diff --git a/README.txt b/README.txt index 843ec44..7585bbf 100644 --- a/README.txt +++ b/README.txt @@ -1,523 +1,523 @@ Name qhull, rbox 2012.1 2012/02/18 Convex hull, Delaunay triangulation, Voronoi diagrams, Halfspace intersection Documentation: html/index.htm http://www.qhull.org/html Available from: [out-of-date] News and a paper: Version 1 (simplicial only): Purpose Qhull is a general dimension convex hull program that reads a set of points from stdin, and outputs the smallest convex set that contains the points to stdout. It also generates Delaunay triangulations, Voronoi diagrams, furthest-site Voronoi diagrams, and halfspace intersections about a point. Rbox is a useful tool in generating input for Qhull; it generates hypercubes, diamonds, cones, circles, simplices, spirals, lattices, and random points. Qhull produces graphical output for Geomview. This helps with understanding the output. Environment requirements Qhull and rbox should run on all 32-bit and 64-bit computers. Use an ANSI C or C++ compiler to compile the program. The software is self-contained. It comes with examples and test scripts. Qhull's C++ interface uses the STL. The C++ test program uses QTestLib from Nokia's Qt Framework. Qhull's C++ interface may change without notice. Eventually, it will move into the qhull shared library. Qhull is copyrighted software. Please read COPYING.txt and REGISTER.txt before using or distributing Qhull. To cite Qhull, please use 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. To contribute to Qhull Qhull is on Gitorious (http://gitorious.org:qhull, git@gitorious.org:qhull/qhull.git) For internal documentation, see html/qh-code.htm To install Qhull Qhull is precompiled for Windows, otherwise it needs compilation. Besides makefiles for gcc, qhull includes CMakeLists.txt for CMake, vcproj/sln files for Microsoft Visual Studio, and .pro files for Qt Creator. It compiles with mingw. Install and build instructions follow. See the end of this document for a list of distributed files. ----------------- -Installing Qhull on Windows +Installing Qhull on Windows 7 (32- or 64-bit), Windows XP, and Windows NT - The zip file contains rbox.exe, qhull.exe, qconvex.exe, qdelaunay.exe, + The zip file contains rbox.exe, qhull.exe, qconvex.exe, qdelaUnay.exe, qhalf.exe, qvoronoi.exe, testqset.exe, user_eg*.exe, documentation files, and source files. To install Qhull: - Unzip the files into a directory. You may use WinZip32 - Click on QHULL-GO or open a command window into Qhull's bin directory. To uninstall Qhull - Delete the qhull directory To learn about Qhull: - Execute 'qconvex' for a synopsis and examples. - Execute 'rbox 10 | qconvex' to compute the convex hull of 10 random points. - Execute 'rbox 10 | qconvex i TO file' to write results to 'file'. - Browse the documentation: qhull\html\index.htm - If an error occurs, Windows sends the error to stdout instead of stderr. Use 'TO xxx' to send normal output to xxx and error output to stdout To improve the command window - Double-click the window bar to increase the size of the window - Right-click the window bar - Select Properties - Check QuickEdit Mode Select text with right-click or Enter Paste text with right-click - Change Font to Lucinda Console - Change Layout to Screen Buffer Height 999, Window Size Height 55 - Change Colors to Screen Background White, Screen Text Black - Click OK - Select 'Modify shortcut that started this window', then OK If you use qhull a lot, install MSYS (www.mingw.org), Road Bash (www.qhull.org/bash), or Cygwin (www.cygwin.com). ----------------- Installing Qhull on Unix with gcc To build Qhull, static libraries, shared library, and C++ interface - Extract Qhull from qhull...tgz or qhull...zip - make - export LD_LIBRARY_PATH=$PWD/lib:$LD_LIBRARY_PATH Or, to build Qhull and libqhullstatic.a - Extract Qhull from qhull...tgz or qhull...zip - cd src/libqhull - make The Makefiles may be edited for other compilers. If 'testqset' exits with an error, qhull is broken ----------------- Installing Qhull with CMake 2.6 or later To build Qhull, static libraries, shared library, and C++ interface - Extract Qhull from qhull...tgz or qhull...zip - cd build - cmake .. - make - make install On Windows, CMake installs to C:/Program Files/qhull See CMakeLists.txt for further build instructions ----------------- Installing Qhull with Qt To build Qhull, static libraries, shared library, C++ interface, and C++ test - Extract Qhull from qhull...tgz or qhull...zip - cd src - qmake - make ----------------- Installing Qhull with Autoconf [WARNING out-of-date] The tar.gz tarball contains documentation, source files, and a config directory [R. Laboissiere]. [Nov 2011] Qhull 2009.1.2 does not include the C++ interface To install Qhull - Extract the files - ./configure - make - make install ------------------- Working with Qhull's C++ interface Qhull's C++ interface is likely to change. Stay current with Gitorious. To clone Qhull's next branch from http://gitorious.org/qhull git init git clone git://gitorious.org/qhull/qhull.git cd qhull git checkout next ... git pull origin next ------------------ Compiling Qhull with Microsoft Visual C++ 2005 or later To compile Qhull with Microsoft Visual C++ - Extract Qhull from Gitorious, qhull...tgz, or qhull...zip - Load solution build/qhull.sln - Build - Project qhulltest requires Qt for DevStudio (http://qt.nokia.com/downloads) Set the QTDIR environment variable to your Qt directory (e.g., c:/qt/4.7.4) If incorrect, precompile will fail with 'Can not locate the file specified' ----------------- Compiling Qhull with Qt Creator Qt (http://qt.nokia.com) is a C++ framework for Windows, Linux, and Macintosh Qhull uses QTestLib to test qhull's C++ interface (qhulltest) To compile Qhull with Qt Creator - Extract Qhull from Gitorious, qhull...tgz, or qhull...zip - Download the Qt SDK from Nokia (http://qt.nokia.com/downloads) - Start Qt Creator - Load src/qhull-all.pro - Build ----------------- Compiling Qhull with mingw on Windows To compile Qhull with MINGW - Extract Qhull from Gitorious, qhull...tgz, or qhull...zip - Install Road Bash (http://www.qhull.org/bash) or install MSYS (http://www.mingw.org/wiki/msys) - Install MINGW (http://www.mingw.org/). Mingw is included with Qt SDK. - make ----------------- Compiling Qhull with cygwin on Windows To compile Qhull with cygwin - Extract Qhull from Gitorious, qhull...tgz, or qhull...zip - Install cygwin (http://www.cygwin.com) - Include packages for gcc, make, ar, and ln - make ----------------- Compiling from Makfile without gcc The file, qhull-src.tgz, contains documentation and source files for qhull and rbox. To unpack the gzip file - tar zxf qhull-src.tgz - cd qhull Compiling qhull and rbox with Makefile - in Makefile, check the CC, CCOPTS1, PRINTMAN, and PRINTC defines - the defaults are gcc and enscript - CCOPTS1 should include the ANSI flag. It defines __STDC__ - in user.h, check the definitions of qh_SECticks and qh_CPUclock. - use '#define qh_CLOCKtype 2' for timing runs longer than 1 hour - type: make - this builds: qhull qconvex qdelaunay qhalf qvoronoi rbox libqhull.a - type: make doc - this prints the man page - See also qhull/html/index.htm - if your compiler reports many errors, it is probably not a ANSI C compiler - you will need to set the -ansi switch or find another compiler - if your compiler warns about missing prototypes for fprintf() etc. - this is ok, your compiler should have these in stdio.h - if your compiler warns about missing prototypes for memset() etc. - include memory.h in qhull_a.h - if your compiler reports "global.c: storage size of 'qh_qh' isn't known" - delete the initializer "={0}" in global.c, stat.c and mem.c - if your compiler warns about "stat.c: improper initializer" - this is ok, the initializer is not used - if you have trouble building libqhull.a with 'ar' - try 'make -f Makefile.txt qhullx' - if the code compiles, the qhull test case will automatically execute - if an error occurs, there's an incompatibility between machines - If you can, try a different compiler - You can turn off the Qhull memory manager with qh_NOmem in mem.h - You can turn off compiler optimization (-O2 in Makefile) - If you find the source of the problem, please let us know - to install the programs and their man pages: - define MANDIR and BINDIR - type 'make install' - if you have Geomview (www.geomview.org) - try 'rbox 100 | qconvex G >a' and load 'a' into Geomview - run 'q_eg' for Geomview examples of Qhull output (see qh-eg.htm) ------------------ Compiling on other machines and compilers Qhull compiles with Borland C++ 5.0 bcc32. A Makefile is included. Execute 'make -f Mborland'. If you use the Borland IDE, set the ANSI option in Options:Project:Compiler:Source:Language-compliance. Qhull compiles with Borland C++ 4.02 for Win32 and DOS Power Pack. Use 'make -f Mborland -D_DPMI'. Qhull 1.0 compiles with Borland C++ 4.02. For rbox 1.0, use "bcc32 -WX -w- -O2-e -erbox -lc rbox.c". Use the same options for Qhull 1.0. [D. Zwick] Qhull compiles with Metrowerks C++ 1.7 with the ANSI option. If you turn on full warnings, the compiler will report a number of unused variables, variables set but not used, and dead code. These are intentional. For example, variables may be initialized (unnecessarily) to prevent warnings about possible use of uninitialized variables. Qhull compiles on the Power Macintosh with Metrowerk's C compiler. It uses the SIOUX interface to read point coordinates and return output. There is no graphical output. For project files, see 'Compiling a custom build'. Instead of using SIOUX, Qhull may be embedded within an application. Some users have reported problems with compiling Qhull under Irix 5.1. It compiles under other versions of Irix. If you have troubles with the memory manager, you can turn it off by defining qh_NOmem in mem.h. ----------------- Distributed files README.txt // Instructions for installing Qhull REGISTER.txt // Qhull registration COPYING.txt // Copyright notice QHULL-GO.lnk // Windows icon for eg/qhull-go.bat Announce.txt // Announcement CMakeLists.txt // CMake build file (2.6 or later) File_id.diz // Package descriptor index.htm // Home page Makefile // Makefile for gcc and other compilers qhull*.md5sum // md5sum for all files bin/* // Qhull executables and dll (.zip only) build/qhull.sln // DevStudio solution and project files (2005 or later) build/*.vcproj config/* // Autoconf files for creating configure (Unix only) eg/* // Test scripts and geomview files from q_eg html/index.htm // Manual html/qh-faq.htm // Frequently asked questions html/qh-get.htm // Download page html/qhull-cpp.xml // C++ style notes as a Road FAQ (www.qhull.org/road) src/Changes.txt // Change history for Qhull and rbox src/qhull-all.pro // Qt project eg/ q_eg // shell script for Geomview examples (eg.01.cube) q_egtest // shell script for Geomview test examples q_test // shell script to test qhull q_test-ok.txt // output from q_test qhulltest-ok.txt // output from qhulltest (Qt only) rbox consists of (bin, html): rbox.exe // Win32 executable (.zip only) rbox.htm // html manual rbox.man // Unix man page rbox.txt qhull consists of (bin, html): qhull.exe // Win32 executables and dlls (.zip only) qconvex.exe qdelaunay.exe qhalf.exe qvoronoi.exe qhull.dll qhull_p.dll qhull-go.bat // command window qconvex.htm // html manual qdelaun.htm qdelau_f.htm qhalf.htm qvoronoi.htm qvoron_f.htm qh-eg.htm qh-code.htm qh-impre.htm index.htm qh-opt*.htm qh-quick.htm qh--*.gif // images for manual normal_voronoi_knauss_oesterle.jpg qhull.man // Unix man page qhull.txt bin/ msvcr80.dll // Visual C++ redistributable file (.zip only) src/ qhull/unix.c // Qhull and rbox applications qconvex/qconvex.c qhalf/qhalf.c qdelaunay/qdelaunay.c qvoronoi/qvoronoi.c rbox/rbox.c user_eg/user_eg.c // example of using qhull_p.dll (requires -Dqh_QHpointer) user_eg2/user_eg2.c // example of using qhull.dll from a user program user_eg3/user_eg3.cpp // example of Qhull's C++ interface with libqhullstatic_p.a qhulltest/qhulltest.cpp // Test of Qhull's C++ interface using Qt's QTestLib qhull-*.pri // Include files for Qt projects src/libqhull libqhull.pro // Qt project for shared library (qhull.dll) index.htm // design documentation for libqhull qh-*.htm qhull-exports.def // Export Definition file for Visual C++ Makefile // Simple gcc Makefile for qhull and libqhullstatic.a Mborland // Makefile for Borland C++ 5.0 libqhull.h // header file for qhull user.h // header file of user definable constants libqhull.c // Quickhull algorithm with partitioning user.c // user re-definable functions usermem.c userprintf.c userprintf_rbox.c qhull_a.h // include files for libqhull/*.c geom.c // geometric routines geom2.c geom.h global.c // global variables io.c // input-output routines io.h mem.c // memory routines, this is stand-alone code mem.h merge.c // merging of non-convex facets merge.h poly.c // polyhedron routines poly2.c poly.h qset.c // set routines, this only depends on mem.c qset.h random.c // utilities w/ Park & Miller's random number generator random.h rboxlib.c // point set generator for rbox stat.c // statistics stat.h src/libqhullp libqhullp.pro // Qt project for shared library (qhull_p.dll) qhull_p-exports.def // Export Definition file for Visual C++ src/libqhullstatic/ libqhullstatic.pro // Qt project for static library src/libqhullstaticp/ libqhullstaticp.pro // Qt project for static library with qh_QHpointer src/libqhullcpp/ libqhullcpp.pro // Qt project for static C++ library Qhull.cpp // Call libqhull.c from C++ Qhull.h qt-qhull.cpp // Supporting methods for Qt qhull_interface.cpp // Another approach to C++ Coordinates.cpp // input classes Coordinates.h PointCoordinates.cpp PointCoordinates.h RboxPoints.cpp // call rboxlib.c from C++ RboxPoints.h QhullFacet.cpp // data structure classes QhullFacet.h QhullHyperplane.cpp QhullHyperplane.h QhullPoint.cpp QhullPoint.h QhullQh.cpp QhullStat.cpp QhullStat.h QhullVertex.cpp QhullVertex.h QhullFacetList.cpp // collection classes QhullFacetList.h QhullFacetSet.cpp QhullFacetSet.h QhullIterator.h QhullLinkedList.h QhullPoints.cpp QhullPoints.h QhullPointSet.cpp QhullPointSet.h QhullRidge.cpp QhullRidge.h QhullSet.cpp QhullSet.h QhullSets.h QhullVertexSet.cpp QhullVertexSet.h functionObjects.h // supporting classes QhullError.cpp QhullError.h QhullQh.cpp QhullQh.h UsingLibQhull.cpp UsingLibQhull.h src/qhulltest/ qhulltest.pro // Qt project for test of C++ interface Coordinates_test.cpp // Test of each class PointCoordinates_test.cpp Point_test.cpp QhullFacetList_test.cpp QhullFacetSet_test.cpp QhullFacet_test.cpp QhullHyperplane_test.cpp QhullLinkedList_test.cpp QhullPointSet_test.cpp QhullPoints_test.cpp QhullPoint_test.cpp QhullRidge_test.cpp QhullSet_test.cpp QhullVertexSet_test.cpp QhullVertex_test.cpp Qhull_test.cpp RboxPoints_test.cpp UsingLibQhull_test.cpp src/road/ RoadError.cpp // Supporting base classes RoadError.h RoadLogEvent.cpp RoadLogEvent.h RoadTest.cpp // Run multiple test files with QTestLib RoadTest.h src/testqset/ testqset.pro // Qt project for test qset.c with mem.c testqset.c ----------------- Authors: C. Bradford Barber Hannu Huhdanpaa (Version 1.0) bradb@shore.net hannu@qhull.org Qhull 1.0 and 2.0 were developed under NSF grants NSF/DMS-8920161 and NSF-CCR-91-15793 750-7504 at the Geometry Center and Harvard University. If you find Qhull useful, please let us know. diff --git a/html/Changes.txt b/html/Changes.txt new file mode 100644 index 0000000..724c6a1 --- /dev/null +++ b/html/Changes.txt @@ -0,0 +1,890 @@ +$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-get.htm b/html/qh-get.htm index ac3ccf5..d3093e9 100644 --- a/html/qh-get.htm +++ b/html/qh-get.htm @@ -1,129 +1,122 @@ Qhull Downloads

Up: Qhull Home Page

[CONE] Qhull Downloads

  • Qhull Home Page

    Qhull computes the convex hull, Delaunay triangulation, Voronoi diagram, halfspace intersection about a point, furthest-site Delaunay triangulation, and furthest-site Voronoi diagram. It runs in 2-d, 3-d, 4-d, and higher dimensions. It implements the Quickhull algorithm for computing the convex hull. Qhull handles roundoff errors from floating point arithmetic. It can approximate a convex hull.

    Visit Qhull News for news, bug reports, change history, and users. If you use Qhull 2003.1 or 2009.1, please upgrade to 2012.1 or apply poly.c-qh_gethash.patch.

  • Download: Qhull 2012.1 for Windows (2.1 Mbytes, readme, md5sum, contents) -

    Type: console programs for - Windows

    +

    Type: console programs for Windows 7 (32- or 64-bit), XP, and NT

    Includes executables, documentation, and sources files. It runs in a command window.

  • Download: Qhull 2012.1 for Unix (670K, readme, md5sum, contents)

    Type: C/C++ source code for 32-bit and 64-bit architectures

    Includes documentation, source files, two Makefile's, CMakeLists.txt, DevStudio projects, and Qt projects. Includes preliminary C++ support and a preliminary Debian/autoconf build.

    Debian, rpm, and Autoconf distributions are needed.

  • Gitorious Qhull (git://gitorious.org/qhull/qhull.git)

    Type: git repository for Qhull. See Changes.txt

    Includes documentation, source files, C++ interface, and test programs. It builds with gcc, mingw, CMake, DevStudio, and Qt Creator.

    • +
  • Download: + Qhull version 2012.1 rpm for OpenSuse 12.1 (707K) +

    Type: Rpm build for OpenSuse 12.1 +

    +
    • + +
  • Download: + Article about Qhull (307K) +

    Type: PDF on ACM Digital Library (from this page only)

    +

    Barber, C.B., Dobkin, D.P., and Huhdanpaa, H.T., + "The Quickhull algorithm for convex hulls," ACM + Transactions on Mathematical Software, 22(4):469-483, Dec 1996 [abstract].

    +
  • Download: libqhull5 2009.1 for Debian Unix (1.3M) -

    Type: Out-of-date C source code for Unix systems. Requires patch - poly.c-qh_gethash.patch +

    Type: Out-of-date C source code for Unix systems. It may segfault if run with more than 2G memory (fix with + poly.c-qh_gethash.patch)

    Qhull 2009.1 for Octave with Autoconf/Automake/Libtool support [R. Laboissiere]. If using gcc 4.1, 4.2, or 4.3, please compile qset.c with -fno-strict-aliasing (otherwise qhull segfaults) [Karas, Krishnaswami]. See Bugs [Apr 2008].

    • - -
  • Download: - Qhull version 2003.1 i686 rpm (670K) -

    Type: Out-of-date rpm build for Mandrake 9.2 and RedHat - [qhull.spec]. - Requires patch poly.c-qh_gethash.patch -

    - -

    For other Linux systems, use the out-of-date src rpm [L. Mazet]. - Requires patch poly.c-qh_gethash.patch -

    - -
    • ----> -
  • Download: - Article about Qhull (307K) -

    Type: PDF on ACM Digital Library (from this page only)

    -

    Barber, C.B., Dobkin, D.P., and Huhdanpaa, H.T., - "The Quickhull algorithm for convex hulls," ACM - Transactions on Mathematical Software, 22(4):469-483, Dec 1996 [abstract].

    -
  • Download: Qhull version 1.0 (92K)

    Type: C source code for 32-bit architectures

    Version 1.0 is a fifth the size of version 2.4. It computes convex hulls and Delaunay triangulations. If a precision error occurs, it stops with an error message. It reports an initialization error for inputs made with 0/1 coordinates.

    Version 1.0 compiles on a PC with Borland C++ 4.02 for Win32 and DOS Power Pack. The options for rbox are "bcc32 -WX -w- -O2-e -erbox -lc rbox.c". The options for qhull are the same. [D. Zwick]

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[HOME] The Geometry Center Home Page

Comments to: qhull@qhull.org
diff --git a/index.htm b/index.htm index 5a8cc94..2053789 100644 --- a/index.htm +++ b/index.htm @@ -1,278 +1,279 @@ 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.

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URL: http://www.qhull.org
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Comments to: qhull@qhull.org
Created: May 17 1995 --- diff --git a/src/Changes.txt b/src/Changes.txt index 0e38be1..14c46bc 100644 --- a/src/Changes.txt +++ b/src/Changes.txt @@ -1,1626 +1,1629 @@ .............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 - 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 - Review email for doc changes before jun'10 - Git: Create signed tags for Qhull versions - Wiki: Add FIXUP to QH11026 for known problems - 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 + - qh-get.htm: List the Window OSs for Qhull [T. Winkler] + - Reconsider Qhull version numbering (e.g., Traveler 4/5/12) + ------------ Qhull 2012.1 2012/02/18 6.3.1.1494 - Fix CMakeLists for libqhull with MATCHES [P. Gajdos] ------------ Qhull 2012.1 2012/02/18 6.3.1.1490 Code changes - Require option 'Qz' for Delaunay triangulation/Voronoi diagram of cocircular/cospherical points [D. Sheehy] - qh_errexit: Do not call qh_printsummary or qh_printstats on qh_ERRinput - Change error QH6227 (all degenerate) from qh_ERRinput to qh_ERRprec - Change error QH6159 (ID overflow) from qh_ERRinput to qh_ERRqhull - eg/q_eg, q_egtest, q_test: Run if qconvex is in $PATH [M. Atzeri] Build changes [M. Atzeri] - Install to share/doc/qhull instead of share/doc/packages/qhull - On Unix systems, install to share/man/man1 instead of man/man1 - CMakeLists: Remove the installation of user_eg* and testqset - CMakeLists: Remove VERSION from qhull executables and libraries - CMakeLists: Define qhull_SOVERSION instead of qhull_MAJOR - CMakeLists: Set SOVERSION for shared libraries - Rename libraries to qhull, qhull_d, qhull_p, and qhull_pd libqhull6_p.vcproj is now libqhull_p.vcproj mingw builds as libqhull.dll cygwin builds as cygqhull-6.dll linux builds as libqhull.so.6.3.1 with symbolic link as libqhull.so - Developers using qhull 2011: libqhull6.so is now libqhull_p.so. Do not use libqhull.so. qhull6.dll is now qhull_p.dll. Do not use qhull.dll. - Merged road/ into libqhullcpp/ and qhulltest/ Moved RoadLogEvent.* and RoadError.* to libqhullcpp Moved RoadTest.* to qhulltest (requires Qt) Installed RoadTest.h in libqhullcpp Doc changes - index.htm: Mathworks uses qhull for n-d - qhull.htm: Fix qhull for qconvex - qdelaun.htm/qvoronoi.htm: Use option 'Qz' for circular/cospherical inputs - make help: Display targets - Makefile: Better messaging ------------ Qhull 2012.1 2012/02/02 6.3.0.1483 Bug fixes - Fixed qset.c for -fno-strict-aliasing. This gcc option is no longer needed (disallow two pointers of differing types to the same memory location) - Fixed error in qh_setappend_set if first set full and second set empty - qh_setdelnth, qh_setdelnth_sorted: fixed wording of error message - qh_setcheck: error message listed size and max backwards. - qh_setequal: Allow NULL set as documented - qh_setindex: Allow NULL set as documented - qh_settemppush: report error if NULL Code changes - Add testqset: low level test of qset.c with mem.c - qh_setendpointer: Implements QSet::endPointer() - Assigned unique error code for qh_gethash Build changes - Added qhull.dll(.so) for Octave and other Debian builds The global data structure qh_qh is statically defined (no qh_QHpointer) Linked user_eg2 with qhull.dll (libqhull.so) instead of qhullstatic Added qh_dllimport to libqhull.h for qhull.dll with MSVC Changed qhull-app-shared.pri to use libqhull (without qh_QHpointer) - Renamed libqhull6.so to libqhull6_p.so Renamed qhull6.dll to qhull6_p.dll The _p libraries (e.g., libqhull6_p.so) require -Dqh_QHpointer Renamed qhull6.vcproj to libqhull6_p.vcproj Added libqhullp/libqhullp.pro for shared library (libqhull6_p.so) Added qhull-app-sharedp.pri for shared libraries with qh_QHpointer - Install libqhull/*.htm files into include/libqhull - Removed libqhull/qhull.h-deprecated [J. Eaton] - Other changes to Makefile builds Added 'make qtestall' as a smoketest of each qhull program src/libqhull/Makefile: Use 'ar -rs ...' instead of ranlib src/libqhull/Makefile: Fixed targets for cleanall - Other changes to DevStudio builds Moved pdb files for qhull libraries to lib/ AdditionalIncludeDirectories: Removed ../src/libqhullcpp Use build-cmake/ for the DevStudio CMake build - Other changes to Qt builds Renamed qhull-libsrc.pri to qhull-libqhull-src.pri - Added explicit d2u conversions to qhull-zip.sh - Fixed \n vs. \r\n issues for Windows source files Draft of Debian/AutoConf build (untested) - Adjusted the Makefile.am's for the new directory structure. - Added testqset to bin_PROGRAMS - config/bootstrap.sh copies program sources into src/libqhull - Kept qh_QHpointer=0 (static global data structure, qh_qh). It is faster. Planning a new interface (qhull7?) which passes qh_qh as a parameter - Added config/changelog from the 2003.1 Debian build - Moved the debian/patches directory to config/ Optional patches to change smoketest message and turn on qh_QHpointer - Deleted the debian directory. It was the old Debian build from 2003.1 Rafael Laboissiere's config directory replaced this build.. - Deleted Make-conf.sh (also the old Debian build) Doc changes - FAQ: Updated notes on computing volume of a Voronoi region - Added direct link to ACM Digital Library for downloading the qhull paper - Added link to Qhull in R - qset.c: Updated notes about NULL sets - qh_setappend: clarify qh_setappend for NULL newelem - qh_setdellast: Fix head note - Add build/README.txt - Add uninstall instructions to README.txt and CMakeLists.txt - Added instructions to create build/*.vcproj to CMakeLists.txt - Update copyright to 2012 - Updated page links. Added Google books, patents, and blogs. ----------- Qhull 2009.1.3 2011/12/06 configure: Add -fno-strict-aliasing if $GCC, Required for gcc 4.1+ ------------ Qhull 2011.2 2011/11/29 6.2.1.1446 Bug fixes - qh_new_qhull: Call qh_prepare_output if !outfile [A. Aldoma] No effect on qhull users since qh_prepare_output is always called. - Replace Qhull-go.pif with Qhull-go.lnk for Windows 7 64-bit [lots] - Error if qh_newhashtable, qh_setnew, or qh_memalloc overflows [X. Cheng] For example, 'rbox 64 D32' overflows hash table for qh_matchnewfacets Qhull uses 32-bit ints for identifiers, counts, and sizes. See "WARN64" - q_eg, q_test: change tail +3 to tail -n +3 [N. Dubray, M. Atzeri] - Qhull-go.bat: Changed 'cmd' to '%comspec%' Build changes - Added src/libqhull/Makefile for simple gcc build of executables and lib - qhulltest.vcproj: Replaced full path to QT with $QTDIR (e.g., c:/qt/4.7.4) - Split userprintf_rbox.c from userprintf.c, Otherwise qhull brings in rboxlib and rbox brings in libqhull - Makefile: qhullx target must be after LIBQHULLS_OBJS - Makefile: Explicitly list rbox dependencies for qhullx target - MBorland: Fixed tabs - Placed $LIBQHULLS_OBJS in same order. Frequently called ones together. - Update file lists for Make-config.sh [O. Lahaye] - CMakeLists: add README.txt,etc. to DOC_INSTALL_DIR [M. Atzeri] - Restored qhull.h-deprecated. qhull.h conflicts with Qhull.h on Windows systems [C. Abela] - make-config.sh: Add warning that it is out-of-date - Remove extra space in '#! /bin/sh' in q_eg, etc. [P. Cheeseman] Source changes - libqhull.h: Added qh_True and qh_False for True/False [A. Mutzel] Did not remove or replace True/False since it is used everywhere - Moved error message from qh_argv_to_command to caller. Avoids dependency. - user_eg3.c: Use '10 D2' as default rbox (e.g., 'user_eg3 rbox qhull d') - user.c, user_eg2.c: Add test of qh_qh as done in user_eg.c - q_test: Removed duplicate test of qhull C-0.02 Documentation - index.html: Added ACM Authorizer link to ACM Trans. Math. Software - Split Delaunay and Voronoi FAQs - FAQ: How to compute the volume of a Voronoi region [C, Brinch] - Add 'FS' to qconvex prompt (total area and volume) - Add clarification to 'Fv' about corner input sites [O. Can] - Qhull-go.bat: Removed out-of-date advice. Added title. - qh-code.htm: Updated the discussion of multi-threading for C++ [I. Pirwani] Qhull 2009.1.2 2011/11/21 - Revert to LF line endings [P. Cheeseman] - Remove out-of-date material from qhull-go.bat - Replaced QHULL-GO with a lnk file Qhull 2011.1 2011/05/23 6.2.0.1385 (exe/dll files unchanged) - delaunay.vcproj: Fixed qhullstatic_d.lib for debug and minrelsize builds - Did not redate the distribution Qhull 2011.1 2011/05/18 6.2.0.1385 (exe/dll files unchanged) - Add 'm' library to shared and static targets on Unix [A. Bouchard] Qhull 2011.1 2011/05/14 6.2.0.1383 (exe/dll files unchanged) - PointCoordinates.cpp: Add #include [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<

