
+                        QhullSetBase(const QhullSetBase &other) : qh_set(other.qh_set), qh_qh(other.qh_qh) {}
+    QhullSetBase &      operator=(const QhullSetBase &other) { qh_set= other.qh_set; qh_qh= other.qh_qh; return *this; }
+                        ~QhullSetBase() {}
 
 private:
                         //!disabled since memory allocation for QhullSet not defined
                         QhullSetBase() {}
-                        //!disabled since qs= qs2 is ambiguous (pointer vs. contents)
-    QhullSetBase       &operator=(const QhullSetBase &);
 public:
 
-#//Conversions
-                        //! Not type-safe since setT may contain any type
-    void                defineAs(setT *s) { qh_set= s ? s : &s_empty_set; }
-    setT               *getSetT() const { return qh_set; }
-    setT              **referenceSetT() { return &qh_set; }
-
-#//Read-only
-    int                 count() const { return QhullSetBase::count(qh_set); }
-    bool                empty() const { return SETfirst_(qh_set)==0; }
-    bool                isEmpty() const { return empty(); }
-    size_t              size() const { return count(); }
-
-#//Element
+#//!\name GetSet
+    countT              count() const { return QhullSetBase::count(qh_set); }
+    void                defineAs(setT *s) { qh_set= s ? s : &s_empty_set; } //!< Not type-safe since setT may contain any type
+    void                forceEmpty() { qh_set= &s_empty_set; }
+    setT *              getSetT() const { return qh_set; }
+    bool                isEmpty() const { return SETempty_(qh_set); }
+    QhullQh *           qh() const { return qh_qh; }
+    setT **             referenceSetT() { return &qh_set; }
+    size_t              size() const { return QhullSetBase::count(qh_set); }
+
+#//!\name Element
 protected:
-    void              **beginPointer() const { return &qh_set->e[0].p; }
-    void              **elementPointer(int idx) const { QHULL_ASSERT(idx>=0 && idxmaxsize); return &SETelem_(qh_set, idx); }
+    void **             beginPointer() const { return &qh_set->e[0].p; }
+    void **             elementPointer(countT idx) const { QHULL_ASSERT(idx>=0 && idxmaxsize); return &SETelem_(qh_set, idx); }
                         //! Always points to 0
-    void              **endPointer() const { return qh_setendpointer(qh_set); }
+    void **             endPointer() const { return qh_setendpointer(qh_set); }
+
+#//!\name Class methods
+    static countT       count(const setT *set);
+    //s may be null
+    static bool         isEmpty(const setT *s) { return SETempty_(s); }
 };//QhullSetBase
 
 
-//! set of pointers to baseT, T.getBaseT()
+//! QhullSet -- A read-only wrapper to Qhull's collection class, setT.
+//!  QhullSet is similar to STL's  and Qt's QVector.
+//!  QhullSet is unrelated to STL and Qt's set and map types (e.g., QSet and QMap)
+//!  T is a Qhull type that defines 'base_type' and getBaseT() (e.g., QhullFacet with base_type 'facetT *'
+//!  A QhullSet does not own its contents -- erase(), clear(), removeFirst(), removeLast(), pop_back(), pop_front(), fromStdList() not defined
+//!  QhullSetIterator is faster than STL-style iterator/const_iterator
+//!  Qhull's FOREACHelement_() [qset_r.h] maybe more efficient than QhullSet.  It uses a NULL terminator instead of an end pointer.  STL requires an end pointer.
+//!  Derived from QhullLinkedList.h and Qt/core/tools/qvector.h
 template 
 class QhullSet : public QhullSetBase {
 
 private:
-#//Fields -- see QhullSetBase
+#//!\name Fields -- see QhullSetBase
 
-#//Class objects
+#//!\name Class objects
     static setT         s_empty_set;  //! Workaround for no setT allocator.  Used if setT* is NULL
 
 public:
-#//Subtypes
-    typedef T         *iterator;
-    typedef const T   *const_iterator;
+#//!\name Defined here
+    class iterator;
+    class const_iterator;
     typedef typename QhullSet::iterator Iterator;
     typedef typename QhullSet::const_iterator ConstIterator;
 
-#//Class methods
-    static int          count(const setT *set);
-                        //s may be null
-    static bool         isEmpty(const setT *s) { return SETempty_(s); }
-
-#//Constructors
-                        //Copy constructor copies pointer but not contents.  Needed for return by value.
-                        QhullSet(const QhullSet &o) : QhullSetBase(o) {}
+#//!\name Constructors
+                        QhullSet(const Qhull &q, setT *s) : QhullSetBase(q, s) { }
+                        QhullSet(QhullQh *qh, setT *s) : QhullSetBase(qh, s) { }
                         //Conversion from setT* is not type-safe.  Implicit conversion for void* to T
-    explicit            QhullSet(setT *s) : QhullSetBase(s) { QHULL_ASSERT(sizeof(T)==sizeof(void *)); }
-                       ~QhullSet() {}
+                        //Copy constructor copies pointer but not contents.  Needed for return by value.
+                        QhullSet(const QhullSet &other) : QhullSetBase(other) {}
+    QhullSet &       operator=(const QhullSet &other) { QhullSetBase::operator=(other); return *this; }
+                        ~QhullSet() {}
 
 private:
-                        //!Disable default constructor and copy assignment.  See QhullSetBase
+                        //!Disable default constructor.  See QhullSetBase
                         QhullSet();
-    QhullSet        &operator=(const QhullSet &);
 public:
 
-#//Conversion
+#//!\name Conversion
 
 #ifndef QHULL_NO_STL
-    std::vector      toStdVector() const;
+    std::vector toStdVector() const;
 #endif
 #ifdef QHULL_USES_QT
-    QList            toQList() const;
+    QList toQList() const;
 #endif
 
-#//Read-only -- see QhullSetBase for count(), empty(), isEmpty(), size()
+#//!\name GetSet -- see QhullSetBase for count(), empty(), isEmpty(), size()
     using QhullSetBase::count;
     using QhullSetBase::isEmpty;
     // operator== defined for QhullSets of the same type
     bool                operator==(const QhullSet &other) const { return qh_setequal(getSetT(), other.getSetT()); }
     bool                operator!=(const QhullSet &other) const { return !operator==(other); }
 
-#//Element access
-    const T            &at(int idx) const { return operator[](idx); }
-    T                  &back() { return last(); }
-    T                  &back() const { return last(); }
+#//!\name Element access
+    const T             at(countT idx) const { return operator[](idx); }
+    T                   back() { return last(); }
+    T                   back() const { return last(); }
     //! end element is NULL
-    const T            *constData() const { return constBegin(); }
-    T                  *data() { return begin(); }
-    const T            *data() const { return begin(); }
-    T                  &first() { QHULL_ASSERT(!isEmpty()); return *begin(); }
-    const T            &first() const { QHULL_ASSERT(!isEmpty()); return *begin(); }
-    T                  &front() { return first(); }
-    const T            &front() const { return first(); }
-    T                  &last() { QHULL_ASSERT(!isEmpty()); return *(end()-1); }
-    const T            &last() const {  QHULL_ASSERT(!isEmpty()); return *(end()-1); }
+    const typename typename T::base_type * constData() const { return reinterpret_cast(beginPointer()); }
+    typename T::base_type *     data() { return reinterpret_cast(beginPointer()); }
+    typename T::base_type *     data() const { return reinterpret_cast(beginPointer()); }
+    typename T::base_type *     endData() { return reinterpret_cast(endPointer()); }
+    typename T::base_type *     endData() const { return reinterpret_cast(endPointer()); }
+    T                   first() { QHULL_ASSERT(!isEmpty()); return T(qh(), *data()); }
+    const T             first() const { QHULL_ASSERT(!isEmpty()); return T(qh(), *data()); }
+    T                   front() { return first(); }
+    const T             front() const { return first(); }
+    T                   last() { QHULL_ASSERT(!isEmpty()); return T(qh(), *(endData()-1)); }
+    const T             last() const {  QHULL_ASSERT(!isEmpty()); return T(qh(), *(endData()-1)); }
     // mid() not available.  No setT constructor
-    T                  &operator[](int idx) { T *n= reinterpret_cast(elementPointer(idx)); QHULL_ASSERT(idx>=0 && n < reinterpret_cast(endPointer())); return *n; }
-    const T            &operator[](int idx) const { const T *n= reinterpret_cast(elementPointer(idx)); QHULL_ASSERT(idx>=0 && n < reinterpret_cast(endPointer())); return *n; }
-    T                  &second() { return operator[](1); }
-    const T            &second() const { return operator[](1); }
-    T                   value(int idx) const;
-    T                   value(int idx, const T &defaultValue) const;
-
-#//Read-write -- Not available, no setT constructor
-
-#//iterator
-    iterator            begin() { return iterator(beginPointer()); }
-    const_iterator      begin() const { return const_iterator(beginPointer()); }
-    const_iterator      constBegin() const { return const_iterator(beginPointer()); }
-    const_iterator      constEnd() const { return const_iterator(endPointer()); }
-    iterator            end() { return iterator(endPointer()); }
-    const_iterator      end() const { return const_iterator(endPointer()); }
-
-#//Search
+    T                   operator[](countT idx) { typename T::base_type *p= reinterpret_cast(elementPointer(idx)); QHULL_ASSERT(idx>=0 && p < endData()); return T(qh(), *p); }
+    const T             operator[](countT idx) const { const typename T::base_type *p= reinterpret_cast(elementPointer(idx)); QHULL_ASSERT(idx>=0 && p < endData()); return T(qh(), *p); }
+    T                   second() { return operator[](1); }
+    const T             second() const { return operator[](1); }
+    T                   value(countT idx) const;
+    T                   value(countT idx, const T &defaultValue) const;
+
+#//!\name Read-write -- Not available, no setT constructor
+
+#//!\name iterator
+    iterator            begin() { return iterator(qh(), reinterpret_cast(beginPointer())); }
+    const_iterator      begin() const { return const_iterator(qh(), data()); }
+    const_iterator      constBegin() const { return const_iterator(qh(), data()); }
+    const_iterator      constEnd() const { return const_iterator(qh(), endData()); }
+    iterator            end() { return iterator(qh(), endData()); }
+    const_iterator      end() const { return const_iterator(qh(), endData()); }
+
+#//!\name Search
     bool                contains(const T &t) const;
-    int                 count(const T &t) const;
-    int                 indexOf(const T &t) const { /* no qh_qh */ return qh_setindex(getSetT(), t.getBaseT()); }
-    int                 lastIndexOf(const T &t) const;
+    countT              count(const T &t) const;
+    countT              indexOf(const T &t) const { /* no qh_qh */ return qh_setindex(getSetT(), t.getBaseT()); }
+    countT              lastIndexOf(const T &t) const;
+
+    // before const_iterator for conversion with comparison operators
+    class iterator {
+        friend class const_iterator;
+    private:
+        typename T::base_type *  i;  // First for debugger
+        QhullQh *       qh_qh;
+
+    public:
+        typedef ptrdiff_t       difference_type;
+        typedef std::bidirectional_iterator_tag  iterator_category;
+        typedef T               value_type;
+
+                        iterator(QhullQh *qh, typename T::base_type *p) : i(p), qh_qh(qh) {}
+                        iterator(const iterator &o) : i(o.i), qh_qh(o.qh_qh) {}
+        iterator &      operator=(const iterator &o) { i= o.i; qh_qh= o.qh_qh; return *this; }
+
+        T               operator*() const { return T(qh_qh, *i); }
+        //operator->() n/a, value-type
+        T               operator[](countT idx) { return T(qh_qh, *(i+idx)); } //!< No error checking
+        bool            operator==(const iterator &o) const { return i == o.i; }
+        bool            operator!=(const iterator &o) const { return !operator==(o); }
+        bool            operator==(const const_iterator &o) const { return (i==reinterpret_cast(o).i); }
+        bool            operator!=(const const_iterator &o) const { return !operator==(o); }
+
+        //! Assumes same point set
+        countT          operator-(const iterator &o) { return (countT)(i-o.i); } //WARN64
+        bool            operator>(const iterator &o) const { return i>o.i; }
+        bool            operator<=(const iterator &o) const { return !operator>(o); }
+        bool            operator<(const iterator &o) const { return i=(const iterator &o) const { return !operator<(o); }
+        bool            operator>(const const_iterator &o) const { return (i > reinterpret_cast(o).i); }
+        bool            operator<=(const const_iterator &o) const { return !operator>(o); }
+        bool            operator<(const const_iterator &o) const { return (i < reinterpret_cast(o).i); }
+        bool            operator>=(const const_iterator &o) const { return !operator<(o); }
+
+        //! No error checking
+        iterator &      operator++() { ++i; return *this; }
+        iterator        operator++(int) { iterator o= *this; ++i; return o; }
+        iterator &      operator--() { --i; return *this; }
+        iterator        operator--(int) { iterator o= *this; --i; return o; }
+        iterator        operator+(countT j) const { return iterator(qh_qh, i+j); }
+        iterator        operator-(countT j) const { return operator+(-j); }
+        iterator &      operator+=(countT j) { i += j; return *this; }
+        iterator &      operator-=(countT j) { i -= j; return *this; }
+    };//QhullPointSet::iterator
+
+    class const_iterator {
+    private:
+        typename T::base_type *  i;  // First for debugger
+        QhullQh *       qh_qh;
+
+    public:
+        typedef ptrdiff_t       difference_type;
+        typedef std::random_access_iterator_tag  iterator_category;
+        typedef T               value_type;
+
+                        const_iterator(QhullQh *qh, typename T::base_type * p) : i(p), qh_qh(qh) {}
+                        const_iterator(const const_iterator &o) : i(o.i), qh_qh(o.qh_qh) {}
+                        const_iterator(const iterator &o) : i(o.i), qh_qh(o.qh_qh) {}
+        const_iterator &operator=(const const_iterator &o) { i= o.i; qh_qh= o.qh_qh; return *this; }
+
+        T               operator*() const { return T(qh_qh, *i); }
+        T               operator[](countT idx) { return T(qh_qh, *(i+idx)); }  //!< No error checking
+        //operator->() n/a, value-type
+        bool            operator==(const const_iterator &o) const { return i == o.i; }
+        bool            operator!=(const const_iterator &o) const { return !operator==(o); }
+
+        //! Assumes same point set
+        countT          operator-(const const_iterator &o) { return (countT)(i-o.i); } //WARN64
+        bool            operator>(const const_iterator &o) const { return i>o.i; }
+        bool            operator<=(const const_iterator &o) const { return !operator>(o); }
+        bool            operator<(const const_iterator &o) const { return i=(const const_iterator &o) const { return !operator<(o); }
+
+        //!< No error checking
+        const_iterator &operator++() { ++i; return *this; }
+        const_iterator  operator++(int) { const_iterator o= *this; ++i; return o; }
+        const_iterator &operator--() { --i; return *this; }
+        const_iterator  operator--(int) { const_iterator o= *this; --i; return o; }
+        const_iterator  operator+(int j) const { return const_iterator(qh_qh, i+j); }
+        const_iterator  operator-(int j) const { return operator+(-j); }
+        const_iterator &operator+=(int j) { i += j; return *this; }
+        const_iterator &operator-=(int j) { i -= j; return *this; }
+    };//QhullPointSet::const_iterator
 
 };//class QhullSet
 
-// FIXUP? can't use QHULL_DECLARE_SEQUENTIAL_ITERATOR because it is not a template
 
+//! Faster then interator/const_iterator due to T::base_type
 template 
 class QhullSetIterator {
 
-#//Subtypes
+#//!\name Subtypes
     typedef typename QhullSet::const_iterator const_iterator;
 
 private:
-#//Fields
-    const_iterator      i;
-    const_iterator      begin_i;
-    const_iterator      end_i;
+#//!\name Fields
+    typename T::base_type *  i;  // First for debugger
+    typename T::base_type *  begin_i;  // must be initialized after i 
+    typename T::base_type *  end_i; 
+    QhullQh *                qh_qh;
 
 public:
-#//Constructors
-                        QhullSetIterator(const QhullSet &s) : i(s.begin()), begin_i(i), end_i(s.end()) {}
-                        QhullSetIterator(const QhullSetIterator &o) : i(o.i), begin_i(o.begin_i), end_i(o.end_i) {}
-    QhullSetIterator &operator=(const QhullSetIterator &o) { i= o.i; begin_i= o.begin_i; end_i= o.end_i; return *this; }
+#//!\name Constructors
+                        QhullSetIterator(const QhullSet &s) : i(s.data()), begin_i(i), end_i(s.endData()), qh_qh(s.qh()) {}
+                        QhullSetIterator(const QhullSetIterator &o) : i(o.i), begin_i(o.begin_i), end_i(o.end_i), qh_qh(o.qh_qh) {}
+    QhullSetIterator &operator=(const QhullSetIterator &o) { i= o.i; begin_i= o.begin_i; end_i= o.end_i; qh_qh= o.qh_qh; return *this; }
 
-#//ReadOnly
-    int                 countRemaining() { return (int)(end_i-begin_i); } // WARN64
+#//!\name ReadOnly
+    countT              countRemaining() { return (countT)(end_i-i); } // WARN64
 
-#//Search
+#//!\name Search
     bool                findNext(const T &t);
     bool                findPrevious(const T &t);
 
-#//Foreach
+#//!\name Foreach
     bool                hasNext() const { return i != end_i; }
     bool                hasPrevious() const { return i != begin_i; }
-    T                   next() { return *i++; }
-    T                   peekNext() const { return *i; }
-    T                   peekPrevious() const { const_iterator p = i; return *--p; }
-    T                   previous() { return *--i; }
+    T                   next() { return T(qh_qh, *i++); }
+    T                   peekNext() const { return T(qh_qh, *i); }
+    T                   peekPrevious() const { typename T::base_type *p = i; return T(qh_qh, *--p); }
+    T                   previous() { return T(qh_qh, *--i); }
     void                toBack() { i = end_i; }
     void                toFront() { i = begin_i; }
 };//class QhullSetIterator
 
-#//== Definitions =========================================
+#//!\name == Definitions =========================================
+
+#//!\name Conversions
 
-#//Conversion
+// See qt-qhull.cpp for QList conversion
 
 #ifndef QHULL_NO_STL
 template 
 std::vector QhullSet::
 toStdVector() const
 {
-    QhullSetIterator i(*this);
+    QhullSet::const_iterator i= begin();
+    QhullSet::const_iterator e= end();
     std::vector vs;
-    vs.reserve(i.countRemaining());
-    while(i.hasNext()){
-        vs.push_back(i.next());
+    while(i!=e){
+        vs.push_back(*i++);
     }
     return vs;
 }//toStdVector
-#endif
+#endif //QHULL_NO_STL
 
 #ifdef QHULL_USES_QT
 template 
 QList QhullSet::
 toQList() const
 {
-    QhullSetIterator i(*this);
+    QhullSet::const_iterator i= begin();
+    QhullSet::const_iterator e= end();
     QList vs;
-    while(i.hasNext()){
-        vs.append(i.next());
+    while(i!=e){
+        vs.append(*i++);
     }
     return vs;
 }//toQList
 #endif
 
-#//Element
+#//!\name Element
 
 template 
 T QhullSet::
-value(int idx) const
+value(countT idx) const
 {
     // Avoid call to qh_setsize() and assert in elementPointer()
-    const T *n= reinterpret_cast(&SETelem_(getSetT(), idx));
-    return (idx>=0 && n(&SETelem_(getSetT(), idx));
+    return (idx>=0 && p
 T QhullSet::
-value(int idx, const T &defaultValue) const
+value(countT idx, const T &defaultValue) const
 {
     // Avoid call to qh_setsize() and assert in elementPointer()
-    const T *n= reinterpret_cast(&SETelem_(getSetT(), idx));
-    return (idx>=0 && n(&SETelem_(getSetT(), idx));
+    return (idx>=0 && p
 bool QhullSet::
 contains(const T &t) const
 {
     setT *s= getSetT();
-    void *e= t.getBaseT();  // contains() is not inline for better error reporting
-    int result= qh_setin(s, e);
+    void *p= t.getBaseT();  // contains() is not inline for better error reporting
+    int result= qh_setin(s, p);
     return result!=0;
 }//contains
 
 template 
-int QhullSet::
+countT QhullSet::
 count(const T &t) const
 {
-    int c= 0;
-    const T *i= data();
-    const T *e= end();
+    countT n= 0;
+    const typename T::base_type *i= data();
+    const typename T::base_type *e= endData();
+    typename T::base_type p= t.getBaseT();
     while(i
-int QhullSet::
+countT QhullSet::
 lastIndexOf(const T &t) const
 {
-    const T *b= begin();
-    const T *i= end();
+    const typename T::base_type *b= data();
+    const typename T::base_type *i= endData();
+    typename T::base_type p= t.getBaseT();
     while(--i>=b){
-        if(*i==t){
+        if(*i==p){
             break;
         }
     }
-    return (int)(i-b); // WARN64
+    return (countT)(i-b); // WARN64
 }//lastIndexOf
 
-#//QhullSetIterator
+#//!\name QhullSetIterator
 
 template 
 bool QhullSetIterator::
 findNext(const T &t)
 {
+    typename T::base_type p= t.getBaseT();
     while(i!=end_i){
-        if(*(++i)==t){
+        if(*(++i)==p){
             return true;
         }
     }
     return false;
 }//findNext
 
 template 
 bool QhullSetIterator::
 findPrevious(const T &t)
 {
+    typename T::base_type p= t.getBaseT();
     while(i!=begin_i){
-        if(*(--i)==t){
+        if(*(--i)==p){
             return true;
         }
     }
     return false;
 }//findPrevious
 
 }//namespace orgQhull
 
 
-#//== Global namespace =========================================
+#//!\name == Global namespace =========================================
 
 template 
 std::ostream &
 operator<<(std::ostream &os, const orgQhull::QhullSet &qs)
 {
-    const T *i= qs.begin();
-    const T *e= qs.end();
+    typename T::base_type *i= qs.data();
+    typename T::base_type *e= qs.endData();
     while(i!=e){
-        os << *i;
-        ++i;
+        os << T(qs.qh(), *i++);
     }
     return os;
 }//operator<<
 
 #endif // QhullSet_H
diff --git a/src/libqhullcpp/QhullSets.h b/src/libqhullcpp/QhullSets.h
index 0eb9f99..1f388e2 100644
--- a/src/libqhullcpp/QhullSets.h
+++ b/src/libqhullcpp/QhullSets.h
@@ -1,27 +1,27 @@
 /****************************************************************************
 **
-** Copyright (c) 2008-2012 C.B. Barber. All rights reserved.
-** $Id: //main/2011/qhull/src/libqhullcpp/QhullSets.h#3 $$Change: 1464 $
-** $DateTime: 2012/01/25 22:58:41 $$Author: bbarber $
+** Copyright (c) 2008-2014 C.B. Barber. All rights reserved.
+** $Id: //main/2011/qhull/src/libqhullcpp/QhullSets.h#4 $$Change: 1707 $
+** $DateTime: 2014/03/26 09:42:11 $$Author: bbarber $
 **
 ****************************************************************************/
 
 #ifndef QHULLSETS_H
 #define QHULLSETS_H
 
 #include "QhullSet.h"
 
 namespace orgQhull {
 
     //See: QhullFacetSet.h
     //See: QhullPointSet.h
     //See: QhullVertexSet.h
 
     // Avoid circular references between QhullFacet, QhullRidge, and QhullVertex
     class QhullRidge;
     typedef QhullSet  QhullRidgeSet;
     typedef QhullSetIterator  QhullRidgeSetIterator;
 
 }//namespace orgQhull
 
 #endif // QHULLSETS_H
diff --git a/src/libqhullcpp/QhullStat.h b/src/libqhullcpp/QhullStat.h
index d4c2a91..685adb3 100644
--- a/src/libqhullcpp/QhullStat.h
+++ b/src/libqhullcpp/QhullStat.h
@@ -1,52 +1,52 @@
 /****************************************************************************
 **
-** Copyright (c) 2008-2012 C.B. Barber. All rights reserved.
-** $Id: //main/2011/qhull/src/libqhullcpp/QhullStat.h#6 $$Change: 1464 $
-** $DateTime: 2012/01/25 22:58:41 $$Author: bbarber $
+** Copyright (c) 2008-2014 C.B. Barber. All rights reserved.
+** $Id: //main/2011/qhull/src/libqhullcpp/QhullStat.h#8 $$Change: 1707 $
+** $DateTime: 2014/03/26 09:42:11 $$Author: bbarber $
 **
 ****************************************************************************/
 
 #ifndef QHULLSTAT_H
 #define QHULLSTAT_H
 
 extern "C" {
-    #include "libqhull/qhull_r.h"
+    #include "libqhullr/qhull_ra.h"
 }
 
 #include 
 #include 
 
 namespace orgQhull {
 
-#//defined here
+#//!\name defined here
     //! QhullStat -- Qhull's statistics, qhstatT, as a C++ class
     //! Statistics defined with zzdef_() control Qhull's behavior, summarize its result, and report precision problems.
     class QhullStat;
 
 class QhullStat : public qhstatT {
 
 private:
-#//Fields (empty) -- POD type equivalent to qhstatT.  No data or virtual members
+#//!\name Fields (empty) -- POD type equivalent to qhstatT.  No data or virtual members
 
 public:
-#//Constants
+#//!\name Constants
 
-#//class methods
+#//!\name class methods
     static void         clearStatistics();
 
-#//constructor, assignment, destructor, invariant
+#//!\name constructor, assignment, destructor, invariant
                         QhullStat();
-                       ~QhullStat();
+                        ~QhullStat();
 
 private:
     //!disable copy constructor and assignment
                         QhullStat(const QhullStat &);
-    QhullStat          &operator=(const QhullStat &);
+    QhullStat &         operator=(const QhullStat &);
 public:
 
-#//Access
+#//!\name Access
 };//class QhullStat
 
 }//namespace orgQhull
 
 #endif // QHULLSTAT_H
diff --git a/src/libqhullcpp/QhullVertex.cpp b/src/libqhullcpp/QhullVertex.cpp
index a62f7b5..88e02a0 100644
--- a/src/libqhullcpp/QhullVertex.cpp
+++ b/src/libqhullcpp/QhullVertex.cpp
@@ -1,94 +1,106 @@
 /****************************************************************************
 **
 ** Copyright (c) 2008-2014 C.B. Barber. All rights reserved.
-** $Id: //main/2011/qhull/src/libqhullcpp/QhullVertex.cpp#3 $$Change: 1464 $
-** $DateTime: 2012/01/25 22:58:41 $$Author: bbarber $
+** $Id: //main/2011/qhull/src/libqhullcpp/QhullVertex.cpp#9 $$Change: 1799 $
+** $DateTime: 2014/12/17 16:17:40 $$Author: bbarber $
 **
 ****************************************************************************/
 
 #//! QhullVertex -- Qhull's vertex structure, vertexT, as a C++ class
 
-#include "UsingLibQhull.h"
+#include "Qhull.h"
 #include "QhullPoint.h"
 #include "QhullFacetSet.h"
 #include "QhullVertex.h"
-#include "QhullVertexSet.h"
 #include "QhullFacet.h"
 
 #ifdef _MSC_VER  // Microsoft Visual C++ -- warning level 4
 #pragma warning( disable : 4611)  // interaction between '_setjmp' and C++ object destruction is non-portable
 #pragma warning( disable : 4996)  // function was declared deprecated(strcpy, localtime, etc.)
 #endif
 
 namespace orgQhull {
 
-#//class statics
+#//!\name Class objects
 vertexT QhullVertex::
 s_empty_vertex= {0,0,0,0,0,
                  0,0,0,0,0,
-                 0,0};
+                 0};
 
-#//ForEach
+#//!\name Constructors
+
+QhullVertex::QhullVertex(const Qhull &q)
+: qh_vertex(&s_empty_vertex)
+, qh_qh(q.qh())
+{
+}//Default
+
+QhullVertex::QhullVertex(const Qhull &q, vertexT *v)
+: qh_vertex(v ? v : &s_empty_vertex)
+, qh_qh(q.qh())
+{
+}//vertexT
+
+#//!\name foreach
 
 //! Return neighboring facets for a vertex
 //! If neither merging nor Voronoi diagram, requires Qhull::defineVertexNeighborFacets() beforehand.
 QhullFacetSet QhullVertex::
 neighborFacets() const
 {
     if(!neighborFacetsDefined()){
         throw QhullError(10034, "Qhull error: neighboring facets of vertex %d not defined.  Please call Qhull::defineVertexNeighborFacets() beforehand.", id());
     }
-    return QhullFacetSet(qh_vertex->neighbors);
+    return QhullFacetSet(qh_qh, qh_vertex->neighbors);
 }//neighborFacets
 
 }//namespace orgQhull
 
-#//Global functions
+#//!\name Global functions
 
 using std::endl;
 using std::ostream;
 using std::string;
 using std::vector;
 using orgQhull::QhullPoint;
 using orgQhull::QhullFacet;
 using orgQhull::QhullFacetSet;
 using orgQhull::QhullFacetSetIterator;
 using orgQhull::QhullVertex;
-using orgQhull::UsingLibQhull;
 
-//! Duplicate of qh_printvertex [io.c]
+//! Duplicate of qh_printvertex [io_r.c]
 ostream &
 operator<<(ostream &os, const QhullVertex::PrintVertex &pr)
 {
     QhullVertex v= *pr.vertex;
     QhullPoint p= v.point();
-    os << "- p" << p.id(pr.run_id) << " (v" << v.id() << "): ";
+    os << "- p" << p.id() << " (v" << v.id() << "): ";
     const realT *c= p.coordinates();
     for(int k= p.dimension(); k--; ){
         os << " " << *c++; // FIXUP QH11010 %5.2g
     }
     if(v.getVertexT()->deleted){
         os << " deleted";
     }
     if(v.getVertexT()->delridge){
         os << " ridgedeleted";
     }
     os << endl;
     if(v.neighborFacetsDefined()){
         QhullFacetSetIterator i= v.neighborFacets();
         if(i.hasNext()){
             os << " neighborFacets:";
-            int count= 0;
+            countT count= 0;
             while(i.hasNext()){
                 if(++count % 100 == 0){
                     os << endl << "     ";
                 }
                 QhullFacet f= i.next();
                 os << " f" << f.id();
             }
             os << endl;
         }
     }
     return os;
 }//<< PrintVertex
 
diff --git a/src/libqhullcpp/QhullVertex.h b/src/libqhullcpp/QhullVertex.h
index 138514b..4a8117b 100644
--- a/src/libqhullcpp/QhullVertex.h
+++ b/src/libqhullcpp/QhullVertex.h
@@ -1,103 +1,105 @@
 /****************************************************************************
 **
-** Copyright (c) 2008-2012 C.B. Barber. All rights reserved.
-** $Id: //main/2011/qhull/src/libqhullcpp/QhullVertex.h#6 $$Change: 1464 $
-** $DateTime: 2012/01/25 22:58:41 $$Author: bbarber $
+** Copyright (c) 2008-2014 C.B. Barber. All rights reserved.
+** $Id: //main/2011/qhull/src/libqhullcpp/QhullVertex.h#11 $$Change: 1800 $
+** $DateTime: 2014/12/17 21:46:45 $$Author: bbarber $
 **
 ****************************************************************************/
 
 #ifndef QHULLVERTEX_H
 #define QHULLVERTEX_H
 
-#include "UsingLibQhull.h"
 #include "QhullPoint.h"
 #include "QhullLinkedList.h"
 #include "QhullSet.h"
 extern "C" {
-    #include "libqhull/qhull_r.h"
+    #include "libqhullr/qhull_ra.h"
 }
 
 #include 
 
 namespace orgQhull {
 
-#//ClassRef
+#//!\name Used here
     class QhullFacetSet;
 
-#//Types
-    //! QhullVertex -- Qhull's vertex structure, vertexT [libqhull.h], as a C++ class
+#//!\name Defined here
+    //! QhullVertex -- Qhull's vertex structure, vertexT [libqhull_r.h], as a C++ class
     class QhullVertex;
     typedef QhullLinkedList QhullVertexList;
     typedef QhullLinkedListIterator QhullVertexListIterator;
 
 
 /*********************
   topological information:
     next,previous       doubly-linked list of all vertices
     neighborFacets           set of adjacent facets (only if qh.VERTEXneighbors)
 
   geometric information:
     point               array of DIM coordinates
 */
 
 class QhullVertex {
 
+#//!\name Defined here
+public:
+    typedef vertexT *   base_type;  // for QhullVertexSet
+
 private:
-#//Fields
-    vertexT            *qh_vertex;
+#//!\name Fields
+    vertexT *           qh_vertex;
+    QhullQh *           qh_qh;
 
-#//Class objects
+#//!\name Class objects
     static vertexT      s_empty_vertex;  // needed for shallow copy
 
 public:
-#//Constants
+#//!\name Constants
 
-#//Constructors
-                        QhullVertex() : qh_vertex(&s_empty_vertex) {}
+#//!\name Constructors
+    explicit            QhullVertex(const Qhull &q);
+                        QhullVertex(const Qhull &q, vertexT *v);
+    explicit            QhullVertex(QhullQh *qh) : qh_vertex(&s_empty_vertex), qh_qh(qh) {}
+                        QhullVertex(QhullQh *qh, vertexT *v) : qh_vertex(v ? v : &s_empty_vertex), qh_qh(qh) {}
                         // Creates an alias.  Does not copy QhullVertex.  Needed for return by value and parameter passing
-                        QhullVertex(const QhullVertex &o) : qh_vertex(o.qh_vertex) {}
+                        QhullVertex(const QhullVertex &other) : qh_vertex(other.qh_vertex), qh_qh(other.qh_qh) {}
                         // Creates an alias.  Does not copy QhullVertex.  Needed for vector
-    QhullVertex        &operator=(const QhullVertex &o) { qh_vertex= o.qh_vertex; return *this; }
-                       ~QhullVertex() {}
-
-#//Conversion
-                        //Implicit conversion from vertexT
-                        QhullVertex(vertexT *v) : qh_vertex(v ? v : &s_empty_vertex) {}
-    vertexT            *getVertexT() const { return qh_vertex; }
-
-#//QhullSet
-    vertexT            *getBaseT() const { return getVertexT(); }
-
-#//getSet
-    int                 dimension() const { return (qh_vertex->dim || !isDefined()) ? qh_vertex->dim : UsingLibQhull::globalVertexDimension(); }
-    int                 id() const { return qh_vertex->id; }
+    QhullVertex &       operator=(const QhullVertex &other) { qh_vertex= other.qh_vertex; qh_qh= other.qh_qh; return *this; }
+                        ~QhullVertex() {}
+
+#//!\name GetSet
+    int                 dimension() const { return qh_qh->hull_dim; }
+    vertexT *           getBaseT() const { return getVertexT(); } //!< For QhullSet
+    vertexT *           getVertexT() const { return qh_vertex; }
+    countT              id() const { return qh_vertex->id; }
     bool                isDefined() const { return qh_vertex != &s_empty_vertex; }
                         //! True if defineVertexNeighborFacets() already called.  Auotomatically set for facet merging, Voronoi diagrams
     bool                neighborFacetsDefined() const { return qh_vertex->neighbors != 0; }
-    QhullVertex         next() const { return qh_vertex->next; }
-    bool                operator==(const QhullVertex &o) const { return qh_vertex==o.qh_vertex; }
-    bool                operator!=(const QhullVertex &o) const { return !operator==(o); }
-    QhullPoint          point() const { return QhullPoint(dimension(), qh_vertex->point); }
-    QhullVertex         previous() const { return qh_vertex->previous; }
-
-#//ForEach
+    QhullVertex         next() const { return QhullVertex(qh_qh, qh_vertex->next); }
+    bool                operator==(const QhullVertex &other) const { return qh_vertex==other.qh_vertex; }
+    bool                operator!=(const QhullVertex &other) const { return !operator==(other); }
+    QhullPoint          point() const { return QhullPoint(qh_qh, qh_vertex->point); }
+    QhullVertex         previous() const { return QhullVertex(qh_qh, qh_vertex->previous); }
+    QhullQh *           qh() const { return qh_qh; }
+
+#//!\name foreach
     //See also QhullVertexList
     QhullFacetSet       neighborFacets() const;
 
-#//IO
+#//!\name IO
     struct PrintVertex{
         const QhullVertex *vertex;
-        int             run_id;
-                        PrintVertex(int qhRunId, const QhullVertex &v) : vertex(&v), run_id(qhRunId) {}
+        const char *    print_message;
+                        PrintVertex(const char *message, const QhullVertex &v) : vertex(&v), print_message(message) {}
     };//PrintVertex
-    PrintVertex         print(int qhRunId) const { return PrintVertex(qhRunId, *this); }
+    PrintVertex         print(const char *message) const { return PrintVertex(message, *this); }
 };//class QhullVertex
 
 }//namespace orgQhull
 
-#//GLobal
+#//!\name GLobal
 
 std::ostream &operator<<(std::ostream &os, const orgQhull::QhullVertex::PrintVertex &pr);
-inline std::ostream &operator<<(std::ostream &os, const orgQhull::QhullVertex &v) { os << v.print(orgQhull::UsingLibQhull::NOqhRunId); return os; }
+inline std::ostream &operator<<(std::ostream &os, const orgQhull::QhullVertex &v) { os << v.print(""); return os; }
 
 #endif // QHULLVERTEX_H
diff --git a/src/libqhullcpp/QhullVertexSet.cpp b/src/libqhullcpp/QhullVertexSet.cpp
index 1c04906..5743bec 100644
--- a/src/libqhullcpp/QhullVertexSet.cpp
+++ b/src/libqhullcpp/QhullVertexSet.cpp
@@ -1,110 +1,145 @@
 /****************************************************************************
 **
 ** Copyright (c) 2009-2014 C.B. Barber. All rights reserved.
-** $Id: //main/2011/qhull/src/libqhullcpp/QhullVertexSet.cpp#5 $$Change: 1464 $
-** $DateTime: 2012/01/25 22:58:41 $$Author: bbarber $
+** $Id: //main/2011/qhull/src/libqhullcpp/QhullVertexSet.cpp#11 $$Change: 1799 $
+** $DateTime: 2014/12/17 16:17:40 $$Author: bbarber $
 **
 ****************************************************************************/
 
 #//! QhullVertexSet -- Qhull's linked Vertexs, as a C++ class
 
 #include "QhullVertex.h"
 #include "QhullVertexSet.h"
 #include "QhullPoint.h"
 #include "QhullRidge.h"
 #include "QhullVertex.h"
+#include "Qhull.h"
+
+#include "UsingLibQhull.h"
 
 using std::string;
 using std::vector;
 
 #ifdef _MSC_VER  // Microsoft Visual C++ -- warning level 4
 #pragma warning( disable : 4611)  /* interaction between '_setjmp' and C++ object destruction is non-portable */
                                     /* setjmp should not be implemented with 'catch' */
 #endif
 
 namespace orgQhull {
 
 QhullVertexSet::
-QhullVertexSet(int qhRunId, facetT *facetlist, setT *facetset, bool allfacets)
-: QhullSet(0)
-, qhsettemp_qhull(0)
+QhullVertexSet(const Qhull &q, facetT *facetlist, setT *facetset, bool allfacets)
+: QhullSet(q.qh(), 0)
 , qhsettemp_defined(false)
 {
-    UsingLibQhull q(qhRunId);
-    int exitCode = setjmp(qh errexit);
-    if(!exitCode){ // no object creation -- destructors skipped on longjmp()
-        setT *vertices= qh_facetvertices(facetlist, facetset, allfacets);
+    QH_TRY_(q.qh()){ // no object creation -- destructors skipped on longjmp()
+        setT *vertices= qh_facetvertices(q.qh(), facetlist, facetset, allfacets);
         defineAs(vertices);
-        qhsettemp_qhull= s_qhull_output;
         qhsettemp_defined= true;
     }
-    q.maybeThrowQhullMessage(exitCode);
+    q.qh()->maybeThrowQhullMessage(QH_TRY_status);
 }//QhullVertexSet facetlist facetset
 
+QhullVertexSet::
+QhullVertexSet(QhullQh *qh, facetT *facetlist, setT *facetset, bool allfacets)
+: QhullSet(qh, 0)
+, qhsettemp_defined(false)
+{
+    QH_TRY_(qh){ // no object creation -- destructors skipped on longjmp()
+        setT *vertices= qh_facetvertices(qh, facetlist, facetset, allfacets);
+        defineAs(vertices);
+        qhsettemp_defined= true;
+    }
+    qh->maybeThrowQhullMessage(QH_TRY_status);
+}//QhullVertexSet facetlist facetset
+
+//! Copy constructor for argument passing and returning a result
+//! Only copies a pointer to the set.
+//! If qhsettemp_defined, transfers ownership to destination, otherwise the set will be freed twice
+//! If qhsettemp_defined and passed by value, the set will be empty on return to caller
+QhullVertexSet::
+QhullVertexSet(QhullVertexSet &other) 
+: QhullSet(other)
+, qhsettemp_defined(other.qhsettemp_defined)
+{
+    other.qhsettemp_defined= false;
+    other.forceEmpty();
+}//copy constructor
+
+//! Copy assignment only copies a pointer to the set.
+//! If qhsettemp_defined, transfers ownership to destination, otherwise the set will be freed twice
+//! If qhsettemp_defined and passed by value, the set will be empty on return to caller
+//! 'other' is not 'const' due to ownership transfer
+QhullVertexSet & QhullVertexSet::
+operator=(QhullVertexSet &other) 
+{
+    QhullSet::operator=(other);
+    qhsettemp_defined= other.qhsettemp_defined;
+    other.qhsettemp_defined= false;
+    other.forceEmpty();
+    return *this;
+}//copy constructor
+
 void QhullVertexSet::
 freeQhSetTemp()
 {
     if(qhsettemp_defined){
-        UsingLibQhull q(qhsettemp_qhull, QhullError::NOthrow);
-        if(q.defined()){
-            int exitCode = setjmp(qh errexit);
-            if(!exitCode){ // no object creation -- destructors skipped on longjmp()
-                qh_settempfree(referenceSetT()); // errors if not top of tempstack or if qhmem corrupted
-            }
-            q.maybeThrowQhullMessage(exitCode, QhullError::NOthrow);
+        qhsettemp_defined= false;
+        QH_TRY_(qh()){ // no object creation -- destructors skipped on longjmp()
+            qh_settempfree(qh(), referenceSetT()); // errors if not top of tempstack or if qhmem corrupted
         }
+        qh()->maybeThrowQhullMessage(QH_TRY_status, QhullError::NOthrow);
     }
 }//freeQhSetTemp
 
 QhullVertexSet::
 ~QhullVertexSet()
 {
     freeQhSetTemp();
 }//~QhullVertexSet
 
 }//namespace orgQhull
 
-#//Global functions
+#//!\name Global functions
 
 using std::endl;
 using std::ostream;
 using orgQhull::QhullPoint;
 using orgQhull::QhullVertex;
 using orgQhull::QhullVertexSet;
 using orgQhull::QhullVertexSetIterator;
 using orgQhull::UsingLibQhull;
 
-//! Print Vertex identifiers to stream.  Space prefix.  From qh_printVertexheader [io.c]
+//! Print Vertex identifiers to stream.  Space prefix.  From qh_printVertexheader [io_r.c]
 ostream &
 operator<<(ostream &os, const QhullVertexSet::PrintIdentifiers &pr)
 {
     if(pr.print_message && *pr.print_message){
         os << pr.print_message;
     }
-    for(QhullVertexSet::const_iterator i=pr.Vertex_set->begin(); i!=pr.Vertex_set->end(); ++i){
+    for(QhullVertexSet::const_iterator i= pr.vertex_set->begin(); i!=pr.vertex_set->end(); ++i){
         const QhullVertex v= *i;
         os << " v" << v.id();
     }
     os << endl;
     return os;
 }//<
 
 namespace orgQhull {
 
-#//ClassRef
-    class               QhullVertex;
+#//!\name Used here
+    class QhullVertex;
 
-#//Types
+#//!\name Defined here
     //! QhullVertexSet -- a set of Qhull Vertices, as a C++ class.
     //! See Qhull
-    class               QhullVertexSet;
-    typedef QhullSetIterator
-                        QhullVertexSetIterator;
+    class QhullVertexSet;
+    typedef QhullSetIterator QhullVertexSetIterator;
 
 class QhullVertexSet : public QhullSet {
 
 private:
-#//Fields
-    Qhull              *qhsettemp_qhull; //! For sets allocated with qh_settemp()
-    bool                qhsettemp_defined;  //! Set was allocated with q_memalloc()
+#//!\name Fields
+    bool                qhsettemp_defined;  //! Set was allocated with qh_settemp()
 
 public:
-#//Constructor
+#//!\name Constructor
+                        QhullVertexSet(const Qhull &q, setT *s) : QhullSet(q, s), qhsettemp_defined(false) {}
+                        QhullVertexSet(const Qhull &q, facetT *facetlist, setT *facetset, bool allfacets);
                         //Conversion from setT* is not type-safe.  Implicit conversion for void* to T
-   explicit             QhullVertexSet(setT *s) : QhullSet(s), qhsettemp_qhull(0), qhsettemp_defined(false) {}
-                        QhullVertexSet(int qhRunId, facetT *facetlist, setT *facetset, bool allfacets);
+                        QhullVertexSet(QhullQh *qh, setT *s) : QhullSet(qh, s), qhsettemp_defined(false) {}
+                        QhullVertexSet(QhullQh *qh, facetT *facetlist, setT *facetset, bool allfacets);
                         //Copy constructor copies pointer but not contents.  Needed for return by value.
-                        QhullVertexSet(const QhullVertexSet &o) : QhullSet(o), qhsettemp_qhull(o.qhsettemp_qhull), qhsettemp_defined(o.qhsettemp_defined) {}
-                       ~QhullVertexSet();
+                        QhullVertexSet(QhullVertexSet &other);
+    QhullVertexSet &    operator=(QhullVertexSet &other);
+                        ~QhullVertexSet();
 
 private:
-                        //!Disable default constructor and copy assignment.  See QhullSetBase
+                        //!Default constructor disabled.  Will implement allocation later
                         QhullVertexSet();
-    QhullVertexSet      &operator=(const QhullVertexSet &);
 public:
 
-#//Constructor, destructor
+#//!\name Destructor
     void                freeQhSetTemp();
 
-#//IO
+#//!\name IO
     struct PrintVertexSet{
-        const QhullVertexSet *Vertex_set;
-        const char     *print_message;
-        int             run_id;
-                        PrintVertexSet(int qhRunId, const char *message, const QhullVertexSet *s) : Vertex_set(s), print_message(message), run_id(qhRunId) {}
+        const QhullVertexSet *vertex_set;
+        const char *    print_message;
+                        
+                        PrintVertexSet(const char *message, const QhullVertexSet *s) : vertex_set(s), print_message(message) {}
     };//PrintVertexSet
-    const PrintVertexSet       print(int qhRunId, const char *message) const { return PrintVertexSet(qhRunId, message, this); }
+    const PrintVertexSet print(const char *message) const { return PrintVertexSet(message, this); }
 
     struct PrintIdentifiers{
-        const QhullVertexSet *Vertex_set;
-        const char     *print_message;
-                        PrintIdentifiers(const char *message, const QhullVertexSet *s) : Vertex_set(s), print_message(message) {}
+        const QhullVertexSet *vertex_set;
+        const char *    print_message;
+                        PrintIdentifiers(const char *message, const QhullVertexSet *s) : vertex_set(s), print_message(message) {}
     };//PrintIdentifiers
     PrintIdentifiers    printIdentifiers(const char *message) const { return PrintIdentifiers(message, this); }
 
 };//class QhullVertexSet
 
 }//namespace orgQhull
 
-#//== Global namespace =========================================
+#//!\name Global
 
 std::ostream &operator<<(std::ostream &os, const orgQhull::QhullVertexSet::PrintVertexSet &pr);
 std::ostream &operator<<(std::ostream &os, const orgQhull::QhullVertexSet::PrintIdentifiers &p);
-inline std::ostream &operator<<(std::ostream &os, const orgQhull::QhullVertexSet &vs) { os << vs.print(orgQhull::UsingLibQhull::NOqhRunId, ""); return os; }
+inline std::ostream &operator<<(std::ostream &os, const orgQhull::QhullVertexSet &vs) { os << vs.print(""); return os; }
 
 #endif // QHULLVERTEXSET_H
diff --git a/src/libqhullcpp/RboxPoints.cpp b/src/libqhullcpp/RboxPoints.cpp
index ee32aa2..bba6877 100644
--- a/src/libqhullcpp/RboxPoints.cpp
+++ b/src/libqhullcpp/RboxPoints.cpp
@@ -1,219 +1,221 @@
 /****************************************************************************
 **
 ** Copyright (c) 2008-2014 C.B. Barber. All rights reserved.
-** $Id: //main/2011/qhull/src/libqhullcpp/RboxPoints.cpp#4 $$Change: 1464 $
-** $DateTime: 2012/01/25 22:58:41 $$Author: bbarber $
+** $Id: //main/2011/qhull/src/libqhullcpp/RboxPoints.cpp#9 $$Change: 1799 $
+** $DateTime: 2014/12/17 16:17:40 $$Author: bbarber $
 **
 ****************************************************************************/
 
 #include "QhullError.h"
 #include "RboxPoints.h"
 
 #include 
 
 using std::cerr;
 using std::endl;
 using std::istream;
 using std::ostream;
 using std::ostringstream;
 using std::string;
 using std::vector;
 using std::ws;
 
 #ifdef _MSC_VER  // Microsoft Visual C++ -- warning level 4
 #pragma warning( disable : 4996)  // function was declared deprecated(strcpy, localtime, etc.)
 #endif
 
 namespace orgQhull {
 
 #//! RboxPoints -- generate random PointCoordinates for qhull (rbox)
+  
 
-#//Global
-
-//! pointer to RboxPoints for qh_fprintf callback
-RboxPoints *rbox_output= 0;
-
-#//Construct
+#//!\name Constructors
 RboxPoints::
 RboxPoints()
-: PointCoordinates("rbox")
+: PointCoordinates(0, "rbox")
 , rbox_new_count(0)
 , rbox_status(qh_ERRnone)
 , rbox_message()
-{}
+{
+    allocateQhullQh();
+}
 
+//! Allocate and generate points according to rboxCommand
+//! For rbox commands, see http://www.qhull.org/html/rbox.htm or html/rbox.htm
+//! Same as appendPoints()
 RboxPoints::
 RboxPoints(const char *rboxCommand)
-: PointCoordinates("rbox")
+: PointCoordinates(0, "rbox")
 , rbox_new_count(0)
 , rbox_status(qh_ERRnone)
 , rbox_message()
 {
+    allocateQhullQh();
     appendPoints(rboxCommand);
 }
 
 RboxPoints::
-RboxPoints(const RboxPoints &other)
-: PointCoordinates(other)
-, rbox_new_count(0)
-, rbox_status(other.rbox_status)
-, rbox_message(other.rbox_message)
-{}
-
-RboxPoints & RboxPoints::
-operator=(const RboxPoints &other)
+~RboxPoints()
 {
-    PointCoordinates::operator=(other);
-    rbox_new_count= other.rbox_new_count;
-    rbox_status= other.rbox_status;
-    rbox_message= other.rbox_message;
-    return *this;
-}//operator=
-
+    delete qh();
+    setQhullQh(0);
+}
 
-RboxPoints::
-~RboxPoints()
-{}
+// RboxPoints and qh_rboxpoints has several fields in qhT (rbox_errexit..cpp_object)
+// It shares last_random with qh_rand and qh_srand
+// The other fields are unused
+void RboxPoints::
+allocateQhullQh()
+{
+    setQhullQh(new QhullQh);
+}//allocateQhullQh
 
-#//Error
+#//!\name Messaging
 
 void RboxPoints::
 clearRboxMessage()
 {
     rbox_status= qh_ERRnone;
     rbox_message.clear();
 }//clearRboxMessage
 
 std::string RboxPoints::
 rboxMessage() const
 {
     if(rbox_status!=qh_ERRnone){
         return rbox_message;
     }
     if(isEmpty()){
         return "rbox warning: no points generated\n";
     }
     return "rbox: OK\n";
 }//rboxMessage
 
 int RboxPoints::
 rboxStatus() const
 {
     return rbox_status;
 }
 
 bool RboxPoints::
 hasRboxMessage() const
 {
     return (rbox_status!=qh_ERRnone);
 }
 
-#//Modify
+#//!\name Methods
 
+//! Appends points as defined by rboxCommand
+//! Appends rboxCommand to comment
+//! For rbox commands, see http://www.qhull.org/html/rbox.htm or html/rbox.htm
 void RboxPoints::
 appendPoints(const char *rboxCommand)
 {
     string s("rbox ");
     s += rboxCommand;
     char *command= const_cast(s.c_str());
-    if(rbox_output){
-        throw QhullError(10001, "Qhull error: Two simultaneous calls to RboxPoints::appendPoints().  Prevent two processes calling appendPoints() at the same time.  Other RboxPoints '%s'", 0, 0, 0, rbox_output->comment().c_str());
+    if(qh()->cpp_object){
+        throw QhullError(10001, "Qhull error: conflicting user of cpp_object for RboxPoints::appendPoints() or corrupted qh_qh");
     }
     if(extraCoordinatesCount()!=0){
         throw QhullError(10067, "Qhull error: Extra coordinates (%d) prior to calling RboxPoints::appendPoints.  Was %s", extraCoordinatesCount(), 0, 0.0, comment().c_str());
     }
-    int previousCount= count();
-    rbox_output= this;              // set rbox_output for qh_fprintf()
-    int status= ::qh_rboxpoints(0, 0, command);
-    rbox_output= 0;
+    countT previousCount= count();
+    qh()->cpp_object= this;           // for qh_fprintf_rbox()
+    int status= qh_rboxpoints(qh(), command);
+    qh()->cpp_object= 0;         
     if(rbox_status==qh_ERRnone){
         rbox_status= status;
     }
     if(rbox_status!=qh_ERRnone){
         throw QhullError(rbox_status, rbox_message);
     }
     if(extraCoordinatesCount()!=0){
         throw QhullError(10002, "Qhull error: extra coordinates (%d) for PointCoordinates (%x)", extraCoordinatesCount(), 0, 0.0, coordinates());
     }
     if(previousCount+newCount()!=count()){
         throw QhullError(10068, "Qhull error: rbox specified %d points but got %d points for command '%s'", newCount(), count()-previousCount, 0.0, comment().c_str());
     }
 }//appendPoints
 
 }//namespace orgQhull
 
-#//Global functions
+#//!\name Global functions
 
 /*---------------------------------
 
-  qh_fprintf_rbox(fp, msgcode, format, list of args )
+  qh_fprintf_rbox(qh, fp, msgcode, format, list of args )
     fp is ignored (replaces qh_fprintf_rbox() in userprintf_rbox.c)
-    rbox_output == RboxPoints
+    cpp_object == RboxPoints
 
 notes:
     only called from qh_rboxpoints()
-    same as fprintf() and Qhull::qh_fprintf()
+    same as fprintf() and Qhull.qh_fprintf()
     fgets() is not trapped like fprintf()
     Do not throw errors from here.  Use qh_errexit_rbox;
+    A similar technique can be used for qh_fprintf to capture all of its output
 */
 extern "C"
-void qh_fprintf_rbox(FILE*, int msgcode, const char *fmt, ... ) {
+void qh_fprintf_rbox(qhT *qh, FILE*, int msgcode, const char *fmt, ... ) {
     va_list args;
 
     using namespace orgQhull;
 
-    RboxPoints *out= rbox_output;
+    if(!qh->cpp_object){
+        qh_errexit_rbox(qh, 10072);
+    }
+    RboxPoints *out= reinterpret_cast(qh->cpp_object);
     va_start(args, fmt);
     if(msgcoderbox_message += newMessage;
         if(out->rbox_statusrbox_status>=MSG_STDERR){
             out->rbox_status= msgcode;
         }
         va_end(args);
         return;
     }
     switch(msgcode){
     case 9391:
     case 9392:
         out->rbox_message += "RboxPoints error: options 'h', 'n' not supported.\n";
-        qh_errexit_rbox(10010);
+        qh_errexit_rbox(qh, 10010);
         /* never returns */
-    case 9393:
+    case 9393:  // FIXUP countT vs. int
         {
             int dimension= va_arg(args, int);
             string command(va_arg(args, char*));
-            int count= va_arg(args, int);
+            countT count= va_arg(args, countT);
             out->setDimension(dimension);
             out->appendComment(" \"");
             out->appendComment(command.substr(command.find(' ')+1));
             out->appendComment("\"");
             out->setNewCount(count);
             out->reservePoints();
         }
         break;
     case 9407:
         *out << va_arg(args, int);
         // fall through
     case 9405:
         *out << va_arg(args, int);
         // fall through
     case 9403:
         *out << va_arg(args, int);
         break;
     case 9408:
         *out << va_arg(args, double);
         // fall through
     case 9406:
         *out << va_arg(args, double);
         // fall through
     case 9404:
         *out << va_arg(args, double);
         break;
     }
     va_end(args);
 } /* qh_fprintf_rbox */
 
diff --git a/src/libqhullcpp/RboxPoints.h b/src/libqhullcpp/RboxPoints.h
index c909e2c..f9e376e 100644
--- a/src/libqhullcpp/RboxPoints.h
+++ b/src/libqhullcpp/RboxPoints.h
@@ -1,66 +1,71 @@
 /****************************************************************************
 **
-** Copyright (c) 2008-2012 C.B. Barber. All rights reserved.
-** $Id: //main/2011/qhull/src/libqhullcpp/RboxPoints.h#6 $$Change: 1464 $
-** $DateTime: 2012/01/25 22:58:41 $$Author: bbarber $
+** Copyright (c) 2008-2014 C.B. Barber. All rights reserved.
+** $Id: //main/2011/qhull/src/libqhullcpp/RboxPoints.h#11 $$Change: 1712 $
+** $DateTime: 2014/03/30 22:34:33 $$Author: bbarber $
 **
 ****************************************************************************/
 
 #ifndef RBOXPOINTS_H
 #define RBOXPOINTS_H
 
 #include "QhullPoint.h"
 #include "PointCoordinates.h"
 extern "C" {
-#include "libqhull/libqhull.h"
+#include "libqhullr/qhull_ra.h"
 }
 
 #include 
 #include 
 #include 
 #include 
 #include 
 #include 
 
 namespace orgQhull {
 
-#//Types
+#//!\name Defined here
     //! RboxPoints -- generate random PointCoordinates for Qhull
     class RboxPoints;
 
-    class RboxPoints : public PointCoordinates {
+class RboxPoints : public PointCoordinates {
 
 private:
-#//Fields and friends
-    int                 rbox_new_count;     //! Number of points for PointCoordinates
+#//!\name Fields and friends
+                        //! qh() is owned by RboxPoints 
+    countT              rbox_new_count;     //! Number of points for PointCoordinates
     int                 rbox_status;    //! error status from rboxpoints.  qh_ERRnone if none.
     std::string         rbox_message;   //! stderr from rboxpoints
-
-    friend void ::qh_fprintf_rbox(FILE *fp, int msgcode, const char *fmt, ... );
+ 
+    // '::' is required for friend references
+    friend void ::qh_fprintf_rbox(qhT *qh, FILE *fp, int msgcode, const char *fmt, ... );
 
 public:
-#//Construct
+#//!\name Construct
                         RboxPoints();
     explicit            RboxPoints(const char *rboxCommand);
-                        RboxPoints(const RboxPoints &other);
-                        RboxPoints &operator=(const RboxPoints &other);
-                       ~RboxPoints();
+                        ~RboxPoints();
+private:                // Disable copy constructor and assignment.  RboxPoints owns QhullQh.
+                        RboxPoints(const RboxPoints &);
+                        RboxPoints &operator=(const RboxPoints &);
+private:
+    void                allocateQhullQh();
 
 public:
-#//GetSet
+#//!\name GetSet
     void                clearRboxMessage();
-    int                 newCount() const { return rbox_new_count; }
+    countT              newCount() const { return rbox_new_count; }
     std::string         rboxMessage() const;
     int                 rboxStatus() const;
     bool                hasRboxMessage() const;
-    void                setNewCount(int pointCount) { QHULL_ASSERT(pointCount>=0); rbox_new_count= pointCount; }
+    void                setNewCount(countT pointCount) { QHULL_ASSERT(pointCount>=0); rbox_new_count= pointCount; }
 
-#//Modify
+#//!\name Modify
     void                appendPoints(const char* rboxCommand);
     using               PointCoordinates::appendPoints;
     void                reservePoints() { reserveCoordinates((count()+newCount())*dimension()); }
 };//class RboxPoints
 
 }//namespace orgQhull
 
 #endif // RBOXPOINTS_H
diff --git a/src/libqhullcpp/RoadError.h b/src/libqhullcpp/RoadError.h
index 41062bb..b20921e 100644
--- a/src/libqhullcpp/RoadError.h
+++ b/src/libqhullcpp/RoadError.h
@@ -1,86 +1,86 @@
 /****************************************************************************
 **
-** Copyright (c) 2008-2012 C.B. Barber. All rights reserved.
-** $Id: //main/2011/qhull/src/libqhullcpp/RoadError.h#1 $$Change: 1490 $
-** $DateTime: 2012/02/19 20:27:01 $$Author: bbarber $
+** Copyright (c) 2008-2014 C.B. Barber. All rights reserved.
+** $Id: //main/2011/qhull/src/libqhullcpp/RoadError.h#4 $$Change: 1712 $
+** $DateTime: 2014/03/30 22:34:33 $$Author: bbarber $
 **
 ****************************************************************************/
 
 #ifndef ROADERROR_H
 #define ROADERROR_H
 
 #include "RoadLogEvent.h"
 
 #include 
 #include 
 #include 
 #include 
 
 using std::endl;
 
 namespace orgQhull {
 
-#//Types
+#//!\name Defined here
     //! RoadError -- Report and log errors
     //!  See discussion in Saylan, G., "Practical C++ error handling in hybrid environments," Dr. Dobb's Journal, p. 50-55, March 2007.
     //!   He uses an auto_ptr to track a stringstream.  It constructs a string on the fly.  RoadError uses the copy constructor to transform RoadLogEvent into a string
     class RoadError;
 
 class RoadError : public std::exception {
 
 private:
-#//Fields
+#//!\name Fields
     int                 error_code;  //! Non-zero code (not logged), maybe returned as program status
     RoadLogEvent        log_event;   //! Format string w/ arguments
     mutable std::string error_message;  //! Formated error message.  Must be after log_event.
 
-#//Class fields
+#//!\name Class fields
     static const char  *  ROADtag;
     static std::ostringstream  global_log; //! May be replaced with any ostream object
 
 public:
-#//Constants
+#//!\name Constants
 
-#//Constructors
+#//!\name Constructors
     RoadError();
     RoadError(const RoadError &other);  //! Called on throw, generates error_message
     RoadError(int code, const std::string &message);
     RoadError(int code, const char *fmt);
     RoadError(int code, const char *fmt, int d);
     RoadError(int code, const char *fmt, int d, int d2);
     RoadError(int code, const char *fmt, int d, int d2, float f);
     RoadError(int code, const char *fmt, int d, int d2, float f, const char *s);
     RoadError(int code, const char *fmt, int d, int d2, float f, const void *x);
     RoadError(int code, const char *fmt, int d, int d2, float f, int i);
     RoadError(int code, const char *fmt, int d, int d2, float f, long long i);
     RoadError(int code, const char *fmt, int d, int d2, float f, double e);
 
-    RoadError          &operator=(const RoadError &other);
-                       ~RoadError() throw() {};
+    RoadError &         operator=(const RoadError &other);
+                        ~RoadError() throw() {};
 
-#//Class methods
+#//!\name Class methods
 
     static void         clearGlobalLog() { global_log.seekp(0); }
     static bool         emptyGlobalLog() { return global_log.tellp()<=0; }
     static const char  *stringGlobalLog() { return global_log.str().c_str(); }
 
-#//Virtual
+#//!\name Virtual
     virtual const char *what() const throw();
 
-#//GetSet
+#//!\name GetSet
     bool                isDefined() const { return log_event.isDefined(); }
     int                 errorCode() const { return error_code; };
    // FIXUP QH11021 should RoadError provide errorMessage().  Currently what()
     RoadLogEvent        roadLogEvent() const { return log_event; };
 
-#//Update
+#//!\name Update
     void                logError() const;
 };//class RoadError
 
 }//namespace orgQhull
 
-#//Global functions
+#//!\name Global
 
-inline std::ostream    &operator<<(std::ostream &os, const orgQhull::RoadError &e) { return os << e.what(); }
+inline std::ostream &   operator<<(std::ostream &os, const orgQhull::RoadError &e) { return os << e.what(); }
 
 #endif // ROADERROR_H
diff --git a/src/libqhullcpp/RoadLogEvent.h b/src/libqhullcpp/RoadLogEvent.h
index bdab15e..722d6e5 100644
--- a/src/libqhullcpp/RoadLogEvent.h
+++ b/src/libqhullcpp/RoadLogEvent.h
@@ -1,77 +1,77 @@
 /****************************************************************************
 **
-** Copyright (c) 2008-2012 C.B. Barber. All rights reserved.
-** $Id: //main/2011/qhull/src/libqhullcpp/RoadLogEvent.h#1 $$Change: 1490 $
-** $DateTime: 2012/02/19 20:27:01 $$Author: bbarber $
+** Copyright (c) 2008-2014 C.B. Barber. All rights reserved.
+** $Id: //main/2011/qhull/src/libqhullcpp/RoadLogEvent.h#4 $$Change: 1712 $
+** $DateTime: 2014/03/30 22:34:33 $$Author: bbarber $
 **
 ****************************************************************************/
 
 #ifndef ROADLOGEVENT_H
 #define ROADLOGEVENT_H
 
 #include 
 #include 
 #include 
 
 namespace orgQhull {
 
-#//Types
+#//!\name Defined here
     //! RoadLogEvent -- Record an event for the RoadLog
     struct RoadLogEvent;
 
 struct RoadLogEvent {
 
 public:
-#//Fields
-    const char     *format_string; //! Format string (a literal with format codes, for logging)
+#//!\name Fields
+    const char *    format_string; //! Format string (a literal with format codes, for logging)
     int             int_1;       //! Integer argument (%d, for logging)
     int             int_2;       //! Integer argument (%d, for logging)
     float           float_1;     //! Float argument (%f, for logging)
     union {                      //! One additional argument (for logging)
         const char *cstr_1;      //!   Cstr argument (%s) -- type checked at construct-time
         const void *void_1;      //!   Void* argument (%x) -- Use upper-case codes for object types
         long long   int64_1;     //!   signed int64 (%i).  Ambiguous if unsigned is also defined.
         double      double_1;    //!   Double argument (%e)
     };
 
-#//Constants
+#//!\name Constants
 
-#//Constructors
+#//!\name Constructors
     RoadLogEvent() : format_string(0), int_1(0), int_2(0), float_1(0), int64_1(0) {};
     explicit RoadLogEvent(const char *fmt) : format_string(fmt), int_1(0), int_2(0), float_1(0), int64_1(0) {};
     RoadLogEvent(const char *fmt, int d) : format_string(fmt), int_1(d), int_2(0), float_1(0), int64_1(0) {};
     RoadLogEvent(const char *fmt, int d, int d2) : format_string(fmt), int_1(d), int_2(d2), float_1(0), int64_1(0) {};
     RoadLogEvent(const char *fmt, int d, int d2, float f) : format_string(fmt), int_1(d), int_2(d2), float_1(f), int64_1(0) {};
     RoadLogEvent(const char *fmt, int d, int d2, float f, const char *s) : format_string(fmt), int_1(d), int_2(d2), float_1(f), cstr_1(s) {};
     RoadLogEvent(const char *fmt, int d, int d2, float f, const void *x) : format_string(fmt), int_1(d), int_2(d2), float_1(f), void_1(x) {};
     RoadLogEvent(const char *fmt, int d, int d2, float f, int i) : format_string(fmt), int_1(d), int_2(d2), float_1(f), int64_1(i) {};
     RoadLogEvent(const char *fmt, int d, int d2, float f, long long i) : format_string(fmt), int_1(d), int_2(d2), float_1(f), int64_1(i) {};
     RoadLogEvent(const char *fmt, int d, int d2, float f, double g) : format_string(fmt), int_1(d), int_2(d2), float_1(f), double_1(g) {};
     ~RoadLogEvent() {};
     //! Default copy constructor and assignment
 
-#//GetSet
+#//!\name GetSet
     bool                isDefined() const { return format_string!=0; }
     int                 int1() const { return int_1; };
     int                 int2() const { return int_2; };
     float               float1() const { return float_1; };
-    const char         *format() const { return format_string; };
-    const char         *cstr1() const { return cstr_1; };
-    const void         *void1() const { return void_1; };
+    const char *        format() const { return format_string; };
+    const char *        cstr1() const { return cstr_1; };
+    const void *        void1() const { return void_1; };
     long long           int64() const { return int64_1; };
     double              double1() const { return double_1; };
 
-#//Conversion
+#//!\name Conversion
 
     std::string        toString(const char* tag, int code) const;
 
 private:
-#//Class helpers
+#//!\name Class helpers
     static bool         firstExtraCode(std::ostream &os, char c, char *extraCode);
 
 
 };//class RoadLogEvent
 
 }//namespace orgQhull
 
 #endif // ROADLOGEVENT_H
diff --git a/src/libqhullcpp/UsingLibQhull.cpp b/src/libqhullcpp/UsingLibQhull.cpp
index 28a9532..7c0ead0 100644
--- a/src/libqhullcpp/UsingLibQhull.cpp
+++ b/src/libqhullcpp/UsingLibQhull.cpp
@@ -1,373 +1,179 @@
 /****************************************************************************
 **
 ** Copyright (c) 2008-2014 C.B. Barber. All rights reserved.
-** $Id: //main/2011/qhull/src/libqhullcpp/UsingLibQhull.cpp#4 $$Change: 1464 $
-** $DateTime: 2012/01/25 22:58:41 $$Author: bbarber $
+** $Id: //main/2011/qhull/src/libqhullcpp/UsingLibQhull.cpp#7 $$Change: 1708 $
+** $DateTime: 2014/03/26 19:13:56 $$Author: bbarber $
 **
 ****************************************************************************/
 
 #//! UsingLibQhull -- Set up qhull C code from C++
 
 #include "Qhull.h"
 #include "UsingLibQhull.h"
 #include "QhullError.h"
 #include "QhullQh.h"
 
 #ifdef _MSC_VER  // Microsoft Visual C++ -- warning level 4
 #endif
 
 namespace orgQhull {
 
 #//Class objects
 
 const double UsingLibQhull::
 DEFAULTdistanceEpsilon= 1e-15*FACTORepsilon; //! ~DISTround*FACTORepsilon for unit cube
 
 const double UsingLibQhull::
 DEFAULTangleEpsilon= 1e-15*FACTORepsilon; //! ~ANGLEround*FACTORepsilon for unit cube
 
     //! Global pointer to Qhull for qh_fprintf callback and QhullError
 Qhull *
 s_qhull_output= 0;
 
 double UsingLibQhull::
 s_angle_epsilon= 0;
 
 double UsingLibQhull::
 s_distance_epsilon= 0;
 
 //! For QhullPoint.id() w/o qhRunId.  Initialized by Qhull
 const coordT *UsingLibQhull::
 s_points_begin= 0;
 const coordT *UsingLibQhull::
 s_points_end= 0;
 int UsingLibQhull::
 s_points_dimension= 0;
 
 int UsingLibQhull::
 s_vertex_dimension= 0;  // FIXUP QH11023: s_vertex_dimension is required if dimension>15.  Cannot store in QhullVertex
 
 bool UsingLibQhull::
 s_has_points= false;
 
 bool UsingLibQhull::
 s_has_angle_epsilon= false;
 
 bool UsingLibQhull::
 s_has_vertex_dimension= false;
 
 bool UsingLibQhull::
 s_has_distance_epsilon= false;
 
 bool UsingLibQhull::
 s_using_libqhull= false;
 
 #//Constructors
 
 //! Grabs global state (qh_qh, qh_qhstat, qhmem.tempstack)
-//! Follow immediately with setjmp(qh errexit), otherwise errors in libqhull are not caught properly
+//! Follow immediately with setjmp(qh->errexit), otherwise errors in libqhull are not caught properly
 //! See qh_restore_qhull [global.c]
 UsingLibQhull::
 UsingLibQhull(Qhull *q)
 : my_qhull(q)
 , qh_exitcode(0)
 {
     checkUsingLibQhull();
     QhullQh *qhullqh= q->qhullQh();
     if(!qhullqh){
         throw QhullError(10014, "Qhull internal error: Qhull.qhullQh() not defined. initializeQhull() not called.");
     }
-    if(qhullqh->run_id != q->qhull_run_id){
-        throw QhullError(10015, "Qhull error: QhullQh.runId %d != Qhull.runId %d.  Overwritten?", qhullqh->run_id, q->qhull_run_id);
-    }
-    // qh.old_qhstat is zero at initialization
-    // qh.old_tempstack is zero when empty
-    // QhullQh() and UsingLibQhull() are the same
-#if qh_QHpointer
-    if(qh_qh){
-        qh old_qhstat= qh_qhstat;
-        qh old_tempstack= qhmem.tempstack;
-    }
-    qh_qh= qhullqh;
-    qh_qhstat= qhullqh->old_qhstat;
-    qhmem.tempstack= qhullqh->old_tempstack;
-    qhullqh->old_qhstat= 0;
-    qhullqh->old_tempstack= 0;
-#else
-    #error FIXUP QH11024 static qh_qh not tested.  Delete the line to try.
-    if(qhullqh!=&qh_qh){
-        throw QhullError(10040, "Qhull internal error: Qhull.qhullQh() is not qh_qh (%x, static).  Overwrite?", 0,0,0.0, &qh_qh);
-    }
-#endif
     s_qhull_output= q;      // set s_qhull_output for qh_fprintf()
-    qh NOerrexit= False;   // assumes setjmp called next
+    qh->NOerrexit= False;   // assumes setjmp called next
 }//UsingLibQhull qhull
 
 //! Same as UsingLibQhull but does not throw exceptions
 //! !defined() on failure.  For use in destructors
 UsingLibQhull::
 UsingLibQhull(Qhull *q, int noThrow)
 : my_qhull(0)  // Fail by default
 , qh_exitcode(0)
 {
     QHULL_UNUSED(noThrow);
 
     QhullQh *qhullqh= q->qhullQh();
-    if(s_using_libqhull){
-        QhullError e(10050, "Qhull error: UsingLibQhull already in use");
-        e.logError();
-    }else if(!qhullqh || qhullqh->run_id != q->qhull_run_id){
-        QhullError e(10051, "Qhull error: Qhull.qhullQh (%x) undefined or QhullQh.runId %d != Qhull.runId %d.  Overwritten?", (qhullqh ? qhullqh->run_id : -1), q->qhull_run_id, 0.0, qhullqh);
-        e.logError();
-    }else{
-        // qh.old_qhstat is zero at initialization
-        // qh.old_tempstack is zero when empty
-        // QhullQh() and UsingLibQhull() are the same
-#if qh_QHpointer
-        if(qh_qh){
-            qh old_qhstat= qh_qhstat;
-            qh old_tempstack= qhmem.tempstack;
-        }
-        qh_qh= qhullqh;
-        qh_qhstat= qhullqh->old_qhstat;
-        qhmem.tempstack= qhullqh->old_tempstack;
-        qhullqh->old_qhstat= 0;
-        qhullqh->old_tempstack= 0;
-#endif
         my_qhull= q;
         s_qhull_output= q;          // set s_qhull_output for qh_fprintf()
         qh NOerrexit= False;   // assumes setjmp called next
     }
 }//UsingLibQhull qhull noThrow
 
 //! Reuses current global state (qh_qh) from prior UsingQhull
 //! Errors if runId is not the same
 UsingLibQhull::
 UsingLibQhull(int qhRunId)
 : my_qhull(0)
 , qh_exitcode(0)
 {
     checkUsingLibQhull();
 #if qh_QHpointer
     if(!qh_qh || !qh_qhstat){
         throw QhullError(10024, "Qhull error: UsingLibQhull is not active (qh_qh %x or qh_qhstat is not defined)", 0,0,0.0, qh_qh);
     }
 #endif
     if(qh run_id!=qhRunId){
         throw QhullError(10036, "Qhull error: qhRunId %d != qh_qh.runId %d.  Is another Qhull active?", qhRunId, qh run_id);
     }
     if(!s_qhull_output){
         throw QhullError(10037, "Qhull error: UsingLibQhull not active(s_qhull_output undefined).  Invoke UsingLibQhull before this call");
     }
     if(s_qhull_output->qhull_run_id!=qhRunId){
         throw QhullError(10046, "Qhull error: qhRunId %d != s_qhull_output.runId %d.  Is another Qhull active", qhRunId, s_qhull_output->qhull_run_id);
     }
     my_qhull= s_qhull_output;
     qh NOerrexit= False;   // assumes setjmp called next
 }//UsingLibQhull runId
 
 //Leaves libqhull active for runId access
 UsingLibQhull::
 ~UsingLibQhull()
 {
     QhullError e= checkRunId();
     if(e.isDefined()){
         e.logError();
     }else{
 #if qh_QHpointer
         if(qh_qh){
             qh NOerrexit= true;
         }
 #else
         qh NOerrexit= true;
 #endif
     }
     s_using_libqhull= false;
 }//~UsingLibQhull
 
 #//Class methods
 
-void UsingLibQhull::
-checkQhullMemoryEmpty()
-{
-    int curlong, totlong, curshort, totshort, maxlong, totbuffer;
-    // qh_memtotal does not error
-    qh_memtotal(&curlong, &totlong, &curshort, &totshort, &maxlong, &totbuffer);
-    if (curlong || totlong){
-        throw QhullError(10026, "Qhull error: qhull did not free %d bytes of long memory (%d pieces).", totlong, curlong);
-    }
-    if (curshort || totshort){
-        throw QhullError(10035, "Qhull error: qhull did not free %d bytes of short memory (%d pieces).", totshort, curshort);
-    }
-}//checkQhullMemoryEmpty
-
-double UsingLibQhull::
-currentAngleEpsilon()
-{
-    if(s_qhull_output && s_qhull_output->initialized()){
-        return s_qhull_output->qhullQh()->ANGLEround*FACTORepsilon;
-    }else if(s_has_angle_epsilon){
-        return s_angle_epsilon;
-    }
-    return UsingLibQhull::DEFAULTangleEpsilon;
-}//currentAngleEpsilon
-
-double UsingLibQhull::
-currentDistanceEpsilon()
-{
-    if(s_qhull_output && s_qhull_output->initialized()){
-        return s_qhull_output->qhullQh()->DISTround*FACTORepsilon;
-    }else if(s_has_distance_epsilon){
-        return s_distance_epsilon;
-    }
-    return UsingLibQhull::DEFAULTdistanceEpsilon;
-}//currentDistanceEpsilon
-
-const coordT *UsingLibQhull::
-currentPoints(int *dimension, const coordT **pointsEnd)
-{
-    if(s_qhull_output && s_qhull_output->initialized()){
-        *dimension= qh hull_dim;
-        *pointsEnd= qh first_point+qh num_points*qh hull_dim;
-        return qh first_point;
-    }else if(s_has_points){
-        *dimension= s_points_dimension;
-        *pointsEnd= s_points_end;
-        return s_points_begin;
-    }
-    throw QhullError(10059, "Qhull error: missing definition for currentPoints().  Need currentQhull() or setGlobalDistanceEpsilon()");
-}//currentPoints
-
-Qhull &UsingLibQhull::
-currentQhull()
-{
-    if(!s_qhull_output){
-        throw QhullError(10055, "Qhull error: currentQhull not defined.  Run qhull first.");
-    }
-    return *s_qhull_output;
-}//currentQhull
-
-// for QhullVertex::dimension() when >= 16
-int UsingLibQhull::
-currentVertexDimension()
-{
-    if(s_qhull_output && s_qhull_output->initialized()){
-        return s_qhull_output->dimension();
-    }else if(s_has_vertex_dimension){
-        return s_vertex_dimension;
-    }
-    throw QhullError(10057, "Qhull error: missing definition for currentVertexDimension().  Need currentQhull() or setGlobalVertexDimension()");
-}//currentVertexDimension
-
-const coordT *UsingLibQhull::
-globalPoints(int *dimension, const coordT **pointsEnd)
-{
-    if(s_has_points){
-        *dimension= s_points_dimension;
-        *pointsEnd= s_points_end;
-        return s_points_begin;
-    }else{
-        return currentPoints(dimension, pointsEnd);
-    }
-}//globalPoints
-
-bool UsingLibQhull::
-hasPoints()
-{
-    return s_has_points || (s_qhull_output && s_qhull_output->initialized());
-}
-
-bool UsingLibQhull::
-hasVertexDimension()
-{
-    return s_has_vertex_dimension || (s_qhull_output && s_qhull_output->initialized());
-}
-
 void UsingLibQhull::
 setGlobals()
 {
     if(s_qhull_output && s_qhull_output->initialized()){
         QhullQh *qqh= s_qhull_output->qhullQh();
         s_angle_epsilon= qqh->ANGLEround*FACTORepsilon;
         s_distance_epsilon= qqh->DISTround*FACTORepsilon;
         s_points_begin= qqh->first_point;
         s_points_dimension= qqh->hull_dim;
         s_points_end= s_points_begin+qqh->num_points*s_points_dimension;
         s_vertex_dimension= qqh->hull_dim;
         s_has_angle_epsilon= true;
         s_has_distance_epsilon= true;
         s_has_points= true;
         s_has_vertex_dimension= true;
     }else{
         throw QhullError(10058, "Qhull error: setGlobals can only be called for currentQhull().  Run qhull first.");
     }
  }//setGlobals
 
 void UsingLibQhull::
 unsetGlobals()
 {
     s_has_angle_epsilon= false;
     s_has_distance_epsilon= false;
     s_has_points= false;
     s_has_vertex_dimension= false;
 }//unsetGlobals
 
-#// Methods
-
-void UsingLibQhull::
-maybeThrowQhullMessage(int exitCode) const
-{
-    my_qhull->maybeThrowQhullMessage(exitCode);
-    QhullError e= checkRunId(); // Check for qhRunId after libqhull returns. For convenience, ought to be at end of libqhull try block
-    if(e.isDefined()){
-        throw e;
-    }
-}//maybeThrowQhullMessage
-
-void UsingLibQhull::
-maybeThrowQhullMessage(int exitCode, int noThrow) const
-{
-    my_qhull->maybeThrowQhullMessage(exitCode, noThrow);
-    QhullError e= checkRunId(); // Check for qhRunId after libqhull returns. For convenience, ought to be at end of libqhull try block
-    if(e.isDefined()){
-        e.logError();
-    }
-}//maybeThrowQhullMessage
-
 #//Helpers
 
-//! Return QhullError for maybeThrowFromDestructor()
-QhullError UsingLibQhull::
-checkRunId() const
-{
-    // Predeclaring QhullError results in four copy constructors, none used here
-#if qh_QHpointer
-    if(qh_qh){ // 0 if ~Qhull
-        if(my_qhull->qhull_run_id!=qh run_id){
-            return QhullError(10047, "Qhull internal error: Global state (qh_qh, run_id %d) changed.  Should be runId %d.  Another thread?", qh run_id, my_qhull->qhull_run_id);
-        }
-    }
-#else
-    if(qh run_id!=0 && my_qhull->qhull_run_id!=qh run_id){
-        return QhullError(10048, "Qhull internal error: Global state (qh_qh, run_id %d) changed.  Should be runId %d.  Another thread?", qh run_id, my_qhull->qhull_run_id);
-    }
-#endif
-    return QhullError();
-}//checkRunId
-
-//! Can not embed UsingLibQhull.  Otherwise allocated a C++ object missed by qh_errexit
-void UsingLibQhull::
-checkUsingLibQhull() const
-{
-    if(s_using_libqhull){
-        if(s_qhull_output){
-            throw QhullError(10049, "Qhull error: UsingLibQhull already in use by QhullQh.runId %d", s_qhull_output->qhull_run_id);
-        }else{
-            throw QhullError(10050, "Qhull error: UsingLibQhull already in use.  No s_qhull_output");
-        }
-    }
-    s_using_libqhull= true;
-}//checkUsingLibQhull
-
 }//namespace orgQhull
 
diff --git a/src/libqhullcpp/UsingLibQhull.h b/src/libqhullcpp/UsingLibQhull.h
index 92273a2..fb3663d 100644
--- a/src/libqhullcpp/UsingLibQhull.h
+++ b/src/libqhullcpp/UsingLibQhull.h
@@ -1,144 +1,141 @@
 /****************************************************************************
 **
-** Copyright (c) 2008-2012 C.B. Barber. All rights reserved.
-** $Id: //main/2011/qhull/src/libqhullcpp/UsingLibQhull.h#6 $$Change: 1464 $
-** $DateTime: 2012/01/25 22:58:41 $$Author: bbarber $
+** Copyright (c) 2008-2014 C.B. Barber. All rights reserved.
+** $Id: //main/2011/qhull/src/libqhullcpp/UsingLibQhull.h#8 $$Change: 1707 $
+** $DateTime: 2014/03/26 09:42:11 $$Author: bbarber $
 **
 ****************************************************************************/
 
 #ifndef USINGlibqhull_H
 #define USINGlibqhull_H
 
 #include "QhullError.h"
 extern "C" {
-#include "libqhull/libqhull.h"
+#include "libqhullr/qhull_ra.h"
 }
 
 namespace orgQhull {
 
-#//Types
+#//!\name Types
     //! UsingLibQhull -- Interface into libqhull and its 'qh' and 'qhstat' macros
     //! Always use with setjmp() for libqhull error handling.
 
 /*******************************
 
 UsingLibQhull is stack based, but as a call
 Qhull declarations are stack-based.  But can't define a
 setjmp environment, since the target goes away.  So must be UsingLibQhull, but can only have one
 setjmp at a time? Can embedded another Using as long as save/restore
 longjmp on exit.
 */
     class UsingLibQhull;
 
     // Defined elsewhere
     class Qhull;
 
-#// Global variables
-extern Qhull           *s_qhull_output; //! Provide qh_fprintf (Qhull.cpp) access to Qhull
-
 class UsingLibQhull {
 
 private:
-#//Fields
-    Qhull              *my_qhull;
+#//!\name Fields
+    Qhull *             my_qhull;
     int                 qh_exitcode;
 
-#//Class globals
+#//!\name Class globals
     //! Global flags
     static bool         s_using_libqhull; //! True if UsingLibQhull is in scope
 
     //! Use global values if s_has_... is set
     static bool         s_has_angle_epsilon; //! True if s_angle_epsilon defined
     static bool         s_has_distance_epsilon; //! True if s_distance_epsilon defined
     static bool         s_has_points;        //! If False (default), Qhull() runs setPointBase()
     static bool         s_has_vertex_dimension; //! True if s_vertex_dimension defined
 
     //! Global values
     static double       s_angle_epsilon;   //! Epsilon for angle equality
     static double       s_distance_epsilon;   //! Epsilon for distance equality
     static const coordT *s_points_begin;            //! For QhullPoint::id() w/o qhRunId.
     static const coordT *s_points_end;            //! For QhullPoint::id() w/o qhRunId.
     static int          s_points_dimension;
     static int          s_vertex_dimension; //! Default dimension (e.g., if Vertex::dimension() >= 16)
 
 public:
-#//Class constants
+#//!\name Class constants
     static const int    NOqhRunId= 0;   //! qh_qh is not available
     static const int    NOthrow= 1;     //! Do not throw from maybeThrowQhullMessage
     static const int    FACTORepsilon= 10;  //!
     static const double DEFAULTdistanceEpsilon; //! ~DISTround*FACTORepsilon for unit cube
     static const double DEFAULTangleEpsilon;    //! ~ANGLEround*FACTORepsilon for unit cube
 
-#//Class members
+#//!\name Class members
     static void         checkQhullMemoryEmpty();
     static double       currentAngleEpsilon();
     static double       currentDistanceEpsilon();
     static const coordT *currentPoints(int *dimension, const coordT **pointsEnd);
-    static Qhull       ¤tQhull();
+    static Qhull &      currentQhull();
     static int          currentVertexDimension();
     static double       globalAngleEpsilon() { return s_has_angle_epsilon ? s_angle_epsilon : currentAngleEpsilon(); }
     static double       globalDistanceEpsilon() { return s_has_distance_epsilon ? s_distance_epsilon : currentDistanceEpsilon(); }
     static double       globalMachineEpsilon() { return REALepsilon; }
     static const coordT *globalPoints(int *dimension, const coordT **pointsEnd);
     static int          globalVertexDimension() { return s_has_vertex_dimension ? s_vertex_dimension : currentVertexDimension(); }
     static bool         hasPoints();        // inline would require Qhull.h
     static bool         hasVertexDimension();
     static void         setGlobalAngleEpsilon(double d) { s_angle_epsilon=d; s_has_angle_epsilon= true; }
     static void         setGlobalDistanceEpsilon(double d) { s_distance_epsilon= d; s_has_distance_epsilon= true; }
     static void         setGlobalPoints(int dimension, const coordT *pointsBegin, const coordT *pointsEnd) { s_points_dimension= dimension; s_points_begin= pointsBegin; s_points_end= pointsEnd; s_has_points= true; }
     static void         setGlobalVertexDimension(int i) { s_vertex_dimension= i; s_has_vertex_dimension= true; }
     static void         setGlobals();
     static void         unsetGlobalAngleEpsilon() { s_has_angle_epsilon= false; }
     static void         unsetGlobalDistanceEpsilon() { s_has_distance_epsilon= false; }
     static void         unsetGlobalPoints() { s_has_points= false; }
     static void         unsetGlobalVertexDimension() { s_has_vertex_dimension= false; }
     static void         unsetGlobals();
 
-#//Constructors
+#//!\name Constructors
                         UsingLibQhull(Qhull *p);
                         UsingLibQhull(Qhull *p, int noThrow);
                         UsingLibQhull(int qhRunId);
-                       ~UsingLibQhull();
+                        ~UsingLibQhull();
 
 private:                //! disable default constructor, copy constructor, and copy assignment
                         UsingLibQhull();
                         UsingLibQhull(const UsingLibQhull &);
-   UsingLibQhull       &operator=(const UsingLibQhull &);
+   UsingLibQhull &      operator=(const UsingLibQhull &);
 public:
 
-#//Methods
-#//Access
+#//!\name Methods
+#//!\name Access
     bool                defined() const { return my_qhull!=0; }
     void                maybeThrowQhullMessage(int exitCode) const;
     void                maybeThrowQhullMessage(int exitCode, int noThrow) const;
 
-#//Helpers
+#//!\name Helpers
 private:
    QhullError           checkRunId() const;
    void                 checkUsingLibQhull() const;
 
 /***********************************
 You may use global variables in 'qh' after declaring UsingLibQhull.  For example
 
   UsingLibQhull q(qhRunId);
   // NOerrors -- no calls that throw libqhull errors
   cout << "Delaunay Mode: " << qh DELAUNAY;
 
 To trap errors from libqhull, UsingLibQhull must be followed by
 
 UsingLibQhull q(qhRunId);
 int exitCode = setjmp(qh errexit);
 if(!exitCode){ // no object creation -- destructors skipped on longjmp()
     calls to libqhull
 }
 q.maybeThrowQhullMessage(exitCode);
 
 The call to setjmp() can not be moved to a method.  The stack must be preserved for error exits from libqhull.
 
 */
 
 };//UsingLibQhull
 
 }//namespace orgQhull
 
 #endif // USINGlibqhull_H
diff --git a/src/libqhullcpp/functionObjects.h b/src/libqhullcpp/functionObjects.h
index 250b0e9..e4da5f9 100644
--- a/src/libqhullcpp/functionObjects.h
+++ b/src/libqhullcpp/functionObjects.h
@@ -1,66 +1,67 @@
 /****************************************************************************
 **
-** Copyright (c) 2008-2012 C.B. Barber. All rights reserved.
-** $Id: //main/2011/qhull/src/libqhullcpp/functionObjects.h#4 $$Change: 1464 $
-** $DateTime: 2012/01/25 22:58:41 $$Author: bbarber $
+** Copyright (c) 2008-2014 C.B. Barber. All rights reserved.
+** $Id: //main/2011/qhull/src/libqhullcpp/functionObjects.h#8 $$Change: 1797 $
+** $DateTime: 2014/12/15 17:23:41 $$Author: bbarber $
 **
 ****************************************************************************/
 
 #ifndef QHFUNCTIONOBJECTS_H
 #define QHFUNCTIONOBJECTS_H
 
 #include 
 #include 
 
 namespace orgQhull {
-#//Type
+
+#//!\name Defined here
 
     //! Sum of absolute values of the elements in a container
     class AbsoluteSumOf;
     //! Sum of the elements in a container
     class SumOf;
     //! Sum of squares of the elements in a container
     class SumSquaresOf;
 
-#//Class
+#//!\name Class
 
 //! Absolute sum of the elements in a container
 class AbsoluteSumOf
 {
 private:
     double sum;
 public:
     inline AbsoluteSumOf() : sum(0.0) {}
     inline void operator()(double v) { sum += fabs(v); }
     inline operator double() { return sum; }
 };//AbsoluteSumOf
 
 //! Sum of the elements in a container
 class SumOf
 {
 private:
     double sum;
 public:
     inline SumOf() : sum(0.0) {}
     inline void operator()(double v) { sum += v; }
     inline operator double() { return sum; }
 };//SumOf
 
 
 //! Sum of squares of the elements in a container
 class SumSquaresOf
 {
 private:
     double sum;
 public:
     inline SumSquaresOf() : sum(0.0) {}
     inline void operator()(double v) { sum += v*v; }
     inline operator double() { return sum; }
 };//SumSquaresOf
 
 
 }//orgQhull
 
 
 #endif //QHFUNCTIONOBJECTS_H
 
diff --git a/src/libqhullcpp/libqhullcpp.pro b/src/libqhullcpp/libqhullcpp.pro
index ba39c37..66abc06 100644
--- a/src/libqhullcpp/libqhullcpp.pro
+++ b/src/libqhullcpp/libqhullcpp.pro
@@ -1,69 +1,68 @@
 # -------------------------------------------------
 # libqhullcpp.pro -- Qt project for Qhull cpp shared library
 # -------------------------------------------------
 
 include(../qhull-warn.pri)
 
 DESTDIR = ../../lib
 TEMPLATE = lib
 CONFIG += staticlib warn_on
 CONFIG -= qt rtti
 build_pass:CONFIG(debug, debug|release):{
    TARGET = qhullcpp_d
    OBJECTS_DIR = Debug
 }else:build_pass:CONFIG(release, debug|release):{
    TARGET = qhullcpp
    OBJECTS_DIR = Release
 }
 MOC_DIR = moc
 
 INCLUDEPATH += ../../src
 INCLUDEPATH += $$PWD # for MOC_DIR
 
 CONFIG += qhull_warn_shadow qhull_warn_conversion
 
 SOURCES += ../libqhullcpp/Coordinates.cpp
 SOURCES += ../libqhullcpp/PointCoordinates.cpp
 SOURCES += ../libqhullcpp/Qhull.cpp
 SOURCES += ../libqhullcpp/QhullFacet.cpp
 SOURCES += ../libqhullcpp/QhullFacetList.cpp
 SOURCES += ../libqhullcpp/QhullFacetSet.cpp
 SOURCES += ../libqhullcpp/QhullHyperplane.cpp
 SOURCES += ../libqhullcpp/QhullPoint.cpp
 SOURCES += ../libqhullcpp/QhullPoints.cpp
 SOURCES += ../libqhullcpp/QhullPointSet.cpp
 SOURCES += ../libqhullcpp/QhullQh.cpp
 SOURCES += ../libqhullcpp/QhullRidge.cpp
 SOURCES += ../libqhullcpp/QhullSet.cpp
 SOURCES += ../libqhullcpp/QhullStat.cpp
 SOURCES += ../libqhullcpp/QhullVertex.cpp
 SOURCES += ../libqhullcpp/QhullVertexSet.cpp
 SOURCES += ../libqhullcpp/RboxPoints.cpp
 SOURCES += ../libqhullcpp/RoadError.cpp
 SOURCES += ../libqhullcpp/RoadLogEvent.cpp
-SOURCES += ../libqhullcpp/UsingLibQhull.cpp
 
 HEADERS += ../libqhullcpp/Coordinates.h
 HEADERS += ../libqhullcpp/functionObjects.h
 HEADERS += ../libqhullcpp/PointCoordinates.h
 HEADERS += ../libqhullcpp/Qhull.h
 HEADERS += ../libqhullcpp/QhullError.h
 HEADERS += ../libqhullcpp/QhullFacet.h
 HEADERS += ../libqhullcpp/QhullFacetList.h
 HEADERS += ../libqhullcpp/QhullFacetSet.h
 HEADERS += ../libqhullcpp/QhullHyperplane.h
 HEADERS += ../libqhullcpp/QhullIterator.h
 HEADERS += ../libqhullcpp/QhullLinkedList.h
 HEADERS += ../libqhullcpp/QhullPoint.h
 HEADERS += ../libqhullcpp/QhullPoints.h
 HEADERS += ../libqhullcpp/QhullPointSet.h
 HEADERS += ../libqhullcpp/QhullQh.h
 HEADERS += ../libqhullcpp/QhullRidge.h
 HEADERS += ../libqhullcpp/QhullSet.h
 HEADERS += ../libqhullcpp/QhullSets.h
 HEADERS += ../libqhullcpp/QhullStat.h
 HEADERS += ../libqhullcpp/QhullVertex.h
+HEADERS += ../libqhullcpp/QhullVertexSet.h
 HEADERS += ../libqhullcpp/RboxPoints.h
 HEADERS += ../libqhullcpp/RoadError.h
 HEADERS += ../libqhullcpp/RoadLogEvent.h
-HEADERS += ../libqhullcpp/UsingLibQhull.h
diff --git a/src/libqhullcpp/qt-qhull.cpp b/src/libqhullcpp/qt-qhull.cpp
index e5b410a..e42c67e 100644
--- a/src/libqhullcpp/qt-qhull.cpp
+++ b/src/libqhullcpp/qt-qhull.cpp
@@ -1,129 +1,130 @@
 /****************************************************************************
 **
 ** Copyright (c) 2009-2014 C.B. Barber. All rights reserved.
-** $Id: //main/2011/qhull/src/libqhullcpp/qt-qhull.cpp#4 $$Change: 1490 $
-** $DateTime: 2012/02/19 20:27:01 $$Author: bbarber $
+** $Id: //main/2011/qhull/src/libqhullcpp/qt-qhull.cpp#7 $$Change: 1800 $
+** $DateTime: 2014/12/17 21:46:45 $$Author: bbarber $
 **
 ****************************************************************************/
 
 #include 
 #include "RoadTest.h"
 
 #ifndef QHULL_USES_QT
 #define QHULL_USES_QT 1
 #endif
 
 #include "Coordinates.h"
 #include "QhullFacetList.h"
 #include "QhullFacetSet.h"
 #include "QhullHyperplane.h"
 #include "QhullPoint.h"
 #include "QhullPoints.h"
 #include "QhullPointSet.h"
 #include "QhullVertex.h"
 #include "QhullVertexSet.h"
 
 namespace orgQhull {
 
 #//Conversions
 
 QList Coordinates::
 toQList() const
 {
     CoordinatesIterator i(*this);
     QList cs;
     while(i.hasNext()){
         cs.append(i.next());
     }
     return cs;
 }//toQList
 
 QList QhullFacetList::
 toQList() const
 {
     QhullLinkedListIterator i(*this);
     QList vs;
     while(i.hasNext()){
         QhullFacet f= i.next();
         if(isSelectAll() || f.isGood()){
             vs.append(f);
         }
     }
     return vs;
 }//toQList
 
 //! Same as PrintVertices
 QList QhullFacetList::
-vertices_toQList(int qhRunId) const
+vertices_toQList() const
 {
     QList vs;
-    QhullVertexSet qvs(qhRunId, first().getFacetT(), NULL, isSelectAll());
+    QhullVertexSet qvs(qh(), first().getFacetT(), NULL, isSelectAll());
     for(QhullVertexSet::iterator i=qvs.begin(); i!=qvs.end(); ++i){
         vs.push_back(*i);
     }
     return vs;
 }//vertices_toQList
 
 QList QhullFacetSet::
 toQList() const
 {
     QhullSetIterator i(*this);
     QList vs;
     while(i.hasNext()){
         QhullFacet f= i.next();
         if(isSelectAll() || f.isGood()){
             vs.append(f);
         }
     }
     return vs;
 }//toQList
 
 #ifdef QHULL_USES_QT
 QList QhullHyperplane::
 toQList() const
 {
     QhullHyperplaneIterator i(*this);
     QList fs;
     while(i.hasNext()){
         fs.append(i.next());
     }
     fs.append(hyperplane_offset);
     return fs;
 }//toQList
 #endif //QHULL_USES_QT
 
 QList QhullPoint::
 toQList() const
 {
     QhullPointIterator i(*this);
     QList vs;
     while(i.hasNext()){
         vs.append(i.next());
     }
     return vs;
 }//toQList
 
 QList QhullPoints::
 toQList() const
 {
     QhullPointsIterator i(*this);
     QList vs;
     while(i.hasNext()){
         vs.append(i.next());
     }
     return vs;
 }//toQList
 
+/******
 QList QhullPointSet::
 toQList() const
 {
     QhullPointSetIterator i(*this);
     QList vs;
     while(i.hasNext()){
         vs.append(i.next());
     }
     return vs;
 }//toQList
-
+*/
 }//orgQhull
 
diff --git a/src/libqhullpcpp/Coordinates.h b/src/libqhullpcpp/Coordinates.h
index 1fca646..1007660 100644
--- a/src/libqhullpcpp/Coordinates.h
+++ b/src/libqhullpcpp/Coordinates.h
@@ -1,311 +1,312 @@
 /****************************************************************************
 **
 ** Copyright (c) 2009-2012 C.B. Barber. All rights reserved.
-** $Id: //main/2011/qhull/src/libqhullpcpp/Coordinates.h#1 $$Change: 1652 $
-** $DateTime: 2014/01/17 09:01:32 $$Author: bbarber $
+** $Id: //main/2011/qhull/src/libqhullpcpp/Coordinates.h#2 $$Change: 1675 $
+** $DateTime: 2014/02/01 09:38:20 $$Author: bbarber $
 **
 ****************************************************************************/
 
 #ifndef QHCOORDINATES_H
 #define QHCOORDINATES_H
 
 #include "QhullError.h"
 #include "QhullIterator.h"
 extern "C" {
     #include "libqhull/qhull_a.h"
 }
 
 
 #include  // ptrdiff_t, size_t
 #include 
 #include 
 
 namespace orgQhull {
 
-#//Types
+#//!\name Types
     //! an allocated vector of point coordinates
     //!  Used by PointCoordinates for RboxPoints
     //!  A QhullPoint refers to previously allocated coordinates
-    class  Coordinates;
-    class  MutableCoordinatesIterator;
+    class Coordinates;
+    class MutableCoordinatesIterator;
 
 
 class Coordinates {
 
 private:
-#//Fields
+#//!\name Fields
     std::vector coordinate_array;
 
 public:
-#//Subtypes
+#//!\name Subtypes
 
-    class                       const_iterator;
-    class                       iterator;
+    class const_iterator;
+    class iterator;
     typedef iterator Iterator;
     typedef const_iterator ConstIterator;
 
     typedef coordT              value_type;
     typedef const value_type   *const_pointer;
-    typedef const value_type   &const_reference;
-    typedef value_type         *pointer;
-    typedef value_type         &reference;
+    typedef const value_type &  const_reference;
+    typedef value_type *        pointer;
+    typedef value_type &        reference;
     typedef ptrdiff_t           difference_type;
     typedef int                 size_type;
 
-#//Construct
+#//!\name Construct
                         Coordinates() {};
     explicit            Coordinates(const std::vector &other) : coordinate_array(other) {}
                         Coordinates(const Coordinates &other) : coordinate_array(other.coordinate_array) {}
-    Coordinates        &operator=(const Coordinates &other) { coordinate_array= other.coordinate_array; return *this; }
-    Coordinates        &operator=(const std::vector &other) { coordinate_array= other; return *this; }
-                       ~Coordinates() {}
+    Coordinates &       operator=(const Coordinates &other) { coordinate_array= other.coordinate_array; return *this; }
+    Coordinates &       operator=(const std::vector &other) { coordinate_array= other; return *this; }
+                        ~Coordinates() {}
 
-#//Conversion
+#//!\name Conversion
 
-    coordT             *data() { return isEmpty() ? 0 : &at(0); }
-    const coordT       *data() const { return const_cast(isEmpty() ? 0 : &at(0)); }
+    coordT *            data() { return isEmpty() ? 0 : &at(0); }
+    const coordT *      data() const { return const_cast(isEmpty() ? 0 : &at(0)); }
 
 #ifndef QHULL_NO_STL
     std::vector toStdVector() const { return coordinate_array; }
 #endif //QHULL_NO_STL
 #ifdef QHULL_USES_QT
     QList      toQList() const;
 #endif //QHULL_USES_QT
 
-#//GetSet
+#//!\name GetSet
     int                count() const { return static_cast(size()); }
     bool               empty() const { return coordinate_array.empty(); }
     bool               isEmpty() const { return empty(); }
     bool               operator==(const Coordinates &other) const  { return coordinate_array==other.coordinate_array; }
     bool               operator!=(const Coordinates &other) const  { return coordinate_array!=other.coordinate_array; }
     size_t             size() const { return coordinate_array.size(); }
 
-#//Element access
-    coordT             &at(int idx) { return coordinate_array.at(idx); }
-    const coordT       &at(int idx) const { return coordinate_array.at(idx); }
-    coordT             &back() { return coordinate_array.back(); }
-    const coordT       &back() const { return coordinate_array.back(); }
-    coordT             &first() { return front(); }
-    const coordT       &first() const { return front(); }
-    coordT             &front() { return coordinate_array.front(); }
-    const coordT       &front() const { return coordinate_array.front(); }
-    coordT             &last() { return back(); }
-    const coordT       &last() const { return back(); }
-    Coordinates        mid(int idx, int length= -1) const;
-    coordT            &operator[](int idx) { return coordinate_array.operator[](idx); }
-    const coordT      &operator[](int idx) const { return coordinate_array.operator[](idx); }
-    coordT             value(int idx, const coordT &defaultValue) const;
-
-#//Iterator
+#//!\name Element access
+    coordT &            at(int idx) { return coordinate_array.at(idx); }
+    const coordT &      at(int idx) const { return coordinate_array.at(idx); }
+    coordT &            back() { return coordinate_array.back(); }
+    const coordT &      back() const { return coordinate_array.back(); }
+    coordT &            first() { return front(); }
+    const coordT &      first() const { return front(); }
+    coordT &            front() { return coordinate_array.front(); }
+    const coordT &      front() const { return coordinate_array.front(); }
+    coordT &            last() { return back(); }
+    const coordT &      last() const { return back(); }
+    Coordinates         mid(int idx, int length= -1) const;
+    coordT &            operator[](int idx) { return coordinate_array.operator[](idx); }
+    const coordT &      operator[](int idx) const { return coordinate_array.operator[](idx); }
+    coordT              value(int idx, const coordT &defaultValue) const;
+
+#//!\name Iterator
     iterator            begin() { return iterator(coordinate_array.begin()); }
     const_iterator      begin() const { return const_iterator(coordinate_array.begin()); }
     const_iterator      constBegin() const { return begin(); }
     const_iterator      constEnd() const { return end(); }
     iterator            end() { return iterator(coordinate_array.end()); }
     const_iterator      end() const { return const_iterator(coordinate_array.end()); }
 
-#//Read-only
+#//!\name Read-only
     Coordinates         operator+(const Coordinates &other) const;
 
-#//Modify
+#//!\name Modify
     void                append(const coordT &c) { push_back(c); }
     void                clear() { coordinate_array.clear(); }
     iterator            erase(iterator idx) { return iterator(coordinate_array.erase(idx.base())); }
     iterator            erase(iterator beginIterator, iterator endIterator) { return iterator(coordinate_array.erase(beginIterator.base(), endIterator.base())); }
     void                insert(int before, const coordT &c) { insert(begin()+before, c); }
     iterator            insert(iterator before, const coordT &c) { return iterator(coordinate_array.insert(before.base(), c)); }
     void                move(int from, int to) { insert(to, takeAt(from)); }
-    Coordinates        &operator+=(const Coordinates &other);
-    Coordinates        &operator+=(const coordT &c) { append(c); return *this; }
-    Coordinates        &operator<<(const Coordinates &other) { return *this += other; }
-    Coordinates        &operator<<(const coordT &c) { return *this += c; }
+    Coordinates &       operator+=(const Coordinates &other);
+    Coordinates &       operator+=(const coordT &c) { append(c); return *this; }
+    Coordinates &       operator<<(const Coordinates &other) { return *this += other; }
+    Coordinates &       operator<<(const coordT &c) { return *this += c; }
     void                pop_back() { coordinate_array.pop_back(); }
     void                pop_front() { removeFirst(); }
     void                prepend(const coordT &c) { insert(begin(), c); }
     void                push_back(const coordT &c) { coordinate_array.push_back(c); }
     void                push_front(const coordT &c) { insert(begin(), c); }
                         //removeAll below
     void                removeAt(int idx) { erase(begin()+idx); }
     void                removeFirst() { erase(begin()); }
     void                removeLast() { erase(--end()); }
     void                replace(int idx, const coordT &c) { (*this)[idx]= c; }
     void                reserve(int i) { coordinate_array.reserve(i); }
     void                swap(int idx, int other);
     coordT              takeAt(int idx);
     coordT              takeFirst() { return takeAt(0); }
     coordT              takeLast();
 
-#//Search
+#//!\name Search
     bool                contains(const coordT &t) const;
     int                 count(const coordT &t) const;
     int                 indexOf(const coordT &t, int from = 0) const;
     int                 lastIndexOf(const coordT &t, int from = -1) const;
     void                removeAll(const coordT &t);
 
-#//Coordinates::iterator -- from QhullPoints, forwarding to coordinate_array
+#//!\name Coordinates::iterator
+    // From QhullPoints, forwarding to coordinate_array
     // before const_iterator for conversion with comparison operators
     class iterator {
 
     private:
         std::vector::iterator i;
-        friend class    const_iterator;
+        friend class const_iterator;
 
     public:
         typedef std::random_access_iterator_tag  iterator_category;
         typedef coordT      value_type;
         typedef value_type *pointer;
         typedef value_type &reference;
         typedef ptrdiff_t   difference_type;
 
                         iterator() {}
                         iterator(const iterator &other) { i= other.i; }
         explicit        iterator(const std::vector::iterator &vi) { i= vi; }
-        iterator       &operator=(const iterator &other) { i= other.i; return *this; }
+        iterator &      operator=(const iterator &other) { i= other.i; return *this; }
         std::vector::iterator &base() { return i; }
                         // No operator-> for base types
-        coordT         &operator*() const { return *i; }
-        coordT         &operator[](int idx) const { return i[idx]; }
+        coordT &        operator*() const { return *i; }
+        coordT &        operator[](int idx) const { return i[idx]; }
 
         bool            operator==(const iterator &other) const { return i==other.i; }
         bool            operator!=(const iterator &other) const { return i!=other.i; }
         bool            operator<(const iterator &other) const { return i(const iterator &other) const { return i>other.i; }
         bool            operator>=(const iterator &other) const { return i>=other.i; }
               // reinterpret_cast to break circular dependency
         bool            operator==(const Coordinates::const_iterator &other) const { return *this==reinterpret_cast(other); }
         bool            operator!=(const Coordinates::const_iterator &other) const { return *this!=reinterpret_cast(other); }
         bool            operator<(const Coordinates::const_iterator &other) const { return *this(other); }
         bool            operator<=(const Coordinates::const_iterator &other) const { return *this<=reinterpret_cast(other); }
         bool            operator>(const Coordinates::const_iterator &other) const { return *this>reinterpret_cast(other); }
         bool            operator>=(const Coordinates::const_iterator &other) const { return *this>=reinterpret_cast(other); }
 
         iterator        operator++() { return iterator(++i); } //FIXUP QH11012 Should return reference, but get reference to temporary
         iterator        operator++(int) { return iterator(i++); }
         iterator        operator--() { return iterator(--i); }
         iterator        operator--(int) { return iterator(i--); }
         iterator        operator+=(int idx) { return iterator(i += idx); }
         iterator        operator-=(int idx) { return iterator(i -= idx); }
         iterator        operator+(int idx) const { return iterator(i+idx); }
         iterator        operator-(int idx) const { return iterator(i-idx); }
         difference_type operator-(iterator other) const { return i-other.i; }
     };//Coordinates::iterator
 
-#//Coordinates::const_iterator
+#//!\name Coordinates::const_iterator
     class const_iterator {
 
     private:
         std::vector::const_iterator i;
 
     public:
         typedef std::random_access_iterator_tag  iterator_category;
         typedef coordT            value_type;
         typedef const value_type *pointer;
         typedef const value_type &reference;
         typedef ptrdiff_t         difference_type;
 
                         const_iterator() {}
                         const_iterator(const const_iterator &other) { i= other.i; }
                         const_iterator(iterator o) : i(o.i) {}
         explicit        const_iterator(const std::vector::const_iterator &vi) { i= vi; }
         const_iterator &operator=(const const_iterator &other) { i= other.i; return *this; }
                         // No operator-> for base types
                         // No reference to a base type for () and []
-        const coordT   &operator*() const { return *i; }
-        const coordT   &operator[](int idx) const { return i[idx]; }
+        const coordT &  operator*() const { return *i; }
+        const coordT &  operator[](int idx) const { return i[idx]; }
 
         bool            operator==(const const_iterator &other) const { return i==other.i; }
         bool            operator!=(const const_iterator &other) const { return i!=other.i; }
         bool            operator<(const const_iterator &other) const { return i(const const_iterator &other) const { return i>other.i; }
         bool            operator>=(const const_iterator &other) const { return i>=other.i; }
 
         const_iterator  operator++() { return const_iterator(++i); } //FIXUP QH11014 -- too much copying
         const_iterator  operator++(int) { return const_iterator(i++); }
         const_iterator  operator--() { return const_iterator(--i); }
         const_iterator  operator--(int) { return const_iterator(i--); }
         const_iterator  operator+=(int idx) { return const_iterator(i += idx); }
         const_iterator  operator-=(int idx) { return const_iterator(i -= idx); }
         const_iterator  operator+(int idx) const { return const_iterator(i+idx); }
         const_iterator  operator-(int idx) const { return const_iterator(i-idx); }
         difference_type operator-(const_iterator other) const { return i-other.i; }
     };//Coordinates::const_iterator
 
 };//Coordinates
 
 //class CoordinatesIterator
 //QHULL_DECLARE_SEQUENTIAL_ITERATOR(Coordinates, coordT)
 
 class CoordinatesIterator
 {
     typedef Coordinates::const_iterator const_iterator;
     const Coordinates *c;
     const_iterator i;
     public:
     inline CoordinatesIterator(const Coordinates &container)
     : c(&container), i(c->constBegin()) {}
     inline CoordinatesIterator &operator=(const Coordinates &container)
     { c = &container; i = c->constBegin(); return *this; }
     inline void toFront() { i = c->constBegin(); }
     inline void toBack() { i = c->constEnd(); }
     inline bool hasNext() const { return i != c->constEnd(); }
     inline const coordT &next() { return *i++; }
     inline const coordT &peekNext() const { return *i; }
     inline bool hasPrevious() const { return i != c->constBegin(); }
     inline const coordT &previous() { return *--i; }
     inline const coordT &peekPrevious() const { const_iterator p = i; return *--p; }
     inline bool findNext(const coordT &t)
     { while (i != c->constEnd()) if (*i++ == t) return true; return false; }
     inline bool findPrevious(const coordT &t)
     { while (i != c->constBegin()) if (*(--i) == t) return true;
     return false;  }
 };//CoordinatesIterator
 
 //class MutableCoordinatesIterator
 //QHULL_DECLARE_MUTABLE_SEQUENTIAL_ITERATOR(Coordinates, coordT)
 class MutableCoordinatesIterator
 {
     typedef Coordinates::iterator iterator;
     typedef Coordinates::const_iterator const_iterator;
     Coordinates *c;
     iterator i, n;
     inline bool item_exists() const { return const_iterator(n) != c->constEnd(); }
     public:
     inline MutableCoordinatesIterator(Coordinates &container)
     : c(&container)
     { i = c->begin(); n = c->end(); }
     inline ~MutableCoordinatesIterator()
     {}
     inline MutableCoordinatesIterator &operator=(Coordinates &container)
     { c = &container;
     i = c->begin(); n = c->end(); return *this; }
     inline void toFront() { i = c->begin(); n = c->end(); }
     inline void toBack() { i = c->end(); n = i; }
     inline bool hasNext() const { return c->constEnd() != const_iterator(i); }
     inline coordT &next() { n = i++; return *n; }
     inline coordT &peekNext() const { return *i; }
     inline bool hasPrevious() const { return c->constBegin() != const_iterator(i); }
     inline coordT &previous() { n = --i; return *n; }
     inline coordT &peekPrevious() const { iterator p = i; return *--p; }
     inline void remove()
     { if (c->constEnd() != const_iterator(n)) { i = c->erase(n); n = c->end(); } }
     inline void setValue(const coordT &t) const { if (c->constEnd() != const_iterator(n)) *n = t; }
     inline coordT &value() { QHULL_ASSERT(item_exists()); return *n; }
     inline const coordT &value() const { QHULL_ASSERT(item_exists()); return *n; }
     inline void insert(const coordT &t) { n = i = c->insert(i, t); ++i; }
     inline bool findNext(const coordT &t)
     { while (c->constEnd() != const_iterator(n = i)) if (*i++ == t) return true; return false; }
     inline bool findPrevious(const coordT &t)
     { while (c->constBegin() != const_iterator(i)) if (*(n = --i) == t) return true;
     n = c->end(); return false;  }
 };//MutableCoordinatesIterator
 
 
 }//namespace orgQhull
 
-#//Global functions
+#//!\name Global
 
 std::ostream &operator<<(std::ostream &os, const orgQhull::Coordinates &c);
 
 #endif // QHCOORDINATES_H
diff --git a/src/libqhullpcpp/PointCoordinates.cpp b/src/libqhullpcpp/PointCoordinates.cpp
index 78f7af1..5a23cc5 100644
--- a/src/libqhullpcpp/PointCoordinates.cpp
+++ b/src/libqhullpcpp/PointCoordinates.cpp
@@ -1,294 +1,295 @@
 /****************************************************************************
 **
 ** Copyright (c) 2009-2014 C.B. Barber. All rights reserved.
-** $Id: //main/2011/qhull/src/libqhullpcpp/PointCoordinates.cpp#1 $$Change: 1652 $
-** $DateTime: 2014/01/17 09:01:32 $$Author: bbarber $
+** $Id: //main/2011/qhull/src/libqhullpcpp/PointCoordinates.cpp#2 $$Change: 1712 $
+** $DateTime: 2014/03/30 22:34:33 $$Author: bbarber $
 **
 ****************************************************************************/
 
 #include "QhullError.h"
 #include "QhullPoint.h"
 #include "PointCoordinates.h"
 
 #include 
 #include 
 
 using std::istream;
 using std::string;
 using std::ws;
 
 #ifdef _MSC_VER  // Microsoft Visual C++ -- warning level 4
 #pragma warning( disable : 4996)  // function was declared deprecated(strcpy, localtime, etc.)
 #endif
 
 namespace orgQhull {
 
 #//! PointCoordinates -- vector of PointCoordinates
 
 #//Construct
 PointCoordinates::
 PointCoordinates()
 : QhullPoints()
 , point_coordinates()
 , point_comment()
 {
     makeValid();
 }
 
 #//Construct
 PointCoordinates::
 PointCoordinates(int pointDimension)
 : QhullPoints(pointDimension)
 , point_coordinates()
 , point_comment()
 {
     makeValid();
 }
 
 PointCoordinates::
 PointCoordinates(const std::string &aComment)
 : QhullPoints()
 , point_coordinates()
 , point_comment(aComment)
 {
     makeValid();
 }
 
 PointCoordinates::
 PointCoordinates(int pointDimension, const std::string &aComment)
 : QhullPoints(pointDimension)
 , point_coordinates()
 , point_comment(aComment)
 {
     makeValid();
 }
 
 PointCoordinates::
 PointCoordinates(int pointDimension, const std::string &aComment, int coordinatesCount, const coordT *c)
 : QhullPoints(pointDimension)
 , point_coordinates()
 , point_comment(aComment)
 {
     append(coordinatesCount, c);
 }
 
 PointCoordinates::
 PointCoordinates(const PointCoordinates &other)
 : QhullPoints(other)
 , point_coordinates(other.point_coordinates)
 , point_comment(other.point_comment)
 {
     makeValid();
 }
 
 PointCoordinates & PointCoordinates::
 operator=(const PointCoordinates &other)
 {
+    QhullPoints::operator=(other);
     point_coordinates= other.point_coordinates;
     point_comment= other.point_comment;
     makeValid();
     return *this;
 }//operator=
 
 PointCoordinates::
 ~PointCoordinates()
 { }
 
 #//GetSet
 
 void PointCoordinates::
 checkValid() const
 {
     if(getCoordinates().data()!=data()
     || getCoordinates().count()!=coordinateCount()){
         throw QhullError(10060, "Qhull error: first point (%x) is not PointCoordinates.data() or count (%d) is not PointCoordinates.count (%d)", coordinateCount(), getCoordinates().count(), 0.0, data());
     }
 }//checkValid
 
 void PointCoordinates::
 setDimension(int i)
 {
     if(i<0){
         throw QhullError(10062, "Qhull error: can not set PointCoordinates dimension to %d", i);
     }
     int currentDimension=QhullPoints::dimension();
     if(currentDimension!=0 && i!=currentDimension){
         throw QhullError(10063, "Qhull error: can not change PointCoordinates dimension (from %d to %d)", currentDimension, i);
     }
     QhullPoints::setDimension(i);
 }//setDimension
 
 //#Foreach
 
 Coordinates::ConstIterator PointCoordinates::
 beginCoordinates(int pointIndex) const
 {
     return point_coordinates.begin()+indexOffset(pointIndex);
 }
 
 Coordinates::Iterator PointCoordinates::
 beginCoordinates(int pointIndex)
 {
     return point_coordinates.begin()+indexOffset(pointIndex);
 }
 
 #//Modify
 
 void PointCoordinates::
 append(int coordinatesCount, const coordT *c)
 {
     if(coordinatesCount<=0){
         return;
     }
     if(includesCoordinates(c)){
         throw QhullError(10065, "Qhull error: can not append a subset of PointCoordinates to itself.  The coordinates for point %d may move.", indexOf(c, QhullError::NOthrow));
     }
     reserveCoordinates(coordinatesCount);
     std::copy(c, c+coordinatesCount, std::back_inserter(point_coordinates));
     makeValid();
 }//append coordT
 
 void PointCoordinates::
 append(const PointCoordinates &other)
 {
     setDimension(other.dimension());
     append(other.coordinateCount(), other.data());
 }//append PointCoordinates
 
 void PointCoordinates::
 append(const QhullPoint &p)
 {
     setDimension(p.dimension());
     append(p.dimension(), p.coordinates());
 }//append QhullPoint
 
 void PointCoordinates::
 appendComment(const std::string &s){
     if(char c= s[0] && point_comment.empty()){
         if(c=='-' || isdigit(c)){
             throw QhullError(10028, "Qhull argument error: comments can not start with a number or minus, %s", 0, 0, 0.0, s.c_str());
         }
     }
     point_comment += s;
 }//appendComment
 
 //! Read PointCoordinates from istream.  First two numbers are dimension and count.  A non-digit starts a rboxCommand.
 //! Overwrites point_comment.  See qh_readpoints [io.c]
 void PointCoordinates::
 appendPoints(istream &in)
 {
     int inDimension, inCount;
     in >> ws >> inDimension >> ws;
     if(!in.good()){
         in.clear();
         string remainder;
         getline(in, remainder);
         throw QhullError(10005, "Qhull error: input did not start with dimension or count -- %s", 0, 0, 0, remainder.c_str());
     }
     char c= (char)in.peek();
     if(c!='-' && !isdigit(c)){         // Comments start with a non-digit
         getline(in, point_comment);
         in >> ws;
     }
     in >> inCount >> ws;
     if(!in.good()){
         in.clear();
         string remainder;
         getline(in, remainder);
         throw QhullError(10009, "Qhull error: input did not start with dimension and count -- %d %s", inDimension, 0, 0, remainder.c_str());
     }
     c= (char)in.peek();
     if(c!='-' && !isdigit(c)){         // Comments start with a non-digit
         getline(in, point_comment);
         in >> ws;
     }
     if(inCount> p >> ws;
         if(in.fail()){
             in.clear();
             string remainder;
             getline(in, remainder);
             throw QhullError(10008, "Qhull error: failed to read coordinate %d  of point %d\n   %s", coordinatesCount % inDimension, coordinatesCount/inDimension, 0, remainder.c_str());
         }else{
             point_coordinates.push_back(p);
             coordinatesCount++;
         }
     }
     if(coordinatesCount != inCount*inDimension){
         if(coordinatesCount%inDimension==0){
             throw QhullError(10006, "Qhull error: expected %d %d-d PointCoordinates but read %i PointCoordinates", int(inCount), inDimension, 0.0, int(coordinatesCount/inDimension));
         }else{
             throw QhullError(10012, "Qhull error: expected %d %d-d PointCoordinates but read %i PointCoordinates plus %f extra coordinates", inCount, inDimension, float(coordinatesCount%inDimension), coordinatesCount/inDimension);
         }
     }
     makeValid();
 }//appendPoints istream
 
 PointCoordinates PointCoordinates::
 operator+(const PointCoordinates &other) const
 {
     PointCoordinates pc= *this;
     pc << other;
     return pc;
 }//operator+
 
 void PointCoordinates::
 reserveCoordinates(int newCoordinates)
 {
     // vector::reserve is not const
     point_coordinates.reserve((int)point_coordinates.size()+newCoordinates); // WARN64
     makeValid();
 }//reserveCoordinates
 
 #//Helpers
 
 int PointCoordinates::
 indexOffset(int i) const {
     int n= i*dimension();
     int coordinatesCount= point_coordinates.count();
     if(i<0 || n>coordinatesCount){
         throw QhullError(10061, "Qhull error: point_coordinates is too short (%d) for point %d", coordinatesCount, i);
     }
     return n;
 }
 
 }//namespace orgQhull
 
 #//Global functions
 
 using std::endl;
 using std::ostream;
 
 using orgQhull::Coordinates;
 using orgQhull::PointCoordinates;
 
 ostream&
 operator<<(ostream &os, const PointCoordinates &p)
 {
     p.checkValid();
     int count= p.count();
     int dimension= p.dimension();
     string comment= p.comment();
     if(comment.empty()){
         os << dimension << endl;
     }else{
         os << dimension << " " << comment << endl;
     }
     os << count << endl;
     Coordinates::ConstIterator c= p.beginCoordinates();
     for(int i=0; i
 #include 
 
 namespace orgQhull {
 
-#//Types
+#//!\name Types
     //! Zero or more points with Coordinates, count, and dimension
     class PointCoordinates;
 
 class PointCoordinates : public QhullPoints {
 
 private:
-#//Field
+#//!\name Fields
     Coordinates         point_coordinates;      //! array of point coordinates
                                                 //! may have extraCoordinates()
     std::string         point_comment;          //! Comment describing PointCoordinates
 
 public:
-#//Construct
+#//!\name Construct
                         PointCoordinates();
     explicit            PointCoordinates(int pointDimension);
     explicit            PointCoordinates(const std::string &aComment);
                         PointCoordinates(int pointDimension, const std::string &aComment);
                         PointCoordinates(int pointDimension, const std::string &aComment, int coordinatesCount, const coordT *c); // may be invalid
                         //! Use append() and appendPoints() for Coordinates and vector
                         PointCoordinates(const PointCoordinates &other);
-    PointCoordinates   &operator=(const PointCoordinates &other);
-    ~PointCoordinates();
+    PointCoordinates &  operator=(const PointCoordinates &other);
+                        ~PointCoordinates();
 
-#//Convert
+#//!\name Convert
     //! QhullPoints coordinates, constData, data, count, size
 #ifndef QHULL_NO_STL
     void                append(const std::vector &otherCoordinates) { if(!otherCoordinates.empty()){ append((int)otherCoordinates.size(), &otherCoordinates[0]); } }
     std::vector toStdVector() const { return point_coordinates.toStdVector(); }
 #endif //QHULL_NO_STL
 #ifdef QHULL_USES_QT
     void                append(const QList &pointCoordinates) { if(!pointCoordinates.isEmpty()){ append(pointCoordinates.count(), &pointCoordinates[0]); } }
     QList       toQList() const { return point_coordinates.toQList(); }
 #endif //QHULL_USES_QT
 
-#//GetSet
+#//!\name GetSet
     //! See QhullPoints for coordinates, coordinateCount, dimension, empty, isEmpty, ==, !=
     void                checkValid() const;
     std::string         comment() const { return point_comment; }
     void                makeValid() { defineAs(point_coordinates.count(), point_coordinates.data()); }
-    const Coordinates  &getCoordinates() const { return point_coordinates; }
+    const Coordinates & getCoordinates() const { return point_coordinates; }
     void                setComment(const std::string &s) { point_comment= s; }
     void                setDimension(int i);
 
 private:
     void                defineAs(int coordinatesCount, coordT *c) { QhullPoints::defineAs(coordinatesCount, c); }
     //! defineAs() otherwise disabled
 public:
 
-#//ElementAccess
+#//!\name ElementAccess
     //! See QhullPoints for at, back, first, front, last, mid, [], value
 
-#//Foreach
+#//!\name Foreach
     //! See QhullPoints for begin, constBegin, end
     Coordinates::ConstIterator  beginCoordinates() const { return point_coordinates.begin(); }
     Coordinates::Iterator       beginCoordinates() { return point_coordinates.begin(); }
     Coordinates::ConstIterator  beginCoordinates(int pointIndex) const;
     Coordinates::Iterator       beginCoordinates(int pointIndex);
     Coordinates::ConstIterator  endCoordinates() const { return point_coordinates.end(); }
     Coordinates::Iterator       endCoordinates() { return point_coordinates.end(); }
 
-#//Search
+#//!\name Search
     //! See QhullPoints for contains, count, indexOf, lastIndexOf
 
-#//Read-only
+#//!\name Read-only
     PointCoordinates    operator+(const PointCoordinates &other) const;
 
-#//Modify
+#//!\name Modify
     //FIXUP QH11001: Add clear() and other modify operators from Coordinates.h.  Include QhullPoint::operator=()
     void                append(int coordinatesCount, const coordT *c);  //! Dimension previously defined
     void                append(const coordT &c) { append(1, &c); } //! Dimension previously defined
     void                append(const QhullPoint &p);
     //! See convert for std::vector and QList
     void                append(const Coordinates &c) { append(c.count(), c.data()); }
     void                append(const PointCoordinates &other);
     void                appendComment(const std::string &s);
     void                appendPoints(std::istream &in);
-    PointCoordinates   &operator+=(const PointCoordinates &other) { append(other); return *this; }
-    PointCoordinates   &operator+=(const coordT &c) { append(c); return *this; }
-    PointCoordinates   &operator+=(const QhullPoint &p) { append(p); return *this; }
-    PointCoordinates   &operator<<(const PointCoordinates &other) { return *this += other; }
-    PointCoordinates   &operator<<(const coordT &c) { return *this += c; }
-    PointCoordinates   &operator<<(const QhullPoint &p) { return *this += p; }
+    PointCoordinates &  operator+=(const PointCoordinates &other) { append(other); return *this; }
+    PointCoordinates &  operator+=(const coordT &c) { append(c); return *this; }
+    PointCoordinates &  operator+=(const QhullPoint &p) { append(p); return *this; }
+    PointCoordinates &  operator<<(const PointCoordinates &other) { return *this += other; }
+    PointCoordinates &  operator<<(const coordT &c) { return *this += c; }
+    PointCoordinates &  operator<<(const QhullPoint &p) { return *this += p; }
     // reserve() is non-const
     void                reserveCoordinates(int newCoordinates);
 
-#//Helpers
+#//!\name Helpers
 private:
     int                 indexOffset(int i) const;
 
 };//PointCoordinates
 
 // No references to QhullPoint.  Prevents use of QHULL_DECLARE_SEQUENTIAL_ITERATOR(PointCoordinates, QhullPoint)
 class PointCoordinatesIterator
 {
     typedef PointCoordinates::const_iterator const_iterator;
     const PointCoordinates *c;
     const_iterator i;
     public:
     inline PointCoordinatesIterator(const PointCoordinates &container)
     : c(&container), i(c->constBegin()) {}
     inline PointCoordinatesIterator &operator=(const PointCoordinates &container)
     { c = &container; i = c->constBegin(); return *this; }
     inline void toFront() { i = c->constBegin(); }
     inline void toBack() { i = c->constEnd(); }
     inline bool hasNext() const { return i != c->constEnd(); }
     inline const QhullPoint next() { return *i++; }
     inline const QhullPoint peekNext() const { return *i; }
     inline bool hasPrevious() const { return i != c->constBegin(); }
     inline const QhullPoint previous() { return *--i; }
     inline const QhullPoint peekPrevious() const { const_iterator p = i; return *--p; }
     inline bool findNext(const QhullPoint &t)
     { while (i != c->constEnd()) if (*i++ == t) return true; return false; }
     inline bool findPrevious(const QhullPoint &t)
     { while (i != c->constBegin()) if (*(--i) == t) return true;
     return false;  }
 };//CoordinatesIterator
 
 // FIXUP QH11002:  Add MutablePointCoordinatesIterator after adding modify operators
 \
 }//namespace orgQhull
 
-#//Global functions
+#//!\name Global
 
-std::ostream           &operator<<(std::ostream &os, const orgQhull::PointCoordinates &p);
+std::ostream &          operator<<(std::ostream &os, const orgQhull::PointCoordinates &p);
 
 #endif // QHPOINTCOORDINATES_H
diff --git a/src/libqhullpcpp/Qhull.cpp b/src/libqhullpcpp/Qhull.cpp
index e19e241..ce6cd5e 100644
--- a/src/libqhullpcpp/Qhull.cpp
+++ b/src/libqhullpcpp/Qhull.cpp
@@ -1,543 +1,543 @@
 /****************************************************************************
 **
 ** Copyright (c) 2008-2014 C.B. Barber. All rights reserved.
-** $Id: //main/2011/qhull/src/libqhullpcpp/Qhull.cpp#1 $$Change: 1652 $
-** $DateTime: 2014/01/17 09:01:32 $$Author: bbarber $
+** $Id: //main/2011/qhull/src/libqhullpcpp/Qhull.cpp#2 $$Change: 1710 $
+** $DateTime: 2014/03/28 22:23:20 $$Author: bbarber $
 **
 ****************************************************************************/
 
 #//! Qhull -- invoke qhull from C++
 #//! Compile libqhull and Qhull together due to use of setjmp/longjmp()
 
 #include "QhullError.h"
 #include "UsingLibQhull.h"
 #include "RboxPoints.h"
 #include "QhullQh.h"
 #include "QhullFacet.h"
 #include "QhullFacetList.h"
 #include "Qhull.h"
 extern "C" {
     #include "libqhull/qhull_a.h"
 }
 
 #include 
 
 using std::cerr;
 using std::string;
 using std::vector;
 using std::ostream;
 
 #ifdef _MSC_VER  // Microsoft Visual C++ -- warning level 4
 #pragma warning( disable : 4611)  // interaction between '_setjmp' and C++ object destruction is non-portable
 #pragma warning( disable : 4996)  // function was declared deprecated(strcpy, localtime, etc.)
 #endif
 
 namespace orgQhull {
 
 #//Global variables
 
 char s_unsupported_options[]=" Fd TI ";
 char s_not_output_options[]= " Fd TI A C d E H P Qb QbB Qbb Qc Qf Qg Qi Qm QJ Qr QR Qs Qt Qv Qx Qz Q0 Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10 Q11 R Tc TC TM TP TR Tv TV TW U v V W ";
 
 #//Constructor, destructor, etc.
 Qhull::
 Qhull()
 : qhull_qh(0)
 , qhull_run_id(UsingLibQhull::NOqhRunId)
 , origin_point()
 , qhull_status(qh_ERRnone)
 , qhull_dimension(0)
 , run_called(false)
 , qh_active(false)
 , qhull_message()
 , error_stream(0)
 , output_stream(0)
 , feasiblePoint()
 , useOutputStream(false)
 {
-    initializeQhull();
+    allocateQhullQh();
 }//Qhull
 
 Qhull::
 Qhull(const RboxPoints &rboxPoints, const char *qhullCommand2)
 : qhull_qh(0)
 , qhull_run_id(UsingLibQhull::NOqhRunId)
 , origin_point()
 , qhull_status(qh_ERRnone)
 , qhull_dimension(0)
 , run_called(false)
 , qh_active(false)
 , qhull_message()
 , error_stream(0)
 , output_stream(0)
 , feasiblePoint()
 , useOutputStream(false)
 {
-    initializeQhull();
+    allocateQhullQh();
     runQhull(rboxPoints, qhullCommand2);
 }//Qhull rbox
 
 Qhull::
 Qhull(const char *rboxCommand2, int pointDimension, int pointCount, const realT *pointCoordinates, const char *qhullCommand2)
 : qhull_qh(0)
 , qhull_run_id(UsingLibQhull::NOqhRunId)
 , origin_point()
 , qhull_status(qh_ERRnone)
 , qhull_dimension(0)
 , run_called(false)
 , qh_active(false)
 , qhull_message()
 , error_stream(0)
 , output_stream(0)
 , feasiblePoint()
 , useOutputStream(false)
 {
-    initializeQhull();
+    allocateQhullQh();
     runQhull(rboxCommand2, pointDimension, pointCount, pointCoordinates, qhullCommand2);
 }//Qhull points
 
 Qhull::
 Qhull(const Qhull &other)
 : qhull_qh(0)
 , qhull_run_id(UsingLibQhull::NOqhRunId)
 , origin_point()
 , qhull_status(qh_ERRnone)
 , qhull_dimension(0)
 , run_called(false)
 , qh_active(false)
 , qhull_message(other.qhull_message)
 , error_stream(other.error_stream)
 , output_stream(other.output_stream)
 , feasiblePoint(other.feasiblePoint)
 , useOutputStream(other.useOutputStream)
 {
     if(other.initialized()){
         throw QhullError(10069, "Qhull error: can not use Qhull copy constructor if initialized() is true");
     }
-    initializeQhull();
+    allocateQhullQh();
 }//copy constructor
 
 Qhull & Qhull::
 operator=(const Qhull &other)
 {
     if(other.initialized() || initialized()){
         throw QhullError(10070, "Qhull error: can not use Qhull copy assignment if initialized() is true");
     }
     qhull_message= other.qhull_message;
     error_stream= other.error_stream;
     output_stream= other.output_stream;
     feasiblePoint= other.feasiblePoint;
     useOutputStream= other.useOutputStream;
     return *this;
 }//copy constructor
 
 void Qhull::
-initializeQhull()
+allocateQhullQh()
 {
     #if qh_QHpointer
         qhull_qh= new QhullQh;
         qhull_qh->old_qhstat= qh_qhstat;
         qhull_qh->old_tempstack= qhmem.tempstack;
         qh_qh= 0;
         qh_qhstat= 0;
     #else
         qhull_qh= new (&qh_qh) QhullQh;
         qhull_qh->old_qhstat= &qh_qhstat;
         qhull_qh->old_tempstack= qhmem.tempstack;
     #endif
     qhmem.tempstack= 0;
     qhull_run_id= qhull_qh->run_id;
-}//initializeQhull
+}//allocateQhullQh
 
 Qhull::
 ~Qhull() throw()
 {
     //! UsingLibQhull is required by ~QhullQh
     UsingLibQhull q(this, QhullError::NOthrow);
     if(q.defined()){
         int exitCode = setjmp(qh errexit);
         if(!exitCode){ // no object creation -- destructors skipped on longjmp()
 #if qh_QHpointer
             delete qhull_qh;
             // clears qhull_qh and qh_qh
             qh_qh= 0;
 #else
             qhull_qh->~QhullQh();
             qhull_qh= 0;
 #endif
             qhull_run_id= UsingLibQhull::NOqhRunId;
             // Except for cerr, does not throw errors
             if(hasQhullMessage()){
                 cerr<< "\nQhull output at end\n"; //FIXUP QH11005: where should error and log messages go on ~Qhull?
                 cerr<num_points*hullDimension(), qhull_qh->first_point);
 }//points
 
 QhullPointSet Qhull::
 otherPoints() const
 {
     return QhullPointSet(hullDimension(), qhull_qh->other_points);
 }//otherPoints
 
 //! Return vertices of the convex hull.
 QhullVertexList Qhull::
 vertexList() const{
     return QhullVertexList(beginVertex(), endVertex());
 }//vertexList
 
 #//Modify
 
 void Qhull::
 outputQhull()
 {
     checkIfQhullInitialized();
     UsingLibQhull q(this);
     int exitCode = setjmp(qh errexit);
     if(!exitCode){ // no object creation -- destructors skipped on longjmp()
         qh_produce_output2();
     }
     maybeThrowQhullMessage(exitCode);
 }//outputQhull
 
 void Qhull::
 outputQhull(const char *outputflags)
 {
     checkIfQhullInitialized();
     UsingLibQhull q(this);
     string cmd(" "); // qh_checkflags skips first word
     cmd += outputflags;
     char *command= const_cast(cmd.c_str());
     int exitCode = setjmp(qh errexit);
     if(!exitCode){ // no object creation -- destructors skipped on longjmp()
         qh_clear_outputflags();
         char *s = qh qhull_command + strlen(qh qhull_command) + 1; //space
         strncat(qh qhull_command, command, sizeof(qh qhull_command)-strlen(qh qhull_command)-1);
         qh_checkflags(command, s_not_output_options);
         qh_initflags(s);
         qh_initqhull_outputflags();
         if(qh KEEPminArea < REALmax/2
            || (0 != qh KEEParea + qh KEEPmerge + qh GOODvertex
                     + qh GOODthreshold + qh GOODpoint + qh SPLITthresholds)){
             facetT *facet;
             qh ONLYgood= False;
             FORALLfacet_(qh facet_list) {
                 facet->good= True;
             }
             qh_prepare_output();
         }
         qh_produce_output2();
         if(qh VERIFYoutput && !qh STOPpoint && !qh STOPcone){
             qh_check_points();
         }
     }
     maybeThrowQhullMessage(exitCode);
 }//outputQhull
 
 void Qhull::
 runQhull(const RboxPoints &rboxPoints, const char *qhullCommand2)
 {
     runQhull(rboxPoints.comment().c_str(), rboxPoints.dimension(), rboxPoints.count(), &*rboxPoints.coordinates(), qhullCommand2);
 }//runQhull, RboxPoints
 
 //! points is a array of points, input sites ('d' or 'v'), or halfspaces with offset last ('H')
 //! Derived from qh_new_qhull [user.c]
 void Qhull::
 runQhull(const char *rboxCommand2, int pointDimension, int pointCount, const realT *rboxPoints, const char *qhullCommand2)
 {
     if(run_called){
         throw QhullError(10027, "Qhull error: runQhull called twice.  Only one call allowed.");
     }
     run_called= true;
     string s("qhull ");
     s += qhullCommand2;
     char *command= const_cast(s.c_str());
     UsingLibQhull q(this);
     int exitCode = setjmp(qh errexit);
     if(!exitCode){ // no object creation -- destructors skipped on longjmp()
         qh_checkflags(command, s_unsupported_options);
         qh_initflags(command);
         *qh rbox_command= '\0';
         strncat( qh rbox_command, rboxCommand2, sizeof(qh rbox_command)-1);
         if(qh DELAUNAY){
             qh PROJECTdelaunay= True;   // qh_init_B() calls qh_projectinput()
         }
         pointT *newPoints= const_cast(rboxPoints);
         int newDimension= pointDimension;
         int newIsMalloc= False;
         if(qh HALFspace){
             --newDimension;
             initializeFeasiblePoint(newDimension);
             newPoints= qh_sethalfspace_all(pointDimension, pointCount, newPoints, qh feasible_point);
             newIsMalloc= True;
         }
         qh_init_B(newPoints, pointCount, newDimension, newIsMalloc);
         qhull_dimension= (qh DELAUNAY ? qh hull_dim - 1 : qh hull_dim);
         qh_qhull();
         qh_check_output();
         qh_prepare_output();
         if(qh VERIFYoutput && !qh STOPpoint && !qh STOPcone){
             qh_check_points();
         }
     }
     for(int k= qhull_dimension; k--; ){  // Do not move up (may throw)
         origin_point << 0.0;
     }
     maybeThrowQhullMessage(exitCode);
 }//runQhull
 
 #//Helpers -- be careful of allocating C++ objects due to setjmp/longjmp() error handling by qh_... routines
 
 void Qhull::
 initializeFeasiblePoint(int hulldim)
 {
     if(qh feasible_string){
         qh_setfeasible(hulldim);
     }else{
         if(feasiblePoint.empty()){
             qh_fprintf(qh ferr, 6209, "qhull error: missing feasible point for halfspace intersection.  Use option 'Hn,n' or set qh.feasiblePoint\n");
             qh_errexit(qh_ERRmem, NULL, NULL);
         }
         if(feasiblePoint.size()!=(size_t)hulldim){
             qh_fprintf(qh ferr, 6210, "qhull error: dimension of feasiblePoint should be %d.  It is %u", hulldim, feasiblePoint.size());
             qh_errexit(qh_ERRmem, NULL, NULL);
         }
         if (!(qh feasible_point= (coordT*)qh_malloc(hulldim * sizeof(coordT)))) {
             qh_fprintf(qh ferr, 6202, "qhull error: insufficient memory for feasible point\n");
             qh_errexit(qh_ERRmem, NULL, NULL);
         }
         coordT *t= qh feasible_point;
         // No qh_... routines after here -- longjmp() ignores destructor
         for(Coordinates::ConstIterator p=feasiblePoint.begin(); p--------------------------------
 
   qh_fprintf(fp, msgcode, format, list of args )
     fp is ignored (replaces qh_fprintf() in userprintf.c)
     s_qhull_output == Qhull
 
 notes:
     only called from libqhull
     same as fprintf() and RboxPoints::qh_fprintf_rbox()
     fgets() is not trapped like fprintf()
     Do not throw errors from here.  Use qh_errexit;
 */
 extern "C"
 void qh_fprintf(FILE *fp, int msgcode, const char *fmt, ... ) {
     va_list args;
 
     using namespace orgQhull;
 
     if(!s_qhull_output){
         fprintf(stderr, "QH10025 Qhull error: UsingLibQhull not declared prior to calling qh_...().  s_qhull_output==NULL.\n");
         qh_exit(10025);
     }
     Qhull *out= s_qhull_output;
     va_start(args, fmt);
     if(msgcode=MSG_ERROR && msgcodeqhull_statusqhull_status>=MSG_WARNING){
                 out->qhull_status= msgcode;
             }
         }
         char newMessage[MSG_MAXLEN];
         // RoadError will add the message tag
         vsnprintf(newMessage, sizeof(newMessage), fmt, args);
         out->appendQhullMessage(newMessage);
         va_end(args);
         return;
     }
     if(out->output_stream && out->useOutputStream){
         char newMessage[MSG_MAXLEN];
         vsnprintf(newMessage, sizeof(newMessage), fmt, args);
         *out->output_stream << newMessage;
         va_end(args);
         return;
     }
     // FIXUP QH11008: how do users trap messages and handle input?  A callback?
     char newMessage[MSG_MAXLEN];
     vsnprintf(newMessage, sizeof(newMessage), fmt, args);
     out->appendQhullMessage(newMessage);
     va_end(args);
 } /* qh_fprintf */
 
diff --git a/src/libqhullpcpp/Qhull.h b/src/libqhullpcpp/Qhull.h
index cc8c4c0..6ed6992 100644
--- a/src/libqhullpcpp/Qhull.h
+++ b/src/libqhullpcpp/Qhull.h
@@ -1,147 +1,147 @@
 /****************************************************************************
 **
 ** Copyright (c) 2008-2012 C.B. Barber. All rights reserved.
-** $Id: //main/2011/qhull/src/libqhullpcpp/Qhull.h#1 $$Change: 1652 $
-** $DateTime: 2014/01/17 09:01:32 $$Author: bbarber $
+** $Id: //main/2011/qhull/src/libqhullpcpp/Qhull.h#3 $$Change: 1710 $
+** $DateTime: 2014/03/28 22:23:20 $$Author: bbarber $
 **
 ****************************************************************************/
 
 #ifndef QHULLCPP_H
 #define QHULLCPP_H
 
 #include "QhullQh.h"
 #include "RboxPoints.h"
 #include "QhullLinkedList.h"
 #include "QhullPoint.h"
 #include "QhullPoints.h"
 #include "QhullVertex.h"
 #include "QhullFacet.h"
 
 #include 
 #include 
 #include 
 #include 
 #include 
 
 #if qh_QHpointer != 1
 #error  qh_QHpointer is not set.  Please set it in user.h or
 #error  compile Qhull with -Dqh_QHpointer.  The C++ classes
 #error  require dynamic allocation for Qhulls global data
 #error  structure qhT (QhullQh).
 #endif
 
 namespace orgQhull {
 
 /***
    Compile qhullcpp and libqhull with the same compiler.  setjmp() and longjmp() must be the same.
 */
 
-#//Types
+#//!\name Types
     //! Qhull -- run Qhull from C++
     class Qhull;
 
     //Defined elsewhere
     class QhullFacetList;
     class RboxPoints;
 
 class Qhull {
 
 private:
-#//Members and friends
-    QhullQh            *qhull_qh;       //! qh_qh for this instance
+#//!\name Members and friends
+    QhullQh *           qhull_qh;       //! qh_qh for this instance
     int                 qhull_run_id;    //! qh.run_id at initialization (catch multiple runs if !qh_QHpointer)
     Coordinates         origin_point;   //! origin for qhull_dimension.  Set by runQhull()
     int                 qhull_status;   //! qh_ERRnone if valid
     int                 qhull_dimension; //! Dimension of result (qh.hull_dim or one less for Delaunay/Voronoi)
     bool                run_called;     //! True at start of runQhull.  Errors if call again.
     bool                qh_active;      //! True if global pointer qh_qh equals qhull_qh
     std::string         qhull_message;
-    std::ostream       *error_stream;   //! overrides errorMessage, use appendQhullMessage()
-    std::ostream       *output_stream;  //! send output to stream
+    std::ostream *      error_stream;   //! overrides errorMessage, use appendQhullMessage()
+    std::ostream *      output_stream;  //! send output to stream
 
     friend void       ::qh_fprintf(FILE *fp, int msgcode, const char *fmt, ... );
-    friend class        UsingLibQhull;
+    friend class UsingLibQhull;
 
-#//Attribute
+#//!\name Attribute
 public:
     Coordinates         feasiblePoint;  //! feasible point for half-space intersection
     bool                useOutputStream; //! Set if using outputStream
     // FIXUP QH11003 feasiblePoint useOutputStream as field or getter?
 
-#//constructor, assignment, destructor, invariant
+#//!\name constructor, assignment, destructor, invariant
                         Qhull();      //! Qhull::runQhull() must be called next
                         Qhull(const RboxPoints &rboxPoints, const char *qhullCommand2);
                         Qhull(const char *rboxCommand2, int pointDimension, int pointCount, const realT *pointCoordinates, const char *qhullCommand2);
                         // Throws error if other.initialized().  Needed for return by value and parameter passing
                         Qhull(const Qhull &other);
                         // Throws error if initialized() or other.initialized().  Needed for vector
-    Qhull              &operator=(const Qhull &other);
-                       ~Qhull() throw();
+    Qhull &             operator=(const Qhull &other);
+                        ~Qhull() throw();
 private:
-    void                initializeQhull();
+    void                allocateQhullQh();
 
 public:
-#//virtual methods
+#//!\name !\name virtual methods
     //FIXUP QH11004 -- qh_memfree, etc. as virtual?
 
-#//Messaging
+#//!\name Messaging
     void                appendQhullMessage(const std::string &s);
     void                clearQhullMessage();
     std::string         qhullMessage() const;
     bool                hasQhullMessage() const;
     int                 qhullStatus() const;
     void                setErrorStream(std::ostream *os);
     void                setOutputStream(std::ostream *os);
 
-#//GetSet
+#//!\name GetSet
     void                checkIfQhullInitialized();
     bool                initialized() const { return qhull_dimension>0; }
     int                 dimension() const { return qhull_dimension; }
     int                 hullDimension() const { return qhullQh()->hull_dim; }
                         // non-const due to QhullPoint
     QhullPoint          origin() { QHULL_ASSERT(initialized()); return QhullPoint(dimension(), origin_point.data()); }
-    QhullQh            *qhullQh() const { return qhull_qh; };
+    QhullQh *           qhullQh() const { return qhull_qh; };
     int                 runId(); // Modifies my_qhull
 
-#//GetQh -- access to qhT (Qhull's global data structure)
-    const char         *qhullCommand() const { return qhull_qh->qhull_command; }
-    const char         *rboxCommand() const { return qhull_qh->rbox_command; }
+#//!\name GetQh -- access to qhT (Qhull's global data structure)
+    const char *        qhullCommand() const { return qhull_qh->qhull_command; }
+    const char *        rboxCommand() const { return qhull_qh->rbox_command; }
     int                 facetCount() const { return qhull_qh->num_facets; }
     int                 vertexCount() const { return qhull_qh->num_vertices; }
 
-#//GetValue
+#//!\name GetValue
     double              area();
     double              volume();
 
-#//ForEach
+#//!\name ForEach
     QhullFacet          beginFacet() const { return QhullFacet(qhull_qh->facet_list); }
     QhullVertex         beginVertex() const { return QhullVertex(qhull_qh->vertex_list); }
     void                defineVertexNeighborFacets(); //!< Automatically called if merging facets or Voronoi diagram
     QhullFacet          endFacet() const { return QhullFacet(qhull_qh->facet_tail); }
     QhullVertex         endVertex() const { return QhullVertex(qhull_qh->vertex_tail); }
     QhullFacetList      facetList() const;
     QhullFacet          firstFacet() const { return beginFacet(); }
     QhullVertex         firstVertex() const { return beginVertex(); }
     QhullPoints         points() const;
     QhullPointSet       otherPoints() const;
                         //! Same as points().coordinates()
-    coordT             *pointCoordinateBegin() const { return qhull_qh->first_point; }
-    coordT             *pointCoordinateEnd() const { return qhull_qh->first_point + qhull_qh->num_points*qhull_qh->hull_dim; }
+    coordT *            pointCoordinateBegin() const { return qhull_qh->first_point; }
+    coordT *            pointCoordinateEnd() const { return qhull_qh->first_point + qhull_qh->num_points*qhull_qh->hull_dim; }
     QhullVertexList     vertexList() const;
 
-#//Modify
+#//!\name Modify
     void                outputQhull();
     void                outputQhull(const char * outputflags);
     void                runQhull(const RboxPoints &rboxPoints, const char *qhullCommand2);
     void                runQhull(const char *rboxCommand2, int pointDimension, int pointCount, const realT *rboxPoints, const char *qhullCommand2);
 
 private:
-#//Helpers
+#//!\name Helpers
     void                initializeFeasiblePoint(int hulldim);
     void                maybeThrowQhullMessage(int exitCode);
     void                maybeThrowQhullMessage(int exitCode, int noThrow) throw();
 };//Qhull
 
 }//namespace orgQhull
 
 #endif // QHULLCPP_H
diff --git a/src/libqhullpcpp/QhullError.h b/src/libqhullpcpp/QhullError.h
index c136c76..8c9bc7c 100644
--- a/src/libqhullpcpp/QhullError.h
+++ b/src/libqhullpcpp/QhullError.h
@@ -1,64 +1,65 @@
 /****************************************************************************
 **
 ** Copyright (c) 2008-2012 C.B. Barber. All rights reserved.
-** $Id: //main/2011/qhull/src/libqhullpcpp/QhullError.h#1 $$Change: 1652 $
-** $DateTime: 2014/01/17 09:01:32 $$Author: bbarber $
+** $Id: //main/2011/qhull/src/libqhullpcpp/QhullError.h#3 $$Change: 1710 $
+** $DateTime: 2014/03/28 22:23:20 $$Author: bbarber $
 **
 ****************************************************************************/
 
 #ifndef QHULLERROR_H
 #define QHULLERROR_H
 
 #include "RoadError.h"
+// No dependencies on libqhull
 
 #include 
 #include 
 #include 
 
 namespace orgQhull {
 
-#//Types
+#//!\name Types
     //! QhullError -- std::exception class for Qhull
     class QhullError;
 
 class QhullError : public RoadError {
 
 public:
-#//Constants
+#//!\name Constants
     enum {
         QHULLfirstError= 10000, //MSG_QHULL_ERROR in Qhull's user.h
-        QHULLlastError= 10070,
+        QHULLlastError= 10073,
         NOthrow= 1 //! For flag to UsingLibQhull()
     };
 
-#//Constructors
+#//!\name Constructors
     // default constructors
     QhullError() : RoadError() {};
     QhullError(const QhullError &other) : RoadError(other) {}
     QhullError(int code, const std::string &message) : RoadError(code, message) {};
     QhullError(int code, const char *fmt) : RoadError(code, fmt) {};
     QhullError(int code, const char *fmt, int d) : RoadError(code, fmt, d) {};
     QhullError(int code, const char *fmt, int d, int d2) : RoadError(code, fmt, d, d2) {};
     QhullError(int code, const char *fmt, int d, int d2, float f) : RoadError(code, fmt, d, d2, f) {};
     QhullError(int code, const char *fmt, int d, int d2, float f, const char *s) : RoadError(code, fmt, d, d2, f, s) {};
     QhullError(int code, const char *fmt, int d, int d2, float f, const void *x) : RoadError(code, fmt, d, d2, f, x) {};
     QhullError(int code, const char *fmt, int d, int d2, float f, int i) : RoadError(code, fmt, d, d2, f, i) {};
     QhullError(int code, const char *fmt, int d, int d2, float f, long long i) : RoadError(code, fmt, d, d2, f, i) {};
     QhullError(int code, const char *fmt, int d, int d2, float f, double e) : RoadError(code, fmt, d, d2, f, e) {};
     QhullError &operator=(const QhullError &other) { this->RoadError::operator=(other); return *this; }
     ~QhullError() throw() {}
 
 };//class QhullError
 
 #ifndef QHULL_1
     #define QHULL_ASSERT assert
 
 #endif
 
 }//namespace orgQhull
 
-#//Global functions
+#//!\name Global
 
 inline std::ostream &operator<<(std::ostream &os, const orgQhull::QhullError &e) { return os << e.what(); }
 
 #endif // QHULLERROR_H
diff --git a/src/libqhullpcpp/QhullFacet.h b/src/libqhullpcpp/QhullFacet.h
index a183196..be9204f 100644
--- a/src/libqhullpcpp/QhullFacet.h
+++ b/src/libqhullpcpp/QhullFacet.h
@@ -1,155 +1,155 @@
 /****************************************************************************
 **
 ** Copyright (c) 2008-2012 C.B. Barber. All rights reserved.
-** $Id: //main/2011/qhull/src/libqhullpcpp/QhullFacet.h#1 $$Change: 1652 $
-** $DateTime: 2014/01/17 09:01:32 $$Author: bbarber $
+** $Id: //main/2011/qhull/src/libqhullpcpp/QhullFacet.h#2 $$Change: 1675 $
+** $DateTime: 2014/02/01 09:38:20 $$Author: bbarber $
 **
 ****************************************************************************/
 
 #ifndef QHULLFACET_H
 #define QHULLFACET_H
 
 #include "Coordinates.h"
 #include "QhullHyperplane.h"
 #include "QhullPoint.h"
 #include "QhullSet.h"
 #include "QhullPointSet.h"
 extern "C" {
     #include "libqhull/qhull_a.h"
 }
 
 #include 
 #include 
 #include 
 
 namespace orgQhull {
 
-#//ClassRef
+#//!\name ClassRef
     class QhullFacetSet;
     class QhullRidge;
     typedef QhullSet  QhullRidgeSet;
     class QhullVertex;
     class QhullVertexSet;
 
-#//Types
+#//!\name Types
     //! QhullFacet -- Qhull's facet structure, facetT [libqhull.h], as a C++ class
     class QhullFacet;
 
 //! A QhullFacet is the C++ equivalent to Qhull's facetT*
 class QhullFacet {
 
 private:
-#//Fields -- no additions (QhullFacetSet of facetT*)
-    facetT             *qh_facet;  //! May be 0 (!isDefined) for corner cases (e.g., *facetSet.end()==0) and tricoplanarOwner()
+#//!\name Fields -- no additions (QhullFacetSet of facetT*)
+    facetT *            qh_facet;  //! May be 0 (!isDefined) for corner cases (e.g., *facetSet.end()==0) and tricoplanarOwner()
 
-#//Class objects
+#//!\name Class objects
     static facetT       s_empty_facet; // needed for shallow copy
 
 public:
-#//Constants
+#//!\name Constants
 
-#//Constructors
+#//!\name Constructors
                         QhullFacet() : qh_facet(&s_empty_facet) {}
                         // Creates an alias.  Does not copy QhullFacet.  Needed for return by value and parameter passing
                         QhullFacet(const QhullFacet &o) : qh_facet(o.qh_facet ? o.qh_facet : &s_empty_facet) {}
                         // Creates an alias.  Does not copy QhullFacet.  Needed for vector
-    QhullFacet         &operator=(const QhullFacet &o) { qh_facet= o.qh_facet ? o.qh_facet : &s_empty_facet; return *this; }
-                       ~QhullFacet() {}
+    QhullFacet &        operator=(const QhullFacet &o) { qh_facet= o.qh_facet ? o.qh_facet : &s_empty_facet; return *this; }
+                        ~QhullFacet() {}
 
-#//Conversion
+#//!\name Conversion
                         //Implicit conversion from facetT
                         QhullFacet(facetT *f) : qh_facet(f ? f : &s_empty_facet) {}
                         // Do not define facetT().  It conflicts with return type facetT*
-    facetT             *getFacetT() const { return qh_facet; }
+    facetT *            getFacetT() const { return qh_facet; }
 
-#//QhullSet
-    facetT             *getBaseT() const { return getFacetT(); }
+#//!\name QhullSet
+    facetT *            getBaseT() const { return getFacetT(); }
 
-#//getSet
+#//!\name getSet
     int                 dimension() const;
     QhullPoint          getCenter(int qhRunId) { return getCenter(qhRunId, qh_PRINTpoints); }
     QhullPoint          getCenter(int qhRunId, qh_PRINT printFormat);
     QhullHyperplane     hyperplane() const { return QhullHyperplane(dimension(), qh_facet->normal, qh_facet->offset); }
     int                 id() const { return qh_facet ? qh_facet->id : -1; }
     QhullHyperplane     innerplane(int qhRunId) const;
     bool                isDefined() const { return qh_facet && qh_facet != &s_empty_facet; }
     bool                isGood() const { return qh_facet && qh_facet->good; }
     bool                isSimplicial() const { return qh_facet->simplicial; }
     bool                isTopOrient() const { return qh_facet->toporient; }
     bool                isTriCoplanar() const { return qh_facet->tricoplanar; }
     bool                isUpperDelaunay() const { return qh_facet->upperdelaunay; }
     QhullFacet          next() const { return qh_facet->next; }
     bool                operator==(const QhullFacet &o) const { return qh_facet==o.qh_facet; }
     bool                operator!=(const QhullFacet &o) const { return !operator==(o); }
     QhullHyperplane     outerplane(int qhRunId) const;
     QhullFacet          previous() const { return qh_facet->previous; }
     QhullFacet          tricoplanarOwner() const;
     QhullPoint          voronoiVertex(int qhRunId);
 
-#//value
+#//!\name value
     //! Undefined if c.size() != dimension()
     double              distance(const Coordinates &c) const { return distance(c.data()); }
     double              distance(const pointT *p) const { return distance(QhullPoint(dimension(), const_cast(p))); }
     double              distance(const QhullPoint &p) const { return hyperplane().distance(p); }
     double              facetArea(int qhRunId);
 
-#//foreach
+#//!\name foreach
     // Can not inline.  Otherwise circular reference
     QhullPointSet       coplanarPoints() const;
     QhullFacetSet       neighborFacets() const;
     QhullPointSet       outsidePoints() const;
     QhullRidgeSet       ridges() const;
     QhullVertexSet      vertices() const;
 
-#//IO
+#//!\name IO
     struct PrintCenter{
-        QhullFacet     *facet;  // non-const due to facet.center()
-        const char     *message;
+        QhullFacet *    facet;  // non-const due to facet.center()
+        const char *    message;
         int             run_id;
         qh_PRINT        print_format;
                         PrintCenter(int qhRunId, QhullFacet &f, qh_PRINT printFormat, const char * s) : facet(&f), message(s), run_id(qhRunId), print_format(printFormat){}
     };//PrintCenter
     PrintCenter         printCenter(int qhRunId, qh_PRINT printFormat, const char *message) { return PrintCenter(qhRunId, *this, printFormat, message); }
 
     struct PrintFacet{
-        QhullFacet     *facet;  // non-const due to f->center()
+        QhullFacet *    facet;  // non-const due to f->center()
         int             run_id;
                         PrintFacet(int qhRunId, QhullFacet &f) : facet(&f), run_id(qhRunId) {}
     };//PrintFacet
     PrintFacet          print(int qhRunId) { return PrintFacet(qhRunId, *this); }
 
     struct PrintFlags{
         const QhullFacet *facet;
-        const char     *message;
+        const char *    message;
                         PrintFlags(const QhullFacet &f, const char *s) : facet(&f), message(s) {}
     };//PrintFlags
     PrintFlags          printFlags(const char *message) const { return PrintFlags(*this, message); }
 
     struct PrintHeader{
-        QhullFacet     *facet;  // non-const due to f->center()
+        QhullFacet *    facet;  // non-const due to f->center()
         int             run_id;
                         PrintHeader(int qhRunId, QhullFacet &f) : facet(&f), run_id(qhRunId) {}
     };//PrintHeader
     PrintHeader         printHeader(int qhRunId) { return PrintHeader(qhRunId, *this); }
 
     struct PrintRidges{
         const QhullFacet *facet;
         int             run_id;
                         PrintRidges(int qhRunId, QhullFacet &f) : facet(&f), run_id(qhRunId) {}
     };//PrintRidges
     PrintRidges         printRidges(int qhRunId) { return PrintRidges(qhRunId, *this); }
 
 };//class QhullFacet
 
 }//namespace orgQhull
 
-#//Global functions
+#//!\name Global
 
 std::ostream &operator<<(std::ostream &os, const orgQhull::QhullFacet::PrintCenter &pr);
 std::ostream &operator<<(std::ostream &os, const orgQhull::QhullFacet::PrintFlags &pr);
 std::ostream &operator<<(std::ostream &os, const orgQhull::QhullFacet::PrintHeader &pr);
 std::ostream &operator<<(std::ostream &os, const orgQhull::QhullFacet::PrintRidges &pr);
 std::ostream &operator<<(std::ostream &os, const orgQhull::QhullFacet::PrintFacet &pr);
 std::ostream &operator<<(std::ostream &os, orgQhull::QhullFacet &f); // non-const due to qh_getcenter()
 
 #endif // QHULLFACET_H
diff --git a/src/libqhullpcpp/QhullFacetList.h b/src/libqhullpcpp/QhullFacetList.h
index afe510e..bf1133e 100644
--- a/src/libqhullpcpp/QhullFacetList.h
+++ b/src/libqhullpcpp/QhullFacetList.h
@@ -1,102 +1,102 @@
 /****************************************************************************
 **
 ** Copyright (c) 2008-2012 C.B. Barber. All rights reserved.
-** $Id: //main/2011/qhull/src/libqhullpcpp/QhullFacetList.h#1 $$Change: 1652 $
-** $DateTime: 2014/01/17 09:01:32 $$Author: bbarber $
+** $Id: //main/2011/qhull/src/libqhullpcpp/QhullFacetList.h#2 $$Change: 1675 $
+** $DateTime: 2014/02/01 09:38:20 $$Author: bbarber $
 **
 ****************************************************************************/
 
 #ifndef QHULLFACETLIST_H
 #define QHULLFACETLIST_H
 
 #include "QhullLinkedList.h"
 #include "QhullFacet.h"
 
 #include 
 
 namespace orgQhull {
 
-#//ClassRef
-    class               QhullFacet;
+#//!\name ClassRef
+    class QhullFacet;
 
-#//Types
+#//!\name Types
     //! QhullFacetList -- List of Qhull facets, as a C++ class.  See QhullFacetSet.h
-    class               QhullFacetList;
+    class QhullFacetList;
     //! QhullFacetListIterator -- if(f.isGood()){ ... }
     typedef QhullLinkedListIterator
                         QhullFacetListIterator;
 
 class QhullFacetList : public QhullLinkedList {
 
-#// Fields
+#//!\name  Fields
 private:
     bool                select_all;   //! True if include bad facets.  Default is false.
 
-#//Constructors
+#//!\name Constructors
 public:
                         QhullFacetList(QhullFacet b, QhullFacet e) : QhullLinkedList(b, e), select_all(false) {}
                         //Copy constructor copies pointer but not contents.  Needed for return by value and parameter passing.
                         QhullFacetList(const QhullFacetList &o) : QhullLinkedList(*o.begin(), *o.end()), select_all(o.select_all) {}
-                       ~QhullFacetList() {}
+                        ~QhullFacetList() {}
 
 private:
                         //!Disable default constructor and copy assignment.  See QhullLinkedList
                         QhullFacetList();
-    QhullFacetList     &operator=(const QhullFacetList &);
+    QhullFacetList &    operator=(const QhullFacetList &);
 public:
 
-#//Conversion
+#//!\name Conversion
 #ifndef QHULL_NO_STL
     std::vector toStdVector() const;
     std::vector vertices_toStdVector(int qhRunId) const;
 #endif //QHULL_NO_STL
 #ifdef QHULL_USES_QT
     QList   toQList() const;
     QList  vertices_toQList(int qhRunId) const;
 #endif //QHULL_USES_QT
 
-#//GetSet
+#//!\name GetSet
     bool                isSelectAll() const { return select_all; }
     void                selectAll() { select_all= true; }
     void                selectGood() { select_all= false; }
 
-#//Read-only
+#//!\name Read-only
                         //! Filtered by facet.isGood().  May be 0 when !isEmpty().
     int                 count() const;
     bool                contains(const QhullFacet &f) const;
     int                 count(const QhullFacet &f) const;
                         //! operator==() does not depend on isGood()
 
-#//IO
+#//!\name IO
     struct PrintFacetList{
         const QhullFacetList *facet_list;
         int             run_id;
                         PrintFacetList(int qhRunId, const QhullFacetList &fl) : facet_list(&fl), run_id(qhRunId) {}
     };//PrintFacetList
     PrintFacetList     print(int qhRunId) const  { return PrintFacetList(qhRunId, *this); }
 
     struct PrintFacets{
         const QhullFacetList *facet_list;
         int             run_id;
                         PrintFacets(int qhRunId, const QhullFacetList &fl) : facet_list(&fl), run_id(qhRunId) {}
     };//PrintFacets
     PrintFacets     printFacets(int qhRunId) const { return PrintFacets(qhRunId, *this); }
 
     struct PrintVertices{
         const QhullFacetList *facet_list;
         int             run_id;   //! Can not be NOrunId due to qh_facetvertices
                         PrintVertices(int qhRunId, const QhullFacetList &fl) : facet_list(&fl), run_id(qhRunId) {}
     };//PrintVertices
     PrintVertices   printVertices(int qhRunId) const { return PrintVertices(qhRunId, *this); }
 };//class QhullFacetList
 
 }//namespace orgQhull
 
-#//== Global namespace =========================================
+#//!\name Global
 
 std::ostream &operator<<(std::ostream &os, const orgQhull::QhullFacetList::PrintFacetList &p);
 std::ostream &operator<<(std::ostream &os, const orgQhull::QhullFacetList::PrintFacets &p);
 std::ostream &operator<<(std::ostream &os, const orgQhull::QhullFacetList::PrintVertices &p);
 std::ostream &operator<<(std::ostream &os, const orgQhull::QhullFacetList &fs);
 
 #endif // QHULLFACETLIST_H
diff --git a/src/libqhullpcpp/QhullFacetSet.h b/src/libqhullpcpp/QhullFacetSet.h
index 95af11c..97e7264 100644
--- a/src/libqhullpcpp/QhullFacetSet.h
+++ b/src/libqhullpcpp/QhullFacetSet.h
@@ -1,94 +1,94 @@
 /****************************************************************************
 **
 ** Copyright (c) 2008-2012 C.B. Barber. All rights reserved.
-** $Id: //main/2011/qhull/src/libqhullpcpp/QhullFacetSet.h#1 $$Change: 1652 $
-** $DateTime: 2014/01/17 09:01:32 $$Author: bbarber $
+** $Id: //main/2011/qhull/src/libqhullpcpp/QhullFacetSet.h#2 $$Change: 1675 $
+** $DateTime: 2014/02/01 09:38:20 $$Author: bbarber $
 **
 ****************************************************************************/
 
 #ifndef QHULLFACETSET_H
 #define QHULLFACETSET_H
 
 #include "QhullSet.h"
 
 #include 
 
 namespace orgQhull {
 
-#//ClassRef
-    class               QhullFacet;
+#//!\name ClassRef
+    class QhullFacet;
 
-#//Types
+#//!\name Types
     //! QhullFacetSet -- a set of Qhull facets, as a C++ class.  See QhullFacetList.h
-    class               QhullFacetSet;
+    class QhullFacetSet;
     typedef QhullSetIterator
                         QhullFacetSetIterator;
 
 class QhullFacetSet : public QhullSet {
 
 private:
-#//Fields
+#//!\name Fields
     bool                select_all;   //! True if include bad facets.  Default is false.
 
 public:
-#//Constructor
+#//!\name Constructor
                         //Conversion from setT* is not type-safe.  Implicit conversion for void* to T
    explicit             QhullFacetSet(setT *s) : QhullSet(s), select_all(false) {}
                         //Copy constructor copies pointer but not contents.  Needed for return by value and parameter passing.
                         QhullFacetSet(const QhullFacetSet &o) : QhullSet(o), select_all(o.select_all) {}
 
 private:
                         //!Disable default constructor and copy assignment.  See QhullSetBase
                         QhullFacetSet();
-    QhullFacetSet      &operator=(const QhullFacetSet &);
+    QhullFacetSet &     operator=(const QhullFacetSet &);
 public:
 
-#//Conversion
+#//!\name Conversion
 #ifndef QHULL_NO_STL
     std::vector toStdVector() const;
 #endif //QHULL_NO_STL
 #ifdef QHULL_USES_QT
     QList   toQList() const;
 #endif //QHULL_USES_QT
 
-#//GetSet
+#//!\name GetSet
     bool                isSelectAll() const { return select_all; }
     void                selectAll() { select_all= true; }
     void                selectGood() { select_all= false; }
 
-#//Read-only
+#//!\name Read-only
                         //! Filtered by facet.isGood().  May be 0 when !isEmpty().
     int                 count() const;
     bool                contains(const QhullFacet &f) const;
     int                 count(const QhullFacet &f) const;
                         //! operator==() does not depend on isGood()
 
-#//IO
+#//!\name IO
     // Not same as QhullFacetList#IO.  A QhullFacetSet is a component of a QhullFacetList.
 
     struct PrintFacetSet{
         const QhullFacetSet *facet_set;
-        const char     *print_message;
+        const char *    print_message;
         int             run_id;
                         PrintFacetSet(int qhRunId, const char *message, const QhullFacetSet *s) : facet_set(s), print_message(message), run_id(qhRunId) {}
     };//PrintFacetSet
     const PrintFacetSet       print(int qhRunId, const char *message) const { return PrintFacetSet(qhRunId, message, this); }
 
     struct PrintIdentifiers{
         const QhullFacetSet *facet_set;
-        const char     *print_message;
+        const char *    print_message;
                         PrintIdentifiers(const char *message, const QhullFacetSet *s) : facet_set(s), print_message(message) {}
     };//PrintIdentifiers
     PrintIdentifiers    printIdentifiers(const char *message) const { return PrintIdentifiers(message, this); }
 
 };//class QhullFacetSet
 
 }//namespace orgQhull
 
-#//== Global namespace =========================================
+#//!\name Global
 
 std::ostream &operator<<(std::ostream &os, const orgQhull::QhullFacetSet &fs);
 std::ostream &operator<<(std::ostream &os, const orgQhull::QhullFacetSet::PrintFacetSet &pr);
 std::ostream &operator<<(std::ostream &os, const orgQhull::QhullFacetSet::PrintIdentifiers &p);
 
 #endif // QHULLFACETSET_H
diff --git a/src/libqhullpcpp/QhullHyperplane.h b/src/libqhullpcpp/QhullHyperplane.h
index 8655f26..4ceaaa1 100644
--- a/src/libqhullpcpp/QhullHyperplane.h
+++ b/src/libqhullpcpp/QhullHyperplane.h
@@ -1,122 +1,122 @@
 /****************************************************************************
 **
 ** Copyright (c) 2009-2012 C.B. Barber. All rights reserved.
-** $Id: //main/2011/qhull/src/libqhullpcpp/QhullHyperplane.h#1 $$Change: 1652 $
-** $DateTime: 2014/01/17 09:01:32 $$Author: bbarber $
+** $Id: //main/2011/qhull/src/libqhullpcpp/QhullHyperplane.h#2 $$Change: 1675 $
+** $DateTime: 2014/02/01 09:38:20 $$Author: bbarber $
 **
 ****************************************************************************/
 
 #ifndef QHHYPERPLANE_H
 #define QHHYPERPLANE_H
 
 #include "QhullError.h"
 #include "QhullIterator.h"
 #include "UsingLibQhull.h"
 extern "C" {
     #include "libqhull/qhull_a.h"
 }
 
 #include 
 
 namespace orgQhull {
-#//ClassRef
+#//!\name ClassRef
     class QhullPoint;
 
-#//Types
+#//!\name Types
     //! QhullHyperplane as an offset, dimension, and pointer to coordinates
     class QhullHyperplane;
     //! Java-style iterator for QhullHyperplane coordinates
     class QhullHyperplaneIterator;
 
 class QhullHyperplane { // Similar to QhullPoint
 
 private:
-#//Fields
-    coordT             *hyperplane_coordinates;  // Keep pointers aligned
+#//!\name Fields
+    coordT *            hyperplane_coordinates;  // Keep pointers aligned
     int                 hyperplane_dimension;
     coordT              hyperplane_offset;
 
 public:
-#//Subtypes
+#//!\name Subtypes
     typedef const coordT *                  iterator;
     typedef const coordT *                  const_iterator;
     typedef QhullHyperplane::iterator       Iterator;
     typedef QhullHyperplane::const_iterator ConstIterator;
 
-#//Construct
+#//!\name Construct
                         QhullHyperplane() : hyperplane_coordinates(0), hyperplane_dimension(0), hyperplane_offset(0.0) {};
                         QhullHyperplane(int hyperplaneDimension, coordT *c, coordT hyperplaneOffset) : hyperplane_coordinates(c), hyperplane_dimension(hyperplaneDimension), hyperplane_offset(hyperplaneOffset) {}
                         // Creates an alias.  Does not copy the hyperplane's coordinates.  Needed for return by value and parameter passing.
                         QhullHyperplane(const QhullHyperplane &other)  : hyperplane_coordinates(other.hyperplane_coordinates), hyperplane_dimension(other.hyperplane_dimension), hyperplane_offset(other.hyperplane_offset) {}
                         // Creates an alias.  Does not copy the hyperplane's coordinates.  Needed for vector
-    QhullHyperplane    &operator=(const QhullHyperplane &other) { hyperplane_coordinates= other.hyperplane_coordinates; hyperplane_dimension= other.hyperplane_dimension; hyperplane_offset= other.hyperplane_offset; return *this; }
-                       ~QhullHyperplane() {}
+    QhullHyperplane &   operator=(const QhullHyperplane &other) { hyperplane_coordinates= other.hyperplane_coordinates; hyperplane_dimension= other.hyperplane_dimension; hyperplane_offset= other.hyperplane_offset; return *this; }
+                        ~QhullHyperplane() {}
 
-#//Conversions --
+#//!\name Conversions --
 //! Includes offset at end
 #ifndef QHULL_NO_STL
     std::vector toStdVector() const;
 #endif //QHULL_NO_STL
 #ifdef QHULL_USES_QT
     QList       toQList() const;
 #endif //QHULL_USES_QT
 
-#//Read-only
+#//!\name Read-only
 public:
-    const coordT       *coordinates() const { return hyperplane_coordinates; }
-    coordT             *coordinates() { return hyperplane_coordinates; }
+    const coordT *      coordinates() const { return hyperplane_coordinates; }
+    coordT *            coordinates() { return hyperplane_coordinates; }
     int                 dimension() const { return hyperplane_dimension; }
     bool                isDefined() const { return hyperplane_coordinates!=0 && hyperplane_dimension>0; }
     coordT              offset() const { return hyperplane_offset; }
 
-#//Define
+#//!\name Define
     void                defineAs(int hyperplaneDimension, coordT *c, coordT hyperplaneOffset) { QHULL_ASSERT(hyperplaneDimension>=0); hyperplane_coordinates= c; hyperplane_dimension= hyperplaneDimension; hyperplane_offset= hyperplaneOffset; }
     //! Creates an alias to other
     void                defineAs(QhullHyperplane &other) { hyperplane_coordinates= other.coordinates(); hyperplane_dimension= other.dimension();  hyperplane_offset= other.offset(); }
     void                setCoordinates(coordT *c) { hyperplane_coordinates= c; }
     void                setDimension(int hyperplaneDimension) { hyperplane_dimension= hyperplaneDimension; }
     void                setOffset(coordT hyperplaneOffset) { hyperplane_offset= hyperplaneOffset; }
 
-#//value
+#//!\name value
     double              distance(const QhullPoint &p) const;
     double              norm() const;
 
-#//iterator
+#//!\name iterator
     iterator            begin() { return hyperplane_coordinates; }
     const_iterator      begin() const { return hyperplane_coordinates; }
     const_iterator      constBegin() const { return hyperplane_coordinates; }
     const_iterator      constEnd() const { return hyperplane_coordinates+hyperplane_dimension; }
     int                 count() { return dimension(); }
     iterator            end() { return hyperplane_coordinates+hyperplane_dimension; }
     const_iterator      end() const { return hyperplane_coordinates+hyperplane_dimension; }
     size_t              size() { return (size_t)dimension(); }
 
-#//Operator
+#//!\name Operator
     bool                operator==(const QhullHyperplane &other) const;
     bool                operator!=(const QhullHyperplane &other) const { return !operator==(other); }
-    const coordT       &operator[](int idx) const { QHULL_ASSERT(idx>=0 && idx=0 && idx=0 && idx=0 && idx
 #include 
 #include 
 //! Avoid dependence on 
 namespace std { struct bidirectional_iterator_tag; struct random_access_iterator_tag; }
 
 namespace orgQhull {
 
-#//Defined here
+#//!\name Defined here
     //! QHULL_DECLARE_SEQUENTIAL_ITERATOR(C) -- Declare a Java-style iterator
     //! QHULL_DECLARE_MUTABLE_SEQUENTIAL_ITERATOR(C) -- Declare a mutable Java-style iterator
     //! QHULL_DECLARE_SET_ITERATOR(C) -- Declare a set iterator
     //! QHULL_DECLARE_MUTABLE_SET_ITERATOR(C) -- Declare a mutable set iterator
     //! Derived from Qt/core/tools/qiterator.h and qset.h/FOREACHsetelement_()
 
 // Changed c to C* as in Mutable...  Assumes c does not go away.
 #define QHULL_DECLARE_SEQUENTIAL_ITERATOR(C, T) \
     \
     class C##Iterator \
     { \
         typedef C::const_iterator const_iterator; \
         const C *c; \
         const_iterator i; \
         public: \
         inline C##Iterator(const C &container) \
         : c(&container), i(c->constBegin()) {} \
         inline C##Iterator &operator=(const C &container) \
         { c = &container; i = c->constBegin(); return *this; } \
         inline void toFront() { i = c->constBegin(); } \
         inline void toBack() { i = c->constEnd(); } \
         inline bool hasNext() const { return i != c->constEnd(); } \
         inline const T &next() { return *i++; } \
         inline const T &peekNext() const { return *i; } \
         inline bool hasPrevious() const { return i != c->constBegin(); } \
         inline const T &previous() { return *--i; } \
         inline const T &peekPrevious() const { const_iterator p = i; return *--p; } \
         inline bool findNext(const T &t) \
         { while (i != c->constEnd()) if (*i++ == t) return true; return false; } \
         inline bool findPrevious(const T &t) \
         { while (i != c->constBegin()) if (*(--i) == t) return true; \
         return false;  } \
     };//C##Iterator
 
 // Remove setShareable() from Q_DECLARE_MUTABLE_SEQUENTIAL_ITERATOR
 // Uses QHULL_ASSERT (assert.h)
 // Duplicated in MutablePointIterator without insert or remove
 #define QHULL_DECLARE_MUTABLE_SEQUENTIAL_ITERATOR(C, T) \
     class Mutable##C##Iterator \
     { \
         typedef C::iterator iterator; \
         typedef C::const_iterator const_iterator; \
         C *c; \
         iterator i, n; \
         inline bool item_exists() const { return const_iterator(n) != c->constEnd(); } \
         public: \
         inline Mutable##C##Iterator(C &container) \
         : c(&container) \
         { i = c->begin(); n = c->end(); } \
         inline ~Mutable##C##Iterator() \
         {} \
         inline Mutable##C##Iterator &operator=(C &container) \
         { c = &container; \
         i = c->begin(); n = c->end(); return *this; } \
         inline void toFront() { i = c->begin(); n = c->end(); } \
         inline void toBack() { i = c->end(); n = i; } \
         inline bool hasNext() const { return c->constEnd() != const_iterator(i); } \
         inline T &next() { n = i++; return *n; } \
         inline T &peekNext() const { return *i; } \
         inline bool hasPrevious() const { return c->constBegin() != const_iterator(i); } \
         inline T &previous() { n = --i; return *n; } \
         inline T &peekPrevious() const { iterator p = i; return *--p; } \
         inline void remove() \
         { if (c->constEnd() != const_iterator(n)) { i = c->erase(n); n = c->end(); } } \
         inline void setValue(const T &t) const { if (c->constEnd() != const_iterator(n)) *n = t; } \
         inline T &value() { QHULL_ASSERT(item_exists()); return *n; } \
         inline const T &value() const { QHULL_ASSERT(item_exists()); return *n; } \
         inline void insert(const T &t) { n = i = c->insert(i, t); ++i; } \
         inline bool findNext(const T &t) \
         { while (c->constEnd() != const_iterator(n = i)) if (*i++ == t) return true; return false; } \
         inline bool findPrevious(const T &t) \
         { while (c->constBegin() != const_iterator(i)) if (*(n = --i) == t) return true; \
         n = c->end(); return false;  } \
     };//Mutable##C##Iterator
 
 #define QHULL_DECLARE_SET_ITERATOR(C) \
 \
     template  \
     class Qhull##C##Iterator \
     { \
         typedef typename Qhull##C::const_iterator const_iterator; \
         Qhull##C c; \
         const_iterator i; \
     public: \
         inline Qhull##C##Iterator(const Qhull##C &container) \
         : c(container), i(c.constBegin()) {} \
         inline Qhull##C##Iterator &operator=(const Qhull##C &container) \
         { c = container; i = c.constBegin(); return *this; } \
         inline void toFront() { i = c.constBegin(); } \
         inline void toBack() { i = c.constEnd(); } \
         inline bool hasNext() const { return i != c.constEnd(); } \
         inline const T &next() { return *i++; } \
         inline const T &peekNext() const { return *i; } \
         inline bool hasPrevious() const { return i != c.constBegin(); } \
         inline const T &previous() { return *--i; } \
         inline const T &peekPrevious() const { const_iterator p = i; return *--p; } \
         inline bool findNext(const T &t) \
         { while (i != c.constEnd()) if (*i++ == t) return true; return false; } \
         inline bool findPrevious(const T &t) \
         { while (i != c.constBegin()) if (*(--i) == t) return true; \
         return false;  } \
     };//Qhull##C##Iterator
 
 #define QHULL_DECLARE_MUTABLE_SET_ITERATOR(C) \
 \
 template  \
 class QhullMutable##C##Iterator \
 { \
     typedef typename Qhull##C::iterator iterator; \
     typedef typename Qhull##C::const_iterator const_iterator; \
     Qhull##C *c; \
     iterator i, n; \
     inline bool item_exists() const { return const_iterator(n) != c->constEnd(); } \
 public: \
     inline Mutable##C##Iterator(Qhull##C &container) \
         : c(&container) \
     { c->setSharable(false); i = c->begin(); n = c->end(); } \
     inline ~Mutable##C##Iterator() \
     { c->setSharable(true); } \
     inline Mutable##C##Iterator &operator=(Qhull##C &container) \
     { c->setSharable(true); c = &container; c->setSharable(false); \
       i = c->begin(); n = c->end(); return *this; } \
     inline void toFront() { i = c->begin(); n = c->end(); } \
     inline void toBack() { i = c->end(); n = i; } \
     inline bool hasNext() const { return c->constEnd() != const_iterator(i); } \
     inline T &next() { n = i++; return *n; } \
     inline T &peekNext() const { return *i; } \
     inline bool hasPrevious() const { return c->constBegin() != const_iterator(i); } \
     inline T &previous() { n = --i; return *n; } \
     inline T &peekPrevious() const { iterator p = i; return *--p; } \
     inline void remove() \
     { if (c->constEnd() != const_iterator(n)) { i = c->erase(n); n = c->end(); } } \
     inline void setValue(const T &t) const { if (c->constEnd() != const_iterator(n)) *n = t; } \
     inline T &value() { Q_ASSERT(item_exists()); return *n; } \
     inline const T &value() const { Q_ASSERT(item_exists()); return *n; } \
     inline void insert(const T &t) { n = i = c->insert(i, t); ++i; } \
     inline bool findNext(const T &t) \
     { while (c->constEnd() != const_iterator(n = i)) if (*i++ == t) return true; return false; } \
     inline bool findPrevious(const T &t) \
     { while (c->constBegin() != const_iterator(i)) if (*(n = --i) == t) return true; \
       n = c->end(); return false;  } \
 };//QhullMutable##C##Iterator
 
 }//namespace orgQhull
 
 #endif // QHULLITERATOR_H
 
diff --git a/src/libqhullpcpp/QhullLinkedList.h b/src/libqhullpcpp/QhullLinkedList.h
index 1a83805..6eacbb6 100644
--- a/src/libqhullpcpp/QhullLinkedList.h
+++ b/src/libqhullpcpp/QhullLinkedList.h
@@ -1,377 +1,375 @@
 /****************************************************************************
 **
 ** Copyright (c) 2008-2012 C.B. Barber. All rights reserved.
-** $Id: //main/2011/qhull/src/libqhullpcpp/QhullLinkedList.h#1 $$Change: 1652 $
-** $DateTime: 2014/01/17 09:01:32 $$Author: bbarber $
+** $Id: //main/2011/qhull/src/libqhullpcpp/QhullLinkedList.h#2 $$Change: 1675 $
+** $DateTime: 2014/02/01 09:38:20 $$Author: bbarber $
 **
 ****************************************************************************/
 
 #ifndef QHULLLINKEDLIST_H
 #define QHULLLINKEDLIST_H
 
 namespace std { struct bidirectional_iterator_tag; struct random_access_iterator_tag; }
 
 #include "QhullError.h"
 
 #ifdef QHULL_USES_QT
 #include 
 #endif
 
 #ifndef QHULL_NO_STL
 #include 
 #endif
 
 namespace orgQhull {
 
-#//Type
+#//!\name Type
     //! QhullLinkedList -- A linked list modeled on QLinkedList.
     //!   T is an opaque type with T(B *b), b=t.getBaseT(), t=t.next(), and t=t.prev().  The end node is a sentinel.
     //!   libqhull owns the contents.
     //!   QhullLinkedList does not define erase(), clear(), removeFirst(), removeLast(), pop_back(), pop_front(), fromStdList()
     //!   Derived from Qt/core/tools/qlinkedlist.h and libqhull.h/FORALLfacets_()
     //! QhullLinkedList::const_iterator -- STL-style iterator
     //! QhullLinkedList::iterator -- STL-style iterator
     //! QhullLinkedListIterator -- Java-style iterator
     //!   Derived from Qt/core/tools/qiterator.h
     //!   Works with Qt's foreach keyword [Qt/src/corelib/global/qglobal.h]
 
 template 
 class QhullLinkedList
 {
 private:
-#//Fields
+#//!\name Fields
     T                   begin_node;
     T                   end_node;     //! Sentinel node at end of list
 
 public:
-#//Subtypes and types
-    class               const_iterator;
-    class               iterator;
+#//!\name Subtypes and types
+    class const_iterator;
+    class iterator;
     typedef const_iterator  ConstIterator;
     typedef iterator    Iterator;
     typedef ptrdiff_t   difference_type;
     typedef int         size_type;
     typedef T           value_type;
     typedef const value_type *const_pointer;
     typedef const value_type &const_reference;
     typedef value_type *pointer;
     typedef value_type &reference;
 
-#//Constructors
+#//!\name Constructors
                         QhullLinkedList(T b, T e) : begin_node(b), end_node(e) {}
                         //Copy constructor copies pointer but not contents.  Needed for return by value and parameter passing.
                         QhullLinkedList(const QhullLinkedList &o) : begin_node(o.begin_node), end_node(o.end_node) {}
-                       ~QhullLinkedList() {}
+                        ~QhullLinkedList() {}
 
 private:
                         //!disabled since a sentinel must be allocated as the private type
                         QhullLinkedList() {}
                         //!disabled since qs= qs2 is ambiguous (pointer vs. contents)
     QhullLinkedList &operator=(const QhullLinkedList &l) {}
 public:
 
-#//Conversions
+#//!\name Conversions
 #ifndef QHULL_NO_STL
     std::vector      toStdVector() const;
 #endif
 #ifdef QHULL_USES_QT
     QList            toQList() const;
 #endif
 
-#//Read-only
+#//!\name Read-only
     int                 count() const;
-                        //count(t) under #//Search
+                        //count(t) under Search
     bool                empty() const { return isEmpty(); }
     bool                isEmpty() const { return (begin_node==end_node); }
     bool                operator==(const QhullLinkedList &o) const;
     bool                operator!=(const QhullLinkedList &o) const { return !operator==(o); }
     size_t              size() const { return count(); }
 
-#//Element access
+#//!\name Element access
     //! Return by value which contains a pointer (e.g., typedef vertexT * QhullVertex).  A reference does not make sense.
     T                   back() const { return last(); }
     T                   first() const { QHULL_ASSERT(!isEmpty()); return *begin(); }
     T                   front() const { return first(); }
     T                   last() const { QHULL_ASSERT(!isEmpty()); return *--end(); }
 
-#//Modify -- Allocation of opaque types not implemented.
+#//!\name Modify -- Allocation of opaque types not implemented.
 