  ---------------------------------
+
+
+   geom2.c
+   infrequently used geometric routines of qhull
+
+   see qh-geom.htm and geom.h
+
+   Copyright (c) 1993-2012 The Geometry Center.
+   $Id: //main/2011/qhull/src/libqhullr/geom2_r.c#1 $$Change: 1640 $
+   $DateTime: 2014/01/15 09:12:08 $$Author: bbarber $
+
+   frequently used code goes into geom.c
+*/
+
+#include "qhull_a.h"
+
+/*================== functions in alphabetic order ============*/
+
+/*---------------------------------
+
+  qh_copypoints( points, numpoints, dimension)
+    return qh_malloc'd copy of points
+*/
+coordT *qh_copypoints(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 ferr, 6004, "qhull error: insufficient memory to copy %d points\n",
+        numpoints);
+    qh_errexit(qh_ERRmem, NULL, NULL);
+  }
+  memcpy((char *)newpoints, (char *)points, (size_t)size);
+  return newpoints;
+} /* copypoints */
+
+/*---------------------------------
+
+  qh_crossproduct( 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(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( 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(realT **rows, int dim, boolT *nearzero) {
+  realT det=0;
+  int i;
+  boolT sign= False;
+
+  *nearzero= False;
+  if (dim < 2) {
+    qh_fprintf(qh ferr, 6005, "qhull internal error (qh_determinate): only implemented for dimension >= 2\n");
+    qh_errexit(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(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( 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(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_(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 hull_dim, maxabs, sumabs);
+  joggle= distround * qh_JOGGLEdefault;
+  maximize_(joggle, REALepsilon * qh_JOGGLEdefault);
+  trace2((qh ferr, 2001, "qh_detjoggle: joggle=%2.2g maxwidth=%2.2g\n", joggle, maxwidth));
+  return joggle;
+} /* detjoggle */
+
+/*---------------------------------
+
+  qh_detroundoff()
+    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(void) {
+
+  qh_option("_max-width", NULL, &qh MAXwidth);
+  if (!qh SETroundoff) {
+    qh DISTround= qh_distround(qh hull_dim, qh MAXabs_coord, qh MAXsumcoord);
+    if (qh RANDOMdist)
+      qh DISTround += qh RANDOMfactor * qh MAXabs_coord;
+    qh_option("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("Angle-premerge-with-random", NULL, &qh premerge_cos);
+  }
+  if (qh postmerge_cos < REALmax/2) {
+    qh postmerge_cos -= qh ANGLEround;
+    if (qh RANDOMdist)
+      qh_option("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("Centrum-premerge-with-random", NULL, &qh premerge_centrum);
+  if (qh RANDOMdist && qh POSTmerge)
+    qh_option("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("_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("_near-inside", NULL, &qh NEARinside);
+  if (qh JOGGLEmax < qh DISTround) {
+    qh_fprintf(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_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("Visible-distance", NULL, &qh MINvisible);
+  }
+  if (qh MAXcoplanar > REALmax/2) {
+    qh MAXcoplanar= qh MINvisible;
+    qh_option("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("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("_wide-facet", NULL, &qh WIDEfacet);
+  if (qh MINvisible > qh MINoutside + 3 * REALepsilon
+  && !qh BESToutside && !qh FORCEoutput)
+    qh_fprintf(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( 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(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 ferr, 6007, "qhull internal error (qh_detsimplex): #points %d < dimension %d\n",
+               i, dim);
+    qh_errexit(qh_ERRqhull, NULL, NULL);
+  }
+  det= qh_determinant(rows, dim, nearzero);
+  trace2((qh ferr, 2002, "qh_detsimplex: det=%2.2g for point p%d, dim %d, nearzero? %d\n",
+          det, qh_pointid(apex), dim, *nearzero));
+  return det;
+} /* detsimplex */
+
+/*---------------------------------
+
+  qh_distnorm( 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
+*/
+realT qh_distnorm(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(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(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 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( 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(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( 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(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 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(facet);
+    FOREACHridge_(facet->ridges)
+      area += qh_facetarea_simplex(qh hull_dim, centrum, ridge->vertices,
+                 NULL, (boolT)(ridge->top == facet),  facet->normal, &facet->offset);
+    if (qh CENTERtype != qh_AScentrum)
+      qh_memfree(centrum, qh normal_size);
+  }
+  if (facet->upperdelaunay && qh DELAUNAY)
+    area= -area;  /* the normal should be [0,...,1] */
+  trace4((qh ferr, 4009, "qh_facetarea: f%d area %2.2g\n", facet->id, area));
+  return area;
+} /* facetarea */
+
+/*---------------------------------
+
+  qh_facetarea_simplex( 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(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 ferr, 6008, "qhull internal error (qh_facetarea_simplex): #points %d != dim %d -1\n",
+               i, dim);
+    qh_errexit(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(rows, dim, &nearzero);
+  if (toporient)
+    area= -area;
+  area *= qh AREAfactor;
+  trace4((qh ferr, 4010, "qh_facetarea_simplex: area=%2.2g for point p%d, toporient %d, nearzero? %d\n",
+          area, qh_pointid(apex), toporient, nearzero));
+  return area;
+} /* facetarea_simplex */
+
+/*---------------------------------
+
+  qh_facetcenter( 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(setT *vertices) {
+  setT *points= qh_settemp(qh_setsize(vertices));
+  vertexT *vertex, **vertexp;
+  pointT *center;
+
+  FOREACHvertex_(vertices)
+    qh_setappend(&points, vertex->point);
+  center= qh_voronoi_center(qh hull_dim-1, points);
+  qh_settempfree(&points);
+  return center;
+} /* facetcenter */
+
+/*---------------------------------
+
+  qh_findgooddist( 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(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(point, facetA, &bestdist);
+    bestfacet= facetA;
+    goodseen= True;
+  }
+  qh_removefacet(facetA);
+  qh_appendfacet(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(point, neighbor, &dist);
+      if (dist > 0) {
+        qh_removefacet(neighbor);
+        qh_appendfacet(neighbor);
+        if (neighbor->good) {
+          goodseen= True;
+          if (dist > bestdist) {
+            bestdist= dist;
+            bestfacet= neighbor;
+          }
+        }
+      }
+    }
+  }
+  if (bestfacet) {
+    *distp= bestdist;
+    trace2((qh ferr, 2003, "qh_findgooddist: p%d is %2.2g above good facet f%d\n",
+      qh_pointid(point), bestdist, bestfacet->id));
+    return bestfacet;
+  }
+  trace4((qh ferr, 4011, "qh_findgooddist: no good facet for p%d above f%d\n",
+      qh_pointid(point), facetA->id));
+  return NULL;
+}  /* findgooddist */
+
+/*---------------------------------
+
+  qh_getarea( 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(facetT *facetlist) {
+  realT area;
+  realT dist;
+  facetT *facet;
+
+  if (qh hasAreaVolume)
+    return;
+  if (qh REPORTfreq)
+    qh_fprintf(qh ferr, 8020, "computing area of each facet and volume of the convex hull\n");
+  else
+    trace1((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(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 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( 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(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( 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(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()
+    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(void) {
+  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 ferr, 6009, "qhull error: insufficient memory to joggle %d points\n",
+          qh num_points);
+      qh_errexit(qh_ERRmem, NULL, NULL);
+    }
+    qh POINTSmalloc= True;
+    if (qh JOGGLEmax == 0.0) {
+      qh JOGGLEmax= qh_detjoggle(qh input_points, qh num_points, qh hull_dim);
+      qh_option("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("QJoggle", NULL, &qh JOGGLEmax);
+  }
+  if (qh build_cnt > 1 && qh JOGGLEmax > fmax_(qh MAXwidth/4, 0.1)) {
+      qh_fprintf(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_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("_joggle-seed", &seed, NULL);
+  trace0((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 hull_dim, qh num_points, qh first_point);
+  }
+} /* joggleinput */
+
+/*---------------------------------
+
+  qh_maxabsval( normal, dim )
+    return pointer to maximum absolute value of a dim vector
+    returns NULL if dim=0
+*/
+realT *qh_maxabsval(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( 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(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 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_ERRinput, NULL, NULL);
+  }
+  set= qh_settemp(2*dimension);
+  for (k=0; k < dimension; k++) {
+    if (points == qh GOODpointp)
+      minimum= maximum= points + dimension;
+    else
+      minimum= maximum= points;
+    FORALLpoint_(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(&set, maximum);
+    qh_setappend(&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 ferr, "qh_maxmin: found the max and min points(by dim):", set);
+  return(set);
+} /* maxmin */
+
+/*---------------------------------
+
+  qh_maxouter()
+    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(void) {
+  realT dist;
+
+  dist= fmax_(qh max_outside, qh DISTround);
+  dist += qh DISTround;
+  trace4((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( 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(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(*simplex);
+  if (sizinit < 2) {
+    if (qh_setsize(maxpoints) >= 2) {
+      FOREACHpoint_(maxpoints) {
+        if (maxcoord < point[0]) {
+          maxcoord= point[0];
+          maxx= point;
+        }
+        if (mincoord > point[0]) {
+          mincoord= point[0];
+          minx= point;
+        }
+      }
+    }else {
+      FORALLpoint_(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(simplex, minx);
+    if (qh_setsize(*simplex) < 2)
+      qh_setunique(simplex, maxx);
+    sizinit= qh_setsize(*simplex);
+    if (sizinit < 2) {
+      qh_precision("input has same x coordinate");
+      if (zzval_(Zsetplane) > qh hull_dim+1) {
+        qh_fprintf(qh ferr, 6012, "qhull precision error (qh_maxsimplex for voronoi_center):\n%d points with the same x coordinate.\n",
+                 qh_setsize(maxpoints)+numpoints);
+        qh_errexit(qh_ERRprec, NULL, NULL);
+      }else {
+        qh_fprintf(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_ERRinput, NULL, NULL);
+      }
+    }
+  }
+  for (k=sizinit; k < dim+1; k++) {
+    maxpoint= NULL;
+    maxdet= -REALmax;
+    FOREACHpoint_(maxpoints) {
+      if (!qh_setin(*simplex, point)) {
+        det= qh_detsimplex(point, *simplex, k, &nearzero);
+        if ((det= fabs_(det)) > maxdet) {
+          maxdet= det;
+          maxpoint= point;
+          maxnearzero= nearzero;
+        }
+      }
+    }
+    if (!maxpoint || maxnearzero) {
+      zinc_(Zsearchpoints);
+      if (!maxpoint) {
+        trace0((qh ferr, 7, "qh_maxsimplex: searching all points for %d-th initial vertex.\n", k+1));
+      }else {
+        trace0((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(maxpoint), maxdet));
+      }
+      FORALLpoint_(points, numpoints) {
+        if (point == qh GOODpointp)
+          continue;
+        if (!qh_setin(*simplex, point)) {
+          det= qh_detsimplex(point, *simplex, k, &nearzero);
+          if ((det= fabs_(det)) > maxdet) {
+            maxdet= det;
+            maxpoint= point;
+            maxnearzero= nearzero;
+          }
+        }
+      }
+    } /* !maxpoint */
+    if (!maxpoint) {
+      qh_fprintf(qh ferr, 6014, "qhull internal error (qh_maxsimplex): not enough points available\n");
+      qh_errexit(qh_ERRqhull, NULL, NULL);
+    }
+    qh_setappend(simplex, maxpoint);
+    trace1((qh ferr, 1002, "qh_maxsimplex: selected point p%d for %d`th initial vertex, det=%2.2g\n",
+            qh_pointid(maxpoint), k+1, maxdet));
+  } /* k */
+} /* maxsimplex */
+
+/*---------------------------------
+
+  qh_minabsval( normal, dim )
+    return minimum absolute value of a dim vector
+*/
+realT qh_minabsval(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 ( vecA, vecB, dim )
+    return index of min abs. difference of two vectors
+*/
+int qh_mindiff(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( facet  )
+    make facet outside oriented via qh.interior_point
+
+  returns:
+    True if facet reversed orientation.
+*/
+boolT qh_orientoutside(facetT *facet) {
+  int k;
+  realT dist;
+
+  qh_distplane(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( 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_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(facetT *facet, realT *outerplane, realT *innerplane) {
+  realT dist, mindist;
+  vertexT *vertex, **vertexp;
+
+  if (outerplane) {
+    if (!qh_MAXoutside || !facet || !qh maxoutdone) {
+      *outerplane= qh_maxouter();       /* 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(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( point1, point2, dim )
+    return distance between two points
+
+  notes:
+    returns distance squared if 'dim' is negative
+*/
+coordT qh_pointdist(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( fp, string, rows, numrow, numcol )
+    print matrix to fp given by row vectors
+    print string as header
+
+  notes:
+    print a vector by qh_printmatrix(fp, "", &vect, 1, len)
+*/
+void qh_printmatrix(FILE *fp, const char *string, realT **rows, int numrow, int numcol) {
+  realT *rowp;
+  realT r; /*bug fix*/
+  int i,k;
+
+  qh_fprintf(fp, 9001, "%s\n", string);
+  for (i=0; i < numrow; i++) {
+    rowp= rows[i];
+    for (k=0; k < numcol; k++) {
+      r= *rowp++;
+      qh_fprintf(fp, 9002, "%6.3g ", r);
+    }
+    qh_fprintf(fp, 9003, "\n");
+  }
+} /* printmatrix */
+
+
+/*---------------------------------
+
+  qh_printpoints( fp, string, points )
+    print pointids to fp for a set of points
+    if string, prints string and 'p' point ids
+*/
+void qh_printpoints(FILE *fp, const char *string, setT *points) {
+  pointT *point, **pointp;
+
+  if (string) {
+    qh_fprintf(fp, 9004, "%s", string);
+    FOREACHpoint_(points)
+      qh_fprintf(fp, 9005, " p%d", qh_pointid(point));
+    qh_fprintf(fp, 9006, "\n");
+  }else {
+    FOREACHpoint_(points)
+      qh_fprintf(fp, 9007, " %d", qh_pointid(point));
+    qh_fprintf(fp, 9008, "\n");
+  }
+} /* printpoints */
+
+
+/*---------------------------------
+
+  qh_projectinput()
+    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(void) {
+  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(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 ferr, 6015, "qhull internal error (qh_projectinput): dimension after projection %d != hull_dim %d\n", newdim, qh hull_dim);
+    qh_errexit(qh_ERRqhull, NULL, NULL);
+  }
+  if (!(newpoints=(coordT*)qh_malloc(newnum*newdim*sizeof(coordT)))){
+    qh_fprintf(qh ferr, 6016, "qhull error: insufficient memory to project %d points\n",
+           qh num_points);
+    qh_errexit(qh_ERRmem, NULL, NULL);
+  }
+  qh_projectpoints(project, qh input_dim+1, qh first_point,
+                    qh num_points, qh input_dim, newpoints, newdim);
+  trace1((qh ferr, 1003, "qh_projectinput: updating lower and upper_bound\n"));
+  qh_projectpoints(project, qh input_dim+1, qh lower_bound,
+                    1, qh input_dim+1, qh lower_bound, newdim+1);
+  qh_projectpoints(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 ferr, 6017, "qhull internal error (qh_projectinput): HALFspace defined without qh.feasible_point\n");
+      qh_errexit(qh_ERRqhull, NULL, NULL);
+    }
+    qh_projectpoints(project, qh input_dim, qh feasible_point,
+                      1, qh input_dim, qh feasible_point, newdim);
+  }
+  qh_memfree(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 ferr, 9, "qh_projectinput: projected points to paraboloid for Delaunay\n"));
+  }else if (qh DELAUNAY)  /* !qh ATinfinity */
+    qh_setdelaunay( qh hull_dim, qh num_points, qh first_point);
+} /* projectinput */
+
+
+/*---------------------------------
+
+  qh_projectpoints( 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(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 ferr, 6018, "qhull internal error (qh_projectpoints): newdim %d should be %d after projection\n",
+      newdim, testdim);
+    qh_errexit(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 ferr, 1004, "qh_projectpoints: projected %d points from dim %d to dim %d\n",
+    numpoints, dim, newdim));
+} /* projectpoints */
+
+
+/*---------------------------------
+
+  qh_rotateinput( 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(realT **rows) {
+
+  if (!qh POINTSmalloc) {
+    qh first_point= qh_copypoints(qh first_point, qh num_points, qh hull_dim);
+    qh POINTSmalloc= True;
+  }
+  qh_rotatepoints(qh first_point, qh num_points, qh hull_dim, rows);
+}  /* rotateinput */
+
+/*---------------------------------
+
+  qh_rotatepoints( 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(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 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()
+    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(void) {
+
+  if (!qh POINTSmalloc) {
+    qh first_point= qh_copypoints(qh first_point, qh num_points, qh hull_dim);
+    qh POINTSmalloc= True;
+  }
+  qh_scalepoints(qh first_point, qh num_points, qh hull_dim,
+       qh lower_bound, qh upper_bound);
+}  /* scaleinput */
+
+/*---------------------------------
+
+  qh_scalelast( 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(coordT *points, int numpoints, int dim, coordT low,
+                   coordT high, coordT newhigh) {
+  realT scale, shift;
+  coordT *coord;
+  int i;
+  boolT nearzero= False;
+
+  trace4((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(newhigh, high - low,
+                  qh MINdenom_1, &nearzero);
+  if (nearzero) {
+    if (qh DELAUNAY)
+      qh_fprintf(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 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_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( 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(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 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_ERRinput, NULL, NULL);
+    }
+    scale= qh_divzero(newhigh - newlow, high - low,
+                  qh MINdenom_1, &nearzero);
+    if (nearzero) {
+      qh_fprintf(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_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 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( 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 hull_dim, 1, point)
+
+    Do not use options 'Qbk', 'QBk', or 'QbB' since they scale
+    the coordinates after the original projection.
+
+*/
+void qh_setdelaunay(int dim, int count, pointT *points) {
+  int i, k;
+  coordT *coordp, coord;
+  realT paraboloid;
+
+  trace0((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(points, count, dim, qh last_low, qh last_high, qh last_newhigh);
+} /* setdelaunay */
+
+
+/*---------------------------------
+
+  qh_sethalfspace( 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(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(*(normp++), -dist, qh MINdenom_1, &zerodiv);
+      if (zerodiv)
+        goto LABELerroroutside;
+    }
+  }
+  *nextp= coordp;
+  if (qh IStracing >= 4) {
+    qh_fprintf(qh ferr, 8021, "qh_sethalfspace: halfspace at offset %6.2g to point: ", *offset);
+    for (k=dim, coordp=coords; k--; ) {
+      r= *coordp++;
+      qh_fprintf(qh ferr, 8022, " %6.2g", r);
+    }
+    qh_fprintf(qh ferr, 8023, "\n");
+  }
+  return True;
+LABELerroroutside:
+  feasiblep= feasible;
+  normp= normal;
+  qh_fprintf(qh ferr, 6023, "qhull input error: feasible point is not clearly inside halfspace\nfeasible point: ");
+  for (k=dim; k--; )
+    qh_fprintf(qh ferr, 8024, qh_REAL_1, r=*(feasiblep++));
+  qh_fprintf(qh ferr, 8025, "\n     halfspace: ");
+  for (k=dim; k--; )
+    qh_fprintf(qh ferr, 8026, qh_REAL_1, r=*(normp++));
+  qh_fprintf(qh ferr, 8027, "\n     at offset: ");
+  qh_fprintf(qh ferr, 8028, qh_REAL_1, *offset);
+  qh_fprintf(qh ferr, 8029, " and distance: ");
+  qh_fprintf(qh ferr, 8030, qh_REAL_1, dist);
+  qh_fprintf(qh ferr, 8031, "\n");
+  return False;
+} /* sethalfspace */
+
+/*---------------------------------
+
+  qh_sethalfspace_all( 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(int dim, int count, coordT *halfspaces, pointT *feasible) {
+  int i, newdim;
+  pointT *newpoints;
+  coordT *coordp, *normalp, *offsetp;
+
+  trace0((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 ferr, 6024, "qhull error: insufficient memory to compute dual of %d halfspaces\n",
+          count);
+    qh_errexit(qh_ERRmem, NULL, NULL);
+  }
+  coordp= newpoints;
+  normalp= halfspaces;
+  for (i=0; i < count; i++) {
+    offsetp= normalp + newdim;
+    if (!qh_sethalfspace(newdim, coordp, &coordp, normalp, offsetp, feasible)) {
+      qh_fprintf(qh ferr, 8032, "The halfspace was at index %d\n", i);
+      qh_errexit(qh_ERRinput, NULL, NULL);
+    }
+    normalp= offsetp + 1;
+  }
+  return newpoints;
+} /* sethalfspace_all */
+
+
+/*---------------------------------
+
+  qh_sharpnewfacets()
+
+  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() {
+  facetT *facet;
+  boolT issharp = False;
+  int *quadrant, k;
+
+  quadrant= (int*)qh_memalloc(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( quadrant, qh hull_dim * sizeof(int));
+  trace3((qh ferr, 3001, "qh_sharpnewfacets: %d\n", issharp));
+  return issharp;
+} /* sharpnewfacets */
+
+/*---------------------------------
+
+  qh_voronoi_center( 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(int dim, setT *points) {
+  pointT *point, **pointp, *point0;
+  pointT *center= (pointT*)qh_memalloc(qh center_size);
+  setT *simplex;
+  int i, j, k, size= qh_setsize(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 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_ERRqhull, NULL, NULL);
+    simplex= points;  /* never executed -- avoids warning */
+  }else {
+    simplex= qh_settemp(dim+1);
+    qh_maxsimplex(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 gm_row, dim, &nearzero);
+  factor= qh_divzero(0.5, det, qh MINdenom, &infinite);
+  if (infinite) {
+    for (k=dim; k--; )
+      center[k]= qh_INFINITE;
+    if (qh IStracing)
+      qh_printpoints(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 gm_row, dim, &nearzero)*factor + point0[i];
+    }
+#ifndef qh_NOtrace
+    if (qh IStracing >= 3) {
+      qh_fprintf(qh ferr, 8033, "qh_voronoi_center: det %2.2g factor %2.2g ", det, factor);
+      qh_printmatrix(qh ferr, "center:", ¢er, 1, dim);
+      if (qh IStracing >= 5) {
+        qh_printpoints(qh ferr, "points", simplex);
+        FOREACHpoint_(simplex)
+          qh_fprintf(qh ferr, 8034, "p%d dist %.2g, ", qh_pointid(point),
+                   qh_pointdist(point, center, dim));
+        qh_fprintf(qh ferr, 8035, "\n");
+      }
+    }
+#endif
+  }
+  if (simplex != points)
+    qh_settempfree(&simplex);
+  return center;
+} /* voronoi_center */
+
diff --git a/src/libqhullr/geom_r.c b/src/libqhullr/geom_r.c
new file mode 100644
index 0000000..55d8221
--- /dev/null
+++ b/src/libqhullr/geom_r.c
@@ -0,0 +1,1234 @@
+/*
  ---------------------------------
+
+   geom.c
+   geometric routines of qhull
+
+   see qh-geom.htm and geom.h
+
+   Copyright (c) 1993-2012 The Geometry Center.
+   $Id: //main/2011/qhull/src/libqhullr/geom_r.c#1 $$Change: 1640 $
+   $DateTime: 2014/01/15 09:12:08 $$Author: bbarber $
+
+   infrequent code goes into geom2.c
+*/
+
+#include "qhull_a.h"
+
+/*---------------------------------
+
+  qh_distplane( 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
+*/
+void qh_distplane(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 ferr, 8001, "qh_distplane: ");
+    qh_fprintf(qh ferr, 8002, qh_REAL_1, *dist);
+    qh_fprintf(qh ferr, 8003, "from p%d to f%d\n", qh_pointid(point), facet->id);
+  }
+  return;
+} /* distplane */
+
+
+/*---------------------------------
+
+  qh_findbest( 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(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(point))) {
+    if (qh TRACElevel > qh IStracing)
+      qh IStracing= qh TRACElevel;
+    qh_fprintf(qh ferr, 8004, "qh_findbest: point p%d starting at f%d isnewfacets? %d, unless %d exit if > %2.2g\n",
+             qh_pointid(point), startfacet->id, isnewfacets, bestoutside, qh MINoutside);
+    qh_fprintf(qh ferr, 8005, "  testhorizon? %d noupper? %d", testhorizon, noupper);
+    qh_fprintf(qh ferr, 8006, "  Last point added was p%d.", qh furthest_id);
+    qh_fprintf(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(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 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(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(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()) {
+        /* seldom used, qh_findbestnew will retest all facets */
+        zinc_(Zfindnewsharp);
+        bestfacet= qh_findbestnew(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(lastfacet, point, &bestdist, numpart);
+  if (testhorizon)
+    bestfacet= qh_findbesthorizon(!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_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(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 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(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 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 ferr, 4003, "qh_findbesthorizon: newbest? %d bestfacet f%d bestdist %2.2g\n", newbest, getid_(bestfacet), *bestdist));
+  return bestfacet;
+}  /* findbesthorizon */
+
+/*---------------------------------
+
+  qh_findbestnew( 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(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 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 ferr, 6002, "qhull internal error (qh_findbestnew): no new facets for point p%d\n",
+              qh furthest_id);
+    qh_errexit(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(point))) {
+    if (qh TRACElevel > qh IStracing)
+      qh IStracing= qh TRACElevel;
+    qh_fprintf(qh ferr, 8008, "qh_findbestnew: point p%d facet f%d. Stop? %d if dist > %2.2g\n",
+             qh_pointid(point), startfacet->id, isdistoutside, distoutside);
+    qh_fprintf(qh ferr, 8009, "  Last point added p%d visitid %d.",  qh furthest_id, visitid);
+    qh_fprintf(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(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_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 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( 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(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(*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 ferr, 4005, "qh_backnormal: zero diagonal at column %d.\n", i));
+    qh_precision("zero diagonal on back substitution");
+  }
+} /* backnormal */
+
+/*---------------------------------
+
+  qh_gausselim( 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(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 ferr, 8011, "qh_gausselim: 0 pivot at column %d. (%2.2g < %2.2g)\n", k, pivot_abs, qh DISTround);
+          qh_printmatrix(qh ferr, "Matrix:", rows, numrow, numcol);
+        }
+        zzinc_(Zgauss0);
+        qh_precision("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 ferr, "qh_gausselem: result", rows, numrow, numcol);
+} /* gausselim */
+
+
+/*---------------------------------
+
+  qh_getangle( 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(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 ferr, 4006, "qh_getangle: %2.2g\n", angle));
+  return(angle);
+} /* getangle */
+
+
+/*---------------------------------
+
+  qh_getcenter( vertices )
+    returns arithmetic center of a set of vertices as a new point
+
+  notes:
+    allocates point array for center
+*/
+pointT *qh_getcenter(setT *vertices) {
+  int k;
+  pointT *center, *coord;
+  vertexT *vertex, **vertexp;
+  int count= qh_setsize(vertices);
+
+  if (count < 2) {
+    qh_fprintf(qh ferr, 6003, "qhull internal error (qh_getcenter): not defined for %d points\n", count);
+    qh_errexit(qh_ERRqhull, NULL, NULL);
+  }
+  center= (pointT *)qh_memalloc(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( facet )
+    returns the centrum for a facet as a new point
+
+  notes:
+    allocates the centrum
+*/
+pointT *qh_getcentrum(facetT *facet) {
+  realT dist;
+  pointT *centrum, *point;
+
+  point= qh_getcenter(facet->vertices);
+  zzinc_(Zcentrumtests);
+  qh_distplane(point, facet, &dist);
+  centrum= qh_projectpoint(point, facet, dist);
+  qh_memfree(point, qh normal_size);
+  trace4((qh ferr, 4007, "qh_getcentrum: for f%d, %d vertices dist= %2.2g\n",
+          facet->id, qh_setsize(facet->vertices), dist));
+  return centrum;
+} /* getcentrum */
+
+
+/*---------------------------------
+
+  qh_getdistance( 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(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(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( normal, dim, toporient )
+    normalize a vector and report if too small
+    does not use min norm
+
+  see:
+    qh_normalize2
+*/
+void qh_normalize(coordT *normal, int dim, boolT toporient) {
+  qh_normalize2( normal, dim, toporient, NULL, NULL);
+} /* normalize */
+
+/*---------------------------------
+
+  qh_normalize2( 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 (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(*colp, norm, qh MINdenom_1, &zerodiv);
+      if (!zerodiv)
+        *colp= temp;
+      else {
+        maxp= qh_maxabsval(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 ferr, 1, "qh_normalize: norm=%2.2g too small during p%d\n",
+               norm, qh furthest_id));
+        return;
+      }
+    }
+  }
+} /* normalize */
+
+
+/*---------------------------------
+
+  qh_projectpoint( 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(pointT *point, facetT *facet, realT dist) {
+  pointT *newpoint, *np, *normal;
+  int normsize= qh normal_size;
+  int k;
+  void **freelistp; /* used !qh_NOmem */
+
+  qh_memalloc_(normsize, freelistp, newpoint, pointT);
+  np= newpoint;
+  normal= facet->normal;
+  for (k=qh hull_dim; k--; )
+    *(np++)= *point++ - dist * *normal++;
+  return(newpoint);
+} /* projectpoint */
+
+
+/*---------------------------------
+
+  qh_setfacetplane( 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(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_(normsize, freelistp, facet->normal, coordT);
+  if (facet == qh tracefacet) {
+    oldtrace= qh IStracing;
+    qh IStracing= 5;
+    qh_fprintf(qh ferr, 8012, "qh_setfacetplane: facet f%d created.\n", facet->id);
+    qh_fprintf(qh ferr, 8013, "  Last point added to hull was p%d.", qh furthest_id);
+    if (zzval_(Ztotmerge))
+      qh_fprintf(qh ferr, 8014, "  Last merge was #%d.", zzval_(Ztotmerge));
+    qh_fprintf(qh ferr, 8015, "\n\nCurrent summary is:\n");
+      qh_printsummary(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 RANDOMa, qh RANDOMb);
+      }
+    }else {
+      FOREACHvertex_(facet->vertices)
+       qh gm_row[i++]= vertex->point;
+    }
+    qh_sethyperplane_det(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 RANDOMa, qh RANDOMb);
+      }
+    }
+    qh_sethyperplane_gauss(qh hull_dim, qh gm_row, point0, facet->toporient,
+                facet->normal, &facet->offset, &nearzero);
+    if (nearzero) {
+      if (qh_orientoutside(facet)) {
+        trace0((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(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() */
+            if (dist > qh TRACEdist)
+              istrace= True;
+          }
+        }else if (-dist > qh TRACEdist)
+          istrace= True;
+        if (istrace) {
+          qh_fprintf(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(vertex->point), vertex->id, dist, facet->id, qh furthest_id);
+          qh_errprint("DISTANT", facet, NULL, NULL, NULL);
+        }
+      }
+    }
+    qh RANDOMdist= qh old_randomdist;
+  }
+  if (qh IStracing >= 3) {
+    qh_fprintf(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 ferr, 8018, "%2.2g ", facet->normal[k]);
+    qh_fprintf(qh ferr, 8019, "\n");
+  }
+  if (facet == qh tracefacet)
+    qh IStracing= oldtrace;
+} /* setfacetplane */
+
+
+/*---------------------------------
+
+  qh_sethyperplane_det( 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(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 (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 (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 (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 ferr, 3, "qh_sethyperplane_det: degenerate norm during p%d.\n", qh furthest_id));
+    zzinc_(Znearlysingular);
+  }
+} /* sethyperplane_det */
+
+
+/*---------------------------------
+
+  qh_sethyperplane_gauss( 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(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(rows, dim-1, dim, &sign, nearzero);
+  for (k=dim-1; k--; ) {
+    if ((rows[k])[k] < 0)
+      sign ^= 1;
+  }
+  if (*nearzero) {
+    zzinc_(Znearlysingular);
+    trace0((qh ferr, 4, "qh_sethyperplane_gauss: nearly singular or axis parallel hyperplane during p%d.\n", qh furthest_id));
+    qh_backnormal(rows, dim-1, dim, sign, normal, &nearzero2);
+  }else {
+    qh_backnormal(rows, dim-1, dim, sign, normal, &nearzero2);
+    if (nearzero2) {
+      zzinc_(Znearlysingular);
+      trace0((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(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
new file mode 100644
index 0000000..bf10577
--- /dev/null
+++ b/src/libqhullr/geom_r.h
@@ -0,0 +1,176 @@
+/*
  ---------------------------------
+
+  geom.h
+    header file for geometric routines
+
+   see qh-geom.htm and geom.c
+
+   Copyright (c) 1993-2012 The Geometry Center.
+   $Id: //main/2011/qhull/src/libqhullr/geom_r.h#1 $$Change: 1640 $
+   $DateTime: 2014/01/15 09:12:08 $$Author: bbarber $
+*/
+
+#ifndef qhDEFgeom
+#define qhDEFgeom 1
+
+#include "libqhull.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(realT **rows, int numrow, int numcol, boolT sign, coordT *normal, boolT *nearzero);
+void    qh_distplane(pointT *point, facetT *facet, realT *dist);
+facetT *qh_findbest(pointT *point, facetT *startfacet,
+                     boolT bestoutside, boolT isnewfacets, boolT noupper,
+                     realT *dist, boolT *isoutside, int *numpart);
+facetT *qh_findbesthorizon(boolT ischeckmax, pointT *point,
+                     facetT *startfacet, boolT noupper, realT *bestdist, int *numpart);
+facetT *qh_findbestnew(pointT *point, facetT *startfacet, realT *dist,
+                     boolT bestoutside, boolT *isoutside, int *numpart);
+void    qh_gausselim(realT **rows, int numrow, int numcol, boolT *sign, boolT *nearzero);
+realT   qh_getangle(pointT *vect1, pointT *vect2);
+pointT *qh_getcenter(setT *vertices);
+pointT *qh_getcentrum(facetT *facet);
+realT   qh_getdistance(facetT *facet, facetT *neighbor, realT *mindist, realT *maxdist);
+void    qh_normalize(coordT *normal, int dim, boolT toporient);
+void    qh_normalize2 (coordT *normal, int dim, boolT toporient,
+            realT *minnorm, boolT *ismin);
+pointT *qh_projectpoint(pointT *point, facetT *facet, realT dist);
+
+void    qh_setfacetplane(facetT *newfacets);
+void    qh_sethyperplane_det(int dim, coordT **rows, coordT *point0,
+              boolT toporient, coordT *normal, realT *offset, boolT *nearzero);
+void    qh_sethyperplane_gauss(int dim, coordT **rows, pointT *point0,
+             boolT toporient, coordT *normal, coordT *offset, boolT *nearzero);
+boolT   qh_sharpnewfacets(void);
+
+/*========= infrequently used code in geom2.c =============*/
+
+coordT *qh_copypoints(coordT *points, int numpoints, int dimension);
+void    qh_crossproduct(int dim, realT vecA[3], realT vecB[3], realT vecC[3]);
+realT   qh_determinant(realT **rows, int dim, boolT *nearzero);
+realT   qh_detjoggle(pointT *points, int numpoints, int dimension);
+void    qh_detroundoff(void);
+realT   qh_detsimplex(pointT *apex, setT *points, int dim, boolT *nearzero);
+realT   qh_distnorm(int dim, pointT *point, pointT *normal, realT *offsetp);
+realT   qh_distround(int dimension, realT maxabs, realT maxsumabs);
+realT   qh_divzero(realT numer, realT denom, realT mindenom1, boolT *zerodiv);
+realT   qh_facetarea(facetT *facet);
+realT   qh_facetarea_simplex(int dim, coordT *apex, setT *vertices,
+          vertexT *notvertex,  boolT toporient, coordT *normal, realT *offset);
+pointT *qh_facetcenter(setT *vertices);
+facetT *qh_findgooddist(pointT *point, facetT *facetA, realT *distp, facetT **facetlist);
+void    qh_getarea(facetT *facetlist);
+boolT   qh_gram_schmidt(int dim, realT **rows);
+boolT   qh_inthresholds(coordT *normal, realT *angle);
+void    qh_joggleinput(void);
+realT  *qh_maxabsval(realT *normal, int dim);
+setT   *qh_maxmin(pointT *points, int numpoints, int dimension);
+realT   qh_maxouter(void);
+void    qh_maxsimplex(int dim, setT *maxpoints, pointT *points, int numpoints, setT **simplex);
+realT   qh_minabsval(realT *normal, int dim);
+int     qh_mindiff(realT *vecA, realT *vecB, int dim);
+boolT   qh_orientoutside(facetT *facet);
+void    qh_outerinner(facetT *facet, realT *outerplane, realT *innerplane);
+coordT  qh_pointdist(pointT *point1, pointT *point2, int dim);
+void    qh_printmatrix(FILE *fp, const char *string, realT **rows, int numrow, int numcol);
+void    qh_printpoints(FILE *fp, const char *string, setT *points);
+void    qh_projectinput(void);
+void    qh_projectpoints(signed char *project, int n, realT *points,
+             int numpoints, int dim, realT *newpoints, int newdim);
+void    qh_rotateinput(realT **rows);
+void    qh_rotatepoints(realT *points, int numpoints, int dim, realT **rows);
+void    qh_scaleinput(void);
+void    qh_scalelast(coordT *points, int numpoints, int dim, coordT low,
+                   coordT high, coordT newhigh);
+void    qh_scalepoints(pointT *points, int numpoints, int dim,
+                realT *newlows, realT *newhighs);
+boolT   qh_sethalfspace(int dim, coordT *coords, coordT **nextp,
+              coordT *normal, coordT *offset, coordT *feasible);
+coordT *qh_sethalfspace_all(int dim, int count, coordT *halfspaces, pointT *feasible);
+pointT *qh_voronoi_center(int dim, setT *points);
+
+#endif /* qhDEFgeom */
+
+
+
diff --git a/src/libqhullr/global_r.c b/src/libqhullr/global_r.c
new file mode 100644
index 0000000..66a4b70
--- /dev/null
+++ b/src/libqhullr/global_r.c
@@ -0,0 +1,2127 @@
+
+/*
  ---------------------------------
+
+   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) 1993-2012 The Geometry Center.
+   $Id: //main/2011/qhull/src/libqhullr/global_r.c#1 $$Change: 1640 $
+   $DateTime: 2014/01/15 09:12:08 $$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_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/libqhullr/io_r.c b/src/libqhullr/io_r.c
new file mode 100644
index 0000000..c552585
--- /dev/null
+++ b/src/libqhullr/io_r.c
@@ -0,0 +1,4060 @@
+/*
  ---------------------------------
+
+   io.c
+   Input/Output routines of qhull application
+
+   see qh-io.htm and io.h
+
+   see user.c for qh_errprint and qh_printfacetlist
+
+   unix.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
+
+   Copyright (c) 1993-2012 The Geometry Center.
+   $Id: //main/2011/qhull/src/libqhullr/io_r.c#1 $$Change: 1640 $
+   $DateTime: 2014/01/15 09:12:08 $$Author: bbarber $
+*/
+
+#include "qhull_a.h"
+
+/*========= -functions in alphabetical order after qh_produce_output()  =====*/
+
+/*---------------------------------
+
+  qh_produce_output()
+  qh_produce_output2()
+    prints out the result of qhull in desired format
+    qh_produce_output2() does not call qh_prepare_output()
+    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(void) {
+    int tempsize= qh_setsize(qhmem.tempstack);
+
+    qh_prepare_output();
+    qh_produce_output2();
+    if (qh_setsize(qhmem.tempstack) != tempsize) {
+        qh_fprintf(qh ferr, 6206, "qhull internal error (qh_produce_output): temporary sets not empty(%d)\n",
+            qh_setsize(qhmem.tempstack));
+        qh_errexit(qh_ERRqhull, NULL, NULL);
+    }
+} /* produce_output */
+
+
+void qh_produce_output2(void) {
+  int i, tempsize= qh_setsize(qhmem.tempstack), d_1;
+
+  if (qh PRINTsummary)
+    qh_printsummary(qh ferr);
+  else if (qh PRINTout[0] == qh_PRINTnone)
+    qh_printsummary(qh fout);
+  for (i=0; i < qh_PRINTEND; i++)
+    qh_printfacets(qh fout, qh PRINTout[i], qh facet_list, NULL, !qh_ALL);
+  qh_allstatistics();
+  if (qh PRINTprecision && !qh MERGING && (qh JOGGLEmax > REALmax/2 || qh RERUN))
+    qh_printstats(qh ferr, qhstat precision, NULL);
+  if (qh VERIFYoutput && (zzval_(Zridge) > 0 || zzval_(Zridgemid) > 0))
+    qh_printstats(qh ferr, qhstat vridges, NULL);
+  if (qh PRINTstatistics) {
+    qh_printstatistics(qh ferr, "");
+    qh_memstatistics(qh ferr);
+    d_1= sizeof(setT) + (qh hull_dim - 1) * SETelemsize;
+    qh_fprintf(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(qhmem.tempstack) != tempsize) {
+    qh_fprintf(qh ferr, 6065, "qhull internal error (qh_produce_output2): temporary sets not empty(%d)\n",
+             qh_setsize(qhmem.tempstack));
+    qh_errexit(qh_ERRqhull, NULL, NULL);
+  }
+} /* produce_output2 */
+
+/*---------------------------------
+
+  dfacet( id )
+    print facet by id, for debugging
+
+*/
+void dfacet(unsigned id) {
+  facetT *facet;
+
+  FORALLfacets {
+    if (facet->id == id) {
+      qh_printfacet(qh fout, facet);
+      break;
+    }
+  }
+} /* dfacet */
+
+
+/*---------------------------------
+
+  dvertex( id )
+    print vertex by id, for debugging
+*/
+void dvertex(unsigned id) {
+  vertexT *vertex;
+
+  FORALLvertices {
+    if (vertex->id == id) {
+      qh_printvertex(qh fout, vertex);
+      break;
+    }
+  }
+} /* dvertex */
+
+
+/*---------------------------------
+
+  qh_compare_vertexpoint( p1, p2 )
+    used by qsort() to order vertices by point id
+*/
+int qh_compare_vertexpoint(const void *p1, const void *p2) {