-#//Search
+#//!\name Search
     bool                contains(const T &t) const;
     int                 count(const T &t) const;
 
-#//Iterator
+#//!\name Iterator
     iterator            begin() { return begin_node; }
     const_iterator      begin() const { return begin_node; }
     const_iterator      constBegin() const { return begin_node; }
     const_iterator      constEnd() const { return end_node; }
     iterator            end() { return end_node; }
     const_iterator      end() const { return end_node; }
 
     class iterator {
 
     private:
         T               i;
-        friend class    const_iterator;
+        friend class const_iterator;
 
     public:
         typedef std::bidirectional_iterator_tag  iterator_category;
         typedef T           value_type;
         typedef value_type *pointer;
         typedef value_type &reference;
         typedef ptrdiff_t   difference_type;
 
                         iterator() : i() {}
                         iterator(T t) : i(t) {}
                         iterator(const iterator &o) : i(o.i) {}
-        iterator       &operator=(const iterator &o) { i= o.i; return *this; }
+        iterator &      operator=(const iterator &o) { i= o.i; return *this; }
 
         T               operator*() const { return i; }
         T               operator->() const { return i; }
         bool            operator==(const iterator &o) const { return i == o.i; }
         bool            operator!=(const iterator &o) const { return !operator==(o); }
         bool            operator==(const const_iterator &o) const { return i==reinterpret_cast(o).i; }
         bool            operator!=(const const_iterator &o) const { return !operator==(o); }
-        iterator       &operator++() { i= i.next(); return *this; }
+        iterator &      operator++() { i= i.next(); return *this; }
         iterator        operator++(int) { iterator o= i; i= i.next(); return o; }
-        iterator       &operator--() { i= i.previous(); return *this; }
+        iterator &      operator--() { i= i.previous(); return *this; }
         iterator        operator--(int) { iterator o= i; i= i.previous(); return o; }
         iterator        operator+(int j) const;
         iterator        operator-(int j) const { return operator+(-j); }
-        iterator       &operator+=(int j) { return *this= *this + j; }
-        iterator       &operator-=(int j) { return *this= *this - j; }
+        iterator &      operator+=(int j) { return *this= *this + j; }
+        iterator &      operator-=(int j) { return *this= *this - j; }
     };//QhullLinkedList::iterator
 
     class const_iterator {
 
     private:
         T               i;
 
     public:
         typedef std::bidirectional_iterator_tag  iterator_category;
         typedef T                 value_type;
         typedef const value_type *pointer;
         typedef const value_type &reference;
         typedef ptrdiff_t         difference_type;
 
                         const_iterator() : i() {}
                         const_iterator(T t) : i(t) {}
                         const_iterator(const const_iterator &o) : i(o.i) {}
                         const_iterator(iterator o) : i(o.i) {}
         const_iterator &operator=(const const_iterator &o) { i= o.i; return *this; }
 
         T               operator*() const { return i; }
         T               operator->() const { return i; }
         bool            operator==(const const_iterator &o) const { return i == o.i; }
         bool            operator!=(const const_iterator &o) const { return !operator==(o); }
                         // No comparisons or iterator diff
         const_iterator &operator++() { i= i.next(); return *this; }
         const_iterator  operator++(int) { const_iterator o= i; i= i.next(); return o; }
         const_iterator &operator--() { i= i.previous(); return *this; }
         const_iterator  operator--(int) { const_iterator o= i; i= i.previous(); return o; }
         const_iterator  operator+(int j) const;
         const_iterator  operator-(int j) const { return operator+(-j); }
         const_iterator &operator+=(int j) { return *this= *this + j; }
         const_iterator &operator-=(int j) { return *this= *this - j; }
     };//QhullLinkedList::const_iterator
 
 };//QhullLinkedList
 
 template 
 class QhullLinkedListIterator // FIXUP QH11016 define QhullMutableLinkedListIterator
 {
     typedef typename QhullLinkedList::const_iterator const_iterator;
     const QhullLinkedList *c;
     const_iterator      i;
 
 public:
                         QhullLinkedListIterator(const QhullLinkedList &container) : c(&container), i(c->constBegin()) {}
                         QhullLinkedListIterator &operator=(const QhullLinkedList &container) { c= &container; i= c->constBegin(); return *this; }
     bool                findNext(const T &t);
     bool                findPrevious(const T &t);
     bool                hasNext() const { return i != c->constEnd(); }
     bool                hasPrevious() const { return i != c->constBegin(); }
     T                   next() { return *i++; }
     T                   peekNext() const { return *i; }
     T                   peekPrevious() const { const_iterator p= i; return *--p; }
     T                   previous() { return *--i; }
     void                toFront() { i= c->constBegin(); }
     void                toBack() { i= c->constEnd(); }
 };//QhullLinkedListIterator
 
-#//== Definitions =========================================
-
-#//Conversion
+#//!\name Conversion
 
 #ifndef QHULL_NO_STL
 template 
 std::vector QhullLinkedList::
 toStdVector() const
 {
     std::vector tmp;
     std::copy(constBegin(), constEnd(), std::back_inserter(tmp));
     return tmp;
 }//toStdVector
 #endif
 
 #ifdef QHULL_USES_QT
 template 
 QList  QhullLinkedList::
 toQList() const
 {
     QhullLinkedListIterator i(*this);
     QList ls;
     while(i.hasNext()){
         ls.append(i.next());
     }
     return ls;
 }//toQList
 #endif
 
-#//Read-only
+#//!\name Read-only
 
 template 
 int QhullLinkedList::
 count() const
 {
     const_iterator i= begin_node;
     int c= 0;
     while(i != end_node){
         c++;
         i++;
     }
     return c;
 }//count
 
-#//Search
+#//!\name Search
 
 template 
 bool QhullLinkedList::
 contains(const T &t) const
 {
     const_iterator i= begin_node;
     while(i != end_node){
         if(i==t){
             return true;
         }
         i++;
     }
     return false;
 }//contains
 
 template 
 int QhullLinkedList::
 count(const T &t) const
 {
     const_iterator i= begin_node;
     int c= 0;
     while(i != end_node){
         if(i==t){
             c++;
         }
         i++;
     }
     return c;
 }//count
 
 template 
 bool QhullLinkedList::
 operator==(const QhullLinkedList &l) const
 {
     if(begin_node==l.begin_node){
         return (end_node==l.end_node);
     }
     T i= begin_node;
     T il= l.begin_node;
     while(i != end_node){
         if(i != il){
             return false;
         }
         i= static_cast(i.next());
         il= static_cast(il.next());
     }
     if(il != l.end_node){
         return false;
     }
     return true;
 }//operator==
 
-#//Iterator
+#//!\name Iterator
 
 template 
 typename QhullLinkedList::iterator  QhullLinkedList::iterator::
 operator+(int j) const
 {
     T n= i;
     if(j>0){
         while(j--){
             n= n.next();
         }
     }else{
         while(j++){
             n= n.previous();
         }
     }
     return iterator(n);
 }//operator+
 
 template 
 typename QhullLinkedList::const_iterator  QhullLinkedList::const_iterator::
 operator+(int j) const
 {
     T n= i;
     if(j>0){
         while(j--){
             n= n.next();
         }
     }else{
         while(j++){
             n= n.previous();
         }
     }
     return const_iterator(n);
 }//operator+
 
-#//QhullLinkedListIterator
+#//!\name QhullLinkedListIterator
 
 template 
 bool QhullLinkedListIterator::
 findNext(const T &t)
 {
     while(i != c->constEnd()){
         if (*i++ == t){
             return true;
         }
     }
     return false;
 }//findNext
 
 template 
 bool QhullLinkedListIterator::
 findPrevious(const T &t)
 {
     while(i!=c->constBegin()){
         if(*(--i)==t){
             return true;
         }
     }
     return false;
 }//findNext
 
 }//namespace orgQhull
 
-#//Global functions
+#//!\name Global
 
 template 
 std::ostream &
 operator<<(std::ostream &os, const orgQhull::QhullLinkedList &qs)
 {
     typename orgQhull::QhullLinkedList::const_iterator i;
     for(i= qs.begin(); i != qs.end(); ++i){
         os << *i;
     }
     return os;
 }//operator<<
 
 #endif // QHULLLINKEDLIST_H
 
diff --git a/src/libqhullpcpp/QhullPoint.cpp b/src/libqhullpcpp/QhullPoint.cpp
index ffe8f3e..9bb26a3 100644
--- a/src/libqhullpcpp/QhullPoint.cpp
+++ b/src/libqhullpcpp/QhullPoint.cpp
@@ -1,177 +1,177 @@
 /****************************************************************************
 **
 ** Copyright (c) 2009-2014 C.B. Barber. All rights reserved.
-** $Id: //main/2011/qhull/src/libqhullpcpp/QhullPoint.cpp#1 $$Change: 1652 $
-** $DateTime: 2014/01/17 09:01:32 $$Author: bbarber $
+** $Id: //main/2011/qhull/src/libqhullpcpp/QhullPoint.cpp#3 $$Change: 1711 $
+** $DateTime: 2014/03/30 12:48:17 $$Author: bbarber $
 **
 ****************************************************************************/
 
 #include "UsingLibQhull.h"
 #include "QhullPoint.h"
 
 #include 
 #include 
 
 #ifdef _MSC_VER  // Microsoft Visual C++ -- warning level 4
 #endif
 
 namespace orgQhull {
 
 #//Class public variables and methods
 
 //! If qhRundID undefined uses QhullPoint::s_points_begin and dimension
 int QhullPoint::
 id(int qhRunId, int dimension, const coordT *c)
 {
     QHULL_UNUSED(dimension);
 
     if(UsingLibQhull::hasPoints()){
         if(qhRunId==UsingLibQhull::NOqhRunId){
             const coordT *pointsEnd;
             int dim;
             const coordT *points= UsingLibQhull::globalPoints(&dim, &pointsEnd);
             if(c>=points && c(c));
         }
     }
     long long i=(long long)c;
     return (int)i; // WARN64
 }//id
 
 #//Conversion
 
 // See qt-qhull.cpp for QList conversion
 
 #ifndef QHULL_NO_STL
 std::vector QhullPoint::
 toStdVector() const
 {
     QhullPointIterator i(*this);
     std::vector vs;
     while(i.hasNext()){
         vs.push_back(i.next());
     }
     return vs;
 }//toStdVector
 #endif //QHULL_NO_STL
 
 #//Operator
 
+//! QhullPoint is equal if it has the same address and dimension, or if the coordinates are within sqrt(qh_qh->distanceEpsilon())
+//! Uses sqrt() since globalDistanceEpsilon is the roundoff for distance to hyperplane, i.e., the inner product
 bool QhullPoint::
 operator==(const QhullPoint &other) const
 {
     if(point_dimension!=other.point_dimension){
         return false;
     }
     const coordT *c= point_coordinates;
     const coordT *c2= other.point_coordinates;
     if(c==c2){
         return true;
     }
     double dist2= 0.0;
     for(int k= point_dimension; k--; ){
         double diff= *c++ - *c2++;
         dist2 += diff*diff;
     }
-    double epsilon= UsingLibQhull::globalDistanceEpsilon();
-    // std::cout << "DEBUG dist2 " << dist2 << " epsilon^2 " << epsilon*epsilon << std::endl;
-    return (dist2<=(epsilon*epsilon));
-}//operator==
+    return (dist2 <= UsingLibQhull::globalDistanceEpsilon());
+ }//operator==
 
 
 #//Value
 
-//! Return distance betweeen two points.
+//! Return distance between two points.
 double QhullPoint::
 distance(const QhullPoint &p) const
 {
     const coordT *c= coordinates();
     const coordT *c2= p.coordinates();
     int dim= dimension();
     QHULL_ASSERT(dim==p.dimension());
     double dist;
 
     switch(dim){
   case 2:
       dist= (c[0]-c2[0])*(c[0]-c2[0]) + (c[1]-c2[1])*(c[1]-c2[1]);
       break;
   case 3:
       dist= (c[0]-c2[0])*(c[0]-c2[0]) + (c[1]-c2[1])*(c[1]-c2[1]) + (c[2]-c2[2])*(c[2]-c2[2]);
       break;
   case 4:
       dist= (c[0]-c2[0])*(c[0]-c2[0]) + (c[1]-c2[1])*(c[1]-c2[1]) + (c[2]-c2[2])*(c[2]-c2[2]) + (c[3]-c2[3])*(c[3]-c2[3]);
       break;
   case 5:
       dist= (c[0]-c2[0])*(c[0]-c2[0]) + (c[1]-c2[1])*(c[1]-c2[1]) + (c[2]-c2[2])*(c[2]-c2[2]) + (c[3]-c2[3])*(c[3]-c2[3]) + (c[4]-c2[4])*(c[4]-c2[4]);
       break;
   case 6:
       dist= (c[0]-c2[0])*(c[0]-c2[0]) + (c[1]-c2[1])*(c[1]-c2[1]) + (c[2]-c2[2])*(c[2]-c2[2]) + (c[3]-c2[3])*(c[3]-c2[3]) + (c[4]-c2[4])*(c[4]-c2[4]) + (c[5]-c2[5])*(c[5]-c2[5]);
       break;
   case 7:
       dist= (c[0]-c2[0])*(c[0]-c2[0]) + (c[1]-c2[1])*(c[1]-c2[1]) + (c[2]-c2[2])*(c[2]-c2[2]) + (c[3]-c2[3])*(c[3]-c2[3]) + (c[4]-c2[4])*(c[4]-c2[4]) + (c[5]-c2[5])*(c[5]-c2[5]) + (c[6]-c2[6])*(c[6]-c2[6]);
       break;
   case 8:
       dist= (c[0]-c2[0])*(c[0]-c2[0]) + (c[1]-c2[1])*(c[1]-c2[1]) + (c[2]-c2[2])*(c[2]-c2[2]) + (c[3]-c2[3])*(c[3]-c2[3]) + (c[4]-c2[4])*(c[4]-c2[4]) + (c[5]-c2[5])*(c[5]-c2[5]) + (c[6]-c2[6])*(c[6]-c2[6]) + (c[7]-c2[7])*(c[7]-c2[7]);
       break;
   default:
       dist= 0.0;
       for(int k=dim; k--; ){
           dist += (*c - *c2) * (*c - *c2);
           ++c;
           ++c2;
       }
       break;
     }
     return sqrt(dist);
 }//distance
 
 }//namespace orgQhull
 
 #//Global functions
 
 using std::ostream;
 using orgQhull::QhullPoint;
 using orgQhull::UsingLibQhull;
 
 #//operator<<
 
 ostream &
 operator<<(ostream &os, const QhullPoint &p)
 {
     os << p.printWithIdentifier(UsingLibQhull::NOqhRunId, "");
     return os;
 }
 
 //! Same as qh_printpointid [io.c]
 ostream &
 operator<<(ostream &os, const QhullPoint::PrintPoint &pr)
 {
-    QhullPoint p= *pr.point; 
+    QhullPoint p= *pr.point;
     int i= p.id(pr.run_id);
     if(pr.point_message){
         if(*pr.point_message){
             os << pr.point_message << " ";
         }
         if(pr.with_identifier && (i!=-1)){
             os << "p" << i << ": ";
         }
     }
     const realT *c= p.coordinates();
     for(int k=p.dimension(); k--; ){
         realT r= *c++;
         if(pr.point_message){
             os << " " << r; // FIXUP QH11010 %8.4g
         }else{
             os << " " << r; // FIXUP QH11010 qh_REAL_1
         }
     }
     os << std::endl;
     return os;
 }//printPoint
 
diff --git a/src/libqhullpcpp/QhullPoint.h b/src/libqhullpcpp/QhullPoint.h
index ca3dc0b..66b6dc2 100644
--- a/src/libqhullpcpp/QhullPoint.h
+++ b/src/libqhullpcpp/QhullPoint.h
@@ -1,130 +1,130 @@
 /****************************************************************************
 **
 ** Copyright (c) 2009-2012 C.B. Barber. All rights reserved.
-** $Id: //main/2011/qhull/src/libqhullpcpp/QhullPoint.h#1 $$Change: 1652 $
-** $DateTime: 2014/01/17 09:01:32 $$Author: bbarber $
+** $Id: //main/2011/qhull/src/libqhullpcpp/QhullPoint.h#2 $$Change: 1675 $
+** $DateTime: 2014/02/01 09:38:20 $$Author: bbarber $
 **
 ****************************************************************************/
 
 #ifndef QHPOINT_H
 #define QHPOINT_H
 
 #include "QhullError.h"
 #include "QhullIterator.h"
 #include "UsingLibQhull.h"
 #include "Coordinates.h"
 extern "C" {
     #include "libqhull/qhull_a.h"
 }
 
 #include 
 
 namespace orgQhull {
 
-#//Types
+#//!\name Types
     //! QhullPoint as a pointer and dimension to shared memory
     class QhullPoint;
     //! Java-style iterator for QhullPoint coordinates
     class QhullPointIterator;
 
 class QhullPoint {
 
     //! A point is a pointer into an array of coordinates.
 
 private:
-#//Fields
-    coordT             *point_coordinates;  // Keep pointers aligned
+#//!\name Fields
+    coordT *            point_coordinates;  // Keep pointers aligned
     int                 point_dimension;
 
 public:
-#//Subtypes
+#//!\name Subtypes
     typedef const coordT *              iterator;
     typedef const coordT *              const_iterator;
     typedef QhullPoint::iterator        Iterator;
     typedef QhullPoint::const_iterator  ConstIterator;
 
-#//Class methods -- Convert point to id w/o QhullQh data structure
+#//!\name Class methods -- Convert point to id w/o QhullQh data structure
     static int          id(const coordT *c) { return QhullPoint::id(UsingLibQhull::NOqhRunId, 0, c); }
     static int          id(int qhRunId, const coordT *c) { return QhullPoint::id(qhRunId, 0, c); }
     static int          id(int qhRunId, int dimension, const coordT *c);
 
-#//Construct
+#//!\name Construct
                         QhullPoint() : point_coordinates(0), point_dimension(0) {};
                         QhullPoint(int pointDimension, coordT *c) : point_coordinates(c), point_dimension(pointDimension) {}
     explicit            QhullPoint(Coordinates &c) : point_coordinates(c.data()), point_dimension(c.count()) {}
                         // Creates an alias.  Does not copy the point.  Needed for return by value and parameter passing.
                         QhullPoint(const QhullPoint &other)  : point_coordinates(other.point_coordinates), point_dimension(other.point_dimension) {}
                         // Creates an alias.  Does not copy the point.  Needed for vector
-    QhullPoint         &operator=(const QhullPoint &other) { point_coordinates= other.point_coordinates; point_dimension= other.point_dimension; return *this; }
-                       ~QhullPoint() {}
+    QhullPoint &        operator=(const QhullPoint &other) { point_coordinates= other.point_coordinates; point_dimension= other.point_dimension; return *this; }
+                        ~QhullPoint() {}
 
-#//Conversions
+#//!\name Conversions
     // see coordinates()
 #ifndef QHULL_NO_STL
     std::vector toStdVector() const;
 #endif //QHULL_NO_STL
 #ifdef QHULL_USES_QT
     QList       toQList() const;
 #endif //QHULL_USES_QT
 
-#//Read-only
+#//!\name Read-only
 public:
-    const coordT       *coordinates() const { return point_coordinates; }
-    coordT             *coordinates() { return point_coordinates; }
+    const coordT *      coordinates() const { return point_coordinates; }
+    coordT *            coordinates() { return point_coordinates; }
     int                 dimension() const { return point_dimension; }
     int                 id(int qhRunId) const { return id(qhRunId, dimension(), coordinates()); }
     int                 id() const { return id(UsingLibQhull::NOqhRunId, dimension(), coordinates()); }
     bool                isDefined() const { return point_coordinates!=0 && point_dimension>0; }
 
-#//Define
+#//!\name Define
     void                advancePoint(int idx) { point_coordinates += idx*point_dimension; }
     void                defineAs(int pointDimension, coordT *c) { QHULL_ASSERT(pointDimension>=0); point_coordinates= c; point_dimension= pointDimension; }
     //! Creates an alias to other
     void                defineAs(QhullPoint &other) { point_coordinates= other.coordinates(); point_dimension= other.dimension(); }
     void                setCoordinates(coordT *c) { point_coordinates= c; }
     void                setDimension(int pointDimension) { point_dimension= pointDimension; }
 
-#//value
+#//!\name value
     double              distance(const QhullPoint &p) const;
 
-#//iterator
+#//!\name iterator
     iterator            begin() { return point_coordinates; }
     const_iterator      begin() const { return point_coordinates; }
     const_iterator      constBegin() const { return point_coordinates; }
     const_iterator      constEnd() const { return point_coordinates+point_dimension; }
     int                 count() { return dimension(); }
     iterator            end() { return point_coordinates+point_dimension; }
     const_iterator      end() const { return point_coordinates+point_dimension; }
     size_t              size() { return (size_t)dimension(); }
 
-#//Operator
+#//!\name Operator
     bool                operator==(const QhullPoint &other) const;
     bool                operator!=(const QhullPoint &other) const { return !operator==(other); }
-    const coordT       &operator[](int idx) const { QHULL_ASSERT(idx>=0 && idx=0 && idx=0 && idx=0 && idx
 
 namespace orgQhull {
 
-#//Types
+#//!\name Types
     //! QhullPointSet -- a set of coordinate pointers with dimension
     // with const_iterator and iterator
-    class               QhullPointSet;
+    class QhullPointSet;
     //! Java-style iterator
     class QhullPointsIterator;
 
-#//Classref
-    class               QhullPoint;
+#//!\name Classref
+    class QhullPoint;
 
 class QhullPointSet : public QhullSet {
 
 private:
-#//Field
+#//!\name Fields
     int                 point_dimension;
 
 public:
-#//Subtypes and types
-    class               const_iterator;
-    class               iterator;
+#//!\name Subtypes and types
+    class const_iterator;
+    class iterator;
     typedef QhullPointSet::const_iterator ConstIterator;
     typedef QhullPointSet::iterator Iterator;
 
     typedef QhullPoint  value_type;
     typedef ptrdiff_t   difference_type;
     typedef int         size_type;
     //typedef const value_type *const_pointer;    // FIXUP QH11019: QhullPointSet does not define pointer or reference due to point_dimension
     //typedef const value_type &const_reference;
     //typedef value_type *pointer;
     //typedef value_type &reference;
 
-#//Construct
+#//!\name Construct
                         //Conversion from setT* is not type-safe.  Implicit conversion for void* to T
                         QhullPointSet(int pointDimension, setT *s) : QhullSet(s), point_dimension(pointDimension) {}
                         //Copy constructor copies pointer but not contents.  Needed for return by value and parameter passing.
                         QhullPointSet(const QhullPointSet &o) : QhullSet(o), point_dimension(o.point_dimension) {}
-                       ~QhullPointSet() {}
+                        ~QhullPointSet() {}
 
 //Default constructor and copy assignment disabled since p= p2 is ambiguous (coord* vs coord)
 private:
                         QhullPointSet();
-    QhullPointSet      &operator=(const QhullPointSet &);
+    QhullPointSet &     operator=(const QhullPointSet &);
 public:
 
-#//Conversions
+#//!\name Conversions
     // inherited -- constData, data
 #ifndef QHULL_NO_STL
     std::vector toStdVector() const;
 #endif
 #ifdef QHULL_USES_QT
     QList   toQList() const;
 #endif
 
-#//Read-only
+#//!\name Read-only
     //inherits count, empty, isEmpty, size
     using QhullSetBase::count;
     int                 dimension() const { return point_dimension; }
     bool                operator==(const QhullPointSet &o) const;
     bool                operator!=(const QhullPointSet &o) const { return !operator==(o); }
 
-#//Element access -- can not return references since QhullPoint must be generated
+#//!\name Element access
+    //! Can not return references since QhullPoint must be generated
     QhullPoint          at(int idx) const { return operator[](idx); }
     QhullPoint          back() const { return last(); }
     //! end element is NULL
     QhullPoint          first() const { QHULL_ASSERT(!isEmpty()); return *begin(); }
     QhullPoint          front() const { return first(); }
     QhullPoint          last() const { QHULL_ASSERT(!isEmpty()); return *(end()-1); }
     // mid() not available.  No setT constructor
     QhullPoint          operator[](int idx) const { return QhullPoint(dimension(), QhullSet::operator[](idx)); }
     QhullPoint          second()  const { return operator[](1); }
     QhullPoint          value(int idx) const;
     // Non-const since copy is an alias
     QhullPoint          value(int idx, QhullPoint &defaultValue) const;
 
-#//iterator
+#//!\name iterator
     iterator            begin() { return iterator(dimension(), reinterpret_cast(beginPointer())); }
     const_iterator      begin() const { return const_iterator(dimension(), reinterpret_cast(beginPointer())); }
     const_iterator      constBegin() const { return const_iterator(dimension(), reinterpret_cast(beginPointer())); }
     const_iterator      constEnd() const { return const_iterator(dimension(), reinterpret_cast(endPointer())); }
     iterator            end() { return iterator(dimension(), reinterpret_cast(endPointer())); }
     const_iterator      end() const { return const_iterator(dimension(), reinterpret_cast(endPointer())); }
 
 //Read-write -- Not available, no setT constructor
 
-#//Search
+#//!\name Search
     bool                contains(const QhullPoint &t) const;
     int                 count(const QhullPoint &t) const;
     int                 indexOf(const QhullPoint &t) const;
     int                 lastIndexOf(const QhullPoint &t) const;
 
     // before const_iterator for conversion with comparison operators
     class iterator {
-        friend class    const_iterator;
+        friend class const_iterator;
 
     private:
-        coordT        **i;
+        coordT **       i;
         int             point_dimension;
 
     public:
         typedef ptrdiff_t   difference_type;
         typedef std::bidirectional_iterator_tag  iterator_category;
         typedef QhullPoint *pointer;
         typedef QhullPoint &reference;
         typedef QhullPoint  value_type;
 
                         iterator() : i(0), point_dimension(0) {}
                         iterator(int dimension, coordT **c) : i(c), point_dimension(dimension) {}
                         iterator(const iterator &o) : i(o.i), point_dimension(o.point_dimension) {}
-        iterator       &operator=(const iterator &o) { i= o.i; point_dimension= o.point_dimension; return *this; }
+        iterator &      operator=(const iterator &o) { i= o.i; point_dimension= o.point_dimension; return *this; }
 
         QhullPoint      operator*() const { return QhullPoint(point_dimension, *i); }
                       //operator->() n/a, value-type
         QhullPoint      operator[](int idx) { return QhullPoint(point_dimension, *(i+idx)); }
         bool            operator==(const iterator &o) const { return i == o.i && point_dimension == o.point_dimension; }
         bool            operator!=(const iterator &o) const { return !operator==(o); }
         bool            operator==(const const_iterator &o) const
         { return i == reinterpret_cast(o).i && point_dimension == reinterpret_cast(o).point_dimension; }
         bool            operator!=(const const_iterator &o) const { return !operator==(o); }
 
         //! Assumes same point set
         int             operator-(const iterator &o) { return (int)(i-o.i); } //WARN64
         bool            operator>(const iterator &o) const { return i>o.i; }
         bool            operator<=(const iterator &o) const { return !operator>(o); }
         bool            operator<(const iterator &o) const { return i=(const iterator &o) const { return !operator<(o); }
         bool            operator>(const const_iterator &o) const
         { return i > reinterpret_cast(o).i; }
         bool            operator<=(const const_iterator &o) const { return !operator>(o); }
         bool            operator<(const const_iterator &o) const
         { return i < reinterpret_cast(o).i; }
         bool            operator>=(const const_iterator &o) const { return !operator<(o); }
 
-        iterator       &operator++() { ++i; return *this; }
+        iterator &      operator++() { ++i; return *this; }
         iterator        operator++(int) { iterator o= *this; ++i; return o; }
-        iterator       &operator--() { --i; return *this; }
+        iterator &      operator--() { --i; return *this; }
         iterator        operator--(int) { iterator o= *this; --i; return o; }
         iterator        operator+(int j) const { return iterator(point_dimension, i+j); }
         iterator        operator-(int j) const { return operator+(-j); }
-        iterator       &operator+=(int j) { i += j; return *this; }
-        iterator       &operator-=(int j) { i -= j; return *this; }
+        iterator &      operator+=(int j) { i += j; return *this; }
+        iterator &      operator-=(int j) { i -= j; return *this; }
     };//QhullPointSet::iterator
 
     class const_iterator {
     private:
-        coordT        **i;
+        coordT **       i;
         int             point_dimension;
 
     public:
         typedef std::random_access_iterator_tag  iterator_category;
         typedef QhullPoint value_type;
         typedef value_type *pointer;
         typedef value_type &reference;
         typedef ptrdiff_t  difference_type;
 
                         const_iterator() : i(0), point_dimension(0) {}
                         const_iterator(int dimension, coordT **c) : i(c), point_dimension(dimension) {}
                         const_iterator(const const_iterator &o) : i(o.i), point_dimension(o.point_dimension) {}
                         const_iterator(iterator o) : i(o.i), point_dimension(o.point_dimension) {}
         const_iterator &operator=(const const_iterator &o) { i= o.i; point_dimension= o.point_dimension; return *this; }
 
         QhullPoint      operator*() const { return QhullPoint(point_dimension, *i); }
         QhullPoint      operator[](int idx) { return QhullPoint(point_dimension, *(i+idx)); }
                       //operator->() n/a, value-type
         bool            operator==(const const_iterator &o) const { return i == o.i && point_dimension == o.point_dimension; }
         bool            operator!=(const const_iterator &o) const { return !operator==(o); }
 
         //! Assumes same point set
         int             operator-(const const_iterator &o) { return (int)(i-o.i); } //WARN64
         bool            operator>(const const_iterator &o) const { return i>o.i; }
         bool            operator<=(const const_iterator &o) const { return !operator>(o); }
         bool            operator<(const const_iterator &o) const { return i=(const const_iterator &o) const { return !operator<(o); }
 
         const_iterator &operator++() { ++i; return *this; }
         const_iterator  operator++(int) { const_iterator o= *this; ++i; return o; }
         const_iterator &operator--() { --i; return *this; }
         const_iterator  operator--(int) { const_iterator o= *this; --i; return o; }
         const_iterator  operator+(int j) const { return const_iterator(point_dimension, i+j); }
         const_iterator  operator-(int j) const { return operator+(-j); }
         const_iterator &operator+=(int j) { i += j; return *this; }
         const_iterator &operator-=(int j) { i -= j; return *this; }
     };//QhullPointSet::const_iterator
 
-#//IO
+#//!\name IO
     struct PrintIdentifiers{
         const QhullPointSet *point_set;
-        const char     *print_message;
+        const char *    print_message;
         int             run_id;
         PrintIdentifiers(const char *message, const QhullPointSet *s) : point_set(s), print_message(message) {}
     };//PrintIdentifiers
     PrintIdentifiers printIdentifiers(const char *message) const { return PrintIdentifiers(message, this); }
 
     struct PrintPointSet{
         const QhullPointSet *point_set;
-        const char     *print_message;
+        const char *    print_message;
         int             run_id;
         PrintPointSet(int qhRunId, const char *message, const QhullPointSet &s) : point_set(&s), print_message(message), run_id(qhRunId) {}
     };//PrintPointSet
     PrintPointSet       print(int qhRunId) const { return PrintPointSet(qhRunId, 0, *this); }
     PrintPointSet       print(int qhRunId, const char *message) const { return PrintPointSet(qhRunId, message, *this); }
 
 };//QhullPointSet
 
 //derived from qiterator.h
 class QhullPointSetIterator { // FIXUP QH11020 define QhullMutablePointSetIterator
     typedef QhullPointSet::const_iterator const_iterator;
     const QhullPointSet *c;
     const_iterator      i;
 
 public:
                         QhullPointSetIterator(const QhullPointSet &container) : c(&container), i(c->constBegin()) {}
     QhullPointSetIterator &operator=(const QhullPointSet &container) { c= &container; i= c->constBegin(); return *this; }
     bool                findNext(const QhullPoint &p);
     bool                findPrevious(const QhullPoint &p);
     bool                hasNext() const { return i != c->constEnd(); }
     bool                hasPrevious() const { return i != c->constBegin(); }
     QhullPoint          next() { return *i++; }
     QhullPoint          peekNext() const { return *i; }
     QhullPoint          peekPrevious() const { const_iterator p= i; return *--p; }
     QhullPoint          previous() { return *--i; }
     void                toBack() { i= c->constEnd(); }
     void                toFront() { i= c->constBegin(); }
 };//QhullPointSetIterator
 
 }//namespace orgQhull
 
-#//Global functions
+#//!\name Global
 
 std::ostream &operator<<(std::ostream &os, const orgQhull::QhullPointSet &fs); // Not inline to avoid using statement
 std::ostream &operator<<(std::ostream &os, const orgQhull::QhullPointSet::PrintIdentifiers &pr);
 std::ostream &operator<<(std::ostream &os, const orgQhull::QhullPointSet::PrintPointSet &pr);
 
 #endif // QHULLPOINTSET_H
diff --git a/src/libqhullpcpp/QhullPoints.cpp b/src/libqhullpcpp/QhullPoints.cpp
index efc94cb..8c3106a 100644
--- a/src/libqhullpcpp/QhullPoints.cpp
+++ b/src/libqhullpcpp/QhullPoints.cpp
@@ -1,235 +1,244 @@
 /****************************************************************************
 **
 ** Copyright (c) 2009-2014 C.B. Barber. All rights reserved.
-** $Id: //main/2011/qhull/src/libqhullpcpp/QhullPoints.cpp#1 $$Change: 1652 $
-** $DateTime: 2014/01/17 09:01:32 $$Author: bbarber $
+** $Id: //main/2011/qhull/src/libqhullpcpp/QhullPoints.cpp#2 $$Change: 1710 $
+** $DateTime: 2014/03/28 22:23:20 $$Author: bbarber $
 **
 ****************************************************************************/
 
 #include "QhullPoints.h"
 
 #include 
 #include 
 
 #ifdef _MSC_VER  // Microsoft Visual C++ -- warning level 4
 #endif
 
 namespace orgQhull {
 
 #//Conversion
 // See qt-qhull.cpp for QList conversion
 
 #ifndef QHULL_NO_STL
 std::vector QhullPoints::
 toStdVector() const
 {
     QhullPointsIterator i(*this);
     std::vector vs;
     while(i.hasNext()){
         vs.push_back(i.next());
     }
     return vs;
 }//toStdVector
 #endif //QHULL_NO_STL
 
 #//Read-only
 
+int QhullPoints::
+extraCoordinatesCount() const
+{
+    if(point_dimension>0){
+        return (int)((point_end-point_first)%(size_t)point_dimension);
+    }
+    return 0;
+}//extraCoordinatesCount
+
 bool QhullPoints::
 operator==(const QhullPoints &other) const
 {
     if(point_dimension!=other.point_dimension || (point_end-point_first) != (other.point_end-other.point_first)){
         return false;
     }
     const coordT *c= point_first;
     const coordT *c2= other.point_first;
     while(c=n){
         n= 0;
     }else if(length<0 || idx+length>=n){
         n -= idx;
     }else{
         n -= idx+length;
     }
     return QhullPoints(point_dimension, n*point_dimension, point_first+idx*point_dimension);
 }//mid
 
 QhullPoint QhullPoints::
 value(int idx) const
 {
     QhullPoint p;
     if(idx>=0 && idx=0 && idxconstEnd()){
         if(*i++ == p){
             return true;
         }
     }
     return false;
 }//findNext
 
 bool QhullPointsIterator::
 findPrevious(const QhullPoint &p)
 {
     while(i!=ps->constBegin()){
         if(*--i == p){
             return true;
         }
     }
     return false;
 }//findPrevious
 
 }//namespace orgQhull
 
 #//Global functions
 
 using std::ostream;
 using orgQhull::QhullPoint;
 using orgQhull::QhullPoints;
 using orgQhull::QhullPointsIterator;
 
 ostream &
 operator<<(ostream &os, const QhullPoints &p)
 {
     QhullPointsIterator i(p);
     while(i.hasNext()){
         os << i.next();
     }
     return os;
 }//operator<
 
 namespace orgQhull {
 
-#//Types
+#//!\name Types
     //! coordinate pointer with dimension
     // with const_iterator and iterator
     class QhullPoints;
     //! Java-style iterator
     class QhullPointsIterator;
 
 class QhullPoints {
 
     // QhullPoints consists of pointers into an array of coordinates.
 
 private:
-#//Field
-    coordT             *point_first;
-    coordT             *point_end;  // end>=first.  Trailing coordinates ignored
+#//!\name Fields
+    coordT *            point_first;
+    coordT *            point_end;  // end>=first.  Trailing coordinates ignored
     int                 point_dimension;  // >= 0
 
 public:
-#//Subtypes
-    class               const_iterator;
-    class               iterator;
+#//!\name Subtypes
+    class const_iterator;
+    class iterator;
     typedef QhullPoints::const_iterator ConstIterator;
     typedef QhullPoints::iterator Iterator;
 
-#//Construct
+#//!\name Construct
                         QhullPoints() : point_first(0), point_end(0), point_dimension(0) {};
                         QhullPoints(int pointDimension) : point_first(0), point_end(0), point_dimension(pointDimension) { QHULL_ASSERT(pointDimension>=0); }
                         QhullPoints(int pointDimension, int coordinateCount2, coordT *c) : point_first(c), point_end(c+coordinateCount2), point_dimension(pointDimension) { QHULL_ASSERT(pointDimension>=0 && coordinateCount2>=0 ); }
                         //Copy constructor copies pointers but not contents.  Needed for return by value and parameter passing.
                         QhullPoints(const QhullPoints &other)  : point_first(other.point_first), point_end(other.point_end), point_dimension(other.point_dimension) {}
-                       ~QhullPoints() {}
+                        ~QhullPoints() {}
 
 //disabled since p= p2 is ambiguous (coord* vs coord)
 private:
-    QhullPoints        &operator=(const QhullPoints &other) { point_first= other.point_first; point_end= other.point_end; point_dimension= other.point_dimension; return *this; }
+    QhullPoints &       operator=(const QhullPoints &other) { point_first= other.point_first; point_end= other.point_end; point_dimension= other.point_dimension; return *this; }
 public:
 
-#//Conversion
-    const coordT       *constData() const { return coordinates(); }
+#//!\name Conversion
+    const coordT *      constData() const { return coordinates(); }
     // See coordinates()
-    coordT             *data() { return coordinates(); }
-    const coordT       *data() const { return coordinates(); }
+    coordT *            data() { return coordinates(); }
+    const coordT *      data() const { return coordinates(); }
 #ifndef QHULL_NO_STL
     std::vector toStdVector() const;
 #endif //QHULL_NO_STL
 #ifdef QHULL_USES_QT
     QList   toQList() const;
 #endif //QHULL_USES_QT
 
-#//GetSet
-    coordT             *coordinates() const { return point_first; }
+#//!\name GetSet
+    coordT *            coordinates() const { return point_first; }
     int                 coordinateCount() const { return (int)(point_end-point_first); } // WARN64
     int                 count() const { return (int)size(); } // WARN64
     void                defineAs(int pointDimension, int coordinatesCount, coordT *c) { QHULL_ASSERT(pointDimension>=0 && coordinatesCount>=0 && c!=0); point_first= c; point_end= c+coordinatesCount; point_dimension= pointDimension; }
     void                defineAs(int coordinatesCount, coordT *c) { QHULL_ASSERT((coordinatesCount>=0 && c!=0) || (c==0 && coordinatesCount==0)); point_first= c; point_end= c+coordinatesCount; }
     void                defineAs(const QhullPoints &other) { point_first= other.point_first; point_end= other.point_end; point_dimension= other.point_dimension; }
     int                 dimension() const { return point_dimension; }
     bool                empty() const { return point_end==point_first; }
-    coordT             *extraCoordinates() const { return extraCoordinatesCount() ? (point_end-extraCoordinatesCount()) : 0; }
+    coordT *            extraCoordinates() const { return extraCoordinatesCount() ? (point_end-extraCoordinatesCount()) : 0; }
     int                 extraCoordinatesCount() const { return point_dimension>0 ? (int)((point_end-point_first)%(size_t)point_dimension) : 0; }  // WARN64
     bool                includesCoordinates(const coordT *c) const { return c>=point_first && c=0); point_dimension= pointDimension; }
     size_t              size() const { return (point_dimension ? (point_end-point_first)/point_dimension : 0); }
 
-#//ElementAccess -- can not return references to QhullPoint
+#//!\name Element access
+    //! Can not return references since QhullPoint must be generated
     QhullPoint          at(int idx) const { coordT *p= point_first+idx*point_dimension; QHULL_ASSERT(p(other)); return *this; }
-        QhullPoint     *operator->() { return this; }
+        iterator &      operator=(const iterator &other) { defineAs( const_cast(other)); return *this; }
+        QhullPoint *    operator->() { return this; }
         // value instead of reference since advancePoint() modifies self
         QhullPoint      operator*() const { return *this; }
         QhullPoint      operator[](int idx) const { QhullPoint n= *this; n.advancePoint(idx); return n; }
         bool            operator==(const iterator &other) const { QHULL_ASSERT(dimension()==other.dimension()); return coordinates()==other.coordinates(); }
         bool            operator!=(const iterator &other) const { return !operator==(other); }
         bool            operator<(const iterator &other) const  { QHULL_ASSERT(dimension()==other.dimension()); return coordinates() < other.coordinates(); }
         bool            operator<=(const iterator &other) const { QHULL_ASSERT(dimension()==other.dimension()); return coordinates() <= other.coordinates(); }
         bool            operator>(const iterator &other) const  { QHULL_ASSERT(dimension()==other.dimension()); return coordinates() > other.coordinates(); }
         bool            operator>=(const iterator &other) const { QHULL_ASSERT(dimension()==other.dimension()); return coordinates() >= other.coordinates(); }
         // reinterpret_cast to break circular dependency
         bool            operator==(const QhullPoints::const_iterator &other) const { QHULL_ASSERT(dimension()==reinterpret_cast(other).dimension()); return coordinates()==reinterpret_cast(other).coordinates(); }
         bool            operator!=(const QhullPoints::const_iterator &other) const { return !operator==(reinterpret_cast(other)); }
         bool            operator<(const QhullPoints::const_iterator &other) const  { QHULL_ASSERT(dimension()==reinterpret_cast(other).dimension()); return coordinates() < reinterpret_cast(other).coordinates(); }
         bool            operator<=(const QhullPoints::const_iterator &other) const { QHULL_ASSERT(dimension()==reinterpret_cast(other).dimension()); return coordinates() <= reinterpret_cast(other).coordinates(); }
         bool            operator>(const QhullPoints::const_iterator &other) const  { QHULL_ASSERT(dimension()==reinterpret_cast(other).dimension()); return coordinates() > reinterpret_cast(other).coordinates(); }
         bool            operator>=(const QhullPoints::const_iterator &other) const { QHULL_ASSERT(dimension()==reinterpret_cast(other).dimension()); return coordinates() >= reinterpret_cast(other).coordinates(); }
-        iterator       &operator++() { advancePoint(1); return *this; }
+        iterator &      operator++() { advancePoint(1); return *this; }
         iterator        operator++(int) { iterator n= *this; operator++(); return iterator(n); }
-        iterator       &operator--() { advancePoint(-1); return *this; }
+        iterator &      operator--() { advancePoint(-1); return *this; }
         iterator        operator--(int) { iterator n= *this; operator--(); return iterator(n); }
-        iterator       &operator+=(int idx) { advancePoint(idx); return *this; }
-        iterator       &operator-=(int idx) { advancePoint(-idx); return *this; }
+        iterator &      operator+=(int idx) { advancePoint(idx); return *this; }
+        iterator &      operator-=(int idx) { advancePoint(-idx); return *this; }
         iterator        operator+(int idx) const { iterator n= *this; n.advancePoint(idx); return n; }
         iterator        operator-(int idx) const { iterator n= *this; n.advancePoint(-idx); return n; }
         difference_type operator-(iterator other) const { QHULL_ASSERT(dimension()==other.dimension()); return (coordinates()-other.coordinates())/dimension(); }
     };//QhullPoints::iterator
 
-#//QhullPoints::const_iterator -- FIXUP QH11018 const_iterator same as iterator
+#//!\name QhullPoints::const_iterator -- FIXUP QH11018 const_iterator same as iterator
     class const_iterator : public QhullPoint {
 
     public:
         typedef std::random_access_iterator_tag  iterator_category;
         typedef QhullPoint          value_type;
         typedef const value_type   *pointer;
-        typedef const value_type   &reference;
+        typedef const value_type &  reference;
         typedef ptrdiff_t           difference_type;
 
                         const_iterator() : QhullPoint() {}
                         const_iterator(const const_iterator &other) : QhullPoint(*other) {}
                         const_iterator(const QhullPoints::iterator &other) : QhullPoint(*other) {}
         explicit        const_iterator(const QhullPoints &ps) : QhullPoint(ps.dimension(), ps.coordinates()) {}
         explicit        const_iterator(int pointDimension, coordT *c): QhullPoint(pointDimension, c) {}
         const_iterator &operator=(const const_iterator &other) { defineAs(const_cast(other)); return *this; }
         // value/non-const since advancePoint(1), etc. modifies self
         QhullPoint      operator*() const { return *this; }
-        QhullPoint     *operator->() { return this; }
+        QhullPoint *    operator->() { return this; }
         QhullPoint      operator[](int idx) const { QhullPoint n= *this; n.advancePoint(idx); return n; }
         bool            operator==(const const_iterator &other) const { QHULL_ASSERT(dimension()==other.dimension()); return coordinates()==other.coordinates(); }
         bool            operator!=(const const_iterator &other) const { return !operator==(other); }
         bool            operator<(const const_iterator &other) const  { QHULL_ASSERT(dimension()==other.dimension()); return coordinates() < other.coordinates(); }
         bool            operator<=(const const_iterator &other) const { QHULL_ASSERT(dimension()==other.dimension()); return coordinates() <= other.coordinates(); }
         bool            operator>(const const_iterator &other) const  { QHULL_ASSERT(dimension()==other.dimension()); return coordinates() > other.coordinates(); }
         bool            operator>=(const const_iterator &other) const { QHULL_ASSERT(dimension()==other.dimension()); return coordinates() >= other.coordinates(); }
         const_iterator &operator++() { advancePoint(1); return *this; }
         const_iterator  operator++(int) { const_iterator n= *this; operator++(); return const_iterator(n); }
         const_iterator &operator--() { advancePoint(-1); return *this; }
         const_iterator  operator--(int) { const_iterator n= *this; operator--(); return const_iterator(n); }
         const_iterator &operator+=(int idx) { advancePoint(idx); return *this; }
         const_iterator &operator-=(int idx) { advancePoint(-idx); return *this; }
         const_iterator  operator+(int idx) const { const_iterator n= *this; n.advancePoint(idx); return n; }
         const_iterator  operator-(int idx) const { const_iterator n= *this; n.advancePoint(-idx); return n; }
         difference_type operator-(const_iterator other) const { QHULL_ASSERT(dimension()==other.dimension()); return (coordinates()-other.coordinates())/dimension(); }
     };//QhullPoints::const_iterator
 
-#//IO
+#//!\name IO
     struct PrintPoints{
         const QhullPoints  *points;
-        const char     *point_message;
+        const char *    point_message;
         int             run_id;
         bool            with_identifier;
         PrintPoints(int qhRunId, const char *message, bool withIdentifier, const QhullPoints &ps) : points(&ps), point_message(message), run_id(qhRunId), with_identifier(withIdentifier) {}
     };//PrintPoints
     PrintPoints          print() const { return  PrintPoints(UsingLibQhull::NOqhRunId, "", false, *this); }
     PrintPoints          print(int qhRunId) const { return PrintPoints(qhRunId, "", true, *this); }
     PrintPoints          print(int qhRunId, const char *message) const { return PrintPoints(qhRunId, message, false, *this); }
     PrintPoints          printWithIdentifier(int qhRunId, const char *message) const { return PrintPoints(qhRunId, message, true, *this); }
     //FIXUP remove message for print()?
 };//QhullPoints
 
 // can't use QHULL_DECLARE_SEQUENTIAL_ITERATOR because next(),etc would return a reference to a temporary
 class QhullPointsIterator
 {
     typedef QhullPoints::const_iterator const_iterator;
 
 private:
-#//Fields
+#//!\name Fields
     const QhullPoints  *ps;
     const_iterator      i;
 
 public:
                         QhullPointsIterator(const QhullPoints &other) : ps(&other), i(ps->constBegin()) {}
     QhullPointsIterator &operator=(const QhullPoints &other) { ps = &other; i = ps->constBegin(); return *this; }
     bool                findNext(const QhullPoint &t);
     bool                findPrevious(const QhullPoint &t);
     bool                hasNext() const { return i != ps->constEnd(); }
     bool                hasPrevious() const { return i != ps->constBegin(); }
     QhullPoint          next() { return *i++; }
     QhullPoint          peekNext() const { return *i; }
     QhullPoint          peekPrevious() const { const_iterator p = i; return *--p; }
     QhullPoint          previous() { return *--i; }
     void                toBack() { i = ps->constEnd(); }
     void                toFront() { i = ps->constBegin(); }
 };//QhullPointsIterator
 
 }//namespace orgQhull
 
-#//Global functions
+#//!\name Global
 
-std::ostream           &operator<<(std::ostream &os, const orgQhull::QhullPoints &p);
-std::ostream           &operator<<(std::ostream &os, const orgQhull::QhullPoints::PrintPoints &pr);
+std::ostream &          operator<<(std::ostream &os, const orgQhull::QhullPoints &p);
+std::ostream &          operator<<(std::ostream &os, const orgQhull::QhullPoints::PrintPoints &pr);
 
 #endif // QHULLPOINTS_H
diff --git a/src/libqhullpcpp/QhullQh.h b/src/libqhullpcpp/QhullQh.h
index 59782f9..6e560ee 100644
--- a/src/libqhullpcpp/QhullQh.h
+++ b/src/libqhullpcpp/QhullQh.h
@@ -1,51 +1,52 @@
 /****************************************************************************
 **
 ** Copyright (c) 2008-2012 C.B. Barber. All rights reserved.
-** $Id: //main/2011/qhull/src/libqhullpcpp/QhullQh.h#1 $$Change: 1652 $
-** $DateTime: 2014/01/17 09:01:32 $$Author: bbarber $
+** $Id: //main/2011/qhull/src/libqhullpcpp/QhullQh.h#2 $$Change: 1675 $
+** $DateTime: 2014/02/01 09:38:20 $$Author: bbarber $
 **
 ****************************************************************************/
 
 #ifndef QHULLQH_H
 #define QHULLQH_H
 
 extern "C" {
     #include "libqhull/qhull_a.h"
 }
 
 #include 
 #include 
 
 namespace orgQhull {
 
-#//defined here
+#//!\name defined here
     //! QhullQh -- Qhull's global data structure, qhT, as a C++ class
     //! See UsingLibQhull.h for C++/C interface to qhT
     class QhullQh;
 
 class QhullQh : public qhT {
 
-#//Constants
+#//!\name Constants
     // Set ignored.  PointSet needs explicit dimension
     // Facet from vertices or ridges.vertices.count
     // Ridge from vertices.count
     // Vertex stored in vertexT?  1->16?
     // QhullPoint needs explicit dimension
 
-#//members (empty) -- POD type equivalent to qhT.  No data or virtual members
+#//!\name Fields
+    //! No fields       POD type equivalent to qhT.  No data or virtual members
 
 public:
-#//constructor, assignment, destructor, invariant
+#//!\name Constructors
     QhullQh();
     ~QhullQh();
 
 private:
     //!disable copy constructor and assignment
                         QhullQh(const QhullQh &);
-    QhullQh            &operator=(const QhullQh &);
+    QhullQh &           operator=(const QhullQh &);
 
 };//class QhullQh
 
 }//namespace orgQhull
 
 #endif // QHULLQH_H
diff --git a/src/libqhullpcpp/QhullRidge.h b/src/libqhullpcpp/QhullRidge.h
index a3e7e4c..3eb32e2 100644
--- a/src/libqhullpcpp/QhullRidge.h
+++ b/src/libqhullpcpp/QhullRidge.h
@@ -1,110 +1,110 @@
 /****************************************************************************
 **
 ** Copyright (c) 2008-2012 C.B. Barber. All rights reserved.
-** $Id: //main/2011/qhull/src/libqhullpcpp/QhullRidge.h#1 $$Change: 1652 $
-** $DateTime: 2014/01/17 09:01:32 $$Author: bbarber $
+** $Id: //main/2011/qhull/src/libqhullpcpp/QhullRidge.h#2 $$Change: 1675 $
+** $DateTime: 2014/02/01 09:38:20 $$Author: bbarber $
 **
 ****************************************************************************/
 
 #ifndef QHULLRIDGE_H
 #define QHULLRIDGE_H
 
 #include "QhullSet.h"
 #include "QhullVertex.h"
 #include "QhullVertexSet.h"
 #include "QhullFacet.h"
 extern "C" {
     #include "libqhull/qhull_a.h"
 }
 
 #include 
 
 namespace orgQhull {
 
-#//ClassRef
+#//!\name ClassRef
     class QhullVertex;
     class QhullVertexSet;
     class QhullFacet;
 
-#//Types
+#//!\name Types
     //! QhullRidge -- Qhull's ridge structure, ridgeT [libqhull.h], as a C++ class
     class QhullRidge;
     typedef QhullSet  QhullRidgeSet;
     typedef QhullSetIterator  QhullRidgeSetIterator;
 
     // see QhullSets.h for QhullRidgeSet and QhullRidgeSetIterator -- avoids circular references
 
 /************************
 a ridge is hull_dim-1 simplex between two neighboring facets.  If the
 facets are non-simplicial, there may be more than one ridge between
 two facets.  E.G. a 4-d hypercube has two triangles between each pair
 of neighboring facets.
 
 topological information:
     vertices            a set of vertices
     top,bottom          neighboring facets with orientation
 
 geometric information:
     tested              True if ridge is clearly convex
     nonconvex           True if ridge is non-convex
 */
 
 class QhullRidge {
 
-#//Fields
-    ridgeT             *qh_ridge;
+#//!\name Fields
+    ridgeT *            qh_ridge;
 
-#//Class objects
+#//!\name Class objects
     static ridgeT       s_empty_ridge;
 
 public:
-#//Constants
+#//!\name Constants
 
-#//Constructors
+#//!\name Constructors
                         QhullRidge() : qh_ridge(&s_empty_ridge) {}
                         // Creates an alias.  Does not copy QhullRidge.  Needed for return by value and parameter passing
                         QhullRidge(const QhullRidge &o) : qh_ridge(o.qh_ridge) {}
                         // Creates an alias.  Does not copy QhullRidge.  Needed for vector
-    QhullRidge         &operator=(const QhullRidge &o) { qh_ridge= o.qh_ridge; return *this; }
-                       ~QhullRidge() {}
+    QhullRidge &        operator=(const QhullRidge &o) { qh_ridge= o.qh_ridge; return *this; }
+                        ~QhullRidge() {}
 
-#//Conversion
+#//!\name Conversion
                         //Implicit conversion from ridgeT
                         QhullRidge(ridgeT *r) : qh_ridge(r ? r : &s_empty_ridge) {}
-    ridgeT             *getRidgeT() const { return qh_ridge; }
+    ridgeT *            getRidgeT() const { return qh_ridge; }
 
-#//QhullSet
-    ridgeT             *getBaseT() const { return getRidgeT(); }
+#//!\name QhullSet
+    ridgeT *            getBaseT() const { return getRidgeT(); }
 
-#//getSet
+#//!\name getSet
     QhullFacet          bottomFacet() const { return QhullFacet(qh_ridge->bottom); }
     int                 dimension() const { return QhullSetBase::count(qh_ridge->vertices); }
     int                 id() const { return qh_ridge->id; }
     bool                isDefined() const { return qh_ridge != &s_empty_ridge; }
     bool                operator==(const QhullRidge &o) const { return qh_ridge==o.qh_ridge; }
     bool                operator!=(const QhullRidge &o) const { return !operator==(o); }
     QhullFacet          otherFacet(QhullFacet f) const { return QhullFacet(qh_ridge->top==f.getFacetT() ? qh_ridge->bottom : qh_ridge->top); }
     QhullFacet          topFacet() const { return QhullFacet(qh_ridge->top); }
 
-#//forEach
+#//!\name forEach
     bool                hasNextRidge3d(const QhullFacet f) const;
     QhullRidge          nextRidge3d(const QhullFacet f) const { return nextRidge3d(f, 0); }
     QhullRidge          nextRidge3d(const QhullFacet f, QhullVertex *nextVertex) const;
     QhullVertexSet      vertices() const { return QhullVertexSet(qh_ridge->vertices); }
 
-#//IO
+#//!\name IO
 
     struct PrintRidge{
         const QhullRidge *ridge;
         int             run_id;
                         PrintRidge(int qhRunId, const QhullRidge &r) : ridge(&r), run_id(qhRunId) {}
     };//PrintRidge
     PrintRidge          print(int qhRunId) const { return PrintRidge(qhRunId, *this); }
 };//class QhullRidge
 
 }//namespace orgQhull
 
 std::ostream &operator<<(std::ostream &os, const orgQhull::QhullRidge &r); 
 std::ostream &operator<<(std::ostream &os, const orgQhull::QhullRidge::PrintRidge &pr);
 
 #endif // QHULLRIDGE_H
diff --git a/src/libqhullpcpp/QhullSet.h b/src/libqhullpcpp/QhullSet.h
index b4b2eb9..c49c09a 100644
--- a/src/libqhullpcpp/QhullSet.h
+++ b/src/libqhullpcpp/QhullSet.h
@@ -1,360 +1,358 @@
 /****************************************************************************
 **
 ** Copyright (c) 2008-2012 C.B. Barber. All rights reserved.
-** $Id: //main/2011/qhull/src/libqhullpcpp/QhullSet.h#1 $$Change: 1652 $
-** $DateTime: 2014/01/17 09:01:32 $$Author: bbarber $
+** $Id: //main/2011/qhull/src/libqhullpcpp/QhullSet.h#2 $$Change: 1675 $
+** $DateTime: 2014/02/01 09:38:20 $$Author: bbarber $
 **
 ****************************************************************************/
 
 #ifndef QhullSet_H
 #define QhullSet_H
 
 #include "QhullError.h"
 extern "C" {
     #include "libqhull/qhull_a.h"
 }
 
 
 #ifndef QHULL_NO_STL
 #include 
 #endif
 
 #ifdef QHULL_USES_QT
  #include 
 #endif
 
 namespace orgQhull {
 
-#//Type
+#//!\name Type
     class QhullSetBase;  //! Base class for QhullSet
     //! QhullSet -- A read-only wrapper to Qhull's collection class, setT.
     //!  QhullSet is similar to STL's  and Qt's QVector.
     //!  QhullSet is unrelated to STL and Qt's set and map types (e.g., QSet and QMap)
     //!  For STL efficiency, QhullSet caches endPointer()
     //!  T must be a pointer type
     //!  A QhullSet does not own its contents -- erase(), clear(), removeFirst(), removeLast(), pop_back(), pop_front(), fromStdList() not defined
     //!  Qhull's FOREACHelement_() [qset.h] is more efficient than QhullSet.  It uses a NULL terminator instead of an end pointer.  STL requires an end pointer.
     //!  Derived from QhullLinkedList.h and Qt/core/tools/qvector.h
 
     //! QhullSetIterator defined below
     //See: QhullPointSet, QhullLinkedList
 
 class QhullSetBase {
 
 private:
-#//Fields --
-    setT               *qh_set;
+#//!\name Fields --
+    setT *              qh_set;
 
-#//Class objects
+#//!\name Class objects
     static setT         s_empty_set;  //! Workaround for no setT allocator.  Used if setT* is NULL
 
 public:
-#//Class methods
+#//!\name Class methods
     static int          count(const setT *set);
     //s may be null
     static bool         isEmpty(const setT *s) { return SETempty_(s); }
 
 
-#//Constructors
+#//!\name Constructors
                         //! Copy constructor copies the pointer but not the set.  Needed for return by value and parameter passing.
                         QhullSetBase(const QhullSetBase &o) : qh_set(o.qh_set) {}
     explicit            QhullSetBase(setT *s) : qh_set(s ? s : &s_empty_set) {}
-                       ~QhullSetBase() {}
+                        ~QhullSetBase() {}
 
 private:
                         //!disabled since memory allocation for QhullSet not defined
                         QhullSetBase() {}
                         //!disabled since qs= qs2 is ambiguous (pointer vs. contents)
-    QhullSetBase       &operator=(const QhullSetBase &);
+    QhullSetBase &      operator=(const QhullSetBase &);
 public:
 
-#//Conversions
+#//!\name Conversions
                         //! Not type-safe since setT may contain any type
     void                defineAs(setT *s) { qh_set= s ? s : &s_empty_set; }
-    setT               *getSetT() const { return qh_set; }
-    setT              **referenceSetT() { return &qh_set; }
+    setT *              getSetT() const { return qh_set; }
+    setT **             referenceSetT() { return &qh_set; }
 
-#//Read-only
+#//!\name Read-only
     int                 count() const { return QhullSetBase::count(qh_set); }
     bool                empty() const { return SETfirst_(qh_set)==0; }
     bool                isEmpty() const { return empty(); }
     size_t              size() const { return count(); }
 
-#//Element
+#//!\name Element
 protected:
-    void              **beginPointer() const { return &qh_set->e[0].p; }
-    void              **elementPointer(int idx) const { QHULL_ASSERT(idx>=0 && idxmaxsize); return &SETelem_(qh_set, idx); }
+    void **             beginPointer() const { return &qh_set->e[0].p; }
+    void **             elementPointer(int idx) const { QHULL_ASSERT(idx>=0 && idxmaxsize); return &SETelem_(qh_set, idx); }
                         //! Always points to 0
-    void              **endPointer() const { return qh_setendpointer(qh_set); }
+    void **             endPointer() const { return qh_setendpointer(qh_set); }
 };//QhullSetBase
 
 
 //! set of pointers to baseT, T.getBaseT()
 template 
 class QhullSet : public QhullSetBase {
 
 private:
-#//Fields -- see QhullSetBase
+#//!\name Fields -- see QhullSetBase
 
-#//Class objects
+#//!\name Class objects
     static setT         s_empty_set;  //! Workaround for no setT allocator.  Used if setT* is NULL
 
 public:
-#//Subtypes
-    typedef T         *iterator;
-    typedef const T   *const_iterator;
+#//!\name Subtypes
+    typedef T *        iterator;
+    typedef const T *  const_iterator;
     typedef typename QhullSet::iterator Iterator;
     typedef typename QhullSet::const_iterator ConstIterator;
 
-#//Class methods
+#//!\name Class methods
     static int          count(const setT *set);
                         //s may be null
     static bool         isEmpty(const setT *s) { return SETempty_(s); }
 
-#//Constructors
+#//!\name Constructors
                         //Copy constructor copies pointer but not contents.  Needed for return by value.
                         QhullSet(const QhullSet &o) : QhullSetBase(o) {}
                         //Conversion from setT* is not type-safe.  Implicit conversion for void* to T
     explicit            QhullSet(setT *s) : QhullSetBase(s) { QHULL_ASSERT(sizeof(T)==sizeof(void *)); }
-                       ~QhullSet() {}
+                        ~QhullSet() {}
 
 private:
                         //!Disable default constructor and copy assignment.  See QhullSetBase
                         QhullSet();
-    QhullSet        &operator=(const QhullSet &);
+    QhullSet &       operator=(const QhullSet &);
 public:
 
-#//Conversion
+#//!\name Conversion
 
 #ifndef QHULL_NO_STL
     std::vector      toStdVector() const;
 #endif
 #ifdef QHULL_USES_QT
     QList            toQList() const;
 #endif
 
-#//Read-only -- see QhullSetBase for count(), empty(), isEmpty(), size()
+#//!\name Read-only -- see QhullSetBase for count(), empty(), isEmpty(), size()
     using QhullSetBase::count;
     using QhullSetBase::isEmpty;
     // operator== defined for QhullSets of the same type
     bool                operator==(const QhullSet &other) const { return qh_setequal(getSetT(), other.getSetT()); }
     bool                operator!=(const QhullSet &other) const { return !operator==(other); }
 
-#//Element access
-    const T            &at(int idx) const { return operator[](idx); }
-    T                  &back() { return last(); }
-    T                  &back() const { return last(); }
+#//!\name Element access
+    const T &           at(int idx) const { return operator[](idx); }
+    T &                 back() { return last(); }
+    T &                 back() const { return last(); }
     //! end element is NULL
-    const T            *constData() const { return constBegin(); }
-    T                  *data() { return begin(); }
-    const T            *data() const { return begin(); }
-    T                  &first() { QHULL_ASSERT(!isEmpty()); return *begin(); }
-    const T            &first() const { QHULL_ASSERT(!isEmpty()); return *begin(); }
-    T                  &front() { return first(); }
-    const T            &front() const { return first(); }
-    T                  &last() { QHULL_ASSERT(!isEmpty()); return *(end()-1); }
-    const T            &last() const {  QHULL_ASSERT(!isEmpty()); return *(end()-1); }
+    const T *           constData() const { return constBegin(); }
+    T *                 data() { return begin(); }
+    const T *           data() const { return begin(); }
+    T &                 first() { QHULL_ASSERT(!isEmpty()); return *begin(); }
+    const T &           first() const { QHULL_ASSERT(!isEmpty()); return *begin(); }
+    T &                 front() { return first(); }
+    const T &           front() const { return first(); }
+    T &                 last() { QHULL_ASSERT(!isEmpty()); return *(end()-1); }
+    const T &           last() const {  QHULL_ASSERT(!isEmpty()); return *(end()-1); }
     // mid() not available.  No setT constructor
-    T                  &operator[](int idx) { T *n= reinterpret_cast(elementPointer(idx)); QHULL_ASSERT(idx>=0 && n < reinterpret_cast(endPointer())); return *n; }
-    const T            &operator[](int idx) const { const T *n= reinterpret_cast(elementPointer(idx)); QHULL_ASSERT(idx>=0 && n < reinterpret_cast(endPointer())); return *n; }
-    T                  &second() { return operator[](1); }
-    const T            &second() const { return operator[](1); }
+    T &                 operator[](int idx) { T *n= reinterpret_cast(elementPointer(idx)); QHULL_ASSERT(idx>=0 && n < reinterpret_cast(endPointer())); return *n; }
+    const T &           operator[](int idx) const { const T *n= reinterpret_cast(elementPointer(idx)); QHULL_ASSERT(idx>=0 && n < reinterpret_cast(endPointer())); return *n; }
+    T &                 second() { return operator[](1); }
+    const T &           second() const { return operator[](1); }
     T                   value(int idx) const;
     T                   value(int idx, const T &defaultValue) const;
 
-#//Read-write -- Not available, no setT constructor
+#//!\name GetSet -- Not available, no setT constructor
 
-#//iterator
+#//!\name iterator
     iterator            begin() { return iterator(beginPointer()); }
     const_iterator      begin() const { return const_iterator(beginPointer()); }
     const_iterator      constBegin() const { return const_iterator(beginPointer()); }
     const_iterator      constEnd() const { return const_iterator(endPointer()); }
     iterator            end() { return iterator(endPointer()); }
     const_iterator      end() const { return const_iterator(endPointer()); }
 
-#//Search
+#//!\name Search
     bool                contains(const T &t) const;
     int                 count(const T &t) const;
     int                 indexOf(const T &t) const { /* no qh_qh */ return qh_setindex(getSetT(), t.getBaseT()); }
     int                 lastIndexOf(const T &t) const;
 
 };//class QhullSet
 
 // FIXUP? can't use QHULL_DECLARE_SEQUENTIAL_ITERATOR because it is not a template
 
 template 
 class QhullSetIterator {
 
-#//Subtypes
+#//!\name Subtypes
     typedef typename QhullSet::const_iterator const_iterator;
 
 private:
-#//Fields
+#//!\name Fields
     const_iterator      i;
     const_iterator      begin_i;
     const_iterator      end_i;
 
 public:
-#//Constructors
+#//!\name Constructors
                         QhullSetIterator(const QhullSet &s) : i(s.begin()), begin_i(i), end_i(s.end()) {}
                         QhullSetIterator(const QhullSetIterator &o) : i(o.i), begin_i(o.begin_i), end_i(o.end_i) {}
     QhullSetIterator &operator=(const QhullSetIterator &o) { i= o.i; begin_i= o.begin_i; end_i= o.end_i; return *this; }
 
-#//ReadOnly
+#//!\name ReadOnly
     int                 countRemaining() { return (int)(end_i-begin_i); } // WARN64
 
-#//Search
+#//!\name Search
     bool                findNext(const T &t);
     bool                findPrevious(const T &t);
 
-#//Foreach
+#//!\name Foreach
     bool                hasNext() const { return i != end_i; }
     bool                hasPrevious() const { return i != begin_i; }
     T                   next() { return *i++; }
     T                   peekNext() const { return *i; }
     T                   peekPrevious() const { const_iterator p = i; return *--p; }
     T                   previous() { return *--i; }
     void                toBack() { i = end_i; }
     void                toFront() { i = begin_i; }
 };//class QhullSetIterator
 
-#//== Definitions =========================================
-
-#//Conversion
+#//!\name Conversion
 
 #ifndef QHULL_NO_STL
 template 
 std::vector QhullSet::
 toStdVector() const
 {
     QhullSetIterator i(*this);
     std::vector vs;
     vs.reserve(i.countRemaining());
     while(i.hasNext()){
         vs.push_back(i.next());
     }
     return vs;
 }//toStdVector
 #endif
 
 #ifdef QHULL_USES_QT
 template 
 QList QhullSet::
 toQList() const
 {
     QhullSetIterator i(*this);
     QList vs;
     while(i.hasNext()){
         vs.append(i.next());
     }
     return vs;
 }//toQList
 #endif
 
-#//Element
+#//!\name Element
 
 template 
 T QhullSet::
 value(int idx) const
 {
     // Avoid call to qh_setsize() and assert in elementPointer()
     const T *n= reinterpret_cast(&SETelem_(getSetT(), idx));
     return (idx>=0 && n
 T QhullSet::
 value(int idx, const T &defaultValue) const
 {
     // Avoid call to qh_setsize() and assert in elementPointer()
     const T *n= reinterpret_cast(&SETelem_(getSetT(), idx));
     return (idx>=0 && n
 bool QhullSet::
 contains(const T &t) const
 {
     setT *s= getSetT();
     void *e= t.getBaseT();  // contains() is not inline for better error reporting
     int result= qh_setin(s, e);
     return result!=0;
 }//contains
 
 template 
 int QhullSet::
 count(const T &t) const
 {
     int c= 0;
     const T *i= data();
     const T *e= end();
     while(i
 int QhullSet::
 lastIndexOf(const T &t) const
 {
     const T *b= begin();
     const T *i= end();
     while(--i>=b){
         if(*i==t){
             break;
         }
     }
     return (int)(i-b); // WARN64
 }//lastIndexOf
 
-#//QhullSetIterator
+#//!\name QhullSetIterator
 
 template 
 bool QhullSetIterator::
 findNext(const T &t)
 {
     while(i!=end_i){
         if(*(++i)==t){
             return true;
         }
     }
     return false;
 }//findNext
 
 template 
 bool QhullSetIterator::
 findPrevious(const T &t)
 {
     while(i!=begin_i){
         if(*(--i)==t){
             return true;
         }
     }
     return false;
 }//findPrevious
 
 }//namespace orgQhull
 
 
-#//== Global namespace =========================================
+#//!\name Global
 
 template 
 std::ostream &
 operator<<(std::ostream &os, const orgQhull::QhullSet &qs)
 {
     const T *i= qs.begin();
     const T *e= qs.end();
     while(i!=e){
         os << *i;
         ++i;
     }
     return os;
 }//operator<<
 
 #endif // QhullSet_H
diff --git a/src/libqhullpcpp/QhullStat.h b/src/libqhullpcpp/QhullStat.h
index 44a594a..59422e9 100644
--- a/src/libqhullpcpp/QhullStat.h
+++ b/src/libqhullpcpp/QhullStat.h
@@ -1,52 +1,53 @@
 /****************************************************************************
 **
 ** Copyright (c) 2008-2012 C.B. Barber. All rights reserved.
-** $Id: //main/2011/qhull/src/libqhullpcpp/QhullStat.h#1 $$Change: 1652 $
-** $DateTime: 2014/01/17 09:01:32 $$Author: bbarber $
+** $Id: //main/2011/qhull/src/libqhullpcpp/QhullStat.h#2 $$Change: 1675 $
+** $DateTime: 2014/02/01 09:38:20 $$Author: bbarber $
 **
 ****************************************************************************/
 
 #ifndef QHULLSTAT_H
 #define QHULLSTAT_H
 
 extern "C" {
     #include "libqhull/qhull_a.h"
 }
 
 #include 
 #include 
 
 namespace orgQhull {
 
-#//defined here
+#//!\name defined here
     //! QhullStat -- Qhull's statistics, qhstatT, as a C++ class
     //! Statistics defined with zzdef_() control Qhull's behavior, summarize its result, and report precision problems.
     class QhullStat;
 
 class QhullStat : public qhstatT {
 
 private:
-#//Fields (empty) -- POD type equivalent to qhstatT.  No data or virtual members
+#//!\name Fields
+    //! No fields       POD type equivalent to qhstatT.  No data or virtual members
 
 public:
-#//Constants
+#//!\name Constants
 
-#//class methods
+#//!\name class methods
     static void         clearStatistics();
 
-#//constructor, assignment, destructor, invariant
+#//!\name constructor, assignment, destructor, invariant
                         QhullStat();
-                       ~QhullStat();
+                        ~QhullStat();
 
 private:
     //!disable copy constructor and assignment
                         QhullStat(const QhullStat &);
-    QhullStat          &operator=(const QhullStat &);
+    QhullStat &         operator=(const QhullStat &);
 public:
 
-#//Access
+#//!\name Access
 };//class QhullStat
 
 }//namespace orgQhull
 
 #endif // QHULLSTAT_H
diff --git a/src/libqhullpcpp/QhullVertex.h b/src/libqhullpcpp/QhullVertex.h
index 58a0a4f..e8b0d94 100644
--- a/src/libqhullpcpp/QhullVertex.h
+++ b/src/libqhullpcpp/QhullVertex.h
@@ -1,103 +1,101 @@
 /****************************************************************************
 **
 ** Copyright (c) 2008-2012 C.B. Barber. All rights reserved.
-** $Id: //main/2011/qhull/src/libqhullpcpp/QhullVertex.h#1 $$Change: 1652 $
-** $DateTime: 2014/01/17 09:01:32 $$Author: bbarber $
+** $Id: //main/2011/qhull/src/libqhullpcpp/QhullVertex.h#2 $$Change: 1675 $
+** $DateTime: 2014/02/01 09:38:20 $$Author: bbarber $
 **
 ****************************************************************************/
 
 #ifndef QHULLVERTEX_H
 #define QHULLVERTEX_H
 
 #include "UsingLibQhull.h"
 #include "QhullPoint.h"
 #include "QhullLinkedList.h"
 #include "QhullSet.h"
 extern "C" {
     #include "libqhull/qhull_a.h"
 }
 
 #include 
 
 namespace orgQhull {
 
-#//ClassRef
+#//!\name ClassRef
     class QhullFacetSet;
 
-#//Types
+#//!\name Types
     //! QhullVertex -- Qhull's vertex structure, vertexT [libqhull.h], as a C++ class
     class QhullVertex;
     typedef QhullLinkedList QhullVertexList;
     typedef QhullLinkedListIterator QhullVertexListIterator;
 
 
 /*********************
   topological information:
     next,previous       doubly-linked list of all vertices
     neighborFacets           set of adjacent facets (only if qh.VERTEXneighbors)
 
   geometric information:
     point               array of DIM coordinates
 */
 
 class QhullVertex {
 
 private:
-#//Fields
-    vertexT            *qh_vertex;
+#//!\name Fields
+    vertexT *           qh_vertex;
 
-#//Class objects
+#//!\name Class objects
     static vertexT      s_empty_vertex;  // needed for shallow copy
 
 public:
-#//Constants
+#//!\name Constants
 
-#//Constructors
+#//!\name Constructors
                         QhullVertex() : qh_vertex(&s_empty_vertex) {}
                         // Creates an alias.  Does not copy QhullVertex.  Needed for return by value and parameter passing
                         QhullVertex(const QhullVertex &o) : qh_vertex(o.qh_vertex) {}
                         // Creates an alias.  Does not copy QhullVertex.  Needed for vector
-    QhullVertex        &operator=(const QhullVertex &o) { qh_vertex= o.qh_vertex; return *this; }
-                       ~QhullVertex() {}
+    QhullVertex &       operator=(const QhullVertex &o) { qh_vertex= o.qh_vertex; return *this; }
+                        ~QhullVertex() {}
 
-#//Conversion
+#//!\name Conversion
                         //Implicit conversion from vertexT
                         QhullVertex(vertexT *v) : qh_vertex(v ? v : &s_empty_vertex) {}
-    vertexT            *getVertexT() const { return qh_vertex; }
+    vertexT *           getVertexT() const { return qh_vertex; }
+    vertexT *           getBaseT() const { return getVertexT(); }
 
-#//QhullSet
-    vertexT            *getBaseT() const { return getVertexT(); }
-
-#//getSet
+#//!\name getSet
     int                 dimension() const { return (qh_vertex->dim || !isDefined()) ? qh_vertex->dim : UsingLibQhull::globalVertexDimension(); }
     int                 id() const { return qh_vertex->id; }
     bool                isDefined() const { return qh_vertex != &s_empty_vertex; }
                         //! True if defineVertexNeighborFacets() already called.  Auotomatically set for facet merging, Voronoi diagrams
     bool                neighborFacetsDefined() const { return qh_vertex->neighbors != 0; }
     QhullVertex         next() const { return qh_vertex->next; }
     bool                operator==(const QhullVertex &o) const { return qh_vertex==o.qh_vertex; }
     bool                operator!=(const QhullVertex &o) const { return !operator==(o); }
     QhullPoint          point() const { return QhullPoint(dimension(), qh_vertex->point); }
     QhullVertex         previous() const { return qh_vertex->previous; }
 
-#//ForEach
+#//!\name ForEach
     //See also QhullVertexList
     QhullFacetSet       neighborFacets() const;
 
-#//IO
+#//!\name IO
     struct PrintVertex{
         const QhullVertex *vertex;
         int             run_id;
                         PrintVertex(int qhRunId, const QhullVertex &v) : vertex(&v), run_id(qhRunId) {}
     };//PrintVertex
     PrintVertex         print(int qhRunId) const { return PrintVertex(qhRunId, *this); }
 };//class QhullVertex
 
 }//namespace orgQhull
 
-#//GLobal
+#//!\name GLobal
 
 std::ostream &operator<<(std::ostream &os, const orgQhull::QhullVertex::PrintVertex &pr);
 inline std::ostream &operator<<(std::ostream &os, const orgQhull::QhullVertex &v) { os << v.print(orgQhull::UsingLibQhull::NOqhRunId); return os; }
 
 #endif // QHULLVERTEX_H
diff --git a/src/libqhullpcpp/QhullVertexSet.h b/src/libqhullpcpp/QhullVertexSet.h
index d912bda..e0845cb 100644
--- a/src/libqhullpcpp/QhullVertexSet.h
+++ b/src/libqhullpcpp/QhullVertexSet.h
@@ -1,79 +1,79 @@
 /****************************************************************************
 **
 ** Copyright (c) 2009-2012 C.B. Barber. All rights reserved.
-** $Id: //main/2011/qhull/src/libqhullpcpp/QhullVertexSet.h#1 $$Change: 1652 $
-** $DateTime: 2014/01/17 09:01:32 $$Author: bbarber $
+** $Id: //main/2011/qhull/src/libqhullpcpp/QhullVertexSet.h#2 $$Change: 1675 $
+** $DateTime: 2014/02/01 09:38:20 $$Author: bbarber $
 **
 ****************************************************************************/
 
 #ifndef QHULLVERTEXSET_H
 #define QHULLVERTEXSET_H
 
 #include "QhullSet.h"
 
 #include 
 
 namespace orgQhull {
 
-#//ClassRef
-    class               QhullVertex;
+#//!\name ClassRef
+    class QhullVertex;
 
-#//Types
+#//!\name Types
     //! QhullVertexSet -- a set of Qhull Vertices, as a C++ class.
     //! See Qhull
-    class               QhullVertexSet;
+    class QhullVertexSet;
     typedef QhullSetIterator
                         QhullVertexSetIterator;
 
 class QhullVertexSet : public QhullSet {
 
 private:
-#//Fields
-    Qhull              *qhsettemp_qhull; //! For sets allocated with qh_settemp()
+#//!\name Fields
+    Qhull *             qhsettemp_qhull; //! For sets allocated with qh_settemp()
     bool                qhsettemp_defined;  //! Set was allocated with q_memalloc()
 
 public:
-#//Constructor
+#//!\name Constructor
                         //Conversion from setT* is not type-safe.  Implicit conversion for void* to T
    explicit             QhullVertexSet(setT *s) : QhullSet(s), qhsettemp_qhull(0), qhsettemp_defined(false) {}
                         QhullVertexSet(int qhRunId, facetT *facetlist, setT *facetset, bool allfacets);
                         //Copy constructor copies pointer but not contents.  Needed for return by value.
                         QhullVertexSet(const QhullVertexSet &o) : QhullSet(o), qhsettemp_qhull(o.qhsettemp_qhull), qhsettemp_defined(o.qhsettemp_defined) {}
-                       ~QhullVertexSet();
+                        ~QhullVertexSet();
 
 private:
                         //!Disable default constructor and copy assignment.  See QhullSetBase
                         QhullVertexSet();
-    QhullVertexSet      &operator=(const QhullVertexSet &);
+    QhullVertexSet &     operator=(const QhullVertexSet &);
 public:
 
-#//Constructor, destructor
+#//!\name Constructor, destructor
     void                freeQhSetTemp();
 
-#//IO
+#//!\name IO
     struct PrintVertexSet{
         const QhullVertexSet *Vertex_set;
-        const char     *print_message;
+        const char *    print_message;
         int             run_id;
                         PrintVertexSet(int qhRunId, const char *message, const QhullVertexSet *s) : Vertex_set(s), print_message(message), run_id(qhRunId) {}
     };//PrintVertexSet
     const PrintVertexSet       print(int qhRunId, const char *message) const { return PrintVertexSet(qhRunId, message, this); }
 
     struct PrintIdentifiers{
         const QhullVertexSet *Vertex_set;
-        const char     *print_message;
+        const char *    print_message;
                         PrintIdentifiers(const char *message, const QhullVertexSet *s) : Vertex_set(s), print_message(message) {}
     };//PrintIdentifiers
     PrintIdentifiers    printIdentifiers(const char *message) const { return PrintIdentifiers(message, this); }
 
 };//class QhullVertexSet
 
 }//namespace orgQhull
 
-#//== Global namespace =========================================
+#//!\name Global
 
 std::ostream &operator<<(std::ostream &os, const orgQhull::QhullVertexSet::PrintVertexSet &pr);
 std::ostream &operator<<(std::ostream &os, const orgQhull::QhullVertexSet::PrintIdentifiers &p);
 inline std::ostream &operator<<(std::ostream &os, const orgQhull::QhullVertexSet &vs) { os << vs.print(orgQhull::UsingLibQhull::NOqhRunId, ""); return os; }
 
 #endif // QHULLVERTEXSET_H
diff --git a/src/libqhullpcpp/RboxPoints.cpp b/src/libqhullpcpp/RboxPoints.cpp
index e25960e..5a248f0 100644
--- a/src/libqhullpcpp/RboxPoints.cpp
+++ b/src/libqhullpcpp/RboxPoints.cpp
@@ -1,219 +1,225 @@
 /****************************************************************************
 **
 ** Copyright (c) 2008-2014 C.B. Barber. All rights reserved.
-** $Id: //main/2011/qhull/src/libqhullpcpp/RboxPoints.cpp#1 $$Change: 1652 $
-** $DateTime: 2014/01/17 09:01:32 $$Author: bbarber $
+** $Id: //main/2011/qhull/src/libqhullpcpp/RboxPoints.cpp#2 $$Change: 1710 $
+** $DateTime: 2014/03/28 22:23:20 $$Author: bbarber $
 **
 ****************************************************************************/
 
 #include "QhullError.h"
 #include "RboxPoints.h"
 
 #include 
 
 using std::cerr;
 using std::endl;
 using std::istream;
 using std::ostream;
 using std::ostringstream;
 using std::string;
 using std::vector;
 using std::ws;
 
 #ifdef _MSC_VER  // Microsoft Visual C++ -- warning level 4
 #pragma warning( disable : 4996)  // function was declared deprecated(strcpy, localtime, etc.)
 #endif
 
 namespace orgQhull {
 
 #//! RboxPoints -- generate random PointCoordinates for qhull (rbox)
 
 #//Global
 
 //! pointer to RboxPoints for qh_fprintf callback
 RboxPoints *rbox_output= 0;
 
 #//Construct
 RboxPoints::
 RboxPoints()
 : PointCoordinates("rbox")
 , rbox_new_count(0)
 , rbox_status(qh_ERRnone)
 , rbox_message()
 {}
 
 RboxPoints::
 RboxPoints(const char *rboxCommand)
-: PointCoordinates("rbox")
+: PointCoordinates("rbox ")
 , rbox_new_count(0)
 , rbox_status(qh_ERRnone)
 , rbox_message()
 {
+    std::string s= comment() + rboxCommand;
+    setComment(s);
     appendPoints(rboxCommand);
 }
 
 RboxPoints::
 RboxPoints(const RboxPoints &other)
 : PointCoordinates(other)
 , rbox_new_count(0)
 , rbox_status(other.rbox_status)
 , rbox_message(other.rbox_message)
 {}
 
 RboxPoints & RboxPoints::
 operator=(const RboxPoints &other)
 {
     PointCoordinates::operator=(other);
     rbox_new_count= other.rbox_new_count;
     rbox_status= other.rbox_status;
     rbox_message= other.rbox_message;
     return *this;
 }//operator=
 
 
 RboxPoints::
 ~RboxPoints()
 {}
 
 #//Error
 
 void RboxPoints::
 clearRboxMessage()
 {
     rbox_status= qh_ERRnone;
     rbox_message.clear();
 }//clearRboxMessage
 
 std::string RboxPoints::
 rboxMessage() const
 {
     if(rbox_status!=qh_ERRnone){
         return rbox_message;
     }
     if(isEmpty()){
         return "rbox warning: no points generated\n";
     }
     return "rbox: OK\n";
 }//rboxMessage
 
 int RboxPoints::
 rboxStatus() const
 {
     return rbox_status;
 }
 
 bool RboxPoints::
 hasRboxMessage() const
 {
     return (rbox_status!=qh_ERRnone);
 }
 
 #//Modify
 
 void RboxPoints::
 appendPoints(const char *rboxCommand)
 {
     string s("rbox ");
     s += rboxCommand;
     char *command= const_cast(s.c_str());
     if(rbox_output){
         throw QhullError(10001, "Qhull error: Two simultaneous calls to RboxPoints::appendPoints().  Prevent two processes calling appendPoints() at the same time.  Other RboxPoints '%s'", 0, 0, 0, rbox_output->comment().c_str());
     }
     if(extraCoordinatesCount()!=0){
         throw QhullError(10067, "Qhull error: Extra coordinates (%d) prior to calling RboxPoints::appendPoints.  Was %s", extraCoordinatesCount(), 0, 0.0, comment().c_str());
     }
     int previousCount= count();
     rbox_output= this;              // set rbox_output for qh_fprintf()
     int status= ::qh_rboxpoints(0, 0, command);
     rbox_output= 0;
     if(rbox_status==qh_ERRnone){
         rbox_status= status;
     }
     if(rbox_status!=qh_ERRnone){
         throw QhullError(rbox_status, rbox_message);
     }
     if(extraCoordinatesCount()!=0){
         throw QhullError(10002, "Qhull error: extra coordinates (%d) for PointCoordinates (%x)", extraCoordinatesCount(), 0, 0.0, coordinates());
     }
     if(previousCount+newCount()!=count()){
         throw QhullError(10068, "Qhull error: rbox specified %d points but got %d points for command '%s'", newCount(), count()-previousCount, 0.0, comment().c_str());
     }
 }//appendPoints
 
 }//namespace orgQhull
 
 #//Global functions
 
 /*---------------------------------
 
   qh_fprintf_rbox(fp, msgcode, format, list of args )
     fp is ignored (replaces qh_fprintf_rbox() in userprintf_rbox.c)
     rbox_output == RboxPoints
 
 notes:
     only called from qh_rboxpoints()
     same as fprintf() and Qhull::qh_fprintf()
     fgets() is not trapped like fprintf()
     Do not throw errors from here.  Use qh_errexit_rbox;
 */
 extern "C"
 void qh_fprintf_rbox(FILE*, int msgcode, const char *fmt, ... ) {
     va_list args;
 
     using namespace orgQhull;
 
+    if(!qh->rbox_output){
+        // No place to write an error message
+        qh_errexit_rbox(10072);
+    }
     RboxPoints *out= rbox_output;
     va_start(args, fmt);
     if(msgcoderbox_message += newMessage;
         if(out->rbox_statusrbox_status>=MSG_STDERR){
             out->rbox_status= msgcode;
         }
         va_end(args);
         return;
     }
     switch(msgcode){
     case 9391:
     case 9392:
         out->rbox_message += "RboxPoints error: options 'h', 'n' not supported.\n";
         qh_errexit_rbox(10010);
         /* never returns */
     case 9393:
         {
             int dimension= va_arg(args, int);
             string command(va_arg(args, char*));
             int count= va_arg(args, int);
             out->setDimension(dimension);
             out->appendComment(" \"");
             out->appendComment(command.substr(command.find(' ')+1));
             out->appendComment("\"");
             out->setNewCount(count);
             out->reservePoints();
         }
         break;
     case 9407:
         *out << va_arg(args, int);
         // fall through
     case 9405:
         *out << va_arg(args, int);
         // fall through
     case 9403:
         *out << va_arg(args, int);
         break;
     case 9408:
         *out << va_arg(args, double);
         // fall through
     case 9406:
         *out << va_arg(args, double);
         // fall through
     case 9404:
         *out << va_arg(args, double);
         break;
     }
     va_end(args);
 } /* qh_fprintf_rbox */
 
diff --git a/src/libqhullpcpp/RboxPoints.h b/src/libqhullpcpp/RboxPoints.h
index 28e14aa..dfe7612 100644
--- a/src/libqhullpcpp/RboxPoints.h
+++ b/src/libqhullpcpp/RboxPoints.h
@@ -1,66 +1,66 @@
 /****************************************************************************
 **
 ** Copyright (c) 2008-2012 C.B. Barber. All rights reserved.
-** $Id: //main/2011/qhull/src/libqhullpcpp/RboxPoints.h#1 $$Change: 1652 $
-** $DateTime: 2014/01/17 09:01:32 $$Author: bbarber $
+** $Id: //main/2011/qhull/src/libqhullpcpp/RboxPoints.h#2 $$Change: 1675 $
+** $DateTime: 2014/02/01 09:38:20 $$Author: bbarber $
 **
 ****************************************************************************/
 
 #ifndef RBOXPOINTS_H
 #define RBOXPOINTS_H
 
 #include "QhullPoint.h"
 #include "PointCoordinates.h"
 extern "C" {
 #include "libqhull/libqhull.h"
 }
 
 #include 
 #include 
 #include 
 #include 
 #include 
 #include 
 
 namespace orgQhull {
 
-#//Types
+#//!\name Types
     //! RboxPoints -- generate random PointCoordinates for Qhull
     class RboxPoints;
 
-    class RboxPoints : public PointCoordinates {
+class RboxPoints : public PointCoordinates {
 
 private:
-#//Fields and friends
+#//!\name Fields and friends
     int                 rbox_new_count;     //! Number of points for PointCoordinates
     int                 rbox_status;    //! error status from rboxpoints.  qh_ERRnone if none.
     std::string         rbox_message;   //! stderr from rboxpoints
 
     friend void ::qh_fprintf_rbox(FILE *fp, int msgcode, const char *fmt, ... );
 
 public:
-#//Construct
+#//!\name Construct
                         RboxPoints();
     explicit            RboxPoints(const char *rboxCommand);
                         RboxPoints(const RboxPoints &other);
                         RboxPoints &operator=(const RboxPoints &other);
-                       ~RboxPoints();
+                        ~RboxPoints();
 
 public:
-#//GetSet
+#//!\name GetSet
     void                clearRboxMessage();
     int                 newCount() const { return rbox_new_count; }
     std::string         rboxMessage() const;
     int                 rboxStatus() const;
     bool                hasRboxMessage() const;
     void                setNewCount(int pointCount) { QHULL_ASSERT(pointCount>=0); rbox_new_count= pointCount; }
 
-#//Modify
+#//!\name Modify
     void                appendPoints(const char* rboxCommand);
     using               PointCoordinates::appendPoints;
     void                reservePoints() { reserveCoordinates((count()+newCount())*dimension()); }
 };//class RboxPoints
 
 }//namespace orgQhull
 
 #endif // RBOXPOINTS_H
diff --git a/src/libqhullpcpp/RoadError.h b/src/libqhullpcpp/RoadError.h
index 1c91154..81ddef2 100644
--- a/src/libqhullpcpp/RoadError.h
+++ b/src/libqhullpcpp/RoadError.h
@@ -1,86 +1,86 @@
 /****************************************************************************
 **
 ** Copyright (c) 2008-2012 C.B. Barber. All rights reserved.
-** $Id: //main/2011/qhull/src/libqhullpcpp/RoadError.h#1 $$Change: 1652 $
-** $DateTime: 2014/01/17 09:01:32 $$Author: bbarber $
+** $Id: //main/2011/qhull/src/libqhullpcpp/RoadError.h#2 $$Change: 1675 $
+** $DateTime: 2014/02/01 09:38:20 $$Author: bbarber $
 **
 ****************************************************************************/
 
 #ifndef ROADERROR_H
 #define ROADERROR_H
 
 #include "RoadLogEvent.h"
 
 #include 
 #include 
 #include 
 #include 
 
 using std::endl;
 
 namespace orgQhull {
 
-#//Types
+#//!\name Types
     //! RoadError -- Report and log errors
     //!  See discussion in Saylan, G., "Practical C++ error handling in hybrid environments," Dr. Dobb's Journal, p. 50-55, March 2007.
     //!   He uses an auto_ptr to track a stringstream.  It constructs a string on the fly.  RoadError uses the copy constructor to transform RoadLogEvent into a string
     class RoadError;
 
 class RoadError : public std::exception {
 
 private:
-#//Fields
+#//!\name Fields
     int                 error_code;  //! Non-zero code (not logged), maybe returned as program status
     RoadLogEvent        log_event;   //! Format string w/ arguments
     mutable std::string error_message;  //! Formated error message.  Must be after log_event.
 
-#//Class fields
-    static const char  *  ROADtag;
+#//!\name Class fields
+    static const char * ROADtag;
     static std::ostringstream  global_log; //! May be replaced with any ostream object
 
 public:
-#//Constants
+#//!\name Constants
 
-#//Constructors
+#//!\name Constructors
     RoadError();
     RoadError(const RoadError &other);  //! Called on throw, generates error_message
     RoadError(int code, const std::string &message);
     RoadError(int code, const char *fmt);
     RoadError(int code, const char *fmt, int d);
     RoadError(int code, const char *fmt, int d, int d2);
     RoadError(int code, const char *fmt, int d, int d2, float f);
     RoadError(int code, const char *fmt, int d, int d2, float f, const char *s);
     RoadError(int code, const char *fmt, int d, int d2, float f, const void *x);
     RoadError(int code, const char *fmt, int d, int d2, float f, int i);
     RoadError(int code, const char *fmt, int d, int d2, float f, long long i);
     RoadError(int code, const char *fmt, int d, int d2, float f, double e);
 
-    RoadError          &operator=(const RoadError &other);
-                       ~RoadError() throw() {};
+    RoadError &         operator=(const RoadError &other);
+                        ~RoadError() throw() {};
 
-#//Class methods
+#//!\name Class methods
 
     static void         clearGlobalLog() { global_log.seekp(0); }
     static bool         emptyGlobalLog() { return global_log.tellp()<=0; }
     static const char  *stringGlobalLog() { return global_log.str().c_str(); }
 
-#//Virtual
+#//!\name Virtual
     virtual const char *what() const throw();
 
-#//GetSet
+#//!\name GetSet
     bool                isDefined() const { return log_event.isDefined(); }
     int                 errorCode() const { return error_code; };
    // FIXUP QH11021 should RoadError provide errorMessage().  Currently what()
     RoadLogEvent        roadLogEvent() const { return log_event; };
 
-#//Update
+#//!\name Update
     void                logError() const;
 };//class RoadError
 
 }//namespace orgQhull
 
-#//Global functions
+#//!\name Global
 
-inline std::ostream    &operator<<(std::ostream &os, const orgQhull::RoadError &e) { return os << e.what(); }
+inline std::ostream &   operator<<(std::ostream &os, const orgQhull::RoadError &e) { return os << e.what(); }
 
 #endif // ROADERROR_H
diff --git a/src/libqhullpcpp/RoadLogEvent.h b/src/libqhullpcpp/RoadLogEvent.h
index 2024a17..38b4657 100644
--- a/src/libqhullpcpp/RoadLogEvent.h
+++ b/src/libqhullpcpp/RoadLogEvent.h
@@ -1,77 +1,77 @@
 /****************************************************************************
 **
 ** Copyright (c) 2008-2012 C.B. Barber. All rights reserved.
-** $Id: //main/2011/qhull/src/libqhullpcpp/RoadLogEvent.h#1 $$Change: 1652 $
-** $DateTime: 2014/01/17 09:01:32 $$Author: bbarber $
+** $Id: //main/2011/qhull/src/libqhullpcpp/RoadLogEvent.h#2 $$Change: 1675 $
+** $DateTime: 2014/02/01 09:38:20 $$Author: bbarber $
 **
 ****************************************************************************/
 
 #ifndef ROADLOGEVENT_H
 #define ROADLOGEVENT_H
 
 #include 
 #include 
 #include 
 
 namespace orgQhull {
 
-#//Types
+#//!\name Types
     //! RoadLogEvent -- Record an event for the RoadLog
     struct RoadLogEvent;
 
 struct RoadLogEvent {
 
 public:
-#//Fields
-    const char     *format_string; //! Format string (a literal with format codes, for logging)
+#//!\name Fields
+    const char *    format_string; //! Format string (a literal with format codes, for logging)
     int             int_1;       //! Integer argument (%d, for logging)
     int             int_2;       //! Integer argument (%d, for logging)
     float           float_1;     //! Float argument (%f, for logging)
     union {                      //! One additional argument (for logging)
         const char *cstr_1;      //!   Cstr argument (%s) -- type checked at construct-time
         const void *void_1;      //!   Void* argument (%x) -- Use upper-case codes for object types
         long long   int64_1;     //!   signed int64 (%i).  Ambiguous if unsigned is also defined.
         double      double_1;    //!   Double argument (%e)
     };
 
-#//Constants
+#//!\name Constants
 
-#//Constructors
+#//!\name Constructors
     RoadLogEvent() : format_string(0), int_1(0), int_2(0), float_1(0), int64_1(0) {};
     explicit RoadLogEvent(const char *fmt) : format_string(fmt), int_1(0), int_2(0), float_1(0), int64_1(0) {};
     RoadLogEvent(const char *fmt, int d) : format_string(fmt), int_1(d), int_2(0), float_1(0), int64_1(0) {};
     RoadLogEvent(const char *fmt, int d, int d2) : format_string(fmt), int_1(d), int_2(d2), float_1(0), int64_1(0) {};
     RoadLogEvent(const char *fmt, int d, int d2, float f) : format_string(fmt), int_1(d), int_2(d2), float_1(f), int64_1(0) {};
     RoadLogEvent(const char *fmt, int d, int d2, float f, const char *s) : format_string(fmt), int_1(d), int_2(d2), float_1(f), cstr_1(s) {};
     RoadLogEvent(const char *fmt, int d, int d2, float f, const void *x) : format_string(fmt), int_1(d), int_2(d2), float_1(f), void_1(x) {};
     RoadLogEvent(const char *fmt, int d, int d2, float f, int i) : format_string(fmt), int_1(d), int_2(d2), float_1(f), int64_1(i) {};
     RoadLogEvent(const char *fmt, int d, int d2, float f, long long i) : format_string(fmt), int_1(d), int_2(d2), float_1(f), int64_1(i) {};
     RoadLogEvent(const char *fmt, int d, int d2, float f, double g) : format_string(fmt), int_1(d), int_2(d2), float_1(f), double_1(g) {};
     ~RoadLogEvent() {};
     //! Default copy constructor and assignment
 
-#//GetSet
+#//!\name GetSet
     bool                isDefined() const { return format_string!=0; }
     int                 int1() const { return int_1; };
     int                 int2() const { return int_2; };
     float               float1() const { return float_1; };
-    const char         *format() const { return format_string; };
-    const char         *cstr1() const { return cstr_1; };
-    const void         *void1() const { return void_1; };
+    const char *        format() const { return format_string; };
+    const char *        cstr1() const { return cstr_1; };
+    const void *        void1() const { return void_1; };
     long long           int64() const { return int64_1; };
     double              double1() const { return double_1; };
 
-#//Conversion
+#//!\name Conversion
 
     std::string        toString(const char* tag, int code) const;
 
 private:
-#//Class helpers
+#//!\name Class helpers
     static bool         firstExtraCode(std::ostream &os, char c, char *extraCode);
 
 
 };//class RoadLogEvent
 
 }//namespace orgQhull
 
 #endif // ROADLOGEVENT_H
diff --git a/src/libqhullpcpp/UsingLibQhull.cpp b/src/libqhullpcpp/UsingLibQhull.cpp
index 9ee3156..f99b15f 100644
--- a/src/libqhullpcpp/UsingLibQhull.cpp
+++ b/src/libqhullpcpp/UsingLibQhull.cpp
@@ -1,373 +1,375 @@
 /****************************************************************************
 **
 ** Copyright (c) 2008-2014 C.B. Barber. All rights reserved.
-** $Id: //main/2011/qhull/src/libqhullpcpp/UsingLibQhull.cpp#1 $$Change: 1652 $
-** $DateTime: 2014/01/17 09:01:32 $$Author: bbarber $
+** $Id: //main/2011/qhull/src/libqhullpcpp/UsingLibQhull.cpp#2 $$Change: 1711 $
+** $DateTime: 2014/03/30 12:48:17 $$Author: bbarber $
 **
 ****************************************************************************/
 
 #//! UsingLibQhull -- Set up qhull C code from C++
 
 #include "Qhull.h"
 #include "UsingLibQhull.h"
 #include "QhullError.h"
 #include "QhullQh.h"
 
 #ifdef _MSC_VER  // Microsoft Visual C++ -- warning level 4
 #endif
 
 namespace orgQhull {
 
 #//Class objects
 
 const double UsingLibQhull::
 DEFAULTdistanceEpsilon= 1e-15*FACTORepsilon; //! ~DISTround*FACTORepsilon for unit cube
 
 const double UsingLibQhull::
 DEFAULTangleEpsilon= 1e-15*FACTORepsilon; //! ~ANGLEround*FACTORepsilon for unit cube
 
     //! Global pointer to Qhull for qh_fprintf callback and QhullError
 Qhull *
 s_qhull_output= 0;
 
 double UsingLibQhull::
 s_angle_epsilon= 0;
 
 double UsingLibQhull::
 s_distance_epsilon= 0;
 
 //! For QhullPoint.id() w/o qhRunId.  Initialized by Qhull
 const coordT *UsingLibQhull::
 s_points_begin= 0;
 const coordT *UsingLibQhull::
 s_points_end= 0;
 int UsingLibQhull::
 s_points_dimension= 0;
 
 int UsingLibQhull::
 s_vertex_dimension= 0;  // FIXUP QH11023: s_vertex_dimension is required if dimension>15.  Cannot store in QhullVertex
 
 bool UsingLibQhull::
 s_has_points= false;
 
 bool UsingLibQhull::
 s_has_angle_epsilon= false;
 
 bool UsingLibQhull::
 s_has_vertex_dimension= false;
 
 bool UsingLibQhull::
 s_has_distance_epsilon= false;
 
 bool UsingLibQhull::
 s_using_libqhull= false;
 
 #//Constructors
 
 //! Grabs global state (qh_qh, qh_qhstat, qhmem.tempstack)
 //! Follow immediately with setjmp(qh errexit), otherwise errors in libqhull are not caught properly
 //! See qh_restore_qhull [global.c]
 UsingLibQhull::
 UsingLibQhull(Qhull *q)
 : my_qhull(q)
 , qh_exitcode(0)
 {
     checkUsingLibQhull();
     QhullQh *qhullqh= q->qhullQh();
     if(!qhullqh){
         throw QhullError(10014, "Qhull internal error: Qhull.qhullQh() not defined. initializeQhull() not called.");
     }
     if(qhullqh->run_id != q->qhull_run_id){
         throw QhullError(10015, "Qhull error: QhullQh.runId %d != Qhull.runId %d.  Overwritten?", qhullqh->run_id, q->qhull_run_id);
     }
     // qh.old_qhstat is zero at initialization
     // qh.old_tempstack is zero when empty
     // QhullQh() and UsingLibQhull() are the same
 #if qh_QHpointer
     if(qh_qh){
         qh old_qhstat= qh_qhstat;
         qh old_tempstack= qhmem.tempstack;
     }
     qh_qh= qhullqh;
     qh_qhstat= qhullqh->old_qhstat;
     qhmem.tempstack= qhullqh->old_tempstack;
     qhullqh->old_qhstat= 0;
     qhullqh->old_tempstack= 0;
 #else
     #error FIXUP QH11024 static qh_qh not tested.  Delete the line to try.
     if(qhullqh!=&qh_qh){
         throw QhullError(10040, "Qhull internal error: Qhull.qhullQh() is not qh_qh (%x, static).  Overwrite?", 0,0,0.0, &qh_qh);
     }
 #endif
     s_qhull_output= q;      // set s_qhull_output for qh_fprintf()
     qh NOerrexit= False;   // assumes setjmp called next
 }//UsingLibQhull qhull
 
 //! Same as UsingLibQhull but does not throw exceptions
 //! !defined() on failure.  For use in destructors
 UsingLibQhull::
 UsingLibQhull(Qhull *q, int noThrow)
 : my_qhull(0)  // Fail by default
 , qh_exitcode(0)
 {
     QHULL_UNUSED(noThrow);
 
     QhullQh *qhullqh= q->qhullQh();
     if(s_using_libqhull){
         QhullError e(10050, "Qhull error: UsingLibQhull already in use");
         e.logError();
     }else if(!qhullqh || qhullqh->run_id != q->qhull_run_id){
         QhullError e(10051, "Qhull error: Qhull.qhullQh (%x) undefined or QhullQh.runId %d != Qhull.runId %d.  Overwritten?", (qhullqh ? qhullqh->run_id : -1), q->qhull_run_id, 0.0, qhullqh);
         e.logError();
     }else{
         // qh.old_qhstat is zero at initialization
         // qh.old_tempstack is zero when empty
         // QhullQh() and UsingLibQhull() are the same
 #if qh_QHpointer
         if(qh_qh){
             qh old_qhstat= qh_qhstat;
             qh old_tempstack= qhmem.tempstack;
         }
         qh_qh= qhullqh;
         qh_qhstat= qhullqh->old_qhstat;
         qhmem.tempstack= qhullqh->old_tempstack;
         qhullqh->old_qhstat= 0;
         qhullqh->old_tempstack= 0;
 #endif
         my_qhull= q;
         s_qhull_output= q;          // set s_qhull_output for qh_fprintf()
         qh NOerrexit= False;   // assumes setjmp called next
     }
 }//UsingLibQhull qhull noThrow
 
 //! Reuses current global state (qh_qh) from prior UsingQhull
 //! Errors if runId is not the same
 UsingLibQhull::
 UsingLibQhull(int qhRunId)
 : my_qhull(0)
 , qh_exitcode(0)
 {
     checkUsingLibQhull();
 #if qh_QHpointer
     if(!qh_qh || !qh_qhstat){
         throw QhullError(10024, "Qhull error: UsingLibQhull is not active (qh_qh %x or qh_qhstat is not defined)", 0,0,0.0, qh_qh);
     }
 #endif
     if(qh run_id!=qhRunId){
         throw QhullError(10036, "Qhull error: qhRunId %d != qh_qh.runId %d.  Is another Qhull active?", qhRunId, qh run_id);
     }
     if(!s_qhull_output){
         throw QhullError(10037, "Qhull error: UsingLibQhull not active(s_qhull_output undefined).  Invoke UsingLibQhull before this call");
     }
     if(s_qhull_output->qhull_run_id!=qhRunId){
         throw QhullError(10046, "Qhull error: qhRunId %d != s_qhull_output.runId %d.  Is another Qhull active", qhRunId, s_qhull_output->qhull_run_id);
     }
     my_qhull= s_qhull_output;
     qh NOerrexit= False;   // assumes setjmp called next
 }//UsingLibQhull runId
 
 //Leaves libqhull active for runId access
 UsingLibQhull::
 ~UsingLibQhull()
 {
     QhullError e= checkRunId();
     if(e.isDefined()){
         e.logError();
     }else{
 #if qh_QHpointer
         if(qh_qh){
             qh NOerrexit= true;
         }
 #else
         qh NOerrexit= true;
 #endif
     }
     s_using_libqhull= false;
 }//~UsingLibQhull
 
 #//Class methods
 
 void UsingLibQhull::
 checkQhullMemoryEmpty()
 {
     int curlong, totlong, curshort, totshort, maxlong, totbuffer;
     // qh_memtotal does not error
     qh_memtotal(&curlong, &totlong, &curshort, &totshort, &maxlong, &totbuffer);
     if (curlong || totlong){
         throw QhullError(10026, "Qhull error: qhull did not free %d bytes of long memory (%d pieces).", totlong, curlong);
     }
     if (curshort || totshort){
         throw QhullError(10035, "Qhull error: qhull did not free %d bytes of short memory (%d pieces).", totshort, curshort);
     }
 }//checkQhullMemoryEmpty
 
+//! Epsilon for distance to hyperplane angle equality
 double UsingLibQhull::
 currentAngleEpsilon()
 {
     if(s_qhull_output && s_qhull_output->initialized()){
         return s_qhull_output->qhullQh()->ANGLEround*FACTORepsilon;
     }else if(s_has_angle_epsilon){
         return s_angle_epsilon;
     }
     return UsingLibQhull::DEFAULTangleEpsilon;
 }//currentAngleEpsilon
 
+//! Epsilon for distance to hyperplane
 double UsingLibQhull::
 currentDistanceEpsilon()
 {
     if(s_qhull_output && s_qhull_output->initialized()){
         return s_qhull_output->qhullQh()->DISTround*FACTORepsilon;
     }else if(s_has_distance_epsilon){
         return s_distance_epsilon;
     }
     return UsingLibQhull::DEFAULTdistanceEpsilon;
 }//currentDistanceEpsilon
 
 const coordT *UsingLibQhull::
 currentPoints(int *dimension, const coordT **pointsEnd)
 {
     if(s_qhull_output && s_qhull_output->initialized()){
         *dimension= qh hull_dim;
         *pointsEnd= qh first_point+qh num_points*qh hull_dim;
         return qh first_point;
     }else if(s_has_points){
         *dimension= s_points_dimension;
         *pointsEnd= s_points_end;
         return s_points_begin;
     }
     throw QhullError(10059, "Qhull error: missing definition for currentPoints().  Need currentQhull() or setGlobalDistanceEpsilon()");
 }//currentPoints
 
 Qhull &UsingLibQhull::
 currentQhull()
 {
     if(!s_qhull_output){
         throw QhullError(10055, "Qhull error: currentQhull not defined.  Run qhull first.");
     }
     return *s_qhull_output;
 }//currentQhull
 
 // for QhullVertex::dimension() when >= 16
 int UsingLibQhull::
 currentVertexDimension()
 {
     if(s_qhull_output && s_qhull_output->initialized()){
         return s_qhull_output->dimension();
     }else if(s_has_vertex_dimension){
         return s_vertex_dimension;
     }
     throw QhullError(10057, "Qhull error: missing definition for currentVertexDimension().  Need currentQhull() or setGlobalVertexDimension()");
 }//currentVertexDimension
 
 const coordT *UsingLibQhull::
 globalPoints(int *dimension, const coordT **pointsEnd)
 {
     if(s_has_points){
         *dimension= s_points_dimension;
         *pointsEnd= s_points_end;
         return s_points_begin;
     }else{
         return currentPoints(dimension, pointsEnd);
     }
 }//globalPoints
 
 bool UsingLibQhull::
 hasPoints()
 {
     return s_has_points || (s_qhull_output && s_qhull_output->initialized());
 }
 
 bool UsingLibQhull::
 hasVertexDimension()
 {
     return s_has_vertex_dimension || (s_qhull_output && s_qhull_output->initialized());
 }
 
 void UsingLibQhull::
 setGlobals()
 {
     if(s_qhull_output && s_qhull_output->initialized()){
         QhullQh *qqh= s_qhull_output->qhullQh();
         s_angle_epsilon= qqh->ANGLEround*FACTORepsilon;
         s_distance_epsilon= qqh->DISTround*FACTORepsilon;
         s_points_begin= qqh->first_point;
         s_points_dimension= qqh->hull_dim;
         s_points_end= s_points_begin+qqh->num_points*s_points_dimension;
         s_vertex_dimension= qqh->hull_dim;
         s_has_angle_epsilon= true;
         s_has_distance_epsilon= true;
         s_has_points= true;
         s_has_vertex_dimension= true;
     }else{
         throw QhullError(10058, "Qhull error: setGlobals can only be called for currentQhull().  Run qhull first.");
     }
  }//setGlobals
 
 void UsingLibQhull::
 unsetGlobals()
 {
     s_has_angle_epsilon= false;
     s_has_distance_epsilon= false;
     s_has_points= false;
     s_has_vertex_dimension= false;
 }//unsetGlobals
 
 #// Methods
 
 void UsingLibQhull::
 maybeThrowQhullMessage(int exitCode) const
 {
     my_qhull->maybeThrowQhullMessage(exitCode);
     QhullError e= checkRunId(); // Check for qhRunId after libqhull returns. For convenience, ought to be at end of libqhull try block
     if(e.isDefined()){
         throw e;
     }
 }//maybeThrowQhullMessage
 
 void UsingLibQhull::
 maybeThrowQhullMessage(int exitCode, int noThrow) const
 {
     my_qhull->maybeThrowQhullMessage(exitCode, noThrow);
     QhullError e= checkRunId(); // Check for qhRunId after libqhull returns. For convenience, ought to be at end of libqhull try block
     if(e.isDefined()){
         e.logError();
     }
 }//maybeThrowQhullMessage
 
 #//Helpers
 
 //! Return QhullError for maybeThrowFromDestructor()
 QhullError UsingLibQhull::
 checkRunId() const
 {
     // Predeclaring QhullError results in four copy constructors, none used here
 #if qh_QHpointer
     if(qh_qh){ // 0 if ~Qhull
         if(my_qhull->qhull_run_id!=qh run_id){
             return QhullError(10047, "Qhull internal error: Global state (qh_qh, run_id %d) changed.  Should be runId %d.  Another thread?", qh run_id, my_qhull->qhull_run_id);
         }
     }
 #else
     if(qh run_id!=0 && my_qhull->qhull_run_id!=qh run_id){
         return QhullError(10048, "Qhull internal error: Global state (qh_qh, run_id %d) changed.  Should be runId %d.  Another thread?", qh run_id, my_qhull->qhull_run_id);
     }
 #endif
     return QhullError();
 }//checkRunId
 
 //! Can not embed UsingLibQhull.  Otherwise allocated a C++ object missed by qh_errexit
 void UsingLibQhull::
 checkUsingLibQhull() const
 {
     if(s_using_libqhull){
         if(s_qhull_output){
             throw QhullError(10049, "Qhull error: UsingLibQhull already in use by QhullQh.runId %d", s_qhull_output->qhull_run_id);
         }else{
             throw QhullError(10050, "Qhull error: UsingLibQhull already in use.  No s_qhull_output");
         }
     }
     s_using_libqhull= true;
 }//checkUsingLibQhull
 
 }//namespace orgQhull
 
diff --git a/src/libqhullpcpp/UsingLibQhull.h b/src/libqhullpcpp/UsingLibQhull.h
index 7b094d8..cc91995 100644
--- a/src/libqhullpcpp/UsingLibQhull.h
+++ b/src/libqhullpcpp/UsingLibQhull.h
@@ -1,144 +1,144 @@
 /****************************************************************************
 **
 ** Copyright (c) 2008-2012 C.B. Barber. All rights reserved.
-** $Id: //main/2011/qhull/src/libqhullpcpp/UsingLibQhull.h#1 $$Change: 1652 $
-** $DateTime: 2014/01/17 09:01:32 $$Author: bbarber $
+** $Id: //main/2011/qhull/src/libqhullpcpp/UsingLibQhull.h#2 $$Change: 1675 $
+** $DateTime: 2014/02/01 09:38:20 $$Author: bbarber $
 **
 ****************************************************************************/
 
 #ifndef USINGlibqhull_H
 #define USINGlibqhull_H
 
 #include "QhullError.h"
 extern "C" {
 #include "libqhull/libqhull.h"
 }
 
 namespace orgQhull {
 
-#//Types
+#//!\name Types
     //! UsingLibQhull -- Interface into libqhull and its 'qh' and 'qhstat' macros
     //! Always use with setjmp() for libqhull error handling.
 
 /*******************************
 
 UsingLibQhull is stack based, but as a call
 Qhull declarations are stack-based.  But can't define a
 setjmp environment, since the target goes away.  So must be UsingLibQhull, but can only have one
 setjmp at a time? Can embedded another Using as long as save/restore
 longjmp on exit.
 */
     class UsingLibQhull;
 
     // Defined elsewhere
     class Qhull;
 
-#// Global variables
-extern Qhull           *s_qhull_output; //! Provide qh_fprintf (Qhull.cpp) access to Qhull
+#//!\name  Global variables
+extern Qhull *          s_qhull_output; //! Provide qh_fprintf (Qhull.cpp) access to Qhull
 
 class UsingLibQhull {
 
 private:
-#//Fields
-    Qhull              *my_qhull;
+#//!\name Fields
+    Qhull *             my_qhull;
     int                 qh_exitcode;
 
-#//Class globals
+#//!\name Class globals
     //! Global flags
     static bool         s_using_libqhull; //! True if UsingLibQhull is in scope
 
     //! Use global values if s_has_... is set
     static bool         s_has_angle_epsilon; //! True if s_angle_epsilon defined
     static bool         s_has_distance_epsilon; //! True if s_distance_epsilon defined
     static bool         s_has_points;        //! If False (default), Qhull() runs setPointBase()
     static bool         s_has_vertex_dimension; //! True if s_vertex_dimension defined
 
     //! Global values
     static double       s_angle_epsilon;   //! Epsilon for angle equality
     static double       s_distance_epsilon;   //! Epsilon for distance equality
     static const coordT *s_points_begin;            //! For QhullPoint::id() w/o qhRunId.
     static const coordT *s_points_end;            //! For QhullPoint::id() w/o qhRunId.
     static int          s_points_dimension;
     static int          s_vertex_dimension; //! Default dimension (e.g., if Vertex::dimension() >= 16)
 
 public:
-#//Class constants
+#//!\name Class constants
     static const int    NOqhRunId= 0;   //! qh_qh is not available
     static const int    NOthrow= 1;     //! Do not throw from maybeThrowQhullMessage
     static const int    FACTORepsilon= 10;  //!
     static const double DEFAULTdistanceEpsilon; //! ~DISTround*FACTORepsilon for unit cube
     static const double DEFAULTangleEpsilon;    //! ~ANGLEround*FACTORepsilon for unit cube
 
-#//Class members
+#//!\name Class members
     static void         checkQhullMemoryEmpty();
     static double       currentAngleEpsilon();
     static double       currentDistanceEpsilon();
     static const coordT *currentPoints(int *dimension, const coordT **pointsEnd);
-    static Qhull       ¤tQhull();
+    static Qhull &      currentQhull();
     static int          currentVertexDimension();
     static double       globalAngleEpsilon() { return s_has_angle_epsilon ? s_angle_epsilon : currentAngleEpsilon(); }
     static double       globalDistanceEpsilon() { return s_has_distance_epsilon ? s_distance_epsilon : currentDistanceEpsilon(); }
     static double       globalMachineEpsilon() { return REALepsilon; }
     static const coordT *globalPoints(int *dimension, const coordT **pointsEnd);
     static int          globalVertexDimension() { return s_has_vertex_dimension ? s_vertex_dimension : currentVertexDimension(); }
     static bool         hasPoints();        // inline would require Qhull.h
     static bool         hasVertexDimension();
     static void         setGlobalAngleEpsilon(double d) { s_angle_epsilon=d; s_has_angle_epsilon= true; }
     static void         setGlobalDistanceEpsilon(double d) { s_distance_epsilon= d; s_has_distance_epsilon= true; }
     static void         setGlobalPoints(int dimension, const coordT *pointsBegin, const coordT *pointsEnd) { s_points_dimension= dimension; s_points_begin= pointsBegin; s_points_end= pointsEnd; s_has_points= true; }
     static void         setGlobalVertexDimension(int i) { s_vertex_dimension= i; s_has_vertex_dimension= true; }
     static void         setGlobals();
     static void         unsetGlobalAngleEpsilon() { s_has_angle_epsilon= false; }
     static void         unsetGlobalDistanceEpsilon() { s_has_distance_epsilon= false; }
     static void         unsetGlobalPoints() { s_has_points= false; }
     static void         unsetGlobalVertexDimension() { s_has_vertex_dimension= false; }
     static void         unsetGlobals();
 
-#//Constructors
+#//!\name Constructors
                         UsingLibQhull(Qhull *p);
                         UsingLibQhull(Qhull *p, int noThrow);
                         UsingLibQhull(int qhRunId);
-                       ~UsingLibQhull();
+                        ~UsingLibQhull();
 
 private:                //! disable default constructor, copy constructor, and copy assignment
                         UsingLibQhull();
                         UsingLibQhull(const UsingLibQhull &);
-   UsingLibQhull       &operator=(const UsingLibQhull &);
+   UsingLibQhull &     operator=(const UsingLibQhull &);
 public:
 
-#//Methods
-#//Access
+#//!\name Methods
+#//!\name Access
     bool                defined() const { return my_qhull!=0; }
     void                maybeThrowQhullMessage(int exitCode) const;
     void                maybeThrowQhullMessage(int exitCode, int noThrow) const;
 
-#//Helpers
+#//!\name Helpers
 private:
    QhullError           checkRunId() const;
    void                 checkUsingLibQhull() const;
 
 /***********************************
 You may use global variables in 'qh' after declaring UsingLibQhull.  For example
 
   UsingLibQhull q(qhRunId);
   // NOerrors -- no calls that throw libqhull errors
   cout << "Delaunay Mode: " << qh DELAUNAY;
 
 To trap errors from libqhull, UsingLibQhull must be followed by
 
 UsingLibQhull q(qhRunId);
 int exitCode = setjmp(qh errexit);
 if(!exitCode){ // no object creation -- destructors skipped on longjmp()
     calls to libqhull
 }
 q.maybeThrowQhullMessage(exitCode);
 
 The call to setjmp() can not be moved to a method.  The stack must be preserved for error exits from libqhull.
 
 */
 
 };//UsingLibQhull
 
 }//namespace orgQhull
 
 #endif // USINGlibqhull_H
diff --git a/src/libqhullpcpp/functionObjects.h b/src/libqhullpcpp/functionObjects.h
index 94c8d7a..732a32b 100644
--- a/src/libqhullpcpp/functionObjects.h
+++ b/src/libqhullpcpp/functionObjects.h
@@ -1,66 +1,66 @@
 /****************************************************************************
 **
 ** Copyright (c) 2008-2012 C.B. Barber. All rights reserved.
-** $Id: //main/2011/qhull/src/libqhullpcpp/functionObjects.h#1 $$Change: 1652 $
-** $DateTime: 2014/01/17 09:01:32 $$Author: bbarber $
+** $Id: //main/2011/qhull/src/libqhullpcpp/functionObjects.h#2 $$Change: 1675 $
+** $DateTime: 2014/02/01 09:38:20 $$Author: bbarber $
 **
 ****************************************************************************/
 
 #ifndef QHFUNCTIONOBJECTS_H
 #define QHFUNCTIONOBJECTS_H
 
 #include 
 #include 
 
 namespace orgQhull {
-#//Type
+#//!\name Type
 
     //! Sum of absolute values of the elements in a container
     class AbsoluteSumOf;
     //! Sum of the elements in a container
     class SumOf;
     //! Sum of squares of the elements in a container
     class SumSquaresOf;
 
-#//Class
+#//!\name Class
 
 //! Absolute sum of the elements in a container
 class AbsoluteSumOf
 {
 private:
     double sum;
 public:
     inline AbsoluteSumOf() : sum(0.0) {}
     inline void operator()(double v) { sum += fabs(v); }
     inline operator double() { return sum; }
 };//AbsoluteSumOf
 
 //! Sum of the elements in a container
 class SumOf
 {
 private:
     double sum;
 public:
     inline SumOf() : sum(0.0) {}
     inline void operator()(double v) { sum += v; }
     inline operator double() { return sum; }
 };//SumOf
 
 
 //! Sum of squares of the elements in a container
 class SumSquaresOf
 {
 private:
     double sum;
 public:
     inline SumSquaresOf() : sum(0.0) {}
     inline void operator()(double v) { sum += v*v; }
     inline operator double() { return sum; }
 };//SumSquaresOf
 
 
 }//orgQhull
 
 
 #endif //QHFUNCTIONOBJECTS_H
 
diff --git a/src/libqhullpcpp/libqhullpcpp.pro b/src/libqhullpcpp/libqhullpcpp.pro
index cf07f5a..ad64c0e 100644
--- a/src/libqhullpcpp/libqhullpcpp.pro
+++ b/src/libqhullpcpp/libqhullpcpp.pro
@@ -1,71 +1,72 @@
 # -------------------------------------------------
 # libqhullpcpp.pro -- Qt project for Qhull cpp shared library based on libqhullp
 # -------------------------------------------------
 
 include(../qhull-warn.pri)
 
 DESTDIR = ../../lib
 TEMPLATE = lib
 CONFIG += staticlib warn_on
 CONFIG -= qt rtti
 build_pass:CONFIG(debug, debug|release):{
    TARGET = qhullcpp_pd
    OBJECTS_DIR = Debug
 }else:build_pass:CONFIG(release, debug|release):{
    TARGET = qhullcpp_p
    OBJECTS_DIR = Release
 }
 MOC_DIR = moc
 
 DEFINES += qh_QHpointer # libqhull/user.h
 
 INCLUDEPATH += ../../src
 INCLUDEPATH += $$PWD # for MOC_DIR
 
 CONFIG += qhull_warn_shadow qhull_warn_conversion
 
 SOURCES += ../libqhullpcpp/Coordinates.cpp
 SOURCES += ../libqhullpcpp/PointCoordinates.cpp
 SOURCES += ../libqhullpcpp/Qhull.cpp
 SOURCES += ../libqhullpcpp/QhullFacet.cpp
 SOURCES += ../libqhullpcpp/QhullFacetList.cpp
 SOURCES += ../libqhullpcpp/QhullFacetSet.cpp
 SOURCES += ../libqhullpcpp/QhullHyperplane.cpp
 SOURCES += ../libqhullpcpp/QhullPoint.cpp
 SOURCES += ../libqhullpcpp/QhullPoints.cpp
 SOURCES += ../libqhullpcpp/QhullPointSet.cpp
 SOURCES += ../libqhullpcpp/QhullQh.cpp
 SOURCES += ../libqhullpcpp/QhullRidge.cpp
 SOURCES += ../libqhullpcpp/QhullSet.cpp
 SOURCES += ../libqhullpcpp/QhullStat.cpp
 SOURCES += ../libqhullpcpp/QhullVertex.cpp
 SOURCES += ../libqhullpcpp/QhullVertexSet.cpp
 SOURCES += ../libqhullpcpp/RboxPoints.cpp
 SOURCES += ../libqhullpcpp/RoadError.cpp
 SOURCES += ../libqhullpcpp/RoadLogEvent.cpp
 SOURCES += ../libqhullpcpp/UsingLibQhull.cpp
 
 HEADERS += ../libqhullpcpp/Coordinates.h
 HEADERS += ../libqhullpcpp/functionObjects.h
 HEADERS += ../libqhullpcpp/PointCoordinates.h
 HEADERS += ../libqhullpcpp/Qhull.h
 HEADERS += ../libqhullpcpp/QhullError.h
 HEADERS += ../libqhullpcpp/QhullFacet.h
 HEADERS += ../libqhullpcpp/QhullFacetList.h
 HEADERS += ../libqhullpcpp/QhullFacetSet.h
 HEADERS += ../libqhullpcpp/QhullHyperplane.h
 HEADERS += ../libqhullpcpp/QhullIterator.h
 HEADERS += ../libqhullpcpp/QhullLinkedList.h
 HEADERS += ../libqhullpcpp/QhullPoint.h
 HEADERS += ../libqhullpcpp/QhullPoints.h
 HEADERS += ../libqhullpcpp/QhullPointSet.h
 HEADERS += ../libqhullpcpp/QhullQh.h
 HEADERS += ../libqhullpcpp/QhullRidge.h
 HEADERS += ../libqhullpcpp/QhullSet.h
 HEADERS += ../libqhullpcpp/QhullSets.h
 HEADERS += ../libqhullpcpp/QhullStat.h
 HEADERS += ../libqhullpcpp/QhullVertex.h
+HEADERS += ../libqhullpcpp/QhullVertexSet.h
 HEADERS += ../libqhullpcpp/RboxPoints.h
 HEADERS += ../libqhullpcpp/RoadError.h
 HEADERS += ../libqhullpcpp/RoadLogEvent.h
 HEADERS += ../libqhullpcpp/UsingLibQhull.h
diff --git a/src/libqhullr/README_r.txt b/src/libqhullr/README_r.txt
index b805949..4c0a7b6 100644
--- a/src/libqhullr/README_r.txt
+++ b/src/libqhullr/README_r.txt
@@ -1,273 +1,311 @@
 Converting libqhull to libqhullr
 
 ==========================
 Todo 
 
 After qmake, need to update HEADER paths for libqhull, libqhullr, libqhullcpp libqhullpcpp
     Path="..\lib
     Path="..\..\src\lib
 
-Remove user_eg7,8,9
-
-Rename qhull_ra.h to qhull_ar.h
-
+countT everywhere, problem of strings
+
+Questions
+    Can construct pointSets, add a mid() function?
+    Does C++ auto create default iterator if another constructor already exists?
+    Change other to o?
+    
+OK
+    QhullQh
+    Coordinates
+    QhullPoint!
+    
+    
+
+create countT for int64 IDs
+change vertexId for 'int'
+
+Get rid of static
+    user.c qh_new_qhull
+    static boolT firstcall = True;
+
+    UsingLibQhull
+    lots
+
+    QhullQh
+    static boolT firstcall = True;
+    
 
 ---
 Convert qhulltest.cpp to libqhullcpp and branch old code
 At initialization, check for compatible libqhull.  Add a version check to libqhull
 
 Convert testqset.c to testqset_r.c
    Try to make qhT and mem_r.c etc. plugable
 Convert user_eg to qhull_r.dll
 Convert user_eg2 to libqhullstatic_r.a
 Convert user_eg3 to libqhullcpp
 Rework user_eg7.cpp,etc for new names, add to README
 
 
 ---
 3>..\..\src\qhullr\unix_r.c(39) : warning C4273: '_isatty' : inconsistent dll linkage
 3>        C:\Program Files\Microsoft Visual Studio 8\VC\INCLUDE\io.h(209) : see previous definition of '_isatty'
 
 ---
 Redo usage note for qhullr.cpp
 
 ---
 /*** uncomment here and qhull_a.h
      if string.h does not define memcpy()
 #include 
 */
 
 ---
 Run through valgrind
 
 ---
 Fix or "sample code" in user_r.h
 
 and in user_r.c
   qh_call_qhull(qh, void )
     template for calling qhull from inside your program
 
 --
 Try with and without qh_NOmem
 
 --
 Update 
   README.txt -- the new subprojects
   CMakeLists.txt
   
 ==============
 Steps to update C code to reentrant qhull (e.g., testqset_r.c, user_eg*.c)
 
 Branch the code to ..._r.c
 
 Rename include files
 #include "qhull_ar.h"
 
 Allocate qh at the top, and remove other references to qh_qh and qh_qhPOINTER
   qhT qh_qh;
   qhT *qh= &qh_qh;
 
 If needed, remove spaces between name and argument list
   {[^a-zA-Z0-9_][a-zA-Z0-9_]*} \(
   \1(
   
 Make the following regexp substitions [DevStudio use {} for grouping instead of ()]
 
   Prefix function declarations with "(qhT *qh, "
   ^{[a-zA-Z0-9]* [a-zA-Z0-9]*\}(
   \1(qhT *qh, 
 
   'qh' is the first argument for most internal calls and qhull calls
   \({[a-zA-Z0-9_]*, }
   (qh, \1
   
   \({[a-zA-Z0-9_]+}\)
   (qh, \1)
   
   \(\)
   (qh)
 
   'qh '
   'qh->'
   
 Other substitions to consider
 
   ("
   (qh, "
   
   (&
   (qh, &
   
   ()
   (qh)
 
 Review the code for obvious errors
 Remove qhT for functions that do not need it
 
 Make the following substitions to correct mistakes made above
   qh, qh,
   qh, 
 
   qh, void
   qh
 Review the code for routines that do not take qh
 
 Compile and fix the errors
 
 ==============
 Steps
 
 Build qhullr.sln from qhull_all.sln
   Shadow build isn't working for header files. libbqhull and libqhullr
    RelativePath="..\..\src\libqhull\
   Doesn't create qhullstatic_rd.lib
   Inconsistent dll linkage for _isatty
   
   include only libqhullstaticr and qhullr
   remove libqhull, libqhullp, libqhullr to avoid double searches
   remove all but testqset from testqset
   
 Replace all include files with _r.h
 
 [qhull_all] Remove all spaces before the parens 'qh_... (...)' 
 [qhull_all] Change copyright to 2014
 
 Checked in source
 
 Check for access to .c and .h files
 
 Add qhmemT *qh before all routines
    # Routines with arguments, 3648+498 occurrences
    {qh_[a-zA-Z0-9_]*[^_]\(}{[^)/]}
    \1qhmemT *qh, \2
 
    # Routines with comment args, 15+ occurrences
    {qh_[a-zA-Z0-9_]*[^_]\(}{[/]}
    \1qhmemT *qh \2
    
 Exceptions 104+55 instances
   qhmemT *qh, void
   qhmemT *qh
 
   # times
   SETtruncate_(qhmemT *qh, 
   _(
   
   qhmemT *qh, qhmemT *qh,
   qhmemT *qh,
 
   qhmemT *qh, qhmemT *qh
   qhmemT *qh
 
 In C code
   ^{  *qh_.*}qhmemT *qh
   \1qh
 
   # 602 occurrences, needs repeat  
   ^{ .*}qhmemT *qh
   \1qh
  
   # 3746 occurrences
   {[^a-z]}qh {[a-zA-Z]}
   \1qh->\2
 
 All files, 891 occurrences
   qhmemT \*qh{[^a-zA-Z]}
   qhT *qh\1
 
   qhT *qh *
   qhT *qh, void *
   
   qhmem.
   qh->qhmem.
   
   # 99 occurrences
   qhstat 
   qh->qhstat.
   
 Removed rboxT from rboxlib_r.c
 
 1138 errors and 438 warnings.
 
 Remove dependency on libqhull_r for statT
 Convert FOREACHsetelement_i_ in libqhull_r.h 
 traceN needs qh for qh_fprintf
 add qh to () calls
 
 Down to 600 errors
 
 Thurs at 7:18p after fixing all of the compile errors and removing qh_qhPOINTER
 
 # Debug version of qhullr
  59 files changed, 8849 insertions(+), 8900 deletions(-)
 
 ISPY-/local/qhull/bin> rbox 100000 t100 s | qhullr
 
 Convex hull of 100000 points in 3-d:
 
   Number of vertices: 100000
   Number of facets: 199996
 
 Statistics for: rbox 100000 t100 s | qhullr
 
   Number of points processed: 100000
   Number of hyperplanes created: 565761
   Number of distance tests for qhull: 4376829
   CPU seconds to compute hull (after input): 1.688
 
 # Release version 2012.1
 
 ISPY-/local/qhull/bin> rbox 100000 t100 s | qhull
 
 Convex hull of 100000 points in 3-d:
 
   Number of vertices: 100000
   Number of facets: 199996
 
 Statistics for: rbox 100000 t100 s | qhull
 
   Number of points processed: 100000
   Number of hyperplanes created: 565761
   Number of distance tests for qhull: 4376829
   CPU seconds to compute hull (after input):  1
 
 # Release version of rboxr and qhullr
 
 ISPY-/local/qhull/bin> rboxr 100000 t100 s | qhullr
 
 Convex hull of 100000 points in 3-d:
 
   Number of vertices: 100000
   Number of facets: 199996
 
 Statistics for: rboxr 100000 t100 s | qhullr
 
   Number of points processed: 100000
   Number of hyperplanes created: 565761
   Number of distance tests for qhull: 4376829
   CPU seconds to compute hull (after input):  1
 
 -----
 Reorganized projects for cpp. 
 
 Fixed up qhull_p-exports.def.  qhull_r-exports.def has no DATA records.
 
 user_eg3 with libqhullpcpp worked correctly the first time
 
 IISPY-/local/qhull/bin>   user_eg3 rbox "100000 t100 s"  qhull
 rbox 100000 t100 s
 
 Results of qhull
 
 Convex hull of 100000 points in 3-d:
 
   Number of vertices: 100000
   Number of facets: 199996
 
 Statistics for: rbox "100000 t100 s" | qhull
 
   Number of points processed: 100000
   Number of hyperplanes created: 565761
   Number of distance tests for qhull: 4376829
   CPU seconds to compute hull (after input): 1.672
-  
\ No newline at end of file
+
+---------------------
+Fix cpp formating with */& associated with type and ~ at column 25
+
+ \~
+   ~
+
+{ *}  &
+ &\1 
+ 
+{ *}  \*\*
+ **\1    
+
+On *.h only in cpp files 
+{ *}  \*
+ *\1    
diff --git a/src/libqhullr/geom2_r.c b/src/libqhullr/geom2_r.c
index e1c025a..4d9b0d6 100644
--- a/src/libqhullr/geom2_r.c
+++ b/src/libqhullr/geom2_r.c
@@ -1,2081 +1,2081 @@
 /*
  ---------------------------------
 
 
-   geom2.c
+   geom2_r.c
    infrequently used geometric routines of qhull
 
-   see qh-geom.htm and geom.h
+   see qh-geom.htm and geom_r.h
 
    Copyright (c) 1993-2014 The Geometry Center.
-   $Id: //main/2011/qhull/src/libqhullr/geom2_r.c#4 $$Change: 1663 $
-   $DateTime: 2014/01/19 17:59:16 $$Author: bbarber $
+   $Id: //main/2011/qhull/src/libqhullr/geom2_r.c#6 $$Change: 1797 $
+   $DateTime: 2014/12/15 17:23:41 $$Author: bbarber $
 
-   frequently used code goes into geom.c
+   frequently used code goes into geom_r.c
 */
 
-#include "qhull_r.h"
+#include "qhull_ra.h"
 
 /*================== functions in alphabetic order ============*/
 
 /*---------------------------------
 
   qh_copypoints(qh, points, numpoints, dimension)
     return qh_malloc'd copy of points
 */
 coordT *qh_copypoints(qhT *qh, coordT *points, int numpoints, int dimension) {
   int size;
   coordT *newpoints;
 
   size= numpoints * dimension * (int)sizeof(coordT);
   if (!(newpoints=(coordT*)qh_malloc((size_t)size))) {
     qh_fprintf(qh, qh->ferr, 6004, "qhull error: insufficient memory to copy %d points\n",
         numpoints);
     qh_errexit(qh, qh_ERRmem, NULL, NULL);
   }
   memcpy((char *)newpoints, (char *)points, (size_t)size);
   return newpoints;
 } /* copypoints */
 
 /*---------------------------------
 
   qh_crossproduct(qh, dim, vecA, vecB, vecC )
     crossproduct of 2 dim vectors
     C= A x B
 
   notes:
     from Glasner, Graphics Gems I, p. 639
     only defined for dim==3
 */
 void qh_crossproduct(qhT *qh, int dim, realT vecA[3], realT vecB[3], realT vecC[3]){
 
   if (dim == 3) {
     vecC[0]=   det2_(vecA[1], vecA[2],
                      vecB[1], vecB[2]);
     vecC[1]= - det2_(vecA[0], vecA[2],
                      vecB[0], vecB[2]);
     vecC[2]=   det2_(vecA[0], vecA[1],
                      vecB[0], vecB[1]);
   }
 } /* vcross */
 
 /*---------------------------------
 
   qh_determinant(qh, rows, dim, nearzero )
     compute signed determinant of a square matrix
     uses qh.NEARzero to test for degenerate matrices
 
   returns:
     determinant
     overwrites rows and the matrix
     if dim == 2 or 3
       nearzero iff determinant < qh->NEARzero[dim-1]
       (!quite correct, not critical)
     if dim >= 4
       nearzero iff diagonal[k] < qh->NEARzero[k]
 */
 realT qh_determinant(qhT *qh, realT **rows, int dim, boolT *nearzero) {
   realT det=0;
   int i;
   boolT sign= False;
 
   *nearzero= False;
   if (dim < 2) {
     qh_fprintf(qh, qh->ferr, 6005, "qhull internal error (qh_determinate): only implemented for dimension >= 2\n");
     qh_errexit(qh, qh_ERRqhull, NULL, NULL);
   }else if (dim == 2) {
     det= det2_(rows[0][0], rows[0][1],
                  rows[1][0], rows[1][1]);
     if (fabs_(det) < qh->NEARzero[1])  /* not really correct, what should this be? */
       *nearzero= True;
   }else if (dim == 3) {
     det= det3_(rows[0][0], rows[0][1], rows[0][2],
                  rows[1][0], rows[1][1], rows[1][2],
                  rows[2][0], rows[2][1], rows[2][2]);
     if (fabs_(det) < qh->NEARzero[2])  /* not really correct, what should this be? */
       *nearzero= True;
   }else {
     qh_gausselim(qh, rows, dim, dim, &sign, nearzero);  /* if nearzero, diagonal still ok*/
     det= 1.0;
     for (i=dim; i--; )
       det *= (rows[i])[i];
     if (sign)
       det= -det;
   }
   return det;
 } /* determinant */
 
 /*---------------------------------
 
   qh_detjoggle(qh, points, numpoints, dimension )
     determine default max joggle for point array
       as qh_distround * qh_JOGGLEdefault
 
   returns:
     initial value for JOGGLEmax from points and REALepsilon
 
   notes:
     computes DISTround since qh_maxmin not called yet
     if qh->SCALElast, last dimension will be scaled later to MAXwidth
 
     loop duplicated from qh_maxmin
 */
 realT qh_detjoggle(qhT *qh, pointT *points, int numpoints, int dimension) {
   realT abscoord, distround, joggle, maxcoord, mincoord;
   pointT *point, *pointtemp;
   realT maxabs= -REALmax;
   realT sumabs= 0;
   realT maxwidth= 0;
   int k;
 
   for (k=0; k < dimension; k++) {
     if (qh->SCALElast && k == dimension-1)
       abscoord= maxwidth;
     else if (qh->DELAUNAY && k == dimension-1) /* will qh_setdelaunay() */
       abscoord= 2 * maxabs * maxabs;  /* may be low by qh->hull_dim/2 */
     else {
       maxcoord= -REALmax;
       mincoord= REALmax;
       FORALLpoint_(qh, points, numpoints) {
         maximize_(maxcoord, point[k]);
         minimize_(mincoord, point[k]);
       }
       maximize_(maxwidth, maxcoord-mincoord);
       abscoord= fmax_(maxcoord, -mincoord);
     }
     sumabs += abscoord;
     maximize_(maxabs, abscoord);
   } /* for k */
   distround= qh_distround(qh, qh->hull_dim, maxabs, sumabs);
   joggle= distround * qh_JOGGLEdefault;
   maximize_(joggle, REALepsilon * qh_JOGGLEdefault);
   trace2((qh, qh->ferr, 2001, "qh_detjoggle: joggle=%2.2g maxwidth=%2.2g\n", joggle, maxwidth));
   return joggle;
 } /* detjoggle */
 
 /*---------------------------------
 
   qh_detroundoff(qh)
     determine maximum roundoff errors from
       REALepsilon, REALmax, REALmin, qh.hull_dim, qh.MAXabs_coord,
       qh.MAXsumcoord, qh.MAXwidth, qh.MINdenom_1
 
     accounts for qh.SETroundoff, qh.RANDOMdist, qh->MERGEexact
       qh.premerge_cos, qh.postmerge_cos, qh.premerge_centrum,
       qh.postmerge_centrum, qh.MINoutside,
       qh_RATIOnearinside, qh_COPLANARratio, qh_WIDEcoplanar
 
   returns:
     sets qh.DISTround, etc. (see below)
     appends precision constants to qh.qhull_options
 
   see:
     qh_maxmin() for qh.NEARzero
 
   design:
     determine qh.DISTround for distance computations
     determine minimum denominators for qh_divzero
     determine qh.ANGLEround for angle computations
     adjust qh.premerge_cos,... for roundoff error
     determine qh.ONEmerge for maximum error due to a single merge
     determine qh.NEARinside, qh.MAXcoplanar, qh.MINvisible,
       qh.MINoutside, qh.WIDEfacet
     initialize qh.max_vertex and qh.minvertex
 */
 void qh_detroundoff(qhT *qh) {
 
   qh_option(qh, "_max-width", NULL, &qh->MAXwidth);
   if (!qh->SETroundoff) {
     qh->DISTround= qh_distround(qh, qh->hull_dim, qh->MAXabs_coord, qh->MAXsumcoord);
     if (qh->RANDOMdist)
       qh->DISTround += qh->RANDOMfactor * qh->MAXabs_coord;
     qh_option(qh, "Error-roundoff", NULL, &qh->DISTround);
   }
   qh->MINdenom= qh->MINdenom_1 * qh->MAXabs_coord;
   qh->MINdenom_1_2= sqrt(qh->MINdenom_1 * qh->hull_dim) ;  /* if will be normalized */
   qh->MINdenom_2= qh->MINdenom_1_2 * qh->MAXabs_coord;
                                               /* for inner product */
   qh->ANGLEround= 1.01 * qh->hull_dim * REALepsilon;
   if (qh->RANDOMdist)
     qh->ANGLEround += qh->RANDOMfactor;
   if (qh->premerge_cos < REALmax/2) {
     qh->premerge_cos -= qh->ANGLEround;
     if (qh->RANDOMdist)
       qh_option(qh, "Angle-premerge-with-random", NULL, &qh->premerge_cos);
   }
   if (qh->postmerge_cos < REALmax/2) {
     qh->postmerge_cos -= qh->ANGLEround;
     if (qh->RANDOMdist)
       qh_option(qh, "Angle-postmerge-with-random", NULL, &qh->postmerge_cos);
   }
   qh->premerge_centrum += 2 * qh->DISTround;    /*2 for centrum and distplane()*/
   qh->postmerge_centrum += 2 * qh->DISTround;
   if (qh->RANDOMdist && (qh->MERGEexact || qh->PREmerge))
     qh_option(qh, "Centrum-premerge-with-random", NULL, &qh->premerge_centrum);
   if (qh->RANDOMdist && qh->POSTmerge)
     qh_option(qh, "Centrum-postmerge-with-random", NULL, &qh->postmerge_centrum);
   { /* compute ONEmerge, max vertex offset for merging simplicial facets */
     realT maxangle= 1.0, maxrho;
 
     minimize_(maxangle, qh->premerge_cos);
     minimize_(maxangle, qh->postmerge_cos);
     /* max diameter * sin theta + DISTround for vertex to its hyperplane */
     qh->ONEmerge= sqrt((realT)qh->hull_dim) * qh->MAXwidth *
       sqrt(1.0 - maxangle * maxangle) + qh->DISTround;
     maxrho= qh->hull_dim * qh->premerge_centrum + qh->DISTround;
     maximize_(qh->ONEmerge, maxrho);
     maxrho= qh->hull_dim * qh->postmerge_centrum + qh->DISTround;
     maximize_(qh->ONEmerge, maxrho);
     if (qh->MERGING)
       qh_option(qh, "_one-merge", NULL, &qh->ONEmerge);
   }
   qh->NEARinside= qh->ONEmerge * qh_RATIOnearinside; /* only used if qh->KEEPnearinside */
   if (qh->JOGGLEmax < REALmax/2 && (qh->KEEPcoplanar || qh->KEEPinside)) {
     realT maxdist;             /* adjust qh.NEARinside for joggle */
     qh->KEEPnearinside= True;
     maxdist= sqrt((realT)qh->hull_dim) * qh->JOGGLEmax + qh->DISTround;
     maxdist= 2*maxdist;        /* vertex and coplanar point can joggle in opposite directions */
     maximize_(qh->NEARinside, maxdist);  /* must agree with qh_nearcoplanar() */
   }
   if (qh->KEEPnearinside)
     qh_option(qh, "_near-inside", NULL, &qh->NEARinside);
   if (qh->JOGGLEmax < qh->DISTround) {
     qh_fprintf(qh, qh->ferr, 6006, "qhull error: the joggle for 'QJn', %.2g, is below roundoff for distance computations, %.2g\n",
          qh->JOGGLEmax, qh->DISTround);
     qh_errexit(qh, qh_ERRinput, NULL, NULL);
   }
   if (qh->MINvisible > REALmax/2) {
     if (!qh->MERGING)
       qh->MINvisible= qh->DISTround;
     else if (qh->hull_dim <= 3)
       qh->MINvisible= qh->premerge_centrum;
     else
       qh->MINvisible= qh_COPLANARratio * qh->premerge_centrum;
     if (qh->APPROXhull && qh->MINvisible > qh->MINoutside)
       qh->MINvisible= qh->MINoutside;
     qh_option(qh, "Visible-distance", NULL, &qh->MINvisible);
   }
   if (qh->MAXcoplanar > REALmax/2) {
     qh->MAXcoplanar= qh->MINvisible;
     qh_option(qh, "U-coplanar-distance", NULL, &qh->MAXcoplanar);
   }
   if (!qh->APPROXhull) {             /* user may specify qh->MINoutside */
     qh->MINoutside= 2 * qh->MINvisible;
     if (qh->premerge_cos < REALmax/2)
       maximize_(qh->MINoutside, (1- qh->premerge_cos) * qh->MAXabs_coord);
     qh_option(qh, "Width-outside", NULL, &qh->MINoutside);
   }
   qh->WIDEfacet= qh->MINoutside;
   maximize_(qh->WIDEfacet, qh_WIDEcoplanar * qh->MAXcoplanar);
   maximize_(qh->WIDEfacet, qh_WIDEcoplanar * qh->MINvisible);
   qh_option(qh, "_wide-facet", NULL, &qh->WIDEfacet);
   if (qh->MINvisible > qh->MINoutside + 3 * REALepsilon
   && !qh->BESToutside && !qh->FORCEoutput)
     qh_fprintf(qh, qh->ferr, 7001, "qhull input warning: minimum visibility V%.2g is greater than \nminimum outside W%.2g.  Flipped facets are likely.\n",
              qh->MINvisible, qh->MINoutside);
   qh->max_vertex= qh->DISTround;
   qh->min_vertex= -qh->DISTround;
   /* numeric constants reported in printsummary */
 } /* detroundoff */
 
 /*---------------------------------
 
   qh_detsimplex(qh, apex, points, dim, nearzero )
     compute determinant of a simplex with point apex and base points
 
   returns:
      signed determinant and nearzero from qh_determinant
 
   notes:
      uses qh.gm_matrix/qh.gm_row (assumes they're big enough)
 
   design:
     construct qm_matrix by subtracting apex from points
     compute determinate
 */
 realT qh_detsimplex(qhT *qh, pointT *apex, setT *points, int dim, boolT *nearzero) {
   pointT *coorda, *coordp, *gmcoord, *point, **pointp;
   coordT **rows;
   int k,  i=0;
   realT det;
 
   zinc_(Zdetsimplex);
   gmcoord= qh->gm_matrix;
   rows= qh->gm_row;
   FOREACHpoint_(points) {
     if (i == dim)
       break;
     rows[i++]= gmcoord;
     coordp= point;
     coorda= apex;
     for (k=dim; k--; )
       *(gmcoord++)= *coordp++ - *coorda++;
   }
   if (i < dim) {
     qh_fprintf(qh, qh->ferr, 6007, "qhull internal error (qh_detsimplex): #points %d < dimension %d\n",
                i, dim);
     qh_errexit(qh, qh_ERRqhull, NULL, NULL);
   }
   det= qh_determinant(qh, rows, dim, nearzero);
   trace2((qh, qh->ferr, 2002, "qh_detsimplex: det=%2.2g for point p%d, dim %d, nearzero? %d\n",
           det, qh_pointid(qh, apex), dim, *nearzero));
   return det;
 } /* detsimplex */
 
 /*---------------------------------
 
   qh_distnorm(qh, dim, point, normal, offset )
     return distance from point to hyperplane at normal/offset
 
   returns:
     dist
 
   notes:
     dist > 0 if point is outside of hyperplane
 
   see:
-    qh_distplane in geom.c
+    qh_distplane in geom_r.c
 */
 realT qh_distnorm(qhT *qh, int dim, pointT *point, pointT *normal, realT *offsetp) {
   coordT *normalp= normal, *coordp= point;
   realT dist;
   int k;
 
   dist= *offsetp;
   for (k=dim; k--; )
     dist += *(coordp++) * *(normalp++);
   return dist;
 } /* distnorm */
 
 /*---------------------------------
 
   qh_distround(qh, dimension, maxabs, maxsumabs )
     compute maximum round-off error for a distance computation
       to a normalized hyperplane
     maxabs is the maximum absolute value of a coordinate
     maxsumabs is the maximum possible sum of absolute coordinate values
 
   returns:
     max dist round for REALepsilon
 
   notes:
     calculate roundoff error according to
     Lemma 3.2-1 of Golub and van Loan "Matrix Computation"
     use sqrt(dim) since one vector is normalized
       or use maxsumabs since one vector is < 1
 */
 realT qh_distround(qhT *qh, int dimension, realT maxabs, realT maxsumabs) {
   realT maxdistsum, maxround;
 
   maxdistsum= sqrt((realT)dimension) * maxabs;
   minimize_( maxdistsum, maxsumabs);
   maxround= REALepsilon * (dimension * maxdistsum * 1.01 + maxabs);
               /* adds maxabs for offset */
   trace4((qh, qh->ferr, 4008, "qh_distround: %2.2g maxabs %2.2g maxsumabs %2.2g maxdistsum %2.2g\n",
                  maxround, maxabs, maxsumabs, maxdistsum));
   return maxround;
 } /* distround */
 
 /*---------------------------------
 
   qh_divzero(qh, numer, denom, mindenom1, zerodiv )
     divide by a number that's nearly zero
     mindenom1= minimum denominator for dividing into 1.0
 
   returns:
     quotient
     sets zerodiv and returns 0.0 if it would overflow
 
   design:
     if numer is nearly zero and abs(numer) < abs(denom)
       return numer/denom
     else if numer is nearly zero
       return 0 and zerodiv
     else if denom/numer non-zero
       return numer/denom
     else
       return 0 and zerodiv
 */
 realT qh_divzero(qhT *qh, realT numer, realT denom, realT mindenom1, boolT *zerodiv) {
   realT temp, numerx, denomx;
 
 
   if (numer < mindenom1 && numer > -mindenom1) {
     numerx= fabs_(numer);
     denomx= fabs_(denom);
     if (numerx < denomx) {
       *zerodiv= False;
       return numer/denom;
     }else {
       *zerodiv= True;
       return 0.0;
     }
   }
   temp= denom/numer;
   if (temp > mindenom1 || temp < -mindenom1) {
     *zerodiv= False;
     return numer/denom;
   }else {
     *zerodiv= True;
     return 0.0;
   }
 } /* divzero */
 
 
 /*---------------------------------
 
   qh_facetarea(qh, facet )
     return area for a facet
 
   notes:
     if non-simplicial,
       uses centrum to triangulate facet and sums the projected areas.
     if (qh->DELAUNAY),
       computes projected area instead for last coordinate
     assumes facet->normal exists
     projecting tricoplanar facets to the hyperplane does not appear to make a difference
 
   design:
     if simplicial
       compute area
     else
       for each ridge
         compute area from centrum to ridge
     negate area if upper Delaunay facet
 */
 realT qh_facetarea(qhT *qh, facetT *facet) {
   vertexT *apex;
   pointT *centrum;
   realT area= 0.0;
   ridgeT *ridge, **ridgep;
 
   if (facet->simplicial) {
     apex= SETfirstt_(facet->vertices, vertexT);
     area= qh_facetarea_simplex(qh, qh->hull_dim, apex->point, facet->vertices,
                     apex, facet->toporient, facet->normal, &facet->offset);
   }else {
     if (qh->CENTERtype == qh_AScentrum)
       centrum= facet->center;
     else
       centrum= qh_getcentrum(qh, facet);
     FOREACHridge_(facet->ridges)
       area += qh_facetarea_simplex(qh, qh->hull_dim, centrum, ridge->vertices,
                  NULL, (boolT)(ridge->top == facet),  facet->normal, &facet->offset);
     if (qh->CENTERtype != qh_AScentrum)
       qh_memfree(qh, centrum, qh->normal_size);
   }
   if (facet->upperdelaunay && qh->DELAUNAY)
     area= -area;  /* the normal should be [0,...,1] */
   trace4((qh, qh->ferr, 4009, "qh_facetarea: f%d area %2.2g\n", facet->id, area));
   return area;
 } /* facetarea */
 
 /*---------------------------------
 
   qh_facetarea_simplex(qh, dim, apex, vertices, notvertex, toporient, normal, offset )
     return area for a simplex defined by
       an apex, a base of vertices, an orientation, and a unit normal
     if simplicial or tricoplanar facet,
       notvertex is defined and it is skipped in vertices
 
   returns:
     computes area of simplex projected to plane [normal,offset]
     returns 0 if vertex too far below plane (qh->WIDEfacet)
       vertex can't be apex of tricoplanar facet
 
   notes:
     if (qh->DELAUNAY),
       computes projected area instead for last coordinate
     uses qh->gm_matrix/gm_row and qh->hull_dim
     helper function for qh_facetarea
 
   design:
     if Notvertex
       translate simplex to apex
     else
       project simplex to normal/offset
       translate simplex to apex
     if Delaunay
       set last row/column to 0 with -1 on diagonal
     else
       set last row to Normal
     compute determinate
     scale and flip sign for area
 */
 realT qh_facetarea_simplex(qhT *qh, int dim, coordT *apex, setT *vertices,
         vertexT *notvertex,  boolT toporient, coordT *normal, realT *offset) {
   pointT *coorda, *coordp, *gmcoord;
   coordT **rows, *normalp;
   int k,  i=0;
   realT area, dist;
   vertexT *vertex, **vertexp;
   boolT nearzero;
 
   gmcoord= qh->gm_matrix;
   rows= qh->gm_row;
   FOREACHvertex_(vertices) {
     if (vertex == notvertex)
       continue;
     rows[i++]= gmcoord;
     coorda= apex;
     coordp= vertex->point;
     normalp= normal;
     if (notvertex) {
       for (k=dim; k--; )
         *(gmcoord++)= *coordp++ - *coorda++;
     }else {
       dist= *offset;
       for (k=dim; k--; )
         dist += *coordp++ * *normalp++;
       if (dist < -qh->WIDEfacet) {
         zinc_(Znoarea);
         return 0.0;
       }
       coordp= vertex->point;
       normalp= normal;
       for (k=dim; k--; )
         *(gmcoord++)= (*coordp++ - dist * *normalp++) - *coorda++;
     }
   }
   if (i != dim-1) {
     qh_fprintf(qh, qh->ferr, 6008, "qhull internal error (qh_facetarea_simplex): #points %d != dim %d -1\n",
                i, dim);
     qh_errexit(qh, qh_ERRqhull, NULL, NULL);
   }
   rows[i]= gmcoord;
   if (qh->DELAUNAY) {
     for (i=0; i < dim-1; i++)
       rows[i][dim-1]= 0.0;
     for (k=dim; k--; )
       *(gmcoord++)= 0.0;
     rows[dim-1][dim-1]= -1.0;
   }else {
     normalp= normal;
     for (k=dim; k--; )
       *(gmcoord++)= *normalp++;
   }
   zinc_(Zdetsimplex);
   area= qh_determinant(qh, rows, dim, &nearzero);
   if (toporient)
     area= -area;
   area *= qh->AREAfactor;
   trace4((qh, qh->ferr, 4010, "qh_facetarea_simplex: area=%2.2g for point p%d, toporient %d, nearzero? %d\n",
           area, qh_pointid(qh, apex), toporient, nearzero));
   return area;
 } /* facetarea_simplex */
 
 /*---------------------------------
 
   qh_facetcenter(qh, vertices )
     return Voronoi center (Voronoi vertex) for a facet's vertices
 
   returns:
     return temporary point equal to the center
 
   see:
     qh_voronoi_center()
 */
 pointT *qh_facetcenter(qhT *qh, setT *vertices) {
   setT *points= qh_settemp(qh, qh_setsize(qh, vertices));
   vertexT *vertex, **vertexp;
   pointT *center;
 
   FOREACHvertex_(vertices)
     qh_setappend(qh, &points, vertex->point);
   center= qh_voronoi_center(qh, qh->hull_dim-1, points);
   qh_settempfree(qh, &points);
   return center;
 } /* facetcenter */
 
 /*---------------------------------
 
   qh_findgooddist(qh, point, facetA, dist, facetlist )
     find best good facet visible for point from facetA
     assumes facetA is visible from point
 
   returns:
     best facet, i.e., good facet that is furthest from point
       distance to best facet
       NULL if none
 
     moves good, visible facets (and some other visible facets)
       to end of qh->facet_list
 
   notes:
     uses qh->visit_id
 
   design:
     initialize bestfacet if facetA is good
     move facetA to end of facetlist
     for each facet on facetlist
       for each unvisited neighbor of facet
         move visible neighbors to end of facetlist
         update best good neighbor
         if no good neighbors, update best facet
 */
 facetT *qh_findgooddist(qhT *qh, pointT *point, facetT *facetA, realT *distp,
                facetT **facetlist) {
   realT bestdist= -REALmax, dist;
   facetT *neighbor, **neighborp, *bestfacet=NULL, *facet;
   boolT goodseen= False;
 
   if (facetA->good) {
     zzinc_(Zcheckpart);  /* calls from check_bestdist occur after print stats */
     qh_distplane(qh, point, facetA, &bestdist);
     bestfacet= facetA;
     goodseen= True;
   }
   qh_removefacet(qh, facetA);
   qh_appendfacet(qh, facetA);
   *facetlist= facetA;
   facetA->visitid= ++qh->visit_id;
   FORALLfacet_(*facetlist) {
     FOREACHneighbor_(facet) {
       if (neighbor->visitid == qh->visit_id)
         continue;
       neighbor->visitid= qh->visit_id;
       if (goodseen && !neighbor->good)
         continue;
       zzinc_(Zcheckpart);
       qh_distplane(qh, point, neighbor, &dist);
       if (dist > 0) {
         qh_removefacet(qh, neighbor);
         qh_appendfacet(qh, neighbor);
         if (neighbor->good) {
           goodseen= True;
           if (dist > bestdist) {
             bestdist= dist;
             bestfacet= neighbor;
           }
         }
       }
     }
   }
   if (bestfacet) {
     *distp= bestdist;
     trace2((qh, qh->ferr, 2003, "qh_findgooddist: p%d is %2.2g above good facet f%d\n",
       qh_pointid(qh, point), bestdist, bestfacet->id));
     return bestfacet;
   }
   trace4((qh, qh->ferr, 4011, "qh_findgooddist: no good facet for p%d above f%d\n",
       qh_pointid(qh, point), facetA->id));
   return NULL;
 }  /* findgooddist */
 
 /*---------------------------------
 
   qh_getarea(qh, facetlist )
     set area of all facets in facetlist
     collect statistics
     nop if hasAreaVolume
 
   returns:
     sets qh->totarea/totvol to total area and volume of convex hull
     for Delaunay triangulation, computes projected area of the lower or upper hull
       ignores upper hull if qh->ATinfinity
 
   notes:
     could compute outer volume by expanding facet area by rays from interior
     the following attempt at perpendicular projection underestimated badly:
       qh.totoutvol += (-dist + facet->maxoutside + qh->DISTround)
                             * area/ qh->hull_dim;
   design:
     for each facet on facetlist
       compute facet->area
       update qh.totarea and qh.totvol
 */
 void qh_getarea(qhT *qh, facetT *facetlist) {
   realT area;
   realT dist;
   facetT *facet;
 
   if (qh->hasAreaVolume)
     return;
   if (qh->REPORTfreq)
     qh_fprintf(qh, qh->ferr, 8020, "computing area of each facet and volume of the convex hull\n");
   else
     trace1((qh, qh->ferr, 1001, "qh_getarea: computing volume and area for each facet\n"));
   qh->totarea= qh->totvol= 0.0;
   FORALLfacet_(facetlist) {
     if (!facet->normal)
       continue;
     if (facet->upperdelaunay && qh->ATinfinity)
       continue;
     if (!facet->isarea) {
       facet->f.area= qh_facetarea(qh, facet);
       facet->isarea= True;
     }
     area= facet->f.area;
     if (qh->DELAUNAY) {
       if (facet->upperdelaunay == qh->UPPERdelaunay)
         qh->totarea += area;
     }else {
       qh->totarea += area;
       qh_distplane(qh, qh->interior_point, facet, &dist);
       qh->totvol += -dist * area/ qh->hull_dim;
     }
     if (qh->PRINTstatistics) {
       wadd_(Wareatot, area);
       wmax_(Wareamax, area);
       wmin_(Wareamin, area);
     }
   }
   qh->hasAreaVolume= True;
 } /* getarea */
 
 /*---------------------------------
 
   qh_gram_schmidt(qh, dim, row )
     implements Gram-Schmidt orthogonalization by rows
 
   returns:
     false if zero norm
     overwrites rows[dim][dim]
 
   notes:
     see Golub & van Loan Algorithm 6.2-2
     overflow due to small divisors not handled
 
   design:
     for each row
       compute norm for row
       if non-zero, normalize row
       for each remaining rowA
         compute inner product of row and rowA
         reduce rowA by row * inner product
 */
 boolT qh_gram_schmidt(qhT *qh, int dim, realT **row) {
   realT *rowi, *rowj, norm;
   int i, j, k;
 
   for (i=0; i < dim; i++) {
     rowi= row[i];
     for (norm= 0.0, k= dim; k--; rowi++)
       norm += *rowi * *rowi;
     norm= sqrt(norm);
     wmin_(Wmindenom, norm);
     if (norm == 0.0)  /* either 0 or overflow due to sqrt */
       return False;
     for (k=dim; k--; )
       *(--rowi) /= norm;
     for (j=i+1; j < dim; j++) {
       rowj= row[j];
       for (norm= 0.0, k=dim; k--; )
         norm += *rowi++ * *rowj++;
       for (k=dim; k--; )
         *(--rowj) -= *(--rowi) * norm;
     }
   }
   return True;
 } /* gram_schmidt */
 
 
 /*---------------------------------
 
   qh_inthresholds(qh, normal, angle )
     return True if normal within qh.lower_/upper_threshold
 
   returns:
     estimate of angle by summing of threshold diffs
       angle may be NULL
       smaller "angle" is better
 
   notes:
     invalid if qh.SPLITthresholds
 
   see:
     qh.lower_threshold in qh_initbuild()
     qh_initthresholds()
 
   design:
     for each dimension
       test threshold
 */
 boolT qh_inthresholds(qhT *qh, coordT *normal, realT *angle) {
   boolT within= True;
   int k;
   realT threshold;
 
   if (angle)
     *angle= 0.0;
   for (k=0; k < qh->hull_dim; k++) {
     threshold= qh->lower_threshold[k];
     if (threshold > -REALmax/2) {
       if (normal[k] < threshold)
         within= False;
       if (angle) {
         threshold -= normal[k];
         *angle += fabs_(threshold);
       }
     }
     if (qh->upper_threshold[k] < REALmax/2) {
       threshold= qh->upper_threshold[k];
       if (normal[k] > threshold)
         within= False;
       if (angle) {
         threshold -= normal[k];
         *angle += fabs_(threshold);
       }
     }
   }
   return within;
 } /* inthresholds */
 
 
 /*---------------------------------
 
   qh_joggleinput(qh)
     randomly joggle input to Qhull by qh.JOGGLEmax
     initial input is qh.first_point/qh.num_points of qh.hull_dim
       repeated calls use qh.input_points/qh.num_points
 
   returns:
     joggles points at qh.first_point/qh.num_points
     copies data to qh.input_points/qh.input_malloc if first time
     determines qh.JOGGLEmax if it was zero
     if qh.DELAUNAY
       computes the Delaunay projection of the joggled points
 
   notes:
     if qh.DELAUNAY, unnecessarily joggles the last coordinate
     the initial 'QJn' may be set larger than qh_JOGGLEmaxincrease
 
   design:
     if qh.DELAUNAY
       set qh.SCALElast for reduced precision errors
     if first call
       initialize qh.input_points to the original input points
       if qh.JOGGLEmax == 0
         determine default qh.JOGGLEmax
     else
       increase qh.JOGGLEmax according to qh.build_cnt
     joggle the input by adding a random number in [-qh.JOGGLEmax,qh.JOGGLEmax]
     if qh.DELAUNAY
       sets the Delaunay projection
 */
 void qh_joggleinput(qhT *qh) {
   int i, seed, size;
   coordT *coordp, *inputp;
   realT randr, randa, randb;
 
   if (!qh->input_points) { /* first call */
     qh->input_points= qh->first_point;
     qh->input_malloc= qh->POINTSmalloc;
     size= qh->num_points * qh->hull_dim * sizeof(coordT);
     if (!(qh->first_point=(coordT*)qh_malloc((size_t)size))) {
       qh_fprintf(qh, qh->ferr, 6009, "qhull error: insufficient memory to joggle %d points\n",
           qh->num_points);
       qh_errexit(qh, qh_ERRmem, NULL, NULL);
     }
     qh->POINTSmalloc= True;
     if (qh->JOGGLEmax == 0.0) {
       qh->JOGGLEmax= qh_detjoggle(qh, qh->input_points, qh->num_points, qh->hull_dim);
       qh_option(qh, "QJoggle", NULL, &qh->JOGGLEmax);
     }
   }else {                 /* repeated call */
     if (!qh->RERUN && qh->build_cnt > qh_JOGGLEretry) {
       if (((qh->build_cnt-qh_JOGGLEretry-1) % qh_JOGGLEagain) == 0) {
         realT maxjoggle= qh->MAXwidth * qh_JOGGLEmaxincrease;
         if (qh->JOGGLEmax < maxjoggle) {
           qh->JOGGLEmax *= qh_JOGGLEincrease;
           minimize_(qh->JOGGLEmax, maxjoggle);
         }
       }
     }
     qh_option(qh, "QJoggle", NULL, &qh->JOGGLEmax);
   }
   if (qh->build_cnt > 1 && qh->JOGGLEmax > fmax_(qh->MAXwidth/4, 0.1)) {
       qh_fprintf(qh, qh->ferr, 6010, "qhull error: the current joggle for 'QJn', %.2g, is too large for the width\nof the input.  If possible, recompile Qhull with higher-precision reals.\n",
                 qh->JOGGLEmax);
       qh_errexit(qh, qh_ERRqhull, NULL, NULL);
   }
   /* for some reason, using qh->ROTATErandom and qh_RANDOMseed does not repeat the run. Use 'TRn' instead */
   seed= qh_RANDOMint;
   qh_option(qh, "_joggle-seed", &seed, NULL);
   trace0((qh, qh->ferr, 6, "qh_joggleinput: joggle input by %2.2g with seed %d\n",
     qh->JOGGLEmax, seed));
   inputp= qh->input_points;
   coordp= qh->first_point;
   randa= 2.0 * qh->JOGGLEmax/qh_RANDOMmax;
   randb= -qh->JOGGLEmax;
   size= qh->num_points * qh->hull_dim;
   for (i=size; i--; ) {
     randr= qh_RANDOMint;
     *(coordp++)= *(inputp++) + (randr * randa + randb);
   }
   if (qh->DELAUNAY) {
     qh->last_low= qh->last_high= qh->last_newhigh= REALmax;
     qh_setdelaunay(qh, qh->hull_dim, qh->num_points, qh->first_point);
   }
 } /* joggleinput */
 
 /*---------------------------------
 
   qh_maxabsval(qh, normal, dim )
     return pointer to maximum absolute value of a dim vector
     returns NULL if dim=0
 */
 realT *qh_maxabsval(qhT *qh, realT *normal, int dim) {
   realT maxval= -REALmax;
   realT *maxp= NULL, *colp, absval;
   int k;
 
   for (k=dim, colp= normal; k--; colp++) {
     absval= fabs_(*colp);
     if (absval > maxval) {
       maxval= absval;
       maxp= colp;
     }
   }
   return maxp;
 } /* maxabsval */
 
 
 /*---------------------------------
 
   qh_maxmin(qh, points, numpoints, dimension )
     return max/min points for each dimension
     determine max and min coordinates
 
   returns:
     returns a temporary set of max and min points
       may include duplicate points. Does not include qh.GOODpoint
     sets qh.NEARzero, qh.MAXabs_coord, qh.MAXsumcoord, qh.MAXwidth
          qh.MAXlastcoord, qh.MINlastcoord
     initializes qh.max_outside, qh.min_vertex, qh.WAScoplanar, qh.ZEROall_ok
 
   notes:
     loop duplicated in qh_detjoggle()
 
   design:
     initialize global precision variables
     checks definition of REAL...
     for each dimension
       for each point
         collect maximum and minimum point
       collect maximum of maximums and minimum of minimums
       determine qh.NEARzero for Gaussian Elimination
 */
 setT *qh_maxmin(qhT *qh, pointT *points, int numpoints, int dimension) {
   int k;
   realT maxcoord, temp;
   pointT *minimum, *maximum, *point, *pointtemp;
   setT *set;
 
   qh->max_outside= 0.0;
   qh->MAXabs_coord= 0.0;
   qh->MAXwidth= -REALmax;
   qh->MAXsumcoord= 0.0;
   qh->min_vertex= 0.0;
   qh->WAScoplanar= False;
   if (qh->ZEROcentrum)
     qh->ZEROall_ok= True;
   if (REALmin < REALepsilon && REALmin < REALmax && REALmin > -REALmax
   && REALmax > 0.0 && -REALmax < 0.0)
     ; /* all ok */
   else {
     qh_fprintf(qh, qh->ferr, 6011, "qhull error: floating point constants in user.h are wrong\n\
 REALepsilon %g REALmin %g REALmax %g -REALmax %g\n",
              REALepsilon, REALmin, REALmax, -REALmax);
     qh_errexit(qh, qh_ERRinput, NULL, NULL);
   }
   set= qh_settemp(qh, 2*dimension);
   for (k=0; k < dimension; k++) {
     if (points == qh->GOODpointp)
       minimum= maximum= points + dimension;
     else
       minimum= maximum= points;
     FORALLpoint_(qh, points, numpoints) {
       if (point == qh->GOODpointp)
         continue;
       if (maximum[k] < point[k])
         maximum= point;
       else if (minimum[k] > point[k])
         minimum= point;
     }
     if (k == dimension-1) {
       qh->MINlastcoord= minimum[k];
       qh->MAXlastcoord= maximum[k];
     }
     if (qh->SCALElast && k == dimension-1)
       maxcoord= qh->MAXwidth;
     else {
       maxcoord= fmax_(maximum[k], -minimum[k]);
       if (qh->GOODpointp) {
         temp= fmax_(qh->GOODpointp[k], -qh->GOODpointp[k]);
         maximize_(maxcoord, temp);
       }
       temp= maximum[k] - minimum[k];
       maximize_(qh->MAXwidth, temp);
     }
     maximize_(qh->MAXabs_coord, maxcoord);
     qh->MAXsumcoord += maxcoord;
     qh_setappend(qh, &set, maximum);
     qh_setappend(qh, &set, minimum);
     /* calculation of qh->NEARzero is based on error formula 4.4-13 of
        Golub & van Loan, authors say n^3 can be ignored and 10 be used in
        place of rho */
     qh->NEARzero[k]= 80 * qh->MAXsumcoord * REALepsilon;
   }
   if (qh->IStracing >=1)
     qh_printpoints(qh, qh->ferr, "qh_maxmin: found the max and min points(by dim):", set);
   return(set);
 } /* maxmin */
 
 /*---------------------------------
 
   qh_maxouter(qh)
     return maximum distance from facet to outer plane
     normally this is qh.max_outside+qh.DISTround
     does not include qh.JOGGLEmax
 
   see:
     qh_outerinner()
 
   notes:
     need to add another qh.DISTround if testing actual point with computation
 
   for joggle:
     qh_setfacetplane() updated qh.max_outer for Wnewvertexmax (max distance to vertex)
     need to use Wnewvertexmax since could have a coplanar point for a high
       facet that is replaced by a low facet
     need to add qh.JOGGLEmax if testing input points
 */
 realT qh_maxouter(qhT *qh) {
   realT dist;
 
   dist= fmax_(qh->max_outside, qh->DISTround);
   dist += qh->DISTround;
   trace4((qh, qh->ferr, 4012, "qh_maxouter: max distance from facet to outer plane is %2.2g max_outside is %2.2g\n", dist, qh->max_outside));
   return dist;
 } /* maxouter */
 
 /*---------------------------------
 
   qh_maxsimplex(qh, dim, maxpoints, points, numpoints, simplex )
     determines maximum simplex for a set of points
     starts from points already in simplex
     skips qh.GOODpointp (assumes that it isn't in maxpoints)
 
   returns:
     simplex with dim+1 points
 
   notes:
     assumes at least pointsneeded points in points
     maximizes determinate for x,y,z,w, etc.
     uses maxpoints as long as determinate is clearly non-zero
 
   design:
     initialize simplex with at least two points
       (find points with max or min x coordinate)
     for each remaining dimension
       add point that maximizes the determinate
         (use points from maxpoints first)
 */
 void qh_maxsimplex(qhT *qh, int dim, setT *maxpoints, pointT *points, int numpoints, setT **simplex) {
   pointT *point, **pointp, *pointtemp, *maxpoint, *minx=NULL, *maxx=NULL;
   boolT nearzero, maxnearzero= False;
   int k, sizinit;
   realT maxdet= -REALmax, det, mincoord= REALmax, maxcoord= -REALmax;
 
   sizinit= qh_setsize(qh, *simplex);
   if (sizinit < 2) {
     if (qh_setsize(qh, maxpoints) >= 2) {
       FOREACHpoint_(maxpoints) {
         if (maxcoord < point[0]) {
           maxcoord= point[0];
           maxx= point;
         }
         if (mincoord > point[0]) {
           mincoord= point[0];
           minx= point;
         }
       }
     }else {
       FORALLpoint_(qh, points, numpoints) {
         if (point == qh->GOODpointp)
           continue;
         if (maxcoord < point[0]) {
           maxcoord= point[0];
           maxx= point;
         }
         if (mincoord > point[0]) {
           mincoord= point[0];
           minx= point;
         }
       }
     }
     qh_setunique(qh, simplex, minx);
     if (qh_setsize(qh, *simplex) < 2)
       qh_setunique(qh, simplex, maxx);
     sizinit= qh_setsize(qh, *simplex);
     if (sizinit < 2) {
       qh_precision(qh, "input has same x coordinate");
       if (zzval_(Zsetplane) > qh->hull_dim+1) {
         qh_fprintf(qh, qh->ferr, 6012, "qhull precision error (qh_maxsimplex for voronoi_center):\n%d points with the same x coordinate.\n",
                  qh_setsize(qh, maxpoints)+numpoints);
         qh_errexit(qh, qh_ERRprec, NULL, NULL);
       }else {
         qh_fprintf(qh, qh->ferr, 6013, "qhull input error: input is less than %d-dimensional since it has the same x coordinate\n", qh->hull_dim);
         qh_errexit(qh, qh_ERRinput, NULL, NULL);
       }
     }
   }
   for (k=sizinit; k < dim+1; k++) {
     maxpoint= NULL;
     maxdet= -REALmax;
     FOREACHpoint_(maxpoints) {
       if (!qh_setin(*simplex, point)) {
         det= qh_detsimplex(qh, point, *simplex, k, &nearzero);
         if ((det= fabs_(det)) > maxdet) {
           maxdet= det;
           maxpoint= point;
           maxnearzero= nearzero;
         }
       }
     }
     if (!maxpoint || maxnearzero) {
       zinc_(Zsearchpoints);
       if (!maxpoint) {
         trace0((qh, qh->ferr, 7, "qh_maxsimplex: searching all points for %d-th initial vertex.\n", k+1));
       }else {
         trace0((qh, qh->ferr, 8, "qh_maxsimplex: searching all points for %d-th initial vertex, better than p%d det %2.2g\n",
                 k+1, qh_pointid(qh, maxpoint), maxdet));
       }
       FORALLpoint_(qh, points, numpoints) {
         if (point == qh->GOODpointp)
           continue;
         if (!qh_setin(*simplex, point)) {
           det= qh_detsimplex(qh, point, *simplex, k, &nearzero);
           if ((det= fabs_(det)) > maxdet) {
             maxdet= det;
             maxpoint= point;
             maxnearzero= nearzero;
           }
         }
       }
     } /* !maxpoint */
     if (!maxpoint) {
       qh_fprintf(qh, qh->ferr, 6014, "qhull internal error (qh_maxsimplex): not enough points available\n");
       qh_errexit(qh, qh_ERRqhull, NULL, NULL);
     }
     qh_setappend(qh, simplex, maxpoint);
     trace1((qh, qh->ferr, 1002, "qh_maxsimplex: selected point p%d for %d`th initial vertex, det=%2.2g\n",
             qh_pointid(qh, maxpoint), k+1, maxdet));
   } /* k */
 } /* maxsimplex */
 
 /*---------------------------------
 
   qh_minabsval(qh, normal, dim )
     return minimum absolute value of a dim vector
 */
 realT qh_minabsval(qhT *qh, realT *normal, int dim) {
   realT minval= 0;
   realT maxval= 0;
   realT *colp;
   int k;
 
   for (k=dim, colp=normal; k--; colp++) {
     maximize_(maxval, *colp);
     minimize_(minval, *colp);
   }
   return fmax_(maxval, -minval);
 } /* minabsval */
 
 
 /*---------------------------------
 
   qh_mindif(qh, vecA, vecB, dim )
     return index of min abs. difference of two vectors
 */
 int qh_mindiff(qhT *qh, realT *vecA, realT *vecB, int dim) {
   realT mindiff= REALmax, diff;
   realT *vecAp= vecA, *vecBp= vecB;
   int k, mink= 0;
 
   for (k=0; k < dim; k++) {
     diff= *vecAp++ - *vecBp++;
     diff= fabs_(diff);
     if (diff < mindiff) {
       mindiff= diff;
       mink= k;
     }
   }
   return mink;
 } /* mindiff */
 
 
 
 /*---------------------------------
 
   qh_orientoutside(qh, facet  )
     make facet outside oriented via qh.interior_point
 
   returns:
     True if facet reversed orientation.
 */
 boolT qh_orientoutside(qhT *qh, facetT *facet) {
   int k;
   realT dist;
 
   qh_distplane(qh, qh->interior_point, facet, &dist);
   if (dist > 0) {
     for (k=qh->hull_dim; k--; )
       facet->normal[k]= -facet->normal[k];
     facet->offset= -facet->offset;
     return True;
   }
   return False;
 } /* orientoutside */
 
 /*---------------------------------
 
   qh_outerinner(qh, facet, outerplane, innerplane  )
     if facet and qh.maxoutdone (i.e., qh_check_maxout)
       returns outer and inner plane for facet
     else
       returns maximum outer and inner plane
     accounts for qh.JOGGLEmax
 
   see:
     qh_maxouter(qh), qh_check_bestdist(), qh_check_points()
 
   notes:
     outerplaner or innerplane may be NULL
     facet is const
     Does not error (QhullFacet)
 
     includes qh.DISTround for actual points
     adds another qh.DISTround if testing with floating point arithmetic
 */
 void qh_outerinner(qhT *qh, facetT *facet, realT *outerplane, realT *innerplane) {
   realT dist, mindist;
   vertexT *vertex, **vertexp;
 
   if (outerplane) {
     if (!qh_MAXoutside || !facet || !qh->maxoutdone) {
       *outerplane= qh_maxouter(qh);       /* includes qh.DISTround */
     }else { /* qh_MAXoutside ... */
 #if qh_MAXoutside
       *outerplane= facet->maxoutside + qh->DISTround;
 #endif
 
     }
     if (qh->JOGGLEmax < REALmax/2)
       *outerplane += qh->JOGGLEmax * sqrt((realT)qh->hull_dim);
   }
   if (innerplane) {
     if (facet) {
       mindist= REALmax;
       FOREACHvertex_(facet->vertices) {
         zinc_(Zdistio);
         qh_distplane(qh, vertex->point, facet, &dist);
         minimize_(mindist, dist);
       }
       *innerplane= mindist - qh->DISTround;
     }else
       *innerplane= qh->min_vertex - qh->DISTround;
     if (qh->JOGGLEmax < REALmax/2)
       *innerplane -= qh->JOGGLEmax * sqrt((realT)qh->hull_dim);
   }
 } /* outerinner */
 
 /*---------------------------------
 
   qh_pointdist(qh, point1, point2, dim )
     return distance between two points
 
   notes:
     returns distance squared if 'dim' is negative
 */
 coordT qh_pointdist(qhT *qh, pointT *point1, pointT *point2, int dim) {
   coordT dist, diff;
   int k;
 
   dist= 0.0;
   for (k= (dim > 0 ? dim : -dim); k--; ) {
     diff= *point1++ - *point2++;
     dist += diff * diff;
   }
   if (dim > 0)
     return(sqrt(dist));
   return dist;
 } /* pointdist */
 
 
 /*---------------------------------
 
   qh_printmatrix(qh, fp, string, rows, numrow, numcol )
     print matrix to fp given by row vectors
     print string as header
 
   notes:
     print a vector by qh_printmatrix(qh, fp, "", &vect, 1, len)
 */
 void qh_printmatrix(qhT *qh, FILE *fp, const char *string, realT **rows, int numrow, int numcol) {
   realT *rowp;
   realT r; /*bug fix*/
   int i,k;
 
   qh_fprintf(qh, fp, 9001, "%s\n", string);
   for (i=0; i < numrow; i++) {
     rowp= rows[i];
     for (k=0; k < numcol; k++) {
       r= *rowp++;
       qh_fprintf(qh, fp, 9002, "%6.3g ", r);
     }
     qh_fprintf(qh, fp, 9003, "\n");
   }
 } /* printmatrix */
 
 
 /*---------------------------------
 
   qh_printpoints(qh, fp, string, points )
     print pointids to fp for a set of points
     if string, prints string and 'p' point ids
 */
 void qh_printpoints(qhT *qh, FILE *fp, const char *string, setT *points) {
   pointT *point, **pointp;
 
   if (string) {
     qh_fprintf(qh, fp, 9004, "%s", string);
     FOREACHpoint_(points)
       qh_fprintf(qh, fp, 9005, " p%d", qh_pointid(qh, point));
     qh_fprintf(qh, fp, 9006, "\n");
   }else {
     FOREACHpoint_(points)
       qh_fprintf(qh, fp, 9007, " %d", qh_pointid(qh, point));
     qh_fprintf(qh, fp, 9008, "\n");
   }
 } /* printpoints */
 
 
 /*---------------------------------
 
   qh_projectinput(qh)
     project input points using qh.lower_bound/upper_bound and qh->DELAUNAY
     if qh.lower_bound[k]=qh.upper_bound[k]= 0,
       removes dimension k
     if halfspace intersection
       removes dimension k from qh.feasible_point
     input points in qh->first_point, num_points, input_dim
 
   returns:
     new point array in qh->first_point of qh->hull_dim coordinates
     sets qh->POINTSmalloc
     if qh->DELAUNAY
       projects points to paraboloid
       lowbound/highbound is also projected
     if qh->ATinfinity
       adds point "at-infinity"
     if qh->POINTSmalloc
       frees old point array
 
   notes:
     checks that qh.hull_dim agrees with qh.input_dim, PROJECTinput, and DELAUNAY
 
 
   design:
     sets project[k] to -1 (delete), 0 (keep), 1 (add for Delaunay)
     determines newdim and newnum for qh->hull_dim and qh->num_points
     projects points to newpoints
     projects qh.lower_bound to itself
     projects qh.upper_bound to itself
     if qh->DELAUNAY
       if qh->ATINFINITY
         projects points to paraboloid
         computes "infinity" point as vertex average and 10% above all points
       else
         uses qh_setdelaunay to project points to paraboloid
 */
 void qh_projectinput(qhT *qh) {
   int k,i;
   int newdim= qh->input_dim, newnum= qh->num_points;
   signed char *project;
   int size= (qh->input_dim+1)*sizeof(*project);
   pointT *newpoints, *coord, *infinity;
   realT paraboloid, maxboloid= 0;
 
   project= (signed char*)qh_memalloc(qh, size);
   memset((char*)project, 0, (size_t)size);
   for (k=0; k < qh->input_dim; k++) {   /* skip Delaunay bound */
     if (qh->lower_bound[k] == 0 && qh->upper_bound[k] == 0) {
       project[k]= -1;
       newdim--;
     }
   }
   if (qh->DELAUNAY) {
     project[k]= 1;
     newdim++;
     if (qh->ATinfinity)
       newnum++;
   }
   if (newdim != qh->hull_dim) {
     qh_fprintf(qh, qh->ferr, 6015, "qhull internal error (qh_projectinput): dimension after projection %d != hull_dim %d\n", newdim, qh->hull_dim);
     qh_errexit(qh, qh_ERRqhull, NULL, NULL);
   }
   if (!(newpoints=(coordT*)qh_malloc(newnum*newdim*sizeof(coordT)))){
     qh_fprintf(qh, qh->ferr, 6016, "qhull error: insufficient memory to project %d points\n",
            qh->num_points);
     qh_errexit(qh, qh_ERRmem, NULL, NULL);
   }
   qh_projectpoints(qh, project, qh->input_dim+1, qh->first_point,
                     qh->num_points, qh->input_dim, newpoints, newdim);
   trace1((qh, qh->ferr, 1003, "qh_projectinput: updating lower and upper_bound\n"));
   qh_projectpoints(qh, project, qh->input_dim+1, qh->lower_bound,
                     1, qh->input_dim+1, qh->lower_bound, newdim+1);
   qh_projectpoints(qh, project, qh->input_dim+1, qh->upper_bound,
                     1, qh->input_dim+1, qh->upper_bound, newdim+1);
   if (qh->HALFspace) {
     if (!qh->feasible_point) {
       qh_fprintf(qh, qh->ferr, 6017, "qhull internal error (qh_projectinput): HALFspace defined without qh.feasible_point\n");
       qh_errexit(qh, qh_ERRqhull, NULL, NULL);
     }
     qh_projectpoints(qh, project, qh->input_dim, qh->feasible_point,
                       1, qh->input_dim, qh->feasible_point, newdim);
   }
   qh_memfree(qh, project, (qh->input_dim+1)*sizeof(*project));
   if (qh->POINTSmalloc)
     qh_free(qh->first_point);
   qh->first_point= newpoints;
   qh->POINTSmalloc= True;
   if (qh->DELAUNAY && qh->ATinfinity) {
     coord= qh->first_point;
     infinity= qh->first_point + qh->hull_dim * qh->num_points;
     for (k=qh->hull_dim-1; k--; )
       infinity[k]= 0.0;
     for (i=qh->num_points; i--; ) {
       paraboloid= 0.0;
       for (k=0; k < qh->hull_dim-1; k++) {
         paraboloid += *coord * *coord;
         infinity[k] += *coord;
         coord++;
       }
       *(coord++)= paraboloid;
       maximize_(maxboloid, paraboloid);
     }
     /* coord == infinity */
     for (k=qh->hull_dim-1; k--; )
       *(coord++) /= qh->num_points;
     *(coord++)= maxboloid * 1.1;
     qh->num_points++;
     trace0((qh, qh->ferr, 9, "qh_projectinput: projected points to paraboloid for Delaunay\n"));
   }else if (qh->DELAUNAY)  /* !qh->ATinfinity */
     qh_setdelaunay(qh, qh->hull_dim, qh->num_points, qh->first_point);
 } /* projectinput */
 
 
 /*---------------------------------
 
   qh_projectpoints(qh, project, n, points, numpoints, dim, newpoints, newdim )
     project points/numpoints/dim to newpoints/newdim
     if project[k] == -1
       delete dimension k
     if project[k] == 1
       add dimension k by duplicating previous column
     n is size of project
 
   notes:
     newpoints may be points if only adding dimension at end
 
   design:
     check that 'project' and 'newdim' agree
     for each dimension
       if project == -1
         skip dimension
       else
         determine start of column in newpoints
         determine start of column in points
           if project == +1, duplicate previous column
         copy dimension (column) from points to newpoints
 */
 void qh_projectpoints(qhT *qh, signed char *project, int n, realT *points,
         int numpoints, int dim, realT *newpoints, int newdim) {
   int testdim= dim, oldk=0, newk=0, i,j=0,k;
   realT *newp, *oldp;
 
   for (k=0; k < n; k++)
     testdim += project[k];
   if (testdim != newdim) {
     qh_fprintf(qh, qh->ferr, 6018, "qhull internal error (qh_projectpoints): newdim %d should be %d after projection\n",
       newdim, testdim);
     qh_errexit(qh, qh_ERRqhull, NULL, NULL);
   }
   for (j=0; j= dim)
           continue;
         oldp= points+oldk;
       }else
         oldp= points+oldk++;
       for (i=numpoints; i--; ) {
         *newp= *oldp;
         newp += newdim;
         oldp += dim;
       }
     }
     if (oldk >= dim)
       break;
   }
   trace1((qh, qh->ferr, 1004, "qh_projectpoints: projected %d points from dim %d to dim %d\n",
     numpoints, dim, newdim));
 } /* projectpoints */
 
 
 /*---------------------------------
 
   qh_rotateinput(qh, rows )
     rotate input using row matrix
     input points given by qh->first_point, num_points, hull_dim
     assumes rows[dim] is a scratch buffer
     if qh->POINTSmalloc, overwrites input points, else mallocs a new array
 
   returns:
     rotated input
     sets qh->POINTSmalloc
 
   design:
     see qh_rotatepoints
 */
 void qh_rotateinput(qhT *qh, realT **rows) {
 
   if (!qh->POINTSmalloc) {
     qh->first_point= qh_copypoints(qh, qh->first_point, qh->num_points, qh->hull_dim);
     qh->POINTSmalloc= True;
   }
   qh_rotatepoints(qh, qh->first_point, qh->num_points, qh->hull_dim, rows);
 }  /* rotateinput */
 
 /*---------------------------------
 
   qh_rotatepoints(qh, points, numpoints, dim, row )
     rotate numpoints points by a d-dim row matrix
     assumes rows[dim] is a scratch buffer
 
   returns:
     rotated points in place
 
   design:
     for each point
       for each coordinate
         use row[dim] to compute partial inner product
       for each coordinate
         rotate by partial inner product
 */
 void qh_rotatepoints(qhT *qh, realT *points, int numpoints, int dim, realT **row) {
   realT *point, *rowi, *coord= NULL, sum, *newval;
   int i,j,k;
 
   if (qh->IStracing >= 1)
     qh_printmatrix(qh, qh->ferr, "qh_rotatepoints: rotate points by", row, dim, dim);
   for (point= points, j= numpoints; j--; point += dim) {
     newval= row[dim];
     for (i=0; i < dim; i++) {
       rowi= row[i];
       coord= point;
       for (sum= 0.0, k= dim; k--; )
         sum += *rowi++ * *coord++;
       *(newval++)= sum;
     }
     for (k=dim; k--; )
       *(--coord)= *(--newval);
   }
 } /* rotatepoints */
 
 
 /*---------------------------------
 
   qh_scaleinput(qh)
     scale input points using qh->low_bound/high_bound
     input points given by qh->first_point, num_points, hull_dim
     if qh->POINTSmalloc, overwrites input points, else mallocs a new array
 
   returns:
     scales coordinates of points to low_bound[k], high_bound[k]
     sets qh->POINTSmalloc
 
   design:
     see qh_scalepoints
 */
 void qh_scaleinput(qhT *qh) {
 
   if (!qh->POINTSmalloc) {
     qh->first_point= qh_copypoints(qh, qh->first_point, qh->num_points, qh->hull_dim);
     qh->POINTSmalloc= True;
   }
   qh_scalepoints(qh, qh->first_point, qh->num_points, qh->hull_dim,
        qh->lower_bound, qh->upper_bound);
 }  /* scaleinput */
 
 /*---------------------------------
 
   qh_scalelast(qh, points, numpoints, dim, low, high, newhigh )
     scale last coordinate to [0,m] for Delaunay triangulations
     input points given by points, numpoints, dim
 
   returns:
     changes scale of last coordinate from [low, high] to [0, newhigh]
     overwrites last coordinate of each point
     saves low/high/newhigh in qh.last_low, etc. for qh_setdelaunay()
 
   notes:
     when called by qh_setdelaunay, low/high may not match actual data
 
   design:
     compute scale and shift factors
     apply to last coordinate of each point
 */
 void qh_scalelast(qhT *qh, coordT *points, int numpoints, int dim, coordT low,
                    coordT high, coordT newhigh) {
   realT scale, shift;
   coordT *coord;
   int i;
   boolT nearzero= False;
 
   trace4((qh, qh->ferr, 4013, "qh_scalelast: scale last coordinate from [%2.2g, %2.2g] to [0,%2.2g]\n",
     low, high, newhigh));
   qh->last_low= low;
   qh->last_high= high;
   qh->last_newhigh= newhigh;
   scale= qh_divzero(qh, newhigh, high - low,
                   qh->MINdenom_1, &nearzero);
   if (nearzero) {
     if (qh->DELAUNAY)
       qh_fprintf(qh, qh->ferr, 6019, "qhull input error: can not scale last coordinate.  Input is cocircular\n   or cospherical.   Use option 'Qz' to add a point at infinity.\n");
     else
       qh_fprintf(qh, qh->ferr, 6020, "qhull input error: can not scale last coordinate.  New bounds [0, %2.2g] are too wide for\nexisting bounds [%2.2g, %2.2g] (width %2.2g)\n",
                 newhigh, low, high, high-low);
     qh_errexit(qh, qh_ERRinput, NULL, NULL);
   }
   shift= - low * newhigh / (high-low);
   coord= points + dim - 1;
   for (i=numpoints; i--; coord += dim)
     *coord= *coord * scale + shift;
 } /* scalelast */
 
 /*---------------------------------
 
   qh_scalepoints(qh, points, numpoints, dim, newlows, newhighs )
     scale points to new lowbound and highbound
     retains old bound when newlow= -REALmax or newhigh= +REALmax
 
   returns:
     scaled points
     overwrites old points
 
   design:
     for each coordinate
       compute current low and high bound
       compute scale and shift factors
       scale all points
       enforce new low and high bound for all points
 */
 void qh_scalepoints(qhT *qh, pointT *points, int numpoints, int dim,
         realT *newlows, realT *newhighs) {
   int i,k;
   realT shift, scale, *coord, low, high, newlow, newhigh, mincoord, maxcoord;
   boolT nearzero= False;
 
   for (k=0; k < dim; k++) {
     newhigh= newhighs[k];
     newlow= newlows[k];
     if (newhigh > REALmax/2 && newlow < -REALmax/2)
       continue;
     low= REALmax;
     high= -REALmax;
     for (i=numpoints, coord=points+k; i--; coord += dim) {
       minimize_(low, *coord);
       maximize_(high, *coord);
     }
     if (newhigh > REALmax/2)
       newhigh= high;
     if (newlow < -REALmax/2)
       newlow= low;
     if (qh->DELAUNAY && k == dim-1 && newhigh < newlow) {
       qh_fprintf(qh, qh->ferr, 6021, "qhull input error: 'Qb%d' or 'QB%d' inverts paraboloid since high bound %.2g < low bound %.2g\n",
                k, k, newhigh, newlow);
       qh_errexit(qh, qh_ERRinput, NULL, NULL);
     }
     scale= qh_divzero(qh, newhigh - newlow, high - low,
                   qh->MINdenom_1, &nearzero);
     if (nearzero) {
       qh_fprintf(qh, qh->ferr, 6022, "qhull input error: %d'th dimension's new bounds [%2.2g, %2.2g] too wide for\nexisting bounds [%2.2g, %2.2g]\n",
               k, newlow, newhigh, low, high);
       qh_errexit(qh, qh_ERRinput, NULL, NULL);
     }
     shift= (newlow * high - low * newhigh)/(high-low);
     coord= points+k;
     for (i=numpoints; i--; coord += dim)
       *coord= *coord * scale + shift;
     coord= points+k;
     if (newlow < newhigh) {
       mincoord= newlow;
       maxcoord= newhigh;
     }else {
       mincoord= newhigh;
       maxcoord= newlow;
     }
     for (i=numpoints; i--; coord += dim) {
       minimize_(*coord, maxcoord);  /* because of roundoff error */
       maximize_(*coord, mincoord);
     }
     trace0((qh, qh->ferr, 10, "qh_scalepoints: scaled %d'th coordinate [%2.2g, %2.2g] to [%.2g, %.2g] for %d points by %2.2g and shifted %2.2g\n",
       k, low, high, newlow, newhigh, numpoints, scale, shift));
   }
 } /* scalepoints */
 
 
 /*---------------------------------
 
   qh_setdelaunay(qh, dim, count, points )
     project count points to dim-d paraboloid for Delaunay triangulation
 
     dim is one more than the dimension of the input set
     assumes dim is at least 3 (i.e., at least a 2-d Delaunay triangulation)
 
     points is a dim*count realT array.  The first dim-1 coordinates
     are the coordinates of the first input point.  array[dim] is
     the first coordinate of the second input point.  array[2*dim] is
     the first coordinate of the third input point.
 
     if qh.last_low defined (i.e., 'Qbb' called qh_scalelast)
       calls qh_scalelast to scale the last coordinate the same as the other points
 
   returns:
     for each point
       sets point[dim-1] to sum of squares of coordinates
     scale points to 'Qbb' if needed
 
   notes:
     to project one point, use
       qh_setdelaunay(qh, qh->hull_dim, 1, point)
 
     Do not use options 'Qbk', 'QBk', or 'QbB' since they scale
     the coordinates after the original projection.
 
 */
 void qh_setdelaunay(qhT *qh, int dim, int count, pointT *points) {
   int i, k;
   coordT *coordp, coord;
   realT paraboloid;
 
   trace0((qh, qh->ferr, 11, "qh_setdelaunay: project %d points to paraboloid for Delaunay triangulation\n", count));
   coordp= points;
   for (i=0; i < count; i++) {
     coord= *coordp++;
     paraboloid= coord*coord;
     for (k=dim-2; k--; ) {
       coord= *coordp++;
       paraboloid += coord*coord;
     }
     *coordp++ = paraboloid;
   }
   if (qh->last_low < REALmax/2)
     qh_scalelast(qh, points, count, dim, qh->last_low, qh->last_high, qh->last_newhigh);
 } /* setdelaunay */
 
 
 /*---------------------------------
 
   qh_sethalfspace(qh, dim, coords, nextp, normal, offset, feasible )
     set point to dual of halfspace relative to feasible point
     halfspace is normal coefficients and offset.
 
   returns:
     false if feasible point is outside of hull (error message already reported)
     overwrites coordinates for point at dim coords
     nextp= next point (coords)
 
   design:
     compute distance from feasible point to halfspace
     divide each normal coefficient by -dist
 */
 boolT qh_sethalfspace(qhT *qh, int dim, coordT *coords, coordT **nextp,
          coordT *normal, coordT *offset, coordT *feasible) {
   coordT *normp= normal, *feasiblep= feasible, *coordp= coords;
   realT dist;
   realT r; /*bug fix*/
   int k;
   boolT zerodiv;
 
   dist= *offset;
   for (k=dim; k--; )
     dist += *(normp++) * *(feasiblep++);
   if (dist > 0)
     goto LABELerroroutside;
   normp= normal;
   if (dist < -qh->MINdenom) {
     for (k=dim; k--; )
       *(coordp++)= *(normp++) / -dist;
   }else {
     for (k=dim; k--; ) {
       *(coordp++)= qh_divzero(qh, *(normp++), -dist, qh->MINdenom_1, &zerodiv);
       if (zerodiv)
         goto LABELerroroutside;
     }
   }
   *nextp= coordp;
   if (qh->IStracing >= 4) {
     qh_fprintf(qh, qh->ferr, 8021, "qh_sethalfspace: halfspace at offset %6.2g to point: ", *offset);
     for (k=dim, coordp=coords; k--; ) {
       r= *coordp++;
       qh_fprintf(qh, qh->ferr, 8022, " %6.2g", r);
     }
     qh_fprintf(qh, qh->ferr, 8023, "\n");
   }
   return True;
 LABELerroroutside:
   feasiblep= feasible;
   normp= normal;
   qh_fprintf(qh, qh->ferr, 6023, "qhull input error: feasible point is not clearly inside halfspace\nfeasible point: ");
   for (k=dim; k--; )
     qh_fprintf(qh, qh->ferr, 8024, qh_REAL_1, r=*(feasiblep++));
   qh_fprintf(qh, qh->ferr, 8025, "\n     halfspace: ");
   for (k=dim; k--; )
     qh_fprintf(qh, qh->ferr, 8026, qh_REAL_1, r=*(normp++));
   qh_fprintf(qh, qh->ferr, 8027, "\n     at offset: ");
   qh_fprintf(qh, qh->ferr, 8028, qh_REAL_1, *offset);
   qh_fprintf(qh, qh->ferr, 8029, " and distance: ");
   qh_fprintf(qh, qh->ferr, 8030, qh_REAL_1, dist);
   qh_fprintf(qh, qh->ferr, 8031, "\n");
   return False;
 } /* sethalfspace */
 
 /*---------------------------------
 
   qh_sethalfspace_all(qh, dim, count, halfspaces, feasible )
     generate dual for halfspace intersection with feasible point
     array of count halfspaces
       each halfspace is normal coefficients followed by offset
       the origin is inside the halfspace if the offset is negative
 
   returns:
     malloc'd array of count X dim-1 points
 
   notes:
     call before qh_init_B or qh_initqhull_globals
     unused/untested code: please email bradb@shore.net if this works ok for you
     If using option 'Fp', also set qh->feasible_point. It is a malloc'd array
       that is freed by qh_freebuffers.
 
   design:
     see qh_sethalfspace
 */
 coordT *qh_sethalfspace_all(qhT *qh, int dim, int count, coordT *halfspaces, pointT *feasible) {
   int i, newdim;
   pointT *newpoints;
   coordT *coordp, *normalp, *offsetp;
 
   trace0((qh, qh->ferr, 12, "qh_sethalfspace_all: compute dual for halfspace intersection\n"));
   newdim= dim - 1;
   if (!(newpoints=(coordT*)qh_malloc(count*newdim*sizeof(coordT)))){
     qh_fprintf(qh, qh->ferr, 6024, "qhull error: insufficient memory to compute dual of %d halfspaces\n",
           count);
     qh_errexit(qh, qh_ERRmem, NULL, NULL);
   }
   coordp= newpoints;
   normalp= halfspaces;
   for (i=0; i < count; i++) {
     offsetp= normalp + newdim;
     if (!qh_sethalfspace(qh, newdim, coordp, &coordp, normalp, offsetp, feasible)) {
       qh_fprintf(qh, qh->ferr, 8032, "The halfspace was at index %d\n", i);
       qh_errexit(qh, qh_ERRinput, NULL, NULL);
     }
     normalp= offsetp + 1;
   }
   return newpoints;
 } /* sethalfspace_all */
 
 
 /*---------------------------------
 
   qh_sharpnewfacets(qh)
 
   returns:
     true if could be an acute angle (facets in different quadrants)
 
   notes:
     for qh_findbest
 
   design:
     for all facets on qh.newfacet_list
       if two facets are in different quadrants
         set issharp
 */
 boolT qh_sharpnewfacets(qhT *qh) {
   facetT *facet;
   boolT issharp = False;
   int *quadrant, k;
 
   quadrant= (int*)qh_memalloc(qh, qh->hull_dim * sizeof(int));
   FORALLfacet_(qh->newfacet_list) {
     if (facet == qh->newfacet_list) {
       for (k=qh->hull_dim; k--; )
         quadrant[ k]= (facet->normal[ k] > 0);
     }else {
       for (k=qh->hull_dim; k--; ) {
         if (quadrant[ k] != (facet->normal[ k] > 0)) {
           issharp= True;
           break;
         }
       }
     }
     if (issharp)
       break;
   }
   qh_memfree(qh, quadrant, qh->hull_dim * sizeof(int));
   trace3((qh, qh->ferr, 3001, "qh_sharpnewfacets: %d\n", issharp));
   return issharp;
 } /* sharpnewfacets */
 
 /*---------------------------------
 
   qh_voronoi_center(qh, dim, points )
     return Voronoi center for a set of points
     dim is the orginal dimension of the points
     gh.gm_matrix/qh.gm_row are scratch buffers
 
   returns:
     center as a temporary point
     if non-simplicial,
       returns center for max simplex of points
 
   notes:
     from Bowyer & Woodwark, A Programmer's Geometry, 1983, p. 65
 
   design:
     if non-simplicial
       determine max simplex for points
     translate point0 of simplex to origin
     compute sum of squares of diagonal
     compute determinate
     compute Voronoi center (see Bowyer & Woodwark)
 */
 pointT *qh_voronoi_center(qhT *qh, int dim, setT *points) {
   pointT *point, **pointp, *point0;
   pointT *center= (pointT*)qh_memalloc(qh, qh->center_size);
   setT *simplex;
   int i, j, k, size= qh_setsize(qh, points);
   coordT *gmcoord;
   realT *diffp, sum2, *sum2row, *sum2p, det, factor;
   boolT nearzero, infinite;
 
   if (size == dim+1)
     simplex= points;
   else if (size < dim+1) {
     qh_fprintf(qh, qh->ferr, 6025, "qhull internal error (qh_voronoi_center):\n  need at least %d points to construct a Voronoi center\n",
              dim+1);
     qh_errexit(qh, qh_ERRqhull, NULL, NULL);
     simplex= points;  /* never executed -- avoids warning */
   }else {
     simplex= qh_settemp(qh, dim+1);
     qh_maxsimplex(qh, dim, points, NULL, 0, &simplex);
   }
   point0= SETfirstt_(simplex, pointT);
   gmcoord= qh->gm_matrix;
   for (k=0; k < dim; k++) {
     qh->gm_row[k]= gmcoord;
     FOREACHpoint_(simplex) {
       if (point != point0)
         *(gmcoord++)= point[k] - point0[k];
     }
   }
   sum2row= gmcoord;
   for (i=0; i < dim; i++) {
     sum2= 0.0;
     for (k=0; k < dim; k++) {
       diffp= qh->gm_row[k] + i;
       sum2 += *diffp * *diffp;
     }
     *(gmcoord++)= sum2;
   }
   det= qh_determinant(qh, qh->gm_row, dim, &nearzero);
   factor= qh_divzero(qh, 0.5, det, qh->MINdenom, &infinite);
   if (infinite) {
     for (k=dim; k--; )
       center[k]= qh_INFINITE;
     if (qh->IStracing)
       qh_printpoints(qh, qh->ferr, "qh_voronoi_center: at infinity for ", simplex);
   }else {
     for (i=0; i < dim; i++) {
       gmcoord= qh->gm_matrix;
       sum2p= sum2row;
       for (k=0; k < dim; k++) {
         qh->gm_row[k]= gmcoord;
         if (k == i) {
           for (j=dim; j--; )
             *(gmcoord++)= *sum2p++;
         }else {
           FOREACHpoint_(simplex) {
             if (point != point0)
               *(gmcoord++)= point[k] - point0[k];
           }
         }
       }
       center[i]= qh_determinant(qh, qh->gm_row, dim, &nearzero)*factor + point0[i];
     }
 #ifndef qh_NOtrace
     if (qh->IStracing >= 3) {
       qh_fprintf(qh, qh->ferr, 8033, "qh_voronoi_center: det %2.2g factor %2.2g ", det, factor);
       qh_printmatrix(qh, qh->ferr, "center:", ¢er, 1, dim);
       if (qh->IStracing >= 5) {
         qh_printpoints(qh, qh->ferr, "points", simplex);
         FOREACHpoint_(simplex)
           qh_fprintf(qh, qh->ferr, 8034, "p%d dist %.2g, ", qh_pointid(qh, point),
                    qh_pointdist(qh, point, center, dim));
         qh_fprintf(qh, qh->ferr, 8035, "\n");
       }
     }
 #endif
   }
   if (simplex != points)
     qh_settempfree(qh, &simplex);
   return center;
 } /* voronoi_center */
 
diff --git a/src/libqhullr/geom_r.c b/src/libqhullr/geom_r.c
index 93605c3..085662c 100644
--- a/src/libqhullr/geom_r.c
+++ b/src/libqhullr/geom_r.c
@@ -1,1234 +1,1234 @@
 /*
  ---------------------------------
 
-   geom.c
+   geom_r.c
    geometric routines of qhull
 
-   see qh-geom.htm and geom.h
+   see qh-geom.htm and geom_r.h
 
    Copyright (c) 1993-2014 The Geometry Center.
-   $Id: //main/2011/qhull/src/libqhullr/geom_r.c#4 $$Change: 1663 $
-   $DateTime: 2014/01/19 17:59:16 $$Author: bbarber $
+   $Id: //main/2011/qhull/src/libqhullr/geom_r.c#6 $$Change: 1797 $
+   $DateTime: 2014/12/15 17:23:41 $$Author: bbarber $
 
-   infrequent code goes into geom2.c
+   infrequent code goes into geom2_r.c
 */
 
-#include "qhull_r.h"
+#include "qhull_ra.h"
 
 /*---------------------------------
 
   qh_distplane(qh, point, facet, dist )
     return distance from point to facet
 
   returns:
     dist
     if qh.RANDOMdist, joggles result
 
   notes:
     dist > 0 if point is above facet (i.e., outside)
     does not error (for qh_sortfacets, qh_outerinner)
 
   see:
-    qh_distnorm in geom2.c
-    qh_distplane [geom.c], QhullFacet::distance, and QhullHyperplane::distance are copies
+    qh_distnorm in geom2_r.c
+    qh_distplane [geom_r.c], QhullFacet::distance, and QhullHyperplane::distance are copies
 */
 void qh_distplane(qhT *qh, pointT *point, facetT *facet, realT *dist) {
   coordT *normal= facet->normal, *coordp, randr;
   int k;
 
   switch (qh->hull_dim){
   case 2:
     *dist= facet->offset + point[0] * normal[0] + point[1] * normal[1];
     break;
   case 3:
     *dist= facet->offset + point[0] * normal[0] + point[1] * normal[1] + point[2] * normal[2];
     break;
   case 4:
     *dist= facet->offset+point[0]*normal[0]+point[1]*normal[1]+point[2]*normal[2]+point[3]*normal[3];
     break;
   case 5:
     *dist= facet->offset+point[0]*normal[0]+point[1]*normal[1]+point[2]*normal[2]+point[3]*normal[3]+point[4]*normal[4];
     break;
   case 6:
     *dist= facet->offset+point[0]*normal[0]+point[1]*normal[1]+point[2]*normal[2]+point[3]*normal[3]+point[4]*normal[4]+point[5]*normal[5];
     break;
   case 7:
     *dist= facet->offset+point[0]*normal[0]+point[1]*normal[1]+point[2]*normal[2]+point[3]*normal[3]+point[4]*normal[4]+point[5]*normal[5]+point[6]*normal[6];
     break;
   case 8:
     *dist= facet->offset+point[0]*normal[0]+point[1]*normal[1]+point[2]*normal[2]+point[3]*normal[3]+point[4]*normal[4]+point[5]*normal[5]+point[6]*normal[6]+point[7]*normal[7];
     break;
   default:
     *dist= facet->offset;
     coordp= point;
     for (k=qh->hull_dim; k--; )
       *dist += *coordp++ * *normal++;
     break;
   }
   zinc_(Zdistplane);
   if (!qh->RANDOMdist && qh->IStracing < 4)
     return;
   if (qh->RANDOMdist) {
     randr= qh_RANDOMint;
     *dist += (2.0 * randr / qh_RANDOMmax - 1.0) *
       qh->RANDOMfactor * qh->MAXabs_coord;
   }
   if (qh->IStracing >= 4) {
     qh_fprintf(qh, qh->ferr, 8001, "qh_distplane: ");
     qh_fprintf(qh, qh->ferr, 8002, qh_REAL_1, *dist);
     qh_fprintf(qh, qh->ferr, 8003, "from p%d to f%d\n", qh_pointid(qh, point), facet->id);
   }
   return;
 } /* distplane */
 
 
 /*---------------------------------
 
   qh_findbest(qh, point, startfacet, bestoutside, qh_ISnewfacets, qh_NOupper, dist, isoutside, numpart )
     find facet that is furthest below a point
     for upperDelaunay facets
       returns facet only if !qh_NOupper and clearly above
 
   input:
     starts search at 'startfacet' (can not be flipped)
     if !bestoutside(qh_ALL), stops at qh.MINoutside
 
   returns:
     best facet (reports error if NULL)
     early out if isoutside defined and bestdist > qh.MINoutside
     dist is distance to facet
     isoutside is true if point is outside of facet
     numpart counts the number of distance tests
 
   see also:
     qh_findbestnew()
 
   notes:
     If merging (testhorizon), searches horizon facets of coplanar best facets because
     after qh_distplane, this and qh_partitionpoint are the most expensive in 3-d
       avoid calls to distplane, function calls, and real number operations.
     caller traces result
     Optimized for outside points.   Tried recording a search set for qh_findhorizon.
     Made code more complicated.
 
   when called by qh_partitionvisible():
     indicated by qh_ISnewfacets
     qh.newfacet_list is list of simplicial, new facets
     qh_findbestnew set if qh_sharpnewfacets returns True (to use qh_findbestnew)
     qh.bestfacet_notsharp set if qh_sharpnewfacets returns False
 
   when called by qh_findfacet(), qh_partitionpoint(), qh_partitioncoplanar(),
                  qh_check_bestdist(), qh_addpoint()
     indicated by !qh_ISnewfacets
     returns best facet in neighborhood of given facet
       this is best facet overall if dist > -   qh.MAXcoplanar
         or hull has at least a "spherical" curvature
 
   design:
     initialize and test for early exit
     repeat while there are better facets
       for each neighbor of facet
         exit if outside facet found
         test for better facet
     if point is inside and partitioning
       test for new facets with a "sharp" intersection
       if so, future calls go to qh_findbestnew()
     test horizon facets
 */
 facetT *qh_findbest(qhT *qh, pointT *point, facetT *startfacet,
                      boolT bestoutside, boolT isnewfacets, boolT noupper,
                      realT *dist, boolT *isoutside, int *numpart) {
   realT bestdist= -REALmax/2 /* avoid underflow */;
   facetT *facet, *neighbor, **neighborp;
   facetT *bestfacet= NULL, *lastfacet= NULL;
   int oldtrace= qh->IStracing;
   unsigned int visitid= ++qh->visit_id;
   int numpartnew=0;
   boolT testhorizon = True; /* needed if precise, e.g., rbox c D6 | qhull Q0 Tv */
 
   zinc_(Zfindbest);
   if (qh->IStracing >= 3 || (qh->TRACElevel && qh->TRACEpoint >= 0 && qh->TRACEpoint == qh_pointid(qh, point))) {
     if (qh->TRACElevel > qh->IStracing)
       qh->IStracing= qh->TRACElevel;
     qh_fprintf(qh, qh->ferr, 8004, "qh_findbest: point p%d starting at f%d isnewfacets? %d, unless %d exit if > %2.2g\n",
              qh_pointid(qh, point), startfacet->id, isnewfacets, bestoutside, qh->MINoutside);
     qh_fprintf(qh, qh->ferr, 8005, "  testhorizon? %d noupper? %d", testhorizon, noupper);
     qh_fprintf(qh, qh->ferr, 8006, "  Last point added was p%d.", qh->furthest_id);
     qh_fprintf(qh, qh->ferr, 8007, "  Last merge was #%d.  max_outside %2.2g\n", zzval_(Ztotmerge), qh->max_outside);
   }
   if (isoutside)
     *isoutside= True;
   if (!startfacet->flipped) {  /* test startfacet */
     *numpart= 1;
     qh_distplane(qh, point, startfacet, dist);  /* this code is duplicated below */
     if (!bestoutside && *dist >= qh->MINoutside
     && (!startfacet->upperdelaunay || !noupper)) {
       bestfacet= startfacet;
       goto LABELreturn_best;
     }
     bestdist= *dist;
     if (!startfacet->upperdelaunay) {
       bestfacet= startfacet;
     }
   }else
     *numpart= 0;
   startfacet->visitid= visitid;
   facet= startfacet;
   while (facet) {
     trace4((qh, qh->ferr, 4001, "qh_findbest: neighbors of f%d, bestdist %2.2g f%d\n",
                 facet->id, bestdist, getid_(bestfacet)));
     lastfacet= facet;
     FOREACHneighbor_(facet) {
       if (!neighbor->newfacet && isnewfacets)
         continue;
       if (neighbor->visitid == visitid)
         continue;
       neighbor->visitid= visitid;
       if (!neighbor->flipped) {  /* code duplicated above */
         (*numpart)++;
         qh_distplane(qh, point, neighbor, dist);
         if (*dist > bestdist) {
           if (!bestoutside && *dist >= qh->MINoutside
           && (!neighbor->upperdelaunay || !noupper)) {
             bestfacet= neighbor;
             goto LABELreturn_best;
           }
           if (!neighbor->upperdelaunay) {
             bestfacet= neighbor;
             bestdist= *dist;
             break; /* switch to neighbor */
           }else if (!bestfacet) {
             bestdist= *dist;
             break; /* switch to neighbor */
           }
         } /* end of *dist>bestdist */
       } /* end of !flipped */
     } /* end of FOREACHneighbor */
     facet= neighbor;  /* non-NULL only if *dist>bestdist */
   } /* end of while facet (directed search) */
   if (isnewfacets) {
     if (!bestfacet) {
       bestdist= -REALmax/2;
       bestfacet= qh_findbestnew(qh, point, startfacet->next, &bestdist, bestoutside, isoutside, &numpartnew);
       testhorizon= False; /* qh_findbestnew calls qh_findbesthorizon */
     }else if (!qh->findbest_notsharp && bestdist < - qh->DISTround) {
       if (qh_sharpnewfacets(qh)) {
         /* seldom used, qh_findbestnew will retest all facets */
         zinc_(Zfindnewsharp);
         bestfacet= qh_findbestnew(qh, point, bestfacet, &bestdist, bestoutside, isoutside, &numpartnew);
         testhorizon= False; /* qh_findbestnew calls qh_findbesthorizon */
         qh->findbestnew= True;
       }else
         qh->findbest_notsharp= True;
     }
   }
   if (!bestfacet)
     bestfacet= qh_findbestlower(qh, lastfacet, point, &bestdist, numpart);
   if (testhorizon)
     bestfacet= qh_findbesthorizon(qh, !qh_IScheckmax, point, bestfacet, noupper, &bestdist, &numpartnew);
   *dist= bestdist;
   if (isoutside && bestdist < qh->MINoutside)
     *isoutside= False;
 LABELreturn_best:
   zadd_(Zfindbesttot, *numpart);
   zmax_(Zfindbestmax, *numpart);
   (*numpart) += numpartnew;
   qh->IStracing= oldtrace;
   return bestfacet;
 }  /* findbest */
 
 
 /*---------------------------------
 
   qh_findbesthorizon(qh, qh_IScheckmax, point, startfacet, qh_NOupper, &bestdist, &numpart )
     search coplanar and better horizon facets from startfacet/bestdist
     ischeckmax turns off statistics and minsearch update
     all arguments must be initialized
   returns(ischeckmax):
     best facet
   returns(!ischeckmax):
     best facet that is not upperdelaunay
     allows upperdelaunay that is clearly outside
   returns:
     bestdist is distance to bestfacet
     numpart -- updates number of distance tests
 
   notes:
     no early out -- use qh_findbest() or qh_findbestnew()
     Searches coplanar or better horizon facets
 
   when called by qh_check_maxout() (qh_IScheckmax)
     startfacet must be closest to the point
       Otherwise, if point is beyond and below startfacet, startfacet may be a local minimum
       even though other facets are below the point.
     updates facet->maxoutside for good, visited facets
     may return NULL
 
     searchdist is qh.max_outside + 2 * DISTround
       + max( MINvisible('Vn'), MAXcoplanar('Un'));
     This setting is a guess.  It must be at least max_outside + 2*DISTround
     because a facet may have a geometric neighbor across a vertex
 
   design:
     for each horizon facet of coplanar best facets
       continue if clearly inside
       unless upperdelaunay or clearly outside
          update best facet
 */
 facetT *qh_findbesthorizon(qhT *qh, boolT ischeckmax, pointT* point, facetT *startfacet, boolT noupper, realT *bestdist, int *numpart) {
   facetT *bestfacet= startfacet;
   realT dist;
   facetT *neighbor, **neighborp, *facet;
   facetT *nextfacet= NULL; /* optimize last facet of coplanarfacetset */
   int numpartinit= *numpart, coplanarfacetset_size;
   unsigned int visitid= ++qh->visit_id;
   boolT newbest= False; /* for tracing */
   realT minsearch, searchdist;  /* skip facets that are too far from point */
 
   if (!ischeckmax) {
     zinc_(Zfindhorizon);
   }else {
 #if qh_MAXoutside
     if ((!qh->ONLYgood || startfacet->good) && *bestdist > startfacet->maxoutside)
       startfacet->maxoutside= *bestdist;
 #endif
   }
   searchdist= qh_SEARCHdist; /* multiple of qh.max_outside and precision constants */
   minsearch= *bestdist - searchdist;
   if (ischeckmax) {
     /* Always check coplanar facets.  Needed for RBOX 1000 s Z1 G1e-13 t996564279 | QHULL Tv */
     minimize_(minsearch, -searchdist);
   }
   coplanarfacetset_size= 0;
   facet= startfacet;
   while (True) {
     trace4((qh, qh->ferr, 4002, "qh_findbesthorizon: neighbors of f%d bestdist %2.2g f%d ischeckmax? %d noupper? %d minsearch %2.2g searchdist %2.2g\n",
                 facet->id, *bestdist, getid_(bestfacet), ischeckmax, noupper,
                 minsearch, searchdist));
     FOREACHneighbor_(facet) {
       if (neighbor->visitid == visitid)
         continue;
       neighbor->visitid= visitid;
       if (!neighbor->flipped) {
         qh_distplane(qh, point, neighbor, &dist);
         (*numpart)++;
         if (dist > *bestdist) {
           if (!neighbor->upperdelaunay || ischeckmax || (!noupper && dist >= qh->MINoutside)) {
             bestfacet= neighbor;
             *bestdist= dist;
             newbest= True;
             if (!ischeckmax) {
               minsearch= dist - searchdist;
               if (dist > *bestdist + searchdist) {
                 zinc_(Zfindjump);  /* everything in qh.coplanarfacetset at least searchdist below */
                 coplanarfacetset_size= 0;
               }
             }
           }
         }else if (dist < minsearch)
           continue;  /* if ischeckmax, dist can't be positive */
 #if qh_MAXoutside
         if (ischeckmax && dist > neighbor->maxoutside)
           neighbor->maxoutside= dist;
 #endif
       } /* end of !flipped */
       if (nextfacet) {
         if (!coplanarfacetset_size++) {
           SETfirst_(qh->coplanarfacetset)= nextfacet;
           SETtruncate_(qh->coplanarfacetset, 1);
         }else
           qh_setappend(qh, &qh->coplanarfacetset, nextfacet); /* Was needed for RBOX 1000 s W1e-13 P0 t996547055 | QHULL d Qbb Qc Tv
                                                  and RBOX 1000 s Z1 G1e-13 t996564279 | qhull Tv  */
       }
       nextfacet= neighbor;
     } /* end of EACHneighbor */
     facet= nextfacet;
     if (facet)
       nextfacet= NULL;
     else if (!coplanarfacetset_size)
       break;
     else if (!--coplanarfacetset_size) {
       facet= SETfirstt_(qh->coplanarfacetset, facetT);
       SETtruncate_(qh->coplanarfacetset, 0);
     }else
       facet= (facetT*)qh_setdellast(qh->coplanarfacetset);
   } /* while True, for each facet in qh.coplanarfacetset */
   if (!ischeckmax) {
     zadd_(Zfindhorizontot, *numpart - numpartinit);
     zmax_(Zfindhorizonmax, *numpart - numpartinit);
     if (newbest)
       zinc_(Zparthorizon);
   }
   trace4((qh, qh->ferr, 4003, "qh_findbesthorizon: newbest? %d bestfacet f%d bestdist %2.2g\n", newbest, getid_(bestfacet), *bestdist));
   return bestfacet;
 }  /* findbesthorizon */
 
 /*---------------------------------
 
   qh_findbestnew(qh, point, startfacet, dist, isoutside, numpart )
     find best newfacet for point
     searches all of qh.newfacet_list starting at startfacet
     searches horizon facets of coplanar best newfacets
     searches all facets if startfacet == qh.facet_list
   returns:
     best new or horizon facet that is not upperdelaunay
     early out if isoutside and not 'Qf'
     dist is distance to facet
     isoutside is true if point is outside of facet
     numpart is number of distance tests
 
   notes:
     Always used for merged new facets (see qh_USEfindbestnew)
     Avoids upperdelaunay facet unless (isoutside and outside)
 
     Uses qh.visit_id, qh.coplanarfacetset.
     If share visit_id with qh_findbest, coplanarfacetset is incorrect.
 
     If merging (testhorizon), searches horizon facets of coplanar best facets because
     a point maybe coplanar to the bestfacet, below its horizon facet,
     and above a horizon facet of a coplanar newfacet.  For example,
       rbox 1000 s Z1 G1e-13 | qhull
       rbox 1000 s W1e-13 P0 t992110337 | QHULL d Qbb Qc
 
     qh_findbestnew() used if
        qh_sharpnewfacets -- newfacets contains a sharp angle
        if many merges, qh_premerge found a merge, or 'Qf' (qh.findbestnew)
 
   see also:
     qh_partitionall() and qh_findbest()
 
   design:
     for each new facet starting from startfacet
       test distance from point to facet
       return facet if clearly outside
       unless upperdelaunay and a lowerdelaunay exists
          update best facet
     test horizon facets
 */
 facetT *qh_findbestnew(qhT *qh, pointT *point, facetT *startfacet,
            realT *dist, boolT bestoutside, boolT *isoutside, int *numpart) {
   realT bestdist= -REALmax/2;
   facetT *bestfacet= NULL, *facet;
   int oldtrace= qh->IStracing, i;
   unsigned int visitid= ++qh->visit_id;
   realT distoutside= 0.0;
   boolT isdistoutside; /* True if distoutside is defined */
   boolT testhorizon = True; /* needed if precise, e.g., rbox c D6 | qhull Q0 Tv */
 
   if (!startfacet) {
     if (qh->MERGING)
       qh_fprintf(qh, qh->ferr, 6001, "qhull precision error (qh_findbestnew): merging has formed and deleted a cone of new facets.  Can not continue.\n");
     else
       qh_fprintf(qh, qh->ferr, 6002, "qhull internal error (qh_findbestnew): no new facets for point p%d\n",
               qh->furthest_id);
     qh_errexit(qh, qh_ERRqhull, NULL, NULL);
   }
   zinc_(Zfindnew);
   if (qh->BESToutside || bestoutside)
     isdistoutside= False;
   else {
     isdistoutside= True;
     distoutside= qh_DISToutside; /* multiple of qh.MINoutside & qh.max_outside, see user.h */
   }
   if (isoutside)
     *isoutside= True;
   *numpart= 0;
   if (qh->IStracing >= 3 || (qh->TRACElevel && qh->TRACEpoint >= 0 && qh->TRACEpoint == qh_pointid(qh, point))) {
     if (qh->TRACElevel > qh->IStracing)
       qh->IStracing= qh->TRACElevel;
     qh_fprintf(qh, qh->ferr, 8008, "qh_findbestnew: point p%d facet f%d. Stop? %d if dist > %2.2g\n",
              qh_pointid(qh, point), startfacet->id, isdistoutside, distoutside);
     qh_fprintf(qh, qh->ferr, 8009, "  Last point added p%d visitid %d.",  qh->furthest_id, visitid);
     qh_fprintf(qh, qh->ferr, 8010, "  Last merge was #%d.\n", zzval_(Ztotmerge));
   }
   /* visit all new facets starting with startfacet, maybe qh->facet_list */
   for (i=0, facet=startfacet; i < 2; i++, facet= qh->newfacet_list) {
     FORALLfacet_(facet) {
       if (facet == startfacet && i)
         break;
       facet->visitid= visitid;
       if (!facet->flipped) {
         qh_distplane(qh, point, facet, dist);
         (*numpart)++;
         if (*dist > bestdist) {
           if (!facet->upperdelaunay || *dist >= qh->MINoutside) {
             bestfacet= facet;
             if (isdistoutside && *dist >= distoutside)
               goto LABELreturn_bestnew;
             bestdist= *dist;
           }
         }
       } /* end of !flipped */
     } /* FORALLfacet from startfacet or qh->newfacet_list */
   }
   if (testhorizon || !bestfacet)
     bestfacet= qh_findbesthorizon(qh, !qh_IScheckmax, point, bestfacet ? bestfacet : startfacet,
                                         !qh_NOupper, &bestdist, numpart);
   *dist= bestdist;
   if (isoutside && *dist < qh->MINoutside)
     *isoutside= False;
 LABELreturn_bestnew:
   zadd_(Zfindnewtot, *numpart);
   zmax_(Zfindnewmax, *numpart);
   trace4((qh, qh->ferr, 4004, "qh_findbestnew: bestfacet f%d bestdist %2.2g\n", getid_(bestfacet), *dist));
   qh->IStracing= oldtrace;
   return bestfacet;
 }  /* findbestnew */
 
 /* ============ hyperplane functions -- keep code together [?] ============ */
 
 /*---------------------------------
 
   qh_backnormal(qh, rows, numrow, numcol, sign, normal, nearzero )
     given an upper-triangular rows array and a sign,
     solve for normal equation x using back substitution over rows U
 
   returns:
      normal= x
 
      if will not be able to divzero() when normalized(qh.MINdenom_2 and qh.MINdenom_1_2),
        if fails on last row
          this means that the hyperplane intersects [0,..,1]
          sets last coordinate of normal to sign
        otherwise
          sets tail of normal to [...,sign,0,...], i.e., solves for b= [0...0]
          sets nearzero
 
   notes:
      assumes numrow == numcol-1
 
      see Golub & van Loan 4.4-9 for back substitution
 
      solves Ux=b where Ax=b and PA=LU
      b= [0,...,0,sign or 0]  (sign is either -1 or +1)
      last row of A= [0,...,0,1]
 
      1) Ly=Pb == y=b since P only permutes the 0's of   b
 
   design:
     for each row from end
       perform back substitution
       if near zero
         use qh_divzero for division
         if zero divide and not last row
           set tail of normal to 0
 */
 void qh_backnormal(qhT *qh, realT **rows, int numrow, int numcol, boolT sign,
         coordT *normal, boolT *nearzero) {
   int i, j;
   coordT *normalp, *normal_tail, *ai, *ak;
   realT diagonal;
   boolT waszero;
   int zerocol= -1;
 
   normalp= normal + numcol - 1;
   *normalp--= (sign ? -1.0 : 1.0);
   for (i=numrow; i--; ) {
     *normalp= 0.0;
     ai= rows[i] + i + 1;
     ak= normalp+1;
     for (j=i+1; j < numcol; j++)
       *normalp -= *ai++ * *ak++;
     diagonal= (rows[i])[i];
     if (fabs_(diagonal) > qh->MINdenom_2)
       *(normalp--) /= diagonal;
     else {
       waszero= False;
       *normalp= qh_divzero(qh, *normalp, diagonal, qh->MINdenom_1_2, &waszero);
       if (waszero) {
         zerocol= i;
         *(normalp--)= (sign ? -1.0 : 1.0);
         for (normal_tail= normalp+2; normal_tail < normal + numcol; normal_tail++)
           *normal_tail= 0.0;
       }else
         normalp--;
     }
   }
   if (zerocol != -1) {
     zzinc_(Zback0);
     *nearzero= True;
     trace4((qh, qh->ferr, 4005, "qh_backnormal: zero diagonal at column %d.\n", i));
     qh_precision(qh, "zero diagonal on back substitution");
   }
 } /* backnormal */
 
 /*---------------------------------
 
   qh_gausselim(qh, rows, numrow, numcol, sign )
     Gaussian elimination with partial pivoting
 
   returns:
     rows is upper triangular (includes row exchanges)
     flips sign for each row exchange
     sets nearzero if pivot[k] < qh.NEARzero[k], else clears it
 
   notes:
     if nearzero, the determinant's sign may be incorrect.
     assumes numrow <= numcol
 
   design:
     for each row
       determine pivot and exchange rows if necessary
       test for near zero
       perform gaussian elimination step
 */
 void qh_gausselim(qhT *qh, realT **rows, int numrow, int numcol, boolT *sign, boolT *nearzero) {
   realT *ai, *ak, *rowp, *pivotrow;
   realT n, pivot, pivot_abs= 0.0, temp;
   int i, j, k, pivoti, flip=0;
 
   *nearzero= False;
   for (k=0; k < numrow; k++) {
     pivot_abs= fabs_((rows[k])[k]);
     pivoti= k;
     for (i=k+1; i < numrow; i++) {
       if ((temp= fabs_((rows[i])[k])) > pivot_abs) {
         pivot_abs= temp;
         pivoti= i;
       }
     }
     if (pivoti != k) {
       rowp= rows[pivoti];
       rows[pivoti]= rows[k];
       rows[k]= rowp;
       *sign ^= 1;
       flip ^= 1;
     }
     if (pivot_abs <= qh->NEARzero[k]) {
       *nearzero= True;
       if (pivot_abs == 0.0) {   /* remainder of column == 0 */
         if (qh->IStracing >= 4) {
           qh_fprintf(qh, qh->ferr, 8011, "qh_gausselim: 0 pivot at column %d. (%2.2g < %2.2g)\n", k, pivot_abs, qh->DISTround);
           qh_printmatrix(qh, qh->ferr, "Matrix:", rows, numrow, numcol);
         }
         zzinc_(Zgauss0);
         qh_precision(qh, "zero pivot for Gaussian elimination");
         goto LABELnextcol;
       }
     }
     pivotrow= rows[k] + k;
     pivot= *pivotrow++;  /* signed value of pivot, and remainder of row */
     for (i=k+1; i < numrow; i++) {
       ai= rows[i] + k;
       ak= pivotrow;
       n= (*ai++)/pivot;   /* divzero() not needed since |pivot| >= |*ai| */
       for (j= numcol - (k+1); j--; )
         *ai++ -= n * *ak++;
     }
   LABELnextcol:
     ;
   }
   wmin_(Wmindenom, pivot_abs);  /* last pivot element */
   if (qh->IStracing >= 5)
     qh_printmatrix(qh, qh->ferr, "qh_gausselem: result", rows, numrow, numcol);
 } /* gausselim */
 
 
 /*---------------------------------
 
   qh_getangle(qh, vect1, vect2 )
     returns the dot product of two vectors
     if qh.RANDOMdist, joggles result
 
   notes:
     the angle may be > 1.0 or < -1.0 because of roundoff errors
 
 */
 realT qh_getangle(qhT *qh, pointT *vect1, pointT *vect2) {
   realT angle= 0, randr;
   int k;
 
   for (k=qh->hull_dim; k--; )
     angle += *vect1++ * *vect2++;
   if (qh->RANDOMdist) {
     randr= qh_RANDOMint;
     angle += (2.0 * randr / qh_RANDOMmax - 1.0) *
       qh->RANDOMfactor;
   }
   trace4((qh, qh->ferr, 4006, "qh_getangle: %2.2g\n", angle));
   return(angle);
 } /* getangle */
 
 
 /*---------------------------------
 
   qh_getcenter(qh, vertices )
     returns arithmetic center of a set of vertices as a new point
 
   notes:
     allocates point array for center
 */
 pointT *qh_getcenter(qhT *qh, setT *vertices) {
   int k;
   pointT *center, *coord;
   vertexT *vertex, **vertexp;
   int count= qh_setsize(qh, vertices);
 
   if (count < 2) {
     qh_fprintf(qh, qh->ferr, 6003, "qhull internal error (qh_getcenter): not defined for %d points\n", count);
     qh_errexit(qh, qh_ERRqhull, NULL, NULL);
   }
   center= (pointT *)qh_memalloc(qh, qh->normal_size);
   for (k=0; k < qh->hull_dim; k++) {
     coord= center+k;
     *coord= 0.0;
     FOREACHvertex_(vertices)
       *coord += vertex->point[k];
     *coord /= count;
   }
   return(center);
 } /* getcenter */
 
 
 /*---------------------------------
 
   qh_getcentrum(qh, facet )
     returns the centrum for a facet as a new point
 
   notes:
     allocates the centrum
 */
 pointT *qh_getcentrum(qhT *qh, facetT *facet) {
   realT dist;
   pointT *centrum, *point;
 
   point= qh_getcenter(qh, facet->vertices);
   zzinc_(Zcentrumtests);
   qh_distplane(qh, point, facet, &dist);
   centrum= qh_projectpoint(qh, point, facet, dist);
   qh_memfree(qh, point, qh->normal_size);
   trace4((qh, qh->ferr, 4007, "qh_getcentrum: for f%d, %d vertices dist= %2.2g\n",
           facet->id, qh_setsize(qh, facet->vertices), dist));
   return centrum;
 } /* getcentrum */
 
 
 /*---------------------------------
 
   qh_getdistance(qh, facet, neighbor, mindist, maxdist )
     returns the maxdist and mindist distance of any vertex from neighbor
 
   returns:
     the max absolute value
 
   design:
     for each vertex of facet that is not in neighbor
       test the distance from vertex to neighbor
 */
 realT qh_getdistance(qhT *qh, facetT *facet, facetT *neighbor, realT *mindist, realT *maxdist) {
   vertexT *vertex, **vertexp;
   realT dist, maxd, mind;
 
   FOREACHvertex_(facet->vertices)
     vertex->seen= False;
   FOREACHvertex_(neighbor->vertices)
     vertex->seen= True;
   mind= 0.0;
   maxd= 0.0;
   FOREACHvertex_(facet->vertices) {
     if (!vertex->seen) {
       zzinc_(Zbestdist);
       qh_distplane(qh, vertex->point, neighbor, &dist);
       if (dist < mind)
         mind= dist;
       else if (dist > maxd)
         maxd= dist;
     }
   }
   *mindist= mind;
   *maxdist= maxd;
   mind= -mind;
   if (maxd > mind)
     return maxd;
   else
     return mind;
 } /* getdistance */
 
 
 /*---------------------------------
 
   qh_normalize(qh, normal, dim, toporient )
     normalize a vector and report if too small
     does not use min norm
 
   see:
     qh_normalize2
 */
 void qh_normalize(qhT *qh, coordT *normal, int dim, boolT toporient) {
   qh_normalize2(qh, normal, dim, toporient, NULL, NULL);
 } /* normalize */
 
 /*---------------------------------
 
   qh_normalize2(qh, normal, dim, toporient, minnorm, ismin )
     normalize a vector and report if too small
     qh.MINdenom/MINdenom1 are the upper limits for divide overflow
 
   returns:
     normalized vector
     flips sign if !toporient
     if minnorm non-NULL,
       sets ismin if normal < minnorm
 
   notes:
     if zero norm
        sets all elements to sqrt(1.0/dim)
     if divide by zero (divzero())
        sets largest element to   +/-1
        bumps Znearlysingular
 
   design:
     computes norm
     test for minnorm
     if not near zero
       normalizes normal
     else if zero norm
       sets normal to standard value
     else
       uses qh_divzero to normalize
       if nearzero
         sets norm to direction of maximum value
 */
 void qh_normalize2(qhT *qh, coordT *normal, int dim, boolT toporient,
             realT *minnorm, boolT *ismin) {
   int k;
   realT *colp, *maxp, norm= 0, temp, *norm1, *norm2, *norm3;
   boolT zerodiv;
 
   norm1= normal+1;
   norm2= normal+2;
   norm3= normal+3;
   if (dim == 2)
     norm= sqrt((*normal)*(*normal) + (*norm1)*(*norm1));
   else if (dim == 3)
     norm= sqrt((*normal)*(*normal) + (*norm1)*(*norm1) + (*norm2)*(*norm2));
   else if (dim == 4) {
     norm= sqrt((*normal)*(*normal) + (*norm1)*(*norm1) + (*norm2)*(*norm2)
                + (*norm3)*(*norm3));
   }else if (dim > 4) {
     norm= (*normal)*(*normal) + (*norm1)*(*norm1) + (*norm2)*(*norm2)
                + (*norm3)*(*norm3);
     for (k=dim-4, colp=normal+4; k--; colp++)
       norm += (*colp) * (*colp);
     norm= sqrt(norm);
   }
   if (minnorm) {
     if (norm < *minnorm)
       *ismin= True;
     else
       *ismin= False;
   }
   wmin_(Wmindenom, norm);
   if (norm > qh->MINdenom) {
     if (!toporient)
       norm= -norm;
     *normal /= norm;
     *norm1 /= norm;
     if (dim == 2)
       ; /* all done */
     else if (dim == 3)
       *norm2 /= norm;
     else if (dim == 4) {
       *norm2 /= norm;
       *norm3 /= norm;
     }else if (dim >4) {
       *norm2 /= norm;
       *norm3 /= norm;
       for (k=dim-4, colp=normal+4; k--; )
         *colp++ /= norm;
     }
   }else if (norm == 0.0) {
     temp= sqrt(1.0/dim);
     for (k=dim, colp=normal; k--; )
       *colp++ = temp;
   }else {
     if (!toporient)
       norm= -norm;
     for (k=dim, colp=normal; k--; colp++) { /* k used below */
       temp= qh_divzero(qh, *colp, norm, qh->MINdenom_1, &zerodiv);
       if (!zerodiv)
         *colp= temp;
       else {
         maxp= qh_maxabsval(qh, normal, dim);
         temp= ((*maxp * norm >= 0.0) ? 1.0 : -1.0);
         for (k=dim, colp=normal; k--; colp++)
           *colp= 0.0;
         *maxp= temp;
         zzinc_(Znearlysingular);
         trace0((qh, qh->ferr, 1, "qh_normalize: norm=%2.2g too small during p%d\n",
                norm, qh->furthest_id));
         return;
       }
     }
   }
 } /* normalize */
 
 
 /*---------------------------------
 
   qh_projectpoint(qh, point, facet, dist )
     project point onto a facet by dist
 
   returns:
     returns a new point
 
   notes:
     if dist= distplane(point,facet)
       this projects point to hyperplane
     assumes qh_memfree_() is valid for normal_size
 */
 pointT *qh_projectpoint(qhT *qh, pointT *point, facetT *facet, realT dist) {
   pointT *newpoint, *np, *normal;
   int normsize= qh->normal_size;
   int k;
   void **freelistp; /* used !qh_NOmem */
 
   qh_memalloc_(qh, normsize, freelistp, newpoint, pointT);
   np= newpoint;
   normal= facet->normal;
   for (k=qh->hull_dim; k--; )
     *(np++)= *point++ - dist * *normal++;
   return(newpoint);
 } /* projectpoint */
 
 
 /*---------------------------------
 
   qh_setfacetplane(qh, facet )
     sets the hyperplane for a facet
     if qh.RANDOMdist, joggles hyperplane
 
   notes:
     uses global buffers qh.gm_matrix and qh.gm_row
     overwrites facet->normal if already defined
     updates Wnewvertex if PRINTstatistics
     sets facet->upperdelaunay if upper envelope of Delaunay triangulation
 
   design:
     copy vertex coordinates to qh.gm_matrix/gm_row
     compute determinate
     if nearzero
       recompute determinate with gaussian elimination
       if nearzero
         force outside orientation by testing interior point
 */
 void qh_setfacetplane(qhT *qh, facetT *facet) {
   pointT *point;
   vertexT *vertex, **vertexp;
   int normsize= qh->normal_size;
   int k,i, oldtrace= 0;
   realT dist;
   void **freelistp; /* used !qh_NOmem */
   coordT *coord, *gmcoord;
   pointT *point0= SETfirstt_(facet->vertices, vertexT)->point;
   boolT nearzero= False;
 
   zzinc_(Zsetplane);
   if (!facet->normal)
     qh_memalloc_(qh, normsize, freelistp, facet->normal, coordT);
   if (facet == qh->tracefacet) {
     oldtrace= qh->IStracing;
     qh->IStracing= 5;
     qh_fprintf(qh, qh->ferr, 8012, "qh_setfacetplane: facet f%d created.\n", facet->id);
     qh_fprintf(qh, qh->ferr, 8013, "  Last point added to hull was p%d.", qh->furthest_id);
     if (zzval_(Ztotmerge))
       qh_fprintf(qh, qh->ferr, 8014, "  Last merge was #%d.", zzval_(Ztotmerge));
     qh_fprintf(qh, qh->ferr, 8015, "\n\nCurrent summary is:\n");
       qh_printsummary(qh, qh->ferr);
   }
   if (qh->hull_dim <= 4) {
     i= 0;
     if (qh->RANDOMdist) {
       gmcoord= qh->gm_matrix;
       FOREACHvertex_(facet->vertices) {
         qh->gm_row[i++]= gmcoord;
         coord= vertex->point;
         for (k=qh->hull_dim; k--; )
           *(gmcoord++)= *coord++ * qh_randomfactor(qh, qh->RANDOMa, qh->RANDOMb);
       }
     }else {
       FOREACHvertex_(facet->vertices)
        qh->gm_row[i++]= vertex->point;
     }
     qh_sethyperplane_det(qh, qh->hull_dim, qh->gm_row, point0, facet->toporient,
                 facet->normal, &facet->offset, &nearzero);
   }
   if (qh->hull_dim > 4 || nearzero) {
     i= 0;
     gmcoord= qh->gm_matrix;
     FOREACHvertex_(facet->vertices) {
       if (vertex->point != point0) {
         qh->gm_row[i++]= gmcoord;
         coord= vertex->point;
         point= point0;
         for (k=qh->hull_dim; k--; )
           *(gmcoord++)= *coord++ - *point++;
       }
     }
     qh->gm_row[i]= gmcoord;  /* for areasimplex */
     if (qh->RANDOMdist) {
       gmcoord= qh->gm_matrix;
       for (i=qh->hull_dim-1; i--; ) {
         for (k=qh->hull_dim; k--; )
           *(gmcoord++) *= qh_randomfactor(qh, qh->RANDOMa, qh->RANDOMb);
       }
     }
     qh_sethyperplane_gauss(qh, qh->hull_dim, qh->gm_row, point0, facet->toporient,
                 facet->normal, &facet->offset, &nearzero);
     if (nearzero) {
       if (qh_orientoutside(qh, facet)) {
         trace0((qh, qh->ferr, 2, "qh_setfacetplane: flipped orientation after testing interior_point during p%d\n", qh->furthest_id));
       /* this is part of using Gaussian Elimination.  For example in 5-d
            1 1 1 1 0
            1 1 1 1 1
            0 0 0 1 0
            0 1 0 0 0
            1 0 0 0 0
            norm= 0.38 0.38 -0.76 0.38 0
          has a determinate of 1, but g.e. after subtracting pt. 0 has
          0's in the diagonal, even with full pivoting.  It does work
          if you subtract pt. 4 instead. */
       }
     }
   }
   facet->upperdelaunay= False;
   if (qh->DELAUNAY) {
     if (qh->UPPERdelaunay) {     /* matches qh_triangulate_facet and qh.lower_threshold in qh_initbuild */
       if (facet->normal[qh->hull_dim -1] >= qh->ANGLEround * qh_ZEROdelaunay)
         facet->upperdelaunay= True;
     }else {
       if (facet->normal[qh->hull_dim -1] > -qh->ANGLEround * qh_ZEROdelaunay)
         facet->upperdelaunay= True;
     }
   }
   if (qh->PRINTstatistics || qh->IStracing || qh->TRACElevel || qh->JOGGLEmax < REALmax) {
     qh->old_randomdist= qh->RANDOMdist;
     qh->RANDOMdist= False;
     FOREACHvertex_(facet->vertices) {
       if (vertex->point != point0) {
         boolT istrace= False;
         zinc_(Zdiststat);
         qh_distplane(qh, vertex->point, facet, &dist);
         dist= fabs_(dist);
         zinc_(Znewvertex);
         wadd_(Wnewvertex, dist);
         if (dist > wwval_(Wnewvertexmax)) {
           wwval_(Wnewvertexmax)= dist;
           if (dist > qh->max_outside) {
             qh->max_outside= dist;  /* used by qh_maxouter(qh) */
             if (dist > qh->TRACEdist)
               istrace= True;
           }
         }else if (-dist > qh->TRACEdist)
           istrace= True;
         if (istrace) {
           qh_fprintf(qh, qh->ferr, 8016, "qh_setfacetplane: ====== vertex p%d(v%d) increases max_outside to %2.2g for new facet f%d last p%d\n",
                 qh_pointid(qh, vertex->point), vertex->id, dist, facet->id, qh->furthest_id);
           qh_errprint(qh, "DISTANT", facet, NULL, NULL, NULL);
         }
       }
     }
     qh->RANDOMdist= qh->old_randomdist;
   }
   if (qh->IStracing >= 3) {
     qh_fprintf(qh, qh->ferr, 8017, "qh_setfacetplane: f%d offset %2.2g normal: ",
              facet->id, facet->offset);
     for (k=0; k < qh->hull_dim; k++)
       qh_fprintf(qh, qh->ferr, 8018, "%2.2g ", facet->normal[k]);
     qh_fprintf(qh, qh->ferr, 8019, "\n");
   }
   if (facet == qh->tracefacet)
     qh->IStracing= oldtrace;
 } /* setfacetplane */
 
 
 /*---------------------------------
 
   qh_sethyperplane_det(qh, dim, rows, point0, toporient, normal, offset, nearzero )
     given dim X dim array indexed by rows[], one row per point,
         toporient(flips all signs),
         and point0 (any row)
     set normalized hyperplane equation from oriented simplex
 
   returns:
     normal (normalized)
     offset (places point0 on the hyperplane)
     sets nearzero if hyperplane not through points
 
   notes:
     only defined for dim == 2..4
     rows[] is not modified
     solves det(P-V_0, V_n-V_0, ..., V_1-V_0)=0, i.e. every point is on hyperplane
     see Bower & Woodworth, A programmer's geometry, Butterworths 1983.
 
   derivation of 3-d minnorm
     Goal: all vertices V_i within qh.one_merge of hyperplane
     Plan: exactly translate the facet so that V_0 is the origin
           exactly rotate the facet so that V_1 is on the x-axis and y_2=0.
           exactly rotate the effective perturbation to only effect n_0
              this introduces a factor of sqrt(3)
     n_0 = ((y_2-y_0)*(z_1-z_0) - (z_2-z_0)*(y_1-y_0)) / norm
     Let M_d be the max coordinate difference
     Let M_a be the greater of M_d and the max abs. coordinate
     Let u be machine roundoff and distround be max error for distance computation
     The max error for n_0 is sqrt(3) u M_a M_d / norm.  n_1 is approx. 1 and n_2 is approx. 0
     The max error for distance of V_1 is sqrt(3) u M_a M_d M_d / norm.  Offset=0 at origin
     Then minnorm = 1.8 u M_a M_d M_d / qh.ONEmerge
     Note that qh.one_merge is approx. 45.5 u M_a and norm is usually about M_d M_d
 
   derivation of 4-d minnorm
     same as above except rotate the facet so that V_1 on x-axis and w_2, y_3, w_3=0
      [if two vertices fixed on x-axis, can rotate the other two in yzw.]
     n_0 = det3_(...) = y_2 det2_(z_1, w_1, z_3, w_3) = - y_2 w_1 z_3
      [all other terms contain at least two factors nearly zero.]
     The max error for n_0 is sqrt(4) u M_a M_d M_d / norm
     Then minnorm = 2 u M_a M_d M_d M_d / qh.ONEmerge
     Note that qh.one_merge is approx. 82 u M_a and norm is usually about M_d M_d M_d
 */
 void qh_sethyperplane_det(qhT *qh, int dim, coordT **rows, coordT *point0,
           boolT toporient, coordT *normal, realT *offset, boolT *nearzero) {
   realT maxround, dist;
   int i;
   pointT *point;
 
 
   if (dim == 2) {
     normal[0]= dY(1,0);
     normal[1]= dX(0,1);
     qh_normalize2(qh, normal, dim, toporient, NULL, NULL);
     *offset= -(point0[0]*normal[0]+point0[1]*normal[1]);
     *nearzero= False;  /* since nearzero norm => incident points */
   }else if (dim == 3) {
     normal[0]= det2_(dY(2,0), dZ(2,0),
                      dY(1,0), dZ(1,0));
     normal[1]= det2_(dX(1,0), dZ(1,0),
                      dX(2,0), dZ(2,0));
     normal[2]= det2_(dX(2,0), dY(2,0),
                      dX(1,0), dY(1,0));
     qh_normalize2(qh, normal, dim, toporient, NULL, NULL);
     *offset= -(point0[0]*normal[0] + point0[1]*normal[1]
                + point0[2]*normal[2]);
     maxround= qh->DISTround;
     for (i=dim; i--; ) {
       point= rows[i];
       if (point != point0) {
         dist= *offset + (point[0]*normal[0] + point[1]*normal[1]
                + point[2]*normal[2]);
         if (dist > maxround || dist < -maxround) {
           *nearzero= True;
           break;
         }
       }
     }
   }else if (dim == 4) {
     normal[0]= - det3_(dY(2,0), dZ(2,0), dW(2,0),
                         dY(1,0), dZ(1,0), dW(1,0),
                         dY(3,0), dZ(3,0), dW(3,0));
     normal[1]=   det3_(dX(2,0), dZ(2,0), dW(2,0),
                         dX(1,0), dZ(1,0), dW(1,0),
                         dX(3,0), dZ(3,0), dW(3,0));
     normal[2]= - det3_(dX(2,0), dY(2,0), dW(2,0),
                         dX(1,0), dY(1,0), dW(1,0),
                         dX(3,0), dY(3,0), dW(3,0));
     normal[3]=   det3_(dX(2,0), dY(2,0), dZ(2,0),
                         dX(1,0), dY(1,0), dZ(1,0),
                         dX(3,0), dY(3,0), dZ(3,0));
     qh_normalize2(qh, normal, dim, toporient, NULL, NULL);
     *offset= -(point0[0]*normal[0] + point0[1]*normal[1]
                + point0[2]*normal[2] + point0[3]*normal[3]);
     maxround= qh->DISTround;
     for (i=dim; i--; ) {
       point= rows[i];
       if (point != point0) {
         dist= *offset + (point[0]*normal[0] + point[1]*normal[1]
                + point[2]*normal[2] + point[3]*normal[3]);
         if (dist > maxround || dist < -maxround) {
           *nearzero= True;
           break;
         }
       }
     }
   }
   if (*nearzero) {
     zzinc_(Zminnorm);
     trace0((qh, qh->ferr, 3, "qh_sethyperplane_det: degenerate norm during p%d.\n", qh->furthest_id));
     zzinc_(Znearlysingular);
   }
 } /* sethyperplane_det */
 
 
 /*---------------------------------
 
   qh_sethyperplane_gauss(qh, dim, rows, point0, toporient, normal, offset, nearzero )
     given(dim-1) X dim array of rows[i]= V_{i+1} - V_0 (point0)
     set normalized hyperplane equation from oriented simplex
 
   returns:
     normal (normalized)
     offset (places point0 on the hyperplane)
 
   notes:
     if nearzero
       orientation may be incorrect because of incorrect sign flips in gausselim
     solves [V_n-V_0,...,V_1-V_0, 0 .. 0 1] * N == [0 .. 0 1]
         or [V_n-V_0,...,V_1-V_0, 0 .. 0 1] * N == [0]
     i.e., N is normal to the hyperplane, and the unnormalized
         distance to [0 .. 1] is either 1 or   0
 
   design:
     perform gaussian elimination
     flip sign for negative values
     perform back substitution
     normalize result
     compute offset
 */
 void qh_sethyperplane_gauss(qhT *qh, int dim, coordT **rows, pointT *point0,
                 boolT toporient, coordT *normal, coordT *offset, boolT *nearzero) {
   coordT *pointcoord, *normalcoef;
   int k;
   boolT sign= toporient, nearzero2= False;
 
   qh_gausselim(qh, rows, dim-1, dim, &sign, nearzero);
   for (k=dim-1; k--; ) {
     if ((rows[k])[k] < 0)
       sign ^= 1;
   }
   if (*nearzero) {
     zzinc_(Znearlysingular);
     trace0((qh, qh->ferr, 4, "qh_sethyperplane_gauss: nearly singular or axis parallel hyperplane during p%d.\n", qh->furthest_id));
     qh_backnormal(qh, rows, dim-1, dim, sign, normal, &nearzero2);
   }else {
     qh_backnormal(qh, rows, dim-1, dim, sign, normal, &nearzero2);
     if (nearzero2) {
       zzinc_(Znearlysingular);
       trace0((qh, qh->ferr, 5, "qh_sethyperplane_gauss: singular or axis parallel hyperplane at normalization during p%d.\n", qh->furthest_id));
     }
   }
   if (nearzero2)
     *nearzero= True;
   qh_normalize2(qh, normal, dim, True, NULL, NULL);
   pointcoord= point0;
   normalcoef= normal;
   *offset= -(*pointcoord++ * *normalcoef++);
   for (k=dim-1; k--; )
     *offset -= *pointcoord++ * *normalcoef++;
 } /* sethyperplane_gauss */
 
 
 
diff --git a/src/libqhullr/geom_r.h b/src/libqhullr/geom_r.h
index 470855e..3db76f6 100644
--- a/src/libqhullr/geom_r.h
+++ b/src/libqhullr/geom_r.h
@@ -1,176 +1,176 @@
 /*
  ---------------------------------
 
-  geom.h
+  geom_r.h
     header file for geometric routines
 
-   see qh-geom.htm and geom.c
+   see qh-geom.htm and geom_r.c
 
    Copyright (c) 1993-2014 The Geometry Center.
-   $Id: //main/2011/qhull/src/libqhullr/geom_r.h#2 $$Change: 1645 $
-   $DateTime: 2014/01/15 12:51:30 $$Author: bbarber $
+   $Id: //main/2011/qhull/src/libqhullr/geom_r.h#6 $$Change: 1797 $
+   $DateTime: 2014/12/15 17:23:41 $$Author: bbarber $
 */
 
 #ifndef qhDEFgeom
 #define qhDEFgeom 1
 
 #include "libqhull_r.h"
 
 /* ============ -macros- ======================== */
 
 /*----------------------------------
 
   fabs_(a)
     returns the absolute value of a
 */
 #define fabs_( a ) ((( a ) < 0 ) ? -( a ):( a ))
 
 /*----------------------------------
 
   fmax_(a,b)
     returns the maximum value of a and b
 */
 #define fmax_( a,b )  ( ( a ) < ( b ) ? ( b ) : ( a ) )
 
 /*----------------------------------
 
   fmin_(a,b)
     returns the minimum value of a and b
 */
 #define fmin_( a,b )  ( ( a ) > ( b ) ? ( b ) : ( a ) )
 
 /*----------------------------------
 
   maximize_(maxval, val)
     set maxval to val if val is greater than maxval
 */
 #define maximize_( maxval, val ) { if (( maxval ) < ( val )) ( maxval )= ( val ); }
 
 /*----------------------------------
 
   minimize_(minval, val)
     set minval to val if val is less than minval
 */
 #define minimize_( minval, val ) { if (( minval ) > ( val )) ( minval )= ( val ); }
 
 /*----------------------------------
 
   det2_(a1, a2,
         b1, b2)
 
     compute a 2-d determinate
 */
 #define det2_( a1,a2,b1,b2 ) (( a1 )*( b2 ) - ( a2 )*( b1 ))
 
 /*----------------------------------
 
   det3_(a1, a2, a3,
        b1, b2, b3,
        c1, c2, c3)
 
     compute a 3-d determinate
 */
 #define det3_( a1,a2,a3,b1,b2,b3,c1,c2,c3 ) ( ( a1 )*det2_( b2,b3,c2,c3 ) \
                 - ( b1 )*det2_( a2,a3,c2,c3 ) + ( c1 )*det2_( a2,a3,b2,b3 ) )
 
 /*----------------------------------
 
   dX( p1, p2 )
   dY( p1, p2 )
   dZ( p1, p2 )
 
     given two indices into rows[],
 
     compute the difference between X, Y, or Z coordinates
 */
 #define dX( p1,p2 )  ( *( rows[p1] ) - *( rows[p2] ))
 #define dY( p1,p2 )  ( *( rows[p1]+1 ) - *( rows[p2]+1 ))
 #define dZ( p1,p2 )  ( *( rows[p1]+2 ) - *( rows[p2]+2 ))
 #define dW( p1,p2 )  ( *( rows[p1]+3 ) - *( rows[p2]+3 ))
 
 /*============= prototypes in alphabetical order, infrequent at end ======= */
 
 void    qh_backnormal(qhT *qh, realT **rows, int numrow, int numcol, boolT sign, coordT *normal, boolT *nearzero);
 void    qh_distplane(qhT *qh, pointT *point, facetT *facet, realT *dist);
 facetT *qh_findbest(qhT *qh, pointT *point, facetT *startfacet,
                      boolT bestoutside, boolT isnewfacets, boolT noupper,
                      realT *dist, boolT *isoutside, int *numpart);
 facetT *qh_findbesthorizon(qhT *qh, boolT ischeckmax, pointT *point,
                      facetT *startfacet, boolT noupper, realT *bestdist, int *numpart);
 facetT *qh_findbestnew(qhT *qh, pointT *point, facetT *startfacet, realT *dist,
                      boolT bestoutside, boolT *isoutside, int *numpart);
 void    qh_gausselim(qhT *qh, realT **rows, int numrow, int numcol, boolT *sign, boolT *nearzero);
 realT   qh_getangle(qhT *qh, pointT *vect1, pointT *vect2);
 pointT *qh_getcenter(qhT *qh, setT *vertices);
 pointT *qh_getcentrum(qhT *qh, facetT *facet);
 realT   qh_getdistance(qhT *qh, facetT *facet, facetT *neighbor, realT *mindist, realT *maxdist);
 void    qh_normalize(qhT *qh, coordT *normal, int dim, boolT toporient);
 void    qh_normalize2(qhT *qh, coordT *normal, int dim, boolT toporient,
             realT *minnorm, boolT *ismin);
 pointT *qh_projectpoint(qhT *qh, pointT *point, facetT *facet, realT dist);
 
 void    qh_setfacetplane(qhT *qh, facetT *newfacets);
 void    qh_sethyperplane_det(qhT *qh, int dim, coordT **rows, coordT *point0,
               boolT toporient, coordT *normal, realT *offset, boolT *nearzero);
 void    qh_sethyperplane_gauss(qhT *qh, int dim, coordT **rows, pointT *point0,
              boolT toporient, coordT *normal, coordT *offset, boolT *nearzero);
 boolT   qh_sharpnewfacets(qhT *qh);
 
-/*========= infrequently used code in geom2.c =============*/
+/*========= infrequently used code in geom2_r.c =============*/
 
 coordT *qh_copypoints(qhT *qh, coordT *points, int numpoints, int dimension);
 void    qh_crossproduct(qhT *qh, int dim, realT vecA[3], realT vecB[3], realT vecC[3]);
 realT   qh_determinant(qhT *qh, realT **rows, int dim, boolT *nearzero);
 realT   qh_detjoggle(qhT *qh, pointT *points, int numpoints, int dimension);
 void    qh_detroundoff(qhT *qh);
 realT   qh_detsimplex(qhT *qh, pointT *apex, setT *points, int dim, boolT *nearzero);
 realT   qh_distnorm(qhT *qh, int dim, pointT *point, pointT *normal, realT *offsetp);
 realT   qh_distround(qhT *qh, int dimension, realT maxabs, realT maxsumabs);
 realT   qh_divzero(qhT *qh, realT numer, realT denom, realT mindenom1, boolT *zerodiv);
 realT   qh_facetarea(qhT *qh, facetT *facet);
 realT   qh_facetarea_simplex(qhT *qh, int dim, coordT *apex, setT *vertices,
           vertexT *notvertex,  boolT toporient, coordT *normal, realT *offset);
 pointT *qh_facetcenter(qhT *qh, setT *vertices);
 facetT *qh_findgooddist(qhT *qh, pointT *point, facetT *facetA, realT *distp, facetT **facetlist);
 void    qh_getarea(qhT *qh, facetT *facetlist);
 boolT   qh_gram_schmidt(qhT *qh, int dim, realT **rows);
 boolT   qh_inthresholds(qhT *qh, coordT *normal, realT *angle);
 void    qh_joggleinput(qhT *qh);
 realT  *qh_maxabsval(qhT *qh, realT *normal, int dim);
 setT   *qh_maxmin(qhT *qh, pointT *points, int numpoints, int dimension);
 realT   qh_maxouter(qhT *qh);
 void    qh_maxsimplex(qhT *qh, int dim, setT *maxpoints, pointT *points, int numpoints, setT **simplex);
 realT   qh_minabsval(qhT *qh, realT *normal, int dim);
 int     qh_mindiff(qhT *qh, realT *vecA, realT *vecB, int dim);
 boolT   qh_orientoutside(qhT *qh, facetT *facet);
 void    qh_outerinner(qhT *qh, facetT *facet, realT *outerplane, realT *innerplane);
 coordT  qh_pointdist(qhT *qh, pointT *point1, pointT *point2, int dim);
 void    qh_printmatrix(qhT *qh, FILE *fp, const char *string, realT **rows, int numrow, int numcol);
 void    qh_printpoints(qhT *qh, FILE *fp, const char *string, setT *points);
 void    qh_projectinput(qhT *qh);
 void    qh_projectpoints(qhT *qh, signed char *project, int n, realT *points,
              int numpoints, int dim, realT *newpoints, int newdim);
 void    qh_rotateinput(qhT *qh, realT **rows);
 void    qh_rotatepoints(qhT *qh, realT *points, int numpoints, int dim, realT **rows);
 void    qh_scaleinput(qhT *qh);
 void    qh_scalelast(qhT *qh, coordT *points, int numpoints, int dim, coordT low,
                    coordT high, coordT newhigh);
 void    qh_scalepoints(qhT *qh, pointT *points, int numpoints, int dim,
                 realT *newlows, realT *newhighs);
 boolT   qh_sethalfspace(qhT *qh, int dim, coordT *coords, coordT **nextp,
               coordT *normal, coordT *offset, coordT *feasible);
 coordT *qh_sethalfspace_all(qhT *qh, int dim, int count, coordT *halfspaces, pointT *feasible);
 pointT *qh_voronoi_center(qhT *qh, int dim, setT *points);
 
 #endif /* qhDEFgeom */
 
 
 
diff --git a/src/libqhullr/global_r.c b/src/libqhullr/global_r.c
index 9595d0e..1b9bdf7 100644
--- a/src/libqhullr/global_r.c
+++ b/src/libqhullr/global_r.c
@@ -1,2003 +1,2007 @@
 
 /*
  ---------------------------------
 
-   global.c
+   global_r.c
    initializes all the globals of the qhull application
 
    see README
 
-   see libqhull.h for qh.globals and function prototypes
+   see libqhull_r.h for qh.globals and function prototypes
 
-   see qhull_r.h for internal functions
+   see qhull_ra.h for internal functions
 
    Copyright (c) 1993-2014 The Geometry Center.
-   $Id: //main/2011/qhull/src/libqhullr/global_r.c#4 $$Change: 1663 $
-   $DateTime: 2014/01/19 17:59:16 $$Author: bbarber $
+   $Id: //main/2011/qhull/src/libqhullr/global_r.c#9 $$Change: 1797 $
+   $DateTime: 2014/12/15 17:23:41 $$Author: bbarber $
  */
 
-#include "qhull_r.h"
+#include "qhull_ra.h"
 
-/*========= qh->definition -- globals defined in libqhull.h =======================*/
+/*========= qh->definition -- globals defined in libqhull_r.h =======================*/
 
 /*----------------------------------
 
   qh_version
     version string by year and date
 
     the revision increases on code changes only
 
   notes:
     change date:    Changes.txt, Announce.txt, index.htm, README.txt,
                     qhull-news.html, Eudora signatures, CMakeLists.txt
     change version: README.txt, qh-get.htm, File_id.diz, Makefile.txt
     change year:    Copying.txt
     check download size
-    recompile user_eg.c, rbox.c, libqhull.c, qconvex.c, qdelaun.c qvoronoi.c, qhalf.c, testqset.c
+    recompile user_eg_r.c, rbox_r.c, libqhull_r.c, qconvex_r.c, qdelaun_r.c qvoronoi_r.c, qhalf_r.c, testqset_r.c
 */
 
 const char *qh_version = "2012.1 2012/02/18";
 
 /*---------------------------------
 
   qh_appendprint(qh, printFormat )
     append printFormat to qh.PRINTout unless already defined
 */
 void qh_appendprint(qhT *qh, qh_PRINT format) {
   int i;
 
   for (i=0; i < qh_PRINTEND; i++) {
     if (qh->PRINTout[i] == format && format != qh_PRINTqhull)
       break;
     if (!qh->PRINTout[i]) {
       qh->PRINTout[i]= format;
       break;
     }
   }
 } /* appendprint */
 
 /*---------------------------------
 
   qh_checkflags(qh, commandStr, hiddenFlags )
     errors if commandStr contains hiddenFlags
     hiddenFlags starts and ends with a space and is space deliminated (checked)
 
   notes:
     ignores first word (e.g., "qconvex i")
     use qh_strtol/strtod since strtol/strtod may or may not skip trailing spaces
 
   see:
     qh_initflags() initializes Qhull according to commandStr
 */
 void qh_checkflags(qhT *qh, char *command, char *hiddenflags) {
   char *s= command, *t, *chkerr; /* qh_skipfilename is non-const */
   char key, opt, prevopt;
   char chkkey[]= "   ";
   char chkopt[]=  "    ";
   char chkopt2[]= "     ";
   boolT waserr= False;
 
   if (*hiddenflags != ' ' || hiddenflags[strlen(hiddenflags)-1] != ' ') {
     qh_fprintf(qh, qh->ferr, 6026, "qhull error (qh_checkflags): hiddenflags must start and end with a space: \"%s\"", hiddenflags);
     qh_errexit(qh, qh_ERRinput, NULL, NULL);
   }
   if (strpbrk(hiddenflags, ",\n\r\t")) {
     qh_fprintf(qh, qh->ferr, 6027, "qhull error (qh_checkflags): hiddenflags contains commas, newlines, or tabs: \"%s\"", hiddenflags);
     qh_errexit(qh, qh_ERRinput, NULL, NULL);
   }
   while (*s && !isspace(*s))  /* skip program name */
     s++;
   while (*s) {
     while (*s && isspace(*s))
       s++;
     if (*s == '-')
       s++;
     if (!*s)
       break;
     key = *s++;
     chkerr = NULL;
     if (key == 'T' && (*s == 'I' || *s == 'O')) {  /* TI or TO 'file name' */
       s= qh_skipfilename(qh, ++s);
       continue;
     }
     chkkey[1]= key;
     if (strstr(hiddenflags, chkkey)) {
       chkerr= chkkey;
     }else if (isupper(key)) {
       opt= ' ';
       prevopt= ' ';
       chkopt[1]= key;
       chkopt2[1]= key;
       while (!chkerr && *s && !isspace(*s)) {
         opt= *s++;
         if (isalpha(opt)) {
           chkopt[2]= opt;
           if (strstr(hiddenflags, chkopt))
             chkerr= chkopt;
           if (prevopt != ' ') {
             chkopt2[2]= prevopt;
             chkopt2[3]= opt;
             if (strstr(hiddenflags, chkopt2))
               chkerr= chkopt2;
           }
         }else if (key == 'Q' && isdigit(opt) && prevopt != 'b'
               && (prevopt == ' ' || islower(prevopt))) {
             chkopt[2]= opt;
             if (strstr(hiddenflags, chkopt))
               chkerr= chkopt;
         }else {
           qh_strtod(s-1, &t);
           if (s < t)
             s= t;
         }
         prevopt= opt;
       }
     }
     if (chkerr) {
       *chkerr= '\'';
       chkerr[strlen(chkerr)-1]=  '\'';
       qh_fprintf(qh, qh->ferr, 6029, "qhull error: option %s is not used with this program.\n             It may be used with qhull.\n", chkerr);
       waserr= True;
     }
   }
   if (waserr)
     qh_errexit(qh, qh_ERRinput, NULL, NULL);
 } /* checkflags */
 
 /*---------------------------------
 
   qh_clear_outputflags(qh)
     Clear output flags for QhullPoints
 */
 void qh_clear_outputflags(qhT *qh) {
   int i,k;
 
   qh->ANNOTATEoutput= False;
   qh->DOintersections= False;
   qh->DROPdim= -1;
   qh->FORCEoutput= False;
   qh->GETarea= False;
   qh->GOODpoint= 0;
   qh->GOODpointp= NULL;
   qh->GOODthreshold= False;
   qh->GOODvertex= 0;
   qh->GOODvertexp= NULL;
   qh->IStracing= 0;
   qh->KEEParea= False;
   qh->KEEPmerge= False;
   qh->KEEPminArea= REALmax;
   qh->PRINTcentrums= False;
   qh->PRINTcoplanar= False;
   qh->PRINTdots= False;
   qh->PRINTgood= False;
   qh->PRINTinner= False;
   qh->PRINTneighbors= False;
   qh->PRINTnoplanes= False;
   qh->PRINToptions1st= False;
   qh->PRINTouter= False;
   qh->PRINTprecision= True;
   qh->PRINTridges= False;
   qh->PRINTspheres= False;
   qh->PRINTstatistics= False;
   qh->PRINTsummary= False;
   qh->PRINTtransparent= False;
   qh->SPLITthresholds= False;
   qh->TRACElevel= 0;
   qh->TRInormals= False;
   qh->USEstdout= False;
   qh->VERIFYoutput= False;
   for (k=qh->input_dim+1; k--; ) {  /* duplicated in qh_initqhull_buffers and qh_clear_ouputflags */
     qh->lower_threshold[k]= -REALmax;
     qh->upper_threshold[k]= REALmax;
     qh->lower_bound[k]= -REALmax;
     qh->upper_bound[k]= REALmax;
   }
 
   for (i=0; i < qh_PRINTEND; i++) {
     qh->PRINTout[i]= qh_PRINTnone;
   }
 
   if (!qh->qhull_commandsiz2)
       qh->qhull_commandsiz2= (int)strlen(qh->qhull_command); /* WARN64 */
   else {
       qh->qhull_command[qh->qhull_commandsiz2]= '\0';
   }
   if (!qh->qhull_optionsiz2)
     qh->qhull_optionsiz2= (int)strlen(qh->qhull_options);  /* WARN64 */
   else {
     qh->qhull_options[qh->qhull_optionsiz2]= '\0';
     qh->qhull_optionlen= qh_OPTIONline;  /* start a new line */
   }
 } /* clear_outputflags */
 
 /*---------------------------------
 
   qh_clock()
     return user CPU time in 100ths (qh_SECtick)
     only defined for qh_CLOCKtype == 2
 
   notes:
     use first value to determine time 0
     from Stevens '92 8.15
 */
 unsigned long qh_clock(qhT *qh) {
 
 #if (qh_CLOCKtype == 2)
   struct tms time;
   static long clktck;  /* initialized first call */
   double ratio, cpu;
   unsigned long ticks;
 
   if (!clktck) {
     if ((clktck= sysconf(_SC_CLK_TCK)) < 0) {
       qh_fprintf(qh, qh->ferr, 6030, "qhull internal error (qh_clock): sysconf() failed.  Use qh_CLOCKtype 1 in user.h\n");
       qh_errexit(qh, qh_ERRqhull, NULL, NULL);
     }
   }
   if (times(&time) == -1) {
     qh_fprintf(qh, qh->ferr, 6031, "qhull internal error (qh_clock): times() failed.  Use qh_CLOCKtype 1 in user.h\n");
     qh_errexit(qh, qh_ERRqhull, NULL, NULL);
   }
   ratio= qh_SECticks / (double)clktck;
   ticks= time.tms_utime * ratio;
   return ticks;
 #else
   qh_fprintf(qh, qh->ferr, 6032, "qhull internal error (qh_clock): use qh_CLOCKtype 2 in user.h\n");
   qh_errexit(qh, qh_ERRqhull, NULL, NULL); /* never returns */
   return 0;
 #endif
 } /* clock */
 
 /*---------------------------------
 
   qh_freebuffers()
     free up global memory buffers
 
   notes:
     must match qh_initbuffers()
 */
 void qh_freebuffers(qhT *qh) {
 
   trace5((qh, qh->ferr, 5001, "qh_freebuffers: freeing up global memory buffers\n"));
   /* allocated by qh_initqhull_buffers */
   qh_memfree(qh, qh->NEARzero, qh->hull_dim * sizeof(realT));
   qh_memfree(qh, qh->lower_threshold, (qh->input_dim+1) * sizeof(realT));
   qh_memfree(qh, qh->upper_threshold, (qh->input_dim+1) * sizeof(realT));
   qh_memfree(qh, qh->lower_bound, (qh->input_dim+1) * sizeof(realT));
   qh_memfree(qh, qh->upper_bound, (qh->input_dim+1) * sizeof(realT));
   qh_memfree(qh, qh->gm_matrix, (qh->hull_dim+1) * qh->hull_dim * sizeof(coordT));
   qh_memfree(qh, qh->gm_row, (qh->hull_dim+1) * sizeof(coordT *));
   qh->NEARzero= qh->lower_threshold= qh->upper_threshold= NULL;
   qh->lower_bound= qh->upper_bound= NULL;
   qh->gm_matrix= NULL;
   qh->gm_row= NULL;
   qh_setfree(qh, &qh->other_points);
   qh_setfree(qh, &qh->del_vertices);
   qh_setfree(qh, &qh->coplanarfacetset);
   if (qh->line)                /* allocated by qh_readinput, freed if no error */
     qh_free(qh->line);
   if (qh->half_space)
     qh_free(qh->half_space);
   if (qh->temp_malloc)
     qh_free(qh->temp_malloc);
   if (qh->feasible_point)      /* allocated by qh_readfeasible */
     qh_free(qh->feasible_point);
   if (qh->feasible_string)     /* allocated by qh_initflags */
     qh_free(qh->feasible_string);
   qh->line= qh->feasible_string= NULL;
   qh->half_space= qh->feasible_point= qh->temp_malloc= NULL;
   /* usually allocated by qh_readinput */
   if (qh->first_point && qh->POINTSmalloc) {
     qh_free(qh->first_point);
     qh->first_point= NULL;
   }
   if (qh->input_points && qh->input_malloc) { /* set by qh_joggleinput */
     qh_free(qh->input_points);
     qh->input_points= NULL;
   }
   trace5((qh, qh->ferr, 5002, "qh_freebuffers: finished\n"));
 } /* freebuffers */
 
 
 /*---------------------------------
 
   qh_freebuild(qh, allmem )
     free global memory used by qh_initbuild and qh_buildhull
     if !allmem,
       does not free short memory (e.g., facetT, freed by qh_memfreeshort)
 
   design:
     free centrums
     free each vertex
     mark unattached ridges
     for each facet
       free ridges
       free outside set, coplanar set, neighbor set, ridge set, vertex set
       free facet
     free hash table
     free interior point
     free merge set
     free temporary sets
 */
 void qh_freebuild(qhT *qh, boolT allmem) {
   facetT *facet;
   vertexT *vertex;
   ridgeT *ridge, **ridgep;
   mergeT *merge, **mergep;
 
   trace1((qh, qh->ferr, 1005, "qh_freebuild: free memory from qh_inithull and qh_buildhull\n"));
   if (qh->del_vertices)
     qh_settruncate(qh, qh->del_vertices, 0);
   if (allmem) {
     while ((vertex= qh->vertex_list)) {
       if (vertex->next)
         qh_delvertex(qh, vertex);
       else {
         qh_memfree(qh, vertex, (int)sizeof(vertexT));
         qh->newvertex_list= qh->vertex_list= NULL;
       }
     }
   }else if (qh->VERTEXneighbors) {
     FORALLvertices
       qh_setfreelong(qh, &(vertex->neighbors));
   }
   qh->VERTEXneighbors= False;
   qh->GOODclosest= NULL;
   if (allmem) {
     FORALLfacets {
       FOREACHridge_(facet->ridges)
         ridge->seen= False;
     }
     FORALLfacets {
       if (facet->visible) {
         FOREACHridge_(facet->ridges) {
           if (!otherfacet_(ridge, facet)->visible)
             ridge->seen= True;  /* an unattached ridge */
         }
       }
     }
     while ((facet= qh->facet_list)) {
       FOREACHridge_(facet->ridges) {
         if (ridge->seen) {
           qh_setfree(qh, &(ridge->vertices));
           qh_memfree(qh, ridge, (int)sizeof(ridgeT));
         }else
           ridge->seen= True;
       }
       qh_setfree(qh, &(facet->outsideset));
       qh_setfree(qh, &(facet->coplanarset));
       qh_setfree(qh, &(facet->neighbors));
       qh_setfree(qh, &(facet->ridges));
       qh_setfree(qh, &(facet->vertices));
       if (facet->next)
         qh_delfacet(qh, facet);
       else {
         qh_memfree(qh, facet, (int)sizeof(facetT));
         qh->visible_list= qh->newfacet_list= qh->facet_list= NULL;
       }
     }
   }else {
     FORALLfacets {
       qh_setfreelong(qh, &(facet->outsideset));
       qh_setfreelong(qh, &(facet->coplanarset));
       if (!facet->simplicial) {
         qh_setfreelong(qh, &(facet->neighbors));
         qh_setfreelong(qh, &(facet->ridges));
         qh_setfreelong(qh, &(facet->vertices));
       }
     }
   }
   qh_setfree(qh, &(qh->hash_table));
   qh_memfree(qh, qh->interior_point, qh->normal_size);
   qh->interior_point= NULL;
   FOREACHmerge_(qh->facet_mergeset)  /* usually empty */
     qh_memfree(qh, merge, (int)sizeof(mergeT));
   qh->facet_mergeset= NULL;  /* temp set */
   qh->degen_mergeset= NULL;  /* temp set */
   qh_settempfree_all(qh);
 } /* freebuild */
 
 /*---------------------------------
 
   qh_freeqhull(qh, allmem )
 
   free global memory
   if !allmem,
     does not free short memory (freed by qh_memfreeshort)
 
 notes:
   sets qh.NOerrexit in case caller forgets to
+  Does not throw errors
 
 see:
   see qh_initqhull_start2()
 
 design:
   free global and temporary memory from qh_initbuild and qh_buildhull
   free buffers
   free statistics
 */
 void qh_freeqhull(qhT *qh, boolT allmem) {
 
-  trace1((qh, qh->ferr, 1006, "qh_freeqhull: free global memory\n"));
   qh->NOerrexit= True;  /* no more setjmp since called at exit and ~QhullQh */
+  trace1((qh, qh->ferr, 1006, "qh_freeqhull: free global memory\n"));
   qh_freebuild(qh, allmem);
   qh_freebuffers(qh);
   /* memset is the same in qh_freeqhull() and qh_initqhull_start2() */
   memset((char *)qh, 0, sizeof(qhT)-sizeof(qhmemT)-sizeof(qhstatT));
   qh->NOerrexit= True;
 } /* freeqhull2 */
 
 /*---------------------------------
 
   qh_init_A(qh, infile, outfile, errfile, argc, argv )
     initialize memory and stdio files
     convert input options to option string (qh.qhull_command)
 
   notes:
     infile may be NULL if qh_readpoints() is not called
 
     errfile should always be defined.  It is used for reporting
     errors.  outfile is used for output and format options.
 
     argc/argv may be 0/NULL
 
     called before error handling initialized
     qh_errexit() may not be used
 */
 void qh_init_A(qhT *qh, FILE *infile, FILE *outfile, FILE *errfile, int argc, char *argv[]) {
   qh_meminit(qh, errfile);
   qh_initqhull_start(qh, infile, outfile, errfile);
   qh_init_qhull_command(qh, argc, argv);
 } /* init_A */
 
 /*---------------------------------
 
   qh_init_B(qh, points, numpoints, dim, ismalloc )
     initialize globals for points array
 
     points has numpoints dim-dimensional points
       points[0] is the first coordinate of the first point
       points[1] is the second coordinate of the first point
       points[dim] is the first coordinate of the second point
 
     ismalloc=True
       Qhull will call qh_free(points) on exit or input transformation
     ismalloc=False
       Qhull will allocate a new point array if needed for input transformation
 
     qh.qhull_command
       is the option string.
       It is defined by qh_init_B(), qh_qhull_command(), or qh_initflags
 
   returns:
     if qh.PROJECTinput or (qh.DELAUNAY and qh.PROJECTdelaunay)
       projects the input to a new point array
 
         if qh.DELAUNAY,
           qh.hull_dim is increased by one
         if qh.ATinfinity,
           qh_projectinput adds point-at-infinity for Delaunay tri.
 
     if qh.SCALEinput
       changes the upper and lower bounds of the input, see qh_scaleinput(qh)
 
     if qh.ROTATEinput
       rotates the input by a random rotation, see qh_rotateinput()
       if qh.DELAUNAY
         rotates about the last coordinate
 
   notes:
     called after points are defined
     qh_errexit() may be used
 */
 void qh_init_B(qhT *qh, coordT *points, int numpoints, int dim, boolT ismalloc) {
   qh_initqhull_globals(qh, points, numpoints, dim, ismalloc);
   if (qh->qhmem.LASTsize == 0)
     qh_initqhull_mem(qh);
-  /* mem.c and qset.c are initialized */
+  /* mem_r.c and qset_r.c are initialized */
   qh_initqhull_buffers(qh);
   qh_initthresholds(qh, qh->qhull_command);
   if (qh->PROJECTinput || (qh->DELAUNAY && qh->PROJECTdelaunay))
     qh_projectinput(qh);
   if (qh->SCALEinput)
     qh_scaleinput(qh);
   if (qh->ROTATErandom >= 0) {
     qh_randommatrix(qh, qh->gm_matrix, qh->hull_dim, qh->gm_row);
     if (qh->DELAUNAY) {
       int k, lastk= qh->hull_dim-1;
       for (k=0; k < lastk; k++) {
         qh->gm_row[k][lastk]= 0.0;
         qh->gm_row[lastk][k]= 0.0;
       }
       qh->gm_row[lastk][lastk]= 1.0;
     }
     qh_gram_schmidt(qh, qh->hull_dim, qh->gm_row);
     qh_rotateinput(qh, qh->gm_row);
   }
 } /* init_B */
 
 /*---------------------------------
 
   qh_init_qhull_command(qh, argc, argv )
     build qh.qhull_command from argc/argv
 
   returns:
     a space-delimited string of options (just as typed)
 
   notes:
     makes option string easy to input and output
 
     argc/argv may be 0/NULL
 */
 void qh_init_qhull_command(qhT *qh, int argc, char *argv[]) {
 
   if (!qh_argv_to_command(argc, argv, qh->qhull_command, (int)sizeof(qh->qhull_command))){
     /* Assumes qh.ferr is defined. */
     qh_fprintf(qh, qh->ferr, 6033, "qhull input error: more than %d characters in command line\n",
           (int)sizeof(qh->qhull_command));
     qh_exit(qh_ERRinput);  /* error reported, can not use qh_errexit */
   }
 } /* init_qhull_command */
 
 /*---------------------------------
 
   qh_initflags(qh, commandStr )
     set flags and initialized constants from commandStr
 
   returns:
     sets qh.qhull_command to command if needed
 
   notes:
     ignores first word (e.g., "qhull d")
     use qh_strtol/strtod since strtol/strtod may or may not skip trailing spaces
 
   see:
     qh_initthresholds() continues processing of 'Pdn' and 'PDn'
-    'prompt' in unix.c for documentation
+    'prompt' in unix_r.c for documentation
 
   design:
     for each space-deliminated option group
       if top-level option
         check syntax
         append approriate option to option string
         set appropriate global variable or append printFormat to print options
       else
         for each sub-option
           check syntax
           append approriate option to option string
           set appropriate global variable or append printFormat to print options
 */
 void qh_initflags(qhT *qh, char *command) {
   int k, i, lastproject;
   char *s= command, *t, *prev_s, *start, key;
   boolT isgeom= False, wasproject;
   realT r;
 
   if (command <= &qh->qhull_command[0] || command > &qh->qhull_command[0] + sizeof(qh->qhull_command)) {
     if (command != &qh->qhull_command[0]) {
       *qh->qhull_command= '\0';
       strncat(qh->qhull_command, command, sizeof(qh->qhull_command)-strlen(qh->qhull_command)-1);
     }
     while (*s && !isspace(*s))  /* skip program name */
       s++;
   }
   while (*s) {
     while (*s && isspace(*s))
       s++;
     if (*s == '-')
       s++;
     if (!*s)
       break;
     prev_s= s;
     switch (*s++) {
     case 'd':
       qh_option(qh, "delaunay", NULL, NULL);
       qh->DELAUNAY= True;
       break;
     case 'f':
       qh_option(qh, "facets", NULL, NULL);
       qh_appendprint(qh, qh_PRINTfacets);
       break;
     case 'i':
       qh_option(qh, "incidence", NULL, NULL);
       qh_appendprint(qh, qh_PRINTincidences);
       break;
     case 'm':
       qh_option(qh, "mathematica", NULL, NULL);
       qh_appendprint(qh, qh_PRINTmathematica);
       break;
     case 'n':
       qh_option(qh, "normals", NULL, NULL);
       qh_appendprint(qh, qh_PRINTnormals);
       break;
     case 'o':
       qh_option(qh, "offFile", NULL, NULL);
       qh_appendprint(qh, qh_PRINToff);
       break;
     case 'p':
       qh_option(qh, "points", NULL, NULL);
       qh_appendprint(qh, qh_PRINTpoints);
       break;
     case 's':
       qh_option(qh, "summary", NULL, NULL);
       qh->PRINTsummary= True;
       break;
     case 'v':
       qh_option(qh, "voronoi", NULL, NULL);
       qh->VORONOI= True;
       qh->DELAUNAY= True;
       break;
     case 'A':
       if (!isdigit(*s) && *s != '.' && *s != '-')
         qh_fprintf(qh, qh->ferr, 7002, "qhull warning: no maximum cosine angle given for option 'An'.  Ignored.\n");
       else {
         if (*s == '-') {
           qh->premerge_cos= -qh_strtod(s, &s);
           qh_option(qh, "Angle-premerge-", NULL, &qh->premerge_cos);
           qh->PREmerge= True;
         }else {
           qh->postmerge_cos= qh_strtod(s, &s);
           qh_option(qh, "Angle-postmerge", NULL, &qh->postmerge_cos);
           qh->POSTmerge= True;
         }
         qh->MERGING= True;
       }
       break;
     case 'C':
       if (!isdigit(*s) && *s != '.' && *s != '-')
         qh_fprintf(qh, qh->ferr, 7003, "qhull warning: no centrum radius given for option 'Cn'.  Ignored.\n");
       else {
         if (*s == '-') {
           qh->premerge_centrum= -qh_strtod(s, &s);
           qh_option(qh, "Centrum-premerge-", NULL, &qh->premerge_centrum);
           qh->PREmerge= True;
         }else {
           qh->postmerge_centrum= qh_strtod(s, &s);
           qh_option(qh, "Centrum-postmerge", NULL, &qh->postmerge_centrum);
           qh->POSTmerge= True;
         }
         qh->MERGING= True;
       }
       break;
     case 'E':
       if (*s == '-')
         qh_fprintf(qh, qh->ferr, 7004, "qhull warning: negative maximum roundoff given for option 'An'.  Ignored.\n");
       else if (!isdigit(*s))
         qh_fprintf(qh, qh->ferr, 7005, "qhull warning: no maximum roundoff given for option 'En'.  Ignored.\n");
       else {
         qh->DISTround= qh_strtod(s, &s);
         qh_option(qh, "Distance-roundoff", NULL, &qh->DISTround);
         qh->SETroundoff= True;
       }
       break;
     case 'H':
       start= s;
       qh->HALFspace= True;
       qh_strtod(s, &t);
       while (t > s)  {
         if (*t && !isspace(*t)) {
           if (*t == ',')
             t++;
           else
             qh_fprintf(qh, qh->ferr, 7006, "qhull warning: origin for Halfspace intersection should be 'Hn,n,n,...'\n");
         }
         s= t;
         qh_strtod(s, &t);
       }
       if (start < t) {
         if (!(qh->feasible_string= (char*)calloc((size_t)(t-start+1), (size_t)1))) {
           qh_fprintf(qh, qh->ferr, 6034, "qhull error: insufficient memory for 'Hn,n,n'\n");
           qh_errexit(qh, qh_ERRmem, NULL, NULL);
         }
         strncpy(qh->feasible_string, start, (size_t)(t-start));
         qh_option(qh, "Halfspace-about", NULL, NULL);
         qh_option(qh, qh->feasible_string, NULL, NULL);
       }else
         qh_option(qh, "Halfspace", NULL, NULL);
       break;
     case 'R':
       if (!isdigit(*s))
         qh_fprintf(qh, qh->ferr, 7007, "qhull warning: missing random perturbation for option 'Rn'.  Ignored\n");
       else {
         qh->RANDOMfactor= qh_strtod(s, &s);
         qh_option(qh, "Random_perturb", NULL, &qh->RANDOMfactor);
         qh->RANDOMdist= True;
       }
       break;
     case 'V':
       if (!isdigit(*s) && *s != '-')
         qh_fprintf(qh, qh->ferr, 7008, "qhull warning: missing visible distance for option 'Vn'.  Ignored\n");
       else {
         qh->MINvisible= qh_strtod(s, &s);
         qh_option(qh, "Visible", NULL, &qh->MINvisible);
       }
       break;
     case 'U':
       if (!isdigit(*s) && *s != '-')
         qh_fprintf(qh, qh->ferr, 7009, "qhull warning: missing coplanar distance for option 'Un'.  Ignored\n");
       else {
         qh->MAXcoplanar= qh_strtod(s, &s);
         qh_option(qh, "U-coplanar", NULL, &qh->MAXcoplanar);
       }
       break;
     case 'W':
       if (*s == '-')
         qh_fprintf(qh, qh->ferr, 7010, "qhull warning: negative outside width for option 'Wn'.  Ignored.\n");
       else if (!isdigit(*s))
         qh_fprintf(qh, qh->ferr, 7011, "qhull warning: missing outside width for option 'Wn'.  Ignored\n");
       else {
         qh->MINoutside= qh_strtod(s, &s);
         qh_option(qh, "W-outside", NULL, &qh->MINoutside);
         qh->APPROXhull= True;
       }
       break;
     /************  sub menus ***************/
     case 'F':
       while (*s && !isspace(*s)) {
         switch (*s++) {
         case 'a':
           qh_option(qh, "Farea", NULL, NULL);
           qh_appendprint(qh, qh_PRINTarea);
           qh->GETarea= True;
           break;
         case 'A':
           qh_option(qh, "FArea-total", NULL, NULL);
           qh->GETarea= True;
           break;
         case 'c':
           qh_option(qh, "Fcoplanars", NULL, NULL);
           qh_appendprint(qh, qh_PRINTcoplanars);
           break;
         case 'C':
           qh_option(qh, "FCentrums", NULL, NULL);
           qh_appendprint(qh, qh_PRINTcentrums);
           break;
         case 'd':
           qh_option(qh, "Fd-cdd-in", NULL, NULL);
           qh->CDDinput= True;
           break;
         case 'D':
           qh_option(qh, "FD-cdd-out", NULL, NULL);
           qh->CDDoutput= True;
           break;
         case 'F':
           qh_option(qh, "FFacets-xridge", NULL, NULL);
           qh_appendprint(qh, qh_PRINTfacets_xridge);
           break;
         case 'i':
           qh_option(qh, "Finner", NULL, NULL);
           qh_appendprint(qh, qh_PRINTinner);
           break;
         case 'I':
           qh_option(qh, "FIDs", NULL, NULL);
           qh_appendprint(qh, qh_PRINTids);
           break;
         case 'm':
           qh_option(qh, "Fmerges", NULL, NULL);
           qh_appendprint(qh, qh_PRINTmerges);
           break;
         case 'M':
           qh_option(qh, "FMaple", NULL, NULL);
           qh_appendprint(qh, qh_PRINTmaple);
           break;
         case 'n':
           qh_option(qh, "Fneighbors", NULL, NULL);
           qh_appendprint(qh, qh_PRINTneighbors);
           break;
         case 'N':
           qh_option(qh, "FNeighbors-vertex", NULL, NULL);
           qh_appendprint(qh, qh_PRINTvneighbors);
           break;
         case 'o':
           qh_option(qh, "Fouter", NULL, NULL);
           qh_appendprint(qh, qh_PRINTouter);
           break;
         case 'O':
           if (qh->PRINToptions1st) {
             qh_option(qh, "FOptions", NULL, NULL);
             qh_appendprint(qh, qh_PRINToptions);
           }else
             qh->PRINToptions1st= True;
           break;
         case 'p':
           qh_option(qh, "Fpoint-intersect", NULL, NULL);
           qh_appendprint(qh, qh_PRINTpointintersect);
           break;
         case 'P':
           qh_option(qh, "FPoint-nearest", NULL, NULL);
           qh_appendprint(qh, qh_PRINTpointnearest);
           break;
         case 'Q':
           qh_option(qh, "FQhull", NULL, NULL);
           qh_appendprint(qh, qh_PRINTqhull);
           break;
         case 's':
           qh_option(qh, "Fsummary", NULL, NULL);
           qh_appendprint(qh, qh_PRINTsummary);
           break;
         case 'S':
           qh_option(qh, "FSize", NULL, NULL);
           qh_appendprint(qh, qh_PRINTsize);
           qh->GETarea= True;
           break;
         case 't':
           qh_option(qh, "Ftriangles", NULL, NULL);
           qh_appendprint(qh, qh_PRINTtriangles);
           break;
         case 'v':
           /* option set in qh_initqhull_globals */
           qh_appendprint(qh, qh_PRINTvertices);
           break;
         case 'V':
           qh_option(qh, "FVertex-average", NULL, NULL);
           qh_appendprint(qh, qh_PRINTaverage);
           break;
         case 'x':
           qh_option(qh, "Fxtremes", NULL, NULL);
           qh_appendprint(qh, qh_PRINTextremes);
           break;
         default:
           s--;
           qh_fprintf(qh, qh->ferr, 7012, "qhull warning: unknown 'F' output option %c, rest ignored\n", (int)s[0]);
           while (*++s && !isspace(*s));
           break;
         }
       }
       break;
     case 'G':
       isgeom= True;
       qh_appendprint(qh, qh_PRINTgeom);
       while (*s && !isspace(*s)) {
         switch (*s++) {
         case 'a':
           qh_option(qh, "Gall-points", NULL, NULL);
           qh->PRINTdots= True;
           break;
         case 'c':
           qh_option(qh, "Gcentrums", NULL, NULL);
           qh->PRINTcentrums= True;
           break;
         case 'h':
           qh_option(qh, "Gintersections", NULL, NULL);
           qh->DOintersections= True;
           break;
         case 'i':
           qh_option(qh, "Ginner", NULL, NULL);
           qh->PRINTinner= True;
           break;
         case 'n':
           qh_option(qh, "Gno-planes", NULL, NULL);
           qh->PRINTnoplanes= True;
           break;
         case 'o':
           qh_option(qh, "Gouter", NULL, NULL);
           qh->PRINTouter= True;
           break;
         case 'p':
           qh_option(qh, "Gpoints", NULL, NULL);
           qh->PRINTcoplanar= True;
           break;
         case 'r':
           qh_option(qh, "Gridges", NULL, NULL);
           qh->PRINTridges= True;
           break;
         case 't':
           qh_option(qh, "Gtransparent", NULL, NULL);
           qh->PRINTtransparent= True;
           break;
         case 'v':
           qh_option(qh, "Gvertices", NULL, NULL);
           qh->PRINTspheres= True;
           break;
         case 'D':
           if (!isdigit(*s))
             qh_fprintf(qh, qh->ferr, 6035, "qhull input error: missing dimension for option 'GDn'\n");
           else {
             if (qh->DROPdim >= 0)
               qh_fprintf(qh, qh->ferr, 7013, "qhull warning: can only drop one dimension.  Previous 'GD%d' ignored\n",
                    qh->DROPdim);
             qh->DROPdim= qh_strtol(s, &s);
             qh_option(qh, "GDrop-dim", &qh->DROPdim, NULL);
           }
           break;
         default:
           s--;
           qh_fprintf(qh, qh->ferr, 7014, "qhull warning: unknown 'G' print option %c, rest ignored\n", (int)s[0]);
           while (*++s && !isspace(*s));
           break;
         }
       }
       break;
     case 'P':
       while (*s && !isspace(*s)) {
         switch (*s++) {
         case 'd': case 'D':  /* see qh_initthresholds() */
           key= s[-1];
           i= qh_strtol(s, &s);
           r= 0;
           if (*s == ':') {
             s++;
             r= qh_strtod(s, &s);
           }
           if (key == 'd')
             qh_option(qh, "Pdrop-facets-dim-less", &i, &r);
           else
             qh_option(qh, "PDrop-facets-dim-more", &i, &r);
           break;
         case 'g':
           qh_option(qh, "Pgood-facets", NULL, NULL);
           qh->PRINTgood= True;
           break;
         case 'G':
           qh_option(qh, "PGood-facet-neighbors", NULL, NULL);
           qh->PRINTneighbors= True;
           break;
         case 'o':
           qh_option(qh, "Poutput-forced", NULL, NULL);
           qh->FORCEoutput= True;
           break;
         case 'p':
           qh_option(qh, "Pprecision-ignore", NULL, NULL);
           qh->PRINTprecision= False;
           break;
         case 'A':
           if (!isdigit(*s))
             qh_fprintf(qh, qh->ferr, 6036, "qhull input error: missing facet count for keep area option 'PAn'\n");
           else {
             qh->KEEParea= qh_strtol(s, &s);
             qh_option(qh, "PArea-keep", &qh->KEEParea, NULL);
             qh->GETarea= True;
           }
           break;
         case 'F':
           if (!isdigit(*s))
             qh_fprintf(qh, qh->ferr, 6037, "qhull input error: missing facet area for option 'PFn'\n");
           else {
             qh->KEEPminArea= qh_strtod(s, &s);
             qh_option(qh, "PFacet-area-keep", NULL, &qh->KEEPminArea);
             qh->GETarea= True;
           }
           break;
         case 'M':
           if (!isdigit(*s))
             qh_fprintf(qh, qh->ferr, 6038, "qhull input error: missing merge count for option 'PMn'\n");
           else {
             qh->KEEPmerge= qh_strtol(s, &s);
             qh_option(qh, "PMerge-keep", &qh->KEEPmerge, NULL);
           }
           break;
         default:
           s--;
           qh_fprintf(qh, qh->ferr, 7015, "qhull warning: unknown 'P' print option %c, rest ignored\n", (int)s[0]);
           while (*++s && !isspace(*s));
           break;
         }
       }
       break;
     case 'Q':
       lastproject= -1;
       while (*s && !isspace(*s)) {
         switch (*s++) {
         case 'b': case 'B':  /* handled by qh_initthresholds */
           key= s[-1];
           if (key == 'b' && *s == 'B') {
             s++;
             r= qh_DEFAULTbox;
             qh->SCALEinput= True;
             qh_option(qh, "QbBound-unit-box", NULL, &r);
             break;
           }
           if (key == 'b' && *s == 'b') {
             s++;
             qh->SCALElast= True;
             qh_option(qh, "Qbbound-last", NULL, NULL);
             break;
           }
           k= qh_strtol(s, &s);
           r= 0.0;
           wasproject= False;
           if (*s == ':') {
             s++;
             if ((r= qh_strtod(s, &s)) == 0.0) {
               t= s;            /* need true dimension for memory allocation */
               while (*t && !isspace(*t)) {
                 if (toupper(*t++) == 'B'
                  && k == qh_strtol(t, &t)
                  && *t++ == ':'
                  && qh_strtod(t, &t) == 0.0) {
                   qh->PROJECTinput++;
                   trace2((qh, qh->ferr, 2004, "qh_initflags: project dimension %d\n", k));
                   qh_option(qh, "Qb-project-dim", &k, NULL);
                   wasproject= True;
                   lastproject= k;
                   break;
                 }
               }
             }
           }
           if (!wasproject) {
             if (lastproject == k && r == 0.0)
               lastproject= -1;  /* doesn't catch all possible sequences */
             else if (key == 'b') {
               qh->SCALEinput= True;
               if (r == 0.0)
                 r= -qh_DEFAULTbox;
               qh_option(qh, "Qbound-dim-low", &k, &r);
             }else {
               qh->SCALEinput= True;
               if (r == 0.0)
                 r= qh_DEFAULTbox;
               qh_option(qh, "QBound-dim-high", &k, &r);
             }
           }
           break;
         case 'c':
           qh_option(qh, "Qcoplanar-keep", NULL, NULL);
           qh->KEEPcoplanar= True;
           break;
         case 'f':
           qh_option(qh, "Qfurthest-outside", NULL, NULL);
           qh->BESToutside= True;
           break;
         case 'g':
           qh_option(qh, "Qgood-facets-only", NULL, NULL);
           qh->ONLYgood= True;
           break;
         case 'i':
           qh_option(qh, "Qinterior-keep", NULL, NULL);
           qh->KEEPinside= True;
           break;
         case 'm':
           qh_option(qh, "Qmax-outside-only", NULL, NULL);
           qh->ONLYmax= True;
           break;
         case 'r':
           qh_option(qh, "Qrandom-outside", NULL, NULL);
           qh->RANDOMoutside= True;
           break;
         case 's':
           qh_option(qh, "Qsearch-initial-simplex", NULL, NULL);
           qh->ALLpoints= True;
           break;
         case 't':
           qh_option(qh, "Qtriangulate", NULL, NULL);
           qh->TRIangulate= True;
           break;
         case 'T':
           qh_option(qh, "QTestPoints", NULL, NULL);
           if (!isdigit(*s))
             qh_fprintf(qh, qh->ferr, 6039, "qhull input error: missing number of test points for option 'QTn'\n");
           else {
             qh->TESTpoints= qh_strtol(s, &s);
             qh_option(qh, "QTestPoints", &qh->TESTpoints, NULL);
           }
           break;
         case 'u':
           qh_option(qh, "QupperDelaunay", NULL, NULL);
           qh->UPPERdelaunay= True;
           break;
         case 'v':
           qh_option(qh, "Qvertex-neighbors-convex", NULL, NULL);
           qh->TESTvneighbors= True;
           break;
         case 'x':
           qh_option(qh, "Qxact-merge", NULL, NULL);
           qh->MERGEexact= True;
           break;
         case 'z':
           qh_option(qh, "Qz-infinity-point", NULL, NULL);
           qh->ATinfinity= True;
           break;
         case '0':
           qh_option(qh, "Q0-no-premerge", NULL, NULL);
           qh->NOpremerge= True;
           break;
         case '1':
           if (!isdigit(*s)) {
             qh_option(qh, "Q1-no-angle-sort", NULL, NULL);
             qh->ANGLEmerge= False;
             break;
           }
           switch (*s++) {
           case '0':
             qh_option(qh, "Q10-no-narrow", NULL, NULL);
             qh->NOnarrow= True;
             break;
           case '1':
             qh_option(qh, "Q11-trinormals Qtriangulate", NULL, NULL);
             qh->TRInormals= True;
             qh->TRIangulate= True;
             break;
           default:
             s--;
             qh_fprintf(qh, qh->ferr, 7016, "qhull warning: unknown 'Q' qhull option 1%c, rest ignored\n", (int)s[0]);
             while (*++s && !isspace(*s));
             break;
           }
           break;
         case '2':
           qh_option(qh, "Q2-no-merge-independent", NULL, NULL);
           qh->MERGEindependent= False;
           goto LABELcheckdigit;
           break; /* no warnings */
         case '3':
           qh_option(qh, "Q3-no-merge-vertices", NULL, NULL);
           qh->MERGEvertices= False;
         LABELcheckdigit:
           if (isdigit(*s))
             qh_fprintf(qh, qh->ferr, 7017, "qhull warning: can not follow '1', '2', or '3' with a digit.  '%c' skipped.\n",
                      *s++);
           break;
         case '4':
           qh_option(qh, "Q4-avoid-old-into-new", NULL, NULL);
           qh->AVOIDold= True;
           break;
         case '5':
           qh_option(qh, "Q5-no-check-outer", NULL, NULL);
           qh->SKIPcheckmax= True;
           break;
         case '6':
           qh_option(qh, "Q6-no-concave-merge", NULL, NULL);
           qh->SKIPconvex= True;
           break;
         case '7':
           qh_option(qh, "Q7-no-breadth-first", NULL, NULL);
           qh->VIRTUALmemory= True;
           break;
         case '8':
           qh_option(qh, "Q8-no-near-inside", NULL, NULL);
           qh->NOnearinside= True;
           break;
         case '9':
           qh_option(qh, "Q9-pick-furthest", NULL, NULL);
           qh->PICKfurthest= True;
           break;
         case 'G':
           i= qh_strtol(s, &t);
           if (qh->GOODpoint)
             qh_fprintf(qh, qh->ferr, 7018, "qhull warning: good point already defined for option 'QGn'.  Ignored\n");
           else if (s == t)
             qh_fprintf(qh, qh->ferr, 7019, "qhull warning: missing good point id for option 'QGn'.  Ignored\n");
           else if (i < 0 || *s == '-') {
             qh->GOODpoint= i-1;
             qh_option(qh, "QGood-if-dont-see-point", &i, NULL);
           }else {
             qh->GOODpoint= i+1;
             qh_option(qh, "QGood-if-see-point", &i, NULL);
           }
           s= t;
           break;
         case 'J':
           if (!isdigit(*s) && *s != '-')
             qh->JOGGLEmax= 0.0;
           else {
             qh->JOGGLEmax= (realT) qh_strtod(s, &s);
             qh_option(qh, "QJoggle", NULL, &qh->JOGGLEmax);
           }
           break;
         case 'R':
           if (!isdigit(*s) && *s != '-')
             qh_fprintf(qh, qh->ferr, 7020, "qhull warning: missing random seed for option 'QRn'.  Ignored\n");
           else {
             qh->ROTATErandom= i= qh_strtol(s, &s);
             if (i > 0)
               qh_option(qh, "QRotate-id", &i, NULL );
             else if (i < -1)
               qh_option(qh, "QRandom-seed", &i, NULL );
           }
           break;
         case 'V':
           i= qh_strtol(s, &t);
           if (qh->GOODvertex)
             qh_fprintf(qh, qh->ferr, 7021, "qhull warning: good vertex already defined for option 'QVn'.  Ignored\n");
           else if (s == t)
             qh_fprintf(qh, qh->ferr, 7022, "qhull warning: no good point id given for option 'QVn'.  Ignored\n");
           else if (i < 0) {
             qh->GOODvertex= i - 1;
             qh_option(qh, "QV-good-facets-not-point", &i, NULL);
           }else {
             qh_option(qh, "QV-good-facets-point", &i, NULL);
             qh->GOODvertex= i + 1;
           }
           s= t;
           break;
         default:
           s--;
           qh_fprintf(qh, qh->ferr, 7023, "qhull warning: unknown 'Q' qhull option %c, rest ignored\n", (int)s[0]);
           while (*++s && !isspace(*s));
           break;
         }
       }
       break;
     case 'T':
       while (*s && !isspace(*s)) {
         if (isdigit(*s) || *s == '-')
           qh->IStracing= qh_strtol(s, &s);
         else switch (*s++) {
         case 'a':
           qh_option(qh, "Tannotate-output", NULL, NULL);
           qh->ANNOTATEoutput= True;
           break;
         case 'c':
           qh_option(qh, "Tcheck-frequently", NULL, NULL);
           qh->CHECKfrequently= True;
           break;
         case 's':
           qh_option(qh, "Tstatistics", NULL, NULL);
           qh->PRINTstatistics= True;
           break;
         case 'v':
           qh_option(qh, "Tverify", NULL, NULL);
           qh->VERIFYoutput= True;
           break;
         case 'z':
           if (qh->ferr == qh_FILEstderr) {
             /* The C++ interface captures the output in qh_fprint_qhull() */
             qh_option(qh, "Tz-stdout", NULL, NULL);
             qh->USEstdout= True;
           }else if (!qh->fout)
             qh_fprintf(qh, qh->ferr, 7024, "qhull warning: output file undefined(stdout).  Option 'Tz' ignored.\n");
           else {
             qh_option(qh, "Tz-stdout", NULL, NULL);
             qh->USEstdout= True;
             qh->ferr= qh->fout;
             qh->qhmem.ferr= qh->fout;
           }
           break;
         case 'C':
           if (!isdigit(*s))
             qh_fprintf(qh, qh->ferr, 7025, "qhull warning: missing point id for cone for trace option 'TCn'.  Ignored\n");
           else {
             i= qh_strtol(s, &s);
             qh_option(qh, "TCone-stop", &i, NULL);
             qh->STOPcone= i + 1;
           }
           break;
         case 'F':
           if (!isdigit(*s))
             qh_fprintf(qh, qh->ferr, 7026, "qhull warning: missing frequency count for trace option 'TFn'.  Ignored\n");
           else {
             qh->REPORTfreq= qh_strtol(s, &s);
             qh_option(qh, "TFacet-log", &qh->REPORTfreq, NULL);
             qh->REPORTfreq2= qh->REPORTfreq/2;  /* for tracemerging() */
           }
           break;
         case 'I':
           if (!isspace(*s))
             qh_fprintf(qh, qh->ferr, 7027, "qhull warning: missing space between 'TI' and filename, %s\n", s);
           while (isspace(*s))
             s++;
           t= qh_skipfilename(qh, s);
           {
             char filename[qh_FILENAMElen];
 
             qh_copyfilename(qh, filename, (int)sizeof(filename), s, (int)(t-s));   /* WARN64 */
             s= t;
             if (!freopen(filename, "r", stdin)) {
               qh_fprintf(qh, qh->ferr, 6041, "qhull error: could not open file \"%s\".", filename);
               qh_errexit(qh, qh_ERRinput, NULL, NULL);
             }else {
               qh_option(qh, "TInput-file", NULL, NULL);
               qh_option(qh, filename, NULL, NULL);
             }
           }
           break;
         case 'O':
             if (!isspace(*s))
                 qh_fprintf(qh, qh->ferr, 7028, "qhull warning: missing space between 'TO' and filename, %s\n", s);
             while (isspace(*s))
                 s++;
             t= qh_skipfilename(qh, s);
             {
               char filename[qh_FILENAMElen];
 
               qh_copyfilename(qh, filename, (int)sizeof(filename), s, (int)(t-s));  /* WARN64 */
               s= t;
               if (!freopen(filename, "w", stdout)) {
                 qh_fprintf(qh, qh->ferr, 6044, "qhull error: could not open file \"%s\".", filename);
                 qh_errexit(qh, qh_ERRinput, NULL, NULL);
               }else {
                 qh_option(qh, "TOutput-file", NULL, NULL);
               qh_option(qh, filename, NULL, NULL);
             }
           }
           break;
         case 'P':
           if (!isdigit(*s))
             qh_fprintf(qh, qh->ferr, 7029, "qhull warning: missing point id for trace option 'TPn'.  Ignored\n");
           else {
             qh->TRACEpoint= qh_strtol(s, &s);
             qh_option(qh, "Trace-point", &qh->TRACEpoint, NULL);
           }
           break;
         case 'M':
           if (!isdigit(*s))
             qh_fprintf(qh, qh->ferr, 7030, "qhull warning: missing merge id for trace option 'TMn'.  Ignored\n");
           else {
             qh->TRACEmerge= qh_strtol(s, &s);
             qh_option(qh, "Trace-merge", &qh->TRACEmerge, NULL);
           }
           break;
         case 'R':
           if (!isdigit(*s))
             qh_fprintf(qh, qh->ferr, 7031, "qhull warning: missing rerun count for trace option 'TRn'.  Ignored\n");
           else {
             qh->RERUN= qh_strtol(s, &s);
             qh_option(qh, "TRerun", &qh->RERUN, NULL);
           }
           break;
         case 'V':
           i= qh_strtol(s, &t);
           if (s == t)
             qh_fprintf(qh, qh->ferr, 7032, "qhull warning: missing furthest point id for trace option 'TVn'.  Ignored\n");
           else if (i < 0) {
             qh->STOPpoint= i - 1;
             qh_option(qh, "TV-stop-before-point", &i, NULL);
           }else {
             qh->STOPpoint= i + 1;
             qh_option(qh, "TV-stop-after-point", &i, NULL);
           }
           s= t;
           break;
         case 'W':
           if (!isdigit(*s))
             qh_fprintf(qh, qh->ferr, 7033, "qhull warning: missing max width for trace option 'TWn'.  Ignored\n");
           else {
             qh->TRACEdist= (realT) qh_strtod(s, &s);
             qh_option(qh, "TWide-trace", NULL, &qh->TRACEdist);
           }
           break;
         default:
           s--;
           qh_fprintf(qh, qh->ferr, 7034, "qhull warning: unknown 'T' trace option %c, rest ignored\n", (int)s[0]);
           while (*++s && !isspace(*s));
           break;
         }
       }
       break;
     default:
       qh_fprintf(qh, qh->ferr, 7035, "qhull warning: unknown flag %c(%x)\n", (int)s[-1],
                (int)s[-1]);
       break;
     }
     if (s-1 == prev_s && *s && !isspace(*s)) {
       qh_fprintf(qh, qh->ferr, 7036, "qhull warning: missing space after flag %c(%x); reserved for menu. Skipped.\n",
                (int)*prev_s, (int)*prev_s);
       while (*s && !isspace(*s))
         s++;
     }
   }
   if (qh->STOPcone && qh->JOGGLEmax < REALmax/2)
     qh_fprintf(qh, qh->ferr, 7078, "qhull warning: 'TCn' (stopCone) ignored when used with 'QJn' (joggle)\n");
   if (isgeom && !qh->FORCEoutput && qh->PRINTout[1])
     qh_fprintf(qh, qh->ferr, 7037, "qhull warning: additional output formats are not compatible with Geomview\n");
   /* set derived values in qh_initqhull_globals */
 } /* initflags */
 
 
 /*---------------------------------
 
   qh_initqhull_buffers(qh)
     initialize global memory buffers
 
   notes:
     must match qh_freebuffers()
 */
 void qh_initqhull_buffers(qhT *qh) {
   int k;
 
   qh->TEMPsize= (qh->qhmem.LASTsize - sizeof(setT))/SETelemsize;
   if (qh->TEMPsize <= 0 || qh->TEMPsize > qh->qhmem.LASTsize)
     qh->TEMPsize= 8;  /* e.g., if qh_NOmem */
   qh->other_points= qh_setnew(qh, qh->TEMPsize);
   qh->del_vertices= qh_setnew(qh, qh->TEMPsize);
   qh->coplanarfacetset= qh_setnew(qh, qh->TEMPsize);
   qh->NEARzero= (realT *)qh_memalloc(qh, qh->hull_dim * sizeof(realT));
   qh->lower_threshold= (realT *)qh_memalloc(qh, (qh->input_dim+1) * sizeof(realT));
   qh->upper_threshold= (realT *)qh_memalloc(qh, (qh->input_dim+1) * sizeof(realT));
   qh->lower_bound= (realT *)qh_memalloc(qh, (qh->input_dim+1) * sizeof(realT));
   qh->upper_bound= (realT *)qh_memalloc(qh, (qh->input_dim+1) * sizeof(realT));
   for (k=qh->input_dim+1; k--; ) {  /* duplicated in qh_initqhull_buffers and qh_clear_ouputflags */
     qh->lower_threshold[k]= -REALmax;
     qh->upper_threshold[k]= REALmax;
     qh->lower_bound[k]= -REALmax;
     qh->upper_bound[k]= REALmax;
   }
   qh->gm_matrix= (coordT *)qh_memalloc(qh, (qh->hull_dim+1) * qh->hull_dim * sizeof(coordT));
   qh->gm_row= (coordT **)qh_memalloc(qh, (qh->hull_dim+1) * sizeof(coordT *));
 } /* initqhull_buffers */
 
 /*---------------------------------
 
   qh_initqhull_globals(qh, points, numpoints, dim, ismalloc )
     initialize globals
     if ismalloc
       points were malloc'd and qhull should free at end
 
   returns:
     sets qh.first_point, num_points, input_dim, hull_dim and others
     seeds random number generator (seed=1 if tracing)
     modifies qh.hull_dim if ((qh.DELAUNAY and qh.PROJECTdelaunay) or qh.PROJECTinput)
     adjust user flags as needed
     also checks DIM3 dependencies and constants
 
   notes:
     do not use qh_point() since an input transformation may move them elsewhere
 
   see:
     qh_initqhull_start() sets default values for non-zero globals
 
   design:
     initialize points array from input arguments
     test for qh.ZEROcentrum
       (i.e., use opposite vertex instead of cetrum for convexity testing)
     initialize qh.CENTERtype, qh.normal_size,
       qh.center_size, qh.TRACEpoint/level,
     initialize and test random numbers
     qh_initqhull_outputflags() -- adjust and test output flags
 */
 void qh_initqhull_globals(qhT *qh, coordT *points, int numpoints, int dim, boolT ismalloc) {
   int seed, pointsneeded, extra= 0, i, randi, k;
   realT randr;
   realT factorial;
 
   time_t timedata;
 
   trace0((qh, qh->ferr, 13, "qh_initqhull_globals: for %s | %s\n", qh->rbox_command,
       qh->qhull_command));
   qh->POINTSmalloc= ismalloc;
   qh->first_point= points;
   qh->num_points= numpoints;
   qh->hull_dim= qh->input_dim= dim;
   if (!qh->NOpremerge && !qh->MERGEexact && !qh->PREmerge && qh->JOGGLEmax > REALmax/2) {
     qh->MERGING= True;
     if (qh->hull_dim <= 4) {
       qh->PREmerge= True;
       qh_option(qh, "_pre-merge", NULL, NULL);
     }else {
       qh->MERGEexact= True;
       qh_option(qh, "Qxact_merge", NULL, NULL);
     }
   }else if (qh->MERGEexact)
     qh->MERGING= True;
   if (!qh->NOpremerge && qh->JOGGLEmax > REALmax/2) {
 #ifdef qh_NOmerge
     qh->JOGGLEmax= 0.0;
 #endif
   }
   if (qh->TRIangulate && qh->JOGGLEmax < REALmax/2 && qh->PRINTprecision)
     qh_fprintf(qh, qh->ferr, 7038, "qhull warning: joggle('QJ') always produces simplicial output.  Triangulated output('Qt') does nothing.\n");
   if (qh->JOGGLEmax < REALmax/2 && qh->DELAUNAY && !qh->SCALEinput && !qh->SCALElast) {
     qh->SCALElast= True;
     qh_option(qh, "Qbbound-last-qj", NULL, NULL);
   }
   if (qh->MERGING && !qh->POSTmerge && qh->premerge_cos > REALmax/2
   && qh->premerge_centrum == 0) {
     qh->ZEROcentrum= True;
     qh->ZEROall_ok= True;
     qh_option(qh, "_zero-centrum", NULL, NULL);
   }
   if (qh->JOGGLEmax < REALmax/2 && REALepsilon > 2e-8 && qh->PRINTprecision)
     qh_fprintf(qh, qh->ferr, 7039, "qhull warning: real epsilon, %2.2g, is probably too large for joggle('QJn')\nRecompile with double precision reals(see user.h).\n",
           REALepsilon);
 #ifdef qh_NOmerge
   if (qh->MERGING) {
     qh_fprintf(qh, qh->ferr, 6045, "qhull input error: merging not installed(qh_NOmerge + 'Qx', 'Cn' or 'An')\n");
     qh_errexit(qh, qh_ERRinput, NULL, NULL);
   }
 #endif
   if (qh->DELAUNAY && qh->KEEPcoplanar && !qh->KEEPinside) {
     qh->KEEPinside= True;
     qh_option(qh, "Qinterior-keep", NULL, NULL);
   }
   if (qh->DELAUNAY && qh->HALFspace) {
     qh_fprintf(qh, qh->ferr, 6046, "qhull input error: can not use Delaunay('d') or Voronoi('v') with halfspace intersection('H')\n");
     qh_errexit(qh, qh_ERRinput, NULL, NULL);
   }
   if (!qh->DELAUNAY && (qh->UPPERdelaunay || qh->ATinfinity)) {
     qh_fprintf(qh, qh->ferr, 6047, "qhull input error: use upper-Delaunay('Qu') or infinity-point('Qz') with Delaunay('d') or Voronoi('v')\n");
     qh_errexit(qh, qh_ERRinput, NULL, NULL);
   }
   if (qh->UPPERdelaunay && qh->ATinfinity) {
     qh_fprintf(qh, qh->ferr, 6048, "qhull input error: can not use infinity-point('Qz') with upper-Delaunay('Qu')\n");
     qh_errexit(qh, qh_ERRinput, NULL, NULL);
   }
   if (qh->SCALElast && !qh->DELAUNAY && qh->PRINTprecision)
     qh_fprintf(qh, qh->ferr, 7040, "qhull input warning: option 'Qbb' (scale-last-coordinate) is normally used with 'd' or 'v'\n");
   qh->DOcheckmax= (!qh->SKIPcheckmax && qh->MERGING );
   qh->KEEPnearinside= (qh->DOcheckmax && !(qh->KEEPinside && qh->KEEPcoplanar)
                           && !qh->NOnearinside);
   if (qh->MERGING)
     qh->CENTERtype= qh_AScentrum;
   else if (qh->VORONOI)
     qh->CENTERtype= qh_ASvoronoi;
   if (qh->TESTvneighbors && !qh->MERGING) {
     qh_fprintf(qh, qh->ferr, 6049, "qhull input error: test vertex neighbors('Qv') needs a merge option\n");
     qh_errexit(qh, qh_ERRinput, NULL ,NULL);
   }
   if (qh->PROJECTinput || (qh->DELAUNAY && qh->PROJECTdelaunay)) {
     qh->hull_dim -= qh->PROJECTinput;
     if (qh->DELAUNAY) {
       qh->hull_dim++;
       if (qh->ATinfinity)
         extra= 1;
     }
   }
   if (qh->hull_dim <= 1) {
     qh_fprintf(qh, qh->ferr, 6050, "qhull error: dimension %d must be > 1\n", qh->hull_dim);
     qh_errexit(qh, qh_ERRinput, NULL, NULL);
   }
   for (k=2, factorial=1.0; k < qh->hull_dim; k++)
     factorial *= k;
   qh->AREAfactor= 1.0 / factorial;
   trace2((qh, qh->ferr, 2005, "qh_initqhull_globals: initialize globals.  dim %d numpoints %d malloc? %d projected %d to hull_dim %d\n",
         dim, numpoints, ismalloc, qh->PROJECTinput, qh->hull_dim));
   qh->normal_size= qh->hull_dim * sizeof(coordT);
   qh->center_size= qh->normal_size - sizeof(coordT);
   pointsneeded= qh->hull_dim+1;
   if (qh->hull_dim > qh_DIMmergeVertex) {
     qh->MERGEvertices= False;
     qh_option(qh, "Q3-no-merge-vertices-dim-high", NULL, NULL);
   }
   if (qh->GOODpoint)
     pointsneeded++;
 #ifdef qh_NOtrace
   if (qh->IStracing) {
     qh_fprintf(qh, qh->ferr, 6051, "qhull input error: tracing is not installed(qh_NOtrace in user.h)");
     qh_errexit(qh, qh_ERRqhull, NULL, NULL);
   }
 #endif
   if (qh->RERUN > 1) {
     qh->TRACElastrun= qh->IStracing; /* qh_build_withrestart duplicates next conditional */
     if (qh->IStracing != -1)
       qh->IStracing= 0;
   }else if (qh->TRACEpoint != -1 || qh->TRACEdist < REALmax/2 || qh->TRACEmerge) {
     qh->TRACElevel= (qh->IStracing? qh->IStracing : 3);
     qh->IStracing= 0;
   }
   if (qh->ROTATErandom == 0 || qh->ROTATErandom == -1) {
     seed= (int)time(&timedata);
     if (qh->ROTATErandom  == -1) {
       seed= -seed;
       qh_option(qh, "QRandom-seed", &seed, NULL );
     }else
       qh_option(qh, "QRotate-random", &seed, NULL);
     qh->ROTATErandom= seed;
   }
   seed= qh->ROTATErandom;
   if (seed == INT_MIN)    /* default value */
     seed= 1;
   else if (seed < 0)
     seed= -seed;
   qh_RANDOMseed_(qh, seed);
   randr= 0.0;
   for (i=1000; i--; ) {
     randi= qh_RANDOMint;
     randr += randi;
     if (randi > qh_RANDOMmax) {
       qh_fprintf(qh, qh->ferr, 8036, "\
 qhull configuration error (qh_RANDOMmax in user.h):\n\
    random integer %d > qh_RANDOMmax(qh, %.8g)\n",
                randi, qh_RANDOMmax);
       qh_errexit(qh, qh_ERRinput, NULL, NULL);
     }
   }
   qh_RANDOMseed_(qh, seed);
   randr = randr/1000;
   if (randr < qh_RANDOMmax * 0.1
   || randr > qh_RANDOMmax * 0.9)
     qh_fprintf(qh, qh->ferr, 8037, "\
 qhull configuration warning (qh_RANDOMmax in user.h):\n\
    average of 1000 random integers (%.2g) is much different than expected (%.2g).\n\
    Is qh_RANDOMmax (%.2g) wrong?\n",
              randr, qh_RANDOMmax * 0.5, qh_RANDOMmax);
   qh->RANDOMa= 2.0 * qh->RANDOMfactor/qh_RANDOMmax;
   qh->RANDOMb= 1.0 - qh->RANDOMfactor;
   if (qh_HASHfactor < 1.1) {
     qh_fprintf(qh, qh->ferr, 6052, "qhull internal error (qh_initqhull_globals): qh_HASHfactor %d must be at least 1.1.  Qhull uses linear hash probing\n",
       qh_HASHfactor);
     qh_errexit(qh, qh_ERRqhull, NULL, NULL);
   }
   if (numpoints+extra < pointsneeded) {
     qh_fprintf(qh, qh->ferr, 6214, "qhull input error: not enough points(%d) to construct initial simplex (need %d)\n",
             numpoints, pointsneeded);
     qh_errexit(qh, qh_ERRinput, NULL, NULL);
   }
   qh_initqhull_outputflags(qh);
 } /* initqhull_globals */
 
 /*---------------------------------
 
   qh_initqhull_mem(qh, )
-    initialize mem.c for qhull
+    initialize mem_r.c for qhull
     qh.hull_dim and qh.normal_size determine some of the allocation sizes
     if qh.MERGING,
       includes ridgeT
     calls qh_user_memsizes(qh) to add up to 10 additional sizes for quick allocation
       (see numsizes below)
 
   returns:
-    mem.c already for qh_memalloc/qh_memfree (errors if called beforehand)
+    mem_r.c already for qh_memalloc/qh_memfree (errors if called beforehand)
 
   notes:
     qh_produceoutput() prints memsizes
 
 */
 void qh_initqhull_mem(qhT *qh) {
   int numsizes;
   int i;
 
   numsizes= 8+10;
   qh_meminitbuffers(qh, qh->IStracing, qh_MEMalign, numsizes,
                      qh_MEMbufsize, qh_MEMinitbuf);
   qh_memsize(qh, (int)sizeof(vertexT));
   if (qh->MERGING) {
     qh_memsize(qh, (int)sizeof(ridgeT));
     qh_memsize(qh, (int)sizeof(mergeT));
   }
   qh_memsize(qh, (int)sizeof(facetT));
   i= sizeof(setT) + (qh->hull_dim - 1) * SETelemsize;  /* ridge.vertices */
   qh_memsize(qh, i);
   qh_memsize(qh, qh->normal_size);        /* normal */
   i += SETelemsize;                 /* facet.vertices, .ridges, .neighbors */
   qh_memsize(qh, i);
   qh_user_memsizes(qh);
   qh_memsetup(qh);
 } /* initqhull_mem */
 
 /*---------------------------------
 
   qh_initqhull_outputflags
     initialize flags concerned with output
 
   returns:
     adjust user flags as needed
 
   see:
     qh_clear_outputflags() resets the flags
 
   design:
     test for qh.PRINTgood (i.e., only print 'good' facets)
     check for conflicting print output options
 */
 void qh_initqhull_outputflags(qhT *qh) {
   boolT printgeom= False, printmath= False, printcoplanar= False;
   int i;
 
   trace3((qh, qh->ferr, 3024, "qh_initqhull_outputflags: %s\n", qh->qhull_command));
   if (!(qh->PRINTgood || qh->PRINTneighbors)) {
     if (qh->KEEParea || qh->KEEPminArea < REALmax/2 || qh->KEEPmerge || qh->DELAUNAY
         || (!qh->ONLYgood && (qh->GOODvertex || qh->GOODpoint))) {
       qh->PRINTgood= True;
       qh_option(qh, "Pgood", NULL, NULL);
     }
   }
   if (qh->PRINTtransparent) {
     if (qh->hull_dim != 4 || !qh->DELAUNAY || qh->VORONOI || qh->DROPdim >= 0) {
       qh_fprintf(qh, qh->ferr, 6215, "qhull input error: transparent Delaunay('Gt') needs 3-d Delaunay('d') w/o 'GDn'\n");
       qh_errexit(qh, qh_ERRinput, NULL, NULL);
     }
     qh->DROPdim = 3;
     qh->PRINTridges = True;
   }
   for (i=qh_PRINTEND; i--; ) {
     if (qh->PRINTout[i] == qh_PRINTgeom)
       printgeom= True;
     else if (qh->PRINTout[i] == qh_PRINTmathematica || qh->PRINTout[i] == qh_PRINTmaple)
       printmath= True;
     else if (qh->PRINTout[i] == qh_PRINTcoplanars)
       printcoplanar= True;
     else if (qh->PRINTout[i] == qh_PRINTpointnearest)
       printcoplanar= True;
     else if (qh->PRINTout[i] == qh_PRINTpointintersect && !qh->HALFspace) {
       qh_fprintf(qh, qh->ferr, 6053, "qhull input error: option 'Fp' is only used for \nhalfspace intersection('Hn,n,n').\n");
       qh_errexit(qh, qh_ERRinput, NULL, NULL);
     }else if (qh->PRINTout[i] == qh_PRINTtriangles && (qh->HALFspace || qh->VORONOI)) {
       qh_fprintf(qh, qh->ferr, 6054, "qhull input error: option 'Ft' is not available for Voronoi vertices or halfspace intersection\n");
       qh_errexit(qh, qh_ERRinput, NULL, NULL);
     }else if (qh->PRINTout[i] == qh_PRINTcentrums && qh->VORONOI) {
       qh_fprintf(qh, qh->ferr, 6055, "qhull input error: option 'FC' is not available for Voronoi vertices('v')\n");
       qh_errexit(qh, qh_ERRinput, NULL, NULL);
     }else if (qh->PRINTout[i] == qh_PRINTvertices) {
       if (qh->VORONOI)
         qh_option(qh, "Fvoronoi", NULL, NULL);
       else
         qh_option(qh, "Fvertices", NULL, NULL);
     }
   }
   if (printcoplanar && qh->DELAUNAY && qh->JOGGLEmax < REALmax/2) {
     if (qh->PRINTprecision)
       qh_fprintf(qh, qh->ferr, 7041, "qhull input warning: 'QJ' (joggle) will usually prevent coincident input sites for options 'Fc' and 'FP'\n");
   }
   if (printmath && (qh->hull_dim > 3 || qh->VORONOI)) {
     qh_fprintf(qh, qh->ferr, 6056, "qhull input error: Mathematica and Maple output is only available for 2-d and 3-d convex hulls and 2-d Delaunay triangulations\n");
     qh_errexit(qh, qh_ERRinput, NULL, NULL);
   }
   if (printgeom) {
     if (qh->hull_dim > 4) {
       qh_fprintf(qh, qh->ferr, 6057, "qhull input error: Geomview output is only available for 2-d, 3-d and 4-d\n");
       qh_errexit(qh, qh_ERRinput, NULL, NULL);
     }
     if (qh->PRINTnoplanes && !(qh->PRINTcoplanar + qh->PRINTcentrums
      + qh->PRINTdots + qh->PRINTspheres + qh->DOintersections + qh->PRINTridges)) {
       qh_fprintf(qh, qh->ferr, 6058, "qhull input error: no output specified for Geomview\n");
       qh_errexit(qh, qh_ERRinput, NULL, NULL);
     }
     if (qh->VORONOI && (qh->hull_dim > 3 || qh->DROPdim >= 0)) {
       qh_fprintf(qh, qh->ferr, 6059, "qhull input error: Geomview output for Voronoi diagrams only for 2-d\n");
       qh_errexit(qh, qh_ERRinput, NULL, NULL);
     }
     /* can not warn about furthest-site Geomview output: no lower_threshold */
     if (qh->hull_dim == 4 && qh->DROPdim == -1 &&
         (qh->PRINTcoplanar || qh->PRINTspheres || qh->PRINTcentrums)) {
       qh_fprintf(qh, qh->ferr, 7042, "qhull input warning: coplanars, vertices, and centrums output not\n\
 available for 4-d output(ignored).  Could use 'GDn' instead.\n");
       qh->PRINTcoplanar= qh->PRINTspheres= qh->PRINTcentrums= False;
     }
   }
   if (!qh->KEEPcoplanar && !qh->KEEPinside && !qh->ONLYgood) {
     if ((qh->PRINTcoplanar && qh->PRINTspheres) || printcoplanar) {
       if (qh->QHULLfinished) {
         qh_fprintf(qh, qh->ferr, 7072, "qhull output warning: ignoring coplanar points, option 'Qc' was not set for the first run of qhull.\n");
       }else {
         qh->KEEPcoplanar = True;
         qh_option(qh, "Qcoplanar", NULL, NULL);
       }
     }
   }
   qh->PRINTdim= qh->hull_dim;
   if (qh->DROPdim >=0) {    /* after Geomview checks */
     if (qh->DROPdim < qh->hull_dim) {
       qh->PRINTdim--;
       if (!printgeom || qh->hull_dim < 3)
         qh_fprintf(qh, qh->ferr, 7043, "qhull input warning: drop dimension 'GD%d' is only available for 3-d/4-d Geomview\n", qh->DROPdim);
     }else
       qh->DROPdim= -1;
   }else if (qh->VORONOI) {
     qh->DROPdim= qh->hull_dim-1;
     qh->PRINTdim= qh->hull_dim-1;
   }
 } /* qh_initqhull_outputflags */
 
 /*---------------------------------
 
   qh_initqhull_start(qh, infile, outfile, errfile )
     allocate memory if needed and call qh_initqhull_start2()
 */
 void qh_initqhull_start(qhT *qh, FILE *infile, FILE *outfile, FILE *errfile) {
 
   qh_initstatistics(qh);
   qh_initqhull_start2(qh, infile, outfile, errfile);
 } /* initqhull_start */
 
 /*---------------------------------
 
   qh_initqhull_start2(qh, infile, outfile, errfile )
     start initialization of qhull
     initialize statistics, stdio, default values for global variables
     assumes qh is allocated
   notes:
     report errors elsewhere, error handling and g_qhull_output [Qhull.cpp, QhullQh()] not in initialized
   see:
     qh_maxmin() determines the precision constants
-    qh_freeqhull2()
+    qh_freeqhull()
 */
 void qh_initqhull_start2(qhT *qh, FILE *infile, FILE *outfile, FILE *errfile) {
   time_t timedata;
   int seed;
 
   qh_CPUclock; /* start the clock(for qh_clock).  One-shot. */
   /* memset is the same in qh_freeqhull() and qh_initqhull_start2() */
   memset((char *)qh, 0, sizeof(qhT)-sizeof(qhmemT)-sizeof(qhstatT));   /* every field is 0, FALSE, NULL */
+  qh->NOerrexit= True;
   qh->ANGLEmerge= True;
   qh->DROPdim= -1;
   qh->ferr= errfile;
   qh->fin= infile;
   qh->fout= outfile;
   qh->furthest_id= -1;
   qh->JOGGLEmax= REALmax;
   qh->KEEPminArea = REALmax;
   qh->last_low= REALmax;
   qh->last_high= REALmax;
   qh->last_newhigh= REALmax;
   qh->last_random= 1;
   qh->max_outside= 0.0;
   qh->max_vertex= 0.0;
   qh->MAXabs_coord= 0.0;
   qh->MAXsumcoord= 0.0;
   qh->MAXwidth= -REALmax;
   qh->MERGEindependent= True;
   qh->MINdenom_1= fmax_(1.0/REALmax, REALmin); /* used by qh_scalepoints */
   qh->MINoutside= 0.0;
   qh->MINvisible= REALmax;
   qh->MAXcoplanar= REALmax;
   qh->outside_err= REALmax;
   qh->premerge_centrum= 0.0;
   qh->premerge_cos= REALmax;
   qh->PRINTprecision= True;
   qh->PRINTradius= 0.0;
   qh->postmerge_cos= REALmax;
   qh->postmerge_centrum= 0.0;
   qh->ROTATErandom= INT_MIN;
   qh->MERGEvertices= True;
   qh->totarea= 0.0;
   qh->totvol= 0.0;
   qh->TRACEdist= REALmax;
   qh->TRACEpoint= -1; /* recompile or use 'TPn' */
   qh->tracefacet_id= UINT_MAX;  /* recompile to trace a facet */
   qh->tracevertex_id= UINT_MAX; /* recompile to trace a vertex */
   seed= (int)time(&timedata);
   qh_RANDOMseed_(qh, seed);
-  qh->run_id= qh_RANDOMint+1; /* disallow 0 [UsingLibQhull::NOqhRunId] */
+  qh->run_id= qh_RANDOMint;
+  if(!qh->run_id)
+      qh->run_id++;  /* guarantee non-zero */
   qh_option(qh, "run-id", &qh->run_id, NULL);
   strcat(qh->qhull, "qhull");
 } /* initqhull_start2 */
 
 /*---------------------------------
 
   qh_initthresholds(qh, commandString )
     set thresholds for printing and scaling from commandString
 
   returns:
     sets qh.GOODthreshold or qh.SPLITthreshold if 'Pd0D1' used
 
   see:
     qh_initflags(), 'Qbk' 'QBk' 'Pdk' and 'PDk'
     qh_inthresholds()
 
   design:
     for each 'Pdn' or 'PDn' option
       check syntax
       set qh.lower_threshold or qh.upper_threshold
     set qh.GOODthreshold if an unbounded threshold is used
     set qh.SPLITthreshold if a bounded threshold is used
 */
 void qh_initthresholds(qhT *qh, char *command) {
   realT value;
   int idx, maxdim, k;
   char *s= command; /* non-const due to strtol */
   char key;
 
   maxdim= qh->input_dim;
   if (qh->DELAUNAY && (qh->PROJECTdelaunay || qh->PROJECTinput))
     maxdim++;
   while (*s) {
     if (*s == '-')
       s++;
     if (*s == 'P') {
       s++;
       while (*s && !isspace(key= *s++)) {
         if (key == 'd' || key == 'D') {
           if (!isdigit(*s)) {
             qh_fprintf(qh, qh->ferr, 7044, "qhull warning: no dimension given for Print option '%c' at: %s.  Ignored\n",
                     key, s-1);
             continue;
           }
           idx= qh_strtol(s, &s);
           if (idx >= qh->hull_dim) {
             qh_fprintf(qh, qh->ferr, 7045, "qhull warning: dimension %d for Print option '%c' is >= %d.  Ignored\n",
                 idx, key, qh->hull_dim);
             continue;
           }
           if (*s == ':') {
             s++;
             value= qh_strtod(s, &s);
             if (fabs((double)value) > 1.0) {
               qh_fprintf(qh, qh->ferr, 7046, "qhull warning: value %2.4g for Print option %c is > +1 or < -1.  Ignored\n",
                       value, key);
               continue;
             }
           }else
             value= 0.0;
           if (key == 'd')
             qh->lower_threshold[idx]= value;
           else
             qh->upper_threshold[idx]= value;
         }
       }
     }else if (*s == 'Q') {
       s++;
       while (*s && !isspace(key= *s++)) {
         if (key == 'b' && *s == 'B') {
           s++;
           for (k=maxdim; k--; ) {
             qh->lower_bound[k]= -qh_DEFAULTbox;
             qh->upper_bound[k]= qh_DEFAULTbox;
           }
         }else if (key == 'b' && *s == 'b')
           s++;
         else if (key == 'b' || key == 'B') {
           if (!isdigit(*s)) {
             qh_fprintf(qh, qh->ferr, 7047, "qhull warning: no dimension given for Qhull option %c.  Ignored\n",
                     key);
             continue;
           }
           idx= qh_strtol(s, &s);
           if (idx >= maxdim) {
             qh_fprintf(qh, qh->ferr, 7048, "qhull warning: dimension %d for Qhull option %c is >= %d.  Ignored\n",
                 idx, key, maxdim);
             continue;
           }
           if (*s == ':') {
             s++;
             value= qh_strtod(s, &s);
           }else if (key == 'b')
             value= -qh_DEFAULTbox;
           else
             value= qh_DEFAULTbox;
           if (key == 'b')
             qh->lower_bound[idx]= value;
           else
             qh->upper_bound[idx]= value;
         }
       }
     }else {
       while (*s && !isspace(*s))
         s++;
     }
     while (isspace(*s))
       s++;
   }
   for (k=qh->hull_dim; k--; ) {
     if (qh->lower_threshold[k] > -REALmax/2) {
       qh->GOODthreshold= True;
       if (qh->upper_threshold[k] < REALmax/2) {
         qh->SPLITthresholds= True;
         qh->GOODthreshold= False;
         break;
       }
     }else if (qh->upper_threshold[k] < REALmax/2)
       qh->GOODthreshold= True;
   }
 } /* initthresholds */
 
 /*---------------------------------
 
   qh_option(qh, option, intVal, realVal )
     add an option description to qh.qhull_options
 
   notes:
     NOerrors -- qh_option can not call qh_errexit() [qh_initqhull_start2]
     will be printed with statistics ('Ts') and errors
     strlen(option) < 40
 */
 void qh_option(qhT *qh, const char *option, int *i, realT *r) {
   char buf[200];
   int len, maxlen;
 
   sprintf(buf, "  %s", option);
   if (i)
     sprintf(buf+strlen(buf), " %d", *i);
   if (r)
     sprintf(buf+strlen(buf), " %2.2g", *r);
   len= (int)strlen(buf);  /* WARN64 */
   qh->qhull_optionlen += len;
   maxlen= sizeof(qh->qhull_options) - len -1;
   maximize_(maxlen, 0);
   if (qh->qhull_optionlen >= qh_OPTIONline && maxlen > 0) {
     qh->qhull_optionlen= len;
     strncat(qh->qhull_options, "\n", (size_t)(maxlen--));
   }
   strncat(qh->qhull_options, buf, (size_t)maxlen);
 } /* option */
 
diff --git a/src/libqhullr/index.htm b/src/libqhullr/index.htm
new file mode 100644
index 0000000..b9ca9d0
--- /dev/null
+++ b/src/libqhullr/index.htm
@@ -0,0 +1,248 @@
+
+
+
+
+Qhull functions, macros, and data structures
+
+
+
+
+
Up: Home page for Qhull

+Up: Qhull manual: Table of Contents 

+Up: Programs
+• Options
+• Output
+• Formats
+• Geomview
+• Print
+• Qhull
+• Precision
+• Trace

+Up: Qhull code

+To: Qhull files

+To: Geom • Global
+• Io • Mem
+• Merge • Poly
+• Qhull • Set
+• Stat • User
+
+

+
+
+
Qhull functions, macros, and data structures

+

+
The following sections provide an overview and index to
+Qhull's functions, macros, and data structures. Each
+section starts with an introduction. If you use Opera, the source code links back to this documentation.
+See also Calling
+Qhull from C programs and Calling Qhull from C++ programs.

+
+
Qhull uses the following conventions:

+

+
+
    
+
  • in code, global variables start with "qh "
+
  • in documentation, global variables start with 'qh.'
+
  • constants start with an upper case word
+
  • important globals include an '_'
+
  • functions, macros, and constants start with "qh_"
    • 
+
  • data types end in "T"
    • 
+
  • macros with arguments end in "_"
    • 
+
  • iterators are macros that use local variables
    • 
+
  • iterators for sets start with "FOREACH"
    • 
+
  • iterators for lists start with "FORALL"
    • 
+
  • qhull options are in single quotes (e.g., 'Pdn')
    • 
+
  • lists are sorted alphabetically
    • 
+
  • preprocessor directives on left margin for older compilers
    • 
+

+

+

+When reading the code, please note that the
+global data structure, 'qh', is a macro.  It
+either expands to "qh_qh." or to
+"qh_qh->". The later is used for
+applications which run concurrent calls to qh_qhull().
+

+When reading code with an editor, a search for
+"procedure
+will locate the header of qh_procedure.  A search for * procedure
+will locate the tail of qh_procedure.
+
+
A useful starting point is libqhull.h.  It defines most
+of Qhull data structures and top-level functions.  Search for 'PFn' to
+determine the corresponding constant in Qhull.  Search for 'Fp' to
+determine the corresponding qh_PRINT... constant.
+Search io.c to learn how the print function is implemented.

+
+
If your web browser loads .c and .h files with an external application,
+change the MIME type of .c and .h files to "text/html".
+Opera does not always work since it treats '<' characters as HTML tags.
+

+Please report documentation and link errors
+to qhull-bug@qhull.org.
+

+
+
Copyright © 1997-2012 C.B. Barber

+
+

+
+
»Qhull files 

+

+
+
This sections lists the .c and .h files for Qhull. Please
+refer to these files for detailed information.

+

+
+

+
Makefile, CMakeLists.txt

+
Makefile is preconfigured for gcc.  CMakeLists.txt supports multiple
+platforms with CMake.
+Qhull includes project files for Visual Studio and Qt.
+

+
+
 

+
libqhull.h 

+
Include file for the Qhull library (libqhull.so, qhull.dll, libqhullstatic.a).
+Data structures are documented under Poly.
+Global variables are documented under Global.
+Other data structures and variables are documented under
+Qhull or Geom.

+
+
 

+
Geom, 
+geom.h, 
+geom.c, 
+geom2.c, 
+random.c, 
+random.h

+
Geometric routines. These routines implement mathematical
+functions such as Gaussian elimination and geometric
+routines needed for Qhull. Frequently used routines are
+in geom.c while infrequent ones are in geom2.c.
+

+
+
 

+
Global, 
+global.c, 
+libqhull.h 

+
Global routines. Qhull uses a global data structure, qh,
+to store globally defined constants, lists, sets, and
+variables.
+global.c initializes and frees these
+structures. 

+
+
 

+
Io, io.h,
+io.c 

+
Input and output routines. Qhull provides a wide range of
+input and output options.

+
+
 

+
Mem, 
+mem.h, 
+mem.c 

+
Memory routines. Qhull provides memory allocation and
+deallocation. It uses quick-fit allocation.

+
+
 

+
Merge, 
+merge.h, 
+merge.c 

+
Merge routines. Qhull handles precision problems by
+merged facets or joggled input. These routines merge simplicial facets,
+merge non-simplicial facets, merge cycles of facets, and
+rename redundant vertices.

+
+
 

+
Poly, 
+poly.h, 
+poly.c, 
+poly2.c, 
+libqhull.h 

+
Polyhedral routines. Qhull produces a polyhedron as a
+list of facets with vertices, neighbors, ridges, and
+geometric information. libqhull.h defines the main
+data structures. Frequently used routines are in poly.c
+while infrequent ones are in poly2.c.

+
+
 

+
Qhull, 
+libqhull.c, 
+libqhull.h, 
+qhull_a.h, 
+unix.c , 
+qconvex.c , 
+qdelaun.c , 
+qhalf.c , 
+qvoronoi.c 

+
Top-level routines. The Quickhull algorithm is
+implemented by libqhull.c. qhull_a.h
+includes all header files. 

+
+
 

+
Set, 
+qset.h, 
+qset.c 

+
Set routines. Qhull implements its data structures as
+sets. A set is an array of pointers that is expanded as
+needed. This is a separate package that may be used in
+other applications. 

+
+
 

+
Stat, 
+stat.h, 
+stat.c 

+
Statistical routines. Qhull maintains statistics about
+its implementation. 

+
+
 

+
User, 
+user.h, 
+user.c, 
+user_eg.c, 
+user_eg2.c, 
+user_eg3.cpp, 
+qhull_interface.cpp

+
User-defined routines. Qhull allows the user to configure
+the code with defined constants and specialized routines.
+

+

+

+
+

+
 

+

+
Up:
+Home page for
+Qhull 

+Up: Qhull manual: Table of Contents 

+Up: Programs
+• Options
+• Output
+• Formats
+• Geomview
+• Print
+• Qhull
+• Precision
+• Trace

+Up: Qhull code: Table of Contents 

+To: Qhull files

+To: Geom •
+Global • Io
+• Mem • Merge
+• Poly • Qhull
+• Set • Stat
+• User

+
+
 

+

+
The
+Geometry Center Home Page 

+
Comments to: qhull@qhull.org
+

+Created: May 2, 1997 ---  Last modified: see top  

+
+
diff --git a/src/libqhullr/io_r.c b/src/libqhullr/io_r.c
index 40feeb2..b7c8380 100644
--- a/src/libqhullr/io_r.c
+++ b/src/libqhullr/io_r.c
@@ -1,4062 +1,4062 @@
 /*
  ---------------------------------
 
-   io.c
+   io_r.c
    Input/Output routines of qhull application
 
-   see qh-io.htm and io.h
+   see qh-io.htm and io_r.h
 
-   see user.c for qh_errprint and qh_printfacetlist
+   see user_r.c for qh_errprint and qh_printfacetlist
 
-   unix.c calls qh_readpoints and qh_produce_output
+   unix_r.c calls qh_readpoints and qh_produce_output
 
-   unix.c and user.c are the only callers of io.c functions
-   This allows the user to avoid loading io.o from qhull.a
+   unix_r.c and user_r.c are the only callers of io_r.c functions
+   This allows the user to avoid loading io_r.o from qhull.a
 
    Copyright (c) 1993-2014 The Geometry Center.
-   $Id: //main/2011/qhull/src/libqhullr/io_r.c#4 $$Change: 1663 $
-   $DateTime: 2014/01/19 17:59:16 $$Author: bbarber $
+   $Id: //main/2011/qhull/src/libqhullr/io_r.c#6 $$Change: 1797 $
+   $DateTime: 2014/12/15 17:23:41 $$Author: bbarber $
 */
 
-#include "qhull_r.h"
+#include "qhull_ra.h"
 
 /*========= -functions in alphabetical order after qh_produce_output(qh)  =====*/
 
 /*---------------------------------
 
   qh_produce_output(qh)
   qh_produce_output2(qh)
     prints out the result of qhull in desired format
     qh_produce_output2(qh) does not call qh_prepare_output(qh)
     if qh.GETarea
       computes and prints area and volume
     qh.PRINTout[] is an array of output formats
 
   notes:
     prints output in qh.PRINTout order
 */
 void qh_produce_output(qhT *qh) {
     int tempsize= qh_setsize(qh, qh->qhmem.tempstack);
 
     qh_prepare_output(qh);
     qh_produce_output2(qh);
     if (qh_setsize(qh, qh->qhmem.tempstack) != tempsize) {
         qh_fprintf(qh, qh->ferr, 6206, "qhull internal error (qh_produce_output): temporary sets not empty(%d)\n",
             qh_setsize(qh, qh->qhmem.tempstack));
         qh_errexit(qh, qh_ERRqhull, NULL, NULL);
     }
 } /* produce_output */
 
 
 void qh_produce_output2(qhT *qh) {
   int i, tempsize= qh_setsize(qh, qh->qhmem.tempstack), d_1;
 
   if (qh->PRINTsummary)
     qh_printsummary(qh, qh->ferr);
   else if (qh->PRINTout[0] == qh_PRINTnone)
     qh_printsummary(qh, qh->fout);
   for (i=0; i < qh_PRINTEND; i++)
     qh_printfacets(qh, qh->fout, qh->PRINTout[i], qh->facet_list, NULL, !qh_ALL);
   qh_allstatistics(qh);
   if (qh->PRINTprecision && !qh->MERGING && (qh->JOGGLEmax > REALmax/2 || qh->RERUN))
     qh_printstats(qh, qh->ferr, qh->qhstat.precision, NULL);
   if (qh->VERIFYoutput && (zzval_(Zridge) > 0 || zzval_(Zridgemid) > 0))
     qh_printstats(qh, qh->ferr, qh->qhstat.vridges, NULL);
   if (qh->PRINTstatistics) {
     qh_printstatistics(qh, qh->ferr, "");
     qh_memstatistics(qh, qh->ferr);
     d_1= sizeof(setT) + (qh->hull_dim - 1) * SETelemsize;
     qh_fprintf(qh, qh->ferr, 8040, "\
     size in bytes: merge %d ridge %d vertex %d facet %d\n\
          normal %d ridge vertices %d facet vertices or neighbors %d\n",
             (int)sizeof(mergeT), (int)sizeof(ridgeT),
             (int)sizeof(vertexT), (int)sizeof(facetT),
             qh->normal_size, d_1, d_1 + SETelemsize);
   }
   if (qh_setsize(qh, qh->qhmem.tempstack) != tempsize) {
     qh_fprintf(qh, qh->ferr, 6065, "qhull internal error (qh_produce_output2): temporary sets not empty(%d)\n",
              qh_setsize(qh, qh->qhmem.tempstack));
     qh_errexit(qh, qh_ERRqhull, NULL, NULL);
   }
 } /* produce_output2 */
 
 /*---------------------------------
 
   qh_dfacet(qh, id )
     print facet by id, for debugging
 
 */
 void qh_dfacet(qhT *qh, unsigned id) {
   facetT *facet;
 
   FORALLfacets {
     if (facet->id == id) {
       qh_printfacet(qh, qh->fout, facet);
       break;
     }
   }
 } /* qh_dfacet */
 
 
 /*---------------------------------
 
   qh_dvertex(qh, id )
     print vertex by id, for debugging
 */
 void qh_dvertex(qhT *qh, unsigned id) {
   vertexT *vertex;
 
   FORALLvertices {
     if (vertex->id == id) {
       qh_printvertex(qh, qh->fout, vertex);
       break;
     }
   }
 } /* qh_dvertex */
 
 
 /*---------------------------------
 
   qh_compare_facetarea(p1, p2 )
     used by qsort() to order facets by area
 */
 int qh_compare_facetarea(const void *p1, const void *p2) {
   const facetT *a= *((facetT *const*)p1), *b= *((facetT *const*)p2);
 
   if (!a->isarea)
     return -1;
   if (!b->isarea)
     return 1;
   if (a->f.area > b->f.area)
     return 1;
   else if (a->f.area == b->f.area)
     return 0;
   return -1;
 } /* compare_facetarea */
 
 /*---------------------------------
 
   qh_compare_facetmerge(p1, p2 )
     used by qsort() to order facets by number of merges
 */
 int qh_compare_facetmerge(const void *p1, const void *p2) {
   const facetT *a= *((facetT *const*)p1), *b= *((facetT *const*)p2);
 
   return(a->nummerge - b->nummerge);
 } /* compare_facetvisit */
 
 /*---------------------------------
 
   qh_compare_facetvisit(p1, p2 )
     used by qsort() to order facets by visit id or id
 */
 int qh_compare_facetvisit(const void *p1, const void *p2) {
   const facetT *a= *((facetT *const*)p1), *b= *((facetT *const*)p2);
   int i,j;
 
   if (!(i= a->visitid))
     i= 0 - a->id; /* do not convert to int, sign distinguishes id from visitid */
   if (!(j= b->visitid))
     j= 0 - b->id;
   return(i - j);
 } /* compare_facetvisit */
 
 /*---------------------------------
 
   qh_compare_vertexpoint( p1, p2 )
     used by qsort() to order vertices by point id
 
   Not usable in qhulllib_r since qh_pointid depends on qh
 
   int qh_compare_vertexpoint(const void *p1, const void *p2) {
   const vertexT *a= *((vertexT *const*)p1), *b= *((vertexT *const*)p2);
 
   return((qh_pointid(qh, a->point) > qh_pointid(qh, b->point)?1:-1));
 }*/
 
 /*---------------------------------
 
   qh_copyfilename(qh, dest, size, source, length )
     copy filename identified by qh_skipfilename()
 
   notes:
     see qh_skipfilename() for syntax
 */
 void qh_copyfilename(qhT *qh, char *filename, int size, const char* source, int length) {
   char c= *source;
 
   if (length > size + 1) {
       qh_fprintf(qh, qh->ferr, 6040, "qhull error: filename is more than %d characters, %s\n",  size-1, source);
       qh_errexit(qh, qh_ERRinput, NULL, NULL);
   }
   strncpy(filename, source, length);
   filename[length]= '\0';
   if (c == '\'' || c == '"') {
     char *s= filename + 1;
     char *t= filename;
     while (*s) {
       if (*s == c) {
           if (s[-1] == '\\')
               t[-1]= c;
       }else
           *t++= *s;
       s++;
     }
     *t= '\0';
   }
 } /* copyfilename */
 
 /*---------------------------------
 
   qh_countfacets(qh, facetlist, facets, printall,
           numfacets, numsimplicial, totneighbors, numridges, numcoplanar, numtricoplanars  )
     count good facets for printing and set visitid
     if allfacets, ignores qh_skipfacet()
 
   notes:
     qh_printsummary and qh_countfacets must match counts
 
   returns:
     numfacets, numsimplicial, total neighbors, numridges, coplanars
     each facet with ->visitid indicating 1-relative position
       ->visitid==0 indicates not good
 
   notes
     numfacets >= numsimplicial
     if qh.NEWfacets,
       does not count visible facets (matches qh_printafacet)
 
   design:
     for all facets on facetlist and in facets set
       unless facet is skipped or visible (i.e., will be deleted)
         mark facet->visitid
         update counts
 */
 void qh_countfacets(qhT *qh, facetT *facetlist, setT *facets, boolT printall,
     int *numfacetsp, int *numsimplicialp, int *totneighborsp, int *numridgesp, int *numcoplanarsp, int *numtricoplanarsp) {
   facetT *facet, **facetp;
   int numfacets= 0, numsimplicial= 0, numridges= 0, totneighbors= 0, numcoplanars= 0, numtricoplanars= 0;
 
   FORALLfacet_(facetlist) {
     if ((facet->visible && qh->NEWfacets)
     || (!printall && qh_skipfacet(qh, facet)))
       facet->visitid= 0;
     else {
       facet->visitid= ++numfacets;
       totneighbors += qh_setsize(qh, facet->neighbors);
       if (facet->simplicial) {
         numsimplicial++;
         if (facet->keepcentrum && facet->tricoplanar)
           numtricoplanars++;
       }else
         numridges += qh_setsize(qh, facet->ridges);
       if (facet->coplanarset)
         numcoplanars += qh_setsize(qh, facet->coplanarset);
     }
   }
 
   FOREACHfacet_(facets) {
     if ((facet->visible && qh->NEWfacets)
     || (!printall && qh_skipfacet(qh, facet)))
       facet->visitid= 0;
     else {
       facet->visitid= ++numfacets;
       totneighbors += qh_setsize(qh, facet->neighbors);
       if (facet->simplicial){
         numsimplicial++;
         if (facet->keepcentrum && facet->tricoplanar)
           numtricoplanars++;
       }else
         numridges += qh_setsize(qh, facet->ridges);
       if (facet->coplanarset)
         numcoplanars += qh_setsize(qh, facet->coplanarset);
     }
   }
   qh->visit_id += numfacets+1;
   *numfacetsp= numfacets;
   *numsimplicialp= numsimplicial;
   *totneighborsp= totneighbors;
   *numridgesp= numridges;
   *numcoplanarsp= numcoplanars;
   *numtricoplanarsp= numtricoplanars;
 } /* countfacets */
 
 /*---------------------------------
 
   qh_detvnorm(qh, vertex, vertexA, centers, offset )
     compute separating plane of the Voronoi diagram for a pair of input sites
     centers= set of facets (i.e., Voronoi vertices)
       facet->visitid= 0 iff vertex-at-infinity (i.e., unbounded)
 
   assumes:
     qh_ASvoronoi and qh_vertexneighbors() already set
 
   returns:
     norm
       a pointer into qh.gm_matrix to qh.hull_dim-1 reals
       copy the data before reusing qh.gm_matrix
     offset
       if 'QVn'
         sign adjusted so that qh.GOODvertexp is inside
       else
         sign adjusted so that vertex is inside
 
     qh.gm_matrix= simplex of points from centers relative to first center
 
   notes:
-    in io.c so that code for 'v Tv' can be removed by removing io.c
+    in io_r.c so that code for 'v Tv' can be removed by removing io_r.c
     returns pointer into qh.gm_matrix to avoid tracking of temporary memory
 
   design:
     determine midpoint of input sites
     build points as the set of Voronoi vertices
     select a simplex from points (if necessary)
       include midpoint if the Voronoi region is unbounded
     relocate the first vertex of the simplex to the origin
     compute the normalized hyperplane through the simplex
     orient the hyperplane toward 'QVn' or 'vertex'
     if 'Tv' or 'Ts'
       if bounded
         test that hyperplane is the perpendicular bisector of the input sites
       test that Voronoi vertices not in the simplex are still on the hyperplane
     free up temporary memory
 */
 pointT *qh_detvnorm(qhT *qh, vertexT *vertex, vertexT *vertexA, setT *centers, realT *offsetp) {
   facetT *facet, **facetp;
   int  i, k, pointid, pointidA, point_i, point_n;
   setT *simplex= NULL;
   pointT *point, **pointp, *point0, *midpoint, *normal, *inpoint;
   coordT *coord, *gmcoord, *normalp;
   setT *points= qh_settemp(qh, qh->TEMPsize);
   boolT nearzero= False;
   boolT unbounded= False;
   int numcenters= 0;
   int dim= qh->hull_dim - 1;
   realT dist, offset, angle, zero= 0.0;
 
   midpoint= qh->gm_matrix + qh->hull_dim * qh->hull_dim;  /* last row */
   for (k=0; k < dim; k++)
     midpoint[k]= (vertex->point[k] + vertexA->point[k])/2;
   FOREACHfacet_(centers) {
     numcenters++;
     if (!facet->visitid)
       unbounded= True;
     else {
       if (!facet->center)
         facet->center= qh_facetcenter(qh, facet->vertices);
       qh_setappend(qh, &points, facet->center);
     }
   }
   if (numcenters > dim) {
     simplex= qh_settemp(qh, qh->TEMPsize);
     qh_setappend(qh, &simplex, vertex->point);
     if (unbounded)
       qh_setappend(qh, &simplex, midpoint);
     qh_maxsimplex(qh, dim, points, NULL, 0, &simplex);
     qh_setdelnth(qh, simplex, 0);
   }else if (numcenters == dim) {
     if (unbounded)
       qh_setappend(qh, &points, midpoint);
     simplex= points;
   }else {
     qh_fprintf(qh, qh->ferr, 6216, "qhull internal error (qh_detvnorm): too few points(%d) to compute separating plane\n", numcenters);
     qh_errexit(qh, qh_ERRqhull, NULL, NULL);
   }
   i= 0;
   gmcoord= qh->gm_matrix;
   point0= SETfirstt_(simplex, pointT);
   FOREACHpoint_(simplex) {
     if (qh->IStracing >= 4)
       qh_printmatrix(qh, qh->ferr, "qh_detvnorm: Voronoi vertex or midpoint",
                               &point, 1, dim);
     if (point != point0) {
       qh->gm_row[i++]= gmcoord;
       coord= point0;
       for (k=dim; k--; )
         *(gmcoord++)= *point++ - *coord++;
     }
   }
   qh->gm_row[i]= gmcoord;  /* does not overlap midpoint, may be used later for qh_areasimplex */
   normal= gmcoord;
   qh_sethyperplane_gauss(qh, dim, qh->gm_row, point0, True,
                 normal, &offset, &nearzero);
   if (qh->GOODvertexp == vertexA->point)
     inpoint= vertexA->point;
   else
     inpoint= vertex->point;
   zinc_(Zdistio);
   dist= qh_distnorm(qh, dim, inpoint, normal, &offset);
   if (dist > 0) {
     offset= -offset;
     normalp= normal;
     for (k=dim; k--; ) {
       *normalp= -(*normalp);
       normalp++;
     }
   }
   if (qh->VERIFYoutput || qh->PRINTstatistics) {
     pointid= qh_pointid(qh, vertex->point);
     pointidA= qh_pointid(qh, vertexA->point);
     if (!unbounded) {
       zinc_(Zdiststat);
       dist= qh_distnorm(qh, dim, midpoint, normal, &offset);
       if (dist < 0)
         dist= -dist;
       zzinc_(Zridgemid);
       wwmax_(Wridgemidmax, dist);
       wwadd_(Wridgemid, dist);
       trace4((qh, qh->ferr, 4014, "qh_detvnorm: points %d %d midpoint dist %2.2g\n",
                  pointid, pointidA, dist));
       for (k=0; k < dim; k++)
         midpoint[k]= vertexA->point[k] - vertex->point[k];  /* overwrites midpoint! */
       qh_normalize(qh, midpoint, dim, False);
       angle= qh_distnorm(qh, dim, midpoint, normal, &zero); /* qh_detangle uses dim+1 */
       if (angle < 0.0)
         angle= angle + 1.0;
       else
         angle= angle - 1.0;
       if (angle < 0.0)
         angle -= angle;
       trace4((qh, qh->ferr, 4015, "qh_detvnorm: points %d %d angle %2.2g nearzero %d\n",
                  pointid, pointidA, angle, nearzero));
       if (nearzero) {
         zzinc_(Zridge0);
         wwmax_(Wridge0max, angle);
         wwadd_(Wridge0, angle);
       }else {
         zzinc_(Zridgeok)
         wwmax_(Wridgeokmax, angle);
         wwadd_(Wridgeok, angle);
       }
     }
     if (simplex != points) {
       FOREACHpoint_i_(qh, points) {
         if (!qh_setin(simplex, point)) {
           facet= SETelemt_(centers, point_i, facetT);
           zinc_(Zdiststat);
           dist= qh_distnorm(qh, dim, point, normal, &offset);
           if (dist < 0)
             dist= -dist;
           zzinc_(Zridge);
           wwmax_(Wridgemax, dist);
           wwadd_(Wridge, dist);
           trace4((qh, qh->ferr, 4016, "qh_detvnorm: points %d %d Voronoi vertex %d dist %2.2g\n",
                              pointid, pointidA, facet->visitid, dist));
         }
       }
     }
   }
   *offsetp= offset;
   if (simplex != points)
     qh_settempfree(qh, &simplex);
   qh_settempfree(qh, &points);
   return normal;
 } /* detvnorm */
 
 /*---------------------------------
 
   qh_detvridge(qh, vertexA )
     determine Voronoi ridge from 'seen' neighbors of vertexA
     include one vertex-at-infinite if an !neighbor->visitid
 
   returns:
     temporary set of centers (facets, i.e., Voronoi vertices)
     sorted by center id
 */
 setT *qh_detvridge(qhT *qh, vertexT *vertex) {
   setT *centers= qh_settemp(qh, qh->TEMPsize);
   setT *tricenters= qh_settemp(qh, qh->TEMPsize);
   facetT *neighbor, **neighborp;
   boolT firstinf= True;
 
   FOREACHneighbor_(vertex) {
     if (neighbor->seen) {
       if (neighbor->visitid) {
         if (!neighbor->tricoplanar || qh_setunique(qh, &tricenters, neighbor->center))
           qh_setappend(qh, ¢ers, neighbor);
       }else if (firstinf) {
         firstinf= False;
         qh_setappend(qh, ¢ers, neighbor);
       }
     }
   }
   qsort(SETaddr_(centers, facetT), (size_t)qh_setsize(qh, centers),
              sizeof(facetT *), qh_compare_facetvisit);
   qh_settempfree(qh, &tricenters);
   return centers;
 } /* detvridge */
 
 /*---------------------------------
 
   qh_detvridge3(qh, atvertex, vertex )
     determine 3-d Voronoi ridge from 'seen' neighbors of atvertex and vertex
     include one vertex-at-infinite for !neighbor->visitid
     assumes all facet->seen2= True
 
   returns:
     temporary set of centers (facets, i.e., Voronoi vertices)
     listed in adjacency order (!oriented)
     all facet->seen2= True
 
   design:
     mark all neighbors of atvertex
     for each adjacent neighbor of both atvertex and vertex
       if neighbor selected
         add neighbor to set of Voronoi vertices
 */
 setT *qh_detvridge3(qhT *qh, vertexT *atvertex, vertexT *vertex) {
   setT *centers= qh_settemp(qh, qh->TEMPsize);
   setT *tricenters= qh_settemp(qh, qh->TEMPsize);
   facetT *neighbor, **neighborp, *facet= NULL;
   boolT firstinf= True;
 
   FOREACHneighbor_(atvertex)
     neighbor->seen2= False;
   FOREACHneighbor_(vertex) {
     if (!neighbor->seen2) {
       facet= neighbor;
       break;
     }
   }
   while (facet) {
     facet->seen2= True;
     if (neighbor->seen) {
       if (facet->visitid) {
         if (!facet->tricoplanar || qh_setunique(qh, &tricenters, facet->center))
           qh_setappend(qh, ¢ers, facet);
       }else if (firstinf) {
         firstinf= False;
         qh_setappend(qh, ¢ers, facet);
       }
     }
     FOREACHneighbor_(facet) {
       if (!neighbor->seen2) {
         if (qh_setin(vertex->neighbors, neighbor))
           break;
         else
           neighbor->seen2= True;
       }
     }
     facet= neighbor;
   }
   if (qh->CHECKfrequently) {
     FOREACHneighbor_(vertex) {
       if (!neighbor->seen2) {
           qh_fprintf(qh, qh->ferr, 6217, "qhull internal error (qh_detvridge3): neighbors of vertex p%d are not connected at facet %d\n",
                  qh_pointid(qh, vertex->point), neighbor->id);
         qh_errexit(qh, qh_ERRqhull, neighbor, NULL);
       }
     }
   }
   FOREACHneighbor_(atvertex)
     neighbor->seen2= True;
   qh_settempfree(qh, &tricenters);
   return centers;
 } /* detvridge3 */
 
 /*---------------------------------
 
   qh_eachvoronoi(qh, fp, printvridge, vertex, visitall, innerouter, inorder )
     if visitall,
       visit all Voronoi ridges for vertex (i.e., an input site)
     else
       visit all unvisited Voronoi ridges for vertex
       all vertex->seen= False if unvisited
     assumes
       all facet->seen= False
       all facet->seen2= True (for qh_detvridge3)
       all facet->visitid == 0 if vertex_at_infinity
                          == index of Voronoi vertex
                          >= qh.num_facets if ignored
     innerouter:
       qh_RIDGEall--  both inner (bounded) and outer(unbounded) ridges
       qh_RIDGEinner- only inner
       qh_RIDGEouter- only outer
 
     if inorder
       orders vertices for 3-d Voronoi diagrams
 
   returns:
     number of visited ridges (does not include previously visited ridges)
 
     if printvridge,
       calls printvridge( fp, vertex, vertexA, centers)
         fp== any pointer (assumes FILE*)
         vertex,vertexA= pair of input sites that define a Voronoi ridge
         centers= set of facets (i.e., Voronoi vertices)
                  ->visitid == index or 0 if vertex_at_infinity
                  ordered for 3-d Voronoi diagram
   notes:
     uses qh.vertex_visit
 
   see:
     qh_eachvoronoi_all()
 
   design:
     mark selected neighbors of atvertex
     for each selected neighbor (either Voronoi vertex or vertex-at-infinity)
       for each unvisited vertex
         if atvertex and vertex share more than d-1 neighbors
           bump totalcount
           if printvridge defined
             build the set of shared neighbors (i.e., Voronoi vertices)
             call printvridge
 */
 int qh_eachvoronoi(qhT *qh, FILE *fp, printvridgeT printvridge, vertexT *atvertex, boolT visitall, qh_RIDGE innerouter, boolT inorder) {
   boolT unbounded;
   int count;
   facetT *neighbor, **neighborp, *neighborA, **neighborAp;
   setT *centers;
   setT *tricenters= qh_settemp(qh, qh->TEMPsize);
 
   vertexT *vertex, **vertexp;
   boolT firstinf;
   unsigned int numfacets= (unsigned int)qh->num_facets;
   int totridges= 0;
 
   qh->vertex_visit++;
   atvertex->seen= True;
   if (visitall) {
     FORALLvertices
       vertex->seen= False;
   }
   FOREACHneighbor_(atvertex) {
     if (neighbor->visitid < numfacets)
       neighbor->seen= True;
   }
   FOREACHneighbor_(atvertex) {
     if (neighbor->seen) {
       FOREACHvertex_(neighbor->vertices) {
         if (vertex->visitid != qh->vertex_visit && !vertex->seen) {
           vertex->visitid= qh->vertex_visit;
           count= 0;
           firstinf= True;
           qh_settruncate(qh, tricenters, 0);
           FOREACHneighborA_(vertex) {
             if (neighborA->seen) {
               if (neighborA->visitid) {
                 if (!neighborA->tricoplanar || qh_setunique(qh, &tricenters, neighborA->center))
                   count++;
               }else if (firstinf) {
                 count++;
                 firstinf= False;
               }
             }
           }
           if (count >= qh->hull_dim - 1) {  /* e.g., 3 for 3-d Voronoi */
             if (firstinf) {
               if (innerouter == qh_RIDGEouter)
                 continue;
               unbounded= False;
             }else {
               if (innerouter == qh_RIDGEinner)
                 continue;
               unbounded= True;
             }
             totridges++;
             trace4((qh, qh->ferr, 4017, "qh_eachvoronoi: Voronoi ridge of %d vertices between sites %d and %d\n",
                   count, qh_pointid(qh, atvertex->point), qh_pointid(qh, vertex->point)));
             if (printvridge && fp) {
               if (inorder && qh->hull_dim == 3+1) /* 3-d Voronoi diagram */
                 centers= qh_detvridge3(qh, atvertex, vertex);
               else
                 centers= qh_detvridge(qh, vertex);
               (*printvridge)(qh, fp, atvertex, vertex, centers, unbounded);
               qh_settempfree(qh, ¢ers);
             }
           }
         }
       }
     }
   }
   FOREACHneighbor_(atvertex)
     neighbor->seen= False;
   qh_settempfree(qh, &tricenters);
   return totridges;
 } /* eachvoronoi */
 
 
 /*---------------------------------
 
   qh_eachvoronoi_all(qh, fp, printvridge, isUpper, innerouter, inorder )
     visit all Voronoi ridges
 
     innerouter:
       see qh_eachvoronoi()
 
     if inorder
       orders vertices for 3-d Voronoi diagrams
 
   returns
     total number of ridges
 
     if isUpper == facet->upperdelaunay  (i.e., a Vornoi vertex)
       facet->visitid= Voronoi vertex index(same as 'o' format)
     else
       facet->visitid= 0
 
     if printvridge,
       calls printvridge( fp, vertex, vertexA, centers)
       [see qh_eachvoronoi]
 
   notes:
     Not used for qhull.exe
     same effect as qh_printvdiagram but ridges not sorted by point id
 */
 int qh_eachvoronoi_all(qhT *qh, FILE *fp, printvridgeT printvridge, boolT isUpper, qh_RIDGE innerouter, boolT inorder) {
   facetT *facet;
   vertexT *vertex;
   int numcenters= 1;  /* vertex 0 is vertex-at-infinity */
   int totridges= 0;
 
   qh_clearcenters(qh, qh_ASvoronoi);
   qh_vertexneighbors(qh);
   maximize_(qh->visit_id, (unsigned) qh->num_facets);
   FORALLfacets {
     facet->visitid= 0;
     facet->seen= False;
     facet->seen2= True;
   }
   FORALLfacets {
     if (facet->upperdelaunay == isUpper)
       facet->visitid= numcenters++;
   }
   FORALLvertices
     vertex->seen= False;
   FORALLvertices {
     if (qh->GOODvertex > 0 && qh_pointid(qh, vertex->point)+1 != qh->GOODvertex)
       continue;
     totridges += qh_eachvoronoi(qh, fp, printvridge, vertex,
                    !qh_ALL, innerouter, inorder);
   }
   return totridges;
 } /* eachvoronoi_all */
 
 /*---------------------------------
 
   qh_facet2point(qh, facet, point0, point1, mindist )
     return two projected temporary vertices for a 2-d facet
     may be non-simplicial
 
   returns:
     point0 and point1 oriented and projected to the facet
     returns mindist (maximum distance below plane)
 */
 void qh_facet2point(qhT *qh, facetT *facet, pointT **point0, pointT **point1, realT *mindist) {
   vertexT *vertex0, *vertex1;
   realT dist;
 
   if (facet->toporient ^ qh_ORIENTclock) {
     vertex0= SETfirstt_(facet->vertices, vertexT);
     vertex1= SETsecondt_(facet->vertices, vertexT);
   }else {
     vertex1= SETfirstt_(facet->vertices, vertexT);
     vertex0= SETsecondt_(facet->vertices, vertexT);
   }
   zadd_(Zdistio, 2);
   qh_distplane(qh, vertex0->point, facet, &dist);
   *mindist= dist;
   *point0= qh_projectpoint(qh, vertex0->point, facet, dist);
   qh_distplane(qh, vertex1->point, facet, &dist);
   minimize_(*mindist, dist);
   *point1= qh_projectpoint(qh, vertex1->point, facet, dist);
 } /* facet2point */
 
 
 /*---------------------------------
 
   qh_facetvertices(qh, facetlist, facets, allfacets )
     returns temporary set of vertices in a set and/or list of facets
     if allfacets, ignores qh_skipfacet()
 
   returns:
     vertices with qh.vertex_visit
 
   notes:
     optimized for allfacets of facet_list
 
   design:
     if allfacets of facet_list
       create vertex set from vertex_list
     else
       for each selected facet in facets or facetlist
         append unvisited vertices to vertex set
 */
 setT *qh_facetvertices(qhT *qh, facetT *facetlist, setT *facets, boolT allfacets) {
   setT *vertices;
   facetT *facet, **facetp;
   vertexT *vertex, **vertexp;
 
   qh->vertex_visit++;
   if (facetlist == qh->facet_list && allfacets && !facets) {
     vertices= qh_settemp(qh, qh->num_vertices);
     FORALLvertices {
       vertex->visitid= qh->vertex_visit;
       qh_setappend(qh, &vertices, vertex);
     }
   }else {
     vertices= qh_settemp(qh, qh->TEMPsize);
     FORALLfacet_(facetlist) {
       if (!allfacets && qh_skipfacet(qh, facet))
         continue;
       FOREACHvertex_(facet->vertices) {
         if (vertex->visitid != qh->vertex_visit) {
           vertex->visitid= qh->vertex_visit;
           qh_setappend(qh, &vertices, vertex);
         }
       }
     }
   }
   FOREACHfacet_(facets) {
     if (!allfacets && qh_skipfacet(qh, facet))
       continue;
     FOREACHvertex_(facet->vertices) {
       if (vertex->visitid != qh->vertex_visit) {
         vertex->visitid= qh->vertex_visit;
         qh_setappend(qh, &vertices, vertex);
       }
     }
   }
   return vertices;
 } /* facetvertices */
 
 /*---------------------------------
 
   qh_geomplanes(qh, facet, outerplane, innerplane )
     return outer and inner planes for Geomview
     qh.PRINTradius is size of vertices and points (includes qh.JOGGLEmax)
 
   notes:
     assume precise calculations in io.c with roundoff covered by qh_GEOMepsilon
 */
 void qh_geomplanes(qhT *qh, facetT *facet, realT *outerplane, realT *innerplane) {
   realT radius;
 
   if (qh->MERGING || qh->JOGGLEmax < REALmax/2) {
     qh_outerinner(qh, facet, outerplane, innerplane);
     radius= qh->PRINTradius;
     if (qh->JOGGLEmax < REALmax/2)
       radius -= qh->JOGGLEmax * sqrt((realT)qh->hull_dim);  /* already accounted for in qh_outerinner() */
     *outerplane += radius;
     *innerplane -= radius;
     if (qh->PRINTcoplanar || qh->PRINTspheres) {
       *outerplane += qh->MAXabs_coord * qh_GEOMepsilon;
       *innerplane -= qh->MAXabs_coord * qh_GEOMepsilon;
     }
   }else
     *innerplane= *outerplane= 0;
 } /* geomplanes */
 
 
 /*---------------------------------
 
   qh_markkeep(qh, facetlist )
     mark good facets that meet qh.KEEParea, qh.KEEPmerge, and qh.KEEPminArea
     ignores visible facets (!part of convex hull)
 
   returns:
     may clear facet->good
     recomputes qh.num_good
 
   design:
     get set of good facets
     if qh.KEEParea
       sort facets by area
       clear facet->good for all but n largest facets
     if qh.KEEPmerge
       sort facets by merge count
       clear facet->good for all but n most merged facets
     if qh.KEEPminarea
       clear facet->good if area too small
     update qh.num_good
 */
 void qh_markkeep(qhT *qh, facetT *facetlist) {
   facetT *facet, **facetp;
   setT *facets= qh_settemp(qh, qh->num_facets);
   int size, count;
 
   trace2((qh, qh->ferr, 2006, "qh_markkeep: only keep %d largest and/or %d most merged facets and/or min area %.2g\n",
           qh->KEEParea, qh->KEEPmerge, qh->KEEPminArea));
   FORALLfacet_(facetlist) {
     if (!facet->visible && facet->good)
       qh_setappend(qh, &facets, facet);
   }
   size= qh_setsize(qh, facets);
   if (qh->KEEParea) {
     qsort(SETaddr_(facets, facetT), (size_t)size,
              sizeof(facetT *), qh_compare_facetarea);
     if ((count= size - qh->KEEParea) > 0) {
       FOREACHfacet_(facets) {
         facet->good= False;
         if (--count == 0)
           break;
       }
     }
   }
   if (qh->KEEPmerge) {
     qsort(SETaddr_(facets, facetT), (size_t)size,
              sizeof(facetT *), qh_compare_facetmerge);
     if ((count= size - qh->KEEPmerge) > 0) {
       FOREACHfacet_(facets) {
         facet->good= False;
         if (--count == 0)
           break;
       }
     }
   }
   if (qh->KEEPminArea < REALmax/2) {
     FOREACHfacet_(facets) {
       if (!facet->isarea || facet->f.area < qh->KEEPminArea)
         facet->good= False;
     }
   }
   qh_settempfree(qh, &facets);
   count= 0;
   FORALLfacet_(facetlist) {
     if (facet->good)
       count++;
   }
   qh->num_good= count;
 } /* markkeep */
 
 
 /*---------------------------------
 
   qh_markvoronoi(qh, facetlist, facets, printall, isLower, numcenters )
     mark voronoi vertices for printing by site pairs
 
   returns:
     temporary set of vertices indexed by pointid
     isLower set if printing lower hull (i.e., at least one facet is lower hull)
     numcenters= total number of Voronoi vertices
     bumps qh.printoutnum for vertex-at-infinity
     clears all facet->seen and sets facet->seen2
 
     if selected
       facet->visitid= Voronoi vertex id
     else if upper hull (or 'Qu' and lower hull)
       facet->visitid= 0
     else
       facet->visitid >= qh->num_facets
 
   notes:
     ignores qh.ATinfinity, if defined
 */
 setT *qh_markvoronoi(qhT *qh, facetT *facetlist, setT *facets, boolT printall, boolT *isLowerp, int *numcentersp) {
   int numcenters=0;
   facetT *facet, **facetp;
   setT *vertices;
   boolT isLower= False;
 
   qh->printoutnum++;
   qh_clearcenters(qh, qh_ASvoronoi);  /* in case, qh_printvdiagram2 called by user */
   qh_vertexneighbors(qh);
   vertices= qh_pointvertex(qh);
   if (qh->ATinfinity)
     SETelem_(vertices, qh->num_points-1)= NULL;
   qh->visit_id++;
   maximize_(qh->visit_id, (unsigned) qh->num_facets);
   FORALLfacet_(facetlist) {
     if (printall || !qh_skipfacet(qh, facet)) {
       if (!facet->upperdelaunay) {
         isLower= True;
         break;
       }
     }
   }
   FOREACHfacet_(facets) {
     if (printall || !qh_skipfacet(qh, facet)) {
       if (!facet->upperdelaunay) {
         isLower= True;
         break;
       }
     }
   }
   FORALLfacets {
     if (facet->normal && (facet->upperdelaunay == isLower))
       facet->visitid= 0;  /* facetlist or facets may overwrite */
     else
       facet->visitid= qh->visit_id;
     facet->seen= False;
     facet->seen2= True;
   }
   numcenters++;  /* qh_INFINITE */
   FORALLfacet_(facetlist) {
     if (printall || !qh_skipfacet(qh, facet))
       facet->visitid= numcenters++;
   }
   FOREACHfacet_(facets) {
     if (printall || !qh_skipfacet(qh, facet))
       facet->visitid= numcenters++;
   }
   *isLowerp= isLower;
   *numcentersp= numcenters;
   trace2((qh, qh->ferr, 2007, "qh_markvoronoi: isLower %d numcenters %d\n", isLower, numcenters));
   return vertices;
 } /* markvoronoi */
 
 /*---------------------------------
 
   qh_order_vertexneighbors(qh, vertex )
     order facet neighbors of a 2-d or 3-d vertex by adjacency
 
   notes:
     does not orient the neighbors
 
   design:
     initialize a new neighbor set with the first facet in vertex->neighbors
     while vertex->neighbors non-empty
       select next neighbor in the previous facet's neighbor set
     set vertex->neighbors to the new neighbor set
 */
 void qh_order_vertexneighbors(qhT *qh, vertexT *vertex) {
   setT *newset;
   facetT *facet, *neighbor, **neighborp;
 
   trace4((qh, qh->ferr, 4018, "qh_order_vertexneighbors: order neighbors of v%d for 3-d\n", vertex->id));
   newset= qh_settemp(qh, qh_setsize(qh, vertex->neighbors));
   facet= (facetT*)qh_setdellast(vertex->neighbors);
   qh_setappend(qh, &newset, facet);
   while (qh_setsize(qh, vertex->neighbors)) {
     FOREACHneighbor_(vertex) {
       if (qh_setin(facet->neighbors, neighbor)) {
         qh_setdel(vertex->neighbors, neighbor);
         qh_setappend(qh, &newset, neighbor);
         facet= neighbor;
         break;
       }
     }
     if (!neighbor) {
       qh_fprintf(qh, qh->ferr, 6066, "qhull internal error (qh_order_vertexneighbors): no neighbor of v%d for f%d\n",
         vertex->id, facet->id);
       qh_errexit(qh, qh_ERRqhull, facet, NULL);
     }
   }
   qh_setfree(qh, &vertex->neighbors);
   qh_settemppop(qh);
   vertex->neighbors= newset;
 } /* order_vertexneighbors */
 
 /*---------------------------------
 
   qh_prepare_output(qh, )
     prepare for qh_produce_output2(qh) according to
       qh.KEEPminArea, KEEParea, KEEPmerge, GOODvertex, GOODthreshold, GOODpoint, ONLYgood, SPLITthresholds
     does not reset facet->good
 
   notes
     except for PRINTstatistics, no-op if previously called with same options
 */
 void qh_prepare_output(qhT *qh) {
   if (qh->VORONOI) {
     qh_clearcenters(qh, qh_ASvoronoi);
     qh_vertexneighbors(qh);
   }
   if (qh->TRIangulate && !qh->hasTriangulation) {
     qh_triangulate(qh);
     if (qh->VERIFYoutput && !qh->CHECKfrequently)
       qh_checkpolygon(qh, qh->facet_list);
   }
   qh_findgood_all(qh, qh->facet_list);
   if (qh->GETarea)
     qh_getarea(qh, qh->facet_list);
   if (qh->KEEParea || qh->KEEPmerge || qh->KEEPminArea < REALmax/2)
     qh_markkeep(qh, qh->facet_list);
   if (qh->PRINTstatistics)
     qh_collectstatistics(qh);
 }
 
 /*---------------------------------
 
   qh_printafacet(qh, fp, format, facet, printall )
     print facet to fp in given output format (see qh.PRINTout)
 
   returns:
     nop if !printall and qh_skipfacet()
     nop if visible facet and NEWfacets and format != PRINTfacets
     must match qh_countfacets
 
   notes
     preserves qh.visit_id
     facet->normal may be null if PREmerge/MERGEexact and STOPcone before merge
 
   see
     qh_printbegin() and qh_printend()
 
   design:
     test for printing facet
     call appropriate routine for format
     or output results directly
 */
 void qh_printafacet(qhT *qh, FILE *fp, qh_PRINT format, facetT *facet, boolT printall) {
   realT color[4], offset, dist, outerplane, innerplane;
   boolT zerodiv;
   coordT *point, *normp, *coordp, **pointp, *feasiblep;
   int k;
   vertexT *vertex, **vertexp;
   facetT *neighbor, **neighborp;
 
   if (!printall && qh_skipfacet(qh, facet))
     return;
   if (facet->visible && qh->NEWfacets && format != qh_PRINTfacets)
     return;
   qh->printoutnum++;
   switch (format) {
   case qh_PRINTarea:
     if (facet->isarea) {
       qh_fprintf(qh, fp, 9009, qh_REAL_1, facet->f.area);
       qh_fprintf(qh, fp, 9010, "\n");
     }else
       qh_fprintf(qh, fp, 9011, "0\n");
     break;
   case qh_PRINTcoplanars:
     qh_fprintf(qh, fp, 9012, "%d", qh_setsize(qh, facet->coplanarset));
     FOREACHpoint_(facet->coplanarset)
       qh_fprintf(qh, fp, 9013, " %d", qh_pointid(qh, point));
     qh_fprintf(qh, fp, 9014, "\n");
     break;
   case qh_PRINTcentrums:
     qh_printcenter(qh, fp, format, NULL, facet);
     break;
   case qh_PRINTfacets:
     qh_printfacet(qh, fp, facet);
     break;
   case qh_PRINTfacets_xridge:
     qh_printfacetheader(qh, fp, facet);
     break;
   case qh_PRINTgeom:  /* either 2 , 3, or 4-d by qh_printbegin */
     if (!facet->normal)
       break;
     for (k=qh->hull_dim; k--; ) {
       color[k]= (facet->normal[k]+1.0)/2.0;
       maximize_(color[k], -1.0);
       minimize_(color[k], +1.0);
     }
     qh_projectdim3(qh, color, color);
     if (qh->PRINTdim != qh->hull_dim)
       qh_normalize2(qh, color, 3, True, NULL, NULL);
     if (qh->hull_dim <= 2)
       qh_printfacet2geom(qh, fp, facet, color);
     else if (qh->hull_dim == 3) {
       if (facet->simplicial)
         qh_printfacet3geom_simplicial(qh, fp, facet, color);
       else
         qh_printfacet3geom_nonsimplicial(qh, fp, facet, color);
     }else {
       if (facet->simplicial)
         qh_printfacet4geom_simplicial(qh, fp, facet, color);
       else
         qh_printfacet4geom_nonsimplicial(qh, fp, facet, color);
     }
     break;
   case qh_PRINTids:
     qh_fprintf(qh, fp, 9015, "%d\n", facet->id);
     break;
   case qh_PRINTincidences:
   case qh_PRINToff:
   case qh_PRINTtriangles:
     if (qh->hull_dim == 3 && format != qh_PRINTtriangles)
       qh_printfacet3vertex(qh, fp, facet, format);
     else if (facet->simplicial || qh->hull_dim == 2 || format == qh_PRINToff)
       qh_printfacetNvertex_simplicial(qh, fp, facet, format);
     else
       qh_printfacetNvertex_nonsimplicial(qh, fp, facet, qh->printoutvar++, format);
     break;
   case qh_PRINTinner:
     qh_outerinner(qh, facet, NULL, &innerplane);
     offset= facet->offset - innerplane;
     goto LABELprintnorm;
     break; /* prevent warning */
   case qh_PRINTmerges:
     qh_fprintf(qh, fp, 9016, "%d\n", facet->nummerge);
     break;
   case qh_PRINTnormals:
     offset= facet->offset;
     goto LABELprintnorm;
     break; /* prevent warning */
   case qh_PRINTouter:
     qh_outerinner(qh, facet, &outerplane, NULL);
     offset= facet->offset - outerplane;
   LABELprintnorm:
     if (!facet->normal) {
       qh_fprintf(qh, fp, 9017, "no normal for facet f%d\n", facet->id);
       break;
     }
     if (qh->CDDoutput) {
       qh_fprintf(qh, fp, 9018, qh_REAL_1, -offset);
       for (k=0; k < qh->hull_dim; k++)
         qh_fprintf(qh, fp, 9019, qh_REAL_1, -facet->normal[k]);
     }else {
       for (k=0; k < qh->hull_dim; k++)
         qh_fprintf(qh, fp, 9020, qh_REAL_1, facet->normal[k]);
       qh_fprintf(qh, fp, 9021, qh_REAL_1, offset);
     }
     qh_fprintf(qh, fp, 9022, "\n");
     break;
   case qh_PRINTmathematica:  /* either 2 or 3-d by qh_printbegin */
   case qh_PRINTmaple:
     if (qh->hull_dim == 2)
       qh_printfacet2math(qh, fp, facet, format, qh->printoutvar++);
     else
       qh_printfacet3math(qh, fp, facet, format, qh->printoutvar++);
     break;
   case qh_PRINTneighbors:
     qh_fprintf(qh, fp, 9023, "%d", qh_setsize(qh, facet->neighbors));
     FOREACHneighbor_(facet)
       qh_fprintf(qh, fp, 9024, " %d",
                neighbor->visitid ? neighbor->visitid - 1: 0 - neighbor->id);
     qh_fprintf(qh, fp, 9025, "\n");
     break;
   case qh_PRINTpointintersect:
     if (!qh->feasible_point) {
       qh_fprintf(qh, qh->ferr, 6067, "qhull input error (qh_printafacet): option 'Fp' needs qh->feasible_point\n");
       qh_errexit(qh, qh_ERRinput, NULL, NULL);
     }
     if (facet->offset > 0)
       goto LABELprintinfinite;
     point= coordp= (coordT*)qh_memalloc(qh, qh->normal_size);
     normp= facet->normal;
     feasiblep= qh->feasible_point;
     if (facet->offset < -qh->MINdenom) {
       for (k=qh->hull_dim; k--; )
         *(coordp++)= (*(normp++) / - facet->offset) + *(feasiblep++);
     }else {
       for (k=qh->hull_dim; k--; ) {
         *(coordp++)= qh_divzero(qh, *(normp++), facet->offset, qh->MINdenom_1,
                                  &zerodiv) + *(feasiblep++);
         if (zerodiv) {
           qh_memfree(qh, point, qh->normal_size);
           goto LABELprintinfinite;
         }
       }
     }
     qh_printpoint(qh, fp, NULL, point);
     qh_memfree(qh, point, qh->normal_size);
     break;
   LABELprintinfinite:
     for (k=qh->hull_dim; k--; )
       qh_fprintf(qh, fp, 9026, qh_REAL_1, qh_INFINITE);
     qh_fprintf(qh, fp, 9027, "\n");
     break;
   case qh_PRINTpointnearest:
     FOREACHpoint_(facet->coplanarset) {
       int id, id2;
       vertex= qh_nearvertex(qh, facet, point, &dist);
       id= qh_pointid(qh, vertex->point);
       id2= qh_pointid(qh, point);
       qh_fprintf(qh, fp, 9028, "%d %d %d " qh_REAL_1 "\n", id, id2, facet->id, dist);
     }
     break;
   case qh_PRINTpoints:  /* VORONOI only by qh_printbegin */
     if (qh->CDDoutput)
       qh_fprintf(qh, fp, 9029, "1 ");
     qh_printcenter(qh, fp, format, NULL, facet);
     break;
   case qh_PRINTvertices:
     qh_fprintf(qh, fp, 9030, "%d", qh_setsize(qh, facet->vertices));
     FOREACHvertex_(facet->vertices)
       qh_fprintf(qh, fp, 9031, " %d", qh_pointid(qh, vertex->point));
     qh_fprintf(qh, fp, 9032, "\n");
     break;
   default:
     break;
   }
 } /* printafacet */
 