+  const vertexT *a= *((vertexT *const*)p1), *b= *((vertexT *const*)p2);
+
+  return((qh_pointid(a->point) > qh_pointid(b->point)?1:-1));
+} /* compare_vertexpoint */
+
+/*---------------------------------
+
+  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_copyfilename( dest, size, source, length )
+    copy filename identified by qh_skipfilename()
+
+  notes:
+    see qh_skipfilename() for syntax
+*/
+void qh_copyfilename(char *filename, int size, const char* source, int length) {
+  char c= *source;
+
+  if (length > size + 1) {
+      qh_fprintf(qh ferr, 6040, "qhull error: filename is more than %d characters, %s\n",  size-1, source);
+      qh_errexit(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( 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(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(facet)))
+      facet->visitid= 0;
+    else {
+      facet->visitid= ++numfacets;
+      totneighbors += qh_setsize(facet->neighbors);
+      if (facet->simplicial) {
+        numsimplicial++;
+        if (facet->keepcentrum && facet->tricoplanar)
+          numtricoplanars++;
+      }else
+        numridges += qh_setsize(facet->ridges);
+      if (facet->coplanarset)
+        numcoplanars += qh_setsize(facet->coplanarset);
+    }
+  }
+
+  FOREACHfacet_(facets) {
+    if ((facet->visible && qh NEWfacets)
+    || (!printall && qh_skipfacet(facet)))
+      facet->visitid= 0;
+    else {
+      facet->visitid= ++numfacets;
+      totneighbors += qh_setsize(facet->neighbors);
+      if (facet->simplicial){
+        numsimplicial++;
+        if (facet->keepcentrum && facet->tricoplanar)
+          numtricoplanars++;
+      }else
+        numridges += qh_setsize(facet->ridges);
+      if (facet->coplanarset)
+        numcoplanars += qh_setsize(facet->coplanarset);
+    }
+  }
+  qh visit_id += numfacets+1;
+  *numfacetsp= numfacets;
+  *numsimplicialp= numsimplicial;
+  *totneighborsp= totneighbors;
+  *numridgesp= numridges;
+  *numcoplanarsp= numcoplanars;
+  *numtricoplanarsp= numtricoplanars;
+} /* countfacets */
+
+/*---------------------------------
+
+  qh_detvnorm( 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
+    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(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 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(facet->vertices);
+      qh_setappend(&points, facet->center);
+    }
+  }
+  if (numcenters > dim) {
+    simplex= qh_settemp(qh TEMPsize);
+    qh_setappend(&simplex, vertex->point);
+    if (unbounded)
+      qh_setappend(&simplex, midpoint);
+    qh_maxsimplex(dim, points, NULL, 0, &simplex);
+    qh_setdelnth(simplex, 0);
+  }else if (numcenters == dim) {
+    if (unbounded)
+      qh_setappend(&points, midpoint);
+    simplex= points;
+  }else {
+    qh_fprintf(qh ferr, 6216, "qhull internal error (qh_detvnorm): too few points(%d) to compute separating plane\n", numcenters);
+    qh_errexit(qh_ERRqhull, NULL, NULL);
+  }
+  i= 0;
+  gmcoord= qh gm_matrix;
+  point0= SETfirstt_(simplex, pointT);
+  FOREACHpoint_(simplex) {
+    if (qh IStracing >= 4)
+      qh_printmatrix(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(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(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(vertex->point);
+    pointidA= qh_pointid(vertexA->point);
+    if (!unbounded) {
+      zinc_(Zdiststat);
+      dist= qh_distnorm(dim, midpoint, normal, &offset);
+      if (dist < 0)
+        dist= -dist;
+      zzinc_(Zridgemid);
+      wwmax_(Wridgemidmax, dist);
+      wwadd_(Wridgemid, dist);
+      trace4((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(midpoint, dim, False);
+      angle= qh_distnorm(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 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_(points) {
+        if (!qh_setin(simplex, point)) {
+          facet= SETelemt_(centers, point_i, facetT);
+          zinc_(Zdiststat);
+          dist= qh_distnorm(dim, point, normal, &offset);
+          if (dist < 0)
+            dist= -dist;
+          zzinc_(Zridge);
+          wwmax_(Wridgemax, dist);
+          wwadd_(Wridge, dist);
+          trace4((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(&simplex);
+  qh_settempfree(&points);
+  return normal;
+} /* detvnorm */
+
+/*---------------------------------
+
+  qh_detvridge( 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(vertexT *vertex) {
+  setT *centers= qh_settemp(qh TEMPsize);
+  setT *tricenters= qh_settemp(qh TEMPsize);
+  facetT *neighbor, **neighborp;
+  boolT firstinf= True;
+
+  FOREACHneighbor_(vertex) {
+    if (neighbor->seen) {
+      if (neighbor->visitid) {
+        if (!neighbor->tricoplanar || qh_setunique(&tricenters, neighbor->center))
+          qh_setappend(¢ers, neighbor);
+      }else if (firstinf) {
+        firstinf= False;
+        qh_setappend(¢ers, neighbor);
+      }
+    }
+  }
+  qsort(SETaddr_(centers, facetT), (size_t)qh_setsize(centers),
+             sizeof(facetT *), qh_compare_facetvisit);
+  qh_settempfree(&tricenters);
+  return centers;
+} /* detvridge */
+
+/*---------------------------------
+
+  qh_detvridge3( 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 (vertexT *atvertex, vertexT *vertex) {
+  setT *centers= qh_settemp(qh TEMPsize);
+  setT *tricenters= qh_settemp(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(&tricenters, facet->center))
+          qh_setappend(¢ers, facet);
+      }else if (firstinf) {
+        firstinf= False;
+        qh_setappend(¢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 ferr, 6217, "qhull internal error (qh_detvridge3): neighbors of vertex p%d are not connected at facet %d\n",
+                 qh_pointid(vertex->point), neighbor->id);
+        qh_errexit(qh_ERRqhull, neighbor, NULL);
+      }
+    }
+  }
+  FOREACHneighbor_(atvertex)
+    neighbor->seen2= True;
+  qh_settempfree(&tricenters);
+  return centers;
+} /* detvridge3 */
+
+/*---------------------------------
+
+  qh_eachvoronoi( 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(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 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(tricenters, 0);
+          FOREACHneighborA_(vertex) {
+            if (neighborA->seen) {
+              if (neighborA->visitid) {
+                if (!neighborA->tricoplanar || qh_setunique(&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 ferr, 4017, "qh_eachvoronoi: Voronoi ridge of %d vertices between sites %d and %d\n",
+                  count, qh_pointid(atvertex->point), qh_pointid(vertex->point)));
+            if (printvridge && fp) {
+              if (inorder && qh hull_dim == 3+1) /* 3-d Voronoi diagram */
+                centers= qh_detvridge3 (atvertex, vertex);
+              else
+                centers= qh_detvridge(vertex);
+              (*printvridge) (fp, atvertex, vertex, centers, unbounded);
+              qh_settempfree(¢ers);
+            }
+          }
+        }
+      }
+    }
+  }
+  FOREACHneighbor_(atvertex)
+    neighbor->seen= False;
+  qh_settempfree(&tricenters);
+  return totridges;
+} /* eachvoronoi */
+
+
+/*---------------------------------
+
+  qh_eachvoronoi_all( 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(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_ASvoronoi);
+  qh_vertexneighbors();
+  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(vertex->point)+1 != qh GOODvertex)
+      continue;
+    totridges += qh_eachvoronoi(fp, printvridge, vertex,
+                   !qh_ALL, innerouter, inorder);
+  }
+  return totridges;
+} /* eachvoronoi_all */
+
+/*---------------------------------
+
+  qh_facet2point( 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(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(vertex0->point, facet, &dist);
+  *mindist= dist;
+  *point0= qh_projectpoint(vertex0->point, facet, dist);
+  qh_distplane(vertex1->point, facet, &dist);
+  minimize_(*mindist, dist);
+  *point1= qh_projectpoint(vertex1->point, facet, dist);
+} /* facet2point */
+
+
+/*---------------------------------
+
+  qh_facetvertices( 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(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 num_vertices);
+    FORALLvertices {
+      vertex->visitid= qh vertex_visit;
+      qh_setappend(&vertices, vertex);
+    }
+  }else {
+    vertices= qh_settemp(qh TEMPsize);
+    FORALLfacet_(facetlist) {
+      if (!allfacets && qh_skipfacet(facet))
+        continue;
+      FOREACHvertex_(facet->vertices) {
+        if (vertex->visitid != qh vertex_visit) {
+          vertex->visitid= qh vertex_visit;
+          qh_setappend(&vertices, vertex);
+        }
+      }
+    }
+  }
+  FOREACHfacet_(facets) {
+    if (!allfacets && qh_skipfacet(facet))
+      continue;
+    FOREACHvertex_(facet->vertices) {
+      if (vertex->visitid != qh vertex_visit) {
+        vertex->visitid= qh vertex_visit;
+        qh_setappend(&vertices, vertex);
+      }
+    }
+  }
+  return vertices;
+} /* facetvertices */
+
+/*---------------------------------
+
+  qh_geomplanes( 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(facetT *facet, realT *outerplane, realT *innerplane) {
+  realT radius;
+
+  if (qh MERGING || qh JOGGLEmax < REALmax/2) {
+    qh_outerinner(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( 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(facetT *facetlist) {
+  facetT *facet, **facetp;
+  setT *facets= qh_settemp(qh num_facets);
+  int size, count;
+
+  trace2((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(&facets, facet);
+  }
+  size= qh_setsize(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(&facets);
+  count= 0;
+  FORALLfacet_(facetlist) {
+    if (facet->good)
+      count++;
+  }
+  qh num_good= count;
+} /* markkeep */
+
+
+/*---------------------------------
+
+  qh_markvoronoi( 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(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_ASvoronoi);  /* in case, qh_printvdiagram2 called by user */
+  qh_vertexneighbors();
+  vertices= qh_pointvertex();
+  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(facet)) {
+      if (!facet->upperdelaunay) {
+        isLower= True;
+        break;
+      }
+    }
+  }
+  FOREACHfacet_(facets) {
+    if (printall || !qh_skipfacet(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(facet))
+      facet->visitid= numcenters++;
+  }
+  FOREACHfacet_(facets) {
+    if (printall || !qh_skipfacet(facet))
+      facet->visitid= numcenters++;
+  }
+  *isLowerp= isLower;
+  *numcentersp= numcenters;
+  trace2((qh ferr, 2007, "qh_markvoronoi: isLower %d numcenters %d\n", isLower, numcenters));
+  return vertices;
+} /* markvoronoi */
+
+/*---------------------------------
+
+  qh_order_vertexneighbors( 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(vertexT *vertex) {
+  setT *newset;
+  facetT *facet, *neighbor, **neighborp;
+
+  trace4((qh ferr, 4018, "qh_order_vertexneighbors: order neighbors of v%d for 3-d\n", vertex->id));
+  newset= qh_settemp(qh_setsize(vertex->neighbors));
+  facet= (facetT*)qh_setdellast(vertex->neighbors);
+  qh_setappend(&newset, facet);
+  while (qh_setsize(vertex->neighbors)) {
+    FOREACHneighbor_(vertex) {
+      if (qh_setin(facet->neighbors, neighbor)) {
+        qh_setdel(vertex->neighbors, neighbor);
+        qh_setappend(&newset, neighbor);
+        facet= neighbor;
+        break;
+      }
+    }
+    if (!neighbor) {
+      qh_fprintf(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_ERRqhull, facet, NULL);
+    }
+  }
+  qh_setfree(&vertex->neighbors);
+  qh_settemppop();
+  vertex->neighbors= newset;
+} /* order_vertexneighbors */
+
+/*---------------------------------
+
+  qh_prepare_output( )
+    prepare for qh_produce_output2() 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(void) {
+  if (qh VORONOI) {
+    qh_clearcenters (qh_ASvoronoi);
+    qh_vertexneighbors();
+  }
+  if (qh TRIangulate && !qh hasTriangulation) {
+    qh_triangulate();
+    if (qh VERIFYoutput && !qh CHECKfrequently)
+      qh_checkpolygon (qh facet_list);
+  }
+  qh_findgood_all (qh facet_list);
+  if (qh GETarea)
+    qh_getarea(qh facet_list);
+  if (qh KEEParea || qh KEEPmerge || qh KEEPminArea < REALmax/2)
+    qh_markkeep (qh facet_list);
+  if (qh PRINTstatistics)
+    qh_collectstatistics();
+}
+
+/*---------------------------------
+
+  qh_printafacet( 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(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(facet))
+    return;
+  if (facet->visible && qh NEWfacets && format != qh_PRINTfacets)
+    return;
+  qh printoutnum++;
+  switch (format) {
+  case qh_PRINTarea:
+    if (facet->isarea) {
+      qh_fprintf(fp, 9009, qh_REAL_1, facet->f.area);
+      qh_fprintf(fp, 9010, "\n");
+    }else
+      qh_fprintf(fp, 9011, "0\n");
+    break;
+  case qh_PRINTcoplanars:
+    qh_fprintf(fp, 9012, "%d", qh_setsize(facet->coplanarset));
+    FOREACHpoint_(facet->coplanarset)
+      qh_fprintf(fp, 9013, " %d", qh_pointid(point));
+    qh_fprintf(fp, 9014, "\n");
+    break;
+  case qh_PRINTcentrums:
+    qh_printcenter(fp, format, NULL, facet);
+    break;
+  case qh_PRINTfacets:
+    qh_printfacet(fp, facet);
+    break;
+  case qh_PRINTfacets_xridge:
+    qh_printfacetheader(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 (color, color);
+    if (qh PRINTdim != qh hull_dim)
+      qh_normalize2 (color, 3, True, NULL, NULL);
+    if (qh hull_dim <= 2)
+      qh_printfacet2geom(fp, facet, color);
+    else if (qh hull_dim == 3) {
+      if (facet->simplicial)
+        qh_printfacet3geom_simplicial(fp, facet, color);
+      else
+        qh_printfacet3geom_nonsimplicial(fp, facet, color);
+    }else {
+      if (facet->simplicial)
+        qh_printfacet4geom_simplicial(fp, facet, color);
+      else
+        qh_printfacet4geom_nonsimplicial(fp, facet, color);
+    }
+    break;
+  case qh_PRINTids:
+    qh_fprintf(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(fp, facet, format);
+    else if (facet->simplicial || qh hull_dim == 2 || format == qh_PRINToff)
+      qh_printfacetNvertex_simplicial(fp, facet, format);
+    else
+      qh_printfacetNvertex_nonsimplicial(fp, facet, qh printoutvar++, format);
+    break;
+  case qh_PRINTinner:
+    qh_outerinner(facet, NULL, &innerplane);
+    offset= facet->offset - innerplane;
+    goto LABELprintnorm;
+    break; /* prevent warning */
+  case qh_PRINTmerges:
+    qh_fprintf(fp, 9016, "%d\n", facet->nummerge);
+    break;
+  case qh_PRINTnormals:
+    offset= facet->offset;
+    goto LABELprintnorm;
+    break; /* prevent warning */
+  case qh_PRINTouter:
+    qh_outerinner(facet, &outerplane, NULL);
+    offset= facet->offset - outerplane;
+  LABELprintnorm:
+    if (!facet->normal) {
+      qh_fprintf(fp, 9017, "no normal for facet f%d\n", facet->id);
+      break;
+    }
+    if (qh CDDoutput) {
+      qh_fprintf(fp, 9018, qh_REAL_1, -offset);
+      for (k=0; k < qh hull_dim; k++)
+        qh_fprintf(fp, 9019, qh_REAL_1, -facet->normal[k]);
+    }else {
+      for (k=0; k < qh hull_dim; k++)
+        qh_fprintf(fp, 9020, qh_REAL_1, facet->normal[k]);
+      qh_fprintf(fp, 9021, qh_REAL_1, offset);
+    }
+    qh_fprintf(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(fp, facet, format, qh printoutvar++);
+    else
+      qh_printfacet3math(fp, facet, format, qh printoutvar++);
+    break;
+  case qh_PRINTneighbors:
+    qh_fprintf(fp, 9023, "%d", qh_setsize(facet->neighbors));
+    FOREACHneighbor_(facet)
+      qh_fprintf(fp, 9024, " %d",
+               neighbor->visitid ? neighbor->visitid - 1: 0 - neighbor->id);
+    qh_fprintf(fp, 9025, "\n");
+    break;
+  case qh_PRINTpointintersect:
+    if (!qh feasible_point) {
+      qh_fprintf(qh ferr, 6067, "qhull input error (qh_printafacet): option 'Fp' needs qh feasible_point\n");
+      qh_errexit( qh_ERRinput, NULL, NULL);
+    }
+    if (facet->offset > 0)
+      goto LABELprintinfinite;
+    point= coordp= (coordT*)qh_memalloc(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(*(normp++), facet->offset, qh MINdenom_1,
+                                 &zerodiv) + *(feasiblep++);
+        if (zerodiv) {
+          qh_memfree(point, qh normal_size);
+          goto LABELprintinfinite;
+        }
+      }
+    }
+    qh_printpoint(fp, NULL, point);
+    qh_memfree(point, qh normal_size);
+    break;
+  LABELprintinfinite:
+    for (k=qh hull_dim; k--; )
+      qh_fprintf(fp, 9026, qh_REAL_1, qh_INFINITE);
+    qh_fprintf(fp, 9027, "\n");
+    break;
+  case qh_PRINTpointnearest:
+    FOREACHpoint_(facet->coplanarset) {
+      int id, id2;
+      vertex= qh_nearvertex(facet, point, &dist);
+      id= qh_pointid(vertex->point);
+      id2= qh_pointid(point);
+      qh_fprintf(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(fp, 9029, "1 ");
+    qh_printcenter(fp, format, NULL, facet);
+    break;
+  case qh_PRINTvertices:
+    qh_fprintf(fp, 9030, "%d", qh_setsize(facet->vertices));
+    FOREACHvertex_(facet->vertices)
+      qh_fprintf(fp, 9031, " %d", qh_pointid(vertex->point));
+    qh_fprintf(fp, 9032, "\n");
+    break;
+  default:
+    break;
+  }
+} /* printafacet */
+
+/*---------------------------------
+
+  qh_printbegin(  )
+    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(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(facetlist, facets, printall, &numfacets, &numsimplicial,
+      &totneighbors, &numridges, &numcoplanars, &numtricoplanars);
+  switch (format) {
+  case qh_PRINTnone:
+    break;
+  case qh_PRINTarea:
+    qh_fprintf(fp, 9033, "%d\n", numfacets);
+    break;
+  case qh_PRINTcoplanars:
+    qh_fprintf(fp, 9034, "%d\n", numfacets);
+    break;
+  case qh_PRINTcentrums:
+    if (qh CENTERtype == qh_ASnone)
+      qh_clearcenters(qh_AScentrum);
+    qh_fprintf(fp, 9035, "%d\n%d\n", qh hull_dim, numfacets);
+    break;
+  case qh_PRINTfacets:
+  case qh_PRINTfacets_xridge:
+    if (facetlist)
+      qh_printvertexlist(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 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 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 ferr, 7051, "qhull warning: output for vertices not implemented in 4-d\n");
+    if (qh PRINTdim == 4 && qh DOintersections && qh PRINTnoplanes)
+      qh_fprintf(qh ferr, 7052, "qhull warning: 'Gnh' generates no output in 4-d\n");
+    if (qh PRINTdim == 2) {
+      qh_fprintf(fp, 9036, "{appearance {linewidth 3} LIST # %s | %s\n",
+              qh rbox_command, qh qhull_command);
+    }else if (qh PRINTdim == 3) {
+      qh_fprintf(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(NULL, facet, &num, printall);
+      FOREACHfacet_(facets)
+        qh_printend4geom(NULL, facet, &num, printall);
+      qh ridgeoutnum= num;
+      qh printoutvar= 0;  /* counts number of ridges in output */
+      qh_fprintf(fp, 9038, "LIST # %s | %s\n", qh rbox_command, qh qhull_command);
+    }
+
+    if (qh PRINTdots) {
+      qh printoutnum++;
+      num= qh num_points + qh_setsize(qh other_points);
+      if (qh DELAUNAY && qh ATinfinity)
+        num--;
+      if (qh PRINTdim == 4)
+        qh_fprintf(fp, 9039, "4VECT %d %d 1\n", num, num);
+      else
+        qh_fprintf(fp, 9040, "VECT %d %d 1\n", num, num);
+
+      for (i=num; i--; ) {
+        if (i % 20 == 0)
+          qh_fprintf(fp, 9041, "\n");
+        qh_fprintf(fp, 9042, "1 ");
+      }
+      qh_fprintf(fp, 9043, "# 1 point per line\n1 ");
+      for (i=num-1; i--; ) { /* num at least 3 for D2 */
+        if (i % 20 == 0)
+          qh_fprintf(fp, 9044, "\n");
+        qh_fprintf(fp, 9045, "0 ");
+      }
+      qh_fprintf(fp, 9046, "# 1 color for all\n");
+      FORALLpoints {
+        if (!qh DELAUNAY || !qh ATinfinity || qh_pointid(point) != qh num_points-1) {
+          if (qh PRINTdim == 4)
+            qh_printpoint(fp, NULL, point);
+            else
+              qh_printpoint3 (fp, point);
+        }
+      }
+      FOREACHpoint_(qh other_points) {
+        if (qh PRINTdim == 4)
+          qh_printpoint(fp, NULL, point);
+        else
+          qh_printpoint3 (fp, point);
+      }
+      qh_fprintf(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(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(facetlist, facets, printall);
+      if (qh PRINTspheres && qh PRINTdim <= 3)
+        qh_printspheres(fp, vertices, qh PRINTradius);
+      if (qh PRINTcoplanar || qh PRINTcentrums) {
+        qh firstcentrum= True;
+        if (qh PRINTcoplanar&& !qh PRINTspheres) {
+          FOREACHvertex_(vertices)
+            qh_printpointvect2 (fp, vertex->point, NULL, qh interior_point, qh PRINTradius);
+        }
+        FORALLfacet_(facetlist) {
+          if (!printall && qh_skipfacet(facet))
+            continue;
+          if (!facet->normal)
+            continue;
+          if (qh PRINTcentrums && qh PRINTdim <= 3)
+            qh_printcentrum(fp, facet, qh PRINTcradius);
+          if (!qh PRINTcoplanar)
+            continue;
+          FOREACHpoint_(facet->coplanarset)
+            qh_printpointvect2 (fp, point, facet->normal, NULL, qh PRINTradius);
+          FOREACHpoint_(facet->outsideset)
+            qh_printpointvect2 (fp, point, facet->normal, NULL, qh PRINTradius);
+        }
+        FOREACHfacet_(facets) {
+          if (!printall && qh_skipfacet(facet))
+            continue;
+          if (!facet->normal)
+            continue;
+          if (qh PRINTcentrums && qh PRINTdim <= 3)
+            qh_printcentrum(fp, facet, qh PRINTcradius);
+          if (!qh PRINTcoplanar)
+            continue;
+          FOREACHpoint_(facet->coplanarset)
+            qh_printpointvect2 (fp, point, facet->normal, NULL, qh PRINTradius);
+          FOREACHpoint_(facet->outsideset)
+            qh_printpointvect2 (fp, point, facet->normal, NULL, qh PRINTradius);
+        }
+      }
+      qh_settempfree(&vertices);
+    }
+    qh visit_id++; /* for printing hyperplane intersections */
+    break;
+  case qh_PRINTids:
+    qh_fprintf(fp, 9049, "%d\n", numfacets);
+    break;
+  case qh_PRINTincidences:
+    if (qh VORONOI && qh PRINTprecision)
+      qh_fprintf(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(fp, 9050, "%d\n", numfacets);
+    else
+      qh_fprintf(fp, 9051, "%d\n", numsimplicial+numridges);
+    break;
+  case qh_PRINTinner:
+  case qh_PRINTnormals:
+  case qh_PRINTouter:
+    if (qh CDDoutput)
+      qh_fprintf(fp, 9052, "%s | %s\nbegin\n    %d %d real\n", qh rbox_command,
+            qh qhull_command, numfacets, qh hull_dim+1);
+    else
+      qh_fprintf(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 ferr, 7054, "qhull warning: output is the Delaunay triangulation\n");
+    if (format == qh_PRINTmaple) {
+      if (qh hull_dim == 2)
+        qh_fprintf(fp, 9054, "PLOT(CURVES(\n");
+      else
+        qh_fprintf(fp, 9055, "PLOT3D(POLYGONS(\n");
+    }else
+      qh_fprintf(fp, 9056, "{\n");
+    qh printoutvar= 0;   /* counts number of facets for notfirst */
+    break;
+  case qh_PRINTmerges:
+    qh_fprintf(fp, 9057, "%d\n", numfacets);
+    break;
+  case qh_PRINTpointintersect:
+    qh_fprintf(fp, 9058, "%d\n%d\n", qh hull_dim, numfacets);
+    break;
+  case qh_PRINTneighbors:
+    qh_fprintf(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(fp, 9060, "%d\n%d %d %d\n", num,
+        qh num_points+qh_setsize(qh other_points), numfacets, totneighbors/2);
+    else { /* qh_PRINTtriangles */
+      qh printoutvar= qh num_points+qh_setsize(qh other_points); /* first centrum */
+      if (qh DELAUNAY)
+        num--;  /* drop last dimension */
+      qh_fprintf(fp, 9061, "%d\n%d %d %d\n", num, qh printoutvar
+        + numfacets - numsimplicial, numsimplicial + numridges, totneighbors/2);
+    }
+    FORALLpoints
+      qh_printpointid(qh fout, NULL, num, point, -1);
+    FOREACHpoint_(qh other_points)
+      qh_printpointid(qh fout, NULL, num, point, -1);
+    if (format == qh_PRINTtriangles && qh hull_dim > 2) {
+      FORALLfacets {
+        if (!facet->simplicial && facet->visitid)
+          qh_printcenter(qh fout, format, NULL, facet);
+      }
+    }
+    break;
+  case qh_PRINTpointnearest:
+    qh_fprintf(fp, 9062, "%d\n", numcoplanars);
+    break;
+  case qh_PRINTpoints:
+    if (!qh VORONOI)
+      goto LABELnoformat;
+    if (qh CDDoutput)
+      qh_fprintf(fp, 9063, "%s | %s\nbegin\n%d %d real\n", qh rbox_command,
+           qh qhull_command, numfacets, qh hull_dim);
+    else
+      qh_fprintf(fp, 9064, "%d\n%d\n", qh hull_dim-1, numfacets);
+    break;
+  case qh_PRINTvertices:
+    qh_fprintf(fp, 9065, "%d\n", numfacets);
+    break;
+  case qh_PRINTsummary:
+  default:
+  LABELnoformat:
+    qh_fprintf(qh ferr, 6068, "qhull internal error (qh_printbegin): can not use this format for dimension %d\n",
+         qh hull_dim);
+    qh_errexit(qh_ERRqhull, NULL, NULL);
+  }
+} /* printbegin */
+
+/*---------------------------------
+
+  qh_printcenter( 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(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(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(facet->vertices);
+      for (k=0; k < num; k++)
+        qh_fprintf(fp, 9067, qh_REAL_1, facet->center[k]);
+    }else {
+      for (k=0; k < num; k++)
+        qh_fprintf(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(facet);
+    for (k=0; k < num; k++)
+      qh_fprintf(fp, 9069, qh_REAL_1, facet->center[k]);
+  }
+  if (format == qh_PRINTgeom && num == 2)
+    qh_fprintf(fp, 9070, " 0\n");
+  else
+    qh_fprintf(fp, 9071, "\n");
+} /* printcenter */
+
+/*---------------------------------
+
+  qh_printcentrum( 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(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(facet);
+    centrum= facet->center;
+  }else {
+    centrum= qh_getcentrum(facet);
+    tempcentrum= True;
+  }
+  qh_fprintf(fp, 9072, "{appearance {-normal -edge normscale 0} ");
+  if (qh firstcentrum) {
+    qh firstcentrum= False;
+    qh_fprintf(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(fp, 9074, "{INST geom { : centrum } transform { # f%d\n", facet->id);
+  apex= SETfirstt_(facet->vertices, vertexT);
+  qh_distplane(apex->point, facet, &dist);
+  projpt= qh_projectpoint(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 (xaxis, xaxis);
+    qh_projectdim3 (normal, normal);
+    qh_normalize2 (normal, qh PRINTdim, True, NULL, NULL);
+  }
+  qh_crossproduct(3, xaxis, normal, yaxis);
+  qh_fprintf(fp, 9075, "%8.4g %8.4g %8.4g 0\n", xaxis[0], xaxis[1], xaxis[2]);
+  qh_fprintf(fp, 9076, "%8.4g %8.4g %8.4g 0\n", yaxis[0], yaxis[1], yaxis[2]);
+  qh_fprintf(fp, 9077, "%8.4g %8.4g %8.4g 0\n", normal[0], normal[1], normal[2]);
+  qh_printpoint3 (fp, centrum);
+  qh_fprintf(fp, 9078, "1 }}}\n");
+  qh_memfree(projpt, qh normal_size);
+  qh_printpointvect(fp, centrum, facet->normal, NULL, radius, green);
+  if (tempcentrum)
+    qh_memfree(centrum, qh normal_size);
+} /* printcentrum */
+
+/*---------------------------------
+
+  qh_printend( fp, format )
+    prints trailer for all output formats
+
+  see:
+    qh_printbegin() and qh_printafacet()
+
+*/
+void qh_printend(FILE *fp, qh_PRINT format, facetT *facetlist, setT *facets, boolT printall) {
+  int num;
+  facetT *facet, **facetp;
+
+  if (!qh printoutnum)
+    qh_fprintf(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(fp, facet,&num, printall);
+      FOREACHfacet_(facets)
+        qh_printend4geom(fp, facet, &num, printall);
+      if (num != qh ridgeoutnum || qh printoutvar != qh ridgeoutnum) {
+        qh_fprintf(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_ERRqhull, NULL, NULL);
+      }
+    }else
+      qh_fprintf(fp, 9079, "}\n");
+    break;
+  case qh_PRINTinner:
+  case qh_PRINTnormals:
+  case qh_PRINTouter:
+    if (qh CDDoutput)
+      qh_fprintf(fp, 9080, "end\n");
+    break;
+  case qh_PRINTmaple:
+    qh_fprintf(fp, 9081, "));\n");
+    break;
+  case qh_PRINTmathematica:
+    qh_fprintf(fp, 9082, "}\n");
+    break;
+  case qh_PRINTpoints:
+    if (qh CDDoutput)
+      qh_fprintf(fp, 9083, "end\n");
+    break;
+  default:
+    break;
+  }
+} /* printend */
+
+/*---------------------------------
+
+  qh_printend4geom( 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(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(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(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(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( 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(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 other_points);
+
+  points= qh_settemp(allpoints);
+  qh_setzero(points, 0, allpoints);
+  vertices= qh_facetvertices(facetlist, facets, printall);
+  FOREACHvertex_(vertices) {
+    id= qh_pointid(vertex->point);
+    if (id >= 0) {
+      SETelem_(points, id)= vertex->point;
+      numpoints++;
+    }
+  }
+  qh_settempfree(&vertices);
+  qh_fprintf(fp, 9086, "%d\n", numpoints);
+  FOREACHpoint_i_(points) {
+    if (point)
+      qh_fprintf(fp, 9087, "%d\n", point_i);
+  }
+  qh_settempfree(&points);
+} /* printextremes */
+
+/*---------------------------------
+
+  qh_printextremes_2d( 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(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(facetlist, facets, printall, &numfacets, &numsimplicial,
+      &totneighbors, &numridges, &numcoplanars, &numtricoplanars); /* marks qh visit_id */
+  vertices= qh_facetvertices(facetlist, facets, printall);
+  qh_fprintf(fp, 9088, "%d\n", qh_setsize(vertices));
+  qh_settempfree(&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 ferr, 6218, "Qhull internal error (qh_printextremes_2d): loop in facet list.  facet %d nextfacet %d\n",
+                 facet->id, nextfacet->id);
+      qh_errexit2 (qh_ERRqhull, facet, nextfacet);
+    }
+    if (facet->visitid) {
+      if (vertexA->visitid != qh vertex_visit) {
+        vertexA->visitid= qh vertex_visit;
+        qh_fprintf(fp, 9089, "%d\n", qh_pointid(vertexA->point));
+      }
+      if (vertexB->visitid != qh vertex_visit) {
+        vertexB->visitid= qh vertex_visit;
+        qh_fprintf(fp, 9090, "%d\n", qh_pointid(vertexB->point));
+      }
+    }
+    facet->visitid= qh visit_id;
+    facet= nextfacet;
+  }while (facet && facet != startfacet);
+} /* printextremes_2d */
+
+/*---------------------------------
+
+  qh_printextremes_d( 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(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(facetlist, facets, printall);
+  qh_vertexneighbors();
+  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(fp, 9091, "%d\n", numpoints);
+  FOREACHvertex_(vertices) {
+    if (vertex->seen)
+      qh_fprintf(fp, 9092, "%d\n", qh_pointid(vertex->point));
+  }
+  qh_settempfree(&vertices);
+} /* printextremes_d */
+
+/*---------------------------------
+
+  qh_printfacet( fp, facet )
+    prints all fields of a facet to fp
+
+  notes:
+    ridges printed in neighbor order
+*/
+void qh_printfacet(FILE *fp, facetT *facet) {
+
+  qh_printfacetheader(fp, facet);
+  if (facet->ridges)
+    qh_printfacetridges(fp, facet);
+} /* printfacet */
+
+
+/*---------------------------------
+
+  qh_printfacet2geom( 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.
+*/
+void qh_printfacet2geom(FILE *fp, facetT *facet, realT color[3]) {
+  pointT *point0, *point1;
+  realT mindist, innerplane, outerplane;
+  int k;
+
+  qh_facet2point(facet, &point0, &point1, &mindist);
+  qh_geomplanes(facet, &outerplane, &innerplane);
+  if (qh PRINTouter || (!qh PRINTnoplanes && !qh PRINTinner))
+    qh_printfacet2geom_points(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(fp, point0, point1, facet, innerplane, color);
+  }
+  qh_memfree(point1, qh normal_size);
+  qh_memfree(point0, qh normal_size);
+} /* printfacet2geom */
+
+/*---------------------------------
+
+  qh_printfacet2geom_points( 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(FILE *fp, pointT *point1, pointT *point2,
+                               facetT *facet, realT offset, realT color[3]) {
+  pointT *p1= point1, *p2= point2;
+
+  qh_fprintf(fp, 9093, "VECT 1 2 1 2 1 # f%d\n", facet->id);
+  if (offset != 0.0) {
+    p1= qh_projectpoint(p1, facet, -offset);
+    p2= qh_projectpoint(p2, facet, -offset);
+  }
+  qh_fprintf(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(p1, qh normal_size);
+    qh_memfree(p2, qh normal_size);
+  }
+  qh_fprintf(fp, 9095, "%8.4g %8.4g %8.4g 1.0\n", color[0], color[1], color[2]);
+} /* printfacet2geom_points */
+
+
+/*---------------------------------
+
+  qh_printfacet2math( 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(FILE *fp, facetT *facet, qh_PRINT format, int notfirst) {
+  pointT *point0, *point1;
+  realT mindist;
+  const char *pointfmt;
+
+  qh_facet2point(facet, &point0, &point1, &mindist);
+  if (notfirst)
+    qh_fprintf(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(fp, 9097, pointfmt, point0[0], point0[1], point1[0], point1[1]);
+  qh_memfree(point1, qh normal_size);
+  qh_memfree(point0, qh normal_size);
+} /* printfacet2math */
+
+
+/*---------------------------------
+
+  qh_printfacet3geom_nonsimplicial( 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(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(facet, &outerplane, &innerplane);
+  vertices= qh_facet3vertex(facet); /* oriented */
+  cntvertices= qh_setsize(vertices);
+  projectedpoints= qh_settemp(cntvertices);
+  FOREACHvertex_(vertices) {
+    zinc_(Zdistio);
+    qh_distplane(vertex->point, facet, &dist);
+    projpt= qh_projectpoint(vertex->point, facet, dist);
+    qh_setappend(&projectedpoints, projpt);
+  }
+  if (qh PRINTouter || (!qh PRINTnoplanes && !qh PRINTinner))
+    qh_printfacet3geom_points(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(fp, projectedpoints, facet, innerplane, color);
+  }
+  FOREACHpoint_(projectedpoints)
+    qh_memfree(point, qh normal_size);
+  qh_settempfree(&projectedpoints);
+  qh_settempfree(&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(fp, facet, neighbor, ridge->vertices, black);
+        if (qh PRINTridges) {
+          vertexA= SETfirstt_(ridge->vertices, vertexT);
+          vertexB= SETsecondt_(ridge->vertices, vertexT);
+          qh_printline3geom(fp, vertexA->point, vertexB->point, green);
+        }
+      }
+    }
+  }
+} /* printfacet3geom_nonsimplicial */
+
+/*---------------------------------
+
+  qh_printfacet3geom_points( 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(FILE *fp, setT *points, facetT *facet, realT offset, realT color[3]) {
+  int k, n= qh_setsize(points), i;
+  pointT *point, **pointp;
+  setT *printpoints;
+
+  qh_fprintf(fp, 9098, "{ OFF %d 1 1 # f%d\n", n, facet->id);
+  if (offset != 0.0) {
+    printpoints= qh_settemp(n);
+    FOREACHpoint_(points)
+      qh_setappend(&printpoints, qh_projectpoint(point, facet, -offset));
+  }else
+    printpoints= points;
+  FOREACHpoint_(printpoints) {
+    for (k=0; k < qh hull_dim; k++) {
+      if (k == qh DROPdim)
+        qh_fprintf(fp, 9099, "0 ");
+      else
+        qh_fprintf(fp, 9100, "%8.4g ", point[k]);
+    }
+    if (printpoints != points)
+      qh_memfree(point, qh normal_size);
+    qh_fprintf(fp, 9101, "\n");
+  }
+  if (printpoints != points)
+    qh_settempfree(&printpoints);
+  qh_fprintf(fp, 9102, "%d ", n);
+  for (i=0; i < n; i++)
+    qh_fprintf(fp, 9103, "%d ", i);
+  qh_fprintf(fp, 9104, "%8.4g %8.4g %8.4g 1.0 }\n", color[0], color[1], color[2]);
+} /* printfacet3geom_points */
+
+
+/*---------------------------------
+
+  qh_printfacet3geom_simplicial(  )
+    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
+    innerplane may be off by qh DISTround.  Maxoutside is calculated elsewhere
+    so a DISTround error may have occured.
+*/
+void qh_printfacet3geom_simplicial(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(facet, &outerplane, &innerplane);
+  vertices= qh_facet3vertex(facet);
+  points= qh_settemp(qh TEMPsize);
+  FOREACHvertex_(vertices)
+    qh_setappend(&points, vertex->point);
+  if (qh PRINTouter || (!qh PRINTnoplanes && !qh PRINTinner))
+    qh_printfacet3geom_points(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(fp, points, facet, innerplane, color);
+  }
+  qh_settempfree(&points);
+  qh_settempfree(&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(facet->vertices, qh hull_dim,
+                          SETindex_(facet->neighbors, neighbor), 0);
+        if (qh DOintersections)
+           qh_printhyperplaneintersection(fp, facet, neighbor, vertices, black);
+        if (qh PRINTridges) {
+          vertexA= SETfirstt_(vertices, vertexT);
+          vertexB= SETsecondt_(vertices, vertexT);
+          qh_printline3geom(fp, vertexA->point, vertexB->point, green);
+        }
+        qh_setfree(&vertices);
+      }
+    }
+  }
+} /* printfacet3geom_simplicial */
+
+/*---------------------------------
+
+  qh_printfacet3math( 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(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(fp, 9105, ",\n");
+  vertices= qh_facet3vertex(facet);
+  points= qh_settemp(qh_setsize(vertices));
+  FOREACHvertex_(vertices) {
+    zinc_(Zdistio);
+    qh_distplane(vertex->point, facet, &dist);
+    point= qh_projectpoint(vertex->point, facet, dist);
+    qh_setappend(&points, point);
+  }
+  if (format == qh_PRINTmaple) {
+    qh_fprintf(fp, 9106, "[");
+    pointfmt= "[%16.8f, %16.8f, %16.8f]";
+    endfmt= "]";
+  }else {
+    qh_fprintf(fp, 9107, "Polygon[{");
+    pointfmt= "{%16.8f, %16.8f, %16.8f}";
+    endfmt= "}]";
+  }
+  FOREACHpoint_(points) {
+    if (firstpoint)
+      firstpoint= False;
+    else
+      qh_fprintf(fp, 9108, ",\n");
+    qh_fprintf(fp, 9109, pointfmt, point[0], point[1], point[2]);
+  }
+  FOREACHpoint_(points)
+    qh_memfree(point, qh normal_size);
+  qh_settempfree(&points);
+  qh_settempfree(&vertices);
+  qh_fprintf(fp, 9110, endfmt);
+} /* printfacet3math */
+
+
+/*---------------------------------
+
+  qh_printfacet3vertex( 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(FILE *fp, facetT *facet, qh_PRINT format) {
+  vertexT *vertex, **vertexp;
+  setT *vertices;
+
+  vertices= qh_facet3vertex(facet);
+  if (format == qh_PRINToff)
+    qh_fprintf(fp, 9111, "%d ", qh_setsize(vertices));
+  FOREACHvertex_(vertices)
+    qh_fprintf(fp, 9112, "%d ", qh_pointid(vertex->point));
+  qh_fprintf(fp, 9113, "\n");
+  qh_settempfree(&vertices);
+} /* printfacet3vertex */
+
+
+/*---------------------------------
+
+  qh_printfacet4geom_nonsimplicial(  )
+    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(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(fp, facet, neighbor, ridge->vertices, color);
+    else {
+      if (qh DROPdim >= 0)
+        qh_fprintf(fp, 9114, "OFF 3 1 1 # f%d\n", facet->id);
+      else {
+        qh printoutvar++;
+        qh_fprintf(fp, 9115, "# r%d between f%d f%d\n", ridge->id, facet->id, neighbor->id);
+      }
+      FOREACHvertex_(ridge->vertices) {
+        zinc_(Zdistio);
+        qh_distplane(vertex->point,facet, &dist);
+        point=qh_projectpoint(vertex->point,facet, dist);
+        for (k=0; k < qh hull_dim; k++) {
+          if (k != qh DROPdim)
+            qh_fprintf(fp, 9116, "%8.4g ", point[k]);
+        }
+        qh_fprintf(fp, 9117, "\n");
+        qh_memfree(point, qh normal_size);
+      }
+      if (qh DROPdim >= 0)
+        qh_fprintf(fp, 9118, "3 0 1 2 %8.4g %8.4g %8.4g\n", color[0], color[1], color[2]);
+    }
+  }
+} /* printfacet4geom_nonsimplicial */
+
+
+/*---------------------------------
+
+  qh_printfacet4geom_simplicial( 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(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(facet->vertices, qh hull_dim,
+                          SETindex_(facet->neighbors, neighbor), 0);
+    if (qh DOintersections)
+      qh_printhyperplaneintersection(fp, facet, neighbor, vertices, color);
+    else {
+      if (qh DROPdim >= 0)
+        qh_fprintf(fp, 9119, "OFF 3 1 1 # ridge between f%d f%d\n",
+                facet->id, neighbor->id);
+      else {
+        qh printoutvar++;
+        qh_fprintf(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(fp, 9121, "%8.4g ", vertex->point[k]);
+        }
+        qh_fprintf(fp, 9122, "\n");
+      }
+      if (qh DROPdim >= 0)
+        qh_fprintf(fp, 9123, "3 0 1 2 %8.4g %8.4g %8.4g\n", color[0], color[1], color[2]);
+    }
+    qh_setfree(&vertices);
+  }
+} /* printfacet4geom_simplicial */
+
+
+/*---------------------------------
+
+  qh_printfacetNvertex_nonsimplicial( fp, facet, id, format )
+    print vertices for an N-d non-simplicial facet
+    triangulates each ridge to the id
+*/
+void qh_printfacetNvertex_nonsimplicial(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(fp, 9124, "%d ", qh hull_dim);
+    qh_fprintf(fp, 9125, "%d ", id);
+    if ((ridge->top == facet) ^ qh_ORIENTclock) {
+      FOREACHvertex_(ridge->vertices)
+        qh_fprintf(fp, 9126, "%d ", qh_pointid(vertex->point));
+    }else {
+      FOREACHvertexreverse12_(ridge->vertices)
+        qh_fprintf(fp, 9127, "%d ", qh_pointid(vertex->point));
+    }
+    qh_fprintf(fp, 9128, "\n");
+  }
+} /* printfacetNvertex_nonsimplicial */
+
+
+/*---------------------------------
+
+  qh_printfacetNvertex_simplicial( 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(FILE *fp, facetT *facet, qh_PRINT format) {
+  vertexT *vertex, **vertexp;
+
+  if (format == qh_PRINToff || format == qh_PRINTtriangles)
+    qh_fprintf(fp, 9129, "%d ", qh_setsize(facet->vertices));
+  if ((facet->toporient ^ qh_ORIENTclock)
+  || (qh hull_dim > 2 && !facet->simplicial)) {
+    FOREACHvertex_(facet->vertices)
+      qh_fprintf(fp, 9130, "%d ", qh_pointid(vertex->point));
+  }else {
+    FOREACHvertexreverse12_(facet->vertices)
+      qh_fprintf(fp, 9131, "%d ", qh_pointid(vertex->point));
+  }
+  qh_fprintf(fp, 9132, "\n");
+} /* printfacetNvertex_simplicial */
+
+
+/*---------------------------------
+
+  qh_printfacetheader( fp, facet )
+    prints header fields of a facet to fp
+
+  notes:
+    for 'f' output and debugging
+    Same as QhullFacet::printHeader()
+*/
+void qh_printfacetheader(FILE *fp, facetT *facet) {
+  pointT *point, **pointp, *furthest;
+  facetT *neighbor, **neighborp;
+  realT dist;
+
+  if (facet == qh_MERGEridge) {
+    qh_fprintf(fp, 9133, " MERGEridge\n");
+    return;
+  }else if (facet == qh_DUPLICATEridge) {
+    qh_fprintf(fp, 9134, " DUPLICATEridge\n");
+    return;
+  }else if (!facet) {
+    qh_fprintf(fp, 9135, " NULLfacet\n");
+    return;
+  }
+  qh old_randomdist= qh RANDOMdist;
+  qh RANDOMdist= False;
+  qh_fprintf(fp, 9136, "- f%d\n", facet->id);
+  qh_fprintf(fp, 9137, "    - flags:");
+  if (facet->toporient)
+    qh_fprintf(fp, 9138, " top");
+  else
+    qh_fprintf(fp, 9139, " bottom");
+  if (facet->simplicial)
+    qh_fprintf(fp, 9140, " simplicial");
+  if (facet->tricoplanar)
+    qh_fprintf(fp, 9141, " tricoplanar");
+  if (facet->upperdelaunay)
+    qh_fprintf(fp, 9142, " upperDelaunay");
+  if (facet->visible)
+    qh_fprintf(fp, 9143, " visible");
+  if (facet->newfacet)
+    qh_fprintf(fp, 9144, " new");
+  if (facet->tested)
+    qh_fprintf(fp, 9145, " tested");
+  if (!facet->good)
+    qh_fprintf(fp, 9146, " notG");
+  if (facet->seen)
+    qh_fprintf(fp, 9147, " seen");
+  if (facet->coplanar)
+    qh_fprintf(fp, 9148, " coplanar");
+  if (facet->mergehorizon)
+    qh_fprintf(fp, 9149, " mergehorizon");
+  if (facet->keepcentrum)
+    qh_fprintf(fp, 9150, " keepcentrum");
+  if (facet->dupridge)
+    qh_fprintf(fp, 9151, " dupridge");
+  if (facet->mergeridge && !facet->mergeridge2)
+    qh_fprintf(fp, 9152, " mergeridge1");
+  if (facet->mergeridge2)
+    qh_fprintf(fp, 9153, " mergeridge2");
+  if (facet->newmerge)
+    qh_fprintf(fp, 9154, " newmerge");
+  if (facet->flipped)
+    qh_fprintf(fp, 9155, " flipped");
+  if (facet->notfurthest)
+    qh_fprintf(fp, 9156, " notfurthest");
+  if (facet->degenerate)
+    qh_fprintf(fp, 9157, " degenerate");
+  if (facet->redundant)
+    qh_fprintf(fp, 9158, " redundant");
+  qh_fprintf(fp, 9159, "\n");
+  if (facet->isarea)
+    qh_fprintf(fp, 9160, "    - area: %2.2g\n", facet->f.area);
+  else if (qh NEWfacets && facet->visible && facet->f.replace)
+    qh_fprintf(fp, 9161, "    - replacement: f%d\n", facet->f.replace->id);
+  else if (facet->newfacet) {
+    if (facet->f.samecycle && facet->f.samecycle != facet)
+      qh_fprintf(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(fp, 9163, "    - owner of normal & centrum is facet f%d\n", facet->f.triowner->id);
+  }else if (facet->f.newcycle)
+    qh_fprintf(fp, 9164, "    - was horizon to f%d\n", facet->f.newcycle->id);
+  if (facet->nummerge)
+    qh_fprintf(fp, 9165, "    - merges: %d\n", facet->nummerge);
+  qh_printpointid(fp, "    - normal: ", qh hull_dim, facet->normal, -1);
+  qh_fprintf(fp, 9166, "    - offset: %10.7g\n", facet->offset);
+  if (qh CENTERtype == qh_ASvoronoi || facet->center)
+    qh_printcenter(fp, qh_PRINTfacets, "    - center: ", facet);
+#if qh_MAXoutside
+  if (facet->maxoutside > qh DISTround)
+    qh_fprintf(fp, 9167, "    - maxoutside: %10.7g\n", facet->maxoutside);
+#endif
+  if (!SETempty_(facet->outsideset)) {
+    furthest= (pointT*)qh_setlast(facet->outsideset);
+    if (qh_setsize(facet->outsideset) < 6) {
+      qh_fprintf(fp, 9168, "    - outside set(furthest p%d):\n", qh_pointid(furthest));
+      FOREACHpoint_(facet->outsideset)
+        qh_printpoint(fp, "     ", point);
+    }else if (qh_setsize(facet->outsideset) < 21) {
+      qh_printpoints(fp, "    - outside set:", facet->outsideset);
+    }else {
+      qh_fprintf(fp, 9169, "    - outside set:  %d points.", qh_setsize(facet->outsideset));
+      qh_printpoint(fp, "  Furthest", furthest);
+    }
+#if !qh_COMPUTEfurthest
+    qh_fprintf(fp, 9170, "    - furthest distance= %2.2g\n", facet->furthestdist);
+#endif
+  }
+  if (!SETempty_(facet->coplanarset)) {
+    furthest= (pointT*)qh_setlast(facet->coplanarset);
+    if (qh_setsize(facet->coplanarset) < 6) {
+      qh_fprintf(fp, 9171, "    - coplanar set(furthest p%d):\n", qh_pointid(furthest));
+      FOREACHpoint_(facet->coplanarset)
+        qh_printpoint(fp, "     ", point);
+    }else if (qh_setsize(facet->coplanarset) < 21) {
+      qh_printpoints(fp, "    - coplanar set:", facet->coplanarset);
+    }else {
+      qh_fprintf(fp, 9172, "    - coplanar set:  %d points.", qh_setsize(facet->coplanarset));
+      qh_printpoint(fp, "  Furthest", furthest);
+    }
+    zinc_(Zdistio);
+    qh_distplane(furthest, facet, &dist);
+    qh_fprintf(fp, 9173, "      furthest distance= %2.2g\n", dist);
+  }
+  qh_printvertices(fp, "    - vertices:", facet->vertices);
+  qh_fprintf(fp, 9174, "    - neighboring facets:");
+  FOREACHneighbor_(facet) {
+    if (neighbor == qh_MERGEridge)
+      qh_fprintf(fp, 9175, " MERGE");
+    else if (neighbor == qh_DUPLICATEridge)
+      qh_fprintf(fp, 9176, " DUP");
+    else
+      qh_fprintf(fp, 9177, " f%d", neighbor->id);
+  }
+  qh_fprintf(fp, 9178, "\n");
+  qh RANDOMdist= qh old_randomdist;
+} /* printfacetheader */
+
+
+/*---------------------------------
+
+  qh_printfacetridges( 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(FILE *fp, facetT *facet) {
+  facetT *neighbor, **neighborp;
+  ridgeT *ridge, **ridgep;
+  int numridges= 0;
+
+
+  if (facet->visible && qh NEWfacets) {
+    qh_fprintf(fp, 9179, "    - ridges(ids may be garbage):");
+    FOREACHridge_(facet->ridges)
+      qh_fprintf(fp, 9180, " r%d", ridge->id);
+    qh_fprintf(fp, 9181, "\n");
+  }else {
+    qh_fprintf(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(fp, ridge);
+        numridges++;
+        ridge= qh_nextridge3d(ridge, facet, NULL);
+        }
+    }else {
+      FOREACHneighbor_(facet) {
+        FOREACHridge_(facet->ridges) {
+          if (otherfacet_(ridge,facet) == neighbor) {
+            ridge->seen= True;
+            qh_printridge(fp, ridge);
+            numridges++;
+          }
+        }
+      }
+    }
+    if (numridges != qh_setsize(facet->ridges)) {
+      qh_fprintf(fp, 9183, "     - all ridges:");
+      FOREACHridge_(facet->ridges)
+        qh_fprintf(fp, 9184, " r%d", ridge->id);
+        qh_fprintf(fp, 9185, "\n");
+    }
+    FOREACHridge_(facet->ridges) {
+      if (!ridge->seen)
+        qh_printridge(fp, ridge);
+    }
+  }
+} /* printfacetridges */
+
+/*---------------------------------
+
+  qh_printfacets( 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(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 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(facetlist, facets, printall);
+    center= qh_getcenter(vertices);
+    qh_fprintf(fp, 9186, "%d 1\n", qh hull_dim);
+    qh_printpointid(fp, NULL, qh hull_dim, center, -1);
+    qh_memfree(center, qh normal_size);
+    qh_settempfree(&vertices);
+  }else if (format == qh_PRINTextremes) {
+    if (qh DELAUNAY)
+      qh_printextremes_d(fp, facetlist, facets, printall);
+    else if (qh hull_dim == 2)
+      qh_printextremes_2d(fp, facetlist, facets, printall);
+    else
+      qh_printextremes(fp, facetlist, facets, printall);
+  }else if (format == qh_PRINToptions)
+    qh_fprintf(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(fp, facetlist, facets, printall);
+  else if (format == qh_PRINTqhull)
+    qh_fprintf(fp, 9188, "%s | %s\n", qh rbox_command, qh qhull_command);
+  else if (format == qh_PRINTsize) {
+    qh_fprintf(fp, 9189, "0\n2 ");
+    qh_fprintf(fp, 9190, qh_REAL_1, qh totarea);
+    qh_fprintf(fp, 9191, qh_REAL_1, qh totvol);
+    qh_fprintf(fp, 9192, "\n");
+  }else if (format == qh_PRINTsummary) {
+    qh_countfacets(facetlist, facets, printall, &numfacets, &numsimplicial,
+      &totneighbors, &numridges, &numcoplanars, &numtricoplanars);
+    vertices= qh_facetvertices(facetlist, facets, printall);
+    qh_fprintf(fp, 9193, "10 %d %d %d %d %d %d %d %d %d %d\n2 ", qh hull_dim,
+                qh num_points + qh_setsize(qh other_points),
+                qh num_vertices, qh num_facets - qh num_visible,
+                qh_setsize(vertices), numfacets, numcoplanars,
+                numfacets - numsimplicial, zzval_(Zdelvertextot),
+                numtricoplanars);
+    qh_settempfree(&vertices);
+    qh_outerinner(NULL, &outerplane, &innerplane);
+    qh_fprintf(fp, 9194, qh_REAL_2n, outerplane, innerplane);
+  }else if (format == qh_PRINTvneighbors)
+    qh_printvneighbors(fp, facetlist, facets, printall);
+  else if (qh VORONOI && format == qh_PRINToff)
+    qh_printvoronoi(fp, format, facetlist, facets, printall);
+  else if (qh VORONOI && format == qh_PRINTgeom) {
+    qh_printbegin(fp, format, facetlist, facets, printall);
+    qh_printvoronoi(fp, format, facetlist, facets, printall);
+    qh_printend(fp, format, facetlist, facets, printall);
+  }else if (qh VORONOI
+  && (format == qh_PRINTvertices || format == qh_PRINTinner || format == qh_PRINTouter))
+    qh_printvdiagram(fp, format, facetlist, facets, printall);
+  else {
+    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, facetlist, facets, printall);
+  }
+  qh RANDOMdist= qh old_randomdist;
+} /* printfacets */
+
+
+/*---------------------------------
+
+  qh_printhyperplaneintersection( 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(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(facet1->normal, facet2->normal);
+  denominator= 1 - costheta * costheta;
+  i= qh_setsize(vertices);
+  if (qh hull_dim == 3)
+    qh_fprintf(fp, 9195, "VECT 1 %d 1 %d 1 ", i, i);
+  else if (qh hull_dim == 4 && qh DROPdim >= 0)
+    qh_fprintf(fp, 9196, "OFF 3 1 1 ");
+  else
+    qh printoutvar++;
+  qh_fprintf(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(vertex->point, facet1, &dist1);
+    qh_distplane(vertex->point, facet2, &dist2);
+    s= qh_divzero(-dist1 + costheta * dist2, denominator,mindenom,&nearzero1);
+    t= qh_divzero(-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 (p, p);
+      qh_fprintf(fp, 9198, "%8.4g %8.4g %8.4g # ", p[0], p[1], p[2]);
+    }else
+      qh_fprintf(fp, 9199, "%8.4g %8.4g %8.4g %8.4g # ", p[0], p[1], p[2], p[3]);
+    if (nearzero1+nearzero2)
+      qh_fprintf(fp, 9200, "p%d(coplanar facets)\n", qh_pointid(vertex->point));
+    else
+      qh_fprintf(fp, 9201, "projected p%d\n", qh_pointid(vertex->point));
+  }
+  if (qh hull_dim == 3)
+    qh_fprintf(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(fp, 9203, "3 0 1 2 %8.4g %8.4g %8.4g 1.0\n", color[0], color[1], color[2]);
+} /* printhyperplaneintersection */
+
+/*---------------------------------
+
+  qh_printline3geom( 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(FILE *fp, pointT *pointA, pointT *pointB, realT color[3]) {
+  int k;
+  realT pA[4], pB[4];
+
+  qh_projectdim3(pointA, pA);
+  qh_projectdim3(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(fp, 9204, "VECT 1 2 1 2 1\n");
+    for (k=0; k < 3; k++)
+       qh_fprintf(fp, 9205, "%8.4g ", pB[k]);
+    qh_fprintf(fp, 9206, " # p%d\n", qh_pointid(pointB));
+  }else
+    qh_fprintf(fp, 9207, "VECT 1 1 1 1 1\n");
+  for (k=0; k < 3; k++)
+    qh_fprintf(fp, 9208, "%8.4g ", pA[k]);
+  qh_fprintf(fp, 9209, " # p%d\n", qh_pointid(pointA));
+  qh_fprintf(fp, 9210, "%8.4g %8.4g %8.4g 1\n", color[0], color[1], color[2]);
+}
+
+/*---------------------------------
+
+  qh_printneighborhood( fp, format, facetA, facetB, printall )
+    print neighborhood of one or two facets
+
+  notes:
+    calls qh_findgood_all()
+    bumps qh.visit_id
+*/
+void qh_printneighborhood(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 facet_list);
+  if (facetA == facetB)
+    facetB= NULL;
+  facets= qh_settemp(2*(qh_setsize(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(&facets, facet);
+    }
+    FOREACHneighbor_(facet) {
+      if (neighbor->visitid == qh visit_id)
+        continue;
+      neighbor->visitid= qh visit_id;
+      if (printall || !qh_skipfacet(neighbor))
+        qh_setappend(&facets, neighbor);
+    }
+  }
+  qh_printfacets(fp, format, NULL, facets, printall);
+  qh_settempfree(&facets);
+} /* printneighborhood */
+
+/*---------------------------------
+
+  qh_printpoint( fp, string, point )
+  qh_printpointid( 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(FILE *fp, const char *string, pointT *point) {
+  int id= qh_pointid( point);
+
+  qh_printpointid( fp, string, qh hull_dim, point, id);
+} /* printpoint */
+
+void qh_printpointid(FILE *fp, const char *string, int dim, pointT *point, int id) {
+  int k;
+  realT r; /*bug fix*/
+
+  if (!point)
+    return;
+  if (string) {
+    qh_fprintf(fp, 9211, "%s", string);
+   if (id != -1)
+      qh_fprintf(fp, 9212, " p%d: ", id);
+  }
+  for (k=dim; k--; ) {
+    r= *point++;
+    if (string)
+      qh_fprintf(fp, 9213, " %8.4g", r);
+    else
+      qh_fprintf(fp, 9214, qh_REAL_1, r);
+  }
+  qh_fprintf(fp, 9215, "\n");
+} /* printpointid */
+
+/*---------------------------------
+
+  qh_printpoint3( fp, point )
+    prints 2-d, 3-d, or 4-d point as Geomview 3-d coordinates
+*/
+void qh_printpoint3 (FILE *fp, pointT *point) {
+  int k;
+  realT p[4];
+
+  qh_projectdim3 (point, p);
+  for (k=0; k < 3; k++)
+    qh_fprintf(fp, 9216, "%8.4g ", p[k]);
+  qh_fprintf(fp, 9217, " # p%d\n", qh_pointid(point));
+} /* printpoint3 */
+
+/*----------------------------------------
+-printpoints- print pointids for a set of points starting at index
+   see geom.c
+*/
+
+/*---------------------------------
+
+  qh_printpoints_out( 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(FILE *fp, facetT *facetlist, setT *facets, boolT printall) {
+  int allpoints= qh num_points + qh_setsize(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(allpoints);
+  qh_setzero(points, 0, allpoints);
+  vertices= qh_facetvertices(facetlist, facets, printall);
+  FOREACHvertex_(vertices) {
+    id= qh_pointid(vertex->point);
+    if (id >= 0)
+      SETelem_(points, id)= vertex->point;
+  }
+  if (qh KEEPinside || qh KEEPcoplanar || qh KEEPnearinside) {
+    FORALLfacet_(facetlist) {
+      if (!printall && qh_skipfacet(facet))
+        continue;
+      FOREACHpoint_(facet->coplanarset) {
+        id= qh_pointid(point);
+        if (id >= 0)
+          SETelem_(points, id)= point;
+      }
+    }
+    FOREACHfacet_(facets) {
+      if (!printall && qh_skipfacet(facet))
+        continue;
+      FOREACHpoint_(facet->coplanarset) {
+        id= qh_pointid(point);
+        if (id >= 0)
+          SETelem_(points, id)= point;
+      }
+    }
+  }
+  qh_settempfree(&vertices);
+  FOREACHpoint_i_(points) {
+    if (point)
+      numpoints++;
+  }
+  if (qh CDDoutput)
+    qh_fprintf(fp, 9218, "%s | %s\nbegin\n%d %d real\n", qh rbox_command,
+             qh qhull_command, numpoints, qh hull_dim + 1);
+  else
+    qh_fprintf(fp, 9219, "%d\n%d\n", qh hull_dim, numpoints);
+  FOREACHpoint_i_(points) {
+    if (point) {
+      if (qh CDDoutput)
+        qh_fprintf(fp, 9220, "1 ");
+      qh_printpoint(fp, NULL, point);
+    }
+  }
+  if (qh CDDoutput)
+    qh_fprintf(fp, 9221, "end\n");
+  qh_settempfree(&points);
+} /* printpoints_out */
+
+
+/*---------------------------------
+
+  qh_printpointvect( 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(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 (diff, qh hull_dim, True, NULL, NULL);
+  for (k=qh hull_dim; k--; )
+    pointA[k]= point[k]+diff[k] * radius;
+  qh_printline3geom(fp, point, pointA, color);
+} /* printpointvect */
+
+/*---------------------------------
+
+  qh_printpointvect2( 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 (FILE *fp, pointT *point, coordT *normal, pointT *center, realT radius) {
+  realT red[3]={1, 0, 0}, yellow[3]={1, 1, 0};
+
+  qh_printpointvect(fp, point, normal, center, radius, red);
+  qh_printpointvect(fp, point, normal, center, -radius, yellow);
+} /* printpointvect2 */
+
+/*---------------------------------
+
+  qh_printridge( fp, ridge )
+    prints the information in a ridge
+
+  notes:
+    for qh_printfacetridges()
+    same as operator<< [QhullRidge.cpp]
+*/
+void qh_printridge(FILE *fp, ridgeT *ridge) {
+
+  qh_fprintf(fp, 9222, "     - r%d", ridge->id);
+  if (ridge->tested)
+    qh_fprintf(fp, 9223, " tested");
+  if (ridge->nonconvex)
+    qh_fprintf(fp, 9224, " nonconvex");
+  qh_fprintf(fp, 9225, "\n");
+  qh_printvertices(fp, "           vertices:", ridge->vertices);
+  if (ridge->top && ridge->bottom)
+    qh_fprintf(fp, 9226, "           between f%d and f%d\n",
+            ridge->top->id, ridge->bottom->id);
+} /* printridge */
+
+/*---------------------------------
+
+  qh_printspheres( fp, vertices, radius )
+    prints 3-d vertices as OFF spheres
+
+  notes:
+    inflated octahedron from Stuart Levy earth/mksphere2
+*/
+void qh_printspheres(FILE *fp, setT *vertices, realT radius) {
+  vertexT *vertex, **vertexp;
+
+  qh printoutnum++;
+  qh_fprintf(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(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 (fp, vertex->point);
+    qh_fprintf(fp, 9229, "1\n");
+  }
+  qh_fprintf(fp, 9230, "}}}\n");
+} /* printspheres */
+
+
+/*----------------------------------------------
+-printsummary-
+                see libqhull.c
+*/
+
+/*---------------------------------
+
+  qh_printvdiagram( 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(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 ferr, 6219, "Qhull internal error (qh_printvdiagram): unknown print format %d.\n", format);
+    qh_errexit(qh_ERRinput, NULL, NULL);
+  }
+  vertices= qh_markvoronoi(facetlist, facets, printall, &isLower, &numcenters);
+  totcount= qh_printvdiagram2 (NULL, NULL, vertices, innerouter, False);
+  qh_fprintf(fp, 9231, "%d\n", totcount);
+  totcount= qh_printvdiagram2 (fp, printvridge, vertices, innerouter, True /* inorder*/);
+  qh_settempfree(&vertices);
+#if 0  /* for testing qh_eachvoronoi_all */
+  qh_fprintf(fp, 9232, "\n");
+  totcount= qh_eachvoronoi_all(fp, printvridge, qh UPPERdelaunay, innerouter, True /* inorder*/);
+  qh_fprintf(fp, 9233, "%d\n", totcount);
+#endif
+} /* printvdiagram */
+
+/*---------------------------------
+
+  qh_printvdiagram2( 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 (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_(vertices) {
+    if (vertex) {
+      if (qh GOODvertex > 0 && qh_pointid(vertex->point)+1 != qh GOODvertex)
+        continue;
+      totcount += qh_eachvoronoi(fp, printvridge, vertex, !qh_ALL, innerouter, inorder);
+    }
+  }
+  return totcount;
+} /* printvdiagram2 */
+
+/*---------------------------------
+
+  qh_printvertex( fp, vertex )
+    prints the information in a vertex
+    Duplicated as operator<< [QhullVertex.cpp]
+*/
+void qh_printvertex(FILE *fp, vertexT *vertex) {
+  pointT *point;
+  int k, count= 0;
+  facetT *neighbor, **neighborp;
+  realT r; /*bug fix*/
+
+  if (!vertex) {
+    qh_fprintf(fp, 9234, "  NULLvertex\n");
+    return;
+  }
+  qh_fprintf(fp, 9235, "- p%d(v%d):", qh_pointid(vertex->point), vertex->id);
+  point= vertex->point;
+  if (point) {
+    for (k=qh hull_dim; k--; ) {
+      r= *point++;
+      qh_fprintf(fp, 9236, " %5.2g", r);
+    }
+  }
+  if (vertex->deleted)
+    qh_fprintf(fp, 9237, " deleted");
+  if (vertex->delridge)
+    qh_fprintf(fp, 9238, " ridgedeleted");
+  qh_fprintf(fp, 9239, "\n");
+  if (vertex->neighbors) {
+    qh_fprintf(fp, 9240, "  neighbors:");
+    FOREACHneighbor_(vertex) {
+      if (++count % 100 == 0)
+        qh_fprintf(fp, 9241, "\n     ");
+      qh_fprintf(fp, 9242, " f%d", neighbor->id);
+    }
+    qh_fprintf(fp, 9243, "\n");
+  }
+} /* printvertex */
+
+
+/*---------------------------------
+
+  qh_printvertexlist( fp, string, facetlist, facets, printall )
+    prints vertices used by a facetlist or facet set
+    tests qh_skipfacet() if !printall
+*/
+void qh_printvertexlist(FILE *fp, const char* string, facetT *facetlist,
+                         setT *facets, boolT printall) {
+  vertexT *vertex, **vertexp;
+  setT *vertices;
+
+  vertices= qh_facetvertices(facetlist, facets, printall);
+  qh_fprintf(fp, 9244, "%s", string);
+  FOREACHvertex_(vertices)
+    qh_printvertex(fp, vertex);
+  qh_settempfree(&vertices);
+} /* printvertexlist */
+
+
+/*---------------------------------
+
+  qh_printvertices( fp, string, vertices )
+    prints vertices in a set
+    duplicated as printVertexSet [QhullVertex.cpp]
+*/
+void qh_printvertices(FILE *fp, const char* string, setT *vertices) {
+  vertexT *vertex, **vertexp;
+
+  qh_fprintf(fp, 9245, "%s", string);
+  FOREACHvertex_(vertices)
+    qh_fprintf(fp, 9246, " p%d(v%d)", qh_pointid(vertex->point), vertex->id);
+  qh_fprintf(fp, 9247, "\n");
+} /* printvertices */
+
+/*---------------------------------
+
+  qh_printvneighbors( 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(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 other_points);
+  vertexT *vertex, **vertexp;
+  int vertex_i, vertex_n;
+  facetT *facet, **facetp, *neighbor, **neighborp;
+  pointT *point, **pointp;
+
+  qh_countfacets(facetlist, facets, printall, &numfacets, &numsimplicial,
+      &totneighbors, &numridges, &numcoplanars, &numtricoplanars);  /* sets facet->visitid */
+  qh_fprintf(fp, 9248, "%d\n", numpoints);
+  qh_vertexneighbors();
+  vertices= qh_facetvertices(facetlist, facets, printall);
+  vertex_points= qh_settemp(numpoints);
+  coplanar_points= qh_settemp(numpoints);
+  qh_setzero(vertex_points, 0, numpoints);
+  qh_setzero(coplanar_points, 0, numpoints);
+  FOREACHvertex_(vertices)
+    qh_point_add(vertex_points, vertex->point, vertex);
+  FORALLfacet_(facetlist) {
+    FOREACHpoint_(facet->coplanarset)
+      qh_point_add(coplanar_points, point, facet);
+  }
+  FOREACHfacet_(facets) {
+    FOREACHpoint_(facet->coplanarset)
+      qh_point_add(coplanar_points, point, facet);
+  }
+  FOREACHvertex_i_(vertex_points) {
+    if (vertex) {
+      numneighbors= qh_setsize(vertex->neighbors);
+      qh_fprintf(fp, 9249, "%d", numneighbors);
+      if (qh hull_dim == 3)
+        qh_order_vertexneighbors(vertex);
+      else if (qh hull_dim >= 4)
+        qsort(SETaddr_(vertex->neighbors, facetT), (size_t)numneighbors,
+             sizeof(facetT *), qh_compare_facetvisit);
+      FOREACHneighbor_(vertex)
+        qh_fprintf(fp, 9250, " %d",
+                 neighbor->visitid ? neighbor->visitid - 1 : 0 - neighbor->id);
+      qh_fprintf(fp, 9251, "\n");
+    }else if ((facet= SETelemt_(coplanar_points, vertex_i, facetT)))
+      qh_fprintf(fp, 9252, "1 %d\n",
+                  facet->visitid ? facet->visitid - 1 : 0 - facet->id);
+    else
+      qh_fprintf(fp, 9253, "0\n");
+  }
+  qh_settempfree(&coplanar_points);
+  qh_settempfree(&vertex_points);
+  qh_settempfree(&vertices);
+} /* printvneighbors */
+
+/*---------------------------------
+
+  qh_printvoronoi( 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(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(facetlist, facets, printall, &isLower, &numcenters);
+  FOREACHvertex_i_(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(fp, 9254, "{appearance {+edge -face} OFF %d %d 1 # Voronoi centers and cells\n",
+                numcenters, numvertices);
+  else
+    qh_fprintf(fp, 9255, "%d\n%d %d 1\n", qh hull_dim-1, numcenters, qh_setsize(vertices));
+  if (format == qh_PRINTgeom) {
+    for (k=qh hull_dim-1; k--; )
+      qh_fprintf(fp, 9256, qh_REAL_1, 0.0);
+    qh_fprintf(fp, 9257, " 0 # infinity not used\n");
+  }else {
+    for (k=qh hull_dim-1; k--; )
+      qh_fprintf(fp, 9258, qh_REAL_1, qh_INFINITE);
+    qh_fprintf(fp, 9259, "\n");
+  }
+  FORALLfacet_(facetlist) {
+    if (facet->visitid && facet->visitid < numfacets) {
+      if (format == qh_PRINTgeom)
+        qh_fprintf(fp, 9260, "# %d f%d\n", vid++, facet->id);
+      qh_printcenter(fp, format, NULL, facet);
+    }
+  }
+  FOREACHfacet_(facets) {
+    if (facet->visitid && facet->visitid < numfacets) {
+      if (format == qh_PRINTgeom)
+        qh_fprintf(fp, 9261, "# %d f%d\n", vid++, facet->id);
+      qh_printcenter(fp, format, NULL, facet);
+    }
+  }
+  FOREACHvertex_i_(vertices) {
+    numneighbors= 0;
+    numinf=0;
+    if (vertex) {
+      if (qh hull_dim == 3)
+        qh_order_vertexneighbors(vertex);
+      else if (qh hull_dim >= 4)
+        qsort(SETaddr_(vertex->neighbors, facetT),
+             (size_t)qh_setsize(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(fp, 9262, "%d", numneighbors);
+        FOREACHneighbor_(vertex) {
+          if (neighbor->visitid && neighbor->visitid < numfacets)
+            qh_fprintf(fp, 9263, " %d", neighbor->visitid);
+        }
+        qh_fprintf(fp, 9264, " # p%d(v%d)\n", vertex_i, vertex->id);
+      }else
+        qh_fprintf(fp, 9265, " # p%d is coplanar or isolated\n", vertex_i);
+    }else {
+      if (numinf)
+        numneighbors++;
+      qh_fprintf(fp, 9266, "%d", numneighbors);
+      if (vertex) {
+        FOREACHneighbor_(vertex) {
+          if (neighbor->visitid == 0) {
+            if (numinf) {
+              numinf= 0;
+              qh_fprintf(fp, 9267, " %d", neighbor->visitid);
+            }
+          }else if (neighbor->visitid < numfacets)
+            qh_fprintf(fp, 9268, " %d", neighbor->visitid);
+        }
+      }
+      qh_fprintf(fp, 9269, "\n");
+    }
+  }
+  if (format == qh_PRINTgeom)
+    qh_fprintf(fp, 9270, "}\n");
+  qh_settempfree(&vertices);
+} /* printvoronoi */
+
+/*---------------------------------
+
+  qh_printvnorm( 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(FILE *fp, vertexT *vertex, vertexT *vertexA, setT *centers, boolT unbounded) {
+  pointT *normal;
+  realT offset;
+  int k;
+  QHULL_UNUSED(unbounded);
+
+  normal= qh_detvnorm(vertex, vertexA, centers, &offset);
+  qh_fprintf(fp, 9271, "%d %d %d ",
+      2+qh hull_dim, qh_pointid(vertex->point), qh_pointid(vertexA->point));
+  for (k=0; k< qh hull_dim-1; k++)
+    qh_fprintf(fp, 9272, qh_REAL_1, normal[k]);
+  qh_fprintf(fp, 9273, qh_REAL_1, offset);
+  qh_fprintf(fp, 9274, "\n");
+} /* printvnorm */
+
+/*---------------------------------
+
+  qh_printvridge( 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(FILE *fp, vertexT *vertex, vertexT *vertexA, setT *centers, boolT unbounded) {
+  facetT *facet, **facetp;
+  QHULL_UNUSED(unbounded);
+
+  qh_fprintf(fp, 9275, "%d %d %d", qh_setsize(centers)+2,
+       qh_pointid(vertex->point), qh_pointid(vertexA->point));
+  FOREACHfacet_(centers)
+    qh_fprintf(fp, 9276, " %d", facet->visitid);
+  qh_fprintf(fp, 9277, "\n");
+} /* printvridge */
+
+/*---------------------------------
+
+  qh_projectdim3( 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 (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( 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(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 ferr, 6070, "qhull input error: feasible point(dim 1 coords) is only valid for halfspace intersection\n");
+    qh_errexit(qh_ERRinput, NULL, NULL);
+  }
+  if (qh feasible_string)
+    qh_fprintf(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 ferr, 6071, "qhull error: insufficient memory for feasible point\n");
+    qh_errexit(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 ferr, 6072, "qhull input error: coordinates for feasible point do not finish out the line: %s\n",
+               s);
+          qh_errexit(qh_ERRinput, NULL, NULL);
+        }
+        return linecount;
+      }
+    }
+  }
+  qh_fprintf(qh ferr, 6073, "qhull input error: only %d coordinates.  Could not read %d-d feasible point.\n",
+           tokcount, dim);
+  qh_errexit(qh_ERRinput, NULL, NULL);
+  return 0;
+} /* readfeasible */
+
+/*---------------------------------
+
+  qh_readpoints( 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(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(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 ferr, 6074, "qhull input error: missing \"begin\" for cdd-formated input\n");
+      qh_errexit(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(diminput, s); /* checks if ok */
+          dimfeasible= diminput;
+          diminput= numinput= 0;
+        }else
+          break;
+      }
+    }
+  }
+  if (!s) {
+    qh_fprintf(qh ferr, 6075, "qhull input error: short input file.  Did not find dimension and number of points\n");
+    qh_errexit(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 ferr, 6220,"qhull input error: dimension %d(first number) should be at least 2\n",
+            diminput);
+    qh_errexit(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 ferr, 6221,"qhull input error: dimension %d(first number, includes offset) should be at least 3 for halfspaces\n",
+            diminput);
+      qh_errexit(qh_ERRinput, NULL, NULL);
+    }
+    if (dimfeasible) {
+      if (dimfeasible != *dimension) {
+        qh_fprintf(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_ERRinput, NULL, NULL);
+      }
+    }else
+      qh_setfeasible(*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 ferr, 6076, "qhull error: insufficient memory to read %d points\n",
+            numinput);
+    qh_errexit(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 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 ferr, 6077, "qhull input error: for cdd format, point at line %d does not start with '1'\n",
+                   linecount);
+            qh_errexit(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(*dimension, coords, &coords, normalp, offsetp, qh feasible_point)) {
+            qh_fprintf(qh ferr, 8048, "The halfspace was on line %d\n", linecount);
+            if (wasbegin)
+              qh_fprintf(qh ferr, 8049, "The input appears to be in cdd format.  If so, you should use option 'Fd'\n");
+            qh_errexit(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 ferr, 6078, "qhull input error: line %d contained more than %d characters\n",
+              linecount, (int) (s - qh line));   /* WARN64 */
+      qh_errexit(qh_ERRinput, NULL, NULL);
+    }
+    isfirst= False;
+  }
+  if (tokcount != maxcount) {
+    newnum= fmin_(numinput, tokcount/diminput);
+    qh_fprintf(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 ferr, 8051, ", line %d is the first comment", firsttext);
+    if (firstshort)
+      qh_fprintf(qh ferr, 8052, ", line %d is the first short\nline", firstshort);
+    if (firstlong)
+      qh_fprintf(qh ferr, 8053, ", line %d is the first long line", firstlong);
+    qh_fprintf(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 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 ferr, 1008,"qh_readpoints: read in %d %d-dimensional points\n",
+          numinput, diminput));
+  return(points);
+} /* readpoints */
+
+
+/*---------------------------------
+
+  qh_setfeasible( 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(int dim) {
+  int tokcount= 0;
+  char *s;
+  coordT *coords, value;
+
+  if (!(s= qh feasible_string)) {
+    qh_fprintf(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_ERRinput, NULL, NULL);
+  }
+  if (!(qh feasible_point= (pointT*)qh_malloc(dim * sizeof(coordT)))) {
+    qh_fprintf(qh ferr, 6079, "qhull error: insufficient memory for 'Hn,n,n'\n");
+    qh_errexit(qh_ERRmem, NULL, NULL);
+  }
+  coords= qh feasible_point;
+  while (*s) {
+    value= qh_strtod(s, &s);
+    if (++tokcount > dim) {
+      qh_fprintf(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( 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(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(facet->normal, NULL));
+} /* skipfacet */
+
+/*---------------------------------
+
+  qh_skipfilename( 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(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 ferr, 6204, "qhull input error: filename expected, none found.\n");
+    qh_errexit(qh_ERRinput, NULL, NULL);
+  }
+  if (c == '\'' || c == '"') {
+    while (*s !=c || s[-1] == '\\') {
+      if (!*s) {
+        qh_fprintf(qh ferr, 6203, "qhull input error: missing quote after filename -- %s\n", filename);
+        qh_errexit(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
new file mode 100644
index 0000000..7549952
--- /dev/null
+++ b/src/libqhullr/io_r.h
@@ -0,0 +1,159 @@
+/*
  ---------------------------------
+
+   io.h
+   declarations of Input/Output functions
+
+   see README, libqhull.h and io.c
+
+   Copyright (c) 1993-2012 The Geometry Center.
+   $Id: //main/2011/qhull/src/libqhullr/io_r.h#1 $$Change: 1640 $
+   $DateTime: 2014/01/15 09:12:08 $$Author: bbarber $
+*/
+
+#ifndef qhDEFio
+#define qhDEFio 1
+
+#include "libqhull.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
+*/
+typedef void (*printvridgeT)(FILE *fp, vertexT *vertex, vertexT *vertexA, setT *centers, boolT unbounded);
+
+/*============== -prototypes in alphabetical order =========*/
+
+void    dfacet(unsigned id);
+void    dvertex(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 used */
+void    qh_copyfilename(char *filename, int size, const char* source, int length);
+void    qh_countfacets(facetT *facetlist, setT *facets, boolT printall,
+              int *numfacetsp, int *numsimplicialp, int *totneighborsp,
+              int *numridgesp, int *numcoplanarsp, int *numnumtricoplanarsp);
+pointT *qh_detvnorm(vertexT *vertex, vertexT *vertexA, setT *centers, realT *offsetp);
+setT   *qh_detvridge(vertexT *vertex);
+setT   *qh_detvridge3 (vertexT *atvertex, vertexT *vertex);
+int     qh_eachvoronoi(FILE *fp, printvridgeT printvridge, vertexT *atvertex, boolT visitall, qh_RIDGE innerouter, boolT inorder);
+int     qh_eachvoronoi_all(FILE *fp, printvridgeT printvridge, boolT isUpper, qh_RIDGE innerouter, boolT inorder);
+void    qh_facet2point(facetT *facet, pointT **point0, pointT **point1, realT *mindist);
+setT   *qh_facetvertices(facetT *facetlist, setT *facets, boolT allfacets);
+void    qh_geomplanes(facetT *facet, realT *outerplane, realT *innerplane);
+void    qh_markkeep(facetT *facetlist);
+setT   *qh_markvoronoi(facetT *facetlist, setT *facets, boolT printall, boolT *isLowerp, int *numcentersp);
+void    qh_order_vertexneighbors(vertexT *vertex);
+void    qh_prepare_output(void);
+void    qh_printafacet(FILE *fp, qh_PRINT format, facetT *facet, boolT printall);
+void    qh_printbegin(FILE *fp, qh_PRINT format, facetT *facetlist, setT *facets, boolT printall);
+void    qh_printcenter(FILE *fp, qh_PRINT format, const char *string, facetT *facet);
+void    qh_printcentrum(FILE *fp, facetT *facet, realT radius);
+void    qh_printend(FILE *fp, qh_PRINT format, facetT *facetlist, setT *facets, boolT printall);
+void    qh_printend4geom(FILE *fp, facetT *facet, int *num, boolT printall);
+void    qh_printextremes(FILE *fp, facetT *facetlist, setT *facets, boolT printall);
+void    qh_printextremes_2d(FILE *fp, facetT *facetlist, setT *facets, boolT printall);
+void    qh_printextremes_d(FILE *fp, facetT *facetlist, setT *facets, boolT printall);
+void    qh_printfacet(FILE *fp, facetT *facet);
+void    qh_printfacet2math(FILE *fp, facetT *facet, qh_PRINT format, int notfirst);
+void    qh_printfacet2geom(FILE *fp, facetT *facet, realT color[3]);
+void    qh_printfacet2geom_points(FILE *fp, pointT *point1, pointT *point2,
+                               facetT *facet, realT offset, realT color[3]);
+void    qh_printfacet3math(FILE *fp, facetT *facet, qh_PRINT format, int notfirst);
+void    qh_printfacet3geom_nonsimplicial(FILE *fp, facetT *facet, realT color[3]);
+void    qh_printfacet3geom_points(FILE *fp, setT *points, facetT *facet, realT offset, realT color[3]);
+void    qh_printfacet3geom_simplicial(FILE *fp, facetT *facet, realT color[3]);
+void    qh_printfacet3vertex(FILE *fp, facetT *facet, qh_PRINT format);
+void    qh_printfacet4geom_nonsimplicial(FILE *fp, facetT *facet, realT color[3]);
+void    qh_printfacet4geom_simplicial(FILE *fp, facetT *facet, realT color[3]);
+void    qh_printfacetNvertex_nonsimplicial(FILE *fp, facetT *facet, int id, qh_PRINT format);
+void    qh_printfacetNvertex_simplicial(FILE *fp, facetT *facet, qh_PRINT format);
+void    qh_printfacetheader(FILE *fp, facetT *facet);
+void    qh_printfacetridges(FILE *fp, facetT *facet);
+void    qh_printfacets(FILE *fp, qh_PRINT format, facetT *facetlist, setT *facets, boolT printall);
+void    qh_printhyperplaneintersection(FILE *fp, facetT *facet1, facetT *facet2,
+                   setT *vertices, realT color[3]);
+void    qh_printneighborhood(FILE *fp, qh_PRINT format, facetT *facetA, facetT *facetB, boolT printall);
+void    qh_printline3geom(FILE *fp, pointT *pointA, pointT *pointB, realT color[3]);
+void    qh_printpoint(FILE *fp, const char *string, pointT *point);
+void    qh_printpointid(FILE *fp, const char *string, int dim, pointT *point, int id);
+void    qh_printpoint3 (FILE *fp, pointT *point);
+void    qh_printpoints_out(FILE *fp, facetT *facetlist, setT *facets, boolT printall);
+void    qh_printpointvect(FILE *fp, pointT *point, coordT *normal, pointT *center, realT radius, realT color[3]);
+void    qh_printpointvect2 (FILE *fp, pointT *point, coordT *normal, pointT *center, realT radius);
+void    qh_printridge(FILE *fp, ridgeT *ridge);
+void    qh_printspheres(FILE *fp, setT *vertices, realT radius);
+void    qh_printvdiagram(FILE *fp, qh_PRINT format, facetT *facetlist, setT *facets, boolT printall);
+int     qh_printvdiagram2 (FILE *fp, printvridgeT printvridge, setT *vertices, qh_RIDGE innerouter, boolT inorder);
+void    qh_printvertex(FILE *fp, vertexT *vertex);
+void    qh_printvertexlist(FILE *fp, const char* string, facetT *facetlist,
+                         setT *facets, boolT printall);
+void    qh_printvertices(FILE *fp, const char* string, setT *vertices);
+void    qh_printvneighbors(FILE *fp, facetT* facetlist, setT *facets, boolT printall);
+void    qh_printvoronoi(FILE *fp, qh_PRINT format, facetT *facetlist, setT *facets, boolT printall);
+void    qh_printvnorm(FILE *fp, vertexT *vertex, vertexT *vertexA, setT *centers, boolT unbounded);
+void    qh_printvridge(FILE *fp, vertexT *vertex, vertexT *vertexA, setT *centers, boolT unbounded);
+void    qh_produce_output(void);
+void    qh_produce_output2(void);
+void    qh_projectdim3 (pointT *source, pointT *destination);
+int     qh_readfeasible(int dim, const char *curline);
+coordT *qh_readpoints(int *numpoints, int *dimension, boolT *ismalloc);
+void    qh_setfeasible(int dim);
+boolT   qh_skipfacet(facetT *facet);
+char   *qh_skipfilename(char *filename);
+
+#endif /* qhDEFio */
diff --git a/src/libqhullr/libqhull_r.c b/src/libqhullr/libqhull_r.c
new file mode 100644
index 0000000..2778f9c
--- /dev/null
+++ b/src/libqhullr/libqhull_r.c
@@ -0,0 +1,1401 @@
+/*
  ---------------------------------
+
+   libqhull.c
+   Quickhull algorithm for convex hulls
+
+   qhull() and top-level routines
+
+   see qh-qhull.htm, libqhull.h, unix.c
+
+   see qhull_a.h for internal functions
+
+   Copyright (c) 1993-2012 The Geometry Center.
+   $Id: //main/2011/qhull/src/libqhullr/libqhull_r.c#1 $$Change: 1640 $
+   $DateTime: 2014/01/15 09:12:08 $$Author: bbarber $
+*/
+
+#include "qhull_a.h"
+
+/*============= functions in alphabetic order after qhull() =======*/
+
+/*---------------------------------
+
+  qh_qhull()
+    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(void) {
+  int numoutside;
+
+  qh hulltime= qh_CPUclock;
+  if (qh RERUN || qh JOGGLEmax < REALmax/2)
+    qh_build_withrestart();
+  else {
+    qh_initbuild();
+    qh_buildhull();
+  }
+  if (!qh STOPpoint && !qh STOPcone) {
+    if (qh ZEROall_ok && !qh TESTvneighbors && qh MERGEexact)
+      qh_checkzero( qh_ALL);
+    if (qh ZEROall_ok && !qh TESTvneighbors && !qh WAScoplanar) {
+      trace2((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("First post-merge", qh premerge_centrum, qh premerge_cos,
+             (qh POSTmerge ? False : qh TESTvneighbors));
+      else if (!qh POSTmerge && qh TESTvneighbors)
+        qh_postmerge("For testing vertex neighbors", qh premerge_centrum,
+             qh premerge_cos, True);
+      if (qh POSTmerge)
+        qh_postmerge("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(/*visible_list, newfacet_list*/ !qh_ALL, &numoutside);
+        qh findbestnew= False;
+        qh_deletevisible(/*qh visible_list*/);
+        qh_resetlists(False, qh_RESETvisible /*qh visible_list newvertex_list newfacet_list */);
+      }
+    }
+    if (qh DOcheckmax){
+      if (qh REPORTfreq) {
+        qh_buildtracing(NULL, NULL);
+        qh_fprintf(qh ferr, 8115, "\nTesting all coplanar points.\n");
+      }
+      qh_check_maxout();
+    }
+    if (qh KEEPnearinside && !qh maxoutdone)
+      qh_nearcoplanar();
+  }
+  if (qh_setsize(qhmem.tempstack) != 0) {
+    qh_fprintf(qh ferr, 6164, "qhull internal error (qh_qhull): temporary sets not empty(%d)\n",
+             qh_setsize(qhmem.tempstack));
+    qh_errexit(qh_ERRqhull, NULL, NULL);
+  }
+  qh hulltime= qh_CPUclock - qh hulltime;
+  qh QHULLfinished= True;
+  trace1((qh ferr, 1036, "Qhull: algorithm completed\n"));
+} /* qhull */
+
+/*---------------------------------
+
+  qh_addpoint( 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(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(furthest) == -1)
+    qh_setappend(&qh other_points, furthest);
+  if (!facet) {
+    qh_fprintf(qh ferr, 6213, "qhull internal error (qh_addpoint): NULL facet.  Need to call qh_findbestfacet first\n");
+    qh_errexit(qh_ERRqhull, NULL, NULL);
+  }
+  if (checkdist) {
+    facet= qh_findbest(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(furthest, facet, &dist);
+      return True;
+    }
+  }
+  qh_buildtracing(furthest, facet);
+  if (qh STOPpoint < 0 && qh furthest_id == -qh STOPpoint-1) {
+    facet->notfurthest= True;
+    return False;
+  }
+  qh_findhorizon(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(False, qh_RESETvisible /*qh visible_list newvertex_list newfacet_list */);
+    return True;
+  }
+  zzinc_(Zprocessed);
+  firstnew= qh facet_id;
+  vertex= qh_makenewfacets(furthest /*visible_list, attaches if !ONLYgood */);
+  qh_makenewplanes(/* 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 newfacet_list, goodhorizon) && !qh GOODclosest) {
+    FORALLnew_facets
+      qh_delfacet(newfacet);
+    qh_delvertex(vertex);
+    qh_resetlists(True, qh_RESETvisible /*qh visible_list newvertex_list newfacet_list */);
+    zinc_(Znotgoodnew);
+    facet->notfurthest= True;
+    return True;
+  }
+  if (qh ONLYgood)
+    qh_attachnewfacets(/*visible_list*/);
+  qh_matchnewfacets();
+  qh_updatevertices();
+  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(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(/*visible_list, newfacet_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 visible_list*/);
+  zmax_(Zmaxvertex, qh num_vertices);
+  qh NEWfacets= False;
+  if (qh IStracing >= 4) {
+    if (qh num_facets < 2000)
+      qh_printlists();
+    qh_printfacetlist(qh newfacet_list, NULL, True);
+    qh_checkpolygon(qh facet_list);
+  }else if (qh CHECKfrequently) {
+    if (qh num_facets < 50)
+      qh_checkpolygon(qh facet_list);
+    else
+      qh_checkpolygon(qh newfacet_list);
+  }
+  if (qh STOPpoint > 0 && qh furthest_id == qh STOPpoint-1)
+    return False;
+  qh_resetlists(True, qh_RESETvisible /*qh visible_list newvertex_list newfacet_list */);
+  /* qh_triangulate(); to test qh.TRInormals */
+  trace2((qh ferr, 2056, "qh_addpoint: added p%d new facets %d new balance %2.2g point balance %2.2g\n",
+    qh_pointid(furthest), numnew, newbalance, pbalance));
+  return True;
+} /* addpoint */
+
+/*---------------------------------
+
+  qh_build_withrestart()
+    allow restarts due to qh.JOGGLEmax while calling qh_buildhull()
+    qh.FIRSTpoint/qh.NUMpoints is point array
+        it may be moved by qh_joggleinput()
+*/
+void qh_build_withrestart(void) {