 /*---------------------------------
 
   qh_printbegin(qh, )
     prints header for all output formats
 
   returns:
     checks for valid format
 
   notes:
     uses qh.visit_id for 3/4off
     changes qh.interior_point if printing centrums
     qh_countfacets clears facet->visitid for non-good facets
 
   see
     qh_printend() and qh_printafacet()
 
   design:
     count facets and related statistics
     print header for format
 */
 void qh_printbegin(qhT *qh, FILE *fp, qh_PRINT format, facetT *facetlist, setT *facets, boolT printall) {
   int numfacets, numsimplicial, numridges, totneighbors, numcoplanars, numtricoplanars;
   int i, num;
   facetT *facet, **facetp;
   vertexT *vertex, **vertexp;
   setT *vertices;
   pointT *point, **pointp, *pointtemp;
 
   qh->printoutnum= 0;
   qh_countfacets(qh, facetlist, facets, printall, &numfacets, &numsimplicial,
       &totneighbors, &numridges, &numcoplanars, &numtricoplanars);
   switch (format) {
   case qh_PRINTnone:
     break;
   case qh_PRINTarea:
     qh_fprintf(qh, fp, 9033, "%d\n", numfacets);
     break;
   case qh_PRINTcoplanars:
     qh_fprintf(qh, fp, 9034, "%d\n", numfacets);
     break;
   case qh_PRINTcentrums:
     if (qh->CENTERtype == qh_ASnone)
       qh_clearcenters(qh, qh_AScentrum);
     qh_fprintf(qh, fp, 9035, "%d\n%d\n", qh->hull_dim, numfacets);
     break;
   case qh_PRINTfacets:
   case qh_PRINTfacets_xridge:
     if (facetlist)
       qh_printvertexlist(qh, fp, "Vertices and facets:\n", facetlist, facets, printall);
     break;
   case qh_PRINTgeom:
     if (qh->hull_dim > 4)  /* qh_initqhull_globals also checks */
       goto LABELnoformat;
     if (qh->VORONOI && qh->hull_dim > 3)  /* PRINTdim == DROPdim == hull_dim-1 */
       goto LABELnoformat;
     if (qh->hull_dim == 2 && (qh->PRINTridges || qh->DOintersections))
       qh_fprintf(qh, qh->ferr, 7049, "qhull warning: output for ridges and intersections not implemented in 2-d\n");
     if (qh->hull_dim == 4 && (qh->PRINTinner || qh->PRINTouter ||
                              (qh->PRINTdim == 4 && qh->PRINTcentrums)))
       qh_fprintf(qh, qh->ferr, 7050, "qhull warning: output for outer/inner planes and centrums not implemented in 4-d\n");
     if (qh->PRINTdim == 4 && (qh->PRINTspheres))
       qh_fprintf(qh, qh->ferr, 7051, "qhull warning: output for vertices not implemented in 4-d\n");
     if (qh->PRINTdim == 4 && qh->DOintersections && qh->PRINTnoplanes)
       qh_fprintf(qh, qh->ferr, 7052, "qhull warning: 'Gnh' generates no output in 4-d\n");
     if (qh->PRINTdim == 2) {
       qh_fprintf(qh, fp, 9036, "{appearance {linewidth 3} LIST # %s | %s\n",
               qh->rbox_command, qh->qhull_command);
     }else if (qh->PRINTdim == 3) {
       qh_fprintf(qh, fp, 9037, "{appearance {+edge -evert linewidth 2} LIST # %s | %s\n",
               qh->rbox_command, qh->qhull_command);
     }else if (qh->PRINTdim == 4) {
       qh->visit_id++;
       num= 0;
       FORALLfacet_(facetlist)    /* get number of ridges to be printed */
         qh_printend4geom(qh, NULL, facet, &num, printall);
       FOREACHfacet_(facets)
         qh_printend4geom(qh, NULL, facet, &num, printall);
       qh->ridgeoutnum= num;
       qh->printoutvar= 0;  /* counts number of ridges in output */
       qh_fprintf(qh, fp, 9038, "LIST # %s | %s\n", qh->rbox_command, qh->qhull_command);
     }
 
     if (qh->PRINTdots) {
       qh->printoutnum++;
       num= qh->num_points + qh_setsize(qh, qh->other_points);
       if (qh->DELAUNAY && qh->ATinfinity)
         num--;
       if (qh->PRINTdim == 4)
         qh_fprintf(qh, fp, 9039, "4VECT %d %d 1\n", num, num);
       else
         qh_fprintf(qh, fp, 9040, "VECT %d %d 1\n", num, num);
 
       for (i=num; i--; ) {
         if (i % 20 == 0)
           qh_fprintf(qh, fp, 9041, "\n");
         qh_fprintf(qh, fp, 9042, "1 ");
       }
       qh_fprintf(qh, fp, 9043, "# 1 point per line\n1 ");
       for (i=num-1; i--; ) { /* num at least 3 for D2 */
         if (i % 20 == 0)
           qh_fprintf(qh, fp, 9044, "\n");
         qh_fprintf(qh, fp, 9045, "0 ");
       }
       qh_fprintf(qh, fp, 9046, "# 1 color for all\n");
       FORALLpoints {
         if (!qh->DELAUNAY || !qh->ATinfinity || qh_pointid(qh, point) != qh->num_points-1) {
           if (qh->PRINTdim == 4)
             qh_printpoint(qh, fp, NULL, point);
             else
               qh_printpoint3(qh, fp, point);
         }
       }
       FOREACHpoint_(qh->other_points) {
         if (qh->PRINTdim == 4)
           qh_printpoint(qh, fp, NULL, point);
         else
           qh_printpoint3(qh, fp, point);
       }
       qh_fprintf(qh, fp, 9047, "0 1 1 1  # color of points\n");
     }
 
     if (qh->PRINTdim == 4  && !qh->PRINTnoplanes)
       /* 4dview loads up multiple 4OFF objects slowly */
       qh_fprintf(qh, fp, 9048, "4OFF %d %d 1\n", 3*qh->ridgeoutnum, qh->ridgeoutnum);
     qh->PRINTcradius= 2 * qh->DISTround;  /* include test DISTround */
     if (qh->PREmerge) {
       maximize_(qh->PRINTcradius, qh->premerge_centrum + qh->DISTround);
     }else if (qh->POSTmerge)
       maximize_(qh->PRINTcradius, qh->postmerge_centrum + qh->DISTround);
     qh->PRINTradius= qh->PRINTcradius;
     if (qh->PRINTspheres + qh->PRINTcoplanar)
       maximize_(qh->PRINTradius, qh->MAXabs_coord * qh_MINradius);
     if (qh->premerge_cos < REALmax/2) {
       maximize_(qh->PRINTradius, (1- qh->premerge_cos) * qh->MAXabs_coord);
     }else if (!qh->PREmerge && qh->POSTmerge && qh->postmerge_cos < REALmax/2) {
       maximize_(qh->PRINTradius, (1- qh->postmerge_cos) * qh->MAXabs_coord);
     }
     maximize_(qh->PRINTradius, qh->MINvisible);
     if (qh->JOGGLEmax < REALmax/2)
       qh->PRINTradius += qh->JOGGLEmax * sqrt((realT)qh->hull_dim);
     if (qh->PRINTdim != 4 &&
         (qh->PRINTcoplanar || qh->PRINTspheres || qh->PRINTcentrums)) {
       vertices= qh_facetvertices(qh, facetlist, facets, printall);
       if (qh->PRINTspheres && qh->PRINTdim <= 3)
         qh_printspheres(qh, fp, vertices, qh->PRINTradius);
       if (qh->PRINTcoplanar || qh->PRINTcentrums) {
         qh->firstcentrum= True;
         if (qh->PRINTcoplanar&& !qh->PRINTspheres) {
           FOREACHvertex_(vertices)
             qh_printpointvect2(qh, fp, vertex->point, NULL, qh->interior_point, qh->PRINTradius);
         }
         FORALLfacet_(facetlist) {
           if (!printall && qh_skipfacet(qh, facet))
             continue;
           if (!facet->normal)
             continue;
           if (qh->PRINTcentrums && qh->PRINTdim <= 3)
             qh_printcentrum(qh, fp, facet, qh->PRINTcradius);
           if (!qh->PRINTcoplanar)
             continue;
           FOREACHpoint_(facet->coplanarset)
             qh_printpointvect2(qh, fp, point, facet->normal, NULL, qh->PRINTradius);
           FOREACHpoint_(facet->outsideset)
             qh_printpointvect2(qh, fp, point, facet->normal, NULL, qh->PRINTradius);
         }
         FOREACHfacet_(facets) {
           if (!printall && qh_skipfacet(qh, facet))
             continue;
           if (!facet->normal)
             continue;
           if (qh->PRINTcentrums && qh->PRINTdim <= 3)
             qh_printcentrum(qh, fp, facet, qh->PRINTcradius);
           if (!qh->PRINTcoplanar)
             continue;
           FOREACHpoint_(facet->coplanarset)
             qh_printpointvect2(qh, fp, point, facet->normal, NULL, qh->PRINTradius);
           FOREACHpoint_(facet->outsideset)
             qh_printpointvect2(qh, fp, point, facet->normal, NULL, qh->PRINTradius);
         }
       }
       qh_settempfree(qh, &vertices);
     }
     qh->visit_id++; /* for printing hyperplane intersections */
     break;
   case qh_PRINTids:
     qh_fprintf(qh, fp, 9049, "%d\n", numfacets);
     break;
   case qh_PRINTincidences:
     if (qh->VORONOI && qh->PRINTprecision)
       qh_fprintf(qh, qh->ferr, 7053, "qhull warning: writing Delaunay.  Use 'p' or 'o' for Voronoi centers\n");
     qh->printoutvar= qh->vertex_id;  /* centrum id for non-simplicial facets */
     if (qh->hull_dim <= 3)
       qh_fprintf(qh, fp, 9050, "%d\n", numfacets);
     else
       qh_fprintf(qh, fp, 9051, "%d\n", numsimplicial+numridges);
     break;
   case qh_PRINTinner:
   case qh_PRINTnormals:
   case qh_PRINTouter:
     if (qh->CDDoutput)
       qh_fprintf(qh, fp, 9052, "%s | %s\nbegin\n    %d %d real\n", qh->rbox_command,
             qh->qhull_command, numfacets, qh->hull_dim+1);
     else
       qh_fprintf(qh, fp, 9053, "%d\n%d\n", qh->hull_dim+1, numfacets);
     break;
   case qh_PRINTmathematica:
   case qh_PRINTmaple:
     if (qh->hull_dim > 3)  /* qh_initbuffers also checks */
       goto LABELnoformat;
     if (qh->VORONOI)
       qh_fprintf(qh, qh->ferr, 7054, "qhull warning: output is the Delaunay triangulation\n");
     if (format == qh_PRINTmaple) {
       if (qh->hull_dim == 2)
         qh_fprintf(qh, fp, 9054, "PLOT(CURVES(\n");
       else
         qh_fprintf(qh, fp, 9055, "PLOT3D(POLYGONS(\n");
     }else
       qh_fprintf(qh, fp, 9056, "{\n");
     qh->printoutvar= 0;   /* counts number of facets for notfirst */
     break;
   case qh_PRINTmerges:
     qh_fprintf(qh, fp, 9057, "%d\n", numfacets);
     break;
   case qh_PRINTpointintersect:
     qh_fprintf(qh, fp, 9058, "%d\n%d\n", qh->hull_dim, numfacets);
     break;
   case qh_PRINTneighbors:
     qh_fprintf(qh, fp, 9059, "%d\n", numfacets);
     break;
   case qh_PRINToff:
   case qh_PRINTtriangles:
     if (qh->VORONOI)
       goto LABELnoformat;
     num = qh->hull_dim;
     if (format == qh_PRINToff || qh->hull_dim == 2)
       qh_fprintf(qh, fp, 9060, "%d\n%d %d %d\n", num,
         qh->num_points+qh_setsize(qh, qh->other_points), numfacets, totneighbors/2);
     else { /* qh_PRINTtriangles */
       qh->printoutvar= qh->num_points+qh_setsize(qh, qh->other_points); /* first centrum */
       if (qh->DELAUNAY)
         num--;  /* drop last dimension */
       qh_fprintf(qh, fp, 9061, "%d\n%d %d %d\n", num, qh->printoutvar
         + numfacets - numsimplicial, numsimplicial + numridges, totneighbors/2);
     }
     FORALLpoints
       qh_printpointid(qh, qh->fout, NULL, num, point, -1);
     FOREACHpoint_(qh->other_points)
       qh_printpointid(qh, qh->fout, NULL, num, point, -1);
     if (format == qh_PRINTtriangles && qh->hull_dim > 2) {
       FORALLfacets {
         if (!facet->simplicial && facet->visitid)
           qh_printcenter(qh, qh->fout, format, NULL, facet);
       }
     }
     break;
   case qh_PRINTpointnearest:
     qh_fprintf(qh, fp, 9062, "%d\n", numcoplanars);
     break;
   case qh_PRINTpoints:
     if (!qh->VORONOI)
       goto LABELnoformat;
     if (qh->CDDoutput)
       qh_fprintf(qh, fp, 9063, "%s | %s\nbegin\n%d %d real\n", qh->rbox_command,
            qh->qhull_command, numfacets, qh->hull_dim);
     else
       qh_fprintf(qh, fp, 9064, "%d\n%d\n", qh->hull_dim-1, numfacets);
     break;
   case qh_PRINTvertices:
     qh_fprintf(qh, fp, 9065, "%d\n", numfacets);
     break;
   case qh_PRINTsummary:
   default:
   LABELnoformat:
     qh_fprintf(qh, qh->ferr, 6068, "qhull internal error (qh_printbegin): can not use this format for dimension %d\n",
          qh->hull_dim);
     qh_errexit(qh, qh_ERRqhull, NULL, NULL);
   }
 } /* printbegin */
 
 /*---------------------------------
 
   qh_printcenter(qh, fp, string, facet )
     print facet->center as centrum or Voronoi center
     string may be NULL.  Don't include '%' codes.
     nop if qh->CENTERtype neither CENTERvoronoi nor CENTERcentrum
     if upper envelope of Delaunay triangulation and point at-infinity
       prints qh_INFINITE instead;
 
   notes:
     defines facet->center if needed
     if format=PRINTgeom, adds a 0 if would otherwise be 2-d
     Same as QhullFacet::printCenter
 */
 void qh_printcenter(qhT *qh, FILE *fp, qh_PRINT format, const char *string, facetT *facet) {
   int k, num;
 
   if (qh->CENTERtype != qh_ASvoronoi && qh->CENTERtype != qh_AScentrum)
     return;
   if (string)
     qh_fprintf(qh, fp, 9066, string);
   if (qh->CENTERtype == qh_ASvoronoi) {
     num= qh->hull_dim-1;
     if (!facet->normal || !facet->upperdelaunay || !qh->ATinfinity) {
       if (!facet->center)
         facet->center= qh_facetcenter(qh, facet->vertices);
       for (k=0; k < num; k++)
         qh_fprintf(qh, fp, 9067, qh_REAL_1, facet->center[k]);
     }else {
       for (k=0; k < num; k++)
         qh_fprintf(qh, fp, 9068, qh_REAL_1, qh_INFINITE);
     }
   }else /* qh->CENTERtype == qh_AScentrum */ {
     num= qh->hull_dim;
     if (format == qh_PRINTtriangles && qh->DELAUNAY)
       num--;
     if (!facet->center)
       facet->center= qh_getcentrum(qh, facet);
     for (k=0; k < num; k++)
       qh_fprintf(qh, fp, 9069, qh_REAL_1, facet->center[k]);
   }
   if (format == qh_PRINTgeom && num == 2)
     qh_fprintf(qh, fp, 9070, " 0\n");
   else
     qh_fprintf(qh, fp, 9071, "\n");
 } /* printcenter */
 
 /*---------------------------------
 
   qh_printcentrum(qh, fp, facet, radius )
     print centrum for a facet in OOGL format
     radius defines size of centrum
     2-d or 3-d only
 
   returns:
     defines facet->center if needed
 */
 void qh_printcentrum(qhT *qh, FILE *fp, facetT *facet, realT radius) {
   pointT *centrum, *projpt;
   boolT tempcentrum= False;
   realT xaxis[4], yaxis[4], normal[4], dist;
   realT green[3]={0, 1, 0};
   vertexT *apex;
   int k;
 
   if (qh->CENTERtype == qh_AScentrum) {
     if (!facet->center)
       facet->center= qh_getcentrum(qh, facet);
     centrum= facet->center;
   }else {
     centrum= qh_getcentrum(qh, facet);
     tempcentrum= True;
   }
   qh_fprintf(qh, fp, 9072, "{appearance {-normal -edge normscale 0} ");
   if (qh->firstcentrum) {
     qh->firstcentrum= False;
     qh_fprintf(qh, fp, 9073, "{INST geom { define centrum CQUAD  # f%d\n\
 -0.3 -0.3 0.0001     0 0 1 1\n\
  0.3 -0.3 0.0001     0 0 1 1\n\
  0.3  0.3 0.0001     0 0 1 1\n\
 -0.3  0.3 0.0001     0 0 1 1 } transform { \n", facet->id);
   }else
     qh_fprintf(qh, fp, 9074, "{INST geom { : centrum } transform { # f%d\n", facet->id);
   apex= SETfirstt_(facet->vertices, vertexT);
   qh_distplane(qh, apex->point, facet, &dist);
   projpt= qh_projectpoint(qh, apex->point, facet, dist);
   for (k=qh->hull_dim; k--; ) {
     xaxis[k]= projpt[k] - centrum[k];
     normal[k]= facet->normal[k];
   }
   if (qh->hull_dim == 2) {
     xaxis[2]= 0;
     normal[2]= 0;
   }else if (qh->hull_dim == 4) {
     qh_projectdim3(qh, xaxis, xaxis);
     qh_projectdim3(qh, normal, normal);
     qh_normalize2(qh, normal, qh->PRINTdim, True, NULL, NULL);
   }
   qh_crossproduct(qh, 3, xaxis, normal, yaxis);
   qh_fprintf(qh, fp, 9075, "%8.4g %8.4g %8.4g 0\n", xaxis[0], xaxis[1], xaxis[2]);
   qh_fprintf(qh, fp, 9076, "%8.4g %8.4g %8.4g 0\n", yaxis[0], yaxis[1], yaxis[2]);
   qh_fprintf(qh, fp, 9077, "%8.4g %8.4g %8.4g 0\n", normal[0], normal[1], normal[2]);
   qh_printpoint3(qh, fp, centrum);
   qh_fprintf(qh, fp, 9078, "1 }}}\n");
   qh_memfree(qh, projpt, qh->normal_size);
   qh_printpointvect(qh, fp, centrum, facet->normal, NULL, radius, green);
   if (tempcentrum)
     qh_memfree(qh, centrum, qh->normal_size);
 } /* printcentrum */
 
 /*---------------------------------
 
   qh_printend(qh, fp, format )
     prints trailer for all output formats
 
   see:
     qh_printbegin() and qh_printafacet()
 
 */
 void qh_printend(qhT *qh, FILE *fp, qh_PRINT format, facetT *facetlist, setT *facets, boolT printall) {
   int num;
   facetT *facet, **facetp;
 
   if (!qh->printoutnum)
     qh_fprintf(qh, qh->ferr, 7055, "qhull warning: no facets printed\n");
   switch (format) {
   case qh_PRINTgeom:
     if (qh->hull_dim == 4 && qh->DROPdim < 0  && !qh->PRINTnoplanes) {
       qh->visit_id++;
       num= 0;
       FORALLfacet_(facetlist)
         qh_printend4geom(qh, fp, facet,&num, printall);
       FOREACHfacet_(facets)
         qh_printend4geom(qh, fp, facet, &num, printall);
       if (num != qh->ridgeoutnum || qh->printoutvar != qh->ridgeoutnum) {
         qh_fprintf(qh, qh->ferr, 6069, "qhull internal error (qh_printend): number of ridges %d != number printed %d and at end %d\n", qh->ridgeoutnum, qh->printoutvar, num);
         qh_errexit(qh, qh_ERRqhull, NULL, NULL);
       }
     }else
       qh_fprintf(qh, fp, 9079, "}\n");
     break;
   case qh_PRINTinner:
   case qh_PRINTnormals:
   case qh_PRINTouter:
     if (qh->CDDoutput)
       qh_fprintf(qh, fp, 9080, "end\n");
     break;
   case qh_PRINTmaple:
     qh_fprintf(qh, fp, 9081, "));\n");
     break;
   case qh_PRINTmathematica:
     qh_fprintf(qh, fp, 9082, "}\n");
     break;
   case qh_PRINTpoints:
     if (qh->CDDoutput)
       qh_fprintf(qh, fp, 9083, "end\n");
     break;
   default:
     break;
   }
 } /* printend */
 
 /*---------------------------------
 
   qh_printend4geom(qh, fp, facet, numridges, printall )
     helper function for qh_printbegin/printend
 
   returns:
     number of printed ridges
 
   notes:
     just counts printed ridges if fp=NULL
     uses facet->visitid
     must agree with qh_printfacet4geom...
 
   design:
     computes color for facet from its normal
     prints each ridge of facet
 */
 void qh_printend4geom(qhT *qh, FILE *fp, facetT *facet, int *nump, boolT printall) {
   realT color[3];
   int i, num= *nump;
   facetT *neighbor, **neighborp;
   ridgeT *ridge, **ridgep;
 
   if (!printall && qh_skipfacet(qh, facet))
     return;
   if (qh->PRINTnoplanes || (facet->visible && qh->NEWfacets))
     return;
   if (!facet->normal)
     return;
   if (fp) {
     for (i=0; i < 3; i++) {
       color[i]= (facet->normal[i]+1.0)/2.0;
       maximize_(color[i], -1.0);
       minimize_(color[i], +1.0);
     }
   }
   facet->visitid= qh->visit_id;
   if (facet->simplicial) {
     FOREACHneighbor_(facet) {
       if (neighbor->visitid != qh->visit_id) {
         if (fp)
           qh_fprintf(qh, fp, 9084, "3 %d %d %d %8.4g %8.4g %8.4g 1 # f%d f%d\n",
                  3*num, 3*num+1, 3*num+2, color[0], color[1], color[2],
                  facet->id, neighbor->id);
         num++;
       }
     }
   }else {
     FOREACHridge_(facet->ridges) {
       neighbor= otherfacet_(ridge, facet);
       if (neighbor->visitid != qh->visit_id) {
         if (fp)
           qh_fprintf(qh, fp, 9085, "3 %d %d %d %8.4g %8.4g %8.4g 1 #r%d f%d f%d\n",
                  3*num, 3*num+1, 3*num+2, color[0], color[1], color[2],
                  ridge->id, facet->id, neighbor->id);
         num++;
       }
     }
   }
   *nump= num;
 } /* printend4geom */
 
 /*---------------------------------
 
   qh_printextremes(qh, fp, facetlist, facets, printall )
     print extreme points for convex hulls or halfspace intersections
 
   notes:
     #points, followed by ids, one per line
 
     sorted by id
     same order as qh_printpoints_out if no coplanar/interior points
 */
 void qh_printextremes(qhT *qh, FILE *fp, facetT *facetlist, setT *facets, boolT printall) {
   setT *vertices, *points;
   pointT *point;
   vertexT *vertex, **vertexp;
   int id;
   int numpoints=0, point_i, point_n;
   int allpoints= qh->num_points + qh_setsize(qh, qh->other_points);
 
   points= qh_settemp(qh, allpoints);
   qh_setzero(qh, points, 0, allpoints);
   vertices= qh_facetvertices(qh, facetlist, facets, printall);
   FOREACHvertex_(vertices) {
     id= qh_pointid(qh, vertex->point);
     if (id >= 0) {
       SETelem_(points, id)= vertex->point;
       numpoints++;
     }
   }
   qh_settempfree(qh, &vertices);
   qh_fprintf(qh, fp, 9086, "%d\n", numpoints);
   FOREACHpoint_i_(qh, points) {
     if (point)
       qh_fprintf(qh, fp, 9087, "%d\n", point_i);
   }
   qh_settempfree(qh, &points);
 } /* printextremes */
 
 /*---------------------------------
 
   qh_printextremes_2d(qh, fp, facetlist, facets, printall )
     prints point ids for facets in qh_ORIENTclock order
 
   notes:
     #points, followed by ids, one per line
     if facetlist/facets are disjoint than the output includes skips
     errors if facets form a loop
     does not print coplanar points
 */
 void qh_printextremes_2d(qhT *qh, FILE *fp, facetT *facetlist, setT *facets, boolT printall) {
   int numfacets, numridges, totneighbors, numcoplanars, numsimplicial, numtricoplanars;
   setT *vertices;
   facetT *facet, *startfacet, *nextfacet;
   vertexT *vertexA, *vertexB;
 
   qh_countfacets(qh, facetlist, facets, printall, &numfacets, &numsimplicial,
       &totneighbors, &numridges, &numcoplanars, &numtricoplanars); /* marks qh->visit_id */
   vertices= qh_facetvertices(qh, facetlist, facets, printall);
   qh_fprintf(qh, fp, 9088, "%d\n", qh_setsize(qh, vertices));
   qh_settempfree(qh, &vertices);
   if (!numfacets)
     return;
   facet= startfacet= facetlist ? facetlist : SETfirstt_(facets, facetT);
   qh->vertex_visit++;
   qh->visit_id++;
   do {
     if (facet->toporient ^ qh_ORIENTclock) {
       vertexA= SETfirstt_(facet->vertices, vertexT);
       vertexB= SETsecondt_(facet->vertices, vertexT);
       nextfacet= SETfirstt_(facet->neighbors, facetT);
     }else {
       vertexA= SETsecondt_(facet->vertices, vertexT);
       vertexB= SETfirstt_(facet->vertices, vertexT);
       nextfacet= SETsecondt_(facet->neighbors, facetT);
     }
     if (facet->visitid == qh->visit_id) {
       qh_fprintf(qh, qh->ferr, 6218, "Qhull internal error (qh_printextremes_2d): loop in facet list.  facet %d nextfacet %d\n",
                  facet->id, nextfacet->id);
       qh_errexit2(qh, qh_ERRqhull, facet, nextfacet);
     }
     if (facet->visitid) {
       if (vertexA->visitid != qh->vertex_visit) {
         vertexA->visitid= qh->vertex_visit;
         qh_fprintf(qh, fp, 9089, "%d\n", qh_pointid(qh, vertexA->point));
       }
       if (vertexB->visitid != qh->vertex_visit) {
         vertexB->visitid= qh->vertex_visit;
         qh_fprintf(qh, fp, 9090, "%d\n", qh_pointid(qh, vertexB->point));
       }
     }
     facet->visitid= qh->visit_id;
     facet= nextfacet;
   }while (facet && facet != startfacet);
 } /* printextremes_2d */
 
 /*---------------------------------
 
   qh_printextremes_d(qh, fp, facetlist, facets, printall )
     print extreme points of input sites for Delaunay triangulations
 
   notes:
     #points, followed by ids, one per line
 
     unordered
 */
 void qh_printextremes_d(qhT *qh, FILE *fp, facetT *facetlist, setT *facets, boolT printall) {
   setT *vertices;
   vertexT *vertex, **vertexp;
   boolT upperseen, lowerseen;
   facetT *neighbor, **neighborp;
   int numpoints=0;
 
   vertices= qh_facetvertices(qh, facetlist, facets, printall);
   qh_vertexneighbors(qh);
   FOREACHvertex_(vertices) {
     upperseen= lowerseen= False;
     FOREACHneighbor_(vertex) {
       if (neighbor->upperdelaunay)
         upperseen= True;
       else
         lowerseen= True;
     }
     if (upperseen && lowerseen) {
       vertex->seen= True;
       numpoints++;
     }else
       vertex->seen= False;
   }
   qh_fprintf(qh, fp, 9091, "%d\n", numpoints);
   FOREACHvertex_(vertices) {
     if (vertex->seen)
       qh_fprintf(qh, fp, 9092, "%d\n", qh_pointid(qh, vertex->point));
   }
   qh_settempfree(qh, &vertices);
 } /* printextremes_d */
 
 /*---------------------------------
 
   qh_printfacet(qh, fp, facet )
     prints all fields of a facet to fp
 
   notes:
     ridges printed in neighbor order
 */
 void qh_printfacet(qhT *qh, FILE *fp, facetT *facet) {
 
   qh_printfacetheader(qh, fp, facet);
   if (facet->ridges)
     qh_printfacetridges(qh, fp, facet);
 } /* printfacet */
 
 
 /*---------------------------------
 
   qh_printfacet2geom(qh, fp, facet, color )
     print facet as part of a 2-d VECT for Geomview
 
     notes:
-      assume precise calculations in io.c with roundoff covered by qh_GEOMepsilon
-      mindist is calculated within io.c.  maxoutside is calculated elsewhere
-      so a DISTround error may have occured.
+      assume precise calculations in io_r.c with roundoff covered by qh_GEOMepsilon
+      mindist is calculated within io_r.c.  maxoutside is calculated elsewhere
+      so a DISTround error may have occurred.
 */
 void qh_printfacet2geom(qhT *qh, FILE *fp, facetT *facet, realT color[3]) {
   pointT *point0, *point1;
   realT mindist, innerplane, outerplane;
   int k;
 
   qh_facet2point(qh, facet, &point0, &point1, &mindist);
   qh_geomplanes(qh, facet, &outerplane, &innerplane);
   if (qh->PRINTouter || (!qh->PRINTnoplanes && !qh->PRINTinner))
     qh_printfacet2geom_points(qh, fp, point0, point1, facet, outerplane, color);
   if (qh->PRINTinner || (!qh->PRINTnoplanes && !qh->PRINTouter &&
                 outerplane - innerplane > 2 * qh->MAXabs_coord * qh_GEOMepsilon)) {
     for (k=3; k--; )
       color[k]= 1.0 - color[k];
     qh_printfacet2geom_points(qh, fp, point0, point1, facet, innerplane, color);
   }
   qh_memfree(qh, point1, qh->normal_size);
   qh_memfree(qh, point0, qh->normal_size);
 } /* printfacet2geom */
 
 /*---------------------------------
 
   qh_printfacet2geom_points(qh, fp, point1, point2, facet, offset, color )
     prints a 2-d facet as a VECT with 2 points at some offset.
     The points are on the facet's plane.
 */
 void qh_printfacet2geom_points(qhT *qh, FILE *fp, pointT *point1, pointT *point2,
                                facetT *facet, realT offset, realT color[3]) {
   pointT *p1= point1, *p2= point2;
 
   qh_fprintf(qh, fp, 9093, "VECT 1 2 1 2 1 # f%d\n", facet->id);
   if (offset != 0.0) {
     p1= qh_projectpoint(qh, p1, facet, -offset);
     p2= qh_projectpoint(qh, p2, facet, -offset);
   }
   qh_fprintf(qh, fp, 9094, "%8.4g %8.4g %8.4g\n%8.4g %8.4g %8.4g\n",
            p1[0], p1[1], 0.0, p2[0], p2[1], 0.0);
   if (offset != 0.0) {
     qh_memfree(qh, p1, qh->normal_size);
     qh_memfree(qh, p2, qh->normal_size);
   }
   qh_fprintf(qh, fp, 9095, "%8.4g %8.4g %8.4g 1.0\n", color[0], color[1], color[2]);
 } /* printfacet2geom_points */
 
 
 /*---------------------------------
 
   qh_printfacet2math(qh, fp, facet, format, notfirst )
     print 2-d Maple or Mathematica output for a facet
     may be non-simplicial
 
   notes:
     use %16.8f since Mathematica 2.2 does not handle exponential format
     see qh_printfacet3math
 */
 void qh_printfacet2math(qhT *qh, FILE *fp, facetT *facet, qh_PRINT format, int notfirst) {
   pointT *point0, *point1;
   realT mindist;
   const char *pointfmt;
 
   qh_facet2point(qh, facet, &point0, &point1, &mindist);
   if (notfirst)
     qh_fprintf(qh, fp, 9096, ",");
   if (format == qh_PRINTmaple)
     pointfmt= "[[%16.8f, %16.8f], [%16.8f, %16.8f]]\n";
   else
     pointfmt= "Line[{{%16.8f, %16.8f}, {%16.8f, %16.8f}}]\n";
   qh_fprintf(qh, fp, 9097, pointfmt, point0[0], point0[1], point1[0], point1[1]);
   qh_memfree(qh, point1, qh->normal_size);
   qh_memfree(qh, point0, qh->normal_size);
 } /* printfacet2math */
 
 
 /*---------------------------------
 
   qh_printfacet3geom_nonsimplicial(qh, fp, facet, color )
     print Geomview OFF for a 3-d nonsimplicial facet.
     if DOintersections, prints ridges to unvisited neighbors(qh->visit_id)
 
   notes
     uses facet->visitid for intersections and ridges
 */
 void qh_printfacet3geom_nonsimplicial(qhT *qh, FILE *fp, facetT *facet, realT color[3]) {
   ridgeT *ridge, **ridgep;
   setT *projectedpoints, *vertices;
   vertexT *vertex, **vertexp, *vertexA, *vertexB;
   pointT *projpt, *point, **pointp;
   facetT *neighbor;
   realT dist, outerplane, innerplane;
   int cntvertices, k;
   realT black[3]={0, 0, 0}, green[3]={0, 1, 0};
 
   qh_geomplanes(qh, facet, &outerplane, &innerplane);
   vertices= qh_facet3vertex(qh, facet); /* oriented */
   cntvertices= qh_setsize(qh, vertices);
   projectedpoints= qh_settemp(qh, cntvertices);
   FOREACHvertex_(vertices) {
     zinc_(Zdistio);
     qh_distplane(qh, vertex->point, facet, &dist);
     projpt= qh_projectpoint(qh, vertex->point, facet, dist);
     qh_setappend(qh, &projectedpoints, projpt);
   }
   if (qh->PRINTouter || (!qh->PRINTnoplanes && !qh->PRINTinner))
     qh_printfacet3geom_points(qh, fp, projectedpoints, facet, outerplane, color);
   if (qh->PRINTinner || (!qh->PRINTnoplanes && !qh->PRINTouter &&
                 outerplane - innerplane > 2 * qh->MAXabs_coord * qh_GEOMepsilon)) {
     for (k=3; k--; )
       color[k]= 1.0 - color[k];
     qh_printfacet3geom_points(qh, fp, projectedpoints, facet, innerplane, color);
   }
   FOREACHpoint_(projectedpoints)
     qh_memfree(qh, point, qh->normal_size);
   qh_settempfree(qh, &projectedpoints);
   qh_settempfree(qh, &vertices);
   if ((qh->DOintersections || qh->PRINTridges)
   && (!facet->visible || !qh->NEWfacets)) {
     facet->visitid= qh->visit_id;
     FOREACHridge_(facet->ridges) {
       neighbor= otherfacet_(ridge, facet);
       if (neighbor->visitid != qh->visit_id) {
         if (qh->DOintersections)
           qh_printhyperplaneintersection(qh, fp, facet, neighbor, ridge->vertices, black);
         if (qh->PRINTridges) {
           vertexA= SETfirstt_(ridge->vertices, vertexT);
           vertexB= SETsecondt_(ridge->vertices, vertexT);
           qh_printline3geom(qh, fp, vertexA->point, vertexB->point, green);
         }
       }
     }
   }
 } /* printfacet3geom_nonsimplicial */
 
 /*---------------------------------
 
   qh_printfacet3geom_points(qh, fp, points, facet, offset )
     prints a 3-d facet as OFF Geomview object.
     offset is relative to the facet's hyperplane
     Facet is determined as a list of points
 */
 void qh_printfacet3geom_points(qhT *qh, FILE *fp, setT *points, facetT *facet, realT offset, realT color[3]) {
   int k, n= qh_setsize(qh, points), i;
   pointT *point, **pointp;
   setT *printpoints;
 
   qh_fprintf(qh, fp, 9098, "{ OFF %d 1 1 # f%d\n", n, facet->id);
   if (offset != 0.0) {
     printpoints= qh_settemp(qh, n);
     FOREACHpoint_(points)
       qh_setappend(qh, &printpoints, qh_projectpoint(qh, point, facet, -offset));
   }else
     printpoints= points;
   FOREACHpoint_(printpoints) {
     for (k=0; k < qh->hull_dim; k++) {
       if (k == qh->DROPdim)
         qh_fprintf(qh, fp, 9099, "0 ");
       else
         qh_fprintf(qh, fp, 9100, "%8.4g ", point[k]);
     }
     if (printpoints != points)
       qh_memfree(qh, point, qh->normal_size);
     qh_fprintf(qh, fp, 9101, "\n");
   }
   if (printpoints != points)
     qh_settempfree(qh, &printpoints);
   qh_fprintf(qh, fp, 9102, "%d ", n);
   for (i=0; i < n; i++)
     qh_fprintf(qh, fp, 9103, "%d ", i);
   qh_fprintf(qh, fp, 9104, "%8.4g %8.4g %8.4g 1.0 }\n", color[0], color[1], color[2]);
 } /* printfacet3geom_points */
 
 
 /*---------------------------------
 
   qh_printfacet3geom_simplicial(qh, )
     print Geomview OFF for a 3-d simplicial facet.
 
   notes:
     may flip color
     uses facet->visitid for intersections and ridges
 
-    assume precise calculations in io.c with roundoff covered by qh_GEOMepsilon
+    assume precise calculations in io_r.c with roundoff covered by qh_GEOMepsilon
     innerplane may be off by qh->DISTround.  Maxoutside is calculated elsewhere
-    so a DISTround error may have occured.
+    so a DISTround error may have occurred.
 */
 void qh_printfacet3geom_simplicial(qhT *qh, FILE *fp, facetT *facet, realT color[3]) {
   setT *points, *vertices;
   vertexT *vertex, **vertexp, *vertexA, *vertexB;
   facetT *neighbor, **neighborp;
   realT outerplane, innerplane;
   realT black[3]={0, 0, 0}, green[3]={0, 1, 0};
   int k;
 
   qh_geomplanes(qh, facet, &outerplane, &innerplane);
   vertices= qh_facet3vertex(qh, facet);
   points= qh_settemp(qh, qh->TEMPsize);
   FOREACHvertex_(vertices)
     qh_setappend(qh, &points, vertex->point);
   if (qh->PRINTouter || (!qh->PRINTnoplanes && !qh->PRINTinner))
     qh_printfacet3geom_points(qh, fp, points, facet, outerplane, color);
   if (qh->PRINTinner || (!qh->PRINTnoplanes && !qh->PRINTouter &&
               outerplane - innerplane > 2 * qh->MAXabs_coord * qh_GEOMepsilon)) {
     for (k=3; k--; )
       color[k]= 1.0 - color[k];
     qh_printfacet3geom_points(qh, fp, points, facet, innerplane, color);
   }
   qh_settempfree(qh, &points);
   qh_settempfree(qh, &vertices);
   if ((qh->DOintersections || qh->PRINTridges)
   && (!facet->visible || !qh->NEWfacets)) {
     facet->visitid= qh->visit_id;
     FOREACHneighbor_(facet) {
       if (neighbor->visitid != qh->visit_id) {
         vertices= qh_setnew_delnthsorted(qh, facet->vertices, qh->hull_dim,
                           SETindex_(facet->neighbors, neighbor), 0);
         if (qh->DOintersections)
            qh_printhyperplaneintersection(qh, fp, facet, neighbor, vertices, black);
         if (qh->PRINTridges) {
           vertexA= SETfirstt_(vertices, vertexT);
           vertexB= SETsecondt_(vertices, vertexT);
           qh_printline3geom(qh, fp, vertexA->point, vertexB->point, green);
         }
         qh_setfree(qh, &vertices);
       }
     }
   }
 } /* printfacet3geom_simplicial */
 
 /*---------------------------------
 
   qh_printfacet3math(qh, fp, facet, notfirst )
     print 3-d Maple or Mathematica output for a facet
 
   notes:
     may be non-simplicial
     use %16.8f since Mathematica 2.2 does not handle exponential format
     see qh_printfacet2math
 */
 void qh_printfacet3math(qhT *qh, FILE *fp, facetT *facet, qh_PRINT format, int notfirst) {
   vertexT *vertex, **vertexp;
   setT *points, *vertices;
   pointT *point, **pointp;
   boolT firstpoint= True;
   realT dist;
   const char *pointfmt, *endfmt;
 
   if (notfirst)
     qh_fprintf(qh, fp, 9105, ",\n");
   vertices= qh_facet3vertex(qh, facet);
   points= qh_settemp(qh, qh_setsize(qh, vertices));
   FOREACHvertex_(vertices) {
     zinc_(Zdistio);
     qh_distplane(qh, vertex->point, facet, &dist);
     point= qh_projectpoint(qh, vertex->point, facet, dist);
     qh_setappend(qh, &points, point);
   }
   if (format == qh_PRINTmaple) {
     qh_fprintf(qh, fp, 9106, "[");
     pointfmt= "[%16.8f, %16.8f, %16.8f]";
     endfmt= "]";
   }else {
     qh_fprintf(qh, fp, 9107, "Polygon[{");
     pointfmt= "{%16.8f, %16.8f, %16.8f}";
     endfmt= "}]";
   }
   FOREACHpoint_(points) {
     if (firstpoint)
       firstpoint= False;
     else
       qh_fprintf(qh, fp, 9108, ",\n");
     qh_fprintf(qh, fp, 9109, pointfmt, point[0], point[1], point[2]);
   }
   FOREACHpoint_(points)
     qh_memfree(qh, point, qh->normal_size);
   qh_settempfree(qh, &points);
   qh_settempfree(qh, &vertices);
   qh_fprintf(qh, fp, 9110, endfmt);
 } /* printfacet3math */
 
 
 /*---------------------------------
 
   qh_printfacet3vertex(qh, fp, facet, format )
     print vertices in a 3-d facet as point ids
 
   notes:
     prints number of vertices first if format == qh_PRINToff
     the facet may be non-simplicial
 */
 void qh_printfacet3vertex(qhT *qh, FILE *fp, facetT *facet, qh_PRINT format) {
   vertexT *vertex, **vertexp;
   setT *vertices;
 
   vertices= qh_facet3vertex(qh, facet);
   if (format == qh_PRINToff)
     qh_fprintf(qh, fp, 9111, "%d ", qh_setsize(qh, vertices));
   FOREACHvertex_(vertices)
     qh_fprintf(qh, fp, 9112, "%d ", qh_pointid(qh, vertex->point));
   qh_fprintf(qh, fp, 9113, "\n");
   qh_settempfree(qh, &vertices);
 } /* printfacet3vertex */
 
 
 /*---------------------------------
 
   qh_printfacet4geom_nonsimplicial(qh, )
     print Geomview 4OFF file for a 4d nonsimplicial facet
     prints all ridges to unvisited neighbors (qh.visit_id)
     if qh.DROPdim
       prints in OFF format
 
   notes:
     must agree with printend4geom()
 */
 void qh_printfacet4geom_nonsimplicial(qhT *qh, FILE *fp, facetT *facet, realT color[3]) {
   facetT *neighbor;
   ridgeT *ridge, **ridgep;
   vertexT *vertex, **vertexp;
   pointT *point;
   int k;
   realT dist;
 
   facet->visitid= qh->visit_id;
   if (qh->PRINTnoplanes || (facet->visible && qh->NEWfacets))
     return;
   FOREACHridge_(facet->ridges) {
     neighbor= otherfacet_(ridge, facet);
     if (neighbor->visitid == qh->visit_id)
       continue;
     if (qh->PRINTtransparent && !neighbor->good)
       continue;
     if (qh->DOintersections)
       qh_printhyperplaneintersection(qh, fp, facet, neighbor, ridge->vertices, color);
     else {
       if (qh->DROPdim >= 0)
         qh_fprintf(qh, fp, 9114, "OFF 3 1 1 # f%d\n", facet->id);
       else {
         qh->printoutvar++;
         qh_fprintf(qh, fp, 9115, "# r%d between f%d f%d\n", ridge->id, facet->id, neighbor->id);
       }
       FOREACHvertex_(ridge->vertices) {
         zinc_(Zdistio);
         qh_distplane(qh, vertex->point,facet, &dist);
         point=qh_projectpoint(qh, vertex->point,facet, dist);
         for (k=0; k < qh->hull_dim; k++) {
           if (k != qh->DROPdim)
             qh_fprintf(qh, fp, 9116, "%8.4g ", point[k]);
         }
         qh_fprintf(qh, fp, 9117, "\n");
         qh_memfree(qh, point, qh->normal_size);
       }
       if (qh->DROPdim >= 0)
         qh_fprintf(qh, fp, 9118, "3 0 1 2 %8.4g %8.4g %8.4g\n", color[0], color[1], color[2]);
     }
   }
 } /* printfacet4geom_nonsimplicial */
 
 
 /*---------------------------------
 
   qh_printfacet4geom_simplicial(qh, fp, facet, color )
     print Geomview 4OFF file for a 4d simplicial facet
     prints triangles for unvisited neighbors (qh.visit_id)
 
   notes:
     must agree with printend4geom()
 */
 void qh_printfacet4geom_simplicial(qhT *qh, FILE *fp, facetT *facet, realT color[3]) {
   setT *vertices;
   facetT *neighbor, **neighborp;
   vertexT *vertex, **vertexp;
   int k;
 
   facet->visitid= qh->visit_id;
   if (qh->PRINTnoplanes || (facet->visible && qh->NEWfacets))
     return;
   FOREACHneighbor_(facet) {
     if (neighbor->visitid == qh->visit_id)
       continue;
     if (qh->PRINTtransparent && !neighbor->good)
       continue;
     vertices= qh_setnew_delnthsorted(qh, facet->vertices, qh->hull_dim,
                           SETindex_(facet->neighbors, neighbor), 0);
     if (qh->DOintersections)
       qh_printhyperplaneintersection(qh, fp, facet, neighbor, vertices, color);
     else {
       if (qh->DROPdim >= 0)
         qh_fprintf(qh, fp, 9119, "OFF 3 1 1 # ridge between f%d f%d\n",
                 facet->id, neighbor->id);
       else {
         qh->printoutvar++;
         qh_fprintf(qh, fp, 9120, "# ridge between f%d f%d\n", facet->id, neighbor->id);
       }
       FOREACHvertex_(vertices) {
         for (k=0; k < qh->hull_dim; k++) {
           if (k != qh->DROPdim)
             qh_fprintf(qh, fp, 9121, "%8.4g ", vertex->point[k]);
         }
         qh_fprintf(qh, fp, 9122, "\n");
       }
       if (qh->DROPdim >= 0)
         qh_fprintf(qh, fp, 9123, "3 0 1 2 %8.4g %8.4g %8.4g\n", color[0], color[1], color[2]);
     }
     qh_setfree(qh, &vertices);
   }
 } /* printfacet4geom_simplicial */
 
 
 /*---------------------------------
 
   qh_printfacetNvertex_nonsimplicial(qh, fp, facet, id, format )
     print vertices for an N-d non-simplicial facet
     triangulates each ridge to the id
 */
 void qh_printfacetNvertex_nonsimplicial(qhT *qh, FILE *fp, facetT *facet, int id, qh_PRINT format) {
   vertexT *vertex, **vertexp;
   ridgeT *ridge, **ridgep;
 
   if (facet->visible && qh->NEWfacets)
     return;
   FOREACHridge_(facet->ridges) {
     if (format == qh_PRINTtriangles)
       qh_fprintf(qh, fp, 9124, "%d ", qh->hull_dim);
     qh_fprintf(qh, fp, 9125, "%d ", id);
     if ((ridge->top == facet) ^ qh_ORIENTclock) {
       FOREACHvertex_(ridge->vertices)
         qh_fprintf(qh, fp, 9126, "%d ", qh_pointid(qh, vertex->point));
     }else {
       FOREACHvertexreverse12_(ridge->vertices)
         qh_fprintf(qh, fp, 9127, "%d ", qh_pointid(qh, vertex->point));
     }
     qh_fprintf(qh, fp, 9128, "\n");
   }
 } /* printfacetNvertex_nonsimplicial */
 
 
 /*---------------------------------
 
   qh_printfacetNvertex_simplicial(qh, fp, facet, format )
     print vertices for an N-d simplicial facet
     prints vertices for non-simplicial facets
       2-d facets (orientation preserved by qh_mergefacet2d)
       PRINToff ('o') for 4-d and higher
 */
 void qh_printfacetNvertex_simplicial(qhT *qh, FILE *fp, facetT *facet, qh_PRINT format) {
   vertexT *vertex, **vertexp;
 
   if (format == qh_PRINToff || format == qh_PRINTtriangles)
     qh_fprintf(qh, fp, 9129, "%d ", qh_setsize(qh, facet->vertices));
   if ((facet->toporient ^ qh_ORIENTclock)
   || (qh->hull_dim > 2 && !facet->simplicial)) {
     FOREACHvertex_(facet->vertices)
       qh_fprintf(qh, fp, 9130, "%d ", qh_pointid(qh, vertex->point));
   }else {
     FOREACHvertexreverse12_(facet->vertices)
       qh_fprintf(qh, fp, 9131, "%d ", qh_pointid(qh, vertex->point));
   }
   qh_fprintf(qh, fp, 9132, "\n");
 } /* printfacetNvertex_simplicial */
 
 
 /*---------------------------------
 
   qh_printfacetheader(qh, fp, facet )
     prints header fields of a facet to fp
 
   notes:
     for 'f' output and debugging
     Same as QhullFacet::printHeader()
 */
 void qh_printfacetheader(qhT *qh, FILE *fp, facetT *facet) {
   pointT *point, **pointp, *furthest;
   facetT *neighbor, **neighborp;
   realT dist;
 
   if (facet == qh_MERGEridge) {
     qh_fprintf(qh, fp, 9133, " MERGEridge\n");
     return;
   }else if (facet == qh_DUPLICATEridge) {
     qh_fprintf(qh, fp, 9134, " DUPLICATEridge\n");
     return;
   }else if (!facet) {
     qh_fprintf(qh, fp, 9135, " NULLfacet\n");
     return;
   }
   qh->old_randomdist= qh->RANDOMdist;
   qh->RANDOMdist= False;
   qh_fprintf(qh, fp, 9136, "- f%d\n", facet->id);
   qh_fprintf(qh, fp, 9137, "    - flags:");
   if (facet->toporient)
     qh_fprintf(qh, fp, 9138, " top");
   else
     qh_fprintf(qh, fp, 9139, " bottom");
   if (facet->simplicial)
     qh_fprintf(qh, fp, 9140, " simplicial");
   if (facet->tricoplanar)
     qh_fprintf(qh, fp, 9141, " tricoplanar");
   if (facet->upperdelaunay)
     qh_fprintf(qh, fp, 9142, " upperDelaunay");
   if (facet->visible)
     qh_fprintf(qh, fp, 9143, " visible");
   if (facet->newfacet)
     qh_fprintf(qh, fp, 9144, " new");
   if (facet->tested)
     qh_fprintf(qh, fp, 9145, " tested");
   if (!facet->good)
     qh_fprintf(qh, fp, 9146, " notG");
   if (facet->seen)
     qh_fprintf(qh, fp, 9147, " seen");
   if (facet->coplanar)
     qh_fprintf(qh, fp, 9148, " coplanar");
   if (facet->mergehorizon)
     qh_fprintf(qh, fp, 9149, " mergehorizon");
   if (facet->keepcentrum)
     qh_fprintf(qh, fp, 9150, " keepcentrum");
   if (facet->dupridge)
     qh_fprintf(qh, fp, 9151, " dupridge");
   if (facet->mergeridge && !facet->mergeridge2)
     qh_fprintf(qh, fp, 9152, " mergeridge1");
   if (facet->mergeridge2)
     qh_fprintf(qh, fp, 9153, " mergeridge2");
   if (facet->newmerge)
     qh_fprintf(qh, fp, 9154, " newmerge");
   if (facet->flipped)
     qh_fprintf(qh, fp, 9155, " flipped");
   if (facet->notfurthest)
     qh_fprintf(qh, fp, 9156, " notfurthest");
   if (facet->degenerate)
     qh_fprintf(qh, fp, 9157, " degenerate");
   if (facet->redundant)
     qh_fprintf(qh, fp, 9158, " redundant");
   qh_fprintf(qh, fp, 9159, "\n");
   if (facet->isarea)
     qh_fprintf(qh, fp, 9160, "    - area: %2.2g\n", facet->f.area);
   else if (qh->NEWfacets && facet->visible && facet->f.replace)
     qh_fprintf(qh, fp, 9161, "    - replacement: f%d\n", facet->f.replace->id);
   else if (facet->newfacet) {
     if (facet->f.samecycle && facet->f.samecycle != facet)
       qh_fprintf(qh, fp, 9162, "    - shares same visible/horizon as f%d\n", facet->f.samecycle->id);
   }else if (facet->tricoplanar /* !isarea */) {
     if (facet->f.triowner)
       qh_fprintf(qh, fp, 9163, "    - owner of normal & centrum is facet f%d\n", facet->f.triowner->id);
   }else if (facet->f.newcycle)
     qh_fprintf(qh, fp, 9164, "    - was horizon to f%d\n", facet->f.newcycle->id);
   if (facet->nummerge)
     qh_fprintf(qh, fp, 9165, "    - merges: %d\n", facet->nummerge);
   qh_printpointid(qh, fp, "    - normal: ", qh->hull_dim, facet->normal, -1);
   qh_fprintf(qh, fp, 9166, "    - offset: %10.7g\n", facet->offset);
   if (qh->CENTERtype == qh_ASvoronoi || facet->center)
     qh_printcenter(qh, fp, qh_PRINTfacets, "    - center: ", facet);
 #if qh_MAXoutside
   if (facet->maxoutside > qh->DISTround)
     qh_fprintf(qh, fp, 9167, "    - maxoutside: %10.7g\n", facet->maxoutside);
 #endif
   if (!SETempty_(facet->outsideset)) {
     furthest= (pointT*)qh_setlast(facet->outsideset);
     if (qh_setsize(qh, facet->outsideset) < 6) {
       qh_fprintf(qh, fp, 9168, "    - outside set(furthest p%d):\n", qh_pointid(qh, furthest));
       FOREACHpoint_(facet->outsideset)
         qh_printpoint(qh, fp, "     ", point);
     }else if (qh_setsize(qh, facet->outsideset) < 21) {
       qh_printpoints(qh, fp, "    - outside set:", facet->outsideset);
     }else {
       qh_fprintf(qh, fp, 9169, "    - outside set:  %d points.", qh_setsize(qh, facet->outsideset));
       qh_printpoint(qh, fp, "  Furthest", furthest);
     }
 #if !qh_COMPUTEfurthest
     qh_fprintf(qh, fp, 9170, "    - furthest distance= %2.2g\n", facet->furthestdist);
 #endif
   }
   if (!SETempty_(facet->coplanarset)) {
     furthest= (pointT*)qh_setlast(facet->coplanarset);
     if (qh_setsize(qh, facet->coplanarset) < 6) {
       qh_fprintf(qh, fp, 9171, "    - coplanar set(furthest p%d):\n", qh_pointid(qh, furthest));
       FOREACHpoint_(facet->coplanarset)
         qh_printpoint(qh, fp, "     ", point);
     }else if (qh_setsize(qh, facet->coplanarset) < 21) {
       qh_printpoints(qh, fp, "    - coplanar set:", facet->coplanarset);
     }else {
       qh_fprintf(qh, fp, 9172, "    - coplanar set:  %d points.", qh_setsize(qh, facet->coplanarset));
       qh_printpoint(qh, fp, "  Furthest", furthest);
     }
     zinc_(Zdistio);
     qh_distplane(qh, furthest, facet, &dist);
     qh_fprintf(qh, fp, 9173, "      furthest distance= %2.2g\n", dist);
   }
   qh_printvertices(qh, fp, "    - vertices:", facet->vertices);
   qh_fprintf(qh, fp, 9174, "    - neighboring facets:");
   FOREACHneighbor_(facet) {
     if (neighbor == qh_MERGEridge)
       qh_fprintf(qh, fp, 9175, " MERGE");
     else if (neighbor == qh_DUPLICATEridge)
       qh_fprintf(qh, fp, 9176, " DUP");
     else
       qh_fprintf(qh, fp, 9177, " f%d", neighbor->id);
   }
   qh_fprintf(qh, fp, 9178, "\n");
   qh->RANDOMdist= qh->old_randomdist;
 } /* printfacetheader */
 
 
 /*---------------------------------
 
   qh_printfacetridges(qh, fp, facet )
     prints ridges of a facet to fp
 
   notes:
     ridges printed in neighbor order
     assumes the ridges exist
     for 'f' output
     same as QhullFacet::printRidges
 */
 void qh_printfacetridges(qhT *qh, FILE *fp, facetT *facet) {
   facetT *neighbor, **neighborp;
   ridgeT *ridge, **ridgep;
   int numridges= 0;
 
 
   if (facet->visible && qh->NEWfacets) {
     qh_fprintf(qh, fp, 9179, "    - ridges(ids may be garbage):");
     FOREACHridge_(facet->ridges)
       qh_fprintf(qh, fp, 9180, " r%d", ridge->id);
     qh_fprintf(qh, fp, 9181, "\n");
   }else {
     qh_fprintf(qh, fp, 9182, "    - ridges:\n");
     FOREACHridge_(facet->ridges)
       ridge->seen= False;
     if (qh->hull_dim == 3) {
       ridge= SETfirstt_(facet->ridges, ridgeT);
       while (ridge && !ridge->seen) {
         ridge->seen= True;
         qh_printridge(qh, fp, ridge);
         numridges++;
         ridge= qh_nextridge3d(qh, ridge, facet, NULL);
         }
     }else {
       FOREACHneighbor_(facet) {
         FOREACHridge_(facet->ridges) {
           if (otherfacet_(ridge,facet) == neighbor) {
             ridge->seen= True;
             qh_printridge(qh, fp, ridge);
             numridges++;
           }
         }
       }
     }
     if (numridges != qh_setsize(qh, facet->ridges)) {
       qh_fprintf(qh, fp, 9183, "     - all ridges:");
       FOREACHridge_(facet->ridges)
         qh_fprintf(qh, fp, 9184, " r%d", ridge->id);
         qh_fprintf(qh, fp, 9185, "\n");
     }
     FOREACHridge_(facet->ridges) {
       if (!ridge->seen)
         qh_printridge(qh, fp, ridge);
     }
   }
 } /* printfacetridges */
 
 /*---------------------------------
 
   qh_printfacets(qh, fp, format, facetlist, facets, printall )
     prints facetlist and/or facet set in output format
 
   notes:
     also used for specialized formats ('FO' and summary)
     turns off 'Rn' option since want actual numbers
 */
 void qh_printfacets(qhT *qh, FILE *fp, qh_PRINT format, facetT *facetlist, setT *facets, boolT printall) {
   int numfacets, numsimplicial, numridges, totneighbors, numcoplanars, numtricoplanars;
   facetT *facet, **facetp;
   setT *vertices;
   coordT *center;
   realT outerplane, innerplane;
 
   qh->old_randomdist= qh->RANDOMdist;
   qh->RANDOMdist= False;
   if (qh->CDDoutput && (format == qh_PRINTcentrums || format == qh_PRINTpointintersect || format == qh_PRINToff))
     qh_fprintf(qh, qh->ferr, 7056, "qhull warning: CDD format is not available for centrums, halfspace\nintersections, and OFF file format.\n");
   if (format == qh_PRINTnone)
     ; /* print nothing */
   else if (format == qh_PRINTaverage) {
     vertices= qh_facetvertices(qh, facetlist, facets, printall);
     center= qh_getcenter(qh, vertices);
     qh_fprintf(qh, fp, 9186, "%d 1\n", qh->hull_dim);
     qh_printpointid(qh, fp, NULL, qh->hull_dim, center, -1);
     qh_memfree(qh, center, qh->normal_size);
     qh_settempfree(qh, &vertices);
   }else if (format == qh_PRINTextremes) {
     if (qh->DELAUNAY)
       qh_printextremes_d(qh, fp, facetlist, facets, printall);
     else if (qh->hull_dim == 2)
       qh_printextremes_2d(qh, fp, facetlist, facets, printall);
     else
       qh_printextremes(qh, fp, facetlist, facets, printall);
   }else if (format == qh_PRINToptions)
     qh_fprintf(qh, fp, 9187, "Options selected for Qhull %s:\n%s\n", qh_version, qh->qhull_options);
   else if (format == qh_PRINTpoints && !qh->VORONOI)
     qh_printpoints_out(qh, fp, facetlist, facets, printall);
   else if (format == qh_PRINTqhull)
     qh_fprintf(qh, fp, 9188, "%s | %s\n", qh->rbox_command, qh->qhull_command);
   else if (format == qh_PRINTsize) {
     qh_fprintf(qh, fp, 9189, "0\n2 ");
     qh_fprintf(qh, fp, 9190, qh_REAL_1, qh->totarea);
     qh_fprintf(qh, fp, 9191, qh_REAL_1, qh->totvol);
     qh_fprintf(qh, fp, 9192, "\n");
   }else if (format == qh_PRINTsummary) {
     qh_countfacets(qh, facetlist, facets, printall, &numfacets, &numsimplicial,
       &totneighbors, &numridges, &numcoplanars, &numtricoplanars);
     vertices= qh_facetvertices(qh, facetlist, facets, printall);
     qh_fprintf(qh, fp, 9193, "10 %d %d %d %d %d %d %d %d %d %d\n2 ", qh->hull_dim,
                 qh->num_points + qh_setsize(qh, qh->other_points),
                 qh->num_vertices, qh->num_facets - qh->num_visible,
                 qh_setsize(qh, vertices), numfacets, numcoplanars,
                 numfacets - numsimplicial, zzval_(Zdelvertextot),
                 numtricoplanars);
     qh_settempfree(qh, &vertices);
     qh_outerinner(qh, NULL, &outerplane, &innerplane);
     qh_fprintf(qh, fp, 9194, qh_REAL_2n, outerplane, innerplane);
   }else if (format == qh_PRINTvneighbors)
     qh_printvneighbors(qh, fp, facetlist, facets, printall);
   else if (qh->VORONOI && format == qh_PRINToff)
     qh_printvoronoi(qh, fp, format, facetlist, facets, printall);
   else if (qh->VORONOI && format == qh_PRINTgeom) {
     qh_printbegin(qh, fp, format, facetlist, facets, printall);
     qh_printvoronoi(qh, fp, format, facetlist, facets, printall);
     qh_printend(qh, fp, format, facetlist, facets, printall);
   }else if (qh->VORONOI
   && (format == qh_PRINTvertices || format == qh_PRINTinner || format == qh_PRINTouter))
     qh_printvdiagram(qh, fp, format, facetlist, facets, printall);
   else {
     qh_printbegin(qh, fp, format, facetlist, facets, printall);
     FORALLfacet_(facetlist)
       qh_printafacet(qh, fp, format, facet, printall);
     FOREACHfacet_(facets)
       qh_printafacet(qh, fp, format, facet, printall);
     qh_printend(qh, fp, format, facetlist, facets, printall);
   }
   qh->RANDOMdist= qh->old_randomdist;
 } /* printfacets */
 
 
 /*---------------------------------
 
   qh_printhyperplaneintersection(qh, fp, facet1, facet2, vertices, color )
     print Geomview OFF or 4OFF for the intersection of two hyperplanes in 3-d or 4-d
 */
 void qh_printhyperplaneintersection(qhT *qh, FILE *fp, facetT *facet1, facetT *facet2,
                    setT *vertices, realT color[3]) {
   realT costheta, denominator, dist1, dist2, s, t, mindenom, p[4];
   vertexT *vertex, **vertexp;
   int i, k;
   boolT nearzero1, nearzero2;
 
   costheta= qh_getangle(qh, facet1->normal, facet2->normal);
   denominator= 1 - costheta * costheta;
   i= qh_setsize(qh, vertices);
   if (qh->hull_dim == 3)
     qh_fprintf(qh, fp, 9195, "VECT 1 %d 1 %d 1 ", i, i);
   else if (qh->hull_dim == 4 && qh->DROPdim >= 0)
     qh_fprintf(qh, fp, 9196, "OFF 3 1 1 ");
   else
     qh->printoutvar++;
   qh_fprintf(qh, fp, 9197, "# intersect f%d f%d\n", facet1->id, facet2->id);
   mindenom= 1 / (10.0 * qh->MAXabs_coord);
   FOREACHvertex_(vertices) {
     zadd_(Zdistio, 2);
     qh_distplane(qh, vertex->point, facet1, &dist1);
     qh_distplane(qh, vertex->point, facet2, &dist2);
     s= qh_divzero(qh, -dist1 + costheta * dist2, denominator,mindenom,&nearzero1);
     t= qh_divzero(qh, -dist2 + costheta * dist1, denominator,mindenom,&nearzero2);
     if (nearzero1 || nearzero2)
       s= t= 0.0;
     for (k=qh->hull_dim; k--; )
       p[k]= vertex->point[k] + facet1->normal[k] * s + facet2->normal[k] * t;
     if (qh->PRINTdim <= 3) {
       qh_projectdim3(qh, p, p);
       qh_fprintf(qh, fp, 9198, "%8.4g %8.4g %8.4g # ", p[0], p[1], p[2]);
     }else
       qh_fprintf(qh, fp, 9199, "%8.4g %8.4g %8.4g %8.4g # ", p[0], p[1], p[2], p[3]);
     if (nearzero1+nearzero2)
       qh_fprintf(qh, fp, 9200, "p%d(coplanar facets)\n", qh_pointid(qh, vertex->point));
     else
       qh_fprintf(qh, fp, 9201, "projected p%d\n", qh_pointid(qh, vertex->point));
   }
   if (qh->hull_dim == 3)
     qh_fprintf(qh, fp, 9202, "%8.4g %8.4g %8.4g 1.0\n", color[0], color[1], color[2]);
   else if (qh->hull_dim == 4 && qh->DROPdim >= 0)
     qh_fprintf(qh, fp, 9203, "3 0 1 2 %8.4g %8.4g %8.4g 1.0\n", color[0], color[1], color[2]);
 } /* printhyperplaneintersection */
 
 /*---------------------------------
 
   qh_printline3geom(qh, fp, pointA, pointB, color )
     prints a line as a VECT
     prints 0's for qh.DROPdim
 
   notes:
     if pointA == pointB,
       it's a 1 point VECT
 */
 void qh_printline3geom(qhT *qh, FILE *fp, pointT *pointA, pointT *pointB, realT color[3]) {
   int k;
   realT pA[4], pB[4];
 
   qh_projectdim3(qh, pointA, pA);
   qh_projectdim3(qh, pointB, pB);
   if ((fabs(pA[0] - pB[0]) > 1e-3) ||
       (fabs(pA[1] - pB[1]) > 1e-3) ||
       (fabs(pA[2] - pB[2]) > 1e-3)) {
     qh_fprintf(qh, fp, 9204, "VECT 1 2 1 2 1\n");
     for (k=0; k < 3; k++)
        qh_fprintf(qh, fp, 9205, "%8.4g ", pB[k]);
     qh_fprintf(qh, fp, 9206, " # p%d\n", qh_pointid(qh, pointB));
   }else
     qh_fprintf(qh, fp, 9207, "VECT 1 1 1 1 1\n");
   for (k=0; k < 3; k++)
     qh_fprintf(qh, fp, 9208, "%8.4g ", pA[k]);
   qh_fprintf(qh, fp, 9209, " # p%d\n", qh_pointid(qh, pointA));
   qh_fprintf(qh, fp, 9210, "%8.4g %8.4g %8.4g 1\n", color[0], color[1], color[2]);
 }
 
 /*---------------------------------
 
   qh_printneighborhood(qh, fp, format, facetA, facetB, printall )
     print neighborhood of one or two facets
 
   notes:
     calls qh_findgood_all()
     bumps qh.visit_id
 */
 void qh_printneighborhood(qhT *qh, FILE *fp, qh_PRINT format, facetT *facetA, facetT *facetB, boolT printall) {
   facetT *neighbor, **neighborp, *facet;
   setT *facets;
 
   if (format == qh_PRINTnone)
     return;
   qh_findgood_all(qh, qh->facet_list);
   if (facetA == facetB)
     facetB= NULL;
   facets= qh_settemp(qh, 2*(qh_setsize(qh, facetA->neighbors)+1));
   qh->visit_id++;
   for (facet= facetA; facet; facet= ((facet == facetA) ? facetB : NULL)) {
     if (facet->visitid != qh->visit_id) {
       facet->visitid= qh->visit_id;
       qh_setappend(qh, &facets, facet);
     }
     FOREACHneighbor_(facet) {
       if (neighbor->visitid == qh->visit_id)
         continue;
       neighbor->visitid= qh->visit_id;
       if (printall || !qh_skipfacet(qh, neighbor))
         qh_setappend(qh, &facets, neighbor);
     }
   }
   qh_printfacets(qh, fp, format, NULL, facets, printall);
   qh_settempfree(qh, &facets);
 } /* printneighborhood */
 
 /*---------------------------------
 
   qh_printpoint(qh, fp, string, point )
   qh_printpointid(qh, fp, string, dim, point, id )
     prints the coordinates of a point
 
   returns:
     if string is defined
       prints 'string p%d' (skips p%d if id=-1)
 
   notes:
     nop if point is NULL
     prints id unless it is undefined (-1)
     Same as QhullPoint's printPoint
 */
 void qh_printpoint(qhT *qh, FILE *fp, const char *string, pointT *point) {
   int id= qh_pointid(qh, point);
 
   qh_printpointid(qh, fp, string, qh->hull_dim, point, id);
 } /* printpoint */
 
 void qh_printpointid(qhT *qh, FILE *fp, const char *string, int dim, pointT *point, int id) {
   int k;
   realT r; /*bug fix*/
 
   if (!point)
     return;
   if (string) {
     qh_fprintf(qh, fp, 9211, "%s", string);
    if (id != -1)
       qh_fprintf(qh, fp, 9212, " p%d: ", id);
   }
   for (k=dim; k--; ) {
     r= *point++;
     if (string)
       qh_fprintf(qh, fp, 9213, " %8.4g", r);
     else
       qh_fprintf(qh, fp, 9214, qh_REAL_1, r);
   }
   qh_fprintf(qh, fp, 9215, "\n");
 } /* printpointid */
 
 /*---------------------------------
 
   qh_printpoint3(qh, fp, point )
     prints 2-d, 3-d, or 4-d point as Geomview 3-d coordinates
 */
 void qh_printpoint3(qhT *qh, FILE *fp, pointT *point) {
   int k;
   realT p[4];
 
   qh_projectdim3(qh, point, p);
   for (k=0; k < 3; k++)
     qh_fprintf(qh, fp, 9216, "%8.4g ", p[k]);
   qh_fprintf(qh, fp, 9217, " # p%d\n", qh_pointid(qh, point));
 } /* printpoint3 */
 
 /*----------------------------------------
 -printpoints- print pointids for a set of points starting at index
-   see geom.c
+   see geom_r.c
 */
 
 /*---------------------------------
 
   qh_printpoints_out(qh, fp, facetlist, facets, printall )
     prints vertices, coplanar/inside points, for facets by their point coordinates
     allows qh.CDDoutput
 
   notes:
     same format as qhull input
     if no coplanar/interior points,
       same order as qh_printextremes
 */
 void qh_printpoints_out(qhT *qh, FILE *fp, facetT *facetlist, setT *facets, boolT printall) {
   int allpoints= qh->num_points + qh_setsize(qh, qh->other_points);
   int numpoints=0, point_i, point_n;
   setT *vertices, *points;
   facetT *facet, **facetp;
   pointT *point, **pointp;
   vertexT *vertex, **vertexp;
   int id;
 
   points= qh_settemp(qh, allpoints);
   qh_setzero(qh, points, 0, allpoints);
   vertices= qh_facetvertices(qh, facetlist, facets, printall);
   FOREACHvertex_(vertices) {
     id= qh_pointid(qh, vertex->point);
     if (id >= 0)
       SETelem_(points, id)= vertex->point;
   }
   if (qh->KEEPinside || qh->KEEPcoplanar || qh->KEEPnearinside) {
     FORALLfacet_(facetlist) {
       if (!printall && qh_skipfacet(qh, facet))
         continue;
       FOREACHpoint_(facet->coplanarset) {
         id= qh_pointid(qh, point);
         if (id >= 0)
           SETelem_(points, id)= point;
       }
     }
     FOREACHfacet_(facets) {
       if (!printall && qh_skipfacet(qh, facet))
         continue;
       FOREACHpoint_(facet->coplanarset) {
         id= qh_pointid(qh, point);
         if (id >= 0)
           SETelem_(points, id)= point;
       }
     }
   }
   qh_settempfree(qh, &vertices);
   FOREACHpoint_i_(qh, points) {
     if (point)
       numpoints++;
   }
   if (qh->CDDoutput)
     qh_fprintf(qh, fp, 9218, "%s | %s\nbegin\n%d %d real\n", qh->rbox_command,
              qh->qhull_command, numpoints, qh->hull_dim + 1);
   else
     qh_fprintf(qh, fp, 9219, "%d\n%d\n", qh->hull_dim, numpoints);
   FOREACHpoint_i_(qh, points) {
     if (point) {
       if (qh->CDDoutput)
         qh_fprintf(qh, fp, 9220, "1 ");
       qh_printpoint(qh, fp, NULL, point);
     }
   }
   if (qh->CDDoutput)
     qh_fprintf(qh, fp, 9221, "end\n");
   qh_settempfree(qh, &points);
 } /* printpoints_out */
 
 
 /*---------------------------------
 
   qh_printpointvect(qh, fp, point, normal, center, radius, color )
     prints a 2-d, 3-d, or 4-d point as 3-d VECT's relative to normal or to center point
 */
 void qh_printpointvect(qhT *qh, FILE *fp, pointT *point, coordT *normal, pointT *center, realT radius, realT color[3]) {
   realT diff[4], pointA[4];
   int k;
 
   for (k=qh->hull_dim; k--; ) {
     if (center)
       diff[k]= point[k]-center[k];
     else if (normal)
       diff[k]= normal[k];
     else
       diff[k]= 0;
   }
   if (center)
     qh_normalize2(qh, diff, qh->hull_dim, True, NULL, NULL);
   for (k=qh->hull_dim; k--; )
     pointA[k]= point[k]+diff[k] * radius;
   qh_printline3geom(qh, fp, point, pointA, color);
 } /* printpointvect */
 
 /*---------------------------------
 
   qh_printpointvect2(qh, fp, point, normal, center, radius )
     prints a 2-d, 3-d, or 4-d point as 2 3-d VECT's for an imprecise point
 */
 void qh_printpointvect2(qhT *qh, FILE *fp, pointT *point, coordT *normal, pointT *center, realT radius) {
   realT red[3]={1, 0, 0}, yellow[3]={1, 1, 0};
 
   qh_printpointvect(qh, fp, point, normal, center, radius, red);
   qh_printpointvect(qh, fp, point, normal, center, -radius, yellow);
 } /* printpointvect2 */
 
 /*---------------------------------
 
   qh_printridge(qh, fp, ridge )
     prints the information in a ridge
 
   notes:
     for qh_printfacetridges()
     same as operator<< [QhullRidge.cpp]
 */
 void qh_printridge(qhT *qh, FILE *fp, ridgeT *ridge) {
 
   qh_fprintf(qh, fp, 9222, "     - r%d", ridge->id);
   if (ridge->tested)
     qh_fprintf(qh, fp, 9223, " tested");
   if (ridge->nonconvex)
     qh_fprintf(qh, fp, 9224, " nonconvex");
   qh_fprintf(qh, fp, 9225, "\n");
   qh_printvertices(qh, fp, "           vertices:", ridge->vertices);
   if (ridge->top && ridge->bottom)
     qh_fprintf(qh, fp, 9226, "           between f%d and f%d\n",
             ridge->top->id, ridge->bottom->id);
 } /* printridge */
 
 /*---------------------------------
 
   qh_printspheres(qh, fp, vertices, radius )
     prints 3-d vertices as OFF spheres
 
   notes:
     inflated octahedron from Stuart Levy earth/mksphere2
 */
 void qh_printspheres(qhT *qh, FILE *fp, setT *vertices, realT radius) {
   vertexT *vertex, **vertexp;
 
   qh->printoutnum++;
   qh_fprintf(qh, fp, 9227, "{appearance {-edge -normal normscale 0} {\n\
 INST geom {define vsphere OFF\n\
 18 32 48\n\
 \n\
 0 0 1\n\
 1 0 0\n\
 0 1 0\n\
 -1 0 0\n\
 0 -1 0\n\
 0 0 -1\n\
 0.707107 0 0.707107\n\
 0 -0.707107 0.707107\n\
 0.707107 -0.707107 0\n\
 -0.707107 0 0.707107\n\
 -0.707107 -0.707107 0\n\
 0 0.707107 0.707107\n\
 -0.707107 0.707107 0\n\
 0.707107 0.707107 0\n\
 0.707107 0 -0.707107\n\
 0 0.707107 -0.707107\n\
 -0.707107 0 -0.707107\n\
 0 -0.707107 -0.707107\n\
 \n\
 3 0 6 11\n\
 3 0 7 6 \n\
 3 0 9 7 \n\
 3 0 11 9\n\
 3 1 6 8 \n\
 3 1 8 14\n\
 3 1 13 6\n\
 3 1 14 13\n\
 3 2 11 13\n\
 3 2 12 11\n\
 3 2 13 15\n\
 3 2 15 12\n\
 3 3 9 12\n\
 3 3 10 9\n\
 3 3 12 16\n\
 3 3 16 10\n\
 3 4 7 10\n\
 3 4 8 7\n\
 3 4 10 17\n\
 3 4 17 8\n\
 3 5 14 17\n\
 3 5 15 14\n\
 3 5 16 15\n\
 3 5 17 16\n\
 3 6 13 11\n\
 3 7 8 6\n\
 3 9 10 7\n\
 3 11 12 9\n\
 3 14 8 17\n\
 3 15 13 14\n\
 3 16 12 15\n\
 3 17 10 16\n} transforms { TLIST\n");
   FOREACHvertex_(vertices) {
     qh_fprintf(qh, fp, 9228, "%8.4g 0 0 0 # v%d\n 0 %8.4g 0 0\n0 0 %8.4g 0\n",
       radius, vertex->id, radius, radius);
     qh_printpoint3(qh, fp, vertex->point);
     qh_fprintf(qh, fp, 9229, "1\n");
   }
   qh_fprintf(qh, fp, 9230, "}}}\n");
 } /* printspheres */
 
 
 /*----------------------------------------------
 -printsummary-
-                see libqhull.c
+                see libqhull_r.c
 */
 
 /*---------------------------------
 
   qh_printvdiagram(qh, fp, format, facetlist, facets, printall )
     print voronoi diagram
       # of pairs of input sites
       #indices site1 site2 vertex1 ...
 
     sites indexed by input point id
       point 0 is the first input point
     vertices indexed by 'o' and 'p' order
       vertex 0 is the 'vertex-at-infinity'
       vertex 1 is the first Voronoi vertex
 
   see:
     qh_printvoronoi()
     qh_eachvoronoi_all()
 
   notes:
     if all facets are upperdelaunay,
       prints upper hull (furthest-site Voronoi diagram)
 */
 void qh_printvdiagram(qhT *qh, FILE *fp, qh_PRINT format, facetT *facetlist, setT *facets, boolT printall) {
   setT *vertices;
   int totcount, numcenters;
   boolT isLower;
   qh_RIDGE innerouter= qh_RIDGEall;
   printvridgeT printvridge= NULL;
 
   if (format == qh_PRINTvertices) {
     innerouter= qh_RIDGEall;
     printvridge= qh_printvridge;
   }else if (format == qh_PRINTinner) {
     innerouter= qh_RIDGEinner;
     printvridge= qh_printvnorm;
   }else if (format == qh_PRINTouter) {
     innerouter= qh_RIDGEouter;
     printvridge= qh_printvnorm;
   }else {
     qh_fprintf(qh, qh->ferr, 6219, "Qhull internal error (qh_printvdiagram): unknown print format %d.\n", format);
     qh_errexit(qh, qh_ERRinput, NULL, NULL);
   }
   vertices= qh_markvoronoi(qh, facetlist, facets, printall, &isLower, &numcenters);
   totcount= qh_printvdiagram2(qh, NULL, NULL, vertices, innerouter, False);
   qh_fprintf(qh, fp, 9231, "%d\n", totcount);
   totcount= qh_printvdiagram2(qh, fp, printvridge, vertices, innerouter, True /* inorder*/);
   qh_settempfree(qh, &vertices);
 #if 0  /* for testing qh_eachvoronoi_all */
   qh_fprintf(qh, fp, 9232, "\n");
   totcount= qh_eachvoronoi_all(qh, fp, printvridge, qh->UPPERdelaunay, innerouter, True /* inorder*/);
   qh_fprintf(qh, fp, 9233, "%d\n", totcount);
 #endif
 } /* printvdiagram */
 
 /*---------------------------------
 
   qh_printvdiagram2(qh, fp, printvridge, vertices, innerouter, inorder )
     visit all pairs of input sites (vertices) for selected Voronoi vertices
     vertices may include NULLs
 
   innerouter:
     qh_RIDGEall   print inner ridges(bounded) and outer ridges(unbounded)
     qh_RIDGEinner print only inner ridges
     qh_RIDGEouter print only outer ridges
 
   inorder:
     print 3-d Voronoi vertices in order
 
   assumes:
     qh_markvoronoi marked facet->visitid for Voronoi vertices
     all facet->seen= False
     all facet->seen2= True
 
   returns:
     total number of Voronoi ridges
     if printvridge,
       calls printvridge( fp, vertex, vertexA, centers) for each ridge
       [see qh_eachvoronoi()]
 
   see:
     qh_eachvoronoi_all()
 */
 int qh_printvdiagram2(qhT *qh, FILE *fp, printvridgeT printvridge, setT *vertices, qh_RIDGE innerouter, boolT inorder) {
   int totcount= 0;
   int vertex_i, vertex_n;
   vertexT *vertex;
 
   FORALLvertices
     vertex->seen= False;
   FOREACHvertex_i_(qh, vertices) {
     if (vertex) {
       if (qh->GOODvertex > 0 && qh_pointid(qh, vertex->point)+1 != qh->GOODvertex)
         continue;
       totcount += qh_eachvoronoi(qh, fp, printvridge, vertex, !qh_ALL, innerouter, inorder);
     }
   }
   return totcount;
 } /* printvdiagram2 */
 
 /*---------------------------------
 
   qh_printvertex(qh, fp, vertex )
     prints the information in a vertex
     Duplicated as operator<< [QhullVertex.cpp]
 */
 void qh_printvertex(qhT *qh, FILE *fp, vertexT *vertex) {
   pointT *point;
   int k, count= 0;
   facetT *neighbor, **neighborp;
   realT r; /*bug fix*/
 
   if (!vertex) {
     qh_fprintf(qh, fp, 9234, "  NULLvertex\n");
     return;
   }
   qh_fprintf(qh, fp, 9235, "- p%d(v%d):", qh_pointid(qh, vertex->point), vertex->id);
   point= vertex->point;
   if (point) {
     for (k=qh->hull_dim; k--; ) {
       r= *point++;
       qh_fprintf(qh, fp, 9236, " %5.2g", r);
     }
   }
   if (vertex->deleted)
     qh_fprintf(qh, fp, 9237, " deleted");
   if (vertex->delridge)
     qh_fprintf(qh, fp, 9238, " ridgedeleted");
   qh_fprintf(qh, fp, 9239, "\n");
   if (vertex->neighbors) {
     qh_fprintf(qh, fp, 9240, "  neighbors:");
     FOREACHneighbor_(vertex) {
       if (++count % 100 == 0)
         qh_fprintf(qh, fp, 9241, "\n     ");
       qh_fprintf(qh, fp, 9242, " f%d", neighbor->id);
     }
     qh_fprintf(qh, fp, 9243, "\n");
   }
 } /* printvertex */
 
 
 /*---------------------------------
 
   qh_printvertexlist(qh, fp, string, facetlist, facets, printall )
     prints vertices used by a facetlist or facet set
     tests qh_skipfacet() if !printall
 */
 void qh_printvertexlist(qhT *qh, FILE *fp, const char* string, facetT *facetlist,
                          setT *facets, boolT printall) {
   vertexT *vertex, **vertexp;
   setT *vertices;
 
   vertices= qh_facetvertices(qh, facetlist, facets, printall);
   qh_fprintf(qh, fp, 9244, "%s", string);
   FOREACHvertex_(vertices)
     qh_printvertex(qh, fp, vertex);
   qh_settempfree(qh, &vertices);
 } /* printvertexlist */
 
 
 /*---------------------------------
 
   qh_printvertices(qh, fp, string, vertices )
     prints vertices in a set
     duplicated as printVertexSet [QhullVertex.cpp]
 */
 void qh_printvertices(qhT *qh, FILE *fp, const char* string, setT *vertices) {
   vertexT *vertex, **vertexp;
 
   qh_fprintf(qh, fp, 9245, "%s", string);
   FOREACHvertex_(vertices)
     qh_fprintf(qh, fp, 9246, " p%d(v%d)", qh_pointid(qh, vertex->point), vertex->id);
   qh_fprintf(qh, fp, 9247, "\n");
 } /* printvertices */
 
 /*---------------------------------
 
   qh_printvneighbors(qh, fp, facetlist, facets, printall )
     print vertex neighbors of vertices in facetlist and facets ('FN')
 
   notes:
     qh_countfacets clears facet->visitid for non-printed facets
 
   design:
     collect facet count and related statistics
     if necessary, build neighbor sets for each vertex
     collect vertices in facetlist and facets
     build a point array for point->vertex and point->coplanar facet
     for each point
       list vertex neighbors or coplanar facet
 */
 void qh_printvneighbors(qhT *qh, FILE *fp, facetT* facetlist, setT *facets, boolT printall) {
   int numfacets, numsimplicial, numridges, totneighbors, numneighbors, numcoplanars, numtricoplanars;
   setT *vertices, *vertex_points, *coplanar_points;
   int numpoints= qh->num_points + qh_setsize(qh, qh->other_points);
   vertexT *vertex, **vertexp;
   int vertex_i, vertex_n;
   facetT *facet, **facetp, *neighbor, **neighborp;
   pointT *point, **pointp;
 
   qh_countfacets(qh, facetlist, facets, printall, &numfacets, &numsimplicial,
       &totneighbors, &numridges, &numcoplanars, &numtricoplanars);  /* sets facet->visitid */
   qh_fprintf(qh, fp, 9248, "%d\n", numpoints);
   qh_vertexneighbors(qh);
   vertices= qh_facetvertices(qh, facetlist, facets, printall);
   vertex_points= qh_settemp(qh, numpoints);
   coplanar_points= qh_settemp(qh, numpoints);
   qh_setzero(qh, vertex_points, 0, numpoints);
   qh_setzero(qh, coplanar_points, 0, numpoints);
   FOREACHvertex_(vertices)
     qh_point_add(qh, vertex_points, vertex->point, vertex);
   FORALLfacet_(facetlist) {
     FOREACHpoint_(facet->coplanarset)
       qh_point_add(qh, coplanar_points, point, facet);
   }
   FOREACHfacet_(facets) {
     FOREACHpoint_(facet->coplanarset)
       qh_point_add(qh, coplanar_points, point, facet);
   }
   FOREACHvertex_i_(qh, vertex_points) {
     if (vertex) {
       numneighbors= qh_setsize(qh, vertex->neighbors);
       qh_fprintf(qh, fp, 9249, "%d", numneighbors);
       if (qh->hull_dim == 3)
         qh_order_vertexneighbors(qh, vertex);
       else if (qh->hull_dim >= 4)
         qsort(SETaddr_(vertex->neighbors, facetT), (size_t)numneighbors,
              sizeof(facetT *), qh_compare_facetvisit);
       FOREACHneighbor_(vertex)
         qh_fprintf(qh, fp, 9250, " %d",
                  neighbor->visitid ? neighbor->visitid - 1 : 0 - neighbor->id);
       qh_fprintf(qh, fp, 9251, "\n");
     }else if ((facet= SETelemt_(coplanar_points, vertex_i, facetT)))
       qh_fprintf(qh, fp, 9252, "1 %d\n",
                   facet->visitid ? facet->visitid - 1 : 0 - facet->id);
     else
       qh_fprintf(qh, fp, 9253, "0\n");
   }
   qh_settempfree(qh, &coplanar_points);
   qh_settempfree(qh, &vertex_points);
   qh_settempfree(qh, &vertices);
 } /* printvneighbors */
 
 /*---------------------------------
 
   qh_printvoronoi(qh, fp, format, facetlist, facets, printall )
     print voronoi diagram in 'o' or 'G' format
     for 'o' format
       prints voronoi centers for each facet and for infinity
       for each vertex, lists ids of printed facets or infinity
       assumes facetlist and facets are disjoint
     for 'G' format
       prints an OFF object
       adds a 0 coordinate to center
       prints infinity but does not list in vertices
 
   see:
     qh_printvdiagram()
 
   notes:
     if 'o',
       prints a line for each point except "at-infinity"
     if all facets are upperdelaunay,
       reverses lower and upper hull
 */
 void qh_printvoronoi(qhT *qh, FILE *fp, qh_PRINT format, facetT *facetlist, setT *facets, boolT printall) {
   int k, numcenters, numvertices= 0, numneighbors, numinf, vid=1, vertex_i, vertex_n;
   facetT *facet, **facetp, *neighbor, **neighborp;
   setT *vertices;
   vertexT *vertex;
   boolT isLower;
   unsigned int numfacets= (unsigned int) qh->num_facets;
 
   vertices= qh_markvoronoi(qh, facetlist, facets, printall, &isLower, &numcenters);
   FOREACHvertex_i_(qh, vertices) {
     if (vertex) {
       numvertices++;
       numneighbors = numinf = 0;
       FOREACHneighbor_(vertex) {
         if (neighbor->visitid == 0)
           numinf= 1;
         else if (neighbor->visitid < numfacets)
           numneighbors++;
       }
       if (numinf && !numneighbors) {
         SETelem_(vertices, vertex_i)= NULL;
         numvertices--;
       }
     }
   }
   if (format == qh_PRINTgeom)
     qh_fprintf(qh, fp, 9254, "{appearance {+edge -face} OFF %d %d 1 # Voronoi centers and cells\n",
                 numcenters, numvertices);
   else
     qh_fprintf(qh, fp, 9255, "%d\n%d %d 1\n", qh->hull_dim-1, numcenters, qh_setsize(qh, vertices));
   if (format == qh_PRINTgeom) {
     for (k=qh->hull_dim-1; k--; )
       qh_fprintf(qh, fp, 9256, qh_REAL_1, 0.0);
     qh_fprintf(qh, fp, 9257, " 0 # infinity not used\n");
   }else {
     for (k=qh->hull_dim-1; k--; )
       qh_fprintf(qh, fp, 9258, qh_REAL_1, qh_INFINITE);
     qh_fprintf(qh, fp, 9259, "\n");
   }
   FORALLfacet_(facetlist) {
     if (facet->visitid && facet->visitid < numfacets) {
       if (format == qh_PRINTgeom)
         qh_fprintf(qh, fp, 9260, "# %d f%d\n", vid++, facet->id);
       qh_printcenter(qh, fp, format, NULL, facet);
     }
   }
   FOREACHfacet_(facets) {
     if (facet->visitid && facet->visitid < numfacets) {
       if (format == qh_PRINTgeom)
         qh_fprintf(qh, fp, 9261, "# %d f%d\n", vid++, facet->id);
       qh_printcenter(qh, fp, format, NULL, facet);
     }
   }
   FOREACHvertex_i_(qh, vertices) {
     numneighbors= 0;
     numinf=0;
     if (vertex) {
       if (qh->hull_dim == 3)
         qh_order_vertexneighbors(qh, vertex);
       else if (qh->hull_dim >= 4)
         qsort(SETaddr_(vertex->neighbors, facetT),
              (size_t)qh_setsize(qh, vertex->neighbors),
              sizeof(facetT *), qh_compare_facetvisit);
       FOREACHneighbor_(vertex) {
         if (neighbor->visitid == 0)
           numinf= 1;
         else if (neighbor->visitid < numfacets)
           numneighbors++;
       }
     }
     if (format == qh_PRINTgeom) {
       if (vertex) {
         qh_fprintf(qh, fp, 9262, "%d", numneighbors);
         FOREACHneighbor_(vertex) {
           if (neighbor->visitid && neighbor->visitid < numfacets)
             qh_fprintf(qh, fp, 9263, " %d", neighbor->visitid);
         }
         qh_fprintf(qh, fp, 9264, " # p%d(v%d)\n", vertex_i, vertex->id);
       }else
         qh_fprintf(qh, fp, 9265, " # p%d is coplanar or isolated\n", vertex_i);
     }else {
       if (numinf)
         numneighbors++;
       qh_fprintf(qh, fp, 9266, "%d", numneighbors);
       if (vertex) {
         FOREACHneighbor_(vertex) {
           if (neighbor->visitid == 0) {
             if (numinf) {
               numinf= 0;
               qh_fprintf(qh, fp, 9267, " %d", neighbor->visitid);
             }
           }else if (neighbor->visitid < numfacets)
             qh_fprintf(qh, fp, 9268, " %d", neighbor->visitid);
         }
       }
       qh_fprintf(qh, fp, 9269, "\n");
     }
   }
   if (format == qh_PRINTgeom)
     qh_fprintf(qh, fp, 9270, "}\n");
   qh_settempfree(qh, &vertices);
 } /* printvoronoi */
 
 /*---------------------------------
 
   qh_printvnorm(qh, fp, vertex, vertexA, centers, unbounded )
     print one separating plane of the Voronoi diagram for a pair of input sites
     unbounded==True if centers includes vertex-at-infinity
 
   assumes:
     qh_ASvoronoi and qh_vertexneighbors() already set
 
   note:
     parameter unbounded is UNUSED by this callback
 
   see:
     qh_printvdiagram()
     qh_eachvoronoi()
 */
 void qh_printvnorm(qhT *qh, FILE *fp, vertexT *vertex, vertexT *vertexA, setT *centers, boolT unbounded) {
   pointT *normal;
   realT offset;
   int k;
   QHULL_UNUSED(unbounded);
 
   normal= qh_detvnorm(qh, vertex, vertexA, centers, &offset);
   qh_fprintf(qh, fp, 9271, "%d %d %d ",
       2+qh->hull_dim, qh_pointid(qh, vertex->point), qh_pointid(qh, vertexA->point));
   for (k=0; k< qh->hull_dim-1; k++)
     qh_fprintf(qh, fp, 9272, qh_REAL_1, normal[k]);
   qh_fprintf(qh, fp, 9273, qh_REAL_1, offset);
   qh_fprintf(qh, fp, 9274, "\n");
 } /* printvnorm */
 
 /*---------------------------------
 
   qh_printvridge(qh, fp, vertex, vertexA, centers, unbounded )
     print one ridge of the Voronoi diagram for a pair of input sites
     unbounded==True if centers includes vertex-at-infinity
 
   see:
     qh_printvdiagram()
 
   notes:
     the user may use a different function
     parameter unbounded is UNUSED
 */
 void qh_printvridge(qhT *qh, FILE *fp, vertexT *vertex, vertexT *vertexA, setT *centers, boolT unbounded) {
   facetT *facet, **facetp;
   QHULL_UNUSED(unbounded);
 
   qh_fprintf(qh, fp, 9275, "%d %d %d", qh_setsize(qh, centers)+2,
        qh_pointid(qh, vertex->point), qh_pointid(qh, vertexA->point));
   FOREACHfacet_(centers)
     qh_fprintf(qh, fp, 9276, " %d", facet->visitid);
   qh_fprintf(qh, fp, 9277, "\n");
 } /* printvridge */
 
 /*---------------------------------
 
   qh_projectdim3(qh, source, destination )
     project 2-d 3-d or 4-d point to a 3-d point
     uses qh.DROPdim and qh.hull_dim
     source and destination may be the same
 
   notes:
     allocate 4 elements to destination just in case
 */
 void qh_projectdim3(qhT *qh, pointT *source, pointT *destination) {
   int i,k;
 
   for (k=0, i=0; k < qh->hull_dim; k++) {
     if (qh->hull_dim == 4) {
       if (k != qh->DROPdim)
         destination[i++]= source[k];
     }else if (k == qh->DROPdim)
       destination[i++]= 0;
     else
       destination[i++]= source[k];
   }
   while (i < 3)
     destination[i++]= 0.0;
 } /* projectdim3 */
 
 /*---------------------------------
 
   qh_readfeasible(qh, dim, curline )
     read feasible point from current line and qh.fin
 
   returns:
     number of lines read from qh.fin
     sets qh.FEASIBLEpoint with malloc'd coordinates
 
   notes:
     checks for qh.HALFspace
     assumes dim > 1
 
   see:
     qh_setfeasible
 */
 int qh_readfeasible(qhT *qh, int dim, const char *curline) {
   boolT isfirst= True;
   int linecount= 0, tokcount= 0;
   const char *s;
   char *t, firstline[qh_MAXfirst+1];
   coordT *coords, value;
 
   if (!qh->HALFspace) {
     qh_fprintf(qh, qh->ferr, 6070, "qhull input error: feasible point(dim 1 coords) is only valid for halfspace intersection\n");
     qh_errexit(qh, qh_ERRinput, NULL, NULL);
   }
   if (qh->feasible_string)
     qh_fprintf(qh, qh->ferr, 7057, "qhull input warning: feasible point(dim 1 coords) overrides 'Hn,n,n' feasible point for halfspace intersection\n");
   if (!(qh->feasible_point= (coordT*)qh_malloc(dim* sizeof(coordT)))) {
     qh_fprintf(qh, qh->ferr, 6071, "qhull error: insufficient memory for feasible point\n");
     qh_errexit(qh, qh_ERRmem, NULL, NULL);
   }
   coords= qh->feasible_point;
   while ((s= (isfirst ?  curline : fgets(firstline, qh_MAXfirst, qh->fin)))) {
     if (isfirst)
       isfirst= False;
     else
       linecount++;
     while (*s) {
       while (isspace(*s))
         s++;
       value= qh_strtod(s, &t);
       if (s == t)
         break;
       s= t;
       *(coords++)= value;
       if (++tokcount == dim) {
         while (isspace(*s))
           s++;
         qh_strtod(s, &t);
         if (s != t) {
           qh_fprintf(qh, qh->ferr, 6072, "qhull input error: coordinates for feasible point do not finish out the line: %s\n",
                s);
           qh_errexit(qh, qh_ERRinput, NULL, NULL);
         }
         return linecount;
       }
     }
   }
   qh_fprintf(qh, qh->ferr, 6073, "qhull input error: only %d coordinates.  Could not read %d-d feasible point.\n",
            tokcount, dim);
   qh_errexit(qh, qh_ERRinput, NULL, NULL);
   return 0;
 } /* readfeasible */
 
 /*---------------------------------
 
   qh_readpoints(qh, numpoints, dimension, ismalloc )
     read points from qh.fin into qh.first_point, qh.num_points
     qh.fin is lines of coordinates, one per vertex, first line number of points
     if 'rbox D4',
       gives message
     if qh.ATinfinity,
       adds point-at-infinity for Delaunay triangulations
 
   returns:
     number of points, array of point coordinates, dimension, ismalloc True
     if qh.DELAUNAY & !qh.PROJECTinput, projects points to paraboloid
         and clears qh.PROJECTdelaunay
     if qh.HALFspace, reads optional feasible point, reads halfspaces,
         converts to dual.
 
   for feasible point in "cdd format" in 3-d:
     3 1
     coordinates
     comments
     begin
     n 4 real/integer
     ...
     end
 
   notes:
     dimension will change in qh_initqhull_globals if qh.PROJECTinput
     uses malloc() since qh_mem not initialized
     FIXUP QH11012: qh_readpoints needs rewriting, too long
 */
 coordT *qh_readpoints(qhT *qh, int *numpoints, int *dimension, boolT *ismalloc) {
   coordT *points, *coords, *infinity= NULL;
   realT paraboloid, maxboloid= -REALmax, value;
   realT *coordp= NULL, *offsetp= NULL, *normalp= NULL;
   char *s= 0, *t, firstline[qh_MAXfirst+1];
   int diminput=0, numinput=0, dimfeasible= 0, newnum, k, tempi;
   int firsttext=0, firstshort=0, firstlong=0, firstpoint=0;
   int tokcount= 0, linecount=0, maxcount, coordcount=0;
   boolT islong, isfirst= True, wasbegin= False;
   boolT isdelaunay= qh->DELAUNAY && !qh->PROJECTinput;
 
   if (qh->CDDinput) {
     while ((s= fgets(firstline, qh_MAXfirst, qh->fin))) {
       linecount++;
       if (qh->HALFspace && linecount == 1 && isdigit(*s)) {
         dimfeasible= qh_strtol(s, &s);
         while (isspace(*s))
           s++;
         if (qh_strtol(s, &s) == 1)
           linecount += qh_readfeasible(qh, dimfeasible, s);
         else
           dimfeasible= 0;
       }else if (!memcmp(firstline, "begin", (size_t)5) || !memcmp(firstline, "BEGIN", (size_t)5))
         break;
       else if (!*qh->rbox_command)
         strncat(qh->rbox_command, s, sizeof(qh->rbox_command)-1);
     }
     if (!s) {
       qh_fprintf(qh, qh->ferr, 6074, "qhull input error: missing \"begin\" for cdd-formated input\n");
       qh_errexit(qh, qh_ERRinput, NULL, NULL);
     }
   }
   while (!numinput && (s= fgets(firstline, qh_MAXfirst, qh->fin))) {
     linecount++;
     if (!memcmp(s, "begin", (size_t)5) || !memcmp(s, "BEGIN", (size_t)5))
       wasbegin= True;
     while (*s) {
       while (isspace(*s))
         s++;
       if (!*s)
         break;
       if (!isdigit(*s)) {
         if (!*qh->rbox_command) {
           strncat(qh->rbox_command, s, sizeof(qh->rbox_command)-1);
           firsttext= linecount;
         }
         break;
       }
       if (!diminput)
         diminput= qh_strtol(s, &s);
       else {
         numinput= qh_strtol(s, &s);
         if (numinput == 1 && diminput >= 2 && qh->HALFspace && !qh->CDDinput) {
           linecount += qh_readfeasible(qh, diminput, s); /* checks if ok */
           dimfeasible= diminput;
           diminput= numinput= 0;
         }else
           break;
       }
     }
   }
   if (!s) {
     qh_fprintf(qh, qh->ferr, 6075, "qhull input error: short input file.  Did not find dimension and number of points\n");
     qh_errexit(qh, qh_ERRinput, NULL, NULL);
   }
   if (diminput > numinput) {
     tempi= diminput;    /* exchange dim and n, e.g., for cdd input format */
     diminput= numinput;
     numinput= tempi;
   }
   if (diminput < 2) {
     qh_fprintf(qh, qh->ferr, 6220,"qhull input error: dimension %d(first number) should be at least 2\n",
             diminput);
     qh_errexit(qh, qh_ERRinput, NULL, NULL);
   }
   if (isdelaunay) {
     qh->PROJECTdelaunay= False;
     if (qh->CDDinput)
       *dimension= diminput;
     else
       *dimension= diminput+1;
     *numpoints= numinput;
     if (qh->ATinfinity)
       (*numpoints)++;
   }else if (qh->HALFspace) {
     *dimension= diminput - 1;
     *numpoints= numinput;
     if (diminput < 3) {
       qh_fprintf(qh, qh->ferr, 6221,"qhull input error: dimension %d(first number, includes offset) should be at least 3 for halfspaces\n",
             diminput);
       qh_errexit(qh, qh_ERRinput, NULL, NULL);
     }
     if (dimfeasible) {
       if (dimfeasible != *dimension) {
         qh_fprintf(qh, qh->ferr, 6222,"qhull input error: dimension %d of feasible point is not one less than dimension %d for halfspaces\n",
           dimfeasible, diminput);
         qh_errexit(qh, qh_ERRinput, NULL, NULL);
       }
     }else
       qh_setfeasible(qh, *dimension);
   }else {
     if (qh->CDDinput)
       *dimension= diminput-1;
     else
       *dimension= diminput;
     *numpoints= numinput;
   }
   qh->normal_size= *dimension * sizeof(coordT); /* for tracing with qh_printpoint */
   if (qh->HALFspace) {
     qh->half_space= coordp= (coordT*)qh_malloc(qh->normal_size + sizeof(coordT));
     if (qh->CDDinput) {
       offsetp= qh->half_space;
       normalp= offsetp + 1;
     }else {
       normalp= qh->half_space;
       offsetp= normalp + *dimension;
     }
   }
   qh->maxline= diminput * (qh_REALdigits + 5);
   maximize_(qh->maxline, 500);
   qh->line= (char*)qh_malloc((qh->maxline+1) * sizeof(char));
   *ismalloc= True;  /* use malloc since memory not setup */
   coords= points= qh->temp_malloc=
         (coordT*)qh_malloc((*numpoints)*(*dimension)*sizeof(coordT));
   if (!coords || !qh->line || (qh->HALFspace && !qh->half_space)) {
     qh_fprintf(qh, qh->ferr, 6076, "qhull error: insufficient memory to read %d points\n",
             numinput);
     qh_errexit(qh, qh_ERRmem, NULL, NULL);
   }
   if (isdelaunay && qh->ATinfinity) {
     infinity= points + numinput * (*dimension);
     for (k= (*dimension) - 1; k--; )
       infinity[k]= 0.0;
   }
   maxcount= numinput * diminput;
   paraboloid= 0.0;
   while ((s= (isfirst ?  s : fgets(qh->line, qh->maxline, qh->fin)))) {
     if (!isfirst) {
       linecount++;
       if (*s == 'e' || *s == 'E') {
         if (!memcmp(s, "end", (size_t)3) || !memcmp(s, "END", (size_t)3)) {
           if (qh->CDDinput )
             break;
           else if (wasbegin)
             qh_fprintf(qh, qh->ferr, 7058, "qhull input warning: the input appears to be in cdd format.  If so, use 'Fd'\n");
         }
       }
     }
     islong= False;
     while (*s) {
       while (isspace(*s))
         s++;
       value= qh_strtod(s, &t);
       if (s == t) {
         if (!*qh->rbox_command)
          strncat(qh->rbox_command, s, sizeof(qh->rbox_command)-1);
         if (*s && !firsttext)
           firsttext= linecount;
         if (!islong && !firstshort && coordcount)
           firstshort= linecount;
         break;
       }
       if (!firstpoint)
         firstpoint= linecount;
       s= t;
       if (++tokcount > maxcount)
         continue;
       if (qh->HALFspace) {
         if (qh->CDDinput)
           *(coordp++)= -value; /* both coefficients and offset */
         else
           *(coordp++)= value;
       }else {
         *(coords++)= value;
         if (qh->CDDinput && !coordcount) {
           if (value != 1.0) {
             qh_fprintf(qh, qh->ferr, 6077, "qhull input error: for cdd format, point at line %d does not start with '1'\n",
                    linecount);
             qh_errexit(qh, qh_ERRinput, NULL, NULL);
           }
           coords--;
         }else if (isdelaunay) {
           paraboloid += value * value;
           if (qh->ATinfinity) {
             if (qh->CDDinput)
               infinity[coordcount-1] += value;
             else
               infinity[coordcount] += value;
           }
         }
       }
       if (++coordcount == diminput) {
         coordcount= 0;
         if (isdelaunay) {
           *(coords++)= paraboloid;
           maximize_(maxboloid, paraboloid);
           paraboloid= 0.0;
         }else if (qh->HALFspace) {
           if (!qh_sethalfspace(qh, *dimension, coords, &coords, normalp, offsetp, qh->feasible_point)) {
             qh_fprintf(qh, qh->ferr, 8048, "The halfspace was on line %d\n", linecount);
             if (wasbegin)
               qh_fprintf(qh, qh->ferr, 8049, "The input appears to be in cdd format.  If so, you should use option 'Fd'\n");
             qh_errexit(qh, qh_ERRinput, NULL, NULL);
           }
           coordp= qh->half_space;
         }
         while (isspace(*s))
           s++;
         if (*s) {
           islong= True;
           if (!firstlong)
             firstlong= linecount;
         }
       }
     }
     if (!islong && !firstshort && coordcount)
       firstshort= linecount;
     if (!isfirst && s - qh->line >= qh->maxline) {
       qh_fprintf(qh, qh->ferr, 6078, "qhull input error: line %d contained more than %d characters\n",
               linecount, (int) (s - qh->line));   /* WARN64 */
       qh_errexit(qh, qh_ERRinput, NULL, NULL);
     }
     isfirst= False;
   }
   if (tokcount != maxcount) {
     newnum= fmin_(numinput, tokcount/diminput);
     qh_fprintf(qh, qh->ferr, 7073,"\
 qhull warning: instead of %d %d-dimensional points, input contains\n\
 %d points and %d extra coordinates.  Line %d is the first\npoint",
        numinput, diminput, tokcount/diminput, tokcount % diminput, firstpoint);
     if (firsttext)
       qh_fprintf(qh, qh->ferr, 8051, ", line %d is the first comment", firsttext);
     if (firstshort)
       qh_fprintf(qh, qh->ferr, 8052, ", line %d is the first short\nline", firstshort);
     if (firstlong)
       qh_fprintf(qh, qh->ferr, 8053, ", line %d is the first long line", firstlong);
     qh_fprintf(qh, qh->ferr, 8054, ".  Continue with %d points.\n", newnum);
     numinput= newnum;
     if (isdelaunay && qh->ATinfinity) {
       for (k= tokcount % diminput; k--; )
         infinity[k] -= *(--coords);
       *numpoints= newnum+1;
     }else {
       coords -= tokcount % diminput;
       *numpoints= newnum;
     }
   }
   if (isdelaunay && qh->ATinfinity) {
     for (k= (*dimension) -1; k--; )
       infinity[k] /= numinput;
     if (coords == infinity)
       coords += (*dimension) -1;
     else {
       for (k=0; k < (*dimension) -1; k++)
         *(coords++)= infinity[k];
     }
     *(coords++)= maxboloid * 1.1;
   }
   if (qh->rbox_command[0]) {
     qh->rbox_command[strlen(qh->rbox_command)-1]= '\0';
     if (!strcmp(qh->rbox_command, "./rbox D4"))
       qh_fprintf(qh, qh->ferr, 8055, "\n\
 This is the qhull test case.  If any errors or core dumps occur,\n\
 recompile qhull with 'make new'.  If errors still occur, there is\n\
 an incompatibility.  You should try a different compiler.  You can also\n\
 change the choices in user.h.  If you discover the source of the problem,\n\
 please send mail to qhull_bug@qhull.org.\n\
 \n\
 Type 'qhull' for a short list of options.\n");
   }
   qh_free(qh->line);
   qh->line= NULL;
   if (qh->half_space) {
     qh_free(qh->half_space);
     qh->half_space= NULL;
   }
   qh->temp_malloc= NULL;
   trace1((qh, qh->ferr, 1008,"qh_readpoints: read in %d %d-dimensional points\n",
           numinput, diminput));
   return(points);
 } /* readpoints */
 
 
 /*---------------------------------
 
   qh_setfeasible(qh, dim )
     set qh.FEASIBLEpoint from qh.feasible_string in "n,n,n" or "n n n" format
 
   notes:
     "n,n,n" already checked by qh_initflags()
     see qh_readfeasible()
 */
 void qh_setfeasible(qhT *qh, int dim) {
   int tokcount= 0;
   char *s;
   coordT *coords, value;
 
   if (!(s= qh->feasible_string)) {
     qh_fprintf(qh, qh->ferr, 6223, "\
 qhull input error: halfspace intersection needs a feasible point.\n\
 Either prepend the input with 1 point or use 'Hn,n,n'.  See manual.\n");
     qh_errexit(qh, qh_ERRinput, NULL, NULL);
   }
   if (!(qh->feasible_point= (pointT*)qh_malloc(dim * sizeof(coordT)))) {
     qh_fprintf(qh, qh->ferr, 6079, "qhull error: insufficient memory for 'Hn,n,n'\n");
     qh_errexit(qh, qh_ERRmem, NULL, NULL);
   }
   coords= qh->feasible_point;
   while (*s) {
     value= qh_strtod(s, &s);
     if (++tokcount > dim) {
       qh_fprintf(qh, qh->ferr, 7059, "qhull input warning: more coordinates for 'H%s' than dimension %d\n",
           qh->feasible_string, dim);
       break;
     }
     *(coords++)= value;
     if (*s)
       s++;
   }
   while (++tokcount <= dim)
     *(coords++)= 0.0;
 } /* setfeasible */
 
 /*---------------------------------
 
   qh_skipfacet(qh, facet )
     returns 'True' if this facet is not to be printed
 
   notes:
     based on the user provided slice thresholds and 'good' specifications
 */
 boolT qh_skipfacet(qhT *qh, facetT *facet) {
   facetT *neighbor, **neighborp;
 
   if (qh->PRINTneighbors) {
     if (facet->good)
       return !qh->PRINTgood;
     FOREACHneighbor_(facet) {
       if (neighbor->good)
         return False;
     }
     return True;
   }else if (qh->PRINTgood)
     return !facet->good;
   else if (!facet->normal)
     return True;
   return(!qh_inthresholds(qh, facet->normal, NULL));
 } /* skipfacet */
 
 /*---------------------------------
 
   qh_skipfilename(qh, string )
     returns pointer to character after filename
 
   notes:
     skips leading spaces
     ends with spacing or eol
     if starts with ' or " ends with the same, skipping \' or \"
     For qhull, qh_argv_to_command() only uses double quotes
 */
 char *qh_skipfilename(qhT *qh, char *filename) {
   char *s= filename;  /* non-const due to return */
   char c;
 
   while (*s && isspace(*s))
     s++;
   c= *s++;
   if (c == '\0') {
     qh_fprintf(qh, qh->ferr, 6204, "qhull input error: filename expected, none found.\n");
     qh_errexit(qh, qh_ERRinput, NULL, NULL);
   }
   if (c == '\'' || c == '"') {
     while (*s !=c || s[-1] == '\\') {
       if (!*s) {
         qh_fprintf(qh, qh->ferr, 6203, "qhull input error: missing quote after filename -- %s\n", filename);
         qh_errexit(qh, qh_ERRinput, NULL, NULL);
       }
       s++;
     }
     s++;
   }
   else while (*s && !isspace(*s))
       s++;
   return s;
 } /* skipfilename */
 
diff --git a/src/libqhullr/io_r.h b/src/libqhullr/io_r.h
index 1620282..1bba4a6 100644
--- a/src/libqhullr/io_r.h
+++ b/src/libqhullr/io_r.h
@@ -1,159 +1,159 @@
 /*
  ---------------------------------
 
-   io.h
+   io_r.h
    declarations of Input/Output functions
 
-   see README, libqhull.h and io.c
+   see README, libqhull_r.h and io_r.c
 
    Copyright (c) 1993-2014 The Geometry Center.
-   $Id: //main/2011/qhull/src/libqhullr/io_r.h#2 $$Change: 1645 $
-   $DateTime: 2014/01/15 12:51:30 $$Author: bbarber $
+   $Id: //main/2011/qhull/src/libqhullr/io_r.h#6 $$Change: 1797 $
+   $DateTime: 2014/12/15 17:23:41 $$Author: bbarber $
 */
 
 #ifndef qhDEFio
 #define qhDEFio 1
 
 #include "libqhull_r.h"
 
 /*============ constants and flags ==================*/
 
 /*----------------------------------
 
   qh_MAXfirst
     maximum length of first two lines of stdin
 */
 #define qh_MAXfirst  200
 
 /*----------------------------------
 
   qh_MINradius
     min radius for Gp and Gv, fraction of maxcoord
 */
 #define qh_MINradius 0.02
 
 /*----------------------------------
 
   qh_GEOMepsilon
     adjust outer planes for 'lines closer' and geomview roundoff.
     This prevents bleed through.
 */
 #define qh_GEOMepsilon 2e-3
 
 /*----------------------------------
 
   qh_WHITESPACE
     possible values of white space
 */
 #define qh_WHITESPACE " \n\t\v\r\f"
 
 
 /*----------------------------------
 
   qh_RIDGE
     to select which ridges to print in qh_eachvoronoi
 */
 typedef enum
 {
     qh_RIDGEall = 0, qh_RIDGEinner, qh_RIDGEouter
 }
 qh_RIDGE;
 
 /*----------------------------------
 
   printvridgeT
     prints results of qh_printvdiagram
 
   see:
-    qh_printvridge for an example
+    qh_printvridge for an example
 */
 typedef void (*printvridgeT)(qhT *qh, FILE *fp, vertexT *vertex, vertexT *vertexA, setT *centers, boolT unbounded);
 
 /*============== -prototypes in alphabetical order =========*/
 
 void    qh_dfacet(qhT *qh, unsigned id);
 void    qh_dvertex(qhT *qh, unsigned id);
 int     qh_compare_facetarea(const void *p1, const void *p2);
 int     qh_compare_facetmerge(const void *p1, const void *p2);
 int     qh_compare_facetvisit(const void *p1, const void *p2);
 /* int  qh_compare_vertexpoint(const void *p1, const void *p2); Not useable since it depends on qh */
 void    qh_copyfilename(qhT *qh, char *filename, int size, const char* source, int length);
 void    qh_countfacets(qhT *qh, facetT *facetlist, setT *facets, boolT printall,
               int *numfacetsp, int *numsimplicialp, int *totneighborsp,
               int *numridgesp, int *numcoplanarsp, int *numnumtricoplanarsp);
 pointT *qh_detvnorm(qhT *qh, vertexT *vertex, vertexT *vertexA, setT *centers, realT *offsetp);
 setT   *qh_detvridge(qhT *qh, vertexT *vertex);
 setT   *qh_detvridge3(qhT *qh, vertexT *atvertex, vertexT *vertex);
 int     qh_eachvoronoi(qhT *qh, FILE *fp, printvridgeT printvridge, vertexT *atvertex, boolT visitall, qh_RIDGE innerouter, boolT inorder);
 int     qh_eachvoronoi_all(qhT *qh, FILE *fp, printvridgeT printvridge, boolT isUpper, qh_RIDGE innerouter, boolT inorder);
 void    qh_facet2point(qhT *qh, facetT *facet, pointT **point0, pointT **point1, realT *mindist);
 setT   *qh_facetvertices(qhT *qh, facetT *facetlist, setT *facets, boolT allfacets);
 void    qh_geomplanes(qhT *qh, facetT *facet, realT *outerplane, realT *innerplane);
 void    qh_markkeep(qhT *qh, facetT *facetlist);
 setT   *qh_markvoronoi(qhT *qh, facetT *facetlist, setT *facets, boolT printall, boolT *isLowerp, int *numcentersp);
 void    qh_order_vertexneighbors(qhT *qh, vertexT *vertex);
 void    qh_prepare_output(qhT *qh);
 void    qh_printafacet(qhT *qh, FILE *fp, qh_PRINT format, facetT *facet, boolT printall);
 void    qh_printbegin(qhT *qh, FILE *fp, qh_PRINT format, facetT *facetlist, setT *facets, boolT printall);
 void    qh_printcenter(qhT *qh, FILE *fp, qh_PRINT format, const char *string, facetT *facet);
 void    qh_printcentrum(qhT *qh, FILE *fp, facetT *facet, realT radius);
 void    qh_printend(qhT *qh, FILE *fp, qh_PRINT format, facetT *facetlist, setT *facets, boolT printall);
 void    qh_printend4geom(qhT *qh, FILE *fp, facetT *facet, int *num, boolT printall);
 void    qh_printextremes(qhT *qh, FILE *fp, facetT *facetlist, setT *facets, boolT printall);
 void    qh_printextremes_2d(qhT *qh, FILE *fp, facetT *facetlist, setT *facets, boolT printall);
 void    qh_printextremes_d(qhT *qh, FILE *fp, facetT *facetlist, setT *facets, boolT printall);
 void    qh_printfacet(qhT *qh, FILE *fp, facetT *facet);
 void    qh_printfacet2math(qhT *qh, FILE *fp, facetT *facet, qh_PRINT format, int notfirst);
 void    qh_printfacet2geom(qhT *qh, FILE *fp, facetT *facet, realT color[3]);
 void    qh_printfacet2geom_points(qhT *qh, FILE *fp, pointT *point1, pointT *point2,
                                facetT *facet, realT offset, realT color[3]);
 void    qh_printfacet3math(qhT *qh, FILE *fp, facetT *facet, qh_PRINT format, int notfirst);
 void    qh_printfacet3geom_nonsimplicial(qhT *qh, FILE *fp, facetT *facet, realT color[3]);
 void    qh_printfacet3geom_points(qhT *qh, FILE *fp, setT *points, facetT *facet, realT offset, realT color[3]);
 void    qh_printfacet3geom_simplicial(qhT *qh, FILE *fp, facetT *facet, realT color[3]);
 void    qh_printfacet3vertex(qhT *qh, FILE *fp, facetT *facet, qh_PRINT format);
 void    qh_printfacet4geom_nonsimplicial(qhT *qh, FILE *fp, facetT *facet, realT color[3]);
 void    qh_printfacet4geom_simplicial(qhT *qh, FILE *fp, facetT *facet, realT color[3]);
 void    qh_printfacetNvertex_nonsimplicial(qhT *qh, FILE *fp, facetT *facet, int id, qh_PRINT format);
 void    qh_printfacetNvertex_simplicial(qhT *qh, FILE *fp, facetT *facet, qh_PRINT format);
 void    qh_printfacetheader(qhT *qh, FILE *fp, facetT *facet);
 void    qh_printfacetridges(qhT *qh, FILE *fp, facetT *facet);
 void    qh_printfacets(qhT *qh, FILE *fp, qh_PRINT format, facetT *facetlist, setT *facets, boolT printall);
 void    qh_printhyperplaneintersection(qhT *qh, FILE *fp, facetT *facet1, facetT *facet2,
                    setT *vertices, realT color[3]);
 void    qh_printneighborhood(qhT *qh, FILE *fp, qh_PRINT format, facetT *facetA, facetT *facetB, boolT printall);
 void    qh_printline3geom(qhT *qh, FILE *fp, pointT *pointA, pointT *pointB, realT color[3]);
 void    qh_printpoint(qhT *qh, FILE *fp, const char *string, pointT *point);
 void    qh_printpointid(qhT *qh, FILE *fp, const char *string, int dim, pointT *point, int id);
 void    qh_printpoint3(qhT *qh, FILE *fp, pointT *point);
 void    qh_printpoints_out(qhT *qh, FILE *fp, facetT *facetlist, setT *facets, boolT printall);
 void    qh_printpointvect(qhT *qh, FILE *fp, pointT *point, coordT *normal, pointT *center, realT radius, realT color[3]);
 void    qh_printpointvect2(qhT *qh, FILE *fp, pointT *point, coordT *normal, pointT *center, realT radius);
 void    qh_printridge(qhT *qh, FILE *fp, ridgeT *ridge);
 void    qh_printspheres(qhT *qh, FILE *fp, setT *vertices, realT radius);
 void    qh_printvdiagram(qhT *qh, FILE *fp, qh_PRINT format, facetT *facetlist, setT *facets, boolT printall);
 int     qh_printvdiagram2(qhT *qh, FILE *fp, printvridgeT printvridge, setT *vertices, qh_RIDGE innerouter, boolT inorder);
 void    qh_printvertex(qhT *qh, FILE *fp, vertexT *vertex);
 void    qh_printvertexlist(qhT *qh, FILE *fp, const char* string, facetT *facetlist,
                          setT *facets, boolT printall);
 void    qh_printvertices(qhT *qh, FILE *fp, const char* string, setT *vertices);
 void    qh_printvneighbors(qhT *qh, FILE *fp, facetT* facetlist, setT *facets, boolT printall);
 void    qh_printvoronoi(qhT *qh, FILE *fp, qh_PRINT format, facetT *facetlist, setT *facets, boolT printall);
 void    qh_printvnorm(qhT *qh, FILE *fp, vertexT *vertex, vertexT *vertexA, setT *centers, boolT unbounded);
 void    qh_printvridge(qhT *qh, FILE *fp, vertexT *vertex, vertexT *vertexA, setT *centers, boolT unbounded);
 void    qh_produce_output(qhT *qh);
 void    qh_produce_output2(qhT *qh);
 void    qh_projectdim3(qhT *qh, pointT *source, pointT *destination);
 int     qh_readfeasible(qhT *qh, int dim, const char *curline);
 coordT *qh_readpoints(qhT *qh, int *numpoints, int *dimension, boolT *ismalloc);
 void    qh_setfeasible(qhT *qh, int dim);
 boolT   qh_skipfacet(qhT *qh, facetT *facet);
 char   *qh_skipfilename(qhT *qh, char *filename);
 
 #endif /* qhDEFio */
diff --git a/src/libqhullr/libqhull_r.c b/src/libqhullr/libqhull_r.c
index 042dd4f..51c70b8 100644
--- a/src/libqhullr/libqhull_r.c
+++ b/src/libqhullr/libqhull_r.c
@@ -1,1401 +1,1403 @@
 /*
  ---------------------------------
 
-   libqhull.c
+   libqhull_r.c
    Quickhull algorithm for convex hulls
 
    qhull() and top-level routines
 
-   see qh-qhull.htm, libqhull.h, unix.c
+   see qh-qhull.htm, libqhull.h, unix_r.c
 
-   see qhull_r.h for internal functions
+   see qhull_ra.h for internal functions
 
    Copyright (c) 1993-2014 The Geometry Center.
-   $Id: //main/2011/qhull/src/libqhullr/libqhull_r.c#4 $$Change: 1663 $
-   $DateTime: 2014/01/19 17:59:16 $$Author: bbarber $
+   $Id: //main/2011/qhull/src/libqhullr/libqhull_r.c#8 $$Change: 1797 $
+   $DateTime: 2014/12/15 17:23:41 $$Author: bbarber $
 */
 
-#include "qhull_r.h"
+#include "qhull_ra.h"
 
 /*============= functions in alphabetic order after qhull() =======*/
 
 /*---------------------------------
 
   qh_qhull(qh)
     compute DIM3 convex hull of qh.num_points starting at qh.first_point
     qh->contains all global options and variables
 
   returns:
     returns polyhedron
       qh.facet_list, qh.num_facets, qh.vertex_list, qh.num_vertices,
 
     returns global variables
       qh.hulltime, qh.max_outside, qh.interior_point, qh.max_vertex, qh.min_vertex
 
     returns precision constants
       qh.ANGLEround, centrum_radius, cos_max, DISTround, MAXabs_coord, ONEmerge
 
   notes:
     unless needed for output
       qh.max_vertex and qh.min_vertex are max/min due to merges
 
   see:
     to add individual points to either qh.num_points
       use qh_addpoint()
 
     if qh.GETarea
       qh_produceoutput() returns qh.totarea and qh.totvol via qh_getarea()
 
   design:
     record starting time
     initialize hull and partition points
     build convex hull
     unless early termination
       update facet->maxoutside for vertices, coplanar, and near-inside points
     error if temporary sets exist
     record end time
 */
 
 void qh_qhull(qhT *qh) {
   int numoutside;
 
   qh->hulltime= qh_CPUclock;
   if (qh->RERUN || qh->JOGGLEmax < REALmax/2)
     qh_build_withrestart(qh);
   else {
     qh_initbuild(qh);
     qh_buildhull(qh);
   }
   if (!qh->STOPpoint && !qh->STOPcone) {
     if (qh->ZEROall_ok && !qh->TESTvneighbors && qh->MERGEexact)
       qh_checkzero(qh, qh_ALL);
     if (qh->ZEROall_ok && !qh->TESTvneighbors && !qh->WAScoplanar) {
       trace2((qh, qh->ferr, 2055, "qh_qhull: all facets are clearly convex and no coplanar points.  Post-merging and check of maxout not needed.\n"));
       qh->DOcheckmax= False;
     }else {
       if (qh->MERGEexact || (qh->hull_dim > qh_DIMreduceBuild && qh->PREmerge))
         qh_postmerge(qh, "First post-merge", qh->premerge_centrum, qh->premerge_cos,
              (qh->POSTmerge ? False : qh->TESTvneighbors));
       else if (!qh->POSTmerge && qh->TESTvneighbors)
         qh_postmerge(qh, "For testing vertex neighbors", qh->premerge_centrum,
              qh->premerge_cos, True);
       if (qh->POSTmerge)
         qh_postmerge(qh, "For post-merging", qh->postmerge_centrum,
              qh->postmerge_cos, qh->TESTvneighbors);
       if (qh->visible_list == qh->facet_list) { /* i.e., merging done */
         qh->findbestnew= True;
         qh_partitionvisible(qh /*qh.visible_list*/, !qh_ALL, &numoutside);
         qh->findbestnew= False;
         qh_deletevisible(qh /*qh.visible_list*/);
         qh_resetlists(qh, False, qh_RESETvisible /*qh.visible_list newvertex_list newfacet_list */);
       }
     }
     if (qh->DOcheckmax){
       if (qh->REPORTfreq) {
         qh_buildtracing(qh, NULL, NULL);
         qh_fprintf(qh, qh->ferr, 8115, "\nTesting all coplanar points.\n");
       }
       qh_check_maxout(qh);
     }
     if (qh->KEEPnearinside && !qh->maxoutdone)
       qh_nearcoplanar(qh);
   }
   if (qh_setsize(qh, qh->qhmem.tempstack) != 0) {
     qh_fprintf(qh, qh->ferr, 6164, "qhull internal error (qh_qhull): temporary sets not empty(%d)\n",
              qh_setsize(qh, qh->qhmem.tempstack));
     qh_errexit(qh, qh_ERRqhull, NULL, NULL);
   }
   qh->hulltime= qh_CPUclock - qh->hulltime;
   qh->QHULLfinished= True;
   trace1((qh, qh->ferr, 1036, "Qhull: algorithm completed\n"));
 } /* qhull */
 
 /*---------------------------------
 
   qh_addpoint(qh, furthest, facet, checkdist )
     add point (usually furthest point) above facet to hull
     if checkdist,
       check that point is above facet.
       if point is not outside of the hull, uses qh_partitioncoplanar()
       assumes that facet is defined by qh_findbestfacet()
     else if facet specified,
       assumes that point is above facet (major damage if below)
     for Delaunay triangulations,
       Use qh_setdelaunay() to lift point to paraboloid and scale by 'Qbb' if needed
       Do not use options 'Qbk', 'QBk', or 'QbB' since they scale the coordinates.
 
   returns:
     returns False if user requested an early termination
      qh.visible_list, newfacet_list, delvertex_list, NEWfacets may be defined
     updates qh.facet_list, qh.num_facets, qh.vertex_list, qh.num_vertices
     clear qh.maxoutdone (will need to call qh_check_maxout() for facet->maxoutside)
     if unknown point, adds a pointer to qh.other_points
       do not deallocate the point's coordinates
 
   notes:
     assumes point is near its best facet and not at a local minimum of a lens
       distributions.  Use qh_findbestfacet to avoid this case.
     uses qh.visible_list, qh.newfacet_list, qh.delvertex_list, qh.NEWfacets
 
   see also:
     qh_triangulate() -- triangulate non-simplicial facets
 
   design:
     add point to other_points if needed
     if checkdist
       if point not above facet
         partition coplanar point
         exit
     exit if pre STOPpoint requested
     find horizon and visible facets for point
     make new facets for point to horizon
     make hyperplanes for point
     compute balance statistics
     match neighboring new facets
     update vertex neighbors and delete interior vertices
     exit if STOPcone requested
     merge non-convex new facets
     if merge found, many merges, or 'Qf'
        use qh_findbestnew() instead of qh_findbest()
     partition outside points from visible facets
     delete visible facets
     check polyhedron if requested
     exit if post STOPpoint requested
     reset working lists of facets and vertices
 */
 boolT qh_addpoint(qhT *qh, pointT *furthest, facetT *facet, boolT checkdist) {
   int goodvisible, goodhorizon;
   vertexT *vertex;
   facetT *newfacet;
   realT dist, newbalance, pbalance;
   boolT isoutside= False;
   int numpart, numpoints, numnew, firstnew;
 
   qh->maxoutdone= False;
   if (qh_pointid(qh, furthest) == -1)
     qh_setappend(qh, &qh->other_points, furthest);
   if (!facet) {
     qh_fprintf(qh, qh->ferr, 6213, "qhull internal error (qh_addpoint): NULL facet.  Need to call qh_findbestfacet first\n");
     qh_errexit(qh, qh_ERRqhull, NULL, NULL);
   }
   if (checkdist) {
     facet= qh_findbest(qh, furthest, facet, !qh_ALL, !qh_ISnewfacets, !qh_NOupper,
                         &dist, &isoutside, &numpart);
     zzadd_(Zpartition, numpart);
     if (!isoutside) {
       zinc_(Znotmax);  /* last point of outsideset is no longer furthest. */
       facet->notfurthest= True;
       qh_partitioncoplanar(qh, furthest, facet, &dist);
       return True;
     }
   }
   qh_buildtracing(qh, furthest, facet);
   if (qh->STOPpoint < 0 && qh->furthest_id == -qh->STOPpoint-1) {
     facet->notfurthest= True;
     return False;
   }
   qh_findhorizon(qh, furthest, facet, &goodvisible, &goodhorizon);
   if (qh->ONLYgood && !(goodvisible+goodhorizon) && !qh->GOODclosest) {
     zinc_(Znotgood);
     facet->notfurthest= True;
     /* last point of outsideset is no longer furthest.  This is ok
        since all points of the outside are likely to be bad */
     qh_resetlists(qh, False, qh_RESETvisible /*qh.visible_list newvertex_list newfacet_list */);
     return True;
   }
   zzinc_(Zprocessed);
   firstnew= qh->facet_id;
   vertex= qh_makenewfacets(qh, furthest /*visible_list, attaches if !ONLYgood */);
   qh_makenewplanes(qh /* newfacet_list */);
   numnew= qh->facet_id - firstnew;
   newbalance= numnew - (realT) (qh->num_facets-qh->num_visible)
                          * qh->hull_dim/qh->num_vertices;
   wadd_(Wnewbalance, newbalance);
   wadd_(Wnewbalance2, newbalance * newbalance);
   if (qh->ONLYgood
   && !qh_findgood(qh, qh->newfacet_list, goodhorizon) && !qh->GOODclosest) {
     FORALLnew_facets
       qh_delfacet(qh, newfacet);
     qh_delvertex(qh, vertex);
     qh_resetlists(qh, True, qh_RESETvisible /*qh.visible_list newvertex_list newfacet_list */);
     zinc_(Znotgoodnew);
     facet->notfurthest= True;
     return True;
   }
   if (qh->ONLYgood)
     qh_attachnewfacets(qh /*visible_list*/);
   qh_matchnewfacets(qh);
   qh_updatevertices(qh);
   if (qh->STOPcone && qh->furthest_id == qh->STOPcone-1) {
     facet->notfurthest= True;
     return False;  /* visible_list etc. still defined */
   }
   qh->findbestnew= False;
   if (qh->PREmerge || qh->MERGEexact) {
     qh_premerge(qh, vertex, qh->premerge_centrum, qh->premerge_cos);
     if (qh_USEfindbestnew)
       qh->findbestnew= True;
     else {
       FORALLnew_facets {
         if (!newfacet->simplicial) {
           qh->findbestnew= True;  /* use qh_findbestnew instead of qh_findbest*/
           break;
         }
       }
     }
   }else if (qh->BESToutside)
     qh->findbestnew= True;
   qh_partitionvisible(qh /*qh.visible_list*/, !qh_ALL, &numpoints);
   qh->findbestnew= False;
   qh->findbest_notsharp= False;
   zinc_(Zpbalance);
   pbalance= numpoints - (realT) qh->hull_dim /* assumes all points extreme */
                 * (qh->num_points - qh->num_vertices)/qh->num_vertices;
   wadd_(Wpbalance, pbalance);
   wadd_(Wpbalance2, pbalance * pbalance);
   qh_deletevisible(qh /*qh.visible_list*/);
   zmax_(Zmaxvertex, qh->num_vertices);
   qh->NEWfacets= False;
   if (qh->IStracing >= 4) {
     if (qh->num_facets < 2000)
       qh_printlists(qh);
     qh_printfacetlist(qh, qh->newfacet_list, NULL, True);
     qh_checkpolygon(qh, qh->facet_list);
   }else if (qh->CHECKfrequently) {
     if (qh->num_facets < 50)
       qh_checkpolygon(qh, qh->facet_list);
     else
       qh_checkpolygon(qh, qh->newfacet_list);
   }
   if (qh->STOPpoint > 0 && qh->furthest_id == qh->STOPpoint-1)
     return False;
   qh_resetlists(qh, True, qh_RESETvisible /*qh.visible_list newvertex_list newfacet_list */);
   /* qh_triangulate(qh); to test qh.TRInormals */
   trace2((qh, qh->ferr, 2056, "qh_addpoint: added p%d new facets %d new balance %2.2g point balance %2.2g\n",
     qh_pointid(qh, furthest), numnew, newbalance, pbalance));
   return True;
 } /* addpoint */
 
 /*---------------------------------
 
   qh_build_withrestart(qh)
     allow restarts due to qh.JOGGLEmax while calling qh_buildhull()
+       qh_errexit always undoes qh_build_withrestart()
     qh.FIRSTpoint/qh.NUMpoints is point array
-        it may be moved by qh_joggleinput(qh)
+       it may be moved by qh_joggleinput(qh)
 */
 void qh_build_withrestart(qhT *qh) {
   int restart;
 
   qh->ALLOWrestart= True;
   while (True) {
     restart= setjmp(qh->restartexit); /* simple statement for CRAY J916 */
     if (restart) {       /* only from qh_precision() */
       zzinc_(Zretry);
       wmax_(Wretrymax, qh->JOGGLEmax);
       /* QH7078 warns about using 'TCn' with 'QJn' */
       qh->STOPcone= -1; /* if break from joggle, prevents normal output */
     }
     if (!qh->RERUN && qh->JOGGLEmax < REALmax/2) {
       if (qh->build_cnt > qh_JOGGLEmaxretry) {
         qh_fprintf(qh, qh->ferr, 6229, "qhull precision error: %d attempts to construct a convex hull\n\
         with joggled input.  Increase joggle above 'QJ%2.2g'\n\
         or modify qh_JOGGLE... parameters in user.h\n",
            qh->build_cnt, qh->JOGGLEmax);
         qh_errexit(qh, qh_ERRqhull, NULL, NULL);
       }
       if (qh->build_cnt && !restart)
         break;
     }else if (qh->build_cnt && qh->build_cnt >= qh->RERUN)
       break;
     qh->STOPcone= 0;
     qh_freebuild(qh, True);  /* first call is a nop */
     qh->build_cnt++;
     if (!qh->qhull_optionsiz)
       qh->qhull_optionsiz= (int)strlen(qh->qhull_options);   /* WARN64 */
     else {
       qh->qhull_options [qh->qhull_optionsiz]= '\0';
       qh->qhull_optionlen= qh_OPTIONline;  /* starts a new line */
     }
     qh_option(qh, "_run", &qh->build_cnt, NULL);
     if (qh->build_cnt == qh->RERUN) {
       qh->IStracing= qh->TRACElastrun;  /* duplicated from qh_initqhull_globals */
       if (qh->TRACEpoint != -1 || qh->TRACEdist < REALmax/2 || qh->TRACEmerge) {
         qh->TRACElevel= (qh->IStracing? qh->IStracing : 3);
         qh->IStracing= 0;
       }
       qh->qhmem.IStracing= qh->IStracing;
     }
     if (qh->JOGGLEmax < REALmax/2)
       qh_joggleinput(qh);
     qh_initbuild(qh);
     qh_buildhull(qh);
     if (qh->JOGGLEmax < REALmax/2 && !qh->MERGING)
       qh_checkconvex(qh, qh->facet_list, qh_ALGORITHMfault);
   }
   qh->ALLOWrestart= False;
 } /* qh_build_withrestart */
 
 /*---------------------------------
 
   qh_buildhull(qh)
     construct a convex hull by adding outside points one at a time
 
   returns:
 
   notes:
     may be called multiple times
     checks facet and vertex lists for incorrect flags
     to recover from STOPcone, call qh_deletevisible and qh_resetlists
 
   design:
     check visible facet and newfacet flags
     check newlist vertex flags and qh.STOPcone/STOPpoint
     for each facet with a furthest outside point
       add point to facet
       exit if qh.STOPcone or qh.STOPpoint requested
     if qh.NARROWhull for initial simplex
       partition remaining outside points to coplanar sets
 */
 void qh_buildhull(qhT *qh) {
   facetT *facet;
   pointT *furthest;
   vertexT *vertex;
   int id;
 
   trace1((qh, qh->ferr, 1037, "qh_buildhull: start build hull\n"));
   FORALLfacets {
     if (facet->visible || facet->newfacet) {
       qh_fprintf(qh, qh->ferr, 6165, "qhull internal error (qh_buildhull): visible or new facet f%d in facet list\n",
                    facet->id);
       qh_errexit(qh, qh_ERRqhull, facet, NULL);
     }
   }
   FORALLvertices {
     if (vertex->newlist) {
       qh_fprintf(qh, qh->ferr, 6166, "qhull internal error (qh_buildhull): new vertex f%d in vertex list\n",
                    vertex->id);
       qh_errprint(qh, "ERRONEOUS", NULL, NULL, NULL, vertex);
       qh_errexit(qh, qh_ERRqhull, NULL, NULL);
     }
     id= qh_pointid(qh, vertex->point);
     if ((qh->STOPpoint>0 && id == qh->STOPpoint-1) ||
         (qh->STOPpoint<0 && id == -qh->STOPpoint-1) ||
         (qh->STOPcone>0 && id == qh->STOPcone-1)) {
       trace1((qh, qh->ferr, 1038,"qh_buildhull: stop point or cone P%d in initial hull\n", id));
       return;
     }
   }
   qh->facet_next= qh->facet_list;      /* advance facet when processed */
   while ((furthest= qh_nextfurthest(qh, &facet))) {
     qh->num_outside--;  /* if ONLYmax, furthest may not be outside */
     if (!qh_addpoint(qh, furthest, facet, qh->ONLYmax))
       break;
   }
   if (qh->NARROWhull) /* move points from outsideset to coplanarset */
     qh_outcoplanar(qh /* facet_list */ );
   if (qh->num_outside && !furthest) {
     qh_fprintf(qh, qh->ferr, 6167, "qhull internal error (qh_buildhull): %d outside points were never processed.\n", qh->num_outside);
     qh_errexit(qh, qh_ERRqhull, NULL, NULL);
   }
   trace1((qh, qh->ferr, 1039, "qh_buildhull: completed the hull construction\n"));
 } /* buildhull */
 
 
 /*---------------------------------
 
   qh_buildtracing(qh, furthest, facet )
     trace an iteration of qh_buildhull() for furthest point and facet
     if !furthest, prints progress message
 
   returns:
     tracks progress with qh.lastreport
     updates qh.furthest_id (-3 if furthest is NULL)
     also resets visit_id, vertext_visit on wrap around
 
   see:
     qh_tracemerging()
 
   design:
     if !furthest
       print progress message
       exit
     if 'TFn' iteration
       print progress message
     else if tracing
       trace furthest point and facet
     reset qh.visit_id and qh.vertex_visit if overflow may occur
     set qh.furthest_id for tracing
 */
 void qh_buildtracing(qhT *qh, pointT *furthest, facetT *facet) {
   realT dist= 0;
   float cpu;
   int total, furthestid;
   time_t timedata;
   struct tm *tp;
   vertexT *vertex;
 
   qh->old_randomdist= qh->RANDOMdist;
   qh->RANDOMdist= False;
   if (!furthest) {
     time(&timedata);
     tp= localtime(&timedata);
     cpu= (float)qh_CPUclock - (float)qh->hulltime;
     cpu /= (float)qh_SECticks;
     total= zzval_(Ztotmerge) - zzval_(Zcyclehorizon) + zzval_(Zcyclefacettot);
     qh_fprintf(qh, qh->ferr, 8118, "\n\
 At %02d:%02d:%02d & %2.5g CPU secs, qhull has created %d facets and merged %d.\n\
  The current hull contains %d facets and %d vertices.  Last point was p%d\n",
       tp->tm_hour, tp->tm_min, tp->tm_sec, cpu, qh->facet_id -1,
       total, qh->num_facets, qh->num_vertices, qh->furthest_id);
     return;
   }
   furthestid= qh_pointid(qh, furthest);
   if (qh->TRACEpoint == furthestid) {
     qh->IStracing= qh->TRACElevel;
     qh->qhmem.IStracing= qh->TRACElevel;
   }else if (qh->TRACEpoint != -1 && qh->TRACEdist < REALmax/2) {
     qh->IStracing= 0;
     qh->qhmem.IStracing= 0;
   }
   if (qh->REPORTfreq && (qh->facet_id-1 > qh->lastreport+qh->REPORTfreq)) {
     qh->lastreport= qh->facet_id-1;
     time(&timedata);
     tp= localtime(&timedata);
     cpu= (float)qh_CPUclock - (float)qh->hulltime;
     cpu /= (float)qh_SECticks;
     total= zzval_(Ztotmerge) - zzval_(Zcyclehorizon) + zzval_(Zcyclefacettot);
     zinc_(Zdistio);
     qh_distplane(qh, furthest, facet, &dist);
     qh_fprintf(qh, qh->ferr, 8119, "\n\
 At %02d:%02d:%02d & %2.5g CPU secs, qhull has created %d facets and merged %d.\n\
  The current hull contains %d facets and %d vertices.  There are %d\n\
  outside points.  Next is point p%d(v%d), %2.2g above f%d.\n",
       tp->tm_hour, tp->tm_min, tp->tm_sec, cpu, qh->facet_id -1,
       total, qh->num_facets, qh->num_vertices, qh->num_outside+1,
       furthestid, qh->vertex_id, dist, getid_(facet));
   }else if (qh->IStracing >=1) {
     cpu= (float)qh_CPUclock - (float)qh->hulltime;
     cpu /= (float)qh_SECticks;
     qh_distplane(qh, furthest, facet, &dist);
     qh_fprintf(qh, qh->ferr, 8120, "qh_addpoint: add p%d(v%d) to hull of %d facets(%2.2g above f%d) and %d outside at %4.4g CPU secs.  Previous was p%d.\n",
       furthestid, qh->vertex_id, qh->num_facets, dist,
       getid_(facet), qh->num_outside+1, cpu, qh->furthest_id);
   }
   zmax_(Zvisit2max, (int)qh->visit_id/2);
   if (qh->visit_id > (unsigned) INT_MAX) {
     zinc_(Zvisit);
     qh->visit_id= 0;
     FORALLfacets
       facet->visitid= 0;
   }
   zmax_(Zvvisit2max, (int)qh->vertex_visit/2);
   if (qh->vertex_visit > (unsigned) INT_MAX/2) { /* 31 bits */
     zinc_(Zvvisit);
     qh->vertex_visit= 0;
     FORALLvertices
       vertex->visitid= 0;
   }
   qh->furthest_id= furthestid;
   qh->RANDOMdist= qh->old_randomdist;
 } /* buildtracing */
 
 /*---------------------------------
 
   qh_errexit2(qh, exitcode, facet, otherfacet )
     return exitcode to system after an error
     report two facets
 
   returns:
     assumes exitcode non-zero
 
   see:
     normally use qh_errexit() in user.c(reports a facet and a ridge)
 */
 void qh_errexit2(qhT *qh, int exitcode, facetT *facet, facetT *otherfacet) {
 
   qh_errprint(qh, "ERRONEOUS", facet, otherfacet, NULL, NULL);
   qh_errexit(qh, exitcode, NULL, NULL);
 } /* errexit2 */
 
 
 /*---------------------------------
 
   qh_findhorizon(qh, point, facet, goodvisible, goodhorizon )
     given a visible facet, find the point's horizon and visible facets
     for all facets, !facet-visible
 
   returns:
     returns qh.visible_list/num_visible with all visible facets
       marks visible facets with ->visible
     updates count of good visible and good horizon facets
     updates qh.max_outside, qh.max_vertex, facet->maxoutside
 
   see:
     similar to qh_delpoint()
 
   design:
     move facet to qh.visible_list at end of qh.facet_list
     for all visible facets
      for each unvisited neighbor of a visible facet
        compute distance of point to neighbor
        if point above neighbor
          move neighbor to end of qh.visible_list
        else if point is coplanar with neighbor
          update qh.max_outside, qh.max_vertex, neighbor->maxoutside
          mark neighbor coplanar (will create a samecycle later)
          update horizon statistics
 */
 void qh_findhorizon(qhT *qh, pointT *point, facetT *facet, int *goodvisible, int *goodhorizon) {
   facetT *neighbor, **neighborp, *visible;
   int numhorizon= 0, coplanar= 0;
   realT dist;
 
   trace1((qh, qh->ferr, 1040,"qh_findhorizon: find horizon for point p%d facet f%d\n",qh_pointid(qh, point),facet->id));
   *goodvisible= *goodhorizon= 0;
   zinc_(Ztotvisible);
   qh_removefacet(qh, facet);  /* visible_list at end of qh->facet_list */
   qh_appendfacet(qh, facet);
   qh->num_visible= 1;
   if (facet->good)
     (*goodvisible)++;
   qh->visible_list= facet;
   facet->visible= True;
   facet->f.replace= NULL;
   if (qh->IStracing >=4)
     qh_errprint(qh, "visible", facet, NULL, NULL, NULL);
   qh->visit_id++;
   FORALLvisible_facets {
     if (visible->tricoplanar && !qh->TRInormals) {
       qh_fprintf(qh, qh->ferr, 6230, "Qhull internal error (qh_findhorizon): does not work for tricoplanar facets.  Use option 'Q11'\n");
       qh_errexit(qh, qh_ERRqhull, visible, NULL);
     }
     visible->visitid= qh->visit_id;
     FOREACHneighbor_(visible) {
       if (neighbor->visitid == qh->visit_id)
         continue;
       neighbor->visitid= qh->visit_id;
       zzinc_(Znumvisibility);
       qh_distplane(qh, point, neighbor, &dist);
       if (dist > qh->MINvisible) {
         zinc_(Ztotvisible);
         qh_removefacet(qh, neighbor);  /* append to end of qh->visible_list */
         qh_appendfacet(qh, neighbor);
         neighbor->visible= True;
         neighbor->f.replace= NULL;
         qh->num_visible++;
         if (neighbor->good)
           (*goodvisible)++;
         if (qh->IStracing >=4)
           qh_errprint(qh, "visible", neighbor, NULL, NULL, NULL);
       }else {
         if (dist > - qh->MAXcoplanar) {
           neighbor->coplanar= True;
           zzinc_(Zcoplanarhorizon);
           qh_precision(qh, "coplanar horizon");
           coplanar++;
           if (qh->MERGING) {
             if (dist > 0) {
               maximize_(qh->max_outside, dist);
               maximize_(qh->max_vertex, dist);
 #if qh_MAXoutside
               maximize_(neighbor->maxoutside, dist);
 #endif
             }else
               minimize_(qh->min_vertex, dist);  /* due to merge later */
           }
           trace2((qh, qh->ferr, 2057, "qh_findhorizon: point p%d is coplanar to horizon f%d, dist=%2.7g < qh->MINvisible(%2.7g)\n",
               qh_pointid(qh, point), neighbor->id, dist, qh->MINvisible));
         }else
           neighbor->coplanar= False;
         zinc_(Ztothorizon);
         numhorizon++;
         if (neighbor->good)
           (*goodhorizon)++;
         if (qh->IStracing >=4)
           qh_errprint(qh, "horizon", neighbor, NULL, NULL, NULL);
       }
     }
   }
   if (!numhorizon) {
     qh_precision(qh, "empty horizon");
     qh_fprintf(qh, qh->ferr, 6168, "qhull precision error (qh_findhorizon): empty horizon\n\
 QhullPoint p%d was above all facets.\n", qh_pointid(qh, point));
     qh_printfacetlist(qh, qh->facet_list, NULL, True);
     qh_errexit(qh, qh_ERRprec, NULL, NULL);
   }
   trace1((qh, qh->ferr, 1041, "qh_findhorizon: %d horizon facets(good %d), %d visible(good %d), %d coplanar\n",
        numhorizon, *goodhorizon, qh->num_visible, *goodvisible, coplanar));
   if (qh->IStracing >= 4 && qh->num_facets < 50)
     qh_printlists(qh);
 } /* findhorizon */
 
 /*---------------------------------
 
   qh_nextfurthest(qh, visible )
     returns next furthest point and visible facet for qh_addpoint()
     starts search at qh.facet_next
 
   returns:
     removes furthest point from outside set
     NULL if none available
     advances qh.facet_next over facets with empty outside sets
 
   design:
     for each facet from qh.facet_next
       if empty outside set
         advance qh.facet_next
       else if qh.NARROWhull
         determine furthest outside point
         if furthest point is not outside
           advance qh.facet_next(point will be coplanar)
     remove furthest point from outside set
 */
 pointT *qh_nextfurthest(qhT *qh, facetT **visible) {
   facetT *facet;
   int size, idx;
   realT randr, dist;
   pointT *furthest;
 
   while ((facet= qh->facet_next) != qh->facet_tail) {
     if (!facet->outsideset) {
       qh->facet_next= facet->next;
       continue;
     }
     SETreturnsize_(facet->outsideset, size);
     if (!size) {
       qh_setfree(qh, &facet->outsideset);
       qh->facet_next= facet->next;
       continue;
     }
     if (qh->NARROWhull) {
       if (facet->notfurthest)
         qh_furthestout(qh, facet);
       furthest= (pointT*)qh_setlast(facet->outsideset);
 #if qh_COMPUTEfurthest
       qh_distplane(qh, furthest, facet, &dist);
       zinc_(Zcomputefurthest);
 #else
       dist= facet->furthestdist;
 #endif
       if (dist < qh->MINoutside) { /* remainder of outside set is coplanar for qh_outcoplanar */
         qh->facet_next= facet->next;
         continue;
       }
     }
     if (!qh->RANDOMoutside && !qh->VIRTUALmemory) {
       if (qh->PICKfurthest) {
         qh_furthestnext(qh /* qh->facet_list */);
         facet= qh->facet_next;
       }
       *visible= facet;
       return((pointT*)qh_setdellast(facet->outsideset));
     }
     if (qh->RANDOMoutside) {
       int outcoplanar = 0;
       if (qh->NARROWhull) {
         FORALLfacets {
           if (facet == qh->facet_next)
             break;
           if (facet->outsideset)
             outcoplanar += qh_setsize(qh, facet->outsideset);
         }
       }
       randr= qh_RANDOMint;
       randr= randr/(qh_RANDOMmax+1);
       idx= (int)floor((qh->num_outside - outcoplanar) * randr);
       FORALLfacet_(qh->facet_next) {
         if (facet->outsideset) {
           SETreturnsize_(facet->outsideset, size);
           if (!size)
             qh_setfree(qh, &facet->outsideset);
           else if (size > idx) {
             *visible= facet;
             return((pointT*)qh_setdelnth(qh, facet->outsideset, idx));
           }else
             idx -= size;
         }
       }
       qh_fprintf(qh, qh->ferr, 6169, "qhull internal error (qh_nextfurthest): num_outside %d is too low\nby at least %d, or a random real %g >= 1.0\n",
               qh->num_outside, idx+1, randr);
       qh_errexit(qh, qh_ERRqhull, NULL, NULL);
     }else { /* VIRTUALmemory */
       facet= qh->facet_tail->previous;
       if (!(furthest= (pointT*)qh_setdellast(facet->outsideset))) {
         if (facet->outsideset)
           qh_setfree(qh, &facet->outsideset);
         qh_removefacet(qh, facet);
         qh_prependfacet(qh, facet, &qh->facet_list);
         continue;
       }
       *visible= facet;
       return furthest;
     }
   }
   return NULL;
 } /* nextfurthest */
 
 /*---------------------------------
 
   qh_partitionall(qh, vertices, points, numpoints )
     partitions all points in points/numpoints to the outsidesets of facets
     vertices= vertices in qh.facet_list(!partitioned)
 
   returns:
     builds facet->outsideset
     does not partition qh.GOODpoint
     if qh.ONLYgood && !qh.MERGING,
       does not partition qh.GOODvertex
 
   notes:
     faster if qh.facet_list sorted by anticipated size of outside set
 
   design:
     initialize pointset with all points
     remove vertices from pointset
     remove qh.GOODpointp from pointset (unless it's qh.STOPcone or qh.STOPpoint)
     for all facets
       for all remaining points in pointset
         compute distance from point to facet
         if point is outside facet
           remove point from pointset (by not reappending)
           update bestpoint
           append point or old bestpoint to facet's outside set
       append bestpoint to facet's outside set (furthest)
     for all points remaining in pointset
       partition point into facets' outside sets and coplanar sets
 */
 void qh_partitionall(qhT *qh, setT *vertices, pointT *points, int numpoints){
   setT *pointset;
   vertexT *vertex, **vertexp;
   pointT *point, **pointp, *bestpoint;
   int size, point_i, point_n, point_end, remaining, i, id;
   facetT *facet;
   realT bestdist= -REALmax, dist, distoutside;
 
   trace1((qh, qh->ferr, 1042, "qh_partitionall: partition all points into outside sets\n"));
   pointset= qh_settemp(qh, numpoints);
   qh->num_outside= 0;
   pointp= SETaddr_(pointset, pointT);
   for (i=numpoints, point= points; i--; point += qh->hull_dim)
     *(pointp++)= point;
   qh_settruncate(qh, pointset, numpoints);
   FOREACHvertex_(vertices) {
     if ((id= qh_pointid(qh, vertex->point)) >= 0)
       SETelem_(pointset, id)= NULL;
   }
   id= qh_pointid(qh, qh->GOODpointp);
   if (id >=0 && qh->STOPcone-1 != id && -qh->STOPpoint-1 != id)
     SETelem_(pointset, id)= NULL;
   if (qh->GOODvertexp && qh->ONLYgood && !qh->MERGING) { /* matches qhull()*/
     if ((id= qh_pointid(qh, qh->GOODvertexp)) >= 0)
       SETelem_(pointset, id)= NULL;
   }
   if (!qh->BESToutside) {  /* matches conditional for qh_partitionpoint below */
     distoutside= qh_DISToutside; /* multiple of qh.MINoutside & qh.max_outside, see user.h */
     zval_(Ztotpartition)= qh->num_points - qh->hull_dim - 1; /*misses GOOD... */
     remaining= qh->num_facets;
     point_end= numpoints;
     FORALLfacets {
       size= point_end/(remaining--) + 100;
       facet->outsideset= qh_setnew(qh, size);
       bestpoint= NULL;
       point_end= 0;
       FOREACHpoint_i_(qh, pointset) {
         if (point) {
           zzinc_(Zpartitionall);
           qh_distplane(qh, point, facet, &dist);
           if (dist < distoutside)
             SETelem_(pointset, point_end++)= point;
           else {
             qh->num_outside++;
             if (!bestpoint) {
               bestpoint= point;
               bestdist= dist;
             }else if (dist > bestdist) {
               qh_setappend(qh, &facet->outsideset, bestpoint);
               bestpoint= point;
               bestdist= dist;
             }else
               qh_setappend(qh, &facet->outsideset, point);
           }
         }
       }
       if (bestpoint) {
         qh_setappend(qh, &facet->outsideset, bestpoint);
 #if !qh_COMPUTEfurthest
         facet->furthestdist= bestdist;
 #endif
       }else
         qh_setfree(qh, &facet->outsideset);
       qh_settruncate(qh, pointset, point_end);
     }
   }
   /* if !qh->BESToutside, pointset contains points not assigned to outsideset */
   if (qh->BESToutside || qh->MERGING || qh->KEEPcoplanar || qh->KEEPinside) {
     qh->findbestnew= True;
     FOREACHpoint_i_(qh, pointset) {
       if (point)
         qh_partitionpoint(qh, point, qh->facet_list);
     }
     qh->findbestnew= False;
   }
   zzadd_(Zpartitionall, zzval_(Zpartition));
   zzval_(Zpartition)= 0;
   qh_settempfree(qh, &pointset);
   if (qh->IStracing >= 4)
     qh_printfacetlist(qh, qh->facet_list, NULL, True);
 } /* partitionall */
 
 
 /*---------------------------------
 
   qh_partitioncoplanar(qh, point, facet, dist )
     partition coplanar point to a facet
     dist is distance from point to facet
     if dist NULL,
       searches for bestfacet and does nothing if inside
     if qh.findbestnew set,
       searches new facets instead of using qh_findbest()
 
   returns:
     qh.max_ouside updated
     if qh.KEEPcoplanar or qh.KEEPinside
       point assigned to best coplanarset
 
   notes:
     facet->maxoutside is updated at end by qh_check_maxout
 
   design:
     if dist undefined
       find best facet for point
       if point sufficiently below facet (depends on qh.NEARinside and qh.KEEPinside)
         exit
     if keeping coplanar/nearinside/inside points
       if point is above furthest coplanar point
         append point to coplanar set (it is the new furthest)
         update qh.max_outside
       else
         append point one before end of coplanar set
     else if point is clearly outside of qh.max_outside and bestfacet->coplanarset
     and bestfacet is more than perpendicular to facet
       repartition the point using qh_findbest() -- it may be put on an outsideset
     else
       update qh.max_outside
 */
 void qh_partitioncoplanar(qhT *qh, pointT *point, facetT *facet, realT *dist) {
   facetT *bestfacet;
   pointT *oldfurthest;
   realT bestdist, dist2= 0, angle;
   int numpart= 0, oldfindbest;
   boolT isoutside;
 
   qh->WAScoplanar= True;
   if (!dist) {
     if (qh->findbestnew)
       bestfacet= qh_findbestnew(qh, point, facet, &bestdist, qh_ALL, &isoutside, &numpart);
     else
       bestfacet= qh_findbest(qh, point, facet, qh_ALL, !qh_ISnewfacets, qh->DELAUNAY,
                           &bestdist, &isoutside, &numpart);
     zinc_(Ztotpartcoplanar);
     zzadd_(Zpartcoplanar, numpart);
     if (!qh->DELAUNAY && !qh->KEEPinside) { /*  for 'd', bestdist skips upperDelaunay facets */
       if (qh->KEEPnearinside) {
         if (bestdist < -qh->NEARinside) {
           zinc_(Zcoplanarinside);
           trace4((qh, qh->ferr, 4062, "qh_partitioncoplanar: point p%d is more than near-inside facet f%d dist %2.2g findbestnew %d\n",
                   qh_pointid(qh, point), bestfacet->id, bestdist, qh->findbestnew));
           return;
         }
       }else if (bestdist < -qh->MAXcoplanar) {
           trace4((qh, qh->ferr, 4063, "qh_partitioncoplanar: point p%d is inside facet f%d dist %2.2g findbestnew %d\n",
                   qh_pointid(qh, point), bestfacet->id, bestdist, qh->findbestnew));
         zinc_(Zcoplanarinside);
         return;
       }
     }
   }else {
     bestfacet= facet;
     bestdist= *dist;
   }
   if (bestdist > qh->max_outside) {
     if (!dist && facet != bestfacet) {
       zinc_(Zpartangle);
       angle= qh_getangle(qh, facet->normal, bestfacet->normal);
       if (angle < 0) {
         /* typically due to deleted vertex and coplanar facets, e.g.,
              RBOX 1000 s Z1 G1e-13 t1001185205 | QHULL Tv */
         zinc_(Zpartflip);
         trace2((qh, qh->ferr, 2058, "qh_partitioncoplanar: repartition point p%d from f%d.  It is above flipped facet f%d dist %2.2g\n",
                 qh_pointid(qh, point), facet->id, bestfacet->id, bestdist));
         oldfindbest= qh->findbestnew;
         qh->findbestnew= False;
         qh_partitionpoint(qh, point, bestfacet);
         qh->findbestnew= oldfindbest;
         return;
       }
     }
     qh->max_outside= bestdist;
     if (bestdist > qh->TRACEdist) {
       qh_fprintf(qh, qh->ferr, 8122, "qh_partitioncoplanar: ====== p%d from f%d increases max_outside to %2.2g of f%d last p%d\n",
                      qh_pointid(qh, point), facet->id, bestdist, bestfacet->id, qh->furthest_id);
       qh_errprint(qh, "DISTANT", facet, bestfacet, NULL, NULL);
     }
   }
   if (qh->KEEPcoplanar + qh->KEEPinside + qh->KEEPnearinside) {
     oldfurthest= (pointT*)qh_setlast(bestfacet->coplanarset);
     if (oldfurthest) {
       zinc_(Zcomputefurthest);
       qh_distplane(qh, oldfurthest, bestfacet, &dist2);
     }
     if (!oldfurthest || dist2 < bestdist)
       qh_setappend(qh, &bestfacet->coplanarset, point);
     else
       qh_setappend2ndlast(qh, &bestfacet->coplanarset, point);
   }
   trace4((qh, qh->ferr, 4064, "qh_partitioncoplanar: point p%d is coplanar with facet f%d(or inside) dist %2.2g\n",
           qh_pointid(qh, point), bestfacet->id, bestdist));
 } /* partitioncoplanar */
 
 /*---------------------------------
 
   qh_partitionpoint(qh, point, facet )
     assigns point to an outside set, coplanar set, or inside set (i.e., dropt)
     if qh.findbestnew
       uses qh_findbestnew() to search all new facets
     else
       uses qh_findbest()
 
   notes:
     after qh_distplane(), this and qh_findbest() are most expensive in 3-d
 
   design:
     find best facet for point
       (either exhaustive search of new facets or directed search from facet)
     if qh.NARROWhull
       retain coplanar and nearinside points as outside points
     if point is outside bestfacet
       if point above furthest point for bestfacet
         append point to outside set (it becomes the new furthest)
         if outside set was empty
           move bestfacet to end of qh.facet_list (i.e., after qh.facet_next)
         update bestfacet->furthestdist
       else
         append point one before end of outside set
     else if point is coplanar to bestfacet
       if keeping coplanar points or need to update qh.max_outside
         partition coplanar point into bestfacet
     else if near-inside point
       partition as coplanar point into bestfacet
     else is an inside point
       if keeping inside points
         partition as coplanar point into bestfacet
 */
 void qh_partitionpoint(qhT *qh, pointT *point, facetT *facet) {
   realT bestdist;
   boolT isoutside;
   facetT *bestfacet;
   int numpart;
 #if qh_COMPUTEfurthest
   realT dist;
 #endif
 
   if (qh->findbestnew)
     bestfacet= qh_findbestnew(qh, point, facet, &bestdist, qh->BESToutside, &isoutside, &numpart);
   else
     bestfacet= qh_findbest(qh, point, facet, qh->BESToutside, qh_ISnewfacets, !qh_NOupper,
                           &bestdist, &isoutside, &numpart);
   zinc_(Ztotpartition);
   zzadd_(Zpartition, numpart);
   if (qh->NARROWhull) {
     if (qh->DELAUNAY && !isoutside && bestdist >= -qh->MAXcoplanar)
       qh_precision(qh, "nearly incident point(narrow hull)");
     if (qh->KEEPnearinside) {
       if (bestdist >= -qh->NEARinside)
         isoutside= True;
     }else if (bestdist >= -qh->MAXcoplanar)
       isoutside= True;
   }
 
   if (isoutside) {
     if (!bestfacet->outsideset
     || !qh_setlast(bestfacet->outsideset)) {
       qh_setappend(qh, &(bestfacet->outsideset), point);
       if (!bestfacet->newfacet) {
         qh_removefacet(qh, bestfacet);  /* make sure it's after qh->facet_next */
         qh_appendfacet(qh, bestfacet);
       }
 #if !qh_COMPUTEfurthest
       bestfacet->furthestdist= bestdist;
 #endif
     }else {
 #if qh_COMPUTEfurthest
       zinc_(Zcomputefurthest);
       qh_distplane(qh, oldfurthest, bestfacet, &dist);
       if (dist < bestdist)
         qh_setappend(qh, &(bestfacet->outsideset), point);
       else
         qh_setappend2ndlast(qh, &(bestfacet->outsideset), point);
 #else
       if (bestfacet->furthestdist < bestdist) {
         qh_setappend(qh, &(bestfacet->outsideset), point);
         bestfacet->furthestdist= bestdist;
       }else
         qh_setappend2ndlast(qh, &(bestfacet->outsideset), point);
 #endif
     }
     qh->num_outside++;
     trace4((qh, qh->ferr, 4065, "qh_partitionpoint: point p%d is outside facet f%d new? %d (or narrowhull)\n",
           qh_pointid(qh, point), bestfacet->id, bestfacet->newfacet));
   }else if (qh->DELAUNAY || bestdist >= -qh->MAXcoplanar) { /* for 'd', bestdist skips upperDelaunay facets */
     zzinc_(Zcoplanarpart);
     if (qh->DELAUNAY)
       qh_precision(qh, "nearly incident point");
     if ((qh->KEEPcoplanar + qh->KEEPnearinside) || bestdist > qh->max_outside)
       qh_partitioncoplanar(qh, point, bestfacet, &bestdist);
     else {
       trace4((qh, qh->ferr, 4066, "qh_partitionpoint: point p%d is coplanar to facet f%d (dropped)\n",
           qh_pointid(qh, point), bestfacet->id));
     }
   }else if (qh->KEEPnearinside && bestdist > -qh->NEARinside) {
     zinc_(Zpartnear);
     qh_partitioncoplanar(qh, point, bestfacet, &bestdist);
   }else {
     zinc_(Zpartinside);
     trace4((qh, qh->ferr, 4067, "qh_partitionpoint: point p%d is inside all facets, closest to f%d dist %2.2g\n",
           qh_pointid(qh, point), bestfacet->id, bestdist));
     if (qh->KEEPinside)
       qh_partitioncoplanar(qh, point, bestfacet, &bestdist);
   }
 } /* partitionpoint */
 
 /*---------------------------------
 
   qh_partitionvisible(qh, allpoints, numoutside )
     partitions points in visible facets to qh.newfacet_list
     qh.visible_list= visible facets
     for visible facets
       1st neighbor (if any) points to a horizon facet or a new facet
     if allpoints(!used),
       repartitions coplanar points
 
   returns:
     updates outside sets and coplanar sets of qh.newfacet_list
     updates qh.num_outside (count of outside points)
 
   notes:
     qh.findbest_notsharp should be clear (extra work if set)
 
   design:
     for all visible facets with outside set or coplanar set
       select a newfacet for visible facet
       if outside set
         partition outside set into new facets
       if coplanar set and keeping coplanar/near-inside/inside points
         if allpoints
           partition coplanar set into new facets, may be assigned outside
         else
           partition coplanar set into coplanar sets of new facets
     for each deleted vertex
       if allpoints
         partition vertex into new facets, may be assigned outside
       else
         partition vertex into coplanar sets of new facets
 */
 void qh_partitionvisible(qhT *qh /*qh.visible_list*/, boolT allpoints, int *numoutside) {
   facetT *visible, *newfacet;
   pointT *point, **pointp;
   int coplanar=0, size;
   unsigned count;
   vertexT *vertex, **vertexp;
 
   if (qh->ONLYmax)
     maximize_(qh->MINoutside, qh->max_vertex);
   *numoutside= 0;
   FORALLvisible_facets {
     if (!visible->outsideset && !visible->coplanarset)
       continue;
     newfacet= visible->f.replace;
     count= 0;
     while (newfacet && newfacet->visible) {
       newfacet= newfacet->f.replace;
       if (count++ > qh->facet_id)
         qh_infiniteloop(qh, visible);
     }
     if (!newfacet)
       newfacet= qh->newfacet_list;
     if (newfacet == qh->facet_tail) {
       qh_fprintf(qh, qh->ferr, 6170, "qhull precision error (qh_partitionvisible): all new facets deleted as\n        degenerate facets. Can not continue.\n");
       qh_errexit(qh, qh_ERRprec, NULL, NULL);
     }
     if (visible->outsideset) {
       size= qh_setsize(qh, visible->outsideset);
       *numoutside += size;
       qh->num_outside -= size;
       FOREACHpoint_(visible->outsideset)
         qh_partitionpoint(qh, point, newfacet);
     }
     if (visible->coplanarset && (qh->KEEPcoplanar + qh->KEEPinside + qh->KEEPnearinside)) {
       size= qh_setsize(qh, visible->coplanarset);
       coplanar += size;
       FOREACHpoint_(visible->coplanarset) {
         if (allpoints) /* not used */
           qh_partitionpoint(qh, point, newfacet);
         else
           qh_partitioncoplanar(qh, point, newfacet, NULL);
       }
     }
   }
   FOREACHvertex_(qh->del_vertices) {
     if (vertex->point) {
       if (allpoints) /* not used */
         qh_partitionpoint(qh, vertex->point, qh->newfacet_list);
       else
         qh_partitioncoplanar(qh, vertex->point, qh->newfacet_list, NULL);
     }
   }
   trace1((qh, qh->ferr, 1043,"qh_partitionvisible: partitioned %d points from outsidesets and %d points from coplanarsets\n", *numoutside, coplanar));
 } /* partitionvisible */
 
 
 
 /*---------------------------------
 
   qh_precision(qh, reason )
     restart on precision errors if not merging and if 'QJn'
 */
 void qh_precision(qhT *qh, const char *reason) {
 
   if (qh->ALLOWrestart && !qh->PREmerge && !qh->MERGEexact) {
     if (qh->JOGGLEmax < REALmax/2) {
       trace0((qh, qh->ferr, 26, "qh_precision: qhull restart because of %s\n", reason));
+      /* May be called repeatedly if qh->ALLOWrestart */
       longjmp(qh->restartexit, qh_ERRprec);
     }
   }
 } /* qh_precision */
 
 /*---------------------------------
 
   qh_printsummary(qh, fp )
     prints summary to fp
 
   notes:
-    not in io.c so that user_eg.c can prevent io.c from loading
+    not in io_r.c so that user_eg.c can prevent io_r.c from loading
     qh_printsummary and qh_countfacets must match counts
 
   design:
     determine number of points, vertices, and coplanar points
     print summary
 */
 void qh_printsummary(qhT *qh, FILE *fp) {
   realT ratio, outerplane, innerplane;
   float cpu;
   int size, id, nummerged, numvertices, numcoplanars= 0, nonsimplicial=0;
   int goodused;
   facetT *facet;
   const char *s;
   int numdel= zzval_(Zdelvertextot);
   int numtricoplanars= 0;
 
   size= qh->num_points + qh_setsize(qh, qh->other_points);
   numvertices= qh->num_vertices - qh_setsize(qh, qh->del_vertices);
   id= qh_pointid(qh, qh->GOODpointp);
   FORALLfacets {
     if (facet->coplanarset)
       numcoplanars += qh_setsize(qh, facet->coplanarset);
     if (facet->good) {
       if (facet->simplicial) {
         if (facet->keepcentrum && facet->tricoplanar)
           numtricoplanars++;
       }else if (qh_setsize(qh, facet->vertices) != qh->hull_dim)
         nonsimplicial++;
     }
   }
   if (id >=0 && qh->STOPcone-1 != id && -qh->STOPpoint-1 != id)
     size--;
   if (qh->STOPcone || qh->STOPpoint)
       qh_fprintf(qh, fp, 9288, "\nAt a premature exit due to 'TVn', 'TCn', 'TRn', or precision error with 'QJn'.");
   if (qh->UPPERdelaunay)
     goodused= qh->GOODvertex + qh->GOODpoint + qh->SPLITthresholds;
   else if (qh->DELAUNAY)
     goodused= qh->GOODvertex + qh->GOODpoint + qh->GOODthreshold;
   else
     goodused= qh->num_good;
   nummerged= zzval_(Ztotmerge) - zzval_(Zcyclehorizon) + zzval_(Zcyclefacettot);
   if (qh->VORONOI) {
     if (qh->UPPERdelaunay)
       qh_fprintf(qh, fp, 9289, "\n\
 Furthest-site Voronoi vertices by the convex hull of %d points in %d-d:\n\n", size, qh->hull_dim);
     else
       qh_fprintf(qh, fp, 9290, "\n\
 Voronoi diagram by the convex hull of %d points in %d-d:\n\n", size, qh->hull_dim);
     qh_fprintf(qh, fp, 9291, "  Number of Voronoi regions%s: %d\n",
               qh->ATinfinity ? " and at-infinity" : "", numvertices);
     if (numdel)
       qh_fprintf(qh, fp, 9292, "  Total number of deleted points due to merging: %d\n", numdel);
     if (numcoplanars - numdel > 0)
       qh_fprintf(qh, fp, 9293, "  Number of nearly incident points: %d\n", numcoplanars - numdel);
     else if (size - numvertices - numdel > 0)
       qh_fprintf(qh, fp, 9294, "  Total number of nearly incident points: %d\n", size - numvertices - numdel);
     qh_fprintf(qh, fp, 9295, "  Number of%s Voronoi vertices: %d\n",
               goodused ? " 'good'" : "", qh->num_good);
     if (nonsimplicial)
       qh_fprintf(qh, fp, 9296, "  Number of%s non-simplicial Voronoi vertices: %d\n",
               goodused ? " 'good'" : "", nonsimplicial);
   }else if (qh->DELAUNAY) {
     if (qh->UPPERdelaunay)
       qh_fprintf(qh, fp, 9297, "\n\
 Furthest-site Delaunay triangulation by the convex hull of %d points in %d-d:\n\n", size, qh->hull_dim);
     else
       qh_fprintf(qh, fp, 9298, "\n\
 Delaunay triangulation by the convex hull of %d points in %d-d:\n\n", size, qh->hull_dim);
     qh_fprintf(qh, fp, 9299, "  Number of input sites%s: %d\n",
               qh->ATinfinity ? " and at-infinity" : "", numvertices);
     if (numdel)
       qh_fprintf(qh, fp, 9300, "  Total number of deleted points due to merging: %d\n", numdel);
     if (numcoplanars - numdel > 0)
       qh_fprintf(qh, fp, 9301, "  Number of nearly incident points: %d\n", numcoplanars - numdel);
     else if (size - numvertices - numdel > 0)
       qh_fprintf(qh, fp, 9302, "  Total number of nearly incident points: %d\n", size - numvertices - numdel);
     qh_fprintf(qh, fp, 9303, "  Number of%s Delaunay regions: %d\n",
               goodused ? " 'good'" : "", qh->num_good);
     if (nonsimplicial)
       qh_fprintf(qh, fp, 9304, "  Number of%s non-simplicial Delaunay regions: %d\n",
               goodused ? " 'good'" : "", nonsimplicial);
   }else if (qh->HALFspace) {
     qh_fprintf(qh, fp, 9305, "\n\
 Halfspace intersection by the convex hull of %d points in %d-d:\n\n", size, qh->hull_dim);
     qh_fprintf(qh, fp, 9306, "  Number of halfspaces: %d\n", size);
     qh_fprintf(qh, fp, 9307, "  Number of non-redundant halfspaces: %d\n", numvertices);
     if (numcoplanars) {
       if (qh->KEEPinside && qh->KEEPcoplanar)
         s= "similar and redundant";
       else if (qh->KEEPinside)
         s= "redundant";
       else
         s= "similar";
       qh_fprintf(qh, fp, 9308, "  Number of %s halfspaces: %d\n", s, numcoplanars);
     }
     qh_fprintf(qh, fp, 9309, "  Number of intersection points: %d\n", qh->num_facets - qh->num_visible);
     if (goodused)
       qh_fprintf(qh, fp, 9310, "  Number of 'good' intersection points: %d\n", qh->num_good);
     if (nonsimplicial)
       qh_fprintf(qh, fp, 9311, "  Number of%s non-simplicial intersection points: %d\n",
               goodused ? " 'good'" : "", nonsimplicial);
   }else {
     qh_fprintf(qh, fp, 9312, "\n\
 Convex hull of %d points in %d-d:\n\n", size, qh->hull_dim);
     qh_fprintf(qh, fp, 9313, "  Number of vertices: %d\n", numvertices);
     if (numcoplanars) {
       if (qh->KEEPinside && qh->KEEPcoplanar)
         s= "coplanar and interior";
       else if (qh->KEEPinside)
         s= "interior";
       else
         s= "coplanar";
       qh_fprintf(qh, fp, 9314, "  Number of %s points: %d\n", s, numcoplanars);
     }
     qh_fprintf(qh, fp, 9315, "  Number of facets: %d\n", qh->num_facets - qh->num_visible);
     if (goodused)
       qh_fprintf(qh, fp, 9316, "  Number of 'good' facets: %d\n", qh->num_good);
     if (nonsimplicial)
       qh_fprintf(qh, fp, 9317, "  Number of%s non-simplicial facets: %d\n",
               goodused ? " 'good'" : "", nonsimplicial);
   }
   if (numtricoplanars)
       qh_fprintf(qh, fp, 9318, "  Number of triangulated facets: %d\n", numtricoplanars);
   qh_fprintf(qh, fp, 9319, "\nStatistics for: %s | %s",
                       qh->rbox_command, qh->qhull_command);
   if (qh->ROTATErandom != INT_MIN)
     qh_fprintf(qh, fp, 9320, " QR%d\n\n", qh->ROTATErandom);
   else
     qh_fprintf(qh, fp, 9321, "\n\n");
   qh_fprintf(qh, fp, 9322, "  Number of points processed: %d\n", zzval_(Zprocessed));
   qh_fprintf(qh, fp, 9323, "  Number of hyperplanes created: %d\n", zzval_(Zsetplane));
   if (qh->DELAUNAY)
     qh_fprintf(qh, fp, 9324, "  Number of facets in hull: %d\n", qh->num_facets - qh->num_visible);
   qh_fprintf(qh, fp, 9325, "  Number of distance tests for qhull: %d\n", zzval_(Zpartition)+
       zzval_(Zpartitionall)+zzval_(Znumvisibility)+zzval_(Zpartcoplanar));
 #if 0  /* NOTE: must print before printstatistics() */
   {realT stddev, ave;
   qh_fprintf(qh, fp, 9326, "  average new facet balance: %2.2g\n",
           wval_(Wnewbalance)/zval_(Zprocessed));
   stddev= qh_stddev(zval_(Zprocessed), wval_(Wnewbalance),
                                  wval_(Wnewbalance2), &ave);
   qh_fprintf(qh, fp, 9327, "  new facet standard deviation: %2.2g\n", stddev);
   qh_fprintf(qh, fp, 9328, "  average partition balance: %2.2g\n",
           wval_(Wpbalance)/zval_(Zpbalance));
   stddev= qh_stddev(zval_(Zpbalance), wval_(Wpbalance),
                                  wval_(Wpbalance2), &ave);
   qh_fprintf(qh, fp, 9329, "  partition standard deviation: %2.2g\n", stddev);
   }
 #endif
   if (nummerged) {
     qh_fprintf(qh, fp, 9330,"  Number of distance tests for merging: %d\n",zzval_(Zbestdist)+
           zzval_(Zcentrumtests)+zzval_(Zdistconvex)+zzval_(Zdistcheck)+
           zzval_(Zdistzero));
     qh_fprintf(qh, fp, 9331,"  Number of distance tests for checking: %d\n",zzval_(Zcheckpart));
     qh_fprintf(qh, fp, 9332,"  Number of merged facets: %d\n", nummerged);
   }
   if (!qh->RANDOMoutside && qh->QHULLfinished) {
     cpu= (float)qh->hulltime;
     cpu /= (float)qh_SECticks;
     wval_(Wcpu)= cpu;
     qh_fprintf(qh, fp, 9333, "  CPU seconds to compute hull (after input): %2.4g\n", cpu);
   }
   if (qh->RERUN) {
     if (!qh->PREmerge && !qh->MERGEexact)
       qh_fprintf(qh, fp, 9334, "  Percentage of runs with precision errors: %4.1f\n",
            zzval_(Zretry)*100.0/qh->build_cnt);  /* careful of order */
   }else if (qh->JOGGLEmax < REALmax/2) {
     if (zzval_(Zretry))
       qh_fprintf(qh, fp, 9335, "  After %d retries, input joggled by: %2.2g\n",
          zzval_(Zretry), qh->JOGGLEmax);
     else
       qh_fprintf(qh, fp, 9336, "  Input joggled by: %2.2g\n", qh->JOGGLEmax);
   }
   if (qh->totarea != 0.0)
     qh_fprintf(qh, fp, 9337, "  %s facet area:   %2.8g\n",
             zzval_(Ztotmerge) ? "Approximate" : "Total", qh->totarea);
   if (qh->totvol != 0.0)
     qh_fprintf(qh, fp, 9338, "  %s volume:       %2.8g\n",
             zzval_(Ztotmerge) ? "Approximate" : "Total", qh->totvol);
   if (qh->MERGING) {
     qh_outerinner(qh, NULL, &outerplane, &innerplane);
     if (outerplane > 2 * qh->DISTround) {
       qh_fprintf(qh, fp, 9339, "  Maximum distance of %spoint above facet: %2.2g",
             (qh->QHULLfinished ? "" : "merged "), outerplane);
       ratio= outerplane/(qh->ONEmerge + qh->DISTround);
       /* don't report ratio if MINoutside is large */
       if (ratio > 0.05 && 2* qh->ONEmerge > qh->MINoutside && qh->JOGGLEmax > REALmax/2)
         qh_fprintf(qh, fp, 9340, " (%.1fx)\n", ratio);
       else
         qh_fprintf(qh, fp, 9341, "\n");
     }
     if (innerplane < -2 * qh->DISTround) {
       qh_fprintf(qh, fp, 9342, "  Maximum distance of %svertex below facet: %2.2g",
             (qh->QHULLfinished ? "" : "merged "), innerplane);
       ratio= -innerplane/(qh->ONEmerge+qh->DISTround);
       if (ratio > 0.05 && qh->JOGGLEmax > REALmax/2)
         qh_fprintf(qh, fp, 9343, " (%.1fx)\n", ratio);
       else
         qh_fprintf(qh, fp, 9344, "\n");
     }
   }
   qh_fprintf(qh, fp, 9345, "\n");
 } /* printsummary */
 
 
diff --git a/src/libqhullr/libqhull_r.h b/src/libqhullr/libqhull_r.h
index 6fb65b0..ea75def 100644
--- a/src/libqhullr/libqhull_r.h
+++ b/src/libqhullr/libqhull_r.h
@@ -1,1091 +1,1090 @@
 /*
  ---------------------------------
 
-   libqhull.h
+   libqhull_r.h
    user-level header file for using qhull.a library
 
-   see qh-qhull.htm, qhull_r.h
+   see qh-qhull.htm, qhull_ra.h
 
    Copyright (c) 1993-2014 The Geometry Center.
-   $Id: //main/2011/qhull/src/libqhullr/libqhull_r.h#3 $$Change: 1651 $
-   $DateTime: 2014/01/17 08:13:57 $$Author: bbarber $
+   $Id: //main/2011/qhull/src/libqhullr/libqhull_r.h#9 $$Change: 1797 $
+   $DateTime: 2014/12/15 17:23:41 $$Author: bbarber $
 
-   includes function prototypes for libqhull.c, geom.c, global.c, io.c, user.c
+   includes function prototypes for libqhull_r.c, geom_r.c, global_r.c, io_r.c, user.c
 
-   use mem.h for mem.c
-   use qset.h for qset.c
+   use mem_r.h for mem_r.c
+   use qset_r.h for qset_r.c
 
-   see unix.c for an example of using libqhull.h
+   see unix_r.c for an example of using libqhull_r.h
 
    recompile qhull if you change this file
 */
 
 #ifndef qhDEFlibqhull
 #define qhDEFlibqhull 1
 
 /*=========================== -included files ==============*/
 
 #include "user_r.h"      /* user definable constants (e.g., realT) */
 
 #include "mem_r.h" 
 /* stat_r.h included realT */
 
 #include 
 #include 
 #include 
 #include 
 
 #ifndef __STDC__
 #ifndef __cplusplus
 #if     !_MSC_VER
 #error  Neither __STDC__ nor __cplusplus is defined.  Please use strict ANSI C or C++ to compile
 #error  Qhull.  You may need to turn off compiler extensions in your project configuration.  If
-#error  your compiler is a standard C compiler, you can delete this warning from libqhull.h
+#error  your compiler is a standard C compiler, you can delete this warning from libqhull_r.h
 #endif
 #endif
 #endif
 
 /*============ constants and basic types ====================*/
 
-extern const char *qh_version; /* defined in global.c */
+extern const char *qh_version; /* defined in global_r.c */
 
 /*----------------------------------
 
   coordT
     coordinates and coefficients are stored as realT (i.e., double)
 
   notes:
     Qhull works well if realT is 'float'.  If so joggle (QJ) is not effective.
 
     Could use 'float' for data and 'double' for calculations (realT vs. coordT)
       This requires many type casts, and adjusted error bounds.
       Also C compilers may do expressions in double anyway.
 */
 #define coordT realT
 
 /*----------------------------------
 
   pointT
     a point is an array of coordinates, usually qh.hull_dim
 */
 #define pointT coordT
 
 /*----------------------------------
 
   flagT
     Boolean flag as a bit
 */
 #define flagT unsigned int
 
 /*----------------------------------
 
   boolT
     boolean value, either True or False
 
   notes:
     needed for portability
     Use qh_False/qh_True as synonyms
 */
 #define boolT unsigned int
 #ifdef False
 #undef False
 #endif
 #ifdef True
 #undef True
 #endif
 #define False 0
 #define True 1
 #define qh_False 0
 #define qh_True 1
 
 #include "stat_r.h" 
 
 /*----------------------------------
 
   qh_CENTER
     to distinguish facet->center
 */
 typedef enum
 {
     qh_ASnone = 0, qh_ASvoronoi, qh_AScentrum
 }
 qh_CENTER;
 
 /*----------------------------------
 
   qh_PRINT
     output formats for printing (qh.PRINTout).
     'Fa' 'FV' 'Fc' 'FC'
 
 
    notes:
    some of these names are similar to qhT names.  The similar names are only
    used in switch statements in qh_printbegin() etc.
 */
 typedef enum {qh_PRINTnone= 0,
   qh_PRINTarea, qh_PRINTaverage,           /* 'Fa' 'FV' 'Fc' 'FC' */
   qh_PRINTcoplanars, qh_PRINTcentrums,
   qh_PRINTfacets, qh_PRINTfacets_xridge,   /* 'f' 'FF' 'G' 'FI' 'Fi' 'Fn' */
   qh_PRINTgeom, qh_PRINTids, qh_PRINTinner, qh_PRINTneighbors,
   qh_PRINTnormals, qh_PRINTouter, qh_PRINTmaple, /* 'n' 'Fo' 'i' 'm' 'Fm' 'FM', 'o' */
   qh_PRINTincidences, qh_PRINTmathematica, qh_PRINTmerges, qh_PRINToff,
   qh_PRINToptions, qh_PRINTpointintersect, /* 'FO' 'Fp' 'FP' 'p' 'FQ' 'FS' */
   qh_PRINTpointnearest, qh_PRINTpoints, qh_PRINTqhull, qh_PRINTsize,
   qh_PRINTsummary, qh_PRINTtriangles,      /* 'Fs' 'Ft' 'Fv' 'FN' 'Fx' */
   qh_PRINTvertices, qh_PRINTvneighbors, qh_PRINTextremes,
   qh_PRINTEND} qh_PRINT;
 
 /*----------------------------------
 
   qh_ALL
     argument flag for selecting everything
 */
 #define qh_ALL      True
 #define qh_NOupper  True     /* argument for qh_findbest */
 #define qh_IScheckmax  True     /* argument for qh_findbesthorizon */
 #define qh_ISnewfacets  True     /* argument for qh_findbest */
 #define qh_RESETvisible  True     /* argument for qh_resetlists */
 
 /*----------------------------------
 
   qh_ERR
     Qhull exit codes, for indicating errors
     See: MSG_ERROR and MSG_WARNING [user.h]
 */
 #define qh_ERRnone  0    /* no error occurred during qhull */
 #define qh_ERRinput 1    /* input inconsistency */
 #define qh_ERRsingular 2 /* singular input data */
 #define qh_ERRprec  3    /* precision error */
-#define qh_ERRmem   4    /* insufficient memory, matches mem.h */
-#define qh_ERRqhull 5    /* internal error detected, matches mem.h */
+#define qh_ERRmem   4    /* insufficient memory, matches mem_r.h */
+#define qh_ERRqhull 5    /* internal error detected, matches mem_r.h */
 
 /*----------------------------------
 
 qh_FILEstderr
 Fake stderr to distinguish error output from normal output
 For C++ interface.  Must redefine qh_fprintf_qhull
 */
 #define qh_FILEstderr ((FILE*)1)
 
 /* ============ -structures- ====================
    each of the following structures is defined by a typedef
    all realT and coordT fields occur at the beginning of a structure
         (otherwise space may be wasted due to alignment)
    define all flags together and pack into 32-bit number
 */
 
 typedef struct vertexT vertexT;
 typedef struct ridgeT ridgeT;
 typedef struct facetT facetT;
 
 #ifndef DEFqhT
 #define DEFqhT 1
 typedef struct qhT qhT;          /* defined below */
 #endif
 
 #ifndef DEFsetT
 #define DEFsetT 1
-typedef struct setT setT;          /* defined in qset.h */
+typedef struct setT setT;          /* defined in qset_r.h */
 #endif
 
 #ifndef DEFqhstatT
 #define DEFqhstatT 1
-typedef struct qhstatT qhstatT;    /* defined in stat.h */
+typedef struct qhstatT qhstatT;    /* defined in stat_r.h */
 #endif
 
 /*----------------------------------
 
   facetT
     defines a facet
 
   notes:
    qhull() generates the hull as a list of facets.
 
   topological information:
     f.previous,next     doubly-linked list of facets
     f.vertices          set of vertices
     f.ridges            set of ridges
     f.neighbors         set of neighbors
     f.toporient         True if facet has top-orientation (else bottom)
 
   geometric information:
     f.offset,normal     hyperplane equation
     f.maxoutside        offset to outer plane -- all points inside
     f.center            centrum for testing convexity
     f.simplicial        True if facet is simplicial
     f.flipped           True if facet does not include qh.interior_point
 
   for constructing hull:
     f.visible           True if facet on list of visible facets (will be deleted)
     f.newfacet          True if facet on list of newly created facets
     f.coplanarset       set of points coplanar with this facet
                         (includes near-inside points for later testing)
     f.outsideset        set of points outside of this facet
     f.furthestdist      distance to furthest point of outside set
     f.visitid           marks visited facets during a loop
     f.replace           replacement facet for to-be-deleted, visible facets
     f.samecycle,newcycle cycle of facets for merging into horizon facet
 
   see below for other flags and fields
 */
 struct facetT {
 #if !qh_COMPUTEfurthest
   coordT   furthestdist;/* distance to furthest point of outsideset */
 #endif
 #if qh_MAXoutside
   coordT   maxoutside;  /* max computed distance of point to facet
                         Before QHULLfinished this is an approximation
                         since maxdist not always set for mergefacet
                         Actual outer plane is +DISTround and
                         computed outer plane is +2*DISTround */
 #endif
   coordT   offset;      /* exact offset of hyperplane from origin */
   coordT  *normal;      /* normal of hyperplane, hull_dim coefficients */
                         /*   if tricoplanar, shared with a neighbor */
   union {               /* in order of testing */
-   realT   area;        /* area of facet, only in io.c if  ->isarea */
+   realT   area;        /* area of facet, only in io_r.c if  ->isarea */
    facetT *replace;     /*  replacement facet if ->visible and NEWfacets
                              is NULL only if qh_mergedegen_redundant or interior */
    facetT *samecycle;   /*  cycle of facets from the same visible/horizon intersection,
                              if ->newfacet */
    facetT *newcycle;    /*  in horizon facet, current samecycle of new facets */
    facetT *trivisible;  /* visible facet for ->tricoplanar facets during qh_triangulate() */
    facetT *triowner;    /* owner facet for ->tricoplanar, !isarea facets w/ ->keepcentrum */
   }f;
   coordT  *center;      /*  centrum for convexity, qh.CENTERtype == qh_AScentrum */
                         /*  Voronoi center, qh.CENTERtype == qh_ASvoronoi */
                         /*   if tricoplanar, shared with a neighbor */
   facetT  *previous;    /* previous facet in the facet_list */
   facetT  *next;        /* next facet in the facet_list */
   setT    *vertices;    /* vertices for this facet, inverse sorted by ID
                            if simplicial, 1st vertex was apex/furthest */
   setT    *ridges;      /* explicit ridges for nonsimplicial facets.
                            for simplicial facets, neighbors define the ridges */
   setT    *neighbors;   /* neighbors of the facet.  If simplicial, the kth
                            neighbor is opposite the kth vertex, and the first
                            neighbor is the horizon facet for the first vertex*/
   setT    *outsideset;  /* set of points outside this facet
                            if non-empty, last point is furthest
                            if NARROWhull, includes coplanars for partitioning*/
   setT    *coplanarset; /* set of points coplanar with this facet
                            > qh.min_vertex and <= facet->max_outside
                            a point is assigned to the furthest facet
                            if non-empty, last point is furthest away */
   unsigned visitid;     /* visit_id, for visiting all neighbors,
                            all uses are independent */
   unsigned id;          /* unique identifier from qh.facet_id */
   unsigned nummerge:9;  /* number of merges */
-#define qh_MAXnummerge 511 /*     2^9-1, 32 flags total, see "flags:" in io.c */
+#define qh_MAXnummerge 511 /*     2^9-1, 32 flags total, see "flags:" in io_r.c */
   flagT    tricoplanar:1; /* True if TRIangulate and simplicial and coplanar with a neighbor */
                           /*   all tricoplanars share the same ->center, ->normal, ->offset, ->maxoutside */
                           /*   all tricoplanars share the same apex */
                           /*   if ->degenerate, does not span facet (one logical ridge) */
                           /*   one tricoplanar has ->keepcentrum and ->coplanarset */
                           /*   during qh_triangulate, f.trivisible points to original facet */
   flagT    newfacet:1;  /* True if facet on qh.newfacet_list (new or merged) */
   flagT    visible:1;   /* True if visible facet (will be deleted) */
   flagT    toporient:1; /* True if created with top orientation
                            after merging, use ridge orientation */
   flagT    simplicial:1;/* True if simplicial facet, ->ridges may be implicit */
   flagT    seen:1;      /* used to perform operations only once, like visitid */
   flagT    seen2:1;     /* used to perform operations only once, like visitid */
   flagT    flipped:1;   /* True if facet is flipped */
   flagT    upperdelaunay:1; /* True if facet is upper envelope of Delaunay triangulation */
   flagT    notfurthest:1; /* True if last point of outsideset is not furthest*/
 
 /*-------- flags primarily for output ---------*/
   flagT    good:1;      /* True if a facet marked good for output */
   flagT    isarea:1;    /* True if facet->f.area is defined */
 
 /*-------- flags for merging ------------------*/
   flagT    dupridge:1;  /* True if duplicate ridge in facet */
   flagT    mergeridge:1; /* True if facet or neighbor contains a qh_MERGEridge
                             ->normal defined (also defined for mergeridge2) */
   flagT    mergeridge2:1; /* True if neighbor contains a qh_MERGEridge (qhT *qh, mark_dupridges */
   flagT    coplanar:1;  /* True if horizon facet is coplanar at last use */
   flagT     mergehorizon:1; /* True if will merge into horizon (->coplanar) */
   flagT     cycledone:1;/* True if mergecycle_all already done */
   flagT    tested:1;    /* True if facet convexity has been tested (false after merge */
   flagT    keepcentrum:1; /* True if keep old centrum after a merge, or marks owner for ->tricoplanar */
   flagT    newmerge:1;  /* True if facet is newly merged for reducevertices */
   flagT    degenerate:1; /* True if facet is degenerate (degen_mergeset or ->tricoplanar) */
   flagT    redundant:1;  /* True if facet is redundant (degen_mergeset) */
 };
 
 
 /*----------------------------------
 
   ridgeT
     defines a ridge
 
   notes:
   a ridge is hull_dim-1 simplex between two neighboring facets.  If the
   facets are non-simplicial, there may be more than one ridge between
   two facets.  E.G. a 4-d hypercube has two triangles between each pair
   of neighboring facets.
 
   topological information:
     vertices            a set of vertices
     top,bottom          neighboring facets with orientation
 
   geometric information:
     tested              True if ridge is clearly convex
     nonconvex           True if ridge is non-convex
 */
 struct ridgeT {
   setT    *vertices;    /* vertices belonging to this ridge, inverse sorted by ID
                            NULL if a degen ridge (matchsame) */
   facetT  *top;         /* top facet this ridge is part of */
   facetT  *bottom;      /* bottom facet this ridge is part of */
   unsigned id:24;       /* unique identifier, =>room for 8 flags, bit field matches qh->ridge_id */
   flagT    seen:1;      /* used to perform operations only once */
   flagT    tested:1;    /* True when ridge is tested for convexity */
   flagT    nonconvex:1; /* True if getmergeset detected a non-convex neighbor
                            only one ridge between neighbors may have nonconvex */
 };
 
 /*----------------------------------
 
   vertexT
      defines a vertex
 
   topological information:
     next,previous       doubly-linked list of all vertices
     neighbors           set of adjacent facets (only if qh.VERTEXneighbors)
 
   geometric information:
     point               array of DIM3 coordinates
 */
 struct vertexT {
   vertexT *next;        /* next vertex in vertex_list */
   vertexT *previous;    /* previous vertex in vertex_list */
   pointT  *point;       /* hull_dim coordinates (coordT) */
   setT    *neighbors;   /* neighboring facets of vertex, qh_vertexneighbors()
-                           inits in io.c or after first merge */
+                           inits in io_r.c or after first merge */
   unsigned visitid:31;  /* for use with qh.vertex_visit, size must match */
   flagT    seen2:1;     /* another seen flag */
-  unsigned id:24;       /* unique identifier, bit field matches qh.vertex_id */
-  unsigned dim:4;       /* dimension of point if non-zero, used by cpp */
+  unsigned id:28;       /* unique identifier, bit field matches qh.vertex_id */
                         /* =>room for 4 flags */
   flagT    seen:1;      /* used to perform operations only once */
   flagT    delridge:1;  /* vertex was part of a deleted ridge */
   flagT    deleted:1;   /* true if vertex on qh.del_vertices */
   flagT    newlist:1;   /* true if vertex on qh.newvertex_list */
 };
 
-#define MAX_vdim 15  /* Maximum size of vertex->dim */
-
 /*======= -global variables -qh ============================*/
 
 /*----------------------------------
 
   qhT
    All global variables for qhull are in qhT.  It includes qhmemT, qhstatT, and rbox globals
 
    This version of Qhull is reentrant, but it is not thread-safe.  
    
    Do not run separate threads on the same instance of qhT.
 */
 
 struct qhT {
 
 /*----------------------------------
 
   qh constants
     configuration flags and constants for Qhull
 
   notes:
     The user configures Qhull by defining flags.  They are
     copied into qh by qh_setflags().  qh-quick.htm#options defines the flags.
 */
   boolT ALLpoints;        /* true 'Qs' if search all points for initial simplex */
   boolT ANGLEmerge;       /* true 'Qa' if sort potential merges by angle */
   boolT APPROXhull;       /* true 'Wn' if MINoutside set */
   realT   MINoutside;     /*   'Wn' min. distance for an outside point */
   boolT ANNOTATEoutput;   /* true 'Ta' if annotate output with message codes */
   boolT ATinfinity;       /* true 'Qz' if point num_points-1 is "at-infinity"
                              for improving precision in Delaunay triangulations */
   boolT AVOIDold;         /* true 'Q4' if avoid old->new merges */
   boolT BESToutside;      /* true 'Qf' if partition points into best outsideset */
   boolT CDDinput;         /* true 'Pc' if input uses CDD format (1.0/offset first) */
   boolT CDDoutput;        /* true 'PC' if print normals in CDD format (offset first) */
   boolT CHECKfrequently;  /* true 'Tc' if checking frequently */
   realT premerge_cos;     /*   'A-n'   cos_max when pre merging */
   realT postmerge_cos;    /*   'An'    cos_max when post merging */
   boolT DELAUNAY;         /* true 'd' if computing DELAUNAY triangulation */
   boolT DOintersections;  /* true 'Gh' if print hyperplane intersections */
   int   DROPdim;          /* drops dim 'GDn' for 4-d -> 3-d output */
   boolT FORCEoutput;      /* true 'Po' if forcing output despite degeneracies */
   int   GOODpoint;        /* 1+n for 'QGn', good facet if visible/not(-) from point n*/
   pointT *GOODpointp;     /*   the actual point */
   boolT GOODthreshold;    /* true if qh.lower_threshold/upper_threshold defined
                              false if qh.SPLITthreshold */
   int   GOODvertex;       /* 1+n, good facet if vertex for point n */
   pointT *GOODvertexp;     /*   the actual point */
   boolT HALFspace;        /* true 'Hn,n,n' if halfspace intersection */
+  boolT ISqhullQh;        /* Set by Qhull.cpp on initialization */
   int   IStracing;        /* trace execution, 0=none, 1=least, 4=most, -1=events */
   int   KEEParea;         /* 'PAn' number of largest facets to keep */
   boolT KEEPcoplanar;     /* true 'Qc' if keeping nearest facet for coplanar points */
   boolT KEEPinside;       /* true 'Qi' if keeping nearest facet for inside points
                               set automatically if 'd Qc' */
   int   KEEPmerge;        /* 'PMn' number of facets to keep with most merges */
   realT KEEPminArea;      /* 'PFn' minimum facet area to keep */
   realT MAXcoplanar;      /* 'Un' max distance below a facet to be coplanar*/
   boolT MERGEexact;       /* true 'Qx' if exact merges (coplanar, degen, dupridge, flipped) */
   boolT MERGEindependent; /* true 'Q2' if merging independent sets */
   boolT MERGING;          /* true if exact-, pre- or post-merging, with angle and centrum tests */
   realT   premerge_centrum;  /*   'C-n' centrum_radius when pre merging.  Default is round-off */
   realT   postmerge_centrum; /*   'Cn' centrum_radius when post merging.  Default is round-off */
   boolT MERGEvertices;    /* true 'Q3' if merging redundant vertices */
   realT MINvisible;       /* 'Vn' min. distance for a facet to be visible */
   boolT NOnarrow;         /* true 'Q10' if no special processing for narrow distributions */
   boolT NOnearinside;     /* true 'Q8' if ignore near-inside points when partitioning */
   boolT NOpremerge;       /* true 'Q0' if no defaults for C-0 or Qx */
   boolT ONLYgood;         /* true 'Qg' if process points with good visible or horizon facets */
   boolT ONLYmax;          /* true 'Qm' if only process points that increase max_outside */
   boolT PICKfurthest;     /* true 'Q9' if process furthest of furthest points*/
   boolT POSTmerge;        /* true if merging after buildhull (Cn or An) */
   boolT PREmerge;         /* true if merging during buildhull (C-n or A-n) */
                         /* NOTE: some of these names are similar to qh_PRINT names */
   boolT PRINTcentrums;    /* true 'Gc' if printing centrums */
   boolT PRINTcoplanar;    /* true 'Gp' if printing coplanar points */
   int   PRINTdim;         /* print dimension for Geomview output */
   boolT PRINTdots;        /* true 'Ga' if printing all points as dots */
   boolT PRINTgood;        /* true 'Pg' if printing good facets */
   boolT PRINTinner;       /* true 'Gi' if printing inner planes */
   boolT PRINTneighbors;   /* true 'PG' if printing neighbors of good facets */
   boolT PRINTnoplanes;    /* true 'Gn' if printing no planes */
   boolT PRINToptions1st;  /* true 'FO' if printing options to stderr */
   boolT PRINTouter;       /* true 'Go' if printing outer planes */
   boolT PRINTprecision;   /* false 'Pp' if not reporting precision problems */
   qh_PRINT PRINTout[qh_PRINTEND]; /* list of output formats to print */
   boolT PRINTridges;      /* true 'Gr' if print ridges */
   boolT PRINTspheres;     /* true 'Gv' if print vertices as spheres */
   boolT PRINTstatistics;  /* true 'Ts' if printing statistics to stderr */
   boolT PRINTsummary;     /* true 's' if printing summary to stderr */
   boolT PRINTtransparent; /* true 'Gt' if print transparent outer ridges */
   boolT PROJECTdelaunay;  /* true if DELAUNAY, no readpoints() and
                              need projectinput() for Delaunay in qh_init_B */
   int   PROJECTinput;     /* number of projected dimensions 'bn:0Bn:0' */
   boolT QUICKhelp;        /* true if quick help message for degen input */
   boolT RANDOMdist;       /* true if randomly change distplane and setfacetplane */
   realT RANDOMfactor;     /*    maximum random perturbation */
   realT RANDOMa;          /*    qh_randomfactor is randr * RANDOMa + RANDOMb */
   realT RANDOMb;
   boolT RANDOMoutside;    /* true if select a random outside point */
   int   REPORTfreq;       /* buildtracing reports every n facets */
   int   REPORTfreq2;      /* tracemerging reports every REPORTfreq/2 facets */
   int   RERUN;            /* 'TRn' rerun qhull n times (qh.build_cnt) */
   int   ROTATErandom;     /* 'QRn' seed, 0 time, >= rotate input */
   boolT SCALEinput;       /* true 'Qbk' if scaling input */
   boolT SCALElast;        /* true 'Qbb' if scale last coord to max prev coord */
   boolT SETroundoff;      /* true 'E' if qh.DISTround is predefined */
   boolT SKIPcheckmax;     /* true 'Q5' if skip qh_check_maxout */
   boolT SKIPconvex;       /* true 'Q6' if skip convexity testing during pre-merge */
   boolT SPLITthresholds;  /* true if upper_/lower_threshold defines a region
                                used only for printing (!for qh.ONLYgood) */
   int   STOPcone;         /* 'TCn' 1+n for stopping after cone for point n */
                           /*       also used by qh_build_withresart for err exit*/
   int   STOPpoint;        /* 'TVn' 'TV-n' 1+n for stopping after/before(-)
                                         adding point n */
   int   TESTpoints;       /* 'QTn' num of test points after qh.num_points.  Test points always coplanar. */
   boolT TESTvneighbors;   /*  true 'Qv' if test vertex neighbors at end */
   int   TRACElevel;       /* 'Tn' conditional IStracing level */
   int   TRACElastrun;     /*  qh.TRACElevel applies to last qh.RERUN */
   int   TRACEpoint;       /* 'TPn' start tracing when point n is a vertex */
   realT TRACEdist;        /* 'TWn' start tracing when merge distance too big */
   int   TRACEmerge;       /* 'TMn' start tracing before this merge */
   boolT TRIangulate;      /* true 'Qt' if triangulate non-simplicial facets */
   boolT TRInormals;       /* true 'Q11' if triangulate duplicates normals (sets Qt) */
   boolT UPPERdelaunay;    /* true 'Qu' if computing furthest-site Delaunay */
   boolT USEstdout;        /* true 'Tz' if using stdout instead of stderr */
   boolT VERIFYoutput;     /* true 'Tv' if verify output at end of qhull */
   boolT VIRTUALmemory;    /* true 'Q7' if depth-first processing in buildhull */
   boolT VORONOI;          /* true 'v' if computing Voronoi diagram */
 
   /*--------input constants ---------*/
   realT AREAfactor;       /* 1/(hull_dim-1)! for converting det's to area */
   boolT DOcheckmax;       /* true if calling qh_check_maxout (qhT *qh, qh_initqhull_globals) */
   char  *feasible_string;  /* feasible point 'Hn,n,n' for halfspace intersection */
   coordT *feasible_point;  /*    as coordinates, both malloc'd */
-  boolT GETarea;          /* true 'Fa', 'FA', 'FS', 'PAn', 'PFn' if compute facet area/Voronoi volume in io.c */
+  boolT GETarea;          /* true 'Fa', 'FA', 'FS', 'PAn', 'PFn' if compute facet area/Voronoi volume in io_r.c */
   boolT KEEPnearinside;   /* true if near-inside points in coplanarset */
   int   hull_dim;         /* dimension of hull, set by initbuffers */
   int   input_dim;        /* dimension of input, set by initbuffers */
   int   num_points;       /* number of input points */
   pointT *first_point;    /* array of input points, see POINTSmalloc */
   boolT POINTSmalloc;     /*   true if qh.first_point/num_points allocated */
   pointT *input_points;   /* copy of original qh.first_point for input points for qh_joggleinput */
   boolT input_malloc;     /* true if qh.input_points malloc'd */
   char  qhull_command[256];/* command line that invoked this program */
   int   qhull_commandsiz2; /*    size of qhull_command at qh_clear_outputflags */
   char  rbox_command[256]; /* command line that produced the input points */
   char  qhull_options[512];/* descriptive list of options */
   int   qhull_optionlen;  /*    length of last line */
   int   qhull_optionsiz;  /*    size of qhull_options at qh_build_withrestart */
   int   qhull_optionsiz2; /*    size of qhull_options at qh_clear_outputflags */
   int   run_id;           /* non-zero, random identifier for this instance of qhull */
   boolT VERTEXneighbors;  /* true if maintaining vertex neighbors */
   boolT ZEROcentrum;      /* true if 'C-0' or 'C-0 Qx'.  sets ZEROall_ok */
   realT *upper_threshold; /* don't print if facet->normal[k]>=upper_threshold[k]
                              must set either GOODthreshold or SPLITthreshold
                              if Delaunay, default is 0.0 for upper envelope */
   realT *lower_threshold; /* don't print if facet->normal[k] <=lower_threshold[k] */
   realT *upper_bound;     /* scale point[k] to new upper bound */
   realT *lower_bound;     /* scale point[k] to new lower bound
                              project if both upper_ and lower_bound == 0 */
 
 /*----------------------------------
 
   qh precision constants
     precision constants for Qhull
 
   notes:
     qh_detroundoff(qh) computes the maximum roundoff error for distance
     and other computations.  It also sets default values for the
     qh constants above.
 */
   realT ANGLEround;       /* max round off error for angles */
   realT centrum_radius;   /* max centrum radius for convexity (roundoff added) */
   realT cos_max;          /* max cosine for convexity (roundoff added) */
-  realT DISTround;        /* max round off error for distances, 'E' overrides */
+  realT DISTround;        /* max round off error for distances, 'E' overrides qh_distround() */
   realT MAXabs_coord;     /* max absolute coordinate */
   realT MAXlastcoord;     /* max last coordinate for qh_scalelast */
   realT MAXsumcoord;      /* max sum of coordinates */
   realT MAXwidth;         /* max rectilinear width of point coordinates */
   realT MINdenom_1;       /* min. abs. value for 1/x */
   realT MINdenom;         /*    use divzero if denominator < MINdenom */
   realT MINdenom_1_2;     /* min. abs. val for 1/x that allows normalization */
   realT MINdenom_2;       /*    use divzero if denominator < MINdenom_2 */
   realT MINlastcoord;     /* min. last coordinate for qh_scalelast */
   boolT NARROWhull;       /* set in qh_initialhull if angle < qh_MAXnarrow */
   realT *NEARzero;        /* hull_dim array for near zero in gausselim */
   realT NEARinside;       /* keep points for qh_check_maxout if close to facet */
   realT ONEmerge;         /* max distance for merging simplicial facets */
   realT outside_err;      /* application's epsilon for coplanar points
                              qh_check_bestdist() qh_check_points() reports error if point outside */
   realT WIDEfacet;        /* size of wide facet for skipping ridge in
                              area computation and locking centrum */
 
 /*----------------------------------
 
   qh internal constants
     internal constants for Qhull
 */
   char qhull[sizeof("qhull")]; /* "qhull" for checking ownership while debugging */
-  jmp_buf errexit;        /* exit label for qh_errexit, defined by setjmp() */
+  jmp_buf errexit;        /* exit label for qh_errexit, defined by setjmp() and NOerrexit */
   char jmpXtra[40];       /* extra bytes in case jmp_buf is defined wrong by compiler */
-  jmp_buf restartexit;    /* restart label for qh_errexit, defined by setjmp() */
+  jmp_buf restartexit;    /* restart label for qh_errexit, defined by setjmp() and ALLOWrestart */
   char jmpXtra2[40];      /* extra bytes in case jmp_buf is defined wrong by compiler*/
   FILE *fin;              /* pointer to input file, init by qh_initqhull_start */
   FILE *fout;             /* pointer to output file */
   FILE *ferr;             /* pointer to error file */
   pointT *interior_point; /* center point of the initial simplex*/
   int normal_size;     /* size in bytes for facet normals and point coords*/
   int center_size;     /* size in bytes for Voronoi centers */
   int   TEMPsize;         /* size for small, temporary sets (in quick mem) */
 
 /*----------------------------------
 
   qh facet and vertex lists
     defines lists of facets, new facets, visible facets, vertices, and
     new vertices.  Includes counts, next ids, and trace ids.
   see:
     qh_resetlists()
 */
   facetT *facet_list;     /* first facet */
   facetT  *facet_tail;     /* end of facet_list (dummy facet) */
   facetT *facet_next;     /* next facet for buildhull()
                              previous facets do not have outside sets
                              NARROWhull: previous facets may have coplanar outside sets for qh_outcoplanar */
   facetT *newfacet_list;  /* list of new facets to end of facet_list */
   facetT *visible_list;   /* list of visible facets preceeding newfacet_list,
                              facet->visible set */
   int       num_visible;  /* current number of visible facets */
   unsigned tracefacet_id;  /* set at init, then can print whenever */
   facetT *tracefacet;     /*   set in newfacet/mergefacet, undone in delfacet*/
   unsigned tracevertex_id;  /* set at buildtracing, can print whenever */
   vertexT *tracevertex;     /*   set in newvertex, undone in delvertex*/
   vertexT *vertex_list;     /* list of all vertices, to vertex_tail */
   vertexT  *vertex_tail;    /*      end of vertex_list (dummy vertex) */
   vertexT *newvertex_list; /* list of vertices in newfacet_list, to vertex_tail
                              all vertices have 'newlist' set */
   int   num_facets;       /* number of facets in facet_list
                              includes visble faces (num_visible) */
   int   num_vertices;     /* number of vertices in facet_list */
   int   num_outside;      /* number of points in outsidesets (for tracing and RANDOMoutside)
                                includes coplanar outsideset points for NARROWhull/qh_outcoplanar() */
   int   num_good;         /* number of good facets (after findgood_all) */
   unsigned facet_id;      /* ID of next, new facet from newfacet() */
   unsigned ridge_id:24;   /* ID of next, new ridge from newridge() */
   unsigned vertex_id:24;  /* ID of next, new vertex from newvertex() */
 
 /*----------------------------------
 
   qh global variables
     defines minimum and maximum distances, next visit ids, several flags,
     and other global variables.
     initialize in qh_initbuild or qh_maxmin if used in qh_buildhull
 */
   unsigned long hulltime; /* ignore time to set up input and randomize */
                           /*   use unsigned to avoid wrap-around errors */
   boolT ALLOWrestart;     /* true if qh_precision can use qh.restartexit */
   int   build_cnt;        /* number of calls to qh_initbuild */
   qh_CENTER CENTERtype;   /* current type of facet->center, qh_CENTER */
   int   furthest_id;      /* pointid of furthest point, for tracing */
   facetT *GOODclosest;    /* closest facet to GOODthreshold in qh_findgood */
   boolT hasAreaVolume;    /* true if totarea, totvol was defined by qh_getarea */
   boolT hasTriangulation; /* true if triangulation created by qh_triangulate */
   realT JOGGLEmax;        /* set 'QJn' if randomly joggle input */
   boolT maxoutdone;       /* set qh_check_maxout(), cleared by qh_addpoint() */
   realT max_outside;      /* maximum distance from a point to a facet,
                                before roundoff, not simplicial vertices
                                actual outer plane is +DISTround and
                                computed outer plane is +2*DISTround */
   realT max_vertex;       /* maximum distance (>0) from vertex to a facet,
                                before roundoff, due to a merge */
   realT min_vertex;       /* minimum distance (<0) from vertex to a facet,
                                before roundoff, due to a merge
                                if qh.JOGGLEmax, qh_makenewplanes sets it
                                recomputed if qh.DOcheckmax, default -qh.DISTround */
   boolT NEWfacets;        /* true while visible facets invalid due to new or merge
                               from makecone/attachnewfacets to deletevisible */
   boolT findbestnew;      /* true if partitioning calls qh_findbestnew */
   boolT findbest_notsharp; /* true if new facets are at least 90 degrees */
   boolT NOerrexit;        /* true if qh.errexit is not available */
   realT PRINTcradius;     /* radius for printing centrums */
   realT PRINTradius;      /* radius for printing vertex spheres and points */
   boolT POSTmerging;      /* true when post merging */
   int   printoutvar;      /* temporary variable for qh_printbegin, etc. */
   int   printoutnum;      /* number of facets printed */
   boolT QHULLfinished;    /* True after qhull() is finished */
   realT totarea;          /* 'FA': total facet area computed by qh_getarea, hasAreaVolume */
   realT totvol;           /* 'FA': total volume computed by qh_getarea, hasAreaVolume */
   unsigned int visit_id;  /* unique ID for searching neighborhoods, */
   unsigned int vertex_visit:31; /* unique ID for searching vertices, reset with qh_buildtracing */
   boolT ZEROall_ok;       /* True if qh_checkzero always succeeds */
   boolT WAScoplanar;      /* True if qh_partitioncoplanar (qhT *qh, qh_check_maxout) */
 
 /*----------------------------------
 
   qh global sets
     defines sets for merging, initial simplex, hashing, extra input points,
     and deleted vertices
 */
   setT *facet_mergeset;   /* temporary set of merges to be done */
   setT *degen_mergeset;   /* temporary set of degenerate and redundant merges */
   setT *hash_table;       /* hash table for matching ridges in qh_matchfacets
                              size is setsize() */
   setT *other_points;     /* additional points */
   setT *del_vertices;     /* vertices to partition and delete with visible
                              facets.  Have deleted set for checkfacet */
 
 /*----------------------------------
 
   qh global buffers
     defines buffers for maxtrix operations, input, and error messages
 */
-  coordT *gm_matrix;      /* (dim+1)Xdim matrix for geom.c */
+  coordT *gm_matrix;      /* (dim+1)Xdim matrix for geom_r.c */
   coordT **gm_row;        /* array of gm_matrix rows */
   char* line;             /* malloc'd input line of maxline+1 chars */
   int maxline;
   coordT *half_space;     /* malloc'd input array for halfspace (qh.normal_size+coordT) */
   coordT *temp_malloc;    /* malloc'd input array for points */
 
-/*----------------------------------
 
   qh static variables
     defines static variables for individual functions
 
   notes:
     do not use 'static' within a function.  Multiple instances of qhull
     may exist.
 
     do not assume zero initialization, 'QPn' may cause a restart
 */
   boolT ERREXITcalled;    /* true during qh_errexit (qhT *qh, prevents duplicate calls */
   boolT firstcentrum;     /* for qh_printcentrum */
   boolT old_randomdist;   /* save RANDOMdist flag during io, tracing, or statistics */
   setT *coplanarfacetset;  /* set of coplanar facets for searching qh_findbesthorizon() */
   realT last_low;         /* qh_scalelast parameters for qh_setdelaunay */
   realT last_high;
   realT last_newhigh;
   unsigned lastreport;    /* for qh_buildtracing */
   int mergereport;        /* for qh_tracemerging */
   setT *old_tempstack;    /* for saving qh->qhmem.tempstack in save_qhull */
   int   ridgeoutnum;      /* number of ridges for 4OFF output (qh_printbegin,etc) */
 
 /*----------------------------------
 
   qh memory management, rbox globals, and statistics
 
-  Replaces global data structures in libqhull.h
+  Replaces global data structures defined for libqhull
 */
-
   int     last_random;    /* Last random number from qh_rand (random_r.c) */
-  jmp_buf rbox_errexit;   /* errexit from rboxlib_r.c */
+  jmp_buf rbox_errexit;   /* errexit from rboxlib_r.c, for qh_rboxpoints only */
+  char    jmpXtra3[40];   /* extra bytes in case jmp_buf is defined wrong by compiler */
   int     rbox_isinteger;
   double  rbox_out_offset;
+  void *  cpp_object;     /* C++ pointer.  Currently used by RboxPoints.qh_fprintf_rbox */
 
   /* Last, otherwise zero'd by qh_initqhull_start2 (global_r.c */
   qhmemT  qhmem;          /* Qhull managed memory (mem_r.h) */
-  /* Last because its size depends on the number of statistics */
+  /* After qhmem because its size depends on the number of statistics */
   qhstatT qhstat;         /* Qhull statistics (stat_r.h) */
 };
 
 /*=========== -macros- =========================*/
 
 /*----------------------------------
 
   otherfacet_(ridge, facet)
     return neighboring facet for a ridge in facet
 */
 #define otherfacet_(ridge, facet) \
                         (((ridge)->top == (facet)) ? (ridge)->bottom : (ridge)->top)
 
 /*----------------------------------
 
   getid_(p)
     return int ID for facet, ridge, or vertex
     return -1 if NULL
 */
 #define getid_(p)       ((p) ? (int)((p)->id) : -1)
 
 /*============== FORALL macros ===================*/
 
 /*----------------------------------
 
   FORALLfacets { ... }
     assign 'facet' to each facet in qh.facet_list
 
   notes:
     uses 'facetT *facet;'
     assumes last facet is a sentinel
     assumes qh defined
 
   see:
     FORALLfacet_( facetlist )
 */
 #define FORALLfacets for (facet=qh->facet_list;facet && facet->next;facet=facet->next)
 
 /*----------------------------------
 
   FORALLpoints { ... }
     assign 'point' to each point in qh.first_point, qh.num_points
 
   notes:
     assumes qh defined
 
   declare:
     coordT *point, *pointtemp;
 */
 #define FORALLpoints FORALLpoint_(qh, qh->first_point, qh->num_points)
 
 /*----------------------------------
 
   FORALLpoint_( qh, points, num) { ... }
     assign 'point' to each point in points array of num points
 
   declare:
     coordT *point, *pointtemp;
 */
 #define FORALLpoint_(qh, points, num) for (point= (points), \
       pointtemp= (points)+qh->hull_dim*(num); point < pointtemp; point += qh->hull_dim)
 
 /*----------------------------------
 
   FORALLvertices { ... }
     assign 'vertex' to each vertex in qh.vertex_list
 
   declare:
     vertexT *vertex;
 
   notes:
     assumes qh.vertex_list terminated with a sentinel
     assumes qh defined
 */
 #define FORALLvertices for (vertex=qh->vertex_list;vertex && vertex->next;vertex= vertex->next)
 
 /*----------------------------------
 
   FOREACHfacet_( facets ) { ... }
     assign 'facet' to each facet in facets
 
   declare:
     facetT *facet, **facetp;
 
   see:
-    FOREACHsetelement_
+    FOREACHsetelement_
 */
 #define FOREACHfacet_(facets)    FOREACHsetelement_(facetT, facets, facet)
 
 /*----------------------------------
 
   FOREACHneighbor_( facet ) { ... }
     assign 'neighbor' to each neighbor in facet->neighbors
 
   FOREACHneighbor_( vertex ) { ... }
     assign 'neighbor' to each neighbor in vertex->neighbors
 
   declare:
     facetT *neighbor, **neighborp;
 
   see:
-    FOREACHsetelement_
+    FOREACHsetelement_
 */
 #define FOREACHneighbor_(facet)  FOREACHsetelement_(facetT, facet->neighbors, neighbor)
 
 /*----------------------------------
 
   FOREACHpoint_( points ) { ... }
     assign 'point' to each point in points set
 
   declare:
     pointT *point, **pointp;
 
   see:
-    FOREACHsetelement_
+    FOREACHsetelement_
 */
 #define FOREACHpoint_(points)    FOREACHsetelement_(pointT, points, point)
 
 /*----------------------------------
 
   FOREACHridge_( ridges ) { ... }
     assign 'ridge' to each ridge in ridges set
 
   declare:
     ridgeT *ridge, **ridgep;
 
   see:
-    FOREACHsetelement_
+    FOREACHsetelement_
 */
 #define FOREACHridge_(ridges)    FOREACHsetelement_(ridgeT, ridges, ridge)
 
 /*----------------------------------
 
   FOREACHvertex_( vertices ) { ... }
     assign 'vertex' to each vertex in vertices set
 
   declare:
     vertexT *vertex, **vertexp;
 
   see:
-    FOREACHsetelement_
+    FOREACHsetelement_
 */
 #define FOREACHvertex_(vertices) FOREACHsetelement_(vertexT, vertices,vertex)
 
 /*----------------------------------
 
   FOREACHfacet_i_( qh, facets ) { ... }
     assign 'facet' and 'facet_i' for each facet in facets set
 
   declare:
     facetT *facet;
     int     facet_n, facet_i;
 
   see:
-    FOREACHsetelement_i_
+    FOREACHsetelement_i_
 */
 #define FOREACHfacet_i_(qh, facets)    FOREACHsetelement_i_(qh, facetT, facets, facet)
 
 /*----------------------------------
 
   FOREACHneighbor_i_( qh, facet ) { ... }
     assign 'neighbor' and 'neighbor_i' for each neighbor in facet->neighbors
 
   FOREACHneighbor_i_( qh, vertex ) { ... }
     assign 'neighbor' and 'neighbor_i' for each neighbor in vertex->neighbors
 
   declare:
     facetT *neighbor;
     int     neighbor_n, neighbor_i;
 
   see:
-    FOREACHsetelement_i_
+    FOREACHsetelement_i_
 */
 #define FOREACHneighbor_i_(qh, facet)  FOREACHsetelement_i_(qh, facetT, facet->neighbors, neighbor)
 
 /*----------------------------------
 
   FOREACHpoint_i_( qh, points ) { ... }
     assign 'point' and 'point_i' for each point in points set
 
   declare:
     pointT *point;
     int     point_n, point_i;
 
   see:
-    FOREACHsetelement_i_
+    FOREACHsetelement_i_
 */
 #define FOREACHpoint_i_(qh, points)    FOREACHsetelement_i_(qh, pointT, points, point)
 
 /*----------------------------------
 
   FOREACHridge_i_( qh, ridges ) { ... }
     assign 'ridge' and 'ridge_i' for each ridge in ridges set
 
   declare:
     ridgeT *ridge;
     int     ridge_n, ridge_i;
 
   see:
-    FOREACHsetelement_i_
+    FOREACHsetelement_i_
 */
 #define FOREACHridge_i_(qh, ridges)    FOREACHsetelement_i_(qh, ridgeT, ridges, ridge)
 
 /*----------------------------------
 
   FOREACHvertex_i_( qh, vertices ) { ... }
     assign 'vertex' and 'vertex_i' for each vertex in vertices set
 
   declare:
     vertexT *vertex;
     int     vertex_n, vertex_i;
 
   see:
-    FOREACHsetelement_i_
+    FOREACHsetelement_i_
 */
 #define FOREACHvertex_i_(qh, vertices) FOREACHsetelement_i_(qh, vertexT, vertices,vertex)
 
-/********* -libqhull.c prototypes (duplicated from qhull_r.h) **********************/
+/********* -libqhull_r.c prototypes (duplicated from qhull_ra.h) **********************/
 
 void    qh_qhull(qhT *qh);
 boolT   qh_addpoint(qhT *qh, pointT *furthest, facetT *facet, boolT checkdist);
 void    qh_printsummary(qhT *qh, FILE *fp);
 
 /********* -user.c prototypes (alphabetical) **********************/
 
 void    qh_errexit(qhT *qh, int exitcode, facetT *facet, ridgeT *ridge);
 void    qh_errprint(qhT *qh, const char* string, facetT *atfacet, facetT *otherfacet, ridgeT *atridge, vertexT *atvertex);
 int     qh_new_qhull(qhT *qh, int dim, int numpoints, coordT *points, boolT ismalloc,
                 char *qhull_cmd, FILE *outfile, FILE *errfile);
 void    qh_printfacetlist(qhT *qh, facetT *facetlist, setT *facets, boolT printall);
 void    qh_printhelp_degenerate(qhT *qh, FILE *fp);
 void    qh_printhelp_narrowhull(qhT *qh, FILE *fp, realT minangle);
 void    qh_printhelp_singular(qhT *qh, FILE *fp);
 void    qh_user_memsizes(qhT *qh);
 
-/********* -usermem.c prototypes (alphabetical) **********************/
+/********* -usermem_r.c prototypes (alphabetical) **********************/
 void    qh_exit(int exitcode);
 void    qh_free(void *mem);
 void   *qh_malloc(size_t size);
 
-/********* -userprintf.c and userprintf_rbox.c prototypes **********************/
+/********* -userprintf_r.c and userprintf_rbox_r.c prototypes **********************/
 void    qh_fprintf(qhT *qh, FILE *fp, int msgcode, const char *fmt, ... );
 void    qh_fprintf_rbox(qhT *qh, FILE *fp, int msgcode, const char *fmt, ... );
 
-/***** -geom.c/geom2.c/random.c prototypes (duplicated from geom.h, random.h) ****************/
+/***** -geom_r.c/geom2_r.c/random_r.c prototypes (duplicated from geom_r.h, random_r.h) ****************/
 
 facetT *qh_findbest(qhT *qh, pointT *point, facetT *startfacet,
                      boolT bestoutside, boolT newfacets, boolT noupper,
                      realT *dist, boolT *isoutside, int *numpart);
 facetT *qh_findbestnew(qhT *qh, pointT *point, facetT *startfacet,
                      realT *dist, boolT bestoutside, boolT *isoutside, int *numpart);
 boolT   qh_gram_schmidt(qhT *qh, int dim, realT **rows);
 void    qh_outerinner(qhT *qh, facetT *facet, realT *outerplane, realT *innerplane);
 void    qh_printsummary(qhT *qh, FILE *fp);
 void    qh_projectinput(qhT *qh);
 void    qh_randommatrix(qhT *qh, realT *buffer, int dim, realT **row);
 void    qh_rotateinput(qhT *qh, realT **rows);
 void    qh_scaleinput(qhT *qh);
 void    qh_setdelaunay(qhT *qh, int dim, int count, pointT *points);
 coordT  *qh_sethalfspace_all(qhT *qh, int dim, int count, coordT *halfspaces, pointT *feasible);
 
-/***** -global.c prototypes (alphabetical) ***********************/
+/***** -global_r.c prototypes (alphabetical) ***********************/
 
 unsigned long qh_clock(qhT *qh);
 void    qh_checkflags(qhT *qh, char *command, char *hiddenflags);
 void    qh_clear_outputflags(qhT *qh);
 void    qh_freebuffers(qhT *qh);
 void    qh_freeqhull(qhT *qh, boolT allmem);
 void    qh_init_A(qhT *qh, FILE *infile, FILE *outfile, FILE *errfile, int argc, char *argv[]);
 void    qh_init_B(qhT *qh, coordT *points, int numpoints, int dim, boolT ismalloc);
 void    qh_init_qhull_command(qhT *qh, int argc, char *argv[]);
 void    qh_initbuffers(qhT *qh, coordT *points, int numpoints, int dim, boolT ismalloc);
 void    qh_initflags(qhT *qh, char *command);
 void    qh_initqhull_buffers(qhT *qh);
 void    qh_initqhull_globals(qhT *qh, coordT *points, int numpoints, int dim, boolT ismalloc);
 void    qh_initqhull_mem(qhT *qh);
 void    qh_initqhull_outputflags(qhT *qh);
 void    qh_initqhull_start(qhT *qh, FILE *infile, FILE *outfile, FILE *errfile);
 void    qh_initqhull_start2(qhT *qh, FILE *infile, FILE *outfile, FILE *errfile);
 void    qh_initthresholds(qhT *qh, char *command);
 void    qh_option(qhT *qh, const char *option, int *i, realT *r);
 
-/***** -io.c prototypes (duplicated from io.h) ***********************/
+/***** -io_r.c prototypes (duplicated from io_r.h) ***********************/
 
 void    qh_dfacet(qhT *qh, unsigned id);
 void    qh_dvertex(qhT *qh, unsigned id);
 void    qh_printneighborhood(qhT *qh, FILE *fp, qh_PRINT format, facetT *facetA, facetT *facetB, boolT printall);
 void    qh_produce_output(qhT *qh);
 coordT *qh_readpoints(qhT *qh, int *numpoints, int *dimension, boolT *ismalloc);
 
 
-/********* -mem.c prototypes (duplicated from mem.h) **********************/
+/********* -mem_r.c prototypes (duplicated from mem_r.h) **********************/
 
 void qh_meminit(qhT *qh, FILE *ferr);
 void qh_memfreeshort(qhT *qh, int *curlong, int *totlong);
 
-/********* -poly.c/poly2.c prototypes (duplicated from poly.h) **********************/
+/********* -poly_r.c/poly2_r.c prototypes (duplicated from poly_r.h) **********************/
 
 void    qh_check_output(qhT *qh);
 void    qh_check_points(qhT *qh);
 setT   *qh_facetvertices(qhT *qh, facetT *facetlist, setT *facets, boolT allfacets);
 facetT *qh_findbestfacet(qhT *qh, pointT *point, boolT bestoutside,
            realT *bestdist, boolT *isoutside);
 vertexT *qh_nearvertex(qhT *qh, facetT *facet, pointT *point, realT *bestdistp);
 pointT *qh_point(qhT *qh, int id);
 setT   *qh_pointfacet(qhT *qh /*qh.facet_list*/);
 int     qh_pointid(qhT *qh, pointT *point);
 setT   *qh_pointvertex(qhT *qh /*qh.facet_list*/);
 void    qh_setvoronoi_all(qhT *qh);
 void    qh_triangulate(qhT *qh /*qh.facet_list*/);
 
-/********* -rboxpoints.c prototypes **********************/
+/********* -rboxpoints_r.c prototypes **********************/
 int     qh_rboxpoints(qhT *qh, char* rbox_command);
 void    qh_errexit_rbox(qhT *qh, int exitcode);
 
-/********* -stat.c prototypes (duplicated from stat.h) **********************/
+/********* -stat_r.c prototypes (duplicated from stat_r.h) **********************/
 
 void    qh_collectstatistics(qhT *qh);
 void    qh_printallstatistics(qhT *qh, FILE *fp, const char *string);
 
 #endif /* qhDEFlibqhull */
diff --git a/src/libqhullr/mem_r.c b/src/libqhullr/mem_r.c
index 2ce3d60..23eef56 100644
--- a/src/libqhullr/mem_r.c
+++ b/src/libqhullr/mem_r.c
@@ -1,529 +1,530 @@
 /*
  ---------------------------------
 
-  mem.c
+  mem_r.c
     memory management routines for qhull
 
-  See libqhull/mem.c for a standalone program.
+  See libqhull/mem_r.c for a standalone program.
 
   To initialize memory:
 
     qh_meminit(qh, stderr);
     qh_meminitbuffers(qh, qh->IStracing, qh_MEMalign, 7, qh_MEMbufsize,qh_MEMinitbuf);
     qh_memsize(qh, (int)sizeof(facetT));
     qh_memsize(qh, (int)sizeof(facetT));
     ...
     qh_memsetup(qh);
 
   To free up all memory buffers:
     qh_memfreeshort(qh, &curlong, &totlong);
 
   if qh_NOmem,
     malloc/free is used instead of mem.c
 
   notes:
     uses Quickfit algorithm (freelists for commonly allocated sizes)
     assumes small sizes for freelists (it discards the tail of memory buffers)
 
   see:
-    qh-mem.htm and mem.h
-    global.c (qh_initbuffers) for an example of using mem.c
+    qh-mem.htm and mem_r.h
+    global_r.c (qh_initbuffers) for an example of using mem_r.c
 
   Copyright (c) 1993-2014 The Geometry Center.
-  $Id: //main/2011/qhull/src/libqhullr/mem_r.c#2 $$Change: 1645 $
-  $DateTime: 2014/01/15 12:51:30 $$Author: bbarber $
+  $Id: //main/2011/qhull/src/libqhullr/mem_r.c#7 $$Change: 1797 $
+  $DateTime: 2014/12/15 17:23:41 $$Author: bbarber $
 */
 
 #include "mem_r.h"
 #include "libqhull_r.h"
 
 #include 
 #include 
 #include 
 
 #ifndef qh_NOmem
 
 /*============= internal functions ==============*/
 
 static int qh_intcompare(const void *i, const void *j);
 
 /*========== functions in alphabetical order ======== */
 
 /*---------------------------------
 
   qh_intcompare( i, j )
     used by qsort and bsearch to compare two integers
 */
 static int qh_intcompare(const void *i, const void *j) {
   return(*((const int *)i) - *((const int *)j));
 } /* intcompare */
 
 
 /*----------------------------------
 
   qh_memalloc( qh, insize )
     returns object of insize bytes
     qhmem is the global memory structure
 
   returns:
     pointer to allocated memory
     errors if insufficient memory
 
   notes:
     use explicit type conversion to avoid type warnings on some compilers
     actual object may be larger than insize
     use qh_memalloc_() for inline code for quick allocations
     logs allocations if 'T5'
 
   design:
     if size < qh->qhmem.LASTsize
       if qh->qhmem.freelists[size] non-empty
         return first object on freelist
       else
         round up request to size of qh->qhmem.freelists[size]
         allocate new allocation buffer if necessary
         allocate object from allocation buffer
     else
       allocate object with qh_malloc() in user.c
 */
 void *qh_memalloc(qhT *qh, int insize) {
   void **freelistp, *newbuffer;
   int idx, size, n;
   int outsize, bufsize;
   void *object;
 
   if (insize<0) {
       qh_fprintf(qh, qh->qhmem.ferr, 6235, "qhull error (qh_memalloc): negative request size (%d).  Did int overflow due to high-D?\n", insize); /* WARN64 */
       qh_errexit(qh, qhmem_ERRmem, NULL, NULL);
   }
   if (insize>=0 && insize <= qh->qhmem.LASTsize) {
     idx= qh->qhmem.indextable[insize];
     outsize= qh->qhmem.sizetable[idx];
     qh->qhmem.totshort += outsize;
     freelistp= qh->qhmem.freelists+idx;
     if ((object= *freelistp)) {
       qh->qhmem.cntquick++;
       qh->qhmem.totfree -= outsize;
       *freelistp= *((void **)*freelistp);  /* replace freelist with next object */
 #ifdef qh_TRACEshort
       n= qh->qhmem.cntshort+qh->qhmem.cntquick+qh->qhmem.freeshort;
       if (qh->qhmem.IStracing >= 5)
           qh_fprintf(qh, qh->qhmem.ferr, 8141, "qh_mem %p n %8d alloc quick: %d bytes (tot %d cnt %d)\n", object, n, outsize, qh->qhmem.totshort, qh->qhmem.cntshort+qh->qhmem.cntquick-qh->qhmem.freeshort);
 #endif
       return(object);
     }else {
       qh->qhmem.cntshort++;
       if (outsize > qh->qhmem.freesize) {
         qh->qhmem.totdropped += qh->qhmem.freesize;
         if (!qh->qhmem.curbuffer)
           bufsize= qh->qhmem.BUFinit;
         else
           bufsize= qh->qhmem.BUFsize;
         if (!(newbuffer= qh_malloc((size_t)bufsize))) {
           qh_fprintf(qh, qh->qhmem.ferr, 6080, "qhull error (qh_memalloc): insufficient memory to allocate short memory buffer (%d bytes)\n", bufsize);
           qh_errexit(qh, qhmem_ERRmem, NULL, NULL);
         }
         *((void **)newbuffer)= qh->qhmem.curbuffer;  /* prepend newbuffer to curbuffer
                                                     list */
         qh->qhmem.curbuffer= newbuffer;
         size= (sizeof(void **) + qh->qhmem.ALIGNmask) & ~qh->qhmem.ALIGNmask;
         qh->qhmem.freemem= (void *)((char *)newbuffer+size);
         qh->qhmem.freesize= bufsize - size;
         qh->qhmem.totbuffer += bufsize - size; /* easier to check */
         /* Periodically test totbuffer.  It matches at beginning and exit of every call */
         n = qh->qhmem.totshort + qh->qhmem.totfree + qh->qhmem.totdropped + qh->qhmem.freesize - outsize;
         if (qh->qhmem.totbuffer != n) {
             qh_fprintf(qh, qh->qhmem.ferr, 6212, "qh_memalloc internal error: short totbuffer %d != totshort+totfree... %d\n", qh->qhmem.totbuffer, n);
             qh_errexit(qh, qhmem_ERRmem, NULL, NULL);
         }
       }
       object= qh->qhmem.freemem;
       qh->qhmem.freemem= (void *)((char *)qh->qhmem.freemem + outsize);
       qh->qhmem.freesize -= outsize;
       qh->qhmem.totunused += outsize - insize;
 #ifdef qh_TRACEshort
       n= qh->qhmem.cntshort+qh->qhmem.cntquick+qh->qhmem.freeshort;
       if (qh->qhmem.IStracing >= 5)
           qh_fprintf(qh, qh->qhmem.ferr, 8140, "qh_mem %p n %8d alloc short: %d bytes (tot %d cnt %d)\n", object, n, outsize, qh->qhmem.totshort, qh->qhmem.cntshort+qh->qhmem.cntquick-qh->qhmem.freeshort);
 #endif
       return object;
     }
   }else {                     /* long allocation */
     if (!qh->qhmem.indextable) {
       qh_fprintf(qh, qh->qhmem.ferr, 6081, "qhull internal error (qh_memalloc): qhmem has not been initialized.\n");
       qh_errexit(qh, qhmem_ERRqhull, NULL, NULL);
     }
     outsize= insize;
     qh->qhmem.cntlong++;
     qh->qhmem.totlong += outsize;
     if (qh->qhmem.maxlong < qh->qhmem.totlong)
       qh->qhmem.maxlong= qh->qhmem.totlong;
     if (!(object= qh_malloc((size_t)outsize))) {
       qh_fprintf(qh, qh->qhmem.ferr, 6082, "qhull error (qh_memalloc): insufficient memory to allocate %d bytes\n", outsize);
       qh_errexit(qh, qhmem_ERRmem, NULL, NULL);
     }
     if (qh->qhmem.IStracing >= 5)
       qh_fprintf(qh, qh->qhmem.ferr, 8057, "qh_mem %p n %8d alloc long: %d bytes (tot %d cnt %d)\n", object, qh->qhmem.cntlong+qh->qhmem.freelong, outsize, qh->qhmem.totlong, qh->qhmem.cntlong-qh->qhmem.freelong);
   }
   return(object);
 } /* memalloc */
 
 
 /*----------------------------------
 
   qh_memfree(qh, object, insize )
     free up an object of size bytes
     size is insize from qh_memalloc
 
   notes:
     object may be NULL
     type checking warns if using (void **)object
     use qh_memfree_() for quick free's of small objects
 
   design:
     if size <= qh->qhmem.LASTsize
       append object to corresponding freelist
     else
       call qh_free(object)
 */
 void qh_memfree(qhT *qh, void *object, int insize) {
   void **freelistp;
   int idx, outsize;
 
   if (!object)
     return;
   if (insize <= qh->qhmem.LASTsize) {
     qh->qhmem.freeshort++;
     idx= qh->qhmem.indextable[insize];
     outsize= qh->qhmem.sizetable[idx];
     qh->qhmem.totfree += outsize;
     qh->qhmem.totshort -= outsize;
     freelistp= qh->qhmem.freelists + idx;
     *((void **)object)= *freelistp;
     *freelistp= object;
 #ifdef qh_TRACEshort
     idx= qh->qhmem.cntshort+qh->qhmem.cntquick+qh->qhmem.freeshort;
     if (qh->qhmem.IStracing >= 5)
         qh_fprintf(qh, qh->qhmem.ferr, 8142, "qh_mem %p n %8d free short: %d bytes (tot %d cnt %d)\n", object, idx, outsize, qh->qhmem.totshort, qh->qhmem.cntshort+qh->qhmem.cntquick-qh->qhmem.freeshort);
 #endif
   }else {
     qh->qhmem.freelong++;
     qh->qhmem.totlong -= insize;
     qh_free(object);
     if (qh->qhmem.IStracing >= 5)
       qh_fprintf(qh, qh->qhmem.ferr, 8058, "qh_mem %p n %8d free long: %d bytes (tot %d cnt %d)\n", object, qh->qhmem.cntlong+qh->qhmem.freelong, insize, qh->qhmem.totlong, qh->qhmem.cntlong-qh->qhmem.freelong);
   }
 } /* memfree */
 
 
 /*---------------------------------
 
   qh_memfreeshort(qh, curlong, totlong )
     frees up all short and qhmem memory allocations
 
   returns:
     number and size of current long allocations
 
   see:
     qh_freeqhull(qh, allMem)
     qh_memtotal(qh, curlong, totlong, curshort, totshort, maxlong, totbuffer);
 */
 void qh_memfreeshort(qhT *qh, int *curlong, int *totlong) {
   void *buffer, *nextbuffer;
   FILE *ferr;
 
   *curlong= qh->qhmem.cntlong - qh->qhmem.freelong;
   *totlong= qh->qhmem.totlong;
   for (buffer= qh->qhmem.curbuffer; buffer; buffer= nextbuffer) {
     nextbuffer= *((void **) buffer);
     qh_free(buffer);
   }
   qh->qhmem.curbuffer= NULL;
   if (qh->qhmem.LASTsize) {
     qh_free(qh->qhmem.indextable);
     qh_free(qh->qhmem.freelists);
     qh_free(qh->qhmem.sizetable);
   }
   ferr= qh->qhmem.ferr;
   memset((char *)&qh->qhmem, 0, sizeof(qh->qhmem));  /* every field is 0, FALSE, NULL */
   qh->qhmem.ferr= ferr;
 } /* memfreeshort */
 
 
 /*----------------------------------
 
   qh_meminit(qh, ferr )
     initialize qhmem and test sizeof( void*)
+    Does not throw errors.  qh_exit on failure
 */
 void qh_meminit(qhT *qh, FILE *ferr) {
 
   memset((char *)&qh->qhmem, 0, sizeof(qh->qhmem));  /* every field is 0, FALSE, NULL */
   if (ferr)
       qh->qhmem.ferr= ferr;
   else
       qh->qhmem.ferr= stderr;
   if (sizeof(void*) < sizeof(int)) {
     qh_fprintf(qh, qh->qhmem.ferr, 6083, "qhull internal error (qh_meminit): sizeof(void*) %d < sizeof(int) %d.  qset.c will not work\n", (int)sizeof(void*), (int)sizeof(int));
     qh_exit(qhmem_ERRqhull);  /* can not use qh_errexit() */
   }
   if (sizeof(void*) > sizeof(ptr_intT)) {
       qh_fprintf(qh, qh->qhmem.ferr, 6084, "qhull internal error (qh_meminit): sizeof(void*) %d > sizeof(ptr_intT) %d. Change ptr_intT in mem.h to 'long long'\n", (int)sizeof(void*), (int)sizeof(ptr_intT));
       qh_exit(qhmem_ERRqhull);  /* can not use qh_errexit() */
   }
 } /* meminit */
 
 /*---------------------------------
 
   qh_meminitbuffers(qh, tracelevel, alignment, numsizes, bufsize, bufinit )
     initialize qhmem
     if tracelevel >= 5, trace memory allocations
     alignment= desired address alignment for memory allocations
     numsizes= number of freelists
     bufsize=  size of additional memory buffers for short allocations
     bufinit=  size of initial memory buffer for short allocations
 */
 void qh_meminitbuffers(qhT *qh, int tracelevel, int alignment, int numsizes, int bufsize, int bufinit) {
 
   qh->qhmem.IStracing= tracelevel;
   qh->qhmem.NUMsizes= numsizes;
   qh->qhmem.BUFsize= bufsize;
   qh->qhmem.BUFinit= bufinit;
   qh->qhmem.ALIGNmask= alignment-1;
   if (qh->qhmem.ALIGNmask & ~qh->qhmem.ALIGNmask) {
     qh_fprintf(qh, qh->qhmem.ferr, 6085, "qhull internal error (qh_meminit): memory alignment %d is not a power of 2\n", alignment);
     qh_errexit(qh, qhmem_ERRqhull, NULL, NULL);
   }
   qh->qhmem.sizetable= (int *) calloc((size_t)numsizes, sizeof(int));
   qh->qhmem.freelists= (void **) calloc((size_t)numsizes, sizeof(void *));
   if (!qh->qhmem.sizetable || !qh->qhmem.freelists) {
     qh_fprintf(qh, qh->qhmem.ferr, 6086, "qhull error (qh_meminit): insufficient memory\n");
     qh_errexit(qh, qhmem_ERRmem, NULL, NULL);
   }
   if (qh->qhmem.IStracing >= 1)
     qh_fprintf(qh, qh->qhmem.ferr, 8059, "qh_meminitbuffers: memory initialized with alignment %d\n", alignment);
 } /* meminitbuffers */
 
 /*---------------------------------
 
   qh_memsetup(qh)
     set up memory after running memsize()
 */
 void qh_memsetup(qhT *qh) {
   int k,i;
 
   qsort(qh->qhmem.sizetable, (size_t)qh->qhmem.TABLEsize, sizeof(int), qh_intcompare);
   qh->qhmem.LASTsize= qh->qhmem.sizetable[qh->qhmem.TABLEsize-1];
   if(qh->qhmem.LASTsize >= qh->qhmem.BUFsize || qh->qhmem.LASTsize >= qh->qhmem.BUFinit) {
     qh_fprintf(qh, qh->qhmem.ferr, 6087, "qhull error (qh_memsetup): largest mem size %d is >= buffer size %d or initial buffer size %d\n",
             qh->qhmem.LASTsize, qh->qhmem.BUFsize, qh->qhmem.BUFinit);
     qh_errexit(qh, qhmem_ERRmem, NULL, NULL);
   }
   if (!(qh->qhmem.indextable= (int *)qh_malloc((qh->qhmem.LASTsize+1) * sizeof(int)))) {
     qh_fprintf(qh, qh->qhmem.ferr, 6088, "qhull error (qh_memsetup): insufficient memory\n");
     qh_errexit(qh, qhmem_ERRmem, NULL, NULL);
   }
   for (k=qh->qhmem.LASTsize+1; k--; )
     qh->qhmem.indextable[k]= k;
   i= 0;
   for (k=0; k <= qh->qhmem.LASTsize; k++) {
     if (qh->qhmem.indextable[k] <= qh->qhmem.sizetable[i])
       qh->qhmem.indextable[k]= i;
     else
       qh->qhmem.indextable[k]= ++i;
   }
 } /* memsetup */
 
 /*---------------------------------
 
   qh_memsize(qh, size )
     define a free list for this size
 */
 void qh_memsize(qhT *qh, int size) {
   int k;
 
   if(qh->qhmem.LASTsize) {
     qh_fprintf(qh, qh->qhmem.ferr, 6089, "qhull error (qh_memsize): called after qhmem_setup\n");
     qh_errexit(qh, qhmem_ERRqhull, NULL, NULL);
   }
   size= (size + qh->qhmem.ALIGNmask) & ~qh->qhmem.ALIGNmask;
   for (k=qh->qhmem.TABLEsize; k--; ) {
     if (qh->qhmem.sizetable[k] == size)
       return;
   }
   if (qh->qhmem.TABLEsize < qh->qhmem.NUMsizes)
     qh->qhmem.sizetable[qh->qhmem.TABLEsize++]= size;
   else
     qh_fprintf(qh, qh->qhmem.ferr, 7060, "qhull warning (memsize): free list table has room for only %d sizes\n", qh->qhmem.NUMsizes);
 } /* memsize */
 
 
 /*---------------------------------
 
   qh_memstatistics(qh, fp )
     print out memory statistics
 
     Verifies that qh->qhmem.totfree == sum of freelists
 */
 void qh_memstatistics(qhT *qh, FILE *fp) {
   int i, count, totfree= 0;
   void *object;
 
   for (i=0; i < qh->qhmem.TABLEsize; i++) {
     count=0;
     for (object= qh->qhmem.freelists[i]; object; object= *((void **)object))
       count++;
     totfree += qh->qhmem.sizetable[i] * count;
   }
   if (totfree != qh->qhmem.totfree) {
       qh_fprintf(qh, qh->qhmem.ferr, 6211, "qh_memstatistics internal error: totfree %d not equal to freelist total %d\n", qh->qhmem.totfree, totfree);
       qh_errexit(qh, qhmem_ERRqhull, NULL, NULL);
   }
   qh_fprintf(qh, fp, 9278, "\nmemory statistics:\n\
 %7d quick allocations\n\
 %7d short allocations\n\
 %7d long allocations\n\
 %7d short frees\n\
 %7d long frees\n\
 %7d bytes of short memory in use\n\
 %7d bytes of short memory in freelists\n\
 %7d bytes of dropped short memory\n\
 %7d bytes of unused short memory (estimated)\n\
 %7d bytes of long memory allocated (max, except for input)\n\
 %7d bytes of long memory in use (in %d pieces)\n\
 %7d bytes of short memory buffers (minus links)\n\
 %7d bytes per short memory buffer (initially %d bytes)\n",
            qh->qhmem.cntquick, qh->qhmem.cntshort, qh->qhmem.cntlong,
            qh->qhmem.freeshort, qh->qhmem.freelong,
            qh->qhmem.totshort, qh->qhmem.totfree,
            qh->qhmem.totdropped + qh->qhmem.freesize, qh->qhmem.totunused,
            qh->qhmem.maxlong, qh->qhmem.totlong, qh->qhmem.cntlong - qh->qhmem.freelong,
            qh->qhmem.totbuffer, qh->qhmem.BUFsize, qh->qhmem.BUFinit);
   if (qh->qhmem.cntlarger) {
     qh_fprintf(qh, fp, 9279, "%7d calls to qh_setlarger\n%7.2g     average copy size\n",
            qh->qhmem.cntlarger, ((float)qh->qhmem.totlarger)/(float)qh->qhmem.cntlarger);
     qh_fprintf(qh, fp, 9280, "  freelists(bytes->count):");
   }
   for (i=0; i < qh->qhmem.TABLEsize; i++) {
     count=0;
     for (object= qh->qhmem.freelists[i]; object; object= *((void **)object))
       count++;
     qh_fprintf(qh, fp, 9281, " %d->%d", qh->qhmem.sizetable[i], count);
   }
   qh_fprintf(qh, fp, 9282, "\n\n");
 } /* memstatistics */
 
 
 /*---------------------------------
 
   qh_NOmem
     turn off quick-fit memory allocation
 
   notes:
     uses qh_malloc() and qh_free() instead
 */
 #else /* qh_NOmem */
 
 void *qh_memalloc(qhT *qh, int insize) {
   void *object;
 
   if (!(object= qh_malloc((size_t)insize))) {
     qh_fprintf(qh, qh->qhmem.ferr, 6090, "qhull error (qh_memalloc): insufficient memory\n");
     qh_errexit(qh, qhmem_ERRmem, NULL, NULL);
   }
   qh->qhmem.cntlong++;
   qh->qhmem.totlong += insize;
   if (qh->qhmem.maxlong < qh->qhmem.totlong)
       qh->qhmem.maxlong= qh->qhmem.totlong;
   if (qh->qhmem.IStracing >= 5)
     qh_fprintf(qh, qh->qhmem.ferr, 8060, "qh_mem %p n %8d alloc long: %d bytes (tot %d cnt %d)\n", object, qh->qhmem.cntlong+qh->qhmem.freelong, insize, qh->qhmem.totlong, qh->qhmem.cntlong-qh->qhmem.freelong);
   return object;
 }
 
 void qh_memfree(qhT *qh, void *object, int insize) {
 
   if (!object)
     return;
   qh_free(object);
   qh->qhmem.freelong++;
   qh->qhmem.totlong -= insize;
   if (qh->qhmem.IStracing >= 5)
     qh_fprintf(qh, qh->qhmem.ferr, 8061, "qh_mem %p n %8d free long: %d bytes (tot %d cnt %d)\n", object, qh->qhmem.cntlong+qh->qhmem.freelong, insize, qh->qhmem.totlong, qh->qhmem.cntlong-qh->qhmem.freelong);
 }
 
 void qh_memfreeshort(qhT *qh, int *curlong, int *totlong) {
   *totlong= qh->qhmem.totlong;
   *curlong= qh->qhmem.cntlong - qh->qhmem.freelong;
   memset((char *)&qh->qhmem, 0, sizeof(qh->qhmem));  /* every field is 0, FALSE, NULL */
 }
 
 void qh_meminit(qhT *qh, FILE *ferr) {
 
   memset((char *)&qh->qhmem, 0, sizeof(qh->qhmem));  /* every field is 0, FALSE, NULL */
   if (ferr)
       qh->qhmem.ferr= ferr;
   else
       qh->qhmem.ferr= stderr;
   if (sizeof(void*) < sizeof(int)) {
     qh_fprintf(qh, qh->qhmem.ferr, 6091, "qhull internal error (qh_meminit): sizeof(void*) %d < sizeof(int) %d.  qset.c will not work\n", (int)sizeof(void*), (int)sizeof(int));
     qh_errexit(qh, qhmem_ERRqhull, NULL, NULL);
   }
 }
 
 void qh_meminitbuffers(qhT *qh, int tracelevel, int alignment, int numsizes, int bufsize, int bufinit) {
 
   qh->qhmem.IStracing= tracelevel;
 }
 
 void qh_memsetup(qhT *qh) {
 
 }
 
 void qh_memsize(qhT *qh, int size) {
 
 }
 
 void qh_memstatistics(qhT *qh, FILE *fp) {
 
   qh_fprintf(qh, fp, 9409, "\nmemory statistics:\n\
 %7d long allocations\n\
 %7d long frees\n\
 %7d bytes of long memory allocated (max, except for input)\n\
 %7d bytes of long memory in use (in %d pieces)\n",
            qh->qhmem.cntlong,
            qh->qhmem.freelong,
            qh->qhmem.maxlong, qh->qhmem.totlong, qh->qhmem.cntlong - qh->qhmem.freelong);
 }
 
 #endif /* qh_NOmem */
 
 /*---------------------------------
 
   qh_memtotal(qh, totlong, curlong, totshort, curshort, maxlong, totbuffer )
     Return the total, allocated long and short memory
 
   returns:
     Returns the total current bytes of long and short allocations
     Returns the current count of long and short allocations
     Returns the maximum long memory and total short buffer (minus one link per buffer)
-    Does not error (UsingLibQhull.cpp)
+    Does not error (for deprecated UsingLibQhull.cpp (libqhullpcpp))
 */
 void qh_memtotal(qhT *qh, int *totlong, int *curlong, int *totshort, int *curshort, int *maxlong, int *totbuffer) {
     *totlong= qh->qhmem.totlong;
     *curlong= qh->qhmem.cntlong - qh->qhmem.freelong;
     *totshort= qh->qhmem.totshort;
     *curshort= qh->qhmem.cntshort + qh->qhmem.cntquick - qh->qhmem.freeshort;
     *maxlong= qh->qhmem.maxlong;
     *totbuffer= qh->qhmem.totbuffer;
 } /* memtotlong */
 
diff --git a/src/libqhullr/mem_r.h b/src/libqhullr/mem_r.h
index 2596372..5e88985 100644
--- a/src/libqhullr/mem_r.h
+++ b/src/libqhullr/mem_r.h
@@ -1,223 +1,223 @@
 /*
  ---------------------------------
 
-   mem.h
+   mem_r.h
      prototypes for memory management functions
 
-   see qh-mem.htm, mem.c and qset.h
+   see qh-mem.htm, mem_r.c and qset_r.h
 
    for error handling, writes message and calls
      qh_errexit(qhT *qh, qhmem_ERRmem, NULL, NULL) if insufficient memory
        and
      qh_errexit(qhT *qh, qhmem_ERRqhull, NULL, NULL) otherwise
 
    Copyright (c) 1993-2014 The Geometry Center.
-   $Id: //main/2011/qhull/src/libqhullr/mem_r.h#2 $$Change: 1645 $
-   $DateTime: 2014/01/15 12:51:30 $$Author: bbarber $
+   $Id: //main/2011/qhull/src/libqhullr/mem_r.h#4 $$Change: 1797 $
+   $DateTime: 2014/12/15 17:23:41 $$Author: bbarber $
 */
 
 #ifndef qhDEFmem
 #define qhDEFmem 1
 
 #include 
 
 #ifndef DEFsetT
 #define DEFsetT 1
-typedef struct setT setT;          /* defined in qset.h */
+typedef struct setT setT;          /* defined in qset_r.h */
 #endif
 
 #ifndef DEFqhT
 #define DEFqhT 1
-typedef struct qhT qhT;          /* defined in libqhull.h */
+typedef struct qhT qhT;          /* defined in libqhull_r.h */
 #endif
 
 /*---------------------------------
 
   qh_NOmem
     turn off quick-fit memory allocation
 
   notes:
-    mem.c implements Quickfit memory allocation for about 20% time
+    mem_r.c implements Quickfit memory allocation for about 20% time
     savings.  If it fails on your machine, try to locate the
     problem, and send the answer to qhull@qhull.org.  If this can
     not be done, define qh_NOmem to use malloc/free instead.
 
    #define qh_NOmem
 */
 
 /*---------------------------------
 
 qh_TRACEshort
 Trace short and quick memory allocations at T5
 
 */
 #define qh_TRACEshort
 
 /*-------------------------------------------
     to avoid bus errors, memory allocation must consider alignment requirements.
-    malloc() automatically takes care of alignment.   Since mem.c manages
+    malloc() automatically takes care of alignment.   Since mem_r.c manages
     its own memory, we need to explicitly specify alignment in
     qh_meminitbuffers().
 
     A safe choice is sizeof(double).  sizeof(float) may be used if doubles
     do not occur in data structures and pointers are the same size.  Be careful
     of machines (e.g., DEC Alpha) with large pointers.  If gcc is available,
     use __alignof__(double) or fmax_(__alignof__(float), __alignof__(void *)).
 
    see qh_MEMalign in user.h for qhull's alignment
 */
 
-#define qhmem_ERRmem 4    /* matches qh_ERRmem in libqhull.h */
-#define qhmem_ERRqhull 5  /* matches qh_ERRqhull in libqhull.h */
+#define qhmem_ERRmem 4    /* matches qh_ERRmem in libqhull_r.h */
+#define qhmem_ERRqhull 5  /* matches qh_ERRqhull in libqhull_r.h */
 
 /*----------------------------------
 
   ptr_intT
     for casting a void * to an integer-type that holds a pointer
-    Used for integer expressions (e.g., computing qh_gethash() in poly.c)
+    Used for integer expressions (e.g., computing qh_gethash() in poly_r.c)
 
   notes:
     WARN64 -- these notes indicate 64-bit issues
     On 64-bit machines, a pointer may be larger than an 'int'.
-    qh_meminit()/mem.c checks that 'ptr_intT' holds a 'void*'
+    qh_meminit()/mem_r.c checks that 'ptr_intT' holds a 'void*'
     ptr_intT is typically a signed value, but not necessarily so
     size_t is typically unsigned, but should match the parameter type
     Qhull uses int instead of size_t except for system calls such as malloc, qsort, qh_malloc, etc.
     This matches Qt convention and is easier to work with.  
 */
 #if _MSC_VER && defined(_WIN64)
 typedef long long ptr_intT;
 #else
 typedef long ptr_intT;
 #endif
 
 /*----------------------------------
 
   qhmemT
-    global memory structure for mem.c
+    global memory structure for mem_r.c
 
  notes:
    users should ignore qhmem except for writing extensions
-   qhmem is allocated in mem.c
+   qhmem is allocated in mem_r.c
 
    qhmem could be swapable like qh and qhstat, but then
    multiple qh's and qhmem's would need to keep in synch.
    A swapable qhmem would also waste memory buffers.  As long
    as memory operations are atomic, there is no problem with
    multiple qh structures being active at the same time.
    If you need separate address spaces, you can swap the
    contents of qh->qhmem.
 */
 typedef struct qhmemT qhmemT;
 
-/* Update qhmem in mem.c if add or remove fields */
+/* Update qhmem in mem_r.c if add or remove fields */
 struct qhmemT {               /* global memory management variables */
   int      BUFsize;           /* size of memory allocation buffer */
   int      BUFinit;           /* initial size of memory allocation buffer */
   int      TABLEsize;         /* actual number of sizes in free list table */
   int      NUMsizes;          /* maximum number of sizes in free list table */
   int      LASTsize;          /* last size in free list table */
   int      ALIGNmask;         /* worst-case alignment, must be 2^n-1 */
   void   **freelists;          /* free list table, linked by offset 0 */
   int     *sizetable;         /* size of each freelist */
   int     *indextable;        /* size->index table */
   void    *curbuffer;         /* current buffer, linked by offset 0 */
   void    *freemem;           /*   free memory in curbuffer */
   int      freesize;          /*   size of freemem in bytes */
   setT    *tempstack;         /* stack of temporary memory, managed by users */
   FILE    *ferr;              /* file for reporting errors when 'qh' may be undefined */
   int      IStracing;         /* =5 if tracing memory allocations */
   int      cntquick;          /* count of quick allocations */
                               /* Note: removing statistics doesn't effect speed */
   int      cntshort;          /* count of short allocations */
   int      cntlong;           /* count of long allocations */
   int      freeshort;         /* count of short memfrees */
   int      freelong;          /* count of long memfrees */
   int      totbuffer;         /* total short memory buffers minus buffer links */
   int      totdropped;        /* total dropped memory at end of short memory buffers (e.g., freesize) */
   int      totfree;           /* total size of free, short memory on freelists */
   int      totlong;           /* total size of long memory in use */
   int      maxlong;           /*   maximum totlong */
   int      totshort;          /* total size of short memory in use */
   int      totunused;         /* total unused short memory (estimated, short size - request size of first allocations) */
   int      cntlarger;         /* count of setlarger's */
   int      totlarger;         /* total copied by setlarger */
 };
 
 
 /*==================== -macros ====================*/
 
 /*----------------------------------
 
   qh_memalloc_(qh, freelistp, insize, object, type)
     returns object of size bytes
         assumes size<=qh->qhmem.LASTsize and void **freelistp is a temp
 */
 
 #if defined qh_NOmem
 #define qh_memalloc_(qh, insize, freelistp, object, type) {\
   object= (type*)qh_memalloc(qh, insize); }
 #elif defined qh_TRACEshort
 #define qh_memalloc_(qh, insize, freelistp, object, type) {\
     freelistp= NULL; /* Avoid warnings */ \
     object= (type*)qh_memalloc(qh, insize); }
 #else /* !qh_NOmem */
 
 #define qh_memalloc_(qh, insize, freelistp, object, type) {\
   freelistp= qh->qhmem.freelists + qh->qhmem.indextable[insize];\
   if ((object= (type*)*freelistp)) {\
     qh->qhmem.totshort += qh->qhmem.sizetable[qh->qhmem.indextable[insize]]; \
     qh->qhmem.totfree -= qh->qhmem.sizetable[qh->qhmem.indextable[insize]]; \
     qh->qhmem.cntquick++;  \
     *freelistp= *((void **)*freelistp);\
   }else object= (type*)qh_memalloc(qh, insize);}
 #endif
 
 /*----------------------------------
 
   qh_memfree_(qh, object, insize, freelistp)
     free up an object
 
   notes:
     object may be NULL
     assumes size<=qh->qhmem.LASTsize and void **freelistp is a temp
 */
 #if defined qh_NOmem
 #define qh_memfree_(qh, object, insize, freelistp) {\
   qh_memfree(qh, object, insize); }
 #elif defined qh_TRACEshort
 #define qh_memfree_(qh, object, insize, freelistp) {\
     freelistp= NULL; /* Avoid warnings */ \
     qh_memfree(qh, object, insize); }
 #else /* !qh_NOmem */
 
 #define qh_memfree_(qh, object, insize, freelistp) {\
   if (object) { \
     qh->qhmem.freeshort++;\
     freelistp= qh->qhmem.freelists + qh->qhmem.indextable[insize];\
     qh->qhmem.totshort -= qh->qhmem.sizetable[qh->qhmem.indextable[insize]]; \
     qh->qhmem.totfree += qh->qhmem.sizetable[qh->qhmem.indextable[insize]]; \
     *((void **)object)= *freelistp;\
     *freelistp= object;}}
 #endif
 
 /*=============== prototypes in alphabetical order ============*/
 
 void *qh_memalloc(qhT *qh, int insize);
 void qh_memfree(qhT *qh, void *object, int insize);
 void qh_memfreeshort(qhT *qh, int *curlong, int *totlong);
 void qh_meminit(qhT *qh, FILE *ferr);
 void qh_meminitbuffers(qhT *qh, int tracelevel, int alignment, int numsizes,
                         int bufsize, int bufinit);
 void qh_memsetup(qhT *qh);
 void qh_memsize(qhT *qh, int size);
 void qh_memstatistics(qhT *qh, FILE *fp);
 void qh_memtotal(qhT *qh, int *totlong, int *curlong, int *totshort, int *curshort, int *maxlong, int *totbuffer);
 
 #endif /* qhDEFmem */
diff --git a/src/libqhullr/merge_r.c b/src/libqhullr/merge_r.c
index a4c98ff..a424e8e 100644
--- a/src/libqhullr/merge_r.c
+++ b/src/libqhullr/merge_r.c
@@ -1,3623 +1,3623 @@
 /*
  ---------------------------------
 
-   merge.c
+   merge_r.c
    merges non-convex facets
 
-   see qh-merge.htm and merge.h
+   see qh-merge.htm and merge_r.h
 
    other modules call qh_premerge() and qh_postmerge()
 
    the user may call qh_postmerge() to perform additional merges.
 
-   To remove deleted facets and vertices (qhull() in libqhull.c):
+   To remove deleted facets and vertices (qhull() in libqhull_r.c):
      qh_partitionvisible(qh, !qh_ALL, &numoutside);  // visible_list, newfacet_list
      qh_deletevisible();         // qh.visible_list
      qh_resetlists(qh, False, qh_RESETvisible);       // qh.visible_list newvertex_list newfacet_list
 
    assumes qh.CENTERtype= centrum
 
    merges occur in qh_mergefacet and in qh_mergecycle
    vertex->neighbors not set until the first merge occurs
 
    Copyright (c) 1993-2014 C.B. Barber.
-   $Id: //main/2011/qhull/src/libqhullr/merge_r.c#4 $$Change: 1663 $
-   $DateTime: 2014/01/19 17:59:16 $$Author: bbarber $
+   $Id: //main/2011/qhull/src/libqhullr/merge_r.c#6 $$Change: 1797 $
+   $DateTime: 2014/12/15 17:23:41 $$Author: bbarber $
 */
 
-#include "qhull_r.h"
+#include "qhull_ra.h"
 
 #ifndef qh_NOmerge
 
 /*===== functions(alphabetical after premerge and postmerge) ======*/
 
 /*---------------------------------
 
   qh_premerge(qh, apex, maxcentrum )
     pre-merge nonconvex facets in qh.newfacet_list for apex
     maxcentrum defines coplanar and concave (qh_test_appendmerge)
 
   returns:
     deleted facets added to qh.visible_list with facet->visible set
 
   notes:
     uses globals, qh.MERGEexact, qh.PREmerge
 
   design:
     mark duplicate ridges in qh.newfacet_list
     merge facet cycles in qh.newfacet_list
     merge duplicate ridges and concave facets in qh.newfacet_list
     check merged facet cycles for degenerate and redundant facets
     merge degenerate and redundant facets
     collect coplanar and concave facets
     merge concave, coplanar, degenerate, and redundant facets
 */
 void qh_premerge(qhT *qh, vertexT *apex, realT maxcentrum, realT maxangle) {
   boolT othermerge= False;
   facetT *newfacet;
 
   if (qh->ZEROcentrum && qh_checkzero(qh, !qh_ALL))
     return;
   trace2((qh, qh->ferr, 2008, "qh_premerge: premerge centrum %2.2g angle %2.2g for apex v%d facetlist f%d\n",
             maxcentrum, maxangle, apex->id, getid_(qh->newfacet_list)));
   if (qh->IStracing >= 4 && qh->num_facets < 50)
     qh_printlists(qh);
   qh->centrum_radius= maxcentrum;
   qh->cos_max= maxangle;
   qh->degen_mergeset= qh_settemp(qh, qh->TEMPsize);
   qh->facet_mergeset= qh_settemp(qh, qh->TEMPsize);
   if (qh->hull_dim >=3) {
     qh_mark_dupridges(qh, qh->newfacet_list); /* facet_mergeset */
     qh_mergecycle_all(qh, qh->newfacet_list, &othermerge);
     qh_forcedmerges(qh, &othermerge /* qh->facet_mergeset */);
     FORALLnew_facets {  /* test samecycle merges */
       if (!newfacet->simplicial && !newfacet->mergeridge)
         qh_degen_redundant_neighbors(qh, newfacet, NULL);
     }
     if (qh_merge_degenredundant(qh))
       othermerge= True;
   }else /* qh->hull_dim == 2 */
     qh_mergecycle_all(qh, qh->newfacet_list, &othermerge);
   qh_flippedmerges(qh, qh->newfacet_list, &othermerge);
   if (!qh->MERGEexact || zzval_(Ztotmerge)) {
     zinc_(Zpremergetot);
     qh->POSTmerging= False;
     qh_getmergeset_initial(qh, qh->newfacet_list);
     qh_all_merges(qh, othermerge, False);
   }
   qh_settempfree(qh, &qh->facet_mergeset);
   qh_settempfree(qh, &qh->degen_mergeset);
 } /* premerge */
 
 /*---------------------------------
 
   qh_postmerge(qh, reason, maxcentrum, maxangle, vneighbors )
     post-merge nonconvex facets as defined by maxcentrum and maxangle
     'reason' is for reporting progress
     if vneighbors,
       calls qh_test_vneighbors at end of qh_all_merge
     if firstmerge,
       calls qh_reducevertices before qh_getmergeset
 
   returns:
     if first call (qh.visible_list != qh.facet_list),
       builds qh.facet_newlist, qh.newvertex_list
     deleted facets added to qh.visible_list with facet->visible
     qh.visible_list == qh.facet_list
 
   notes:
 
 
   design:
     if first call
       set qh.visible_list and qh.newfacet_list to qh.facet_list
       add all facets to qh.newfacet_list
       mark non-simplicial facets, facet->newmerge
       set qh.newvertext_list to qh.vertex_list
       add all vertices to qh.newvertex_list
       if a pre-merge occured
         set vertex->delridge {will retest the ridge}
         if qh.MERGEexact
           call qh_reducevertices()
       if no pre-merging
         merge flipped facets
     determine non-convex facets
     merge all non-convex facets
 */
 void qh_postmerge(qhT *qh, const char *reason, realT maxcentrum, realT maxangle,
                       boolT vneighbors) {
   facetT *newfacet;
   boolT othermerges= False;
   vertexT *vertex;
 
   if (qh->REPORTfreq || qh->IStracing) {
     qh_buildtracing(qh, NULL, NULL);
     qh_printsummary(qh, qh->ferr);
     if (qh->PRINTstatistics)
       qh_printallstatistics(qh, qh->ferr, "reason");
     qh_fprintf(qh, qh->ferr, 8062, "\n%s with 'C%.2g' and 'A%.2g'\n",
         reason, maxcentrum, maxangle);
   }
   trace2((qh, qh->ferr, 2009, "qh_postmerge: postmerge.  test vneighbors? %d\n",
             vneighbors));
   qh->centrum_radius= maxcentrum;
   qh->cos_max= maxangle;
   qh->POSTmerging= True;
   qh->degen_mergeset= qh_settemp(qh, qh->TEMPsize);
   qh->facet_mergeset= qh_settemp(qh, qh->TEMPsize);
   if (qh->visible_list != qh->facet_list) {  /* first call */
     qh->NEWfacets= True;
     qh->visible_list= qh->newfacet_list= qh->facet_list;
     FORALLnew_facets {
       newfacet->newfacet= True;
        if (!newfacet->simplicial)
         newfacet->newmerge= True;
      zinc_(Zpostfacets);
     }
     qh->newvertex_list= qh->vertex_list;
     FORALLvertices
       vertex->newlist= True;
     if (qh->VERTEXneighbors) { /* a merge has occurred */
       FORALLvertices
         vertex->delridge= True; /* test for redundant, needed? */
       if (qh->MERGEexact) {
         if (qh->hull_dim <= qh_DIMreduceBuild)
           qh_reducevertices(qh); /* was skipped during pre-merging */
       }
     }
     if (!qh->PREmerge && !qh->MERGEexact)
       qh_flippedmerges(qh, qh->newfacet_list, &othermerges);
   }
   qh_getmergeset_initial(qh, qh->newfacet_list);
   qh_all_merges(qh, False, vneighbors);
   qh_settempfree(qh, &qh->facet_mergeset);
   qh_settempfree(qh, &qh->degen_mergeset);
 } /* post_merge */
 
 /*---------------------------------
 
   qh_all_merges(qh, othermerge, vneighbors )
     merge all non-convex facets
 
     set othermerge if already merged facets (for qh_reducevertices)
     if vneighbors
       tests vertex neighbors for convexity at end
     qh.facet_mergeset lists the non-convex ridges in qh_newfacet_list
     qh.degen_mergeset is defined
     if qh.MERGEexact && !qh.POSTmerging,
       does not merge coplanar facets
 
   returns:
     deleted facets added to qh.visible_list with facet->visible
     deleted vertices added qh.delvertex_list with vertex->delvertex
 
   notes:
     unless !qh.MERGEindependent,
       merges facets in independent sets
     uses qh.newfacet_list as argument since merges call qh_removefacet()
 
   design:
     while merges occur
       for each merge in qh.facet_mergeset
         unless one of the facets was already merged in this pass
           merge the facets
         test merged facets for additional merges
         add merges to qh.facet_mergeset
       if vertices record neighboring facets
         rename redundant vertices
           update qh.facet_mergeset
     if vneighbors ??
       tests vertex neighbors for convexity at end
 */
 void qh_all_merges(qhT *qh, boolT othermerge, boolT vneighbors) {
   facetT *facet1, *facet2;
   mergeT *merge;
   boolT wasmerge= True, isreduce;
   void **freelistp;  /* used !qh_NOmem */
   vertexT *vertex;
   mergeType mergetype;
   int numcoplanar=0, numconcave=0, numdegenredun= 0, numnewmerges= 0;
 
   trace2((qh, qh->ferr, 2010, "qh_all_merges: starting to merge facets beginning from f%d\n",
             getid_(qh->newfacet_list)));
   while (True) {
     wasmerge= False;
     while (qh_setsize(qh, qh->facet_mergeset)) {
       while ((merge= (mergeT*)qh_setdellast(qh->facet_mergeset))) {
         facet1= merge->facet1;
         facet2= merge->facet2;
         mergetype= merge->type;
         qh_memfree_(qh, merge, (int)sizeof(mergeT), freelistp);
         if (facet1->visible || facet2->visible) /*deleted facet*/
           continue;
         if ((facet1->newfacet && !facet1->tested)
                 || (facet2->newfacet && !facet2->tested)) {
           if (qh->MERGEindependent && mergetype <= MRGanglecoplanar)
             continue;      /* perform independent sets of merges */
         }
         qh_merge_nonconvex(qh, facet1, facet2, mergetype);
         numdegenredun += qh_merge_degenredundant(qh);
         numnewmerges++;
         wasmerge= True;
         if (mergetype == MRGconcave)
           numconcave++;
         else /* MRGcoplanar or MRGanglecoplanar */
           numcoplanar++;
       } /* while setdellast */
       if (qh->POSTmerging && qh->hull_dim <= qh_DIMreduceBuild
       && numnewmerges > qh_MAXnewmerges) {
         numnewmerges= 0;
         qh_reducevertices(qh);  /* otherwise large post merges too slow */
       }
       qh_getmergeset(qh, qh->newfacet_list); /* facet_mergeset */
     } /* while mergeset */
     if (qh->VERTEXneighbors) {
       isreduce= False;
       if (qh->hull_dim >=4 && qh->POSTmerging) {
         FORALLvertices
           vertex->delridge= True;
         isreduce= True;
       }
       if ((wasmerge || othermerge) && (!qh->MERGEexact || qh->POSTmerging)
           && qh->hull_dim <= qh_DIMreduceBuild) {
         othermerge= False;
         isreduce= True;
       }
       if (isreduce) {
         if (qh_reducevertices(qh)) {
           qh_getmergeset(qh, qh->newfacet_list); /* facet_mergeset */
           continue;
         }
       }
     }
     if (vneighbors && qh_test_vneighbors(qh /* qh->newfacet_list */))
       continue;
     break;
   } /* while (True) */
   if (qh->CHECKfrequently && !qh->MERGEexact) {
     qh->old_randomdist= qh->RANDOMdist;
     qh->RANDOMdist= False;
     qh_checkconvex(qh, qh->newfacet_list, qh_ALGORITHMfault);
     /* qh_checkconnect(qh); [this is slow and it changes the facet order] */
     qh->RANDOMdist= qh->old_randomdist;
   }
   trace1((qh, qh->ferr, 1009, "qh_all_merges: merged %d coplanar facets %d concave facets and %d degen or redundant facets.\n",
     numcoplanar, numconcave, numdegenredun));
   if (qh->IStracing >= 4 && qh->num_facets < 50)
     qh_printlists(qh);
 } /* all_merges */
 
 
 /*---------------------------------
 
   qh_appendmergeset(qh, facet, neighbor, mergetype, angle )
     appends an entry to qh.facet_mergeset or qh.degen_mergeset
 
     angle ignored if NULL or !qh.ANGLEmerge
 
   returns:
     merge appended to facet_mergeset or degen_mergeset
       sets ->degenerate or ->redundant if degen_mergeset
 
   see:
     qh_test_appendmerge()
 
   design:
     allocate merge entry
     if regular merge
       append to qh.facet_mergeset
     else if degenerate merge and qh.facet_mergeset is all degenerate
       append to qh.degen_mergeset
     else if degenerate merge
       prepend to qh.degen_mergeset
     else if redundant merge
       append to qh.degen_mergeset
 */
 void qh_appendmergeset(qhT *qh, facetT *facet, facetT *neighbor, mergeType mergetype, realT *angle) {
   mergeT *merge, *lastmerge;
   void **freelistp; /* used !qh_NOmem */
 
   if (facet->redundant)
     return;
   if (facet->degenerate && mergetype == MRGdegen)
     return;
   qh_memalloc_(qh, (int)sizeof(mergeT), freelistp, merge, mergeT);
   merge->facet1= facet;
   merge->facet2= neighbor;
   merge->type= mergetype;
   if (angle && qh->ANGLEmerge)
     merge->angle= *angle;
   if (mergetype < MRGdegen)
     qh_setappend(qh, &(qh->facet_mergeset), merge);
   else if (mergetype == MRGdegen) {
     facet->degenerate= True;
     if (!(lastmerge= (mergeT*)qh_setlast(qh->degen_mergeset))
     || lastmerge->type == MRGdegen)
       qh_setappend(qh, &(qh->degen_mergeset), merge);
     else
       qh_setaddnth(qh, &(qh->degen_mergeset), 0, merge);
   }else if (mergetype == MRGredundant) {
     facet->redundant= True;
     qh_setappend(qh, &(qh->degen_mergeset), merge);
   }else /* mergetype == MRGmirror */ {
     if (facet->redundant || neighbor->redundant) {
       qh_fprintf(qh, qh->ferr, 6092, "qhull error (qh_appendmergeset): facet f%d or f%d is already a mirrored facet\n",
            facet->id, neighbor->id);
       qh_errexit2(qh, qh_ERRqhull, facet, neighbor);
     }
     if (!qh_setequal(facet->vertices, neighbor->vertices)) {
       qh_fprintf(qh, qh->ferr, 6093, "qhull error (qh_appendmergeset): mirrored facets f%d and f%d do not have the same vertices\n",
            facet->id, neighbor->id);
       qh_errexit2(qh, qh_ERRqhull, facet, neighbor);
     }
     facet->redundant= True;
     neighbor->redundant= True;
     qh_setappend(qh, &(qh->degen_mergeset), merge);
   }
 } /* appendmergeset */
 
 
 /*---------------------------------
 
   qh_basevertices(qh, samecycle )
     return temporary set of base vertices for samecycle
     samecycle is first facet in the cycle
     assumes apex is SETfirst_( samecycle->vertices )
 
   returns:
     vertices(settemp)
     all ->seen are cleared
 
   notes:
     uses qh_vertex_visit;
 
   design:
     for each facet in samecycle
       for each unseen vertex in facet->vertices
         append to result
 */
 setT *qh_basevertices(qhT *qh, facetT *samecycle) {
   facetT *same;
   vertexT *apex, *vertex, **vertexp;
   setT *vertices= qh_settemp(qh, qh->TEMPsize);
 
   apex= SETfirstt_(samecycle->vertices, vertexT);
   apex->visitid= ++qh->vertex_visit;
   FORALLsame_cycle_(samecycle) {
     if (same->mergeridge)
       continue;
     FOREACHvertex_(same->vertices) {
       if (vertex->visitid != qh->vertex_visit) {
         qh_setappend(qh, &vertices, vertex);
         vertex->visitid= qh->vertex_visit;
         vertex->seen= False;
       }
     }
   }
   trace4((qh, qh->ferr, 4019, "qh_basevertices: found %d vertices\n",
          qh_setsize(qh, vertices)));
   return vertices;
 } /* basevertices */
 
 /*---------------------------------
 
   qh_checkconnect(qh)
     check that new facets are connected
     new facets are on qh.newfacet_list
 
   notes:
     this is slow and it changes the order of the facets
     uses qh.visit_id
 
   design:
     move first new facet to end of qh.facet_list
     for all newly appended facets
       append unvisited neighbors to end of qh.facet_list
     for all new facets
       report error if unvisited
 */
 void qh_checkconnect(qhT *qh /* qh->newfacet_list */) {
   facetT *facet, *newfacet, *errfacet= NULL, *neighbor, **neighborp;
 
   facet= qh->newfacet_list;
   qh_removefacet(qh, facet);
   qh_appendfacet(qh, facet);
   facet->visitid= ++qh->visit_id;
   FORALLfacet_(facet) {
     FOREACHneighbor_(facet) {
       if (neighbor->visitid != qh->visit_id) {
         qh_removefacet(qh, neighbor);
         qh_appendfacet(qh, neighbor);
         neighbor->visitid= qh->visit_id;
       }
     }
   }
   FORALLnew_facets {
     if (newfacet->visitid == qh->visit_id)
       break;
     qh_fprintf(qh, qh->ferr, 6094, "qhull error: f%d is not attached to the new facets\n",
          newfacet->id);
     errfacet= newfacet;
   }
   if (errfacet)
     qh_errexit(qh, qh_ERRqhull, errfacet, NULL);
 } /* checkconnect */
 
 /*---------------------------------
 
   qh_checkzero(qh, testall )
     check that facets are clearly convex for qh.DISTround with qh.MERGEexact
 
     if testall,
       test all facets for qh.MERGEexact post-merging
     else
       test qh.newfacet_list
 
     if qh.MERGEexact,
       allows coplanar ridges
       skips convexity test while qh.ZEROall_ok
 
   returns:
     True if all facets !flipped, !dupridge, normal
          if all horizon facets are simplicial
          if all vertices are clearly below neighbor
          if all opposite vertices of horizon are below
     clears qh.ZEROall_ok if any problems or coplanar facets
 
   notes:
     uses qh.vertex_visit
     horizon facets may define multiple new facets
 
   design:
     for all facets in qh.newfacet_list or qh.facet_list
       check for flagged faults (flipped, etc.)
     for all facets in qh.newfacet_list or qh.facet_list
       for each neighbor of facet
         skip horizon facets for qh.newfacet_list
         test the opposite vertex
       if qh.newfacet_list
         test the other vertices in the facet's horizon facet
 */
 boolT qh_checkzero(qhT *qh, boolT testall) {
   facetT *facet, *neighbor, **neighborp;
   facetT *horizon, *facetlist;
   int neighbor_i;
   vertexT *vertex, **vertexp;
   realT dist;
 
   if (testall)
     facetlist= qh->facet_list;
   else {
     facetlist= qh->newfacet_list;
     FORALLfacet_(facetlist) {
       horizon= SETfirstt_(facet->neighbors, facetT);
       if (!horizon->simplicial)
         goto LABELproblem;
       if (facet->flipped || facet->dupridge || !facet->normal)
         goto LABELproblem;
     }
     if (qh->MERGEexact && qh->ZEROall_ok) {
       trace2((qh, qh->ferr, 2011, "qh_checkzero: skip convexity check until first pre-merge\n"));
       return True;
     }
   }
   FORALLfacet_(facetlist) {
     qh->vertex_visit++;
     neighbor_i= 0;
     horizon= NULL;
     FOREACHneighbor_(facet) {
       if (!neighbor_i && !testall) {
         horizon= neighbor;
         neighbor_i++;
         continue; /* horizon facet tested in qh_findhorizon */
       }
       vertex= SETelemt_(facet->vertices, neighbor_i++, vertexT);
       vertex->visitid= qh->vertex_visit;
       zzinc_(Zdistzero);
       qh_distplane(qh, vertex->point, neighbor, &dist);
       if (dist >= -qh->DISTround) {
         qh->ZEROall_ok= False;
         if (!qh->MERGEexact || testall || dist > qh->DISTround)
           goto LABELnonconvex;
       }
     }
     if (!testall) {
       FOREACHvertex_(horizon->vertices) {
         if (vertex->visitid != qh->vertex_visit) {
           zzinc_(Zdistzero);
           qh_distplane(qh, vertex->point, facet, &dist);
           if (dist >= -qh->DISTround) {
             qh->ZEROall_ok= False;
             if (!qh->MERGEexact || dist > qh->DISTround)
               goto LABELnonconvex;
           }
           break;
         }
       }
     }
   }
   trace2((qh, qh->ferr, 2012, "qh_checkzero: testall %d, facets are %s\n", testall,
         (qh->MERGEexact && !testall) ?
            "not concave, flipped, or duplicate ridged" : "clearly convex"));
   return True;
 
  LABELproblem:
   qh->ZEROall_ok= False;
   trace2((qh, qh->ferr, 2013, "qh_checkzero: facet f%d needs pre-merging\n",
        facet->id));
   return False;
 
  LABELnonconvex:
   trace2((qh, qh->ferr, 2014, "qh_checkzero: facet f%d and f%d are not clearly convex.  v%d dist %.2g\n",
          facet->id, neighbor->id, vertex->id, dist));
   return False;
 } /* checkzero */
 
 /*---------------------------------
 
   qh_compareangle(angle1, angle2 )
     used by qsort() to order merges by angle
 */
 int qh_compareangle(const void *p1, const void *p2) {
   const mergeT *a= *((mergeT *const*)p1), *b= *((mergeT *const*)p2);
 
   return((a->angle > b->angle) ? 1 : -1);
 } /* compareangle */
 
 /*---------------------------------
 
   qh_comparemerge(merge1, merge2 )
     used by qsort() to order merges
 */
 int qh_comparemerge(const void *p1, const void *p2) {
   const mergeT *a= *((mergeT *const*)p1), *b= *((mergeT *const*)p2);
 
   return(a->type - b->type);
 } /* comparemerge */
 
 /*---------------------------------
 
   qh_comparevisit(vertex1, vertex2 )
     used by qsort() to order vertices by their visitid
 */
 int qh_comparevisit(const void *p1, const void *p2) {
   const vertexT *a= *((vertexT *const*)p1), *b= *((vertexT *const*)p2);
 
   return(a->visitid - b->visitid);
 } /* comparevisit */
 
 /*---------------------------------
 
   qh_copynonconvex(qh, atridge )
     set non-convex flag on other ridges (if any) between same neighbors
 
   notes:
     may be faster if use smaller ridge set
 
   design:
     for each ridge of atridge's top facet
       if ridge shares the same neighbor
         set nonconvex flag
 */
 void qh_copynonconvex(qhT *qh, ridgeT *atridge) {
   facetT *facet, *otherfacet;
   ridgeT *ridge, **ridgep;
 
   facet= atridge->top;
   otherfacet= atridge->bottom;
   FOREACHridge_(facet->ridges) {
     if (otherfacet == otherfacet_(ridge, facet) && ridge != atridge) {
       ridge->nonconvex= True;
       trace4((qh, qh->ferr, 4020, "qh_copynonconvex: moved nonconvex flag from r%d to r%d\n",
               atridge->id, ridge->id));
       break;
     }
   }
 } /* copynonconvex */
 
 /*---------------------------------
 
   qh_degen_redundant_facet(qh, facet )
     check facet for degen. or redundancy
 
   notes:
     bumps vertex_visit
     called if a facet was redundant but no longer is (qh_merge_degenredundant)
     qh_appendmergeset() only appends first reference to facet (i.e., redundant)
 
   see:
     qh_degen_redundant_neighbors()
 
   design:
     test for redundant neighbor
     test for degenerate facet
 */
 void qh_degen_redundant_facet(qhT *qh, facetT *facet) {
   vertexT *vertex, **vertexp;
   facetT *neighbor, **neighborp;
 
   trace4((qh, qh->ferr, 4021, "qh_degen_redundant_facet: test facet f%d for degen/redundant\n",
           facet->id));
   FOREACHneighbor_(facet) {
     qh->vertex_visit++;
     FOREACHvertex_(neighbor->vertices)
       vertex->visitid= qh->vertex_visit;
     FOREACHvertex_(facet->vertices) {
       if (vertex->visitid != qh->vertex_visit)
         break;
     }
     if (!vertex) {
       qh_appendmergeset(qh, facet, neighbor, MRGredundant, NULL);
       trace2((qh, qh->ferr, 2015, "qh_degen_redundant_facet: f%d is contained in f%d.  merge\n", facet->id, neighbor->id));
       return;
     }
   }
   if (qh_setsize(qh, facet->neighbors) < qh->hull_dim) {
     qh_appendmergeset(qh, facet, facet, MRGdegen, NULL);
     trace2((qh, qh->ferr, 2016, "qh_degen_redundant_neighbors: f%d is degenerate.\n", facet->id));
   }
 } /* degen_redundant_facet */
 
 
 /*---------------------------------
 
   qh_degen_redundant_neighbors(qh, facet, delfacet,  )
     append degenerate and redundant neighbors to facet_mergeset
     if delfacet,
       only checks neighbors of both delfacet and facet
     also checks current facet for degeneracy
 
   notes:
     bumps vertex_visit
     called for each qh_mergefacet() and qh_mergecycle()
     merge and statistics occur in merge_nonconvex
     qh_appendmergeset() only appends first reference to facet (i.e., redundant)
       it appends redundant facets after degenerate ones
 
     a degenerate facet has fewer than hull_dim neighbors
     a redundant facet's vertices is a subset of its neighbor's vertices
     tests for redundant merges first (appendmergeset is nop for others)
     in a merge, only needs to test neighbors of merged facet
 
   see:
     qh_merge_degenredundant() and qh_degen_redundant_facet()
 
   design:
     test for degenerate facet
     test for redundant neighbor
     test for degenerate neighbor
 */
 void qh_degen_redundant_neighbors(qhT *qh, facetT *facet, facetT *delfacet) {
   vertexT *vertex, **vertexp;
   facetT *neighbor, **neighborp;
   int size;
 
   trace4((qh, qh->ferr, 4022, "qh_degen_redundant_neighbors: test neighbors of f%d with delfacet f%d\n",
           facet->id, getid_(delfacet)));
   if ((size= qh_setsize(qh, facet->neighbors)) < qh->hull_dim) {
     qh_appendmergeset(qh, facet, facet, MRGdegen, NULL);
     trace2((qh, qh->ferr, 2017, "qh_degen_redundant_neighbors: f%d is degenerate with %d neighbors.\n", facet->id, size));
   }
   if (!delfacet)
     delfacet= facet;
   qh->vertex_visit++;
   FOREACHvertex_(facet->vertices)
     vertex->visitid= qh->vertex_visit;
   FOREACHneighbor_(delfacet) {
     /* uses early out instead of checking vertex count */
     if (neighbor == facet)
       continue;
     FOREACHvertex_(neighbor->vertices) {
       if (vertex->visitid != qh->vertex_visit)
         break;
     }
     if (!vertex) {
       qh_appendmergeset(qh, neighbor, facet, MRGredundant, NULL);
       trace2((qh, qh->ferr, 2018, "qh_degen_redundant_neighbors: f%d is contained in f%d.  merge\n", neighbor->id, facet->id));
     }
   }
   FOREACHneighbor_(delfacet) {   /* redundant merges occur first */
     if (neighbor == facet)
       continue;
     if ((size= qh_setsize(qh, neighbor->neighbors)) < qh->hull_dim) {
       qh_appendmergeset(qh, neighbor, neighbor, MRGdegen, NULL);
       trace2((qh, qh->ferr, 2019, "qh_degen_redundant_neighbors: f%d is degenerate with %d neighbors.  Neighbor of f%d.\n", neighbor->id, size, facet->id));
     }
   }
 } /* degen_redundant_neighbors */
 
 
 /*---------------------------------
 
   qh_find_newvertex(qh, oldvertex, vertices, ridges )
     locate new vertex for renaming old vertex
     vertices is a set of possible new vertices
       vertices sorted by number of deleted ridges
 
   returns:
     newvertex or NULL
       each ridge includes both vertex and oldvertex
     vertices sorted by number of deleted ridges
 
   notes:
     modifies vertex->visitid
     new vertex is in one of the ridges
     renaming will not cause a duplicate ridge
     renaming will minimize the number of deleted ridges
     newvertex may not be adjacent in the dual (though unlikely)
 
   design:
     for each vertex in vertices
       set vertex->visitid to number of references in ridges
     remove unvisited vertices
     set qh.vertex_visit above all possible values
     sort vertices by number of references in ridges
     add each ridge to qh.hash_table
     for each vertex in vertices
       look for a vertex that would not cause a duplicate ridge after a rename
 */
 vertexT *qh_find_newvertex(qhT *qh, vertexT *oldvertex, setT *vertices, setT *ridges) {
   vertexT *vertex, **vertexp;
   setT *newridges;
   ridgeT *ridge, **ridgep;
   int size, hashsize;
   int hash;
 
 #ifndef qh_NOtrace
   if (qh->IStracing >= 4) {
     qh_fprintf(qh, qh->ferr, 8063, "qh_find_newvertex: find new vertex for v%d from ",
              oldvertex->id);
     FOREACHvertex_(vertices)
       qh_fprintf(qh, qh->ferr, 8064, "v%d ", vertex->id);
     FOREACHridge_(ridges)
       qh_fprintf(qh, qh->ferr, 8065, "r%d ", ridge->id);
     qh_fprintf(qh, qh->ferr, 8066, "\n");
   }
 #endif
   FOREACHvertex_(vertices)
     vertex->visitid= 0;
   FOREACHridge_(ridges) {
     FOREACHvertex_(ridge->vertices)
       vertex->visitid++;
   }
   FOREACHvertex_(vertices) {
     if (!vertex->visitid) {
       qh_setdelnth(qh, vertices, SETindex_(vertices,vertex));
       vertexp--; /* repeat since deleted this vertex */
     }
   }
   qh->vertex_visit += (unsigned int)qh_setsize(qh, ridges);
   if (!qh_setsize(qh, vertices)) {
     trace4((qh, qh->ferr, 4023, "qh_find_newvertex: vertices not in ridges for v%d\n",
             oldvertex->id));
     return NULL;
   }
   qsort(SETaddr_(vertices, vertexT), (size_t)qh_setsize(qh, vertices),
                 sizeof(vertexT *), qh_comparevisit);
   /* can now use qh->vertex_visit */
   if (qh->PRINTstatistics) {
     size= qh_setsize(qh, vertices);
     zinc_(Zintersect);
     zadd_(Zintersecttot, size);
     zmax_(Zintersectmax, size);
   }
   hashsize= qh_newhashtable(qh, qh_setsize(qh, ridges));
   FOREACHridge_(ridges)
     qh_hashridge(qh, qh->hash_table, hashsize, ridge, oldvertex);
   FOREACHvertex_(vertices) {
     newridges= qh_vertexridges(qh, vertex);
     FOREACHridge_(newridges) {
       if (qh_hashridge_find(qh, qh->hash_table, hashsize, ridge, vertex, oldvertex, &hash)) {
         zinc_(Zdupridge);
         break;
       }
     }
     qh_settempfree(qh, &newridges);
     if (!ridge)
       break;  /* found a rename */
   }
   if (vertex) {
     /* counted in qh_renamevertex */
     trace2((qh, qh->ferr, 2020, "qh_find_newvertex: found v%d for old v%d from %d vertices and %d ridges.\n",
       vertex->id, oldvertex->id, qh_setsize(qh, vertices), qh_setsize(qh, ridges)));
   }else {
     zinc_(Zfindfail);
     trace0((qh, qh->ferr, 14, "qh_find_newvertex: no vertex for renaming v%d(all duplicated ridges) during p%d\n",
       oldvertex->id, qh->furthest_id));
   }
   qh_setfree(qh, &qh->hash_table);
   return vertex;
 } /* find_newvertex */
 
 /*---------------------------------
 
   qh_findbest_test(qh, testcentrum, facet, neighbor, bestfacet, dist, mindist, maxdist )
     test neighbor of facet for qh_findbestneighbor()
     if testcentrum,
       tests centrum (assumes it is defined)
     else
       tests vertices
 
   returns:
     if a better facet (i.e., vertices/centrum of facet closer to neighbor)
       updates bestfacet, dist, mindist, and maxdist
 */
 void qh_findbest_test(qhT *qh, boolT testcentrum, facetT *facet, facetT *neighbor,
       facetT **bestfacet, realT *distp, realT *mindistp, realT *maxdistp) {
   realT dist, mindist, maxdist;
 
   if (testcentrum) {
     zzinc_(Zbestdist);
     qh_distplane(qh, facet->center, neighbor, &dist);
     dist *= qh->hull_dim; /* estimate furthest vertex */
     if (dist < 0) {
       maxdist= 0;
       mindist= dist;
       dist= -dist;
     }else {
       mindist= 0;
       maxdist= dist;
     }
   }else
     dist= qh_getdistance(qh, facet, neighbor, &mindist, &maxdist);
   if (dist < *distp) {
     *bestfacet= neighbor;
     *mindistp= mindist;
     *maxdistp= maxdist;
     *distp= dist;
   }
 } /* findbest_test */
 
 /*---------------------------------
 
   qh_findbestneighbor(qh, facet, dist, mindist, maxdist )
     finds best neighbor (least dist) of a facet for merging
 
   returns:
     returns min and max distances and their max absolute value
 
   notes:
     avoids merging old into new
     assumes ridge->nonconvex only set on one ridge between a pair of facets
     could use an early out predicate but not worth it
 
   design:
     if a large facet
       will test centrum
     else
       will test vertices
     if a large facet
       test nonconvex neighbors for best merge
     else
       test all neighbors for the best merge
     if testing centrum
       get distance information
 */
 facetT *qh_findbestneighbor(qhT *qh, facetT *facet, realT *distp, realT *mindistp, realT *maxdistp) {
   facetT *neighbor, **neighborp, *bestfacet= NULL;
   ridgeT *ridge, **ridgep;
   boolT nonconvex= True, testcentrum= False;
   int size= qh_setsize(qh, facet->vertices);
 
   *distp= REALmax;
   if (size > qh_BESTcentrum2 * qh->hull_dim + qh_BESTcentrum) {
     testcentrum= True;
     zinc_(Zbestcentrum);
     if (!facet->center)
        facet->center= qh_getcentrum(qh, facet);
   }
   if (size > qh->hull_dim + qh_BESTnonconvex) {
     FOREACHridge_(facet->ridges) {
       if (ridge->nonconvex) {
         neighbor= otherfacet_(ridge, facet);
         qh_findbest_test(qh, testcentrum, facet, neighbor,
                           &bestfacet, distp, mindistp, maxdistp);
       }
     }
   }
   if (!bestfacet) {
     nonconvex= False;
     FOREACHneighbor_(facet)
       qh_findbest_test(qh, testcentrum, facet, neighbor,
                         &bestfacet, distp, mindistp, maxdistp);
   }
   if (!bestfacet) {
     qh_fprintf(qh, qh->ferr, 6095, "qhull internal error (qh_findbestneighbor): no neighbors for f%d\n", facet->id);
 
     qh_errexit(qh, qh_ERRqhull, facet, NULL);
   }
   if (testcentrum)
     qh_getdistance(qh, facet, bestfacet, mindistp, maxdistp);
   trace3((qh, qh->ferr, 3002, "qh_findbestneighbor: f%d is best neighbor for f%d testcentrum? %d nonconvex? %d dist %2.2g min %2.2g max %2.2g\n",
      bestfacet->id, facet->id, testcentrum, nonconvex, *distp, *mindistp, *maxdistp));
   return(bestfacet);
 } /* findbestneighbor */
 
 
 /*---------------------------------
 
   qh_flippedmerges(qh, facetlist, wasmerge )
     merge flipped facets into best neighbor
     assumes qh.facet_mergeset at top of temporary stack
 
   returns:
     no flipped facets on facetlist
     sets wasmerge if merge occurred
     degen/redundant merges passed through
 
   notes:
     othermerges not needed since qh.facet_mergeset is empty before & after
       keep it in case of change
 
   design:
     append flipped facets to qh.facetmergeset
     for each flipped merge
       find best neighbor
       merge facet into neighbor
       merge degenerate and redundant facets
     remove flipped merges from qh.facet_mergeset
 */
 void qh_flippedmerges(qhT *qh, facetT *facetlist, boolT *wasmerge) {
   facetT *facet, *neighbor, *facet1;
   realT dist, mindist, maxdist;
   mergeT *merge, **mergep;
   setT *othermerges;
   int nummerge=0;
 
   trace4((qh, qh->ferr, 4024, "qh_flippedmerges: begin\n"));
   FORALLfacet_(facetlist) {
     if (facet->flipped && !facet->visible)
       qh_appendmergeset(qh, facet, facet, MRGflip, NULL);
   }
   othermerges= qh_settemppop(qh); /* was facet_mergeset */
   qh->facet_mergeset= qh_settemp(qh, qh->TEMPsize);
   qh_settemppush(qh, othermerges);
   FOREACHmerge_(othermerges) {
     facet1= merge->facet1;
     if (merge->type != MRGflip || facet1->visible)
       continue;
     if (qh->TRACEmerge-1 == zzval_(Ztotmerge))
       qh->qhmem.IStracing= qh->IStracing= qh->TRACElevel;
     neighbor= qh_findbestneighbor(qh, facet1, &dist, &mindist, &maxdist);
     trace0((qh, qh->ferr, 15, "qh_flippedmerges: merge flipped f%d into f%d dist %2.2g during p%d\n",
       facet1->id, neighbor->id, dist, qh->furthest_id));
     qh_mergefacet(qh, facet1, neighbor, &mindist, &maxdist, !qh_MERGEapex);
     nummerge++;
     if (qh->PRINTstatistics) {
       zinc_(Zflipped);
       wadd_(Wflippedtot, dist);
       wmax_(Wflippedmax, dist);
     }
     qh_merge_degenredundant(qh);
   }
   FOREACHmerge_(othermerges) {
     if (merge->facet1->visible || merge->facet2->visible)
       qh_memfree(qh, merge, (int)sizeof(mergeT));
     else
       qh_setappend(qh, &qh->facet_mergeset, merge);
   }
   qh_settempfree(qh, &othermerges);
   if (nummerge)
     *wasmerge= True;
   trace1((qh, qh->ferr, 1010, "qh_flippedmerges: merged %d flipped facets into a good neighbor\n", nummerge));
 } /* flippedmerges */
 
 
 /*---------------------------------
 
   qh_forcedmerges(qh, wasmerge )
     merge duplicated ridges
 
   returns:
     removes all duplicate ridges on facet_mergeset
     wasmerge set if merge
     qh.facet_mergeset may include non-forced merges(none for now)
     qh.degen_mergeset includes degen/redun merges
 
   notes:
     duplicate ridges occur when the horizon is pinched,
         i.e. a subridge occurs in more than two horizon ridges.
      could rename vertices that pinch the horizon
     assumes qh_merge_degenredundant() has not be called
     othermerges isn't needed since facet_mergeset is empty afterwards
       keep it in case of change
 
   design:
     for each duplicate ridge
       find current facets by chasing f.replace links
       determine best direction for facet
       merge one facet into the other
       remove duplicate ridges from qh.facet_mergeset
 */
 void qh_forcedmerges(qhT *qh, boolT *wasmerge) {
   facetT *facet1, *facet2;
   mergeT *merge, **mergep;
   realT dist1, dist2, mindist1, mindist2, maxdist1, maxdist2;
   setT *othermerges;
   int nummerge=0, numflip=0;
 
   if (qh->TRACEmerge-1 == zzval_(Ztotmerge))
     qh->qhmem.IStracing= qh->IStracing= qh->TRACElevel;
   trace4((qh, qh->ferr, 4025, "qh_forcedmerges: begin\n"));
   othermerges= qh_settemppop(qh); /* was facet_mergeset */
   qh->facet_mergeset= qh_settemp(qh, qh->TEMPsize);
   qh_settemppush(qh, othermerges);
   FOREACHmerge_(othermerges) {
     if (merge->type != MRGridge)
         continue;
     facet1= merge->facet1;
     facet2= merge->facet2;
     while (facet1->visible)      /* must exist, no qh_merge_degenredunant */
       facet1= facet1->f.replace; /* previously merged facet */
     while (facet2->visible)
       facet2= facet2->f.replace; /* previously merged facet */
     if (facet1 == facet2)
       continue;
     if (!qh_setin(facet2->neighbors, facet1)) {
       qh_fprintf(qh, qh->ferr, 6096, "qhull internal error (qh_forcedmerges): f%d and f%d had a duplicate ridge but as f%d and f%d they are no longer neighbors\n",
                merge->facet1->id, merge->facet2->id, facet1->id, facet2->id);
       qh_errexit2(qh, qh_ERRqhull, facet1, facet2);
     }
     if (qh->TRACEmerge-1 == zzval_(Ztotmerge))
       qh->qhmem.IStracing= qh->IStracing= qh->TRACElevel;
     dist1= qh_getdistance(qh, facet1, facet2, &mindist1, &maxdist1);
     dist2= qh_getdistance(qh, facet2, facet1, &mindist2, &maxdist2);
     trace0((qh, qh->ferr, 16, "qh_forcedmerges: duplicate ridge between f%d and f%d, dist %2.2g and reverse dist %2.2g during p%d\n",
             facet1->id, facet2->id, dist1, dist2, qh->furthest_id));
     if (dist1 < dist2)
       qh_mergefacet(qh, facet1, facet2, &mindist1, &maxdist1, !qh_MERGEapex);
     else {
       qh_mergefacet(qh, facet2, facet1, &mindist2, &maxdist2, !qh_MERGEapex);
       dist1= dist2;
       facet1= facet2;
     }
     if (facet1->flipped) {
       zinc_(Zmergeflipdup);
       numflip++;
     }else
       nummerge++;
     if (qh->PRINTstatistics) {
       zinc_(Zduplicate);
       wadd_(Wduplicatetot, dist1);
       wmax_(Wduplicatemax, dist1);
     }
   }
   FOREACHmerge_(othermerges) {
     if (merge->type == MRGridge)
       qh_memfree(qh, merge, (int)sizeof(mergeT));
     else
       qh_setappend(qh, &qh->facet_mergeset, merge);
   }
   qh_settempfree(qh, &othermerges);
   if (nummerge)
     *wasmerge= True;
   trace1((qh, qh->ferr, 1011, "qh_forcedmerges: merged %d facets and %d flipped facets across duplicated ridges\n",
                 nummerge, numflip));
 } /* forcedmerges */
 
 
 /*---------------------------------
 
   qh_getmergeset(qh, facetlist )
     determines nonconvex facets on facetlist
     tests !tested ridges and nonconvex ridges of !tested facets
 
   returns:
     returns sorted qh.facet_mergeset of facet-neighbor pairs to be merged
     all ridges tested
 
   notes:
     assumes no nonconvex ridges with both facets tested
     uses facet->tested/ridge->tested to prevent duplicate tests
     can not limit tests to modified ridges since the centrum changed
     uses qh.visit_id
 
   see:
     qh_getmergeset_initial()
 
   design:
     for each facet on facetlist
       for each ridge of facet
         if untested ridge
           test ridge for convexity
           if non-convex
             append ridge to qh.facet_mergeset
     sort qh.facet_mergeset by angle
 */
 void qh_getmergeset(qhT *qh, facetT *facetlist) {
   facetT *facet, *neighbor, **neighborp;
   ridgeT *ridge, **ridgep;
   int nummerges;
 
   nummerges= qh_setsize(qh, qh->facet_mergeset);
   trace4((qh, qh->ferr, 4026, "qh_getmergeset: started.\n"));
   qh->visit_id++;
   FORALLfacet_(facetlist) {
     if (facet->tested)
       continue;
     facet->visitid= qh->visit_id;
     facet->tested= True;  /* must be non-simplicial due to merge */
     FOREACHneighbor_(facet)
       neighbor->seen= False;
     FOREACHridge_(facet->ridges) {
       if (ridge->tested && !ridge->nonconvex)
         continue;
       /* if tested & nonconvex, need to append merge */
       neighbor= otherfacet_(ridge, facet);
       if (neighbor->seen) {
         ridge->tested= True;
         ridge->nonconvex= False;
       }else if (neighbor->visitid != qh->visit_id) {
         ridge->tested= True;
         ridge->nonconvex= False;
         neighbor->seen= True;      /* only one ridge is marked nonconvex */
         if (qh_test_appendmerge(qh, facet, neighbor))
           ridge->nonconvex= True;
       }
     }
   }
   nummerges= qh_setsize(qh, qh->facet_mergeset);
   if (qh->ANGLEmerge)
     qsort(SETaddr_(qh->facet_mergeset, mergeT), (size_t)nummerges, sizeof(mergeT *), qh_compareangle);
   else
     qsort(SETaddr_(qh->facet_mergeset, mergeT), (size_t)nummerges, sizeof(mergeT *), qh_comparemerge);
   if (qh->POSTmerging) {
     zadd_(Zmergesettot2, nummerges);
   }else {
     zadd_(Zmergesettot, nummerges);
     zmax_(Zmergesetmax, nummerges);
   }
   trace2((qh, qh->ferr, 2021, "qh_getmergeset: %d merges found\n", nummerges));
 } /* getmergeset */
 
 
 /*---------------------------------
 
   qh_getmergeset_initial(qh, facetlist )
     determine initial qh.facet_mergeset for facets
     tests all facet/neighbor pairs on facetlist
 
   returns:
     sorted qh.facet_mergeset with nonconvex ridges
     sets facet->tested, ridge->tested, and ridge->nonconvex
 
   notes:
     uses visit_id, assumes ridge->nonconvex is False
 
   see:
     qh_getmergeset()
 
   design:
     for each facet on facetlist
       for each untested neighbor of facet
         test facet and neighbor for convexity
         if non-convex
           append merge to qh.facet_mergeset
           mark one of the ridges as nonconvex
     sort qh.facet_mergeset by angle
 */
 void qh_getmergeset_initial(qhT *qh, facetT *facetlist) {
   facetT *facet, *neighbor, **neighborp;
   ridgeT *ridge, **ridgep;
   int nummerges;
 
   qh->visit_id++;
   FORALLfacet_(facetlist) {
     facet->visitid= qh->visit_id;
     facet->tested= True;
     FOREACHneighbor_(facet) {
       if (neighbor->visitid != qh->visit_id) {
         if (qh_test_appendmerge(qh, facet, neighbor)) {
           FOREACHridge_(neighbor->ridges) {
             if (facet == otherfacet_(ridge, neighbor)) {
               ridge->nonconvex= True;
               break;    /* only one ridge is marked nonconvex */
             }
           }
         }
       }
     }
     FOREACHridge_(facet->ridges)
       ridge->tested= True;
   }
   nummerges= qh_setsize(qh, qh->facet_mergeset);
   if (qh->ANGLEmerge)
     qsort(SETaddr_(qh->facet_mergeset, mergeT), (size_t)nummerges, sizeof(mergeT *), qh_compareangle);
   else
     qsort(SETaddr_(qh->facet_mergeset, mergeT), (size_t)nummerges, sizeof(mergeT *), qh_comparemerge);
   if (qh->POSTmerging) {
     zadd_(Zmergeinittot2, nummerges);
   }else {
     zadd_(Zmergeinittot, nummerges);
     zmax_(Zmergeinitmax, nummerges);
   }
   trace2((qh, qh->ferr, 2022, "qh_getmergeset_initial: %d merges found\n", nummerges));
 } /* getmergeset_initial */
 
 
 /*---------------------------------
 
   qh_hashridge(qh, hashtable, hashsize, ridge, oldvertex )
     add ridge to hashtable without oldvertex
 
   notes:
     assumes hashtable is large enough
 
   design:
     determine hash value for ridge without oldvertex
     find next empty slot for ridge
 */
 void qh_hashridge(qhT *qh, setT *hashtable, int hashsize, ridgeT *ridge, vertexT *oldvertex) {
   int hash;
   ridgeT *ridgeA;
 
   hash= qh_gethash(qh, hashsize, ridge->vertices, qh->hull_dim-1, 0, oldvertex);
   while (True) {
     if (!(ridgeA= SETelemt_(hashtable, hash, ridgeT))) {
       SETelem_(hashtable, hash)= ridge;
       break;
     }else if (ridgeA == ridge)
       break;
     if (++hash == hashsize)
       hash= 0;
   }
 } /* hashridge */
 
 
 /*---------------------------------
 
   qh_hashridge_find(qh, hashtable, hashsize, ridge, vertex, oldvertex, hashslot )
     returns matching ridge without oldvertex in hashtable
       for ridge without vertex
     if oldvertex is NULL
       matches with any one skip
 
   returns:
     matching ridge or NULL
     if no match,
       if ridge already in   table
         hashslot= -1
       else
         hashslot= next NULL index
 
   notes:
     assumes hashtable is large enough
     can't match ridge to itself
 
   design:
     get hash value for ridge without vertex
     for each hashslot
       return match if ridge matches ridgeA without oldvertex
 */
 ridgeT *qh_hashridge_find(qhT *qh, setT *hashtable, int hashsize, ridgeT *ridge,
               vertexT *vertex, vertexT *oldvertex, int *hashslot) {
   int hash;
   ridgeT *ridgeA;
 
   *hashslot= 0;
   zinc_(Zhashridge);
   hash= qh_gethash(qh, hashsize, ridge->vertices, qh->hull_dim-1, 0, vertex);
   while ((ridgeA= SETelemt_(hashtable, hash, ridgeT))) {
     if (ridgeA == ridge)
       *hashslot= -1;
     else {
       zinc_(Zhashridgetest);
       if (qh_setequal_except(ridge->vertices, vertex, ridgeA->vertices, oldvertex))
         return ridgeA;
     }
     if (++hash == hashsize)
       hash= 0;
   }
   if (!*hashslot)
     *hashslot= hash;
   return NULL;
 } /* hashridge_find */
 
 
 /*---------------------------------
 
   qh_makeridges(qh, facet )
     creates explicit ridges between simplicial facets
 
   returns:
     facet with ridges and without qh_MERGEridge
     ->simplicial is False
 
   notes:
     allows qh_MERGEridge flag
     uses existing ridges
     duplicate neighbors ok if ridges already exist (qh_mergecycle_ridges)
 
   see:
     qh_mergecycle_ridges()
 
   design:
     look for qh_MERGEridge neighbors
     mark neighbors that already have ridges
     for each unprocessed neighbor of facet
       create a ridge for neighbor and facet
     if any qh_MERGEridge neighbors
       delete qh_MERGEridge flags (already handled by qh_mark_dupridges)
 */
 void qh_makeridges(qhT *qh, facetT *facet) {
   facetT *neighbor, **neighborp;
   ridgeT *ridge, **ridgep;
   int neighbor_i, neighbor_n;
   boolT toporient, mergeridge= False;
 
   if (!facet->simplicial)
     return;
   trace4((qh, qh->ferr, 4027, "qh_makeridges: make ridges for f%d\n", facet->id));
   facet->simplicial= False;
   FOREACHneighbor_(facet) {
     if (neighbor == qh_MERGEridge)
       mergeridge= True;
     else
       neighbor->seen= False;
   }
   FOREACHridge_(facet->ridges)
     otherfacet_(ridge, facet)->seen= True;
   FOREACHneighbor_i_(qh, facet) {
     if (neighbor == qh_MERGEridge)
       continue;  /* fixed by qh_mark_dupridges */
     else if (!neighbor->seen) {  /* no current ridges */
       ridge= qh_newridge(qh);
       ridge->vertices= qh_setnew_delnthsorted(qh, facet->vertices, qh->hull_dim,
                                                           neighbor_i, 0);
       toporient= facet->toporient ^ (neighbor_i & 0x1);
       if (toporient) {
         ridge->top= facet;
         ridge->bottom= neighbor;
       }else {
         ridge->top= neighbor;
         ridge->bottom= facet;
       }
 #if 0 /* this also works */
       flip= (facet->toporient ^ neighbor->toporient)^(skip1 & 0x1) ^ (skip2 & 0x1);
       if (facet->toporient ^ (skip1 & 0x1) ^ flip) {
         ridge->top= neighbor;
         ridge->bottom= facet;
       }else {
         ridge->top= facet;
         ridge->bottom= neighbor;
       }
 #endif
       qh_setappend(qh, &(facet->ridges), ridge);
       qh_setappend(qh, &(neighbor->ridges), ridge);
     }
   }
   if (mergeridge) {
     while (qh_setdel(facet->neighbors, qh_MERGEridge))
       ; /* delete each one */
   }
 } /* makeridges */
 
 
 /*---------------------------------
 
   qh_mark_dupridges(qh, facetlist )
     add duplicated ridges to qh.facet_mergeset
     facet->dupridge is true
 
   returns:
     duplicate ridges on qh.facet_mergeset
     ->mergeridge/->mergeridge2 set
     duplicate ridges marked by qh_MERGEridge and both sides facet->dupridge
     no MERGEridges in neighbor sets
 
   notes:
     duplicate ridges occur when the horizon is pinched,
         i.e. a subridge occurs in more than two horizon ridges.
     could rename vertices that pinch the horizon
     uses qh.visit_id
 
   design:
     for all facets on facetlist
       if facet contains a duplicate ridge
         for each neighbor of facet
           if neighbor marked qh_MERGEridge (one side of the merge)
             set facet->mergeridge
           else
             if neighbor contains a duplicate ridge
             and the back link is qh_MERGEridge
               append duplicate ridge to qh.facet_mergeset
    for each duplicate ridge
      make ridge sets in preparation for merging
      remove qh_MERGEridge from neighbor set
    for each duplicate ridge
      restore the missing neighbor from the neighbor set that was qh_MERGEridge
      add the missing ridge for this neighbor
 */
 void qh_mark_dupridges(qhT *qh, facetT *facetlist) {
   facetT *facet, *neighbor, **neighborp;
   int nummerge=0;
   mergeT *merge, **mergep;
 
 
   trace4((qh, qh->ferr, 4028, "qh_mark_dupridges: identify duplicate ridges\n"));
   FORALLfacet_(facetlist) {
     if (facet->dupridge) {
       FOREACHneighbor_(facet) {
         if (neighbor == qh_MERGEridge) {
           facet->mergeridge= True;
           continue;
         }
         if (neighbor->dupridge
         && !qh_setin(neighbor->neighbors, facet)) { /* qh_MERGEridge */
           qh_appendmergeset(qh, facet, neighbor, MRGridge, NULL);
           facet->mergeridge2= True;
           facet->mergeridge= True;
           nummerge++;
         }
       }
     }
   }
   if (!nummerge)
     return;
   FORALLfacet_(facetlist) {            /* gets rid of qh_MERGEridge */
     if (facet->mergeridge && !facet->mergeridge2)
       qh_makeridges(qh, facet);
   }
   FOREACHmerge_(qh->facet_mergeset) {   /* restore the missing neighbors */
     if (merge->type == MRGridge) {
       qh_setappend(qh, &merge->facet2->neighbors, merge->facet1);
       qh_makeridges(qh, merge->facet1);   /* and the missing ridges */
     }
   }
   trace1((qh, qh->ferr, 1012, "qh_mark_dupridges: found %d duplicated ridges\n",
                 nummerge));
 } /* mark_dupridges */
 
 /*---------------------------------
 
   qh_maydropneighbor(qh, facet )
     drop neighbor relationship if no ridge between facet and neighbor
 
   returns:
     neighbor sets updated
     appends degenerate facets to qh.facet_mergeset
 
   notes:
     won't cause redundant facets since vertex inclusion is the same
     may drop vertex and neighbor if no ridge
     uses qh.visit_id
 
   design:
     visit all neighbors with ridges
     for each unvisited neighbor of facet
       delete neighbor and facet from the neighbor sets
       if neighbor becomes degenerate
         append neighbor to qh.degen_mergeset
     if facet is degenerate
       append facet to qh.degen_mergeset
 */
 void qh_maydropneighbor(qhT *qh, facetT *facet) {
   ridgeT *ridge, **ridgep;
   realT angledegen= qh_ANGLEdegen;
   facetT *neighbor, **neighborp;
 
   qh->visit_id++;
   trace4((qh, qh->ferr, 4029, "qh_maydropneighbor: test f%d for no ridges to a neighbor\n",
           facet->id));
   FOREACHridge_(facet->ridges) {
     ridge->top->visitid= qh->visit_id;
     ridge->bottom->visitid= qh->visit_id;
   }
   FOREACHneighbor_(facet) {
     if (neighbor->visitid != qh->visit_id) {
       trace0((qh, qh->ferr, 17, "qh_maydropneighbor: facets f%d and f%d are no longer neighbors during p%d\n",
             facet->id, neighbor->id, qh->furthest_id));
       zinc_(Zdropneighbor);
       qh_setdel(facet->neighbors, neighbor);
       neighborp--;  /* repeat, deleted a neighbor */
       qh_setdel(neighbor->neighbors, facet);
       if (qh_setsize(qh, neighbor->neighbors) < qh->hull_dim) {
         zinc_(Zdropdegen);
         qh_appendmergeset(qh, neighbor, neighbor, MRGdegen, &angledegen);
         trace2((qh, qh->ferr, 2023, "qh_maydropneighbors: f%d is degenerate.\n", neighbor->id));
       }
     }
   }
   if (qh_setsize(qh, facet->neighbors) < qh->hull_dim) {
     zinc_(Zdropdegen);
     qh_appendmergeset(qh, facet, facet, MRGdegen, &angledegen);
     trace2((qh, qh->ferr, 2024, "qh_maydropneighbors: f%d is degenerate.\n", facet->id));
   }
 } /* maydropneighbor */
 
 
 /*---------------------------------
 
   qh_merge_degenredundant(qh)
     merge all degenerate and redundant facets
     qh.degen_mergeset contains merges from qh_degen_redundant_neighbors()
 
   returns:
     number of merges performed
     resets facet->degenerate/redundant
     if deleted (visible) facet has no neighbors
       sets ->f.replace to NULL
 
   notes:
     redundant merges happen before degenerate ones
     merging and renaming vertices can result in degen/redundant facets
 
   design:
     for each merge on qh.degen_mergeset
       if redundant merge
         if non-redundant facet merged into redundant facet
           recheck facet for redundancy
         else
           merge redundant facet into other facet
 */
 int qh_merge_degenredundant(qhT *qh) {
   int size;
   mergeT *merge;
   facetT *bestneighbor, *facet1, *facet2;
   realT dist, mindist, maxdist;
   vertexT *vertex, **vertexp;
   int nummerges= 0;
   mergeType mergetype;
 
   while ((merge= (mergeT*)qh_setdellast(qh->degen_mergeset))) {
     facet1= merge->facet1;
     facet2= merge->facet2;
     mergetype= merge->type;
     qh_memfree(qh, merge, (int)sizeof(mergeT));
     if (facet1->visible)
       continue;
     facet1->degenerate= False;
     facet1->redundant= False;
     if (qh->TRACEmerge-1 == zzval_(Ztotmerge))
       qh->qhmem.IStracing= qh->IStracing= qh->TRACElevel;
     if (mergetype == MRGredundant) {
       zinc_(Zneighbor);
       while (facet2->visible) {
         if (!facet2->f.replace) {
           qh_fprintf(qh, qh->ferr, 6097, "qhull internal error (qh_merge_degenredunant): f%d redundant but f%d has no replacement\n",
                facet1->id, facet2->id);
           qh_errexit2(qh, qh_ERRqhull, facet1, facet2);
         }
         facet2= facet2->f.replace;
       }
       if (facet1 == facet2) {
         qh_degen_redundant_facet(qh, facet1); /* in case of others */
         continue;
       }
       trace2((qh, qh->ferr, 2025, "qh_merge_degenredundant: facet f%d is contained in f%d, will merge\n",
             facet1->id, facet2->id));
       qh_mergefacet(qh, facet1, facet2, NULL, NULL, !qh_MERGEapex);
       /* merge distance is already accounted for */
       nummerges++;
     }else {  /* mergetype == MRGdegen, other merges may have fixed */
       if (!(size= qh_setsize(qh, facet1->neighbors))) {
         zinc_(Zdelfacetdup);
         trace2((qh, qh->ferr, 2026, "qh_merge_degenredundant: facet f%d has no neighbors.  Deleted\n", facet1->id));
         qh_willdelete(qh, facet1, NULL);
         FOREACHvertex_(facet1->vertices) {
           qh_setdel(vertex->neighbors, facet1);
           if (!SETfirst_(vertex->neighbors)) {
             zinc_(Zdegenvertex);
             trace2((qh, qh->ferr, 2027, "qh_merge_degenredundant: deleted v%d because f%d has no neighbors\n",
                  vertex->id, facet1->id));
             vertex->deleted= True;
             qh_setappend(qh, &qh->del_vertices, vertex);
           }
         }
         nummerges++;
       }else if (size < qh->hull_dim) {
         bestneighbor= qh_findbestneighbor(qh, facet1, &dist, &mindist, &maxdist);
         trace2((qh, qh->ferr, 2028, "qh_merge_degenredundant: facet f%d has %d neighbors, merge into f%d dist %2.2g\n",
               facet1->id, size, bestneighbor->id, dist));
         qh_mergefacet(qh, facet1, bestneighbor, &mindist, &maxdist, !qh_MERGEapex);
         nummerges++;
         if (qh->PRINTstatistics) {
           zinc_(Zdegen);
           wadd_(Wdegentot, dist);
           wmax_(Wdegenmax, dist);
         }
       } /* else, another merge fixed the degeneracy and redundancy tested */
     }
   }
   return nummerges;
 } /* merge_degenredundant */
 
 /*---------------------------------
 
   qh_merge_nonconvex(qh, facet1, facet2, mergetype )
     remove non-convex ridge between facet1 into facet2
     mergetype gives why the facet's are non-convex
 
   returns:
     merges one of the facets into the best neighbor
 
   design:
     if one of the facets is a new facet
       prefer merging new facet into old facet
     find best neighbors for both facets
     merge the nearest facet into its best neighbor
     update the statistics
 */
 void qh_merge_nonconvex(qhT *qh, facetT *facet1, facetT *facet2, mergeType mergetype) {
   facetT *bestfacet, *bestneighbor, *neighbor;
   realT dist, dist2, mindist, mindist2, maxdist, maxdist2;
 
   if (qh->TRACEmerge-1 == zzval_(Ztotmerge))
     qh->qhmem.IStracing= qh->IStracing= qh->TRACElevel;
   trace3((qh, qh->ferr, 3003, "qh_merge_nonconvex: merge #%d for f%d and f%d type %d\n",
       zzval_(Ztotmerge) + 1, facet1->id, facet2->id, mergetype));
   /* concave or coplanar */
   if (!facet1->newfacet) {
     bestfacet= facet2;   /* avoid merging old facet if new is ok */
     facet2= facet1;
     facet1= bestfacet;
   }else
     bestfacet= facet1;
   bestneighbor= qh_findbestneighbor(qh, bestfacet, &dist, &mindist, &maxdist);
   neighbor= qh_findbestneighbor(qh, facet2, &dist2, &mindist2, &maxdist2);
   if (dist < dist2) {
     qh_mergefacet(qh, bestfacet, bestneighbor, &mindist, &maxdist, !qh_MERGEapex);
   }else if (qh->AVOIDold && !facet2->newfacet
   && ((mindist >= -qh->MAXcoplanar && maxdist <= qh->max_outside)
        || dist * 1.5 < dist2)) {
     zinc_(Zavoidold);
     wadd_(Wavoidoldtot, dist);
     wmax_(Wavoidoldmax, dist);
     trace2((qh, qh->ferr, 2029, "qh_merge_nonconvex: avoid merging old facet f%d dist %2.2g.  Use f%d dist %2.2g instead\n",
            facet2->id, dist2, facet1->id, dist2));
     qh_mergefacet(qh, bestfacet, bestneighbor, &mindist, &maxdist, !qh_MERGEapex);
   }else {
     qh_mergefacet(qh, facet2, neighbor, &mindist2, &maxdist2, !qh_MERGEapex);
     dist= dist2;
   }
   if (qh->PRINTstatistics) {
     if (mergetype == MRGanglecoplanar) {
       zinc_(Zacoplanar);
       wadd_(Wacoplanartot, dist);
       wmax_(Wacoplanarmax, dist);
     }else if (mergetype == MRGconcave) {
       zinc_(Zconcave);
       wadd_(Wconcavetot, dist);
       wmax_(Wconcavemax, dist);
     }else { /* MRGcoplanar */
       zinc_(Zcoplanar);
       wadd_(Wcoplanartot, dist);
       wmax_(Wcoplanarmax, dist);
     }
   }
 } /* merge_nonconvex */
 
 /*---------------------------------
 
   qh_mergecycle(qh, samecycle, newfacet )
     merge a cycle of facets starting at samecycle into a newfacet
     newfacet is a horizon facet with ->normal
     samecycle facets are simplicial from an apex
 
   returns:
     initializes vertex neighbors on first merge
     samecycle deleted (placed on qh.visible_list)
     newfacet at end of qh.facet_list
     deleted vertices on qh.del_vertices
 
   see:
     qh_mergefacet()
     called by qh_mergecycle_all() for multiple, same cycle facets
 
   design:
     make vertex neighbors if necessary
     make ridges for newfacet
     merge neighbor sets of samecycle into newfacet
     merge ridges of samecycle into newfacet
     merge vertex neighbors of samecycle into newfacet
     make apex of samecycle the apex of newfacet
     if newfacet wasn't a new facet
       add its vertices to qh.newvertex_list
     delete samecycle facets a make newfacet a newfacet
 */
 void qh_mergecycle(qhT *qh, facetT *samecycle, facetT *newfacet) {
   int traceonce= False, tracerestore= 0;
   vertexT *apex;
 #ifndef qh_NOtrace
   facetT *same;
 #endif
 
   if (newfacet->tricoplanar) {
     if (!qh->TRInormals) {
       qh_fprintf(qh, qh->ferr, 6224, "Qhull internal error (qh_mergecycle): does not work for tricoplanar facets.  Use option 'Q11'\n");
       qh_errexit(qh, qh_ERRqhull, newfacet, NULL);
     }
     newfacet->tricoplanar= False;
     newfacet->keepcentrum= False;
   }
   if (!qh->VERTEXneighbors)
     qh_vertexneighbors(qh);
   zzinc_(Ztotmerge);
   if (qh->REPORTfreq2 && qh->POSTmerging) {
     if (zzval_(Ztotmerge) > qh->mergereport + qh->REPORTfreq2)
       qh_tracemerging(qh);
   }
 #ifndef qh_NOtrace
   if (qh->TRACEmerge == zzval_(Ztotmerge))
     qh->qhmem.IStracing= qh->IStracing= qh->TRACElevel;
   trace2((qh, qh->ferr, 2030, "qh_mergecycle: merge #%d for facets from cycle f%d into coplanar horizon f%d\n",
         zzval_(Ztotmerge), samecycle->id, newfacet->id));
   if (newfacet == qh->tracefacet) {
     tracerestore= qh->IStracing;
     qh->IStracing= 4;
     qh_fprintf(qh, qh->ferr, 8068, "qh_mergecycle: ========= trace merge %d of samecycle %d into trace f%d, furthest is p%d\n",
                zzval_(Ztotmerge), samecycle->id, newfacet->id,  qh->furthest_id);
     traceonce= True;
   }
   if (qh->IStracing >=4) {
     qh_fprintf(qh, qh->ferr, 8069, "  same cycle:");
     FORALLsame_cycle_(samecycle)
       qh_fprintf(qh, qh->ferr, 8070, " f%d", same->id);
     qh_fprintf(qh, qh->ferr, 8071, "\n");
   }
   if (qh->IStracing >=4)
     qh_errprint(qh, "MERGING CYCLE", samecycle, newfacet, NULL, NULL);
 #endif /* !qh_NOtrace */
   apex= SETfirstt_(samecycle->vertices, vertexT);
   qh_makeridges(qh, newfacet);
   qh_mergecycle_neighbors(qh, samecycle, newfacet);
   qh_mergecycle_ridges(qh, samecycle, newfacet);
   qh_mergecycle_vneighbors(qh, samecycle, newfacet);
   if (SETfirstt_(newfacet->vertices, vertexT) != apex)
     qh_setaddnth(qh, &newfacet->vertices, 0, apex);  /* apex has last id */
   if (!newfacet->newfacet)
     qh_newvertices(qh, newfacet->vertices);
   qh_mergecycle_facets(qh, samecycle, newfacet);
   qh_tracemerge(qh, samecycle, newfacet);
   /* check for degen_redundant_neighbors after qh_forcedmerges() */
   if (traceonce) {
     qh_fprintf(qh, qh->ferr, 8072, "qh_mergecycle: end of trace facet\n");
     qh->IStracing= tracerestore;
   }
 } /* mergecycle */
 
 /*---------------------------------
 
   qh_mergecycle_all(qh, facetlist, wasmerge )
     merge all samecycles of coplanar facets into horizon
     don't merge facets with ->mergeridge (these already have ->normal)
     all facets are simplicial from apex
     all facet->cycledone == False
 
   returns:
     all newfacets merged into coplanar horizon facets
     deleted vertices on  qh.del_vertices
     sets wasmerge if any merge
 
   see:
     calls qh_mergecycle for multiple, same cycle facets
 
   design:
     for each facet on facetlist
       skip facets with duplicate ridges and normals
       check that facet is in a samecycle (->mergehorizon)
       if facet only member of samecycle
         sets vertex->delridge for all vertices except apex
         merge facet into horizon
       else
         mark all facets in samecycle
         remove facets with duplicate ridges from samecycle
         merge samecycle into horizon (deletes facets from facetlist)
 */
 void qh_mergecycle_all(qhT *qh, facetT *facetlist, boolT *wasmerge) {
   facetT *facet, *same, *prev, *horizon;
   facetT *samecycle= NULL, *nextfacet, *nextsame;
   vertexT *apex, *vertex, **vertexp;
   int cycles=0, total=0, facets, nummerge;
 
   trace2((qh, qh->ferr, 2031, "qh_mergecycle_all: begin\n"));
   for (facet= facetlist; facet && (nextfacet= facet->next); facet= nextfacet) {
     if (facet->normal)
       continue;
     if (!facet->mergehorizon) {
       qh_fprintf(qh, qh->ferr, 6225, "Qhull internal error (qh_mergecycle_all): f%d without normal\n", facet->id);
       qh_errexit(qh, qh_ERRqhull, facet, NULL);
     }
     horizon= SETfirstt_(facet->neighbors, facetT);
     if (facet->f.samecycle == facet) {
       zinc_(Zonehorizon);
       /* merge distance done in qh_findhorizon */
       apex= SETfirstt_(facet->vertices, vertexT);
       FOREACHvertex_(facet->vertices) {
         if (vertex != apex)
           vertex->delridge= True;
       }
       horizon->f.newcycle= NULL;
       qh_mergefacet(qh, facet, horizon, NULL, NULL, qh_MERGEapex);
     }else {
       samecycle= facet;
       facets= 0;
       prev= facet;
       for (same= facet->f.samecycle; same;  /* FORALLsame_cycle_(facet) */
            same= (same == facet ? NULL :nextsame)) { /* ends at facet */
         nextsame= same->f.samecycle;
         if (same->cycledone || same->visible)
           qh_infiniteloop(qh, same);
         same->cycledone= True;
         if (same->normal) {
           prev->f.samecycle= same->f.samecycle; /* unlink ->mergeridge */
           same->f.samecycle= NULL;
         }else {
           prev= same;
           facets++;
         }
       }
       while (nextfacet && nextfacet->cycledone)  /* will delete samecycle */
         nextfacet= nextfacet->next;
       horizon->f.newcycle= NULL;
       qh_mergecycle(qh, samecycle, horizon);
       nummerge= horizon->nummerge + facets;
       if (nummerge > qh_MAXnummerge)
         horizon->nummerge= qh_MAXnummerge;
       else
         horizon->nummerge= (short unsigned int)nummerge;
       zzinc_(Zcyclehorizon);
       total += facets;
       zzadd_(Zcyclefacettot, facets);
       zmax_(Zcyclefacetmax, facets);
     }
     cycles++;
   }
   if (cycles)
     *wasmerge= True;
   trace1((qh, qh->ferr, 1013, "qh_mergecycle_all: merged %d same cycles or facets into coplanar horizons\n", cycles));
 } /* mergecycle_all */
 
 /*---------------------------------
 
   qh_mergecycle_facets(qh, samecycle, newfacet )
     finish merge of samecycle into newfacet
 
   returns:
     samecycle prepended to visible_list for later deletion and partitioning
       each facet->f.replace == newfacet
 
     newfacet moved to end of qh.facet_list
       makes newfacet a newfacet (get's facet1->id if it was old)
       sets newfacet->newmerge
       clears newfacet->center (unless merging into a large facet)
       clears newfacet->tested and ridge->tested for facet1
 
     adds neighboring facets to facet_mergeset if redundant or degenerate
 
   design:
     make newfacet a new facet and set its flags
     move samecycle facets to qh.visible_list for later deletion
     unless newfacet is large
       remove its centrum
 */
 void qh_mergecycle_facets(qhT *qh, facetT *samecycle, facetT *newfacet) {
   facetT *same, *next;
 
   trace4((qh, qh->ferr, 4030, "qh_mergecycle_facets: make newfacet new and samecycle deleted\n"));
   qh_removefacet(qh, newfacet);  /* append as a newfacet to end of qh->facet_list */
   qh_appendfacet(qh, newfacet);
   newfacet->newfacet= True;
   newfacet->simplicial= False;
   newfacet->newmerge= True;
 
   for (same= samecycle->f.samecycle; same; same= (same == samecycle ?  NULL : next)) {
     next= same->f.samecycle;  /* reused by willdelete */
     qh_willdelete(qh, same, newfacet);
   }
   if (newfacet->center
       && qh_setsize(qh, newfacet->vertices) <= qh->hull_dim + qh_MAXnewcentrum) {
     qh_memfree(qh, newfacet->center, qh->normal_size);
     newfacet->center= NULL;
   }
   trace3((qh, qh->ferr, 3004, "qh_mergecycle_facets: merged facets from cycle f%d into f%d\n",
              samecycle->id, newfacet->id));
 } /* mergecycle_facets */
 
 /*---------------------------------
 
   qh_mergecycle_neighbors(qh, samecycle, newfacet )
     add neighbors for samecycle facets to newfacet
 
   returns:
     newfacet with updated neighbors and vice-versa
     newfacet has ridges
     all neighbors of newfacet marked with qh.visit_id
     samecycle facets marked with qh.visit_id-1
     ridges updated for simplicial neighbors of samecycle with a ridge
 
   notes:
     assumes newfacet not in samecycle
     usually, samecycle facets are new, simplicial facets without internal ridges
       not so if horizon facet is coplanar to two different samecycles
 
   see:
     qh_mergeneighbors()
 
   design:
     check samecycle
     delete neighbors from newfacet that are also in samecycle
     for each neighbor of a facet in samecycle
       if neighbor is simplicial
         if first visit
           move the neighbor relation to newfacet
           update facet links for its ridges
         else
           make ridges for neighbor
           remove samecycle reference
       else
         update neighbor sets
 */
 void qh_mergecycle_neighbors(qhT *qh, facetT *samecycle, facetT *newfacet) {
   facetT *same, *neighbor, **neighborp;
   int delneighbors= 0, newneighbors= 0;
   unsigned int samevisitid;
   ridgeT *ridge, **ridgep;
 
   samevisitid= ++qh->visit_id;
   FORALLsame_cycle_(samecycle) {
     if (same->visitid == samevisitid || same->visible)
       qh_infiniteloop(qh, samecycle);
     same->visitid= samevisitid;
   }
   newfacet->visitid= ++qh->visit_id;
   trace4((qh, qh->ferr, 4031, "qh_mergecycle_neighbors: delete shared neighbors from newfacet\n"));
   FOREACHneighbor_(newfacet) {
     if (neighbor->visitid == samevisitid) {
       SETref_(neighbor)= NULL;  /* samecycle neighbors deleted */
       delneighbors++;
     }else
       neighbor->visitid= qh->visit_id;
   }
   qh_setcompact(qh, newfacet->neighbors);
 
   trace4((qh, qh->ferr, 4032, "qh_mergecycle_neighbors: update neighbors\n"));
   FORALLsame_cycle_(samecycle) {
     FOREACHneighbor_(same) {
       if (neighbor->visitid == samevisitid)
         continue;
       if (neighbor->simplicial) {
         if (neighbor->visitid != qh->visit_id) {
           qh_setappend(qh, &newfacet->neighbors, neighbor);
           qh_setreplace(qh, neighbor->neighbors, same, newfacet);
           newneighbors++;
           neighbor->visitid= qh->visit_id;
           FOREACHridge_(neighbor->ridges) { /* update ridge in case of qh_makeridges */
             if (ridge->top == same) {
               ridge->top= newfacet;
               break;
             }else if (ridge->bottom == same) {
               ridge->bottom= newfacet;
               break;
             }
           }
         }else {
           qh_makeridges(qh, neighbor);
           qh_setdel(neighbor->neighbors, same);
           /* same can't be horizon facet for neighbor */
         }
       }else { /* non-simplicial neighbor */
         qh_setdel(neighbor->neighbors, same);
         if (neighbor->visitid != qh->visit_id) {
           qh_setappend(qh, &neighbor->neighbors, newfacet);
           qh_setappend(qh, &newfacet->neighbors, neighbor);
           neighbor->visitid= qh->visit_id;
           newneighbors++;
         }
       }
     }
   }
   trace2((qh, qh->ferr, 2032, "qh_mergecycle_neighbors: deleted %d neighbors and added %d\n",
              delneighbors, newneighbors));
 } /* mergecycle_neighbors */
 
 /*---------------------------------
 
   qh_mergecycle_ridges(qh, samecycle, newfacet )
     add ridges/neighbors for facets in samecycle to newfacet
     all new/old neighbors of newfacet marked with qh.visit_id
     facets in samecycle marked with qh.visit_id-1
     newfacet marked with qh.visit_id
 
   returns:
     newfacet has merged ridges
 
   notes:
     ridge already updated for simplicial neighbors of samecycle with a ridge
 
   see:
     qh_mergeridges()
     qh_makeridges()
 
   design:
     remove ridges between newfacet and samecycle
     for each facet in samecycle
       for each ridge in facet
         update facet pointers in ridge
         skip ridges processed in qh_mergecycle_neighors
         free ridges between newfacet and samecycle
         free ridges between facets of samecycle (on 2nd visit)
         append remaining ridges to newfacet
       if simpilicial facet
         for each neighbor of facet
           if simplicial facet
           and not samecycle facet or newfacet
             make ridge between neighbor and newfacet
 */
 void qh_mergecycle_ridges(qhT *qh, facetT *samecycle, facetT *newfacet) {
   facetT *same, *neighbor= NULL;
   int numold=0, numnew=0;
   int neighbor_i, neighbor_n;
   unsigned int samevisitid;
   ridgeT *ridge, **ridgep;
   boolT toporient;
   void **freelistp; /* used !qh_NOmem */
 
   trace4((qh, qh->ferr, 4033, "qh_mergecycle_ridges: delete shared ridges from newfacet\n"));
   samevisitid= qh->visit_id -1;
   FOREACHridge_(newfacet->ridges) {
     neighbor= otherfacet_(ridge, newfacet);
     if (neighbor->visitid == samevisitid)
       SETref_(ridge)= NULL; /* ridge free'd below */
   }
   qh_setcompact(qh, newfacet->ridges);
 
   trace4((qh, qh->ferr, 4034, "qh_mergecycle_ridges: add ridges to newfacet\n"));
   FORALLsame_cycle_(samecycle) {
     FOREACHridge_(same->ridges) {
       if (ridge->top == same) {
         ridge->top= newfacet;
         neighbor= ridge->bottom;
       }else if (ridge->bottom == same) {
         ridge->bottom= newfacet;
         neighbor= ridge->top;
       }else if (ridge->top == newfacet || ridge->bottom == newfacet) {
         qh_setappend(qh, &newfacet->ridges, ridge);
         numold++;  /* already set by qh_mergecycle_neighbors */
         continue;
       }else {
         qh_fprintf(qh, qh->ferr, 6098, "qhull internal error (qh_mergecycle_ridges): bad ridge r%d\n", ridge->id);
         qh_errexit(qh, qh_ERRqhull, NULL, ridge);
       }
       if (neighbor == newfacet) {
         qh_setfree(qh, &(ridge->vertices));
         qh_memfree_(qh, ridge, (int)sizeof(ridgeT), freelistp);
         numold++;
       }else if (neighbor->visitid == samevisitid) {
         qh_setdel(neighbor->ridges, ridge);
         qh_setfree(qh, &(ridge->vertices));
         qh_memfree_(qh, ridge, (int)sizeof(ridgeT), freelistp);
         numold++;
       }else {
         qh_setappend(qh, &newfacet->ridges, ridge);
         numold++;
       }
     }
     if (same->ridges)
       qh_settruncate(qh, same->ridges, 0);
     if (!same->simplicial)
       continue;
     FOREACHneighbor_i_(qh, same) {       /* note: !newfact->simplicial */
       if (neighbor->visitid != samevisitid && neighbor->simplicial) {
         ridge= qh_newridge(qh);
         ridge->vertices= qh_setnew_delnthsorted(qh, same->vertices, qh->hull_dim,
                                                           neighbor_i, 0);
         toporient= same->toporient ^ (neighbor_i & 0x1);
         if (toporient) {
           ridge->top= newfacet;
           ridge->bottom= neighbor;
         }else {
           ridge->top= neighbor;
           ridge->bottom= newfacet;
         }
         qh_setappend(qh, &(newfacet->ridges), ridge);
         qh_setappend(qh, &(neighbor->ridges), ridge);
         numnew++;
       }
     }
   }
 
   trace2((qh, qh->ferr, 2033, "qh_mergecycle_ridges: found %d old ridges and %d new ones\n",
              numold, numnew));
 } /* mergecycle_ridges */
 
 /*---------------------------------
 
   qh_mergecycle_vneighbors(qh, samecycle, newfacet )
     create vertex neighbors for newfacet from vertices of facets in samecycle
     samecycle marked with visitid == qh.visit_id - 1
 
   returns:
     newfacet vertices with updated neighbors
     marks newfacet with qh.visit_id-1
     deletes vertices that are merged away
     sets delridge on all vertices (faster here than in mergecycle_ridges)
 
   see:
     qh_mergevertex_neighbors()
 
   design:
     for each vertex of samecycle facet
       set vertex->delridge
       delete samecycle facets from vertex neighbors
       append newfacet to vertex neighbors
       if vertex only in newfacet
         delete it from newfacet
         add it to qh.del_vertices for later deletion
 */
 void qh_mergecycle_vneighbors(qhT *qh, facetT *samecycle, facetT *newfacet) {
   facetT *neighbor, **neighborp;
   unsigned int mergeid;
   vertexT *vertex, **vertexp, *apex;
   setT *vertices;
 
   trace4((qh, qh->ferr, 4035, "qh_mergecycle_vneighbors: update vertex neighbors for newfacet\n"));
   mergeid= qh->visit_id - 1;
   newfacet->visitid= mergeid;
   vertices= qh_basevertices(qh, samecycle); /* temp */
   apex= SETfirstt_(samecycle->vertices, vertexT);
   qh_setappend(qh, &vertices, apex);
   FOREACHvertex_(vertices) {
     vertex->delridge= True;
     FOREACHneighbor_(vertex) {
       if (neighbor->visitid == mergeid)
         SETref_(neighbor)= NULL;
     }
     qh_setcompact(qh, vertex->neighbors);
     qh_setappend(qh, &vertex->neighbors, newfacet);
     if (!SETsecond_(vertex->neighbors)) {
       zinc_(Zcyclevertex);
       trace2((qh, qh->ferr, 2034, "qh_mergecycle_vneighbors: deleted v%d when merging cycle f%d into f%d\n",
         vertex->id, samecycle->id, newfacet->id));
       qh_setdelsorted(newfacet->vertices, vertex);
       vertex->deleted= True;
       qh_setappend(qh, &qh->del_vertices, vertex);
     }
   }
   qh_settempfree(qh, &vertices);
   trace3((qh, qh->ferr, 3005, "qh_mergecycle_vneighbors: merged vertices from cycle f%d into f%d\n",
              samecycle->id, newfacet->id));
 } /* mergecycle_vneighbors */
 
 /*---------------------------------
 
   qh_mergefacet(qh, facet1, facet2, mindist, maxdist, mergeapex )
     merges facet1 into facet2
     mergeapex==qh_MERGEapex if merging new facet into coplanar horizon
 
   returns:
     qh.max_outside and qh.min_vertex updated
     initializes vertex neighbors on first merge
 
   returns:
     facet2 contains facet1's vertices, neighbors, and ridges
       facet2 moved to end of qh.facet_list
       makes facet2 a newfacet
       sets facet2->newmerge set
       clears facet2->center (unless merging into a large facet)
       clears facet2->tested and ridge->tested for facet1
 
     facet1 prepended to visible_list for later deletion and partitioning
       facet1->f.replace == facet2
 
     adds neighboring facets to facet_mergeset if redundant or degenerate
 
   notes:
     mindist/maxdist may be NULL (only if both NULL)
     traces merge if fmax_(maxdist,-mindist) > TRACEdist
 
   see:
     qh_mergecycle()
 
   design:
     trace merge and check for degenerate simplex
     make ridges for both facets
     update qh.max_outside, qh.max_vertex, qh.min_vertex
     update facet2->maxoutside and keepcentrum
     update facet2->nummerge
     update tested flags for facet2
     if facet1 is simplicial
       merge facet1 into facet2
     else
       merge facet1's neighbors into facet2
       merge facet1's ridges into facet2
       merge facet1's vertices into facet2
       merge facet1's vertex neighbors into facet2
       add facet2's vertices to qh.new_vertexlist
       unless qh_MERGEapex
         test facet2 for degenerate or redundant neighbors
       move facet1 to qh.visible_list for later deletion
       move facet2 to end of qh.newfacet_list
 */
 void qh_mergefacet(qhT *qh, facetT *facet1, facetT *facet2, realT *mindist, realT *maxdist, boolT mergeapex) {
   boolT traceonce= False;
   vertexT *vertex, **vertexp;
   int tracerestore=0, nummerge;
 
   if (facet1->tricoplanar || facet2->tricoplanar) {
     if (!qh->TRInormals) {
       qh_fprintf(qh, qh->ferr, 6226, "Qhull internal error (qh_mergefacet): does not work for tricoplanar facets.  Use option 'Q11'\n");
       qh_errexit2(qh, qh_ERRqhull, facet1, facet2);
     }
     if (facet2->tricoplanar) {
       facet2->tricoplanar= False;
       facet2->keepcentrum= False;
     }
   }
   zzinc_(Ztotmerge);
   if (qh->REPORTfreq2 && qh->POSTmerging) {
     if (zzval_(Ztotmerge) > qh->mergereport + qh->REPORTfreq2)
       qh_tracemerging(qh);
   }
 #ifndef qh_NOtrace
   if (qh->build_cnt >= qh->RERUN) {
     if (mindist && (-*mindist > qh->TRACEdist || *maxdist > qh->TRACEdist)) {
       tracerestore= 0;
       qh->IStracing= qh->TRACElevel;
       traceonce= True;
       qh_fprintf(qh, qh->ferr, 8075, "qh_mergefacet: ========= trace wide merge #%d(%2.2g) for f%d into f%d, last point was p%d\n", zzval_(Ztotmerge),
              fmax_(-*mindist, *maxdist), facet1->id, facet2->id, qh->furthest_id);
     }else if (facet1 == qh->tracefacet || facet2 == qh->tracefacet) {
       tracerestore= qh->IStracing;
       qh->IStracing= 4;
       traceonce= True;
       qh_fprintf(qh, qh->ferr, 8076, "qh_mergefacet: ========= trace merge #%d involving f%d, furthest is p%d\n",
                  zzval_(Ztotmerge), qh->tracefacet_id,  qh->furthest_id);
     }
   }
   if (qh->IStracing >= 2) {
     realT mergemin= -2;
     realT mergemax= -2;
 
     if (mindist) {
       mergemin= *mindist;
       mergemax= *maxdist;
     }
     qh_fprintf(qh, qh->ferr, 8077, "qh_mergefacet: #%d merge f%d into f%d, mindist= %2.2g, maxdist= %2.2g\n",
     zzval_(Ztotmerge), facet1->id, facet2->id, mergemin, mergemax);
   }
 #endif /* !qh_NOtrace */
   if (facet1 == facet2 || facet1->visible || facet2->visible) {
     qh_fprintf(qh, qh->ferr, 6099, "qhull internal error (qh_mergefacet): either f%d and f%d are the same or one is a visible facet\n",
              facet1->id, facet2->id);
     qh_errexit2(qh, qh_ERRqhull, facet1, facet2);
   }
   if (qh->num_facets - qh->num_visible <= qh->hull_dim + 1) {
     qh_fprintf(qh, qh->ferr, 6227, "\n\
 qhull precision error: Only %d facets remain.  Can not merge another\n\
 pair.  The input is too degenerate or the convexity constraints are\n\
 too strong.\n", qh->hull_dim+1);
     if (qh->hull_dim >= 5 && !qh->MERGEexact)
       qh_fprintf(qh, qh->ferr, 8079, "Option 'Qx' may avoid this problem.\n");
     qh_errexit(qh, qh_ERRprec, NULL, NULL);
   }
   if (!qh->VERTEXneighbors)
     qh_vertexneighbors(qh);
   qh_makeridges(qh, facet1);
   qh_makeridges(qh, facet2);
   if (qh->IStracing >=4)
     qh_errprint(qh, "MERGING", facet1, facet2, NULL, NULL);
   if (mindist) {
     maximize_(qh->max_outside, *maxdist);
     maximize_(qh->max_vertex, *maxdist);
 #if qh_MAXoutside
     maximize_(facet2->maxoutside, *maxdist);
 #endif
     minimize_(qh->min_vertex, *mindist);
     if (!facet2->keepcentrum
     && (*maxdist > qh->WIDEfacet || *mindist < -qh->WIDEfacet)) {
       facet2->keepcentrum= True;
       zinc_(Zwidefacet);
     }
   }
   nummerge= facet1->nummerge + facet2->nummerge + 1;
   if (nummerge >= qh_MAXnummerge)
     facet2->nummerge= qh_MAXnummerge;
   else
     facet2->nummerge= (short unsigned int)nummerge;
   facet2->newmerge= True;
   facet2->dupridge= False;
   qh_updatetested(qh, facet1, facet2);
   if (qh->hull_dim > 2 && qh_setsize(qh, facet1->vertices) == qh->hull_dim)
     qh_mergesimplex(qh, facet1, facet2, mergeapex);
   else {
     qh->vertex_visit++;
     FOREACHvertex_(facet2->vertices)
       vertex->visitid= qh->vertex_visit;
     if (qh->hull_dim == 2)
       qh_mergefacet2d(qh, facet1, facet2);
     else {
       qh_mergeneighbors(qh, facet1, facet2);
       qh_mergevertices(qh, facet1->vertices, &facet2->vertices);
     }
     qh_mergeridges(qh, facet1, facet2);
     qh_mergevertex_neighbors(qh, facet1, facet2);
     if (!facet2->newfacet)
       qh_newvertices(qh, facet2->vertices);
   }
   if (!mergeapex)
     qh_degen_redundant_neighbors(qh, facet2, facet1);
   if (facet2->coplanar || !facet2->newfacet) {
     zinc_(Zmergeintohorizon);
   }else if (!facet1->newfacet && facet2->newfacet) {
     zinc_(Zmergehorizon);
   }else {
     zinc_(Zmergenew);
   }
   qh_willdelete(qh, facet1, facet2);
   qh_removefacet(qh, facet2);  /* append as a newfacet to end of qh->facet_list */
   qh_appendfacet(qh, facet2);
   facet2->newfacet= True;
   facet2->tested= False;
   qh_tracemerge(qh, facet1, facet2);
   if (traceonce) {
     qh_fprintf(qh, qh->ferr, 8080, "qh_mergefacet: end of wide tracing\n");
     qh->IStracing= tracerestore;
   }
 } /* mergefacet */
 
 
 /*---------------------------------
 
   qh_mergefacet2d(qh, facet1, facet2 )
     in 2d, merges neighbors and vertices of facet1 into facet2
 
   returns:
     build ridges for neighbors if necessary
     facet2 looks like a simplicial facet except for centrum, ridges
       neighbors are opposite the corresponding vertex
       maintains orientation of facet2
 
   notes:
     qh_mergefacet() retains non-simplicial structures
       they are not needed in 2d, but later routines may use them
     preserves qh.vertex_visit for qh_mergevertex_neighbors()
 
   design:
     get vertices and neighbors
     determine new vertices and neighbors
     set new vertices and neighbors and adjust orientation
     make ridges for new neighbor if needed
 */
 void qh_mergefacet2d(qhT *qh, facetT *facet1, facetT *facet2) {
   vertexT *vertex1A, *vertex1B, *vertex2A, *vertex2B, *vertexA, *vertexB;
   facetT *neighbor1A, *neighbor1B, *neighbor2A, *neighbor2B, *neighborA, *neighborB;
 
   vertex1A= SETfirstt_(facet1->vertices, vertexT);
   vertex1B= SETsecondt_(facet1->vertices, vertexT);
   vertex2A= SETfirstt_(facet2->vertices, vertexT);
   vertex2B= SETsecondt_(facet2->vertices, vertexT);
   neighbor1A= SETfirstt_(facet1->neighbors, facetT);
   neighbor1B= SETsecondt_(facet1->neighbors, facetT);
   neighbor2A= SETfirstt_(facet2->neighbors, facetT);
   neighbor2B= SETsecondt_(facet2->neighbors, facetT);
   if (vertex1A == vertex2A) {
     vertexA= vertex1B;
     vertexB= vertex2B;
     neighborA= neighbor2A;
     neighborB= neighbor1A;
   }else if (vertex1A == vertex2B) {
     vertexA= vertex1B;
     vertexB= vertex2A;
     neighborA= neighbor2B;
     neighborB= neighbor1A;
   }else if (vertex1B == vertex2A) {
     vertexA= vertex1A;
     vertexB= vertex2B;
     neighborA= neighbor2A;
     neighborB= neighbor1B;
   }else { /* 1B == 2B */
     vertexA= vertex1A;
     vertexB= vertex2A;
     neighborA= neighbor2B;
     neighborB= neighbor1B;
   }
   /* vertexB always from facet2, neighborB always from facet1 */
   if (vertexA->id > vertexB->id) {
     SETfirst_(facet2->vertices)= vertexA;
     SETsecond_(facet2->vertices)= vertexB;
     if (vertexB == vertex2A)
       facet2->toporient= !facet2->toporient;
     SETfirst_(facet2->neighbors)= neighborA;
     SETsecond_(facet2->neighbors)= neighborB;
   }else {
     SETfirst_(facet2->vertices)= vertexB;
     SETsecond_(facet2->vertices)= vertexA;
     if (vertexB == vertex2B)
       facet2->toporient= !facet2->toporient;
     SETfirst_(facet2->neighbors)= neighborB;
     SETsecond_(facet2->neighbors)= neighborA;
   }
   qh_makeridges(qh, neighborB);
   qh_setreplace(qh, neighborB->neighbors, facet1, facet2);
   trace4((qh, qh->ferr, 4036, "qh_mergefacet2d: merged v%d and neighbor f%d of f%d into f%d\n",
        vertexA->id, neighborB->id, facet1->id, facet2->id));
 } /* mergefacet2d */
 
 
 /*---------------------------------
 
   qh_mergeneighbors(qh, facet1, facet2 )
     merges the neighbors of facet1 into facet2
 
   see:
     qh_mergecycle_neighbors()
 
   design:
     for each neighbor of facet1
       if neighbor is also a neighbor of facet2
         if neighbor is simpilicial
           make ridges for later deletion as a degenerate facet
         update its neighbor set
       else
         move the neighbor relation to facet2
     remove the neighbor relation for facet1 and facet2
 */
 void qh_mergeneighbors(qhT *qh, facetT *facet1, facetT *facet2) {
   facetT *neighbor, **neighborp;
 
   trace4((qh, qh->ferr, 4037, "qh_mergeneighbors: merge neighbors of f%d and f%d\n",
           facet1->id, facet2->id));
   qh->visit_id++;
   FOREACHneighbor_(facet2) {
     neighbor->visitid= qh->visit_id;
   }
   FOREACHneighbor_(facet1) {
     if (neighbor->visitid == qh->visit_id) {
       if (neighbor->simplicial)    /* is degen, needs ridges */
         qh_makeridges(qh, neighbor);
       if (SETfirstt_(neighbor->neighbors, facetT) != facet1) /*keep newfacet->horizon*/
         qh_setdel(neighbor->neighbors, facet1);
       else {
         qh_setdel(neighbor->neighbors, facet2);
         qh_setreplace(qh, neighbor->neighbors, facet1, facet2);
       }
     }else if (neighbor != facet2) {
       qh_setappend(qh, &(facet2->neighbors), neighbor);
       qh_setreplace(qh, neighbor->neighbors, facet1, facet2);
     }
   }
   qh_setdel(facet1->neighbors, facet2);  /* here for makeridges */
   qh_setdel(facet2->neighbors, facet1);
 } /* mergeneighbors */
 
 
 /*---------------------------------
 
   qh_mergeridges(qh, facet1, facet2 )
     merges the ridge set of facet1 into facet2
 
   returns:
     may delete all ridges for a vertex
     sets vertex->delridge on deleted ridges
 
   see:
     qh_mergecycle_ridges()
 
   design:
     delete ridges between facet1 and facet2
       mark (delridge) vertices on these ridges for later testing
     for each remaining ridge
       rename facet1 to facet2
 */
 void qh_mergeridges(qhT *qh, facetT *facet1, facetT *facet2) {
   ridgeT *ridge, **ridgep;
   vertexT *vertex, **vertexp;
 
   trace4((qh, qh->ferr, 4038, "qh_mergeridges: merge ridges of f%d and f%d\n",
           facet1->id, facet2->id));
   FOREACHridge_(facet2->ridges) {
     if ((ridge->top == facet1) || (ridge->bottom == facet1)) {
       FOREACHvertex_(ridge->vertices)
         vertex->delridge= True;
       qh_delridge(qh, ridge);  /* expensive in high-d, could rebuild */
       ridgep--; /*repeat*/
     }
   }
   FOREACHridge_(facet1->ridges) {
     if (ridge->top == facet1)
       ridge->top= facet2;
     else
       ridge->bottom= facet2;
     qh_setappend(qh, &(facet2->ridges), ridge);
   }
 } /* mergeridges */
 
 
 /*---------------------------------
 
   qh_mergesimplex(qh, facet1, facet2, mergeapex )
     merge simplicial facet1 into facet2
     mergeapex==qh_MERGEapex if merging samecycle into horizon facet
       vertex id is latest (most recently created)
     facet1 may be contained in facet2
     ridges exist for both facets
 
   returns:
     facet2 with updated vertices, ridges, neighbors
     updated neighbors for facet1's vertices
     facet1 not deleted
     sets vertex->delridge on deleted ridges
 
   notes:
     special case code since this is the most common merge
     called from qh_mergefacet()
 
   design:
     if qh_MERGEapex
       add vertices of facet2 to qh.new_vertexlist if necessary
       add apex to facet2
     else
       for each ridge between facet1 and facet2
         set vertex->delridge
       determine the apex for facet1 (i.e., vertex to be merged)
       unless apex already in facet2
         insert apex into vertices for facet2
       add vertices of facet2 to qh.new_vertexlist if necessary
       add apex to qh.new_vertexlist if necessary
       for each vertex of facet1
         if apex
           rename facet1 to facet2 in its vertex neighbors
         else
           delete facet1 from vertex neighors
           if only in facet2
             add vertex to qh.del_vertices for later deletion
       for each ridge of facet1
         delete ridges between facet1 and facet2
         append other ridges to facet2 after renaming facet to facet2
 */
 void qh_mergesimplex(qhT *qh, facetT *facet1, facetT *facet2, boolT mergeapex) {
   vertexT *vertex, **vertexp, *apex;
   ridgeT *ridge, **ridgep;
   boolT issubset= False;
   int vertex_i= -1, vertex_n;
   facetT *neighbor, **neighborp, *otherfacet;
 
   if (mergeapex) {
     if (!facet2->newfacet)
       qh_newvertices(qh, facet2->vertices);  /* apex is new */
     apex= SETfirstt_(facet1->vertices, vertexT);
     if (SETfirstt_(facet2->vertices, vertexT) != apex)
       qh_setaddnth(qh, &facet2->vertices, 0, apex);  /* apex has last id */
     else
       issubset= True;
   }else {
     zinc_(Zmergesimplex);
     FOREACHvertex_(facet1->vertices)
       vertex->seen= False;
     FOREACHridge_(facet1->ridges) {
       if (otherfacet_(ridge, facet1) == facet2) {
         FOREACHvertex_(ridge->vertices) {
           vertex->seen= True;
           vertex->delridge= True;
         }
         break;
       }
     }
     FOREACHvertex_(facet1->vertices) {
       if (!vertex->seen)
         break;  /* must occur */
     }
     apex= vertex;
     trace4((qh, qh->ferr, 4039, "qh_mergesimplex: merge apex v%d of f%d into facet f%d\n",
           apex->id, facet1->id, facet2->id));
     FOREACHvertex_i_(qh, facet2->vertices) {
       if (vertex->id < apex->id) {
         break;
       }else if (vertex->id == apex->id) {
         issubset= True;
         break;
       }
     }
     if (!issubset)
       qh_setaddnth(qh, &facet2->vertices, vertex_i, apex);
     if (!facet2->newfacet)
       qh_newvertices(qh, facet2->vertices);
     else if (!apex->newlist) {
       qh_removevertex(qh, apex);
       qh_appendvertex(qh, apex);
     }
   }
   trace4((qh, qh->ferr, 4040, "qh_mergesimplex: update vertex neighbors of f%d\n",
           facet1->id));
   FOREACHvertex_(facet1->vertices) {
     if (vertex == apex && !issubset)
       qh_setreplace(qh, vertex->neighbors, facet1, facet2);
     else {
       qh_setdel(vertex->neighbors, facet1);
       if (!SETsecond_(vertex->neighbors))
         qh_mergevertex_del(qh, vertex, facet1, facet2);
     }
   }
   trace4((qh, qh->ferr, 4041, "qh_mergesimplex: merge ridges and neighbors of f%d into f%d\n",
           facet1->id, facet2->id));
   qh->visit_id++;
   FOREACHneighbor_(facet2)
     neighbor->visitid= qh->visit_id;
   FOREACHridge_(facet1->ridges) {
     otherfacet= otherfacet_(ridge, facet1);
     if (otherfacet == facet2) {
       qh_setdel(facet2->ridges, ridge);
       qh_setfree(qh, &(ridge->vertices));
       qh_memfree(qh, ridge, (int)sizeof(ridgeT));
       qh_setdel(facet2->neighbors, facet1);
     }else {
       qh_setappend(qh, &facet2->ridges, ridge);
       if (otherfacet->visitid != qh->visit_id) {
         qh_setappend(qh, &facet2->neighbors, otherfacet);
         qh_setreplace(qh, otherfacet->neighbors, facet1, facet2);
         otherfacet->visitid= qh->visit_id;
       }else {
         if (otherfacet->simplicial)    /* is degen, needs ridges */
           qh_makeridges(qh, otherfacet);
         if (SETfirstt_(otherfacet->neighbors, facetT) != facet1)
           qh_setdel(otherfacet->neighbors, facet1);
         else {   /*keep newfacet->neighbors->horizon*/
           qh_setdel(otherfacet->neighbors, facet2);
           qh_setreplace(qh, otherfacet->neighbors, facet1, facet2);
         }
       }
       if (ridge->top == facet1) /* wait until after qh_makeridges */
         ridge->top= facet2;
       else
         ridge->bottom= facet2;
     }
   }
   SETfirst_(facet1->ridges)= NULL; /* it will be deleted */
   trace3((qh, qh->ferr, 3006, "qh_mergesimplex: merged simplex f%d apex v%d into facet f%d\n",
           facet1->id, getid_(apex), facet2->id));
 } /* mergesimplex */
 
 /*---------------------------------
 
   qh_mergevertex_del(qh, vertex, facet1, facet2 )
     delete a vertex because of merging facet1 into facet2
 
   returns:
     deletes vertex from facet2
     adds vertex to qh.del_vertices for later deletion
 */
 void qh_mergevertex_del(qhT *qh, vertexT *vertex, facetT *facet1, facetT *facet2) {
 
   zinc_(Zmergevertex);
   trace2((qh, qh->ferr, 2035, "qh_mergevertex_del: deleted v%d when merging f%d into f%d\n",
           vertex->id, facet1->id, facet2->id));
   qh_setdelsorted(facet2->vertices, vertex);
   vertex->deleted= True;
   qh_setappend(qh, &qh->del_vertices, vertex);
 } /* mergevertex_del */
 
 /*---------------------------------
 
   qh_mergevertex_neighbors(qh, facet1, facet2 )
     merge the vertex neighbors of facet1 to facet2
 
   returns:
     if vertex is current qh.vertex_visit
       deletes facet1 from vertex->neighbors
     else
       renames facet1 to facet2 in vertex->neighbors
     deletes vertices if only one neighbor
 
   notes:
     assumes vertex neighbor sets are good
 */
 void qh_mergevertex_neighbors(qhT *qh, facetT *facet1, facetT *facet2) {
   vertexT *vertex, **vertexp;
 
   trace4((qh, qh->ferr, 4042, "qh_mergevertex_neighbors: merge vertex neighbors of f%d and f%d\n",
           facet1->id, facet2->id));
   if (qh->tracevertex) {
     qh_fprintf(qh, qh->ferr, 8081, "qh_mergevertex_neighbors: of f%d and f%d at furthest p%d f0= %p\n",
              facet1->id, facet2->id, qh->furthest_id, qh->tracevertex->neighbors->e[0].p);
     qh_errprint(qh, "TRACE", NULL, NULL, NULL, qh->tracevertex);
   }
   FOREACHvertex_(facet1->vertices) {
     if (vertex->visitid != qh->vertex_visit)
       qh_setreplace(qh, vertex->neighbors, facet1, facet2);
     else {
       qh_setdel(vertex->neighbors, facet1);
       if (!SETsecond_(vertex->neighbors))
         qh_mergevertex_del(qh, vertex, facet1, facet2);
     }
   }
   if (qh->tracevertex)
     qh_errprint(qh, "TRACE", NULL, NULL, NULL, qh->tracevertex);
 } /* mergevertex_neighbors */
 
 
 /*---------------------------------
 
   qh_mergevertices(qh, vertices1, vertices2 )
     merges the vertex set of facet1 into facet2
 
   returns:
     replaces vertices2 with merged set
     preserves vertex_visit for qh_mergevertex_neighbors
     updates qh.newvertex_list
 
   design:
     create a merged set of both vertices (in inverse id order)
 */
 void qh_mergevertices(qhT *qh, setT *vertices1, setT **vertices2) {
   int newsize= qh_setsize(qh, vertices1)+qh_setsize(qh, *vertices2) - qh->hull_dim + 1;
   setT *mergedvertices;
   vertexT *vertex, **vertexp, **vertex2= SETaddr_(*vertices2, vertexT);
 
   mergedvertices= qh_settemp(qh, newsize);
   FOREACHvertex_(vertices1) {
     if (!*vertex2 || vertex->id > (*vertex2)->id)
       qh_setappend(qh, &mergedvertices, vertex);
     else {
       while (*vertex2 && (*vertex2)->id > vertex->id)
         qh_setappend(qh, &mergedvertices, *vertex2++);
       if (!*vertex2 || (*vertex2)->id < vertex->id)
         qh_setappend(qh, &mergedvertices, vertex);
       else
         qh_setappend(qh, &mergedvertices, *vertex2++);
     }
   }
   while (*vertex2)
     qh_setappend(qh, &mergedvertices, *vertex2++);
   if (newsize < qh_setsize(qh, mergedvertices)) {
     qh_fprintf(qh, qh->ferr, 6100, "qhull internal error (qh_mergevertices): facets did not share a ridge\n");
     qh_errexit(qh, qh_ERRqhull, NULL, NULL);
   }
   qh_setfree(qh, vertices2);
   *vertices2= mergedvertices;
   qh_settemppop(qh);
 } /* mergevertices */
 
 
 /*---------------------------------
 
   qh_neighbor_intersections(qh, vertex )
     return intersection of all vertices in vertex->neighbors except for vertex
 
   returns:
     returns temporary set of vertices
     does not include vertex
     NULL if a neighbor is simplicial
     NULL if empty set
 
   notes:
     used for renaming vertices
 
   design:
     initialize the intersection set with vertices of the first two neighbors
     delete vertex from the intersection
     for each remaining neighbor
       intersect its vertex set with the intersection set
       return NULL if empty
     return the intersection set
 */
 setT *qh_neighbor_intersections(qhT *qh, vertexT *vertex) {
   facetT *neighbor, **neighborp, *neighborA, *neighborB;
   setT *intersect;
   int neighbor_i, neighbor_n;
 
   FOREACHneighbor_(vertex) {
     if (neighbor->simplicial)
       return NULL;
   }
   neighborA= SETfirstt_(vertex->neighbors, facetT);
   neighborB= SETsecondt_(vertex->neighbors, facetT);
   zinc_(Zintersectnum);
   if (!neighborA)
     return NULL;
   if (!neighborB)
     intersect= qh_setcopy(qh, neighborA->vertices, 0);
   else
     intersect= qh_vertexintersect_new(qh, neighborA->vertices, neighborB->vertices);
   qh_settemppush(qh, intersect);
   qh_setdelsorted(intersect, vertex);
   FOREACHneighbor_i_(qh, vertex) {
     if (neighbor_i >= 2) {
       zinc_(Zintersectnum);
       qh_vertexintersect(qh, &intersect, neighbor->vertices);
       if (!SETfirst_(intersect)) {
         zinc_(Zintersectfail);
         qh_settempfree(qh, &intersect);
         return NULL;
       }
     }
   }
   trace3((qh, qh->ferr, 3007, "qh_neighbor_intersections: %d vertices in neighbor intersection of v%d\n",
           qh_setsize(qh, intersect), vertex->id));
   return intersect;
 } /* neighbor_intersections */
 
 /*---------------------------------
 
   qh_newvertices(qh, vertices )
     add vertices to end of qh.vertex_list (marks as new vertices)
 
   returns:
     vertices on qh.newvertex_list
     vertex->newlist set
 */
 void qh_newvertices(qhT *qh, setT *vertices) {
   vertexT *vertex, **vertexp;
 
   FOREACHvertex_(vertices) {
     if (!vertex->newlist) {
       qh_removevertex(qh, vertex);
       qh_appendvertex(qh, vertex);
     }
   }
 } /* newvertices */
 
 /*---------------------------------
 
   qh_reducevertices(qh)
     reduce extra vertices, shared vertices, and redundant vertices
     facet->newmerge is set if merged since last call
     if !qh.MERGEvertices, only removes extra vertices
 
   returns:
     True if also merged degen_redundant facets
     vertices are renamed if possible
     clears facet->newmerge and vertex->delridge
 
   notes:
     ignored if 2-d
 
   design:
     merge any degenerate or redundant facets
     for each newly merged facet
       remove extra vertices
     if qh.MERGEvertices
       for each newly merged facet
         for each vertex
           if vertex was on a deleted ridge
             rename vertex if it is shared
       remove delridge flag from new vertices
 */
 boolT qh_reducevertices(qhT *qh) {
   int numshare=0, numrename= 0;
   boolT degenredun= False;
   facetT *newfacet;
   vertexT *vertex, **vertexp;
 
   if (qh->hull_dim == 2)
     return False;
   if (qh_merge_degenredundant(qh))
     degenredun= True;
  LABELrestart:
   FORALLnew_facets {
     if (newfacet->newmerge) {
       if (!qh->MERGEvertices)
         newfacet->newmerge= False;
       qh_remove_extravertices(qh, newfacet);
     }
   }
   if (!qh->MERGEvertices)
     return False;
   FORALLnew_facets {
     if (newfacet->newmerge) {
       newfacet->newmerge= False;
       FOREACHvertex_(newfacet->vertices) {
         if (vertex->delridge) {
           if (qh_rename_sharedvertex(qh, vertex, newfacet)) {
             numshare++;
             vertexp--; /* repeat since deleted vertex */
           }
         }
       }
     }
   }
   FORALLvertex_(qh->newvertex_list) {
     if (vertex->delridge && !vertex->deleted) {
       vertex->delridge= False;
       if (qh->hull_dim >= 4 && qh_redundant_vertex(qh, vertex)) {
         numrename++;
         if (qh_merge_degenredundant(qh)) {
           degenredun= True;
           goto LABELrestart;
         }
       }
     }
   }
   trace1((qh, qh->ferr, 1014, "qh_reducevertices: renamed %d shared vertices and %d redundant vertices. Degen? %d\n",
           numshare, numrename, degenredun));
   return degenredun;
 } /* reducevertices */
 
 /*---------------------------------
 
   qh_redundant_vertex(qh, vertex )
     detect and rename a redundant vertex
     vertices have full vertex->neighbors
 
   returns:
     returns true if find a redundant vertex
       deletes vertex(vertex->deleted)
 
   notes:
     only needed if vertex->delridge and hull_dim >= 4
     may add degenerate facets to qh.facet_mergeset
     doesn't change vertex->neighbors or create redundant facets
 
   design:
     intersect vertices of all facet neighbors of vertex
     determine ridges for these vertices
     if find a new vertex for vertex amoung these ridges and vertices
       rename vertex to the new vertex
 */
 vertexT *qh_redundant_vertex(qhT *qh, vertexT *vertex) {
   vertexT *newvertex= NULL;
   setT *vertices, *ridges;
 
   trace3((qh, qh->ferr, 3008, "qh_redundant_vertex: check if v%d can be renamed\n", vertex->id));
   if ((vertices= qh_neighbor_intersections(qh, vertex))) {
     ridges= qh_vertexridges(qh, vertex);
     if ((newvertex= qh_find_newvertex(qh, vertex, vertices, ridges)))
       qh_renamevertex(qh, vertex, newvertex, ridges, NULL, NULL);
     qh_settempfree(qh, &ridges);
     qh_settempfree(qh, &vertices);
   }
   return newvertex;
 } /* redundant_vertex */
 
 /*---------------------------------
 
   qh_remove_extravertices(qh, facet )
     remove extra vertices from non-simplicial facets
 
   returns:
     returns True if it finds them
 
   design:
     for each vertex in facet
       if vertex not in a ridge (i.e., no longer used)
         delete vertex from facet
         delete facet from vertice's neighbors
         unless vertex in another facet
           add vertex to qh.del_vertices for later deletion
 */
 boolT qh_remove_extravertices(qhT *qh, facetT *facet) {
   ridgeT *ridge, **ridgep;
   vertexT *vertex, **vertexp;
   boolT foundrem= False;
 
   trace4((qh, qh->ferr, 4043, "qh_remove_extravertices: test f%d for extra vertices\n",
           facet->id));
   FOREACHvertex_(facet->vertices)
     vertex->seen= False;
   FOREACHridge_(facet->ridges) {
     FOREACHvertex_(ridge->vertices)
       vertex->seen= True;
   }
   FOREACHvertex_(facet->vertices) {
     if (!vertex->seen) {
       foundrem= True;
       zinc_(Zremvertex);
       qh_setdelsorted(facet->vertices, vertex);
       qh_setdel(vertex->neighbors, facet);
       if (!qh_setsize(qh, vertex->neighbors)) {
         vertex->deleted= True;
         qh_setappend(qh, &qh->del_vertices, vertex);
         zinc_(Zremvertexdel);
         trace2((qh, qh->ferr, 2036, "qh_remove_extravertices: v%d deleted because it's lost all ridges\n", vertex->id));
       }else
         trace3((qh, qh->ferr, 3009, "qh_remove_extravertices: v%d removed from f%d because it's lost all ridges\n", vertex->id, facet->id));
       vertexp--; /*repeat*/
     }
   }
   return foundrem;
 } /* remove_extravertices */
 
 /*---------------------------------
 
   qh_rename_sharedvertex(qh, vertex, facet )
     detect and rename if shared vertex in facet
     vertices have full ->neighbors
 
   returns:
     newvertex or NULL
     the vertex may still exist in other facets (i.e., a neighbor was pinched)
     does not change facet->neighbors
     updates vertex->neighbors
 
   notes:
     a shared vertex for a facet is only in ridges to one neighbor
     this may undo a pinched facet
 
     it does not catch pinches involving multiple facets.  These appear
       to be difficult to detect, since an exhaustive search is too expensive.
 
   design:
     if vertex only has two neighbors
       determine the ridges that contain the vertex
       determine the vertices shared by both neighbors
       if can find a new vertex in this set
         rename the vertex to the new vertex
 */
 vertexT *qh_rename_sharedvertex(qhT *qh, vertexT *vertex, facetT *facet) {
   facetT *neighbor, **neighborp, *neighborA= NULL;
   setT *vertices, *ridges;
   vertexT *newvertex;
 
   if (qh_setsize(qh, vertex->neighbors) == 2) {
     neighborA= SETfirstt_(vertex->neighbors, facetT);
     if (neighborA == facet)
       neighborA= SETsecondt_(vertex->neighbors, facetT);
   }else if (qh->hull_dim == 3)
     return NULL;
   else {
     qh->visit_id++;
     FOREACHneighbor_(facet)
       neighbor->visitid= qh->visit_id;
     FOREACHneighbor_(vertex) {
       if (neighbor->visitid == qh->visit_id) {
         if (neighborA)
           return NULL;
         neighborA= neighbor;
       }
     }
     if (!neighborA) {
       qh_fprintf(qh, qh->ferr, 6101, "qhull internal error (qh_rename_sharedvertex): v%d's neighbors not in f%d\n",
         vertex->id, facet->id);
       qh_errprint(qh, "ERRONEOUS", facet, NULL, NULL, vertex);
       qh_errexit(qh, qh_ERRqhull, NULL, NULL);
     }
   }
   /* the vertex is shared by facet and neighborA */
   ridges= qh_settemp(qh, qh->TEMPsize);
   neighborA->visitid= ++qh->visit_id;
   qh_vertexridges_facet(qh, vertex, facet, &ridges);
   trace2((qh, qh->ferr, 2037, "qh_rename_sharedvertex: p%d(v%d) is shared by f%d(%d ridges) and f%d\n",
     qh_pointid(qh, vertex->point), vertex->id, facet->id, qh_setsize(qh, ridges), neighborA->id));
   zinc_(Zintersectnum);
   vertices= qh_vertexintersect_new(qh, facet->vertices, neighborA->vertices);
   qh_setdel(vertices, vertex);
   qh_settemppush(qh, vertices);
   if ((newvertex= qh_find_newvertex(qh, vertex, vertices, ridges)))
     qh_renamevertex(qh, vertex, newvertex, ridges, facet, neighborA);
   qh_settempfree(qh, &vertices);
   qh_settempfree(qh, &ridges);
   return newvertex;
 } /* rename_sharedvertex */
 
 /*---------------------------------
 
   qh_renameridgevertex(qh, ridge, oldvertex, newvertex )
     renames oldvertex as newvertex in ridge
 
   returns:
 
   design:
     delete oldvertex from ridge
     if newvertex already in ridge
       copy ridge->noconvex to another ridge if possible
       delete the ridge
     else
       insert newvertex into the ridge
       adjust the ridge's orientation
 */
 void qh_renameridgevertex(qhT *qh, ridgeT *ridge, vertexT *oldvertex, vertexT *newvertex) {
   int nth= 0, oldnth;
   facetT *temp;
   vertexT *vertex, **vertexp;
 
   oldnth= qh_setindex(ridge->vertices, oldvertex);
   qh_setdelnthsorted(qh, ridge->vertices, oldnth);
   FOREACHvertex_(ridge->vertices) {
     if (vertex == newvertex) {
       zinc_(Zdelridge);
       if (ridge->nonconvex) /* only one ridge has nonconvex set */
         qh_copynonconvex(qh, ridge);
       qh_delridge(qh, ridge);
       trace2((qh, qh->ferr, 2038, "qh_renameridgevertex: ridge r%d deleted.  It contained both v%d and v%d\n",
         ridge->id, oldvertex->id, newvertex->id));
       return;
     }
     if (vertex->id < newvertex->id)
       break;
     nth++;
   }
   qh_setaddnth(qh, &ridge->vertices, nth, newvertex);
   if (abs(oldnth - nth)%2) {
     trace3((qh, qh->ferr, 3010, "qh_renameridgevertex: swapped the top and bottom of ridge r%d\n",
             ridge->id));
     temp= ridge->top;
     ridge->top= ridge->bottom;
     ridge->bottom= temp;
   }
 } /* renameridgevertex */
 
 
 /*---------------------------------
 
   qh_renamevertex(qh, oldvertex, newvertex, ridges, oldfacet, neighborA )
     renames oldvertex as newvertex in ridges
     gives oldfacet/neighborA if oldvertex is shared between two facets
 
   returns:
     oldvertex may still exist afterwards
 
 
   notes:
     can not change neighbors of newvertex (since it's a subset)
 
   design:
     for each ridge in ridges
       rename oldvertex to newvertex and delete degenerate ridges
     if oldfacet not defined
       for each neighbor of oldvertex
         delete oldvertex from neighbor's vertices
         remove extra vertices from neighbor
       add oldvertex to qh.del_vertices
     else if oldvertex only between oldfacet and neighborA
       delete oldvertex from oldfacet and neighborA
       add oldvertex to qh.del_vertices
     else oldvertex is in oldfacet and neighborA and other facets (i.e., pinched)
       delete oldvertex from oldfacet
       delete oldfacet from oldvertice's neighbors
       remove extra vertices (e.g., oldvertex) from neighborA
 */
 void qh_renamevertex(qhT *qh, vertexT *oldvertex, vertexT *newvertex, setT *ridges, facetT *oldfacet, facetT *neighborA) {
   facetT *neighbor, **neighborp;
   ridgeT *ridge, **ridgep;
   boolT istrace= False;
 
   if (qh->IStracing >= 2 || oldvertex->id == qh->tracevertex_id ||
         newvertex->id == qh->tracevertex_id)
     istrace= True;
   FOREACHridge_(ridges)
     qh_renameridgevertex(qh, ridge, oldvertex, newvertex);
   if (!oldfacet) {
     zinc_(Zrenameall);
     if (istrace)
       qh_fprintf(qh, qh->ferr, 8082, "qh_renamevertex: renamed v%d to v%d in several facets\n",
                oldvertex->id, newvertex->id);
     FOREACHneighbor_(oldvertex) {
       qh_maydropneighbor(qh, neighbor);
       qh_setdelsorted(neighbor->vertices, oldvertex);
       if (qh_remove_extravertices(qh, neighbor))
         neighborp--; /* neighbor may be deleted */
     }
     if (!oldvertex->deleted) {
       oldvertex->deleted= True;
       qh_setappend(qh, &qh->del_vertices, oldvertex);
     }
   }else if (qh_setsize(qh, oldvertex->neighbors) == 2) {
     zinc_(Zrenameshare);
     if (istrace)
       qh_fprintf(qh, qh->ferr, 8083, "qh_renamevertex: renamed v%d to v%d in oldfacet f%d\n",
                oldvertex->id, newvertex->id, oldfacet->id);
     FOREACHneighbor_(oldvertex)
       qh_setdelsorted(neighbor->vertices, oldvertex);
     oldvertex->deleted= True;
     qh_setappend(qh, &qh->del_vertices, oldvertex);
   }else {
     zinc_(Zrenamepinch);
     if (istrace || qh->IStracing)
       qh_fprintf(qh, qh->ferr, 8084, "qh_renamevertex: renamed pinched v%d to v%d between f%d and f%d\n",
                oldvertex->id, newvertex->id, oldfacet->id, neighborA->id);
     qh_setdelsorted(oldfacet->vertices, oldvertex);
     qh_setdel(oldvertex->neighbors, oldfacet);
     qh_remove_extravertices(qh, neighborA);
   }
 } /* renamevertex */
 
 
 /*---------------------------------
 
   qh_test_appendmerge(qh, facet, neighbor )
     tests facet/neighbor for convexity
     appends to mergeset if non-convex
     if pre-merging,
       nop if qh.SKIPconvex, or qh.MERGEexact and coplanar
 
   returns:
     true if appends facet/neighbor to mergeset
     sets facet->center as needed
     does not change facet->seen
 
   design:
     if qh.cos_max is defined
       if the angle between facet normals is too shallow
         append an angle-coplanar merge to qh.mergeset
         return True
     make facet's centrum if needed
     if facet's centrum is above the neighbor
       set isconcave
     else
       if facet's centrum is not below the neighbor
         set iscoplanar
       make neighbor's centrum if needed
       if neighbor's centrum is above the facet
         set isconcave
       else if neighbor's centrum is not below the facet
         set iscoplanar
    if isconcave or iscoplanar
      get angle if needed
      append concave or coplanar merge to qh.mergeset
 */
 boolT qh_test_appendmerge(qhT *qh, facetT *facet, facetT *neighbor) {
   realT dist, dist2= -REALmax, angle= -REALmax;
   boolT isconcave= False, iscoplanar= False, okangle= False;
 
   if (qh->SKIPconvex && !qh->POSTmerging)
     return False;
   if ((!qh->MERGEexact || qh->POSTmerging) && qh->cos_max < REALmax/2) {
     angle= qh_getangle(qh, facet->normal, neighbor->normal);
     zinc_(Zangletests);
     if (angle > qh->cos_max) {
       zinc_(Zcoplanarangle);
       qh_appendmergeset(qh, facet, neighbor, MRGanglecoplanar, &angle);
       trace2((qh, qh->ferr, 2039, "qh_test_appendmerge: coplanar angle %4.4g between f%d and f%d\n",
          angle, facet->id, neighbor->id));
       return True;
     }else
       okangle= True;
   }
   if (!facet->center)
     facet->center= qh_getcentrum(qh, facet);
   zzinc_(Zcentrumtests);
   qh_distplane(qh, facet->center, neighbor, &dist);
   if (dist > qh->centrum_radius)
     isconcave= True;
   else {
     if (dist > -qh->centrum_radius)
       iscoplanar= True;
     if (!neighbor->center)
       neighbor->center= qh_getcentrum(qh, neighbor);
     zzinc_(Zcentrumtests);
     qh_distplane(qh, neighbor->center, facet, &dist2);
     if (dist2 > qh->centrum_radius)
       isconcave= True;
     else if (!iscoplanar && dist2 > -qh->centrum_radius)
       iscoplanar= True;
   }
   if (!isconcave && (!iscoplanar || (qh->MERGEexact && !qh->POSTmerging)))
     return False;
   if (!okangle && qh->ANGLEmerge) {
     angle= qh_getangle(qh, facet->normal, neighbor->normal);
     zinc_(Zangletests);
   }
   if (isconcave) {
     zinc_(Zconcaveridge);
     if (qh->ANGLEmerge)
       angle += qh_ANGLEconcave + 0.5;
     qh_appendmergeset(qh, facet, neighbor, MRGconcave, &angle);
     trace0((qh, qh->ferr, 18, "qh_test_appendmerge: concave f%d to f%d dist %4.4g and reverse dist %4.4g angle %4.4g during p%d\n",
            facet->id, neighbor->id, dist, dist2, angle, qh->furthest_id));
   }else /* iscoplanar */ {
     zinc_(Zcoplanarcentrum);
     qh_appendmergeset(qh, facet, neighbor, MRGcoplanar, &angle);
     trace2((qh, qh->ferr, 2040, "qh_test_appendmerge: coplanar f%d to f%d dist %4.4g, reverse dist %4.4g angle %4.4g\n",
               facet->id, neighbor->id, dist, dist2, angle));
   }
   return True;
 } /* test_appendmerge */
 
 /*---------------------------------
 
   qh_test_vneighbors(qh)
     test vertex neighbors for convexity
     tests all facets on qh.newfacet_list
 
   returns:
     true if non-convex vneighbors appended to qh.facet_mergeset
     initializes vertex neighbors if needed
 
   notes:
     assumes all facet neighbors have been tested
     this can be expensive
     this does not guarantee that a centrum is below all facets
       but it is unlikely
     uses qh.visit_id
 
   design:
     build vertex neighbors if necessary
     for all new facets
       for all vertices
         for each unvisited facet neighbor of the vertex
           test new facet and neighbor for convexity
 */
 boolT qh_test_vneighbors(qhT *qh /* qh->newfacet_list */) {
   facetT *newfacet, *neighbor, **neighborp;
   vertexT *vertex, **vertexp;
   int nummerges= 0;
 
   trace1((qh, qh->ferr, 1015, "qh_test_vneighbors: testing vertex neighbors for convexity\n"));
   if (!qh->VERTEXneighbors)
     qh_vertexneighbors(qh);
   FORALLnew_facets
     newfacet->seen= False;
   FORALLnew_facets {
     newfacet->seen= True;
     newfacet->visitid= qh->visit_id++;
     FOREACHneighbor_(newfacet)
       newfacet->visitid= qh->visit_id;
     FOREACHvertex_(newfacet->vertices) {
       FOREACHneighbor_(vertex) {
         if (neighbor->seen || neighbor->visitid == qh->visit_id)
           continue;
         if (qh_test_appendmerge(qh, newfacet, neighbor))
           nummerges++;
       }
     }
   }
   zadd_(Ztestvneighbor, nummerges);
   trace1((qh, qh->ferr, 1016, "qh_test_vneighbors: found %d non-convex, vertex neighbors\n",
            nummerges));
   return (nummerges > 0);
 } /* test_vneighbors */
 
 /*---------------------------------
 
   qh_tracemerge(qh, facet1, facet2 )
     print trace message after merge
 */
 void qh_tracemerge(qhT *qh, facetT *facet1, facetT *facet2) {
   boolT waserror= False;
 
 #ifndef qh_NOtrace
   if (qh->IStracing >= 4)
     qh_errprint(qh, "MERGED", facet2, NULL, NULL, NULL);
   if (facet2 == qh->tracefacet || (qh->tracevertex && qh->tracevertex->newlist)) {
     qh_fprintf(qh, qh->ferr, 8085, "qh_tracemerge: trace facet and vertex after merge of f%d and f%d, furthest p%d\n", facet1->id, facet2->id, qh->furthest_id);
     if (facet2 != qh->tracefacet)
       qh_errprint(qh, "TRACE", qh->tracefacet,
         (qh->tracevertex && qh->tracevertex->neighbors) ?
            SETfirstt_(qh->tracevertex->neighbors, facetT) : NULL,
         NULL, qh->tracevertex);
   }
   if (qh->tracevertex) {
     if (qh->tracevertex->deleted)
       qh_fprintf(qh, qh->ferr, 8086, "qh_tracemerge: trace vertex deleted at furthest p%d\n",
             qh->furthest_id);
     else
       qh_checkvertex(qh, qh->tracevertex);
   }
   if (qh->tracefacet) {
     qh_checkfacet(qh, qh->tracefacet, True, &waserror);
     if (waserror)
       qh_errexit(qh, qh_ERRqhull, qh->tracefacet, NULL);
   }
 #endif /* !qh_NOtrace */
   if (qh->CHECKfrequently || qh->IStracing >= 4) { /* can't check polygon here */
     qh_checkfacet(qh, facet2, True, &waserror);
     if (waserror)
       qh_errexit(qh, qh_ERRqhull, NULL, NULL);
   }
 } /* tracemerge */
 
 /*---------------------------------
 
   qh_tracemerging(qh)
     print trace message during POSTmerging
 
   returns:
     updates qh.mergereport
 
   notes:
     called from qh_mergecycle() and qh_mergefacet()
 
   see:
     qh_buildtracing()
 */
 void qh_tracemerging(qhT *qh) {
   realT cpu;
   int total;
   time_t timedata;
   struct tm *tp;
 
   qh->mergereport= zzval_(Ztotmerge);
   time(&timedata);
   tp= localtime(&timedata);
   cpu= qh_CPUclock;
   cpu /= qh_SECticks;
   total= zzval_(Ztotmerge) - zzval_(Zcyclehorizon) + zzval_(Zcyclefacettot);
   qh_fprintf(qh, qh->ferr, 8087, "\n\
 At %d:%d:%d & %2.5g CPU secs, qhull has merged %d facets.  The hull\n\
   contains %d facets and %d vertices.\n",
       tp->tm_hour, tp->tm_min, tp->tm_sec, cpu,
       total, qh->num_facets - qh->num_visible,
       qh->num_vertices-qh_setsize(qh, qh->del_vertices));
 } /* tracemerging */
 
 /*---------------------------------
 
   qh_updatetested(qh, facet1, facet2 )
     clear facet2->tested and facet1->ridge->tested for merge
 
   returns:
     deletes facet2->center unless it's already large
       if so, clears facet2->ridge->tested
 
   design:
     clear facet2->tested
     clear ridge->tested for facet1's ridges
     if facet2 has a centrum
       if facet2 is large
         set facet2->keepcentrum
       else if facet2 has 3 vertices due to many merges, or not large and post merging
         clear facet2->keepcentrum
       unless facet2->keepcentrum
         clear facet2->center to recompute centrum later
         clear ridge->tested for facet2's ridges
 */
 void qh_updatetested(qhT *qh, facetT *facet1, facetT *facet2) {
   ridgeT *ridge, **ridgep;
   int size;
 
   facet2->tested= False;
   FOREACHridge_(facet1->ridges)
     ridge->tested= False;
   if (!facet2->center)
     return;
   size= qh_setsize(qh, facet2->vertices);
   if (!facet2->keepcentrum) {
     if (size > qh->hull_dim + qh_MAXnewcentrum) {
       facet2->keepcentrum= True;
       zinc_(Zwidevertices);
     }
   }else if (size <= qh->hull_dim + qh_MAXnewcentrum) {
     /* center and keepcentrum was set */
     if (size == qh->hull_dim || qh->POSTmerging)
       facet2->keepcentrum= False; /* if many merges need to recompute centrum */
   }
   if (!facet2->keepcentrum) {
     qh_memfree(qh, facet2->center, qh->normal_size);
     facet2->center= NULL;
     FOREACHridge_(facet2->ridges)
       ridge->tested= False;
   }
 } /* updatetested */
 
 /*---------------------------------
 
   qh_vertexridges(qh, vertex )
     return temporary set of ridges adjacent to a vertex
     vertex->neighbors defined
 
   ntoes:
     uses qh.visit_id
     does not include implicit ridges for simplicial facets
 
   design:
     for each neighbor of vertex
       add ridges that include the vertex to ridges
 */
 setT *qh_vertexridges(qhT *qh, vertexT *vertex) {
   facetT *neighbor, **neighborp;
   setT *ridges= qh_settemp(qh, qh->TEMPsize);
   int size;
 
   qh->visit_id++;
   FOREACHneighbor_(vertex)
     neighbor->visitid= qh->visit_id;
   FOREACHneighbor_(vertex) {
     if (*neighborp)   /* no new ridges in last neighbor */
       qh_vertexridges_facet(qh, vertex, neighbor, &ridges);
   }
   if (qh->PRINTstatistics || qh->IStracing) {
     size= qh_setsize(qh, ridges);
     zinc_(Zvertexridge);
     zadd_(Zvertexridgetot, size);
     zmax_(Zvertexridgemax, size);
     trace3((qh, qh->ferr, 3011, "qh_vertexridges: found %d ridges for v%d\n",
              size, vertex->id));
   }
   return ridges;
 } /* vertexridges */
 
 /*---------------------------------
 
   qh_vertexridges_facet(qh, vertex, facet, ridges )
     add adjacent ridges for vertex in facet
     neighbor->visitid==qh.visit_id if it hasn't been visited
 
   returns:
     ridges updated
     sets facet->visitid to qh.visit_id-1
 
   design:
     for each ridge of facet
       if ridge of visited neighbor (i.e., unprocessed)
         if vertex in ridge
           append ridge to vertex
     mark facet processed
 */
 void qh_vertexridges_facet(qhT *qh, vertexT *vertex, facetT *facet, setT **ridges) {
   ridgeT *ridge, **ridgep;
   facetT *neighbor;
 