+  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 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_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(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("_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;
+      }
+      qhmem.IStracing= qh IStracing;
+    }
+    if (qh JOGGLEmax < REALmax/2)
+      qh_joggleinput();
+    qh_initbuild();
+    qh_buildhull();
+    if (qh JOGGLEmax < REALmax/2 && !qh MERGING)
+      qh_checkconvex(qh facet_list, qh_ALGORITHMfault);
+  }
+  qh ALLOWrestart= False;
+} /* qh_build_withrestart */
+
+/*---------------------------------
+
+  qh_buildhull()
+    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(void) {
+  facetT *facet;
+  pointT *furthest;
+  vertexT *vertex;
+  int id;
+
+  trace1((qh ferr, 1037, "qh_buildhull: start build hull\n"));
+  FORALLfacets {
+    if (facet->visible || facet->newfacet) {
+      qh_fprintf(qh ferr, 6165, "qhull internal error (qh_buildhull): visible or new facet f%d in facet list\n",
+                   facet->id);
+      qh_errexit(qh_ERRqhull, facet, NULL);
+    }
+  }
+  FORALLvertices {
+    if (vertex->newlist) {
+      qh_fprintf(qh ferr, 6166, "qhull internal error (qh_buildhull): new vertex f%d in vertex list\n",
+                   vertex->id);
+      qh_errprint("ERRONEOUS", NULL, NULL, NULL, vertex);
+      qh_errexit(qh_ERRqhull, NULL, NULL);
+    }
+    id= qh_pointid(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 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(&facet))) {
+    qh num_outside--;  /* if ONLYmax, furthest may not be outside */
+    if (!qh_addpoint(furthest, facet, qh ONLYmax))
+      break;
+  }
+  if (qh NARROWhull) /* move points from outsideset to coplanarset */
+    qh_outcoplanar( /* facet_list */ );
+  if (qh num_outside && !furthest) {
+    qh_fprintf(qh ferr, 6167, "qhull internal error (qh_buildhull): %d outside points were never processed.\n", qh num_outside);
+    qh_errexit(qh_ERRqhull, NULL, NULL);
+  }
+  trace1((qh ferr, 1039, "qh_buildhull: completed the hull construction\n"));
+} /* buildhull */
+
+
+/*---------------------------------
+
+  qh_buildtracing( 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(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 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(furthest);
+  if (qh TRACEpoint == furthestid) {
+    qh IStracing= qh TRACElevel;
+    qhmem.IStracing= qh TRACElevel;
+  }else if (qh TRACEpoint != -1 && qh TRACEdist < REALmax/2) {
+    qh IStracing= 0;
+    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(furthest, facet, &dist);
+    qh_fprintf(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(furthest, facet, &dist);
+    qh_fprintf(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( 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(int exitcode, facetT *facet, facetT *otherfacet) {
+
+  qh_errprint("ERRONEOUS", facet, otherfacet, NULL, NULL);
+  qh_errexit(exitcode, NULL, NULL);
+} /* errexit2 */
+
+
+/*---------------------------------
+
+  qh_findhorizon( 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(pointT *point, facetT *facet, int *goodvisible, int *goodhorizon) {
+  facetT *neighbor, **neighborp, *visible;
+  int numhorizon= 0, coplanar= 0;
+  realT dist;
+
+  trace1((qh ferr, 1040,"qh_findhorizon: find horizon for point p%d facet f%d\n",qh_pointid(point),facet->id));
+  *goodvisible= *goodhorizon= 0;
+  zinc_(Ztotvisible);
+  qh_removefacet(facet);  /* visible_list at end of qh facet_list */
+  qh_appendfacet(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("visible", facet, NULL, NULL, NULL);
+  qh visit_id++;
+  FORALLvisible_facets {
+    if (visible->tricoplanar && !qh TRInormals) {
+      qh_fprintf(qh ferr, 6230, "Qhull internal error (qh_findhorizon): does not work for tricoplanar facets.  Use option 'Q11'\n");
+      qh_errexit(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(point, neighbor, &dist);
+      if (dist > qh MINvisible) {
+        zinc_(Ztotvisible);
+        qh_removefacet(neighbor);  /* append to end of qh visible_list */
+        qh_appendfacet(neighbor);
+        neighbor->visible= True;
+        neighbor->f.replace= NULL;
+        qh num_visible++;
+        if (neighbor->good)
+          (*goodvisible)++;
+        if (qh IStracing >=4)
+          qh_errprint("visible", neighbor, NULL, NULL, NULL);
+      }else {
+        if (dist > - qh MAXcoplanar) {
+          neighbor->coplanar= True;
+          zzinc_(Zcoplanarhorizon);
+          qh_precision("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 ferr, 2057, "qh_findhorizon: point p%d is coplanar to horizon f%d, dist=%2.7g < qh MINvisible(%2.7g)\n",
+              qh_pointid(point), neighbor->id, dist, qh MINvisible));
+        }else
+          neighbor->coplanar= False;
+        zinc_(Ztothorizon);
+        numhorizon++;
+        if (neighbor->good)
+          (*goodhorizon)++;
+        if (qh IStracing >=4)
+          qh_errprint("horizon", neighbor, NULL, NULL, NULL);
+      }
+    }
+  }
+  if (!numhorizon) {
+    qh_precision("empty horizon");
+    qh_fprintf(qh ferr, 6168, "qhull precision error (qh_findhorizon): empty horizon\n\
+QhullPoint p%d was above all facets.\n", qh_pointid(point));
+    qh_printfacetlist(qh facet_list, NULL, True);
+    qh_errexit(qh_ERRprec, NULL, NULL);
+  }
+  trace1((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();
+} /* findhorizon */
+
+/*---------------------------------
+
+  qh_nextfurthest( 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(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(&facet->outsideset);
+      qh facet_next= facet->next;
+      continue;
+    }
+    if (qh NARROWhull) {
+      if (facet->notfurthest)
+        qh_furthestout(facet);
+      furthest= (pointT*)qh_setlast(facet->outsideset);
+#if qh_COMPUTEfurthest
+      qh_distplane(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 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( 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(&facet->outsideset);
+          else if (size > idx) {
+            *visible= facet;
+            return((pointT*)qh_setdelnth(facet->outsideset, idx));
+          }else
+            idx -= size;
+        }
+      }
+      qh_fprintf(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_ERRqhull, NULL, NULL);
+    }else { /* VIRTUALmemory */
+      facet= qh facet_tail->previous;
+      if (!(furthest= (pointT*)qh_setdellast(facet->outsideset))) {
+        if (facet->outsideset)
+          qh_setfree(&facet->outsideset);
+        qh_removefacet(facet);
+        qh_prependfacet(facet, &qh facet_list);
+        continue;
+      }
+      *visible= facet;
+      return furthest;
+    }
+  }
+  return NULL;
+} /* nextfurthest */
+
+/*---------------------------------
+
+  qh_partitionall( 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(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 ferr, 1042, "qh_partitionall: partition all points into outside sets\n"));
+  pointset= qh_settemp(numpoints);
+  qh num_outside= 0;
+  pointp= SETaddr_(pointset, pointT);
+  for (i=numpoints, point= points; i--; point += qh hull_dim)
+    *(pointp++)= point;
+  qh_settruncate(pointset, numpoints);
+  FOREACHvertex_(vertices) {
+    if ((id= qh_pointid(vertex->point)) >= 0)
+      SETelem_(pointset, id)= NULL;
+  }
+  id= qh_pointid(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 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(size);
+      bestpoint= NULL;
+      point_end= 0;
+      FOREACHpoint_i_(pointset) {
+        if (point) {
+          zzinc_(Zpartitionall);
+          qh_distplane(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(&facet->outsideset, bestpoint);
+              bestpoint= point;
+              bestdist= dist;
+            }else
+              qh_setappend(&facet->outsideset, point);
+          }
+        }
+      }
+      if (bestpoint) {
+        qh_setappend(&facet->outsideset, bestpoint);
+#if !qh_COMPUTEfurthest
+        facet->furthestdist= bestdist;
+#endif
+      }else
+        qh_setfree(&facet->outsideset);
+      qh_settruncate(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_(pointset) {
+      if (point)
+        qh_partitionpoint(point, qh facet_list);
+    }
+    qh findbestnew= False;
+  }
+  zzadd_(Zpartitionall, zzval_(Zpartition));
+  zzval_(Zpartition)= 0;
+  qh_settempfree(&pointset);
+  if (qh IStracing >= 4)
+    qh_printfacetlist(qh facet_list, NULL, True);
+} /* partitionall */
+
+
+/*---------------------------------
+
+  qh_partitioncoplanar( 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(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(point, facet, &bestdist, qh_ALL, &isoutside, &numpart);
+    else
+      bestfacet= qh_findbest(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 ferr, 4062, "qh_partitioncoplanar: point p%d is more than near-inside facet f%d dist %2.2g findbestnew %d\n",
+                  qh_pointid(point), bestfacet->id, bestdist, qh findbestnew));
+          return;
+        }
+      }else if (bestdist < -qh MAXcoplanar) {
+          trace4((qh ferr, 4063, "qh_partitioncoplanar: point p%d is inside facet f%d dist %2.2g findbestnew %d\n",
+                  qh_pointid(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(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 ferr, 2058, "qh_partitioncoplanar: repartition point p%d from f%d.  It is above flipped facet f%d dist %2.2g\n",
+                qh_pointid(point), facet->id, bestfacet->id, bestdist));
+        oldfindbest= qh findbestnew;
+        qh findbestnew= False;
+        qh_partitionpoint(point, bestfacet);
+        qh findbestnew= oldfindbest;
+        return;
+      }
+    }
+    qh max_outside= bestdist;
+    if (bestdist > qh TRACEdist) {
+      qh_fprintf(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(point), facet->id, bestdist, bestfacet->id, qh furthest_id);
+      qh_errprint("DISTANT", facet, bestfacet, NULL, NULL);
+    }
+  }
+  if (qh KEEPcoplanar + qh KEEPinside + qh KEEPnearinside) {
+    oldfurthest= (pointT*)qh_setlast(bestfacet->coplanarset);
+    if (oldfurthest) {
+      zinc_(Zcomputefurthest);
+      qh_distplane(oldfurthest, bestfacet, &dist2);
+    }
+    if (!oldfurthest || dist2 < bestdist)
+      qh_setappend(&bestfacet->coplanarset, point);
+    else
+      qh_setappend2ndlast(&bestfacet->coplanarset, point);
+  }
+  trace4((qh ferr, 4064, "qh_partitioncoplanar: point p%d is coplanar with facet f%d(or inside) dist %2.2g\n",
+          qh_pointid(point), bestfacet->id, bestdist));
+} /* partitioncoplanar */
+
+/*---------------------------------
+
+  qh_partitionpoint( 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(pointT *point, facetT *facet) {
+  realT bestdist;
+  boolT isoutside;
+  facetT *bestfacet;
+  int numpart;
+#if qh_COMPUTEfurthest
+  realT dist;
+#endif
+
+  if (qh findbestnew)
+    bestfacet= qh_findbestnew(point, facet, &bestdist, qh BESToutside, &isoutside, &numpart);
+  else
+    bestfacet= qh_findbest(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("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(&(bestfacet->outsideset), point);
+      if (!bestfacet->newfacet) {
+        qh_removefacet(bestfacet);  /* make sure it's after qh facet_next */
+        qh_appendfacet(bestfacet);
+      }
+#if !qh_COMPUTEfurthest
+      bestfacet->furthestdist= bestdist;
+#endif
+    }else {
+#if qh_COMPUTEfurthest
+      zinc_(Zcomputefurthest);
+      qh_distplane(oldfurthest, bestfacet, &dist);
+      if (dist < bestdist)
+        qh_setappend(&(bestfacet->outsideset), point);
+      else
+        qh_setappend2ndlast(&(bestfacet->outsideset), point);
+#else
+      if (bestfacet->furthestdist < bestdist) {
+        qh_setappend(&(bestfacet->outsideset), point);
+        bestfacet->furthestdist= bestdist;
+      }else
+        qh_setappend2ndlast(&(bestfacet->outsideset), point);
+#endif
+    }
+    qh num_outside++;
+    trace4((qh ferr, 4065, "qh_partitionpoint: point p%d is outside facet f%d new? %d (or narrowhull)\n",
+          qh_pointid(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("nearly incident point");
+    if ((qh KEEPcoplanar + qh KEEPnearinside) || bestdist > qh max_outside)
+      qh_partitioncoplanar(point, bestfacet, &bestdist);
+    else {
+      trace4((qh ferr, 4066, "qh_partitionpoint: point p%d is coplanar to facet f%d (dropped)\n",
+          qh_pointid(point), bestfacet->id));
+    }
+  }else if (qh KEEPnearinside && bestdist > -qh NEARinside) {
+    zinc_(Zpartnear);
+    qh_partitioncoplanar(point, bestfacet, &bestdist);
+  }else {
+    zinc_(Zpartinside);
+    trace4((qh ferr, 4067, "qh_partitionpoint: point p%d is inside all facets, closest to f%d dist %2.2g\n",
+          qh_pointid(point), bestfacet->id, bestdist));
+    if (qh KEEPinside)
+      qh_partitioncoplanar(point, bestfacet, &bestdist);
+  }
+} /* partitionpoint */
+
+/*---------------------------------
+
+  qh_partitionvisible( 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(/*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(visible);
+    }
+    if (!newfacet)
+      newfacet= qh newfacet_list;
+    if (newfacet == qh facet_tail) {
+      qh_fprintf(qh ferr, 6170, "qhull precision error (qh_partitionvisible): all new facets deleted as\n        degenerate facets. Can not continue.\n");
+      qh_errexit(qh_ERRprec, NULL, NULL);
+    }
+    if (visible->outsideset) {
+      size= qh_setsize(visible->outsideset);
+      *numoutside += size;
+      qh num_outside -= size;
+      FOREACHpoint_(visible->outsideset)
+        qh_partitionpoint(point, newfacet);
+    }
+    if (visible->coplanarset && (qh KEEPcoplanar + qh KEEPinside + qh KEEPnearinside)) {
+      size= qh_setsize(visible->coplanarset);
+      coplanar += size;
+      FOREACHpoint_(visible->coplanarset) {
+        if (allpoints) /* not used */
+          qh_partitionpoint(point, newfacet);
+        else
+          qh_partitioncoplanar(point, newfacet, NULL);
+      }
+    }
+  }
+  FOREACHvertex_(qh del_vertices) {
+    if (vertex->point) {
+      if (allpoints) /* not used */
+        qh_partitionpoint(vertex->point, qh newfacet_list);
+      else
+        qh_partitioncoplanar(vertex->point, qh newfacet_list, NULL);
+    }
+  }
+  trace1((qh ferr, 1043,"qh_partitionvisible: partitioned %d points from outsidesets and %d points from coplanarsets\n", *numoutside, coplanar));
+} /* partitionvisible */
+
+
+
+/*---------------------------------
+
+  qh_precision( reason )
+    restart on precision errors if not merging and if 'QJn'
+*/
+void qh_precision(const char *reason) {
+
+  if (qh ALLOWrestart && !qh PREmerge && !qh MERGEexact) {
+    if (qh JOGGLEmax < REALmax/2) {
+      trace0((qh ferr, 26, "qh_precision: qhull restart because of %s\n", reason));
+      longjmp(qh restartexit, qh_ERRprec);
+    }
+  }
+} /* qh_precision */
+
+/*---------------------------------
+
+  qh_printsummary( fp )
+    prints summary to fp
+
+  notes:
+    not in io.c so that user_eg.c can prevent io.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(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 other_points);
+  numvertices= qh num_vertices - qh_setsize(qh del_vertices);
+  id= qh_pointid(qh GOODpointp);
+  FORALLfacets {
+    if (facet->coplanarset)
+      numcoplanars += qh_setsize( facet->coplanarset);
+    if (facet->good) {
+      if (facet->simplicial) {
+        if (facet->keepcentrum && facet->tricoplanar)
+          numtricoplanars++;
+      }else if (qh_setsize(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(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(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(fp, 9290, "\n\
+Voronoi diagram by the convex hull of %d points in %d-d:\n\n", size, qh hull_dim);
+    qh_fprintf(fp, 9291, "  Number of Voronoi regions%s: %d\n",
+              qh ATinfinity ? " and at-infinity" : "", numvertices);
+    if (numdel)
+      qh_fprintf(fp, 9292, "  Total number of deleted points due to merging: %d\n", numdel);
+    if (numcoplanars - numdel > 0)
+      qh_fprintf(fp, 9293, "  Number of nearly incident points: %d\n", numcoplanars - numdel);
+    else if (size - numvertices - numdel > 0)
+      qh_fprintf(fp, 9294, "  Total number of nearly incident points: %d\n", size - numvertices - numdel);
+    qh_fprintf(fp, 9295, "  Number of%s Voronoi vertices: %d\n",
+              goodused ? " 'good'" : "", qh num_good);
+    if (nonsimplicial)
+      qh_fprintf(fp, 9296, "  Number of%s non-simplicial Voronoi vertices: %d\n",
+              goodused ? " 'good'" : "", nonsimplicial);
+  }else if (qh DELAUNAY) {
+    if (qh UPPERdelaunay)
+      qh_fprintf(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(fp, 9298, "\n\
+Delaunay triangulation by the convex hull of %d points in %d-d:\n\n", size, qh hull_dim);
+    qh_fprintf(fp, 9299, "  Number of input sites%s: %d\n",
+              qh ATinfinity ? " and at-infinity" : "", numvertices);
+    if (numdel)
+      qh_fprintf(fp, 9300, "  Total number of deleted points due to merging: %d\n", numdel);
+    if (numcoplanars - numdel > 0)
+      qh_fprintf(fp, 9301, "  Number of nearly incident points: %d\n", numcoplanars - numdel);
+    else if (size - numvertices - numdel > 0)
+      qh_fprintf(fp, 9302, "  Total number of nearly incident points: %d\n", size - numvertices - numdel);
+    qh_fprintf(fp, 9303, "  Number of%s Delaunay regions: %d\n",
+              goodused ? " 'good'" : "", qh num_good);
+    if (nonsimplicial)
+      qh_fprintf(fp, 9304, "  Number of%s non-simplicial Delaunay regions: %d\n",
+              goodused ? " 'good'" : "", nonsimplicial);
+  }else if (qh HALFspace) {
+    qh_fprintf(fp, 9305, "\n\
+Halfspace intersection by the convex hull of %d points in %d-d:\n\n", size, qh hull_dim);
+    qh_fprintf(fp, 9306, "  Number of halfspaces: %d\n", size);
+    qh_fprintf(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(fp, 9308, "  Number of %s halfspaces: %d\n", s, numcoplanars);
+    }
+    qh_fprintf(fp, 9309, "  Number of intersection points: %d\n", qh num_facets - qh num_visible);
+    if (goodused)
+      qh_fprintf(fp, 9310, "  Number of 'good' intersection points: %d\n", qh num_good);
+    if (nonsimplicial)
+      qh_fprintf(fp, 9311, "  Number of%s non-simplicial intersection points: %d\n",
+              goodused ? " 'good'" : "", nonsimplicial);
+  }else {
+    qh_fprintf(fp, 9312, "\n\
+Convex hull of %d points in %d-d:\n\n", size, qh hull_dim);
+    qh_fprintf(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(fp, 9314, "  Number of %s points: %d\n", s, numcoplanars);
+    }
+    qh_fprintf(fp, 9315, "  Number of facets: %d\n", qh num_facets - qh num_visible);
+    if (goodused)
+      qh_fprintf(fp, 9316, "  Number of 'good' facets: %d\n", qh num_good);
+    if (nonsimplicial)
+      qh_fprintf(fp, 9317, "  Number of%s non-simplicial facets: %d\n",
+              goodused ? " 'good'" : "", nonsimplicial);
+  }
+  if (numtricoplanars)
+      qh_fprintf(fp, 9318, "  Number of triangulated facets: %d\n", numtricoplanars);
+  qh_fprintf(fp, 9319, "\nStatistics for: %s | %s",
+                      qh rbox_command, qh qhull_command);
+  if (qh ROTATErandom != INT_MIN)
+    qh_fprintf(fp, 9320, " QR%d\n\n", qh ROTATErandom);
+  else
+    qh_fprintf(fp, 9321, "\n\n");
+  qh_fprintf(fp, 9322, "  Number of points processed: %d\n", zzval_(Zprocessed));
+  qh_fprintf(fp, 9323, "  Number of hyperplanes created: %d\n", zzval_(Zsetplane));
+  if (qh DELAUNAY)
+    qh_fprintf(fp, 9324, "  Number of facets in hull: %d\n", qh num_facets - qh num_visible);
+  qh_fprintf(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(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(fp, 9327, "  new facet standard deviation: %2.2g\n", stddev);
+  qh_fprintf(fp, 9328, "  average partition balance: %2.2g\n",
+          wval_(Wpbalance)/zval_(Zpbalance));
+  stddev= qh_stddev(zval_(Zpbalance), wval_(Wpbalance),
+                                 wval_(Wpbalance2), &ave);
+  qh_fprintf(fp, 9329, "  partition standard deviation: %2.2g\n", stddev);
+  }
+#endif
+  if (nummerged) {
+    qh_fprintf(fp, 9330,"  Number of distance tests for merging: %d\n",zzval_(Zbestdist)+
+          zzval_(Zcentrumtests)+zzval_(Zdistconvex)+zzval_(Zdistcheck)+
+          zzval_(Zdistzero));
+    qh_fprintf(fp, 9331,"  Number of distance tests for checking: %d\n",zzval_(Zcheckpart));
+    qh_fprintf(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(fp, 9333, "  CPU seconds to compute hull (after input): %2.4g\n", cpu);
+  }
+  if (qh RERUN) {
+    if (!qh PREmerge && !qh MERGEexact)
+      qh_fprintf(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(fp, 9335, "  After %d retries, input joggled by: %2.2g\n",
+         zzval_(Zretry), qh JOGGLEmax);
+    else
+      qh_fprintf(fp, 9336, "  Input joggled by: %2.2g\n", qh JOGGLEmax);
+  }
+  if (qh totarea != 0.0)
+    qh_fprintf(fp, 9337, "  %s facet area:   %2.8g\n",
+            zzval_(Ztotmerge) ? "Approximate" : "Total", qh totarea);
+  if (qh totvol != 0.0)
+    qh_fprintf(fp, 9338, "  %s volume:       %2.8g\n",
+            zzval_(Ztotmerge) ? "Approximate" : "Total", qh totvol);
+  if (qh MERGING) {
+    qh_outerinner(NULL, &outerplane, &innerplane);
+    if (outerplane > 2 * qh DISTround) {
+      qh_fprintf(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(fp, 9340, " (%.1fx)\n", ratio);
+      else
+        qh_fprintf(fp, 9341, "\n");
+    }
+    if (innerplane < -2 * qh DISTround) {
+      qh_fprintf(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(fp, 9343, " (%.1fx)\n", ratio);
+      else
+        qh_fprintf(fp, 9344, "\n");
+    }
+  }
+  qh_fprintf(fp, 9345, "\n");
+} /* printsummary */
+
+
diff --git a/src/libqhullr/libqhull_r.h b/src/libqhullr/libqhull_r.h
new file mode 100644
index 0000000..e2d61f2
--- /dev/null
+++ b/src/libqhullr/libqhull_r.h
@@ -0,0 +1,1100 @@
+/*
  ---------------------------------
+
+   libqhull.h
+   user-level header file for using qhull.a library
+
+   see qh-qhull.htm, qhull_a.h
+
+   Copyright (c) 1993-2012 The Geometry Center.
+   $Id: //main/2011/qhull/src/libqhullr/libqhull_r.h#1 $$Change: 1640 $
+   $DateTime: 2014/01/15 09:12:08 $$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 qh 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 */
+  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 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    dfacet( unsigned id);
+void    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/libqhullr/mem_r.c b/src/libqhullr/mem_r.c
new file mode 100644
index 0000000..6a36620
--- /dev/null
+++ b/src/libqhullr/mem_r.c
@@ -0,0 +1,543 @@
+/*
  ---------------------------------
+
+  mem.c
+    memory management routines for qhull
+
+  This is a standalone program.
+
+  To initialize memory:
+
+    qh_meminit(stderr);
+    qh_meminitbuffers(qh IStracing, qh_MEMalign, 7, qh_MEMbufsize,qh_MEMinitbuf);
+    qh_memsize((int)sizeof(facetT));
+    qh_memsize((int)sizeof(facetT));
+    ...
+    qh_memsetup();
+
+  To free up all memory buffers:
+    qh_memfreeshort(&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
+
+  Copyright (c) 1993-2012 The Geometry Center.
+  $Id: //main/2011/qhull/src/libqhullr/mem_r.c#1 $$Change: 1640 $
+  $DateTime: 2014/01/15 09:12:08 $$Author: bbarber $
+*/
+
+#include "mem.h"
+#include 
+#include 
+#include 
+
+#ifndef qhDEFlibqhull
+typedef struct ridgeT ridgeT;
+typedef struct facetT facetT;
+#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
+void    qh_errexit(int exitcode, facetT *, ridgeT *);
+void    qh_exit(int exitcode);
+void    qh_fprintf(FILE *fp, int msgcode, const char *fmt, ... );
+void    qh_free(void *mem);
+void   *qh_malloc(size_t size);
+#endif
+
+/*============ -global data structure ==============
+    see mem.h for definition
+*/
+
+qhmemT qhmem= {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};     /* remove "= {0}" if this causes a compiler error */
+
+#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( 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 < qhmem.LASTsize
+      if qhmem.freelists[size] non-empty
+        return first object on freelist
+      else
+        round up request to size of 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(int insize) {
+  void **freelistp, *newbuffer;
+  int idx, size, n;
+  int outsize, bufsize;
+  void *object;
+
+  if (insize<0) {
+      qh_fprintf(qhmem.ferr, 6235, "qhull error (qh_memalloc): negative request size (%d).  Did int overflow due to high-D?\n", insize); /* WARN64 */
+      qh_errexit(qhmem_ERRmem, NULL, NULL);
+  }
+  if (insize>=0 && insize <= qhmem.LASTsize) {
+    idx= qhmem.indextable[insize];
+    outsize= qhmem.sizetable[idx];
+    qhmem.totshort += outsize;
+    freelistp= qhmem.freelists+idx;
+    if ((object= *freelistp)) {
+      qhmem.cntquick++;
+      qhmem.totfree -= outsize;
+      *freelistp= *((void **)*freelistp);  /* replace freelist with next object */
+#ifdef qh_TRACEshort
+      n= qhmem.cntshort+qhmem.cntquick+qhmem.freeshort;
+      if (qhmem.IStracing >= 5)
+          qh_fprintf(qhmem.ferr, 8141, "qh_mem %p n %8d alloc quick: %d bytes (tot %d cnt %d)\n", object, n, outsize, qhmem.totshort, qhmem.cntshort+qhmem.cntquick-qhmem.freeshort);
+#endif
+      return(object);
+    }else {
+      qhmem.cntshort++;
+      if (outsize > qhmem .freesize) {
+        qhmem .totdropped += qhmem .freesize;
+        if (!qhmem.curbuffer)
+          bufsize= qhmem.BUFinit;
+        else
+          bufsize= qhmem.BUFsize;
+        if (!(newbuffer= qh_malloc((size_t)bufsize))) {
+          qh_fprintf(qhmem.ferr, 6080, "qhull error (qh_memalloc): insufficient memory to allocate short memory buffer (%d bytes)\n", bufsize);
+          qh_errexit(qhmem_ERRmem, NULL, NULL);
+        }
+        *((void **)newbuffer)= qhmem.curbuffer;  /* prepend newbuffer to curbuffer
+                                                    list */
+        qhmem.curbuffer= newbuffer;
+        size= (sizeof(void **) + qhmem.ALIGNmask) & ~qhmem.ALIGNmask;
+        qhmem.freemem= (void *)((char *)newbuffer+size);
+        qhmem.freesize= bufsize - size;
+        qhmem.totbuffer += bufsize - size; /* easier to check */
+        /* Periodically test totbuffer.  It matches at beginning and exit of every call */
+        n = qhmem.totshort + qhmem.totfree + qhmem.totdropped + qhmem.freesize - outsize;
+        if (qhmem.totbuffer != n) {
+            qh_fprintf(qhmem.ferr, 6212, "qh_memalloc internal error: short totbuffer %d != totshort+totfree... %d\n", qhmem.totbuffer, n);
+            qh_errexit(qhmem_ERRmem, NULL, NULL);
+        }
+      }
+      object= qhmem.freemem;
+      qhmem.freemem= (void *)((char *)qhmem.freemem + outsize);
+      qhmem.freesize -= outsize;
+      qhmem.totunused += outsize - insize;
+#ifdef qh_TRACEshort
+      n= qhmem.cntshort+qhmem.cntquick+qhmem.freeshort;
+      if (qhmem.IStracing >= 5)
+          qh_fprintf(qhmem.ferr, 8140, "qh_mem %p n %8d alloc short: %d bytes (tot %d cnt %d)\n", object, n, outsize, qhmem.totshort, qhmem.cntshort+qhmem.cntquick-qhmem.freeshort);
+#endif
+      return object;
+    }
+  }else {                     /* long allocation */
+    if (!qhmem.indextable) {
+      qh_fprintf(qhmem.ferr, 6081, "qhull internal error (qh_memalloc): qhmem has not been initialized.\n");
+      qh_errexit(qhmem_ERRqhull, NULL, NULL);
+    }
+    outsize= insize;
+    qhmem .cntlong++;
+    qhmem .totlong += outsize;
+    if (qhmem.maxlong < qhmem.totlong)
+      qhmem.maxlong= qhmem.totlong;
+    if (!(object= qh_malloc((size_t)outsize))) {
+      qh_fprintf(qhmem.ferr, 6082, "qhull error (qh_memalloc): insufficient memory to allocate %d bytes\n", outsize);
+      qh_errexit(qhmem_ERRmem, NULL, NULL);
+    }
+    if (qhmem.IStracing >= 5)
+      qh_fprintf(qhmem.ferr, 8057, "qh_mem %p n %8d alloc long: %d bytes (tot %d cnt %d)\n", object, qhmem.cntlong+qhmem.freelong, outsize, qhmem.totlong, qhmem.cntlong-qhmem.freelong);
+  }
+  return(object);
+} /* memalloc */
+
+
+/*----------------------------------
+
+  qh_memfree( 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 <= qhmem.LASTsize
+      append object to corresponding freelist
+    else
+      call qh_free(object)
+*/
+void qh_memfree(void *object, int insize) {
+  void **freelistp;
+  int idx, outsize;
+
+  if (!object)
+    return;
+  if (insize <= qhmem.LASTsize) {
+    qhmem .freeshort++;
+    idx= qhmem.indextable[insize];
+    outsize= qhmem.sizetable[idx];
+    qhmem .totfree += outsize;
+    qhmem .totshort -= outsize;
+    freelistp= qhmem.freelists + idx;
+    *((void **)object)= *freelistp;
+    *freelistp= object;
+#ifdef qh_TRACEshort
+    idx= qhmem.cntshort+qhmem.cntquick+qhmem.freeshort;
+    if (qhmem.IStracing >= 5)
+        qh_fprintf(qhmem.ferr, 8142, "qh_mem %p n %8d free short: %d bytes (tot %d cnt %d)\n", object, idx, outsize, qhmem.totshort, qhmem.cntshort+qhmem.cntquick-qhmem.freeshort);
+#endif
+  }else {
+    qhmem .freelong++;
+    qhmem .totlong -= insize;
+    qh_free(object);
+    if (qhmem.IStracing >= 5)
+      qh_fprintf(qhmem.ferr, 8058, "qh_mem %p n %8d free long: %d bytes (tot %d cnt %d)\n", object, qhmem.cntlong+qhmem.freelong, insize, qhmem.totlong, qhmem.cntlong-qhmem.freelong);
+  }
+} /* memfree */
+
+
+/*---------------------------------
+
+  qh_memfreeshort( curlong, totlong )
+    frees up all short and qhmem memory allocations
+
+  returns:
+    number and size of current long allocations
+
+  see:
+    qh_freeqhull(allMem)
+    qh_memtotal(curlong, totlong, curshort, totshort, maxlong, totbuffer);
+*/
+void qh_memfreeshort(int *curlong, int *totlong) {
+  void *buffer, *nextbuffer;
+  FILE *ferr;
+
+  *curlong= qhmem .cntlong - qhmem .freelong;
+  *totlong= qhmem .totlong;
+  for (buffer= qhmem.curbuffer; buffer; buffer= nextbuffer) {
+    nextbuffer= *((void **) buffer);
+    qh_free(buffer);
+  }
+  qhmem.curbuffer= NULL;
+  if (qhmem .LASTsize) {
+    qh_free(qhmem .indextable);
+    qh_free(qhmem .freelists);
+    qh_free(qhmem .sizetable);
+  }
+  ferr= qhmem.ferr;
+  memset((char *)&qhmem, 0, sizeof(qhmem));  /* every field is 0, FALSE, NULL */
+  qhmem.ferr= ferr;
+} /* memfreeshort */
+
+
+/*----------------------------------
+
+  qh_meminit( ferr )
+    initialize qhmem and test sizeof( void*)
+*/
+void qh_meminit(FILE *ferr) {
+
+  memset((char *)&qhmem, 0, sizeof(qhmem));  /* every field is 0, FALSE, NULL */
+  qhmem.ferr= ferr;
+  if (sizeof(void*) < sizeof(int)) {
+    qh_fprintf(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(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( 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(int tracelevel, int alignment, int numsizes, int bufsize, int bufinit) {
+
+  qhmem.IStracing= tracelevel;
+  qhmem.NUMsizes= numsizes;
+  qhmem.BUFsize= bufsize;
+  qhmem.BUFinit= bufinit;
+  qhmem.ALIGNmask= alignment-1;
+  if (qhmem.ALIGNmask & ~qhmem.ALIGNmask) {
+    qh_fprintf(qhmem.ferr, 6085, "qhull internal error (qh_meminit): memory alignment %d is not a power of 2\n", alignment);
+    qh_errexit(qhmem_ERRqhull, NULL, NULL);
+  }
+  qhmem.sizetable= (int *) calloc((size_t)numsizes, sizeof(int));
+  qhmem.freelists= (void **) calloc((size_t)numsizes, sizeof(void *));
+  if (!qhmem.sizetable || !qhmem.freelists) {
+    qh_fprintf(qhmem.ferr, 6086, "qhull error (qh_meminit): insufficient memory\n");
+    qh_errexit(qhmem_ERRmem, NULL, NULL);
+  }
+  if (qhmem.IStracing >= 1)
+    qh_fprintf(qhmem.ferr, 8059, "qh_meminitbuffers: memory initialized with alignment %d\n", alignment);
+} /* meminitbuffers */
+
+/*---------------------------------
+
+  qh_memsetup()
+    set up memory after running memsize()
+*/
+void qh_memsetup(void) {
+  int k,i;
+
+  qsort(qhmem.sizetable, (size_t)qhmem.TABLEsize, sizeof(int), qh_intcompare);
+  qhmem.LASTsize= qhmem.sizetable[qhmem.TABLEsize-1];
+  if (qhmem .LASTsize >= qhmem .BUFsize || qhmem.LASTsize >= qhmem .BUFinit) {
+    qh_fprintf(qhmem.ferr, 6087, "qhull error (qh_memsetup): largest mem size %d is >= buffer size %d or initial buffer size %d\n",
+            qhmem .LASTsize, qhmem .BUFsize, qhmem .BUFinit);
+    qh_errexit(qhmem_ERRmem, NULL, NULL);
+  }
+  if (!(qhmem.indextable= (int *)qh_malloc((qhmem.LASTsize+1) * sizeof(int)))) {
+    qh_fprintf(qhmem.ferr, 6088, "qhull error (qh_memsetup): insufficient memory\n");
+    qh_errexit(qhmem_ERRmem, NULL, NULL);
+  }
+  for (k=qhmem.LASTsize+1; k--; )
+    qhmem.indextable[k]= k;
+  i= 0;
+  for (k=0; k <= qhmem.LASTsize; k++) {
+    if (qhmem.indextable[k] <= qhmem.sizetable[i])
+      qhmem.indextable[k]= i;
+    else
+      qhmem.indextable[k]= ++i;
+  }
+} /* memsetup */
+
+/*---------------------------------
+
+  qh_memsize( size )
+    define a free list for this size
+*/
+void qh_memsize(int size) {
+  int k;
+
+  if (qhmem .LASTsize) {
+    qh_fprintf(qhmem.ferr, 6089, "qhull error (qh_memsize): called after qhmem_setup\n");
+    qh_errexit(qhmem_ERRqhull, NULL, NULL);
+  }
+  size= (size + qhmem.ALIGNmask) & ~qhmem.ALIGNmask;
+  for (k=qhmem.TABLEsize; k--; ) {
+    if (qhmem.sizetable[k] == size)
+      return;
+  }
+  if (qhmem.TABLEsize < qhmem.NUMsizes)
+    qhmem.sizetable[qhmem.TABLEsize++]= size;
+  else
+    qh_fprintf(qhmem.ferr, 7060, "qhull warning (memsize): free list table has room for only %d sizes\n", qhmem.NUMsizes);
+} /* memsize */
+
+
+/*---------------------------------
+
+  qh_memstatistics( fp )
+    print out memory statistics
+
+    Verifies that qhmem.totfree == sum of freelists
+*/
+void qh_memstatistics(FILE *fp) {
+  int i, count, totfree= 0;
+  void *object;
+
+  for (i=0; i < qhmem.TABLEsize; i++) {
+    count=0;
+    for (object= qhmem .freelists[i]; object; object= *((void **)object))
+      count++;
+    totfree += qhmem.sizetable[i] * count;
+  }
+  if (totfree != qhmem .totfree) {
+      qh_fprintf(qhmem.ferr, 6211, "qh_memstatistics internal error: totfree %d not equal to freelist total %d\n", qhmem.totfree, totfree);
+      qh_errexit(qhmem_ERRqhull, NULL, NULL);
+  }
+  qh_fprintf(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",
+           qhmem .cntquick, qhmem .cntshort, qhmem .cntlong,
+           qhmem .freeshort, qhmem .freelong,
+           qhmem .totshort, qhmem .totfree,
+           qhmem .totdropped + qhmem .freesize, qhmem .totunused,
+           qhmem .maxlong, qhmem .totlong, qhmem .cntlong - qhmem .freelong,
+           qhmem .totbuffer, qhmem .BUFsize, qhmem .BUFinit);
+  if (qhmem.cntlarger) {
+    qh_fprintf(fp, 9279, "%7d calls to qh_setlarger\n%7.2g     average copy size\n",
+           qhmem.cntlarger, ((float)qhmem.totlarger)/(float)qhmem.cntlarger);
+    qh_fprintf(fp, 9280, "  freelists(bytes->count):");
+  }
+  for (i=0; i < qhmem.TABLEsize; i++) {
+    count=0;
+    for (object= qhmem .freelists[i]; object; object= *((void **)object))
+      count++;
+    qh_fprintf(fp, 9281, " %d->%d", qhmem.sizetable[i], count);
+  }
+  qh_fprintf(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(int insize) {
+  void *object;
+
+  if (!(object= qh_malloc((size_t)insize))) {
+    qh_fprintf(qhmem.ferr, 6090, "qhull error (qh_memalloc): insufficient memory\n");
+    qh_errexit(qhmem_ERRmem, NULL, NULL);
+  }
+  qhmem .cntlong++;
+  qhmem .totlong += insize;
+  if (qhmem.maxlong < qhmem.totlong)
+      qhmem.maxlong= qhmem.totlong;
+  if (qhmem.IStracing >= 5)
+    qh_fprintf(qhmem.ferr, 8060, "qh_mem %p n %8d alloc long: %d bytes (tot %d cnt %d)\n", object, qhmem.cntlong+qhmem.freelong, insize, qhmem.totlong, qhmem.cntlong-qhmem.freelong);
+  return object;
+}
+
+void qh_memfree(void *object, int insize) {
+
+  if (!object)
+    return;
+  qh_free(object);
+  qhmem .freelong++;
+  qhmem .totlong -= insize;
+  if (qhmem.IStracing >= 5)
+    qh_fprintf(qhmem.ferr, 8061, "qh_mem %p n %8d free long: %d bytes (tot %d cnt %d)\n", object, qhmem.cntlong+qhmem.freelong, insize, qhmem.totlong, qhmem.cntlong-qhmem.freelong);
+}
+
+void qh_memfreeshort(int *curlong, int *totlong) {
+  *totlong= qhmem .totlong;
+  *curlong= qhmem .cntlong - qhmem .freelong;
+  memset((char *)&qhmem, 0, sizeof(qhmem));  /* every field is 0, FALSE, NULL */
+}
+
+void qh_meminit(FILE *ferr) {
+
+  memset((char *)&qhmem, 0, sizeof(qhmem));  /* every field is 0, FALSE, NULL */
+  qhmem.ferr= ferr;
+  if (sizeof(void*) < sizeof(int)) {
+    qh_fprintf(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(qhmem_ERRqhull, NULL, NULL);
+  }
+}
+
+void qh_meminitbuffers(int tracelevel, int alignment, int numsizes, int bufsize, int bufinit) {
+
+  qhmem.IStracing= tracelevel;
+}
+
+void qh_memsetup(void) {
+
+}
+
+void qh_memsize(int size) {
+
+}
+
+void qh_memstatistics(FILE *fp) {
+
+  qh_fprintf(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",
+           qhmem .cntlong,
+           qhmem .freelong,
+           qhmem .maxlong, qhmem .totlong, qhmem .cntlong - qhmem .freelong);
+}
+
+#endif /* qh_NOmem */
+
+/*---------------------------------
+
+  qh_memtotal( 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)
+*/
+void qh_memtotal(int *totlong, int *curlong, int *totshort, int *curshort, int *maxlong, int *totbuffer) {
+    *totlong= qhmem .totlong;
+    *curlong= qhmem .cntlong - qhmem .freelong;
+    *totshort= qhmem .totshort;
+    *curshort= qhmem .cntshort + qhmem .cntquick - qhmem .freeshort;
+    *maxlong= qhmem .maxlong;
+    *totbuffer= qhmem .totbuffer;
+} /* memtotlong */
+
diff --git a/src/libqhullr/mem_r.h b/src/libqhullr/mem_r.h
new file mode 100644
index 0000000..eec2845
--- /dev/null
+++ b/src/libqhullr/mem_r.h
@@ -0,0 +1,219 @@
+/*
  ---------------------------------
+
+   mem.h
+     prototypes for memory management functions
+
+   see qh-mem.htm, mem.c and qset.h
+
+   for error handling, writes message and calls
+     qh_errexit(qhmem_ERRmem, NULL, NULL) if insufficient memory
+       and
+     qh_errexit(qhmem_ERRqhull, NULL, NULL) otherwise
+
+   Copyright (c) 1993-2012 The Geometry Center.
+   $Id: //main/2011/qhull/src/libqhullr/mem_r.h#1 $$Change: 1640 $
+   $DateTime: 2014/01/15 09:12:08 $$Author: bbarber $
+*/
+
+#ifndef qhDEFmem
+#define qhDEFmem 1
+
+#include 
+
+/*---------------------------------
+
+  qh_NOmem
+    turn off quick-fit memory allocation
+
+  notes:
+    mem.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
+    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 */
+
+/*----------------------------------
+
+  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)
+
+  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*'
+    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
+
+ notes:
+   users should ignore qhmem except for writing extensions
+   qhmem is allocated in mem.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 qhmem.
+*/
+typedef struct qhmemT qhmemT;
+extern qhmemT qhmem;
+
+#ifndef DEFsetT
+#define DEFsetT 1
+typedef struct setT setT;          /* defined in qset.h */
+#endif
+
+/* Update qhmem in mem.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, only user is qh_fprintf() */
+  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_(insize, object, type)
+    returns object of size bytes
+        assumes size<=qhmem.LASTsize and void **freelistp is a temp
+*/
+
+#if defined qh_NOmem
+#define qh_memalloc_(insize, freelistp, object, type) {\
+  object= (type*)qh_memalloc(insize); }
+#elif defined qh_TRACEshort
+#define qh_memalloc_(insize, freelistp, object, type) {\
+    freelistp= NULL; /* Avoid warnings */ \
+    object= (type*)qh_memalloc(insize); }
+#else /* !qh_NOmem */
+
+#define qh_memalloc_(insize, freelistp, object, type) {\
+  freelistp= qhmem.freelists + qhmem.indextable[insize];\
+  if ((object= (type*)*freelistp)) {\
+    qhmem.totshort += qhmem.sizetable[qhmem.indextable[insize]]; \
+    qhmem.totfree -= qhmem.sizetable[qhmem.indextable[insize]]; \
+    qhmem.cntquick++;  \
+    *freelistp= *((void **)*freelistp);\
+  }else object= (type*)qh_memalloc(insize);}
+#endif
+
+/*----------------------------------
+
+  qh_memfree_(object, insize)
+    free up an object
+
+  notes:
+    object may be NULL
+    assumes size<=qhmem.LASTsize and void **freelistp is a temp
+*/
+#if defined qh_NOmem
+#define qh_memfree_(object, insize, freelistp) {\
+  qh_memfree(object, insize); }
+#elif defined qh_TRACEshort
+#define qh_memfree_(object, insize, freelistp) {\
+    freelistp= NULL; /* Avoid warnings */ \
+    qh_memfree(object, insize); }
+#else /* !qh_NOmem */
+
+#define qh_memfree_(object, insize, freelistp) {\
+  if (object) { \
+    qhmem .freeshort++;\
+    freelistp= qhmem.freelists + qhmem.indextable[insize];\
+    qhmem.totshort -= qhmem.sizetable[qhmem.indextable[insize]]; \
+    qhmem.totfree += qhmem.sizetable[qhmem.indextable[insize]]; \
+    *((void **)object)= *freelistp;\
+    *freelistp= object;}}
+#endif
+
+/*=============== prototypes in alphabetical order ============*/
+
+void *qh_memalloc(int insize);
+void qh_memfree(void *object, int insize);
+void qh_memfreeshort(int *curlong, int *totlong);
+void qh_meminit(FILE *ferr);
+void qh_meminitbuffers(int tracelevel, int alignment, int numsizes,
+                        int bufsize, int bufinit);
+void qh_memsetup(void);
+void qh_memsize(int size);
+void qh_memstatistics(FILE *fp);
+void qh_memtotal(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
new file mode 100644
index 0000000..45d286f
--- /dev/null
+++ b/src/libqhullr/merge_r.c
@@ -0,0 +1,3623 @@
+/*
  ---------------------------------
+
+   merge.c
+   merges non-convex facets
+
+   see qh-merge.htm and merge.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):
+     qh_partitionvisible(!qh_ALL, &numoutside);  // visible_list, newfacet_list
+     qh_deletevisible();         // qh.visible_list
+     qh_resetlists(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) 1993-2012 C.B. Barber.
+   $Id: //main/2011/qhull/src/libqhullr/merge_r.c#1 $$Change: 1640 $
+   $DateTime: 2014/01/15 09:12:08 $$Author: bbarber $
+*/
+
+#include "qhull_a.h"
+
+#ifndef qh_NOmerge
+
+/*===== functions(alphabetical after premerge and postmerge) ======*/
+
+/*---------------------------------
+
+  qh_premerge( 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(vertexT *apex, realT maxcentrum, realT maxangle) {
+  boolT othermerge= False;
+  facetT *newfacet;
+
+  if (qh ZEROcentrum && qh_checkzero(!qh_ALL))
+    return;
+  trace2((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 centrum_radius= maxcentrum;
+  qh cos_max= maxangle;
+  qh degen_mergeset= qh_settemp(qh TEMPsize);
+  qh facet_mergeset= qh_settemp(qh TEMPsize);
+  if (qh hull_dim >=3) {
+    qh_mark_dupridges(qh newfacet_list); /* facet_mergeset */
+    qh_mergecycle_all(qh newfacet_list, &othermerge);
+    qh_forcedmerges(&othermerge /* qh facet_mergeset */);
+    FORALLnew_facets {  /* test samecycle merges */
+      if (!newfacet->simplicial && !newfacet->mergeridge)