   FOREACHridge_(facet->ridges) {
     neighbor= otherfacet_(ridge, facet);
     if (neighbor->visitid == qh->visit_id
     && qh_setin(ridge->vertices, vertex))
       qh_setappend(qh, ridges, ridge);
   }
   facet->visitid= qh->visit_id-1;
 } /* vertexridges_facet */
 
 /*---------------------------------
 
   qh_willdelete(qh, facet, replace )
     moves facet to visible list
     sets facet->f.replace to replace (may be NULL)
 
   returns:
     bumps qh.num_visible
 */
 void qh_willdelete(qhT *qh, facetT *facet, facetT *replace) {
 
   qh_removefacet(qh, facet);
   qh_prependfacet(qh, facet, &qh->visible_list);
   qh->num_visible++;
   facet->visible= True;
   facet->f.replace= replace;
 } /* willdelete */
 
 #else /* qh_NOmerge */
 void qh_premerge(qhT *qh, vertexT *apex, realT maxcentrum, realT maxangle) {
 }
 void qh_postmerge(qhT *qh, const char *reason, realT maxcentrum, realT maxangle,
                       boolT vneighbors) {
 }
 boolT qh_checkzero(qhT *qh, boolT testall) {
    }
 #endif /* qh_NOmerge */
 
diff --git a/src/libqhullr/merge_r.h b/src/libqhullr/merge_r.h
index 5b099dc..807e0b2 100644
--- a/src/libqhullr/merge_r.h
+++ b/src/libqhullr/merge_r.h
@@ -1,178 +1,178 @@
 /*
  ---------------------------------
 
-   merge.h
-   header file for merge.c
+   merge_r.h
+   header file for merge_r.c
 
-   see qh-merge.htm and merge.c
+   see qh-merge.htm and merge_r.c
 
    Copyright (c) 1993-2014 C.B. Barber.
-   $Id: //main/2011/qhull/src/libqhullr/merge_r.h#2 $$Change: 1645 $
-   $DateTime: 2014/01/15 12:51:30 $$Author: bbarber $
+   $Id: //main/2011/qhull/src/libqhullr/merge_r.h#6 $$Change: 1797 $
+   $DateTime: 2014/12/15 17:23:41 $$Author: bbarber $
 */
 
 #ifndef qhDEFmerge
 #define qhDEFmerge 1
 
 #include "libqhull_r.h"
 
 
 /*============ -constants- ==============*/
 
 /*----------------------------------
 
   qh_ANGLEredundant
     indicates redundant merge in mergeT->angle
 */
 #define qh_ANGLEredundant 6.0
 
 /*----------------------------------
 
   qh_ANGLEdegen
     indicates degenerate facet in mergeT->angle
 */
 #define qh_ANGLEdegen     5.0
 
 /*----------------------------------
 
   qh_ANGLEconcave
     offset to indicate concave facets in mergeT->angle
 
   notes:
     concave facets are assigned the range of [2,4] in mergeT->angle
     roundoff error may make the angle less than 2
 */
 #define qh_ANGLEconcave  1.5
 
 /*----------------------------------
 
   MRG... (mergeType)
     indicates the type of a merge (mergeT->type)
 */
 typedef enum {  /* in sort order for facet_mergeset */
   MRGnone= 0,
   MRGcoplanar,          /* centrum coplanar */
   MRGanglecoplanar,     /* angle coplanar */
                         /* could detect half concave ridges */
   MRGconcave,           /* concave ridge */
   MRGflip,              /* flipped facet. facet1 == facet2 */
   MRGridge,             /* duplicate ridge (qh_MERGEridge) */
                         /* degen and redundant go onto degen_mergeset */
   MRGdegen,             /* degenerate facet (!enough neighbors) facet1 == facet2 */
   MRGredundant,         /* redundant facet (vertex subset) */
                         /* merge_degenredundant assumes degen < redundant */
   MRGmirror,            /* mirror facet from qh_triangulate */
   ENDmrg
 } mergeType;
 
 /*----------------------------------
 
   qh_MERGEapex
     flag for qh_mergefacet() to indicate an apex merge
 */
 #define qh_MERGEapex     True
 
 /*============ -structures- ====================*/
 
 /*----------------------------------
 
   mergeT
     structure used to merge facets
 */
 
 typedef struct mergeT mergeT;
 struct mergeT {         /* initialize in qh_appendmergeset */
   realT   angle;        /* angle between normals of facet1 and facet2 */
   facetT *facet1;       /* will merge facet1 into facet2 */
   facetT *facet2;
   mergeType type;
 };
 
 
 /*=========== -macros- =========================*/
 
 /*----------------------------------
 
   FOREACHmerge_( merges ) {...}
     assign 'merge' to each merge in merges
 
   notes:
     uses 'mergeT *merge, **mergep;'
     if qh_mergefacet(),
       restart since qh.facet_mergeset may change
-    see FOREACHsetelement_
+    see FOREACHsetelement_
 */
 #define FOREACHmerge_( merges ) FOREACHsetelement_(mergeT, merges, merge)
 
 /*============ prototypes in alphabetical order after pre/postmerge =======*/
 
 void    qh_premerge(qhT *qh, vertexT *apex, realT maxcentrum, realT maxangle);
 void    qh_postmerge(qhT *qh, const char *reason, realT maxcentrum, realT maxangle,
              boolT vneighbors);
 void    qh_all_merges(qhT *qh, boolT othermerge, boolT vneighbors);
 void    qh_appendmergeset(qhT *qh, facetT *facet, facetT *neighbor, mergeType mergetype, realT *angle);
 setT   *qh_basevertices(qhT *qh, facetT *samecycle);
 void    qh_checkconnect(qhT *qh /* qh.new_facets */);
 boolT   qh_checkzero(qhT *qh, boolT testall);
 int     qh_compareangle(const void *p1, const void *p2);
 int     qh_comparemerge(const void *p1, const void *p2);
 int     qh_comparevisit(const void *p1, const void *p2);
 void    qh_copynonconvex(qhT *qh, ridgeT *atridge);
 void    qh_degen_redundant_facet(qhT *qh, facetT *facet);
 void    qh_degen_redundant_neighbors(qhT *qh, facetT *facet, facetT *delfacet);
 vertexT *qh_find_newvertex(qhT *qh, vertexT *oldvertex, setT *vertices, setT *ridges);
 void    qh_findbest_test(qhT *qh, boolT testcentrum, facetT *facet, facetT *neighbor,
            facetT **bestfacet, realT *distp, realT *mindistp, realT *maxdistp);
 facetT *qh_findbestneighbor(qhT *qh, facetT *facet, realT *distp, realT *mindistp, realT *maxdistp);
 void    qh_flippedmerges(qhT *qh, facetT *facetlist, boolT *wasmerge);
 void    qh_forcedmerges(qhT *qh, boolT *wasmerge);
 void    qh_getmergeset(qhT *qh, facetT *facetlist);
 void    qh_getmergeset_initial(qhT *qh, facetT *facetlist);
 void    qh_hashridge(qhT *qh, setT *hashtable, int hashsize, ridgeT *ridge, vertexT *oldvertex);
 ridgeT *qh_hashridge_find(qhT *qh, setT *hashtable, int hashsize, ridgeT *ridge,
               vertexT *vertex, vertexT *oldvertex, int *hashslot);
 void    qh_makeridges(qhT *qh, facetT *facet);
 void    qh_mark_dupridges(qhT *qh, facetT *facetlist);
 void    qh_maydropneighbor(qhT *qh, facetT *facet);
 int     qh_merge_degenredundant(qhT *qh);
 void    qh_merge_nonconvex(qhT *qh, facetT *facet1, facetT *facet2, mergeType mergetype);
 void    qh_mergecycle(qhT *qh, facetT *samecycle, facetT *newfacet);
 void    qh_mergecycle_all(qhT *qh, facetT *facetlist, boolT *wasmerge);
 void    qh_mergecycle_facets(qhT *qh, facetT *samecycle, facetT *newfacet);
 void    qh_mergecycle_neighbors(qhT *qh, facetT *samecycle, facetT *newfacet);
 void    qh_mergecycle_ridges(qhT *qh, facetT *samecycle, facetT *newfacet);
 void    qh_mergecycle_vneighbors(qhT *qh, facetT *samecycle, facetT *newfacet);
 void    qh_mergefacet(qhT *qh, facetT *facet1, facetT *facet2, realT *mindist, realT *maxdist, boolT mergeapex);
 void    qh_mergefacet2d(qhT *qh, facetT *facet1, facetT *facet2);
 void    qh_mergeneighbors(qhT *qh, facetT *facet1, facetT *facet2);
 void    qh_mergeridges(qhT *qh, facetT *facet1, facetT *facet2);
 void    qh_mergesimplex(qhT *qh, facetT *facet1, facetT *facet2, boolT mergeapex);
 void    qh_mergevertex_del(qhT *qh, vertexT *vertex, facetT *facet1, facetT *facet2);
 void    qh_mergevertex_neighbors(qhT *qh, facetT *facet1, facetT *facet2);
 void    qh_mergevertices(qhT *qh, setT *vertices1, setT **vertices);
 setT   *qh_neighbor_intersections(qhT *qh, vertexT *vertex);
 void    qh_newvertices(qhT *qh, setT *vertices);
 boolT   qh_reducevertices(qhT *qh);
 vertexT *qh_redundant_vertex(qhT *qh, vertexT *vertex);
 boolT   qh_remove_extravertices(qhT *qh, facetT *facet);
 vertexT *qh_rename_sharedvertex(qhT *qh, vertexT *vertex, facetT *facet);
 void    qh_renameridgevertex(qhT *qh, ridgeT *ridge, vertexT *oldvertex, vertexT *newvertex);
 void    qh_renamevertex(qhT *qh, vertexT *oldvertex, vertexT *newvertex, setT *ridges,
                         facetT *oldfacet, facetT *neighborA);
 boolT   qh_test_appendmerge(qhT *qh, facetT *facet, facetT *neighbor);
 boolT   qh_test_vneighbors(qhT *qh /* qh.newfacet_list */);
 void    qh_tracemerge(qhT *qh, facetT *facet1, facetT *facet2);
 void    qh_tracemerging(qhT *qh);
 void    qh_updatetested(qhT *qh, facetT *facet1, facetT *facet2);
 setT   *qh_vertexridges(qhT *qh, vertexT *vertex);
 void    qh_vertexridges_facet(qhT *qh, vertexT *vertex, facetT *facet, setT **ridges);
 void    qh_willdelete(qhT *qh, facetT *facet, facetT *replace);
 
 #endif /* qhDEFmerge */
diff --git a/src/libqhullr/poly2_r.c b/src/libqhullr/poly2_r.c
index 9ad9327..b312a5c 100644
--- a/src/libqhullr/poly2_r.c
+++ b/src/libqhullr/poly2_r.c
@@ -1,3154 +1,3153 @@
 /*
  ---------------------------------
 
-   poly2.c
-   implements polygons and simplices
+   poly2_r.c
+   implements polygons and simplicies
 
-   see qh-poly.htm, poly.h and libqhull.h
+   see qh-poly.htm, poly_r.h and libqhull_r.h
 
-   frequently used code is in poly.c
+   frequently used code is in poly_r.c
 
    Copyright (c) 1993-2014 The Geometry Center.
-   $Id: //main/2011/qhull/src/libqhullr/poly2_r.c#4 $$Change: 1663 $
-   $DateTime: 2014/01/19 17:59:16 $$Author: bbarber $
+   $Id: //main/2011/qhull/src/libqhullr/poly2_r.c#7 $$Change: 1797 $
+   $DateTime: 2014/12/15 17:23:41 $$Author: bbarber $
 */
 
-#include "qhull_r.h"
+#include "qhull_ra.h"
 
 /*======== functions in alphabetical order ==========*/
 
 /*---------------------------------
 
   qh_addhash(qh, newelem, hashtable, hashsize, hash )
     add newelem to linear hash table at hash if not already there
 */
 void qh_addhash(qhT *qh, void *newelem, setT *hashtable, int hashsize, int hash) {
   int scan;
   void *elem;
 
   for (scan= (int)hash; (elem= SETelem_(hashtable, scan));
        scan= (++scan >= hashsize ? 0 : scan)) {
     if (elem == newelem)
       break;
   }
   /* loop terminates because qh_HASHfactor >= 1.1 by qh_initbuffers */
   if (!elem)
     SETelem_(hashtable, scan)= newelem;
 } /* addhash */
 
 /*---------------------------------
 
   qh_check_bestdist(qh)
     check that all points are within max_outside of the nearest facet
     if qh.ONLYgood,
       ignores !good facets
 
   see:
     qh_check_maxout(), qh_outerinner()
 
   notes:
     only called from qh_check_points()
       seldom used since qh.MERGING is almost always set
     if notverified>0 at end of routine
       some points were well inside the hull.  If the hull contains
       a lens-shaped component, these points were not verified.  Use
       options 'Qi Tv' to verify all points.  (Exhaustive check also verifies)
 
   design:
     determine facet for each point (if any)
     for each point
       start with the assigned facet or with the first facet
       find the best facet for the point and check all coplanar facets
       error if point is outside of facet
 */
 void qh_check_bestdist(qhT *qh) {
   boolT waserror= False, unassigned;
   facetT *facet, *bestfacet, *errfacet1= NULL, *errfacet2= NULL;
   facetT *facetlist;
   realT dist, maxoutside, maxdist= -REALmax;
   pointT *point;
   int numpart= 0, facet_i, facet_n, notgood= 0, notverified= 0;
   setT *facets;
 
   trace1((qh, qh->ferr, 1020, "qh_check_bestdist: check points below nearest facet.  Facet_list f%d\n",
       qh->facet_list->id));
   maxoutside= qh_maxouter(qh);
   maxoutside += qh->DISTround;
   /* one more qh.DISTround for check computation */
   trace1((qh, qh->ferr, 1021, "qh_check_bestdist: check that all points are within %2.2g of best facet\n", maxoutside));
   facets= qh_pointfacet(qh /*qh.facet_list*/);
   if (!qh_QUICKhelp && qh->PRINTprecision)
     qh_fprintf(qh, qh->ferr, 8091, "\n\
 qhull output completed.  Verifying that %d points are\n\
 below %2.2g of the nearest %sfacet.\n",
              qh_setsize(qh, facets), maxoutside, (qh->ONLYgood ?  "good " : ""));
   FOREACHfacet_i_(qh, facets) {  /* for each point with facet assignment */
     if (facet)
       unassigned= False;
     else {
       unassigned= True;
       facet= qh->facet_list;
     }
     point= qh_point(qh, facet_i);
     if (point == qh->GOODpointp)
       continue;
     qh_distplane(qh, point, facet, &dist);
     numpart++;
     bestfacet= qh_findbesthorizon(qh, !qh_IScheckmax, point, facet, qh_NOupper, &dist, &numpart);
     /* occurs after statistics reported */
     maximize_(maxdist, dist);
     if (dist > maxoutside) {
       if (qh->ONLYgood && !bestfacet->good
           && !((bestfacet= qh_findgooddist(qh, point, bestfacet, &dist, &facetlist))
                && dist > maxoutside))
         notgood++;
       else {
         waserror= True;
         qh_fprintf(qh, qh->ferr, 6109, "qhull precision error: point p%d is outside facet f%d, distance= %6.8g maxoutside= %6.8g\n",
                 facet_i, bestfacet->id, dist, maxoutside);
         if (errfacet1 != bestfacet) {
           errfacet2= errfacet1;
           errfacet1= bestfacet;
         }
       }
     }else if (unassigned && dist < -qh->MAXcoplanar)
       notverified++;
   }
   qh_settempfree(qh, &facets);
   if (notverified && !qh->DELAUNAY && !qh_QUICKhelp && qh->PRINTprecision)
     qh_fprintf(qh, qh->ferr, 8092, "\n%d points were well inside the hull.  If the hull contains\n\
 a lens-shaped component, these points were not verified.  Use\n\
 options 'Qci Tv' to verify all points.\n", notverified);
   if (maxdist > qh->outside_err) {
     qh_fprintf(qh, qh->ferr, 6110, "qhull precision error (qh_check_bestdist): a coplanar point is %6.2g from convex hull.  The maximum value(qh.outside_err) is %6.2g\n",
               maxdist, qh->outside_err);
     qh_errexit2(qh, qh_ERRprec, errfacet1, errfacet2);
   }else if (waserror && qh->outside_err > REALmax/2)
     qh_errexit2(qh, qh_ERRprec, errfacet1, errfacet2);
   /* else if waserror, the error was logged to qh.ferr but does not effect the output */
   trace0((qh, qh->ferr, 20, "qh_check_bestdist: max distance outside %2.2g\n", maxdist));
 } /* check_bestdist */
 
 /*---------------------------------
 
   qh_check_maxout(qh)
     updates qh.max_outside by checking all points against bestfacet
     if qh.ONLYgood, ignores !good facets
 
   returns:
     updates facet->maxoutside via qh_findbesthorizon()
     sets qh.maxoutdone
     if printing qh.min_vertex (qh_outerinner),
       it is updated to the current vertices
     removes inside/coplanar points from coplanarset as needed
 
   notes:
     defines coplanar as min_vertex instead of MAXcoplanar
     may not need to check near-inside points because of qh.MAXcoplanar
       and qh.KEEPnearinside (before it was -DISTround)
 
   see also:
     qh_check_bestdist()
 
   design:
     if qh.min_vertex is needed
       for all neighbors of all vertices
         test distance from vertex to neighbor
     determine facet for each point (if any)
     for each point with an assigned facet
       find the best facet for the point and check all coplanar facets
         (updates outer planes)
     remove near-inside points from coplanar sets
 */
 #ifndef qh_NOmerge
 void qh_check_maxout(qhT *qh) {
   facetT *facet, *bestfacet, *neighbor, **neighborp, *facetlist;
   realT dist, maxoutside, minvertex, old_maxoutside;
   pointT *point;
   int numpart= 0, facet_i, facet_n, notgood= 0;
   setT *facets, *vertices;
   vertexT *vertex;
 
   trace1((qh, qh->ferr, 1022, "qh_check_maxout: check and update maxoutside for each facet.\n"));
   maxoutside= minvertex= 0;
   if (qh->VERTEXneighbors
   && (qh->PRINTsummary || qh->KEEPinside || qh->KEEPcoplanar
         || qh->TRACElevel || qh->PRINTstatistics
         || qh->PRINTout[0] == qh_PRINTsummary || qh->PRINTout[0] == qh_PRINTnone)) {
     trace1((qh, qh->ferr, 1023, "qh_check_maxout: determine actual maxoutside and minvertex\n"));
     vertices= qh_pointvertex(qh /*qh.facet_list*/);
     FORALLvertices {
       FOREACHneighbor_(vertex) {
         zinc_(Zdistvertex);  /* distance also computed by main loop below */
         qh_distplane(qh, vertex->point, neighbor, &dist);
         minimize_(minvertex, dist);
         if (-dist > qh->TRACEdist || dist > qh->TRACEdist
         || neighbor == qh->tracefacet || vertex == qh->tracevertex)
           qh_fprintf(qh, qh->ferr, 8093, "qh_check_maxout: p%d(v%d) is %.2g from f%d\n",
                     qh_pointid(qh, vertex->point), vertex->id, dist, neighbor->id);
       }
     }
     if (qh->MERGING) {
       wmin_(Wminvertex, qh->min_vertex);
     }
     qh->min_vertex= minvertex;
     qh_settempfree(qh, &vertices);
   }
   facets= qh_pointfacet(qh /*qh.facet_list*/);
   do {
     old_maxoutside= fmax_(qh->max_outside, maxoutside);
     FOREACHfacet_i_(qh, facets) {     /* for each point with facet assignment */
       if (facet) {
         point= qh_point(qh, facet_i);
         if (point == qh->GOODpointp)
           continue;
         zzinc_(Ztotcheck);
         qh_distplane(qh, point, facet, &dist);
         numpart++;
         bestfacet= qh_findbesthorizon(qh, qh_IScheckmax, point, facet, !qh_NOupper, &dist, &numpart);
         if (bestfacet && dist > maxoutside) {
           if (qh->ONLYgood && !bestfacet->good
           && !((bestfacet= qh_findgooddist(qh, point, bestfacet, &dist, &facetlist))
                && dist > maxoutside))
             notgood++;
           else
             maxoutside= dist;
         }
         if (dist > qh->TRACEdist || (bestfacet && bestfacet == qh->tracefacet))
           qh_fprintf(qh, qh->ferr, 8094, "qh_check_maxout: p%d is %.2g above f%d\n",
                      qh_pointid(qh, point), dist, bestfacet->id);
       }
     }
   }while
     (maxoutside > 2*old_maxoutside);
     /* if qh.maxoutside increases substantially, qh_SEARCHdist is not valid
           e.g., RBOX 5000 s Z1 G1e-13 t1001200614 | qhull */
   zzadd_(Zcheckpart, numpart);
   qh_settempfree(qh, &facets);
   wval_(Wmaxout)= maxoutside - qh->max_outside;
   wmax_(Wmaxoutside, qh->max_outside);
   qh->max_outside= maxoutside;
   qh_nearcoplanar(qh /*qh.facet_list*/);
   qh->maxoutdone= True;
   trace1((qh, qh->ferr, 1024, "qh_check_maxout: maxoutside %2.2g, min_vertex %2.2g, outside of not good %d\n",
        maxoutside, qh->min_vertex, notgood));
 } /* check_maxout */
 #else /* qh_NOmerge */
 void qh_check_maxout(qhT *qh) {
 }
 #endif
 
 /*---------------------------------
 
   qh_check_output(qh)
     performs the checks at the end of qhull algorithm
     Maybe called after voronoi output.  Will recompute otherwise centrums are Voronoi centers instead
 */
 void qh_check_output(qhT *qh) {
   int i;
 
   if (qh->STOPcone)
     return;
   if (qh->VERIFYoutput | qh->IStracing | qh->CHECKfrequently) {
     qh_checkpolygon(qh, qh->facet_list);
     qh_checkflipped_all(qh, qh->facet_list);
     qh_checkconvex(qh, qh->facet_list, qh_ALGORITHMfault);
   }else if (!qh->MERGING && qh_newstats(qh, qh->qhstat.precision, &i)) {
     qh_checkflipped_all(qh, qh->facet_list);
     qh_checkconvex(qh, qh->facet_list, qh_ALGORITHMfault);
   }
 } /* check_output */
 
 
 
 /*---------------------------------
 
   qh_check_point(qh, point, facet, maxoutside, maxdist, errfacet1, errfacet2 )
     check that point is less than maxoutside from facet
 */
 void qh_check_point(qhT *qh, pointT *point, facetT *facet, realT *maxoutside, realT *maxdist, facetT **errfacet1, facetT **errfacet2) {
   realT dist;
 
   /* occurs after statistics reported */
   qh_distplane(qh, point, facet, &dist);
   if (dist > *maxoutside) {
     if (*errfacet1 != facet) {
       *errfacet2= *errfacet1;
       *errfacet1= facet;
     }
     qh_fprintf(qh, qh->ferr, 6111, "qhull precision error: point p%d is outside facet f%d, distance= %6.8g maxoutside= %6.8g\n",
               qh_pointid(qh, point), facet->id, dist, *maxoutside);
   }
   maximize_(*maxdist, dist);
 } /* qh_check_point */
 
 
 /*---------------------------------
 
   qh_check_points(qh)
     checks that all points are inside all facets
 
   notes:
     if many points and qh_check_maxout not called (i.e., !qh.MERGING),
        calls qh_findbesthorizon (seldom done).
     ignores flipped facets
     maxoutside includes 2 qh.DISTrounds
       one qh.DISTround for the computed distances in qh_check_points
     qh_printafacet and qh_printsummary needs only one qh.DISTround
     the computation for qh.VERIFYdirect does not account for qh.other_points
 
   design:
     if many points
       use qh_check_bestdist()
     else
       for all facets
         for all points
           check that point is inside facet
 */
 void qh_check_points(qhT *qh) {
   facetT *facet, *errfacet1= NULL, *errfacet2= NULL;
   realT total, maxoutside, maxdist= -REALmax;
   pointT *point, **pointp, *pointtemp;
   boolT testouter;
 
   maxoutside= qh_maxouter(qh);
   maxoutside += qh->DISTround;
   /* one more qh.DISTround for check computation */
   trace1((qh, qh->ferr, 1025, "qh_check_points: check all points below %2.2g of all facet planes\n",
           maxoutside));
   if (qh->num_good)   /* miss counts other_points and !good facets */
      total= (float)qh->num_good * (float)qh->num_points;
   else
      total= (float)qh->num_facets * (float)qh->num_points;
   if (total >= qh_VERIFYdirect && !qh->maxoutdone) {
     if (!qh_QUICKhelp && qh->SKIPcheckmax && qh->MERGING)
       qh_fprintf(qh, qh->ferr, 7075, "qhull input warning: merging without checking outer planes('Q5' or 'Po').\n\
 Verify may report that a point is outside of a facet.\n");
     qh_check_bestdist(qh);
   }else {
     if (qh_MAXoutside && qh->maxoutdone)
       testouter= True;
     else
       testouter= False;
     if (!qh_QUICKhelp) {
       if (qh->MERGEexact)
         qh_fprintf(qh, qh->ferr, 7076, "qhull input warning: exact merge ('Qx').  Verify may report that a point\n\
 is outside of a facet.  See qh-optq.htm#Qx\n");
       else if (qh->SKIPcheckmax || qh->NOnearinside)
         qh_fprintf(qh, qh->ferr, 7077, "qhull input warning: no outer plane check ('Q5') or no processing of\n\
 near-inside points ('Q8').  Verify may report that a point is outside\n\
 of a facet.\n");
     }
     if (qh->PRINTprecision) {
       if (testouter)
         qh_fprintf(qh, qh->ferr, 8098, "\n\
 Output completed.  Verifying that all points are below outer planes of\n\
 all %sfacets.  Will make %2.0f distance computations.\n",
               (qh->ONLYgood ?  "good " : ""), total);
       else
         qh_fprintf(qh, qh->ferr, 8099, "\n\
 Output completed.  Verifying that all points are below %2.2g of\n\
 all %sfacets.  Will make %2.0f distance computations.\n",
               maxoutside, (qh->ONLYgood ?  "good " : ""), total);
     }
     FORALLfacets {
       if (!facet->good && qh->ONLYgood)
         continue;
       if (facet->flipped)
         continue;
       if (!facet->normal) {
         qh_fprintf(qh, qh->ferr, 7061, "qhull warning (qh_check_points): missing normal for facet f%d\n", facet->id);
         continue;
       }
       if (testouter) {
 #if qh_MAXoutside
         maxoutside= facet->maxoutside + 2* qh->DISTround;
         /* one DISTround to actual point and another to computed point */
 #endif
       }
       FORALLpoints {
         if (point != qh->GOODpointp)
           qh_check_point(qh, point, facet, &maxoutside, &maxdist, &errfacet1, &errfacet2);
       }
       FOREACHpoint_(qh->other_points) {
         if (point != qh->GOODpointp)
           qh_check_point(qh, point, facet, &maxoutside, &maxdist, &errfacet1, &errfacet2);
       }
     }
     if (maxdist > qh->outside_err) {
       qh_fprintf(qh, qh->ferr, 6112, "qhull precision error (qh_check_points): a coplanar point is %6.2g from convex hull.  The maximum value(qh.outside_err) is %6.2g\n",
                 maxdist, qh->outside_err );
       qh_errexit2(qh, qh_ERRprec, errfacet1, errfacet2 );
     }else if (errfacet1 && qh->outside_err > REALmax/2)
         qh_errexit2(qh, qh_ERRprec, errfacet1, errfacet2 );
     /* else if errfacet1, the error was logged to qh.ferr but does not effect the output */
     trace0((qh, qh->ferr, 21, "qh_check_points: max distance outside %2.2g\n", maxdist));
   }
 } /* check_points */
 
 
 /*---------------------------------
 
   qh_checkconvex(qh, facetlist, fault )
     check that each ridge in facetlist is convex
     fault = qh_DATAfault if reporting errors
           = qh_ALGORITHMfault otherwise
 
   returns:
     counts Zconcaveridges and Zcoplanarridges
     errors if concaveridge or if merging an coplanar ridge
 
   note:
     if not merging,
       tests vertices for neighboring simplicial facets
     else if ZEROcentrum,
       tests vertices for neighboring simplicial   facets
     else
       tests centrums of neighboring facets
 
   design:
     for all facets
       report flipped facets
       if ZEROcentrum and simplicial neighbors
         test vertices for neighboring simplicial facets
       else
         test centrum against all neighbors
 */
 void qh_checkconvex(qhT *qh, facetT *facetlist, int fault) {
   facetT *facet, *neighbor, **neighborp, *errfacet1=NULL, *errfacet2=NULL;
   vertexT *vertex;
   realT dist;
   pointT *centrum;
   boolT waserror= False, centrum_warning= False, tempcentrum= False, allsimplicial;
   int neighbor_i;
 
   trace1((qh, qh->ferr, 1026, "qh_checkconvex: check all ridges are convex\n"));
   if (!qh->RERUN) {
     zzval_(Zconcaveridges)= 0;
     zzval_(Zcoplanarridges)= 0;
   }
   FORALLfacet_(facetlist) {
     if (facet->flipped) {
       qh_precision(qh, "flipped facet");
       qh_fprintf(qh, qh->ferr, 6113, "qhull precision error: f%d is flipped(interior point is outside)\n",
                facet->id);
       errfacet1= facet;
       waserror= True;
       continue;
     }
     if (qh->MERGING && (!qh->ZEROcentrum || !facet->simplicial || facet->tricoplanar))
       allsimplicial= False;
     else {
       allsimplicial= True;
       neighbor_i= 0;
       FOREACHneighbor_(facet) {
         vertex= SETelemt_(facet->vertices, neighbor_i++, vertexT);
         if (!neighbor->simplicial || neighbor->tricoplanar) {
           allsimplicial= False;
           continue;
         }
         qh_distplane(qh, vertex->point, neighbor, &dist);
         if (dist > -qh->DISTround) {
           if (fault == qh_DATAfault) {
             qh_precision(qh, "coplanar or concave ridge");
             qh_fprintf(qh, qh->ferr, 6114, "qhull precision error: initial simplex is not convex. Distance=%.2g\n", dist);
             qh_errexit(qh, qh_ERRsingular, NULL, NULL);
           }
           if (dist > qh->DISTround) {
             zzinc_(Zconcaveridges);
             qh_precision(qh, "concave ridge");
             qh_fprintf(qh, qh->ferr, 6115, "qhull precision error: f%d is concave to f%d, since p%d(v%d) is %6.4g above\n",
               facet->id, neighbor->id, qh_pointid(qh, vertex->point), vertex->id, dist);
             errfacet1= facet;
             errfacet2= neighbor;
             waserror= True;
           }else if (qh->ZEROcentrum) {
             if (dist > 0) {     /* qh_checkzero checks that dist < - qh->DISTround */
               zzinc_(Zcoplanarridges);
               qh_precision(qh, "coplanar ridge");
               qh_fprintf(qh, qh->ferr, 6116, "qhull precision error: f%d is clearly not convex to f%d, since p%d(v%d) is %6.4g above\n",
                 facet->id, neighbor->id, qh_pointid(qh, vertex->point), vertex->id, dist);
               errfacet1= facet;
               errfacet2= neighbor;
               waserror= True;
             }
           }else {
             zzinc_(Zcoplanarridges);
             qh_precision(qh, "coplanar ridge");
             trace0((qh, qh->ferr, 22, "qhull precision error: f%d may be coplanar to f%d, since p%d(v%d) is within %6.4g during p%d\n",
               facet->id, neighbor->id, qh_pointid(qh, vertex->point), vertex->id, dist, qh->furthest_id));
           }
         }
       }
     }
     if (!allsimplicial) {
       if (qh->CENTERtype == qh_AScentrum) {
         if (!facet->center)
           facet->center= qh_getcentrum(qh, facet);
         centrum= facet->center;
       }else {
         if (!centrum_warning && (!facet->simplicial || facet->tricoplanar)) {
            centrum_warning= True;
            qh_fprintf(qh, qh->ferr, 7062, "qhull warning: recomputing centrums for convexity test.  This may lead to false, precision errors.\n");
         }
         centrum= qh_getcentrum(qh, facet);
         tempcentrum= True;
       }
       FOREACHneighbor_(facet) {
         if (qh->ZEROcentrum && facet->simplicial && neighbor->simplicial)
           continue;
         if (facet->tricoplanar || neighbor->tricoplanar)
           continue;
         zzinc_(Zdistconvex);
         qh_distplane(qh, centrum, neighbor, &dist);
         if (dist > qh->DISTround) {
           zzinc_(Zconcaveridges);
           qh_precision(qh, "concave ridge");
           qh_fprintf(qh, qh->ferr, 6117, "qhull precision error: f%d is concave to f%d.  Centrum of f%d is %6.4g above f%d\n",
             facet->id, neighbor->id, facet->id, dist, neighbor->id);
           errfacet1= facet;
           errfacet2= neighbor;
           waserror= True;
         }else if (dist >= 0.0) {   /* if arithmetic always rounds the same,
                                      can test against centrum radius instead */
           zzinc_(Zcoplanarridges);
           qh_precision(qh, "coplanar ridge");
           qh_fprintf(qh, qh->ferr, 6118, "qhull precision error: f%d is coplanar or concave to f%d.  Centrum of f%d is %6.4g above f%d\n",
             facet->id, neighbor->id, facet->id, dist, neighbor->id);
           errfacet1= facet;
           errfacet2= neighbor;
           waserror= True;
         }
       }
       if (tempcentrum)
         qh_memfree(qh, centrum, qh->normal_size);
     }
   }
   if (waserror && !qh->FORCEoutput)
     qh_errexit2(qh, qh_ERRprec, errfacet1, errfacet2);
 } /* checkconvex */
 
 
 /*---------------------------------
 
   qh_checkfacet(qh, facet, newmerge, waserror )
     checks for consistency errors in facet
-    newmerge set if from merge.c
+    newmerge set if from merge_r.c
 
   returns:
     sets waserror if any error occurs
 
   checks:
     vertex ids are inverse sorted
     unless newmerge, at least hull_dim neighbors and vertices (exactly if simplicial)
     if non-simplicial, at least as many ridges as neighbors
     neighbors are not duplicated
     ridges are not duplicated
     in 3-d, ridges=verticies
     (qh.hull_dim-1) ridge vertices
     neighbors are reciprocated
     ridge neighbors are facet neighbors and a ridge for every neighbor
     simplicial neighbors match facetintersect
     vertex intersection matches vertices of common ridges
     vertex neighbors and facet vertices agree
     all ridges have distinct vertex sets
 
   notes:
     uses neighbor->seen
 
   design:
     check sets
     check vertices
     check sizes of neighbors and vertices
     check for qh_MERGEridge and qh_DUPLICATEridge flags
     check neighbor set
     check ridge set
     check ridges, neighbors, and vertices
 */
 void qh_checkfacet(qhT *qh, facetT *facet, boolT newmerge, boolT *waserrorp) {
   facetT *neighbor, **neighborp, *errother=NULL;
   ridgeT *ridge, **ridgep, *errridge= NULL, *ridge2;
   vertexT *vertex, **vertexp;
   unsigned previousid= INT_MAX;
   int numneighbors, numvertices, numridges=0, numRvertices=0;
   boolT waserror= False;
   int skipA, skipB, ridge_i, ridge_n, i;
   setT *intersection;
 
   if (facet->visible) {
     qh_fprintf(qh, qh->ferr, 6119, "qhull internal error (qh_checkfacet): facet f%d is on the visible_list\n",
       facet->id);
     qh_errexit(qh, qh_ERRqhull, facet, NULL);
   }
   if (!facet->normal) {
     qh_fprintf(qh, qh->ferr, 6120, "qhull internal error (qh_checkfacet): facet f%d does not have  a normal\n",
       facet->id);
     waserror= True;
   }
   qh_setcheck(qh, facet->vertices, "vertices for f", facet->id);
   qh_setcheck(qh, facet->ridges, "ridges for f", facet->id);
   qh_setcheck(qh, facet->outsideset, "outsideset for f", facet->id);
   qh_setcheck(qh, facet->coplanarset, "coplanarset for f", facet->id);
   qh_setcheck(qh, facet->neighbors, "neighbors for f", facet->id);
   FOREACHvertex_(facet->vertices) {
     if (vertex->deleted) {
       qh_fprintf(qh, qh->ferr, 6121, "qhull internal error (qh_checkfacet): deleted vertex v%d in f%d\n", vertex->id, facet->id);
       qh_errprint(qh, "ERRONEOUS", NULL, NULL, NULL, vertex);
       waserror= True;
     }
     if (vertex->id >= previousid) {
       qh_fprintf(qh, qh->ferr, 6122, "qhull internal error (qh_checkfacet): vertices of f%d are not in descending id order at v%d\n", facet->id, vertex->id);
       waserror= True;
       break;
     }
     previousid= vertex->id;
   }
   numneighbors= qh_setsize(qh, facet->neighbors);
   numvertices= qh_setsize(qh, facet->vertices);
   numridges= qh_setsize(qh, facet->ridges);
   if (facet->simplicial) {
     if (numvertices+numneighbors != 2*qh->hull_dim
     && !facet->degenerate && !facet->redundant) {
       qh_fprintf(qh, qh->ferr, 6123, "qhull internal error (qh_checkfacet): for simplicial facet f%d, #vertices %d + #neighbors %d != 2*qh->hull_dim\n",
                 facet->id, numvertices, numneighbors);
       qh_setprint(qh, qh->ferr, "", facet->neighbors);
       waserror= True;
     }
   }else { /* non-simplicial */
     if (!newmerge
     &&(numvertices < qh->hull_dim || numneighbors < qh->hull_dim)
     && !facet->degenerate && !facet->redundant) {
       qh_fprintf(qh, qh->ferr, 6124, "qhull internal error (qh_checkfacet): for facet f%d, #vertices %d or #neighbors %d < qh->hull_dim\n",
          facet->id, numvertices, numneighbors);
        waserror= True;
     }
     /* in 3-d, can get a vertex twice in an edge list, e.g., RBOX 1000 s W1e-13 t995849315 D2 | QHULL d Tc Tv TP624 TW1e-13 T4 */
     if (numridges < numneighbors
     ||(qh->hull_dim == 3 && numvertices > numridges && !qh->NEWfacets)
     ||(qh->hull_dim == 2 && numridges + numvertices + numneighbors != 6)) {
       if (!facet->degenerate && !facet->redundant) {
         qh_fprintf(qh, qh->ferr, 6125, "qhull internal error (qh_checkfacet): for facet f%d, #ridges %d < #neighbors %d or(3-d) > #vertices %d or(2-d) not all 2\n",
             facet->id, numridges, numneighbors, numvertices);
         waserror= True;
       }
     }
   }
   FOREACHneighbor_(facet) {
     if (neighbor == qh_MERGEridge || neighbor == qh_DUPLICATEridge) {
       qh_fprintf(qh, qh->ferr, 6126, "qhull internal error (qh_checkfacet): facet f%d still has a MERGE or DUP neighbor\n", facet->id);
       qh_errexit(qh, qh_ERRqhull, facet, NULL);
     }
     neighbor->seen= True;
   }
   FOREACHneighbor_(facet) {
     if (!qh_setin(neighbor->neighbors, facet)) {
       qh_fprintf(qh, qh->ferr, 6127, "qhull internal error (qh_checkfacet): facet f%d has neighbor f%d, but f%d does not have neighbor f%d\n",
               facet->id, neighbor->id, neighbor->id, facet->id);
       errother= neighbor;
       waserror= True;
     }
     if (!neighbor->seen) {
       qh_fprintf(qh, qh->ferr, 6128, "qhull internal error (qh_checkfacet): facet f%d has a duplicate neighbor f%d\n",
               facet->id, neighbor->id);
       errother= neighbor;
       waserror= True;
     }
     neighbor->seen= False;
   }
   FOREACHridge_(facet->ridges) {
     qh_setcheck(qh, ridge->vertices, "vertices for r", ridge->id);
     ridge->seen= False;
   }
   FOREACHridge_(facet->ridges) {
     if (ridge->seen) {
       qh_fprintf(qh, qh->ferr, 6129, "qhull internal error (qh_checkfacet): facet f%d has a duplicate ridge r%d\n",
               facet->id, ridge->id);
       errridge= ridge;
       waserror= True;
     }
     ridge->seen= True;
     numRvertices= qh_setsize(qh, ridge->vertices);
     if (numRvertices != qh->hull_dim - 1) {
       qh_fprintf(qh, qh->ferr, 6130, "qhull internal error (qh_checkfacet): ridge between f%d and f%d has %d vertices\n",
                 ridge->top->id, ridge->bottom->id, numRvertices);
       errridge= ridge;
       waserror= True;
     }
     neighbor= otherfacet_(ridge, facet);
     neighbor->seen= True;
     if (!qh_setin(facet->neighbors, neighbor)) {
       qh_fprintf(qh, qh->ferr, 6131, "qhull internal error (qh_checkfacet): for facet f%d, neighbor f%d of ridge r%d not in facet\n",
            facet->id, neighbor->id, ridge->id);
       errridge= ridge;
       waserror= True;
     }
   }
   if (!facet->simplicial) {
     FOREACHneighbor_(facet) {
       if (!neighbor->seen) {
         qh_fprintf(qh, qh->ferr, 6132, "qhull internal error (qh_checkfacet): facet f%d does not have a ridge for neighbor f%d\n",
               facet->id, neighbor->id);
         errother= neighbor;
         waserror= True;
       }
       intersection= qh_vertexintersect_new(qh, facet->vertices, neighbor->vertices);
       qh_settemppush(qh, intersection);
       FOREACHvertex_(facet->vertices) {
         vertex->seen= False;
         vertex->seen2= False;
       }
       FOREACHvertex_(intersection)
         vertex->seen= True;
       FOREACHridge_(facet->ridges) {
         if (neighbor != otherfacet_(ridge, facet))
             continue;
         FOREACHvertex_(ridge->vertices) {
           if (!vertex->seen) {
             qh_fprintf(qh, qh->ferr, 6133, "qhull internal error (qh_checkfacet): vertex v%d in r%d not in f%d intersect f%d\n",
                   vertex->id, ridge->id, facet->id, neighbor->id);
             qh_errexit(qh, qh_ERRqhull, facet, ridge);
           }
           vertex->seen2= True;
         }
       }
       if (!newmerge) {
         FOREACHvertex_(intersection) {
           if (!vertex->seen2) {
             if (qh->IStracing >=3 || !qh->MERGING) {
               qh_fprintf(qh, qh->ferr, 6134, "qhull precision error (qh_checkfacet): vertex v%d in f%d intersect f%d but\n\
  not in a ridge.  This is ok under merging.  Last point was p%d\n",
                      vertex->id, facet->id, neighbor->id, qh->furthest_id);
               if (!qh->FORCEoutput && !qh->MERGING) {
                 qh_errprint(qh, "ERRONEOUS", facet, neighbor, NULL, vertex);
                 if (!qh->MERGING)
                   qh_errexit(qh, qh_ERRqhull, NULL, NULL);
               }
             }
           }
         }
       }
       qh_settempfree(qh, &intersection);
     }
   }else { /* simplicial */
     FOREACHneighbor_(facet) {
       if (neighbor->simplicial) {
         skipA= SETindex_(facet->neighbors, neighbor);
         skipB= qh_setindex(neighbor->neighbors, facet);
         if (!qh_setequal_skip(facet->vertices, skipA, neighbor->vertices, skipB)) {
           qh_fprintf(qh, qh->ferr, 6135, "qhull internal error (qh_checkfacet): facet f%d skip %d and neighbor f%d skip %d do not match \n",
                    facet->id, skipA, neighbor->id, skipB);
           errother= neighbor;
           waserror= True;
         }
       }
     }
   }
   if (qh->hull_dim < 5 && (qh->IStracing > 2 || qh->CHECKfrequently)) {
     FOREACHridge_i_(qh, facet->ridges) {           /* expensive */
       for (i=ridge_i+1; i < ridge_n; i++) {
         ridge2= SETelemt_(facet->ridges, i, ridgeT);
         if (qh_setequal(ridge->vertices, ridge2->vertices)) {
           qh_fprintf(qh, qh->ferr, 6227, "Qhull internal error (qh_checkfacet): ridges r%d and r%d have the same vertices\n",
                   ridge->id, ridge2->id);
           errridge= ridge;
           waserror= True;
         }
       }
     }
   }
   if (waserror) {
     qh_errprint(qh, "ERRONEOUS", facet, errother, errridge, NULL);
     *waserrorp= True;
   }
 } /* checkfacet */
 
 
 /*---------------------------------
 
   qh_checkflipped_all(qh, facetlist )
     checks orientation of facets in list against interior point
 */
 void qh_checkflipped_all(qhT *qh, facetT *facetlist) {
   facetT *facet;
   boolT waserror= False;
   realT dist;
 
   if (facetlist == qh->facet_list)
     zzval_(Zflippedfacets)= 0;
   FORALLfacet_(facetlist) {
     if (facet->normal && !qh_checkflipped(qh, facet, &dist, !qh_ALL)) {
       qh_fprintf(qh, qh->ferr, 6136, "qhull precision error: facet f%d is flipped, distance= %6.12g\n",
               facet->id, dist);
       if (!qh->FORCEoutput) {
         qh_errprint(qh, "ERRONEOUS", facet, NULL, NULL, NULL);
         waserror= True;
       }
     }
   }
   if (waserror) {
     qh_fprintf(qh, qh->ferr, 8101, "\n\
 A flipped facet occurs when its distance to the interior point is\n\
 greater than %2.2g, the maximum roundoff error.\n", -qh->DISTround);
     qh_errexit(qh, qh_ERRprec, NULL, NULL);
   }
 } /* checkflipped_all */
 
 /*---------------------------------
 
   qh_checkpolygon(qh, facetlist )
     checks the correctness of the structure
 
   notes:
     call with either qh.facet_list or qh.newfacet_list
     checks num_facets and num_vertices if qh.facet_list
 
   design:
     for each facet
       checks facet and outside set
     initializes vertexlist
     for each facet
       checks vertex set
     if checking all facets(qh.facetlist)
       check facet count
       if qh.VERTEXneighbors
         check vertex neighbors and count
       check vertex count
 */
 void qh_checkpolygon(qhT *qh, facetT *facetlist) {
   facetT *facet;
   vertexT *vertex, **vertexp, *vertexlist;
   int numfacets= 0, numvertices= 0, numridges= 0;
   int totvneighbors= 0, totvertices= 0;
   boolT waserror= False, nextseen= False, visibleseen= False;
 
   trace1((qh, qh->ferr, 1027, "qh_checkpolygon: check all facets from f%d\n", facetlist->id));
   if (facetlist != qh->facet_list || qh->ONLYgood)
     nextseen= True;
   FORALLfacet_(facetlist) {
     if (facet == qh->visible_list)
       visibleseen= True;
     if (!facet->visible) {
       if (!nextseen) {
         if (facet == qh->facet_next)
           nextseen= True;
         else if (qh_setsize(qh, facet->outsideset)) {
           if (!qh->NARROWhull
 #if !qh_COMPUTEfurthest
                || facet->furthestdist >= qh->MINoutside
 #endif
                         ) {
             qh_fprintf(qh, qh->ferr, 6137, "qhull internal error (qh_checkpolygon): f%d has outside points before qh->facet_next\n",
                      facet->id);
             qh_errexit(qh, qh_ERRqhull, facet, NULL);
           }
         }
       }
       numfacets++;
       qh_checkfacet(qh, facet, False, &waserror);
     }
   }
   if (qh->visible_list && !visibleseen && facetlist == qh->facet_list) {
     qh_fprintf(qh, qh->ferr, 6138, "qhull internal error (qh_checkpolygon): visible list f%d no longer on facet list\n", qh->visible_list->id);
     qh_printlists(qh);
     qh_errexit(qh, qh_ERRqhull, qh->visible_list, NULL);
   }
   if (facetlist == qh->facet_list)
     vertexlist= qh->vertex_list;
   else if (facetlist == qh->newfacet_list)
     vertexlist= qh->newvertex_list;
   else
     vertexlist= NULL;
   FORALLvertex_(vertexlist) {
     vertex->seen= False;
     vertex->visitid= 0;
   }
   FORALLfacet_(facetlist) {
     if (facet->visible)
       continue;
     if (facet->simplicial)
       numridges += qh->hull_dim;
     else
       numridges += qh_setsize(qh, facet->ridges);
     FOREACHvertex_(facet->vertices) {
       vertex->visitid++;
       if (!vertex->seen) {
         vertex->seen= True;
         numvertices++;
         if (qh_pointid(qh, vertex->point) == -1) {
           qh_fprintf(qh, qh->ferr, 6139, "qhull internal error (qh_checkpolygon): unknown point %p for vertex v%d first_point %p\n",
                    vertex->point, vertex->id, qh->first_point);
           waserror= True;
         }
       }
     }
   }
   qh->vertex_visit += (unsigned int)numfacets;
   if (facetlist == qh->facet_list) {
     if (numfacets != qh->num_facets - qh->num_visible) {
       qh_fprintf(qh, qh->ferr, 6140, "qhull internal error (qh_checkpolygon): actual number of facets is %d, cumulative facet count is %d - %d visible facets\n",
               numfacets, qh->num_facets, qh->num_visible);
       waserror= True;
     }
     qh->vertex_visit++;
     if (qh->VERTEXneighbors) {
       FORALLvertices {
         qh_setcheck(qh, vertex->neighbors, "neighbors for v", vertex->id);
         if (vertex->deleted)
           continue;
         totvneighbors += qh_setsize(qh, vertex->neighbors);
       }
       FORALLfacet_(facetlist)
         totvertices += qh_setsize(qh, facet->vertices);
       if (totvneighbors != totvertices) {
         qh_fprintf(qh, qh->ferr, 6141, "qhull internal error (qh_checkpolygon): vertex neighbors inconsistent.  Totvneighbors %d, totvertices %d\n",
                 totvneighbors, totvertices);
         waserror= True;
       }
     }
     if (numvertices != qh->num_vertices - qh_setsize(qh, qh->del_vertices)) {
       qh_fprintf(qh, qh->ferr, 6142, "qhull internal error (qh_checkpolygon): actual number of vertices is %d, cumulative vertex count is %d\n",
               numvertices, qh->num_vertices - qh_setsize(qh, qh->del_vertices));
       waserror= True;
     }
     if (qh->hull_dim == 2 && numvertices != numfacets) {
       qh_fprintf(qh, qh->ferr, 6143, "qhull internal error (qh_checkpolygon): #vertices %d != #facets %d\n",
         numvertices, numfacets);
       waserror= True;
     }
     if (qh->hull_dim == 3 && numvertices + numfacets - numridges/2 != 2) {
       qh_fprintf(qh, qh->ferr, 7063, "qhull warning: #vertices %d + #facets %d - #edges %d != 2\n\
         A vertex appears twice in a edge list.  May occur during merging.",
         numvertices, numfacets, numridges/2);
       /* occurs if lots of merging and a vertex ends up twice in an edge list.  e.g., RBOX 1000 s W1e-13 t995849315 D2 | QHULL d Tc Tv */
     }
   }
   if (waserror)
     qh_errexit(qh, qh_ERRqhull, NULL, NULL);
 } /* checkpolygon */
 
 
 /*---------------------------------
 
   qh_checkvertex(qh, vertex )
     check vertex for consistency
     checks vertex->neighbors
 
   notes:
     neighbors checked efficiently in checkpolygon
 */
 void qh_checkvertex(qhT *qh, vertexT *vertex) {
   boolT waserror= False;
   facetT *neighbor, **neighborp, *errfacet=NULL;
 
   if (qh_pointid(qh, vertex->point) == -1) {
     qh_fprintf(qh, qh->ferr, 6144, "qhull internal error (qh_checkvertex): unknown point id %p\n", vertex->point);
     waserror= True;
   }
   if (vertex->id >= qh->vertex_id) {
     qh_fprintf(qh, qh->ferr, 6145, "qhull internal error (qh_checkvertex): unknown vertex id %d\n", vertex->id);
     waserror= True;
   }
   if (!waserror && !vertex->deleted) {
     if (qh_setsize(qh, vertex->neighbors)) {
       FOREACHneighbor_(vertex) {
         if (!qh_setin(neighbor->vertices, vertex)) {
           qh_fprintf(qh, qh->ferr, 6146, "qhull internal error (qh_checkvertex): neighbor f%d does not contain v%d\n", neighbor->id, vertex->id);
           errfacet= neighbor;
           waserror= True;
         }
       }
     }
   }
   if (waserror) {
     qh_errprint(qh, "ERRONEOUS", NULL, NULL, NULL, vertex);
     qh_errexit(qh, qh_ERRqhull, errfacet, NULL);
   }
 } /* checkvertex */
 
 /*---------------------------------
 
   qh_clearcenters(qh, type )
     clear old data from facet->center
 
   notes:
     sets new centertype
     nop if CENTERtype is the same
 */
 void qh_clearcenters(qhT *qh, qh_CENTER type) {
   facetT *facet;
 
   if (qh->CENTERtype != type) {
     FORALLfacets {
       if (facet->tricoplanar && !facet->keepcentrum)
           facet->center= NULL;
       else if (qh->CENTERtype == qh_ASvoronoi){
         if (facet->center) {
           qh_memfree(qh, facet->center, qh->center_size);
           facet->center= NULL;
         }
       }else /* qh->CENTERtype == qh_AScentrum */ {
         if (facet->center) {
           qh_memfree(qh, facet->center, qh->normal_size);
           facet->center= NULL;
         }
       }
     }
     qh->CENTERtype= type;
   }
   trace2((qh, qh->ferr, 2043, "qh_clearcenters: switched to center type %d\n", type));
 } /* clearcenters */
 
 /*---------------------------------
 
   qh_createsimplex(qh, vertices )
     creates a simplex from a set of vertices
 
   returns:
     initializes qh.facet_list to the simplex
     initializes qh.newfacet_list, .facet_tail
     initializes qh.vertex_list, .newvertex_list, .vertex_tail
 
   design:
     initializes lists
     for each vertex
       create a new facet
     for each new facet
       create its neighbor set
 */
 void qh_createsimplex(qhT *qh, setT *vertices) {
   facetT *facet= NULL, *newfacet;
   boolT toporient= True;
   int vertex_i, vertex_n, nth;
   setT *newfacets= qh_settemp(qh, qh->hull_dim+1);
   vertexT *vertex;
 
   qh->facet_list= qh->newfacet_list= qh->facet_tail= qh_newfacet(qh);
   qh->num_facets= qh->num_vertices= qh->num_visible= 0;
   qh->vertex_list= qh->newvertex_list= qh->vertex_tail= qh_newvertex(qh, NULL);
   FOREACHvertex_i_(qh, vertices) {
     newfacet= qh_newfacet(qh);
     newfacet->vertices= qh_setnew_delnthsorted(qh, vertices, vertex_n,
                                                 vertex_i, 0);
     newfacet->toporient= (unsigned char)toporient;
     qh_appendfacet(qh, newfacet);
     newfacet->newfacet= True;
     qh_appendvertex(qh, vertex);
     qh_setappend(qh, &newfacets, newfacet);
     toporient ^= True;
   }
   FORALLnew_facets {
     nth= 0;
     FORALLfacet_(qh->newfacet_list) {
       if (facet != newfacet)
         SETelem_(newfacet->neighbors, nth++)= facet;
     }
     qh_settruncate(qh, newfacet->neighbors, qh->hull_dim);
   }
   qh_settempfree(qh, &newfacets);
   trace1((qh, qh->ferr, 1028, "qh_createsimplex: created simplex\n"));
 } /* createsimplex */
 
 /*---------------------------------
 
   qh_delridge(qh, ridge )
     deletes ridge from data structures it belongs to
     frees up its memory
 
   notes:
-    in merge.c, caller sets vertex->delridge for each vertex
+    in merge_r.c, caller sets vertex->delridge for each vertex
     ridges also freed in qh_freeqhull
 */
 void qh_delridge(qhT *qh, ridgeT *ridge) {
   void **freelistp; /* used !qh_NOmem */
 
   qh_setdel(ridge->top->ridges, ridge);
   qh_setdel(ridge->bottom->ridges, ridge);
   qh_setfree(qh, &(ridge->vertices));
   qh_memfree_(qh, ridge, (int)sizeof(ridgeT), freelistp);
 } /* delridge */
 
 
 /*---------------------------------
 
   qh_delvertex(qh, vertex )
     deletes a vertex and frees its memory
 
   notes:
     assumes vertex->adjacencies have been updated if needed
     unlinks from vertex_list
 */
 void qh_delvertex(qhT *qh, vertexT *vertex) {
 
   if (vertex == qh->tracevertex)
     qh->tracevertex= NULL;
   qh_removevertex(qh, vertex);
   qh_setfree(qh, &vertex->neighbors);
   qh_memfree(qh, vertex, (int)sizeof(vertexT));
 } /* delvertex */
 
 
 /*---------------------------------
 
   qh_facet3vertex(qh, )
     return temporary set of 3-d vertices in qh_ORIENTclock order
 
   design:
     if simplicial facet
       build set from facet->vertices with facet->toporient
     else
       for each ridge in order
         build set from ridge's vertices
 */
 setT *qh_facet3vertex(qhT *qh, facetT *facet) {
   ridgeT *ridge, *firstridge;
   vertexT *vertex;
   int cntvertices, cntprojected=0;
   setT *vertices;
 
   cntvertices= qh_setsize(qh, facet->vertices);
   vertices= qh_settemp(qh, cntvertices);
   if (facet->simplicial) {
     if (cntvertices != 3) {
       qh_fprintf(qh, qh->ferr, 6147, "qhull internal error (qh_facet3vertex): only %d vertices for simplicial facet f%d\n",
                   cntvertices, facet->id);
       qh_errexit(qh, qh_ERRqhull, facet, NULL);
     }
     qh_setappend(qh, &vertices, SETfirst_(facet->vertices));
     if (facet->toporient ^ qh_ORIENTclock)
       qh_setappend(qh, &vertices, SETsecond_(facet->vertices));
     else
       qh_setaddnth(qh, &vertices, 0, SETsecond_(facet->vertices));
     qh_setappend(qh, &vertices, SETelem_(facet->vertices, 2));
   }else {
     ridge= firstridge= SETfirstt_(facet->ridges, ridgeT);   /* no infinite */
     while ((ridge= qh_nextridge3d(qh, ridge, facet, &vertex))) {
       qh_setappend(qh, &vertices, vertex);
       if (++cntprojected > cntvertices || ridge == firstridge)
         break;
     }
     if (!ridge || cntprojected != cntvertices) {
       qh_fprintf(qh, qh->ferr, 6148, "qhull internal error (qh_facet3vertex): ridges for facet %d don't match up.  got at least %d\n",
                   facet->id, cntprojected);
       qh_errexit(qh, qh_ERRqhull, facet, ridge);
     }
   }
   return vertices;
 } /* facet3vertex */
 
 /*---------------------------------
 
   qh_findbestfacet(qh, point, bestoutside, bestdist, isoutside )
     find facet that is furthest below a point
 
     for Delaunay triangulations,
       Use qh_setdelaunay() to lift point to paraboloid and scale by 'Qbb' if needed
       Do not use options 'Qbk', 'QBk', or 'QbB' since they scale the coordinates.
 
   returns:
     if bestoutside is set (e.g., qh_ALL)
       returns best facet that is not upperdelaunay
       if Delaunay and inside, point is outside circumsphere of bestfacet
     else
       returns first facet below point
       if point is inside, returns nearest, !upperdelaunay facet
     distance to facet
     isoutside set if outside of facet
 
   notes:
     For tricoplanar facets, this finds one of the tricoplanar facets closest
     to the point.  For Delaunay triangulations, the point may be inside a
     different tricoplanar facet. See locate a facet with qh_findbestfacet()
 
     If inside, qh_findbestfacet performs an exhaustive search
        this may be too conservative.  Sometimes it is clearly required.
 
     qh_findbestfacet is not used by qhull.
     uses qh.visit_id and qh.coplanarset
 
   see:
-    qh_findbest
+    qh_findbest
 */
 facetT *qh_findbestfacet(qhT *qh, pointT *point, boolT bestoutside,
            realT *bestdist, boolT *isoutside) {
   facetT *bestfacet= NULL;
   int numpart, totpart= 0;
 
   bestfacet= qh_findbest(qh, point, qh->facet_list,
                             bestoutside, !qh_ISnewfacets, bestoutside /* qh_NOupper */,
                             bestdist, isoutside, &totpart);
   if (*bestdist < -qh->DISTround) {
     bestfacet= qh_findfacet_all(qh, point, bestdist, isoutside, &numpart);
     totpart += numpart;
     if ((isoutside && bestoutside)
     || (!isoutside && bestfacet->upperdelaunay)) {
       bestfacet= qh_findbest(qh, point, bestfacet,
                             bestoutside, False, bestoutside,
                             bestdist, isoutside, &totpart);
       totpart += numpart;
     }
   }
   trace3((qh, qh->ferr, 3014, "qh_findbestfacet: f%d dist %2.2g isoutside %d totpart %d\n",
           bestfacet->id, *bestdist, *isoutside, totpart));
   return bestfacet;
 } /* findbestfacet */
 
 /*---------------------------------
 
   qh_findbestlower(qh, facet, point, bestdist, numpart )
     returns best non-upper, non-flipped neighbor of facet for point
     if needed, searches vertex neighbors
 
   returns:
     returns bestdist and updates numpart
 
   notes:
     if Delaunay and inside, point is outside of circumsphere of bestfacet
     called by qh_findbest() for points above an upperdelaunay facet
 
 */
 facetT *qh_findbestlower(qhT *qh, facetT *upperfacet, pointT *point, realT *bestdistp, int *numpart) {
   facetT *neighbor, **neighborp, *bestfacet= NULL;
   realT bestdist= -REALmax/2 /* avoid underflow */;
   realT dist;
   vertexT *vertex;
 
   zinc_(Zbestlower);
   FOREACHneighbor_(upperfacet) {
     if (neighbor->upperdelaunay || neighbor->flipped)
       continue;
     (*numpart)++;
     qh_distplane(qh, point, neighbor, &dist);
     if (dist > bestdist) {
       bestfacet= neighbor;
       bestdist= dist;
     }
   }
   if (!bestfacet) {
     zinc_(Zbestlowerv);
     /* rarely called, numpart does not count nearvertex computations */
     vertex= qh_nearvertex(qh, upperfacet, point, &dist);
     qh_vertexneighbors(qh);
     FOREACHneighbor_(vertex) {
       if (neighbor->upperdelaunay || neighbor->flipped)
         continue;
       (*numpart)++;
       qh_distplane(qh, point, neighbor, &dist);
       if (dist > bestdist) {
         bestfacet= neighbor;
         bestdist= dist;
       }
     }
   }
   if (!bestfacet) {
     qh_fprintf(qh, qh->ferr, 6228, "\n\
 Qhull internal error (qh_findbestlower): all neighbors of facet %d are flipped or upper Delaunay.\n\
 Please report this error to qhull_bug@qhull.org with the input and all of the output.\n",
        upperfacet->id);
     qh_errexit(qh, qh_ERRqhull, upperfacet, NULL);
   }
   *bestdistp= bestdist;
   trace3((qh, qh->ferr, 3015, "qh_findbestlower: f%d dist %2.2g for f%d p%d\n",
           bestfacet->id, bestdist, upperfacet->id, qh_pointid(qh, point)));
   return bestfacet;
 } /* findbestlower */
 
 /*---------------------------------
 
   qh_findfacet_all(qh, point, bestdist, isoutside, numpart )
     exhaustive search for facet below a point
 
     for Delaunay triangulations,
       Use qh_setdelaunay() to lift point to paraboloid and scale by 'Qbb' if needed
       Do not use options 'Qbk', 'QBk', or 'QbB' since they scale the coordinates.
 
   returns:
     returns first facet below point
     if point is inside,
       returns nearest facet
     distance to facet
     isoutside if point is outside of the hull
     number of distance tests
 
   notes:
     for library users, not used by Qhull
 */
 facetT *qh_findfacet_all(qhT *qh, pointT *point, realT *bestdist, boolT *isoutside,
                           int *numpart) {
   facetT *bestfacet= NULL, *facet;
   realT dist;
   int totpart= 0;
 
   *bestdist= -REALmax;
   *isoutside= False;
   FORALLfacets {
     if (facet->flipped || !facet->normal)
       continue;
     totpart++;
     qh_distplane(qh, point, facet, &dist);
     if (dist > *bestdist) {
       *bestdist= dist;
       bestfacet= facet;
       if (dist > qh->MINoutside) {
         *isoutside= True;
         break;
       }
     }
   }
   *numpart= totpart;
   trace3((qh, qh->ferr, 3016, "qh_findfacet_all: f%d dist %2.2g isoutside %d totpart %d\n",
           getid_(bestfacet), *bestdist, *isoutside, totpart));
   return bestfacet;
 } /* findfacet_all */
 
 /*---------------------------------
 
   qh_findgood(qh, facetlist, goodhorizon )
     identify good facets for qh.PRINTgood
     if qh.GOODvertex>0
       facet includes point as vertex
       if !match, returns goodhorizon
       inactive if qh.MERGING
     if qh.GOODpoint
       facet is visible or coplanar (>0) or not visible (<0)
     if qh.GOODthreshold
       facet->normal matches threshold
     if !goodhorizon and !match,
       selects facet with closest angle
       sets GOODclosest
 
   returns:
     number of new, good facets found
     determines facet->good
     may update qh.GOODclosest
 
   notes:
     qh_findgood_all further reduces the good region
 
   design:
     count good facets
     mark good facets for qh.GOODpoint
     mark good facets for qh.GOODthreshold
     if necessary
       update qh.GOODclosest
 */
 int qh_findgood(qhT *qh, facetT *facetlist, int goodhorizon) {
   facetT *facet, *bestfacet= NULL;
   realT angle, bestangle= REALmax, dist;
   int  numgood=0;
 
   FORALLfacet_(facetlist) {
     if (facet->good)
       numgood++;
   }
   if (qh->GOODvertex>0 && !qh->MERGING) {
     FORALLfacet_(facetlist) {
       if (!qh_isvertex(qh, qh->GOODvertexp, facet->vertices)) {
         facet->good= False;
         numgood--;
       }
     }
   }
   if (qh->GOODpoint && numgood) {
     FORALLfacet_(facetlist) {
       if (facet->good && facet->normal) {
         zinc_(Zdistgood);
         qh_distplane(qh, qh->GOODpointp, facet, &dist);
         if ((qh->GOODpoint > 0) ^ (dist > 0.0)) {
           facet->good= False;
           numgood--;
         }
       }
     }
   }
   if (qh->GOODthreshold && (numgood || goodhorizon || qh->GOODclosest)) {
     FORALLfacet_(facetlist) {
       if (facet->good && facet->normal) {
         if (!qh_inthresholds(qh, facet->normal, &angle)) {
           facet->good= False;
           numgood--;
           if (angle < bestangle) {
             bestangle= angle;
             bestfacet= facet;
           }
         }
       }
     }
     if (!numgood && (!goodhorizon || qh->GOODclosest)) {
       if (qh->GOODclosest) {
         if (qh->GOODclosest->visible)
           qh->GOODclosest= NULL;
         else {
           qh_inthresholds(qh, qh->GOODclosest->normal, &angle);
           if (angle < bestangle)
             bestfacet= qh->GOODclosest;
         }
       }
       if (bestfacet && bestfacet != qh->GOODclosest) {
         if (qh->GOODclosest)
           qh->GOODclosest->good= False;
         qh->GOODclosest= bestfacet;
         bestfacet->good= True;
         numgood++;
         trace2((qh, qh->ferr, 2044, "qh_findgood: f%d is closest(%2.2g) to thresholds\n",
            bestfacet->id, bestangle));
         return numgood;
       }
     }else if (qh->GOODclosest) { /* numgood > 0 */
       qh->GOODclosest->good= False;
       qh->GOODclosest= NULL;
     }
   }
   zadd_(Zgoodfacet, numgood);
   trace2((qh, qh->ferr, 2045, "qh_findgood: found %d good facets with %d good horizon\n",
                numgood, goodhorizon));
   if (!numgood && qh->GOODvertex>0 && !qh->MERGING)
     return goodhorizon;
   return numgood;
 } /* findgood */
 
 /*---------------------------------
 
   qh_findgood_all(qh, facetlist )
     apply other constraints for good facets (used by qh.PRINTgood)
     if qh.GOODvertex
       facet includes (>0) or doesn't include (<0) point as vertex
       if last good facet and ONLYgood, prints warning and continues
     if qh.SPLITthresholds
       facet->normal matches threshold, or if none, the closest one
     calls qh_findgood
     nop if good not used
 
   returns:
     clears facet->good if not good
     sets qh.num_good
 
   notes:
     this is like qh_findgood but more restrictive
 
   design:
     uses qh_findgood to mark good facets
     marks facets for qh.GOODvertex
     marks facets for qh.SPLITthreholds
 */
 void qh_findgood_all(qhT *qh, facetT *facetlist) {
   facetT *facet, *bestfacet=NULL;
   realT angle, bestangle= REALmax;
   int  numgood=0, startgood;
 
   if (!qh->GOODvertex && !qh->GOODthreshold && !qh->GOODpoint
   && !qh->SPLITthresholds)
     return;
   if (!qh->ONLYgood)
     qh_findgood(qh, qh->facet_list, 0);
   FORALLfacet_(facetlist) {
     if (facet->good)
       numgood++;
   }
   if (qh->GOODvertex <0 || (qh->GOODvertex > 0 && qh->MERGING)) {
     FORALLfacet_(facetlist) {
       if (facet->good && ((qh->GOODvertex > 0) ^ !!qh_isvertex(qh, qh->GOODvertexp, facet->vertices))) {
         if (!--numgood) {
           if (qh->ONLYgood) {
             qh_fprintf(qh, qh->ferr, 7064, "qhull warning: good vertex p%d does not match last good facet f%d.  Ignored.\n",
                qh_pointid(qh, qh->GOODvertexp), facet->id);
             return;
           }else if (qh->GOODvertex > 0)
             qh_fprintf(qh, qh->ferr, 7065, "qhull warning: point p%d is not a vertex('QV%d').\n",
                 qh->GOODvertex-1, qh->GOODvertex-1);
           else
             qh_fprintf(qh, qh->ferr, 7066, "qhull warning: point p%d is a vertex for every facet('QV-%d').\n",
                 -qh->GOODvertex - 1, -qh->GOODvertex - 1);
         }
         facet->good= False;
       }
     }
   }
   startgood= numgood;
   if (qh->SPLITthresholds) {
     FORALLfacet_(facetlist) {
       if (facet->good) {
         if (!qh_inthresholds(qh, facet->normal, &angle)) {
           facet->good= False;
           numgood--;
           if (angle < bestangle) {
             bestangle= angle;
             bestfacet= facet;
           }
         }
       }
     }
     if (!numgood && bestfacet) {
       bestfacet->good= True;
       numgood++;
       trace0((qh, qh->ferr, 23, "qh_findgood_all: f%d is closest(%2.2g) to thresholds\n",
            bestfacet->id, bestangle));
       return;
     }
   }
   qh->num_good= numgood;
   trace0((qh, qh->ferr, 24, "qh_findgood_all: %d good facets remain out of %d facets\n",
         numgood, startgood));
 } /* findgood_all */
 
 /*---------------------------------
 
   qh_furthestnext()
     set qh.facet_next to facet with furthest of all furthest points
     searches all facets on qh.facet_list
 
   notes:
     this may help avoid precision problems
 */
 void qh_furthestnext(qhT *qh /* qh->facet_list */) {
   facetT *facet, *bestfacet= NULL;
   realT dist, bestdist= -REALmax;
 
   FORALLfacets {
     if (facet->outsideset) {
 #if qh_COMPUTEfurthest
       pointT *furthest;
       furthest= (pointT*)qh_setlast(facet->outsideset);
       zinc_(Zcomputefurthest);
       qh_distplane(qh, furthest, facet, &dist);
 #else
       dist= facet->furthestdist;
 #endif
       if (dist > bestdist) {
         bestfacet= facet;
         bestdist= dist;
       }
     }
   }
   if (bestfacet) {
     qh_removefacet(qh, bestfacet);
     qh_prependfacet(qh, bestfacet, &qh->facet_next);
     trace1((qh, qh->ferr, 1029, "qh_furthestnext: made f%d next facet(dist %.2g)\n",
             bestfacet->id, bestdist));
   }
 } /* furthestnext */
 
 /*---------------------------------
 
   qh_furthestout(qh, facet )
     make furthest outside point the last point of outsideset
 
   returns:
     updates facet->outsideset
     clears facet->notfurthest
     sets facet->furthestdist
 
   design:
     determine best point of outsideset
     make it the last point of outsideset
 */
 void qh_furthestout(qhT *qh, facetT *facet) {
   pointT *point, **pointp, *bestpoint= NULL;
   realT dist, bestdist= -REALmax;
 
   FOREACHpoint_(facet->outsideset) {
     qh_distplane(qh, point, facet, &dist);
     zinc_(Zcomputefurthest);
     if (dist > bestdist) {
       bestpoint= point;
       bestdist= dist;
     }
   }
   if (bestpoint) {
     qh_setdel(facet->outsideset, point);
     qh_setappend(qh, &facet->outsideset, point);
 #if !qh_COMPUTEfurthest
     facet->furthestdist= bestdist;
 #endif
   }
   facet->notfurthest= False;
   trace3((qh, qh->ferr, 3017, "qh_furthestout: p%d is furthest outside point of f%d\n",
           qh_pointid(qh, point), facet->id));
 } /* furthestout */
 
 
 /*---------------------------------
 
   qh_infiniteloop(qh, facet )
     report infinite loop error due to facet
 */
 void qh_infiniteloop(qhT *qh, facetT *facet) {
 
   qh_fprintf(qh, qh->ferr, 6149, "qhull internal error (qh_infiniteloop): potential infinite loop detected\n");
   qh_errexit(qh, qh_ERRqhull, facet, NULL);
 } /* qh_infiniteloop */
 
 /*---------------------------------
 
   qh_initbuild()
     initialize hull and outside sets with point array
     qh.FIRSTpoint/qh.NUMpoints is point array
     if qh.GOODpoint
       adds qh.GOODpoint to initial hull
 
   returns:
     qh_facetlist with initial hull
     points partioned into outside sets, coplanar sets, or inside
     initializes qh.GOODpointp, qh.GOODvertexp,
 
   design:
     initialize global variables used during qh_buildhull
     determine precision constants and points with max/min coordinate values
       if qh.SCALElast, scale last coordinate(for 'd')
     build initial simplex
     partition input points into facets of initial simplex
     set up lists
     if qh.ONLYgood
       check consistency
       add qh.GOODvertex if defined
 */
 void qh_initbuild(qhT *qh) {
   setT *maxpoints, *vertices;
   facetT *facet;
   int i, numpart;
   realT dist;
   boolT isoutside;
 
   qh->furthest_id= -1;
   qh->lastreport= 0;
   qh->facet_id= qh->vertex_id= qh->ridge_id= 0;
   qh->visit_id= qh->vertex_visit= 0;
   qh->maxoutdone= False;
 
   if (qh->GOODpoint > 0)
     qh->GOODpointp= qh_point(qh, qh->GOODpoint-1);
   else if (qh->GOODpoint < 0)
     qh->GOODpointp= qh_point(qh, -qh->GOODpoint-1);
   if (qh->GOODvertex > 0)
     qh->GOODvertexp= qh_point(qh, qh->GOODvertex-1);
   else if (qh->GOODvertex < 0)
     qh->GOODvertexp= qh_point(qh, -qh->GOODvertex-1);
   if ((qh->GOODpoint
        && (qh->GOODpointp < qh->first_point  /* also catches !GOODpointp */
            || qh->GOODpointp > qh_point(qh, qh->num_points-1)))
     || (qh->GOODvertex
         && (qh->GOODvertexp < qh->first_point  /* also catches !GOODvertexp */
             || qh->GOODvertexp > qh_point(qh, qh->num_points-1)))) {
     qh_fprintf(qh, qh->ferr, 6150, "qhull input error: either QGn or QVn point is > p%d\n",
              qh->num_points-1);
     qh_errexit(qh, qh_ERRinput, NULL, NULL);
   }
   maxpoints= qh_maxmin(qh, qh->first_point, qh->num_points, qh->hull_dim);
   if (qh->SCALElast)
     qh_scalelast(qh, qh->first_point, qh->num_points, qh->hull_dim,
                qh->MINlastcoord, qh->MAXlastcoord, qh->MAXwidth);
   qh_detroundoff(qh);
   if (qh->DELAUNAY && qh->upper_threshold[qh->hull_dim-1] > REALmax/2
                   && qh->lower_threshold[qh->hull_dim-1] < -REALmax/2) {
     for (i=qh_PRINTEND; i--; ) {
       if (qh->PRINTout[i] == qh_PRINTgeom && qh->DROPdim < 0
           && !qh->GOODthreshold && !qh->SPLITthresholds)
         break;  /* in this case, don't set upper_threshold */
     }
     if (i < 0) {
       if (qh->UPPERdelaunay) { /* matches qh.upperdelaunay in qh_setfacetplane */
         qh->lower_threshold[qh->hull_dim-1]= qh->ANGLEround * qh_ZEROdelaunay;
         qh->GOODthreshold= True;
       }else {
         qh->upper_threshold[qh->hull_dim-1]= -qh->ANGLEround * qh_ZEROdelaunay;
         if (!qh->GOODthreshold)
           qh->SPLITthresholds= True; /* build upper-convex hull even if Qg */
           /* qh_initqhull_globals errors if Qg without Pdk/etc. */
       }
     }
   }
   vertices= qh_initialvertices(qh, qh->hull_dim, maxpoints, qh->first_point, qh->num_points);
   qh_initialhull(qh, vertices);  /* initial qh->facet_list */
   qh_partitionall(qh, vertices, qh->first_point, qh->num_points);
   if (qh->PRINToptions1st || qh->TRACElevel || qh->IStracing) {
     if (qh->TRACElevel || qh->IStracing)
       qh_fprintf(qh, qh->ferr, 8103, "\nTrace level %d for %s | %s\n",
          qh->IStracing ? qh->IStracing : qh->TRACElevel, qh->rbox_command, qh->qhull_command);
     qh_fprintf(qh, qh->ferr, 8104, "Options selected for Qhull %s:\n%s\n", qh_version, qh->qhull_options);
   }
   qh_resetlists(qh, False, qh_RESETvisible /*qh.visible_list newvertex_list newfacet_list */);
   qh->facet_next= qh->facet_list;
   qh_furthestnext(qh /* qh->facet_list */);
   if (qh->PREmerge) {
     qh->cos_max= qh->premerge_cos;
     qh->centrum_radius= qh->premerge_centrum;
   }
   if (qh->ONLYgood) {
     if (qh->GOODvertex > 0 && qh->MERGING) {
       qh_fprintf(qh, qh->ferr, 6151, "qhull input error: 'Qg QVn' (only good vertex) does not work with merging.\nUse 'QJ' to joggle the input or 'Q0' to turn off merging.\n");
       qh_errexit(qh, qh_ERRinput, NULL, NULL);
     }
     if (!(qh->GOODthreshold || qh->GOODpoint
          || (!qh->MERGEexact && !qh->PREmerge && qh->GOODvertexp))) {
       qh_fprintf(qh, qh->ferr, 6152, "qhull input error: 'Qg' (ONLYgood) needs a good threshold('Pd0D0'), a\n\
 good point(QGn or QG-n), or a good vertex with 'QJ' or 'Q0' (QVn).\n");
       qh_errexit(qh, qh_ERRinput, NULL, NULL);
     }
     if (qh->GOODvertex > 0  && !qh->MERGING  /* matches qh_partitionall */
         && !qh_isvertex(qh, qh->GOODvertexp, vertices)) {
       facet= qh_findbestnew(qh, qh->GOODvertexp, qh->facet_list,
                           &dist, !qh_ALL, &isoutside, &numpart);
       zadd_(Zdistgood, numpart);
       if (!isoutside) {
         qh_fprintf(qh, qh->ferr, 6153, "qhull input error: point for QV%d is inside initial simplex.  It can not be made a vertex.\n",
                qh_pointid(qh, qh->GOODvertexp));
         qh_errexit(qh, qh_ERRinput, NULL, NULL);
       }
       if (!qh_addpoint(qh, qh->GOODvertexp, facet, False)) {
         qh_settempfree(qh, &vertices);
         qh_settempfree(qh, &maxpoints);
         return;
       }
     }
     qh_findgood(qh, qh->facet_list, 0);
   }
   qh_settempfree(qh, &vertices);
   qh_settempfree(qh, &maxpoints);
   trace1((qh, qh->ferr, 1030, "qh_initbuild: initial hull created and points partitioned\n"));
 } /* initbuild */
 
 /*---------------------------------
 
   qh_initialhull(qh, vertices )
     constructs the initial hull as a DIM3 simplex of vertices
 
   design:
     creates a simplex (initializes lists)
     determines orientation of simplex
     sets hyperplanes for facets
     doubles checks orientation (in case of axis-parallel facets with Gaussian elimination)
     checks for flipped facets and qh.NARROWhull
     checks the result
 */
 void qh_initialhull(qhT *qh, setT *vertices) {
   facetT *facet, *firstfacet, *neighbor, **neighborp;
   realT dist, angle, minangle= REALmax;
 #ifndef qh_NOtrace
   int k;
 #endif
 
   qh_createsimplex(qh, vertices);  /* qh->facet_list */
   qh_resetlists(qh, False, qh_RESETvisible);
   qh->facet_next= qh->facet_list;      /* advance facet when processed */
   qh->interior_point= qh_getcenter(qh, vertices);
   firstfacet= qh->facet_list;
   qh_setfacetplane(qh, firstfacet);
   zinc_(Znumvisibility); /* needs to be in printsummary */
   qh_distplane(qh, qh->interior_point, firstfacet, &dist);
   if (dist > 0) {
     FORALLfacets
       facet->toporient ^= (unsigned char)True;
   }
   FORALLfacets
     qh_setfacetplane(qh, facet);
   FORALLfacets {
     if (!qh_checkflipped(qh, facet, NULL, qh_ALL)) {/* due to axis-parallel facet */
       trace1((qh, qh->ferr, 1031, "qh_initialhull: initial orientation incorrect.  Correct all facets\n"));
       facet->flipped= False;
       FORALLfacets {
         facet->toporient ^= (unsigned char)True;
         qh_orientoutside(qh, facet);
       }
       break;
     }
   }
   FORALLfacets {
     if (!qh_checkflipped(qh, facet, NULL, !qh_ALL)) {  /* can happen with 'R0.1' */
       if (qh->DELAUNAY && ! qh->ATinfinity) {
         if (qh->UPPERdelaunay)
           qh_fprintf(qh, qh->ferr, 6240, "Qhull input error: Can not compute the upper Delaunay triangulation or upper Voronoi diagram of cocircular/cospherical points.\n");
         else
           qh_fprintf(qh, qh->ferr, 6239, "Qhull input error: Use option 'Qz' for the Delaunay triangulation or Voronoi diagram of cocircular/cospherical points.  Option 'Qz' adds a point \"at infinity\" (above the corresponding paraboloid).\n");
         qh_errexit(qh, qh_ERRinput, NULL, NULL);
       }
       qh_precision(qh, "initial facet is coplanar with interior point");
       qh_fprintf(qh, qh->ferr, 6154, "qhull precision error: initial facet %d is coplanar with the interior point\n",
                    facet->id);
       qh_errexit(qh, qh_ERRsingular, facet, NULL);
     }
     FOREACHneighbor_(facet) {
       angle= qh_getangle(qh, facet->normal, neighbor->normal);
       minimize_( minangle, angle);
     }
   }
   if (minangle < qh_MAXnarrow && !qh->NOnarrow) {
     realT diff= 1.0 + minangle;
 
     qh->NARROWhull= True;
     qh_option(qh, "_narrow-hull", NULL, &diff);
     if (minangle < qh_WARNnarrow && !qh->RERUN && qh->PRINTprecision)
       qh_printhelp_narrowhull(qh, qh->ferr, minangle);
   }
   zzval_(Zprocessed)= qh->hull_dim+1;
   qh_checkpolygon(qh, qh->facet_list);
   qh_checkconvex(qh, qh->facet_list,   qh_DATAfault);
 #ifndef qh_NOtrace
   if (qh->IStracing >= 1) {
     qh_fprintf(qh, qh->ferr, 8105, "qh_initialhull: simplex constructed, interior point:");
     for (k=0; k < qh->hull_dim; k++)
       qh_fprintf(qh, qh->ferr, 8106, " %6.4g", qh->interior_point[k]);
     qh_fprintf(qh, qh->ferr, 8107, "\n");
   }
 #endif
 } /* initialhull */
 
 /*---------------------------------
 
   qh_initialvertices(qh, dim, maxpoints, points, numpoints )
     determines a non-singular set of initial vertices
     maxpoints may include duplicate points
 
   returns:
     temporary set of dim+1 vertices in descending order by vertex id
     if qh.RANDOMoutside && !qh.ALLpoints
       picks random points
     if dim >= qh_INITIALmax,
       uses min/max x and max points with non-zero determinants
 
   notes:
     unless qh.ALLpoints,
       uses maxpoints as long as determinate is non-zero
 */
 setT *qh_initialvertices(qhT *qh, int dim, setT *maxpoints, pointT *points, int numpoints) {
   pointT *point, **pointp;
   setT *vertices, *simplex, *tested;
   realT randr;
   int idx, point_i, point_n, k;
   boolT nearzero= False;
 
   vertices= qh_settemp(qh, dim + 1);
   simplex= qh_settemp(qh, dim+1);
   if (qh->ALLpoints)
     qh_maxsimplex(qh, dim, NULL, points, numpoints, &simplex);
   else if (qh->RANDOMoutside) {
     while (qh_setsize(qh, simplex) != dim+1) {
       randr= qh_RANDOMint;
       randr= randr/(qh_RANDOMmax+1);
       idx= (int)floor(qh->num_points * randr);
       while (qh_setin(simplex, qh_point(qh, idx))) {
             idx++; /* in case qh_RANDOMint always returns the same value */
         idx= idx < qh->num_points ? idx : 0;
       }
       qh_setappend(qh, &simplex, qh_point(qh, idx));
     }
   }else if (qh->hull_dim >= qh_INITIALmax) {
     tested= qh_settemp(qh, dim+1);
     qh_setappend(qh, &simplex, SETfirst_(maxpoints));   /* max and min X coord */
     qh_setappend(qh, &simplex, SETsecond_(maxpoints));
     qh_maxsimplex(qh, fmin_(qh_INITIALsearch, dim), maxpoints, points, numpoints, &simplex);
     k= qh_setsize(qh, simplex);
     FOREACHpoint_i_(qh, maxpoints) {
       if (point_i & 0x1) {     /* first pick up max. coord. points */
         if (!qh_setin(simplex, point) && !qh_setin(tested, point)){
           qh_detsimplex(qh, point, simplex, k, &nearzero);
           if (nearzero)
             qh_setappend(qh, &tested, point);
           else {
             qh_setappend(qh, &simplex, point);
             if (++k == dim)  /* use search for last point */
               break;
           }
         }
       }
     }
     while (k != dim && (point= (pointT*)qh_setdellast(maxpoints))) {
       if (!qh_setin(simplex, point) && !qh_setin(tested, point)){
         qh_detsimplex(qh, point, simplex, k, &nearzero);
         if (nearzero)
           qh_setappend(qh, &tested, point);
         else {
           qh_setappend(qh, &simplex, point);
           k++;
         }
       }
     }
     idx= 0;
     while (k != dim && (point= qh_point(qh, idx++))) {
       if (!qh_setin(simplex, point) && !qh_setin(tested, point)){
         qh_detsimplex(qh, point, simplex, k, &nearzero);
         if (!nearzero){
           qh_setappend(qh, &simplex, point);
           k++;
         }
       }
     }
     qh_settempfree(qh, &tested);
     qh_maxsimplex(qh, dim, maxpoints, points, numpoints, &simplex);
   }else
     qh_maxsimplex(qh, dim, maxpoints, points, numpoints, &simplex);
   FOREACHpoint_(simplex)
     qh_setaddnth(qh, &vertices, 0, qh_newvertex(qh, point)); /* descending order */
   qh_settempfree(qh, &simplex);
   return vertices;
 } /* initialvertices */
 
 
 /*---------------------------------
 
   qh_isvertex(qh, )
     returns vertex if point is in vertex set, else returns NULL
 
   notes:
     for qh.GOODvertex
 */
 vertexT *qh_isvertex(qhT *qh, pointT *point, setT *vertices) {
   vertexT *vertex, **vertexp;
 
   FOREACHvertex_(vertices) {
     if (vertex->point == point)
       return vertex;
   }
   return NULL;
 } /* isvertex */
 
 /*---------------------------------
 
   qh_makenewfacets(qh, point )
     make new facets from point and qh.visible_list
 
   returns:
     qh.newfacet_list= list of new facets with hyperplanes and ->newfacet
     qh.newvertex_list= list of vertices in new facets with ->newlist set
 
     if (qh.ONLYgood)
       newfacets reference horizon facets, but not vice versa
       ridges reference non-simplicial horizon ridges, but not vice versa
       does not change existing facets
     else
       sets qh.NEWfacets
       new facets attached to horizon facets and ridges
       for visible facets,
         visible->r.replace is corresponding new facet
 
   see also:
     qh_makenewplanes() -- make hyperplanes for facets
     qh_attachnewfacets() -- attachnewfacets if not done here(qh->ONLYgood)
     qh_matchnewfacets() -- match up neighbors
     qh_updatevertices() -- update vertex neighbors and delvertices
     qh_deletevisible() -- delete visible facets
     qh_checkpolygon() --check the result
     qh_triangulate() -- triangulate a non-simplicial facet
 
   design:
     for each visible facet
       make new facets to its horizon facets
       update its f.replace
       clear its neighbor set
 */
 vertexT *qh_makenewfacets(qhT *qh, pointT *point /*visible_list*/) {
   facetT *visible, *newfacet= NULL, *newfacet2= NULL, *neighbor, **neighborp;
   vertexT *apex;
   int numnew=0;
 
   qh->newfacet_list= qh->facet_tail;
   qh->newvertex_list= qh->vertex_tail;
   apex= qh_newvertex(qh, point);
   qh_appendvertex(qh, apex);
   qh->visit_id++;
   if (!qh->ONLYgood)
     qh->NEWfacets= True;
   FORALLvisible_facets {
     FOREACHneighbor_(visible)
       neighbor->seen= False;
     if (visible->ridges) {
       visible->visitid= qh->visit_id;
       newfacet2= qh_makenew_nonsimplicial(qh, visible, apex, &numnew);
     }
     if (visible->simplicial)
       newfacet= qh_makenew_simplicial(qh, visible, apex, &numnew);
     if (!qh->ONLYgood) {
       if (newfacet2)  /* newfacet is null if all ridges defined */
         newfacet= newfacet2;
       if (newfacet)
         visible->f.replace= newfacet;
       else
         zinc_(Zinsidevisible);
       SETfirst_(visible->neighbors)= NULL;
     }
   }
   trace1((qh, qh->ferr, 1032, "qh_makenewfacets: created %d new facets from point p%d to horizon\n",
           numnew, qh_pointid(qh, point)));
   if (qh->IStracing >= 4)
     qh_printfacetlist(qh, qh->newfacet_list, NULL, qh_ALL);
   return apex;
 } /* makenewfacets */
 
 /*---------------------------------
 
   qh_matchduplicates(qh, atfacet, atskip, hashsize, hashcount )
     match duplicate ridges in qh.hash_table for atfacet/atskip
     duplicates marked with ->dupridge and qh_DUPLICATEridge
 
   returns:
     picks match with worst merge (min distance apart)
     updates hashcount
 
   see also:
     qh_matchneighbor
 
   notes:
 
   design:
     compute hash value for atfacet and atskip
     repeat twice -- once to make best matches, once to match the rest
       for each possible facet in qh.hash_table
         if it is a matching facet and pass 2
           make match
           unless tricoplanar, mark match for merging (qh_MERGEridge)
           [e.g., tricoplanar RBOX s 1000 t993602376 | QHULL C-1e-3 d Qbb FA Qt]
         if it is a matching facet and pass 1
           test if this is a better match
       if pass 1,
         make best match (it will not be merged)
 */
 #ifndef qh_NOmerge
 void qh_matchduplicates(qhT *qh, facetT *atfacet, int atskip, int hashsize, int *hashcount) {
   boolT same, ismatch;
   int hash, scan;
   facetT *facet, *newfacet, *maxmatch= NULL, *maxmatch2= NULL, *nextfacet;
   int skip, newskip, nextskip= 0, maxskip= 0, maxskip2= 0, makematch;
   realT maxdist= -REALmax, mindist, dist2, low, high;
 
   hash= qh_gethash(qh, hashsize, atfacet->vertices, qh->hull_dim, 1,
                      SETelem_(atfacet->vertices, atskip));
   trace2((qh, qh->ferr, 2046, "qh_matchduplicates: find duplicate matches for f%d skip %d hash %d hashcount %d\n",
           atfacet->id, atskip, hash, *hashcount));
   for (makematch= 0; makematch < 2; makematch++) {
     qh->visit_id++;
     for (newfacet= atfacet, newskip= atskip; newfacet; newfacet= nextfacet, newskip= nextskip) {
       zinc_(Zhashlookup);
       nextfacet= NULL;
       newfacet->visitid= qh->visit_id;
       for (scan= hash; (facet= SETelemt_(qh->hash_table, scan, facetT));
            scan= (++scan >= hashsize ? 0 : scan)) {
         if (!facet->dupridge || facet->visitid == qh->visit_id)
           continue;
         zinc_(Zhashtests);
         if (qh_matchvertices(qh, 1, newfacet->vertices, newskip, facet->vertices, &skip, &same)) {
           ismatch= (same == (boolT)(newfacet->toporient ^ facet->toporient));
           if (SETelemt_(facet->neighbors, skip, facetT) != qh_DUPLICATEridge) {
             if (!makematch) {
               qh_fprintf(qh, qh->ferr, 6155, "qhull internal error (qh_matchduplicates): missing dupridge at f%d skip %d for new f%d skip %d hash %d\n",
                      facet->id, skip, newfacet->id, newskip, hash);
               qh_errexit2(qh, qh_ERRqhull, facet, newfacet);
             }
           }else if (ismatch && makematch) {
             if (SETelemt_(newfacet->neighbors, newskip, facetT) == qh_DUPLICATEridge) {
               SETelem_(facet->neighbors, skip)= newfacet;
               if (newfacet->tricoplanar)
                 SETelem_(newfacet->neighbors, newskip)= facet;
               else
                 SETelem_(newfacet->neighbors, newskip)= qh_MERGEridge;
               *hashcount -= 2; /* removed two unmatched facets */
               trace4((qh, qh->ferr, 4059, "qh_matchduplicates: duplicate f%d skip %d matched with new f%d skip %d merge\n",
                     facet->id, skip, newfacet->id, newskip));
             }
           }else if (ismatch) {
             mindist= qh_getdistance(qh, facet, newfacet, &low, &high);
             dist2= qh_getdistance(qh, newfacet, facet, &low, &high);
             minimize_(mindist, dist2);
             if (mindist > maxdist) {
               maxdist= mindist;
               maxmatch= facet;
               maxskip= skip;
               maxmatch2= newfacet;
               maxskip2= newskip;
             }
             trace3((qh, qh->ferr, 3018, "qh_matchduplicates: duplicate f%d skip %d new f%d skip %d at dist %2.2g, max is now f%d f%d\n",
                     facet->id, skip, newfacet->id, newskip, mindist,
                     maxmatch->id, maxmatch2->id));
           }else { /* !ismatch */
             nextfacet= facet;
             nextskip= skip;
           }
         }
         if (makematch && !facet
         && SETelemt_(facet->neighbors, skip, facetT) == qh_DUPLICATEridge) {
           qh_fprintf(qh, qh->ferr, 6156, "qhull internal error (qh_matchduplicates): no MERGEridge match for duplicate f%d skip %d at hash %d\n",
                      newfacet->id, newskip, hash);
           qh_errexit(qh, qh_ERRqhull, newfacet, NULL);
         }
       }
     } /* end of for each new facet at hash */
     if (!makematch) {
       if (!maxmatch) {
         qh_fprintf(qh, qh->ferr, 6157, "qhull internal error (qh_matchduplicates): no maximum match at duplicate f%d skip %d at hash %d\n",
                      atfacet->id, atskip, hash);
         qh_errexit(qh, qh_ERRqhull, atfacet, NULL);
       }
       SETelem_(maxmatch->neighbors, maxskip)= maxmatch2;
       SETelem_(maxmatch2->neighbors, maxskip2)= maxmatch;
       *hashcount -= 2; /* removed two unmatched facets */
       zzinc_(Zmultiridge);
       trace0((qh, qh->ferr, 25, "qh_matchduplicates: duplicate f%d skip %d matched with new f%d skip %d keep\n",
               maxmatch->id, maxskip, maxmatch2->id, maxskip2));
       qh_precision(qh, "ridge with multiple neighbors");
       if (qh->IStracing >= 4)
         qh_errprint(qh, "DUPLICATED/MATCH", maxmatch, maxmatch2, NULL, NULL);
     }
   }
 } /* matchduplicates */
 
 /*---------------------------------
 
   qh_nearcoplanar()
     for all facets, remove near-inside points from facet->coplanarset
     coplanar points defined by innerplane from qh_outerinner()
 
   returns:
     if qh->KEEPcoplanar && !qh->KEEPinside
       facet->coplanarset only contains coplanar points
     if qh.JOGGLEmax
       drops inner plane by another qh.JOGGLEmax diagonal since a
         vertex could shift out while a coplanar point shifts in
 
   notes:
     used for qh.PREmerge and qh.JOGGLEmax
     must agree with computation of qh.NEARcoplanar in qh_detroundoff(qh)
   design:
     if not keeping coplanar or inside points
       free all coplanar sets
     else if not keeping both coplanar and inside points
       remove !coplanar or !inside points from coplanar sets
 */
 void qh_nearcoplanar(qhT *qh /* qh.facet_list */) {
   facetT *facet;
   pointT *point, **pointp;
   int numpart;
   realT dist, innerplane;
 
   if (!qh->KEEPcoplanar && !qh->KEEPinside) {
     FORALLfacets {
       if (facet->coplanarset)
         qh_setfree(qh, &facet->coplanarset);
     }
   }else if (!qh->KEEPcoplanar || !qh->KEEPinside) {
     qh_outerinner(qh, NULL, NULL, &innerplane);
     if (qh->JOGGLEmax < REALmax/2)
       innerplane -= qh->JOGGLEmax * sqrt((realT)qh->hull_dim);
     numpart= 0;
     FORALLfacets {
       if (facet->coplanarset) {
         FOREACHpoint_(facet->coplanarset) {
           numpart++;
           qh_distplane(qh, point, facet, &dist);
           if (dist < innerplane) {
             if (!qh->KEEPinside)
               SETref_(point)= NULL;
           }else if (!qh->KEEPcoplanar)
             SETref_(point)= NULL;
         }
         qh_setcompact(qh, facet->coplanarset);
       }
     }
     zzadd_(Zcheckpart, numpart);
   }
 } /* nearcoplanar */
 
 /*---------------------------------
 
   qh_nearvertex(qh, facet, point, bestdist )
     return nearest vertex in facet to point
 
   returns:
     vertex and its distance
 
   notes:
     if qh.DELAUNAY
       distance is measured in the input set
     searches neighboring tricoplanar facets (requires vertexneighbors)
       Slow implementation.  Recomputes vertex set for each point.
     The vertex set could be stored in the qh.keepcentrum facet.
 */
 vertexT *qh_nearvertex(qhT *qh, facetT *facet, pointT *point, realT *bestdistp) {
   realT bestdist= REALmax, dist;
   vertexT *bestvertex= NULL, *vertex, **vertexp, *apex;
   coordT *center;
   facetT *neighbor, **neighborp;
   setT *vertices;
   int dim= qh->hull_dim;
 
   if (qh->DELAUNAY)
     dim--;
   if (facet->tricoplanar) {
     if (!qh->VERTEXneighbors || !facet->center) {
       qh_fprintf(qh, qh->ferr, 6158, "qhull internal error (qh_nearvertex): qh.VERTEXneighbors and facet->center required for tricoplanar facets\n");
       qh_errexit(qh, qh_ERRqhull, facet, NULL);
     }
     vertices= qh_settemp(qh, qh->TEMPsize);
     apex= SETfirstt_(facet->vertices, vertexT);
     center= facet->center;
     FOREACHneighbor_(apex) {
       if (neighbor->center == center) {
         FOREACHvertex_(neighbor->vertices)
           qh_setappend(qh, &vertices, vertex);
       }
     }
   }else
     vertices= facet->vertices;
   FOREACHvertex_(vertices) {
     dist= qh_pointdist(qh, vertex->point, point, -dim);
     if (dist < bestdist) {
       bestdist= dist;
       bestvertex= vertex;
     }
   }
   if (facet->tricoplanar)
     qh_settempfree(qh, &vertices);
   *bestdistp= sqrt(bestdist);
   trace3((qh, qh->ferr, 3019, "qh_nearvertex: v%d dist %2.2g for f%d p%d\n",
         bestvertex->id, *bestdistp, facet->id, qh_pointid(qh, point)));
   return bestvertex;
 } /* nearvertex */
 
 /*---------------------------------
 
   qh_newhashtable(qh, newsize )
     returns size of qh.hash_table of at least newsize slots
 
   notes:
     assumes qh.hash_table is NULL
     qh_HASHfactor determines the number of extra slots
     size is not divisible by 2, 3, or 5
 */
 int qh_newhashtable(qhT *qh, int newsize) {
   int size;
 
   size= ((newsize+1)*qh_HASHfactor) | 0x1;  /* odd number */
   while (True) {
     if (newsize<0 || size<0) {
         qh_fprintf(qh, qh->qhmem.ferr, 6236, "qhull error (qh_newhashtable): negative request (%d) or size (%d).  Did int overflow due to high-D?\n", newsize, size); /* WARN64 */
         qh_errexit(qh, qhmem_ERRmem, NULL, NULL);
     }
     if ((size%3) && (size%5))
       break;
     size += 2;
     /* loop terminates because there is an infinite number of primes */
   }
   qh->hash_table= qh_setnew(qh, size);
   qh_setzero(qh, qh->hash_table, 0, size);
   return size;
 } /* newhashtable */
 
 /*---------------------------------
 
   qh_newvertex(qh, point )
     returns a new vertex for point
 */
 vertexT *qh_newvertex(qhT *qh, pointT *point) {
   vertexT *vertex;
 
   zinc_(Ztotvertices);
   vertex= (vertexT *)qh_memalloc(qh, (int)sizeof(vertexT));
   memset((char *) vertex, (size_t)0, sizeof(vertexT));
   if (qh->vertex_id == 0xFFFFFF) {
     qh_fprintf(qh, qh->ferr, 6159, "qhull error: more than %d vertices.  ID field overflows and two vertices\n\
 may have the same identifier.  Vertices will not be sorted correctly.\n", 0xFFFFFF);
     qh_errexit(qh, qh_ERRqhull, NULL, NULL);
   }
   if (qh->vertex_id == qh->tracevertex_id)
     qh->tracevertex= vertex;
   vertex->id= qh->vertex_id++;
   vertex->point= point;
-  vertex->dim= (unsigned char)(qh->hull_dim <= MAX_vdim ? qh->hull_dim : 0);
   trace4((qh, qh->ferr, 4060, "qh_newvertex: vertex p%d(v%d) created\n", qh_pointid(qh, vertex->point),
           vertex->id));
   return(vertex);
 } /* newvertex */
 
 /*---------------------------------
 
   qh_nextridge3d(qh, atridge, facet, vertex )
     return next ridge and vertex for a 3d facet
     returns NULL on error
     [for QhullFacet::nextRidge3d] Does not call qh_errexit nor access qhT.
 
   notes:
     in qh_ORIENTclock order
     this is a O(n^2) implementation to trace all ridges
     be sure to stop on any 2nd visit
     same as QhullRidge::nextRidge3d
     does not use qhT or qh_errexit [QhullFacet.cpp]
 
   design:
     for each ridge
       exit if it is the ridge after atridge
 */
 ridgeT *qh_nextridge3d(qhT *qh, ridgeT *atridge, facetT *facet, vertexT **vertexp) {
   vertexT *atvertex, *vertex, *othervertex;
   ridgeT *ridge, **ridgep;
 
   if ((atridge->top == facet) ^ qh_ORIENTclock)
     atvertex= SETsecondt_(atridge->vertices, vertexT);
   else
     atvertex= SETfirstt_(atridge->vertices, vertexT);
   FOREACHridge_(facet->ridges) {
     if (ridge == atridge)
       continue;
     if ((ridge->top == facet) ^ qh_ORIENTclock) {
       othervertex= SETsecondt_(ridge->vertices, vertexT);
       vertex= SETfirstt_(ridge->vertices, vertexT);
     }else {
       vertex= SETsecondt_(ridge->vertices, vertexT);
       othervertex= SETfirstt_(ridge->vertices, vertexT);
     }
     if (vertex == atvertex) {
       if (vertexp)
         *vertexp= othervertex;
       return ridge;
     }
   }
   return NULL;
 } /* nextridge3d */
 #else /* qh_NOmerge */
 void qh_matchduplicates(qhT *qh, facetT *atfacet, int atskip, int hashsize, int *hashcount) {
 }
 ridgeT *qh_nextridge3d(qhT *qh, ridgeT *atridge, facetT *facet, vertexT **vertexp) {
 
   return NULL;
 }
 #endif /* qh_NOmerge */
 
 /*---------------------------------
 
   qh_outcoplanar()
     move points from all facets' outsidesets to their coplanarsets
 
   notes:
     for post-processing under qh.NARROWhull
 
   design:
     for each facet
       for each outside point for facet
         partition point into coplanar set
 */
 void qh_outcoplanar(qhT *qh /* facet_list */) {
   pointT *point, **pointp;
   facetT *facet;
   realT dist;
 
   trace1((qh, qh->ferr, 1033, "qh_outcoplanar: move outsideset to coplanarset for qh->NARROWhull\n"));
   FORALLfacets {
     FOREACHpoint_(facet->outsideset) {
       qh->num_outside--;
       if (qh->KEEPcoplanar || qh->KEEPnearinside) {
         qh_distplane(qh, point, facet, &dist);
         zinc_(Zpartition);
         qh_partitioncoplanar(qh, point, facet, &dist);
       }
     }
     qh_setfree(qh, &facet->outsideset);
   }
 } /* outcoplanar */
 
 /*---------------------------------
 
   qh_point(qh, id )
     return point for a point id, or NULL if unknown
 
   alternative code:
     return((pointT *)((unsigned   long)qh.first_point
            + (unsigned long)((id)*qh.normal_size)));
 */
 pointT *qh_point(qhT *qh, int id) {
 
   if (id < 0)
     return NULL;
   if (id < qh->num_points)
     return qh->first_point + id * qh->hull_dim;
   id -= qh->num_points;
   if (id < qh_setsize(qh, qh->other_points))
     return SETelemt_(qh->other_points, id, pointT);
   return NULL;
 } /* point */
 
 /*---------------------------------
 
   qh_point_add(qh, set, point, elem )
     stores elem at set[point.id]
 
   returns:
     access function for qh_pointfacet and qh_pointvertex
 
   notes:
     checks point.id
 */
 void qh_point_add(qhT *qh, setT *set, pointT *point, void *elem) {
   int id, size;
 
   SETreturnsize_(set, size);
   if ((id= qh_pointid(qh, point)) < 0)
     qh_fprintf(qh, qh->ferr, 7067, "qhull internal warning (point_add): unknown point %p id %d\n",
       point, id);
   else if (id >= size) {
     qh_fprintf(qh, qh->ferr, 6160, "qhull internal errror(point_add): point p%d is out of bounds(%d)\n",
              id, size);
     qh_errexit(qh, qh_ERRqhull, NULL, NULL);
   }else
     SETelem_(set, id)= elem;
 } /* point_add */
 
 
 /*---------------------------------
 
   qh_pointfacet()
     return temporary set of facet for each point
     the set is indexed by point id
 
   notes:
     vertices assigned to one of the facets
     coplanarset assigned to the facet
     outside set assigned to the facet
     NULL if no facet for point (inside)
       includes qh.GOODpointp
 
   access:
     FOREACHfacet_i_(qh, facets) { ... }
     SETelem_(facets, i)
 
   design:
     for each facet
       add each vertex
       add each coplanar point
       add each outside point
 */
 setT *qh_pointfacet(qhT *qh /*qh.facet_list*/) {
   int numpoints= qh->num_points + qh_setsize(qh, qh->other_points);
   setT *facets;
   facetT *facet;
   vertexT *vertex, **vertexp;
   pointT *point, **pointp;
 
   facets= qh_settemp(qh, numpoints);
   qh_setzero(qh, facets, 0, numpoints);
   qh->vertex_visit++;
   FORALLfacets {
     FOREACHvertex_(facet->vertices) {
       if (vertex->visitid != qh->vertex_visit) {
         vertex->visitid= qh->vertex_visit;
         qh_point_add(qh, facets, vertex->point, facet);
       }
     }
     FOREACHpoint_(facet->coplanarset)
       qh_point_add(qh, facets, point, facet);
     FOREACHpoint_(facet->outsideset)
       qh_point_add(qh, facets, point, facet);
   }
   return facets;
 } /* pointfacet */
 
 /*---------------------------------
 
   qh_pointvertex(qh, )
     return temporary set of vertices indexed by point id
     entry is NULL if no vertex for a point
       this will include qh.GOODpointp
 
   access:
     FOREACHvertex_i_(qh, vertices) { ... }
     SETelem_(vertices, i)
 */
 setT *qh_pointvertex(qhT *qh /*qh.facet_list*/) {
   int numpoints= qh->num_points + qh_setsize(qh, qh->other_points);
   setT *vertices;
   vertexT *vertex;
 
   vertices= qh_settemp(qh, numpoints);
   qh_setzero(qh, vertices, 0, numpoints);
   FORALLvertices
     qh_point_add(qh, vertices, vertex->point, vertex);
   return vertices;
 } /* pointvertex */
 
 
 /*---------------------------------
 
   qh_prependfacet(qh, facet, facetlist )
     prepend facet to the start of a facetlist
 
   returns:
     increments qh.numfacets
     updates facetlist, qh.facet_list, facet_next
 
   notes:
     be careful of prepending since it can lose a pointer.
       e.g., can lose _next by deleting and then prepending before _next
 */
 void qh_prependfacet(qhT *qh, facetT *facet, facetT **facetlist) {
   facetT *prevfacet, *list;
 
 
   trace4((qh, qh->ferr, 4061, "qh_prependfacet: prepend f%d before f%d\n",
           facet->id, getid_(*facetlist)));
   if (!*facetlist)
     (*facetlist)= qh->facet_tail;
   list= *facetlist;
   prevfacet= list->previous;
   facet->previous= prevfacet;
   if (prevfacet)
     prevfacet->next= facet;
   list->previous= facet;
   facet->next= *facetlist;
   if (qh->facet_list == list)  /* this may change *facetlist */
     qh->facet_list= facet;
   if (qh->facet_next == list)
     qh->facet_next= facet;
   *facetlist= facet;
   qh->num_facets++;
 } /* prependfacet */
 
 
 /*---------------------------------
 
   qh_printhashtable(qh, fp )
     print hash table to fp
 
   notes:
-    not in I/O to avoid bringing io.c in
+    not in I/O to avoid bringing io_r.c in
 
   design:
     for each hash entry
       if defined
         if unmatched or will merge (NULL, qh_MERGEridge, qh_DUPLICATEridge)
           print entry and neighbors
 */
 void qh_printhashtable(qhT *qh, FILE *fp) {
   facetT *facet, *neighbor;
   int id, facet_i, facet_n, neighbor_i= 0, neighbor_n= 0;
   vertexT *vertex, **vertexp;
 
   FOREACHfacet_i_(qh, qh->hash_table) {
     if (facet) {
       FOREACHneighbor_i_(qh, facet) {
         if (!neighbor || neighbor == qh_MERGEridge || neighbor == qh_DUPLICATEridge)
           break;
       }
       if (neighbor_i == neighbor_n)
         continue;
       qh_fprintf(qh, fp, 9283, "hash %d f%d ", facet_i, facet->id);
       FOREACHvertex_(facet->vertices)
         qh_fprintf(qh, fp, 9284, "v%d ", vertex->id);
       qh_fprintf(qh, fp, 9285, "\n neighbors:");
       FOREACHneighbor_i_(qh, facet) {
         if (neighbor == qh_MERGEridge)
           id= -3;
         else if (neighbor == qh_DUPLICATEridge)
           id= -2;
         else
           id= getid_(neighbor);
         qh_fprintf(qh, fp, 9286, " %d", id);
       }
       qh_fprintf(qh, fp, 9287, "\n");
     }
   }
 } /* printhashtable */
 
 
 /*---------------------------------
 
   qh_printlists(qh, fp )
     print out facet and vertex list for debugging (without 'f/v' tags)
 */
 void qh_printlists(qhT *qh) {
   facetT *facet;
   vertexT *vertex;
   int count= 0;
 
   qh_fprintf(qh, qh->ferr, 8108, "qh_printlists: facets:");
   FORALLfacets {
     if (++count % 100 == 0)
       qh_fprintf(qh, qh->ferr, 8109, "\n     ");
     qh_fprintf(qh, qh->ferr, 8110, " %d", facet->id);
   }
   qh_fprintf(qh, qh->ferr, 8111, "\n  new facets %d visible facets %d next facet for qh_addpoint %d\n  vertices(new %d):",
      getid_(qh->newfacet_list), getid_(qh->visible_list), getid_(qh->facet_next),
      getid_(qh->newvertex_list));
   count = 0;
   FORALLvertices {
     if (++count % 100 == 0)
       qh_fprintf(qh, qh->ferr, 8112, "\n     ");
     qh_fprintf(qh, qh->ferr, 8113, " %d", vertex->id);
   }
   qh_fprintf(qh, qh->ferr, 8114, "\n");
 } /* printlists */
 
 /*---------------------------------
 
   qh_resetlists(qh, stats, qh_RESETvisible )
     reset newvertex_list, newfacet_list, visible_list
     if stats,
       maintains statistics
 
   returns:
     visible_list is empty if qh_deletevisible was called
 */
 void qh_resetlists(qhT *qh, boolT stats, boolT resetVisible /*qh.newvertex_list newfacet_list visible_list*/) {
   vertexT *vertex;
   facetT *newfacet, *visible;
   int totnew=0, totver=0;
 
   if (stats) {
     FORALLvertex_(qh->newvertex_list)
       totver++;
     FORALLnew_facets
       totnew++;
     zadd_(Zvisvertextot, totver);
     zmax_(Zvisvertexmax, totver);
     zadd_(Znewfacettot, totnew);
     zmax_(Znewfacetmax, totnew);
   }
   FORALLvertex_(qh->newvertex_list)
     vertex->newlist= False;
   qh->newvertex_list= NULL;
   FORALLnew_facets
     newfacet->newfacet= False;
   qh->newfacet_list= NULL;
   if (resetVisible) {
     FORALLvisible_facets {
       visible->f.replace= NULL;
       visible->visible= False;
     }
     qh->num_visible= 0;
   }
   qh->visible_list= NULL; /* may still have visible facets via qh_triangulate */
   qh->NEWfacets= False;
 } /* resetlists */
 
 /*---------------------------------
 
   qh_setvoronoi_all(qh)
     compute Voronoi centers for all facets
     includes upperDelaunay facets if qh.UPPERdelaunay ('Qu')
 
   returns:
     facet->center is the Voronoi center
 
   notes:
     this is unused/untested code
       please email bradb@shore.net if this works ok for you
 
   use:
     FORALLvertices {...} to locate the vertex for a point.
     FOREACHneighbor_(vertex) {...} to visit the Voronoi centers for a Voronoi cell.
 */
 void qh_setvoronoi_all(qhT *qh) {
   facetT *facet;
 
   qh_clearcenters(qh, qh_ASvoronoi);
   qh_vertexneighbors(qh);
 
   FORALLfacets {
     if (!facet->normal || !facet->upperdelaunay || qh->UPPERdelaunay) {
       if (!facet->center)
         facet->center= qh_facetcenter(qh, facet->vertices);
     }
   }
 } /* setvoronoi_all */
 
 #ifndef qh_NOmerge
 
 /*---------------------------------
 
   qh_triangulate()
     triangulate non-simplicial facets on qh.facet_list,
     if qh->VORONOI, sets Voronoi centers of non-simplicial facets
     nop if hasTriangulation
 
   returns:
     all facets simplicial
     each tricoplanar facet has ->f.triowner == owner of ->center,normal,etc.
 
   notes:
     call after qh_check_output since may switch to Voronoi centers
     Output may overwrite ->f.triowner with ->f.area
 */
 void qh_triangulate(qhT *qh /*qh.facet_list*/) {
   facetT *facet, *nextfacet, *owner;
   int onlygood= qh->ONLYgood;
   facetT *neighbor, *visible= NULL, *facet1, *facet2, *new_facet_list= NULL;
   facetT *orig_neighbor= NULL, *otherfacet;
   vertexT *new_vertex_list= NULL;
   mergeT *merge;
   mergeType mergetype;
   int neighbor_i, neighbor_n;
 
   if (qh->hasTriangulation)
       return;
   trace1((qh, qh->ferr, 1034, "qh_triangulate: triangulate non-simplicial facets\n"));
   if (qh->hull_dim == 2)
     return;
   if (qh->VORONOI) {  /* otherwise lose Voronoi centers [could rebuild vertex set from tricoplanar] */
     qh_clearcenters(qh, qh_ASvoronoi);
     qh_vertexneighbors(qh);
   }
   qh->ONLYgood= False; /* for makenew_nonsimplicial */
   qh->visit_id++;
   qh->NEWfacets= True;
   qh->degen_mergeset= qh_settemp(qh, qh->TEMPsize);
   qh->newvertex_list= qh->vertex_tail;
   for (facet= qh->facet_list; facet && facet->next; facet= nextfacet) { /* non-simplicial facets moved to end */
     nextfacet= facet->next;
     if (facet->visible || facet->simplicial)
       continue;
     /* triangulate all non-simplicial facets, otherwise merging does not work, e.g., RBOX c P-0.1 P+0.1 P+0.1 D3 | QHULL d Qt Tv */
     if (!new_facet_list)
       new_facet_list= facet;  /* will be moved to end */
     qh_triangulate_facet(qh, facet, &new_vertex_list);
   }
   trace2((qh, qh->ferr, 2047, "qh_triangulate: delete null facets from f%d -- apex same as second vertex\n", getid_(new_facet_list)));
   for (facet= new_facet_list; facet && facet->next; facet= nextfacet) { /* null facets moved to end */
     nextfacet= facet->next;
     if (facet->visible)
       continue;
     if (facet->ridges) {
       if (qh_setsize(qh, facet->ridges) > 0) {
         qh_fprintf(qh, qh->ferr, 6161, "qhull error (qh_triangulate): ridges still defined for f%d\n", facet->id);
         qh_errexit(qh, qh_ERRqhull, facet, NULL);
       }
       qh_setfree(qh, &facet->ridges);
     }
     if (SETfirst_(facet->vertices) == SETsecond_(facet->vertices)) {
       zinc_(Ztrinull);
       qh_triangulate_null(qh, facet);
     }
   }
   trace2((qh, qh->ferr, 2048, "qh_triangulate: delete %d or more mirror facets -- same vertices and neighbors\n", qh_setsize(qh, qh->degen_mergeset)));
   qh->visible_list= qh->facet_tail;
   while ((merge= (mergeT*)qh_setdellast(qh->degen_mergeset))) {
     facet1= merge->facet1;
     facet2= merge->facet2;
     mergetype= merge->type;
     qh_memfree(qh, merge, (int)sizeof(mergeT));
     if (mergetype == MRGmirror) {
       zinc_(Ztrimirror);
       qh_triangulate_mirror(qh, facet1, facet2);
     }
   }
   qh_settempfree(qh, &qh->degen_mergeset);
   trace2((qh, qh->ferr, 2049, "qh_triangulate: update neighbor lists for vertices from v%d\n", getid_(new_vertex_list)));
   qh->newvertex_list= new_vertex_list;  /* all vertices of new facets */
   qh->visible_list= NULL;
   qh_updatevertices(qh /*qh.newvertex_list, empty newfacet_list and visible_list*/);
   qh_resetlists(qh, False, !qh_RESETvisible /*qh.newvertex_list, empty newfacet_list and visible_list*/);
 
   trace2((qh, qh->ferr, 2050, "qh_triangulate: identify degenerate tricoplanar facets from f%d\n", getid_(new_facet_list)));
   trace2((qh, qh->ferr, 2051, "qh_triangulate: and replace facet->f.triowner with tricoplanar facets that own center, normal, etc.\n"));
   FORALLfacet_(new_facet_list) {
     if (facet->tricoplanar && !facet->visible) {
       FOREACHneighbor_i_(qh, facet) {
         if (neighbor_i == 0) {  /* first iteration */
           if (neighbor->tricoplanar)
             orig_neighbor= neighbor->f.triowner;
           else
             orig_neighbor= neighbor;
         }else {
           if (neighbor->tricoplanar)
             otherfacet= neighbor->f.triowner;
           else
             otherfacet= neighbor;
           if (orig_neighbor == otherfacet) {
             zinc_(Ztridegen);
             facet->degenerate= True;
             break;
           }
         }
       }
     }
   }
 
   trace2((qh, qh->ferr, 2052, "qh_triangulate: delete visible facets -- non-simplicial, null, and mirrored facets\n"));
   owner= NULL;
   visible= NULL;
   for (facet= new_facet_list; facet && facet->next; facet= nextfacet) { /* may delete facet */
     nextfacet= facet->next;
     if (facet->visible) {
       if (facet->tricoplanar) { /* a null or mirrored facet */
         qh_delfacet(qh, facet);
         qh->num_visible--;
       }else {  /* a non-simplicial facet followed by its tricoplanars */
         if (visible && !owner) {
           /*  RBOX 200 s D5 t1001471447 | QHULL Qt C-0.01 Qx Qc Tv Qt -- f4483 had 6 vertices/neighbors and 8 ridges */
           trace2((qh, qh->ferr, 2053, "qh_triangulate: all tricoplanar facets degenerate for non-simplicial facet f%d\n",
                        visible->id));
           qh_delfacet(qh, visible);
           qh->num_visible--;
         }
         visible= facet;
         owner= NULL;
       }
     }else if (facet->tricoplanar) {
       if (facet->f.triowner != visible) {
         qh_fprintf(qh, qh->ferr, 6162, "qhull error (qh_triangulate): tricoplanar facet f%d not owned by its visible, non-simplicial facet f%d\n", facet->id, getid_(visible));
         qh_errexit2(qh, qh_ERRqhull, facet, visible);
       }
       if (owner)
         facet->f.triowner= owner;
       else if (!facet->degenerate) {
         owner= facet;
         nextfacet= visible->next; /* rescan tricoplanar facets with owner */
         facet->keepcentrum= True;  /* one facet owns ->normal, etc. */
         facet->coplanarset= visible->coplanarset;
         facet->outsideset= visible->outsideset;
         visible->coplanarset= NULL;
         visible->outsideset= NULL;
         if (!qh->TRInormals) { /* center and normal copied to tricoplanar facets */
           visible->center= NULL;
           visible->normal= NULL;
         }
         qh_delfacet(qh, visible);
         qh->num_visible--;
       }
     }
   }
   if (visible && !owner) {
     trace2((qh, qh->ferr, 2054, "qh_triangulate: all tricoplanar facets degenerate for last non-simplicial facet f%d\n",
                  visible->id));
     qh_delfacet(qh, visible);
     qh->num_visible--;
   }
   qh->NEWfacets= False;
   qh->ONLYgood= onlygood; /* restore value */
   if (qh->CHECKfrequently)
     qh_checkpolygon(qh, qh->facet_list);
   qh->hasTriangulation= True;
 } /* triangulate */
 
 
 /*---------------------------------
 
   qh_triangulate_facet(qh, facetA)
     triangulate a non-simplicial facet
       if qh.CENTERtype=qh_ASvoronoi, sets its Voronoi center
   returns:
     qh.newfacet_list == simplicial facets
       facet->tricoplanar set and ->keepcentrum false
       facet->degenerate set if duplicated apex
       facet->f.trivisible set to facetA
       facet->center copied from facetA (created if qh_ASvoronoi)
         qh_eachvoronoi, qh_detvridge, qh_detvridge3 assume centers copied
       facet->normal,offset,maxoutside copied from facetA
 
   notes:
       qh_makenew_nonsimplicial uses neighbor->seen for the same
 
   see also:
       qh_addpoint() -- add a point
       qh_makenewfacets() -- construct a cone of facets for a new vertex
 
   design:
       if qh_ASvoronoi,
          compute Voronoi center (facet->center)
       select first vertex (highest ID to preserve ID ordering of ->vertices)
       triangulate from vertex to ridges
       copy facet->center, normal, offset
       update vertex neighbors
 */
 void qh_triangulate_facet(qhT *qh, facetT *facetA, vertexT **first_vertex) {
   facetT *newfacet;
   facetT *neighbor, **neighborp;
   vertexT *apex;
   int numnew=0;
 
   trace3((qh, qh->ferr, 3020, "qh_triangulate_facet: triangulate facet f%d\n", facetA->id));
 
   if (qh->IStracing >= 4)
     qh_printfacet(qh, qh->ferr, facetA);
   FOREACHneighbor_(facetA) {
     neighbor->seen= False;
     neighbor->coplanar= False;
   }
   if (qh->CENTERtype == qh_ASvoronoi && !facetA->center  /* matches upperdelaunay in qh_setfacetplane() */
         && fabs_(facetA->normal[qh->hull_dim -1]) >= qh->ANGLEround * qh_ZEROdelaunay) {
     facetA->center= qh_facetcenter(qh, facetA->vertices);
   }
   qh_willdelete(qh, facetA, NULL);
   qh->newfacet_list= qh->facet_tail;
   facetA->visitid= qh->visit_id;
   apex= SETfirstt_(facetA->vertices, vertexT);
   qh_makenew_nonsimplicial(qh, facetA, apex, &numnew);
   SETfirst_(facetA->neighbors)= NULL;
   FORALLnew_facets {
     newfacet->tricoplanar= True;
     newfacet->f.trivisible= facetA;
     newfacet->degenerate= False;
     newfacet->upperdelaunay= facetA->upperdelaunay;
     newfacet->good= facetA->good;
     if (qh->TRInormals) {
       newfacet->keepcentrum= True;
       newfacet->normal= qh_copypoints(qh, facetA->normal, 1, qh->hull_dim);
       if (qh->CENTERtype == qh_AScentrum)
         newfacet->center= qh_getcentrum(qh, newfacet);
       else
         newfacet->center= qh_copypoints(qh, facetA->center, 1, qh->hull_dim);
     }else {
       newfacet->keepcentrum= False;
       newfacet->normal= facetA->normal;
       newfacet->center= facetA->center;
     }
     newfacet->offset= facetA->offset;
 #if qh_MAXoutside
     newfacet->maxoutside= facetA->maxoutside;
 #endif
   }
   qh_matchnewfacets(qh /*qh.newfacet_list*/);
   zinc_(Ztricoplanar);
   zadd_(Ztricoplanartot, numnew);
   zmax_(Ztricoplanarmax, numnew);
   qh->visible_list= NULL;
   if (!(*first_vertex))
     (*first_vertex)= qh->newvertex_list;
   qh->newvertex_list= NULL;
   qh_updatevertices(qh /*qh.newfacet_list, empty visible_list and newvertex_list*/);
   qh_resetlists(qh, False, !qh_RESETvisible /*qh.newfacet_list, empty visible_list and newvertex_list*/);
 } /* triangulate_facet */
 
 /*---------------------------------
 
   qh_triangulate_link(qh, oldfacetA, facetA, oldfacetB, facetB)
     relink facetA to facetB via oldfacets
   returns:
     adds mirror facets to qh->degen_mergeset (4-d and up only)
   design:
     if they are already neighbors, the opposing neighbors become MRGmirror facets
 */
 void qh_triangulate_link(qhT *qh, facetT *oldfacetA, facetT *facetA, facetT *oldfacetB, facetT *facetB) {
   int errmirror= False;
 
   trace3((qh, qh->ferr, 3021, "qh_triangulate_link: relink old facets f%d and f%d between neighbors f%d and f%d\n",
          oldfacetA->id, oldfacetB->id, facetA->id, facetB->id));
   if (qh_setin(facetA->neighbors, facetB)) {
     if (!qh_setin(facetB->neighbors, facetA))
       errmirror= True;
     else
       qh_appendmergeset(qh, facetA, facetB, MRGmirror, NULL);
   }else if (qh_setin(facetB->neighbors, facetA))
     errmirror= True;
   if (errmirror) {
     qh_fprintf(qh, qh->ferr, 6163, "qhull error (qh_triangulate_link): mirror facets f%d and f%d do not match for old facets f%d and f%d\n",
        facetA->id, facetB->id, oldfacetA->id, oldfacetB->id);
     qh_errexit2(qh, qh_ERRqhull, facetA, facetB);
   }
   qh_setreplace(qh, facetB->neighbors, oldfacetB, facetA);
   qh_setreplace(qh, facetA->neighbors, oldfacetA, facetB);
 } /* triangulate_link */
 
 /*---------------------------------
 
   qh_triangulate_mirror(qh, facetA, facetB)
     delete mirrored facets from qh_triangulate_null() and qh_triangulate_mirror
       a mirrored facet shares the same vertices of a logical ridge
   design:
     since a null facet duplicates the first two vertices, the opposing neighbors absorb the null facet
     if they are already neighbors, the opposing neighbors become MRGmirror facets
 */
 void qh_triangulate_mirror(qhT *qh, facetT *facetA, facetT *facetB) {
   facetT *neighbor, *neighborB;
   int neighbor_i, neighbor_n;
 
   trace3((qh, qh->ferr, 3022, "qh_triangulate_mirror: delete mirrored facets f%d and f%d\n",
          facetA->id, facetB->id));
   FOREACHneighbor_i_(qh, facetA) {
     neighborB= SETelemt_(facetB->neighbors, neighbor_i, facetT);
     if (neighbor == neighborB)
       continue; /* occurs twice */
     qh_triangulate_link(qh, facetA, neighbor, facetB, neighborB);
   }
   qh_willdelete(qh, facetA, NULL);
   qh_willdelete(qh, facetB, NULL);
 } /* triangulate_mirror */
 
 /*---------------------------------
 
   qh_triangulate_null(qh, facetA)
     remove null facetA from qh_triangulate_facet()
       a null facet has vertex #1 (apex) == vertex #2
   returns:
     adds facetA to ->visible for deletion after qh_updatevertices
     qh->degen_mergeset contains mirror facets (4-d and up only)
   design:
     since a null facet duplicates the first two vertices, the opposing neighbors absorb the null facet
     if they are already neighbors, the opposing neighbors become MRGmirror facets
 */
 void qh_triangulate_null(qhT *qh, facetT *facetA) {
   facetT *neighbor, *otherfacet;
 
   trace3((qh, qh->ferr, 3023, "qh_triangulate_null: delete null facet f%d\n", facetA->id));
   neighbor= SETfirstt_(facetA->neighbors, facetT);
   otherfacet= SETsecondt_(facetA->neighbors, facetT);
   qh_triangulate_link(qh, facetA, neighbor, facetA, otherfacet);
   qh_willdelete(qh, facetA, NULL);
 } /* triangulate_null */
 
 #else /* qh_NOmerge */
 void qh_triangulate(qhT *qh) {
 }
 #endif /* qh_NOmerge */
 
    /*---------------------------------
 
   qh_vertexintersect(qh, vertexsetA, vertexsetB )
     intersects two vertex sets (inverse id ordered)
     vertexsetA is a temporary set at the top of qh->qhmem.tempstack
 
   returns:
     replaces vertexsetA with the intersection
 
   notes:
     could overwrite vertexsetA if currently too slow
 */
 void qh_vertexintersect(qhT *qh, setT **vertexsetA,setT *vertexsetB) {
   setT *intersection;
 
   intersection= qh_vertexintersect_new(qh, *vertexsetA, vertexsetB);
   qh_settempfree(qh, vertexsetA);
   *vertexsetA= intersection;
   qh_settemppush(qh, intersection);
 } /* vertexintersect */
 
 /*---------------------------------
 
   qh_vertexintersect_new(qh, )
     intersects two vertex sets (inverse id ordered)
 
   returns:
     a new set
 */
 setT *qh_vertexintersect_new(qhT *qh, setT *vertexsetA,setT *vertexsetB) {
   setT *intersection= qh_setnew(qh, qh->hull_dim - 1);
   vertexT **vertexA= SETaddr_(vertexsetA, vertexT);
   vertexT **vertexB= SETaddr_(vertexsetB, vertexT);
 
   while (*vertexA && *vertexB) {
     if (*vertexA  == *vertexB) {
       qh_setappend(qh, &intersection, *vertexA);
       vertexA++; vertexB++;
     }else {
       if ((*vertexA)->id > (*vertexB)->id)
         vertexA++;
       else
         vertexB++;
     }
   }
   return intersection;
 } /* vertexintersect_new */
 
 /*---------------------------------
 
   qh_vertexneighbors(qh)
     for each vertex in qh.facet_list,
       determine its neighboring facets
 
   returns:
     sets qh.VERTEXneighbors
       nop if qh.VERTEXneighbors already set
       qh_addpoint() will maintain them
 
   notes:
     assumes all vertex->neighbors are NULL
 
   design:
     for each facet
       for each vertex
         append facet to vertex->neighbors
 */
 void qh_vertexneighbors(qhT *qh /*qh.facet_list*/) {
   facetT *facet;
   vertexT *vertex, **vertexp;
 
   if (qh->VERTEXneighbors)
     return;
   trace1((qh, qh->ferr, 1035, "qh_vertexneighbors: determing neighboring facets for each vertex\n"));
   qh->vertex_visit++;
   FORALLfacets {
     if (facet->visible)
       continue;
     FOREACHvertex_(facet->vertices) {
       if (vertex->visitid != qh->vertex_visit) {
         vertex->visitid= qh->vertex_visit;
         vertex->neighbors= qh_setnew(qh, qh->hull_dim);
       }
       qh_setappend(qh, &vertex->neighbors, facet);
     }
   }
   qh->VERTEXneighbors= True;
 } /* vertexneighbors */
 
 /*---------------------------------
 
   qh_vertexsubset(qh, vertexsetA, vertexsetB )
     returns True if vertexsetA is a subset of vertexsetB
     assumes vertexsets are sorted
 
   note:
     empty set is a subset of any other set
 */
 boolT qh_vertexsubset(qhT *qh, setT *vertexsetA, setT *vertexsetB) {
   vertexT **vertexA= (vertexT **) SETaddr_(vertexsetA, vertexT);
   vertexT **vertexB= (vertexT **) SETaddr_(vertexsetB, vertexT);
 
   while (True) {
     if (!*vertexA)
       return True;
     if (!*vertexB)
       return False;
     if ((*vertexA)->id > (*vertexB)->id)
       return False;
     if (*vertexA  == *vertexB)
       vertexA++;
     vertexB++;
   }
   return False; /* avoid warnings */
 } /* vertexsubset */
diff --git a/src/libqhullr/poly_r.c b/src/libqhullr/poly_r.c
index 126c9f3..b1040fd 100644
--- a/src/libqhullr/poly_r.c
+++ b/src/libqhullr/poly_r.c
@@ -1,1199 +1,1199 @@
 /*
  ---------------------------------
 
-   poly.c
+   poly_r.c
    implements polygons and simplices
 
-   see qh-poly.htm, poly.h and libqhull.h
+   see qh-poly.htm, poly_r.h and libqhull_r.h
 
-   infrequent code is in poly2.c
+   infrequent code is in poly2_r.c
    (all but top 50 and their callers 12/3/95)
 
    Copyright (c) 1993-2014 The Geometry Center.
-   $Id: //main/2011/qhull/src/libqhullr/poly_r.c#4 $$Change: 1663 $
-   $DateTime: 2014/01/19 17:59:16 $$Author: bbarber $
+   $Id: //main/2011/qhull/src/libqhullr/poly_r.c#7 $$Change: 1799 $
+   $DateTime: 2014/12/17 16:17:40 $$Author: bbarber $
 */
 
-#include "qhull_r.h"
+#include "qhull_ra.h"
 
 /*======== functions in alphabetical order ==========*/
 
 /*---------------------------------
 
   qh_appendfacet(qh, facet )
     appends facet to end of qh.facet_list,
 
   returns:
     updates qh.newfacet_list, facet_next, facet_list
     increments qh.numfacets
 
   notes:
     assumes qh.facet_list/facet_tail is defined (createsimplex)
 
   see:
     qh_removefacet()
 
 */
 void qh_appendfacet(qhT *qh, facetT *facet) {
   facetT *tail= qh->facet_tail;
 
   if (tail == qh->newfacet_list)
     qh->newfacet_list= facet;
   if (tail == qh->facet_next)
     qh->facet_next= facet;
   facet->previous= tail->previous;
   facet->next= tail;
   if (tail->previous)
     tail->previous->next= facet;
   else
     qh->facet_list= facet;
   tail->previous= facet;
   qh->num_facets++;
   trace4((qh, qh->ferr, 4044, "qh_appendfacet: append f%d to facet_list\n", facet->id));
 } /* appendfacet */
 
 
 /*---------------------------------
 
   qh_appendvertex(qh, vertex )
     appends vertex to end of qh.vertex_list,
 
   returns:
     sets vertex->newlist
     updates qh.vertex_list, newvertex_list
     increments qh.num_vertices
 
   notes:
     assumes qh.vertex_list/vertex_tail is defined (createsimplex)
 
 */
 void qh_appendvertex(qhT *qh, vertexT *vertex) {
   vertexT *tail= qh->vertex_tail;
 
   if (tail == qh->newvertex_list)
     qh->newvertex_list= vertex;
   vertex->newlist= True;
   vertex->previous= tail->previous;
   vertex->next= tail;
   if (tail->previous)
     tail->previous->next= vertex;
   else
     qh->vertex_list= vertex;
   tail->previous= vertex;
   qh->num_vertices++;
   trace4((qh, qh->ferr, 4045, "qh_appendvertex: append v%d to vertex_list\n", vertex->id));
 } /* appendvertex */
 
 
 /*---------------------------------
 
   qh_attachnewfacets(qh, )
     attach horizon facets to new facets in qh.newfacet_list
     newfacets have neighbor and ridge links to horizon but not vice versa
     only needed for qh.ONLYgood
 
   returns:
     set qh.NEWfacets
     horizon facets linked to new facets
       ridges changed from visible facets to new facets
       simplicial ridges deleted
     qh.visible_list, no ridges valid
     facet->f.replace is a newfacet (if any)
 
   design:
     delete interior ridges and neighbor sets by
       for each visible, non-simplicial facet
         for each ridge
           if last visit or if neighbor is simplicial
             if horizon neighbor
               delete ridge for horizon's ridge set
             delete ridge
         erase neighbor set
     attach horizon facets and new facets by
       for all new facets
         if corresponding horizon facet is simplicial
           locate corresponding visible facet {may be more than one}
           link visible facet to new facet
           replace visible facet with new facet in horizon
         else it's non-simplicial
           for all visible neighbors of the horizon facet
             link visible neighbor to new facet
             delete visible neighbor from horizon facet
           append new facet to horizon's neighbors
           the first ridge of the new facet is the horizon ridge
           link the new facet into the horizon ridge
 */
 void qh_attachnewfacets(qhT *qh /* qh.visible_list, newfacet_list */) {
   facetT *newfacet= NULL, *neighbor, **neighborp, *horizon, *visible;
   ridgeT *ridge, **ridgep;
 
   qh->NEWfacets= True;
   trace3((qh, qh->ferr, 3012, "qh_attachnewfacets: delete interior ridges\n"));
   qh->visit_id++;
   FORALLvisible_facets {
     visible->visitid= qh->visit_id;
     if (visible->ridges) {
       FOREACHridge_(visible->ridges) {
         neighbor= otherfacet_(ridge, visible);
         if (neighbor->visitid == qh->visit_id
             || (!neighbor->visible && neighbor->simplicial)) {
           if (!neighbor->visible)  /* delete ridge for simplicial horizon */
             qh_setdel(neighbor->ridges, ridge);
           qh_setfree(qh, &(ridge->vertices)); /* delete on 2nd visit */
           qh_memfree(qh, ridge, (int)sizeof(ridgeT));
         }
       }
       SETfirst_(visible->ridges)= NULL;
     }
     SETfirst_(visible->neighbors)= NULL;
   }
   trace1((qh, qh->ferr, 1017, "qh_attachnewfacets: attach horizon facets to new facets\n"));
   FORALLnew_facets {
     horizon= SETfirstt_(newfacet->neighbors, facetT);
     if (horizon->simplicial) {
       visible= NULL;
       FOREACHneighbor_(horizon) {   /* may have more than one horizon ridge */
         if (neighbor->visible) {
           if (visible) {
             if (qh_setequal_skip(newfacet->vertices, 0, horizon->vertices,
                                   SETindex_(horizon->neighbors, neighbor))) {
               visible= neighbor;
               break;
             }
           }else
             visible= neighbor;
         }
       }
       if (visible) {
         visible->f.replace= newfacet;
         qh_setreplace(qh, horizon->neighbors, visible, newfacet);
       }else {
         qh_fprintf(qh, qh->ferr, 6102, "qhull internal error (qh_attachnewfacets): couldn't find visible facet for horizon f%d of newfacet f%d\n",
                  horizon->id, newfacet->id);
         qh_errexit2(qh, qh_ERRqhull, horizon, newfacet);
       }
     }else { /* non-simplicial, with a ridge for newfacet */
       FOREACHneighbor_(horizon) {    /* may hold for many new facets */
         if (neighbor->visible) {
           neighbor->f.replace= newfacet;
           qh_setdelnth(qh, horizon->neighbors,
                         SETindex_(horizon->neighbors, neighbor));
           neighborp--; /* repeat */
         }
       }
       qh_setappend(qh, &horizon->neighbors, newfacet);
       ridge= SETfirstt_(newfacet->ridges, ridgeT);
       if (ridge->top == horizon)
         ridge->bottom= newfacet;
       else
         ridge->top= newfacet;
       }
   } /* newfacets */
   if (qh->PRINTstatistics) {
     FORALLvisible_facets {
       if (!visible->f.replace)
         zinc_(Zinsidevisible);
     }
   }
 } /* attachnewfacets */
 
 /*---------------------------------
 
   qh_checkflipped(qh, facet, dist, allerror )
     checks facet orientation to interior point
 
     if allerror set,
       tests against qh.DISTround
     else
       tests against 0 since tested against DISTround before
 
   returns:
     False if it flipped orientation (sets facet->flipped)
     distance if non-NULL
 */
 boolT qh_checkflipped(qhT *qh, facetT *facet, realT *distp, boolT allerror) {
   realT dist;
 
   if (facet->flipped && !distp)
     return False;
   zzinc_(Zdistcheck);
   qh_distplane(qh, qh->interior_point, facet, &dist);
   if (distp)
     *distp= dist;
   if ((allerror && dist > -qh->DISTround)|| (!allerror && dist >= 0.0)) {
     facet->flipped= True;
     zzinc_(Zflippedfacets);
     trace0((qh, qh->ferr, 19, "qh_checkflipped: facet f%d is flipped, distance= %6.12g during p%d\n",
               facet->id, dist, qh->furthest_id));
     qh_precision(qh, "flipped facet");
     return False;
   }
   return True;
 } /* checkflipped */
 
 /*---------------------------------
 
   qh_delfacet(qh, facet )
     removes facet from facet_list and frees up its memory
 
   notes:
     assumes vertices and ridges already freed
 */
 void qh_delfacet(qhT *qh, facetT *facet) {
   void **freelistp; /* used !qh_NOmem */
 
   trace4((qh, qh->ferr, 4046, "qh_delfacet: delete f%d\n", facet->id));
   if (facet == qh->tracefacet)
     qh->tracefacet= NULL;
   if (facet == qh->GOODclosest)
     qh->GOODclosest= NULL;
   qh_removefacet(qh, facet);
   if (!facet->tricoplanar || facet->keepcentrum) {
     qh_memfree_(qh, facet->normal, qh->normal_size, freelistp);
     if (qh->CENTERtype == qh_ASvoronoi) {   /* uses macro calls */
       qh_memfree_(qh, facet->center, qh->center_size, freelistp);
     }else /* AScentrum */ {
       qh_memfree_(qh, facet->center, qh->normal_size, freelistp);
     }
   }
   qh_setfree(qh, &(facet->neighbors));
   if (facet->ridges)
     qh_setfree(qh, &(facet->ridges));
   qh_setfree(qh, &(facet->vertices));
   if (facet->outsideset)
     qh_setfree(qh, &(facet->outsideset));
   if (facet->coplanarset)
     qh_setfree(qh, &(facet->coplanarset));
   qh_memfree_(qh, facet, (int)sizeof(facetT), freelistp);
 } /* delfacet */
 
 
 /*---------------------------------
 
   qh_deletevisible()
     delete visible facets and vertices
 
   returns:
     deletes each facet and removes from facetlist
     at exit, qh.visible_list empty (== qh.newfacet_list)
 
   notes:
     ridges already deleted
     horizon facets do not reference facets on qh.visible_list
     new facets in qh.newfacet_list
     uses   qh.visit_id;
 */
 void qh_deletevisible(qhT *qh /*qh.visible_list*/) {
   facetT *visible, *nextfacet;
   vertexT *vertex, **vertexp;
   int numvisible= 0, numdel= qh_setsize(qh, qh->del_vertices);
 
   trace1((qh, qh->ferr, 1018, "qh_deletevisible: delete %d visible facets and %d vertices\n",
          qh->num_visible, numdel));
   for (visible= qh->visible_list; visible && visible->visible;
                 visible= nextfacet) { /* deleting current */
     nextfacet= visible->next;
     numvisible++;
     qh_delfacet(qh, visible);
   }
   if (numvisible != qh->num_visible) {
     qh_fprintf(qh, qh->ferr, 6103, "qhull internal error (qh_deletevisible): qh->num_visible %d is not number of visible facets %d\n",
              qh->num_visible, numvisible);
     qh_errexit(qh, qh_ERRqhull, NULL, NULL);
   }
   qh->num_visible= 0;
   zadd_(Zvisfacettot, numvisible);
   zmax_(Zvisfacetmax, numvisible);
   zzadd_(Zdelvertextot, numdel);
   zmax_(Zdelvertexmax, numdel);
   FOREACHvertex_(qh->del_vertices)
     qh_delvertex(qh, vertex);
   qh_settruncate(qh, qh->del_vertices, 0);
 } /* deletevisible */
 
 /*---------------------------------
 
   qh_facetintersect(qh, facetA, facetB, skipa, skipB, prepend )
     return vertices for intersection of two simplicial facets
     may include 1 prepended entry (if more, need to settemppush)
 
   returns:
     returns set of qh.hull_dim-1 + prepend vertices
     returns skipped index for each test and checks for exactly one
 
   notes:
     does not need settemp since set in quick memory
 
   see also:
     qh_vertexintersect and qh_vertexintersect_new
     use qh_setnew_delnthsorted to get nth ridge (no skip information)
 
   design:
     locate skipped vertex by scanning facet A's neighbors
     locate skipped vertex by scanning facet B's neighbors
     intersect the vertex sets
 */
 setT *qh_facetintersect(qhT *qh, facetT *facetA, facetT *facetB,
                          int *skipA,int *skipB, int prepend) {
   setT *intersect;
   int dim= qh->hull_dim, i, j;
   facetT **neighborsA, **neighborsB;
 
   neighborsA= SETaddr_(facetA->neighbors, facetT);
   neighborsB= SETaddr_(facetB->neighbors, facetT);
   i= j= 0;
   if (facetB == *neighborsA++)
     *skipA= 0;
   else if (facetB == *neighborsA++)
     *skipA= 1;
   else if (facetB == *neighborsA++)
     *skipA= 2;
   else {
     for (i=3; i < dim; i++) {
       if (facetB == *neighborsA++) {
         *skipA= i;
         break;
       }
     }
   }
   if (facetA == *neighborsB++)
     *skipB= 0;
   else if (facetA == *neighborsB++)
     *skipB= 1;
   else if (facetA == *neighborsB++)
     *skipB= 2;
   else {
     for (j=3; j < dim; j++) {
       if (facetA == *neighborsB++) {
         *skipB= j;
         break;
       }
     }
   }
   if (i >= dim || j >= dim) {
     qh_fprintf(qh, qh->ferr, 6104, "qhull internal error (qh_facetintersect): f%d or f%d not in others neighbors\n",
             facetA->id, facetB->id);
     qh_errexit2(qh, qh_ERRqhull, facetA, facetB);
   }
   intersect= qh_setnew_delnthsorted(qh, facetA->vertices, qh->hull_dim, *skipA, prepend);
   trace4((qh, qh->ferr, 4047, "qh_facetintersect: f%d skip %d matches f%d skip %d\n",
           facetA->id, *skipA, facetB->id, *skipB));
   return(intersect);
 } /* facetintersect */
 
 /*---------------------------------
 
   qh_gethash(qh, hashsize, set, size, firstindex, skipelem )
     return hashvalue for a set with firstindex and skipelem
 
   notes:
     returned hash is in [0,hashsize)
     assumes at least firstindex+1 elements
     assumes skipelem is NULL, in set, or part of hash
 
     hashes memory addresses which may change over different runs of the same data
     using sum for hash does badly in high d
 */
 int qh_gethash(qhT *qh, int hashsize, setT *set, int size, int firstindex, void *skipelem) {
   void **elemp= SETelemaddr_(set, firstindex, void);
   ptr_intT hash = 0, elem;
   unsigned result;
   int i;
 #ifdef _MSC_VER                   /* Microsoft Visual C++ -- warn about 64-bit issues */
 #pragma warning( push)            /* WARN64 -- ptr_intT holds a 64-bit pointer */
 #pragma warning( disable : 4311)  /* 'type cast': pointer truncation from 'void*' to 'ptr_intT' */
 #endif
 
   switch (size-firstindex) {
   case 1:
     hash= (ptr_intT)(*elemp) - (ptr_intT) skipelem;
     break;
   case 2:
     hash= (ptr_intT)(*elemp) + (ptr_intT)elemp[1] - (ptr_intT) skipelem;
     break;
   case 3:
     hash= (ptr_intT)(*elemp) + (ptr_intT)elemp[1] + (ptr_intT)elemp[2]
       - (ptr_intT) skipelem;
     break;
   case 4:
     hash= (ptr_intT)(*elemp) + (ptr_intT)elemp[1] + (ptr_intT)elemp[2]
       + (ptr_intT)elemp[3] - (ptr_intT) skipelem;
     break;
   case 5:
     hash= (ptr_intT)(*elemp) + (ptr_intT)elemp[1] + (ptr_intT)elemp[2]
       + (ptr_intT)elemp[3] + (ptr_intT)elemp[4] - (ptr_intT) skipelem;
     break;
   case 6:
     hash= (ptr_intT)(*elemp) + (ptr_intT)elemp[1] + (ptr_intT)elemp[2]
       + (ptr_intT)elemp[3] + (ptr_intT)elemp[4]+ (ptr_intT)elemp[5]
       - (ptr_intT) skipelem;
     break;
   default:
     hash= 0;
     i= 3;
     do {     /* this is about 10% in 10-d */
       if ((elem= (ptr_intT)*elemp++) != (ptr_intT)skipelem) {
         hash ^= (elem << i) + (elem >> (32-i));
         i += 3;
         if (i >= 32)
           i -= 32;
       }
     }while (*elemp);
     break;
   }
   if (hashsize<0) {
     qh_fprintf(qh, qh->ferr, 6202, "qhull internal error: negative hashsize %d passed to qh_gethash [poly.c]\n", hashsize);
     qh_errexit2(qh, qh_ERRqhull, NULL, NULL);
   }
   result= (unsigned)hash;
   result %= (unsigned)hashsize;
   /* result= 0; for debugging */
   return result;
 #ifdef _MSC_VER
 #pragma warning( pop)
 #endif
 } /* gethash */
 
 /*---------------------------------
 
   qh_makenewfacet(qh, vertices, toporient, horizon )
     creates a toporient? facet from vertices
 
   returns:
     returns newfacet
       adds newfacet to qh.facet_list
       newfacet->vertices= vertices
       if horizon
         newfacet->neighbor= horizon, but not vice versa
     newvertex_list updated with vertices
 */
 facetT *qh_makenewfacet(qhT *qh, setT *vertices, boolT toporient,facetT *horizon) {
   facetT *newfacet;
   vertexT *vertex, **vertexp;
 
   FOREACHvertex_(vertices) {
     if (!vertex->newlist) {
       qh_removevertex(qh, vertex);
       qh_appendvertex(qh, vertex);
     }
   }
   newfacet= qh_newfacet(qh);
   newfacet->vertices= vertices;
   newfacet->toporient= (unsigned char)toporient;
   if (horizon)
     qh_setappend(qh, &(newfacet->neighbors), horizon);
   qh_appendfacet(qh, newfacet);
   return(newfacet);
 } /* makenewfacet */
 
 
 /*---------------------------------
 
   qh_makenewplanes()
     make new hyperplanes for facets on qh.newfacet_list
 
   returns:
     all facets have hyperplanes or are marked for   merging
     doesn't create hyperplane if horizon is coplanar (will merge)
     updates qh.min_vertex if qh.JOGGLEmax
 
   notes:
     facet->f.samecycle is defined for facet->mergehorizon facets
 */
 void qh_makenewplanes(qhT *qh /* qh.newfacet_list */) {
   facetT *newfacet;
 
   FORALLnew_facets {
     if (!newfacet->mergehorizon)
       qh_setfacetplane(qh, newfacet);
   }
   if (qh->JOGGLEmax < REALmax/2)
     minimize_(qh->min_vertex, -wwval_(Wnewvertexmax));
 } /* makenewplanes */
 
 /*---------------------------------
 
   qh_makenew_nonsimplicial(qh, visible, apex, numnew )
     make new facets for ridges of a visible facet
 
   returns:
     first newfacet, bumps numnew as needed
     attaches new facets if !qh.ONLYgood
     marks ridge neighbors for simplicial visible
     if (qh.ONLYgood)
       ridges on newfacet, horizon, and visible
     else
       ridge and neighbors between newfacet and   horizon
       visible facet's ridges are deleted
 
   notes:
     qh.visit_id if visible has already been processed
     sets neighbor->seen for building f.samecycle
       assumes all 'seen' flags initially false
 
   design:
     for each ridge of visible facet
       get neighbor of visible facet
       if neighbor was already processed
         delete the ridge (will delete all visible facets later)
       if neighbor is a horizon facet
         create a new facet
         if neighbor coplanar
           adds newfacet to f.samecycle for later merging
         else
           updates neighbor's neighbor set
           (checks for non-simplicial facet with multiple ridges to visible facet)
         updates neighbor's ridge set
         (checks for simplicial neighbor to non-simplicial visible facet)
         (deletes ridge if neighbor is simplicial)
 
 */
 #ifndef qh_NOmerge
 facetT *qh_makenew_nonsimplicial(qhT *qh, facetT *visible, vertexT *apex, int *numnew) {
   void **freelistp; /* used !qh_NOmem */
   ridgeT *ridge, **ridgep;
   facetT *neighbor, *newfacet= NULL, *samecycle;
   setT *vertices;
   boolT toporient;
   int ridgeid;
 
   FOREACHridge_(visible->ridges) {
     ridgeid= ridge->id;
     neighbor= otherfacet_(ridge, visible);
     if (neighbor->visible) {
       if (!qh->ONLYgood) {
         if (neighbor->visitid == qh->visit_id) {
           qh_setfree(qh, &(ridge->vertices));  /* delete on 2nd visit */
           qh_memfree_(qh, ridge, (int)sizeof(ridgeT), freelistp);
         }
       }
     }else {  /* neighbor is an horizon facet */
       toporient= (ridge->top == visible);
       vertices= qh_setnew(qh, qh->hull_dim); /* makes sure this is quick */
       qh_setappend(qh, &vertices, apex);
       qh_setappend_set(qh, &vertices, ridge->vertices);
       newfacet= qh_makenewfacet(qh, vertices, toporient, neighbor);
       (*numnew)++;
       if (neighbor->coplanar) {
         newfacet->mergehorizon= True;
         if (!neighbor->seen) {
           newfacet->f.samecycle= newfacet;
           neighbor->f.newcycle= newfacet;
         }else {
           samecycle= neighbor->f.newcycle;
           newfacet->f.samecycle= samecycle->f.samecycle;
           samecycle->f.samecycle= newfacet;
         }
       }
       if (qh->ONLYgood) {
         if (!neighbor->simplicial)
           qh_setappend(qh, &(newfacet->ridges), ridge);
       }else {  /* qh_attachnewfacets */
         if (neighbor->seen) {
           if (neighbor->simplicial) {
             qh_fprintf(qh, qh->ferr, 6105, "qhull internal error (qh_makenew_nonsimplicial): simplicial f%d sharing two ridges with f%d\n",
                    neighbor->id, visible->id);
             qh_errexit2(qh, qh_ERRqhull, neighbor, visible);
           }
           qh_setappend(qh, &(neighbor->neighbors), newfacet);
         }else
           qh_setreplace(qh, neighbor->neighbors, visible, newfacet);
         if (neighbor->simplicial) {
           qh_setdel(neighbor->ridges, ridge);
           qh_setfree(qh, &(ridge->vertices));
           qh_memfree(qh, ridge, (int)sizeof(ridgeT));
         }else {
           qh_setappend(qh, &(newfacet->ridges), ridge);
           if (toporient)
             ridge->top= newfacet;
           else
             ridge->bottom= newfacet;
         }
       trace4((qh, qh->ferr, 4048, "qh_makenew_nonsimplicial: created facet f%d from v%d and r%d of horizon f%d\n",
             newfacet->id, apex->id, ridgeid, neighbor->id));
       }
     }
     neighbor->seen= True;
   } /* for each ridge */
   if (!qh->ONLYgood)
     SETfirst_(visible->ridges)= NULL;
   return newfacet;
 } /* makenew_nonsimplicial */
 #else /* qh_NOmerge */
 facetT *qh_makenew_nonsimplicial(qhT *qh, facetT *visible, vertexT *apex, int *numnew) {
   return NULL;
 }
 #endif /* qh_NOmerge */
 
 /*---------------------------------
 
   qh_makenew_simplicial(qh, visible, apex, numnew )
     make new facets for simplicial visible facet and apex
 
   returns:
     attaches new facets if (!qh.ONLYgood)
       neighbors between newfacet and horizon
 
   notes:
     nop if neighbor->seen or neighbor->visible(see qh_makenew_nonsimplicial)
 
   design:
     locate neighboring horizon facet for visible facet
     determine vertices and orientation
     create new facet
     if coplanar,
       add new facet to f.samecycle
     update horizon facet's neighbor list
 */
 facetT *qh_makenew_simplicial(qhT *qh, facetT *visible, vertexT *apex, int *numnew) {
   facetT *neighbor, **neighborp, *newfacet= NULL;
   setT *vertices;
   boolT flip, toporient;
   int horizonskip, visibleskip;
 
   FOREACHneighbor_(visible) {
     if (!neighbor->seen && !neighbor->visible) {
       vertices= qh_facetintersect(qh, neighbor,visible, &horizonskip, &visibleskip, 1);
       SETfirst_(vertices)= apex;
       flip= ((horizonskip & 0x1) ^ (visibleskip & 0x1));
       if (neighbor->toporient)
         toporient= horizonskip & 0x1;
       else
         toporient= (horizonskip & 0x1) ^ 0x1;
       newfacet= qh_makenewfacet(qh, vertices, toporient, neighbor);
       (*numnew)++;
       if (neighbor->coplanar && (qh->PREmerge || qh->MERGEexact)) {
 #ifndef qh_NOmerge
         newfacet->f.samecycle= newfacet;
         newfacet->mergehorizon= True;
 #endif
       }
       if (!qh->ONLYgood)
         SETelem_(neighbor->neighbors, horizonskip)= newfacet;
       trace4((qh, qh->ferr, 4049, "qh_makenew_simplicial: create facet f%d top %d from v%d and horizon f%d skip %d top %d and visible f%d skip %d, flip? %d\n",
             newfacet->id, toporient, apex->id, neighbor->id, horizonskip,
               neighbor->toporient, visible->id, visibleskip, flip));
     }
   }
   return newfacet;
 } /* makenew_simplicial */
 
 /*---------------------------------
 
   qh_matchneighbor(qh, newfacet, newskip, hashsize, hashcount )
     either match subridge of newfacet with neighbor or add to hash_table
 
   returns:
     duplicate ridges are unmatched and marked by qh_DUPLICATEridge
 
   notes:
     ridge is newfacet->vertices w/o newskip vertex
     do not allocate memory (need to free hash_table cleanly)
     uses linear hash chains
 
   see also:
     qh_matchduplicates
 
   design:
     for each possible matching facet in qh.hash_table
       if vertices match
         set ismatch, if facets have opposite orientation
         if ismatch and matching facet doesn't have a match
           match the facets by updating their neighbor sets
         else
           indicate a duplicate ridge
           set facet hyperplane for later testing
           add facet to hashtable
           unless the other facet was already a duplicate ridge
             mark both facets with a duplicate ridge
             add other facet (if defined) to hash table
 */
 void qh_matchneighbor(qhT *qh, facetT *newfacet, int newskip, int hashsize, int *hashcount) {
   boolT newfound= False;   /* True, if new facet is already in hash chain */
   boolT same, ismatch;
   int hash, scan;
   facetT *facet, *matchfacet;
   int skip, matchskip;
 
   hash= qh_gethash(qh, hashsize, newfacet->vertices, qh->hull_dim, 1,
                      SETelem_(newfacet->vertices, newskip));
   trace4((qh, qh->ferr, 4050, "qh_matchneighbor: newfacet f%d skip %d hash %d hashcount %d\n",
           newfacet->id, newskip, hash, *hashcount));
   zinc_(Zhashlookup);
   for (scan= hash; (facet= SETelemt_(qh->hash_table, scan, facetT));
        scan= (++scan >= hashsize ? 0 : scan)) {
     if (facet == newfacet) {
       newfound= True;
       continue;
     }
     zinc_(Zhashtests);
     if (qh_matchvertices(qh, 1, newfacet->vertices, newskip, facet->vertices, &skip, &same)) {
       if (SETelem_(newfacet->vertices, newskip) ==
           SETelem_(facet->vertices, skip)) {
         qh_precision(qh, "two facets with the same vertices");
         qh_fprintf(qh, qh->ferr, 6106, "qhull precision error: Vertex sets are the same for f%d and f%d.  Can not force output.\n",
           facet->id, newfacet->id);
         qh_errexit2(qh, qh_ERRprec, facet, newfacet);
       }
       ismatch= (same == (boolT)((newfacet->toporient ^ facet->toporient)));
       matchfacet= SETelemt_(facet->neighbors, skip, facetT);
       if (ismatch && !matchfacet) {
         SETelem_(facet->neighbors, skip)= newfacet;
         SETelem_(newfacet->neighbors, newskip)= facet;
         (*hashcount)--;
         trace4((qh, qh->ferr, 4051, "qh_matchneighbor: f%d skip %d matched with new f%d skip %d\n",
            facet->id, skip, newfacet->id, newskip));
         return;
       }
       if (!qh->PREmerge && !qh->MERGEexact) {
         qh_precision(qh, "a ridge with more than two neighbors");
         qh_fprintf(qh, qh->ferr, 6107, "qhull precision error: facets f%d, f%d and f%d meet at a ridge with more than 2 neighbors.  Can not continue.\n",
                  facet->id, newfacet->id, getid_(matchfacet));
         qh_errexit2(qh, qh_ERRprec, facet, newfacet);
       }
       SETelem_(newfacet->neighbors, newskip)= qh_DUPLICATEridge;
       newfacet->dupridge= True;
       if (!newfacet->normal)
         qh_setfacetplane(qh, newfacet);
       qh_addhash(qh, newfacet, qh->hash_table, hashsize, hash);
       (*hashcount)++;
       if (!facet->normal)
         qh_setfacetplane(qh, facet);
       if (matchfacet != qh_DUPLICATEridge) {
         SETelem_(facet->neighbors, skip)= qh_DUPLICATEridge;
         facet->dupridge= True;
         if (!facet->normal)
           qh_setfacetplane(qh, facet);
         if (matchfacet) {
           matchskip= qh_setindex(matchfacet->neighbors, facet);
           SETelem_(matchfacet->neighbors, matchskip)= qh_DUPLICATEridge;
           matchfacet->dupridge= True;
           if (!matchfacet->normal)
             qh_setfacetplane(qh, matchfacet);
           qh_addhash(qh, matchfacet, qh->hash_table, hashsize, hash);
           *hashcount += 2;
         }
       }
       trace4((qh, qh->ferr, 4052, "qh_matchneighbor: new f%d skip %d duplicates ridge for f%d skip %d matching f%d ismatch %d at hash %d\n",
            newfacet->id, newskip, facet->id, skip,
            (matchfacet == qh_DUPLICATEridge ? -2 : getid_(matchfacet)),
            ismatch, hash));
       return; /* end of duplicate ridge */
     }
   }
   if (!newfound)
     SETelem_(qh->hash_table, scan)= newfacet;  /* same as qh_addhash */
   (*hashcount)++;
   trace4((qh, qh->ferr, 4053, "qh_matchneighbor: no match for f%d skip %d at hash %d\n",
            newfacet->id, newskip, hash));
 } /* matchneighbor */
 
 
 /*---------------------------------
 
   qh_matchnewfacets()
     match newfacets in qh.newfacet_list to their newfacet neighbors
 
   returns:
     qh.newfacet_list with full neighbor sets
       get vertices with nth neighbor by deleting nth vertex
     if qh.PREmerge/MERGEexact or qh.FORCEoutput
       sets facet->flippped if flipped normal (also prevents point partitioning)
     if duplicate ridges and qh.PREmerge/MERGEexact
       sets facet->dupridge
       missing neighbor links identifies extra ridges to be merging (qh_MERGEridge)
 
   notes:
     newfacets already have neighbor[0] (horizon facet)
     assumes qh.hash_table is NULL
     vertex->neighbors has not been updated yet
     do not allocate memory after qh.hash_table (need to free it cleanly)
 
   design:
     delete neighbor sets for all new facets
     initialize a hash table
     for all new facets
       match facet with neighbors
     if unmatched facets (due to duplicate ridges)
       for each new facet with a duplicate ridge
         match it with a facet
     check for flipped facets
 */
 void qh_matchnewfacets(qhT *qh /* qh.newfacet_list */) {
   int numnew=0, hashcount=0, newskip;
   facetT *newfacet, *neighbor;
   int dim= qh->hull_dim, hashsize, neighbor_i, neighbor_n;
   setT *neighbors;
 #ifndef qh_NOtrace
   int facet_i, facet_n, numfree= 0;
   facetT *facet;
 #endif
 
   trace1((qh, qh->ferr, 1019, "qh_matchnewfacets: match neighbors for new facets.\n"));
   FORALLnew_facets {
     numnew++;
     {  /* inline qh_setzero(qh, newfacet->neighbors, 1, qh->hull_dim); */
       neighbors= newfacet->neighbors;
       neighbors->e[neighbors->maxsize].i= dim+1; /*may be overwritten*/
       memset((char *)SETelemaddr_(neighbors, 1, void), 0, dim * SETelemsize);
     }
   }
 
   qh_newhashtable(qh, numnew*(qh->hull_dim-1)); /* twice what is normally needed,
                                      but every ridge could be DUPLICATEridge */
   hashsize= qh_setsize(qh, qh->hash_table);
   FORALLnew_facets {
     for (newskip=1; newskiphull_dim; newskip++) /* furthest/horizon already matched */
       qh_matchneighbor(qh, newfacet, newskip, hashsize, &hashcount);
 #if 0   /* use the following to trap hashcount errors */
     {
       int count= 0, k;
       facetT *facet, *neighbor;
 
       count= 0;
       FORALLfacet_(qh->newfacet_list) {  /* newfacet already in use */
         for (k=1; k < qh->hull_dim; k++) {
           neighbor= SETelemt_(facet->neighbors, k, facetT);
           if (!neighbor || neighbor == qh_DUPLICATEridge)
             count++;
         }
         if (facet == newfacet)
           break;
       }
       if (count != hashcount) {
         qh_fprintf(qh, qh->ferr, 8088, "qh_matchnewfacets: after adding facet %d, hashcount %d != count %d\n",
                  newfacet->id, hashcount, count);
         qh_errexit(qh, qh_ERRqhull, newfacet, NULL);
       }
     }
 #endif  /* end of trap code */
   }
   if (hashcount) {
     FORALLnew_facets {
       if (newfacet->dupridge) {
         FOREACHneighbor_i_(qh, newfacet) {
           if (neighbor == qh_DUPLICATEridge) {
             qh_matchduplicates(qh, newfacet, neighbor_i, hashsize, &hashcount);
                     /* this may report MERGEfacet */
           }
         }
       }
     }
   }
   if (hashcount) {
     qh_fprintf(qh, qh->ferr, 6108, "qhull internal error (qh_matchnewfacets): %d neighbors did not match up\n",
         hashcount);
     qh_printhashtable(qh, qh->ferr);
     qh_errexit(qh, qh_ERRqhull, NULL, NULL);
   }
 #ifndef qh_NOtrace
   if (qh->IStracing >= 2) {
     FOREACHfacet_i_(qh, qh->hash_table) {
       if (!facet)
         numfree++;
     }
     qh_fprintf(qh, qh->ferr, 8089, "qh_matchnewfacets: %d new facets, %d unused hash entries .  hashsize %d\n",
              numnew, numfree, qh_setsize(qh, qh->hash_table));
   }
 #endif /* !qh_NOtrace */
   qh_setfree(qh, &qh->hash_table);
   if (qh->PREmerge || qh->MERGEexact) {
     if (qh->IStracing >= 4)
       qh_printfacetlist(qh, qh->newfacet_list, NULL, qh_ALL);
     FORALLnew_facets {
       if (newfacet->normal)
         qh_checkflipped(qh, newfacet, NULL, qh_ALL);
     }
   }else if (qh->FORCEoutput)
     qh_checkflipped_all(qh, qh->newfacet_list);  /* prints warnings for flipped */
 } /* matchnewfacets */
 
 
 /*---------------------------------
 
   qh_matchvertices(qh, firstindex, verticesA, skipA, verticesB, skipB, same )
     tests whether vertices match with a single skip
     starts match at firstindex since all new facets have a common vertex
 
   returns:
     true if matched vertices
     skip index for each set
     sets same iff vertices have the same orientation
 
   notes:
     assumes skipA is in A and both sets are the same size
 
   design:
     set up pointers
     scan both sets checking for a match
     test orientation
 */
 boolT qh_matchvertices(qhT *qh, int firstindex, setT *verticesA, int skipA,
        setT *verticesB, int *skipB, boolT *same) {
   vertexT **elemAp, **elemBp, **skipBp=NULL, **skipAp;
 
   elemAp= SETelemaddr_(verticesA, firstindex, vertexT);
   elemBp= SETelemaddr_(verticesB, firstindex, vertexT);
   skipAp= SETelemaddr_(verticesA, skipA, vertexT);
   do if (elemAp != skipAp) {
     while (*elemAp != *elemBp++) {
       if (skipBp)
         return False;
       skipBp= elemBp;  /* one extra like FOREACH */
     }
   }while (*(++elemAp));
   if (!skipBp)
     skipBp= ++elemBp;
   *skipB= SETindex_(verticesB, skipB); /* i.e., skipBp - verticesB */
   *same= !((skipA & 0x1) ^ (*skipB & 0x1)); /* result is 0 or 1 */
   trace4((qh, qh->ferr, 4054, "qh_matchvertices: matched by skip %d(v%d) and skip %d(v%d) same? %d\n",
           skipA, (*skipAp)->id, *skipB, (*(skipBp-1))->id, *same));
   return(True);
 } /* matchvertices */
 
 /*---------------------------------
 
   qh_newfacet(qh)
     return a new facet
 
   returns:
     all fields initialized or cleared   (NULL)
     preallocates neighbors set
 */
 facetT *qh_newfacet(qhT *qh) {
   facetT *facet;
   void **freelistp; /* used !qh_NOmem */
 
   qh_memalloc_(qh, (int)sizeof(facetT), freelistp, facet, facetT);
   memset((char *)facet, (size_t)0, sizeof(facetT));
   if (qh->facet_id == qh->tracefacet_id)
     qh->tracefacet= facet;
   facet->id= qh->facet_id++;
   facet->neighbors= qh_setnew(qh, qh->hull_dim);
 #if !qh_COMPUTEfurthest
   facet->furthestdist= 0.0;
 #endif
 #if qh_MAXoutside
   if (qh->FORCEoutput && qh->APPROXhull)
     facet->maxoutside= qh->MINoutside;
   else
     facet->maxoutside= qh->DISTround;
 #endif
   facet->simplicial= True;
   facet->good= True;
   facet->newfacet= True;
   trace4((qh, qh->ferr, 4055, "qh_newfacet: created facet f%d\n", facet->id));
   return(facet);
 } /* newfacet */
 
 
 /*---------------------------------
 
   qh_newridge()
     return a new ridge
 */
 ridgeT *qh_newridge(qhT *qh) {
   ridgeT *ridge;
   void **freelistp;   /* used !qh_NOmem */
 
   qh_memalloc_(qh, (int)sizeof(ridgeT), freelistp, ridge, ridgeT);
   memset((char *)ridge, (size_t)0, sizeof(ridgeT));
   zinc_(Ztotridges);
   if (qh->ridge_id == 0xFFFFFF) {
     qh_fprintf(qh, qh->ferr, 7074, "\
 qhull warning: more than %d ridges.  ID field overflows and two ridges\n\
 may have the same identifier.  Otherwise output ok.\n", 0xFFFFFF);
   }
   ridge->id= qh->ridge_id++;
   trace4((qh, qh->ferr, 4056, "qh_newridge: created ridge r%d\n", ridge->id));
   return(ridge);
 } /* newridge */
 
 
 /*---------------------------------
 
   qh_pointid(qh, )
     return id for a point,
     returns -3 if null, -2 if interior, or -1 if not known
 
   alternative code:
     unsigned long id;
     id= ((unsigned long)point - (unsigned long)qh.first_point)/qh.normal_size;
 
   notes:
     WARN64 -- id truncated to 32-bits, at most 2G points
     NOerrors returned (QhullPoint::id)
     if point not in point array
       the code does a comparison of unrelated pointers.
 */
 int qh_pointid(qhT *qh, pointT *point) {
   ptr_intT offset, id;
 
-  if (!point)
+  if (!point || !qh)
     return -3;
   else if (point == qh->interior_point)
     return -2;
   else if (point >= qh->first_point
   && point < qh->first_point + qh->num_points * qh->hull_dim) {
     offset= (ptr_intT)(point - qh->first_point);
     id= offset / qh->hull_dim;
   }else if ((id= qh_setindex(qh->other_points, point)) != -1)
     id += qh->num_points;
   else
     return -1;
   return (int)id;
 } /* pointid */
 
 /*---------------------------------
 
   qh_removefacet(qh, facet )
     unlinks facet from qh.facet_list,
 
   returns:
     updates qh.facet_list .newfacet_list .facet_next visible_list
     decrements qh.num_facets
 
   see:
     qh_appendfacet
 */
 void qh_removefacet(qhT *qh, facetT *facet) {
   facetT *next= facet->next, *previous= facet->previous;
 
   if (facet == qh->newfacet_list)
     qh->newfacet_list= next;
   if (facet == qh->facet_next)
     qh->facet_next= next;
   if (facet == qh->visible_list)
     qh->visible_list= next;
   if (previous) {
     previous->next= next;
     next->previous= previous;
   }else {  /* 1st facet in qh->facet_list */
     qh->facet_list= next;
     qh->facet_list->previous= NULL;
   }
   qh->num_facets--;
   trace4((qh, qh->ferr, 4057, "qh_removefacet: remove f%d from facet_list\n", facet->id));
 } /* removefacet */
 
 
 /*---------------------------------
 
   qh_removevertex(qh, vertex )
     unlinks vertex from qh.vertex_list,
 
   returns:
     updates qh.vertex_list .newvertex_list
     decrements qh.num_vertices
 */
 void qh_removevertex(qhT *qh, vertexT *vertex) {
   vertexT *next= vertex->next, *previous= vertex->previous;
 
   if (vertex == qh->newvertex_list)
     qh->newvertex_list= next;
   if (previous) {
     previous->next= next;
     next->previous= previous;
   }else {  /* 1st vertex in qh->vertex_list */
     qh->vertex_list= vertex->next;
     qh->vertex_list->previous= NULL;
   }
   qh->num_vertices--;
   trace4((qh, qh->ferr, 4058, "qh_removevertex: remove v%d from vertex_list\n", vertex->id));
 } /* removevertex */
 
 
 /*---------------------------------
 
   qh_updatevertices()
     update vertex neighbors and delete interior vertices
 
   returns:
     if qh.VERTEXneighbors, updates neighbors for each vertex
       if qh.newvertex_list,
          removes visible neighbors  from vertex neighbors
       if qh.newfacet_list
          adds new facets to vertex neighbors
     if qh.visible_list
        interior vertices added to qh.del_vertices for later partitioning
 
   design:
     if qh.VERTEXneighbors
       deletes references to visible facets from vertex neighbors
       appends new facets to the neighbor list for each vertex
       checks all vertices of visible facets
         removes visible facets from neighbor lists
         marks unused vertices for deletion
 */
 void qh_updatevertices(qhT *qh /*qh.newvertex_list, newfacet_list, visible_list*/) {
   facetT *newfacet= NULL, *neighbor, **neighborp, *visible;
   vertexT *vertex, **vertexp;
 
   trace3((qh, qh->ferr, 3013, "qh_updatevertices: delete interior vertices and update vertex->neighbors\n"));
   if (qh->VERTEXneighbors) {
     FORALLvertex_(qh->newvertex_list) {
       FOREACHneighbor_(vertex) {
         if (neighbor->visible)
           SETref_(neighbor)= NULL;
       }
       qh_setcompact(qh, vertex->neighbors);
     }
     FORALLnew_facets {
       FOREACHvertex_(newfacet->vertices)
         qh_setappend(qh, &vertex->neighbors, newfacet);
     }
     FORALLvisible_facets {
       FOREACHvertex_(visible->vertices) {
         if (!vertex->newlist && !vertex->deleted) {
           FOREACHneighbor_(vertex) { /* this can happen under merging */
             if (!neighbor->visible)
               break;
           }
           if (neighbor)
             qh_setdel(vertex->neighbors, visible);
           else {
             vertex->deleted= True;
             qh_setappend(qh, &qh->del_vertices, vertex);
             trace2((qh, qh->ferr, 2041, "qh_updatevertices: delete vertex p%d(v%d) in f%d\n",
                   qh_pointid(qh, vertex->point), vertex->id, visible->id));
           }
         }
       }
     }
   }else {  /* !VERTEXneighbors */
     FORALLvisible_facets {
       FOREACHvertex_(visible->vertices) {
         if (!vertex->newlist && !vertex->deleted) {
           vertex->deleted= True;
           qh_setappend(qh, &qh->del_vertices, vertex);
           trace2((qh, qh->ferr, 2042, "qh_updatevertices: delete vertex p%d(v%d) in f%d\n",
                   qh_pointid(qh, vertex->point), vertex->id, visible->id));
         }
       }
     }
   }
 } /* updatevertices */
 
 
 
diff --git a/src/libqhullr/poly_r.h b/src/libqhullr/poly_r.h
index 7ece5da..dc27d33 100644
--- a/src/libqhullr/poly_r.h
+++ b/src/libqhullr/poly_r.h
@@ -1,295 +1,295 @@
 /*
  ---------------------------------
 
-   poly.h
-   header file for poly.c and poly2.c
+   poly_r.h
+   header file for poly_r.c and poly2_r.c
 
-   see qh-poly.htm, libqhull.h and poly.c
+   see qh-poly.htm, libqhull_r.h and poly_r.c
 
    Copyright (c) 1993-2014 The Geometry Center.
-   $Id: //main/2011/qhull/src/libqhullr/poly_r.h#2 $$Change: 1645 $
-   $DateTime: 2014/01/15 12:51:30 $$Author: bbarber $
+   $Id: //main/2011/qhull/src/libqhullr/poly_r.h#6 $$Change: 1797 $
+   $DateTime: 2014/12/15 17:23:41 $$Author: bbarber $
 */
 
 #ifndef qhDEFpoly
 #define qhDEFpoly 1
 
 #include "libqhull_r.h"
 
 /*===============   constants ========================== */
 
 /*----------------------------------
 
   ALGORITHMfault
     use as argument to checkconvex() to report errors during buildhull
 */
 #define qh_ALGORITHMfault 0
 
 /*----------------------------------
 
   DATAfault
     use as argument to checkconvex() to report errors during initialhull
 */
 #define qh_DATAfault 1
 
 /*----------------------------------
 
   DUPLICATEridge
     special value for facet->neighbor to indicate a duplicate ridge
 
   notes:
     set by matchneighbor, used by matchmatch and mark_dupridge
 */
 #define qh_DUPLICATEridge (facetT *)1L
 
 /*----------------------------------
 
   MERGEridge       flag in facet
     special value for facet->neighbor to indicate a merged ridge
 
   notes:
     set by matchneighbor, used by matchmatch and mark_dupridge
 */
 #define qh_MERGEridge (facetT *)2L
 
 
 /*============ -structures- ====================*/
 
 /*=========== -macros- =========================*/
 
 /*----------------------------------
 
   FORALLfacet_( facetlist ) { ... }
     assign 'facet' to each facet in facetlist
 
   notes:
     uses 'facetT *facet;'
     assumes last facet is a sentinel
 
   see:
     FORALLfacets
 */
 #define FORALLfacet_( facetlist ) if (facetlist ) for ( facet=( facetlist ); facet && facet->next; facet= facet->next )
 
 /*----------------------------------
 
   FORALLnew_facets { ... }
     assign 'newfacet' to each facet in qh.newfacet_list
 
   notes:
     uses 'facetT *newfacet;'
     at exit, newfacet==NULL
 */
 #define FORALLnew_facets for ( newfacet=qh->newfacet_list;newfacet && newfacet->next;newfacet=newfacet->next )
 
 /*----------------------------------
 
   FORALLvertex_( vertexlist ) { ... }
     assign 'vertex' to each vertex in vertexlist
 
   notes:
     uses 'vertexT *vertex;'
     at exit, vertex==NULL
 */
 #define FORALLvertex_( vertexlist ) for (vertex=( vertexlist );vertex && vertex->next;vertex= vertex->next )
 
 /*----------------------------------
 
   FORALLvisible_facets { ... }
     assign 'visible' to each visible facet in qh.visible_list
 
   notes:
     uses 'vacetT *visible;'
     at exit, visible==NULL
 */
 #define FORALLvisible_facets for (visible=qh->visible_list; visible && visible->visible; visible= visible->next)
 
 /*----------------------------------
 
   FORALLsame_( newfacet ) { ... }
     assign 'same' to each facet in newfacet->f.samecycle
 
   notes:
     uses 'facetT *same;'
     stops when it returns to newfacet
 */
 #define FORALLsame_(newfacet) for (same= newfacet->f.samecycle; same != newfacet; same= same->f.samecycle)
 
 /*----------------------------------
 
   FORALLsame_cycle_( newfacet ) { ... }
     assign 'same' to each facet in newfacet->f.samecycle
 
   notes:
     uses 'facetT *same;'
     at exit, same == NULL
 */
 #define FORALLsame_cycle_(newfacet) \
      for (same= newfacet->f.samecycle; \
          same; same= (same == newfacet ?  NULL : same->f.samecycle))
 
 /*----------------------------------
 
   FOREACHneighborA_( facet ) { ... }
     assign 'neighborA' to each neighbor in facet->neighbors
 
   FOREACHneighborA_( vertex ) { ... }
     assign 'neighborA' to each neighbor in vertex->neighbors
 
   declare:
     facetT *neighborA, **neighborAp;
 
   see:
-    FOREACHsetelement_
+    FOREACHsetelement_
 */
 #define FOREACHneighborA_(facet)  FOREACHsetelement_(facetT, facet->neighbors, neighborA)
 
 /*----------------------------------
 
   FOREACHvisible_( facets ) { ... }
     assign 'visible' to each facet in facets
 
   notes:
     uses 'facetT *facet, *facetp;'
-    see FOREACHsetelement_
+    see FOREACHsetelement_
 */
 #define FOREACHvisible_(facets) FOREACHsetelement_(facetT, facets, visible)
 
 /*----------------------------------
 
   FOREACHnewfacet_( facets ) { ... }
     assign 'newfacet' to each facet in facets
 
   notes:
     uses 'facetT *newfacet, *newfacetp;'
-    see FOREACHsetelement_
+    see FOREACHsetelement_
 */
 #define FOREACHnewfacet_(facets) FOREACHsetelement_(facetT, facets, newfacet)
 
 /*----------------------------------
 
   FOREACHvertexA_( vertices ) { ... }
     assign 'vertexA' to each vertex in vertices
 
   notes:
     uses 'vertexT *vertexA, *vertexAp;'
-    see FOREACHsetelement_
+    see FOREACHsetelement_
 */
 #define FOREACHvertexA_(vertices) FOREACHsetelement_(vertexT, vertices, vertexA)
 
 /*----------------------------------
 
   FOREACHvertexreverse12_( vertices ) { ... }
     assign 'vertex' to each vertex in vertices
     reverse order of first two vertices
 
   notes:
     uses 'vertexT *vertex, *vertexp;'
-    see FOREACHsetelement_
+    see FOREACHsetelement_
 */
 #define FOREACHvertexreverse12_(vertices) FOREACHsetelementreverse12_(vertexT, vertices, vertex)
 
 
-/*=============== prototypes poly.c in alphabetical order ================*/
+/*=============== prototypes poly_r.c in alphabetical order ================*/
 
 void    qh_appendfacet(qhT *qh, facetT *facet);
 void    qh_appendvertex(qhT *qh, vertexT *vertex);
 void    qh_attachnewfacets(qhT *qh /* qh.visible_list, newfacet_list */);
 boolT   qh_checkflipped(qhT *qh, facetT *facet, realT *dist, boolT allerror);
 void    qh_delfacet(qhT *qh, facetT *facet);
 void    qh_deletevisible(qhT *qh /* qh.visible_list, qh.horizon_list */);
 setT   *qh_facetintersect(qhT *qh, facetT *facetA, facetT *facetB, int *skipAp,int *skipBp, int extra);
 int     qh_gethash(qhT *qh, int hashsize, setT *set, int size, int firstindex, void *skipelem);
 facetT *qh_makenewfacet(qhT *qh, setT *vertices, boolT toporient, facetT *facet);
 void    qh_makenewplanes(qhT *qh /* qh.newfacet_list */);
 facetT *qh_makenew_nonsimplicial(qhT *qh, facetT *visible, vertexT *apex, int *numnew);
 facetT *qh_makenew_simplicial(qhT *qh, facetT *visible, vertexT *apex, int *numnew);
 void    qh_matchneighbor(qhT *qh, facetT *newfacet, int newskip, int hashsize,
                           int *hashcount);
 void    qh_matchnewfacets(qhT *qh);
 boolT   qh_matchvertices(qhT *qh, int firstindex, setT *verticesA, int skipA,
                           setT *verticesB, int *skipB, boolT *same);
 facetT *qh_newfacet(qhT *qh);
 ridgeT *qh_newridge(qhT *qh);
 int     qh_pointid(qhT *qh, pointT *point);
 void    qh_removefacet(qhT *qh, facetT *facet);
 void    qh_removevertex(qhT *qh, vertexT *vertex);
 void    qh_updatevertices(qhT *qh);
 
 
-/*========== -prototypes poly2.c in alphabetical order ===========*/
+/*========== -prototypes poly2_r.c in alphabetical order ===========*/
 
 void    qh_addhash(qhT *qh, void *newelem, setT *hashtable, int hashsize, int hash);
 void    qh_check_bestdist(qhT *qh);
 void    qh_check_maxout(qhT *qh);
 void    qh_check_output(qhT *qh);
 void    qh_check_point(qhT *qh, pointT *point, facetT *facet, realT *maxoutside, realT *maxdist, facetT **errfacet1, facetT **errfacet2);
 void    qh_check_points(qhT *qh);
 void    qh_checkconvex(qhT *qh, facetT *facetlist, int fault);
 void    qh_checkfacet(qhT *qh, facetT *facet, boolT newmerge, boolT *waserrorp);
 void    qh_checkflipped_all(qhT *qh, facetT *facetlist);
 void    qh_checkpolygon(qhT *qh, facetT *facetlist);
 void    qh_checkvertex(qhT *qh, vertexT *vertex);
 void    qh_clearcenters(qhT *qh, qh_CENTER type);
 void    qh_createsimplex(qhT *qh, setT *vertices);
 void    qh_delridge(qhT *qh, ridgeT *ridge);
 void    qh_delvertex(qhT *qh, vertexT *vertex);
 setT   *qh_facet3vertex(qhT *qh, facetT *facet);
 facetT *qh_findbestfacet(qhT *qh, pointT *point, boolT bestoutside,
            realT *bestdist, boolT *isoutside);
 facetT *qh_findbestlower(qhT *qh, facetT *upperfacet, pointT *point, realT *bestdistp, int *numpart);
 facetT *qh_findfacet_all(qhT *qh, pointT *point, realT *bestdist, boolT *isoutside,
                           int *numpart);
 int     qh_findgood(qhT *qh, facetT *facetlist, int goodhorizon);
 void    qh_findgood_all(qhT *qh, facetT *facetlist);
 void    qh_furthestnext(qhT *qh /* qh.facet_list */);
 void    qh_furthestout(qhT *qh, facetT *facet);
 void    qh_infiniteloop(qhT *qh, facetT *facet);
 void    qh_initbuild(qhT *qh);
 void    qh_initialhull(qhT *qh, setT *vertices);
 setT   *qh_initialvertices(qhT *qh, int dim, setT *maxpoints, pointT *points, int numpoints);
 vertexT *qh_isvertex(qhT *qh, pointT *point, setT *vertices);
 vertexT *qh_makenewfacets(qhT *qh, pointT *point /*horizon_list, visible_list*/);
 void    qh_matchduplicates(qhT *qh, facetT *atfacet, int atskip, int hashsize, int *hashcount);
 void    qh_nearcoplanar(qhT *qh /* qh.facet_list */);
 vertexT *qh_nearvertex(qhT *qh, facetT *facet, pointT *point, realT *bestdistp);
 int     qh_newhashtable(qhT *qh, int newsize);
 vertexT *qh_newvertex(qhT *qh, pointT *point);
 ridgeT *qh_nextridge3d(qhT *qh, ridgeT *atridge, facetT *facet, vertexT **vertexp);
 void    qh_outcoplanar(qhT *qh /* qh.facet_list */);
 pointT *qh_point(qhT *qh, int id);
 void    qh_point_add(qhT *qh, setT *set, pointT *point, void *elem);
 setT   *qh_pointfacet(qhT *qh /*qh.facet_list*/);
 setT   *qh_pointvertex(qhT *qh /*qh.facet_list*/);
 void    qh_prependfacet(qhT *qh, facetT *facet, facetT **facetlist);
 void    qh_printhashtable(qhT *qh, FILE *fp);
 void    qh_printlists(qhT *qh);
 void    qh_resetlists(qhT *qh, boolT stats, boolT resetVisible /*qh.newvertex_list newfacet_list visible_list*/);
 void    qh_setvoronoi_all(qhT *qh);
 void    qh_triangulate(qhT *qh /*qh.facet_list*/);
 void    qh_triangulate_facet(qhT *qh, facetT *facetA, vertexT **first_vertex);
 void    qh_triangulate_link(qhT *qh, facetT *oldfacetA, facetT *facetA, facetT *oldfacetB, facetT *facetB);
 void    qh_triangulate_mirror(qhT *qh, facetT *facetA, facetT *facetB);
 void    qh_triangulate_null(qhT *qh, facetT *facetA);
 void    qh_vertexintersect(qhT *qh, setT **vertexsetA,setT *vertexsetB);
 setT   *qh_vertexintersect_new(qhT *qh, setT *vertexsetA,setT *vertexsetB);
 void    qh_vertexneighbors(qhT *qh /*qh.facet_list*/);
 boolT   qh_vertexsubset(qhT *qh, setT *vertexsetA, setT *vertexsetB);
 
 
 #endif /* qhDEFpoly */
diff --git a/src/libqhullr/qh-geom.htm b/src/libqhullr/qh-geom.htm
new file mode 100644
index 0000000..8aeab33
--- /dev/null
+++ b/src/libqhullr/qh-geom.htm
@@ -0,0 +1,293 @@
+
+
+
+
+geom.c, geom2.c -- geometric and floating point routines
+
+
+
+
+
Up: Home page for Qhull

+Up: Qhull manual: Table of Contents 

+Up: Programs
+• Options
+• Output
+• Formats
+• Geomview
+• Print
+• Qhull
+• Precision
+• Trace

+Up: Qhull code: Table of Contents

+To: Qhull functions, macros, and data structures

+To: Geom • Global
+• Io • Mem
+• Merge • Poly
+• Qhull • Set
+• Stat • User
+

+
+

+
+
+
geom.c, geom2.c, random.c -- geometric and floating point routines

+

+
Geometrically, a vertex is a point with d coordinates
+and a facet is a halfspace. A halfspace is defined by an
+oriented hyperplane through the facet's vertices. A hyperplane
+is defined by d normalized coefficients and an offset. A
+point is above a facet if its distance to the facet is
+positive.

+
+
Qhull uses floating point coordinates for input points,
+vertices, halfspace equations, centrums, and an interior point.

+
+
Qhull may be configured for single precision or double
+precision floating point arithmetic (see realT
+). 

+
+
Each floating point operation may incur round-off error (see
+Merge). The maximum error for distance
+computations is determined at initialization. The roundoff error
+in halfspace computation is accounted for by computing the
+distance from vertices to the halfspace. 

+

+
Copyright © 1995-2012 C.B. Barber

+

+
» Geom
+• Global •
+Io • Mem •
+Merge • Poly •
+Qhull • Set •
+Stat • User 

+
+
Index to geom.c,
+geom2.c, geom.h,
+random.c, random.h
+

+
+
+
+
»geometric data types
+and constants

+
+
    
+
  • coordT coordinates and
+coefficients are stored as realT
    • 
+
  • pointT a point is an array
+of DIM3 coordinates 
    • 
+

+
+
»mathematical macros

+
+
    
+
  • fabs_ returns the absolute
+value of a 
    • 
+
  • fmax_ returns the maximum
+value of a and b 
    • 
+
  • fmin_ returns the minimum
+value of a and b 
    • 
+
  • maximize_ maximize a value
+
    • 
+
  • minimize_ minimize a value
+
    • 
+
  • det2_ compute a 2-d
+determinate 
    • 
+
  • det3_ compute a 3-d
+determinate 
    • 
+
  • dX, dY, dZ compute the difference
+between two coordinates 
    • 
+

+
+
»mathematical functions

+
+
+
+
»computational geometry functions

+
+
+
+
»point array functions

+
+
+
»geometric facet functions

+
+
+
»geometric roundoff functions

+
    
+
  • qh_detjoggle determine
+default joggle for points and distance roundoff error
    • 
+
  • qh_detroundoff
+determine maximum roundoff error and other precision constants
    • 
+
  • qh_distround compute
+maximum roundoff error due to a distance computation to a
+normalized hyperplane
    • 
+
  • qh_divzero divide by a
+number that is nearly zero 
    • 
+
  • qh_maxouter return maximum outer
+plane
    • 
+
  • qh_outerinner return actual
+outer and inner planes
+

+
+
 

+

+
Up:
+Home page for
+Qhull 

+Up: Qhull manual: Table of Contents 

+Up: Programs
+• Options
+• Output
+• Formats
+• Geomview
+• Print
+• Qhull
+• Precision
+• Trace

+Up: Qhull code: Table of Contents 

+To: Qhull functions, macros, and data structures

+To: Geom •
+Global • Io
+• Mem • Merge
+• Poly • Qhull
+• Set • Stat
+• User

+
+
+
 

+

+
The
+Geometry Center Home Page 

+
Comments to: qhull@qhull.org
+

+Created: May 2, 1997 ---  Last modified: see top  

+
+
diff --git a/src/libqhullr/qh-globa.htm b/src/libqhullr/qh-globa.htm
new file mode 100644
index 0000000..d89f59c
--- /dev/null
+++ b/src/libqhullr/qh-globa.htm
@@ -0,0 +1,161 @@
+
+
+
+
+global.c -- global variables and their functions
+
+
+
+
+
Up: Home page for Qhull

+Up: Qhull manual: Table of Contents 

+Up: Programs
+• Options
+• Output
+• Formats
+• Geomview
+• Print
+• Qhull
+• Precision
+• Trace

+Up: Qhull code: Table of Contents

+To: Qhull functions, macros, and data structures

+To: Geom • Global
+• Io • Mem
+• Merge • Poly
+• Qhull • Set
+• Stat • User
+

+
+

+
+
+
global.c -- global variables and their functions

+

+
Qhull uses a global data structure, qh, to store
+globally defined constants, lists, sets, and variables. This
+allows multiple instances of Qhull to execute at the same time.
+The structure may be statically allocated or
+dynamically allocated with malloc().  See
+QHpointer.
+

+

+
Copyright © 1995-2012 C.B. Barber

+

+
» Geom
+• Global •
+Io • Mem •
+Merge • Poly •
+Qhull • Set •
+Stat • User 

+
+
Index to global.c and
+libqhull.h

+
+
+
+
»Qhull's global
+variables

+
+
+
+
»Global variable and
+initialization routines

+
+
+
+
 

+

+
Up:
+Home page for
+Qhull 

+Up: Qhull manual: Table of Contents 

+Up: Programs
+• Options
+• Output
+• Formats
+• Geomview
+• Print
+• Qhull
+• Precision
+• Trace

+Up: Qhull code: Table of Contents 

+To: Qhull functions, macros, and data structures

+To: Geom •
+Global • Io
+• Mem • Merge
+• Poly • Qhull
+• Set • Stat
+• User

+
 

+

+
The
+Geometry Center Home Page 

+
Comments to: qhull@qhull.org
+

+Created: May 2, 1997 ---  Last modified: see top  

+
+
diff --git a/src/libqhullr/qh-io.htm b/src/libqhullr/qh-io.htm
new file mode 100644
index 0000000..0ea8f48
--- /dev/null
+++ b/src/libqhullr/qh-io.htm
@@ -0,0 +1,303 @@
+
+
+
+
+io.c -- input and output operations
+
+
+
+
+
Up: Home page for Qhull

+Up: Qhull manual: Table of Contents 

+Up: Programs
+• Options
+• Output
+• Formats
+• Geomview
+• Print
+• Qhull
+• Precision
+• Trace

+Up: Qhull code: Table of Contents

+To: Qhull functions, macros, and data structures

+To: Geom • Global
+• Io • Mem
+• Merge • Poly
+• Qhull • Set
+• Stat • User
+

+

+
+
io.c -- input and output operations

+

+
+
Qhull provides a wide range of input
+and output options. To organize the code, most output formats use
+the same driver: 

+
+
+    qh_printbegin( fp, format, facetlist, facets, printall );
+
+    FORALLfacet_( facetlist )
+      qh_printafacet( fp, format, facet, printall );
+
+    FOREACHfacet_( facets )
+      qh_printafacet( fp, format, facet, printall );
+
+    qh_printend( fp, format );
+

+
+
Note the 'printall' flag. It selects whether or not
+qh_skipfacet() is tested. 

+
+

+
Copyright © 1995-2012 C.B. Barber

+

+
» Geom •
+Global • Io •
+Mem • Merge •
+Poly • Qhull •
+Set • Stat •
+User 

+
+
Index to io.c and io.h

+
+
+
+
»io.h constants and types

+
+
    
+
  • qh_MAXfirst maximum length
+of first two lines of stdin 
    • 
+
  • qh_WHITESPACE possible
+values of white space 
    • 
+
  • printvridgeT function to
+print results of qh_printvdiagram or qh_eachvoronoi
    • 
+

+
+
»User level functions

+
+
+
+
»Print functions for all
+output formats

+
+
+
+
»Text output functions

+
+
+
»Text utility functions

+
+
+
»Geomview output functions

+
+
»Geomview utility functions

+
+

+
 

+

+
Up:
+Home page for
+Qhull 

+Up: Qhull manual: Table of Contents 

+Up: Programs
+• Options
+• Output
+• Formats
+• Geomview
+• Print
+• Qhull
+• Precision
+• Trace

+Up: Qhull code: Table of Contents 

+To: Qhull functions, macros, and data structures

+To: Geom •
+Global • Io
+• Mem • Merge
+• Poly • Qhull
+• Set • Stat
+• User

+

+
 

+

+
The
+Geometry Center Home Page 

+
Comments to: qhull@qhull.org
+

+Created: May 2, 1997 ---  Last modified: see top  

+
+
diff --git a/src/libqhullr/qh-mem.htm b/src/libqhullr/qh-mem.htm
new file mode 100644
index 0000000..4bba0af
--- /dev/null
+++ b/src/libqhullr/qh-mem.htm
@@ -0,0 +1,141 @@
+
+
+
+
+mem.c -- memory operations
+
+
+
+
+
Up: Home page for Qhull

+Up: Qhull manual: Table of Contents 

+Up: Programs
+• Options
+• Output
+• Formats
+• Geomview
+• Print
+• Qhull
+• Precision
+• Trace

+Up: Qhull code: Table of Contents

+To: Qhull functions, macros, and data structures

+To: Geom • Global
+• Io • Mem
+• Merge • Poly
+• Qhull • Set
+• Stat • User
+

+

+
+
mem.c -- memory operations

+

+
Qhull uses quick-fit memory allocation. It maintains a
+set of free lists for a variety of small allocations. A
+small request returns a block from the best fitting free
+list. If the free list is empty, Qhull allocates a block
+from a reserved buffer. 

+
Use 'T5' to trace memory allocations.

+
+

+
Copyright © 1995-2012 C.B. Barber

+

+
» Geom
+• Global •
+Io • Mem
+• Merge • Poly
+• Qhull • Set
+• Stat • User
+

+
Index to mem.c and
+mem.h

+
+
»mem.h data types and constants

+
    
+
  • ptr_intT for casting
+a void* to an integer-type 
    • 
+
  • qhmemT global memory
+structure for mem.c 
    • 
+
  • qh_NOmem disable memory allocation
    • 
+

+
»mem.h macros

+
+
»User level
+functions

+
+
+
»Initialization and
+termination functions

+
+
+
 

+

+
Up:
+Home page for
+Qhull 

+Up: Qhull manual: Table of Contents 

+Up: Programs
+• Options
+• Output
+• Formats
+• Geomview
+• Print
+• Qhull
+• Precision
+• Trace

+Up: Qhull code: Table of Contents 

+To: Qhull functions, macros, and data structures

+To: Geom •
+Global • Io
+• Mem • Merge
+• Poly • Qhull
+• Set • Stat
+• User

+

+
 

+

+
The
+Geometry Center Home Page 

+
Comments to: qhull@qhull.org
+

+Created: May 2, 1997 ---  Last modified: see top  

+
+
diff --git a/src/libqhullr/qh-merge.htm b/src/libqhullr/qh-merge.htm
new file mode 100644
index 0000000..2bc92b4
--- /dev/null
+++ b/src/libqhullr/qh-merge.htm
@@ -0,0 +1,364 @@
+
+
+
+
+merge.c -- facet merge operations
+
+
+
+
+
Up: Home page for Qhull

+Up: Qhull manual: Table of Contents 

+Up: Programs
+• Options
+• Output
+• Formats
+• Geomview
+• Print
+• Qhull
+• Precision
+• Trace

+Up: Qhull code: Table of Contents

+To: Qhull functions, macros, and data structures

+To: Geom • Global
+• Io • Mem
+• Merge • Poly
+• Qhull • Set
+• Stat • User
+

+

+
+
merge.c -- facet merge operations

+

+
Qhull handles precision problems by merged facets or joggled input.
+Except for redundant vertices, it corrects a problem by
+merging two facets. When done, all facets are clearly
+convex. See Imprecision in Qhull
+for further information. 

+
Users may joggle the input ('QJn')
+instead of merging facets. 

+
Qhull detects and corrects the following problems: 

+
    
+
  • More than two facets meeting at a ridge. When
+Qhull creates facets, it creates an even number
+of facets for each ridge. A convex hull always
+has two facets for each ridge. More than two
+facets may be created if non-adjacent facets
+share a vertex. This is called a duplicate
+ridge. In 2-d, a duplicate ridge would
+create a loop of facets. 
    • 
+

+
    
+
  • A facet contained in another facet. Facet
+merging may leave all vertices of one facet as a
+subset of the vertices of another facet. This is
+called a redundant facet. 
    • 
+

+
    
+
  • A facet with fewer than three neighbors. Facet
+merging may leave a facet with one or two
+neighbors. This is called a degenerate facet.
+
    • 
+

+
    
+
  • A facet with flipped orientation. A
+facet's hyperplane may define a halfspace that
+does not include the interior point.This is
+called a flipped facet. 
    • 
+

+
    
+
  • A coplanar horizon facet. A
+newly processed point may be coplanar with an
+horizon facet. Qhull creates a new facet without
+a hyperplane. It links new facets for the same
+horizon facet together. This is called a samecycle.
+The new facet or samecycle is merged into the
+horizon facet. 
    • 
+

+
    
+
  • Concave facets. A facet's centrum may be
+above a neighboring facet. If so, the facets meet
+at a concave angle. 
    • 
+

+
    
+
  • Coplanar facets. A facet's centrum may be
+coplanar with a neighboring facet (i.e., it is
+neither clearly below nor clearly above the
+facet's hyperplane). Qhull removes coplanar
+facets in independent sets sorted by angle.
    • 
+

+
    
+
  • Redundant vertex. A vertex may have fewer
+than three neighboring facets. If so, it is
+redundant and may be renamed to an adjacent
+vertex without changing the topological
+structure.This is called a redundant vertex.
+
    • 
+

+

+
Copyright © 1995-2012 C.B. Barber

+

+
» Geom
+• Global
+• Io • Mem
+• Merge • Poly
+• Qhull • Set
+• Stat • User
+

+
Index to merge.c and
+merge.h

+
+
+
»merge.h data
+types, macros, and global sets

+
    
+
  • mergeT structure to
+identify a merge of two facets
    • 
+
  • FOREACHmerge_
+assign 'merge' to each merge in merges 
    • 
+
  • qh global sets
+qh.facet_mergeset contains non-convex merges
+while qh.degen_mergeset contains degenerate and
+redundant facets
    • 
+

+
»merge.h
+constants

+
+
»top-level merge
+functions

+
+
+
»functions for
+identifying merges

+
+
+
»functions for
+determining the best merge

+
+
+
»functions for
+merging facets

+
+
+
»functions for
+merging a cycle of facets

+
If a point is coplanar with an horizon facet, the
+corresponding new facets are linked together (a samecycle)
+for merging.

+
+
»functions
+for renaming a vertex

+
+
+
»functions
+for identifying vertices for renaming

+
+
+
»functions for check and
+trace

+
+
+
 

+

+
Up:
+Home page for
+Qhull 

+Up: Qhull manual: Table of Contents 

+Up: Programs
+• Options
+• Output
+• Formats
+• Geomview
+• Print
+• Qhull
+• Precision
+• Trace

+Up: Qhull code: Table of Contents 

+To: Qhull functions, macros, and data structures

+To: Geom •
+Global • Io
+• Mem • Merge
+• Poly • Qhull
+• Set • Stat
+• User

+

+
 

+

+
The
+Geometry Center Home Page 

+
Comments to: qhull@qhull.org
+

+Created: May 2, 1997 ---  Last modified: see top  

+
+
diff --git a/src/libqhullr/qh-poly.htm b/src/libqhullr/qh-poly.htm
new file mode 100644
index 0000000..1bb5937
--- /dev/null
+++ b/src/libqhullr/qh-poly.htm
@@ -0,0 +1,481 @@
+
+
+
+
+poly.c, poly2.c -- polyhedron operations
+
+
+
+
+
Up: Home page for Qhull

+Up: Qhull manual: Table of Contents 

+Up: Programs
+• Options
+• Output
+• Formats
+• Geomview
+• Print
+• Qhull
+• Precision
+• Trace

+Up: Qhull code: Table of Contents

+To: Qhull functions, macros, and data structures

+To: Geom • Global
+• Io • Mem
+• Merge • Poly
+• Qhull • Set
+• Stat • User
+

+

+
+
poly.c, poly2.c -- polyhedron operations

+

+
+
Qhull uses dimension-free terminology. Qhull builds a
+polyhedron in dimension d. A polyhedron is a
+simplicial complex of faces with geometric information for the
+top and bottom-level faces. A (d-1)-face is a facet,
+a (d-2)-face is a ridge, and a 0-face
+is a vertex. For example in 3-d, a facet is a polygon
+and a ridge is an edge. A facet is built from a ridge (the base)
+and a vertex (the apex). See
+Qhull's data structures.

+
+
Qhull's primary data structure is a polyhedron. A
+polyhedron is a list of facets. Each facet has a set of
+neighboring facets and a set of vertices. Each facet has a
+hyperplane. For example, a tetrahedron has four facets.
+If its vertices are a, b, c, d, and its facets
+are 1, 2, 3, 4, the tetrahedron is 

+

+
    
+
  • facet 1 
      
+    
    • vertices: b c d 
      • 
+    
    • neighbors: 2 3 4 
      • 
+
    
+
    • 
+
  • facet 2 
      
+    
    • vertices: a c d 
      • 
+    
    • neighbors: 1 3 4 
      • 
+
    
+
    • 
+
  • facet 3 
      
+    
    • vertices: a b d 
      • 
+    
    • neighbors: 1 2 4 
      • 
+
    
+
    • 
+
  • facet 4 
      
+    
    • vertices: a b c 
      • 
+    
    • neighbors: 1 2 3 
      • 
+
    
+
    • 
+

+

+
A facet may be simplicial or non-simplicial. In 3-d, a
+simplicial facet has three vertices and three
+neighbors. A nonsimplicial facet has more than
+three vertices and more than three neighbors. A
+nonsimplicial facet has a set of ridges and a centrum. 

+

+A simplicial facet has an orientation. An orientation
+is either top or bottom.
+The flag, facet->toporient,
+defines the orientation of the facet's vertices.  For example in 3-d,
+'top' is left-handed orientation (i.e., the vertex order follows the direction
+of the left-hand fingers when the thumb is pointing away from the center).
+Except for axis-parallel facets in 5-d and higher, topological orientation
+determines the geometric orientation of the facet's hyperplane.
+
+
A nonsimplicial facet is due to merging two or more
+facets. The facet's ridge set determine a simplicial
+decomposition of the facet. Each ridge is a 1-face (i.e.,
+it has two vertices and two neighboring facets). The
+orientation of a ridge is determined by the order of the
+neighboring facets. The flag, facet->toporient,is
+ignored. 

+
A nonsimplicial facet has a centrum for testing
+convexity. A centrum is a point on the facet's
+hyperplane that is near the center of the facet. Except
+for large facets, it is the arithmetic average of the
+facet's vertices. 

+
A nonsimplicial facet is an approximation that is
+defined by offsets from the facet's hyperplane. When
+Qhull finishes, the outer plane is above all
+points while the inner plane is below the facet's
+vertices. This guarantees that any exact convex hull
+passes between the inner and outer planes. The outer
+plane is defined by facet->maxoutside while
+the inner plane is computed from the facet's vertices.

+
+
Qhull 3.1 includes triangulation of non-simplicial facets
+('Qt').
+These facets,
+called tricoplanar, share the same normal. centrum, and Voronoi center.
+One facet (keepcentrum) owns these data structures.
+While tricoplanar facets are more accurate than the simplicial facets from
+joggled input, they
+may have zero area or flipped orientation.
+
+

+
Copyright © 1995-2012 C.B. Barber

+

+
» Geom
+• Global
+• Io • Mem
+• Merge • Poly
+• Qhull • Set
+• Stat • User
+

+
Index to poly.c,
+poly2.c, poly.h,
+and libqhull.h

+
+
»Data
+types and global lists for polyhedrons

+
+
»poly.h constants

+
    
+
  • ALGORITHMfault
+flag to not report errors in qh_checkconvex() 
    • 
+
  • DATAfault flag to
+report errors in qh_checkconvex() 
    • 
+
  • DUPLICATEridge
+special value for facet->neighbor to indicate
+a duplicate ridge 
    • 
+
  • MERGEridge
+special value for facet->neighbor to indicate
+a merged ridge 
    • 
+

+
»Global FORALL
+macros

+
+
»FORALL macros

+
+
»FOREACH macros

+
+
»Indexed
+FOREACH macros

+
    
+
  • FOREACHfacet_i_
+assign 'facet' and 'facet_i' to each facet in
+facet set 
    • 
+
  • FOREACHneighbor_i_
+assign 'neighbor' and 'neighbor_i' to each facet
+in facet->neighbors or vertex->neighbors
    • 
+
  • FOREACHpoint_i_
+assign 'point' and 'point_i' to each point in
+points set 
    • 
+
  • FOREACHridge_i_
+assign 'ridge' and 'ridge_i' to each ridge in
+ridges set 
    • 
+
  • FOREACHvertex_i_
+assign 'vertex' and 'vertex_i' to each vertex in
+vertices set 
    • 
+
  • FOREACHvertexreverse12_
+assign 'vertex' to each vertex in vertex set;
+reverse the order of first two vertices 
    • 
+

+
»Other macros for polyhedrons

+
    
+
  • getid_ return ID for
+a facet, ridge, or vertex 
    • 
+
  • otherfacet_
+return neighboring facet for a ridge in a facet 
    • 
+

+
»Facetlist
+functions

+
+
»Facet
+functions

+
+
»Vertex,
+ridge, and point functions

+
+
»Hashtable functions

+
+
»Allocation and
+deallocation functions

+
+
»Check
+functions

+
+
+
+
 

+

+
Up:
+Home page for
+Qhull 

+Up: Qhull manual: Table of Contents 

+Up: Programs
+• Options
+• Output
+• Formats
+• Geomview
+• Print
+• Qhull
+• Precision
+• Trace

+Up: Qhull code: Table of Contents 

+To: Qhull functions, macros, and data structures

+To: Geom •
+Global • Io
+• Mem • Merge
+• Poly • Qhull
+• Set • Stat
+• User

+

+
 

+

+
The
+Geometry Center Home Page 

+
Comments to: qhull@qhull.org
+

+Created: May 2, 1997 ---  Last modified: see top  

+
+
diff --git a/src/libqhullr/qh-qhull.htm b/src/libqhullr/qh-qhull.htm
new file mode 100644
index 0000000..df877f3
--- /dev/null
+++ b/src/libqhullr/qh-qhull.htm
@@ -0,0 +1,277 @@
+
+
+
+
+libqhull.c -- top-level functions and basic data types
+
+
+
+
+
Up: Home page for Qhull

+Up: Qhull manual: Table of Contents 

+Up: Programs
+• Options
+• Output
+• Formats
+• Geomview
+• Print
+• Qhull
+• Precision
+• Trace

+Up: Qhull code: Table of Contents

+To: Qhull functions, macros, and data structures

+To: Geom • Global
+• Io • Mem
+• Merge • Poly
+• Qhull • Set
+• Stat • User
+

+

+
+
libqhull.c -- top-level functions and basic data types

+

+
Qhull implements the Quickhull algorithm for computing
+the convex hull. The Quickhull algorithm combines two
+well-known algorithms: the 2-d quickhull algorithm and
+the n-d beneath-beyond algorithm. See
+Description of Qhull. 

+
This section provides an index to the top-level
+functions and base data types.  The top-level header file, libqhull.h,
+contains prototypes for these functions.

+

+
Copyright © 1995-2012 C.B. Barber

+

+
» Geom
+• Global
+• Io • Mem
+• Merge • Poly
+• Qhull • Set
+• Stat • User
+

+
Index to libqhull.c,
+libqhull.h, and
+unix.c

+
+
+
»libqhull.h and unix.c
+data types and constants

+
    
+
  • flagT Boolean flag as
+a bit 
    • 
+
  • boolT boolean value,
+either True or False 
    • 
+
  • CENTERtype to
+distinguish facet->center 
    • 
+
  • qh_PRINT output
+formats for printing (qh.PRINTout) 
    • 
+
  • qh_ALL argument flag
+for selecting everything 
    • 
+
  • qh_ERR Qhull exit
+codes for indicating errors 
    • 
+
  • qh_FILEstderr Fake stderr
+to distinguish error output from normal output [C++ only]
    • 
+
  • qh_prompt version and long prompt for Qhull
    • 
+
  • qh_prompt2 synopsis for Qhull
    • 
+
  • qh_prompt3 concise prompt for Qhull
    • 
+
  • qh_version version stamp
    • 
+

+
+
»libqhull.h other
+macros

+
    
+
  • traceN print trace
+message if qh.IStracing >= N. 
    • 
+
  • QHULL_UNUSED declare an
+ unused variable to avoid warnings. 
    • 
+

+
+
»Quickhull
+routines in call order

+
+
+
»Top-level routines for initializing and terminating Qhull (in other modules)

+
+
+
»Top-level routines for reading and modifying the input (in other modules)

+
+
+
»Top-level routines for calling Qhull (in other modules)

+
+
+
»Top-level routines for returning results (in other modules)

+
+
+
»Top-level routines for testing and debugging (in other modules)

+
+
+
 

+

+
Up:
+Home page for
+Qhull 

+Up: Qhull manual: Table of Contents 

+Up: Programs
+• Options
+• Output
+• Formats
+• Geomview
+• Print
+• Qhull
+• Precision
+• Trace

+Up: Qhull code: Table of Contents 

+To: Qhull functions, macros, and data structures

+To: Geom •
+Global • Io
+• Mem • Merge
+• Poly • Qhull
+• Set • Stat
+• User

+

+
 

+

+
The
+Geometry Center Home Page 

+
Comments to: qhull@qhull.org
+

+Created: May 2, 1997 ---  Last modified: see top  

+
+
diff --git a/src/libqhullr/qh-set.htm b/src/libqhullr/qh-set.htm
new file mode 100644
index 0000000..1fbd366
--- /dev/null
+++ b/src/libqhullr/qh-set.htm
@@ -0,0 +1,306 @@
+
+
+
+
+qset.c -- set data type and operations
+
+
+
+
+
Up: Home page for Qhull

+Up: Qhull manual: Table of Contents 

+Up: Programs
+• Options
+• Output
+• Formats
+• Geomview
+• Print
+• Qhull
+• Precision
+• Trace

+Up: Qhull code: Table of Contents

+To: Qhull functions, macros, and data structures

+To: Geom • Global
+• Io • Mem
+• Merge • Poly
+• Qhull • Set
+• Stat • User
+

+

+
+
qset.c -- set data type and operations

+

+
Qhull's data structures are constructed from sets. The
+functions and macros in qset.c construct, iterate, and
+modify these sets. They are the most frequently called
+functions in Qhull. For this reason, efficiency is the
+primary concern. 

+
In Qhull, a set is represented by an unordered
+array of pointers with a maximum size and a NULL
+terminator (setT).
+Most sets correspond to mathematical sets
+(i.e., the pointers are unique). Some sets are sorted to
+enforce uniqueness. Some sets are ordered. For example,
+the order of vertices in a ridge determine the ridge's
+orientation. If you reverse the order of adjacent
+vertices, the orientation reverses. Some sets are not
+mathematical sets. They may be indexed as an array and
+they may include NULL pointers. 

+
The most common operation on a set is to iterate its
+members. This is done with a 'FOREACH...' macro. Each set
+has a custom macro. For example, 'FOREACHvertex_'
+iterates over a set of vertices. Each vertex is assigned
+to the variable 'vertex' from the pointer 'vertexp'. 

+
Most sets are constructed by appending elements to the
+set. The last element of a set is either NULL or the
+index of the terminating NULL for a partially full set.
+If a set is full, appending an element copies the set to
+a larger array. 

+
+

+
Copyright © 1995-2012 C.B. Barber

+

+
» Geom
+• Global •
+Io • Mem •
+Merge • Poly
+• Qhull • Set
+• Stat • User
+

+
Index to qset.c and
+qset.h

+
+
»Data types and
+constants

+
    
+
  • SETelemsize size
+of a set element in bytes 
    • 
+
  • setT a set with a
+maximum size and a current size
    • 
+
  • qh global sets
+global sets for temporary sets, etc. 
    • 
+

+
»FOREACH macros

+
+
»Access and
+size macros

+
+
»Internal macros

+
    
+
  • SETsizeaddr_
+return pointer to end element of a set (indicates
+current size) 
    • 
+

+
+
»address macros

+
    
+
  • SETaddr_ return
+address of a set's elements 
    • 
+
  • SETelemaddr_
+return address of the n'th element of a set 
    • 
+
  • SETref_ l.h.s. for
+modifying the current element in a FOREACH
+iteration 
    • 
+

+
+
»Allocation and
+deallocation functions

+
+
+
»Access and
+predicate functions 

+
+
+
»Add functions

+
+
+
»Check and print functions

+
+
+
»Copy, compact, and zero functions

+
+
+
»Delete functions

+
+
+
»Temporary set functions

+
+
+
 

+

+
Up:
+Home page for
+Qhull 

+Up: Qhull manual: Table of Contents 

+Up: Programs
+• Options
+• Output
+• Formats
+• Geomview
+• Print
+• Qhull
+• Precision
+• Trace

+Up: Qhull code: Table of Contents 

+To: Qhull functions, macros, and data structures

+To: Geom •
+Global • Io
+• Mem • Merge
+• Poly • Qhull
+• Set • Stat
+• User

+

+
 

+

+
The
+Geometry Center Home Page 

+
Comments to: qhull@qhull.org
+

+Created: May 2, 1997 ---  Last modified: see top  

+
+
diff --git a/src/libqhullr/qh-stat.htm b/src/libqhullr/qh-stat.htm
new file mode 100644
index 0000000..53c6158
--- /dev/null
+++ b/src/libqhullr/qh-stat.htm
@@ -0,0 +1,161 @@
+
+
+
+
+stat.c -- statistical operations
+
+
+
+
+
Up: Home page for Qhull

+Up: Qhull manual: Table of Contents 

+Up: Programs
+• Options
+• Output
+• Formats
+• Geomview
+• Print
+• Qhull
+• Precision
+• Trace

+Up: Qhull code: Table of Contents

+To: Qhull functions, macros, and data structures

+To: Geom • Global
+• Io • Mem
+• Merge • Poly
+• Qhull • Set
+• Stat • User
+

+

+
+
stat.c -- statistical operations

+

+
Qhull records many statistics. These functions and
+macros make it inexpensive to add a statistic.
+
As with Qhull's global variables, the statistics data structure is
+accessed by a macro, 'qhstat'.  If qh_QHpointer is defined, the macro
+is 'qh_qhstat->', otherwise the macro is 'qh_qhstat.'.
+Statistics
+may be turned off in user.h. If so, all but the 'zz'
+statistics are ignored.

+

+
Copyright © 1995-2012 C.B. Barber

+

+
» Geom
+• Global
+• Io • Mem
+• Merge • Poly
+• Qhull • Set
+• Stat • User
+

+
Index to stat.c and
+stat.h

+
+
+
»stat.h types

+
    
+
  • intrealT union of
+integer and real
    • 
+
  • qhstat global data
+structure for statistics 
    • 
+

+
»stat.h
+constants

+
    
+
  • qh_KEEPstatistics 0 turns off most statistics
    • 
+
  • Z..., W... integer (Z) and real (W) statistics
+
    • 
+
  • ZZstat Z.../W... statistics that
+remain defined if qh_KEEPstatistics=0
+
    • 
+
  • ztype zdoc, zinc, etc.
+for definining statistics 
    • 
+

+
»stat.h macros

+
    
+
  • MAYdebugx called
+frequently for error trapping 
    • 
+
  • zadd_/wadd_ add value
+to an integer or real statistic 
    • 
+
  • zdef_ define a
+statistic 
    • 
+
  • zinc_ increment an
+integer statistic 
    • 
+
  • zmax_/wmax_ update
+integer or real maximum statistic 
    • 
+
  • zmin_/wmin_ update
+integer or real minimum statistic 
    • 
+
  • zval_/wval_ set or
+return value of a statistic 
    • 
+

+
+
»stat.c
+functions

+
+
+
 

+

+
Up:
+Home page for
+Qhull 

+Up: Qhull manual: Table of Contents 

+Up: Programs
+• Options
+• Output
+• Formats
+• Geomview
+• Print
+• Qhull
+• Precision
+• Trace

+Up: Qhull code: Table of Contents 

+To: Qhull functions, macros, and data structures

+To: Geom •
+Global • Io
+• Mem • Merge
+• Poly • Qhull
+• Set • Stat
+• User

+

+
 

+

+
The
+Geometry Center Home Page 

+
Comments to: qhull@qhull.org
+

+Created: May 2, 1997 ---  Last modified: see top  

+
+
diff --git a/src/libqhull/qh-user.htm b/src/libqhullr/qh-user.htm
similarity index 98%
copy from src/libqhull/qh-user.htm
copy to src/libqhullr/qh-user.htm
index a8afed4..b917920 100644
--- a/src/libqhull/qh-user.htm
+++ b/src/libqhullr/qh-user.htm
@@ -1,263 +1,265 @@
 
 
 
 
 user.c -- user-definable operations
 
 
 
 
 
Up: Home page for Qhull

 Up: Qhull manual: Table of Contents 

 Up: Programs
 • Options
 • Output
 • Formats
 • Geomview
 • Print
 • Qhull
 • Precision
 • Trace

 Up: Qhull code: Table of Contents

 To: Qhull functions, macros, and data structures

 To: Geom • Global
 • Io • Mem
 • Merge • Poly
 • Qhull • Set
 • Stat • User
 

 

 
user.c -- user-definable operations

 

 
This section contains functions and constants that the
 user may want to change. 

 
 

 
Copyright © 1995-2012 C.B. Barber

 

 
» Geom
 • Global
 • Io • Mem
 • Merge • Poly
 • Qhull • Set
 • Stat • User
 

 
Index to user.c, usermem.c, userprintf.c, userprintf_rbox.c and
 user.h

 
 
 
»Qhull library constants

 
 
 
 
»user.h data
 types and configuration macros

 
 
 
»definition constants

 
    
 
  • qh_DEFAULTbox
 define default box size for rbox, 'Qbb', and 'QbB' (Geomview expects 0.5) 
    • 
 
  • qh_INFINITE on
 output, indicates Voronoi center at infinity 
    • 
 
  • qh_ORIENTclock
 define convention for orienting facets
    • 
 
  • qh_ZEROdelaunay
 define facets that are ignored in Delaunay triangulations
    • 
 

 
 
»joggle constants

 
 
 
»performance
 related constants

 
 
 
»memory constants

 
 
 
»conditional compilation

 
 
 
»merge
 constants

 
 
 
»user.c
 functions

 
 
 
»usermem.c
 functions

 
    
 
  • qh_exit exit program, same as exit().
    • 
 
  • qh_free free memory, same as free().
    • 
 
  • qh_malloc allocate memory, same as malloc()
    • 
 

 
 
»userprintf.c
  and userprintf_rbox,c functions

 
    
 
  • qh_fprintf print
 information from Qhull, sames as fprintf(). 
    • 
 
  • qh_fprintf_rbox print
 information from Rbox, sames as fprintf(). 
    • 
 

 
 
 

 

 
Up:
 Home page for
 Qhull 

 Up: Qhull manual: Table of Contents 

 Up: Programs
 • Options
 • Output
 • Formats
 • Geomview
 • Print
 • Qhull
 • Precision
 • Trace

 Up: Qhull code: Table of Contents 

 To: Qhull functions, macros, and data structures

 To: Geom •
 Global • Io
 • Mem • Merge
 • Poly • Qhull
 • Set • Stat
 • User

 

 
 

 

 
The
 Geometry Center Home Page 

 
Comments to: qhull@qhull.org
 

 Created: May 2, 1997 ---  Last modified: see top  

 
 
diff --git a/src/libqhullr/qhull_r.h b/src/libqhullr/qhull_r.h
deleted file mode 100644
index 902b623..0000000
--- a/src/libqhullr/qhull_r.h
+++ /dev/null
@@ -1,151 +0,0 @@
-/*
  ---------------------------------
-
-   qhull_r.h
-   all header files for compiling qhull with reentrant code
-
-   see qh-qhull.htm
-
-   see libqhull_r.h for user-level definitions
-
-   see user_r.h for user-definable constants
-
-   defines internal functions for libqhull.c global.c
-
-   Copyright (c) 1993-2014 The Geometry Center.
-   $Id: //main/2011/qhull/src/libqhullr/qhull_r.h#2 $$Change: 1663 $
-   $DateTime: 2014/01/19 17:59:16 $$Author: bbarber $
-
-   Notes:  grep for ((" and (" to catch fprintf("lkasdjf");
-           full parens around (x?y:z)
-           use '#include qhull/qhull_r.h' to avoid name clashes
-*/
-
-#ifndef qhDEFqhulla
-#define qhDEFqhulla 1
-
-#include "libqhull_r.h"  /* Defines data types */
-
-#include "stat_r.h"
-#include "random_r.h"
-#include "mem_r.h"
-#include "qset_r.h"
-#include "geom_r.h"
-#include "merge_r.h"
-#include "poly_r.h"
-#include "io_r.h"
-
-#include 
-#include 
-#include 
-#include     /* some compilers will not need float.h */
-#include 
-#include 
-#include 
-#include 
-#include 
-/*** uncomment here and qset.c
-     if string.h does not define memcpy()
-#include 
-*/
-
-#if qh_CLOCKtype == 2  /* defined in user.h from libqhull.h */
-#include 
-#include 
-#include 
-#endif
-
-#ifdef _MSC_VER  /* Microsoft Visual C++ -- warning level 4 */
-#pragma warning( disable : 4100)  /* unreferenced formal parameter */
-#pragma warning( disable : 4127)  /* conditional expression is constant */
-#pragma warning( disable : 4706)  /* assignment within conditional function */
-#pragma warning( disable : 4996)  /* function was declared deprecated(strcpy, localtime, etc.) */
-#endif
-
-/* ======= -macros- =========== */
-
-/*----------------------------------
-
-  traceN((qh, qh->ferr, 0Nnnn, "format\n", vars));
-    calls qh_fprintf if qh.IStracing >= N
-
-    Add debugging traps to the end of qh_fprintf
-
-  notes:
-    removing tracing reduces code size but doesn't change execution speed
-*/
-#ifndef qh_NOtrace
-#define trace0(args) {if (qh->IStracing) qh_fprintf args;}
-#define trace1(args) {if (qh->IStracing >= 1) qh_fprintf args;}
-#define trace2(args) {if (qh->IStracing >= 2) qh_fprintf args;}
-#define trace3(args) {if (qh->IStracing >= 3) qh_fprintf args;}
-#define trace4(args) {if (qh->IStracing >= 4) qh_fprintf args;}
-#define trace5(args) {if (qh->IStracing >= 5) qh_fprintf args;}
-#else /* qh_NOtrace */
-#define trace0(args) {}
-#define trace1(args) {}
-#define trace2(args) {}
-#define trace3(args) {}
-#define trace4(args) {}
-#define trace5(args) {}
-#endif /* qh_NOtrace */
-
-/*----------------------------------
-
-*/
-
-/* See Qt's qglobal.h */
-#if !defined(SAG_COM) && (defined(WIN64) || defined(_WIN64) || defined(__WIN64__) || defined(WIN32) || defined(_WIN32) || defined(__WIN32__) || defined(__NT__))
-#   define QHULL_OS_WIN
-#elif defined(__MWERKS__) && defined(__INTEL__)
-#   define QHULL_OS_WIN
-#endif
-#if defined(__INTEL_COMPILER) && !defined(QHULL_OS_WIN)
-template 
-inline void qhullUnused(T &x) { (void)x; }
-#  define QHULL_UNUSED(x) qhullUnused(x);
-#else
-#  define QHULL_UNUSED(x) (void)x;
-#endif
-
-/***** -libqhull.c prototypes (alphabetical after qhull) ********************/
-
-void    qh_qhull(qhT *qh);
-boolT   qh_addpoint(qhT *qh, pointT *furthest, facetT *facet, boolT checkdist);
-void    qh_buildhull(qhT *qh);
-void    qh_buildtracing(qhT *qh, pointT *furthest, facetT *facet);
-void    qh_build_withrestart(qhT *qh);
-void    qh_errexit2(qhT *qh, int exitcode, facetT *facet, facetT *otherfacet);
-void    qh_findhorizon(qhT *qh, pointT *point, facetT *facet, int *goodvisible,int *goodhorizon);
-pointT *qh_nextfurthest(qhT *qh, facetT **visible);
-void    qh_partitionall(qhT *qh, setT *vertices, pointT *points,int npoints);
-void    qh_partitioncoplanar(qhT *qh, pointT *point, facetT *facet, realT *dist);
-void    qh_partitionpoint(qhT *qh, pointT *point, facetT *facet);
-void    qh_partitionvisible(qhT *qh, boolT allpoints, int *numpoints);
-void    qh_precision(qhT *qh, const char *reason);
-void    qh_printsummary(qhT *qh, FILE *fp);
-
-/***** -global.c internal prototypes (alphabetical) ***********************/
-
-void    qh_appendprint(qhT *qh, qh_PRINT format);
-void    qh_freebuild(qhT *qh, boolT allmem);
-void    qh_freebuffers(qhT *qh);
-void    qh_initbuffers(qhT *qh, coordT *points, int numpoints, int dim, boolT ismalloc);
-
-/***** -stat.c internal prototypes (alphabetical) ***********************/
-
-void    qh_allstatA(qhT *qh);
-void    qh_allstatB(qhT *qh);
-void    qh_allstatC(qhT *qh);
-void    qh_allstatD(qhT *qh);
-void    qh_allstatE(qhT *qh);
-void    qh_allstatE2(qhT *qh);
-void    qh_allstatF(qhT *qh);
-void    qh_allstatG(qhT *qh);
-void    qh_allstatH(qhT *qh);
-void    qh_freebuffers(qhT *qh);
-void    qh_initbuffers(qhT *qh, coordT *points, int numpoints, int dim, boolT ismalloc);
-
-#endif /* qhDEFqhulla */
diff --git a/src/libqhullr/qhull_ra.h b/src/libqhullr/qhull_ra.h
index 9845417..552e973 100644
--- a/src/libqhullr/qhull_ra.h
+++ b/src/libqhullr/qhull_ra.h
@@ -1,151 +1,151 @@
 /*
  ---------------------------------
 
-   qhull_r.h
+   qhull_ra.h
    all header files for compiling qhull with reentrant code
 
    see qh-qhull.htm
 
    see libqhull_r.h for user-level definitions
 
    see user_r.h for user-definable constants
 
-   defines internal functions for libqhull.c global.c
+   defines internal functions for libqhull_r.c global_r.c
 
    Copyright (c) 1993-2014 The Geometry Center.
-   $Id: //main/2011/qhull/src/libqhullr/qhull_ra.h#4 $$Change: 1663 $
-   $DateTime: 2014/01/19 17:59:16 $$Author: bbarber $
+   $Id: //main/2011/qhull/src/libqhullr/qhull_ra.h#7 $$Change: 1797 $
+   $DateTime: 2014/12/15 17:23:41 $$Author: bbarber $
 
    Notes:  grep for ((" and (" to catch fprintf("lkasdjf");
            full parens around (x?y:z)
-           use '#include qhull/qhull_r.h' to avoid name clashes
+           use '#include qhull/qhull_ra.h' to avoid name clashes
 */
 
 #ifndef qhDEFqhulla
 #define qhDEFqhulla 1
 
 #include "libqhull_r.h"  /* Defines data types */
 
 #include "stat_r.h"
 #include "random_r.h"
 #include "mem_r.h"
 #include "qset_r.h"
 #include "geom_r.h"
 #include "merge_r.h"
 #include "poly_r.h"
 #include "io_r.h"
 
 #include 
 #include 
 #include 
 #include     /* some compilers will not need float.h */
 #include 
 #include 
 #include 
 #include 
 #include 
-/*** uncomment here and qset.c
+/*** uncomment here and qset_r.c
      if string.h does not define memcpy()
 #include 
 */
 
-#if qh_CLOCKtype == 2  /* defined in user.h from libqhull.h */
+#if qh_CLOCKtype == 2  /* defined in user_r.h from libqhull_r.h */
 #include 
 #include 
 #include 
 #endif
 
 #ifdef _MSC_VER  /* Microsoft Visual C++ -- warning level 4 */
 #pragma warning( disable : 4100)  /* unreferenced formal parameter */
 #pragma warning( disable : 4127)  /* conditional expression is constant */
 #pragma warning( disable : 4706)  /* assignment within conditional function */
 #pragma warning( disable : 4996)  /* function was declared deprecated(strcpy, localtime, etc.) */
 #endif
 
 /* ======= -macros- =========== */
 
 /*----------------------------------
 
   traceN((qh, qh->ferr, 0Nnnn, "format\n", vars));
     calls qh_fprintf if qh.IStracing >= N
 
     Add debugging traps to the end of qh_fprintf
 
   notes:
     removing tracing reduces code size but doesn't change execution speed
 */
 #ifndef qh_NOtrace
 #define trace0(args) {if (qh->IStracing) qh_fprintf args;}
 #define trace1(args) {if (qh->IStracing >= 1) qh_fprintf args;}
 #define trace2(args) {if (qh->IStracing >= 2) qh_fprintf args;}
 #define trace3(args) {if (qh->IStracing >= 3) qh_fprintf args;}
 #define trace4(args) {if (qh->IStracing >= 4) qh_fprintf args;}
 #define trace5(args) {if (qh->IStracing >= 5) qh_fprintf args;}
 #else /* qh_NOtrace */
 #define trace0(args) {}
 #define trace1(args) {}
 #define trace2(args) {}
 #define trace3(args) {}
 #define trace4(args) {}
 #define trace5(args) {}
 #endif /* qh_NOtrace */
 
 /*----------------------------------
 
 */
 
 /* See Qt's qglobal.h */
 #if !defined(SAG_COM) && (defined(WIN64) || defined(_WIN64) || defined(__WIN64__) || defined(WIN32) || defined(_WIN32) || defined(__WIN32__) || defined(__NT__))
 #   define QHULL_OS_WIN
 #elif defined(__MWERKS__) && defined(__INTEL__)
 #   define QHULL_OS_WIN
 #endif
 #if defined(__INTEL_COMPILER) && !defined(QHULL_OS_WIN)
 template 
 inline void qhullUnused(T &x) { (void)x; }
 #  define QHULL_UNUSED(x) qhullUnused(x);
 #else
 #  define QHULL_UNUSED(x) (void)x;
 #endif
 
-/***** -libqhull.c prototypes (alphabetical after qhull) ********************/
+/***** -libqhull_r.c prototypes (alphabetical after qhull) ********************/
 
 void    qh_qhull(qhT *qh);
 boolT   qh_addpoint(qhT *qh, pointT *furthest, facetT *facet, boolT checkdist);
 void    qh_buildhull(qhT *qh);
 void    qh_buildtracing(qhT *qh, pointT *furthest, facetT *facet);
 void    qh_build_withrestart(qhT *qh);
 void    qh_errexit2(qhT *qh, int exitcode, facetT *facet, facetT *otherfacet);
 void    qh_findhorizon(qhT *qh, pointT *point, facetT *facet, int *goodvisible,int *goodhorizon);
 pointT *qh_nextfurthest(qhT *qh, facetT **visible);
 void    qh_partitionall(qhT *qh, setT *vertices, pointT *points,int npoints);
 void    qh_partitioncoplanar(qhT *qh, pointT *point, facetT *facet, realT *dist);
 void    qh_partitionpoint(qhT *qh, pointT *point, facetT *facet);
 void    qh_partitionvisible(qhT *qh, boolT allpoints, int *numpoints);
 void    qh_precision(qhT *qh, const char *reason);
 void    qh_printsummary(qhT *qh, FILE *fp);
 
-/***** -global.c internal prototypes (alphabetical) ***********************/
+/***** -global_r.c internal prototypes (alphabetical) ***********************/
 
 void    qh_appendprint(qhT *qh, qh_PRINT format);
 void    qh_freebuild(qhT *qh, boolT allmem);
 void    qh_freebuffers(qhT *qh);
 void    qh_initbuffers(qhT *qh, coordT *points, int numpoints, int dim, boolT ismalloc);
 
-/***** -stat.c internal prototypes (alphabetical) ***********************/
+/***** -stat_r.c internal prototypes (alphabetical) ***********************/
 
 void    qh_allstatA(qhT *qh);
 void    qh_allstatB(qhT *qh);
 void    qh_allstatC(qhT *qh);
 void    qh_allstatD(qhT *qh);
 void    qh_allstatE(qhT *qh);
 void    qh_allstatE2(qhT *qh);
 void    qh_allstatF(qhT *qh);
 void    qh_allstatG(qhT *qh);
 void    qh_allstatH(qhT *qh);
 void    qh_freebuffers(qhT *qh);
 void    qh_initbuffers(qhT *qh, coordT *points, int numpoints, int dim, boolT ismalloc);
 
 #endif /* qhDEFqhulla */
diff --git a/src/libqhullr/qset_r.c b/src/libqhullr/qset_r.c
index e4d156f..724d5b4 100644
--- a/src/libqhullr/qset_r.c
+++ b/src/libqhullr/qset_r.c
@@ -1,1340 +1,1340 @@
 /*
  ---------------------------------
 
-   qset.c
+   qset_r.c
    implements set manipulations needed for quickhull
 
-   see qh-set.htm and qset.h
+   see qh-set.htm and qset_r.h
 
    Be careful of strict aliasing (two pointers of different types
    that reference the same location).  The last slot of a set is
    either the actual size of the set plus 1, or the NULL terminator
    of the set (i.e., setelemT).
 
    Copyright (c) 1993-2014 The Geometry Center.
-   $Id: //main/2011/qhull/src/libqhullr/qset_r.c#3 $$Change: 1651 $
-   $DateTime: 2014/01/17 08:13:57 $$Author: bbarber $
+   $Id: //main/2011/qhull/src/libqhullr/qset_r.c#6 $$Change: 1797 $
+   $DateTime: 2014/12/15 17:23:41 $$Author: bbarber $
 */
 
 #include "qset_r.h"
 #include "libqhull_r.h" /* for qhT */
 #include "mem_r.h"
 #include 
 #include 
-/*** uncomment here and qhull_r.h
+/*** uncomment here and qhull_ra.h
      if string.h does not define memcpy()
 #include 
 */
 
 #ifndef qhDEFlibqhull
 typedef struct ridgeT ridgeT;
 typedef struct facetT facetT;
 void    qh_errexit(qhT *qh, int exitcode, facetT *, ridgeT *);
 void    qh_fprintf(qhT *qh, FILE *fp, int msgcode, const char *fmt, ... );
 #  ifdef _MSC_VER  /* Microsoft Visual C++ -- warning level 4 */
 #  pragma warning( disable : 4127)  /* conditional expression is constant */
 #  pragma warning( disable : 4706)  /* assignment within conditional function */
 #  endif
 #endif
 
 /*=============== internal macros ===========================*/
 
 /*============ functions in alphabetical order ===================*/
 
 /*----------------------------------
 
   qh_setaddnth(qh, setp, nth, newelem)
     adds newelem as n'th element of sorted or unsorted *setp
 
   notes:
     *setp and newelem must be defined
     *setp may be a temp set
     nth=0 is first element
     errors if nth is out of bounds
 
   design:
     expand *setp if empty or full
     move tail of *setp up one
     insert newelem
 */
 void qh_setaddnth(qhT *qh, setT **setp, int nth, void *newelem) {
   int oldsize, i;
   setelemT *sizep;          /* avoid strict aliasing */
   setelemT *oldp, *newp;
 
   if (!*setp || (sizep= SETsizeaddr_(*setp))->i==0) {
     qh_setlarger(qh, setp);
     sizep= SETsizeaddr_(*setp);
   }
   oldsize= sizep->i - 1;
   if (nth < 0 || nth > oldsize) {
     qh_fprintf(qh, qh->qhmem.ferr, 6171, "qhull internal error (qh_setaddnth): nth %d is out-of-bounds for set:\n", nth);
     qh_setprint(qh, qh->qhmem.ferr, "", *setp);
     qh_errexit(qh, qhmem_ERRqhull, NULL, NULL);
   }
   sizep->i++;
   oldp= (setelemT *)SETelemaddr_(*setp, oldsize, void);   /* NULL */
   newp= oldp+1;
   for (i=oldsize-nth+1; i--; )  /* move at least NULL  */
     (newp--)->p= (oldp--)->p;       /* may overwrite *sizep */
   newp->p= newelem;
 } /* setaddnth */
 
 
 /*----------------------------------
 
   setaddsorted( setp, newelem )
     adds an newelem into sorted *setp
 
   notes:
     *setp and newelem must be defined
     *setp may be a temp set
     nop if newelem already in set
 
   design:
     find newelem's position in *setp
     insert newelem
 */
 void qh_setaddsorted(qhT *qh, setT **setp, void *newelem) {
   int newindex=0;
   void *elem, **elemp;
 
   FOREACHelem_(*setp) {          /* could use binary search instead */
     if (elem < newelem)
       newindex++;
     else if (elem == newelem)
       return;
     else
       break;
   }
   qh_setaddnth(qh, setp, newindex, newelem);
 } /* setaddsorted */
 
 
 /*---------------------------------
 
   qh_setappend(qh, setp, newelem)
     append newelem to *setp
 
   notes:
     *setp may be a temp set
     *setp and newelem may be NULL
 
   design:
     expand *setp if empty or full
     append newelem to *setp
 
 */
 void qh_setappend(qhT *qh, setT **setp, void *newelem) {
   setelemT *sizep;  /* Avoid strict aliasing.  Writing to *endp may overwrite *sizep */
   setelemT *endp;
   int count;
 
   if (!newelem)
     return;
   if (!*setp || (sizep= SETsizeaddr_(*setp))->i==0) {
     qh_setlarger(qh, setp);
     sizep= SETsizeaddr_(*setp);
   }
   count= (sizep->i)++ - 1;
   endp= (setelemT *)SETelemaddr_(*setp, count, void);
   (endp++)->p= newelem;
   endp->p= NULL;
 } /* setappend */
 
 /*---------------------------------
 
   qh_setappend_set(qh, setp, setA)
     appends setA to *setp
 
   notes:
     *setp can not be a temp set
     *setp and setA may be NULL
 
   design:
     setup for copy
     expand *setp if it is too small
     append all elements of setA to *setp
 */
 void qh_setappend_set(qhT *qh, setT **setp, setT *setA) {
   int sizeA, size;
   setT *oldset;
   setelemT *sizep;
 
   if (!setA)
     return;
   SETreturnsize_(setA, sizeA);
   if (!*setp)
     *setp= qh_setnew(qh, sizeA);
   sizep= SETsizeaddr_(*setp);
   if (!(size= sizep->i))
     size= (*setp)->maxsize;
   else
     size--;
   if (size + sizeA > (*setp)->maxsize) {
     oldset= *setp;
     *setp= qh_setcopy(qh, oldset, sizeA);
     qh_setfree(qh, &oldset);
     sizep= SETsizeaddr_(*setp);
   }
   if (sizeA > 0) {
     sizep->i= size+sizeA+1;   /* memcpy may overwrite */
     memcpy((char *)&((*setp)->e[size].p), (char *)&(setA->e[0].p), (size_t)(sizeA+1) * SETelemsize);
   }
 } /* setappend_set */
 
 
 /*---------------------------------
 
   qh_setappend2ndlast(qh, setp, newelem )
     makes newelem the next to the last element in *setp
 
   notes:
     *setp must have at least one element
     newelem must be defined
     *setp may be a temp set
 
   design:
     expand *setp if empty or full
     move last element of *setp up one
     insert newelem
 */
 void qh_setappend2ndlast(qhT *qh, setT **setp, void *newelem) {
     setelemT *sizep;  /* Avoid strict aliasing.  Writing to *endp may overwrite *sizep */
     setelemT *endp, *lastp;
     int count;
 
     if (!*setp || (sizep= SETsizeaddr_(*setp))->i==0) {
         qh_setlarger(qh, setp);
         sizep= SETsizeaddr_(*setp);
     }
     count= (sizep->i)++ - 1;
     endp= (setelemT *)SETelemaddr_(*setp, count, void); /* NULL */
     lastp= endp-1;
     *(endp++)= *lastp;
     endp->p= NULL;    /* may overwrite *sizep */
     lastp->p= newelem;
 } /* setappend2ndlast */
 
 /*---------------------------------
 
   qh_setcheck(qh, set, typename, id )
     check set for validity
     report errors with typename and id
 
   design:
     checks that maxsize, actual size, and NULL terminator agree
 */
 void qh_setcheck(qhT *qh, setT *set, const char *tname, unsigned id) {
   int maxsize, size;
   int waserr= 0;
 
   if (!set)
     return;
   SETreturnsize_(set, size);
   maxsize= set->maxsize;
   if (size > maxsize || !maxsize) {
     qh_fprintf(qh, qh->qhmem.ferr, 6172, "qhull internal error (qh_setcheck): actual size %d of %s%d is greater than max size %d\n",
              size, tname, id, maxsize);
     waserr= 1;
   }else if (set->e[size].p) {
     qh_fprintf(qh, qh->qhmem.ferr, 6173, "qhull internal error (qh_setcheck): %s%d(size %d max %d) is not null terminated.\n",
              tname, id, size-1, maxsize);
     waserr= 1;
   }
   if (waserr) {
     qh_setprint(qh, qh->qhmem.ferr, "ERRONEOUS", set);
     qh_errexit(qh, qhmem_ERRqhull, NULL, NULL);
   }
 } /* setcheck */
 
 
 /*---------------------------------
 
   qh_setcompact(qh, set )
     remove internal NULLs from an unsorted set
 
   returns:
     updated set
 
   notes:
     set may be NULL
     it would be faster to swap tail of set into holes, like qh_setdel
 
   design:
     setup pointers into set
     skip NULLs while copying elements to start of set
     update the actual size
 */
 void qh_setcompact(qhT *qh, setT *set) {
   int size;
   void **destp, **elemp, **endp, **firstp;
 
   if (!set)
     return;
   SETreturnsize_(set, size);
   destp= elemp= firstp= SETaddr_(set, void);
   endp= destp + size;
   while (1) {
     if (!(*destp++ = *elemp++)) {
       destp--;
       if (elemp > endp)
         break;
     }
   }
   qh_settruncate(qh, set, (int)(destp-firstp));   /* WARN64 */
 } /* setcompact */
 
 
 /*---------------------------------
 
   qh_setcopy(qh, set, extra )
     make a copy of a sorted or unsorted set with extra slots
 
   returns:
     new set
 
   design:
     create a newset with extra slots
     copy the elements to the newset
 
 */
 setT *qh_setcopy(qhT *qh, setT *set, int extra) {
   setT *newset;
   int size;
 
   if (extra < 0)
     extra= 0;
   SETreturnsize_(set, size);
   newset= qh_setnew(qh, size+extra);
   SETsizeaddr_(newset)->i= size+1;    /* memcpy may overwrite */
   memcpy((char *)&(newset->e[0].p), (char *)&(set->e[0].p), (size_t)(size+1) * SETelemsize);
   return(newset);
 } /* setcopy */
 
 
 /*---------------------------------
 
   qh_setdel(set, oldelem )
     delete oldelem from an unsorted set
 
   returns:
     returns oldelem if found
     returns NULL otherwise
 
   notes:
     set may be NULL
     oldelem must not be NULL;
     only deletes one copy of oldelem in set
 
   design:
     locate oldelem
     update actual size if it was full
     move the last element to the oldelem's location
 */
 void *qh_setdel(setT *set, void *oldelem) {
   setelemT *sizep;
   setelemT *elemp;
   setelemT *lastp;
 
   if (!set)
     return NULL;
   elemp= (setelemT *)SETaddr_(set, void);
   while (elemp->p != oldelem && elemp->p)
     elemp++;
   if (elemp->p) {
     sizep= SETsizeaddr_(set);
     if (!(sizep->i)--)         /*  if was a full set */
       sizep->i= set->maxsize;  /*     *sizep= (maxsize-1)+ 1 */
     lastp= (setelemT *)SETelemaddr_(set, sizep->i-1, void);
     elemp->p= lastp->p;      /* may overwrite itself */
     lastp->p= NULL;
     return oldelem;
   }
   return NULL;
 } /* setdel */
 
 
 /*---------------------------------
 
   qh_setdellast(set)
     return last element of set or NULL
 
   notes:
     deletes element from set
     set may be NULL
 
   design:
     return NULL if empty
     if full set
       delete last element and set actual size
     else
       delete last element and update actual size
 */
 void *qh_setdellast(setT *set) {
   int setsize;  /* actually, actual_size + 1 */
   int maxsize;
   setelemT *sizep;
   void *returnvalue;
 
   if (!set || !(set->e[0].p))
     return NULL;
   sizep= SETsizeaddr_(set);
   if ((setsize= sizep->i)) {
     returnvalue= set->e[setsize - 2].p;
     set->e[setsize - 2].p= NULL;
     sizep->i--;
   }else {
     maxsize= set->maxsize;
     returnvalue= set->e[maxsize - 1].p;
     set->e[maxsize - 1].p= NULL;
     sizep->i= maxsize;
   }
   return returnvalue;
 } /* setdellast */
 
 
 /*---------------------------------
 
   qh_setdelnth(qh, set, nth )
     deletes nth element from unsorted set
     0 is first element
 
   returns:
     returns the element (needs type conversion)
 
   notes:
     errors if nth invalid
 
   design:
     setup points and check nth
     delete nth element and overwrite with last element
 */
 void *qh_setdelnth(qhT *qh, setT *set, int nth) {
   void *elem;
   setelemT *sizep;
   setelemT *elemp, *lastp;
 
   elemp= (setelemT *)SETelemaddr_(set, nth, void);
   sizep= SETsizeaddr_(set);
   if ((sizep->i--)==0)         /*  if was a full set */
     sizep->i= set->maxsize;  /*     *sizep= (maxsize-1)+ 1 */
   if (nth < 0 || nth >= sizep->i) {
     qh_fprintf(qh, qh->qhmem.ferr, 6174, "qhull internal error (qh_setdelnth): nth %d is out-of-bounds for set:\n", nth);
     qh_setprint(qh, qh->qhmem.ferr, "", set);
     qh_errexit(qh, qhmem_ERRqhull, NULL, NULL);
   }
   lastp= (setelemT *)SETelemaddr_(set, sizep->i-1, void);
   elem= elemp->p;
   elemp->p= lastp->p;      /* may overwrite itself */
   lastp->p= NULL;
   return elem;
 } /* setdelnth */
 
 /*---------------------------------
 
   qh_setdelnthsorted(qh, set, nth )
     deletes nth element from sorted set
 
   returns:
     returns the element (use type conversion)
 
   notes:
     errors if nth invalid
 
   see also:
     setnew_delnthsorted
 
   design:
     setup points and check nth
     copy remaining elements down one
     update actual size
 */
 void *qh_setdelnthsorted(qhT *qh, setT *set, int nth) {
   void *elem;
   setelemT *sizep;
   setelemT *newp, *oldp;
 
   sizep= SETsizeaddr_(set);
   if (nth < 0 || (sizep->i && nth >= sizep->i-1) || nth >= set->maxsize) {
     qh_fprintf(qh, qh->qhmem.ferr, 6175, "qhull internal error (qh_setdelnthsorted): nth %d is out-of-bounds for set:\n", nth);
     qh_setprint(qh, qh->qhmem.ferr, "", set);
     qh_errexit(qh, qhmem_ERRqhull, NULL, NULL);
   }
   newp= (setelemT *)SETelemaddr_(set, nth, void);
   elem= newp->p;
   oldp= newp+1;
   while (((newp++)->p= (oldp++)->p))
     ; /* copy remaining elements and NULL */
   if ((sizep->i--)==0)         /*  if was a full set */
     sizep->i= set->maxsize;  /*     *sizep= (max size-1)+ 1 */
   return elem;
 } /* setdelnthsorted */
 
 
 /*---------------------------------
 
   qh_setdelsorted(set, oldelem )
     deletes oldelem from sorted set
 
   returns:
     returns oldelem if it was deleted
 
   notes:
     set may be NULL
 
   design:
     locate oldelem in set
     copy remaining elements down one
     update actual size
 */
 void *qh_setdelsorted(setT *set, void *oldelem) {
   setelemT *sizep;
   setelemT *newp, *oldp;
 
   if (!set)
     return NULL;
   newp= (setelemT *)SETaddr_(set, void);
   while(newp->p != oldelem && newp->p)
     newp++;
   if (newp->p) {
     oldp= newp+1;
     while (((newp++)->p= (oldp++)->p))
       ; /* copy remaining elements */
     sizep= SETsizeaddr_(set);
     if ((sizep->i--)==0)    /*  if was a full set */
       sizep->i= set->maxsize;  /*     *sizep= (max size-1)+ 1 */
     return oldelem;
   }
   return NULL;
 } /* setdelsorted */
 
 
 /*---------------------------------
 
   qh_setduplicate(qh, set, elemsize )
     duplicate a set of elemsize elements
 
   notes:
     use setcopy if retaining old elements
 
   design:
     create a new set
     for each elem of the old set
       create a newelem
       append newelem to newset
 */
 setT *qh_setduplicate(qhT *qh, setT *set, int elemsize) {
   void          *elem, **elemp, *newElem;
   setT          *newSet;
   int           size;
 
   if (!(size= qh_setsize(qh, set)))
     return NULL;
   newSet= qh_setnew(qh, size);
   FOREACHelem_(set) {
     newElem= qh_memalloc(qh, elemsize);
     memcpy(newElem, elem, (size_t)elemsize);
     qh_setappend(qh, &newSet, newElem);
   }
   return newSet;
 } /* setduplicate */
 
 
 /*---------------------------------
 
   qh_setendpointer( set )
     Returns pointer to NULL terminator of a set's elements
     set can not be NULL
 
 */
 void **qh_setendpointer(setT *set) {
 
   setelemT *sizep= SETsizeaddr_(set);
   int n= sizep->i;
   return (n ? &set->e[n-1].p : &sizep->p);
 } /* qh_setendpointer */
 
 /*---------------------------------
 
   qh_setequal( setA, setB )
     returns 1 if two sorted sets are equal, otherwise returns 0
 
   notes:
     either set may be NULL
 
   design:
     check size of each set
     setup pointers
     compare elements of each set
 */
 int qh_setequal(setT *setA, setT *setB) {
   void **elemAp, **elemBp;
   int sizeA= 0, sizeB= 0;
 
   if (setA) {
     SETreturnsize_(setA, sizeA);
   }
   if (setB) {
     SETreturnsize_(setB, sizeB);
   }
   if (sizeA != sizeB)
     return 0;
   if (!sizeA)
     return 1;
   elemAp= SETaddr_(setA, void);
   elemBp= SETaddr_(setB, void);
   if (!memcmp((char *)elemAp, (char *)elemBp, sizeA*SETelemsize))
     return 1;
   return 0;
 } /* setequal */
 
 
 /*---------------------------------
 
   qh_setequal_except( setA, skipelemA, setB, skipelemB )
     returns 1 if sorted setA and setB are equal except for skipelemA & B
 
   returns:
     false if either skipelemA or skipelemB are missing
 
   notes:
     neither set may be NULL
 
     if skipelemB is NULL,
       can skip any one element of setB
 
   design:
     setup pointers
     search for skipelemA, skipelemB, and mismatches
     check results
 */
 int qh_setequal_except(setT *setA, void *skipelemA, setT *setB, void *skipelemB) {
   void **elemA, **elemB;
   int skip=0;
 
   elemA= SETaddr_(setA, void);
   elemB= SETaddr_(setB, void);
   while (1) {
     if (*elemA == skipelemA) {
       skip++;
       elemA++;
     }
     if (skipelemB) {
       if (*elemB == skipelemB) {
         skip++;
         elemB++;
       }
     }else if (*elemA != *elemB) {
       skip++;
       if (!(skipelemB= *elemB++))
         return 0;
     }
     if (!*elemA)
       break;
     if (*elemA++ != *elemB++)
       return 0;
   }
   if (skip != 2 || *elemB)
     return 0;
   return 1;
 } /* setequal_except */
 
 
 /*---------------------------------
 
   qh_setequal_skip( setA, skipA, setB, skipB )
     returns 1 if sorted setA and setB are equal except for elements skipA & B
 
   returns:
     false if different size
 
   notes:
     neither set may be NULL
 
   design:
     setup pointers
     search for mismatches while skipping skipA and skipB
 */
 int qh_setequal_skip(setT *setA, int skipA, setT *setB, int skipB) {
   void **elemA, **elemB, **skipAp, **skipBp;
 
   elemA= SETaddr_(setA, void);
   elemB= SETaddr_(setB, void);
   skipAp= SETelemaddr_(setA, skipA, void);
   skipBp= SETelemaddr_(setB, skipB, void);
   while (1) {
     if (elemA == skipAp)
       elemA++;
     if (elemB == skipBp)
       elemB++;
     if (!*elemA)
       break;
     if (*elemA++ != *elemB++)
       return 0;
   }
   if (*elemB)
     return 0;
   return 1;
 } /* setequal_skip */
 
 
 /*---------------------------------
 
   qh_setfree(qh, setp )
     frees the space occupied by a sorted or unsorted set
 
   returns:
     sets setp to NULL
 
   notes:
     set may be NULL
 
   design:
     free array
     free set
 */
 void qh_setfree(qhT *qh, setT **setp) {
   int size;
   void **freelistp;  /* used !qh_NOmem */
 
   if (*setp) {
     size= sizeof(setT) + ((*setp)->maxsize)*SETelemsize;
     if (size <= qh->qhmem.LASTsize) {
       qh_memfree_(qh, *setp, size, freelistp);
     }else
       qh_memfree(qh, *setp, size);
     *setp= NULL;
   }
 } /* setfree */
 
 
 /*---------------------------------
 
   qh_setfree2(qh, setp, elemsize )
     frees the space occupied by a set and its elements
 
   notes:
     set may be NULL
 
   design:
     free each element
     free set
 */
 void qh_setfree2(qhT *qh, setT **setp, int elemsize) {
   void          *elem, **elemp;
 
   FOREACHelem_(*setp)
     qh_memfree(qh, elem, elemsize);
   qh_setfree(qh, setp);
 } /* setfree2 */
 
 
 
 /*---------------------------------
 
   qh_setfreelong(qh, setp )
     frees a set only if it's in long memory
 
   returns:
     sets setp to NULL if it is freed
 
   notes:
     set may be NULL
 
   design:
     if set is large
       free it
 */
 void qh_setfreelong(qhT *qh, setT **setp) {
   int size;
 
   if (*setp) {
     size= sizeof(setT) + ((*setp)->maxsize)*SETelemsize;
     if (size > qh->qhmem.LASTsize) {
       qh_memfree(qh, *setp, size);
       *setp= NULL;
     }
   }
 } /* setfreelong */
 
 
 /*---------------------------------
 
   qh_setin(set, setelem )
     returns 1 if setelem is in a set, 0 otherwise
 
   notes:
     set may be NULL or unsorted
 
   design:
     scans set for setelem
 */
 int qh_setin(setT *set, void *setelem) {
   void *elem, **elemp;
 
   FOREACHelem_(set) {
     if (elem == setelem)
       return 1;
   }
   return 0;
 } /* setin */
 
 
 /*---------------------------------
 
   qh_setindex(set, atelem )
     returns the index of atelem in set.
     returns -1, if not in set or maxsize wrong
 
   notes:
     set may be NULL and may contain nulls.
     NOerrors returned (qh_pointid, QhullPoint::id)
 
   design:
     checks maxsize
     scans set for atelem
 */
 int qh_setindex(setT *set, void *atelem) {
   void **elem;
   int size, i;
 
   if (!set)
     return -1;
   SETreturnsize_(set, size);
   if (size > set->maxsize)
     return -1;
   elem= SETaddr_(set, void);
   for (i=0; i < size; i++) {
     if (*elem++ == atelem)
       return i;
   }
   return -1;
 } /* setindex */
 
 
 /*---------------------------------
 
   qh_setlarger(qh, oldsetp )
     returns a larger set that contains all elements of *oldsetp
 
   notes:
     the set is at least twice as large
     if temp set, updates qh->qhmem.tempstack
 
   design:
     creates a new set
     copies the old set to the new set
     updates pointers in tempstack
     deletes the old set
 */
 void qh_setlarger(qhT *qh, setT **oldsetp) {
   int size= 1;
   setT *newset, *set, **setp, *oldset;
   setelemT *sizep;
   setelemT *newp, *oldp;
 
   if (*oldsetp) {
     oldset= *oldsetp;
     SETreturnsize_(oldset, size);
     qh->qhmem.cntlarger++;
     qh->qhmem.totlarger += size+1;
     newset= qh_setnew(qh, 2 * size);
     oldp= (setelemT *)SETaddr_(oldset, void);
     newp= (setelemT *)SETaddr_(newset, void);
     memcpy((char *)newp, (char *)oldp, (size_t)(size+1) * SETelemsize);
     sizep= SETsizeaddr_(newset);
     sizep->i= size+1;
     FOREACHset_((setT *)qh->qhmem.tempstack) {
       if (set == oldset)
         *(setp-1)= newset;
     }
     qh_setfree(qh, oldsetp);
   }else
     newset= qh_setnew(qh, 3);
   *oldsetp= newset;
 } /* setlarger */
 
 
 /*---------------------------------
 
   qh_setlast( set )
     return last element of set or NULL (use type conversion)
 
   notes:
     set may be NULL
 
   design:
     return last element
 */
 void *qh_setlast(setT *set) {
   int size;
 
   if (set) {
     size= SETsizeaddr_(set)->i;
     if (!size)
       return SETelem_(set, set->maxsize - 1);
     else if (size > 1)
       return SETelem_(set, size - 2);
   }
   return NULL;
 } /* setlast */
 
 
 /*---------------------------------
 
   qh_setnew(qh, setsize )
     creates and allocates space for a set
 
   notes:
     setsize means the number of elements (!including the NULL terminator)
     use qh_settemp/qh_setfreetemp if set is temporary
 
   design:
     allocate memory for set
     roundup memory if small set
     initialize as empty set
 */
 setT *qh_setnew(qhT *qh, int setsize) {
   setT *set;
   int sizereceived; /* used !qh_NOmem */
   int size;
   void **freelistp; /* used !qh_NOmem */
 
   if (!setsize)
     setsize++;
   size= sizeof(setT) + setsize * SETelemsize;
   if (size>0 && size <= qh->qhmem.LASTsize) {
     qh_memalloc_(qh, size, freelistp, set, setT);
 #ifndef qh_NOmem
     sizereceived= qh->qhmem.sizetable[ qh->qhmem.indextable[size]];
     if (sizereceived > size)
       setsize += (sizereceived - size)/SETelemsize;
 #endif
   }else
     set= (setT*)qh_memalloc(qh, size);
   set->maxsize= setsize;
   set->e[setsize].i= 1;
   set->e[0].p= NULL;
   return(set);
 } /* setnew */
 
 
 /*---------------------------------
 
   qh_setnew_delnthsorted(qh, set, size, nth, prepend )
     creates a sorted set not containing nth element
     if prepend, the first prepend elements are undefined
 
   notes:
     set must be defined
     checks nth
     see also: setdelnthsorted
 
   design:
     create new set
     setup pointers and allocate room for prepend'ed entries
     append head of old set to new set
     append tail of old set to new set
 */
 setT *qh_setnew_delnthsorted(qhT *qh, setT *set, int size, int nth, int prepend) {
   setT *newset;
   void **oldp, **newp;
   int tailsize= size - nth -1, newsize;
 
   if (tailsize < 0) {
     qh_fprintf(qh, qh->qhmem.ferr, 6176, "qhull internal error (qh_setnew_delnthsorted): nth %d is out-of-bounds for set:\n", nth);
     qh_setprint(qh, qh->qhmem.ferr, "", set);
     qh_errexit(qh, qhmem_ERRqhull, NULL, NULL);
   }
   newsize= size-1 + prepend;
   newset= qh_setnew(qh, newsize);
   newset->e[newset->maxsize].i= newsize+1;  /* may be overwritten */
   oldp= SETaddr_(set, void);
   newp= SETaddr_(newset, void) + prepend;
   switch (nth) {
   case 0:
     break;
   case 1:
     *(newp++)= *oldp++;
     break;
   case 2:
     *(newp++)= *oldp++;
     *(newp++)= *oldp++;
     break;
   case 3:
     *(newp++)= *oldp++;
     *(newp++)= *oldp++;
     *(newp++)= *oldp++;
     break;
   case 4:
     *(newp++)= *oldp++;
     *(newp++)= *oldp++;
     *(newp++)= *oldp++;
     *(newp++)= *oldp++;
     break;
   default:
     memcpy((char *)newp, (char *)oldp, (size_t)nth * SETelemsize);
     newp += nth;
     oldp += nth;
     break;
   }
   oldp++;
   switch (tailsize) {
   case 0:
     break;
   case 1:
     *(newp++)= *oldp++;
     break;
   case 2:
     *(newp++)= *oldp++;
     *(newp++)= *oldp++;
     break;
   case 3:
     *(newp++)= *oldp++;
     *(newp++)= *oldp++;
     *(newp++)= *oldp++;
     break;
   case 4:
     *(newp++)= *oldp++;
     *(newp++)= *oldp++;
     *(newp++)= *oldp++;
     *(newp++)= *oldp++;
     break;
   default:
     memcpy((char *)newp, (char *)oldp, (size_t)tailsize * SETelemsize);
     newp += tailsize;
   }
   *newp= NULL;
   return(newset);
 } /* setnew_delnthsorted */
 
 
 /*---------------------------------
 
   qh_setprint(qh, fp, string, set )
     print set elements to fp with identifying string
 
   notes:
     never errors
 */
 void qh_setprint(qhT *qh, FILE *fp, const char* string, setT *set) {
   int size, k;
 
   if (!set)
     qh_fprintf(qh, fp, 9346, "%s set is null\n", string);
   else {
     SETreturnsize_(set, size);
     qh_fprintf(qh, fp, 9347, "%s set=%p maxsize=%d size=%d elems=",
              string, set, set->maxsize, size);
     if (size > set->maxsize)
       size= set->maxsize+1;
     for (k=0; k < size; k++)
       qh_fprintf(qh, fp, 9348, " %p", set->e[k].p);
     qh_fprintf(qh, fp, 9349, "\n");
   }
 } /* setprint */
 
 /*---------------------------------
 
   qh_setreplace(qh, set, oldelem, newelem )
     replaces oldelem in set with newelem
 
   notes:
     errors if oldelem not in the set
     newelem may be NULL, but it turns the set into an indexed set (no FOREACH)
 
   design:
     find oldelem
     replace with newelem
 */
 void qh_setreplace(qhT *qh, setT *set, void *oldelem, void *newelem) {
   void **elemp;
 
   elemp= SETaddr_(set, void);
   while (*elemp != oldelem && *elemp)
     elemp++;
   if (*elemp)
     *elemp= newelem;
   else {
     qh_fprintf(qh, qh->qhmem.ferr, 6177, "qhull internal error (qh_setreplace): elem %p not found in set\n",
        oldelem);
     qh_setprint(qh, qh->qhmem.ferr, "", set);
     qh_errexit(qh, qhmem_ERRqhull, NULL, NULL);
   }
 } /* setreplace */
 
 
 /*---------------------------------
 
   qh_setsize(qh, set )
     returns the size of a set
 
   notes:
     errors if set's maxsize is incorrect
     same as SETreturnsize_(set)
-    same code for qh_setsize [qset.c] and QhullSetBase::count
+    same code for qh_setsize [qset_r.c] and QhullSetBase::count
 
   design:
     determine actual size of set from maxsize
 */
 int qh_setsize(qhT *qh, setT *set) {
   int size;
   setelemT *sizep;
 
   if (!set)
     return(0);
   sizep= SETsizeaddr_(set);
   if ((size= sizep->i)) {
     size--;
     if (size > set->maxsize) {
       qh_fprintf(qh, qh->qhmem.ferr, 6178, "qhull internal error (qh_setsize): current set size %d is greater than maximum size %d\n",
                size, set->maxsize);
       qh_setprint(qh, qh->qhmem.ferr, "set: ", set);
       qh_errexit(qh, qhmem_ERRqhull, NULL, NULL);
     }
   }else
     size= set->maxsize;
   return size;
 } /* setsize */
 
 /*---------------------------------
 
   qh_settemp(qh, setsize )
     return a stacked, temporary set of upto setsize elements
 
   notes:
     use settempfree or settempfree_all to release from qh->qhmem.tempstack
     see also qh_setnew
 
   design:
     allocate set
     append to qh->qhmem.tempstack
 
 */
 setT *qh_settemp(qhT *qh, int setsize) {
   setT *newset;
 
   newset= qh_setnew(qh, setsize);
   qh_setappend(qh, &qh->qhmem.tempstack, newset);
   if (qh->qhmem.IStracing >= 5)
     qh_fprintf(qh, qh->qhmem.ferr, 8123, "qh_settemp: temp set %p of %d elements, depth %d\n",
        newset, newset->maxsize, qh_setsize(qh, qh->qhmem.tempstack));
   return newset;
 } /* settemp */
 
 /*---------------------------------
 
   qh_settempfree(qh, set )
     free temporary set at top of qh->qhmem.tempstack
 
   notes:
     nop if set is NULL
     errors if set not from previous   qh_settemp
 
   to locate errors:
     use 'T2' to find source and then find mis-matching qh_settemp
 
   design:
     check top of qh->qhmem.tempstack
     free it
 */
 void qh_settempfree(qhT *qh, setT **set) {
   setT *stackedset;
 
   if (!*set)
     return;
   stackedset= qh_settemppop(qh);
   if (stackedset != *set) {
     qh_settemppush(qh, stackedset);
     qh_fprintf(qh, qh->qhmem.ferr, 6179, "qhull internal error (qh_settempfree): set %p(size %d) was not last temporary allocated(depth %d, set %p, size %d)\n",
              *set, qh_setsize(qh, *set), qh_setsize(qh, qh->qhmem.tempstack)+1,
              stackedset, qh_setsize(qh, stackedset));
     qh_errexit(qh, qhmem_ERRqhull, NULL, NULL);
   }
   qh_setfree(qh, set);
 } /* settempfree */
 
 /*---------------------------------
 
   qh_settempfree_all(qh)
     free all temporary sets in qh->qhmem.tempstack
 
   design:
     for each set in tempstack
       free set
     free qh->qhmem.tempstack
 */
 void qh_settempfree_all(qhT *qh) {
   setT *set, **setp;
 
   FOREACHset_(qh->qhmem.tempstack)
     qh_setfree(qh, &set);
   qh_setfree(qh, &qh->qhmem.tempstack);
 } /* settempfree_all */
 
 /*---------------------------------
 
   qh_settemppop(qh)
     pop and return temporary set from qh->qhmem.tempstack
 
   notes:
     the returned set is permanent
 
   design:
     pop and check top of qh->qhmem.tempstack
 */
 setT *qh_settemppop(qhT *qh) {
   setT *stackedset;
 
   stackedset= (setT*)qh_setdellast(qh->qhmem.tempstack);
   if (!stackedset) {
     qh_fprintf(qh, qh->qhmem.ferr, 6180, "qhull internal error (qh_settemppop): pop from empty temporary stack\n");
     qh_errexit(qh, qhmem_ERRqhull, NULL, NULL);
   }
   if (qh->qhmem.IStracing >= 5)
     qh_fprintf(qh, qh->qhmem.ferr, 8124, "qh_settemppop: depth %d temp set %p of %d elements\n",
        qh_setsize(qh, qh->qhmem.tempstack)+1, stackedset, qh_setsize(qh, stackedset));
   return stackedset;
 } /* settemppop */
 
 /*---------------------------------
 
   qh_settemppush(qh, set )
     push temporary set unto qh->qhmem.tempstack (makes it temporary)
 
   notes:
     duplicates settemp() for tracing
 
   design:
     append set to tempstack
 */
 void qh_settemppush(qhT *qh, setT *set) {
     if (!set) {
         fprintf (qh->qhmem.ferr, "qhull error (qh_settemppush): can not push a NULL temp\n");
         qh_errexit(qh, qhmem_ERRqhull, NULL, NULL);
     }
   qh_setappend(qh, &qh->qhmem.tempstack, set);
   if (qh->qhmem.IStracing >= 5)
     qh_fprintf(qh, qh->qhmem.ferr, 8125, "qh_settemppush: depth %d temp set %p of %d elements\n",
       qh_setsize(qh, qh->qhmem.tempstack), set, qh_setsize(qh, set));
 } /* settemppush */
 
 
 /*---------------------------------
 
   qh_settruncate(qh, set, size )
     truncate set to size elements
 
   notes:
     set must be defined
 
   see:
     SETtruncate_
 
   design:
     check size
     update actual size of set
 */
 void qh_settruncate(qhT *qh, setT *set, int size) {
 
   if (size < 0 || size > set->maxsize) {
     qh_fprintf(qh, qh->qhmem.ferr, 6181, "qhull internal error (qh_settruncate): size %d out of bounds for set:\n", size);
     qh_setprint(qh, qh->qhmem.ferr, "", set);
     qh_errexit(qh, qhmem_ERRqhull, NULL, NULL);
   }
   set->e[set->maxsize].i= size+1;   /* maybe overwritten */
   set->e[size].p= NULL;
 } /* settruncate */
 
 /*---------------------------------
 
   qh_setunique(qh, set, elem )
     add elem to unsorted set unless it is already in set
 
   notes:
     returns 1 if it is appended
 
   design:
     if elem not in set
       append elem to set
 */
 int qh_setunique(qhT *qh, setT **set, void *elem) {
 
   if (!qh_setin(*set, elem)) {
     qh_setappend(qh, set, elem);
     return 1;
   }
   return 0;
 } /* setunique */
 
 /*---------------------------------
 
   qh_setzero(qh, set, index, size )
     zero elements from index on
     set actual size of set to size
 
   notes:
     set must be defined
     the set becomes an indexed set (can not use FOREACH...)
 
   see also:
     qh_settruncate
 
   design:
     check index and size
     update actual size
     zero elements starting at e[index]
 */
 void qh_setzero(qhT *qh, setT *set, int idx, int size) {
   int count;
 
   if (idx < 0 || idx >= size || size > set->maxsize) {
     qh_fprintf(qh, qh->qhmem.ferr, 6182, "qhull internal error (qh_setzero): index %d or size %d out of bounds for set:\n", idx, size);
     qh_setprint(qh, qh->qhmem.ferr, "", set);
     qh_errexit(qh, qhmem_ERRqhull, NULL, NULL);
   }
   set->e[set->maxsize].i=  size+1;  /* may be overwritten */
   count= size - idx + 1;   /* +1 for NULL terminator */
   memset((char *)SETelemaddr_(set, idx, void), 0, (size_t)count * SETelemsize);
 } /* setzero */
 
 
diff --git a/src/libqhullr/qset_r.h b/src/libqhullr/qset_r.h
index babb809..5290b94 100644
--- a/src/libqhullr/qset_r.h
+++ b/src/libqhullr/qset_r.h
@@ -1,493 +1,498 @@
 /*
  ---------------------------------
 
-   qset.h
-     header file for qset.c that implements set
+   qset_r.h
+     header file for qset_r.c that implements set
 
-   see qh-set.htm and qset.c
+   see qh-set.htm and qset_r.c
 
-   only uses mem.c, malloc/free
+   only uses mem_r.c, malloc/free
 
    for error handling, writes message and calls
       qh_errexit(qhT *qh, qhmem_ERRqhull, NULL, NULL);
 
    set operations satisfy the following properties:
     - sets have a max size, the actual size (if different) is stored at the end
     - every set is NULL terminated
     - sets may be sorted or unsorted, the caller must distinguish this
 
    Copyright (c) 1993-2014 The Geometry Center.
-   $Id: //main/2011/qhull/src/libqhullr/qset_r.h#4 $$Change: 1663 $
-   $DateTime: 2014/01/19 17:59:16 $$Author: bbarber $
+   $Id: //main/2011/qhull/src/libqhullr/qset_r.h#8 $$Change: 1797 $
+   $DateTime: 2014/12/15 17:23:41 $$Author: bbarber $
 */
 
 #ifndef qhDEFset
 #define qhDEFset 1
 
 #include 
 
 /*================= -structures- ===============*/
 
 #ifndef DEFsetT
 #define DEFsetT 1
 typedef struct setT setT;   /* a set is a sorted or unsorted array of pointers */
 #endif
 
 #ifndef DEFqhT
 #define DEFqhT 1
 typedef struct qhT qhT;          /* defined in libqhull_r.h */
 #endif
 
+#ifndef DEFcountT
+#define DEFcountT 1
+typedef int countT;          /* defined in user_r.h */
+#endif
+
 /*------------------------------------------
 
 setT
   a set or list of pointers with maximum size and actual size.
 
 variations:
   unsorted, unique   -- a list of unique pointers with NULL terminator
                            user guarantees uniqueness
   sorted             -- a sorted list of unique pointers with NULL terminator
-                           qset.c guarantees uniqueness
+                           qset_r.c guarantees uniqueness
   unsorted           -- a list of pointers terminated with NULL
   indexed            -- an array of pointers with NULL elements
 
 structure for set of n elements:
 
         --------------
         |  maxsize
         --------------
         |  e[0] - a pointer, may be NULL for indexed sets
         --------------
         |  e[1]
 
         --------------
         |  ...
         --------------
         |  e[n-1]
         --------------
         |  e[n] = NULL
         --------------
         |  ...
         --------------
         |  e[maxsize] - n+1 or NULL (determines actual size of set)
         --------------
 
 */
 
 /*-- setelemT -- internal type to allow both pointers and indices
 */
 typedef union setelemT setelemT;
 union setelemT {
   void    *p;
-  int      i;         /* integer used for e[maxSize] */
+  countT   i;         /* integer used for e[maxSize] */
 };
 
 struct setT {
-  int maxsize;          /* maximum number of elements (except NULL) */
+  countT maxsize;          /* maximum number of elements (except NULL) */
   setelemT e[1];        /* array of pointers, tail is NULL */
                         /* last slot (unless NULL) is actual size+1
                            e[maxsize]==NULL or e[e[maxsize]-1]==NULL */
                         /* this may generate a warning since e[] contains
                            maxsize elements */
 };
 
 /*=========== -constants- =========================*/
 
 /*-------------------------------------
 
   SETelemsize
     size of a set element in bytes
 */
 #define SETelemsize ((int)sizeof(setelemT))
 
 
 /*=========== -macros- =========================*/
 
 /*-------------------------------------
 
    FOREACHsetelement_(type, set, variable)
      define FOREACH iterator
 
    declare:
      assumes *variable and **variablep are declared
      no space in "variable)" [DEC Alpha cc compiler]
 
    each iteration:
      variable is set element
      variablep is one beyond variable.
 
    to repeat an element:
      variablep--; / *repeat* /
 
    at exit:
      variable is NULL at end of loop
 
    example:
      #define FOREACHfacet_( facets ) FOREACHsetelement_( facetT, facets, facet )
 
    notes:
      use FOREACHsetelement_i_() if need index or include NULLs
 
    WARNING:
      nested loops can't use the same variable (define another FOREACH)
 
      needs braces if nested inside another FOREACH
      this includes intervening blocks, e.g. FOREACH...{ if () FOREACH...} )
 */
 #define FOREACHsetelement_(type, set, variable) \
         if (((variable= NULL), set)) for (\
           variable##p= (type **)&((set)->e[0].p); \
           (variable= *variable##p++);)
 
 /*------------------------------------------
 
    FOREACHsetelement_i_(qh, type, set, variable)
      define indexed FOREACH iterator
 
    declare:
      type *variable, variable_n, variable_i;
 
    each iteration:
      variable is set element, may be NULL
      variable_i is index, variable_n is qh_setsize()
 
    to repeat an element:
      variable_i--; variable_n-- repeats for deleted element
 
    at exit:
      variable==NULL and variable_i==variable_n
 
    example:
      #define FOREACHfacet_i_( qh, facets ) FOREACHsetelement_i_( qh, facetT, facets, facet )
 
    WARNING:
      nested loops can't use the same variable (define another FOREACH)
 
      needs braces if nested inside another FOREACH
      this includes intervening blocks, e.g. FOREACH...{ if () FOREACH...} )
 */
 #define FOREACHsetelement_i_(qh, type, set, variable) \
         if (((variable= NULL), set)) for (\
           variable##_i= 0, variable= (type *)((set)->e[0].p), \
                    variable##_n= qh_setsize(qh, set);\
           variable##_i < variable##_n;\
           variable= (type *)((set)->e[++variable##_i].p) )
 
 /*----------------------------------------
 
    FOREACHsetelementreverse_(qh, type, set, variable)-
      define FOREACH iterator in reverse order
 
    declare:
      assumes *variable and **variablep are declared
-     also declare 'int variabletemp'
+     also declare 'countT variabletemp'
 
    each iteration:
      variable is set element
 
    to repeat an element:
      variabletemp++; / *repeat* /
 
    at exit:
      variable is NULL
 
    example:
      #define FOREACHvertexreverse_( vertices ) FOREACHsetelementreverse_( vertexT, vertices, vertex )
 
    notes:
      use FOREACHsetelementreverse12_() to reverse first two elements
      WARNING: needs braces if nested inside another FOREACH
 */
 #define FOREACHsetelementreverse_(qh, type, set, variable) \
         if (((variable= NULL), set)) for (\
            variable##temp= qh_setsize(qh, set)-1, variable= qh_setlast(qh, set);\
            variable; variable= \
            ((--variable##temp >= 0) ? SETelemt_(set, variable##temp, type) : NULL))
 
 /*-------------------------------------
 
    FOREACHsetelementreverse12_(type, set, variable)-
      define FOREACH iterator with e[1] and e[0] reversed
 
    declare:
      assumes *variable and **variablep are declared
 
    each iteration:
      variable is set element
      variablep is one after variable.
 
    to repeat an element:
      variablep--; / *repeat* /
 
    at exit:
      variable is NULL at end of loop
 
    example
      #define FOREACHvertexreverse12_( vertices ) FOREACHsetelementreverse12_( vertexT, vertices, vertex )
 
    notes:
      WARNING: needs braces if nested inside another FOREACH
 */
 #define FOREACHsetelementreverse12_(type, set, variable) \
         if (((variable= NULL), set)) for (\
           variable##p= (type **)&((set)->e[1].p); \
           (variable= *variable##p); \
           variable##p == ((type **)&((set)->e[0].p))?variable##p += 2: \
               (variable##p == ((type **)&((set)->e[1].p))?variable##p--:variable##p++))
 
 /*-------------------------------------
 
    FOREACHelem_( set )-
      iterate elements in a set
 
    declare:
      void *elem, *elemp;
 
    each iteration:
      elem is set element
      elemp is one beyond
 
    to repeat an element:
      elemp--; / *repeat* /
 
    at exit:
      elem == NULL at end of loop
 
    example:
      FOREACHelem_(set) {
 
    notes:
      WARNING: needs braces if nested inside another FOREACH
 */
 #define FOREACHelem_(set) FOREACHsetelement_(void, set, elem)
 
 /*-------------------------------------
 
    FOREACHset_( set )-
      iterate a set of sets
 
    declare:
      setT *set, **setp;
 
    each iteration:
      set is set element
      setp is one beyond
 
    to repeat an element:
      setp--; / *repeat* /
 
    at exit:
      set == NULL at end of loop
 
    example
      FOREACHset_(sets) {
 
    notes:
      WARNING: needs braces if nested inside another FOREACH
 */
 #define FOREACHset_(sets) FOREACHsetelement_(setT, sets, set)
 
 /*-------------------------------------------
 
    SETindex_( set, elem )
      return index of elem in set
 
    notes:
      for use with FOREACH iteration
      WARN64 -- Maximum set size is 2G
 
    example:
      i= SETindex_(ridges, ridge)
 */
-#define SETindex_(set, elem) ((int)((void **)elem##p - (void **)&(set)->e[1].p))
+#define SETindex_(set, elem) ((countT)((void **)elem##p - (void **)&(set)->e[1].p))
 
 /*-----------------------------------------
 
    SETref_( elem )
      l.h.s. for modifying the current element in a FOREACH iteration
 
    example:
      SETref_(ridge)= anotherridge;
 */
 #define SETref_(elem) (elem##p[-1])
 
 /*-----------------------------------------
 
    SETelem_(set, n)
      return the n'th element of set
 
    notes:
       assumes that n is valid [0..size] and that set is defined
       use SETelemt_() for type cast
 */
 #define SETelem_(set, n)           ((set)->e[n].p)
 
 /*-----------------------------------------
 
    SETelemt_(set, n, type)
      return the n'th element of set as a type
 
    notes:
       assumes that n is valid [0..size] and that set is defined
 */
 #define SETelemt_(set, n, type)    ((type*)((set)->e[n].p))
 
 /*-----------------------------------------
 
    SETelemaddr_(set, n, type)
      return address of the n'th element of a set
 
    notes:
       assumes that n is valid [0..size] and set is defined
 */
 #define SETelemaddr_(set, n, type) ((type **)(&((set)->e[n].p)))
 
 /*-----------------------------------------
 
    SETfirst_(set)
      return first element of set
 
 */
 #define SETfirst_(set)             ((set)->e[0].p)
 
 /*-----------------------------------------
 
    SETfirstt_(set, type)
      return first element of set as a type
 
 */
 #define SETfirstt_(set, type)      ((type*)((set)->e[0].p))
 
 /*-----------------------------------------
 
    SETsecond_(set)
      return second element of set
 
 */
 #define SETsecond_(set)            ((set)->e[1].p)
 
 /*-----------------------------------------
 
    SETsecondt_(set, type)
      return second element of set as a type
 */
 #define SETsecondt_(set, type)     ((type*)((set)->e[1].p))
 
 /*-----------------------------------------
 
    SETaddr_(set, type)
        return address of set's elements
 */
 #define SETaddr_(set,type)         ((type **)(&((set)->e[0].p)))
 
 /*-----------------------------------------
 
    SETreturnsize_(set, size)
      return size of a set
 
    notes:
       set must be defined
       use qh_setsize(qhT *qh, set) unless speed is critical
 */
 #define SETreturnsize_(set, size) (((size)= ((set)->e[(set)->maxsize].i))?(--(size)):((size)= (set)->maxsize))
 
 /*-----------------------------------------
 
    SETempty_(set)
      return true(1) if set is empty
 
    notes:
       set may be NULL
 */
 #define SETempty_(set)            (!set || (SETfirst_(set) ? 0 : 1))
 
 /*---------------------------------
 
   SETsizeaddr_(set)
     return pointer to 'actual size+1' of set (set CANNOT be NULL!!)
     Its type is setelemT* for strict aliasing
     All SETelemaddr_ must be cast to setelemT
 
 
   notes:
     *SETsizeaddr==NULL or e[*SETsizeaddr-1].p==NULL
 */
 #define SETsizeaddr_(set) (&((set)->e[(set)->maxsize]))
 
 /*-----------------------------------------
 
    SETtruncate_(set, size)
      truncate set to size
 
    see:
      qh_settruncate()
 
 */
 #define SETtruncate_(set, size) {set->e[set->maxsize].i= size+1; /* maybe overwritten */ \
       set->e[size].p= NULL;}
 
 /*======= prototypes in alphabetical order ============*/
 
 void  qh_setaddsorted(qhT *qh, setT **setp, void *elem);
-void  qh_setaddnth(qhT *qh, setT **setp, int nth, void *newelem);
+void  qh_setaddnth(qhT *qh, setT **setp, countT nth, void *newelem);
 void  qh_setappend(qhT *qh, setT **setp, void *elem);
 void  qh_setappend_set(qhT *qh, setT **setp, setT *setA);
 void  qh_setappend2ndlast(qhT *qh, setT **setp, void *elem);
 void  qh_setcheck(qhT *qh, setT *set, const char *tname, unsigned id);
 void  qh_setcompact(qhT *qh, setT *set);
-setT *qh_setcopy(qhT *qh, setT *set, int extra);
+setT *qh_setcopy(qhT *qh, setT *set, countT extra);
 void *qh_setdel(setT *set, void *elem);
 void *qh_setdellast(setT *set);
-void *qh_setdelnth(qhT *qh, setT *set, int nth);
-void *qh_setdelnthsorted(qhT *qh, setT *set, int nth);
+void *qh_setdelnth(qhT *qh, setT *set, countT nth);
+void *qh_setdelnthsorted(qhT *qh, setT *set, countT nth);
 void *qh_setdelsorted(setT *set, void *newelem);
 setT *qh_setduplicate(qhT *qh, setT *set, int elemsize);
 void **qh_setendpointer(setT *set);
 int   qh_setequal(setT *setA, setT *setB);
 int   qh_setequal_except(setT *setA, void *skipelemA, setT *setB, void *skipelemB);
 int   qh_setequal_skip(setT *setA, int skipA, setT *setB, int skipB);
 void  qh_setfree(qhT *qh, setT **set);
 void  qh_setfree2(qhT *qh, setT **setp, int elemsize);
 void  qh_setfreelong(qhT *qh, setT **set);
 int   qh_setin(setT *set, void *setelem);
-int   qh_setindex(setT *set, void *setelem);
+countT qh_setindex(setT *set, void *setelem);
 void  qh_setlarger(qhT *qh, setT **setp);
 void *qh_setlast(setT *set);
-setT *qh_setnew(qhT *qh, int size);
-setT *qh_setnew_delnthsorted(qhT *qh, setT *set, int size, int nth, int prepend);
+setT *qh_setnew(qhT *qh, countT size);
+setT *qh_setnew_delnthsorted(qhT *qh, setT *set, countT size, countT nth, countT prepend);
 void  qh_setprint(qhT *qh, FILE *fp, const char* string, setT *set);
 void  qh_setreplace(qhT *qh, setT *set, void *oldelem, void *newelem);
-int   qh_setsize(qhT *qh, setT *set);
-setT *qh_settemp(qhT *qh, int setsize);
+countT qh_setsize(qhT *qh, setT *set);
+setT *qh_settemp(qhT *qh, countT setsize);
 void  qh_settempfree(qhT *qh, setT **set);
 void  qh_settempfree_all(qhT *qh);
 setT *qh_settemppop(qhT *qh);
 void  qh_settemppush(qhT *qh, setT *set);
-void  qh_settruncate(qhT *qh, setT *set, int size);
+void  qh_settruncate(qhT *qh, setT *set, countT size);
 int   qh_setunique(qhT *qh, setT **set, void *elem);
-void  qh_setzero(qhT *qh, setT *set, int idx, int size);
+void  qh_setzero(qhT *qh, setT *set, countT idx, countT size);
 
 
 #endif /* qhDEFset */
diff --git a/src/libqhullr/random_r.c b/src/libqhullr/random_r.c
index c2ff5ef..c35702b 100644
--- a/src/libqhullr/random_r.c
+++ b/src/libqhullr/random_r.c
@@ -1,245 +1,245 @@
 /*
  ---------------------------------
 
-   random.c -- utilities
+   random_r.c -- utilities
      Park & Miller's minimimal standard random number generator
      argc/argv conversion
 
-     Used by rbox.  Do not use 'qh' 
+     Used by rbox_r.c  Do not use 'qh' 
 */
 
 #include "libqhull_r.h"
 #include 
 #include 
 #include 
 
 #ifdef _MSC_VER  /* Microsoft Visual C++ -- warning level 4 */
 #pragma warning( disable : 4706)  /* assignment within conditional function */
 #pragma warning( disable : 4996)  /* function was declared deprecated(strcpy, localtime, etc.) */
 #endif
 
 /*---------------------------------
 
  qh_argv_to_command(argc, argv, command, max_size )
 
     build command from argc/argv
     max_size is at least
 
  returns:
     a space-delimited string of options (just as typed)
     returns false if max_size is too short
 
  notes:
     silently removes
     makes option string easy to input and output
     matches qh_argv_to_command_size()
 
     argc may be 0
 */
 int qh_argv_to_command(int argc, char *argv[], char* command, int max_size) {
   int i, remaining;
   char *s;
   *command= '\0';  /* max_size > 0 */
 
   if (argc) {
     if ((s= strrchr( argv[0], '\\')) /* get filename w/o .exe extension */
     || (s= strrchr( argv[0], '/')))
         s++;
     else
         s= argv[0];
     if ((int)strlen(s) < max_size)   /* WARN64 */
         strcpy(command, s);
     else
         goto error_argv;
     if ((s= strstr(command, ".EXE"))
     ||  (s= strstr(command, ".exe")))
         *s= '\0';
   }
   for (i=1; i < argc; i++) {
     s= argv[i];
     remaining= max_size - (int)strlen(command) - (int)strlen(s) - 2;   /* WARN64 */
     if (!*s || strchr(s, ' ')) {
       char *t= command + strlen(command);
       remaining -= 2;
       if (remaining < 0) {
         goto error_argv;
       }
       *t++= ' ';
       *t++= '"';
       while (*s) {
         if (*s == '"') {
           if (--remaining < 0)
             goto error_argv;
           *t++= '\\';
         }
         *t++= *s++;
       }
       *t++= '"';
       *t= '\0';
     }else if (remaining < 0) {
       goto error_argv;
     }else
       strcat(command, " ");
       strcat(command, s);
   }
   return 1;
 
 error_argv:
   return 0;
 } /* argv_to_command */
 
 /*---------------------------------
 
 qh_argv_to_command_size(argc, argv )
 
     return size to allocate for qh_argv_to_command()
 
 notes:
     argc may be 0
     actual size is usually shorter
 */
 int qh_argv_to_command_size(int argc, char *argv[]) {
     unsigned int count= 1; /* null-terminator if argc==0 */
     int i;
     char *s;
 
     for (i=0; i0 && strchr(argv[i], ' ')) {
         count += 2;  /* quote delimiters */
         for (s=argv[i]; *s; s++) {
           if (*s == '"') {
             count++;
           }
         }
       }
     }
     return count;
 } /* argv_to_command_size */
 
 /*---------------------------------
 
   qh_rand()
   qh_srand(qh, seed )
     generate pseudo-random number between 1 and 2^31 -2
 
   notes:
     For qhull and rbox, called from qh_RANDOMint(),etc. [user.h]
 
     From Park & Miller's minimal standard random number generator
       Communications of the ACM, 31:1192-1201, 1988.
     Does not use 0 or 2^31 -1
       this is silently enforced by qh_srand()
     Can make 'Rn' much faster by moving qh_rand to qh_distplane
 */
 
 /* Global variables and constants */
 
 #define qh_rand_a 16807
 #define qh_rand_m 2147483647
 #define qh_rand_q 127773  /* m div a */
 #define qh_rand_r 2836    /* m mod a */
 
 int qh_rand(qhT *qh) {
     int lo, hi, test;
     int seed = qh->last_random;
 
     hi = seed / qh_rand_q;  /* seed div q */
     lo = seed % qh_rand_q;  /* seed mod q */
     test = qh_rand_a * lo - qh_rand_r * hi;
     if (test > 0)
         seed= test;
     else
         seed= test + qh_rand_m;
     qh->last_random= seed;
     /* seed = seed < qh_RANDOMmax/2 ? 0 : qh_RANDOMmax;  for testing */
     /* seed = qh_RANDOMmax;  for testing */
     return seed;
 } /* rand */
 
 void qh_srand(qhT *qh, int seed) {
     if (seed < 1)
         qh->last_random= 1;
     else if (seed >= qh_rand_m)
         qh->last_random= qh_rand_m - 1;
     else
         qh->last_random= seed;
 } /* qh_srand */
 
 /*---------------------------------
 
 qh_randomfactor(qh, scale, offset )
   return a random factor r * scale + offset
 
 notes:
-  qh.RANDOMa/b are defined in global.c
+  qh.RANDOMa/b are defined in global_r.c
   qh_RANDOMint requires 'qh'
 */
 realT qh_randomfactor(qhT *qh, realT scale, realT offset) {
     realT randr;
 
     randr= qh_RANDOMint;
     return randr * scale + offset;
 } /* randomfactor */
 
 /*---------------------------------
 
 qh_randommatrix(qh, buffer, dim, rows )
   generate a random dim X dim matrix in range [-1,1]
   assumes buffer is [dim+1, dim]
 
   returns:
     sets buffer to random numbers
     sets rows to rows of buffer
     sets row[dim] as scratch row
 
   notes:
     qh_RANDOMint requires 'qh'
 */
 void qh_randommatrix(qhT *qh, realT *buffer, int dim, realT **rows) {
     int i, k;
     realT **rowi, *coord, realr;
 
     coord= buffer;
     rowi= rows;
     for (i=0; i < dim; i++) {
         *(rowi++)= coord;
         for (k=0; k < dim; k++) {
             realr= qh_RANDOMint;
             *(coord++)= 2.0 * realr/(qh_RANDOMmax+1) - 1.0;
         }
     }
     *rowi= coord;
 } /* randommatrix */
 
 /*---------------------------------
 
   qh_strtol( s, endp) qh_strtod( s, endp)
     internal versions of strtol() and strtod()
     does not skip trailing spaces
   notes:
     some implementations of strtol()/strtod() skip trailing spaces
 */
 double qh_strtod(const char *s, char **endp) {
   double result;
 
   result= strtod(s, endp);
   if (s < (*endp) && (*endp)[-1] == ' ')
     (*endp)--;
   return result;
 } /* strtod */
 
 int qh_strtol(const char *s, char **endp) {
   int result;
 
   result= (int) strtol(s, endp, 10);     /* WARN64 */
   if (s< (*endp) && (*endp)[-1] == ' ')
     (*endp)--;
   return result;
 } /* strtol */
diff --git a/src/libqhullr/random_r.h b/src/libqhullr/random_r.h
index a8e8c96..a1557be 100644
--- a/src/libqhullr/random_r.h
+++ b/src/libqhullr/random_r.h
@@ -1,34 +1,34 @@
 /*
  ---------------------------------
 
   random.h
     header file for random routines
 
-   see qh-geom.htm and random.c
+   see qh-geom.htm and random_r.c
 
    Copyright (c) 1993-2014 The Geometry Center.
-   $Id: //main/2011/qhull/src/libqhullr/random_r.h#2 $$Change: 1645 $
-   $DateTime: 2014/01/15 12:51:30 $$Author: bbarber $
+   $Id: //main/2011/qhull/src/libqhullr/random_r.h#6 $$Change: 1797 $
+   $DateTime: 2014/12/15 17:23:41 $$Author: bbarber $
 */
 
 #ifndef qhDEFrandom
 #define qhDEFrandom 1
 
 #include "libqhull_r.h"
 
 /*============= prototypes in alphabetical order ======= */
 
 
 int     qh_argv_to_command(int argc, char *argv[], char* command, int max_size);
 int     qh_argv_to_command_size(int argc, char *argv[]);
 int     qh_rand(qhT *qh);
 void    qh_srand(qhT *qh, int seed);
 realT   qh_randomfactor(qhT *qh, realT scale, realT offset);
 void    qh_randommatrix(qhT *qh, realT *buffer, int dim, realT **row);
 int     qh_strtol(const char *s, char **endp);
 double  qh_strtod(const char *s, char **endp);
 
 #endif /* qhDEFrandom */
 
 
 
diff --git a/src/libqhullr/rboxlib_r.c b/src/libqhullr/rboxlib_r.c
index 5f5720d..ec84adf 100644
--- a/src/libqhullr/rboxlib_r.c
+++ b/src/libqhullr/rboxlib_r.c
@@ -1,772 +1,771 @@
 /*
  ---------------------------------
 
-   rboxlib.c
+   rboxlib_r.c
      Generate input points
 
    notes:
-     For documentation, see prompt[] of rbox.c
+     For documentation, see prompt[] of rbox_r.c
      50 points generated for 'rbox D4'
 
    WARNING:
-     incorrect range if qh_RANDOMmax is defined wrong (user.h)
+     incorrect range if qh_RANDOMmax is defined wrong (user_r.h)
 */
 
 #include "random_r.h"
 #include "libqhull_r.h"
 
 #include 
 #include 
 #include 
 #include 
 #include 
 #include 
 #include 
 #include 
 
 #ifdef _MSC_VER  /* Microsoft Visual C++ */
 #pragma warning( disable : 4706)  /* assignment within conditional expression. */
 #pragma warning( disable : 4996)  /* this function (strncat,sprintf,strcpy) or variable may be unsafe. */
 #endif
 
 #define MAXdim 200
 #define PI 3.1415926535897932384
 
 /* ------------------------------ prototypes ----------------*/
 int qh_roundi(qhT *qh, double a);
 void qh_out1(qhT *qh, double a);
 void qh_out2n(qhT *qh, double a, double b);
 void qh_out3n(qhT *qh, double a, double b, double c);
 
 void    qh_fprintf_rbox(qhT *qh, FILE *fp, int msgcode, const char *fmt, ... );
 void    qh_free(void *mem);
 void   *qh_malloc(size_t size);
 int     qh_rand(qhT *qh);
 void    qh_srand(qhT *qh, int seed);
 
-
-/* ------------------------------ globals -------------------*/
-
 /*---------------------------------
 
   qh_rboxpoints(qh, rbox_command )
     Generate points to qh->fout according to rbox options
     Report errors on qh->ferr
 
   returns:
     0 (qh_ERRnone) on success
     1 (qh_ERRinput) on input error
     4 (qh_ERRmem) on memory error
     5 (qh_ERRqhull) on internal error
 
   notes:
-    To avoid stdio, redefine qh_malloc, qh_free, and qh_fprintf_rbox (user.c)
+    To avoid using stdio, redefine qh_malloc, qh_free, and qh_fprintf_rbox (user.c)
 
   design:
     Straight line code (consider defining a struct and functions):
 
     Parse arguments into variables
     Determine the number of points
     Generate the points
 */
 int qh_rboxpoints(qhT *qh, char* rbox_command) {
   int i,j,k;
   int gendim;
   int cubesize, diamondsize, seed=0, count, apex;
   int dim=3 , numpoints= 0, totpoints, addpoints=0;
   int issphere=0, isaxis=0,  iscdd= 0, islens= 0, isregular=0, iswidth=0, addcube=0;
   int isgap=0, isspiral=0, NOcommand= 0, adddiamond=0;
   int israndom=0, istime=0;
   int isbox=0, issimplex=0, issimplex2=0, ismesh=0;
   double width=0.0, gap=0.0, radius= 0.0;
   double coord[MAXdim], offset, meshm=3.0, meshn=4.0, meshr=5.0;
   double *simplex= NULL, *simplexp;
   int nthroot, mult[MAXdim];
   double norm, factor, randr, rangap, lensangle= 0, lensbase= 1;
   double anglediff, angle, x, y, cube= 0.0, diamond= 0.0;
   double box= qh_DEFAULTbox; /* scale all numbers before output */
   double randmax= qh_RANDOMmax;
   char command[200], seedbuf[200];
   char *s= command, *t, *first_point= NULL;
   time_t timedata;
   int exitcode;
 
   exitcode= setjmp(qh->rbox_errexit);
   if (exitcode) {
     /* same code for error exit and normal return */
     if (simplex)
         qh_free(simplex);
     return exitcode;
   }
 
   *command= '\0';
   strncat(command, rbox_command, sizeof(command)-strlen(command)-1);
 
   while (*s && !isspace(*s))  /* skip program name */
     s++;
   while (*s) {
     while (*s && isspace(*s))
       s++;
     if (*s == '-')
       s++;
     if (!*s)
       break;
     if (isdigit(*s)) {
       numpoints= qh_strtol(s, &s);
       continue;
     }
     /* ============= read flags =============== */
     switch (*s++) {
     case 'c':
       addcube= 1;
       t= s;
       while (isspace(*t))
         t++;
       if (*t == 'G')
         cube= qh_strtod(++t, &s);
       break;
     case 'd':
       adddiamond= 1;
       t= s;
       while (isspace(*t))
         t++;
       if (*t == 'G')
         diamond= qh_strtod(++t, &s);
       break;
     case 'h':
       iscdd= 1;
       break;
     case 'l':
       isspiral= 1;
       break;
     case 'n':
       NOcommand= 1;
       break;
     case 'r':
       isregular= 1;
       break;
     case 's':
       issphere= 1;
       break;
     case 't':
       istime= 1;
       if (isdigit(*s)) {
         seed= qh_strtol(s, &s);
         israndom= 0;
       }else
         israndom= 1;
       break;
     case 'x':
       issimplex= 1;
       break;
     case 'y':
       issimplex2= 1;
       break;
     case 'z':
       qh->rbox_isinteger= 1;
       break;
     case 'B':
       box= qh_strtod(s, &s);
       isbox= 1;
       break;
     case 'D':
       dim= qh_strtol(s, &s);
       if (dim < 1
       || dim > MAXdim) {
         qh_fprintf_rbox(qh, qh->ferr, 6189, "rbox error: dimension, D%d, out of bounds (>=%d or <=0)", dim, MAXdim);
         qh_errexit_rbox(qh, qh_ERRinput);
       }
       break;
     case 'G':
       if (isdigit(*s))
         gap= qh_strtod(s, &s);
       else
         gap= 0.5;
       isgap= 1;
       break;
     case 'L':
       if (isdigit(*s))
         radius= qh_strtod(s, &s);
       else
         radius= 10;
       islens= 1;
       break;
     case 'M':
       ismesh= 1;
       if (*s)
         meshn= qh_strtod(s, &s);
       if (*s == ',') {
         ++s;
         meshm= qh_strtod(s, &s);
       }else
         meshm= 0.0;
       if (*s == ',') {
         ++s;
         meshr= qh_strtod(s, &s);
       }else
         meshr= sqrt(meshn*meshn + meshm*meshm);
       if (*s && !isspace(*s)) {
         qh_fprintf_rbox(qh, qh->ferr, 7069, "rbox warning: assuming 'M3,4,5' since mesh args are not integers or reals\n");
         meshn= 3.0, meshm=4.0, meshr=5.0;
       }
       break;
     case 'O':
       qh->rbox_out_offset= qh_strtod(s, &s);
       break;
     case 'P':
       if (!first_point)
         first_point= s-1;
       addpoints++;
       while (*s && !isspace(*s))   /* read points later */
         s++;
       break;
     case 'W':
       width= qh_strtod(s, &s);
       iswidth= 1;
       break;
     case 'Z':
       if (isdigit(*s))
         radius= qh_strtod(s, &s);
       else
         radius= 1.0;
       isaxis= 1;
       break;
     default:
       qh_fprintf_rbox(qh, qh->ferr, 7070, "rbox error: unknown flag at %s.\nExecute 'rbox' without arguments for documentation.\n", s);
       qh_errexit_rbox(qh, qh_ERRinput);
     }
     if (*s && !isspace(*s)) {
       qh_fprintf_rbox(qh, qh->ferr, 7071, "rbox error: missing space between flags at %s.\n", s);
       qh_errexit_rbox(qh, qh_ERRinput);
     }
   }
 
   /* ============= defaults, constants, and sizes =============== */
   if (qh->rbox_isinteger && !isbox)
     box= qh_DEFAULTzbox;
   if (addcube) {
     cubesize= (int)floor(ldexp(1.0,dim)+0.5);
     if (cube == 0.0)
       cube= box;
   }else
     cubesize= 0;
   if (adddiamond) {
     diamondsize= 2*dim;
     if (diamond == 0.0)
       diamond= box;
   }else
     diamondsize= 0;
   if (islens) {
     if (isaxis) {
         qh_fprintf_rbox(qh, qh->ferr, 6190, "rbox error: can not combine 'Ln' with 'Zn'\n");
         qh_errexit_rbox(qh, qh_ERRinput);
     }
     if (radius <= 1.0) {
         qh_fprintf_rbox(qh, qh->ferr, 6191, "rbox error: lens radius %.2g should be greater than 1.0\n",
                radius);
         qh_errexit_rbox(qh, qh_ERRinput);
     }
     lensangle= asin(1.0/radius);
     lensbase= radius * cos(lensangle);
   }
 
   if (!numpoints) {
     if (issimplex2)
         ; /* ok */
     else if (isregular + issimplex + islens + issphere + isaxis + isspiral + iswidth + ismesh) {
         qh_fprintf_rbox(qh, qh->ferr, 6192, "rbox error: missing count\n");
         qh_errexit_rbox(qh, qh_ERRinput);
     }else if (adddiamond + addcube + addpoints)
         ; /* ok */
     else {
         numpoints= 50;  /* ./rbox D4 is the test case */
         issphere= 1;
     }
   }
   if ((issimplex + islens + isspiral + ismesh > 1)
   || (issimplex + issphere + isspiral + ismesh > 1)) {
     qh_fprintf_rbox(qh, qh->ferr, 6193, "rbox error: can only specify one of 'l', 's', 'x', 'Ln', or 'Mn,m,r' ('Ln s' is ok).\n");
     qh_errexit_rbox(qh, qh_ERRinput);
   }
 
   /* ============= print header with total points =============== */
   if (issimplex || ismesh)
     totpoints= numpoints;
   else if (issimplex2)
     totpoints= numpoints+dim+1;
   else if (isregular) {
     totpoints= numpoints;
     if (dim == 2) {
         if (islens)
           totpoints += numpoints - 2;
     }else if (dim == 3) {
         if (islens)
           totpoints += 2 * numpoints;
       else if (isgap)
         totpoints += 1 + numpoints;
       else
         totpoints += 2;
     }
   }else
     totpoints= numpoints + isaxis;
   totpoints += cubesize + diamondsize + addpoints;
 
   /* ============= seed randoms =============== */
   if (istime == 0) {
     for (s=command; *s; s++) {
       if (issimplex2 && *s == 'y') /* make 'y' same seed as 'x' */
         i= 'x';
       else
         i= *s;
       seed= 11*seed + i;
     }
   }else if (israndom) {
     seed= (int)time(&timedata);
     sprintf(seedbuf, " t%d", seed);  /* appends an extra t, not worth removing */
     strncat(command, seedbuf, sizeof(command)-strlen(command)-1);
     t= strstr(command, " t ");
     if (t)
       strcpy(t+1, t+3); /* remove " t " */
   } /* else, seed explicitly set to n */
   qh_RANDOMseed_(qh, seed);
 
   /* ============= print header =============== */
 
   if (iscdd)
       qh_fprintf_rbox(qh, qh->fout, 9391, "%s\nbegin\n        %d %d %s\n",
       NOcommand ? "" : command,
       totpoints, dim+1,
       qh->rbox_isinteger ? "integer" : "real");
   else if (NOcommand)
       qh_fprintf_rbox(qh, qh->fout, 9392, "%d\n%d\n", dim, totpoints);
   else
       qh_fprintf_rbox(qh, qh->fout, 9393, "%d %s\n%d\n", dim, command, totpoints);
 
   /* ============= explicit points =============== */
   if ((s= first_point)) {
     while (s && *s) { /* 'P' */
       count= 0;
       if (iscdd)
         qh_out1(qh, 1.0);
       while (*++s) {
         qh_out1(qh, qh_strtod(s, &s));
         count++;
         if (isspace(*s) || !*s)
           break;
         if (*s != ',') {
           qh_fprintf_rbox(qh, qh->ferr, 6194, "rbox error: missing comma after coordinate in %s\n\n", s);
           qh_errexit_rbox(qh, qh_ERRinput);
         }
       }
       if (count < dim) {
         for (k=dim-count; k--; )
           qh_out1(qh, 0.0);
       }else if (count > dim) {
         qh_fprintf_rbox(qh, qh->ferr, 6195, "rbox error: %d coordinates instead of %d coordinates in %s\n\n",
                   count, dim, s);
         qh_errexit_rbox(qh, qh_ERRinput);
       }
       qh_fprintf_rbox(qh, qh->fout, 9394, "\n");
       while ((s= strchr(s, 'P'))) {
         if (isspace(s[-1]))
           break;
       }
     }
   }
 
   /* ============= simplex distribution =============== */
   if (issimplex+issimplex2) {
     if (!(simplex= (double*)qh_malloc( dim * (dim+1) * sizeof(double)))) {
       qh_fprintf_rbox(qh, qh->ferr, 6196, "rbox error: insufficient memory for simplex\n");
       qh_errexit_rbox(qh, qh_ERRmem); /* qh_ERRmem */
     }
     simplexp= simplex;
     if (isregular) {
       for (i=0; ifout, 9395, "\n");
       }
     }
     for (j=0; jfout, 9396, "\n");
     }
     isregular= 0; /* continue with isbox */
     numpoints= 0;
   }
 
   /* ============= mesh distribution =============== */
   if (ismesh) {
     nthroot= (int)(pow((double)numpoints, 1.0/dim) + 0.99999);
     for (k=dim; k--; )
       mult[k]= 0;
     for (i=0; i < numpoints; i++) {
       for (k=0; k < dim; k++) {
         if (k == 0)
           qh_out1(qh, mult[0] * meshn + mult[1] * (-meshm));
         else if (k == 1)
           qh_out1(qh, mult[0] * meshm + mult[1] * meshn);
         else
           qh_out1(qh, mult[k] * meshr );
       }
       qh_fprintf_rbox(qh, qh->fout, 9397, "\n");
       for (k=0; k < dim; k++) {
         if (++mult[k] < nthroot)
           break;
         mult[k]= 0;
       }
     }
   }
   /* ============= regular points for 's' =============== */
   else if (isregular && !islens) {
     if (dim != 2 && dim != 3) {
       qh_fprintf_rbox(qh, qh->ferr, 6197, "rbox error: regular points can be used only in 2-d and 3-d\n\n");
       qh_errexit_rbox(qh, qh_ERRinput);
     }
     if (!isaxis || radius == 0.0) {
       isaxis= 1;
       radius= 1.0;
     }
     if (dim == 3) {
       if (iscdd)
         qh_out1(qh, 1.0);
       qh_out3n(qh, 0.0, 0.0, -box);
       if (!isgap) {
         if (iscdd)
           qh_out1(qh, 1.0);
         qh_out3n(qh, 0.0, 0.0, box);
       }
     }
     angle= 0.0;
     anglediff= 2.0 * PI/numpoints;
     for (i=0; i < numpoints; i++) {
       angle += anglediff;
       x= radius * cos(angle);
       y= radius * sin(angle);
       if (dim == 2) {
         if (iscdd)
           qh_out1(qh, 1.0);
         qh_out2n(qh, x*box, y*box);
       }else {
         norm= sqrt(1.0 + x*x + y*y);
         if (iscdd)
           qh_out1(qh, 1.0);
         qh_out3n(qh, box*x/norm, box*y/norm, box/norm);
         if (isgap) {
           x *= 1-gap;
           y *= 1-gap;
           norm= sqrt(1.0 + x*x + y*y);
           if (iscdd)
             qh_out1(qh, 1.0);
           qh_out3n(qh, box*x/norm, box*y/norm, box/norm);
         }
       }
     }
   }
   /* ============= regular points for 'r Ln D2' =============== */
   else if (isregular && islens && dim == 2) {
     double cos_0;
 
     angle= lensangle;
     anglediff= 2 * lensangle/(numpoints - 1);
     cos_0= cos(lensangle);
     for (i=0; i < numpoints; i++, angle -= anglediff) {
       x= radius * sin(angle);
       y= radius * (cos(angle) - cos_0);
       if (iscdd)
         qh_out1(qh, 1.0);
       qh_out2n(qh, x*box, y*box);
       if (i != 0 && i != numpoints - 1) {
         if (iscdd)
           qh_out1(qh, 1.0);
         qh_out2n(qh, x*box, -y*box);
       }
     }
   }
   /* ============= regular points for 'r Ln D3' =============== */
   else if (isregular && islens && dim != 2) {
     if (dim != 3) {
       qh_fprintf_rbox(qh, qh->ferr, 6198, "rbox error: regular points can be used only in 2-d and 3-d\n\n");
       qh_errexit_rbox(qh, qh_ERRinput);
     }
     angle= 0.0;
     anglediff= 2* PI/numpoints;
     if (!isgap) {
       isgap= 1;
       gap= 0.5;
     }
     offset= sqrt(radius * radius - (1-gap)*(1-gap)) - lensbase;
     for (i=0; i < numpoints; i++, angle += anglediff) {
       x= cos(angle);
       y= sin(angle);
       if (iscdd)
         qh_out1(qh, 1.0);
       qh_out3n(qh, box*x, box*y, 0.0);
       x *= 1-gap;
       y *= 1-gap;
       if (iscdd)
         qh_out1(qh, 1.0);
       qh_out3n(qh, box*x, box*y, box * offset);
       if (iscdd)
         qh_out1(qh, 1.0);
       qh_out3n(qh, box*x, box*y, -box * offset);
     }
   }
   /* ============= apex of 'Zn' distribution + gendim =============== */
   else {
     if (isaxis) {
       gendim= dim-1;
       if (iscdd)
         qh_out1(qh, 1.0);
       for (j=0; j < gendim; j++)
         qh_out1(qh, 0.0);
       qh_out1(qh, -box);
       qh_fprintf_rbox(qh, qh->fout, 9398, "\n");
     }else if (islens)
       gendim= dim-1;
     else
       gendim= dim;
     /* ============= generate random point in unit cube =============== */
     for (i=0; i < numpoints; i++) {
       norm= 0.0;
       for (j=0; j < gendim; j++) {
         randr= qh_RANDOMint;
         coord[j]= 2.0 * randr/randmax - 1.0;
         norm += coord[j] * coord[j];
       }
       norm= sqrt(norm);
       /* ============= dim-1 point of 'Zn' distribution ========== */
       if (isaxis) {
         if (!isgap) {
           isgap= 1;
           gap= 1.0;
         }
         randr= qh_RANDOMint;
         rangap= 1.0 - gap * randr/randmax;
         factor= radius * rangap / norm;
         for (j=0; jferr, 6199, "rbox error: spiral distribution is available only in 3d\n\n");
-          longjmp(qh->rbox_errexit, qh_ERRinput);
+          qh_errexit_rbox(qh, qh_ERRinput);
         }
         coord[0]= cos(2*PI*i/(numpoints - 1));
         coord[1]= sin(2*PI*i/(numpoints - 1));
         coord[2]= 2.0*(double)i/(double)(numpoints-1) - 1.0;
       /* ============= point of 's' distribution =============== */
       }else if (issphere) {
         factor= 1.0/norm;
         if (iswidth) {
           randr= qh_RANDOMint;
           factor *= 1.0 - width * randr/randmax;
         }
         for (j=0; j randmax/2)
           coord[dim-1]= -coord[dim-1];
       /* ============= project 'Wn' point toward boundary =============== */
       }else if (iswidth && !issphere) {
         j= qh_RANDOMint % gendim;
         if (coord[j] < 0)
           coord[j]= -1.0 - coord[j] * width;
         else
           coord[j]= 1.0 - coord[j] * width;
       }
       /* ============= write point =============== */
       if (iscdd)
         qh_out1(qh, 1.0);
       for (k=0; k < dim; k++)
         qh_out1(qh, coord[k] * box);
       qh_fprintf_rbox(qh, qh->fout, 9399, "\n");
     }
   }
 
   /* ============= write cube vertices =============== */
   if (addcube) {
     for (j=0; j=0; k--) {
         if (j & ( 1 << k))
           qh_out1(qh, cube);
         else
           qh_out1(qh, -cube);
       }
       qh_fprintf_rbox(qh, qh->fout, 9400, "\n");
     }
   }
 
   /* ============= write diamond vertices =============== */
   if (adddiamond) {
     for (j=0; j=0; k--) {
         if (j/2 != k)
           qh_out1(qh, 0.0);
         else if (j & 0x1)
           qh_out1(qh, diamond);
         else
           qh_out1(qh, -diamond);
       }
       qh_fprintf_rbox(qh, qh->fout, 9401, "\n");
     }
   }
 
   if (iscdd)
     qh_fprintf_rbox(qh, qh->fout, 9402, "end\nhull\n");
 
   /* same code for error exit and normal return */
   if (simplex)
     qh_free(simplex);
   return qh_ERRnone;
 } /* rboxpoints */
 
 /*------------------------------------------------
-outxxx - output functions
+outxxx - output functions for qh_rboxpoints
 */
 int qh_roundi(qhT *qh, double a) {
   if (a < 0.0) {
     if (a - 0.5 < INT_MIN) {
       qh_fprintf_rbox(qh, qh->ferr, 6200, "rbox input error: negative coordinate %2.2g is too large.  Reduce 'Bn'\n", a);
       qh_errexit_rbox(qh, qh_ERRinput);
     }
     return (int)(a - 0.5);
   }else {
     if (a + 0.5 > INT_MAX) {
       qh_fprintf_rbox(qh, qh->ferr, 6201, "rbox input error: coordinate %2.2g is too large.  Reduce 'Bn'\n", a);
       qh_errexit_rbox(qh, qh_ERRinput);
     }
     return (int)(a + 0.5);
   }
 } /* qh_roundi */
 
 void qh_out1(qhT *qh, double a) {
 
   if (qh->rbox_isinteger)
     qh_fprintf_rbox(qh, qh->fout, 9403, "%d ", qh_roundi(qh, a+qh->rbox_out_offset));
   else
     qh_fprintf_rbox(qh, qh->fout, 9404, qh_REAL_1, a+qh->rbox_out_offset);
 } /* qh_out1 */
 
 void qh_out2n(qhT *qh, double a, double b) {
 
   if (qh->rbox_isinteger)
     qh_fprintf_rbox(qh, qh->fout, 9405, "%d %d\n", qh_roundi(qh, a+qh->rbox_out_offset), qh_roundi(qh, b+qh->rbox_out_offset));
   else
     qh_fprintf_rbox(qh, qh->fout, 9406, qh_REAL_2n, a+qh->rbox_out_offset, b+qh->rbox_out_offset);
 } /* qh_out2n */
 
 void qh_out3n(qhT *qh, double a, double b, double c) {
 
   if (qh->rbox_isinteger)
     qh_fprintf_rbox(qh, qh->fout, 9407, "%d %d %d\n", qh_roundi(qh, a+qh->rbox_out_offset), qh_roundi(qh, b+qh->rbox_out_offset), qh_roundi(qh, c+qh->rbox_out_offset));
   else
     qh_fprintf_rbox(qh, qh->fout, 9408, qh_REAL_3n, a+qh->rbox_out_offset, b+qh->rbox_out_offset, c+qh->rbox_out_offset);
 } /* qh_out3n */
 
+/*------------------------------------------------
+   Only called from qh_rboxpoints or qh_fprintf_rbox
+   qh_fprintf_rbox is only called from qh_rboxpoints
+*/
 void qh_errexit_rbox(qhT *qh, int exitcode)
 {
-    if(qh)
-      longjmp(qh->rbox_errexit, exitcode);
-    qh_exit(exitcode);
+    longjmp(qh->rbox_errexit, exitcode);
 } /* qh_errexit_rbox */
 
diff --git a/src/libqhullr/stat_r.c b/src/libqhullr/stat_r.c
index 9fa3cb9..0e563df 100644
--- a/src/libqhullr/stat_r.c
+++ b/src/libqhullr/stat_r.c
@@ -1,683 +1,683 @@
 /*
  ---------------------------------
 
-   stat.c
+   stat_r.c
    contains all statistics that are collected for qhull
 
-   see qh-stat.htm and stat.h
+   see qh-stat.htm and stat_r.h
 
    Copyright (c) 1993-2014 The Geometry Center.
-   $Id: //main/2011/qhull/src/libqhullr/stat_r.c#4 $$Change: 1663 $
-   $DateTime: 2014/01/19 17:59:16 $$Author: bbarber $
+   $Id: //main/2011/qhull/src/libqhullr/stat_r.c#6 $$Change: 1797 $
+   $DateTime: 2014/12/15 17:23:41 $$Author: bbarber $
 */
 
-#include "qhull_r.h"
+#include "qhull_ra.h"
 
 /*========== functions in alphabetic order ================*/
 
 /*---------------------------------
 
   qh_allstatA()
     define statistics in groups of 20
 
   notes:
     (otherwise, 'gcc -O2' uses too much memory)
     uses qhstat.next 
 */
 void qh_allstatA(qhT *qh) {
 
    /* zdef_(type,name,doc,average) */
   zzdef_(zdoc, Zdoc2, "precision statistics", -1);
   zdef_(zinc, Znewvertex, NULL, -1);
   zdef_(wadd, Wnewvertex, "ave. distance of a new vertex to a facet(!0s)", Znewvertex);
   zzdef_(wmax, Wnewvertexmax, "max. distance of a new vertex to a facet", -1);
   zdef_(wmax, Wvertexmax, "max. distance of an output vertex to a facet", -1);
   zdef_(wmin, Wvertexmin, "min. distance of an output vertex to a facet", -1);
   zdef_(wmin, Wmindenom, "min. denominator in hyperplane computation", -1);
 
   qh->qhstat.precision= qh->qhstat.next;  /* call qh_precision for each of these */
   zzdef_(zdoc, Zdoc3, "precision problems (corrected unless 'Q0' or an error)", -1);
   zzdef_(zinc, Zcoplanarridges, "coplanar half ridges in output", -1);
   zzdef_(zinc, Zconcaveridges, "concave half ridges in output", -1);
   zzdef_(zinc, Zflippedfacets, "flipped facets", -1);
   zzdef_(zinc, Zcoplanarhorizon, "coplanar horizon facets for new vertices", -1);
   zzdef_(zinc, Zcoplanarpart, "coplanar points during partitioning", -1);
   zzdef_(zinc, Zminnorm, "degenerate hyperplanes recomputed with gaussian elimination", -1);
   zzdef_(zinc, Znearlysingular, "nearly singular or axis-parallel hyperplanes", -1);
   zzdef_(zinc, Zback0, "zero divisors during back substitute", -1);
   zzdef_(zinc, Zgauss0, "zero divisors during gaussian elimination", -1);
   zzdef_(zinc, Zmultiridge, "ridges with multiple neighbors", -1);
 }
 void qh_allstatB(qhT *qh) {
   zzdef_(zdoc, Zdoc1, "summary information", -1);
   zdef_(zinc, Zvertices, "number of vertices in output", -1);
   zdef_(zinc, Znumfacets, "number of facets in output", -1);
   zdef_(zinc, Znonsimplicial, "number of non-simplicial facets in output", -1);
   zdef_(zinc, Znowsimplicial, "number of simplicial facets that were merged", -1);
   zdef_(zinc, Znumridges, "number of ridges in output", -1);
   zdef_(zadd, Znumridges, "average number of ridges per facet", Znumfacets);
   zdef_(zmax, Zmaxridges, "maximum number of ridges", -1);
   zdef_(zadd, Znumneighbors, "average number of neighbors per facet", Znumfacets);
   zdef_(zmax, Zmaxneighbors, "maximum number of neighbors", -1);
   zdef_(zadd, Znumvertices, "average number of vertices per facet", Znumfacets);
   zdef_(zmax, Zmaxvertices, "maximum number of vertices", -1);
   zdef_(zadd, Znumvneighbors, "average number of neighbors per vertex", Zvertices);
   zdef_(zmax, Zmaxvneighbors, "maximum number of neighbors", -1);
   zdef_(wadd, Wcpu, "cpu seconds for qhull after input", -1);
   zdef_(zinc, Ztotvertices, "vertices created altogether", -1);
   zzdef_(zinc, Zsetplane, "facets created altogether", -1);
   zdef_(zinc, Ztotridges, "ridges created altogether", -1);
   zdef_(zinc, Zpostfacets, "facets before post merge", -1);
   zdef_(zadd, Znummergetot, "average merges per facet(at most 511)", Znumfacets);
   zdef_(zmax, Znummergemax, "  maximum merges for a facet(at most 511)", -1);
   zdef_(zinc, Zangle, NULL, -1);
   zdef_(wadd, Wangle, "average angle(cosine) of facet normals for all ridges", Zangle);
   zdef_(wmax, Wanglemax, "  maximum angle(cosine) of facet normals across a ridge", -1);
   zdef_(wmin, Wanglemin, "  minimum angle(cosine) of facet normals across a ridge", -1);
   zdef_(wadd, Wareatot, "total area of facets", -1);
   zdef_(wmax, Wareamax, "  maximum facet area", -1);
   zdef_(wmin, Wareamin, "  minimum facet area", -1);
 }
 void qh_allstatC(qhT *qh) {
   zdef_(zdoc, Zdoc9, "build hull statistics", -1);
   zzdef_(zinc, Zprocessed, "points processed", -1);
   zzdef_(zinc, Zretry, "retries due to precision problems", -1);
   zdef_(wmax, Wretrymax, "  max. random joggle", -1);
   zdef_(zmax, Zmaxvertex, "max. vertices at any one time", -1);
   zdef_(zinc, Ztotvisible, "ave. visible facets per iteration", Zprocessed);
   zdef_(zinc, Zinsidevisible, "  ave. visible facets without an horizon neighbor", Zprocessed);
   zdef_(zadd, Zvisfacettot,  "  ave. facets deleted per iteration", Zprocessed);
   zdef_(zmax, Zvisfacetmax,  "    maximum", -1);
   zdef_(zadd, Zvisvertextot, "ave. visible vertices per iteration", Zprocessed);
   zdef_(zmax, Zvisvertexmax, "    maximum", -1);
   zdef_(zinc, Ztothorizon, "ave. horizon facets per iteration", Zprocessed);
   zdef_(zadd, Znewfacettot,  "ave. new or merged facets per iteration", Zprocessed);
   zdef_(zmax, Znewfacetmax,  "    maximum(includes initial simplex)", -1);
   zdef_(wadd, Wnewbalance, "average new facet balance", Zprocessed);
   zdef_(wadd, Wnewbalance2, "  standard deviation", -1);
   zdef_(wadd, Wpbalance, "average partition balance", Zpbalance);
   zdef_(wadd, Wpbalance2, "  standard deviation", -1);
   zdef_(zinc, Zpbalance, "  number of trials", -1);
   zdef_(zinc, Zsearchpoints, "searches of all points for initial simplex", -1);
   zdef_(zinc, Zdetsimplex, "determinants computed(area & initial hull)", -1);
   zdef_(zinc, Znoarea, "determinants not computed because vertex too low", -1);
   zdef_(zinc, Znotmax, "points ignored(!above max_outside)", -1);
   zdef_(zinc, Znotgood, "points ignored(!above a good facet)", -1);
   zdef_(zinc, Znotgoodnew, "points ignored(didn't create a good new facet)", -1);
   zdef_(zinc, Zgoodfacet, "good facets found", -1);
   zzdef_(zinc, Znumvisibility, "distance tests for facet visibility", -1);
   zdef_(zinc, Zdistvertex, "distance tests to report minimum vertex", -1);
   zzdef_(zinc, Ztotcheck, "points checked for facets' outer planes", -1);
   zzdef_(zinc, Zcheckpart, "  ave. distance tests per check", Ztotcheck);
 }
 void qh_allstatD(qhT *qh) {
   zdef_(zinc, Zvisit, "resets of visit_id", -1);
   zdef_(zinc, Zvvisit, "  resets of vertex_visit", -1);
   zdef_(zmax, Zvisit2max, "  max visit_id/2", -1);
   zdef_(zmax, Zvvisit2max, "  max vertex_visit/2", -1);
 
   zdef_(zdoc, Zdoc4, "partitioning statistics(see previous for outer planes)", -1);
   zzdef_(zadd, Zdelvertextot, "total vertices deleted", -1);
   zdef_(zmax, Zdelvertexmax, "    maximum vertices deleted per iteration", -1);
   zdef_(zinc, Zfindbest, "calls to findbest", -1);
   zdef_(zadd, Zfindbesttot, " ave. facets tested", Zfindbest);
   zdef_(zmax, Zfindbestmax, " max. facets tested", -1);
   zdef_(zadd, Zfindcoplanar, " ave. coplanar search", Zfindbest);
   zdef_(zinc, Zfindnew, "calls to findbestnew", -1);
   zdef_(zadd, Zfindnewtot, " ave. facets tested", Zfindnew);
   zdef_(zmax, Zfindnewmax, " max. facets tested", -1);
   zdef_(zinc, Zfindnewjump, " ave. clearly better", Zfindnew);
   zdef_(zinc, Zfindnewsharp, " calls due to qh_sharpnewfacets", -1);
   zdef_(zinc, Zfindhorizon, "calls to findhorizon", -1);
   zdef_(zadd, Zfindhorizontot, " ave. facets tested", Zfindhorizon);
   zdef_(zmax, Zfindhorizonmax, " max. facets tested", -1);
   zdef_(zinc, Zfindjump,       " ave. clearly better", Zfindhorizon);
   zdef_(zinc, Zparthorizon, " horizon facets better than bestfacet", -1);
   zdef_(zinc, Zpartangle, "angle tests for repartitioned coplanar points", -1);
   zdef_(zinc, Zpartflip, "  repartitioned coplanar points for flipped orientation", -1);
 }
 void qh_allstatE(qhT *qh) {
   zdef_(zinc, Zpartinside, "inside points", -1);
   zdef_(zinc, Zpartnear, "  inside points kept with a facet", -1);
   zdef_(zinc, Zcoplanarinside, "  inside points that were coplanar with a facet", -1);
   zdef_(zinc, Zbestlower, "calls to findbestlower", -1);
   zdef_(zinc, Zbestlowerv, "  with search of vertex neighbors", -1);
   zdef_(wadd, Wmaxout, "difference in max_outside at final check", -1);
   zzdef_(zinc, Zpartitionall, "distance tests for initial partition", -1);
   zdef_(zinc, Ztotpartition, "partitions of a point", -1);
   zzdef_(zinc, Zpartition, "distance tests for partitioning", -1);
   zzdef_(zinc, Zdistcheck, "distance tests for checking flipped facets", -1);
   zzdef_(zinc, Zdistconvex, "distance tests for checking convexity", -1);
   zdef_(zinc, Zdistgood, "distance tests for checking good point", -1);
   zdef_(zinc, Zdistio, "distance tests for output", -1);
   zdef_(zinc, Zdiststat, "distance tests for statistics", -1);
   zdef_(zinc, Zdistplane, "total number of distance tests", -1);
   zdef_(zinc, Ztotpartcoplanar, "partitions of coplanar points or deleted vertices", -1);
   zzdef_(zinc, Zpartcoplanar, "   distance tests for these partitions", -1);
   zdef_(zinc, Zcomputefurthest, "distance tests for computing furthest", -1);
 }
 void qh_allstatE2(qhT *qh) {
   zdef_(zdoc, Zdoc5, "statistics for matching ridges", -1);
   zdef_(zinc, Zhashlookup, "total lookups for matching ridges of new facets", -1);
   zdef_(zinc, Zhashtests, "average number of tests to match a ridge", Zhashlookup);
   zdef_(zinc, Zhashridge, "total lookups of subridges(duplicates and boundary)", -1);
   zdef_(zinc, Zhashridgetest, "average number of tests per subridge", Zhashridge);
   zdef_(zinc, Zdupsame, "duplicated ridges in same merge cycle", -1);
   zdef_(zinc, Zdupflip, "duplicated ridges with flipped facets", -1);
 
   zdef_(zdoc, Zdoc6, "statistics for determining merges", -1);
   zdef_(zinc, Zangletests, "angles computed for ridge convexity", -1);
   zdef_(zinc, Zbestcentrum, "best merges used centrum instead of vertices",-1);
   zzdef_(zinc, Zbestdist, "distance tests for best merge", -1);
   zzdef_(zinc, Zcentrumtests, "distance tests for centrum convexity", -1);
   zzdef_(zinc, Zdistzero, "distance tests for checking simplicial convexity", -1);
   zdef_(zinc, Zcoplanarangle, "coplanar angles in getmergeset", -1);
   zdef_(zinc, Zcoplanarcentrum, "coplanar centrums in getmergeset", -1);
   zdef_(zinc, Zconcaveridge, "concave ridges in getmergeset", -1);
 }
 void qh_allstatF(qhT *qh) {
   zdef_(zdoc, Zdoc7, "statistics for merging", -1);
   zdef_(zinc, Zpremergetot, "merge iterations", -1);
   zdef_(zadd, Zmergeinittot, "ave. initial non-convex ridges per iteration", Zpremergetot);
   zdef_(zadd, Zmergeinitmax, "  maximum", -1);
   zdef_(zadd, Zmergesettot, "  ave. additional non-convex ridges per iteration", Zpremergetot);
   zdef_(zadd, Zmergesetmax, "  maximum additional in one pass", -1);
   zdef_(zadd, Zmergeinittot2, "initial non-convex ridges for post merging", -1);
   zdef_(zadd, Zmergesettot2, "  additional non-convex ridges", -1);
   zdef_(wmax, Wmaxoutside, "max distance of vertex or coplanar point above facet(w/roundoff)", -1);
   zdef_(wmin, Wminvertex, "max distance of merged vertex below facet(or roundoff)", -1);
   zdef_(zinc, Zwidefacet, "centrums frozen due to a wide merge", -1);
   zdef_(zinc, Zwidevertices, "centrums frozen due to extra vertices", -1);
   zzdef_(zinc, Ztotmerge, "total number of facets or cycles of facets merged", -1);
   zdef_(zinc, Zmergesimplex, "merged a simplex", -1);
   zdef_(zinc, Zonehorizon, "simplices merged into coplanar horizon", -1);
   zzdef_(zinc, Zcyclehorizon, "cycles of facets merged into coplanar horizon", -1);
   zzdef_(zadd, Zcyclefacettot, "  ave. facets per cycle", Zcyclehorizon);
   zdef_(zmax, Zcyclefacetmax, "  max. facets", -1);
   zdef_(zinc, Zmergeintohorizon, "new facets merged into horizon", -1);
   zdef_(zinc, Zmergenew, "new facets merged", -1);
   zdef_(zinc, Zmergehorizon, "horizon facets merged into new facets", -1);
   zdef_(zinc, Zmergevertex, "vertices deleted by merging", -1);
   zdef_(zinc, Zcyclevertex, "vertices deleted by merging into coplanar horizon", -1);
   zdef_(zinc, Zdegenvertex, "vertices deleted by degenerate facet", -1);
   zdef_(zinc, Zmergeflipdup, "merges due to flipped facets in duplicated ridge", -1);
   zdef_(zinc, Zneighbor, "merges due to redundant neighbors", -1);
   zdef_(zadd, Ztestvneighbor, "non-convex vertex neighbors", -1);
 }
 void qh_allstatG(qhT *qh) {
   zdef_(zinc, Zacoplanar, "merges due to angle coplanar facets", -1);
   zdef_(wadd, Wacoplanartot, "  average merge distance", Zacoplanar);
   zdef_(wmax, Wacoplanarmax, "  maximum merge distance", -1);
   zdef_(zinc, Zcoplanar, "merges due to coplanar facets", -1);
   zdef_(wadd, Wcoplanartot, "  average merge distance", Zcoplanar);
   zdef_(wmax, Wcoplanarmax, "  maximum merge distance", -1);
   zdef_(zinc, Zconcave, "merges due to concave facets", -1);
   zdef_(wadd, Wconcavetot, "  average merge distance", Zconcave);
   zdef_(wmax, Wconcavemax, "  maximum merge distance", -1);
   zdef_(zinc, Zavoidold, "coplanar/concave merges due to avoiding old merge", -1);
   zdef_(wadd, Wavoidoldtot, "  average merge distance", Zavoidold);
   zdef_(wmax, Wavoidoldmax, "  maximum merge distance", -1);
   zdef_(zinc, Zdegen, "merges due to degenerate facets", -1);
   zdef_(wadd, Wdegentot, "  average merge distance", Zdegen);
   zdef_(wmax, Wdegenmax, "  maximum merge distance", -1);
   zdef_(zinc, Zflipped, "merges due to removing flipped facets", -1);
   zdef_(wadd, Wflippedtot, "  average merge distance", Zflipped);
   zdef_(wmax, Wflippedmax, "  maximum merge distance", -1);
   zdef_(zinc, Zduplicate, "merges due to duplicated ridges", -1);
   zdef_(wadd, Wduplicatetot, "  average merge distance", Zduplicate);
   zdef_(wmax, Wduplicatemax, "  maximum merge distance", -1);
 }
 void qh_allstatH(qhT *qh) {
   zdef_(zdoc, Zdoc8, "renamed vertex statistics", -1);
   zdef_(zinc, Zrenameshare, "renamed vertices shared by two facets", -1);
   zdef_(zinc, Zrenamepinch, "renamed vertices in a pinched facet", -1);
   zdef_(zinc, Zrenameall, "renamed vertices shared by multiple facets", -1);
   zdef_(zinc, Zfindfail, "rename failures due to duplicated ridges", -1);
   zdef_(zinc, Zdupridge, "  duplicate ridges detected", -1);
   zdef_(zinc, Zdelridge, "deleted ridges due to renamed vertices", -1);
   zdef_(zinc, Zdropneighbor, "dropped neighbors due to renamed vertices", -1);
   zdef_(zinc, Zdropdegen, "degenerate facets due to dropped neighbors", -1);
   zdef_(zinc, Zdelfacetdup, "  facets deleted because of no neighbors", -1);
   zdef_(zinc, Zremvertex, "vertices removed from facets due to no ridges", -1);
   zdef_(zinc, Zremvertexdel, "  deleted", -1);
   zdef_(zinc, Zintersectnum, "vertex intersections for locating redundant vertices", -1);
   zdef_(zinc, Zintersectfail, "intersections failed to find a redundant vertex", -1);
   zdef_(zinc, Zintersect, "intersections found redundant vertices", -1);
   zdef_(zadd, Zintersecttot, "   ave. number found per vertex", Zintersect);
   zdef_(zmax, Zintersectmax, "   max. found for a vertex", -1);
   zdef_(zinc, Zvertexridge, NULL, -1);
   zdef_(zadd, Zvertexridgetot, "  ave. number of ridges per tested vertex", Zvertexridge);
   zdef_(zmax, Zvertexridgemax, "  max. number of ridges per tested vertex", -1);
 
   zdef_(zdoc, Zdoc10, "memory usage statistics(in bytes)", -1);
   zdef_(zadd, Zmemfacets, "for facets and their normals, neighbor and vertex sets", -1);
   zdef_(zadd, Zmemvertices, "for vertices and their neighbor sets", -1);
   zdef_(zadd, Zmempoints, "for input points and outside and coplanar sets",-1);
   zdef_(zadd, Zmemridges, "for ridges and their vertex sets", -1);
 } /* allstat */
 
 void qh_allstatI(qhT *qh) {
   qh->qhstat.vridges= qh->qhstat.next;
   zzdef_(zdoc, Zdoc11, "Voronoi ridge statistics", -1);
   zzdef_(zinc, Zridge, "non-simplicial Voronoi vertices for all ridges", -1);
   zzdef_(wadd, Wridge, "  ave. distance to ridge", Zridge);
   zzdef_(wmax, Wridgemax, "  max. distance to ridge", -1);
   zzdef_(zinc, Zridgemid, "bounded ridges", -1);
   zzdef_(wadd, Wridgemid, "  ave. distance of midpoint to ridge", Zridgemid);
   zzdef_(wmax, Wridgemidmax, "  max. distance of midpoint to ridge", -1);
   zzdef_(zinc, Zridgeok, "bounded ridges with ok normal", -1);
   zzdef_(wadd, Wridgeok, "  ave. angle to ridge", Zridgeok);
   zzdef_(wmax, Wridgeokmax, "  max. angle to ridge", -1);
   zzdef_(zinc, Zridge0, "bounded ridges with near-zero normal", -1);
   zzdef_(wadd, Wridge0, "  ave. angle to ridge", Zridge0);
   zzdef_(wmax, Wridge0max, "  max. angle to ridge", -1);
 
   zdef_(zdoc, Zdoc12, "Triangulation statistics(Qt)", -1);
   zdef_(zinc, Ztricoplanar, "non-simplicial facets triangulated", -1);
   zdef_(zadd, Ztricoplanartot, "  ave. new facets created(may be deleted)", Ztricoplanar);
   zdef_(zmax, Ztricoplanarmax, "  max. new facets created", -1);
   zdef_(zinc, Ztrinull, "null new facets deleted(duplicated vertex)", -1);
   zdef_(zinc, Ztrimirror, "mirrored pairs of new facets deleted(same vertices)", -1);
   zdef_(zinc, Ztridegen, "degenerate new facets in output(same ridge)", -1);
 } /* allstat */
 
 /*---------------------------------
 
   qh_allstatistics()
     reset printed flag for all statistics
 */
 void qh_allstatistics(qhT *qh) {
   int i;
 
   for(i=ZEND; i--; )
     qh->qhstat.printed[i]= False;
 } /* allstatistics */
 
 #if qh_KEEPstatistics
 /*---------------------------------
 
   qh_collectstatistics()
     collect statistics for qh.facet_list
 
 */
 void qh_collectstatistics(qhT *qh) {
   facetT *facet, *neighbor, **neighborp;
   vertexT *vertex, **vertexp;
   realT dotproduct, dist;
   int sizneighbors, sizridges, sizvertices, i;
 
   qh->old_randomdist= qh->RANDOMdist;
   qh->RANDOMdist= False;
   zval_(Zmempoints)= qh->num_points * qh->normal_size +
                              sizeof(qhT) + sizeof(qhstatT);
   zval_(Zmemfacets)= 0;
   zval_(Zmemridges)= 0;
   zval_(Zmemvertices)= 0;
   zval_(Zangle)= 0;
   wval_(Wangle)= 0.0;
   zval_(Znumridges)= 0;
   zval_(Znumfacets)= 0;
   zval_(Znumneighbors)= 0;
   zval_(Znumvertices)= 0;
   zval_(Znumvneighbors)= 0;
   zval_(Znummergetot)= 0;
   zval_(Znummergemax)= 0;
   zval_(Zvertices)= qh->num_vertices - qh_setsize(qh, qh->del_vertices);
   if (qh->MERGING || qh->APPROXhull || qh->JOGGLEmax < REALmax/2)
     wmax_(Wmaxoutside, qh->max_outside);
   if (qh->MERGING)
     wmin_(Wminvertex, qh->min_vertex);
   FORALLfacets
     facet->seen= False;
   if (qh->DELAUNAY) {
     FORALLfacets {
       if (facet->upperdelaunay != qh->UPPERdelaunay)
         facet->seen= True; /* remove from angle statistics */
     }
   }
   FORALLfacets {
     if (facet->visible && qh->NEWfacets)
       continue;
     sizvertices= qh_setsize(qh, facet->vertices);
     sizneighbors= qh_setsize(qh, facet->neighbors);
     sizridges= qh_setsize(qh, facet->ridges);
     zinc_(Znumfacets);
     zadd_(Znumvertices, sizvertices);
     zmax_(Zmaxvertices, sizvertices);
     zadd_(Znumneighbors, sizneighbors);
     zmax_(Zmaxneighbors, sizneighbors);
     zadd_(Znummergetot, facet->nummerge);
     i= facet->nummerge; /* avoid warnings */
     zmax_(Znummergemax, i);
     if (!facet->simplicial) {
       if (sizvertices == qh->hull_dim) {
         zinc_(Znowsimplicial);
       }else {
         zinc_(Znonsimplicial);
       }
     }
     if (sizridges) {
       zadd_(Znumridges, sizridges);
       zmax_(Zmaxridges, sizridges);
     }
     zadd_(Zmemfacets, sizeof(facetT) + qh->normal_size + 2*sizeof(setT)
        + SETelemsize * (sizneighbors + sizvertices));
     if (facet->ridges) {
       zadd_(Zmemridges,
          sizeof(setT) + SETelemsize * sizridges + sizridges *
          (sizeof(ridgeT) + sizeof(setT) + SETelemsize * (qh->hull_dim-1))/2);
     }
     if (facet->outsideset)
       zadd_(Zmempoints, sizeof(setT) + SETelemsize * qh_setsize(qh, facet->outsideset));
     if (facet->coplanarset)
       zadd_(Zmempoints, sizeof(setT) + SETelemsize * qh_setsize(qh, facet->coplanarset));
     if (facet->seen) /* Delaunay upper envelope */
       continue;
     facet->seen= True;
     FOREACHneighbor_(facet) {
       if (neighbor == qh_DUPLICATEridge || neighbor == qh_MERGEridge
           || neighbor->seen || !facet->normal || !neighbor->normal)
         continue;
       dotproduct= qh_getangle(qh, facet->normal, neighbor->normal);
       zinc_(Zangle);
       wadd_(Wangle, dotproduct);
       wmax_(Wanglemax, dotproduct)
       wmin_(Wanglemin, dotproduct)
     }
     if (facet->normal) {
       FOREACHvertex_(facet->vertices) {
         zinc_(Zdiststat);
         qh_distplane(qh, vertex->point, facet, &dist);
         wmax_(Wvertexmax, dist);
         wmin_(Wvertexmin, dist);
       }
     }
   }
   FORALLvertices {
     if (vertex->deleted)
       continue;
     zadd_(Zmemvertices, sizeof(vertexT));
     if (vertex->neighbors) {
       sizneighbors= qh_setsize(qh, vertex->neighbors);
       zadd_(Znumvneighbors, sizneighbors);
       zmax_(Zmaxvneighbors, sizneighbors);
       zadd_(Zmemvertices, sizeof(vertexT) + SETelemsize * sizneighbors);
     }
   }
   qh->RANDOMdist= qh->old_randomdist;
 } /* collectstatistics */
 #endif /* qh_KEEPstatistics */
 
 /*---------------------------------
 
   qh_initstatistics(qh)
     initialize statistics
     Requires
 
   notes:
   NOerrors -- qh_initstatistics can not use qh_errexit(), qh_fprintf, or qh.ferr  
   On first call, only qhmem.ferr is defined.  qh_memalloc is not setup.  
   Also invoked by QhullQh().
 */
 void qh_initstatistics(qhT *qh) {
   int i;
   realT realx;
   int intx;
 
   qh->qhstat.next= 0;
   qh_allstatA(qh);
   qh_allstatB(qh);
   qh_allstatC(qh);
   qh_allstatD(qh);
   qh_allstatE(qh);
   qh_allstatE2(qh);
   qh_allstatF(qh);
   qh_allstatG(qh);
   qh_allstatH(qh);
   qh_allstatI(qh);
   if (qh->qhstat.next > (int)sizeof(qh->qhstat.id)) {
     qh_fprintf(qh, qh->qhmem.ferr, 6184, "qhull error (qh_initstatistics): increase size of qhstat.id[].\n\
       qhstat.next %d should be <= sizeof(qh->qhstat.id) %d\n", qh->qhstat.next, (int)sizeof(qh->qhstat.id));
 #if 0 /* for locating error, Znumridges should be duplicated */
     for(i=0; i < ZEND; i++) {
       int j;
       for(j=i+1; j < ZEND; j++) {
         if (qh->qhstat.id[i] == qh->qhstat.id[j]) {
           qh_fprintf(qh, qh->qhmem.ferr, 6185, "qhull error (qh_initstatistics): duplicated statistic %d at indices %d and %d\n",
               qh->qhstat.id[i], i, j);
         }
       }
     }
 #endif
     qh_exit(qh_ERRqhull);  /* can not use qh_errexit() */
   }
   qh->qhstat.init[zinc].i= 0;
   qh->qhstat.init[zadd].i= 0;
   qh->qhstat.init[zmin].i= INT_MAX;
   qh->qhstat.init[zmax].i= INT_MIN;
   qh->qhstat.init[wadd].r= 0;
   qh->qhstat.init[wmin].r= REALmax;
   qh->qhstat.init[wmax].r= -REALmax;
   for(i=0; i < ZEND; i++) {
     if (qh->qhstat.type[i] > ZTYPEreal) {
       realx= qh->qhstat.init[(unsigned char)(qh->qhstat.type[i])].r;
       qh->qhstat.stats[i].r= realx;
     }else if (qh->qhstat.type[i] != zdoc) {
       intx= qh->qhstat.init[(unsigned char)(qh->qhstat.type[i])].i;
       qh->qhstat.stats[i].i= intx;
     }
   }
 } /* initstatistics */
 
 /*---------------------------------
 
   qh_newstats(qh, )
     returns True if statistics for zdoc
 
   returns:
     next zdoc
 */
 boolT qh_newstats(qhT *qh, int idx, int *nextindex) {
   boolT isnew= False;
   int start, i;
 
   if (qh->qhstat.type[qh->qhstat.id[idx]] == zdoc)
     start= idx+1;
   else
     start= idx;
   for(i= start; i < qh->qhstat.next && qh->qhstat.type[qh->qhstat.id[i]] != zdoc; i++) {
     if (!qh_nostatistic(qh, qh->qhstat.id[i]) && !qh->qhstat.printed[qh->qhstat.id[i]])
         isnew= True;
   }
   *nextindex= i;
   return isnew;
 } /* newstats */
 
 /*---------------------------------
 
   qh_nostatistic(qh, index )
     true if no statistic to print
 */
 boolT qh_nostatistic(qhT *qh, int i) {
 
   if ((qh->qhstat.type[i] > ZTYPEreal
        &&qh->qhstat.stats[i].r == qh->qhstat.init[(unsigned char)(qh->qhstat.type[i])].r)
       || (qh->qhstat.type[i] < ZTYPEreal
           &&qh->qhstat.stats[i].i == qh->qhstat.init[(unsigned char)(qh->qhstat.type[i])].i))
     return True;
   return False;
 } /* nostatistic */
 
 #if qh_KEEPstatistics
 /*---------------------------------
 
   qh_printallstatistics(qh, fp, string )
     print all statistics with header 'string'
 */
 void qh_printallstatistics(qhT *qh, FILE *fp, const char *string) {
 
   qh_allstatistics(qh);
   qh_collectstatistics(qh);
   qh_printstatistics(qh, fp, string);
   qh_memstatistics(qh, fp);
 }
 
 
 /*---------------------------------
 
   qh_printstatistics(qh, fp, string )
     print statistics to a file with header 'string'
     skips statistics with qhstat.printed[] (reset with qh_allstatistics)
 
   see:
     qh_printallstatistics()
 */
 void qh_printstatistics(qhT *qh, FILE *fp, const char *string) {
   int i, k;
   realT ave;
 
   if (qh->num_points != qh->num_vertices) {
     wval_(Wpbalance)= 0;
     wval_(Wpbalance2)= 0;
   }else
     wval_(Wpbalance2)= qh_stddev(zval_(Zpbalance), wval_(Wpbalance),
                                  wval_(Wpbalance2), &ave);
   wval_(Wnewbalance2)= qh_stddev(zval_(Zprocessed), wval_(Wnewbalance),
                                  wval_(Wnewbalance2), &ave);
   qh_fprintf(qh, fp, 9350, "\n\
 %s\n\
  qhull invoked by: %s | %s\n%s with options:\n%s\n", string, qh->rbox_command,
      qh->qhull_command, qh_version, qh->qhull_options);
   qh_fprintf(qh, fp, 9351, "\nprecision constants:\n\
  %6.2g max. abs. coordinate in the (transformed) input('Qbd:n')\n\
  %6.2g max. roundoff error for distance computation('En')\n\
  %6.2g max. roundoff error for angle computations\n\
  %6.2g min. distance for outside points ('Wn')\n\
  %6.2g min. distance for visible facets ('Vn')\n\
  %6.2g max. distance for coplanar facets ('Un')\n\
  %6.2g max. facet width for recomputing centrum and area\n\
 ",
   qh->MAXabs_coord, qh->DISTround, qh->ANGLEround, qh->MINoutside,
         qh->MINvisible, qh->MAXcoplanar, qh->WIDEfacet);
   if (qh->KEEPnearinside)
     qh_fprintf(qh, fp, 9352, "\
  %6.2g max. distance for near-inside points\n", qh->NEARinside);
   if (qh->premerge_cos < REALmax/2) qh_fprintf(qh, fp, 9353, "\
  %6.2g max. cosine for pre-merge angle\n", qh->premerge_cos);
   if (qh->PREmerge) qh_fprintf(qh, fp, 9354, "\
  %6.2g radius of pre-merge centrum\n", qh->premerge_centrum);
   if (qh->postmerge_cos < REALmax/2) qh_fprintf(qh, fp, 9355, "\
  %6.2g max. cosine for post-merge angle\n", qh->postmerge_cos);
   if (qh->POSTmerge) qh_fprintf(qh, fp, 9356, "\
  %6.2g radius of post-merge centrum\n", qh->postmerge_centrum);
   qh_fprintf(qh, fp, 9357, "\
  %6.2g max. distance for merging two simplicial facets\n\
  %6.2g max. roundoff error for arithmetic operations\n\
  %6.2g min. denominator for divisions\n\
   zero diagonal for Gauss: ", qh->ONEmerge, REALepsilon, qh->MINdenom);
   for(k=0; k < qh->hull_dim; k++)
     qh_fprintf(qh, fp, 9358, "%6.2e ", qh->NEARzero[k]);
   qh_fprintf(qh, fp, 9359, "\n\n");
   for(i=0 ; i < qh->qhstat.next; )
     qh_printstats(qh, fp, i, &i);
 } /* printstatistics */
 #endif /* qh_KEEPstatistics */
 
 /*---------------------------------
 
   qh_printstatlevel(qh, fp, id )
     print level information for a statistic
 
   notes:
     nop if id >= ZEND, printed, or same as initial value
 */
 void qh_printstatlevel(qhT *qh, FILE *fp, int id, int start) {
 #define NULLfield "       "
 
   if (id >= ZEND || qh->qhstat.printed[id])
     return;
   if (qh->qhstat.type[id] == zdoc) {
     qh_fprintf(qh, fp, 9360, "%s\n", qh->qhstat.doc[id]);
     return;
   }
   start= 0; /* not used */
   if (qh_nostatistic(qh, id) || !qh->qhstat.doc[id])
     return;
   qh->qhstat.printed[id]= True;
   if (qh->qhstat.count[id] != -1
       && qh->qhstat.stats[(unsigned char)(qh->qhstat.count[id])].i == 0)
     qh_fprintf(qh, fp, 9361, " *0 cnt*");
   else if (qh->qhstat.type[id] >= ZTYPEreal && qh->qhstat.count[id] == -1)
     qh_fprintf(qh, fp, 9362, "%7.2g", qh->qhstat.stats[id].r);
   else if (qh->qhstat.type[id] >= ZTYPEreal && qh->qhstat.count[id] != -1)
     qh_fprintf(qh, fp, 9363, "%7.2g", qh->qhstat.stats[id].r/ qh->qhstat.stats[(unsigned char)(qh->qhstat.count[id])].i);
   else if (qh->qhstat.type[id] < ZTYPEreal && qh->qhstat.count[id] == -1)
     qh_fprintf(qh, fp, 9364, "%7d", qh->qhstat.stats[id].i);
   else if (qh->qhstat.type[id] < ZTYPEreal && qh->qhstat.count[id] != -1)
     qh_fprintf(qh, fp, 9365, "%7.3g", (realT) qh->qhstat.stats[id].i / qh->qhstat.stats[(unsigned char)(qh->qhstat.count[id])].i);
   qh_fprintf(qh, fp, 9366, " %s\n", qh->qhstat.doc[id]);
 } /* printstatlevel */
 
 
 /*---------------------------------
 
   qh_printstats(qh, fp, index, nextindex )
     print statistics for a zdoc group
 
   returns:
     next zdoc if non-null
 */
 void qh_printstats(qhT *qh, FILE *fp, int idx, int *nextindex) {
   int j, nexti;
 
   if (qh_newstats(qh, idx, &nexti)) {
     qh_fprintf(qh, fp, 9367, "\n");
     for (j=idx; jqhstat.id[j], 0);
   }
   if (nextindex)
     *nextindex= nexti;
 } /* printstats */
 
 #if qh_KEEPstatistics
 
 /*---------------------------------
 
   qh_stddev(num, tot, tot2, ave )
     compute the standard deviation and average from statistics
 
     tot2 is the sum of the squares
   notes:
     computes r.m.s.:
       (x-ave)^2
       == x^2 - 2x tot/num +   (tot/num)^2
       == tot2 - 2 tot tot/num + tot tot/num
       == tot2 - tot ave
 */
 realT qh_stddev(int num, realT tot, realT tot2, realT *ave) {
   realT stddev;
 
   *ave= tot/num;
   stddev= sqrt(tot2/num - *ave * *ave);
   return stddev;
 } /* stddev */
 
 #endif /* qh_KEEPstatistics */
 
 #if !qh_KEEPstatistics
 void    qh_collectstatistics(qhT *qh) {}
 void    qh_printallstatistics(qhT *qh, FILE *fp, char *string) {};
 void    qh_printstatistics(qhT *qh, FILE *fp, char *string) {}
 #endif
 
diff --git a/src/libqhullr/stat_r.h b/src/libqhullr/stat_r.h
index fa6149b..f86f221 100644
--- a/src/libqhullr/stat_r.h
+++ b/src/libqhullr/stat_r.h
@@ -1,523 +1,523 @@
 /*
  ---------------------------------
 
-   stat.h
+   stat_r.h
      contains all statistics that are collected for qhull
 
-   see qh-stat.htm and stat.c
+   see qh-stat.htm and stat_r.c
 
    Copyright (c) 1993-2014 The Geometry Center.
-   $Id: //main/2011/qhull/src/libqhullr/stat_r.h#2 $$Change: 1645 $
-   $DateTime: 2014/01/15 12:51:30 $$Author: bbarber $
+   $Id: //main/2011/qhull/src/libqhullr/stat_r.h#6 $$Change: 1797 $
+   $DateTime: 2014/12/15 17:23:41 $$Author: bbarber $
 
    recompile qhull if you change this file
 
    Integer statistics are Z* while real statistics are W*.
 
    define MAYdebugx to call a routine at every statistic event
 
 */
 
 #ifndef qhDEFstat
 #define qhDEFstat 1
 
 /* Depends on realT.  Do not include libqhull_r to avoid circular dependency */
 
 #ifndef DEFqhT
 #define DEFqhT 1
 typedef struct qhT qhT;         /* Defined by libqhull_r.h */
 #endif
 
 #ifndef DEFqhstatT
 #define DEFqhstatT 1
 typedef struct qhstatT qhstatT; /* Defined here */
 #endif
 
 /*---------------------------------
 
   qh_KEEPstatistics
     0 turns off statistic gathering (except zzdef/zzinc/zzadd/zzval/wwval)
 */
 #ifndef qh_KEEPstatistics
 #define qh_KEEPstatistics 1
 #endif
 
 /*---------------------------------
 
   Zxxx for integers, Wxxx for reals
 
   notes:
-    be sure that all statistics are defined in stat.c
+    be sure that all statistics are defined in stat_r.c
       otherwise initialization may core dump
     can pick up all statistics by:
       grep '[zw].*_[(][ZW]' *.c >z.x
     remove trailers with query">-
     remove leaders with  query-replace-regexp [ ^I]+  (
 */
 #if qh_KEEPstatistics
 enum qh_statistics {     /* alphabetical after Z/W */
     Zacoplanar,
     Wacoplanarmax,
     Wacoplanartot,
     Zangle,
     Wangle,
     Wanglemax,
     Wanglemin,
     Zangletests,
     Wareatot,
     Wareamax,
     Wareamin,
     Zavoidold,
     Wavoidoldmax,
     Wavoidoldtot,
     Zback0,
     Zbestcentrum,
     Zbestdist,
     Zbestlower,
     Zbestlowerv,
     Zcentrumtests,
     Zcheckpart,
     Zcomputefurthest,
     Zconcave,
     Wconcavemax,
     Wconcavetot,
     Zconcaveridges,
     Zconcaveridge,
     Zcoplanar,
     Wcoplanarmax,
     Wcoplanartot,
     Zcoplanarangle,
     Zcoplanarcentrum,
     Zcoplanarhorizon,
     Zcoplanarinside,
     Zcoplanarpart,
     Zcoplanarridges,
     Wcpu,
     Zcyclefacetmax,
     Zcyclefacettot,
     Zcyclehorizon,
     Zcyclevertex,
     Zdegen,
     Wdegenmax,
     Wdegentot,
     Zdegenvertex,
     Zdelfacetdup,
     Zdelridge,
     Zdelvertextot,
     Zdelvertexmax,
     Zdetsimplex,
     Zdistcheck,
     Zdistconvex,
     Zdistgood,
     Zdistio,
     Zdistplane,
     Zdiststat,
     Zdistvertex,
     Zdistzero,
     Zdoc1,
     Zdoc2,
     Zdoc3,
     Zdoc4,
     Zdoc5,
     Zdoc6,
     Zdoc7,
     Zdoc8,
     Zdoc9,
     Zdoc10,
     Zdoc11,
     Zdoc12,
     Zdropdegen,
     Zdropneighbor,
     Zdupflip,
     Zduplicate,
     Wduplicatemax,
     Wduplicatetot,
     Zdupridge,
     Zdupsame,
     Zflipped,
     Wflippedmax,
     Wflippedtot,
     Zflippedfacets,
     Zfindbest,
     Zfindbestmax,
     Zfindbesttot,
     Zfindcoplanar,
     Zfindfail,
     Zfindhorizon,
     Zfindhorizonmax,
     Zfindhorizontot,
     Zfindjump,
     Zfindnew,
     Zfindnewmax,
     Zfindnewtot,
     Zfindnewjump,
     Zfindnewsharp,
     Zgauss0,
     Zgoodfacet,
     Zhashlookup,
     Zhashridge,
     Zhashridgetest,
     Zhashtests,
     Zinsidevisible,
     Zintersect,
     Zintersectfail,
     Zintersectmax,
     Zintersectnum,
     Zintersecttot,
     Zmaxneighbors,
     Wmaxout,
     Wmaxoutside,
     Zmaxridges,
     Zmaxvertex,
     Zmaxvertices,
     Zmaxvneighbors,
     Zmemfacets,
     Zmempoints,
     Zmemridges,
     Zmemvertices,
     Zmergeflipdup,
     Zmergehorizon,
     Zmergeinittot,
     Zmergeinitmax,
     Zmergeinittot2,
     Zmergeintohorizon,
     Zmergenew,
     Zmergesettot,
     Zmergesetmax,
     Zmergesettot2,
     Zmergesimplex,
     Zmergevertex,
     Wmindenom,
     Wminvertex,
     Zminnorm,
     Zmultiridge,
     Znearlysingular,
     Zneighbor,
     Wnewbalance,
     Wnewbalance2,
     Znewfacettot,
     Znewfacetmax,
     Znewvertex,
     Wnewvertex,
     Wnewvertexmax,
     Znoarea,
     Znonsimplicial,
     Znowsimplicial,
     Znotgood,
     Znotgoodnew,
     Znotmax,
     Znumfacets,
     Znummergemax,
     Znummergetot,
     Znumneighbors,
     Znumridges,
     Znumvertices,
     Znumvisibility,
     Znumvneighbors,
     Zonehorizon,
     Zpartangle,
     Zpartcoplanar,
     Zpartflip,
     Zparthorizon,
     Zpartinside,
     Zpartition,
     Zpartitionall,
     Zpartnear,
     Zpbalance,
     Wpbalance,
     Wpbalance2,
     Zpostfacets,
     Zpremergetot,
     Zprocessed,
     Zremvertex,
     Zremvertexdel,
     Zrenameall,
     Zrenamepinch,
     Zrenameshare,
     Zretry,
     Wretrymax,
     Zridge,
     Wridge,
     Wridgemax,
     Zridge0,
     Wridge0,
     Wridge0max,
     Zridgemid,
     Wridgemid,
     Wridgemidmax,
     Zridgeok,
     Wridgeok,
     Wridgeokmax,
     Zsearchpoints,
     Zsetplane,
     Ztestvneighbor,
     Ztotcheck,
     Ztothorizon,
     Ztotmerge,
     Ztotpartcoplanar,
     Ztotpartition,
     Ztotridges,
     Ztotvertices,
     Ztotvisible,
     Ztricoplanar,
     Ztricoplanarmax,
     Ztricoplanartot,
     Ztridegen,
     Ztrimirror,
     Ztrinull,
     Wvertexmax,
     Wvertexmin,
     Zvertexridge,
     Zvertexridgetot,
     Zvertexridgemax,
     Zvertices,
     Zvisfacettot,
     Zvisfacetmax,
     Zvisit,
     Zvisit2max,
     Zvisvertextot,
     Zvisvertexmax,
     Zvvisit,
     Zvvisit2max,
     Zwidefacet,
     Zwidevertices,
     ZEND};
 
 /*---------------------------------
 
   Zxxx/Wxxx statistics that remain defined if qh_KEEPstatistics=0
 
   notes:
     be sure to use zzdef, zzinc, etc. with these statistics (no double checking!)
 */
 #else
 enum qh_statistics {     /* for zzdef etc. macros */
   Zback0,
   Zbestdist,
   Zcentrumtests,
   Zcheckpart,
   Zconcaveridges,
   Zcoplanarhorizon,
   Zcoplanarpart,
   Zcoplanarridges,
   Zcyclefacettot,
   Zcyclehorizon,
   Zdelvertextot,
   Zdistcheck,
   Zdistconvex,
   Zdistzero,
   Zdoc1,
   Zdoc2,
   Zdoc3,
   Zdoc11,
   Zflippedfacets,
   Zgauss0,
   Zminnorm,
   Zmultiridge,
   Znearlysingular,
   Wnewvertexmax,
   Znumvisibility,
   Zpartcoplanar,
   Zpartition,
   Zpartitionall,
   Zprocessed,
   Zretry,
   Zridge,
   Wridge,
   Wridgemax,
   Zridge0,
   Wridge0,
   Wridge0max,
   Zridgemid,
   Wridgemid,
   Wridgemidmax,
   Zridgeok,
   Wridgeok,
   Wridgeokmax,
   Zsetplane,
   Ztotcheck,
   Ztotmerge,
     ZEND};
 #endif
 
 /*---------------------------------
 
   ztype
     the type of a statistic sets its initial value.
 
   notes:
     The type should be the same as the macro for collecting the statistic
 */
 enum ztypes {zdoc,zinc,zadd,zmax,zmin,ZTYPEreal,wadd,wmax,wmin,ZTYPEend};
 
 /*========== macros and constants =============*/
 
 /*----------------------------------
 
   MAYdebugx
     define as maydebug() to be called frequently for error trapping
 */
 #define MAYdebugx
 
 /*----------------------------------
 
   zzdef_, zdef_( type, name, doc, -1)
     define a statistic (assumes 'qhstat.next= 0;')
 
   zdef_( type, name, doc, count)
     define an averaged statistic
     printed as name/count
 */
 #define zzdef_(stype,name,string,cnt) qh->qhstat.id[qh->qhstat.next++]=name; \
    qh->qhstat.doc[name]= string; qh->qhstat.count[name]= cnt; qh->qhstat.type[name]= stype
 #if qh_KEEPstatistics
 #define zdef_(stype,name,string,cnt) qh->qhstat.id[qh->qhstat.next++]=name; \
    qh->qhstat.doc[name]= string; qh->qhstat.count[name]= cnt; qh->qhstat.type[name]= stype
 #else
 #define zdef_(type,name,doc,count)
 #endif
 
 /*----------------------------------
 
   zzinc_( name ), zinc_( name)
     increment an integer statistic
 */
 #define zzinc_(id) {MAYdebugx; qh->qhstat.stats[id].i++;}
 #if qh_KEEPstatistics
 #define zinc_(id) {MAYdebugx; qh->qhstat.stats[id].i++;}
 #else
 #define zinc_(id) {}
 #endif
 
 /*----------------------------------
 
   zzadd_( name, value ), zadd_( name, value ), wadd_( name, value )
     add value to an integer or real statistic
 */
 #define zzadd_(id, val) {MAYdebugx; qh->qhstat.stats[id].i += (val);}
 #define wwadd_(id, val) {MAYdebugx; qh->qhstat.stats[id].r += (val);}
 #if qh_KEEPstatistics
 #define zadd_(id, val) {MAYdebugx; qh->qhstat.stats[id].i += (val);}
 #define wadd_(id, val) {MAYdebugx; qh->qhstat.stats[id].r += (val);}
 #else
 #define zadd_(id, val) {}
 #define wadd_(id, val) {}
 #endif
 
 /*----------------------------------
 
   zzval_( name ), zval_( name ), wwval_( name )
     set or return value of a statistic
 */
 #define zzval_(id) ((qh->qhstat.stats[id]).i)
 #define wwval_(id) ((qh->qhstat.stats[id]).r)
 #if qh_KEEPstatistics
 #define zval_(id) ((qh->qhstat.stats[id]).i)
 #define wval_(id) ((qh->qhstat.stats[id]).r)
 #else
 #define zval_(id) qh->qhstat.tempi
 #define wval_(id) qh->qhstat.tempr
 #endif
 
 /*----------------------------------
 
   zmax_( id, val ), wmax_( id, value )
     maximize id with val
 */
 #define wwmax_(id, val) {MAYdebugx; maximize_(qh->qhstat.stats[id].r,(val));}
 #if qh_KEEPstatistics
 #define zmax_(id, val) {MAYdebugx; maximize_(qh->qhstat.stats[id].i,(val));}
 #define wmax_(id, val) {MAYdebugx; maximize_(qh->qhstat.stats[id].r,(val));}
 #else
 #define zmax_(id, val) {}
 #define wmax_(id, val) {}
 #endif
 
 /*----------------------------------
 
   zmin_( id, val ), wmin_( id, value )
     minimize id with val
 */
 #if qh_KEEPstatistics
 #define zmin_(id, val) {MAYdebugx; minimize_(qh->qhstat.stats[id].i,(val));}
 #define wmin_(id, val) {MAYdebugx; minimize_(qh->qhstat.stats[id].r,(val));}
 #else
 #define zmin_(id, val) {}
 #define wmin_(id, val) {}
 #endif
 
-/*================== stat.h types ==============*/
+/*================== stat_r.h types ==============*/
 
 
 /*----------------------------------
 
   intrealT
     union of integer and real, used for statistics
 */
 typedef union intrealT intrealT;    /* union of int and realT */
 union intrealT {
     int i;
     realT r;
 };
 
 /*----------------------------------
 
   qhstat
     Data structure for statistics, similar to qh and qhrbox
 
     Allocated as part of qhT (libqhull_r.h)
 */
 
 struct qhstatT {
   intrealT   stats[ZEND];     /* integer and real statistics */
   unsigned   char id[ZEND+10]; /* id's in print order */
   const char *doc[ZEND];       /* array of documentation strings */
   short int  count[ZEND];     /* -1 if none, else index of count to use */
   char       type[ZEND];      /* type, see ztypes above */
   char       printed[ZEND];   /* true, if statistic has been printed */
   intrealT   init[ZTYPEend];  /* initial values by types, set initstatistics */
 
   int        next;            /* next index for zdef_ */
   int        precision;       /* index for precision problems */
   int        vridges;         /* index for Voronoi ridges */
   int        tempi;
   realT      tempr;
 };
 
 /*========== function prototypes ===========*/
 
 void    qh_allstatA(qhT *qh);
 void    qh_allstatB(qhT *qh);
 void    qh_allstatC(qhT *qh);
 void    qh_allstatD(qhT *qh);
 void    qh_allstatE(qhT *qh);
 void    qh_allstatE2(qhT *qh);
 void    qh_allstatF(qhT *qh);
 void    qh_allstatG(qhT *qh);
 void    qh_allstatH(qhT *qh);
 void    qh_allstatI(qhT *qh);
 void    qh_allstatistics(qhT *qh);
 void    qh_collectstatistics(qhT *qh);
 void    qh_initstatistics(qhT *qh);
 boolT   qh_newstats(qhT *qh, int idx, int *nextindex);
 boolT   qh_nostatistic(qhT *qh, int i);
 void    qh_printallstatistics(qhT *qh, FILE *fp, const char *string);
 void    qh_printstatistics(qhT *qh, FILE *fp, const char *string);
 void    qh_printstatlevel(qhT *qh, FILE *fp, int id, int start);
 void    qh_printstats(qhT *qh, FILE *fp, int idx, int *nextindex);
 realT   qh_stddev(int num, realT tot, realT tot2, realT *ave);
 
 #endif   /* qhDEFstat */
diff --git a/src/libqhullr/user_r.c b/src/libqhullr/user_r.c
index f52e650..85c5cab 100644
--- a/src/libqhullr/user_r.c
+++ b/src/libqhullr/user_r.c
@@ -1,512 +1,513 @@
 /*
  ---------------------------------
 
    user.c
    user redefinable functions
 
-   see user2.c for qh_fprintf, qh_malloc, qh_free
+   see user2_r.c for qh_fprintf, qh_malloc, qh_free
 
    see README.txt  see COPYING.txt for copyright information.
 
-   see libqhull.h for data structures, macros, and user-callable functions.
+   see libqhull_r.h for data structures, macros, and user-callable functions.
 
-   see user_eg.c, unix.c, and qhull_interface.cpp for examples.
+   see user_eg_r.c, unix_r.c, and qhull_interface.cpp for examples.
 
    see user.h for user-definable constants
 
-      use qh_NOmem in mem.h to turn off memory management
+      use qh_NOmem in mem_r.h to turn off memory management
       use qh_NOmerge in user.h to turn off facet merging
       set qh_KEEPstatistics in user.h to 0 to turn off statistics
 
    This is unsupported software.  You're welcome to make changes,
    but you're on your own if something goes wrong.  Use 'Tc' to
    check frequently.  Usually qhull will report an error if
    a data structure becomes inconsistent.  If so, it also reports
    the last point added to the hull, e.g., 102.  You can then trace
    the execution of qhull with "T4P102".
 
    Please report any errors that you fix to qhull@qhull.org
 
    call_qhull is a template for calling qhull from within your application
 
    if you recompile and load this module, then user.o will not be loaded
    from qhull.a
 
    you can add additional quick allocation sizes in qh_user_memsizes
 
    if the other functions here are redefined to not use qh_print...,
-   then io.o will not be loaded from qhull.a.  See user_eg.c for an
+   then io.o will not be loaded from qhull.a.  See user_eg_r.c for an
    example.  We recommend keeping io.o for the extra debugging
    information it supplies.
 */
 
-#include "qhull_r.h"
+#include "qhull_ra.h"
 
 #include 
 
 /*---------------------------------
 
   qh_call_qhull(qh, void )
     template for calling qhull from inside your program
     remove #if 0, #endif to compile
 
   returns:
-    exit code(see qh_ERR... in libqhull.h)
+    exit code(see qh_ERR... in libqhull_r.h)
     all memory freed
 
   notes:
     This can be called any number of times.
 
   see:
     qh_call_qhull_once()
 
 */
 #if 0
 {
   int dim;                  /* dimension of points */
   int numpoints;            /* number of points */
   coordT *points;           /* array of coordinates for each point */
   boolT ismalloc;           /* True if qhull should free points in qh_freeqhull() or reallocation */
   char flags[]= "qhull Tv"; /* option flags for qhull, see qh_opt.htm */
   FILE *outfile= stdout;    /* output from qh_produce_output(qh)
                                use NULL to skip qh_produce_output(qh) */
   FILE *errfile= stderr;    /* error messages from qhull code */
   int exitcode;             /* 0 if no error from qhull */
   facetT *facet;            /* set by FORALLfacets */
   int curlong, totlong;     /* memory remaining after qh_memfreeshort */
 
   /* initialize dim, numpoints, points[], ismalloc here */
   exitcode= qh_new_qhull(qh, dim, numpoints, points, ismalloc,
                       flags, outfile, errfile);
   if (!exitcode) {                  /* if no error */
     /* 'qh->facet_list' contains the convex hull */
     FORALLfacets {
        /* ... your code ... */
     }
   }
   qh_freeqhull(qh, !qh_ALL);
   qh_memfreeshort(qh, &curlong, &totlong);
   if (curlong || totlong)
     qh_fprintf(qh, errfile, 7068, "qhull internal warning (main): did not free %d bytes of long memory(%d pieces)\n", totlong, curlong);
 }
 #endif
 
 /*---------------------------------
 
   qh_new_qhull(qh, dim, numpoints, points, ismalloc, qhull_cmd, outfile, errfile )
     build new qhull data structure and return exitcode (0 if no errors)
 
   notes:
     do not modify points until finished with results.
       The qhull data structure contains pointers into the points array.
     do not call qhull functions before qh_new_qhull().
       The qhull data structure is not initialized until qh_new_qhull().
 
     outfile may be null
     qhull_cmd must start with "qhull "
     projects points to a new point array for Delaunay triangulations ('d' and 'v')
     transforms points into a new point array for halfspace intersection ('H')
 
   see:
     user_eg.c for an example
 */
 int qh_new_qhull(qhT *qh, int dim, int numpoints, coordT *points, boolT ismalloc,
                 char *qhull_cmd, FILE *outfile, FILE *errfile) {
   int exitcode, hulldim;
   boolT new_ismalloc;
   static boolT firstcall = True;
   coordT *new_points;
 
   if (firstcall) {
     qh_meminit(qh, errfile);
     firstcall= False;
   }
   if (strncmp(qhull_cmd,"qhull ", (size_t)6)) {
     qh_fprintf(qh, errfile, 6186, "qhull error (qh_new_qhull): start qhull_cmd argument with \"qhull \"\n");
     qh_exit(qh_ERRinput);
   }
   qh_initqhull_start(qh, NULL, outfile, errfile);
   trace1((qh, qh->ferr, 1044, "qh_new_qhull: build new Qhull for %d %d-d points with %s\n", numpoints, dim, qhull_cmd));
   exitcode = setjmp(qh->errexit);
   if (!exitcode)
   {
     qh->NOerrexit = False;
     qh_initflags(qh, qhull_cmd);
     if (qh->DELAUNAY)
       qh->PROJECTdelaunay= True;
     if (qh->HALFspace) {
       /* points is an array of halfspaces,
          the last coordinate of each halfspace is its offset */
       hulldim= dim-1;
       qh_setfeasible(qh, hulldim);
       new_points= qh_sethalfspace_all(qh, dim, numpoints, points, qh->feasible_point);
       new_ismalloc= True;
       if (ismalloc)
         qh_free(points);
     }else {
       hulldim= dim;
       new_points= points;
       new_ismalloc= ismalloc;
     }
     qh_init_B(qh, new_points, numpoints, hulldim, new_ismalloc);
     qh_qhull(qh);
     qh_check_output(qh);
     if (outfile) {
       qh_produce_output(qh);
     }else {
       qh_prepare_output(qh);
     }
     if (qh->VERIFYoutput && !qh->STOPpoint && !qh->STOPcone)
       qh_check_points(qh);
   }
   qh->NOerrexit = True;
   return exitcode;
 } /* new_qhull */
 
 /*---------------------------------
 
   qh_errexit(qh, exitcode, facet, ridge )
     report and exit from an error
     report facet and ridge if non-NULL
     reports useful information such as last point processed
     set qh.FORCEoutput to print neighborhood of facet
 
   see:
-    qh_errexit2() in libqhull.c for printing 2 facets
+    qh_errexit2() in libqhull_r.c for printing 2 facets
 
   design:
     check for error within error processing
     compute qh.hulltime
     print facet and ridge (if any)
     report commandString, options, qh.furthest_id
     print summary and statistics (including precision statistics)
     if qh_ERRsingular
       print help text for singular data set
     exit program via long jump (if defined) or exit()
 */
 void qh_errexit(qhT *qh, int exitcode, facetT *facet, ridgeT *ridge) {
 
   if (qh->ERREXITcalled) {
     qh_fprintf(qh, qh->ferr, 8126, "\nqhull error while processing previous error.  Exit program\n");
     qh_exit(qh_ERRqhull);
   }
   qh->ERREXITcalled= True;
   if (!qh->QHULLfinished)
     qh->hulltime= qh_CPUclock - qh->hulltime;
   qh_errprint(qh, "ERRONEOUS", facet, NULL, ridge, NULL);
   qh_fprintf(qh, qh->ferr, 8127, "\nWhile executing: %s | %s\n", qh->rbox_command, qh->qhull_command);
   qh_fprintf(qh, qh->ferr, 8128, "Options selected for Qhull %s:\n%s\n", qh_version, qh->qhull_options);
   if (qh->furthest_id >= 0) {
     qh_fprintf(qh, qh->ferr, 8129, "Last point added to hull was p%d.", qh->furthest_id);
     if (zzval_(Ztotmerge))
       qh_fprintf(qh, qh->ferr, 8130, "  Last merge was #%d.", zzval_(Ztotmerge));
     if (qh->QHULLfinished)
       qh_fprintf(qh, qh->ferr, 8131, "\nQhull has finished constructing the hull.");
     else if (qh->POSTmerging)
       qh_fprintf(qh, qh->ferr, 8132, "\nQhull has started post-merging.");
     qh_fprintf(qh, qh->ferr, 8133, "\n");
   }
   if (qh->FORCEoutput && (qh->QHULLfinished || (!facet && !ridge)))
     qh_produce_output(qh);
   else if (exitcode != qh_ERRinput) {
     if (exitcode != qh_ERRsingular && zzval_(Zsetplane) > qh->hull_dim+1) {
       qh_fprintf(qh, qh->ferr, 8134, "\nAt error exit:\n");
       qh_printsummary(qh, qh->ferr);
       if (qh->PRINTstatistics) {
         qh_collectstatistics(qh);
         qh_printstatistics(qh, qh->ferr, "at error exit");
         qh_memstatistics(qh, qh->ferr);
       }
     }
     if (qh->PRINTprecision)
       qh_printstats(qh, qh->ferr, qh->qhstat.precision, NULL);
   }
   if (!exitcode)
     exitcode= qh_ERRqhull;
   else if (exitcode == qh_ERRsingular)
     qh_printhelp_singular(qh, qh->ferr);
   else if (exitcode == qh_ERRprec && !qh->PREmerge)
     qh_printhelp_degenerate(qh, qh->ferr);
   if (qh->NOerrexit) {
     qh_fprintf(qh, qh->ferr, 6187, "qhull error while ending program.  Exit program\n");
     qh_exit(qh_ERRqhull);
   }
   qh->ERREXITcalled= False;
   qh->NOerrexit= True;
+  qh->ALLOWrestart= False;  /* longjmp will undo qh_build_withrestart */
   longjmp(qh->errexit, exitcode);
 } /* errexit */
 
 
 /*---------------------------------
 
   qh_errprint(qh, fp, string, atfacet, otherfacet, atridge, atvertex )
     prints out the information of facets and ridges to fp
     also prints neighbors and geomview output
 
   notes:
     except for string, any parameter may be NULL
 */
 void qh_errprint(qhT *qh, const char *string, facetT *atfacet, facetT *otherfacet, ridgeT *atridge, vertexT *atvertex) {
   int i;
 
   if (atfacet) {
     qh_fprintf(qh, qh->ferr, 8135, "%s FACET:\n", string);
     qh_printfacet(qh, qh->ferr, atfacet);
   }
   if (otherfacet) {
     qh_fprintf(qh, qh->ferr, 8136, "%s OTHER FACET:\n", string);
     qh_printfacet(qh, qh->ferr, otherfacet);
   }
   if (atridge) {
     qh_fprintf(qh, qh->ferr, 8137, "%s RIDGE:\n", string);
     qh_printridge(qh, qh->ferr, atridge);
     if (atridge->top && atridge->top != atfacet && atridge->top != otherfacet)
       qh_printfacet(qh, qh->ferr, atridge->top);
     if (atridge->bottom
         && atridge->bottom != atfacet && atridge->bottom != otherfacet)
       qh_printfacet(qh, qh->ferr, atridge->bottom);
     if (!atfacet)
       atfacet= atridge->top;
     if (!otherfacet)
       otherfacet= otherfacet_(atridge, atfacet);
   }
   if (atvertex) {
     qh_fprintf(qh, qh->ferr, 8138, "%s VERTEX:\n", string);
     qh_printvertex(qh, qh->ferr, atvertex);
   }
   if (qh->fout && qh->FORCEoutput && atfacet && !qh->QHULLfinished && !qh->IStracing) {
     qh_fprintf(qh, qh->ferr, 8139, "ERRONEOUS and NEIGHBORING FACETS to output\n");
     for (i=0; i < qh_PRINTEND; i++)  /* use fout for geomview output */
       qh_printneighborhood(qh, qh->fout, qh->PRINTout[i], atfacet, otherfacet,
                             !qh_ALL);
   }
 } /* errprint */
 
 
 /*---------------------------------
 
   qh_printfacetlist(qh, fp, facetlist, facets, printall )
     print all fields for a facet list and/or set of facets to fp
     if !printall,
       only prints good facets
 
   notes:
     also prints all vertices
 */
 void qh_printfacetlist(qhT *qh, facetT *facetlist, setT *facets, boolT printall) {
   facetT *facet, **facetp;
 
   qh_printbegin(qh, qh->ferr, qh_PRINTfacets, facetlist, facets, printall);
   FORALLfacet_(facetlist)
     qh_printafacet(qh, qh->ferr, qh_PRINTfacets, facet, printall);
   FOREACHfacet_(facets)
     qh_printafacet(qh, qh->ferr, qh_PRINTfacets, facet, printall);
   qh_printend(qh, qh->ferr, qh_PRINTfacets, facetlist, facets, printall);
 } /* printfacetlist */
 
 
 /*---------------------------------
 
   qh_printhelp_degenerate(qh, fp )
     prints descriptive message for precision error
 
   notes:
     no message if qh_QUICKhelp
 */
 void qh_printhelp_degenerate(qhT *qh, FILE *fp) {
 
   if (qh->MERGEexact || qh->PREmerge || qh->JOGGLEmax < REALmax/2)
     qh_fprintf(qh, fp, 9368, "\n\
 A Qhull error has occurred.  Qhull should have corrected the above\n\
 precision error.  Please send the input and all of the output to\n\
 qhull_bug@qhull.org\n");
   else if (!qh_QUICKhelp) {
     qh_fprintf(qh, fp, 9369, "\n\
 Precision problems were detected during construction of the convex hull.\n\
 This occurs because convex hull algorithms assume that calculations are\n\
 exact, but floating-point arithmetic has roundoff errors.\n\
 \n\
 To correct for precision problems, do not use 'Q0'.  By default, Qhull\n\
 selects 'C-0' or 'Qx' and merges non-convex facets.  With option 'QJ',\n\
 Qhull joggles the input to prevent precision problems.  See \"Imprecision\n\
 in Qhull\" (qh-impre.htm).\n\
 \n\
 If you use 'Q0', the output may include\n\
 coplanar ridges, concave ridges, and flipped facets.  In 4-d and higher,\n\
 Qhull may produce a ridge with four neighbors or two facets with the same \n\
 vertices.  Qhull reports these events when they occur.  It stops when a\n\
 concave ridge, flipped facet, or duplicate facet occurs.\n");
 #if REALfloat
     qh_fprintf(qh, fp, 9370, "\
 \n\
 Qhull is currently using single precision arithmetic.  The following\n\
 will probably remove the precision problems:\n\
   - recompile qhull for realT precision(#define REALfloat 0 in user.h).\n");
 #endif
     if (qh->DELAUNAY && !qh->SCALElast && qh->MAXabs_coord > 1e4)
       qh_fprintf(qh, fp, 9371, "\
 \n\
 When computing the Delaunay triangulation of coordinates > 1.0,\n\
   - use 'Qbb' to scale the last coordinate to [0,m] (max previous coordinate)\n");
     if (qh->DELAUNAY && !qh->ATinfinity)
       qh_fprintf(qh, fp, 9372, "\
 When computing the Delaunay triangulation:\n\
   - use 'Qz' to add a point at-infinity.  This reduces precision problems.\n");
 
     qh_fprintf(qh, fp, 9373, "\
 \n\
 If you need triangular output:\n\
   - use option 'Qt' to triangulate the output\n\
   - use option 'QJ' to joggle the input points and remove precision errors\n\
   - use option 'Ft'.  It triangulates non-simplicial facets with added points.\n\
 \n\
 If you must use 'Q0',\n\
 try one or more of the following options.  They can not guarantee an output.\n\
   - use 'QbB' to scale the input to a cube.\n\
   - use 'Po' to produce output and prevent partitioning for flipped facets\n\
   - use 'V0' to set min. distance to visible facet as 0 instead of roundoff\n\
   - use 'En' to specify a maximum roundoff error less than %2.2g.\n\
   - options 'Qf', 'Qbb', and 'QR0' may also help\n",
                qh->DISTround);
     qh_fprintf(qh, fp, 9374, "\
 \n\
 To guarantee simplicial output:\n\
   - use option 'Qt' to triangulate the output\n\
   - use option 'QJ' to joggle the input points and remove precision errors\n\
   - use option 'Ft' to triangulate the output by adding points\n\
   - use exact arithmetic (see \"Imprecision in Qhull\", qh-impre.htm)\n\
 ");
   }
 } /* printhelp_degenerate */
 
 
 /*---------------------------------
 
   qh_printhelp_narrowhull(qh, minangle )
     Warn about a narrow hull
 
   notes:
     Alternatively, reduce qh_WARNnarrow in user.h
 
 */
 void qh_printhelp_narrowhull(qhT *qh, FILE *fp, realT minangle) {
 
     qh_fprintf(qh, fp, 9375, "qhull precision warning: \n\
 The initial hull is narrow (cosine of min. angle is %.16f).\n\
 Is the input lower dimensional (e.g., on a plane in 3-d)?  Qhull may\n\
 produce a wide facet.  Options 'QbB' (scale to unit box) or 'Qbb' (scale\n\
 last coordinate) may remove this warning.  Use 'Pp' to skip this warning.\n\
 See 'Limitations' in qh-impre.htm.\n",
           -minangle);   /* convert from angle between normals to angle between facets */
 } /* printhelp_narrowhull */
 
 /*---------------------------------
 
   qh_printhelp_singular(qh, fp )
     prints descriptive message for singular input
 */
 void qh_printhelp_singular(qhT *qh, FILE *fp) {
   facetT *facet;
   vertexT *vertex, **vertexp;
   realT min, max, *coord, dist;
   int i,k;
 
   qh_fprintf(qh, fp, 9376, "\n\
 The input to qhull appears to be less than %d dimensional, or a\n\
 computation has overflowed.\n\n\
 Qhull could not construct a clearly convex simplex from points:\n",
            qh->hull_dim);
   qh_printvertexlist(qh, fp, "", qh->facet_list, NULL, qh_ALL);
   if (!qh_QUICKhelp)
     qh_fprintf(qh, fp, 9377, "\n\
 The center point is coplanar with a facet, or a vertex is coplanar\n\
 with a neighboring facet.  The maximum round off error for\n\
 computing distances is %2.2g.  The center point, facets and distances\n\
 to the center point are as follows:\n\n", qh->DISTround);
   qh_printpointid(qh, fp, "center point", qh->hull_dim, qh->interior_point, -1);
   qh_fprintf(qh, fp, 9378, "\n");
   FORALLfacets {
     qh_fprintf(qh, fp, 9379, "facet");
     FOREACHvertex_(facet->vertices)
       qh_fprintf(qh, fp, 9380, " p%d", qh_pointid(qh, vertex->point));
     zinc_(Zdistio);
     qh_distplane(qh, qh->interior_point, facet, &dist);
     qh_fprintf(qh, fp, 9381, " distance= %4.2g\n", dist);
   }
   if (!qh_QUICKhelp) {
     if (qh->HALFspace)
       qh_fprintf(qh, fp, 9382, "\n\
 These points are the dual of the given halfspaces.  They indicate that\n\
 the intersection is degenerate.\n");
     qh_fprintf(qh, fp, 9383,"\n\
 These points either have a maximum or minimum x-coordinate, or\n\
 they maximize the determinant for k coordinates.  Trial points\n\
 are first selected from points that maximize a coordinate.\n");
     if (qh->hull_dim >= qh_INITIALmax)
       qh_fprintf(qh, fp, 9384, "\n\
 Because of the high dimension, the min x-coordinate and max-coordinate\n\
 points are used if the determinant is non-zero.  Option 'Qs' will\n\
 do a better, though much slower, job.  Instead of 'Qs', you can change\n\
 the points by randomly rotating the input with 'QR0'.\n");
   }
   qh_fprintf(qh, fp, 9385, "\nThe min and max coordinates for each dimension are:\n");
   for (k=0; k < qh->hull_dim; k++) {
     min= REALmax;
     max= -REALmin;
     for (i=qh->num_points, coord= qh->first_point+k; i--; coord += qh->hull_dim) {
       maximize_(max, *coord);
       minimize_(min, *coord);
     }
     qh_fprintf(qh, fp, 9386, "  %d:  %8.4g  %8.4g  difference= %4.4g\n", k, min, max, max-min);
   }
   if (!qh_QUICKhelp) {
     qh_fprintf(qh, fp, 9387, "\n\
 If the input should be full dimensional, you have several options that\n\
 may determine an initial simplex:\n\
   - use 'QJ'  to joggle the input and make it full dimensional\n\
   - use 'QbB' to scale the points to the unit cube\n\
   - use 'QR0' to randomly rotate the input for different maximum points\n\
   - use 'Qs'  to search all points for the initial simplex\n\
   - use 'En'  to specify a maximum roundoff error less than %2.2g.\n\
   - trace execution with 'T3' to see the determinant for each point.\n",
                      qh->DISTround);
 #if REALfloat
     qh_fprintf(qh, fp, 9388, "\
-  - recompile qhull for realT precision(#define REALfloat 0 in libqhull.h).\n");
+  - recompile qhull for realT precision(#define REALfloat 0 in libqhull_r.h).\n");
 #endif
     qh_fprintf(qh, fp, 9389, "\n\
 If the input is lower dimensional:\n\
   - use 'QJ' to joggle the input and make it full dimensional\n\
   - use 'Qbk:0Bk:0' to delete coordinate k from the input.  You should\n\
     pick the coordinate with the least range.  The hull will have the\n\
     correct topology.\n\
   - determine the flat containing the points, rotate the points\n\
     into a coordinate plane, and delete the other coordinates.\n\
   - add one or more points to make the input full dimensional.\n\
 ");
   }
 } /* printhelp_singular */
 
 /*---------------------------------
 
   qh_user_memsizes(qh)
     allocate up to 10 additional, quick allocation sizes
 
   notes:
     increase maximum number of allocations in qh_initqhull_mem()
 */
 void qh_user_memsizes(qhT *qh) {
 
   /* qh_memsize(qh, size); */
 } /* user_memsizes */
 
 
diff --git a/src/libqhullr/user_r.h b/src/libqhullr/user_r.h
index 9a13c9d..ce69ee1 100644
--- a/src/libqhullr/user_r.h
+++ b/src/libqhullr/user_r.h
@@ -1,807 +1,827 @@
 /*
  ---------------------------------
 
    user.h
    user redefinable constants
 
    see qh-user.htm.  see COPYING for copyright information.
 