+        qh_degen_redundant_neighbors(newfacet, NULL);
+    }
+    if (qh_merge_degenredundant())
+      othermerge= True;
+  }else /* qh hull_dim == 2 */
+    qh_mergecycle_all(qh newfacet_list, &othermerge);
+  qh_flippedmerges(qh newfacet_list, &othermerge);
+  if (!qh MERGEexact || zzval_(Ztotmerge)) {
+    zinc_(Zpremergetot);
+    qh POSTmerging= False;
+    qh_getmergeset_initial(qh newfacet_list);
+    qh_all_merges(othermerge, False);
+  }
+  qh_settempfree(&qh facet_mergeset);
+  qh_settempfree(&qh degen_mergeset);
+} /* premerge */
+
+/*---------------------------------
+
+  qh_postmerge( 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(const char *reason, realT maxcentrum, realT maxangle,
+                      boolT vneighbors) {
+  facetT *newfacet;
+  boolT othermerges= False;
+  vertexT *vertex;
+
+  if (qh REPORTfreq || qh IStracing) {
+    qh_buildtracing(NULL, NULL);
+    qh_printsummary(qh ferr);
+    if (qh PRINTstatistics)
+      qh_printallstatistics(qh ferr, "reason");
+    qh_fprintf(qh ferr, 8062, "\n%s with 'C%.2g' and 'A%.2g'\n",
+        reason, maxcentrum, maxangle);
+  }
+  trace2((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 TEMPsize);
+  qh facet_mergeset= qh_settemp(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(); /* was skipped during pre-merging */
+      }
+    }
+    if (!qh PREmerge && !qh MERGEexact)
+      qh_flippedmerges(qh newfacet_list, &othermerges);
+  }
+  qh_getmergeset_initial(qh newfacet_list);
+  qh_all_merges(False, vneighbors);
+  qh_settempfree(&qh facet_mergeset);
+  qh_settempfree(&qh degen_mergeset);
+} /* post_merge */
+
+/*---------------------------------
+
+  qh_all_merges( 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(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 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 facet_mergeset)) {
+      while ((merge= (mergeT*)qh_setdellast(qh facet_mergeset))) {
+        facet1= merge->facet1;
+        facet2= merge->facet2;
+        mergetype= merge->type;
+        qh_memfree_(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(facet1, facet2, mergetype);
+        numdegenredun += qh_merge_degenredundant();
+        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();  /* otherwise large post merges too slow */
+      }
+      qh_getmergeset(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_getmergeset(qh newfacet_list); /* facet_mergeset */
+          continue;
+        }
+      }
+    }
+    if (vneighbors && qh_test_vneighbors(/* qh newfacet_list */))
+      continue;
+    break;
+  } /* while (True) */
+  if (qh CHECKfrequently && !qh MERGEexact) {
+    qh old_randomdist= qh RANDOMdist;
+    qh RANDOMdist= False;
+    qh_checkconvex(qh newfacet_list, qh_ALGORITHMfault);
+    /* qh_checkconnect(); [this is slow and it changes the facet order] */
+    qh RANDOMdist= qh old_randomdist;
+  }
+  trace1((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();
+} /* all_merges */
+
+
+/*---------------------------------
+
+  qh_appendmergeset( 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(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_((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 facet_mergeset), merge);
+  else if (mergetype == MRGdegen) {
+    facet->degenerate= True;
+    if (!(lastmerge= (mergeT*)qh_setlast(qh degen_mergeset))
+    || lastmerge->type == MRGdegen)
+      qh_setappend(&(qh degen_mergeset), merge);
+    else
+      qh_setaddnth(&(qh degen_mergeset), 0, merge);
+  }else if (mergetype == MRGredundant) {
+    facet->redundant= True;
+    qh_setappend(&(qh degen_mergeset), merge);
+  }else /* mergetype == MRGmirror */ {
+    if (facet->redundant || neighbor->redundant) {
+      qh_fprintf(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_ERRqhull, facet, neighbor);
+    }
+    if (!qh_setequal(facet->vertices, neighbor->vertices)) {
+      qh_fprintf(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_ERRqhull, facet, neighbor);
+    }
+    facet->redundant= True;
+    neighbor->redundant= True;
+    qh_setappend(&(qh degen_mergeset), merge);
+  }
+} /* appendmergeset */
+
+
+/*---------------------------------
+
+  qh_basevertices( 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(facetT *samecycle) {
+  facetT *same;
+  vertexT *apex, *vertex, **vertexp;
+  setT *vertices= qh_settemp(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(&vertices, vertex);
+        vertex->visitid= qh vertex_visit;
+        vertex->seen= False;
+      }
+    }
+  }
+  trace4((qh ferr, 4019, "qh_basevertices: found %d vertices\n",
+         qh_setsize(vertices)));
+  return vertices;
+} /* basevertices */
+
+/*---------------------------------
+
+  qh_checkconnect()
+    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(void /* qh newfacet_list */) {
+  facetT *facet, *newfacet, *errfacet= NULL, *neighbor, **neighborp;
+
+  facet= qh newfacet_list;
+  qh_removefacet(facet);
+  qh_appendfacet(facet);
+  facet->visitid= ++qh visit_id;
+  FORALLfacet_(facet) {
+    FOREACHneighbor_(facet) {
+      if (neighbor->visitid != qh visit_id) {
+        qh_removefacet(neighbor);
+        qh_appendfacet(neighbor);
+        neighbor->visitid= qh visit_id;
+      }
+    }
+  }
+  FORALLnew_facets {
+    if (newfacet->visitid == qh visit_id)
+      break;
+    qh_fprintf(qh ferr, 6094, "qhull error: f%d is not attached to the new facets\n",
+         newfacet->id);
+    errfacet= newfacet;
+  }
+  if (errfacet)
+    qh_errexit(qh_ERRqhull, errfacet, NULL);
+} /* checkconnect */
+
+/*---------------------------------
+
+  qh_checkzero( 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(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 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(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(vertex->point, facet, &dist);
+          if (dist >= -qh DISTround) {
+            qh ZEROall_ok= False;
+            if (!qh MERGEexact || dist > qh DISTround)
+              goto LABELnonconvex;
+          }
+          break;
+        }
+      }
+    }
+  }
+  trace2((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 ferr, 2013, "qh_checkzero: facet f%d needs pre-merging\n",
+       facet->id));
+  return False;
+
+ LABELnonconvex:
+  trace2((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( 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(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 ferr, 4020, "qh_copynonconvex: moved nonconvex flag from r%d to r%d\n",
+              atridge->id, ridge->id));
+      break;
+    }
+  }
+} /* copynonconvex */
+
+/*---------------------------------
+
+  qh_degen_redundant_facet( 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(facetT *facet) {
+  vertexT *vertex, **vertexp;
+  facetT *neighbor, **neighborp;
+
+  trace4((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(facet, neighbor, MRGredundant, NULL);
+      trace2((qh ferr, 2015, "qh_degen_redundant_facet: f%d is contained in f%d.  merge\n", facet->id, neighbor->id));
+      return;
+    }
+  }
+  if (qh_setsize(facet->neighbors) < qh hull_dim) {
+    qh_appendmergeset(facet, facet, MRGdegen, NULL);
+    trace2((qh ferr, 2016, "qh_degen_redundant_neighbors: f%d is degenerate.\n", facet->id));
+  }
+} /* degen_redundant_facet */
+
+
+/*---------------------------------
+
+  qh_degen_redundant_neighbors( 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(facetT *facet, facetT *delfacet) {
+  vertexT *vertex, **vertexp;
+  facetT *neighbor, **neighborp;
+  int size;
+
+  trace4((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(facet->neighbors)) < qh hull_dim) {
+    qh_appendmergeset(facet, facet, MRGdegen, NULL);
+    trace2((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(neighbor, facet, MRGredundant, NULL);
+      trace2((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(neighbor->neighbors)) < qh hull_dim) {
+      qh_appendmergeset(neighbor, neighbor, MRGdegen, NULL);
+      trace2((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( 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(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 ferr, 8063, "qh_find_newvertex: find new vertex for v%d from ",
+             oldvertex->id);
+    FOREACHvertex_(vertices)
+      qh_fprintf(qh ferr, 8064, "v%d ", vertex->id);
+    FOREACHridge_(ridges)
+      qh_fprintf(qh ferr, 8065, "r%d ", ridge->id);
+    qh_fprintf(qh ferr, 8066, "\n");
+  }
+#endif
+  FOREACHvertex_(vertices)
+    vertex->visitid= 0;
+  FOREACHridge_(ridges) {
+    FOREACHvertex_(ridge->vertices)
+      vertex->visitid++;
+  }
+  FOREACHvertex_(vertices) {
+    if (!vertex->visitid) {
+      qh_setdelnth(vertices, SETindex_(vertices,vertex));
+      vertexp--; /* repeat since deleted this vertex */
+    }
+  }
+  qh vertex_visit += (unsigned int)qh_setsize(ridges);
+  if (!qh_setsize(vertices)) {
+    trace4((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(vertices),
+                sizeof(vertexT *), qh_comparevisit);
+  /* can now use qh vertex_visit */
+  if (qh PRINTstatistics) {
+    size= qh_setsize(vertices);
+    zinc_(Zintersect);
+    zadd_(Zintersecttot, size);
+    zmax_(Zintersectmax, size);
+  }
+  hashsize= qh_newhashtable(qh_setsize(ridges));
+  FOREACHridge_(ridges)
+    qh_hashridge(qh hash_table, hashsize, ridge, oldvertex);
+  FOREACHvertex_(vertices) {
+    newridges= qh_vertexridges(vertex);
+    FOREACHridge_(newridges) {
+      if (qh_hashridge_find(qh hash_table, hashsize, ridge, vertex, oldvertex, &hash)) {
+        zinc_(Zdupridge);
+        break;
+      }
+    }
+    qh_settempfree(&newridges);
+    if (!ridge)
+      break;  /* found a rename */
+  }
+  if (vertex) {
+    /* counted in qh_renamevertex */
+    trace2((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(vertices), qh_setsize(ridges)));
+  }else {
+    zinc_(Zfindfail);
+    trace0((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 hash_table);
+  return vertex;
+} /* find_newvertex */
+
+/*---------------------------------
+
+  qh_findbest_test( 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(boolT testcentrum, facetT *facet, facetT *neighbor,
+      facetT **bestfacet, realT *distp, realT *mindistp, realT *maxdistp) {
+  realT dist, mindist, maxdist;
+
+  if (testcentrum) {
+    zzinc_(Zbestdist);
+    qh_distplane(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(facet, neighbor, &mindist, &maxdist);
+  if (dist < *distp) {
+    *bestfacet= neighbor;
+    *mindistp= mindist;
+    *maxdistp= maxdist;
+    *distp= dist;
+  }
+} /* findbest_test */
+
+/*---------------------------------
+
+  qh_findbestneighbor( 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(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(facet->vertices);
+
+  *distp= REALmax;
+  if (size > qh_BESTcentrum2 * qh hull_dim + qh_BESTcentrum) {
+    testcentrum= True;
+    zinc_(Zbestcentrum);
+    if (!facet->center)
+       facet->center= qh_getcentrum(facet);
+  }
+  if (size > qh hull_dim + qh_BESTnonconvex) {
+    FOREACHridge_(facet->ridges) {
+      if (ridge->nonconvex) {
+        neighbor= otherfacet_(ridge, facet);
+        qh_findbest_test(testcentrum, facet, neighbor,
+                          &bestfacet, distp, mindistp, maxdistp);
+      }
+    }
+  }
+  if (!bestfacet) {
+    nonconvex= False;
+    FOREACHneighbor_(facet)
+      qh_findbest_test(testcentrum, facet, neighbor,
+                        &bestfacet, distp, mindistp, maxdistp);
+  }
+  if (!bestfacet) {
+    qh_fprintf(qh ferr, 6095, "qhull internal error (qh_findbestneighbor): no neighbors for f%d\n", facet->id);
+
+    qh_errexit(qh_ERRqhull, facet, NULL);
+  }
+  if (testcentrum)
+    qh_getdistance(facet, bestfacet, mindistp, maxdistp);
+  trace3((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( 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(facetT *facetlist, boolT *wasmerge) {
+  facetT *facet, *neighbor, *facet1;
+  realT dist, mindist, maxdist;
+  mergeT *merge, **mergep;
+  setT *othermerges;
+  int nummerge=0;
+
+  trace4((qh ferr, 4024, "qh_flippedmerges: begin\n"));
+  FORALLfacet_(facetlist) {
+    if (facet->flipped && !facet->visible)
+      qh_appendmergeset(facet, facet, MRGflip, NULL);
+  }
+  othermerges= qh_settemppop(); /* was facet_mergeset */
+  qh facet_mergeset= qh_settemp(qh TEMPsize);
+  qh_settemppush(othermerges);
+  FOREACHmerge_(othermerges) {
+    facet1= merge->facet1;
+    if (merge->type != MRGflip || facet1->visible)
+      continue;
+    if (qh TRACEmerge-1 == zzval_(Ztotmerge))
+      qhmem.IStracing= qh IStracing= qh TRACElevel;
+    neighbor= qh_findbestneighbor(facet1, &dist, &mindist, &maxdist);
+    trace0((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(facet1, neighbor, &mindist, &maxdist, !qh_MERGEapex);
+    nummerge++;
+    if (qh PRINTstatistics) {
+      zinc_(Zflipped);
+      wadd_(Wflippedtot, dist);
+      wmax_(Wflippedmax, dist);
+    }
+    qh_merge_degenredundant();
+  }
+  FOREACHmerge_(othermerges) {
+    if (merge->facet1->visible || merge->facet2->visible)
+      qh_memfree(merge, (int)sizeof(mergeT));
+    else
+      qh_setappend(&qh facet_mergeset, merge);
+  }
+  qh_settempfree(&othermerges);
+  if (nummerge)
+    *wasmerge= True;
+  trace1((qh ferr, 1010, "qh_flippedmerges: merged %d flipped facets into a good neighbor\n", nummerge));
+} /* flippedmerges */
+
+
+/*---------------------------------
+
+  qh_forcedmerges( 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(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))
+    qhmem.IStracing= qh IStracing= qh TRACElevel;
+  trace4((qh ferr, 4025, "qh_forcedmerges: begin\n"));
+  othermerges= qh_settemppop(); /* was facet_mergeset */
+  qh facet_mergeset= qh_settemp(qh TEMPsize);
+  qh_settemppush(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 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_ERRqhull, facet1, facet2);
+    }
+    if (qh TRACEmerge-1 == zzval_(Ztotmerge))
+      qhmem.IStracing= qh IStracing= qh TRACElevel;
+    dist1= qh_getdistance(facet1, facet2, &mindist1, &maxdist1);
+    dist2= qh_getdistance(facet2, facet1, &mindist2, &maxdist2);
+    trace0((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(facet1, facet2, &mindist1, &maxdist1, !qh_MERGEapex);
+    else {
+      qh_mergefacet(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(merge, (int)sizeof(mergeT));
+    else
+      qh_setappend(&qh facet_mergeset, merge);
+  }
+  qh_settempfree(&othermerges);
+  if (nummerge)
+    *wasmerge= True;
+  trace1((qh ferr, 1011, "qh_forcedmerges: merged %d facets and %d flipped facets across duplicated ridges\n",
+                nummerge, numflip));
+} /* forcedmerges */
+
+
+/*---------------------------------
+
+  qh_getmergeset( 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(facetT *facetlist) {
+  facetT *facet, *neighbor, **neighborp;
+  ridgeT *ridge, **ridgep;
+  int nummerges;
+
+  nummerges= qh_setsize(qh facet_mergeset);
+  trace4((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(facet, neighbor))
+          ridge->nonconvex= True;
+      }
+    }
+  }
+  nummerges= qh_setsize(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 ferr, 2021, "qh_getmergeset: %d merges found\n", nummerges));
+} /* getmergeset */
+
+
+/*---------------------------------
+
+  qh_getmergeset_initial( 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(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(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 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 ferr, 2022, "qh_getmergeset_initial: %d merges found\n", nummerges));
+} /* getmergeset_initial */
+
+
+/*---------------------------------
+
+  qh_hashridge( 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(setT *hashtable, int hashsize, ridgeT *ridge, vertexT *oldvertex) {
+  int hash;
+  ridgeT *ridgeA;
+
+  hash= qh_gethash(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( 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(setT *hashtable, int hashsize, ridgeT *ridge,
+              vertexT *vertex, vertexT *oldvertex, int *hashslot) {
+  int hash;
+  ridgeT *ridgeA;
+
+  *hashslot= 0;
+  zinc_(Zhashridge);
+  hash= qh_gethash(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( 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(facetT *facet) {
+  facetT *neighbor, **neighborp;
+  ridgeT *ridge, **ridgep;
+  int neighbor_i, neighbor_n;
+  boolT toporient, mergeridge= False;
+
+  if (!facet->simplicial)
+    return;
+  trace4((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_(facet) {
+    if (neighbor == qh_MERGEridge)
+      continue;  /* fixed by qh_mark_dupridges */
+    else if (!neighbor->seen) {  /* no current ridges */
+      ridge= qh_newridge();
+      ridge->vertices= qh_setnew_delnthsorted(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(&(facet->ridges), ridge);
+      qh_setappend(&(neighbor->ridges), ridge);
+    }
+  }
+  if (mergeridge) {
+    while (qh_setdel(facet->neighbors, qh_MERGEridge))
+      ; /* delete each one */
+  }
+} /* makeridges */
+
+
+/*---------------------------------
+
+  qh_mark_dupridges( 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(facetT *facetlist) {
+  facetT *facet, *neighbor, **neighborp;
+  int nummerge=0;
+  mergeT *merge, **mergep;
+
+
+  trace4((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(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(facet);
+  }
+  FOREACHmerge_(qh facet_mergeset) {   /* restore the missing neighbors */
+    if (merge->type == MRGridge) {
+      qh_setappend(&merge->facet2->neighbors, merge->facet1);
+      qh_makeridges(merge->facet1);   /* and the missing ridges */
+    }
+  }
+  trace1((qh ferr, 1012, "qh_mark_dupridges: found %d duplicated ridges\n",
+                nummerge));
+} /* mark_dupridges */
+
+/*---------------------------------
+
+  qh_maydropneighbor( 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(facetT *facet) {
+  ridgeT *ridge, **ridgep;
+  realT angledegen= qh_ANGLEdegen;
+  facetT *neighbor, **neighborp;
+
+  qh visit_id++;
+  trace4((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 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(neighbor->neighbors) < qh hull_dim) {
+        zinc_(Zdropdegen);
+        qh_appendmergeset(neighbor, neighbor, MRGdegen, &angledegen);
+        trace2((qh ferr, 2023, "qh_maydropneighbors: f%d is degenerate.\n", neighbor->id));
+      }
+    }
+  }
+  if (qh_setsize(facet->neighbors) < qh hull_dim) {
+    zinc_(Zdropdegen);
+    qh_appendmergeset(facet, facet, MRGdegen, &angledegen);
+    trace2((qh ferr, 2024, "qh_maydropneighbors: f%d is degenerate.\n", facet->id));
+  }
+} /* maydropneighbor */
+
+
+/*---------------------------------
+
+  qh_merge_degenredundant()
+    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(void) {
+  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(merge, (int)sizeof(mergeT));
+    if (facet1->visible)
+      continue;
+    facet1->degenerate= False;
+    facet1->redundant= False;
+    if (qh TRACEmerge-1 == zzval_(Ztotmerge))
+      qhmem.IStracing= qh IStracing= qh TRACElevel;
+    if (mergetype == MRGredundant) {
+      zinc_(Zneighbor);
+      while (facet2->visible) {
+        if (!facet2->f.replace) {
+          qh_fprintf(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_ERRqhull, facet1, facet2);
+        }
+        facet2= facet2->f.replace;
+      }
+      if (facet1 == facet2) {
+        qh_degen_redundant_facet(facet1); /* in case of others */
+        continue;
+      }
+      trace2((qh ferr, 2025, "qh_merge_degenredundant: facet f%d is contained in f%d, will merge\n",
+            facet1->id, facet2->id));
+      qh_mergefacet(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(facet1->neighbors))) {
+        zinc_(Zdelfacetdup);
+        trace2((qh ferr, 2026, "qh_merge_degenredundant: facet f%d has no neighbors.  Deleted\n", facet1->id));
+        qh_willdelete(facet1, NULL);
+        FOREACHvertex_(facet1->vertices) {
+          qh_setdel(vertex->neighbors, facet1);
+          if (!SETfirst_(vertex->neighbors)) {
+            zinc_(Zdegenvertex);
+            trace2((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 del_vertices, vertex);
+          }
+        }
+        nummerges++;
+      }else if (size < qh hull_dim) {
+        bestneighbor= qh_findbestneighbor(facet1, &dist, &mindist, &maxdist);
+        trace2((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(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( 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(facetT *facet1, facetT *facet2, mergeType mergetype) {
+  facetT *bestfacet, *bestneighbor, *neighbor;
+  realT dist, dist2, mindist, mindist2, maxdist, maxdist2;
+
+  if (qh TRACEmerge-1 == zzval_(Ztotmerge))
+    qhmem.IStracing= qh IStracing= qh TRACElevel;
+  trace3((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(bestfacet, &dist, &mindist, &maxdist);
+  neighbor= qh_findbestneighbor(facet2, &dist2, &mindist2, &maxdist2);
+  if (dist < dist2) {
+    qh_mergefacet(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 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(bestfacet, bestneighbor, &mindist, &maxdist, !qh_MERGEapex);
+  }else {
+    qh_mergefacet(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( 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(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 ferr, 6224, "Qhull internal error (qh_mergecycle): does not work for tricoplanar facets.  Use option 'Q11'\n");
+      qh_errexit(qh_ERRqhull, newfacet, NULL);
+    }
+    newfacet->tricoplanar= False;
+    newfacet->keepcentrum= False;
+  }
+  if (!qh VERTEXneighbors)
+    qh_vertexneighbors();
+  zzinc_(Ztotmerge);
+  if (qh REPORTfreq2 && qh POSTmerging) {
+    if (zzval_(Ztotmerge) > qh mergereport + qh REPORTfreq2)
+      qh_tracemerging();
+  }
+#ifndef qh_NOtrace
+  if (qh TRACEmerge == zzval_(Ztotmerge))
+    qhmem.IStracing= qh IStracing= qh TRACElevel;
+  trace2((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 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 ferr, 8069, "  same cycle:");
+    FORALLsame_cycle_(samecycle)
+      qh_fprintf(qh ferr, 8070, " f%d", same->id);
+    qh_fprintf(qh ferr, 8071, "\n");
+  }
+  if (qh IStracing >=4)
+    qh_errprint("MERGING CYCLE", samecycle, newfacet, NULL, NULL);
+#endif /* !qh_NOtrace */
+  apex= SETfirstt_(samecycle->vertices, vertexT);
+  qh_makeridges(newfacet);
+  qh_mergecycle_neighbors(samecycle, newfacet);
+  qh_mergecycle_ridges(samecycle, newfacet);
+  qh_mergecycle_vneighbors(samecycle, newfacet);
+  if (SETfirstt_(newfacet->vertices, vertexT) != apex)
+    qh_setaddnth(&newfacet->vertices, 0, apex);  /* apex has last id */
+  if (!newfacet->newfacet)
+    qh_newvertices(newfacet->vertices);
+  qh_mergecycle_facets(samecycle, newfacet);
+  qh_tracemerge(samecycle, newfacet);
+  /* check for degen_redundant_neighbors after qh_forcedmerges() */
+  if (traceonce) {
+    qh_fprintf(qh ferr, 8072, "qh_mergecycle: end of trace facet\n");
+    qh IStracing= tracerestore;
+  }
+} /* mergecycle */
+
+/*---------------------------------
+
+  qh_mergecycle_all( 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(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 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 ferr, 6225, "Qhull internal error (qh_mergecycle_all): f%d without normal\n", facet->id);
+      qh_errexit(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(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(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(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 ferr, 1013, "qh_mergecycle_all: merged %d same cycles or facets into coplanar horizons\n", cycles));
+} /* mergecycle_all */
+
+/*---------------------------------
+
+  qh_mergecycle_facets( 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(facetT *samecycle, facetT *newfacet) {
+  facetT *same, *next;
+
+  trace4((qh ferr, 4030, "qh_mergecycle_facets: make newfacet new and samecycle deleted\n"));
+  qh_removefacet(newfacet);  /* append as a newfacet to end of qh facet_list */
+  qh_appendfacet(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(same, newfacet);
+  }
+  if (newfacet->center
+      && qh_setsize(newfacet->vertices) <= qh hull_dim + qh_MAXnewcentrum) {
+    qh_memfree(newfacet->center, qh normal_size);
+    newfacet->center= NULL;
+  }
+  trace3((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( 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(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(samecycle);
+    same->visitid= samevisitid;
+  }
+  newfacet->visitid= ++qh visit_id;
+  trace4((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(newfacet->neighbors);
+
+  trace4((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(&newfacet->neighbors, neighbor);
+          qh_setreplace(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(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(&neighbor->neighbors, newfacet);
+          qh_setappend(&newfacet->neighbors, neighbor);
+          neighbor->visitid= qh visit_id;
+          newneighbors++;
+        }
+      }
+    }
+  }
+  trace2((qh ferr, 2032, "qh_mergecycle_neighbors: deleted %d neighbors and added %d\n",
+             delneighbors, newneighbors));
+} /* mergecycle_neighbors */
+
+/*---------------------------------
+
+  qh_mergecycle_ridges( 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(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 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(newfacet->ridges);
+
+  trace4((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(&newfacet->ridges, ridge);
+        numold++;  /* already set by qh_mergecycle_neighbors */
+        continue;
+      }else {
+        qh_fprintf(qh ferr, 6098, "qhull internal error (qh_mergecycle_ridges): bad ridge r%d\n", ridge->id);
+        qh_errexit(qh_ERRqhull, NULL, ridge);
+      }
+      if (neighbor == newfacet) {
+        qh_setfree(&(ridge->vertices));
+        qh_memfree_(ridge, (int)sizeof(ridgeT), freelistp);
+        numold++;
+      }else if (neighbor->visitid == samevisitid) {
+        qh_setdel(neighbor->ridges, ridge);
+        qh_setfree(&(ridge->vertices));
+        qh_memfree_(ridge, (int)sizeof(ridgeT), freelistp);
+        numold++;
+      }else {
+        qh_setappend(&newfacet->ridges, ridge);
+        numold++;
+      }
+    }
+    if (same->ridges)
+      qh_settruncate(same->ridges, 0);
+    if (!same->simplicial)
+      continue;
+    FOREACHneighbor_i_(same) {       /* note: !newfact->simplicial */
+      if (neighbor->visitid != samevisitid && neighbor->simplicial) {
+        ridge= qh_newridge();
+        ridge->vertices= qh_setnew_delnthsorted(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(&(newfacet->ridges), ridge);
+        qh_setappend(&(neighbor->ridges), ridge);
+        numnew++;
+      }
+    }
+  }
+
+  trace2((qh ferr, 2033, "qh_mergecycle_ridges: found %d old ridges and %d new ones\n",
+             numold, numnew));
+} /* mergecycle_ridges */
+
+/*---------------------------------
+
+  qh_mergecycle_vneighbors( 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(facetT *samecycle, facetT *newfacet) {
+  facetT *neighbor, **neighborp;
+  unsigned int mergeid;
+  vertexT *vertex, **vertexp, *apex;
+  setT *vertices;
+
+  trace4((qh ferr, 4035, "qh_mergecycle_vneighbors: update vertex neighbors for newfacet\n"));
+  mergeid= qh visit_id - 1;
+  newfacet->visitid= mergeid;
+  vertices= qh_basevertices(samecycle); /* temp */
+  apex= SETfirstt_(samecycle->vertices, vertexT);
+  qh_setappend(&vertices, apex);
+  FOREACHvertex_(vertices) {
+    vertex->delridge= True;
+    FOREACHneighbor_(vertex) {
+      if (neighbor->visitid == mergeid)
+        SETref_(neighbor)= NULL;
+    }
+    qh_setcompact(vertex->neighbors);
+    qh_setappend(&vertex->neighbors, newfacet);
+    if (!SETsecond_(vertex->neighbors)) {
+      zinc_(Zcyclevertex);
+      trace2((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 del_vertices, vertex);
+    }
+  }
+  qh_settempfree(&vertices);
+  trace3((qh ferr, 3005, "qh_mergecycle_vneighbors: merged vertices from cycle f%d into f%d\n",
+             samecycle->id, newfacet->id));
+} /* mergecycle_vneighbors */
+
+/*---------------------------------
+
+  qh_mergefacet( 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(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 ferr, 6226, "Qhull internal error (qh_mergefacet): does not work for tricoplanar facets.  Use option 'Q11'\n");
+      qh_errexit2 (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();
+  }
+#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 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 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 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 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_ERRqhull, facet1, facet2);
+  }
+  if (qh num_facets - qh num_visible <= qh hull_dim + 1) {
+    qh_fprintf(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 ferr, 8079, "Option 'Qx' may avoid this problem.\n");
+    qh_errexit(qh_ERRprec, NULL, NULL);
+  }
+  if (!qh VERTEXneighbors)
+    qh_vertexneighbors();
+  qh_makeridges(facet1);
+  qh_makeridges(facet2);
+  if (qh IStracing >=4)
+    qh_errprint("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  (facet1, facet2);
+  if (qh hull_dim > 2 && qh_setsize(facet1->vertices) == qh hull_dim)
+    qh_mergesimplex(facet1, facet2, mergeapex);
+  else {
+    qh vertex_visit++;
+    FOREACHvertex_(facet2->vertices)
+      vertex->visitid= qh vertex_visit;
+    if (qh hull_dim == 2)
+      qh_mergefacet2d(facet1, facet2);
+    else {
+      qh_mergeneighbors(facet1, facet2);
+      qh_mergevertices(facet1->vertices, &facet2->vertices);
+    }
+    qh_mergeridges(facet1, facet2);
+    qh_mergevertex_neighbors(facet1, facet2);
+    if (!facet2->newfacet)
+      qh_newvertices(facet2->vertices);
+  }
+  if (!mergeapex)
+    qh_degen_redundant_neighbors(facet2, facet1);
+  if (facet2->coplanar || !facet2->newfacet) {
+    zinc_(Zmergeintohorizon);
+  }else if (!facet1->newfacet && facet2->newfacet) {
+    zinc_(Zmergehorizon);
+  }else {
+    zinc_(Zmergenew);
+  }
+  qh_willdelete(facet1, facet2);
+  qh_removefacet(facet2);  /* append as a newfacet to end of qh facet_list */
+  qh_appendfacet(facet2);
+  facet2->newfacet= True;
+  facet2->tested= False;
+  qh_tracemerge(facet1, facet2);
+  if (traceonce) {
+    qh_fprintf(qh ferr, 8080, "qh_mergefacet: end of wide tracing\n");
+    qh IStracing= tracerestore;
+  }
+} /* mergefacet */
+
+
+/*---------------------------------
+
+  qh_mergefacet2d( 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(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(neighborB);
+  qh_setreplace(neighborB->neighbors, facet1, facet2);
+  trace4((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( 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(facetT *facet1, facetT *facet2) {
+  facetT *neighbor, **neighborp;
+
+  trace4((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(neighbor);
+      if (SETfirstt_(neighbor->neighbors, facetT) != facet1) /*keep newfacet->horizon*/
+        qh_setdel(neighbor->neighbors, facet1);
+      else {
+        qh_setdel(neighbor->neighbors, facet2);
+        qh_setreplace(neighbor->neighbors, facet1, facet2);
+      }
+    }else if (neighbor != facet2) {
+      qh_setappend(&(facet2->neighbors), neighbor);
+      qh_setreplace(neighbor->neighbors, facet1, facet2);
+    }
+  }
+  qh_setdel(facet1->neighbors, facet2);  /* here for makeridges */
+  qh_setdel(facet2->neighbors, facet1);
+} /* mergeneighbors */
+
+
+/*---------------------------------
+
+  qh_mergeridges( 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(facetT *facet1, facetT *facet2) {
+  ridgeT *ridge, **ridgep;
+  vertexT *vertex, **vertexp;
+
+  trace4((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(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(&(facet2->ridges), ridge);
+  }
+} /* mergeridges */
+
+
+/*---------------------------------
+
+  qh_mergesimplex( 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(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(facet2->vertices);  /* apex is new */
+    apex= SETfirstt_(facet1->vertices, vertexT);
+    if (SETfirstt_(facet2->vertices, vertexT) != apex)
+      qh_setaddnth(&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 ferr, 4039, "qh_mergesimplex: merge apex v%d of f%d into facet f%d\n",
+          apex->id, facet1->id, facet2->id));
+    FOREACHvertex_i_(facet2->vertices) {
+      if (vertex->id < apex->id) {
+        break;
+      }else if (vertex->id == apex->id) {
+        issubset= True;
+        break;
+      }
+    }
+    if (!issubset)
+      qh_setaddnth(&facet2->vertices, vertex_i, apex);
+    if (!facet2->newfacet)
+      qh_newvertices(facet2->vertices);
+    else if (!apex->newlist) {
+      qh_removevertex(apex);
+      qh_appendvertex(apex);
+    }
+  }
+  trace4((qh ferr, 4040, "qh_mergesimplex: update vertex neighbors of f%d\n",
+          facet1->id));
+  FOREACHvertex_(facet1->vertices) {
+    if (vertex == apex && !issubset)
+      qh_setreplace(vertex->neighbors, facet1, facet2);
+    else {
+      qh_setdel(vertex->neighbors, facet1);
+      if (!SETsecond_(vertex->neighbors))
+        qh_mergevertex_del(vertex, facet1, facet2);
+    }
+  }
+  trace4((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(&(ridge->vertices));
+      qh_memfree(ridge, (int)sizeof(ridgeT));
+      qh_setdel(facet2->neighbors, facet1);
+    }else {
+      qh_setappend(&facet2->ridges, ridge);
+      if (otherfacet->visitid != qh visit_id) {
+        qh_setappend(&facet2->neighbors, otherfacet);
+        qh_setreplace(otherfacet->neighbors, facet1, facet2);
+        otherfacet->visitid= qh visit_id;
+      }else {
+        if (otherfacet->simplicial)    /* is degen, needs ridges */
+          qh_makeridges(otherfacet);
+        if (SETfirstt_(otherfacet->neighbors, facetT) != facet1)
+          qh_setdel(otherfacet->neighbors, facet1);
+        else {   /*keep newfacet->neighbors->horizon*/
+          qh_setdel(otherfacet->neighbors, facet2);
+          qh_setreplace(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 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( 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(vertexT *vertex, facetT *facet1, facetT *facet2) {
+
+  zinc_(Zmergevertex);
+  trace2((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 del_vertices, vertex);
+} /* mergevertex_del */
+
+/*---------------------------------
+
+  qh_mergevertex_neighbors( 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(facetT *facet1, facetT *facet2) {
+  vertexT *vertex, **vertexp;
+
+  trace4((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 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("TRACE", NULL, NULL, NULL, qh tracevertex);
+  }
+  FOREACHvertex_(facet1->vertices) {
+    if (vertex->visitid != qh vertex_visit)
+      qh_setreplace(vertex->neighbors, facet1, facet2);
+    else {
+      qh_setdel(vertex->neighbors, facet1);
+      if (!SETsecond_(vertex->neighbors))
+        qh_mergevertex_del(vertex, facet1, facet2);
+    }
+  }
+  if (qh tracevertex)
+    qh_errprint("TRACE", NULL, NULL, NULL, qh tracevertex);
+} /* mergevertex_neighbors */
+
+
+/*---------------------------------
+
+  qh_mergevertices( 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(setT *vertices1, setT **vertices2) {
+  int newsize= qh_setsize(vertices1)+qh_setsize(*vertices2) - qh hull_dim + 1;
+  setT *mergedvertices;
+  vertexT *vertex, **vertexp, **vertex2= SETaddr_(*vertices2, vertexT);
+
+  mergedvertices= qh_settemp(newsize);
+  FOREACHvertex_(vertices1) {
+    if (!*vertex2 || vertex->id > (*vertex2)->id)
+      qh_setappend(&mergedvertices, vertex);
+    else {
+      while (*vertex2 && (*vertex2)->id > vertex->id)
+        qh_setappend(&mergedvertices, *vertex2++);
+      if (!*vertex2 || (*vertex2)->id < vertex->id)
+        qh_setappend(&mergedvertices, vertex);
+      else
+        qh_setappend(&mergedvertices, *vertex2++);
+    }
+  }
+  while (*vertex2)
+    qh_setappend(&mergedvertices, *vertex2++);
+  if (newsize < qh_setsize(mergedvertices)) {
+    qh_fprintf(qh ferr, 6100, "qhull internal error (qh_mergevertices): facets did not share a ridge\n");
+    qh_errexit(qh_ERRqhull, NULL, NULL);
+  }
+  qh_setfree(vertices2);
+  *vertices2= mergedvertices;
+  qh_settemppop();
+} /* mergevertices */
+
+
+/*---------------------------------
+
+  qh_neighbor_intersections( 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(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(neighborA->vertices, 0);
+  else
+    intersect= qh_vertexintersect_new(neighborA->vertices, neighborB->vertices);
+  qh_settemppush(intersect);
+  qh_setdelsorted(intersect, vertex);
+  FOREACHneighbor_i_(vertex) {
+    if (neighbor_i >= 2) {
+      zinc_(Zintersectnum);
+      qh_vertexintersect(&intersect, neighbor->vertices);
+      if (!SETfirst_(intersect)) {
+        zinc_(Zintersectfail);
+        qh_settempfree(&intersect);
+        return NULL;
+      }
+    }
+  }
+  trace3((qh ferr, 3007, "qh_neighbor_intersections: %d vertices in neighbor intersection of v%d\n",
+          qh_setsize(intersect), vertex->id));
+  return intersect;
+} /* neighbor_intersections */
+
+/*---------------------------------
+
+  qh_newvertices( 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(setT *vertices) {
+  vertexT *vertex, **vertexp;
+
+  FOREACHvertex_(vertices) {
+    if (!vertex->newlist) {
+      qh_removevertex(vertex);
+      qh_appendvertex(vertex);
+    }
+  }
+} /* newvertices */
+
+/*---------------------------------
+
+  qh_reducevertices()
+    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(void) {
+  int numshare=0, numrename= 0;
+  boolT degenredun= False;
+  facetT *newfacet;
+  vertexT *vertex, **vertexp;
+
+  if (qh hull_dim == 2)
+    return False;
+  if (qh_merge_degenredundant())
+    degenredun= True;
+ LABELrestart:
+  FORALLnew_facets {
+    if (newfacet->newmerge) {
+      if (!qh MERGEvertices)
+        newfacet->newmerge= False;
+      qh_remove_extravertices(newfacet);
+    }
+  }
+  if (!qh MERGEvertices)
+    return False;
+  FORALLnew_facets {
+    if (newfacet->newmerge) {
+      newfacet->newmerge= False;
+      FOREACHvertex_(newfacet->vertices) {
+        if (vertex->delridge) {
+          if (qh_rename_sharedvertex(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(vertex)) {
+        numrename++;
+        if (qh_merge_degenredundant()) {
+          degenredun= True;
+          goto LABELrestart;
+        }
+      }
+    }
+  }
+  trace1((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( 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(vertexT *vertex) {
+  vertexT *newvertex= NULL;
+  setT *vertices, *ridges;
+
+  trace3((qh ferr, 3008, "qh_redundant_vertex: check if v%d can be renamed\n", vertex->id));
+  if ((vertices= qh_neighbor_intersections(vertex))) {
+    ridges= qh_vertexridges(vertex);
+    if ((newvertex= qh_find_newvertex(vertex, vertices, ridges)))
+      qh_renamevertex(vertex, newvertex, ridges, NULL, NULL);
+    qh_settempfree(&ridges);
+    qh_settempfree(&vertices);
+  }
+  return newvertex;
+} /* redundant_vertex */
+
+/*---------------------------------
+
+  qh_remove_extravertices( 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(facetT *facet) {
+  ridgeT *ridge, **ridgep;
+  vertexT *vertex, **vertexp;
+  boolT foundrem= False;
+
+  trace4((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(vertex->neighbors)) {
+        vertex->deleted= True;
+        qh_setappend(&qh del_vertices, vertex);
+        zinc_(Zremvertexdel);
+        trace2((qh ferr, 2036, "qh_remove_extravertices: v%d deleted because it's lost all ridges\n", vertex->id));
+      }else
+        trace3((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( 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(vertexT *vertex, facetT *facet) {
+  facetT *neighbor, **neighborp, *neighborA= NULL;
+  setT *vertices, *ridges;
+  vertexT *newvertex;
+
+  if (qh_setsize(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 ferr, 6101, "qhull internal error (qh_rename_sharedvertex): v%d's neighbors not in f%d\n",
+        vertex->id, facet->id);
+      qh_errprint("ERRONEOUS", facet, NULL, NULL, vertex);
+      qh_errexit(qh_ERRqhull, NULL, NULL);
+    }
+  }
+  /* the vertex is shared by facet and neighborA */
+  ridges= qh_settemp(qh TEMPsize);
+  neighborA->visitid= ++qh visit_id;
+  qh_vertexridges_facet(vertex, facet, &ridges);
+  trace2((qh ferr, 2037, "qh_rename_sharedvertex: p%d(v%d) is shared by f%d(%d ridges) and f%d\n",
+    qh_pointid(vertex->point), vertex->id, facet->id, qh_setsize(ridges), neighborA->id));
+  zinc_(Zintersectnum);
+  vertices= qh_vertexintersect_new(facet->vertices, neighborA->vertices);
+  qh_setdel(vertices, vertex);
+  qh_settemppush(vertices);
+  if ((newvertex= qh_find_newvertex(vertex, vertices, ridges)))
+    qh_renamevertex(vertex, newvertex, ridges, facet, neighborA);
+  qh_settempfree(&vertices);
+  qh_settempfree(&ridges);
+  return newvertex;
+} /* rename_sharedvertex */
+
+/*---------------------------------
+
+  qh_renameridgevertex( 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(ridgeT *ridge, vertexT *oldvertex, vertexT *newvertex) {
+  int nth= 0, oldnth;
+  facetT *temp;
+  vertexT *vertex, **vertexp;
+
+  oldnth= qh_setindex(ridge->vertices, oldvertex);
+  qh_setdelnthsorted(ridge->vertices, oldnth);
+  FOREACHvertex_(ridge->vertices) {
+    if (vertex == newvertex) {
+      zinc_(Zdelridge);
+      if (ridge->nonconvex) /* only one ridge has nonconvex set */
+        qh_copynonconvex(ridge);
+      qh_delridge(ridge);
+      trace2((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(&ridge->vertices, nth, newvertex);
+  if (abs(oldnth - nth)%2) {
+    trace3((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( 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(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(ridge, oldvertex, newvertex);
+  if (!oldfacet) {
+    zinc_(Zrenameall);
+    if (istrace)
+      qh_fprintf(qh ferr, 8082, "qh_renamevertex: renamed v%d to v%d in several facets\n",
+               oldvertex->id, newvertex->id);
+    FOREACHneighbor_(oldvertex) {
+      qh_maydropneighbor(neighbor);
+      qh_setdelsorted(neighbor->vertices, oldvertex);
+      if (qh_remove_extravertices(neighbor))
+        neighborp--; /* neighbor may be deleted */
+    }
+    if (!oldvertex->deleted) {
+      oldvertex->deleted= True;
+      qh_setappend(&qh del_vertices, oldvertex);
+    }
+  }else if (qh_setsize(oldvertex->neighbors) == 2) {
+    zinc_(Zrenameshare);
+    if (istrace)
+      qh_fprintf(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 del_vertices, oldvertex);