-   before reading any code, review libqhull.h for data structure definitions and
-   the "qh" macro.
+   before reading any code, review libqhull_r.h for data structure definitions
 
 Sections:
    ============= qhull library constants ======================
    ============= data types and configuration macros ==========
    ============= performance related constants ================
    ============= memory constants =============================
    ============= joggle constants =============================
    ============= conditional compilation ======================
    ============= -merge constants- ============================
 
 Code flags --
   NOerrors -- the code does not call qh_errexit()
   WARN64 -- the code may be incompatible with 64-bit pointers
 
 */
 
 #include 
 
 #ifndef qhDEFuser
 #define qhDEFuser 1
 
 /*============================================================*/
 /*============= qhull library constants ======================*/
 /*============================================================*/
 
 /*----------------------------------
 
   FILENAMElen -- max length for TI and TO filenames
 
 */
 
 #define qh_FILENAMElen 500
 
 /*----------------------------------
 
   msgcode -- Unique message codes for qh_fprintf
 
   If add new messages, assign these values and increment in user.h and user_r.h
+  See QhullError.h for 10000 errors.
 
   def counters =  [27, 1047, 2059, 3025, 4068, 5003,
      6243, 7079, 8143, 9410, 10000, 11026]
 
-  See: qh_ERR* [libqhull.h]
+  See: qh_ERR* [libqhull_r.h]
 */
 
 #define MSG_TRACE0 0
 #define MSG_TRACE1 1000
 #define MSG_TRACE2 2000
 #define MSG_TRACE3 3000
 #define MSG_TRACE4 4000
 #define MSG_TRACE5 5000
 #define MSG_ERROR  6000   /* errors written to qh.ferr */
 #define MSG_WARNING 7000
 #define MSG_STDERR  8000  /* log messages Written to qh.ferr */
 #define MSG_OUTPUT  9000
-#define MSG_QHULL_ERROR 10000 /* errors thrown by QhullError [QhullError.h] */
+#define MSG_QHULL_ERROR 10000 /* errors thrown by QhullError.cpp */
 #define MSG_FIXUP  11000  /* FIXUP QH11... */
 #define MSG_MAXLEN  3000 /* qh_printhelp_degenerate() in user.c */
 
 
 /*----------------------------------
 
   qh_OPTIONline -- max length of an option line 'FO'
 */
 #define qh_OPTIONline 80
 
 /*============================================================*/
 /*============= data types and configuration macros ==========*/
 /*============================================================*/
 
 /*----------------------------------
 
   realT
     set the size of floating point numbers
 
   qh_REALdigits
     maximimum number of significant digits
 
   qh_REAL_1, qh_REAL_2n, qh_REAL_3n
     format strings for printf
 
   qh_REALmax, qh_REALmin
     maximum and minimum (near zero) values
 
   qh_REALepsilon
     machine roundoff.  Maximum roundoff error for addition and multiplication.
 
   notes:
    Select whether to store floating point numbers in single precision (float)
    or double precision (double).
 
    Use 'float' to save about 8% in time and 25% in space.  This is particularly
    helpful if high-d where convex hulls are space limited.  Using 'float' also
    reduces the printed size of Qhull's output since numbers have 8 digits of
    precision.
 
    Use 'double' when greater arithmetic precision is needed.  This is needed
    for Delaunay triangulations and Voronoi diagrams when you are not merging
    facets.
 
    If 'double' gives insufficient precision, your data probably includes
    degeneracies.  If so you should use facet merging (done by default)
    or exact arithmetic (see imprecision section of manual, qh-impre.htm).
    You may also use option 'Po' to force output despite precision errors.
 
    You may use 'long double', but many format statements need to be changed
    and you may need a 'long double' square root routine.  S. Grundmann
    (sg@eeiwzb.et.tu-dresden.de) has done this.  He reports that the code runs
    much slower with little gain in precision.
 
    WARNING: on some machines,    int f(){realT a= REALmax;return (a == REALmax);}
       returns False.  Use (a > REALmax/2) instead of (a == REALmax).
 
    REALfloat =   1      all numbers are 'float' type
              =   0      all numbers are 'double' type
 */
 #define REALfloat 0
 
 #if (REALfloat == 1)
 #define realT float
 #define REALmax FLT_MAX
 #define REALmin FLT_MIN
 #define REALepsilon FLT_EPSILON
 #define qh_REALdigits 8   /* maximum number of significant digits */
 #define qh_REAL_1 "%6.8g "
 #define qh_REAL_2n "%6.8g %6.8g\n"
 #define qh_REAL_3n "%6.8g %6.8g %6.8g\n"
 
 #elif (REALfloat == 0)
 #define realT double
 #define REALmax DBL_MAX
 #define REALmin DBL_MIN
 #define REALepsilon DBL_EPSILON
 #define qh_REALdigits 16    /* maximum number of significant digits */
 #define qh_REAL_1 "%6.16g "
 #define qh_REAL_2n "%6.16g %6.16g\n"
 #define qh_REAL_3n "%6.16g %6.16g %6.16g\n"
 
 #else
 #error unknown float option
 #endif
 
+/*----------------------------------
+  
+  countT
+    The type for counts and identifiers (e.g., the number of points, vertex identifiers)
+
+    Typically 'int' or 'long long'.   
+
+    May be defined as a unsigned valued (? FIXUP)
+
+    Also defined in qset_r.h
+*/
+
+#ifndef DEFcountT
+#define DEFcountT 1
+typedef int countT;          
+#endif
+#define COUNTmax 0x7fffffff
+
+
 /*----------------------------------
 
   qh_CPUclock
     define the clock() function for reporting the total time spent by Qhull
     returns CPU ticks as a 'long int'
     qh_CPUclock is only used for reporting the total time spent by Qhull
 
   qh_SECticks
     the number of clock ticks per second
 
   notes:
     looks for CLOCKS_PER_SEC, CLOCKS_PER_SECOND, or assumes microseconds
     to define a custom clock, set qh_CLOCKtype to 0
 
     if your system does not use clock() to return CPU ticks, replace
     qh_CPUclock with the corresponding function.  It is converted
     to 'unsigned long' to prevent wrap-around during long runs.  By default,
      defines clock_t as 'long'
 
    Set qh_CLOCKtype to
 
      1          for CLOCKS_PER_SEC, CLOCKS_PER_SECOND, or microsecond
                 Note:  may fail if more than 1 hour elapsed time
 
-     2          use qh_clock() with POSIX times() (see global.c)
+     2          use qh_clock() with POSIX times() (see global_r.c)
 */
 #define qh_CLOCKtype 1  /* change to the desired number */
 
 #if (qh_CLOCKtype == 1)
 
 #if defined(CLOCKS_PER_SECOND)
 #define qh_CPUclock    ((unsigned long)clock())  /* return CPU clock */
 #define qh_SECticks CLOCKS_PER_SECOND
 
 #elif defined(CLOCKS_PER_SEC)
 #define qh_CPUclock    ((unsigned long)clock())  /* return CPU clock */
 #define qh_SECticks CLOCKS_PER_SEC
 
 #elif defined(CLK_TCK)
 #define qh_CPUclock    ((unsigned long)clock())  /* return CPU clock */
 #define qh_SECticks CLK_TCK
 
 #else
 #define qh_CPUclock    ((unsigned long)clock())  /* return CPU clock */
 #define qh_SECticks 1E6
 #endif
 
 #elif (qh_CLOCKtype == 2)
 #define qh_CPUclock    qh_clock()  /* return CPU clock */
 #define qh_SECticks 100
 
 #else /* qh_CLOCKtype == ? */
 #error unknown clock option
 #endif
 
 /*----------------------------------
 
   qh_RANDOMtype, qh_RANDOMmax, qh_RANDOMseed
     define random number generator
 
     qh_RANDOMint generates a random integer between 0 and qh_RANDOMmax.
     qh_RANDOMseed sets the random number seed for qh_RANDOMint
 
   Set qh_RANDOMtype (default 5) to:
     1       for random() with 31 bits (UCB)
     2       for rand() with RAND_MAX or 15 bits (system 5)
     3       for rand() with 31 bits (Sun)
     4       for lrand48() with 31 bits (Solaris)
     5       for qh_rand(qh) with 31 bits (included with Qhull, requires 'qh')
 
   notes:
     Random numbers are used by rbox to generate point sets.  Random
     numbers are used by Qhull to rotate the input ('QRn' option),
     simulate a randomized algorithm ('Qr' option), and to simulate
     roundoff errors ('Rn' option).
 
     Random number generators differ between systems.  Most systems provide
     rand() but the period varies.  The period of rand() is not critical
     since qhull does not normally use random numbers.
 
     The default generator is Park & Miller's minimal standard random
     number generator [CACM 31:1195 '88].  It is included with Qhull.
 
     If qh_RANDOMmax is wrong, qhull will report a warning and Geomview
     output will likely be invisible.
 */
 #define qh_RANDOMtype 5   /* *** change to the desired number *** */
 
 #if (qh_RANDOMtype == 1)
 #define qh_RANDOMmax ((realT)0x7fffffffUL)  /* 31 bits, random()/MAX */
 #define qh_RANDOMint random()
 #define qh_RANDOMseed_(qh, seed) srandom(seed);
 
 #elif (qh_RANDOMtype == 2)
 #ifdef RAND_MAX
 #define qh_RANDOMmax ((realT)RAND_MAX)
 #else
 #define qh_RANDOMmax ((realT)32767)   /* 15 bits (System 5) */
 #endif
 #define qh_RANDOMint  rand()
 #define qh_RANDOMseed_(qh, seed) srand((unsigned)seed);
 
 #elif (qh_RANDOMtype == 3)
 #define qh_RANDOMmax ((realT)0x7fffffffUL)  /* 31 bits, Sun */
 #define qh_RANDOMint  rand()
 #define qh_RANDOMseed_(qh, seed) srand((unsigned)seed);
 
 #elif (qh_RANDOMtype == 4)
 #define qh_RANDOMmax ((realT)0x7fffffffUL)  /* 31 bits, lrand38()/MAX */
 #define qh_RANDOMint lrand48()
 #define qh_RANDOMseed_(qh, seed) srand48(seed);
 
 #elif (qh_RANDOMtype == 5)  /* 'qh' is an implicit parameter */
 #define qh_RANDOMmax ((realT)2147483646UL)  /* 31 bits, qh_rand/MAX */
 #define qh_RANDOMint qh_rand(qh)
 #define qh_RANDOMseed_(qh, seed) qh_srand(qh, seed);
 /* unlike rand(), never returns 0 */
 
 #else
 #error: unknown random option
 #endif
 
 /*----------------------------------
 
   qh_ORIENTclock
     0 for inward pointing normals by Geomview convention
 */
 #define qh_ORIENTclock 0
 
 
 /*============================================================*/
 /*============= joggle constants =============================*/
 /*============================================================*/
 
 /*----------------------------------
 
 qh_JOGGLEdefault
 default qh.JOGGLEmax is qh.DISTround * qh_JOGGLEdefault
 
 notes:
 rbox s r 100 | qhull QJ1e-15 QR0 generates 90% faults at distround 7e-16
 rbox s r 100 | qhull QJ1e-14 QR0 generates 70% faults
 rbox s r 100 | qhull QJ1e-13 QR0 generates 35% faults
 rbox s r 100 | qhull QJ1e-12 QR0 generates 8% faults
 rbox s r 100 | qhull QJ1e-11 QR0 generates 1% faults
 rbox s r 100 | qhull QJ1e-10 QR0 generates 0% faults
 rbox 1000 W0 | qhull QJ1e-12 QR0 generates 86% faults
 rbox 1000 W0 | qhull QJ1e-11 QR0 generates 20% faults
 rbox 1000 W0 | qhull QJ1e-10 QR0 generates 2% faults
 the later have about 20 points per facet, each of which may interfere
 
 pick a value large enough to avoid retries on most inputs
 */
 #define qh_JOGGLEdefault 30000.0
 
 /*----------------------------------
 
 qh_JOGGLEincrease
 factor to increase qh.JOGGLEmax on qh_JOGGLEretry or qh_JOGGLEagain
 */
 #define qh_JOGGLEincrease 10.0
 
 /*----------------------------------
 
 qh_JOGGLEretry
 if ZZretry = qh_JOGGLEretry, increase qh.JOGGLEmax
 
 notes:
 try twice at the original value in case of bad luck the first time
 */
 #define qh_JOGGLEretry 2
 
 /*----------------------------------
 
 qh_JOGGLEagain
 every following qh_JOGGLEagain, increase qh.JOGGLEmax
 
 notes:
 1 is OK since it's already failed qh_JOGGLEretry times
 */
 #define qh_JOGGLEagain 1
 
 /*----------------------------------
 
 qh_JOGGLEmaxincrease
 maximum qh.JOGGLEmax due to qh_JOGGLEincrease
 relative to qh.MAXwidth
 
 notes:
 qh.joggleinput will retry at this value until qh_JOGGLEmaxretry
 */
 #define qh_JOGGLEmaxincrease 1e-2
 
 /*----------------------------------
 
 qh_JOGGLEmaxretry
 stop after qh_JOGGLEmaxretry attempts
 */
 #define qh_JOGGLEmaxretry 100
 
 /*============================================================*/
 /*============= performance related constants ================*/
 /*============================================================*/
 
 /*----------------------------------
 
   qh_HASHfactor
     total hash slots / used hash slots.  Must be at least 1.1.
 
   notes:
     =2 for at worst 50% occupancy for qh.hash_table and normally 25% occupancy
 */
 #define qh_HASHfactor 2
 
 /*----------------------------------
 
   qh_VERIFYdirect
     with 'Tv' verify all points against all facets if op count is smaller
 
   notes:
     if greater, calls qh_check_bestdist() instead
 */
 #define qh_VERIFYdirect 1000000
 
 /*----------------------------------
 
   qh_INITIALsearch
      if qh_INITIALmax, search points up to this dimension
 */
 #define qh_INITIALsearch 6
 
 /*----------------------------------
 
   qh_INITIALmax
     if dim >= qh_INITIALmax, use min/max coordinate points for initial simplex
 
   notes:
     from points with non-zero determinants
     use option 'Qs' to override (much slower)
 */
 #define qh_INITIALmax 8
 
 /*============================================================*/
 /*============= memory constants =============================*/
 /*============================================================*/
 
 /*----------------------------------
 
   qh_MEMalign
-    memory alignment for qh_meminitbuffers() in global.c
+    memory alignment for qh_meminitbuffers() in global_r.c
 
   notes:
     to avoid bus errors, memory allocation must consider alignment requirements.
-    malloc() automatically takes care of alignment.   Since mem.c manages
+    malloc() automatically takes care of alignment.   Since mem_r.c manages
     its own memory, we need to explicitly specify alignment in
     qh_meminitbuffers().
 
     A safe choice is sizeof(double).  sizeof(float) may be used if doubles
     do not occur in data structures and pointers are the same size.  Be careful
     of machines (e.g., DEC Alpha) with large pointers.
 
     If using gcc, best alignment is [fmax_() is defined in geom_r.h]
               #define qh_MEMalign fmax_(__alignof__(realT),__alignof__(void *))
 */
 #define qh_MEMalign ((int)(fmax_(sizeof(realT), sizeof(void *))))
 
 /*----------------------------------
 
   qh_MEMbufsize
     size of additional memory buffers
 
   notes:
-    used for qh_meminitbuffers() in global.c
+    used for qh_meminitbuffers() in global_r.c
 */
 #define qh_MEMbufsize 0x10000       /* allocate 64K memory buffers */
 
 /*----------------------------------
 
   qh_MEMinitbuf
     size of initial memory buffer
 
   notes:
-    use for qh_meminitbuffers() in global.c
+    use for qh_meminitbuffers() in global_r.c
 */
 #define qh_MEMinitbuf 0x20000      /* initially allocate 128K buffer */
 
 /*----------------------------------
 
   qh_INFINITE
     on output, indicates Voronoi center at infinity
 */
 #define qh_INFINITE  -10.101
 
 /*----------------------------------
 
   qh_DEFAULTbox
     default box size (Geomview expects 0.5)
 
   qh_DEFAULTbox
     default box size for integer coorindate (rbox only)
 */
 #define qh_DEFAULTbox 0.5
 #define qh_DEFAULTzbox 1e6
 
 /*============================================================*/
 /*============= conditional compilation ======================*/
 /*============================================================*/
 
 /*----------------------------------
 
   __cplusplus
     defined by C++ compilers
 
   __MSC_VER
     defined by Microsoft Visual C++
 
   __MWERKS__ && __INTEL__
     defined by Metrowerks when compiling for Intel-based Macintosh
 
   __STDC__
     defined for strict ANSI C
 */
 
 /*----------------------------------
 
   qh_COMPUTEfurthest
     compute furthest distance to an outside point instead of storing it with the facet
     =1 to compute furthest
 
   notes:
     computing furthest saves memory but costs time
       about 40% more distance tests for partitioning
       removes facet->furthestdist
 */
 #define qh_COMPUTEfurthest 0
 
 /*----------------------------------
 
   qh_KEEPstatistics
     =0 removes most of statistic gathering and reporting
 
   notes:
     if 0, code size is reduced by about 4%.
 */
 #define qh_KEEPstatistics 1
 
 /*----------------------------------
 
   qh_MAXoutside
     record outer plane for each facet
     =1 to record facet->maxoutside
 
   notes:
     this takes a realT per facet and slightly slows down qhull
     it produces better outer planes for geomview output
 */
 #define qh_MAXoutside 1
 
 /*----------------------------------
 
   qh_NOmerge
     disables facet merging if defined
 
   notes:
     This saves about 10% space.
 
     Unless 'Q0'
       qh_NOmerge sets 'QJ' to avoid precision errors
 
     #define qh_NOmerge
 
   see:
-    qh_NOmem in mem.c
+    qh_NOmem in mem_r.c
 
-    see user.c/user_eg.c for removing io.o
+    see user_r.c/user_eg.c for removing io_r.o
 */
 
 /*----------------------------------
 
   qh_NOtrace
     no tracing if defined
 
   notes:
     This saves about 5% space.
 
     #define qh_NOtrace
 */
 
 #if 0  /* sample code */
     exitcode= qh_new_qhull(qhT *qh, dim, numpoints, points, ismalloc,
                       flags, outfile, errfile);
     qh_freeqhull(qhT *qh, !qh_ALL); /* frees long memory used by second call */
     qh_memfreeshort(qhT *qh, &curlong, &totlong);  /* frees short memory and memory allocator */
 #endif
 
 /*----------------------------------
 
   qh_QUICKhelp
     =1 to use abbreviated help messages, e.g., for degenerate inputs
 */
 #define qh_QUICKhelp    0
 
 /*============================================================*/
 /*============= -merge constants- ============================*/
 /*============================================================*/
 /*
    These constants effect facet merging.  You probably will not need
    to modify them.  They effect the performance of facet merging.
 */
 
 /*----------------------------------
 
   qh_DIMmergeVertex
     max dimension for vertex merging (it is not effective in high-d)
 */
 #define qh_DIMmergeVertex 6
 
 /*----------------------------------
 
   qh_DIMreduceBuild
      max dimension for vertex reduction during build (slow in high-d)
 */
 #define qh_DIMreduceBuild 5
 
 /*----------------------------------
 
   qh_BESTcentrum
      if > 2*dim+n vertices, qh_findbestneighbor() tests centrums (faster)
      else, qh_findbestneighbor() tests all vertices (much better merges)
 
   qh_BESTcentrum2
      if qh_BESTcentrum2 * DIM3 + BESTcentrum < #vertices tests centrums
 */
 #define qh_BESTcentrum 20
 #define qh_BESTcentrum2 2
 
 /*----------------------------------
 
   qh_BESTnonconvex
     if > dim+n neighbors, qh_findbestneighbor() tests nonconvex ridges.
 
   notes:
     It is needed because qh_findbestneighbor is slow for large facets
 */
 #define qh_BESTnonconvex 15
 
 /*----------------------------------
 
   qh_MAXnewmerges
     if >n newmerges, qh_merge_nonconvex() calls qh_reducevertices_centrums.
 
   notes:
     It is needed because postmerge can merge many facets at once
 */
 #define qh_MAXnewmerges 2
 
 /*----------------------------------
 
   qh_MAXnewcentrum
     if <= dim+n vertices (n approximates the number of merges),
       reset the centrum in qh_updatetested() and qh_mergecycle_facets()
 
   notes:
     needed to reduce cost and because centrums may move too much if
     many vertices in high-d
 */
 #define qh_MAXnewcentrum 5
 
 /*----------------------------------
 
   qh_COPLANARratio
     for 3-d+ merging, qh.MINvisible is n*premerge_centrum
 
   notes:
     for non-merging, it's DISTround
 */
 #define qh_COPLANARratio 3
 
 /*----------------------------------
 
   qh_DISToutside
     When is a point clearly outside of a facet?
     Stops search in qh_findbestnew or qh_partitionall
     qh_findbest uses qh.MINoutside since since it is only called if no merges.
 
   notes:
     'Qf' always searches for best facet
     if !qh.MERGING, same as qh.MINoutside.
     if qh_USEfindbestnew, increase value since neighboring facets may be ill-behaved
       [Note: Zdelvertextot occurs normally with interior points]
             RBOX 1000 s Z1 G1e-13 t1001188774 | QHULL Tv
     When there is a sharp edge, need to move points to a
     clearly good facet; otherwise may be lost in another partitioning.
     if too big then O(n^2) behavior for partitioning in cone
     if very small then important points not processed
     Needed in qh_partitionall for
       RBOX 1000 s Z1 G1e-13 t1001032651 | QHULL Tv
     Needed in qh_findbestnew for many instances of
       RBOX 1000 s Z1 G1e-13 t | QHULL Tv
 
   See:
     qh_DISToutside -- when is a point clearly outside of a facet
     qh_SEARCHdist -- when is facet coplanar with the best facet?
     qh_USEfindbestnew -- when to use qh_findbestnew for qh_partitionpoint()
 */
 #define qh_DISToutside ((qh_USEfindbestnew ? 2 : 1) * \
      fmax_((qh->MERGING ? 2 : 1)*qh->MINoutside, qh->max_outside))
 
 /*----------------------------------
 
   qh_RATIOnearinside
     ratio of qh.NEARinside to qh.ONEmerge for retaining inside points for
     qh_check_maxout().
 
   notes:
     This is overkill since do not know the correct value.
     It effects whether 'Qc' reports all coplanar points
     Not used for 'd' since non-extreme points are coplanar
 */
 #define qh_RATIOnearinside 5
 
 /*----------------------------------
 
   qh_SEARCHdist
     When is a facet coplanar with the best facet?
     qh_findbesthorizon: all coplanar facets of the best facet need to be searched.
 
   See:
     qh_DISToutside -- when is a point clearly outside of a facet
     qh_SEARCHdist -- when is facet coplanar with the best facet?
     qh_USEfindbestnew -- when to use qh_findbestnew for qh_partitionpoint()
 */
 #define qh_SEARCHdist ((qh_USEfindbestnew ? 2 : 1) * \
       (qh->max_outside + 2 * qh->DISTround + fmax_( qh->MINvisible, qh->MAXcoplanar)));
 
 /*----------------------------------
 
   qh_USEfindbestnew
      Always use qh_findbestnew for qh_partitionpoint, otherwise use
      qh_findbestnew if merged new facet or sharpnewfacets.
 
   See:
     qh_DISToutside -- when is a point clearly outside of a facet
     qh_SEARCHdist -- when is facet coplanar with the best facet?
     qh_USEfindbestnew -- when to use qh_findbestnew for qh_partitionpoint()
 */
 #define qh_USEfindbestnew (zzval_(Ztotmerge) > 50)
 
 /*----------------------------------
 
   qh_WIDEcoplanar
     n*MAXcoplanar or n*MINvisible for a WIDEfacet
 
     if vertex is further than qh.WIDEfacet from the hyperplane
     then its ridges are not counted in computing the area, and
     the facet's centrum is frozen.
 
   notes:
    qh.WIDEfacet= max(qh.MAXoutside,qh_WIDEcoplanar*qh.MAXcoplanar,
       qh_WIDEcoplanar * qh.MINvisible);
 */
 #define qh_WIDEcoplanar 6
 
 /*----------------------------------
 
   qh_MAXnarrow
     max. cosine in initial hull that sets qh.NARROWhull
 
   notes:
     If qh.NARROWhull, the initial partition does not make
     coplanar points.  If narrow, a coplanar point can be
     coplanar to two facets of opposite orientations and
     distant from the exact convex hull.
 
     Conservative estimate.  Don't actually see problems until it is -1.0
 */
 #define qh_MAXnarrow -0.99999999
 
 /*----------------------------------
 
   qh_WARNnarrow
     max. cosine in initial hull to warn about qh.NARROWhull
 
   notes:
     this is a conservative estimate.
     Don't actually see problems until it is -1.0.  See qh-impre.htm
 */
 #define qh_WARNnarrow -0.999999999999999
 
 /*----------------------------------
 
   qh_ZEROdelaunay
     a zero Delaunay facet occurs for input sites coplanar with their convex hull
     the last normal coefficient of a zero Delaunay facet is within
         qh_ZEROdelaunay * qh.ANGLEround of 0
 
   notes:
     qh_ZEROdelaunay does not allow for joggled input ('QJ').
 
     You can avoid zero Delaunay facets by surrounding the input with a box.
 
     Use option 'PDk:-n' to explicitly define zero Delaunay facets
       k= dimension of input sites (e.g., 3 for 3-d Delaunay triangulation)
       n= the cutoff for zero Delaunay facets (e.g., 'PD3:-1e-12')
 */
 #define qh_ZEROdelaunay 2
 
 #endif /* qh_DEFuser */
 
 
 
diff --git a/src/libqhullr/usermem_r.c b/src/libqhullr/usermem_r.c
index fb661fb..83c89b4 100644
--- a/src/libqhullr/usermem_r.c
+++ b/src/libqhullr/usermem_r.c
@@ -1,64 +1,64 @@
 /*
  ---------------------------------
 
-   usermem.c
+   usermem_r.c
    qh_exit(), qh_free(), and qh_malloc()
 
    See README.txt.
 
    If you redefine one of these functions you must redefine all of them.
    If you recompile and load this file, then usermem.o will not be loaded
    from qhull.a or qhull.lib
 
-   See libqhull.h for data structures, macros, and user-callable functions.
-   See user.c for qhull-related, redefinable functions
-   see user.h for user-definable constants
-   See userprintf.c for qh_fprintf and userprintf_rbox,c for qh_fprintf_rbox
+   See libqhull_r.h for data structures, macros, and user-callable functions.
+   See user_r.c for qhull-related, redefinable functions
+   see user_r.h for user-definable constants
+   See userprintf_r.c for qh_fprintf and userprintf_rbox_r.c for qh_fprintf_rbox
 
    Please report any errors that you fix to qhull@qhull.org
 */
 
 #include "libqhull_r.h"
 
 #include 
 
 /*---------------------------------
 
   qh_exit( exitcode )
     exit program
 
   notes:
     same as exit()
 */
 void qh_exit(int exitcode) {
     exit(exitcode);
 } /* exit */
 
 /*---------------------------------
 
   qh_free(qhT *qh, mem )
     free memory
 
   notes:
     same as free()
 */
 void qh_free(void *mem) {
     free(mem);
 } /* free */
 
 /*---------------------------------
 
     qh_malloc( mem )
       allocate memory
 
     notes:
       same as malloc()
 */
 void *qh_malloc(size_t size) {
     return malloc(size);
 } /* malloc */
 
 
diff --git a/src/libqhullr/userprintf_r.c b/src/libqhullr/userprintf_r.c
index 46965f9..2fbf288 100644
--- a/src/libqhullr/userprintf_r.c
+++ b/src/libqhullr/userprintf_r.c
@@ -1,64 +1,64 @@
 /*
  ---------------------------------
 
-   userprintf.c
+   userprintf_r.c
    qh_fprintf()
 
    see README.txt  see COPYING.txt for copyright information.
 
-   If you recompile and load this file, then userprintf.o will not be loaded
+   If you recompile and load this file, then userprintf_r.o will not be loaded
    from qhull.a or qhull.lib
 
-   See libqhull.h for data structures, macros, and user-callable functions.
-   See user.c for qhull-related, redefinable functions
-   see user.h for user-definable constants
-   See usermem.c for qh_exit(), qh_free(), and qh_malloc()
+   See libqhull_r.h for data structures, macros, and user-callable functions.
+   See user_r.c for qhull-related, redefinable functions
+   see user_r.h for user-definable constants
+   See usermem_r.c for qh_exit(), qh_free(), and qh_malloc()
    see Qhull.cpp and RboxPoints.cpp for examples.
 
    Please report any errors that you fix to qhull@qhull.org
 */
 
 #include "libqhull_r.h"
 
 #include 
 #include 
 #include 
 
 /*---------------------------------
 
    qh_fprintf(qh, fp, msgcode, format, list of args )
      print arguments to *fp according to format
-     Use qh_fprintf_rbox() for rboxlib.c
+     Use qh_fprintf_rbox() for rboxlib_r.c
 
    notes:
      same as fprintf()
      fgets() is not trapped like fprintf()
      exit qh_fprintf via qh_errexit()
      may be called for errors in qh_initstatistics and qh_meminit
 */
 
 void qh_fprintf(qhT *qh, FILE *fp, int msgcode, const char *fmt, ... ) {
     va_list args;
 
     if (!fp) {
         if(!qh)
             fprintf(stderr, "QH6241 qh_fprintf: fp and qh not defined for '%s'", fmt);
         else
             fprintf(qh->qhmem.ferr, "QH6232 qh_fprintf: fp is 0.  Was wrong qh_fprintf called for '%s'", fmt);
-        fprintf(qh->qhmem.ferr, "QH6232 Qhull internal error (userprintf.c): fp is 0.  Wrong qh_fprintf called.\n");
+        fprintf(qh->qhmem.ferr, "QH6232 Qhull internal error (userprintf_r.c): fp is 0.  Wrong qh_fprintf called.\n");
         qh_errexit(qh, 6232, NULL, NULL);
     }
     va_start(args, fmt);
     if (qh && qh->ANNOTATEoutput) {
       fprintf(fp, "[QH%.4d]", msgcode);
     }else if (msgcode >= MSG_ERROR && msgcode < MSG_STDERR ) {
       fprintf(fp, "QH%.4d ", msgcode);
     }
     vfprintf(fp, fmt, args);
     va_end(args);
 
     /* Place debugging traps here. Use with option 'Tn' */
 
 } /* qh_fprintf */
 
diff --git a/src/libqhullr/userprintf_rbox_r.c b/src/libqhullr/userprintf_rbox_r.c
index ce706a6..5af87f6 100644
--- a/src/libqhullr/userprintf_rbox_r.c
+++ b/src/libqhullr/userprintf_rbox_r.c
@@ -1,53 +1,53 @@
 /*
  ---------------------------------
 
-   userprintf_rbox.c
+   userprintf_rbox_r.c
    qh_fprintf_rbox()
 
    see README.txt  see COPYING.txt for copyright information.
 
-   If you recompile and load this file, then userprintf_rbox.o will not be loaded
+   If you recompile and load this file, then userprintf_rbox_r.o will not be loaded
    from qhull.a or qhull.lib
 
-   See libqhull.h for data structures, macros, and user-callable functions.
-   See user.c for qhull-related, redefinable functions
-   see user.h for user-definable constants
-   See usermem.c for qh_exit(), qh_free(), and qh_malloc()
+   See libqhull_r.h for data structures, macros, and user-callable functions.
+   See user_r.c for qhull-related, redefinable functions
+   see user_r.h for user-definable constants
+   See usermem_r.c for qh_exit(), qh_free(), and qh_malloc()
    see Qhull.cpp and RboxPoints.cpp for examples.
 
    Please report any errors that you fix to qhull@qhull.org
 */
 
 #include "libqhull_r.h"
 
 #include 
 #include 
 #include 
 
 /*---------------------------------
 
    qh_fprintf_rbox(qh, fp, msgcode, format, list of args )
      print arguments to *fp according to format
-     Use qh_fprintf_rbox() for rboxlib.c
+     Use qh_fprintf_rbox() for rboxlib_r.c
 
    notes:
      same as fprintf()
      fgets() is not trapped like fprintf()
      exit qh_fprintf_rbox via qh_errexit_rbox()
 */
 
 void qh_fprintf_rbox(qhT *qh, FILE *fp, int msgcode, const char *fmt, ... ) {
     va_list args;
 
     if (!fp) {
-        fprintf(stderr, "QH6231 Qhull internal error (userprintf.c): fp is 0.  Wrong qh_fprintf_rbox called.\n");
+        fprintf(stderr, "QH6231 Qhull internal error (userprintf_r.c): fp is 0.  Wrong qh_fprintf_rbox called.\n");
         qh_errexit_rbox(qh, 6231);
     }
     if (msgcode >= MSG_ERROR && msgcode < MSG_STDERR)
       fprintf(fp, "QH%.4d ", msgcode);
     va_start(args, fmt);
     vfprintf(fp, fmt, args);
     va_end(args);
 } /* qh_fprintf_rbox */
 
diff --git a/src/qhulltest/PointCoordinates_test.cpp b/src/qhulltest/PointCoordinates_test.cpp
index 1c4e1cf..608a9fb 100644
--- a/src/qhulltest/PointCoordinates_test.cpp
+++ b/src/qhulltest/PointCoordinates_test.cpp
@@ -1,397 +1,396 @@
 /****************************************************************************
 **
 ** Copyright (c) 2009-2014 C.B. Barber. All rights reserved.
-** $Id: //main/2011/qhull/src/qhulltest/PointCoordinates_test.cpp#6 $$Change: 1490 $
-** $DateTime: 2012/02/19 20:27:01 $$Author: bbarber $
+** $Id: //main/2011/qhull/src/qhulltest/PointCoordinates_test.cpp#8 $$Change: 1708 $
+** $DateTime: 2014/03/26 19:13:56 $$Author: bbarber $
 **
 ****************************************************************************/
 
 //pre-compiled headers
 #include 
 #include "RoadTest.h" // QT_VERSION
 
 #include "PointCoordinates.h"
 #include "QhullError.h"
 #include "RboxPoints.h"
 #include "Qhull.h"
 
 using std::cout;
 using std::endl;
 using std::ostringstream;
 using std::ostream;
 using std::string;
 using std::stringstream;
 
 namespace orgQhull {
 
 class PointCoordinates_test : public RoadTest
 {
     Q_OBJECT
 
 #//Test slots
 private slots:
     void t_construct();
     void t_convert();
     void t_getset();
     void t_element();
     void t_foreach();
     void t_search();
     void t_modify();
     void t_append_points();
     void t_coord_iterator();
     void t_io();
 };//PointCoordinates_test
 
 void
 add_PointCoordinates_test()
 {
     new PointCoordinates_test();
 }
 
 void PointCoordinates_test::
 t_construct()
 {
     PointCoordinates pc;
     QCOMPARE(pc.size(), 0U);
     QCOMPARE(pc.coordinateCount(), 0);
     QCOMPARE(pc.dimension(), 0);
     QCOMPARE(pc.coordinates(), (coordT *)0);
     QVERIFY(pc.isEmpty());
     pc.checkValid();
     PointCoordinates pc7(2);
     QCOMPARE(pc7.dimension(), 2);
     QCOMPARE(pc7.count(), 0);
     QVERIFY(pc7.isEmpty());
     QVERIFY(pc7.comment().empty());
     pc7.checkValid();
     PointCoordinates pc2("Test pc2");
     QCOMPARE(pc2.count(), 0);
     QVERIFY(pc2.isEmpty());
     QCOMPARE(pc2.comment(), std::string("Test pc2"));
     pc2.checkValid();
     PointCoordinates pc3(3, "Test 3-d pc3");
     QCOMPARE(pc3.dimension(), 3);
     QVERIFY(pc3.isEmpty());
     pc3.checkValid();
     coordT c[]= { 0.0, 1.0, 2.0, 3.0, 4.0, 5.0 };
     PointCoordinates pc4(2, "Test 2-d pc4", 6, c);
     QCOMPARE(pc4.dimension(), 2);
     QCOMPARE(pc4.count(), 3);
     QCOMPARE(pc4.size(), 3u);
     QVERIFY(!pc4.isEmpty());
-    QVERIFY(!pc4.empty());
     pc4.checkValid();
     QhullPoint p= pc4[2];
     QCOMPARE(p[1], 5.0);
     // QhullPoint refers to PointCoordinates
     p[1] += 1.0;
     QCOMPARE(pc4[2][1], 6.0);
     PointCoordinates pc5(4, "Test 4-d pc5 with insufficient coordinates", 6, c);
     QCOMPARE(pc5.dimension(), 4);
     QCOMPARE(pc5.count(), 1);
     QCOMPARE(pc5.extraCoordinatesCount(), 2);
     QCOMPARE(pc5.extraCoordinates()[1], 5.0);
     QVERIFY(!pc5.isEmpty());;
     std::vector vc;
     vc.push_back(3.0);
     vc.push_back(4.0);
     vc.push_back(5.0);
     vc.push_back(6.0);
     vc.push_back(7.0);
     vc.push_back(9.0);
     pc5.append(2, &vc[3]); // Copy of vc[]
     pc5.checkValid();
     QhullPoint p5(4, &vc[1]);
     QCOMPARE(pc5[1], p5);
     PointCoordinates pc6(pc5); // Makes copy of point_coordinates
     QCOMPARE(pc6[1], p5);
     QVERIFY(pc6==pc5);
     QhullPoint p6= pc5[1];  // Refers to pc5.coordinates
     pc5[1][0] += 1.0;
     QCOMPARE(pc5[1], p6);
     QVERIFY(pc5[1]!=p5);
     QVERIFY(pc6!=pc5);
     pc6= pc5;
     QVERIFY(pc6==pc5);
     PointCoordinates pc8;
     pc6= pc8;
     QVERIFY(pc6!=pc5);
     QVERIFY(pc6.isEmpty());
 }//t_construct
 
 void PointCoordinates_test::
 t_convert()
 {
     //defineAs tested above
     coordT c[]= {0.0, 1.0, 2.0, 3.0, 4.0, 5.0};
     PointCoordinates ps(3, "two 3-d points", 6, c);
     QCOMPARE(ps.dimension(), 3);
     QCOMPARE(ps.size(), 2u);
     const coordT *c2= ps.constData();
     QVERIFY(c!=c2);
     QCOMPARE(c[0], c2[0]);
     const coordT *c3= ps.data();
     QCOMPARE(c3, c2);
     coordT *c4= ps.data();
     QCOMPARE(c4, c2);
     std::vector vs= ps.toStdVector();
     QCOMPARE(vs.size(), 6u);
     QCOMPARE(vs[5], 5.0);
     QList qs= ps.toQList();
     QCOMPARE(qs.size(), 6);
     QCOMPARE(qs[5], 5.0);
 }//t_convert
 
 void PointCoordinates_test::
 t_getset()
 {
     // See t_construct() for test of coordinates, coordinateCount, dimension, empty, isEmpty, ==, !=
     // See t_construct() for test of checkValid, comment, setDimension
     PointCoordinates pc("Coordinates c");
     pc.setComment("New comment");
     QCOMPARE(pc.comment(), std::string("New comment"));
     pc.checkValid();
     pc.makeValid();  // A no-op
     pc.checkValid();
     Coordinates cs= pc.getCoordinates();
     QVERIFY(cs.isEmpty());
     PointCoordinates pc2(pc);
     pc.setDimension(3);
     QVERIFY(pc2!=pc);
     coordT c[]= {0.0, 1.0, 2.0, 3.0, 4.0, 5.0};
     pc.append(6, c);
     pc.checkValid();
     pc.makeValid();  // A no-op
     QhullPoint p= pc[0];
     QCOMPARE(p[2], 2.0);
     try{
         pc.setDimension(2);
         QFAIL("setDimension(2) did not fail for 3-d.");
     }catch (const std::exception &e) {
         const char *s= e.what();
         cout << "INFO   : Caught " << s;
     }
 }//t_getset
 
 void PointCoordinates_test::
 t_element()
 {
     coordT c[]= {0.0, 1.0, 2.0, 3.0, 4.0, 5.0};
     PointCoordinates pc(2, "2-d points", 6, c);
     QhullPoint p= pc.at(0);
     QCOMPARE(p, pc[0]);
     QCOMPARE(p, pc.first());
     QCOMPARE(p, pc.value(0));
     p= pc.back();
     QCOMPARE(p, pc[2]);
     QCOMPARE(p, pc.last());
     QCOMPARE(p, pc.value(2));
     QhullPoints ps= pc.mid(1, 2);
     QCOMPARE(ps[1], p);
 }//t_element
 
 void PointCoordinates_test::
 t_foreach()
 {
     coordT c[]= {0.0, 1.0, 2.0, 3.0, 4.0, 5.0};
     PointCoordinates pc(2, "2-d points", 6, c);
     QhullPoints::Iterator i= pc.begin();
     QhullPoint p= pc[0];
     QCOMPARE(*i, p);
     QCOMPARE((*i)[0], 0.0);
     QhullPoint p3= pc[2];
     i= pc.end();
     QCOMPARE(i[-1], p3);
     const PointCoordinates pc2(2, "2-d points", 6, c);
     QhullPoints::ConstIterator i2= pc.begin();
     const QhullPoint p0= pc2[0];
     QCOMPARE(*i2, p0);
     QCOMPARE((*i2)[0], 0.0);
     QhullPoints::ConstIterator i3= i2;
     QCOMPARE(i3, i2);
     QCOMPARE((*i3)[0], 0.0);
     i3= pc.constEnd();
     --i3;
     QhullPoint p2= pc2[2];
     QCOMPARE(*i3, p2);
     i= pc.end();
     QVERIFY(i-1==i3);
     i2= pc2.end();
     QVERIFY(i2-1!=i3);
     QCOMPARE(*(i2-1), *i3);
     foreach(QhullPoint p3, pc){ //Qt only
         QVERIFY(p3[0]>=0.0);
         QVERIFY(p3[0]<=5.0);
     }
     Coordinates::ConstIterator i4= pc.beginCoordinates();
     QCOMPARE(*i4, 0.0);
     Coordinates::Iterator i5= pc.beginCoordinates();
     QCOMPARE(*i5, 0.0);
     i4= pc.beginCoordinates(1);
     QCOMPARE(*i4, 2.0);
     i5= pc.beginCoordinates(1);
     QCOMPARE(*i5, 2.0);
     i4= pc.endCoordinates();
     QCOMPARE(*--i4, 5.0);
     i5= pc.endCoordinates();
     QCOMPARE(*--i5, 5.0);
 }//t_foreach
 
 void PointCoordinates_test::
 t_search()
 {
     coordT c[]= {0.0, 1.0, 2.0, 3.0, 4.0, 5.0};
     PointCoordinates pc(2, "2-d points", 6, c);
     QhullPoint p0= pc[0];
     QhullPoint p2= pc[2];
     QVERIFY(pc.contains(p0));
     QVERIFY(pc.contains(p2));
     QCOMPARE(pc.count(p0), 1);
     QCOMPARE(pc.indexOf(p2), 2);
     QCOMPARE(pc.lastIndexOf(p0), 0);
 }//t_search
 
 void PointCoordinates_test::
 t_modify()
 {
     coordT c[]= {0.0, 1.0, 2.0, 3.0, 4.0, 5.0};
     PointCoordinates pc(2, "2-d points", 6, c);
     coordT c3[]= {0.0, 1.0, 2.0, 3.0, 4.0, 5.0};
     PointCoordinates pc5(2);
     pc5.append(6, c3); // 0-5
     QVERIFY(pc5==pc);
     PointCoordinates pc2(2, "2-d");
     coordT c2[]= {6.0, 7.0, 8.0, 9.0, 10.0, 11.0};
     pc2.append(6, c2);
     QCOMPARE(pc2.count(), 3);
     pc2.append(14.0);
     QCOMPARE(pc2.count(), 3);
     QCOMPARE(pc2.extraCoordinatesCount(), 1);
     pc2.append(15.0); // 6-11, 14,15
     QCOMPARE(pc2.count(), 4);
     QCOMPARE(pc2.extraCoordinatesCount(), 0);
     QhullPoint p(pc[0]);
     pc2.append(p); // 6-11, 14,15, 0,1
     QCOMPARE(pc2.count(), 5);
     QCOMPARE(pc2.extraCoordinatesCount(), 0);
     QCOMPARE(pc2.lastIndexOf(p), 4);
     pc.append(pc2); // Invalidates p
     QCOMPARE(pc.count(), 8); // 0-11, 14,15, 0,1
     QCOMPARE(pc.extraCoordinatesCount(), 0);
     QCOMPARE(pc.lastIndexOf(pc[0]), 7);
     pc.appendComment(" operators");
     QCOMPARE(pc.comment(), std::string("2-d points operators"));
     pc.checkValid();
     // see t_append_points for appendPoints
     PointCoordinates pc3= pc+pc2;
     pc3.checkValid();
     QCOMPARE(pc3.count(), 13);
     QCOMPARE(pc3[6][0], 14.0);
     QCOMPARE(pc3[8][0], 6.0);
     pc3 += pc;
     QCOMPARE(pc3.count(), 21);
     QCOMPARE(pc3[14][0], 2.0);
     pc3 += 12.0;
     pc3 += 14.0;
     QCOMPARE(pc3.count(), 22);
     QCOMPARE(pc3.last()[0], 12.0);
     // QhullPoint p3= pc3.first(); // += throws error because append may move the data
     QhullPoint p3= pc2.first();
     pc3 += p3;
     QCOMPARE(pc3.count(), 23);
     QCOMPARE(pc3.last()[0], 6.0);
     pc3 << pc;
     QCOMPARE(pc3.count(), 31);
     QCOMPARE(pc3.last()[0], 0.0);
     pc3 << 12.0 << 14.0;
     QCOMPARE(pc3.count(), 32);
     QCOMPARE(pc3.last()[0], 12.0);
     PointCoordinates pc4(pc3);
     pc4.reserveCoordinates(100);
     QVERIFY(pc3==pc4);
 }//t_modify
 
 void PointCoordinates_test::
 t_append_points()
 {
     PointCoordinates pc(2, "stringstream");
     stringstream s("2 3 1 2 3 4 5 6");
     pc.appendPoints(s);
     QCOMPARE(pc.count(), 3);
 }//t_append_points
 
 void PointCoordinates_test::
 t_coord_iterator()
 {
     PointCoordinates c(2);
     c << 0.0 << 1.0 << 2.0 << 3.0 << 4.0 << 5.0;
     PointCoordinatesIterator i(c);
     QhullPoint p0(c[0]);
     QhullPoint p1(c[1]);
     QhullPoint p2(c[2]);
     coordT c2[] = {-1.0, -2.0};
     QhullPoint p3(2, c2);
     PointCoordinatesIterator i2= c;
     QVERIFY(i.findNext(p1));
     QVERIFY(!i.findNext(p1));
     QVERIFY(!i.findNext(p2));
     QVERIFY(!i.findNext(p3));
     QVERIFY(i.findPrevious(p2));
     QVERIFY(!i.findPrevious(p2));
     QVERIFY(!i.findPrevious(p0));
     QVERIFY(!i.findPrevious(p3));
     QVERIFY(i2.findNext(p2));
     QVERIFY(i2.findPrevious(p0));
     QVERIFY(i2.findNext(p1));
     QVERIFY(i2.findPrevious(p0));
     QVERIFY(i2.hasNext());
     QVERIFY(!i2.hasPrevious());
     QVERIFY(i.hasNext());
     QVERIFY(!i.hasPrevious());
     i.toBack();
     i2.toFront();
     QVERIFY(!i.hasNext());
     QVERIFY(i.hasPrevious());
     QVERIFY(i2.hasNext());
     QVERIFY(!i2.hasPrevious());
     PointCoordinates c3;
     PointCoordinatesIterator i3= c3;
     QVERIFY(!i3.hasNext());
     QVERIFY(!i3.hasPrevious());
     i3.toBack();
     QVERIFY(!i3.hasNext());
     QVERIFY(!i3.hasPrevious());
     QCOMPARE(i.peekPrevious(), p2);
     QCOMPARE(i.previous(), p2);
     QCOMPARE(i.previous(), p1);
     QCOMPARE(i.previous(), p0);
     QVERIFY(!i.hasPrevious());
     QCOMPARE(i.peekNext(), p0);
     // i.peekNext()= 1.0; // compiler error
     QCOMPARE(i.next(), p0);
     QCOMPARE(i.peekNext(), p1);
     QCOMPARE(i.next(), p1);
     QCOMPARE(i.next(), p2);
     QVERIFY(!i.hasNext());
     i.toFront();
     QCOMPARE(i.next(), p0);
 }//t_coord_iterator
 
 void PointCoordinates_test::
 t_io()
 {
     PointCoordinates c;
     c << 1.0 << 2.0 << 3.0 << 1.0 << 2.0 << 3.0;
     ostringstream os;
     os << "PointCoordinates 0-d\n" << c;
     c.setDimension(2);
     os << "PointCoordinates 1-3-2\n" << c;
     cout << os.str();
     QString s= QString::fromStdString(os.str());
     QCOMPARE(s.count("0"), 3);
     QCOMPARE(s.count("2"), 4);
 }//t_io
 
 }//orgQhull
 
 #include "moc/PointCoordinates_test.moc"
diff --git a/src/qhulltest/QhullFacetList_test.cpp b/src/qhulltest/QhullFacetList_test.cpp
index 8a0b516..3070647 100644
--- a/src/qhulltest/QhullFacetList_test.cpp
+++ b/src/qhulltest/QhullFacetList_test.cpp
@@ -1,172 +1,173 @@
 /****************************************************************************
 **
 ** Copyright (c) 2008-2014 C.B. Barber. All rights reserved.
-** $Id: //main/2011/qhull/src/qhulltest/QhullFacetList_test.cpp#4 $$Change: 1490 $
-** $DateTime: 2012/02/19 20:27:01 $$Author: bbarber $
+** $Id: //main/2011/qhull/src/qhulltest/QhullFacetList_test.cpp#6 $$Change: 1709 $
+** $DateTime: 2014/03/26 22:27:14 $$Author: bbarber $
 **
 ****************************************************************************/
 
 //pre-compiled headers
 #include 
 #include "RoadTest.h" // QT_VERSION
 
 #include "QhullFacetList.h"
 #include "QhullError.h"
 #include "QhullFacet.h"
 #include "QhullVertexSet.h"
 #include "Qhull.h"
 
 using std::cout;
 using std::endl;
 using std::ostringstream;
 using std::ostream;
 using std::string;
 
 namespace orgQhull {
 
 class QhullFacetList_test : public RoadTest
 {
     Q_OBJECT
 
 #//Test slots
 private slots:
     void cleanup();
     void t_construct();
     void t_convert();
     void t_readonly();
     void t_foreach();
     void t_io();
 };//QhullFacetList_test
 
 void
 add_QhullFacetList_test()
 {
     new QhullFacetList_test();
 }
 
 //Executed after each testcase
 void QhullFacetList_test::
 cleanup()
 {
     UsingLibQhull::checkQhullMemoryEmpty();
     RoadTest::cleanup();
 }
 
 void QhullFacetList_test::
 t_construct()
 {
     RboxPoints rcube("c");
     Qhull q(rcube,"QR0");  // rotated unit cube
     QhullFacetList fs2= q.facetList();
     QVERIFY(!fs2.isEmpty());
     QCOMPARE(fs2.count(),6);
     QhullFacetList fs3(q.endFacet(), q.endFacet());
     QVERIFY(fs3.isEmpty());
     QhullFacetList fs4(q.endFacet().previous(), q.endFacet());
     QCOMPARE(fs4.count(), 1);
     QhullFacetList fs5(q.beginFacet(), q.endFacet());
     QCOMPARE(fs2.count(), fs5.count());
     QVERIFY(fs2==fs5);
     QhullFacetList fs6= fs2; // copy constructor
     QVERIFY(fs6==fs2);
     std::vector fv= fs2.toStdVector();
     QCOMPARE(fv.size(), 6u);
 }//t_construct
 
 void QhullFacetList_test::
 t_convert()
 {
     RboxPoints rcube("c");
     Qhull q(rcube,"QR0 QV2");  // rotated unit cube
     QhullFacetList fs2= q.facetList();
     QVERIFY(!fs2.isSelectAll());
     QVERIFY(!fs2.isEmpty());
     QCOMPARE(fs2.count(),3);
     std::vector fv= fs2.toStdVector();
     QCOMPARE(fv.size(), 3u);
     QList fv2= fs2.toQList();
     QCOMPARE(fv2.size(), 3);
-    std::vector fv5= fs2.vertices_toStdVector(q.runId());
+    std::vector fv5= fs2.vertices_toStdVector();
     QCOMPARE(fv5.size(), 7u);
-    QList fv6= fs2.vertices_toQList(q.runId());
+    QList fv6= fs2.vertices_toQList();
     QCOMPARE(fv6.size(), 7);
     fs2.selectAll();
     QVERIFY(fs2.isSelectAll());
     std::vector fv3= fs2.toStdVector();
     QCOMPARE(fv3.size(), 6u);
     QList fv4= fs2.toQList();
     QCOMPARE(fv4.size(), 6);
-    std::vector fv7= fs2.vertices_toStdVector(q.runId());
+    std::vector fv7= fs2.vertices_toStdVector();
     QCOMPARE(fv7.size(), 8u);
-    QList fv8= fs2.vertices_toQList(q.runId());
+    QList fv8= fs2.vertices_toQList();
     QCOMPARE(fv8.size(), 8);
 }//t_convert
 
 //! Spot check properties and read-only.  See QhullLinkedList_test
 void QhullFacetList_test::
 t_readonly()
 {
     RboxPoints rcube("c");
     Qhull q(rcube,"QV0");  // good facets are adjacent to point 0
     QhullFacetList fs= q.facetList();
     QVERIFY(!fs.isSelectAll());
     QCOMPARE(fs.count(), 3);
     QCOMPARE(fs.first(), q.firstFacet());
     fs.selectAll();
     QVERIFY(fs.isSelectAll());
     QCOMPARE(fs.count(), 6);
     fs.selectGood();
     QVERIFY(!fs.isSelectAll());
     QCOMPARE(fs.count(), 3);
     fs.selectAll();
     QVERIFY(fs.isSelectAll());
     QCOMPARE(fs.count(), 6);
     QhullFacet f= fs.first();
     QhullFacet f2= fs.last();
     fs.selectAll();
     QVERIFY(fs.contains(f));
     QVERIFY(fs.contains(f2));
     QVERIFY(f.isGood());
     QVERIFY(!f2.isGood());
     fs.selectGood();
     QVERIFY(fs.contains(f));
     QVERIFY(!fs.contains(f2));
 }//t_readonly
 
 void QhullFacetList_test::
 t_foreach()
 {
     RboxPoints rcube("c");
     // Spot check predicates and accessors.  See QhullLinkedList_test
     Qhull q(rcube,"Qt QR0");  // triangulation of rotated unit cube
     QhullFacetList fs= q.facetList();
     QVERIFY(fs.contains(q.firstFacet()));
     QhullFacet f= q.firstFacet().next();
     QVERIFY(fs.contains(f));
     QCOMPARE(fs.first(), *fs.begin());
     QCOMPARE(*(fs.end()-1), fs.last());
     QCOMPARE(fs.first(), q.firstFacet());
     QCOMPARE(*fs.begin(), q.beginFacet());
     QCOMPARE(*fs.end(), q.endFacet());
 }//t_foreach
 
 void QhullFacetList_test::
 t_io()
 {
     RboxPoints rcube("c");
     {
         Qhull q(rcube,"QR0 QV0");   // good facets are adjacent to point 0
         QhullFacetList fs= q.facetList();
         ostringstream os;
-        os << fs.print(q.runId()); // Runs all print options
-        os << "\nFacets only\n" << fs; // printVertices() requires a runId
+        os << fs.print(); // Runs all print options
+        os << "\nFacets only\n" << fs; 
+        os << "\nVertices\n" << fs.printVertices()
         cout << os.str();
         QString facets= QString::fromStdString(os.str());
         QCOMPARE(facets.count("(v"), 7+12*3*2);
         QCOMPARE(facets.count(QRegExp("f\\d")), 3*7 + 13*3*2);
     }
 }//t_io
 
 }//orgQhull
 
 #include "moc/QhullFacetList_test.moc"
diff --git a/src/qhulltest/QhullFacetSet_test.cpp b/src/qhulltest/QhullFacetSet_test.cpp
index 427e5f5..7b9ae8f 100644
--- a/src/qhulltest/QhullFacetSet_test.cpp
+++ b/src/qhulltest/QhullFacetSet_test.cpp
@@ -1,153 +1,153 @@
 /****************************************************************************
 **
 ** Copyright (c) 2008-2014 C.B. Barber. All rights reserved.
-** $Id: //main/2011/qhull/src/qhulltest/QhullFacetSet_test.cpp#4 $$Change: 1490 $
-** $DateTime: 2012/02/19 20:27:01 $$Author: bbarber $
+** $Id: //main/2011/qhull/src/qhulltest/QhullFacetSet_test.cpp#6 $$Change: 1709 $
+** $DateTime: 2014/03/26 22:27:14 $$Author: bbarber $
 **
 ****************************************************************************/
 
 //pre-compiled headers
 #include 
 #include "RoadTest.h"
 
 #include "QhullFacetSet.h"
 #include "QhullError.h"
 #include "QhullFacet.h"
 #include "Qhull.h"
 
 using std::cout;
 using std::endl;
 using std::ostringstream;
 using std::ostream;
 using std::string;
 
 namespace orgQhull {
 
 class QhullFacetSet_test : public RoadTest
 {
     Q_OBJECT
 
 #//Test slots
 private slots:
     void cleanup();
     void t_construct();
     void t_convert();
     void t_readonly();
     void t_foreach();
     void t_io();
 };//QhullFacetSet_test
 
 void
 add_QhullFacetSet_test()
 {
     new QhullFacetSet_test();
 }
 
 //Executed after each testcase
 void QhullFacetSet_test::
 cleanup()
 {
     RoadTest::cleanup();
     UsingLibQhull::checkQhullMemoryEmpty();
 }
 
 void QhullFacetSet_test::
 t_construct()
 {
     RboxPoints rcube("c");
     Qhull q(rcube,"QR0");  // rotated unit cube
     QhullFacet f= q.firstFacet();
     QhullFacetSet fs2= f.neighborFacets();
     QVERIFY(!fs2.isEmpty());
     QCOMPARE(fs2.count(),4);
     QhullFacetSet fs4= fs2; // copy constructor
     QVERIFY(fs4==fs2);
     QhullFacetSet fs3(q.qhullQh()->facet_mergeset);
     QVERIFY(fs3.isEmpty());
 }//t_construct
 
 void QhullFacetSet_test::
 t_convert()
 {
     RboxPoints rcube("c");
     Qhull q2(rcube,"QR0 QV2");  // rotated unit cube
     QhullFacet f2= q2.firstFacet();
     QhullFacetSet fs2= f2.neighborFacets();
     QVERIFY(!fs2.isSelectAll());
     QCOMPARE(fs2.count(),2);
     std::vector fv= fs2.toStdVector();
     QCOMPARE(fv.size(), 2u);
     QList fv2= fs2.toQList();
     QCOMPARE(fv2.size(), 2);
     fs2.selectAll();
     QVERIFY(fs2.isSelectAll());
     std::vector fv3= fs2.toStdVector();
     QCOMPARE(fv3.size(), 4u);
     QList fv4= fs2.toQList();
     QCOMPARE(fv4.size(), 4);
 }//t_convert
 
 //! Spot check properties and read-only.  See QhullSet_test
 void QhullFacetSet_test::
 t_readonly()
 {
     RboxPoints rcube("c");
     Qhull q(rcube,"QV0");  // good facets are adjacent to point 0
     QhullFacetSet fs= q.firstFacet().neighborFacets();
     QVERIFY(!fs.isSelectAll());
     QCOMPARE(fs.count(), 2);
     fs.selectAll();
     QVERIFY(fs.isSelectAll());
     QCOMPARE(fs.count(), 4);
     fs.selectGood();
     QVERIFY(!fs.isSelectAll());
     QCOMPARE(fs.count(), 2);
     QhullFacet f= fs.first();
     QhullFacet f2= fs.last();
     fs.selectAll();
     QVERIFY(fs.contains(f));
     QVERIFY(fs.contains(f2));
     QVERIFY(f.isGood());
     QVERIFY(!f2.isGood());
     fs.selectGood();
     QVERIFY(fs.contains(f));
     QVERIFY(!fs.contains(f2));
 }//t_readonly
 
 void QhullFacetSet_test::
 t_foreach()
 {
     RboxPoints rcube("c");
     // Spot check predicates and accessors.  See QhullLinkedList_test
     Qhull q(rcube,"QR0");  // rotated unit cube
     QhullFacetSet fs= q.firstFacet().neighborFacets();
     QVERIFY(!fs.contains(q.firstFacet()));
     QVERIFY(fs.contains(fs.first()));
     QhullFacet f= q.firstFacet().next();
     if(!fs.contains(f)){
         f= f.next();
     }
     QVERIFY(fs.contains(f));
     QCOMPARE(fs.first(), *fs.begin());
     QCOMPARE(*(fs.end()-1), fs.last());
 }//t_foreach
 
 void QhullFacetSet_test::
 t_io()
 {
     RboxPoints rcube("c");
     {
         Qhull q(rcube,"QR0 QV0");   // good facets are adjacent to point 0
         QhullFacetSet fs= q.firstFacet().neighborFacets();
         ostringstream os;
-        os << fs.print(q.runId(), "Neighbors of first facet with point 0");
+        os << fs.print("Neighbors of first facet with point 0");
         os << fs.printIdentifiers("\nFacet identifiers: ");
         cout << os.str();
         QString facets= QString::fromStdString(os.str());
         QCOMPARE(facets.count(QRegExp(" f[0-9]")), 2+13*2);
     }
 }//t_io
 
 }//orgQhull
 
 #include "moc/QhullFacetSet_test.moc"
diff --git a/src/qhulltest/QhullFacet_test.cpp b/src/qhulltest/QhullFacet_test.cpp
index d486499..1ea4795 100644
--- a/src/qhulltest/QhullFacet_test.cpp
+++ b/src/qhulltest/QhullFacet_test.cpp
@@ -1,264 +1,264 @@
 /****************************************************************************
 **
 ** Copyright (c) 2008-2014 C.B. Barber. All rights reserved.
-** $Id: //main/2011/qhull/src/qhulltest/QhullFacet_test.cpp#6 $$Change: 1490 $
-** $DateTime: 2012/02/19 20:27:01 $$Author: bbarber $
+** $Id: //main/2011/qhull/src/qhulltest/QhullFacet_test.cpp#9 $$Change: 1709 $
+** $DateTime: 2014/03/26 22:27:14 $$Author: bbarber $
 **
 ****************************************************************************/
 
 //pre-compiled headers
 #include 
 #include "RoadTest.h"
 
 #include "QhullFacet.h"
 #include "QhullError.h"
 #include "Coordinates.h"
 #include "RboxPoints.h"
 #include "QhullFacetList.h"
 #include "QhullFacetSet.h"
 #include "QhullPointSet.h"
 #include "QhullRidge.h"
 #include "Qhull.h"
 
 using std::cout;
 using std::endl;
 using std::ostringstream;
 using std::ostream;
 using std::string;
 
 namespace orgQhull {
 
 class QhullFacet_test : public RoadTest
 {
     Q_OBJECT
 
 #//Test slots
 private slots:
     void cleanup();
     void t_constructConvert();
     void t_getSet();
     void t_value();
     void t_foreach();
     void t_io();
 };//QhullFacet_test
 
 void
 add_QhullFacet_test()
 {
     new QhullFacet_test();
 }
 
 //Executed after each testcase
 void QhullFacet_test::
 cleanup()
 {
     UsingLibQhull::checkQhullMemoryEmpty();
     RoadTest::cleanup();
 }
 
 void QhullFacet_test::
 t_constructConvert()
 {
     // Qhull.runQhull() constructs QhullFacets as facetT
     QhullFacet f;
     QVERIFY(!f.isDefined());
     QCOMPARE(f.dimension(),0);
     RboxPoints rcube("c");
     Qhull q(rcube,"Qt QR0");  // triangulation of rotated unit cube
     QhullFacet f2(q.beginFacet());
     QCOMPARE(f2.dimension(),3);
     f= f2; // copy assignment
     QVERIFY(f.isDefined());
     QCOMPARE(f.dimension(),3);
     QhullFacet f5= f2;
     QVERIFY(f5==f2);
     QVERIFY(f5==f);
     QhullFacet f3= f2.getFacetT();
     QCOMPARE(f,f3);
     QhullFacet f4= f2.getBaseT();
     QCOMPARE(f,f4);
 }//t_constructConvert
 
 void QhullFacet_test::
 t_getSet()
 {
     RboxPoints rcube("c");
     {
         Qhull q(rcube,"Qt QR0");  // triangulation of rotated unit cube
         QCOMPARE(q.facetCount(), 12);
         QCOMPARE(q.vertexCount(), 8);
         QhullFacetListIterator i(q.facetList());
         while(i.hasNext()){
             const QhullFacet f= i.next();
             cout << f.id() << endl;
             QCOMPARE(f.dimension(),3);
             QVERIFY(f.id()>0 && f.id()<=39);
             QVERIFY(f.isDefined());
             if(i.hasNext()){
                 QCOMPARE(f.next(), i.peekNext());
                 QVERIFY(f.next()!=f);
             }
             QVERIFY(i.hasPrevious());
             QCOMPARE(f, i.peekPrevious());
         }
         QhullFacetListIterator i2(i);
         QEXPECT_FAIL("", "ListIterator copy constructor not reset to BOT", Continue);
         QVERIFY(!i2.hasPrevious());
 
         // test tricoplanarOwner
         QhullFacet facet = q.beginFacet();
         QhullFacet tricoplanarOwner = facet.tricoplanarOwner();
         int tricoplanarCount= 0;
         i.toFront();
         while(i.hasNext()){
             const QhullFacet f= i.next();
             if(f.tricoplanarOwner()==tricoplanarOwner){
                 tricoplanarCount++;
             }
         }
         QCOMPARE(tricoplanarCount, 2);
         int tricoplanarCount2= 0;
         foreach (QhullFacet f, q.facetList()){  // Qt only
             QhullHyperplane h= f.hyperplane();
             cout << "Hyperplane: " << h << endl;
             QCOMPARE(h.count(), 3);
             QCOMPARE(h.offset(), -0.5);
             double n= h.norm();
             QCOMPARE(n, 1.0);
-            QhullHyperplane hi= f.innerplane(q.runId());
+            QhullHyperplane hi= f.innerplane();
             QCOMPARE(hi.count(), 3);
             double innerOffset= hi.offset()+0.5;
             cout << "InnerPlane: " << hi << "innerOffset+0.5 " << innerOffset << endl;
             QVERIFY(innerOffset >= 0.0);
-            QhullHyperplane ho= f.outerplane(q.runId());
+            QhullHyperplane ho= f.outerplane();
             QCOMPARE(ho.count(), 3);
             double outerOffset= ho.offset()+0.5;
             cout << "OuterPlane: " << ho << "outerOffset+0.5 " << outerOffset << endl;
             QVERIFY(outerOffset <= 0.0);
             QVERIFY(outerOffset-innerOffset < 1e-7);
             for(int k= 0; k<3; k++){
                 QVERIFY(ho[k]==hi[k]);
                 QVERIFY(ho[k]==h[k]);
             }
-            QhullPoint center= f.getCenter(q.runId());
+            QhullPoint center= f.getCenter();
             cout << "Center: " << center << endl;
             double d= f.distance(center);
             QVERIFY(d < innerOffset-outerOffset);
-            QhullPoint center2= f.getCenter(q.runId(), qh_PRINTcentrums);
+            QhullPoint center2= f.getCenter(qh_PRINTcentrums);
             QCOMPARE(center, center2);
             if(f.tricoplanarOwner()==tricoplanarOwner){
                 tricoplanarCount2++;
             }
         }
         QCOMPARE(tricoplanarCount2, 2);
         Qhull q2(rcube,"d Qz Qt QR0");  // 3-d triangulation of Delaunay triangulation (the cube)
         QhullFacet f2= q2.firstFacet();
-        QhullPoint center3= f2.getCenter(q.runId(), qh_PRINTtriangles);
+        QhullPoint center3= f2.getCenter(qh_PRINTtriangles);
         QCOMPARE(center3.dimension(), 3);
-        QhullPoint center4= f2.getCenter(q.runId());
+        QhullPoint center4= f2.getCenter();
         QCOMPARE(center4.dimension(), 3);
         for(int k= 0; k<3; k++){
             QVERIFY(center4[k]==center3[k]);
         }
         Qhull q3(rcube,"v Qz QR0");  // Voronoi diagram of a cube (one vertex)
 
         UsingLibQhull::setGlobalDistanceEpsilon(1e-12); // Voronoi vertices are not necessarily within distance episilon
         foreach(QhullFacet f, q3.facetList()){ //Qt only
             if(f.isGood()){
                 QhullPoint p= f.voronoiVertex(q3.runId());
                 cout << p.print(q3.runId(), "Voronoi vertex: ")
                     << " DistanceEpsilon " << UsingLibQhull::globalDistanceEpsilon() << endl;
                 QCOMPARE(p, q3.origin());
             }
         }
     }
 }//t_getSet
 
 void QhullFacet_test::
 t_value()
 {
     RboxPoints rcube("c");
     {
         Qhull q(rcube, "");
         coordT c[]= {0.0, 0.0, 0.0};
         foreach (QhullFacet f, q.facetList()){  // Qt only
             double d= f.distance(q.origin());
             QCOMPARE(d, -0.5);
             double d0= f.distance(c);
             QCOMPARE(d0, -0.5);
-            double facetArea= f.facetArea(q.runId());
+            double facetArea= f.facetArea();
             QCOMPARE(facetArea, 1.0);
             #if qh_MAXoutside
                 double maxoutside= f.getFacetT()->maxoutside;
                 QVERIFY(maxoutside<1e-7);
             #endif
         }
     }
 }//t_value
 
 void QhullFacet_test::
 t_foreach()
 {
     RboxPoints rcube("c W0 300");  // cube plus 300 points on its surface
     {
         Qhull q(rcube, "QR0 Qc"); // keep coplanars, thick facet, and rotate the cube
         int coplanarCount= 0;
         foreach(const QhullFacet f, q.facetList()){
             QhullPointSet coplanars= f.coplanarPoints();
             coplanarCount += coplanars.count();
             QhullFacetSet neighbors= f.neighborFacets();
             QCOMPARE(neighbors.count(), 4);
             QhullPointSet outsides= f.outsidePoints();
             QCOMPARE(outsides.count(), 0);
             QhullRidgeSet ridges= f.ridges();
             QCOMPARE(ridges.count(), 4);
             QhullVertexSet vertices= f.vertices();
             QCOMPARE(vertices.count(), 4);
             int ridgeCount= 0;
             QhullRidge r= ridges.first();
             for(int r0= r.id(); ridgeCount==0 || r.id()!=r0; r= r.nextRidge3d(f)){
                 ++ridgeCount;
                 if(!r.hasNextRidge3d(f)){
                     QFAIL("Unexpected simplicial facet.  They only have ridges to non-simplicial neighbors.");
                 }
             }
             QCOMPARE(ridgeCount, 4);
         }
         QCOMPARE(coplanarCount, 300);
     }
 }//t_foreach
 
 void QhullFacet_test::
 t_io()
 {
     RboxPoints rcube("c");
     {
         Qhull q(rcube, "");
         QhullFacet f= q.beginFacet();
         cout << f;
         ostringstream os;
-        os << f.printHeader(q.runId());
+        os << f.printHeader();
         os << f.printFlags("    - flags:");
-        os << f.printCenter(q.runId(), qh_PRINTfacets, "    - center:");
-        os << f.printRidges(q.runId());
+        os << f.printCenter(qh_PRINTfacets, "    - center:");
+        os << f.printRidges();
         cout << os.str();
         ostringstream os2;
-        os2 << f.print(q.runId());  // invokes print*()
+        os2 << f.print();  // invokes print*()
         QString facetString2= QString::fromStdString(os2.str());
         facetString2.replace(QRegExp("\\s\\s+"), " ");
         ostringstream os3;
         q.setOutputStream(&os3);
         q.outputQhull("f");
         QString facetsString= QString::fromStdString(os3.str());
         QString facetString3= facetsString.mid(facetsString.indexOf("- f1\n"));
         facetString3= facetString3.left(facetString3.indexOf("\n- f")+1);
         facetString3.replace(QRegExp("\\s\\s+"), " ");
         QCOMPARE(facetString2, facetString3);
     }
 }//t_io
 
 // toQhullFacet is static_cast only
 
 }//orgQhull
 
 #include "moc/QhullFacet_test.moc"
diff --git a/src/qhulltest/QhullHyperplane_test.cpp b/src/qhulltest/QhullHyperplane_test.cpp
index 129a27c..0df84fd 100644
--- a/src/qhulltest/QhullHyperplane_test.cpp
+++ b/src/qhulltest/QhullHyperplane_test.cpp
@@ -1,412 +1,412 @@
 /****************************************************************************
 **
 ** Copyright (c) 2009-2014 C.B. Barber. All rights reserved.
-** $Id: //main/2011/qhull/src/qhulltest/QhullHyperplane_test.cpp#6 $$Change: 1490 $
-** $DateTime: 2012/02/19 20:27:01 $$Author: bbarber $
+** $Id: //main/2011/qhull/src/qhulltest/QhullHyperplane_test.cpp#8 $$Change: 1709 $
+** $DateTime: 2014/03/26 22:27:14 $$Author: bbarber $
 **
 ****************************************************************************/
 
 //pre-compiled headers
 #include 
 #include 
 #include "RoadTest.h"
 
 #include "QhullHyperplane.h"
 #include "QhullError.h"
 #include "RboxPoints.h"
 #include "QhullFacet.h"
 #include "QhullFacetList.h"
 #include "Qhull.h"
 #include 
 
 using std::cout;
 using std::endl;
 using std::ostringstream;
 using std::ostream;
 using std::string;
 
 namespace orgQhull {
 
 class QhullHyperplane_test : public RoadTest
 {
     Q_OBJECT
 
 #//Test slots
 private slots:
     void cleanup();
     void t_construct();
     void t_convert();
     void t_readonly();
     void t_define();
     void t_value();
     void t_operator();
     void t_iterator();
     void t_const_iterator();
     void t_qhullHyperplane_iterator();
     void t_io();
 };//QhullHyperplane_test
 
 void
 add_QhullHyperplane_test()
 {
     new QhullHyperplane_test();
 }
 
 //Executed after each testcase
 void QhullHyperplane_test::
 cleanup()
 {
     UsingLibQhull::checkQhullMemoryEmpty();
     RoadTest::cleanup();
 }
 
 void QhullHyperplane_test::
 t_construct()
 {
     // Qhull.runQhull() constructs QhullFacets as facetT
     QhullHyperplane h;
     QVERIFY(!h.isDefined());
     QCOMPARE(h.dimension(),0);
     QCOMPARE(h.coordinates(),static_cast(0));
     RboxPoints rcube("c");
     Qhull q(rcube,"Qt QR0");  // triangulation of rotated unit cube
     QhullFacet f= q.firstFacet();
     QhullHyperplane h2(f.hyperplane());
     QVERIFY(h2.isDefined());
     QCOMPARE(h2.dimension(),3);
     // h= h2;  // copy assignment disabled, ambiguous
     QhullHyperplane h3(h2.dimension(), h2.coordinates(), h2.offset());
     QCOMPARE(h2, h3);
     QhullHyperplane h5= h2; // copy constructor
     QVERIFY(h5==h2);
 }//t_construct
 
 void QhullHyperplane_test::
 t_convert()
 {
     RboxPoints rcube("c");
     Qhull q(rcube,"Qt QR0");  // triangulation of rotated unit cube
     QhullHyperplane h= q.firstFacet().hyperplane();
     std::vector fs= h.toStdVector();
     QCOMPARE(fs.size(), 4u);
     double offset= fs.back();
     fs.pop_back();
     QCOMPARE(offset, -0.5);
 
     double squareNorm= inner_product(fs.begin(), fs.end(), fs.begin(), 0.0);
     QCOMPARE(squareNorm, 1.0);
     QList qs= h.toQList();
     QCOMPARE(qs.size(), 4);
     double offset2= qs.takeLast();
     QCOMPARE(offset2, -0.5);
     double squareNorm2= std::inner_product(qs.begin(), qs.end(), qs.begin(), 0.0);
     QCOMPARE(squareNorm2, 1.0);
 }//t_convert
 
 void QhullHyperplane_test::
 t_readonly()
 {
     RboxPoints rcube("c");
     {
         Qhull q(rcube,"Qt QR0");  // triangulation of rotated unit cube
         QhullFacetList fs= q.facetList();
         QhullFacetListIterator i(fs);
         while(i.hasNext()){
             QhullFacet f= i.next();
             QhullHyperplane h= f.hyperplane();
             int id= f.id();
             cout << "h" << id << endl;
             QVERIFY(h.isDefined());
             QCOMPARE(h.dimension(),3);
             const coordT *c= h.coordinates();
             coordT *c2= h.coordinates();
             QCOMPARE(c, c2);
             const coordT *c3= h.begin();
             QCOMPARE(c, c3);
             QCOMPARE(h.offset(), -0.5);
             int j= h.end()-h.begin();
             QCOMPARE(j, 3);
             double squareNorm= std::inner_product(h.begin(), h.end(), h.begin(), 0.0);
             QCOMPARE(squareNorm, 1.0);
         }
         QhullHyperplane h2= fs.first().hyperplane();
         QhullHyperplane h3= fs.last().hyperplane();
         QVERIFY(h2!=h3);
         QVERIFY(h3.coordinates()!=h2.coordinates());
     }
 }//t_readonly
 
 void QhullHyperplane_test::
 t_define()
 {
     RboxPoints rcube("c");
     {
         Qhull q(rcube,"Qt QR0");  // triangulation of rotated unit cube
         QhullFacetList fs= q.facetList();
         QhullHyperplane h= fs.first().hyperplane();
         QhullHyperplane h2= h;
         QVERIFY(h==h2);
         QhullHyperplane h3= fs.last().hyperplane();
         QVERIFY(h2!=h3);
 
         QhullHyperplane h4= h3;
         h4.defineAs(h2);
         QVERIFY(h2==h4);
         QhullHyperplane p5= h3;
         p5.defineAs(h2.dimension(), h2.coordinates(), h2.offset());
         QVERIFY(h2==p5);
         QhullHyperplane h6= h3;
         h6.setCoordinates(h2.coordinates());
         QCOMPARE(h2.coordinates(), h6.coordinates());
         h6.setOffset(h2.offset());
         QCOMPARE(h2.offset(), h6.offset());
         QVERIFY(h2==h6);
         h6.setDimension(2);
         QCOMPARE(h6.dimension(), 2);
         QVERIFY(h2!=h6);
     }
 }//t_define
 
 void QhullHyperplane_test::
 t_value()
 {
     RboxPoints rcube("c G1");
     Qhull q(rcube,"Qt QR0");  // triangulation of rotated unit cube
     const QhullHyperplane h= q.firstFacet().hyperplane();
     double dist= h.distance(q.origin());
     QCOMPARE(dist, -1.0);
     double norm= h.norm();
     QCOMPARE(norm, 1.0);
 }//t_value
 
 void QhullHyperplane_test::
 t_operator()
 {
     RboxPoints rcube("c");
     Qhull q(rcube,"Qt QR0");  // triangulation of rotated unit cube
     const QhullHyperplane h= q.firstFacet().hyperplane();
     //operator== and operator!= tested elsewhere
     const coordT *c= h.coordinates();
     for(int k=h.dimension(); k--; ){
         QCOMPARE(c[k], h[k]);
     }
     //h[0]= 10.0; // compiler error, const
     QhullHyperplane h2= q.firstFacet().hyperplane();
     h2[0]= 10.0;  // Overwrites Hyperplane coordinate!
     QCOMPARE(h2[0], 10.0);
 }//t_operator
 
 void QhullHyperplane_test::
 t_iterator()
 {
     RboxPoints rcube("c");
     {
         QhullHyperplane h2;
         QCOMPARE(h2.begin(), h2.end());
         QCOMPARE(h2.count(), 0);
         QCOMPARE(h2.size(), 0u);
         Qhull q(rcube,"QR0");  // rotated unit cube
         QhullHyperplane h= q.firstFacet().hyperplane();
         QCOMPARE(h.count(), 3);
         QCOMPARE(h.size(), 3u);
         QhullHyperplane::Iterator i= h.begin();
         QhullHyperplane::iterator i2= h.begin();
         QVERIFY(i==i2);
         QVERIFY(i>=i2);
         QVERIFY(i<=i2);
         i= h.begin();
         QVERIFY(i==i2);
         i2= h.end();
         QVERIFY(i!=i2);
         double d3= *i;
         i2--;
         double d2= *i2;
         QCOMPARE(d3, h[0]);
         QCOMPARE(d2, h[2]);
         QhullHyperplane::Iterator i3(i2);
         QCOMPARE(*i2, *i3);
 
         (i3= i)++;
         QCOMPARE((*i3), h[1]);
         QVERIFY(i==i);
         QVERIFY(i!=i2);
         QVERIFY(ii);
         QVERIFY(i2>=i);
 
         QhullHyperplane::ConstIterator i4= h.begin();
         QVERIFY(i==i4); // iterator COMP const_iterator
         QVERIFY(i<=i4);
         QVERIFY(i>=i4);
         QVERIFY(i4==i); // const_iterator COMP iterator
         QVERIFY(i4<=i);
         QVERIFY(i4>=i);
         QVERIFY(i>=i4);
         QVERIFY(i4<=i);
         QVERIFY(i2!=i4);
         QVERIFY(i2>i4);
         QVERIFY(i2>=i4);
         QVERIFY(i4!=i2);
         QVERIFY(i4i);
         QVERIFY(i4>=i);
 
         i= h.begin();
         i2= h.begin();
         QCOMPARE(i, i2++);
         QCOMPARE(*i2, h[1]);
         QCOMPARE(++i, i2);
         QCOMPARE(i, i2--);
         QCOMPARE(i2, h.begin());
         QCOMPARE(--i, i2);
         QCOMPARE(i2 += 3, h.end());
         QCOMPARE(i2 -= 3, h.begin());
         QCOMPARE(i2+0, h.begin());
         QCOMPARE(i2+3, h.end());
         i2 += 3;
         i= i2-0;
         QCOMPARE(i, i2);
         i= i2-3;
         QCOMPARE(i, h.begin());
         QCOMPARE(i2-i, 3);
 
         //h.begin end tested above
 
         // QhullHyperplane is const-only
     }
 }//t_iterator
 
 void QhullHyperplane_test::
 t_const_iterator()
 {
     RboxPoints rcube("c");
     {
         Qhull q(rcube,"QR0");  // rotated unit cube
         QhullHyperplane h= q.firstFacet().hyperplane();
         QhullHyperplane::ConstIterator i= h.begin();
         QhullHyperplane::const_iterator i2= h.begin();
         QVERIFY(i==i2);
         QVERIFY(i>=i2);
         QVERIFY(i<=i2);
         i= h.begin();
         QVERIFY(i==i2);
         i2= h.end();
         QVERIFY(i!=i2);
         double d3= *i;
         i2--;
         double d2= *i2;
         QCOMPARE(d3, h[0]);
         QCOMPARE(d2, h[2]);
         QhullHyperplane::ConstIterator i3(i2);
         QCOMPARE(*i2, *i3);
 
         (i3= i)++;
         QCOMPARE((*i3), h[1]);
         QVERIFY(i==i);
         QVERIFY(i!=i2);
         QVERIFY(ii);
         QVERIFY(i2>=i);
 
         // See t_iterator for const_iterator COMP iterator
 
         i= h.begin();
         i2= h.constBegin();
         QCOMPARE(i, i2++);
         QCOMPARE(*i2, h[1]);
         QCOMPARE(++i, i2);
         QCOMPARE(i, i2--);
         QCOMPARE(i2, h.constBegin());
         QCOMPARE(--i, i2);
         QCOMPARE(i2+=3, h.constEnd());
         QCOMPARE(i2-=3, h.constBegin());
         QCOMPARE(i2+0, h.constBegin());
         QCOMPARE(i2+3, h.constEnd());
         i2 += 3;
         i= i2-0;
         QCOMPARE(i, i2);
         i= i2-3;
         QCOMPARE(i, h.constBegin());
         QCOMPARE(i2-i, 3);
 
         // QhullHyperplane is const-only
     }
 }//t_const_iterator
 
 void QhullHyperplane_test::
 t_qhullHyperplane_iterator()
 {
     QhullHyperplane h2;
     QhullHyperplaneIterator i= h2;
     QCOMPARE(h2.dimension(), 0);
     QVERIFY(!i.hasNext());
     QVERIFY(!i.hasPrevious());
     i.toBack();
     QVERIFY(!i.hasNext());
     QVERIFY(!i.hasPrevious());
 
     RboxPoints rcube("c");
     Qhull q(rcube,"QR0");  // rotated unit cube
     QhullHyperplane h = q.firstFacet().hyperplane();
     QhullHyperplaneIterator i2(h);
     QCOMPARE(h.dimension(), 3);
     i= h;
     QVERIFY(i2.hasNext());
     QVERIFY(!i2.hasPrevious());
     QVERIFY(i.hasNext());
     QVERIFY(!i.hasPrevious());
     i2.toBack();
     i.toFront();
     QVERIFY(!i2.hasNext());
     QVERIFY(i2.hasPrevious());
     QVERIFY(i.hasNext());
     QVERIFY(!i.hasPrevious());
 
     // i at front, i2 at end/back, 3 coordinates
     QCOMPARE(i.peekNext(), h[0]);
     QCOMPARE(i2.peekPrevious(), h[2]);
     QCOMPARE(i2.previous(), h[2]);
     QCOMPARE(i2.previous(), h[1]);
     QCOMPARE(i2.previous(), h[0]);
     QVERIFY(!i2.hasPrevious());
     QCOMPARE(i.peekNext(), h[0]);
     // i.peekNext()= 1.0; // compiler error, i is const
     QCOMPARE(i.next(), h[0]);
     QCOMPARE(i.peekNext(), h[1]);
     QCOMPARE(i.next(), h[1]);
     QCOMPARE(i.next(), h[2]);
     QVERIFY(!i.hasNext());
     i.toFront();
     QCOMPARE(i.next(), h[0]);
 }//t_qhullHyperplane_iterator
 
 void QhullHyperplane_test::
 t_io()
 {
     RboxPoints rcube("c");
     {
         Qhull q(rcube, "");
         QhullHyperplane h= q.firstFacet().hyperplane();
         ostringstream os;
         os << "Hyperplane:\n";
         os << h;
-        os << "Hyperplane w/ runId:\n";
+        os << "Hyperplane as print(), FIXUP drop?\n";
         os << h.print();
         os << h.print(" and a message ", " offset ");
         cout << os.str();
         QString s= QString::fromStdString(os.str());
         QCOMPARE(s.count("1"), 3);
         // QCOMPARE(s.count(QRegExp("f\\d")), 3*7 + 13*3*2);
     }
 }//t_io
 
 
 }//orgQhull
 
 #include "moc/QhullHyperplane_test.moc"
diff --git a/src/qhulltest/QhullLinkedList_test.cpp b/src/qhulltest/QhullLinkedList_test.cpp
index 57381b9..873fc59 100644
--- a/src/qhulltest/QhullLinkedList_test.cpp
+++ b/src/qhulltest/QhullLinkedList_test.cpp
@@ -1,330 +1,328 @@
 /****************************************************************************
 **
 ** Copyright (c) 2009-2014 C.B. Barber. All rights reserved.
-** $Id: //main/2011/qhull/src/qhulltest/QhullLinkedList_test.cpp#4 $$Change: 1490 $
-** $DateTime: 2012/02/19 20:27:01 $$Author: bbarber $
+** $Id: //main/2011/qhull/src/qhulltest/QhullLinkedList_test.cpp#6 $$Change: 1708 $
+** $DateTime: 2014/03/26 19:13:56 $$Author: bbarber $
 **
 ****************************************************************************/
 
 //pre-compiled headers
 #include 
 #include "RoadTest.h"
 
 #include "QhullLinkedList.h"
 #include "Qhull.h"
 
 namespace orgQhull {
 
 class QhullLinkedList_test : public RoadTest
 {
     Q_OBJECT
 
 #//Test slots
 private slots:
     void cleanup();
     void t_construct();
     void t_convert();
     void t_element();
     void t_search();
     void t_iterator();
     void t_const_iterator();
     void t_QhullLinkedList_iterator();
     void t_io();
 };//QhullLinkedList_test
 
 void
 add_QhullLinkedList_test()
 {
     new QhullLinkedList_test();
 }
 
 //Executed after each testcase
 void QhullLinkedList_test::
 cleanup()
 {
     UsingLibQhull::checkQhullMemoryEmpty();
     RoadTest::cleanup();
 }
 
 void QhullLinkedList_test::
 t_construct()
 {
     // QhullLinkedList vs; //private (compiler error).  No memory allocation
     RboxPoints rcube("c");
     {
         Qhull q(rcube,"Qt QR0");  // triangulation of rotated unit cube
         QCOMPARE(q.facetCount(), 12);
         QhullVertexList vs = QhullVertexList(q.beginVertex(), q.endVertex());
         QCOMPARE(vs.count(), 8);
         QCOMPARE(vs.size(), 8u);
         QVERIFY(!vs.isEmpty());
         QhullVertexList vs2 = q.vertexList();
         QCOMPARE(vs2.count(), 8);
         QCOMPARE(vs2.size(),8u);
         QVERIFY(!vs2.isEmpty());
-        QVERIFY(!vs2.empty());
         QVERIFY(vs==vs2);
         // vs= vs2; // disabled.  Would not copy the vertices
         QhullVertexList vs3= vs2; // copy constructor
         QVERIFY(vs3==vs2);
     }
 }//t_construct
 
 void QhullLinkedList_test::
 t_convert()
 {
     RboxPoints rcube("c");
     {
         Qhull q(rcube,"Qt QR0");  // triangulation of rotated unit cube
         QCOMPARE(q.facetCount(), 12);
         QhullVertexList vs = q.vertexList();
         QCOMPARE(vs.size(), 8u);
         QVERIFY(!vs.isEmpty());
-        QVERIFY(!vs.empty());
         std::vector vs2= vs.toStdVector();
         QCOMPARE(vs2.size(), vs.size());
         QhullVertexList::Iterator i= vs.begin();
         for(int k= 0; k<(int)vs2.size(); k++){
             QCOMPARE(vs2[k], *i++);
         }
         QList vs3= vs.toQList();
         QCOMPARE(vs3.count(), vs.count());
         i= vs.begin();
         for(int k= 0; k
 #include "RoadTest.h" // QT_VERSION
 
 #include "QhullPointSet.h"
 #include "RboxPoints.h"
 #include "QhullPoint.h"
 #include "QhullFacet.h"
 #include "QhullFacetList.h"
 #include "Qhull.h"
 
 using std::cout;
 using std::endl;
 using std::ostringstream;
 
 namespace orgQhull {
 
 class QhullPointSet_test : public RoadTest
 {
     Q_OBJECT
 
 #//Test slots
 private slots:
     void cleanup();
     void t_construct();
     void t_convert();
     void t_element();
     void t_iterator();
     void t_const_iterator();
     void t_search();
     void t_pointset_iterator();
     void t_io();
 };//QhullPointSet_test
 
 void
 add_QhullPointSet_test()
 {
     new QhullPointSet_test();
 }
 
 //Executed after each testcase
 void QhullPointSet_test::
 cleanup()
 {
-    UsingLibQhull::checkQhullMemoryEmpty();
     RoadTest::cleanup();
 }
 
 void QhullPointSet_test::
 t_construct()
 {
+    // Default constructor is disallowed (i.e., private)
     RboxPoints rcube("c W0 1000");
     Qhull q(rcube,"Qc");  // cube with 1000 coplanar points
     int coplanarCount= 0;
     foreach(QhullFacet f, q.facetList()){
-        QhullPointSet ps(q.dimension(), f.getFacetT()->outsideset);
-        QCOMPARE(ps.dimension(), 3);
+        QhullPointSet ps(q, f.getFacetT()->outsideset);
         QVERIFY(ps.isEmpty());
-        QVERIFY(ps.empty());
         QCOMPARE(ps.count(), 0);
         QCOMPARE(ps.size(), 0u);
-        QhullPointSet ps2(q.dimension(), f.getFacetT()->coplanarset);
-        QCOMPARE(ps2.dimension(), 3);
+        QhullPointSet ps2(q.qh(), f.getFacetT()->coplanarset);
         QVERIFY(!ps2.isEmpty());
-        QVERIFY(!ps2.empty());
         coplanarCount += ps2.count();
         QCOMPARE(ps2.count(), (int)ps2.size());
         QhullPointSet ps3(ps2);
-        QCOMPARE(ps3.dimension(), 3);
         QVERIFY(!ps3.isEmpty());
         QCOMPARE(ps3.count(), ps2.count());
         QVERIFY(ps3==ps2);
         QVERIFY(ps3!=ps);
-        // ps4= ps3; //compiler error
+        QhullPointSet ps4= ps3;
+        QVERIFY(ps4==ps2);
     }
     QCOMPARE(coplanarCount, 1000);
+    q.checkAndFreeQhullMemory();
 }//t_construct
 
 void QhullPointSet_test::
 t_convert()
 {
     RboxPoints rcube("c W0 1000");
     Qhull q(rcube,"Qc");  // cube with 1000 coplanar points
     QhullFacet f= q.firstFacet();
     QhullPointSet ps= f.coplanarPoints();
-    QCOMPARE(ps.dimension(), 3);
     QVERIFY(ps.count()>=1);   // Sometimes no coplanar points
     std::vector vs= ps.toStdVector();
     QCOMPARE(vs.size(), ps.size());
     QhullPoint p= ps[0];
     QhullPoint p2= vs[0];
     QCOMPARE(p, p2);
     QList qs= ps.toQList();
     QCOMPARE(qs.size(), static_cast(ps.size()));
     QhullPoint p3= qs[0];
     QCOMPARE(p3, p);
+    q.checkAndFreeQhullMemory();
 }//t_convert
 
 // readonly tested in t_construct
-//   dimension, empty, isEmpty, ==, !=, size
+//   empty, isEmpty, ==, !=, size
 
 void QhullPointSet_test::
 t_element()
 {
     RboxPoints rcube("c W0 1000");
     Qhull q(rcube,"Qc");  // cube with 1000 coplanar points
     QhullFacet f= q.firstFacet();
     QhullPointSet ps= f.coplanarPoints();
     QVERIFY(ps.count()>=3);  // Sometimes no coplanar points
     QhullPoint p= ps[0];
     QCOMPARE(p, ps[0]);
     QhullPoint p2= ps[ps.count()-1];
     QCOMPARE(ps.at(1), ps[1]);
+    QCOMPARE(ps.second(), ps[1]);
     QCOMPARE(ps.first(), p);
     QCOMPARE(ps.front(), ps.first());
     QCOMPARE(ps.last(), p2);
     QCOMPARE(ps.back(), ps.last());
-    QhullPoint p8;
+    QhullPoint p8(q);
     QCOMPARE(ps.value(2), ps[2]);
     QCOMPARE(ps.value(-1), p8);
     QCOMPARE(ps.value(ps.count()), p8);
     QCOMPARE(ps.value(ps.count(), p), p);
     QVERIFY(ps.value(1, p)!=p);
     QhullPointSet ps8= f.coplanarPoints();
     QhullPointSet::Iterator i= ps8.begin();
     foreach(QhullPoint p9, ps){  // Qt only
         QCOMPARE(p9.dimension(), 3);
         QCOMPARE(p9, *i++);
     }
+    q.checkAndFreeQhullMemory();
 }//t_element
 
 void QhullPointSet_test::
 t_iterator()
 {
     RboxPoints rcube("c W0 1000");
     Qhull q(rcube,"Qc");  // cube with 1000 coplanar points
     QhullFacet f= q.firstFacet();
     QhullPointSet ps= f.coplanarPoints();
     QVERIFY(ps.count()>=3);  // Sometimes no coplanar points
     QhullPointSet::Iterator i= ps.begin();
     QhullPointSet::iterator i2= ps.begin();
     QVERIFY(i==i2);
     QVERIFY(i>=i2);
     QVERIFY(i<=i2);
     i= ps.begin();
     QVERIFY(i==i2);
     i2= ps.end();
     QVERIFY(i!=i2);
     QhullPoint p= *i;
-    QCOMPARE(p.dimension(), ps.dimension());
+    QCOMPARE(p.dimension(), q.dimension());
     QCOMPARE(p, ps[0]);
     i2--;
     QhullPoint p2= *i2;
-    QCOMPARE(p2.dimension(), ps.dimension());
+    QCOMPARE(p2.dimension(), q.dimension());
     QCOMPARE(p2, ps.last());
     QhullPointSet::Iterator i5(i2);
     QCOMPARE(*i2, *i5);
     QhullPointSet::Iterator i3= i+1;
     QVERIFY(i!=i3);
     QCOMPARE(i[1], *i3);
     (i3= i)++;
     QCOMPARE((*i3)[0], ps[1][0]);
     QCOMPARE((*i3).dimension(), 3);
 
     QVERIFY(i==i);
     QVERIFY(i!=i3);
     QVERIFY(ii);
     QVERIFY(i3>=i);
 
     QhullPointSet::ConstIterator i4= ps.begin();
     QVERIFY(i==i4); // iterator COMP const_iterator
     QVERIFY(i<=i4);
     QVERIFY(i>=i4);
     QVERIFY(i4==i); // const_iterator COMP iterator
     QVERIFY(i4<=i);
     QVERIFY(i4>=i);
     QVERIFY(i>=i4);
     QVERIFY(i4<=i);
     QVERIFY(i2!=i4);
     QVERIFY(i2>i4);
     QVERIFY(i2>=i4);
     QVERIFY(i4!=i2);
     QVERIFY(i4i);
     QVERIFY(i4>=i);
+    i4= ps.constBegin();
+    QVERIFY(i==i4); // iterator COMP const_iterator
+    QCOMPARE(i4+ps.count(), ps.constEnd());
 
     i= ps.begin();
     i2= ps.begin();
     QCOMPARE(i, i2++);
     QCOMPARE(*i2, ps[1]);
     QCOMPARE(++i, i2);
     QCOMPARE(i, i2--);
     QCOMPARE(i2, ps.begin());
     QCOMPARE(--i, i2);
     QCOMPARE(i2+=ps.count(), ps.end());
     QCOMPARE(i2-=ps.count(), ps.begin());
     QCOMPARE(i2+0, ps.begin());
     QCOMPARE(i2+ps.count(), ps.end());
     i2 += ps.count();
     i= i2-0;
     QCOMPARE(i, i2);
     i= i2-ps.count();
     QCOMPARE(i, ps.begin());
     QCOMPARE(i2-i, ps.count());
 
     //ps.begin end tested above
 
     // QhullPointSet is const-only
+    q.checkAndFreeQhullMemory();
 }//t_iterator
 
 void QhullPointSet_test::
 t_const_iterator()
 {
     RboxPoints rcube("c W0 1000");
     Qhull q(rcube,"Qc");  // cube with 1000 coplanar points
     QhullFacet f= q.firstFacet();
     QhullPointSet ps= f.coplanarPoints();
     QVERIFY(ps.count()>=3);  // Sometimes no coplanar points
     QhullPointSet::ConstIterator i= ps.begin();
     QhullPointSet::const_iterator i2= ps.begin();
     QVERIFY(i==i2);
     QVERIFY(i>=i2);
     QVERIFY(i<=i2);
 
     // See t_iterator for const_iterator COMP iterator
 
     i= ps.begin();
     QVERIFY(i==i2);
     i2= ps.end();
     QVERIFY(i!=i2);
     QhullPoint p= *i; // QhullPoint is the base class for QhullPointSet::iterator
-    QCOMPARE(p.dimension(), ps.dimension());
+    QCOMPARE(p.dimension(), q.dimension());
     QCOMPARE(p, ps[0]);
     i2--;
     QhullPoint p2= *i2;
-    QCOMPARE(p2.dimension(), ps.dimension());
+    QCOMPARE(p2.dimension(), q.dimension());
     QCOMPARE(p2, ps.last());
     QhullPointSet::ConstIterator i5(i2);
     QCOMPARE(*i2, *i5);
 
 
     QhullPointSet::ConstIterator i3= i+1;
     QVERIFY(i!=i3);
     QCOMPARE(i[1], *i3);
 
     QVERIFY(i==i);
     QVERIFY(i!=i3);
     QVERIFY(ii);
     QVERIFY(i3>=i);
 
     // QhullPointSet is const-only
+    q.checkAndFreeQhullMemory();
 }//t_const_iterator
 
 
 void QhullPointSet_test::
 t_search()
 {
     RboxPoints rcube("c W0 1000");
     Qhull q(rcube,"Qc");  // cube with 1000 coplanar points
     QhullFacet f= q.firstFacet();
     QhullPointSet ps= f.coplanarPoints();
     QVERIFY(ps.count()>=3);  // Sometimes no coplanar points
     QhullPoint p= ps.first();
     QhullPoint p2= ps.last();
     QVERIFY(ps.contains(p));
     QVERIFY(ps.contains(p2));
     QVERIFY(p!=p2);
     QhullPoint p3= ps[2];
     QVERIFY(ps.contains(p3));
     QVERIFY(p!=p3);
-    QhullPoint p4;
     QCOMPARE(ps.indexOf(p), 0);
     QCOMPARE(ps.indexOf(p2), ps.count()-1);
     QCOMPARE(ps.indexOf(p3), 2);
+    QhullPoint p4(q);
     QCOMPARE(ps.indexOf(p4), -1);
     QCOMPARE(ps.lastIndexOf(p), 0);
     QCOMPARE(ps.lastIndexOf(p2), ps.count()-1);
     QCOMPARE(ps.lastIndexOf(p3), 2);
     QCOMPARE(ps.lastIndexOf(p4), -1);
+    q.checkAndFreeQhullMemory();
 }//t_search
 
 void QhullPointSet_test::
 t_pointset_iterator()
 {
     RboxPoints rcube("c W0 1000");
     Qhull q(rcube,"Qc");  // cube with 1000 coplanar points
     QhullFacet f= q.firstFacet();
     QhullPointSet ps2= f.outsidePoints();
     QVERIFY(ps2.count()==0); // No outside points after constructing the convex hull
     QhullPointSetIterator i2= ps2;
+    QCOMPARE(i2.countRemaining(), 0);
     QVERIFY(!i2.hasNext());
     QVERIFY(!i2.hasPrevious());
     i2.toBack();
     QVERIFY(!i2.hasNext());
     QVERIFY(!i2.hasPrevious());
 
     QhullPointSet ps= f.coplanarPoints();
     QVERIFY(ps.count()>=3);  // Sometimes no coplanar points
     QhullPointSetIterator i(ps);
     i2= ps;
+    QCOMPARE(i2.countRemaining(), ps.count());
     QVERIFY(i2.hasNext());
     QVERIFY(!i2.hasPrevious());
     QVERIFY(i.hasNext());
     QVERIFY(!i.hasPrevious());
     i2.toBack();
+    QCOMPARE(i2.countRemaining(), 0);
     i.toFront();
+    QCOMPARE(i.countRemaining(), ps.count());
+    QCOMPARE(i2.countRemaining(), 0);
     QVERIFY(!i2.hasNext());
     QVERIFY(i2.hasPrevious());
     QVERIFY(i.hasNext());
     QVERIFY(!i.hasPrevious());
 
     QhullPoint p= ps[0];
     QhullPoint p2(ps[0]);
     QCOMPARE(p, p2);
     QVERIFY(p==p2);
     QhullPoint p3(ps.last());
  // p2[0]= 0.0;
     QVERIFY(p==p2);
     QCOMPARE(i2.peekPrevious(), p3);
     QCOMPARE(i2.previous(), p3);
     QCOMPARE(i2.previous(), ps[ps.count()-2]);
     QVERIFY(i2.hasPrevious());
     QCOMPARE(i.peekNext(), p);
     // i.peekNext()= 1.0; // compiler error
     QCOMPARE(i.next(), p);
+    QCOMPARE(i.countRemaining(), ps.count()-1);
     QhullPoint p4= i.peekNext();
     QVERIFY(p4!=p3);
     QCOMPARE(i.next(), p4);
     QVERIFY(i.hasNext());
     i.toFront();
     QCOMPARE(i.next(), p);
+    q.checkAndFreeQhullMemory();
 }//t_pointset_iterator
 
 void QhullPointSet_test::
 t_io()
 {
     ostringstream os;
     RboxPoints rcube("c W0 120");
     Qhull q(rcube,"Qc");  // cube with 100 coplanar points
     QhullFacet f= q.firstFacet();
     QhullPointSet ps= f.coplanarPoints();
     QVERIFY(ps.count()>=3);  // Sometimes no coplanar points
     os << "QhullPointSet from coplanarPoints\n" << ps << endl;
-    os << "\nRunId\n" << ps.print(q.runId());
-    os << ps.print(q.runId(), "\nRunId w/ message\n");
+    os << ps.print("\nWith message\n");
+    os << ps.printIdentifiers("\nCoplanar points: ");
+    os << "\nAs a point set:\n";
+    os << ps;
     cout << os.str();
     QString s= QString::fromStdString(os.str());
-    QCOMPARE(s.count("p"), 3*ps.count()+1);
-    // QCOMPARE(s.count(QRegExp("f\\d")), 3*7 + 13*3*2);
+    QCOMPARE(s.count(" 0.5\n"), 3*ps.count());
+    QCOMPARE(s.count("p"), ps.count()+4);
+    q.checkAndFreeQhullMemory();
 }//t_io
 
 }//orgQhull
 
 #include "moc/QhullPointSet_test.moc"
diff --git a/src/qhulltest/QhullPoint_test.cpp b/src/qhulltest/QhullPoint_test.cpp
index ff8b605..58fbac5 100644
--- a/src/qhulltest/QhullPoint_test.cpp
+++ b/src/qhulltest/QhullPoint_test.cpp
@@ -1,397 +1,447 @@
 /****************************************************************************
 **
 ** Copyright (c) 2008-2014 C.B. Barber. All rights reserved.
-** $Id: //main/2011/qhull/src/qhulltest/QhullPoint_test.cpp#4 $$Change: 1490 $
-** $DateTime: 2012/02/19 20:27:01 $$Author: bbarber $
+** $Id: //main/2011/qhull/src/qhulltest/QhullPoint_test.cpp#10 $$Change: 1799 $
+** $DateTime: 2014/12/17 16:17:40 $$Author: bbarber $
 **
 ****************************************************************************/
 
 //pre-compiled headers
 #include 
 #include "RoadTest.h"
 
 #include "QhullPoint.h"
 #include "Coordinates.h"
 #include "RboxPoints.h"
 #include "QhullError.h"
 #include "QhullFacet.h"
 #include "QhullPoint.h"
 #include "Qhull.h"
 
 #include 
 
 using std::cout;
 using std::endl;
 using std::ostringstream;
 using std::ostream;
 using std::string;
 
 namespace orgQhull {
 
 class QhullPoint_test : public RoadTest
 {
     Q_OBJECT
 
 #//Test slots
 private slots:
     void cleanup();
     void t_construct();
     void t_convert();
     void t_readonly();
     void t_define();
     void t_operator();
     void t_iterator();
     void t_const_iterator();
     void t_qhullpoint_iterator();
+    void t_method();
     void t_io();
 };//QhullPoint_test
 
 void
 add_QhullPoint_test()
 {
     new QhullPoint_test();
 }
 
 //Executed after each test
 void QhullPoint_test::
 cleanup()
 {
-    UsingLibQhull::checkQhullMemoryEmpty();
     RoadTest::cleanup();
 }
 
 void QhullPoint_test::
 t_construct()
 {
-    // Qhull.runQhull() constructs QhullFacets as facetT
-    QhullPoint p;
+    QhullPoint p12;
+    QVERIFY(!p12.isDefined());
+    QCOMPARE(p12.coordinates(), (coordT *)0);
+    QCOMPARE(p12.dimension(), 0);
+    QCOMPARE(p12.qh(), (QhullQh *)0);
+    QCOMPARE(p12.id(), -3);
+    QCOMPARE(p12.begin(), p12.end());
+    QCOMPARE(p12.constBegin(), p12.constEnd());
+
+    RboxPoints rcube("c");
+    Qhull q(rcube, "Qt QR0");  // triangulation of rotated unit cube
+    QhullPoint p(q);
     QVERIFY(!p.isDefined());
-    QCOMPARE(p.dimension(),0);
+    QCOMPARE(p.dimension(),3);
     QCOMPARE(p.coordinates(),static_cast(0));
-    RboxPoints rcube("c");
-    Qhull q(rcube,"Qt QR0");  // triangulation of rotated unit cube
+    QhullPoint p7(q.qh());
+    QCOMPARE(p, p7);
+
+    // copy constructor and copy assignment
     QhullVertex v2(q.beginVertex());
     QhullPoint p2(v2.point());
     QVERIFY(p2.isDefined());
     QCOMPARE(p2.dimension(),3);
-    // p= p2;  // copy assignment disabled, ambiguous
-    QhullPoint p3(p2.dimension(), p2.coordinates());
-    QCOMPARE(p2, p3);
+    QVERIFY(p2!=p12);
+    p= p2;  
+    QCOMPARE(p, p2);
+
+    QhullPoint p3(q, p2.dimension(), p2.coordinates());
+    QCOMPARE(p3, p2);
+    QhullPoint p8(q, p2.coordinates()); // Qhull defines dimension
+    QCOMPARE(p8, p2);
+    QhullPoint p9(q.qh(), p2.dimension(), p2.coordinates());
+    QCOMPARE(p9, p2);
+    QhullPoint p10(q.qh(), p2.coordinates()); // Qhull defines dimension
+    QCOMPARE(p10, p2);
+
     Coordinates c;
     c << 0.0 << 0.0 << 0.0;
-    QhullPoint p6(c);
+    QhullPoint p6(q, c);
     QCOMPARE(p6, q.origin());
+    QhullPoint p11(q.qh(), c);
+    QCOMPARE(p11, q.origin());
+
     QhullPoint p5= p2; // copy constructor
     QVERIFY(p5==p2);
+    q.checkAndFreeQhullMemory();
 }//t_construct
 
 void QhullPoint_test::
 t_convert()
 {
     RboxPoints rcube("c");
     Qhull q(rcube,"Qt QR0");  // triangulation of rotated unit cube
     QhullVertex v= q.firstVertex();
     QhullPoint p= v.point();
     std::vector vs= p.toStdVector();
     QCOMPARE(vs.size(), 3u);
     for(int k=3; k--; ){
         QCOMPARE(vs[k], p[k]);
     }
     QList qs= p.toQList();
     QCOMPARE(qs.size(), 3);
     for(int k=3; k--; ){
         QCOMPARE(qs[k], p[k]);
     }
+    q.checkAndFreeQhullMemory();
 }//t_convert
 
 void QhullPoint_test::
 t_readonly()
 {
     RboxPoints rcube("c");
     {
         Qhull q(rcube,"Qt QR0");  // triangulation of rotated unit cube
         QhullVertexList vs= q.vertexList();
+        cout << "Point ids in 'rbox c'\n";
         QhullVertexListIterator i(vs);
         while(i.hasNext()){
             QhullPoint p= i.next().point();
-            int id= p.id(q.runId());
+            int id= p.id();
             cout << "p" << id << endl;
             QVERIFY(p.isDefined());
             QCOMPARE(p.dimension(),3);
             QCOMPARE(id, p.id());
             QVERIFY(p.id()>=0 && p.id()<9);
             const coordT *c= p.coordinates();
             coordT *c2= p.coordinates();
             QCOMPARE(c, c2);
             QCOMPARE(p.dimension(), 3);
+            QCOMPARE(q.qh(), p.qh());
         }
         QhullPoint p2= vs.first().point();
         QhullPoint p3= vs.last().point();
         QVERIFY(p2!=p3);
         QVERIFY(p3.coordinates()!=p2.coordinates());
+        q.checkAndFreeQhullMemory();
     }
 }//t_readonly
 
 void QhullPoint_test::
 t_define()
 {
     RboxPoints rcube("c");
     {
         Qhull q(rcube,"Qt QR0");  // triangulation of rotated unit cube
         QhullVertexList vs= q.vertexList();
         QhullPoint p= vs.first().point();
         QhullPoint p2= p;
         QVERIFY(p==p2);
         QhullPoint p3= vs.last().point();
         QVERIFY(p2!=p3);
         int idx= (p3.coordinates()-p2.coordinates())/p2.dimension();
         QVERIFY(idx>-8 && idx<8);
         p2.advancePoint(idx);
         QVERIFY(p2==p3);
         p2.advancePoint(-idx);
         QVERIFY(p2==p);
         p2.advancePoint(0);
         QVERIFY(p2==p);
 
         QhullPoint p4= p3;
+        QVERIFY(p4==p3);
         p4.defineAs(p2);
         QVERIFY(p2==p4);
         QhullPoint p5= p3;
         p5.defineAs(p2.dimension(), p2.coordinates());
         QVERIFY(p2==p5);
         QhullPoint p6= p3;
         p6.setCoordinates(p2.coordinates());
         QCOMPARE(p2.coordinates(), p6.coordinates());
         QVERIFY(p2==p6);
         p6.setDimension(2);
         QCOMPARE(p6.dimension(), 2);
         QVERIFY(p2!=p6);
+        q.checkAndFreeQhullMemory();
     }
 }//t_define
 
 void QhullPoint_test::
 t_operator()
 {
     RboxPoints rcube("c");
     Qhull q(rcube,"Qt QR0");  // triangulation of rotated unit cube
     const QhullPoint p= q.firstVertex().point();
     //operator== and operator!= tested elsewhere
     const coordT *c= p.coordinates();
     for(int k=p.dimension(); k--; ){
         QCOMPARE(c[k], p[k]);
     }
     //p[0]= 10.0; // compiler error, const
     QhullPoint p2= q.firstVertex().point();
     p2[0]= 10.0;  // Overwrites point coordinate
     QCOMPARE(p2[0], 10.0);
+    q.checkAndFreeQhullMemory();
 }//t_operator
 
 void QhullPoint_test::
 t_iterator()
 {
     RboxPoints rcube("c");
     {
-        QhullPoint p2;
-        QCOMPARE(p2.begin(), p2.end());
         Qhull q(rcube,"QR0");  // rotated unit cube
+        QhullPoint p2(q);
+        QCOMPARE(p2.begin(), p2.end());
+
         QhullPoint p= q.firstVertex().point();
         QhullPoint::Iterator i= p.begin();
         QhullPoint::iterator i2= p.begin();
         QVERIFY(i==i2);
         QVERIFY(i>=i2);
         QVERIFY(i<=i2);
         i= p.begin();
         QVERIFY(i==i2);
         i2= p.end();
         QVERIFY(i!=i2);
         double d3= *i;
         i2--;
         double d2= *i2;
         QCOMPARE(d3, p[0]);
         QCOMPARE(d2, p[2]);
         QhullPoint::Iterator i3(i2);
         QCOMPARE(*i2, *i3);
 
         (i3= i)++;
         QCOMPARE((*i3), p[1]);
         QVERIFY(i==i);
         QVERIFY(i!=i2);
         QVERIFY(ii);
         QVERIFY(i2>=i);
 
         QhullPoint::ConstIterator i4= p.begin();
         QVERIFY(i==i4); // iterator COMP const_iterator
         QVERIFY(i<=i4);
         QVERIFY(i>=i4);
         QVERIFY(i4==i); // const_iterator COMP iterator
         QVERIFY(i4<=i);
         QVERIFY(i4>=i);
         QVERIFY(i>=i4);
         QVERIFY(i4<=i);
         QVERIFY(i2!=i4);
         QVERIFY(i2>i4);
         QVERIFY(i2>=i4);
         QVERIFY(i4!=i2);
         QVERIFY(i4i);
         QVERIFY(i4>=i);
 
         i= p.begin();
         i2= p.begin();
         QCOMPARE(i, i2++);
         QCOMPARE(*i2, p[1]);
         QCOMPARE(++i, i2);
         QCOMPARE(i, i2--);
         QCOMPARE(i2, p.begin());
         QCOMPARE(--i, i2);
         QCOMPARE(i2 += 3, p.end());
         QCOMPARE(i2 -= 3, p.begin());
         QCOMPARE(i2+0, p.begin());
         QCOMPARE(i2+3, p.end());
         i2 += 3;
         i= i2-0;
         QCOMPARE(i, i2);
         i= i2-3;
         QCOMPARE(i, p.begin());
         QCOMPARE(i2-i, 3);
 
         //p.begin end tested above
 
         // QhullPoint is const-only
+        q.checkAndFreeQhullMemory();
     }
 }//t_iterator
 
 void QhullPoint_test::
 t_const_iterator()
 {
     RboxPoints rcube("c");
     {
         Qhull q(rcube,"QR0");  // rotated unit cube
         QhullPoint p= q.firstVertex().point();
         QhullPoint::ConstIterator i= p.begin();
         QhullPoint::const_iterator i2= p.begin();
         QVERIFY(i==i2);
         QVERIFY(i>=i2);
         QVERIFY(i<=i2);
         i= p.begin();
         QVERIFY(i==i2);
         i2= p.end();
         QVERIFY(i!=i2);
         double d3= *i;
         i2--;
         double d2= *i2;
         QCOMPARE(d3, p[0]);
         QCOMPARE(d2, p[2]);
         QhullPoint::ConstIterator i3(i2);
         QCOMPARE(*i2, *i3);
 
         (i3= i)++;
         QCOMPARE((*i3), p[1]);
         QVERIFY(i==i);
         QVERIFY(i!=i2);
         QVERIFY(ii);
         QVERIFY(i2>=i);
 
         // See t_iterator for const_iterator COMP iterator
 
         i= p.begin();
         i2= p.constBegin();
         QCOMPARE(i, i2++);
         QCOMPARE(*i2, p[1]);
         QCOMPARE(++i, i2);
         QCOMPARE(i, i2--);
         QCOMPARE(i2, p.constBegin());
         QCOMPARE(--i, i2);
         QCOMPARE(i2+=3, p.constEnd());
         QCOMPARE(i2-=3, p.constBegin());
         QCOMPARE(i2+0, p.constBegin());
         QCOMPARE(i2+3, p.constEnd());
         i2 += 3;
         i= i2-0;
         QCOMPARE(i, i2);
         i= i2-3;
         QCOMPARE(i, p.constBegin());
         QCOMPARE(i2-i, 3);
 
         // QhullPoint is const-only
+        q.checkAndFreeQhullMemory();
     }
 }//t_const_iterator
 
 void QhullPoint_test::
 t_qhullpoint_iterator()
 {
-    QhullPoint p2;
+    RboxPoints rcube("c");
+    Qhull q(rcube,"QR0");  // rotated unit cube
+
+    QhullPoint p2(q);
     QhullPointIterator i= p2;
-    QCOMPARE(p2.dimension(), 0);
+    QCOMPARE(p2.dimension(), 3);
     QVERIFY(!i.hasNext());
     QVERIFY(!i.hasPrevious());
     i.toBack();
     QVERIFY(!i.hasNext());
     QVERIFY(!i.hasPrevious());
 
-    RboxPoints rcube("c");
-    Qhull q(rcube,"QR0");  // rotated unit cube
     QhullPoint p = q.firstVertex().point();
     QhullPointIterator i2(p);
     QCOMPARE(p.dimension(), 3);
     i= p;
     QVERIFY(i2.hasNext());
     QVERIFY(!i2.hasPrevious());
     QVERIFY(i.hasNext());
     QVERIFY(!i.hasPrevious());
     i2.toBack();
     i.toFront();
     QVERIFY(!i2.hasNext());
     QVERIFY(i2.hasPrevious());
     QVERIFY(i.hasNext());
     QVERIFY(!i.hasPrevious());
 
     // i at front, i2 at end/back, 3 coordinates
     QCOMPARE(i.peekNext(), p[0]);
     QCOMPARE(i2.peekPrevious(), p[2]);
     QCOMPARE(i2.previous(), p[2]);
     QCOMPARE(i2.previous(), p[1]);
     QCOMPARE(i2.previous(), p[0]);
     QVERIFY(!i2.hasPrevious());
     QCOMPARE(i.peekNext(), p[0]);
     // i.peekNext()= 1.0; // compiler error, i is const
     QCOMPARE(i.next(), p[0]);
     QCOMPARE(i.peekNext(), p[1]);
     QCOMPARE(i.next(), p[1]);
     QCOMPARE(i.next(), p[2]);
     QVERIFY(!i.hasNext());
     i.toFront();
     QCOMPARE(i.next(), p[0]);
+    q.checkAndFreeQhullMemory();
+}//t_qhullpoint_iterator
+
+void QhullPoint_test::
+t_method()
+{
+    // advancePoint tested above
+    RboxPoints rcube("c");
+    Qhull q(rcube, "");
+    QhullPoint p = q.firstVertex().point();
+    double dist= p.distance(q.origin());
+    QCOMPARE(dist, sqrt(double(2.0+1.0))/2); // half diagonal of unit cube
+    q.checkAndFreeQhullMemory();
 }//t_qhullpoint_iterator
 
 void QhullPoint_test::
 t_io()
 {
     RboxPoints rcube("c");
     {
         Qhull q(rcube, "");
         QhullPoint p= q.beginVertex().point();
         ostringstream os;
-        os << "Point w/o runId:\n";
+        os << "Point:\n";
         os << p;
-        os << "Point w/ runId:\n";
-        os << p.print(q.runId()) << p.print(q.runId(), " and a message ");
-        os << p.printWithIdentifier(q.runId(), " Point with id and a message ");
+        os << "Point w/ print:\n";
+        os << p.print(" message ");
+        os << p.printWithIdentifier(" Point with id and a message ");
         cout << os.str();
         QString s= QString::fromStdString(os.str());
-        QCOMPARE(s.count("p"), 3);
-        // QCOMPARE(s.count(QRegExp("f\\d")), 3*7 + 13*3*2);
+        QCOMPARE(s.count("p"), 2);
+        q.checkAndFreeQhullMemory();
     }
 }//t_io
 
 }//orgQhull
 
 #include "moc/QhullPoint_test.moc"
diff --git a/src/qhulltest/QhullPoints_test.cpp b/src/qhulltest/QhullPoints_test.cpp
index 8203f32..532451c 100644
--- a/src/qhulltest/QhullPoints_test.cpp
+++ b/src/qhulltest/QhullPoints_test.cpp
@@ -1,481 +1,478 @@
 /****************************************************************************
 **
 ** Copyright (p) 2009-2014 C.B. Barber. All rights reserved.
-** $Id: //main/2011/qhull/src/qhulltest/QhullPoints_test.cpp#6 $$Change: 1490 $
-** $DateTime: 2012/02/19 20:27:01 $$Author: bbarber $
+** $Id: //main/2011/qhull/src/qhulltest/QhullPoints_test.cpp#9 $$Change: 1709 $
+** $DateTime: 2014/03/26 22:27:14 $$Author: bbarber $
 **
 ****************************************************************************/
 
 //pre-compiled header
 #include 
 #include "RoadTest.h" // QT_VERSION
 
 #include "QhullPoints.h"
 #include "RboxPoints.h"
 #include "Qhull.h"
 
 using std::cout;
 using std::endl;
 using std::ostringstream;
 
 namespace orgQhull {
 
 class QhullPoints_test : public RoadTest
 {
     Q_OBJECT
 
 #//Test slots
 private slots:
     void cleanup();
     void t_construct();
     void t_convert();
     void t_getset();
     void t_element();
     void t_iterator();
     void t_const_iterator();
     void t_search();
     void t_points_iterator();
     void t_io();
 };//QhullPoints_test
 
 void
 add_QhullPoints_test()
 {
     new QhullPoints_test();
 }
 
 //Executed after each testcase
 void QhullPoints_test::
 cleanup()
 {
     UsingLibQhull::checkQhullMemoryEmpty();
     RoadTest::cleanup();
 }
 
 void QhullPoints_test::
 t_construct()
 {
     QhullPoints ps;
     QCOMPARE(ps.dimension(), 0);
     QVERIFY(ps.isEmpty());
-    QVERIFY(ps.empty());
     QCOMPARE(ps.count(), 0);
     QCOMPARE(ps.size(), 0u);
     QCOMPARE(ps.coordinateCount(), 0);
     coordT c[]= {0.0, 1.0, 2.0, 3.0, 4.0, 5.0};
     QhullPoints ps2;
     ps2.defineAs(2, 6, c);
     QCOMPARE(ps2.dimension(), 2);
     QVERIFY(!ps2.isEmpty());
-    QVERIFY(!ps2.empty());
     QCOMPARE(ps2.count(), 3);
     QCOMPARE(ps2.size(), 3u);
     QCOMPARE(ps2.coordinates(), c);
     QhullPoints ps7(3);
     QCOMPARE(ps7.dimension(), 3);
     QVERIFY(ps7.isEmpty());
     QhullPoints ps3(2, 6, c);
     QCOMPARE(ps3.dimension(), 2);
     QVERIFY(!ps3.isEmpty());
     QCOMPARE(ps3.coordinates(), ps2.coordinates());
     QVERIFY(ps3==ps2);
     QVERIFY(ps3!=ps);
     QhullPoints ps4= ps3;
     QVERIFY(ps4==ps3);
     // ps4= ps3; //compiler error
     QhullPoints ps5(ps4);
     QVERIFY(ps5==ps4);
     QVERIFY(!(ps5!=ps4));
     coordT c2[]= {0.0, 1.0, 2.0, 3.0, 4.0, 5.0};
     QhullPoints ps6(2, 6, c2);
     QVERIFY(ps6==ps2);
 }//t_construct
 
 void QhullPoints_test::
 t_convert()
 {
     //defineAs tested above
     coordT c[]= {0.0, 1.0, 2.0, 3.0, 4.0, 5.0};
     QhullPoints ps(3, 6, c);
     QCOMPARE(ps.dimension(), 3);
     QCOMPARE(ps.size(), 2u);
     const coordT *c2= ps.constData();
     QCOMPARE(c, c2);
     const coordT *c3= ps.data();
     QCOMPARE(c, c3);
     coordT *c4= ps.data();
     QCOMPARE(c, c4);
     std::vector vs= ps.toStdVector();
     QCOMPARE(vs.size(), 2u);
     QhullPoint p= vs[1];
     QCOMPARE(p[2], 5.0);
     QList qs= ps.toQList();
     QCOMPARE(qs.size(), 2);
     QhullPoint p2= qs[1];
     QCOMPARE(p2[2], 5.0);
 }//t_convert
 
 void QhullPoints_test::
 t_getset()
 {
-    //See t_construct for coordinates, count, defineAs, dimension, empty, isempty, ==, !=, size
+    //See t_construct for coordinates, count, defineAs, dimension, isempty, ==, !=, size
     coordT c[]= {0.0, 1.0, 2.0, 3.0, 4.0, 5.0};
     QhullPoints ps(3, 6, c);
     QhullPoints ps2(3, 6, c);
     QCOMPARE(ps2.dimension(), 3);
     QCOMPARE(ps2.coordinates(), c);
     QCOMPARE(ps2.count(), 2);
     QCOMPARE(ps2.coordinateCount(), 6);
     coordT c2[]= {-1.0, -2.0, -3.0, -4.0, -5.0, -6.0};
     ps2.defineAs(6, c2);
     QCOMPARE(ps2.coordinates(), c2);
     QCOMPARE(ps2.count(), 2);
     QCOMPARE(ps2.size(), 2u);
     QCOMPARE(ps2.dimension(), 3);
     QVERIFY(!ps2.isEmpty());
     QVERIFY(ps!=ps2);
     // ps2= ps; // assignment not available, compiler error
     ps2.defineAs(ps);
     QVERIFY(ps==ps2);
     ps2.setDimension(2);
     QCOMPARE(ps2.dimension(), 2);
     QCOMPARE(ps2.coordinates(), c);
     QVERIFY(!ps2.isEmpty());
     QCOMPARE(ps2.count(), 3);
     QCOMPARE(ps2.size(), 3u);
     QVERIFY(ps!=ps2);
     QhullPoints ps3(3);
     ps3.defineAs(5, c2);
     QCOMPARE(ps3.count(), 1);
     QCOMPARE(ps3.extraCoordinatesCount(), 2);
     QCOMPARE(ps3.extraCoordinates()[0], -4.0);
     QVERIFY(ps3.includesCoordinates(ps3.data()));
     QVERIFY(ps3.includesCoordinates(ps3.data()+ps3.count()-1));
     QVERIFY(!ps3.includesCoordinates(ps3.data()-1));
     QVERIFY(!ps3.includesCoordinates(ps3.data()+ps3.coordinateCount()));
 }//t_getset
 
 
 void QhullPoints_test::
 t_element()
 {
     coordT c[]= {0.0, 1.0, 2.0, 3.0, 4.0, 5.0};
     QhullPoints ps(2, 6, c);
     QhullPoint p(2, c);
     QCOMPARE(ps[0], p);
     QCOMPARE(ps.at(1), ps[1]);
     QCOMPARE(ps.first(), p);
     QCOMPARE(ps.front(), ps.first());
     QCOMPARE(ps.last(), ps.at(2));
     QCOMPARE(ps.back(), ps.last());
     QhullPoints ps2= ps.mid(2);
     QCOMPARE(ps2.count(), 1);
     QhullPoints ps3= ps.mid(3);
     QVERIFY(ps3.isEmpty());
-    QVERIFY(ps3.empty());
     QhullPoints ps4= ps.mid(10);
     QVERIFY(ps4.isEmpty());
     QhullPoints ps5= ps.mid(-1);
     QVERIFY(ps5.isEmpty());
     QhullPoints ps6= ps.mid(1, 1);
     QCOMPARE(ps6.count(), 1);
     QCOMPARE(ps6[0], ps[1]);
     QhullPoints ps7= ps.mid(1, 10);
     QCOMPARE(ps7.count(), 2);
     QCOMPARE(ps7[1], ps[2]);
     QhullPoint p8;
     QCOMPARE(ps.value(2), ps[2]);
     QCOMPARE(ps.value(-1), p8);
     QCOMPARE(ps.value(3), p8);
     QCOMPARE(ps.value(3, p), p);
     QVERIFY(ps.value(1, p)!=p);
     foreach(QhullPoint p9, ps){  // Qt only
         QCOMPARE(p9.dimension(), 2);
         QVERIFY(p9[0]==0.0 || p9[0]==2.0 || p9[0]==4.0);
     }
 }//t_element
 
 void QhullPoints_test::
 t_iterator()
 {
     coordT c[]= {0.0, 1.0, 2.0};
     QhullPoints ps(1, 3, c);
     QhullPoints::Iterator i(ps);
     QhullPoints::iterator i2= ps.begin();
     QVERIFY(i==i2);
     QVERIFY(i>=i2);
     QVERIFY(i<=i2);
     i= ps.begin();
     QVERIFY(i==i2);
     i2= ps.end();
     QVERIFY(i!=i2);
     QhullPoint p(i); // QhullPoint is the base class for QhullPoints::iterator
     QCOMPARE(p.dimension(), ps.dimension());
     QCOMPARE(p.coordinates(), ps.coordinates());
     i2--;
     QhullPoint p2= *i2;
     QCOMPARE(p[0], 0.0);
     QCOMPARE(p2[0], 2.0);
     QhullPoints::Iterator i5(i2);
     QCOMPARE(*i2, *i5);
     coordT c3[]= {0.0, -1.0, -2.0};
     QhullPoints::Iterator i3(1, c3);
     QVERIFY(i!=i3);
     QCOMPARE(*i, *i3);
 
     (i3= i)++;
     QCOMPARE((*i3)[0], 1.0);
     QCOMPARE(i3->dimension(), 1);
     QCOMPARE(i3[0][0], 1.0);
     QCOMPARE(i3[0], ps[1]);
 
     QVERIFY(i==i);
     QVERIFY(i!=i2);
     QVERIFY(ii);
     QVERIFY(i2>=i);
 
     QhullPoints::ConstIterator i4(1, c);
     QVERIFY(i==i4); // iterator COMP const_iterator
     QVERIFY(i<=i4);
     QVERIFY(i>=i4);
     QVERIFY(i4==i); // const_iterator COMP iterator
     QVERIFY(i4<=i);
     QVERIFY(i4>=i);
     QVERIFY(i>=i4);
     QVERIFY(i4<=i);
     QVERIFY(i2!=i4);
     QVERIFY(i2>i4);
     QVERIFY(i2>=i4);
     QVERIFY(i4!=i2);
     QVERIFY(i4i);
     QVERIFY(i4>=i);
 
     i= ps.begin();
     i2= ps.begin();
     QCOMPARE(i, i2++);
     QCOMPARE(*i2, ps[1]);
     QCOMPARE(++i, i2);
     QCOMPARE(i, i2--);
     QCOMPARE(i2, ps.begin());
     QCOMPARE(--i, i2);
     QCOMPARE(i2+=3, ps.end());
     QCOMPARE(i2-=3, ps.begin());
     QCOMPARE(i2+0, ps.begin());
     QCOMPARE(i2+3, ps.end());
     i2 += 3;
     i= i2-0;
     QCOMPARE(i, i2);
     i= i2-3;
     QCOMPARE(i, ps.begin());
     QCOMPARE(i2-i, 3);
 
     //ps.begin end tested above
 
     // QhullPoints is const-only
 }//t_iterator
 
 void QhullPoints_test::
 t_const_iterator()
 {
     coordT c[]= {0.0, 1.0, 2.0};
     const QhullPoints ps(1, 3, c);
     QhullPoints::ConstIterator i(ps);
     QhullPoints::const_iterator i2= ps.begin();
     QVERIFY(i==i2);
     QVERIFY(i>=i2);
     QVERIFY(i<=i2);
     i= ps.begin();
     QVERIFY(i==i2);
     i2= ps.end();
     QVERIFY(i!=i2);
     QhullPoint p(i);
     QCOMPARE(p.dimension(), ps.dimension());
     QCOMPARE(p.coordinates(), ps.coordinates());
     i2--;
     QhullPoint p2= *i2;
     QCOMPARE(p[0], 0.0);
     QCOMPARE(p2[0], 2.0);
     QhullPoints::ConstIterator i5(i2);
     QCOMPARE(*i2, *i5);
     coordT c3[]= {0.0, -1.0, -2.0};
     QhullPoints::ConstIterator i3(1, c3);
     QVERIFY(i!=i3);
     QCOMPARE(*i, *i3);
 
     (i3= i)++;
     QCOMPARE((*i3)[0], 1.0);
     QCOMPARE(i3->dimension(), 1);
     QCOMPARE(i3[0][0], 1.0);
     QCOMPARE(i3[0][0], 1.0);
     QCOMPARE(i3[0], ps[1]);
 
     QVERIFY(i==i);
     QVERIFY(i!=i2);
     QVERIFY(ii);
     QVERIFY(i2>=i);
 
     // See t_iterator for const_iterator COMP iterator
 
     i= ps.begin();
     i2= ps.constBegin();
     QCOMPARE(i, i2++);
     QCOMPARE(*i2, ps[1]);
     QCOMPARE(++i, i2);
     QCOMPARE(i, i2--);
     QCOMPARE(i2, ps.constBegin());
     QCOMPARE(--i, i2);
     QCOMPARE(i2+=3, ps.constEnd());
     QCOMPARE(i2-=3, ps.constBegin());
     QCOMPARE(i2+0, ps.constBegin());
     QCOMPARE(i2+3, ps.constEnd());
     i2 += 3;
     i= i2-0;
     QCOMPARE(i, i2);
     i= i2-3;
     QCOMPARE(i, ps.constBegin());
     QCOMPARE(i2-i, 3);
 
     // QhullPoints is const-only
 }//t_const_iterator
 
 
 void QhullPoints_test::
 t_search()
 {
     coordT c[]= {0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 0, 1};
     QhullPoints ps(2, 8, c); //2-d array of 4 points
     QhullPoint p= ps.first();
     QhullPoint p2= ps.last();
     QVERIFY(ps.contains(p));
     QVERIFY(ps.contains(p2));
     QVERIFY(p==p2);
     QhullPoint p5= ps[2];
     QVERIFY(p!=p5);
     QVERIFY(ps.contains(p5));
     coordT c2[]= {0.0, 1.0, 2.0, 3.0};
     QhullPoint p3(2, c2); //2-d point
     QVERIFY(ps.contains(p3));
     QhullPoint p4(3, c2); //3-d point
     QVERIFY(!ps.contains(p4));
     p4.defineAs(2, c); //2-d point
     QVERIFY(ps.contains(p4));
     p4.defineAs(2, c+1); //2-d point
     QVERIFY(!ps.contains(p4));
     QhullPoint p6(2, c2+2); //2-d point
     QCOMPARE(ps.count(p), 2);
     QCOMPARE(ps.count(p2), 2);
     QCOMPARE(ps.count(p3), 2);
     QCOMPARE(ps.count(p4), 0);
     QCOMPARE(ps.count(p6), 1);
     QCOMPARE(ps.indexOf(&ps[0][0]), 0);
     //QCOMPARE(ps.indexOf(ps.end()), -1); //ps.end() is a QhullPoint which may match
     QCOMPARE(ps.indexOf(0), -1);
     QCOMPARE(ps.indexOf(&ps[3][0]), 3);
     QCOMPARE(ps.indexOf(&ps[3][1], QhullError::NOthrow), 3);
     QCOMPARE(ps.indexOf(ps.data()+ps.coordinateCount(), QhullError::NOthrow), -1);
     QCOMPARE(ps.indexOf(p), 0);
     QCOMPARE(ps.indexOf(p2), 0);
     QCOMPARE(ps.indexOf(p3), 0);
     QCOMPARE(ps.indexOf(p4), -1);
     QCOMPARE(ps.indexOf(p5), 2);
     QCOMPARE(ps.indexOf(p6), 1);
     QCOMPARE(ps.lastIndexOf(p), 3);
     QCOMPARE(ps.lastIndexOf(p4), -1);
     QCOMPARE(ps.lastIndexOf(p6), 1);
     QhullPoints ps2(3);
     QCOMPARE(ps2.indexOf(ps2.data()), -1);
     QCOMPARE(ps2.indexOf(ps2.data()+1, QhullError::NOthrow), -1);
     QCOMPARE(ps2.indexOf(p), -1);
     QCOMPARE(ps2.lastIndexOf(p), -1);
     QhullPoints ps3;
     QCOMPARE(ps3.indexOf(ps3.data()), -1);
     QCOMPARE(ps3.indexOf(ps3.data()+1, QhullError::NOthrow), -1);
     QCOMPARE(ps3.indexOf(p), -1);
     QCOMPARE(ps3.lastIndexOf(p), -1);
     QhullPoints ps4(2, 0, c);
     QCOMPARE(ps4.indexOf(p), -1);
     QCOMPARE(ps4.lastIndexOf(p), -1);
 }//t_search
 
 void QhullPoints_test::
 t_points_iterator()
 {
     coordT c2[]= {0.0};
     QhullPoints ps2(0, 0, c2); // 0-dimensional
     QhullPointsIterator i2= ps2;
     QVERIFY(!i2.hasNext());
     QVERIFY(!i2.hasPrevious());
     i2.toBack();
     QVERIFY(!i2.hasNext());
     QVERIFY(!i2.hasPrevious());
 
     coordT c[]= {0.0, 1.0, 2.0, 3.0, 4.0, 5.0};
     QhullPoints ps(3, 6, c); // 3-dimensional
     QhullPointsIterator i(ps);
     i2= ps;
     QVERIFY(i2.hasNext());
     QVERIFY(!i2.hasPrevious());
     QVERIFY(i.hasNext());
     QVERIFY(!i.hasPrevious());
     i2.toBack();
     i.toFront();
     QVERIFY(!i2.hasNext());
     QVERIFY(i2.hasPrevious());
     QVERIFY(i.hasNext());
     QVERIFY(!i.hasPrevious());
 
     QhullPoint p= ps[0];
     QhullPoint p2(ps[0]);
     QCOMPARE(p, p2);
     QVERIFY(p==p2);
     QhullPoint p3(ps[1]);
  // p2[0]= 0.0;
     QVERIFY(p==p2);
     QCOMPARE(i2.peekPrevious(), p3);
     QCOMPARE(i2.previous(), p3);
     QCOMPARE(i2.previous(), p);
     QVERIFY(!i2.hasPrevious());
     QCOMPARE(i.peekNext(), p);
     // i.peekNext()= 1.0; // compiler error
     QCOMPARE(i.next(), p);
     QCOMPARE(i.peekNext(), p3);
     QCOMPARE(i.next(), p3);
     QVERIFY(!i.hasNext());
     i.toFront();
     QCOMPARE(i.next(), p);
 }//t_points_iterator
 
 void QhullPoints_test::
 t_io()
 {
     QhullPoints ps;
     ostringstream os;
     os << "Empty QhullPoints\n" << ps << endl;
     coordT c[]= {0.0, 1.0, 2.0, 3.0, 4.0, 5.0};
     QhullPoints ps2(3, 6, c); // 3-dimensional explicit
     os << "QhullPoints from c[]\n" << ps2 << endl;
     RboxPoints rcube("c");
     Qhull q(rcube,"Qt QR0");  // triangulation of rotated unit cube
     QhullPoints ps3= q.points();
     os << "QhullPoints\n" << ps3;
-    os << "RunId\n" << ps3.print(q.runId());
-    os << ps3.print(q.runId(), "RunId w/ message\n");
-    os << ps3.printWithIdentifier(q.runId(), "RunId w/ identifiers\n");
+    os << "RunId\n" << ps3.print();
+    os << ps3.print("RunId w/ message\n");
+    os << ps3.printWithIdentifier("RunId w/ identifiers\n");
     cout << os.str();
     QString s= QString::fromStdString(os.str());
     QCOMPARE(s.count("p"), 3*8+3);
     // QCOMPARE(s.count(QRegExp("f\\d")), 3*7 + 13*3*2);
 }//t_io
 
 }//orgQhull
 
 #include "moc/QhullPoints_test.moc"
diff --git a/src/qhulltest/QhullRidge_test.cpp b/src/qhulltest/QhullRidge_test.cpp
index 302e6f4..70e68ed 100644
--- a/src/qhulltest/QhullRidge_test.cpp
+++ b/src/qhulltest/QhullRidge_test.cpp
@@ -1,163 +1,163 @@
 /****************************************************************************
 **
 ** Copyright (c) 2008-2014 C.B. Barber. All rights reserved.
-** $Id: //main/2011/qhull/src/qhulltest/QhullRidge_test.cpp#5 $$Change: 1490 $
-** $DateTime: 2012/02/19 20:27:01 $$Author: bbarber $
+** $Id: //main/2011/qhull/src/qhulltest/QhullRidge_test.cpp#7 $$Change: 1709 $
+** $DateTime: 2014/03/26 22:27:14 $$Author: bbarber $
 **
 ****************************************************************************/
 
 //pre-compiled headers
 #include 
 #include "RoadTest.h"
 
 #include "QhullRidge.h"
 #include "QhullError.h"
 #include "RboxPoints.h"
 #include "QhullFacet.h"
 #include "Qhull.h"
 
 using std::cout;
 using std::endl;
 using std::ostringstream;
 using std::ostream;
 using std::string;
 
 namespace orgQhull {
 
 class QhullRidge_test : public RoadTest
 {
     Q_OBJECT
 
 #//Test slots
 private slots:
     void cleanup();
     void t_construct();
     void t_getSet();
     void t_foreach();
     void t_io();
 };//QhullRidge_test
 
 void
 add_QhullRidge_test()
 {
     new QhullRidge_test();
 }
 
 //Executed after each testcase
 void QhullRidge_test::
 cleanup()
 {
     UsingLibQhull::checkQhullMemoryEmpty();
     RoadTest::cleanup();
 }
 
 void QhullRidge_test::
 t_construct()
 {
     // Qhull.runQhull() constructs QhullFacets as facetT
     QhullRidge r;
     QVERIFY(!r.isDefined());
     QCOMPARE(r.dimension(),0);
     RboxPoints rcube("c");
     Qhull q(rcube,"QR0");  // triangulation of rotated unit cube
     QhullFacet f(q.firstFacet());
     QhullRidgeSet rs(f.ridges());
     QVERIFY(!rs.isEmpty()); // Simplicial facets do not have ridges()
     QhullRidge r2(rs.first());
     QCOMPARE(r2.dimension(), 2); // One dimension lower than the facet
     r= r2;
     QVERIFY(r.isDefined());
     QCOMPARE(r.dimension(), 2);
     QhullRidge r3= r2.getRidgeT();
     QCOMPARE(r,r3);
     QhullRidge r4= r2.getBaseT();
     QCOMPARE(r,r4);
     QhullRidge r5= r2; // copy constructor
     QVERIFY(r5==r2);
     QVERIFY(r5==r);
 }//t_construct
 
 void QhullRidge_test::
 t_getSet()
 {
     RboxPoints rcube("c");
     {
         Qhull q(rcube,"QR0");  // triangulation of rotated unit cube
         QCOMPARE(q.facetCount(), 6);
         QCOMPARE(q.vertexCount(), 8);
         QhullFacet f(q.firstFacet());
         QhullRidgeSet rs= f.ridges();
         QhullRidgeSetIterator i(rs);
         while(i.hasNext()){
             const QhullRidge r= i.next();
             cout << r.id() << endl;
             QVERIFY(r.bottomFacet()!=r.topFacet());
             QCOMPARE(r.dimension(), 2); // Ridge one-dimension less than facet
             QVERIFY(r.id()>=0 && r.id()<9*27);
             QVERIFY(r.isDefined());
             QVERIFY(r==r);
             QVERIFY(r==i.peekPrevious());
             QCOMPARE(r.otherFacet(r.bottomFacet()),r.topFacet());
             QCOMPARE(r.otherFacet(r.topFacet()),r.bottomFacet());
         }
         QhullRidgeSetIterator i2(i);
         QEXPECT_FAIL("", "SetIterator copy constructor not reset to BOT", Continue);
         QVERIFY(!i2.hasPrevious());
     }
 }//t_getSet
 
 void QhullRidge_test::
 t_foreach()
 {
     RboxPoints rcube("c");  // cube
     {
         Qhull q(rcube, "QR0"); // rotated cube
         QhullFacet f(q.firstFacet());
         foreach (QhullRidge r, f.ridges()){  // Qt only
             QhullVertexSet vs= r.vertices();
             QCOMPARE(vs.count(), 2);
             foreach (QhullVertex v, vs){  // Qt only
                 QVERIFY(f.vertices().contains(v));
             }
         }
         QhullRidgeSet rs= f.ridges();
         QhullRidge r= rs.first();
         QhullRidge r2= r;
         QList vs;
         int count= 0;
         while(!count || r2!=r){
             ++count;
             QhullVertex v;
             QVERIFY2(r2.hasNextRidge3d(f),"A cube should only have non-simplicial facets.");
             QhullRidge r3= r2.nextRidge3d(f, &v);
             QVERIFY(!vs.contains(v));
             vs << v;
             r2= r2.nextRidge3d(f);
             QCOMPARE(r3, r2);
         }
         QCOMPARE(vs.count(), rs.count());
         QCOMPARE(count, rs.count());
     }
 }//t_foreach
 
 void QhullRidge_test::
 t_io()
 {
     RboxPoints rcube("c");
     {
         Qhull q(rcube, "");
         QhullFacet f(q.firstFacet());
         QhullRidgeSet rs= f.ridges();
         QhullRidge r= rs.first();
         ostringstream os;
-        os << "Ridges Without runId\n" << rs << "Ridge\n" << r;
-        os << "Ridge with runId\n" << r.print(q.runId());
+        os << "Ridges\n" << rs << "Ridge\n" << r;
+        os << "Ridge with runId FIXUP\n" << r.print();
         cout << os.str();
         QString s= QString::fromStdString(os.str());
         QCOMPARE(s.count(" r"), 6+2);
     }
 }//t_io
 
 }//orgQhull
 
 #include "moc/QhullRidge_test.moc"
diff --git a/src/qhulltest/QhullSet_test.cpp b/src/qhulltest/QhullSet_test.cpp
index 866b6de..f328c3a 100644
--- a/src/qhulltest/QhullSet_test.cpp
+++ b/src/qhulltest/QhullSet_test.cpp
@@ -1,435 +1,432 @@
 /****************************************************************************
 **
 ** Copyright (c) 2009-2014 C.B. Barber. All rights reserved.
-** $Id: //main/2011/qhull/src/qhulltest/QhullSet_test.cpp#4 $$Change: 1490 $
-** $DateTime: 2012/02/19 20:27:01 $$Author: bbarber $
+** $Id: //main/2011/qhull/src/qhulltest/QhullSet_test.cpp#6 $$Change: 1708 $
+** $DateTime: 2014/03/26 19:13:56 $$Author: bbarber $
 **
 ****************************************************************************/
 
 //pre-compiled headers
 #include 
 #include 
 #include "RoadTest.h" // QT_VERSION
 
 #include "QhullRidge.h"
 #include "QhullFacetSet.h"
 #include "Qhull.h"
 
 using std::cout;
 using std::endl;
 
 namespace orgQhull {
 
 class QhullSet_test : public RoadTest
 {
     Q_OBJECT
 
 #//Test slots
 private slots:
     void cleanup();
     void t_qhullsetbase();
     void t_convert();
     void t_element();
     void t_search();
     void t_iterator();
     void t_const_iterator();
     void t_qhullset_iterator();
     void t_io();
 };//QhullSet_test
 
 void
 add_QhullSet_test()
 {
     new QhullSet_test();
 }
 
 //Executed after each testcase
 void QhullSet_test::
 cleanup()
 {
     UsingLibQhull::checkQhullMemoryEmpty();
     RoadTest::cleanup();
 }
 
 // Test QhullFacetSet and QhullSet.
 // Use QhullRidgeSet to test methods overloaded by QhullFacetSet
 
 void QhullSet_test::
 t_qhullsetbase()
 {
     RboxPoints rcube("c");
     {
         Qhull q(rcube,"QR0");  // triangulation of rotated unit cube
         // Fake an empty set.  Default constructor not defined.  No memory allocation.
         QhullFacet f4 = q.beginFacet();
         QhullFacetSet fs = f4.neighborFacets();
         fs.defineAs(q.qhullQh()->other_points); // Force an empty set
         QVERIFY(fs.isEmpty());
-        QVERIFY(fs.empty());
         QCOMPARE(fs.count(), 0);
         QCOMPARE(fs.size(), 0u);
         QCOMPARE(fs.begin(), fs.end()); // beginPointer(), endPointer()
         QVERIFY(QhullSetBase::isEmpty(fs.getSetT()));
 
         QhullRidgeSet rs = f4.ridges();
         QVERIFY(!rs.isEmpty());
-        QVERIFY(!rs.empty());
         QCOMPARE(rs.count(), 4);
         QCOMPARE(rs.size(), 4u);
         QVERIFY(rs.begin()!=rs.end());
         QVERIFY(!QhullSetBase::isEmpty(rs.getSetT()));
         QhullRidgeSet rs2= rs; // copy constructor
         // rs= rs2; // disabled.  Would not copy ridges
         QCOMPARE(rs2, rs);
 
         QCOMPARE(q.facetCount(), 6);
         QhullFacet f = q.beginFacet();
         QhullFacetSet fs2 = f.neighborFacets();
         QCOMPARE(fs2.count(), 4);
         QCOMPARE(fs2.size(), 4u);
         QVERIFY(!fs2.isEmpty());
         QVERIFY(!QhullSetBase::isEmpty(fs2.getSetT()));
-        QVERIFY(!fs2.empty());
         QVERIFY(fs!=fs2);
         setT *s= fs2.getSetT();
         fs.defineAs(s);
         QVERIFY(fs==fs2);
         QCOMPARE(fs[1], fs2[1]); // elementPointer
         QhullFacetSet fs3(fs2);
         QVERIFY(fs3==fs);
         // fs= fs2; // disabled.  Would not copy facets
         QhullFacetSet fs4= fs2; // copy constructor
         QVERIFY(fs4==fs2);
     }
 }//t_qhullsetbase
 
 // constructors tested by t_qhullsetbase
 
 void QhullSet_test::
 t_convert()
 {
     RboxPoints rcube("c");
     {
         Qhull q(rcube,"QR0");  // rotated unit cube
         QhullFacet f= q.firstFacet();
         f= f.next();
         QhullRidgeSet rs= f.ridges();
         QCOMPARE(rs.count(),4);
         std::vector rv= rs.toStdVector();
         QCOMPARE(rv.size(), 4u);
         QList rv2= rs.toQList();
         QCOMPARE(rv2.size(), 4);
         std::vector::iterator i= rv.begin();
         foreach(QhullRidge r, rv2){  // Qt only
             QhullRidge r2= *i++;
             QCOMPARE(r, r2);
         }
 
         Qhull q2(rcube,"Qt QR0");  // triangulation of rotated unit cube
         QCOMPARE(q2.facetCount(), 12);
         QhullFacet f2 = q2.beginFacet();
         QhullFacetSet fs = f2.neighborFacets();
         QCOMPARE(fs.size(), 3U);
         std::vector vs= fs.toStdVector();
         QCOMPARE(vs.size(), fs.size());
         for(int k= fs.count(); k--; ){
             QCOMPARE(vs[k], fs[k]);
         }
         QList qv= fs.toQList();
         QCOMPARE(qv.count(), fs.count());
         for(int k= fs.count(); k--; ){
             QCOMPARE(qv[k], fs[k]);
         }
     }
 }//t_convert
 
 //ReadOnly (count, isEmpty) tested by t_convert
 //  operator== tested by t_search
 
 void QhullSet_test::
 t_element()
 {
     RboxPoints rcube("c");
     Qhull q(rcube,"QR0");  // rotated unit cube
     QhullFacet f = q.beginFacet();
     QhullFacetSet fs = f.neighborFacets();
 
     QCOMPARE(fs.at(1), fs[1]);
     QCOMPARE(fs.first(), fs[0]);
     QCOMPARE(fs.front(), fs.first());
     QCOMPARE(fs.last(), fs.at(3));
     QCOMPARE(fs.back(), fs.last());
     QhullFacet *d= fs.data();
     const QhullFacet *d2= fs.data();
     const QhullFacet *d3= fs.constData();
     QVERIFY(d==d2);
     QVERIFY(d2==d3);
     QCOMPARE(*d, fs.first());
     QCOMPARE(d+4, fs.end());
     QCOMPARE((d+4)->getFacetT(), static_cast(0));
     QhullFacet f4= *(d+4);
     QVERIFY(!f4.isDefined());
     QCOMPARE(fs.second(), fs[1]);
     const QhullFacet f2= fs.second();
     QVERIFY(f2==fs[1]);
     const QhullFacet f3= fs[1];
     QCOMPARE(f2, f3);
 
     QCOMPARE(fs.value(2), fs[2]);
     QCOMPARE(fs.value(-1), QhullFacet());
     QCOMPARE(fs.value(10), QhullFacet());
     QCOMPARE(fs.value(2, f), fs[2]);
     QCOMPARE(fs.value(4, f), f);
     // mid() not available (read-only)
 }//t_element
 
 void QhullSet_test::
 t_search()
 {
     RboxPoints rcube("c");
     Qhull q(rcube,"QR0");  // rotated unit cube
     QhullFacet f = q.beginFacet();
     QhullFacetSet fs = f.neighborFacets();
     QhullFacet f2= *fs.begin();
     QhullFacet f3= fs.last();
     QVERIFY(fs.contains(f2));
     QVERIFY(fs.contains(f3));
     QVERIFY(!fs.contains(f));
 
     QhullFacetSet fs2= f2.neighborFacets();
     QVERIFY(fs==fs);
     QVERIFY(fs!=fs2);
     QCOMPARE(fs.count(f2), 1);
     QCOMPARE(fs.count(f3), 1);
     QCOMPARE(fs.count(f), 0);
     QCOMPARE(fs.indexOf(f2), 0);
     QCOMPARE(fs.indexOf(f3), 3);
     QCOMPARE(fs.indexOf(f), -1);
     QCOMPARE(fs.lastIndexOf(f2), 0);
     QCOMPARE(fs.lastIndexOf(f3), 3);
     QCOMPARE(fs.lastIndexOf(f), -1);
 }//t_search
 
 void QhullSet_test::
 t_iterator()
 {
     RboxPoints rcube("c");
     {
         Qhull q(rcube,"QR0");  // rotated unit cube
         QhullFacet f = q.beginFacet();
         QhullFacetSet fs = f.neighborFacets();
         QhullFacetSet::Iterator i= fs.begin();
         QhullFacetSet::iterator i2= fs.begin();
         QVERIFY(i==i2);
         QVERIFY(i>=i2);
         QVERIFY(i<=i2);
         i= fs.begin();
         QVERIFY(i==i2);
         i2= fs.end();
         QVERIFY(i!=i2);
         QhullFacet f3(*i);
         i2--;
         QhullFacet f2= *i2;
         QCOMPARE(f3.id(), fs[0].id());
         QCOMPARE(f2.id(), fs[3].id());
         QhullFacetSet::Iterator i3(i2);
         QCOMPARE(*i2, *i3);
 
         (i3= i)++;
         QCOMPARE((*i3).id(), fs[1].id());
         QVERIFY(i==i);
         QVERIFY(i!=i2);
         QVERIFY(ii);
         QVERIFY(i2>=i);
 
         QhullFacetSet::ConstIterator i4= fs.begin();
         QVERIFY(i==i4); // iterator COMP const_iterator
         QVERIFY(i<=i4);
         QVERIFY(i>=i4);
         QVERIFY(i4==i); // const_iterator COMP iterator
         QVERIFY(i4<=i);
         QVERIFY(i4>=i);
         QVERIFY(i>=i4);
         QVERIFY(i4<=i);
         QVERIFY(i2!=i4);
         QVERIFY(i2>i4);
         QVERIFY(i2>=i4);
         QVERIFY(i4!=i2);
         QVERIFY(i4i);
         QVERIFY(i4>=i);
 
         i= fs.begin();
         i2= fs.begin();
         QCOMPARE(i, i2++);
         QCOMPARE(*i2, fs[1]);
         QCOMPARE(++i, i2);
         QCOMPARE(i, i2--);
         QCOMPARE(i2, fs.begin());
         QCOMPARE(--i, i2);
         QCOMPARE(i2 += 4, fs.end());
         QCOMPARE(i2 -= 4, fs.begin());
         QCOMPARE(i2+0, fs.begin());
         QCOMPARE(i2+4, fs.end());
         i2 += 4;
         i= i2-0;
         QCOMPARE(i, i2);
         i= i2-4;
         QCOMPARE(i, fs.begin());
         QCOMPARE(i2-i, 4);
 
         //fs.begin end tested above
 
         // QhullFacetSet is const-only
     }
 }//t_iterator
 
 void QhullSet_test::
 t_const_iterator()
 {
     RboxPoints rcube("c");
     {
         Qhull q(rcube,"QR0");  // rotated unit cube
         QhullFacet f = q.beginFacet();
         QhullFacetSet fs = f.neighborFacets();
         QhullFacetSet::ConstIterator i= fs.begin();
         QhullFacetSet::const_iterator i2= fs.begin();
         QVERIFY(i==i2);
         QVERIFY(i>=i2);
         QVERIFY(i<=i2);
         i= fs.begin();
         QVERIFY(i==i2);
         i2= fs.end();
         QVERIFY(i!=i2);
         QhullFacet f3(*i);
         i2--;
         QhullFacet f2= *i2;
         QCOMPARE(f3.id(), fs[0].id());
         QCOMPARE(f2.id(), fs[3].id());
         QhullFacetSet::ConstIterator i3(i2);
         QCOMPARE(*i2, *i3);
 
         (i3= i)++;
         QCOMPARE((*i3).id(), fs[1].id());
         QVERIFY(i==i);
         QVERIFY(i!=i2);
         QVERIFY(ii);
         QVERIFY(i2>=i);
 
         // See t_iterator for const_iterator COMP iterator
 
         i= fs.begin();
         i2= fs.constBegin();
         QCOMPARE(i, i2++);
         QCOMPARE(*i2, fs[1]);
         QCOMPARE(++i, i2);
         QCOMPARE(i, i2--);
         QCOMPARE(i2, fs.constBegin());
         QCOMPARE(--i, i2);
         QCOMPARE(i2+=4, fs.constEnd());
         QCOMPARE(i2-=4, fs.constBegin());
         QCOMPARE(i2+0, fs.constBegin());
         QCOMPARE(i2+4, fs.constEnd());
         i2 += 4;
         i= i2-0;
         QCOMPARE(i, i2);
         i= i2-4;
         QCOMPARE(i, fs.constBegin());
         QCOMPARE(i2-i, 4);
 
         // QhullFacetSet is const-only
     }
 }//t_const_iterator
 
 void QhullSet_test::
 t_qhullset_iterator()
 {
     RboxPoints rcube("c");
     Qhull q(rcube,"QR0");  // rotated unit cube
     // Fake an empty set.  Default constructor not defined.  No memory allocation.
     QhullFacet f = q.beginFacet();
     QhullFacetSet fs = f.neighborFacets();
     fs.defineAs(q.qhullQh()->other_points);
     QhullFacetSetIterator i= fs;
     QCOMPARE(fs.count(), 0);
     QVERIFY(!i.hasNext());
     QVERIFY(!i.hasPrevious());
     i.toBack();
     QVERIFY(!i.hasNext());
     QVERIFY(!i.hasPrevious());
 
     QhullFacet f2 = q.beginFacet();
     QhullFacetSet fs2 = f2.neighborFacets();
     QhullFacetSetIterator i2(fs2);
     QCOMPARE(fs2.count(), 4);
     i= fs2;
     QVERIFY(i2.hasNext());
     QVERIFY(!i2.hasPrevious());
     QVERIFY(i.hasNext());
     QVERIFY(!i.hasPrevious());
     i2.toBack();
     i.toFront();
     QVERIFY(!i2.hasNext());
     QVERIFY(i2.hasPrevious());
     QVERIFY(i.hasNext());
     QVERIFY(!i.hasPrevious());
 
     // i at front, i2 at end/back, 4 neighbors
     QhullFacetSet fs3 = f2.neighborFacets(); // same as fs2
     QhullFacet f3(fs2[0]);
     QhullFacet f4= fs3[0];
     QCOMPARE(f3, f4);
     QVERIFY(f3==f4);
     QhullFacet f5(fs3[1]);
     QVERIFY(f4!=f5);
     QhullFacet f6(fs3[2]);
     QhullFacet f7(fs3[3]);
     QCOMPARE(i2.peekPrevious(), f7);
     QCOMPARE(i2.previous(), f7);
     QCOMPARE(i2.previous(), f6);
     QCOMPARE(i2.previous(), f5);
     QCOMPARE(i2.previous(), f4);
     QVERIFY(!i2.hasPrevious());
     QCOMPARE(i.peekNext(), f4);
     // i.peekNext()= 1.0; // compiler error
     QCOMPARE(i.next(), f4);
     QCOMPARE(i.peekNext(), f5);
     QCOMPARE(i.next(), f5);
     QCOMPARE(i.next(), f6);
     QCOMPARE(i.next(), f7);
     QVERIFY(!i.hasNext());
     i.toFront();
     QCOMPARE(i.next(), f4);
 }//t_qhullset_iterator
 
 void QhullSet_test::
 t_io()
 {
     RboxPoints rcube("c");
     Qhull q(rcube,"QR0");  // rotated unit cube
     // Fake an empty set.  Default constructor not defined.  No memory allocation.
     QhullFacet f= q.beginFacet();
     QhullFacetSet fs= f.neighborFacets();
     fs.defineAs(q.qhullQh()->other_points);
     cout << "INFO:     empty set" << fs << std::endl;
     QhullFacet f2= q.beginFacet();
     QhullFacetSet fs2= f2.neighborFacets();
     cout << "INFO:   Neighboring facets\n";
     cout << fs2 << std::endl;
 
     QhullRidgeSet rs= f.ridges();
     cout << "INFO:   Ridges for a facet\n";
     cout << rs << std::endl;
 }//t_io
 
 }//namespace orgQhull
 
 #include "moc/QhullSet_test.moc"
diff --git a/src/qhulltest/QhullVertex_test.cpp b/src/qhulltest/QhullVertex_test.cpp
index c850d81..c807f6e 100644
--- a/src/qhulltest/QhullVertex_test.cpp
+++ b/src/qhulltest/QhullVertex_test.cpp
@@ -1,184 +1,184 @@
 /****************************************************************************
 **
 ** Copyright (c) 2008-2014 C.B. Barber. All rights reserved.
-** $Id: //main/2011/qhull/src/qhulltest/QhullVertex_test.cpp#6 $$Change: 1490 $
-** $DateTime: 2012/02/19 20:27:01 $$Author: bbarber $
+** $Id: //main/2011/qhull/src/qhulltest/QhullVertex_test.cpp#8 $$Change: 1709 $
+** $DateTime: 2014/03/26 22:27:14 $$Author: bbarber $
 **
 ****************************************************************************/
 //pre-compiled headers
 #include 
 #include "RoadTest.h"
 
 #include "QhullVertex.h"
 #include "Coordinates.h"
 #include "QhullError.h"
 #include "RboxPoints.h"
 #include "QhullFacet.h"
 #include "QhullFacetSet.h"
 #include "QhullVertexSet.h"
 #include "Qhull.h"
 
 using std::cout;
 using std::endl;
 using std::ostringstream;
 using std::ostream;
 using std::string;
 
 namespace orgQhull {
 
 class QhullVertex_test : public RoadTest
 {
     Q_OBJECT
 
 #//Test slots
 private slots:
     void cleanup();
     void t_constructConvert();
     void t_getSet();
     void t_foreach();
     void t_io();
 };//QhullVertex_test
 
 void
 add_QhullVertex_test()
 {
     new QhullVertex_test();
 }
 
 //Executed after each testcase
 void QhullVertex_test::
 cleanup()
 {
     UsingLibQhull::checkQhullMemoryEmpty();
     RoadTest::cleanup();
 }
 
 void QhullVertex_test::
 t_constructConvert()
 {
     // Qhull.runQhull() constructs QhullFacets as facetT
     QhullVertex v;
     QVERIFY(!v.isDefined());
     QCOMPARE(v.dimension(),0);
     RboxPoints rcube("c");
     Qhull q(rcube,"Qt QR0");  // triangulation of rotated unit cube
     QhullVertex v2(q.beginVertex());
     QCOMPARE(v2.dimension(),3);
     v= v2;  // copy assignment
     QVERIFY(v.isDefined());
     QCOMPARE(v.dimension(),3);
     QhullVertex v5= v2; // copy constructor
     QVERIFY(v5==v2);
     QVERIFY(v5==v);
     QhullVertex v3= v2.getVertexT();
     QCOMPARE(v,v3);
     QhullVertex v4= v2.getBaseT();
     QCOMPARE(v,v4);
 }//t_constructConvert
 
 void QhullVertex_test::
 t_getSet()
 {
     RboxPoints rcube("c");
     {
         Qhull q(rcube,"Qt QR0");  // triangulation of rotated unit cube
         QCOMPARE(q.facetCount(), 12);
         QCOMPARE(q.vertexCount(), 8);
 
         // Also spot-test QhullVertexList.  See QhullLinkedList_test.cpp
         QhullVertexList vs= q.vertexList();
         QhullVertexListIterator i(vs);
         while(i.hasNext()){
             const QhullVertex v= i.next();
             cout << v.id() << endl;
             QCOMPARE(v.dimension(),3);
             QVERIFY(v.id()>=0 && v.id()<9);
             QVERIFY(v.isDefined());
             if(i.hasNext()){
                 QCOMPARE(v.next(), i.peekNext());
                 QVERIFY(v.next()!=v);
                 QVERIFY(v.next().previous()==v);
             }
             QVERIFY(i.hasPrevious());
             QCOMPARE(v, i.peekPrevious());
         }
         QhullVertexListIterator i2(i);
         QEXPECT_FAIL("", "ListIterator copy constructor not reset to BOT", Continue);
         QVERIFY(!i2.hasPrevious());
 
         // test point()
         foreach (QhullVertex v, q.vertexList()){  // Qt only
             QhullPoint p= v.point();
-            int j= p.id(q.runId());
-            cout << "Point " << j << ":\n" << p.print(q.runId()) << endl;
+            int j= p.id();
+            cout << "Point " << j << ":\n" << p.print() << endl;
             QVERIFY(j>=0 && j<8);
         }
     }
 }//t_getSet
 
 void QhullVertex_test::
 t_foreach()
 {
     RboxPoints rcube("c W0 300");  // 300 points on surface of cube
     {
         Qhull q(rcube, "QR0 Qc"); // keep coplanars, thick facet, and rotate the cube
         foreach (QhullVertex v, q.vertexList()){  // Qt only
             QhullFacetSet fs= v.neighborFacets();
             QCOMPARE(fs.count(), 3);
             foreach (QhullFacet f, fs){  // Qt only
                 QVERIFY(f.vertices().contains(v));
             }
         }
     }
 }//t_foreach
 
 void QhullVertex_test::
 t_io()
 {
     RboxPoints rcube("c");
     {
         Qhull q(rcube, "");
         QhullVertex v= q.beginVertex();
         ostringstream os;
         os << "Vertex and vertices w/o runId:\n";
         os << v;
         QhullVertexSet vs= q.firstFacet().vertices();
         os << vs;
-        os << "Vertex and vertices w/ runId:\n";
-        os << v.print(q.runId());
-        os << vs.print(q.runId(), "vertices:");
+        os << "Vertex and vertices w/ FIXUP runId:\n";
+        os << v.print();
+        os << vs.print("vertices:");
         cout << os.str();
         QString s= QString::fromStdString(os.str());
         QCOMPARE(s.count("(v"), 10);
         QCOMPARE(s.count(": f"), 2);
     }
     RboxPoints r10("10 D3");  // Without QhullVertex::facetNeighbors
     {
         Qhull q(r10, "");
         QhullVertex v= q.beginVertex();
         ostringstream os;
         os << "\nTry again with simplicial facets.  No neighboring facets listed for vertices.\n";
-        os << "Vertex and vertices w/o runId:\n";
+        os << "Vertex and vertices:\n";
         os << v;
         q.defineVertexNeighborFacets();
         os << "This time with neighborFacets() defined for all vertices:\n";
         os << v;
         cout << os.str();
         QString s= QString::fromStdString(os.str());
         QCOMPARE(s.count(": f"), 1);
 
         Qhull q2(r10, "v"); // Voronoi diagram
         QhullVertex v2= q2.beginVertex();
         ostringstream os2;
         os2 << "\nTry again with Voronoi diagram of simplicial facets.  Neighboring facets automatically defined for vertices.\n";
-        os2 << "Vertex and vertices w/o runId:\n";
+        os2 << "Vertex and vertices:\n";
         os2 << v2;
         cout << os2.str();
         QString s2= QString::fromStdString(os2.str());
         QCOMPARE(s2.count(": f"), 1);
     }
 }//t_io
 
 }//orgQhull
 
 #include "moc/QhullVertex_test.moc"
diff --git a/src/qhulltest/Qhull_test.cpp b/src/qhulltest/Qhull_test.cpp
index 4d4dc43..e6abc79 100644
--- a/src/qhulltest/Qhull_test.cpp
+++ b/src/qhulltest/Qhull_test.cpp
@@ -1,380 +1,375 @@
 /****************************************************************************
 **
 ** Copyright (c) 2008-2014 C.B. Barber. All rights reserved.
-** $Id: //main/2011/qhull/src/qhulltest/Qhull_test.cpp#5 $$Change: 1490 $
-** $DateTime: 2012/02/19 20:27:01 $$Author: bbarber $
+** $Id: //main/2011/qhull/src/qhulltest/Qhull_test.cpp#7 $$Change: 1709 $
+** $DateTime: 2014/03/26 22:27:14 $$Author: bbarber $
 **
 ****************************************************************************/
 
 //pre-compiled headers
 #include 
 #include "RoadTest.h" // QT_VERSION
 
 #include "Qhull.h"
 #include "QhullError.h"
 #include "RboxPoints.h"
 #include "QhullFacetList.h"
 
 using std::cout;
 using std::endl;
 using std::string;
 
 namespace orgQhull {
 
 //! Test C++ interface to Qhull
 //! See eg/q_test for tests of Qhull commands
 class Qhull_test : public RoadTest
 {
     Q_OBJECT
 
 #//Test slots
 private slots:
     void cleanup();
     void t_construct();
     void t_attribute();
     void t_message();
     void t_getSet();
     void t_getQh();
     void t_getValue();
     void t_foreach();
     void t_modify();
 };//Qhull_test
 
 void
 add_Qhull_test()
 {
     new Qhull_test();
 }
 
 //Executed after each testcase
 void Qhull_test::
 cleanup()
 {
     UsingLibQhull::checkQhullMemoryEmpty();
     RoadTest::cleanup();
 }
 
 void Qhull_test::
 t_construct()
 {
     {
         Qhull q;
         QCOMPARE(q.dimension(),0);
         QVERIFY(q.qhullQh()!=0);
-        QVERIFY(q.runId()!=0);
         QCOMPARE(QString(q.qhullCommand()),QString(""));
         QCOMPARE(QString(q.rboxCommand()),QString(""));
         try{
             QCOMPARE(q.area(),0.0);
             QFAIL("area() did not fail.");
         }catch (const std::exception &e) {
             cout << "INFO   : Caught " << e.what();
         }
         Qhull q2(q);  // Copy constructor and copy assignment OK if not q.initialized()
         QCOMPARE(q2.dimension(),0);
         q= q2;
         QCOMPARE(q.dimension(),0);
     }
     {
         RboxPoints rbox("10000");
         Qhull q(rbox, "QR0"); // Random points in a randomly rotated cube.
         QCOMPARE(q.dimension(),3);
         QVERIFY(q.volume() < 1.0);
         QVERIFY(q.volume() > 0.99);
         try{
             Qhull q2(q);
             QFAIL("Copy constructor did not fail for initialized Qhull.");
         }catch (const std::exception &e) {
             cout << "INFO   : Caught " << e.what();
         }
         try{
             Qhull q3;
             q3= q;
             QFAIL("Copy assignment did not fail for initialized Qhull source.");
         }catch (const std::exception &e) {
             cout << "INFO   : Caught " << e.what();
         }
         QCOMPARE(q.dimension(),3);
         try{
             Qhull q4;
             q= q4;
             QFAIL("Copy assignment did not fail for initialized Qhull destination.");
         }catch (const std::exception &e) {
             cout << "INFO   : Caught " << e.what();
         }
         QCOMPARE(q.dimension(),3);
     }
     {
         double points[] = {
             0, 0,
             1, 0,
             1, 1
         };
         Qhull q("triangle", 2, 3, points, "");
         QCOMPARE(q.dimension(),2);
         QCOMPARE(q.facetCount(),3);
         QCOMPARE(q.vertexCount(),3);
         QCOMPARE(q.dimension(),2);
         QCOMPARE(q.area(), 2.0+sqrt(2.0)); // length of boundary
         QCOMPARE(q.volume(), 0.5);        // the 2-d area
     }
 }//t_construct
 
 void Qhull_test::
 t_attribute()
 {
     RboxPoints rcube("c");
     {
         double normals[] = {
             0,  -1, -0.5,
            -1,   0, -0.5,
             1,   0, -0.5,
             0,   1, -0.5
         };
         Qhull q;
         q.feasiblePoint << 0.0 << 0.0;
         Coordinates c(std::vector(2, 0.0));
         QVERIFY(q.feasiblePoint==c);
         q.setOutputStream(&cout);
         q.runQhull("normals of square", 3, 4, normals, "H"); // halfspace intersect
         QCOMPARE(q.facetList().count(), 4); // Vertices of square
         cout << "Expecting summary of halfspace intersect\n";
         q.outputQhull();
         q.useOutputStream= false;
         cout << "Expecting no output from qh_fprintf() in Qhull.cpp\n";
         q.outputQhull();
     }
 }//t_attribute
 
 //! No QhullMessage for errors outside of qhull
 void Qhull_test::
 t_message()
 {
     RboxPoints rcube("c");
     {
         Qhull q;
         QCOMPARE(q.qhullMessage(), string(""));
         QCOMPARE(q.qhullStatus(), qh_ERRnone);
         QVERIFY(!q.hasQhullMessage());
         try{
             q.runQhull(rcube, "Fd");
             QFAIL("runQhull Fd did not fail.");
         }catch (const std::exception &e) {
             const char *s= e.what();
             cout << "INFO   : Caught " << s;
             QCOMPARE(QString::fromStdString(s).left(6), QString("QH6029"));
             // FIXUP QH11025 -- review decision to clearQhullMessage at QhullError()            // Cleared when copied to QhullError
             QVERIFY(!q.hasQhullMessage());
             // QCOMPARE(q.qhullMessage(), QString::fromStdString(s).remove(0, 7));
             // QCOMPARE(q.qhullStatus(), 6029);
             q.clearQhullMessage();
             QVERIFY(!q.hasQhullMessage());
         }
         q.appendQhullMessage("Append 1");
         QVERIFY(q.hasQhullMessage());
         QCOMPARE(QString::fromStdString(q.qhullMessage()), QString("Append 1"));
         q.appendQhullMessage("\nAppend 2\n");
         QCOMPARE(QString::fromStdString(q.qhullMessage()), QString("Append 1\nAppend 2\n"));
         q.clearQhullMessage();
         QVERIFY(!q.hasQhullMessage());
         QCOMPARE(QString::fromStdString(q.qhullMessage()), QString(""));
     }
     {
         cout << "INFO   : Error stream without output stream\n";
         Qhull q;
         q.setErrorStream(&cout);
         q.setOutputStream(0);
         try{
             q.runQhull(rcube, "Fd");
             QFAIL("runQhull Fd did not fail.");
         }catch (const QhullError &e) {
             cout << "INFO   : Caught " << e;
             QCOMPARE(e.errorCode(), 6029);
         }
         //FIXUP QH11026 Qhullmessage cleared when QhullError thrown.  Switched to e
         //QVERIFY(q.hasQhullMessage());
         //QCOMPARE(QString::fromStdString(q.qhullMessage()).left(6), QString("QH6029"));
         q.clearQhullMessage();
         QVERIFY(!q.hasQhullMessage());
     }
     {
         cout << "INFO   : Error output sent to output stream without error stream\n";
         Qhull q;
         q.setErrorStream(0);
         q.setOutputStream(&cout);
         try{
             q.runQhull(rcube, "Tz H0");
             QFAIL("runQhull TZ did not fail.");
         }catch (const std::exception &e) {
             const char *s= e.what();
             cout << "INFO   : Caught " << s;
             QCOMPARE(QString::fromAscii(s).left(6), QString("QH6023"));
         }
         //FIXUP QH11026 Qhullmessage cleared when QhullError thrown.  Switched to e
         //QVERIFY(q.hasQhullMessage());
         //QCOMPARE(QString::fromStdString(q.qhullMessage()).left(17), QString("qhull: no message"));
         //QCOMPARE(q.qhullStatus(), 6023);
         q.clearQhullMessage();
         QVERIFY(!q.hasQhullMessage());
     }
     {
         cout << "INFO   : No error stream or output stream\n";
         Qhull q;
         q.setErrorStream(0);
         q.setOutputStream(0);
         try{
             q.runQhull(rcube, "Fd");
             QFAIL("outputQhull did not fail.");
         }catch (const std::exception &e) {
             const char *s= e.what();
             cout << "INFO   : Caught " << s;
             QCOMPARE(QString::fromAscii(s).left(6), QString("QH6029"));
         }
         //FIXUP QH11026 Qhullmessage cleared when QhullError thrown.  Switched to e
         //QVERIFY(q.hasQhullMessage());
         //QCOMPARE(QString::fromStdString(q.qhullMessage()).left(9), QString("qhull err"));
         //QCOMPARE(q.qhullStatus(), 6029);
         q.clearQhullMessage();
         QVERIFY(!q.hasQhullMessage());
     }
 }//t_message
 
 void Qhull_test::
 t_getSet()
 {
     RboxPoints rcube("c");
     {
         Qhull q;
         QVERIFY(!q.initialized());
         q.runQhull(rcube, "s");
         QVERIFY(q.initialized());
         QCOMPARE(q.dimension(), 3);
         QhullPoint p= q.origin();
         QCOMPARE(p.dimension(), 3);
         QCOMPARE(p[0]+p[1]+p[2], 0.0);
-        QVERIFY(q.runId()!=0);
         q.setErrorStream(&cout);
         q.outputQhull();
     }
     {
         Qhull q;
         q.runQhull(rcube, "");
         q.setOutputStream(&cout);
         q.outputQhull();
     }
-    // qhullQh -- UsingLibQhull [Qhull.cpp]
-    // runId -- UsingLibQhull [Qhull.cpp]
 }//t_getSet
 
 void Qhull_test::
 t_getQh()
 {
     RboxPoints rcube("c");
     {
         Qhull q;
         q.runQhull(rcube, "s");
         QCOMPARE(QString(q.qhullCommand()), QString("qhull s"));
         QCOMPARE(QString(q.rboxCommand()), QString("rbox \"c\""));
         QCOMPARE(q.facetCount(), 6);
         QCOMPARE(q.vertexCount(), 8);
         // Sample fields from Qhull's qhT [libqhull.h]
         QCOMPARE(q.qhullQh()->ALLpoints, 0u);
         QCOMPARE(q.qhullQh()->GOODpoint, 0);
         QCOMPARE(q.qhullQh()->IStracing, 0);
         QCOMPARE(q.qhullQh()->MAXcoplanar+1.0, 1.0); // fuzzy compare
         QCOMPARE(q.qhullQh()->MERGING, 1u);
         QCOMPARE(q.qhullQh()->input_dim, 3);
         QCOMPARE(QString(q.qhullQh()->qhull_options).left(8), QString("  run-id"));
-        QCOMPARE(q.qhullQh()->run_id, q.runId());
         QCOMPARE(q.qhullQh()->num_facets, 6);
         QCOMPARE(q.qhullQh()->hasTriangulation, 0u);
         QCOMPARE(q.qhullQh()->max_outside - q.qhullQh()->min_vertex + 1.0, 1.0); // fuzzy compare
         QCOMPARE(*q.qhullQh()->gm_matrix+1.0, 1.0); // fuzzy compare
     }
 }//t_getQh
 
 void Qhull_test::
 t_getValue()
 {
     RboxPoints rcube("c");
     {
         Qhull q;
         q.runQhull(rcube, "");
         QCOMPARE(q.area(), 6.0);
         QCOMPARE(q.volume(), 1.0);
     }
 }//t_getValue
 
 void Qhull_test::
 t_foreach()
 {
     RboxPoints rcube("c");
     {
         Qhull q;
         QCOMPARE(q.beginFacet(),q.endFacet());
         QCOMPARE(q.beginVertex(),q.endVertex());
         q.runQhull(rcube, "");
         QCOMPARE(q.facetList().count(), 6);
 
         // defineVertexNeighborFacets() tested in QhullVertex_test::t_io()
 
         QhullFacetList facets(q.beginFacet(), q.endFacet());
         QCOMPARE(facets.count(), 6);
         QCOMPARE(q.firstFacet(), q.beginFacet());
         QhullVertexList vertices(q.beginVertex(), q.endVertex());
         QCOMPARE(vertices.count(), 8);
         QCOMPARE(q.firstVertex(), q.beginVertex());
         QhullPoints ps= q.points();
         QCOMPARE(ps.count(), 8);
         QhullPointSet ps2= q.otherPoints();
         QCOMPARE(ps2.count(), 0);
         // ps2= q.otherPoints(); //disabled, would not copy the points
         QCOMPARE(q.facetCount(), 6);
         QCOMPARE(q.vertexCount(), 8);
         coordT *c= q.pointCoordinateBegin(); // of q.points()
         QVERIFY(*c==0.5 || *c==-0.5);
         coordT *c3= q.pointCoordinateEnd();
         QVERIFY(c3[-1]==0.5 || c3[-1]==-0.5);
         QCOMPARE(c3-c, 8*3);
         QCOMPARE(q.vertexList().count(), 8);
     }
 }//t_foreach
 
 void Qhull_test::
 t_modify()
 {
     //addPoint() tested in t_foreach
     RboxPoints diamond("d");
     Qhull q(diamond, "o");
     q.setOutputStream(&cout);
     cout << "Expecting vertexList and facetList of a 3-d diamond.\n";
     q.outputQhull();
     cout << "Expecting normals of a 3-d diamond.\n";
     q.outputQhull("n");
     // runQhull tested in t_attribute(), t_message(), etc.
 }//t_modify
 
 }//orgQhull
 
 // Redefine Qhull's usermem.c
 void qh_exit(int exitcode) {
     cout << "FAIL!  : Qhull called qh_exit().  Qhull's error handling not available.\n.. See the corresponding Qhull:qhull_message or setErrorStream().\n";
     exit(exitcode);
 }
 void qh_free(void *mem) {
     free(mem);
 }
 void *qh_malloc(size_t size) {
     return malloc(size);
 }
 
 #if 0
 template<> char * QTest::
 toString(const std::string &s)
 {
     QByteArray ba = s.c_str();
     return qstrdup(ba.data());
 }
 #endif
 
 #include "moc/Qhull_test.moc"
diff --git a/src/qhulltest/UsingLibQhull_test.cpp b/src/qhulltest/UsingLibQhull_test.cpp
index 79d2b34..56aa27a 100644
--- a/src/qhulltest/UsingLibQhull_test.cpp
+++ b/src/qhulltest/UsingLibQhull_test.cpp
@@ -1,210 +1,208 @@
 /****************************************************************************
 **
 ** Copyright (c) 2008-2014 C.B. Barber. All rights reserved.
-** $Id: //main/2011/qhull/src/qhulltest/UsingLibQhull_test.cpp#4 $$Change: 1490 $
-** $DateTime: 2012/02/19 20:27:01 $$Author: bbarber $
+** $Id: //main/2011/qhull/src/qhulltest/UsingLibQhull_test.cpp#6 $$Change: 1709 $
+** $DateTime: 2014/03/26 22:27:14 $$Author: bbarber $
 **
 ****************************************************************************/
 
 //pre-compiled headers
 #include 
 #include "RoadTest.h" // QT_VERSION
 
 #include "UsingLibQhull.h"
 #include "QhullError.h"
 #include "Qhull.h"
 
 using std::cout;
 using std::endl;
 using std::string;
 
 namespace orgQhull {
 
 //! Test C++ interface to Qhull
 //! See eg/q_test for tests of Qhull commands
 class UsingLibQhull_test : public RoadTest
 {
     Q_OBJECT
 
 #//Test slots
 private slots:
     void cleanup();
     void t_classMembers();
     void t_globalPoints();
     void t_UsingLibQhull();
     void t_methods();
     void t_cleanuptestcase();
 };//UsingLibQhull_test
 
 void
 add_UsingLibQhull_test()
 {
     new UsingLibQhull_test();
 }
 
 //Executed after each testcase
 void UsingLibQhull_test::
 cleanup()
 {
     UsingLibQhull::checkQhullMemoryEmpty();
     RoadTest::cleanup();
 }
 
 void UsingLibQhull_test::
 t_classMembers()
 {
     {
         //checkQhullMemoryEmpty tested by cleanup()
         QCOMPARE(UsingLibQhull::globalMachineEpsilon()+1.0, 1.0);
         RboxPoints r10("10");
         Qhull q(r10,"v");  // voronoi diagram of 10 points
         UsingLibQhull::unsetGlobalAngleEpsilon();
         UsingLibQhull::unsetGlobalDistanceEpsilon();
         cout << "MachineEpsilon " << UsingLibQhull::globalMachineEpsilon()
             << " angleEpsilon " << UsingLibQhull::globalAngleEpsilon()
             << " distanceEpsilon " << UsingLibQhull::globalDistanceEpsilon()
             << endl;
         QCOMPARE(UsingLibQhull::currentAngleEpsilon()+1.0, 1.0);
         QVERIFY(UsingLibQhull::currentAngleEpsilon() > UsingLibQhull::globalMachineEpsilon());
         QCOMPARE(UsingLibQhull::currentDistanceEpsilon()+1.0, 1.0);
         QVERIFY(UsingLibQhull::currentDistanceEpsilon() >= UsingLibQhull::currentAngleEpsilon());
-        QCOMPARE(UsingLibQhull::currentQhull().runId(), q.runId());
         QCOMPARE(UsingLibQhull::globalAngleEpsilon()+1.0, UsingLibQhull::currentAngleEpsilon()+1.0);
         QCOMPARE(UsingLibQhull::currentVertexDimension(), q.dimension());
         QCOMPARE(UsingLibQhull::globalDistanceEpsilon()+1.0, UsingLibQhull::currentDistanceEpsilon()+1.0);
         UsingLibQhull::setGlobalAngleEpsilon(1.0);
         UsingLibQhull::setGlobalDistanceEpsilon(1.0);
         cout << " Global angleEpsilon " << UsingLibQhull::globalAngleEpsilon()
             << " distanceEpsilon " << UsingLibQhull::globalDistanceEpsilon()
             << endl;
         QCOMPARE(UsingLibQhull::globalAngleEpsilon(), UsingLibQhull::globalDistanceEpsilon());
         QVERIFY(UsingLibQhull::currentAngleEpsilon() != UsingLibQhull::globalAngleEpsilon());
         UsingLibQhull::setGlobalVertexDimension(3);
         QCOMPARE(UsingLibQhull::globalVertexDimension(), UsingLibQhull::currentVertexDimension());
         UsingLibQhull::setGlobalVertexDimension(2);
         QCOMPARE(UsingLibQhull::globalVertexDimension(), 2);
         QCOMPARE(UsingLibQhull::currentVertexDimension(), q.dimension());
         QVERIFY(UsingLibQhull::currentDistanceEpsilon() != UsingLibQhull::globalDistanceEpsilon());
         UsingLibQhull::unsetGlobalAngleEpsilon();
         UsingLibQhull::unsetGlobalVertexDimension();
         UsingLibQhull::unsetGlobalDistanceEpsilon();
         QCOMPARE(UsingLibQhull::currentAngleEpsilon()+1.0, UsingLibQhull::globalAngleEpsilon()+1.0);
         QCOMPARE(UsingLibQhull::globalVertexDimension(), UsingLibQhull::currentVertexDimension());
         QCOMPARE(UsingLibQhull::currentDistanceEpsilon()+1.0, UsingLibQhull::globalDistanceEpsilon()+1.0);
         UsingLibQhull::setGlobals();
     }
     QCOMPARE(UsingLibQhull::globalAngleEpsilon()+1.0, 1.0);
     QCOMPARE(UsingLibQhull::globalVertexDimension(), 4); // 'v'.  VertexDimension is only used for QhullVertex where dim>15
     QCOMPARE(UsingLibQhull::globalDistanceEpsilon()+1.0, 1.0);
     UsingLibQhull::unsetGlobals();
     try{
         cout << UsingLibQhull::globalVertexDimension();
         QFAIL("Did not throw error for undefined dimension.");
     }catch(const std::exception &e){
         cout << "INFO     Caught error -- " << e.what() << endl;
     }
 }//t_classMembers
 
 void UsingLibQhull_test::
 t_globalPoints()
 {
     const coordT *r10PointsBegin;
     {
         RboxPoints r10("10");
         Qhull q(r10,"v");  // voronoi diagram of 10 points
         UsingLibQhull::unsetGlobalPoints();
         int dimension;
         const coordT *pointsEnd;
         const coordT *pointsBegin= UsingLibQhull::globalPoints(&dimension, &pointsEnd);
         cout << "pointsBegin " << pointsBegin
             << " pointsEnd " << pointsEnd
             << " dimension " << dimension
             << endl;
         int dimension2;
         const coordT *pointsEnd2;
         const coordT *pointsBegin2= UsingLibQhull::currentPoints(&dimension2, &pointsEnd2);
         QCOMPARE(pointsBegin2, pointsBegin);
         QCOMPARE(pointsEnd2, pointsEnd);
         QCOMPARE(dimension2, dimension);
         coordT c[]= { 1.0,2.0, 3.0,4.0, 5.0,6.0 };
         UsingLibQhull::setGlobalPoints(2, c, c+3*2);
         pointsBegin= UsingLibQhull::globalPoints(&dimension, &pointsEnd);
         QCOMPARE(pointsBegin, c);
         QCOMPARE(pointsEnd[-1], 6.0);
         QCOMPARE(dimension, 2);
         UsingLibQhull::unsetGlobalPoints();
         pointsBegin= UsingLibQhull::globalPoints(&dimension, &pointsEnd);
         QCOMPARE(pointsBegin, pointsBegin2);
         QCOMPARE(pointsEnd, pointsEnd2);
         QCOMPARE(dimension, dimension2);
         UsingLibQhull::setGlobals();
         r10PointsBegin= pointsBegin;
     }
     int dimension3;
     const coordT *pointsEnd3;
     const coordT *pointsBegin3= UsingLibQhull::currentPoints(&dimension3, &pointsEnd3);
     QCOMPARE(pointsBegin3, r10PointsBegin); // Memory was freed
     QCOMPARE(pointsEnd3, r10PointsBegin+10*4);
     QCOMPARE(dimension3, 4);
     UsingLibQhull::unsetGlobals();
     try{
         pointsBegin3= UsingLibQhull::globalPoints(&dimension3, &pointsEnd3);
         QFAIL("Did not throw error for undefined global points.");
     }catch(const std::exception &e){
         cout << "INFO     Caught error -- " << e.what() << endl;
     }
 }//t_globalPoints
 
 void UsingLibQhull_test::
 t_UsingLibQhull()
 {
     {
         Qhull q;
         UsingLibQhull uq(&q); // Normally created in a method using 'this'
 
         try{
             Qhull q2; // If qh_QHpointer, QhullQh() calls usinlibqhull()
             UsingLibQhull uq2(&q2);
             QFAIL("UsingLibQhull did not fail.");
         }catch (const std::exception &e) {
             cout << "INFO   : Caught " << e.what();
         }
     }
     Qhull q3;
     UsingLibQhull uq3(&q3);
     // UsingLibQhull uq4; // Default constructors disabled.
 }//t_UsingLibQhull
 
 void UsingLibQhull_test::
 t_methods()
 {
     Qhull q;
     UsingLibQhull u(&q); // Normally created in a method using 'this'
     QVERIFY(u.defined());
     u.maybeThrowQhullMessage(0);  // Nothing thrown
     try{
         u.maybeThrowQhullMessage(1);
         QFAIL("maybeThrowQhullMessage(1) did not fail.");
     }catch (const std::exception &e) {
         cout << "INFO   : Caught " << e.what();
     }
-    // Can not check checkRunId() in maybeThrowQhullMessage().  Requires another thread.
     u.maybeThrowQhullMessage(2, UsingLibQhull::NOthrow);
     try{
         throw QhullError(10054, "Report previous NOthrow error");
     }catch (const std::exception &e) {
         cout << "INFO   : " << e.what();
     }
 }//t_methods
 
 // Executed after last test
 void UsingLibQhull_test::
 t_cleanuptestcase()
 {
     UsingLibQhull::unsetGlobals();
 }//t_cleanuptestcase
 
 }//orgQhull
 
 #include "moc/UsingLibQhull_test.moc"
 
diff --git a/src/qhulltest/qhulltest.cpp b/src/qhulltest/qhulltest.cpp
index 567750e..9221f63 100644
--- a/src/qhulltest/qhulltest.cpp
+++ b/src/qhulltest/qhulltest.cpp
@@ -1,86 +1,87 @@
 /****************************************************************************
 **
 ** Copyright (c) 2008-2014 C.B. Barber. All rights reserved.
-** $Id: //main/2011/qhull/src/qhulltest/qhulltest.cpp#5 $$Change: 1490 $
-** $DateTime: 2012/02/19 20:27:01 $$Author: bbarber $
+** $Id: //main/2011/qhull/src/qhulltest/qhulltest.cpp#10 $$Change: 1799 $
+** $DateTime: 2014/12/17 16:17:40 $$Author: bbarber $
 **
 ****************************************************************************/
 
 //pre-compiled headers
 #include 
 #include 
 #include 
 #include 
 #include "RoadTest.h"
 
 #include "../libqhullcpp/RoadError.h"
 
 using std::cout;
 using std::endl;
 
 namespace orgQhull {
 
 void addQhullTests(QStringList &args)
 {
-    TESTadd_(add_QhullVertex_test); //copy
+    TESTadd_(add_QhullPointSet_test); //copy
+    TESTadd_(add_QhullPoint_test); //copy
 
     if(args.contains("--all")){
         args.removeAll("--all");
         // up-to-date
+    /**FIXUP
         TESTadd_(add_Coordinates_test);
         TESTadd_(add_PointCoordinates_test);
         TESTadd_(add_QhullFacet_test);
         TESTadd_(add_QhullFacetList_test);
         TESTadd_(add_QhullFacetSet_test);
         TESTadd_(add_QhullHyperplane_test);
         TESTadd_(add_QhullLinkedList_test);
         TESTadd_(add_QhullPoint_test);
         TESTadd_(add_QhullPoints_test);
         TESTadd_(add_QhullPointSet_test);
         TESTadd_(add_QhullRidge_test);
         TESTadd_(add_QhullSet_test);
         TESTadd_(add_QhullVertex_test);
         TESTadd_(add_RboxPoints_test);
-        TESTadd_(add_UsingLibQhull_test);
-        // needs review
         // qhullStat
         TESTadd_(add_Qhull_test);
+    */
     }//--all
 }//addQhullTests
 
 int main(int argc, char *argv[])
 {
     QCoreApplication app(argc, argv);
     QStringList args= app.arguments();
     bool isAll= args.contains("--all");
     addQhullTests(args);
     int status=1010;
     try{
         status= RoadTest::runTests(args);
     }catch(const std::exception &e){
         cout << "FAIL!  : runTests() did not catch error\n";
         cout << e.what() << endl;
         if(!RoadError::emptyGlobalLog()){
             cout << RoadError::stringGlobalLog() << endl;
             RoadError::clearGlobalLog();
         }
     }
     if(!RoadError::emptyGlobalLog()){
         cout << RoadError::stringGlobalLog() << endl;
         RoadError::clearGlobalLog();
     }
     if(isAll){
         cout << "Finished test of libqhullcpp.  Test libqhull with eg/q_test" << endl;
     }else{
         cout << "Finished test of one class.  Test all classes with 'qhulltest --all'" << endl;
     }
     return status;
 }
 
 }//orgQhull
 
 int main(int argc, char *argv[])
 {
     return orgQhull::main(argc, argv); // Needs RoadTest:: for TESTadd_() linkage
 }
 
diff --git a/src/qhulltest/qhulltest.pro b/src/qhulltest/qhulltest.pro
index dce1404..53623e4 100644
--- a/src/qhulltest/qhulltest.pro
+++ b/src/qhulltest/qhulltest.pro
@@ -1,34 +1,34 @@
 # -------------------------------------------------
 # qhulltest.pro -- Qt project for qhulltest.exe (QTestLib)
+# cd $qh/build/qhulltest && qmake -tp vc -r ../../src/qhulltest/qhulltest.pro
 # -------------------------------------------------
 
 include(../qhull-app-cpp.pri)
 
 TARGET = qhulltest
 CONFIG += qtestlib
 MOC_DIR = moc
 INCLUDEPATH += ..  # for MOC_DIR
 
 PRECOMPILED_HEADER = RoadTest.h
 
 SOURCES += ../libqhullcpp/qt-qhull.cpp
 SOURCES += Coordinates_test.cpp
 SOURCES += PointCoordinates_test.cpp
 SOURCES += Qhull_test.cpp
 SOURCES += QhullFacet_test.cpp
 SOURCES += QhullFacetList_test.cpp
 SOURCES += QhullFacetSet_test.cpp
 SOURCES += QhullHyperplane_test.cpp
 SOURCES += QhullLinkedList_test.cpp
 SOURCES += QhullPoint_test.cpp
 SOURCES += QhullPoints_test.cpp
 SOURCES += QhullPointSet_test.cpp
 SOURCES += QhullRidge_test.cpp
 SOURCES += QhullSet_test.cpp
 SOURCES += qhulltest.cpp
 SOURCES += QhullVertex_test.cpp
 SOURCES += RboxPoints_test.cpp
 SOURCES += RoadTest.cpp
-SOURCES += UsingLibQhull_test.cpp
 
 HEADERS += RoadTest.h
diff --git a/src/user_eg3/user_eg3.cpp b/src/user_eg3/user_eg3.cpp
index a94b552..5459484 100644
--- a/src/user_eg3/user_eg3.cpp
+++ b/src/user_eg3/user_eg3.cpp
@@ -1,156 +1,157 @@
 #//! user_eg3.cpp -- Invoke rbox and qhull from C++
 
 #include "RboxPoints.h"
 #include "QhullError.h"
 #include "QhullQh.h"
 #include "QhullFacet.h"
 #include "QhullFacetList.h"
 #include "QhullLinkedList.h"
 #include "QhullVertex.h"
 #include "Qhull.h"
 
 #include    /* for printf() of help message */
 #include 
 
 using std::cerr;
 using std::cin;
 using std::cout;
 using std::endl;
 
 using orgQhull::Qhull;
 using orgQhull::QhullError;
 using orgQhull::QhullFacet;
 using orgQhull::QhullFacetList;
 using orgQhull::QhullQh;
 using orgQhull::RboxPoints;
 using orgQhull::QhullVertex;
 using orgQhull::QhullVertexSet;
 
 int main(int argc, char **argv);
 int user_eg3(int argc, char **argv);
 
 char prompt[]= "\n\
 user_eg3 -- demonstrate calling rbox and qhull from C++.\n\
 \n\
   eg-100                       Run the example in qh-code.htm\n\
   rbox \"200 D4\" ...            Generate points from rbox\n\
   qhull \"d p\" ...              Run qhull and produce output\n\
   qhull-cout \"o\" ...           Run qhull and produce output to cout\n\
   facets                       Print facets when done\n\
 \n\
 For example\n\
   user_eg3 rbox qhull\n\
   user_eg3 rbox qhull d\n\
   user_eg3 rbox \"10 D2\"  \"2 D2\" qhull  \"s p\" facets\n\
 \n\
 ";
 
 
 /*--------------------------------------------
 -user_eg3-  main procedure of user_eg3 application
 */
 int main(int argc, char **argv) {
 
     if(argc==1){
         cout << prompt;
         return 1;
     }
     try{
         return user_eg3(argc, argv);
     }catch(QhullError &e){
         cerr << e.what() << std::endl;
         return e.errorCode();
     }
 }//main
 
 int user_eg3(int argc, char **argv)
 {
-    bool printFacets= false;
+    bool printFacets= false;  // FIXUP not used
     if(strcmp(argv[1], "eg-100")==0){
-        RboxPoints rbox;
-        rbox.appendPoints("100");
-        Qhull qhull;
-        qhull.runQhull(rbox, "");
-        QhullFacetList facets= qhull.facetList();
+        RboxPoints rbox("100");
+        Qhull q(rbox, "");
+        QhullFacetList facets= q.facetList();
         cout << facets;
         return 0;
     }
+    return 0;
+#if 0
     RboxPoints rbox;
     Qhull qhull;
     int readingRbox= 0;
     int readingQhull= 0;
     for(int i=1; i