+  }else {
+    zinc_(Zrenamepinch);
+    if (istrace || qh IStracing)
+      qh_fprintf(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(neighborA);
+  }
+} /* renamevertex */
+
+
+/*---------------------------------
+
+  qh_test_appendmerge( 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(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(facet->normal, neighbor->normal);
+    zinc_(Zangletests);
+    if (angle > qh cos_max) {
+      zinc_(Zcoplanarangle);
+      qh_appendmergeset(facet, neighbor, MRGanglecoplanar, &angle);
+      trace2((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(facet);
+  zzinc_(Zcentrumtests);
+  qh_distplane(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(neighbor);
+    zzinc_(Zcentrumtests);
+    qh_distplane(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(facet->normal, neighbor->normal);
+    zinc_(Zangletests);
+  }
+  if (isconcave) {
+    zinc_(Zconcaveridge);
+    if (qh ANGLEmerge)
+      angle += qh_ANGLEconcave + 0.5;
+    qh_appendmergeset(facet, neighbor, MRGconcave, &angle);
+    trace0((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(facet, neighbor, MRGcoplanar, &angle);
+    trace2((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()
+    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(void /* qh newfacet_list */) {
+  facetT *newfacet, *neighbor, **neighborp;
+  vertexT *vertex, **vertexp;
+  int nummerges= 0;
+
+  trace1((qh ferr, 1015, "qh_test_vneighbors: testing vertex neighbors for convexity\n"));
+  if (!qh VERTEXneighbors)
+    qh_vertexneighbors();
+  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(newfacet, neighbor))
+          nummerges++;
+      }
+    }
+  }
+  zadd_(Ztestvneighbor, nummerges);
+  trace1((qh ferr, 1016, "qh_test_vneighbors: found %d non-convex, vertex neighbors\n",
+           nummerges));
+  return (nummerges > 0);
+} /* test_vneighbors */
+
+/*---------------------------------
+
+  qh_tracemerge( facet1, facet2 )
+    print trace message after merge
+*/
+void qh_tracemerge(facetT *facet1, facetT *facet2) {
+  boolT waserror= False;
+
+#ifndef qh_NOtrace
+  if (qh IStracing >= 4)
+    qh_errprint("MERGED", facet2, NULL, NULL, NULL);
+  if (facet2 == qh tracefacet || (qh tracevertex && qh tracevertex->newlist)) {
+    qh_fprintf(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("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 ferr, 8086, "qh_tracemerge: trace vertex deleted at furthest p%d\n",
+            qh furthest_id);
+    else
+      qh_checkvertex(qh tracevertex);
+  }
+  if (qh tracefacet) {
+    qh_checkfacet(qh tracefacet, True, &waserror);
+    if (waserror)
+      qh_errexit(qh_ERRqhull, qh tracefacet, NULL);
+  }
+#endif /* !qh_NOtrace */
+  if (qh CHECKfrequently || qh IStracing >= 4) { /* can't check polygon here */
+    qh_checkfacet(facet2, True, &waserror);
+    if (waserror)
+      qh_errexit(qh_ERRqhull, NULL, NULL);
+  }
+} /* tracemerge */
+
+/*---------------------------------
+
+  qh_tracemerging()
+    print trace message during POSTmerging
+
+  returns:
+    updates qh.mergereport
+
+  notes:
+    called from qh_mergecycle() and qh_mergefacet()
+
+  see:
+    qh_buildtracing()
+*/
+void qh_tracemerging(void) {
+  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 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 del_vertices));
+} /* tracemerging */
+
+/*---------------------------------
+
+  qh_updatetested( 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(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(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(facet2->center, qh normal_size);
+    facet2->center= NULL;
+    FOREACHridge_(facet2->ridges)
+      ridge->tested= False;
+  }
+} /* updatetested */
+
+/*---------------------------------
+
+  qh_vertexridges( 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(vertexT *vertex) {
+  facetT *neighbor, **neighborp;
+  setT *ridges= qh_settemp(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(vertex, neighbor, &ridges);
+  }
+  if (qh PRINTstatistics || qh IStracing) {
+    size= qh_setsize(ridges);
+    zinc_(Zvertexridge);
+    zadd_(Zvertexridgetot, size);
+    zmax_(Zvertexridgemax, size);
+    trace3((qh ferr, 3011, "qh_vertexridges: found %d ridges for v%d\n",
+             size, vertex->id));
+  }
+  return ridges;
+} /* vertexridges */
+
+/*---------------------------------
+
+  qh_vertexridges_facet( 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(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(ridges, ridge);
+  }
+  facet->visitid= qh visit_id-1;
+} /* vertexridges_facet */
+
+/*---------------------------------
+
+  qh_willdelete( facet, replace )
+    moves facet to visible list
+    sets facet->f.replace to replace (may be NULL)
+
+  returns:
+    bumps qh.num_visible
+*/
+void qh_willdelete(facetT *facet, facetT *replace) {
+
+  qh_removefacet(facet);
+  qh_prependfacet(facet, &qh visible_list);
+  qh num_visible++;
+  facet->visible= True;
+  facet->f.replace= replace;
+} /* willdelete */
+
+#else /* qh_NOmerge */
+void qh_premerge(vertexT *apex, realT maxcentrum, realT maxangle) {
+}
+void qh_postmerge(const char *reason, realT maxcentrum, realT maxangle,
+                      boolT vneighbors) {
+}
+boolT qh_checkzero(boolT testall) {
+   }
+#endif /* qh_NOmerge */
+
diff --git a/src/libqhullr/merge_r.h b/src/libqhullr/merge_r.h
new file mode 100644
index 0000000..ddb90cd
--- /dev/null
+++ b/src/libqhullr/merge_r.h
@@ -0,0 +1,178 @@
+/*
  ---------------------------------
+
+   merge.h
+   header file for merge.c
+
+   see qh-merge.htm and merge.c
+
+   Copyright (c) 1993-2012 C.B. Barber.
+   $Id: //main/2011/qhull/src/libqhullr/merge_r.h#1 $$Change: 1640 $
+   $DateTime: 2014/01/15 09:12:08 $$Author: bbarber $
+*/
+
+#ifndef qhDEFmerge
+#define qhDEFmerge 1
+
+#include "libqhull.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_
+*/
+#define FOREACHmerge_( merges ) FOREACHsetelement_(mergeT, merges, merge)
+
+/*============ prototypes in alphabetical order after pre/postmerge =======*/
+
+void    qh_premerge(vertexT *apex, realT maxcentrum, realT maxangle);
+void    qh_postmerge(const char *reason, realT maxcentrum, realT maxangle,
+             boolT vneighbors);
+void    qh_all_merges(boolT othermerge, boolT vneighbors);
+void    qh_appendmergeset(facetT *facet, facetT *neighbor, mergeType mergetype, realT *angle);
+setT   *qh_basevertices( facetT *samecycle);
+void    qh_checkconnect(void /* qh new_facets */);
+boolT   qh_checkzero(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(ridgeT *atridge);
+void    qh_degen_redundant_facet(facetT *facet);
+void    qh_degen_redundant_neighbors(facetT *facet, facetT *delfacet);
+vertexT *qh_find_newvertex(vertexT *oldvertex, setT *vertices, setT *ridges);
+void    qh_findbest_test(boolT testcentrum, facetT *facet, facetT *neighbor,
+           facetT **bestfacet, realT *distp, realT *mindistp, realT *maxdistp);
+facetT *qh_findbestneighbor(facetT *facet, realT *distp, realT *mindistp, realT *maxdistp);
+void    qh_flippedmerges(facetT *facetlist, boolT *wasmerge);
+void    qh_forcedmerges( boolT *wasmerge);
+void    qh_getmergeset(facetT *facetlist);
+void    qh_getmergeset_initial(facetT *facetlist);
+void    qh_hashridge(setT *hashtable, int hashsize, ridgeT *ridge, vertexT *oldvertex);
+ridgeT *qh_hashridge_find(setT *hashtable, int hashsize, ridgeT *ridge,
+              vertexT *vertex, vertexT *oldvertex, int *hashslot);
+void    qh_makeridges(facetT *facet);
+void    qh_mark_dupridges(facetT *facetlist);
+void    qh_maydropneighbor(facetT *facet);
+int     qh_merge_degenredundant(void);
+void    qh_merge_nonconvex( facetT *facet1, facetT *facet2, mergeType mergetype);
+void    qh_mergecycle(facetT *samecycle, facetT *newfacet);
+void    qh_mergecycle_all(facetT *facetlist, boolT *wasmerge);
+void    qh_mergecycle_facets( facetT *samecycle, facetT *newfacet);
+void    qh_mergecycle_neighbors(facetT *samecycle, facetT *newfacet);
+void    qh_mergecycle_ridges(facetT *samecycle, facetT *newfacet);
+void    qh_mergecycle_vneighbors( facetT *samecycle, facetT *newfacet);
+void    qh_mergefacet(facetT *facet1, facetT *facet2, realT *mindist, realT *maxdist, boolT mergeapex);
+void    qh_mergefacet2d(facetT *facet1, facetT *facet2);
+void    qh_mergeneighbors(facetT *facet1, facetT *facet2);
+void    qh_mergeridges(facetT *facet1, facetT *facet2);
+void    qh_mergesimplex(facetT *facet1, facetT *facet2, boolT mergeapex);
+void    qh_mergevertex_del(vertexT *vertex, facetT *facet1, facetT *facet2);
+void    qh_mergevertex_neighbors(facetT *facet1, facetT *facet2);
+void    qh_mergevertices(setT *vertices1, setT **vertices);
+setT   *qh_neighbor_intersections(vertexT *vertex);
+void    qh_newvertices(setT *vertices);
+boolT   qh_reducevertices(void);
+vertexT *qh_redundant_vertex(vertexT *vertex);
+boolT   qh_remove_extravertices(facetT *facet);
+vertexT *qh_rename_sharedvertex(vertexT *vertex, facetT *facet);
+void    qh_renameridgevertex(ridgeT *ridge, vertexT *oldvertex, vertexT *newvertex);
+void    qh_renamevertex(vertexT *oldvertex, vertexT *newvertex, setT *ridges,
+                        facetT *oldfacet, facetT *neighborA);
+boolT   qh_test_appendmerge(facetT *facet, facetT *neighbor);
+boolT   qh_test_vneighbors(void /* qh newfacet_list */);
+void    qh_tracemerge(facetT *facet1, facetT *facet2);
+void    qh_tracemerging(void);
+void    qh_updatetested( facetT *facet1, facetT *facet2);
+setT   *qh_vertexridges(vertexT *vertex);
+void    qh_vertexridges_facet(vertexT *vertex, facetT *facet, setT **ridges);
+void    qh_willdelete(facetT *facet, facetT *replace);
+
+#endif /* qhDEFmerge */
diff --git a/src/libqhullr/poly2_r.c b/src/libqhullr/poly2_r.c
new file mode 100644
index 0000000..5267239
--- /dev/null
+++ b/src/libqhullr/poly2_r.c
@@ -0,0 +1,3154 @@
+/*
  ---------------------------------
+
+   poly2.c
+   implements polygons and simplices
+
+   see qh-poly.htm, poly.h and libqhull.h
+
+   frequently used code is in poly.c
+
+   Copyright (c) 1993-2012 The Geometry Center.
+   $Id: //main/2011/qhull/src/libqhullr/poly2_r.c#1 $$Change: 1640 $
+   $DateTime: 2014/01/15 09:12:08 $$Author: bbarber $
+*/
+
+#include "qhull_a.h"
+
+/*======== functions in alphabetical order ==========*/
+
+/*---------------------------------
+
+  qh_addhash( newelem, hashtable, hashsize, hash )
+    add newelem to linear hash table at hash if not already there
+*/
+void qh_addhash(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()
+    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(void) {
+  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 ferr, 1020, "qh_check_bestdist: check points below nearest facet.  Facet_list f%d\n",
+      qh facet_list->id));
+  maxoutside= qh_maxouter();
+  maxoutside += qh DISTround;
+  /* one more qh.DISTround for check computation */
+  trace1((qh ferr, 1021, "qh_check_bestdist: check that all points are within %2.2g of best facet\n", maxoutside));
+  facets= qh_pointfacet(/*qh facet_list*/);
+  if (!qh_QUICKhelp && qh PRINTprecision)
+    qh_fprintf(qh ferr, 8091, "\n\
+qhull output completed.  Verifying that %d points are\n\
+below %2.2g of the nearest %sfacet.\n",
+             qh_setsize(facets), maxoutside, (qh ONLYgood ?  "good " : ""));
+  FOREACHfacet_i_(facets) {  /* for each point with facet assignment */
+    if (facet)
+      unassigned= False;
+    else {
+      unassigned= True;
+      facet= qh facet_list;
+    }
+    point= qh_point(facet_i);
+    if (point == qh GOODpointp)
+      continue;
+    qh_distplane(point, facet, &dist);
+    numpart++;
+    bestfacet= qh_findbesthorizon(!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(point, bestfacet, &dist, &facetlist))
+               && dist > maxoutside))
+        notgood++;
+      else {
+        waserror= True;
+        qh_fprintf(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(&facets);
+  if (notverified && !qh DELAUNAY && !qh_QUICKhelp && qh PRINTprecision)
+    qh_fprintf(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 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_ERRprec, errfacet1, errfacet2);
+  }else if (waserror && qh outside_err > REALmax/2)
+    qh_errexit2 (qh_ERRprec, errfacet1, errfacet2);
+  /* else if waserror, the error was logged to qh.ferr but does not effect the output */
+  trace0((qh ferr, 20, "qh_check_bestdist: max distance outside %2.2g\n", maxdist));
+} /* check_bestdist */
+
+/*---------------------------------
+
+  qh_check_maxout()
+    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(void) {
+  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 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 ferr, 1023, "qh_check_maxout: determine actual maxoutside and minvertex\n"));
+    vertices= qh_pointvertex(/*qh facet_list*/);
+    FORALLvertices {
+      FOREACHneighbor_(vertex) {
+        zinc_(Zdistvertex);  /* distance also computed by main loop below */
+        qh_distplane(vertex->point, neighbor, &dist);
+        minimize_(minvertex, dist);
+        if (-dist > qh TRACEdist || dist > qh TRACEdist
+        || neighbor == qh tracefacet || vertex == qh tracevertex)
+          qh_fprintf(qh ferr, 8093, "qh_check_maxout: p%d(v%d) is %.2g from f%d\n",
+                    qh_pointid(vertex->point), vertex->id, dist, neighbor->id);
+      }
+    }
+    if (qh MERGING) {
+      wmin_(Wminvertex, qh min_vertex);
+    }
+    qh min_vertex= minvertex;
+    qh_settempfree(&vertices);
+  }
+  facets= qh_pointfacet(/*qh facet_list*/);
+  do {
+    old_maxoutside= fmax_(qh max_outside, maxoutside);
+    FOREACHfacet_i_(facets) {     /* for each point with facet assignment */
+      if (facet) {
+        point= qh_point(facet_i);
+        if (point == qh GOODpointp)
+          continue;
+        zzinc_(Ztotcheck);
+        qh_distplane(point, facet, &dist);
+        numpart++;
+        bestfacet= qh_findbesthorizon(qh_IScheckmax, point, facet, !qh_NOupper, &dist, &numpart);
+        if (bestfacet && dist > maxoutside) {
+          if (qh ONLYgood && !bestfacet->good
+          && !((bestfacet= qh_findgooddist(point, bestfacet, &dist, &facetlist))
+               && dist > maxoutside))
+            notgood++;
+          else
+            maxoutside= dist;
+        }
+        if (dist > qh TRACEdist || (bestfacet && bestfacet == qh tracefacet))
+          qh_fprintf(qh ferr, 8094, "qh_check_maxout: p%d is %.2g above f%d\n",
+                     qh_pointid(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(&facets);
+  wval_(Wmaxout)= maxoutside - qh max_outside;
+  wmax_(Wmaxoutside, qh max_outside);
+  qh max_outside= maxoutside;
+  qh_nearcoplanar(/*qh.facet_list*/);
+  qh maxoutdone= True;
+  trace1((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(void) {
+}
+#endif
+
+/*---------------------------------
+
+  qh_check_output()
+    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(void) {
+  int i;
+
+  if (qh STOPcone)
+    return;
+  if (qh VERIFYoutput | qh IStracing | qh CHECKfrequently) {
+    qh_checkpolygon(qh facet_list);
+    qh_checkflipped_all(qh facet_list);
+    qh_checkconvex(qh facet_list, qh_ALGORITHMfault);
+  }else if (!qh MERGING && qh_newstats(qhstat precision, &i)) {
+    qh_checkflipped_all(qh facet_list);
+    qh_checkconvex(qh facet_list, qh_ALGORITHMfault);
+  }
+} /* check_output */
+
+
+
+/*---------------------------------
+
+  qh_check_point( point, facet, maxoutside, maxdist, errfacet1, errfacet2 )
+    check that point is less than maxoutside from facet
+*/
+void qh_check_point(pointT *point, facetT *facet, realT *maxoutside, realT *maxdist, facetT **errfacet1, facetT **errfacet2) {
+  realT dist;
+
+  /* occurs after statistics reported */
+  qh_distplane(point, facet, &dist);
+  if (dist > *maxoutside) {
+    if (*errfacet1 != facet) {
+      *errfacet2= *errfacet1;
+      *errfacet1= facet;
+    }
+    qh_fprintf(qh ferr, 6111, "qhull precision error: point p%d is outside facet f%d, distance= %6.8g maxoutside= %6.8g\n",
+              qh_pointid(point), facet->id, dist, *maxoutside);
+  }
+  maximize_(*maxdist, dist);
+} /* qh_check_point */
+
+
+/*---------------------------------
+
+  qh_check_points()
+    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(void) {
+  facetT *facet, *errfacet1= NULL, *errfacet2= NULL;
+  realT total, maxoutside, maxdist= -REALmax;
+  pointT *point, **pointp, *pointtemp;
+  boolT testouter;
+
+  maxoutside= qh_maxouter();
+  maxoutside += qh DISTround;
+  /* one more qh.DISTround for check computation */
+  trace1((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 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();
+  }else {
+    if (qh_MAXoutside && qh maxoutdone)
+      testouter= True;
+    else
+      testouter= False;
+    if (!qh_QUICKhelp) {
+      if (qh MERGEexact)
+        qh_fprintf(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 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 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 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 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(point, facet, &maxoutside, &maxdist, &errfacet1, &errfacet2);
+      }
+      FOREACHpoint_(qh other_points) {
+        if (point != qh GOODpointp)
+          qh_check_point(point, facet, &maxoutside, &maxdist, &errfacet1, &errfacet2);
+      }
+    }
+    if (maxdist > qh outside_err) {
+      qh_fprintf(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_ERRprec, errfacet1, errfacet2 );
+    }else if (errfacet1 && qh outside_err > REALmax/2)
+        qh_errexit2( qh_ERRprec, errfacet1, errfacet2 );
+    /* else if errfacet1, the error was logged to qh.ferr but does not effect the output */
+    trace0((qh ferr, 21, "qh_check_points: max distance outside %2.2g\n", maxdist));
+  }
+} /* check_points */
+
+
+/*---------------------------------
+
+  qh_checkconvex( 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(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 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("flipped facet");
+      qh_fprintf(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(vertex->point, neighbor, &dist);
+        if (dist > -qh DISTround) {
+          if (fault == qh_DATAfault) {
+            qh_precision("coplanar or concave ridge");
+            qh_fprintf(qh ferr, 6114, "qhull precision error: initial simplex is not convex. Distance=%.2g\n", dist);
+            qh_errexit(qh_ERRsingular, NULL, NULL);
+          }
+          if (dist > qh DISTround) {
+            zzinc_(Zconcaveridges);
+            qh_precision("concave ridge");
+            qh_fprintf(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(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("coplanar ridge");
+              qh_fprintf(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(vertex->point), vertex->id, dist);
+              errfacet1= facet;
+              errfacet2= neighbor;
+              waserror= True;
+            }
+          }else {
+            zzinc_(Zcoplanarridges);
+            qh_precision("coplanar ridge");
+            trace0((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(vertex->point), vertex->id, dist, qh furthest_id));
+          }
+        }
+      }
+    }
+    if (!allsimplicial) {
+      if (qh CENTERtype == qh_AScentrum) {
+        if (!facet->center)
+          facet->center= qh_getcentrum(facet);
+        centrum= facet->center;
+      }else {
+        if (!centrum_warning && (!facet->simplicial || facet->tricoplanar)) {
+           centrum_warning= True;
+           qh_fprintf(qh ferr, 7062, "qhull warning: recomputing centrums for convexity test.  This may lead to false, precision errors.\n");
+        }
+        centrum= qh_getcentrum(facet);
+        tempcentrum= True;
+      }
+      FOREACHneighbor_(facet) {
+        if (qh ZEROcentrum && facet->simplicial && neighbor->simplicial)
+          continue;
+        if (facet->tricoplanar || neighbor->tricoplanar)
+          continue;
+        zzinc_(Zdistconvex);
+        qh_distplane(centrum, neighbor, &dist);
+        if (dist > qh DISTround) {
+          zzinc_(Zconcaveridges);
+          qh_precision("concave ridge");
+          qh_fprintf(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("coplanar ridge");
+          qh_fprintf(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(centrum, qh normal_size);
+    }
+  }
+  if (waserror && !qh FORCEoutput)
+    qh_errexit2 (qh_ERRprec, errfacet1, errfacet2);
+} /* checkconvex */
+
+
+/*---------------------------------
+
+  qh_checkfacet( facet, newmerge, waserror )
+    checks for consistency errors in facet
+    newmerge set if from merge.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(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 ferr, 6119, "qhull internal error (qh_checkfacet): facet f%d is on the visible_list\n",
+      facet->id);
+    qh_errexit(qh_ERRqhull, facet, NULL);
+  }
+  if (!facet->normal) {
+    qh_fprintf(qh ferr, 6120, "qhull internal error (qh_checkfacet): facet f%d does not have  a normal\n",
+      facet->id);
+    waserror= True;
+  }
+  qh_setcheck(facet->vertices, "vertices for f", facet->id);
+  qh_setcheck(facet->ridges, "ridges for f", facet->id);
+  qh_setcheck(facet->outsideset, "outsideset for f", facet->id);
+  qh_setcheck(facet->coplanarset, "coplanarset for f", facet->id);
+  qh_setcheck(facet->neighbors, "neighbors for f", facet->id);
+  FOREACHvertex_(facet->vertices) {
+    if (vertex->deleted) {
+      qh_fprintf(qh ferr, 6121, "qhull internal error (qh_checkfacet): deleted vertex v%d in f%d\n", vertex->id, facet->id);
+      qh_errprint("ERRONEOUS", NULL, NULL, NULL, vertex);
+      waserror= True;
+    }
+    if (vertex->id >= previousid) {
+      qh_fprintf(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(facet->neighbors);
+  numvertices= qh_setsize(facet->vertices);
+  numridges= qh_setsize(facet->ridges);
+  if (facet->simplicial) {
+    if (numvertices+numneighbors != 2*qh hull_dim
+    && !facet->degenerate && !facet->redundant) {
+      qh_fprintf(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 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 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 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 ferr, 6126, "qhull internal error (qh_checkfacet): facet f%d still has a MERGE or DUP neighbor\n", facet->id);
+      qh_errexit(qh_ERRqhull, facet, NULL);
+    }
+    neighbor->seen= True;
+  }
+  FOREACHneighbor_(facet) {
+    if (!qh_setin(neighbor->neighbors, facet)) {
+      qh_fprintf(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 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(ridge->vertices, "vertices for r", ridge->id);
+    ridge->seen= False;
+  }
+  FOREACHridge_(facet->ridges) {
+    if (ridge->seen) {
+      qh_fprintf(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(ridge->vertices);
+    if (numRvertices != qh hull_dim - 1) {
+      qh_fprintf(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 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 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(facet->vertices, neighbor->vertices);
+      qh_settemppush(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 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_ERRqhull, facet, ridge);
+          }
+          vertex->seen2= True;
+        }
+      }
+      if (!newmerge) {
+        FOREACHvertex_(intersection) {
+          if (!vertex->seen2) {
+            if (qh IStracing >=3 || !qh MERGING) {
+              qh_fprintf(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("ERRONEOUS", facet, neighbor, NULL, vertex);
+                if (!qh MERGING)
+                  qh_errexit(qh_ERRqhull, NULL, NULL);
+              }
+            }
+          }
+        }
+      }
+      qh_settempfree(&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 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_(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 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("ERRONEOUS", facet, errother, errridge, NULL);
+    *waserrorp= True;
+  }
+} /* checkfacet */
+
+
+/*---------------------------------
+
+  qh_checkflipped_all( facetlist )
+    checks orientation of facets in list against interior point
+*/
+void qh_checkflipped_all(facetT *facetlist) {
+  facetT *facet;
+  boolT waserror= False;
+  realT dist;
+
+  if (facetlist == qh facet_list)
+    zzval_(Zflippedfacets)= 0;
+  FORALLfacet_(facetlist) {
+    if (facet->normal && !qh_checkflipped(facet, &dist, !qh_ALL)) {
+      qh_fprintf(qh ferr, 6136, "qhull precision error: facet f%d is flipped, distance= %6.12g\n",
+              facet->id, dist);
+      if (!qh FORCEoutput) {
+        qh_errprint("ERRONEOUS", facet, NULL, NULL, NULL);
+        waserror= True;
+      }
+    }
+  }
+  if (waserror) {
+    qh_fprintf(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_ERRprec, NULL, NULL);
+  }
+} /* checkflipped_all */
+
+/*---------------------------------
+
+  qh_checkpolygon( 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(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 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(facet->outsideset)) {
+          if (!qh NARROWhull
+#if !qh_COMPUTEfurthest
+               || facet->furthestdist >= qh MINoutside
+#endif
+                        ) {
+            qh_fprintf(qh ferr, 6137, "qhull internal error (qh_checkpolygon): f%d has outside points before qh facet_next\n",
+                     facet->id);
+            qh_errexit(qh_ERRqhull, facet, NULL);
+          }
+        }
+      }
+      numfacets++;
+      qh_checkfacet(facet, False, &waserror);
+    }
+  }
+  if (qh visible_list && !visibleseen && facetlist == qh facet_list) {
+    qh_fprintf(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_errexit(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(facet->ridges);
+    FOREACHvertex_(facet->vertices) {
+      vertex->visitid++;
+      if (!vertex->seen) {
+        vertex->seen= True;
+        numvertices++;
+        if (qh_pointid(vertex->point) == -1) {
+          qh_fprintf(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 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(vertex->neighbors, "neighbors for v", vertex->id);
+        if (vertex->deleted)
+          continue;
+        totvneighbors += qh_setsize(vertex->neighbors);
+      }
+      FORALLfacet_(facetlist)
+        totvertices += qh_setsize(facet->vertices);
+      if (totvneighbors != totvertices) {
+        qh_fprintf(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 del_vertices)) {
+      qh_fprintf(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 del_vertices));
+      waserror= True;
+    }
+    if (qh hull_dim == 2 && numvertices != numfacets) {
+      qh_fprintf(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 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_ERRqhull, NULL, NULL);
+} /* checkpolygon */
+
+
+/*---------------------------------
+
+  qh_checkvertex( vertex )
+    check vertex for consistency
+    checks vertex->neighbors
+
+  notes:
+    neighbors checked efficiently in checkpolygon
+*/
+void qh_checkvertex(vertexT *vertex) {
+  boolT waserror= False;
+  facetT *neighbor, **neighborp, *errfacet=NULL;
+
+  if (qh_pointid(vertex->point) == -1) {
+    qh_fprintf(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 ferr, 6145, "qhull internal error (qh_checkvertex): unknown vertex id %d\n", vertex->id);
+    waserror= True;
+  }
+  if (!waserror && !vertex->deleted) {
+    if (qh_setsize(vertex->neighbors)) {
+      FOREACHneighbor_(vertex) {
+        if (!qh_setin(neighbor->vertices, vertex)) {
+          qh_fprintf(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("ERRONEOUS", NULL, NULL, NULL, vertex);
+    qh_errexit(qh_ERRqhull, errfacet, NULL);
+  }
+} /* checkvertex */
+
+/*---------------------------------
+
+  qh_clearcenters( type )
+    clear old data from facet->center
+
+  notes:
+    sets new centertype
+    nop if CENTERtype is the same
+*/
+void qh_clearcenters(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(facet->center, qh center_size);
+          facet->center= NULL;
+        }
+      }else /* qh CENTERtype == qh_AScentrum */ {
+        if (facet->center) {
+          qh_memfree(facet->center, qh normal_size);
+          facet->center= NULL;
+        }
+      }
+    }
+    qh CENTERtype= type;
+  }
+  trace2((qh ferr, 2043, "qh_clearcenters: switched to center type %d\n", type));
+} /* clearcenters */
+
+/*---------------------------------
+
+  qh_createsimplex( 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(setT *vertices) {
+  facetT *facet= NULL, *newfacet;
+  boolT toporient= True;
+  int vertex_i, vertex_n, nth;
+  setT *newfacets= qh_settemp(qh hull_dim+1);
+  vertexT *vertex;
+
+  qh facet_list= qh newfacet_list= qh facet_tail= qh_newfacet();
+  qh num_facets= qh num_vertices= qh num_visible= 0;
+  qh vertex_list= qh newvertex_list= qh vertex_tail= qh_newvertex(NULL);
+  FOREACHvertex_i_(vertices) {
+    newfacet= qh_newfacet();
+    newfacet->vertices= qh_setnew_delnthsorted(vertices, vertex_n,
+                                                vertex_i, 0);
+    newfacet->toporient= (unsigned char)toporient;
+    qh_appendfacet(newfacet);
+    newfacet->newfacet= True;
+    qh_appendvertex(vertex);
+    qh_setappend(&newfacets, newfacet);
+    toporient ^= True;
+  }
+  FORALLnew_facets {
+    nth= 0;
+    FORALLfacet_(qh newfacet_list) {
+      if (facet != newfacet)
+        SETelem_(newfacet->neighbors, nth++)= facet;
+    }
+    qh_settruncate(newfacet->neighbors, qh hull_dim);
+  }
+  qh_settempfree(&newfacets);
+  trace1((qh ferr, 1028, "qh_createsimplex: created simplex\n"));
+} /* createsimplex */
+
+/*---------------------------------
+
+  qh_delridge( ridge )
+    deletes ridge from data structures it belongs to
+    frees up its memory
+
+  notes:
+    in merge.c, caller sets vertex->delridge for each vertex
+    ridges also freed in qh_freeqhull
+*/
+void qh_delridge(ridgeT *ridge) {
+  void **freelistp; /* used !qh_NOmem */
+
+  qh_setdel(ridge->top->ridges, ridge);
+  qh_setdel(ridge->bottom->ridges, ridge);
+  qh_setfree(&(ridge->vertices));
+  qh_memfree_(ridge, (int)sizeof(ridgeT), freelistp);
+} /* delridge */
+
+
+/*---------------------------------
+
+  qh_delvertex( vertex )
+    deletes a vertex and frees its memory
+
+  notes:
+    assumes vertex->adjacencies have been updated if needed
+    unlinks from vertex_list
+*/
+void qh_delvertex(vertexT *vertex) {
+
+  if (vertex == qh tracevertex)
+    qh tracevertex= NULL;
+  qh_removevertex(vertex);
+  qh_setfree(&vertex->neighbors);
+  qh_memfree(vertex, (int)sizeof(vertexT));
+} /* delvertex */
+
+
+/*---------------------------------
+
+  qh_facet3vertex(  )
+    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(facetT *facet) {
+  ridgeT *ridge, *firstridge;
+  vertexT *vertex;
+  int cntvertices, cntprojected=0;
+  setT *vertices;
+
+  cntvertices= qh_setsize(facet->vertices);
+  vertices= qh_settemp(cntvertices);
+  if (facet->simplicial) {
+    if (cntvertices != 3) {
+      qh_fprintf(qh ferr, 6147, "qhull internal error (qh_facet3vertex): only %d vertices for simplicial facet f%d\n",
+                  cntvertices, facet->id);
+      qh_errexit(qh_ERRqhull, facet, NULL);
+    }
+    qh_setappend(&vertices, SETfirst_(facet->vertices));
+    if (facet->toporient ^ qh_ORIENTclock)
+      qh_setappend(&vertices, SETsecond_(facet->vertices));
+    else
+      qh_setaddnth(&vertices, 0, SETsecond_(facet->vertices));
+    qh_setappend(&vertices, SETelem_(facet->vertices, 2));
+  }else {
+    ridge= firstridge= SETfirstt_(facet->ridges, ridgeT);   /* no infinite */
+    while ((ridge= qh_nextridge3d(ridge, facet, &vertex))) {
+      qh_setappend(&vertices, vertex);
+      if (++cntprojected > cntvertices || ridge == firstridge)
+        break;
+    }
+    if (!ridge || cntprojected != cntvertices) {
+      qh_fprintf(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_ERRqhull, facet, ridge);
+    }
+  }
+  return vertices;
+} /* facet3vertex */
+
+/*---------------------------------
+
+  qh_findbestfacet( 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
+*/
+facetT *qh_findbestfacet(pointT *point, boolT bestoutside,
+           realT *bestdist, boolT *isoutside) {
+  facetT *bestfacet= NULL;
+  int numpart, totpart= 0;
+
+  bestfacet= qh_findbest(point, qh facet_list,
+                            bestoutside, !qh_ISnewfacets, bestoutside /* qh_NOupper */,
+                            bestdist, isoutside, &totpart);
+  if (*bestdist < -qh DISTround) {
+    bestfacet= qh_findfacet_all(point, bestdist, isoutside, &numpart);
+    totpart += numpart;
+    if ((isoutside && bestoutside)
+    || (!isoutside && bestfacet->upperdelaunay)) {
+      bestfacet= qh_findbest(point, bestfacet,
+                            bestoutside, False, bestoutside,
+                            bestdist, isoutside, &totpart);
+      totpart += numpart;
+    }
+  }
+  trace3((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( 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(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(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(upperfacet, point, &dist);
+    qh_vertexneighbors();
+    FOREACHneighbor_(vertex) {
+      if (neighbor->upperdelaunay || neighbor->flipped)
+        continue;
+      (*numpart)++;
+      qh_distplane(point, neighbor, &dist);
+      if (dist > bestdist) {
+        bestfacet= neighbor;
+        bestdist= dist;
+      }
+    }
+  }
+  if (!bestfacet) {
+    qh_fprintf(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_ERRqhull, upperfacet, NULL);
+  }
+  *bestdistp= bestdist;
+  trace3((qh ferr, 3015, "qh_findbestlower: f%d dist %2.2g for f%d p%d\n",
+          bestfacet->id, bestdist, upperfacet->id, qh_pointid(point)));
+  return bestfacet;
+} /* findbestlower */
+
+/*---------------------------------
+
+  qh_findfacet_all( 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(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(point, facet, &dist);
+    if (dist > *bestdist) {
+      *bestdist= dist;
+      bestfacet= facet;
+      if (dist > qh MINoutside) {
+        *isoutside= True;
+        break;
+      }
+    }
+  }
+  *numpart= totpart;
+  trace3((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( 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(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 GOODvertexp, facet->vertices)) {
+        facet->good= False;
+        numgood--;
+      }
+    }
+  }
+  if (qh GOODpoint && numgood) {
+    FORALLfacet_(facetlist) {
+      if (facet->good && facet->normal) {
+        zinc_(Zdistgood);
+        qh_distplane(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(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 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 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 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( 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(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 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 GOODvertexp, facet->vertices))) {
+        if (!--numgood) {
+          if (qh ONLYgood) {
+            qh_fprintf(qh ferr, 7064, "qhull warning: good vertex p%d does not match last good facet f%d.  Ignored.\n",
+               qh_pointid(qh GOODvertexp), facet->id);
+            return;
+          }else if (qh GOODvertex > 0)
+            qh_fprintf(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 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(facet->normal, &angle)) {
+          facet->good= False;
+          numgood--;
+          if (angle < bestangle) {
+            bestangle= angle;
+            bestfacet= facet;
+          }
+        }
+      }
+    }
+    if (!numgood && bestfacet) {
+      bestfacet->good= True;
+      numgood++;
+      trace0((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 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(void /* 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(furthest, facet, &dist);
+#else
+      dist= facet->furthestdist;
+#endif
+      if (dist > bestdist) {
+        bestfacet= facet;
+        bestdist= dist;
+      }
+    }
+  }
+  if (bestfacet) {
+    qh_removefacet(bestfacet);
+    qh_prependfacet(bestfacet, &qh facet_next);
+    trace1((qh ferr, 1029, "qh_furthestnext: made f%d next facet(dist %.2g)\n",
+            bestfacet->id, bestdist));
+  }
+} /* furthestnext */
+
+/*---------------------------------
+
+  qh_furthestout( 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(facetT *facet) {
+  pointT *point, **pointp, *bestpoint= NULL;
+  realT dist, bestdist= -REALmax;
+
+  FOREACHpoint_(facet->outsideset) {
+    qh_distplane(point, facet, &dist);
+    zinc_(Zcomputefurthest);
+    if (dist > bestdist) {
+      bestpoint= point;
+      bestdist= dist;
+    }
+  }
+  if (bestpoint) {
+    qh_setdel(facet->outsideset, point);
+    qh_setappend(&facet->outsideset, point);
+#if !qh_COMPUTEfurthest
+    facet->furthestdist= bestdist;
+#endif
+  }
+  facet->notfurthest= False;
+  trace3((qh ferr, 3017, "qh_furthestout: p%d is furthest outside point of f%d\n",
+          qh_pointid(point), facet->id));
+} /* furthestout */
+
+
+/*---------------------------------
+
+  qh_infiniteloop( facet )
+    report infinite loop error due to facet
+*/
+void qh_infiniteloop(facetT *facet) {
+
+  qh_fprintf(qh ferr, 6149, "qhull internal error (qh_infiniteloop): potential infinite loop detected\n");
+  qh_errexit(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( void) {
+  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 GOODpoint-1);
+  else if (qh GOODpoint < 0)
+    qh GOODpointp= qh_point(-qh GOODpoint-1);
+  if (qh GOODvertex > 0)
+    qh GOODvertexp= qh_point(qh GOODvertex-1);
+  else if (qh GOODvertex < 0)
+    qh GOODvertexp= qh_point(-qh GOODvertex-1);
+  if ((qh GOODpoint
+       && (qh GOODpointp < qh first_point  /* also catches !GOODpointp */
+           || qh GOODpointp > qh_point(qh num_points-1)))
+    || (qh GOODvertex
+        && (qh GOODvertexp < qh first_point  /* also catches !GOODvertexp */
+            || qh GOODvertexp > qh_point(qh num_points-1)))) {
+    qh_fprintf(qh ferr, 6150, "qhull input error: either QGn or QVn point is > p%d\n",
+             qh num_points-1);
+    qh_errexit(qh_ERRinput, NULL, NULL);
+  }
+  maxpoints= qh_maxmin(qh first_point, qh num_points, qh hull_dim);
+  if (qh SCALElast)
+    qh_scalelast(qh first_point, qh num_points, qh hull_dim,
+               qh MINlastcoord, qh MAXlastcoord, qh MAXwidth);
+  qh_detroundoff();
+  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 hull_dim, maxpoints, qh first_point, qh num_points);
+  qh_initialhull(vertices);  /* initial qh facet_list */
+  qh_partitionall(vertices, qh first_point, qh num_points);
+  if (qh PRINToptions1st || qh TRACElevel || qh IStracing) {
+    if (qh TRACElevel || qh IStracing)
+      qh_fprintf(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 ferr, 8104, "Options selected for Qhull %s:\n%s\n", qh_version, qh qhull_options);
+  }
+  qh_resetlists(False, qh_RESETvisible /*qh visible_list newvertex_list newfacet_list */);
+  qh facet_next= qh facet_list;
+  qh_furthestnext(/* 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 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_ERRinput, NULL, NULL);
+    }
+    if (!(qh GOODthreshold || qh GOODpoint
+         || (!qh MERGEexact && !qh PREmerge && qh GOODvertexp))) {
+      qh_fprintf(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_ERRinput, NULL, NULL);
+    }
+    if (qh GOODvertex > 0  && !qh MERGING  /* matches qh_partitionall */
+        && !qh_isvertex(qh GOODvertexp, vertices)) {
+      facet= qh_findbestnew(qh GOODvertexp, qh facet_list,
+                          &dist, !qh_ALL, &isoutside, &numpart);
+      zadd_(Zdistgood, numpart);
+      if (!isoutside) {
+        qh_fprintf(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 GOODvertexp));
+        qh_errexit(qh_ERRinput, NULL, NULL);
+      }
+      if (!qh_addpoint(qh GOODvertexp, facet, False)) {
+        qh_settempfree(&vertices);
+        qh_settempfree(&maxpoints);
+        return;
+      }
+    }
+    qh_findgood(qh facet_list, 0);
+  }
+  qh_settempfree(&vertices);
+  qh_settempfree(&maxpoints);
+  trace1((qh ferr, 1030, "qh_initbuild: initial hull created and points partitioned\n"));
+} /* initbuild */
+
+/*---------------------------------
+
+  qh_initialhull( 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(setT *vertices) {
+  facetT *facet, *firstfacet, *neighbor, **neighborp;
+  realT dist, angle, minangle= REALmax;
+#ifndef qh_NOtrace
+  int k;
+#endif
+
+  qh_createsimplex(vertices);  /* qh facet_list */
+  qh_resetlists(False, qh_RESETvisible);
+  qh facet_next= qh facet_list;      /* advance facet when processed */
+  qh interior_point= qh_getcenter(vertices);
+  firstfacet= qh facet_list;
+  qh_setfacetplane(firstfacet);
+  zinc_(Znumvisibility); /* needs to be in printsummary */
+  qh_distplane(qh interior_point, firstfacet, &dist);
+  if (dist > 0) {
+    FORALLfacets
+      facet->toporient ^= (unsigned char)True;
+  }
+  FORALLfacets
+    qh_setfacetplane(facet);
+  FORALLfacets {
+    if (!qh_checkflipped(facet, NULL, qh_ALL)) {/* due to axis-parallel facet */
+      trace1((qh ferr, 1031, "qh_initialhull: initial orientation incorrect.  Correct all facets\n"));
+      facet->flipped= False;
+      FORALLfacets {
+        facet->toporient ^= (unsigned char)True;
+        qh_orientoutside(facet);
+      }
+      break;
+    }
+  }
+  FORALLfacets {
+    if (!qh_checkflipped(facet, NULL, !qh_ALL)) {  /* can happen with 'R0.1' */
+      if (qh DELAUNAY && ! qh ATinfinity) {
+        if (qh UPPERdelaunay)
+          qh_fprintf(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 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_ERRinput, NULL, NULL);
+      }
+      qh_precision("initial facet is coplanar with interior point");
+      qh_fprintf(qh ferr, 6154, "qhull precision error: initial facet %d is coplanar with the interior point\n",
+                   facet->id);
+      qh_errexit(qh_ERRsingular, facet, NULL);
+    }
+    FOREACHneighbor_(facet) {
+      angle= qh_getangle(facet->normal, neighbor->normal);
+      minimize_( minangle, angle);
+    }
+  }
+  if (minangle < qh_MAXnarrow && !qh NOnarrow) {
+    realT diff= 1.0 + minangle;
+
+    qh NARROWhull= True;
+    qh_option("_narrow-hull", NULL, &diff);
+    if (minangle < qh_WARNnarrow && !qh RERUN && qh PRINTprecision)
+      qh_printhelp_narrowhull(qh ferr, minangle);
+  }
+  zzval_(Zprocessed)= qh hull_dim+1;
+  qh_checkpolygon(qh facet_list);
+  qh_checkconvex(qh facet_list,   qh_DATAfault);
+#ifndef qh_NOtrace
+  if (qh IStracing >= 1) {
+    qh_fprintf(qh ferr, 8105, "qh_initialhull: simplex constructed, interior point:");
+    for (k=0; k < qh hull_dim; k++)
+      qh_fprintf(qh ferr, 8106, " %6.4g", qh interior_point[k]);
+    qh_fprintf(qh ferr, 8107, "\n");
+  }
+#endif
+} /* initialhull */
+
+/*---------------------------------
+
+  qh_initialvertices( 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(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(dim + 1);
+  simplex= qh_settemp(dim+1);
+  if (qh ALLpoints)
+    qh_maxsimplex(dim, NULL, points, numpoints, &simplex);
+  else if (qh RANDOMoutside) {
+    while (qh_setsize(simplex) != dim+1) {
+      randr= qh_RANDOMint;
+      randr= randr/(qh_RANDOMmax+1);
+      idx= (int)floor(qh num_points * randr);
+      while (qh_setin(simplex, qh_point(idx))) {
+            idx++; /* in case qh_RANDOMint always returns the same value */
+        idx= idx < qh num_points ? idx : 0;
+      }
+      qh_setappend(&simplex, qh_point(idx));
+    }
+  }else if (qh hull_dim >= qh_INITIALmax) {
+    tested= qh_settemp(dim+1);
+    qh_setappend(&simplex, SETfirst_(maxpoints));   /* max and min X coord */
+    qh_setappend(&simplex, SETsecond_(maxpoints));
+    qh_maxsimplex(fmin_(qh_INITIALsearch, dim), maxpoints, points, numpoints, &simplex);
+    k= qh_setsize(simplex);
+    FOREACHpoint_i_(maxpoints) {
+      if (point_i & 0x1) {     /* first pick up max. coord. points */
+        if (!qh_setin(simplex, point) && !qh_setin(tested, point)){
+          qh_detsimplex(point, simplex, k, &nearzero);
+          if (nearzero)
+            qh_setappend(&tested, point);
+          else {
+            qh_setappend(&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(point, simplex, k, &nearzero);
+        if (nearzero)
+          qh_setappend(&tested, point);
+        else {
+          qh_setappend(&simplex, point);
+          k++;
+        }
+      }
+    }
+    idx= 0;
+    while (k != dim && (point= qh_point(idx++))) {
+      if (!qh_setin(simplex, point) && !qh_setin(tested, point)){
+        qh_detsimplex(point, simplex, k, &nearzero);
+        if (!nearzero){
+          qh_setappend(&simplex, point);
+          k++;
+        }
+      }
+    }
+    qh_settempfree(&tested);
+    qh_maxsimplex(dim, maxpoints, points, numpoints, &simplex);
+  }else
+    qh_maxsimplex(dim, maxpoints, points, numpoints, &simplex);
+  FOREACHpoint_(simplex)
+    qh_setaddnth(&vertices, 0, qh_newvertex(point)); /* descending order */
+  qh_settempfree(&simplex);
+  return vertices;
+} /* initialvertices */
+
+
+/*---------------------------------
+
+  qh_isvertex(  )
+    returns vertex if point is in vertex set, else returns NULL
+
+  notes:
+    for qh.GOODvertex
+*/
+vertexT *qh_isvertex(pointT *point, setT *vertices) {
+  vertexT *vertex, **vertexp;
+
+  FOREACHvertex_(vertices) {
+    if (vertex->point == point)
+      return vertex;
+  }
+  return NULL;
+} /* isvertex */
+
+/*---------------------------------
+
+  qh_makenewfacets( 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(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(point);
+  qh_appendvertex(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(visible, apex, &numnew);
+    }
+    if (visible->simplicial)
+      newfacet= qh_makenew_simplicial(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 ferr, 1032, "qh_makenewfacets: created %d new facets from point p%d to horizon\n",
+          numnew, qh_pointid(point)));
+  if (qh IStracing >= 4)
+    qh_printfacetlist(qh newfacet_list, NULL, qh_ALL);
+  return apex;
+} /* makenewfacets */
+
+/*---------------------------------
+
+  qh_matchduplicates( 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(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(hashsize, atfacet->vertices, qh hull_dim, 1,
+                     SETelem_(atfacet->vertices, atskip));
+  trace2((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(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 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_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 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(facet, newfacet, &low, &high);
+            dist2= qh_getdistance(newfacet, facet, &low, &high);
+            minimize_(mindist, dist2);
+            if (mindist > maxdist) {
+              maxdist= mindist;
+              maxmatch= facet;
+              maxskip= skip;
+              maxmatch2= newfacet;
+              maxskip2= newskip;
+            }
+            trace3((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 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_ERRqhull, newfacet, NULL);
+        }
+      }
+    } /* end of for each new facet at hash */
+    if (!makematch) {
+      if (!maxmatch) {
+        qh_fprintf(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_ERRqhull, atfacet, NULL);
+      }
+      SETelem_(maxmatch->neighbors, maxskip)= maxmatch2;
+      SETelem_(maxmatch2->neighbors, maxskip2)= maxmatch;
+      *hashcount -= 2; /* removed two unmatched facets */
+      zzinc_(Zmultiridge);
+      trace0((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("ridge with multiple neighbors");
+      if (qh IStracing >= 4)
+        qh_errprint("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()
+  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(void /* qh.facet_list */) {
+  facetT *facet;
+  pointT *point, **pointp;
+  int numpart;
+  realT dist, innerplane;
+
+  if (!qh KEEPcoplanar && !qh KEEPinside) {
+    FORALLfacets {
+      if (facet->coplanarset)
+        qh_setfree( &facet->coplanarset);
+    }
+  }else if (!qh KEEPcoplanar || !qh KEEPinside) {
+    qh_outerinner(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(point, facet, &dist);
+          if (dist < innerplane) {
+            if (!qh KEEPinside)
+              SETref_(point)= NULL;
+          }else if (!qh KEEPcoplanar)
+            SETref_(point)= NULL;
+        }
+        qh_setcompact(facet->coplanarset);
+      }
+    }
+    zzadd_(Zcheckpart, numpart);
+  }
+} /* nearcoplanar */
+
+/*---------------------------------
+
+  qh_nearvertex( 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(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 ferr, 6158, "qhull internal error (qh_nearvertex): qh.VERTEXneighbors and facet->center required for tricoplanar facets\n");
+      qh_errexit(qh_ERRqhull, facet, NULL);
+    }
+    vertices= qh_settemp(qh TEMPsize);
+    apex= SETfirstt_(facet->vertices, vertexT);
+    center= facet->center;
+    FOREACHneighbor_(apex) {
+      if (neighbor->center == center) {
+        FOREACHvertex_(neighbor->vertices)
+          qh_setappend(&vertices, vertex);
+      }
+    }
+  }else
+    vertices= facet->vertices;
+  FOREACHvertex_(vertices) {
+    dist= qh_pointdist(vertex->point, point, -dim);
+    if (dist < bestdist) {
+      bestdist= dist;
+      bestvertex= vertex;
+    }
+  }
+  if (facet->tricoplanar)
+    qh_settempfree(&vertices);
+  *bestdistp= sqrt(bestdist);
+  trace3((qh ferr, 3019, "qh_nearvertex: v%d dist %2.2g for f%d p%d\n",
+        bestvertex->id, *bestdistp, facet->id, qh_pointid(point)));
+  return bestvertex;
+} /* nearvertex */
+
+/*---------------------------------
+
+  qh_newhashtable( 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(int newsize) {
+  int size;
+
+  size= ((newsize+1)*qh_HASHfactor) | 0x1;  /* odd number */
+  while (True) {
+    if (newsize<0 || size<0) {
+        qh_fprintf(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(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(size);
+  qh_setzero(qh hash_table, 0, size);
+  return size;
+} /* newhashtable */
+
+/*---------------------------------
+
+  qh_newvertex( point )
+    returns a new vertex for point
+*/
+vertexT *qh_newvertex(pointT *point) {
+  vertexT *vertex;
+
+  zinc_(Ztotvertices);
+  vertex= (vertexT *)qh_memalloc((int)sizeof(vertexT));
+  memset((char *) vertex, (size_t)0, sizeof(vertexT));
+  if (qh vertex_id == 0xFFFFFF) {
+    qh_fprintf(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_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 ferr, 4060, "qh_newvertex: vertex p%d(v%d) created\n", qh_pointid(vertex->point),
+          vertex->id));
+  return(vertex);
+} /* newvertex */
+
+/*---------------------------------
+
+  qh_nextridge3d( 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 qh_qh.
+
+  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 qh_qh or qh_errexit [QhullFacet.cpp]
+
+  design:
+    for each ridge
+      exit if it is the ridge after atridge
+*/
+ridgeT *qh_nextridge3d(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(facetT *atfacet, int atskip, int hashsize, int *hashcount) {
+}
+ridgeT *qh_nextridge3d(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(void /* facet_list */) {
+  pointT *point, **pointp;
+  facetT *facet;
+  realT dist;
+
+  trace1((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(point, facet, &dist);
+        zinc_(Zpartition);
+        qh_partitioncoplanar(point, facet, &dist);
+      }
+    }
+    qh_setfree(&facet->outsideset);
+  }
+} /* outcoplanar */
+
+/*---------------------------------
+
+  qh_point( 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(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 other_points))
+    return SETelemt_(qh other_points, id, pointT);
+  return NULL;
+} /* point */
+
+/*---------------------------------
+
+  qh_point_add( 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(setT *set, pointT *point, void *elem) {
+  int id, size;
+
+  SETreturnsize_(set, size);
+  if ((id= qh_pointid(point)) < 0)
+    qh_fprintf(qh ferr, 7067, "qhull internal warning (point_add): unknown point %p id %d\n",
+      point, id);
+  else if (id >= size) {
+    qh_fprintf(qh ferr, 6160, "qhull internal errror(point_add): point p%d is out of bounds(%d)\n",
+             id, size);
+    qh_errexit(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_(facets) { ... }
+    SETelem_(facets, i)
+
+  design:
+    for each facet
+      add each vertex
+      add each coplanar point
+      add each outside point
+*/
+setT *qh_pointfacet(void /*qh facet_list*/) {
+  int numpoints= qh num_points + qh_setsize(qh other_points);
+  setT *facets;
+  facetT *facet;
+  vertexT *vertex, **vertexp;
+  pointT *point, **pointp;
+
+  facets= qh_settemp(numpoints);
+  qh_setzero(facets, 0, numpoints);
+  qh vertex_visit++;
+  FORALLfacets {
+    FOREACHvertex_(facet->vertices) {
+      if (vertex->visitid != qh vertex_visit) {
+        vertex->visitid= qh vertex_visit;
+        qh_point_add(facets, vertex->point, facet);
+      }
+    }
+    FOREACHpoint_(facet->coplanarset)
+      qh_point_add(facets, point, facet);
+    FOREACHpoint_(facet->outsideset)
+      qh_point_add(facets, point, facet);
+  }
+  return facets;
+} /* pointfacet */
+
+/*---------------------------------
+
+  qh_pointvertex(  )
+    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_(vertices) { ... }
+    SETelem_(vertices, i)
+*/
+setT *qh_pointvertex(void /*qh facet_list*/) {
+  int numpoints= qh num_points + qh_setsize(qh other_points);
+  setT *vertices;
+  vertexT *vertex;
+
+  vertices= qh_settemp(numpoints);
+  qh_setzero(vertices, 0, numpoints);
+  FORALLvertices
+    qh_point_add(vertices, vertex->point, vertex);
+  return vertices;
+} /* pointvertex */
+
+
+/*---------------------------------
+
+  qh_prependfacet( 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(facetT *facet, facetT **facetlist) {
+  facetT *prevfacet, *list;
+
+
+  trace4((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( fp )
+    print hash table to fp
+
+  notes:
+    not in I/O to avoid bringing io.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(FILE *fp) {
+  facetT *facet, *neighbor;
+  int id, facet_i, facet_n, neighbor_i= 0, neighbor_n= 0;
+  vertexT *vertex, **vertexp;
+
+  FOREACHfacet_i_(qh hash_table) {
+    if (facet) {
+      FOREACHneighbor_i_(facet) {
+        if (!neighbor || neighbor == qh_MERGEridge || neighbor == qh_DUPLICATEridge)
+          break;
+      }
+      if (neighbor_i == neighbor_n)
+        continue;
+      qh_fprintf(fp, 9283, "hash %d f%d ", facet_i, facet->id);
+      FOREACHvertex_(facet->vertices)
+        qh_fprintf(fp, 9284, "v%d ", vertex->id);
+      qh_fprintf(fp, 9285, "\n neighbors:");
+      FOREACHneighbor_i_(facet) {
+        if (neighbor == qh_MERGEridge)
+          id= -3;
+        else if (neighbor == qh_DUPLICATEridge)
+          id= -2;
+        else
+          id= getid_(neighbor);
+        qh_fprintf(fp, 9286, " %d", id);
+      }
+      qh_fprintf(fp, 9287, "\n");
+    }
+  }
+} /* printhashtable */
+
+
+/*---------------------------------
+
+  qh_printlists( fp )
+    print out facet and vertex list for debugging (without 'f/v' tags)
+*/
+void qh_printlists(void) {
+  facetT *facet;
+  vertexT *vertex;
+  int count= 0;
+
+  qh_fprintf(qh ferr, 8108, "qh_printlists: facets:");
+  FORALLfacets {
+    if (++count % 100 == 0)
+      qh_fprintf(qh ferr, 8109, "\n     ");
+    qh_fprintf(qh ferr, 8110, " %d", facet->id);
+  }
+  qh_fprintf(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 ferr, 8112, "\n     ");
+    qh_fprintf(qh ferr, 8113, " %d", vertex->id);
+  }
+  qh_fprintf(qh ferr, 8114, "\n");
+} /* printlists */
+
+/*---------------------------------
+
+  qh_resetlists( 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(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()
+    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(void) {
+  facetT *facet;
+
+  qh_clearcenters(qh_ASvoronoi);
+  qh_vertexneighbors();
+
+  FORALLfacets {
+    if (!facet->normal || !facet->upperdelaunay || qh UPPERdelaunay) {
+      if (!facet->center)
+        facet->center= qh_facetcenter(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(void /*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 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_ASvoronoi);
+    qh_vertexneighbors();
+  }
+  qh ONLYgood= False; /* for makenew_nonsimplicial */
+  qh visit_id++;
+  qh NEWfacets= True;
+  qh degen_mergeset= qh_settemp(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(facet, &new_vertex_list);
+  }
+  trace2((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(facet->ridges) > 0) {
+        qh_fprintf(qh ferr, 6161, "qhull error (qh_triangulate): ridges still defined for f%d\n", facet->id);
+        qh_errexit(qh_ERRqhull, facet, NULL);
+      }
+      qh_setfree(&facet->ridges);
+    }
+    if (SETfirst_(facet->vertices) == SETsecond_(facet->vertices)) {
+      zinc_(Ztrinull);
+      qh_triangulate_null(facet);
+    }
+  }
+  trace2((qh ferr, 2048, "qh_triangulate: delete %d or more mirror facets -- same vertices and neighbors\n", qh_setsize(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(merge, (int)sizeof(mergeT));
+    if (mergetype == MRGmirror) {
+      zinc_(Ztrimirror);
+      qh_triangulate_mirror(facet1, facet2);
+    }
+  }
+  qh_settempfree(&qh degen_mergeset);
+  trace2((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 newvertex_list, empty newfacet_list and visible_list*/);
+  qh_resetlists(False, !qh_RESETvisible /*qh newvertex_list, empty newfacet_list and visible_list*/);
+
+  trace2((qh ferr, 2050, "qh_triangulate: identify degenerate tricoplanar facets from f%d\n", getid_(new_facet_list)));
+  trace2((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_(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 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(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 ferr, 2053, "qh_triangulate: all tricoplanar facets degenerate for non-simplicial facet f%d\n",
+                       visible->id));
+          qh_delfacet(visible);
+          qh num_visible--;
+        }
+        visible= facet;
+        owner= NULL;
+      }
+    }else if (facet->tricoplanar) {
+      if (facet->f.triowner != visible) {
+        qh_fprintf(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_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(visible);
+        qh num_visible--;
+      }
+    }
+  }
+  if (visible && !owner) {
+    trace2((qh ferr, 2054, "qh_triangulate: all tricoplanar facets degenerate for last non-simplicial facet f%d\n",
+                 visible->id));
+    qh_delfacet(visible);
+    qh num_visible--;
+  }
+  qh NEWfacets= False;
+  qh ONLYgood= onlygood; /* restore value */
+  if (qh CHECKfrequently)
+    qh_checkpolygon(qh facet_list);
+  qh hasTriangulation= True;
+} /* triangulate */
+
+
+/*---------------------------------
+
+  qh_triangulate_facet(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(facetT *facetA, vertexT **first_vertex) {
+  facetT *newfacet;
+  facetT *neighbor, **neighborp;
+  vertexT *apex;
+  int numnew=0;
+
+  trace3((qh ferr, 3020, "qh_triangulate_facet: triangulate facet f%d\n", facetA->id));
+
+  if (qh IStracing >= 4)
+    qh_printfacet(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(facetA->vertices);
+  }
+  qh_willdelete(facetA, NULL);
+  qh newfacet_list= qh facet_tail;
+  facetA->visitid= qh visit_id;
+  apex= SETfirstt_(facetA->vertices, vertexT);
+  qh_makenew_nonsimplicial(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(facetA->normal, 1, qh hull_dim);
+      if (qh CENTERtype == qh_AScentrum)
+        newfacet->center= qh_getcentrum(newfacet);
+      else
+        newfacet->center= qh_copypoints(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 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 newfacet_list, empty visible_list and newvertex_list*/);
+  qh_resetlists(False, !qh_RESETvisible /*qh newfacet_list, empty visible_list and newvertex_list*/);
+} /* triangulate_facet */
+
+/*---------------------------------
+
+  qh_triangulate_link(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(facetT *oldfacetA, facetT *facetA, facetT *oldfacetB, facetT *facetB) {
+  int errmirror= False;
+
+  trace3((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(facetA, facetB, MRGmirror, NULL);
+  }else if (qh_setin(facetB->neighbors, facetA))
+    errmirror= True;
+  if (errmirror) {
+    qh_fprintf(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_ERRqhull, facetA, facetB);
+  }
+  qh_setreplace(facetB->neighbors, oldfacetB, facetA);
+  qh_setreplace(facetA->neighbors, oldfacetA, facetB);
+} /* triangulate_link */
+
+/*---------------------------------
+
+  qh_triangulate_mirror(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(facetT *facetA, facetT *facetB) {
+  facetT *neighbor, *neighborB;
+  int neighbor_i, neighbor_n;
+
+  trace3((qh ferr, 3022, "qh_triangulate_mirror: delete mirrored facets f%d and f%d\n",
+         facetA->id, facetB->id));
+  FOREACHneighbor_i_(facetA) {
+    neighborB= SETelemt_(facetB->neighbors, neighbor_i, facetT);
+    if (neighbor == neighborB)
+      continue; /* occurs twice */
+    qh_triangulate_link(facetA, neighbor, facetB, neighborB);
+  }
+  qh_willdelete(facetA, NULL);
+  qh_willdelete(facetB, NULL);
+} /* triangulate_mirror */
+
+/*---------------------------------
+
+  qh_triangulate_null(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(facetT *facetA) {
+  facetT *neighbor, *otherfacet;
+
+  trace3((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(facetA, neighbor, facetA, otherfacet);
+  qh_willdelete(facetA, NULL);
+} /* triangulate_null */
+
+#else /* qh_NOmerge */
+void qh_triangulate(void) {
+}
+#endif /* qh_NOmerge */
+
+   /*---------------------------------
+
+  qh_vertexintersect( vertexsetA, vertexsetB )
+    intersects two vertex sets (inverse id ordered)
+    vertexsetA is a temporary set at the top of qhmem.tempstack
+
+  returns:
+    replaces vertexsetA with the intersection
+
+  notes:
+    could overwrite vertexsetA if currently too slow
+*/
+void qh_vertexintersect(setT **vertexsetA,setT *vertexsetB) {
+  setT *intersection;
+
+  intersection= qh_vertexintersect_new(*vertexsetA, vertexsetB);
+  qh_settempfree(vertexsetA);
+  *vertexsetA= intersection;
+  qh_settemppush(intersection);
+} /* vertexintersect */
+
+/*---------------------------------
+
+  qh_vertexintersect_new(  )
+    intersects two vertex sets (inverse id ordered)
+
+  returns:
+    a new set
+*/
+setT *qh_vertexintersect_new(setT *vertexsetA,setT *vertexsetB) {
+  setT *intersection= qh_setnew(qh hull_dim - 1);
+  vertexT **vertexA= SETaddr_(vertexsetA, vertexT);
+  vertexT **vertexB= SETaddr_(vertexsetB, vertexT);
+
+  while (*vertexA && *vertexB) {
+    if (*vertexA  == *vertexB) {
+      qh_setappend(&intersection, *vertexA);
+      vertexA++; vertexB++;
+    }else {
+      if ((*vertexA)->id > (*vertexB)->id)
+        vertexA++;
+      else
+        vertexB++;
+    }
+  }
+  return intersection;
+} /* vertexintersect_new */
+
+/*---------------------------------
+
+  qh_vertexneighbors()
+    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(void /*qh facet_list*/) {
+  facetT *facet;
+  vertexT *vertex, **vertexp;
+
+  if (qh VERTEXneighbors)
+    return;
+  trace1((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 hull_dim);
+      }
+      qh_setappend(&vertex->neighbors, facet);
+    }
+  }
+  qh VERTEXneighbors= True;
+} /* vertexneighbors */
+
+/*---------------------------------
+
+  qh_vertexsubset( 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(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
new file mode 100644
index 0000000..a066ae4
--- /dev/null
+++ b/src/libqhullr/poly_r.c
@@ -0,0 +1,1199 @@
+/*
  ---------------------------------
+
+   poly.c
+   implements polygons and simplices
+
+   see qh-poly.htm, poly.h and libqhull.h
+
+   infrequent code is in poly2.c
+   (all but top 50 and their callers 12/3/95)
+
+   Copyright (c) 1993-2012 The Geometry Center.
+   $Id: //main/2011/qhull/src/libqhullr/poly_r.c#1 $$Change: 1640 $
+   $DateTime: 2014/01/15 09:12:08 $$Author: bbarber $
+*/
+
+#include "qhull_a.h"
+
+/*======== functions in alphabetical order ==========*/
+
+/*---------------------------------
+
+  qh_appendfacet( 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(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 ferr, 4044, "qh_appendfacet: append f%d to facet_list\n", facet->id));
+} /* appendfacet */
+
+
+/*---------------------------------
+
+  qh_appendvertex( 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(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 ferr, 4045, "qh_appendvertex: append v%d to vertex_list\n", vertex->id));
+} /* appendvertex */
+
+
+/*---------------------------------
+
+  qh_attachnewfacets( )
+    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(void ) {
+  facetT *newfacet= NULL, *neighbor, **neighborp, *horizon, *visible;
+  ridgeT *ridge, **ridgep;
+
+  qh NEWfacets= True;
+  trace3((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(&(ridge->vertices)); /* delete on 2nd visit */
+          qh_memfree(ridge, (int)sizeof(ridgeT));
+        }
+      }
+      SETfirst_(visible->ridges)= NULL;
+    }
+    SETfirst_(visible->neighbors)= NULL;
+  }
+  trace1((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(horizon->neighbors, visible, newfacet);
+      }else {
+        qh_fprintf(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_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(horizon->neighbors,
+                        SETindex_(horizon->neighbors, neighbor));
+          neighborp--; /* repeat */
+        }
+      }
+      qh_setappend(&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( 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(facetT *facet, realT *distp, boolT allerror) {
+  realT dist;
+
+  if (facet->flipped && !distp)
+    return False;
+  zzinc_(Zdistcheck);
+  qh_distplane(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 ferr, 19, "qh_checkflipped: facet f%d is flipped, distance= %6.12g during p%d\n",
+              facet->id, dist, qh furthest_id));
+    qh_precision("flipped facet");
+    return False;
+  }
+  return True;
+} /* checkflipped */
+
+/*---------------------------------
+
+  qh_delfacet( facet )
+    removes facet from facet_list and frees up its memory
+
+  notes:
+    assumes vertices and ridges already freed
+*/
+void qh_delfacet(facetT *facet) {
+  void **freelistp; /* used !qh_NOmem */
+
+  trace4((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(facet);
+  if (!facet->tricoplanar || facet->keepcentrum) {
+    qh_memfree_(facet->normal, qh normal_size, freelistp);
+    if (qh CENTERtype == qh_ASvoronoi) {   /* uses macro calls */
+      qh_memfree_(facet->center, qh center_size, freelistp);
+    }else /* AScentrum */ {
+      qh_memfree_(facet->center, qh normal_size, freelistp);
+    }
+  }
+  qh_setfree(&(facet->neighbors));
+  if (facet->ridges)
+    qh_setfree(&(facet->ridges));
+  qh_setfree(&(facet->vertices));
+  if (facet->outsideset)
+    qh_setfree(&(facet->outsideset));
+  if (facet->coplanarset)
+    qh_setfree(&(facet->coplanarset));
+  qh_memfree_(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(void /*qh visible_list*/) {
+  facetT *visible, *nextfacet;
+  vertexT *vertex, **vertexp;
+  int numvisible= 0, numdel= qh_setsize(qh del_vertices);
+
+  trace1((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(visible);
+  }
+  if (numvisible != qh num_visible) {
+    qh_fprintf(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_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(vertex);
+  qh_settruncate(qh del_vertices, 0);
+} /* deletevisible */
+
+/*---------------------------------
+
+  qh_facetintersect( 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(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 ferr, 6104, "qhull internal error (qh_facetintersect): f%d or f%d not in others neighbors\n",
+            facetA->id, facetB->id);
+    qh_errexit2 (qh_ERRqhull, facetA, facetB);
+  }
+  intersect= qh_setnew_delnthsorted(facetA->vertices, qh hull_dim, *skipA, prepend);
+  trace4((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( 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(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 ferr, 6202, "qhull internal error: negative hashsize %d passed to qh_gethash [poly.c]\n", hashsize);
+    qh_errexit2 (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( 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(setT *vertices, boolT toporient,facetT *horizon) {
+  facetT *newfacet;
+  vertexT *vertex, **vertexp;
+
+  FOREACHvertex_(vertices) {
+    if (!vertex->newlist) {
+      qh_removevertex(vertex);
+      qh_appendvertex(vertex);
+    }
+  }
+  newfacet= qh_newfacet();
+  newfacet->vertices= vertices;
+  newfacet->toporient= (unsigned char)toporient;
+  if (horizon)
+    qh_setappend(&(newfacet->neighbors), horizon);
+  qh_appendfacet(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(void /* newfacet_list */) {
+  facetT *newfacet;
+
+  FORALLnew_facets {
+    if (!newfacet->mergehorizon)
+      qh_setfacetplane(newfacet);
+  }
+  if (qh JOGGLEmax < REALmax/2)
+    minimize_(qh min_vertex, -wwval_(Wnewvertexmax));
+} /* makenewplanes */
+
+/*---------------------------------
+
+  qh_makenew_nonsimplicial( 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(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(&(ridge->vertices));  /* delete on 2nd visit */
+          qh_memfree_(ridge, (int)sizeof(ridgeT), freelistp);
+        }
+      }
+    }else {  /* neighbor is an horizon facet */
+      toporient= (ridge->top == visible);
+      vertices= qh_setnew(qh hull_dim); /* makes sure this is quick */
+      qh_setappend(&vertices, apex);
+      qh_setappend_set(&vertices, ridge->vertices);
+      newfacet= qh_makenewfacet(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(&(newfacet->ridges), ridge);
+      }else {  /* qh_attachnewfacets */
+        if (neighbor->seen) {
+          if (neighbor->simplicial) {
+            qh_fprintf(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_ERRqhull, neighbor, visible);
+          }
+          qh_setappend(&(neighbor->neighbors), newfacet);
+        }else
+          qh_setreplace(neighbor->neighbors, visible, newfacet);
+        if (neighbor->simplicial) {
+          qh_setdel(neighbor->ridges, ridge);
+          qh_setfree(&(ridge->vertices));
+          qh_memfree(ridge, (int)sizeof(ridgeT));
+        }else {
+          qh_setappend(&(newfacet->ridges), ridge);
+          if (toporient)
+            ridge->top= newfacet;
+          else
+            ridge->bottom= newfacet;
+        }
+      trace4((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(facetT *visible, vertexT *apex, int *numnew) {
+  return NULL;
+}
+#endif /* qh_NOmerge */
+
+/*---------------------------------
+
+  qh_makenew_simplicial( 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(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(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(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 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( 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(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(hashsize, newfacet->vertices, qh hull_dim, 1,
+                     SETelem_(newfacet->vertices, newskip));
+  trace4((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(1, newfacet->vertices, newskip, facet->vertices, &skip, &same)) {
+      if (SETelem_(newfacet->vertices, newskip) ==
+          SETelem_(facet->vertices, skip)) {
+        qh_precision("two facets with the same vertices");
+        qh_fprintf(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_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 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("a ridge with more than two neighbors");
+        qh_fprintf(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_ERRprec, facet, newfacet);
+      }
+      SETelem_(newfacet->neighbors, newskip)= qh_DUPLICATEridge;
+      newfacet->dupridge= True;
+      if (!newfacet->normal)
+        qh_setfacetplane(newfacet);
+      qh_addhash(newfacet, qh hash_table, hashsize, hash);
+      (*hashcount)++;
+      if (!facet->normal)
+        qh_setfacetplane(facet);
+      if (matchfacet != qh_DUPLICATEridge) {
+        SETelem_(facet->neighbors, skip)= qh_DUPLICATEridge;
+        facet->dupridge= True;
+        if (!facet->normal)
+          qh_setfacetplane(facet);
+        if (matchfacet) {
+          matchskip= qh_setindex(matchfacet->neighbors, facet);
+          SETelem_(matchfacet->neighbors, matchskip)= qh_DUPLICATEridge;
+          matchfacet->dupridge= True;
+          if (!matchfacet->normal)
+            qh_setfacetplane(matchfacet);
+          qh_addhash(matchfacet, qh hash_table, hashsize, hash);
+          *hashcount += 2;
+        }
+      }
+      trace4((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 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(void /* 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 ferr, 1019, "qh_matchnewfacets: match neighbors for new facets.\n"));
+  FORALLnew_facets {
+    numnew++;
+    {  /* inline qh_setzero(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(numnew*(qh hull_dim-1)); /* twice what is normally needed,
+                                     but every ridge could be DUPLICATEridge */
+  hashsize= qh_setsize(qh hash_table);
+  FORALLnew_facets {
+    for (newskip=1; newskipneighbors, k, facetT);
+          if (!neighbor || neighbor == qh_DUPLICATEridge)
+            count++;
+        }
+        if (facet == newfacet)
+          break;
+      }
+      if (count != hashcount) {
+        qh_fprintf(qh ferr, 8088, "qh_matchnewfacets: after adding facet %d, hashcount %d != count %d\n",
+                 newfacet->id, hashcount, count);
+        qh_errexit(qh_ERRqhull, newfacet, NULL);
+      }
+    }
+#endif  /* end of trap code */
+  }
+  if (hashcount) {
+    FORALLnew_facets {
+      if (newfacet->dupridge) {
+        FOREACHneighbor_i_(newfacet) {
+          if (neighbor == qh_DUPLICATEridge) {
+            qh_matchduplicates(newfacet, neighbor_i, hashsize, &hashcount);
+                    /* this may report MERGEfacet */
+          }
+        }
+      }
+    }
+  }
+  if (hashcount) {
+    qh_fprintf(qh ferr, 6108, "qhull internal error (qh_matchnewfacets): %d neighbors did not match up\n",
+        hashcount);
+    qh_printhashtable(qh ferr);
+    qh_errexit(qh_ERRqhull, NULL, NULL);
+  }
+#ifndef qh_NOtrace
+  if (qh IStracing >= 2) {
+    FOREACHfacet_i_(qh hash_table) {
+      if (!facet)
+        numfree++;
+    }
+    qh_fprintf(qh ferr, 8089, "qh_matchnewfacets: %d new facets, %d unused hash entries .  hashsize %d\n",
+             numnew, numfree, qh_setsize(qh hash_table));
+  }
+#endif /* !qh_NOtrace */
+  qh_setfree(&qh hash_table);
+  if (qh PREmerge || qh MERGEexact) {
+    if (qh IStracing >= 4)
+      qh_printfacetlist(qh newfacet_list, NULL, qh_ALL);
+    FORALLnew_facets {
+      if (newfacet->normal)
+        qh_checkflipped(newfacet, NULL, qh_ALL);
+    }
+  }else if (qh FORCEoutput)
+    qh_checkflipped_all(qh newfacet_list);  /* prints warnings for flipped */
+} /* matchnewfacets */
+
+
+/*---------------------------------
+
+  qh_matchvertices( 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(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 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()
+    return a new facet
+
+  returns:
+    all fields initialized or cleared   (NULL)
+    preallocates neighbors set
+*/
+facetT *qh_newfacet(void) {
+  facetT *facet;
+  void **freelistp; /* used !qh_NOmem */
+
+  qh_memalloc_((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 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 ferr, 4055, "qh_newfacet: created facet f%d\n", facet->id));
+  return(facet);
+} /* newfacet */
+
+
+/*---------------------------------
+
+  qh_newridge()
+    return a new ridge
+*/
+ridgeT *qh_newridge(void) {
+  ridgeT *ridge;
+  void **freelistp;   /* used !qh_NOmem */
+
+  qh_memalloc_((int)sizeof(ridgeT), freelistp, ridge, ridgeT);
+  memset((char *)ridge, (size_t)0, sizeof(ridgeT));
+  zinc_(Ztotridges);
+  if (qh ridge_id == 0xFFFFFF) {
+    qh_fprintf(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 ferr, 4056, "qh_newridge: created ridge r%d\n", ridge->id));
+  return(ridge);
+} /* newridge */
+
+
+/*---------------------------------
+
+  qh_pointid(  )
+    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(pointT *point) {
+  ptr_intT offset, id;
+
+  if (!point)
+    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( 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(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 ferr, 4057, "qh_removefacet: remove f%d from facet_list\n", facet->id));
+} /* removefacet */
+
+
+/*---------------------------------
+
+  qh_removevertex( vertex )
+    unlinks vertex from qh.vertex_list,
+
+  returns:
+    updates qh.vertex_list .newvertex_list
+    decrements qh.num_vertices
+*/
+void qh_removevertex(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 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(void /*qh newvertex_list, newfacet_list, visible_list*/) {
+  facetT *newfacet= NULL, *neighbor, **neighborp, *visible;
+  vertexT *vertex, **vertexp;
+
+  trace3((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(vertex->neighbors);
+    }
+    FORALLnew_facets {
+      FOREACHvertex_(newfacet->vertices)
+        qh_setappend(&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 del_vertices, vertex);
+            trace2((qh ferr, 2041, "qh_updatevertices: delete vertex p%d(v%d) in f%d\n",
+                  qh_pointid(vertex->point), vertex->id, visible->id));
+          }
+        }
+      }
+    }
+  }else {  /* !VERTEXneighbors */
+    FORALLvisible_facets {
+      FOREACHvertex_(visible->vertices) {
+        if (!vertex->newlist && !vertex->deleted) {
+          vertex->deleted= True;
+          qh_setappend(&qh del_vertices, vertex);
+          trace2((qh ferr, 2042, "qh_updatevertices: delete vertex p%d(v%d) in f%d\n",
+                  qh_pointid(vertex->point), vertex->id, visible->id));
+        }
+      }
+    }
+  }
+} /* updatevertices */
+
+
+
diff --git a/src/libqhullr/poly_r.h b/src/libqhullr/poly_r.h
new file mode 100644
index 0000000..4ae1552
--- /dev/null
+++ b/src/libqhullr/poly_r.h
@@ -0,0 +1,295 @@
+/*
  ---------------------------------
+
+   poly.h
+   header file for poly.c and poly2.c
+
+   see qh-poly.htm, libqhull.h and poly.c
+
+   Copyright (c) 1993-2012 The Geometry Center.
+   $Id: //main/2011/qhull/src/libqhullr/poly_r.h#1 $$Change: 1640 $
+   $DateTime: 2014/01/15 09:12:08 $$Author: bbarber $
+*/
+
+#ifndef qhDEFpoly
+#define qhDEFpoly 1
+
+#include "libqhull.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_
+*/
+#define FOREACHneighborA_(facet)  FOREACHsetelement_(facetT, facet->neighbors, neighborA)
+
+/*----------------------------------
+
+  FOREACHvisible_( facets ) { ... }
+    assign 'visible' to each facet in facets
+
+  notes:
+    uses 'facetT *facet, *facetp;'
+    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_
+*/
+#define FOREACHnewfacet_(facets) FOREACHsetelement_(facetT, facets, newfacet)
+
+/*----------------------------------
+
+  FOREACHvertexA_( vertices ) { ... }
+    assign 'vertexA' to each vertex in vertices
+
+  notes:
+    uses 'vertexT *vertexA, *vertexAp;'
+    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_
+*/
+#define FOREACHvertexreverse12_(vertices) FOREACHsetelementreverse12_(vertexT, vertices, vertex)
+
+
+/*=============== prototypes poly.c in alphabetical order ================*/
+
+void    qh_appendfacet(facetT *facet);
+void    qh_appendvertex(vertexT *vertex);
+void    qh_attachnewfacets(void);
+boolT   qh_checkflipped(facetT *facet, realT *dist, boolT allerror);
+void    qh_delfacet(facetT *facet);
+void    qh_deletevisible(void /*qh visible_list, qh horizon_list*/);
+setT   *qh_facetintersect(facetT *facetA, facetT *facetB, int *skipAp,int *skipBp, int extra);
+int     qh_gethash(int hashsize, setT *set, int size, int firstindex, void *skipelem);
+facetT *qh_makenewfacet(setT *vertices, boolT toporient, facetT *facet);
+void    qh_makenewplanes(void /* newfacet_list */);
+facetT *qh_makenew_nonsimplicial(facetT *visible, vertexT *apex, int *numnew);
+facetT *qh_makenew_simplicial(facetT *visible, vertexT *apex, int *numnew);
+void    qh_matchneighbor(facetT *newfacet, int newskip, int hashsize,
+                          int *hashcount);
+void    qh_matchnewfacets(void);
+boolT   qh_matchvertices(int firstindex, setT *verticesA, int skipA,
+                          setT *verticesB, int *skipB, boolT *same);
+facetT *qh_newfacet(void);
+ridgeT *qh_newridge(void);
+int     qh_pointid(pointT *point);
+void    qh_removefacet(facetT *facet);
+void    qh_removevertex(vertexT *vertex);
+void    qh_updatevertices(void);
+
+
+/*========== -prototypes poly2.c in alphabetical order ===========*/
+
+void    qh_addhash(void* newelem, setT *hashtable, int hashsize, int hash);
+void    qh_check_bestdist(void);
+void    qh_check_maxout(void);
+void    qh_check_output(void);
+void    qh_check_point(pointT *point, facetT *facet, realT *maxoutside, realT *maxdist, facetT **errfacet1, facetT **errfacet2);
+void    qh_check_points(void);
+void    qh_checkconvex(facetT *facetlist, int fault);
+void    qh_checkfacet(facetT *facet, boolT newmerge, boolT *waserrorp);
+void    qh_checkflipped_all(facetT *facetlist);
+void    qh_checkpolygon(facetT *facetlist);
+void    qh_checkvertex(vertexT *vertex);
+void    qh_clearcenters(qh_CENTER type);
+void    qh_createsimplex(setT *vertices);
+void    qh_delridge(ridgeT *ridge);
+void    qh_delvertex(vertexT *vertex);
+setT   *qh_facet3vertex(facetT *facet);
+facetT *qh_findbestfacet(pointT *point, boolT bestoutside,
+           realT *bestdist, boolT *isoutside);
+facetT *qh_findbestlower(facetT *upperfacet, pointT *point, realT *bestdistp, int *numpart);
+facetT *qh_findfacet_all(pointT *point, realT *bestdist, boolT *isoutside,
+                          int *numpart);
+int     qh_findgood(facetT *facetlist, int goodhorizon);
+void    qh_findgood_all(facetT *facetlist);
+void    qh_furthestnext(void /* qh facet_list */);
+void    qh_furthestout(facetT *facet);
+void    qh_infiniteloop(facetT *facet);
+void    qh_initbuild(void);
+void    qh_initialhull(setT *vertices);
+setT   *qh_initialvertices(int dim, setT *maxpoints, pointT *points, int numpoints);
+vertexT *qh_isvertex(pointT *point, setT *vertices);
+vertexT *qh_makenewfacets(pointT *point /*horizon_list, visible_list*/);
+void    qh_matchduplicates(facetT *atfacet, int atskip, int hashsize, int *hashcount);
+void    qh_nearcoplanar(void /* qh.facet_list */);
+vertexT *qh_nearvertex(facetT *facet, pointT *point, realT *bestdistp);
+int     qh_newhashtable(int newsize);
+vertexT *qh_newvertex(pointT *point);
+ridgeT *qh_nextridge3d(ridgeT *atridge, facetT *facet, vertexT **vertexp);
+void    qh_outcoplanar(void /* facet_list */);
+pointT *qh_point(int id);
+void    qh_point_add(setT *set, pointT *point, void *elem);
+setT   *qh_pointfacet(void /*qh facet_list*/);
+setT   *qh_pointvertex(void /*qh facet_list*/);
+void    qh_prependfacet(facetT *facet, facetT **facetlist);
+void    qh_printhashtable(FILE *fp);
+void    qh_printlists(void);
+void    qh_resetlists(boolT stats, boolT resetVisible /*qh newvertex_list newfacet_list visible_list*/);
+void    qh_setvoronoi_all(void);
+void    qh_triangulate(void /*qh facet_list*/);
+void    qh_triangulate_facet(facetT *facetA, vertexT **first_vertex);
+void    qh_triangulate_link(facetT *oldfacetA, facetT *facetA, facetT *oldfacetB, facetT *facetB);
+void    qh_triangulate_mirror(facetT *facetA, facetT *facetB);
+void    qh_triangulate_null(facetT *facetA);
+void    qh_vertexintersect(setT **vertexsetA,setT *vertexsetB);
+setT   *qh_vertexintersect_new(setT *vertexsetA,setT *vertexsetB);
+void    qh_vertexneighbors(void /*qh facet_list*/);
+boolT   qh_vertexsubset(setT *vertexsetA, setT *vertexsetB);
+
+
+#endif /* qhDEFpoly */
diff --git a/src/libqhullr/qhull-exports_r.def b/src/libqhullr/qhull-exports_r.def
new file mode 100644
index 0000000..8f9cca9
--- /dev/null
+++ b/src/libqhullr/qhull-exports_r.def
@@ -0,0 +1,412 @@
+; qhull-exports.def -- msvc module-definition file
+;
+;   Generated from depends.exe by cut-and-paste of exported symbols by mingw gcc
+;   [mar'11] 399 symbols 
+;   Annotate as DATA qh_qh qh_qhstat qhmem qhull_inuse rbox_inuse
+;   Same as ../libqhullp/qhull_p-exports.def without qh_save_qhull and qh_restore_qhull
+;
+; $Id: //main/2011/qhull/src/libqhullr/qhull-exports_r.def#1 $$Change: 1640 $
+; $DateTime: 2014/01/15 09:12:08 $$Author: bbarber $
+; 
+; Define qhull_VERSION in CMakeLists.txt, Makefile, qhull-exports.def, qhull_p-exports.def, and qhull-warn.pri
+VERSION 6.3
+EXPORTS
+dfacet
+dvertex
+out1
+out2n
+out3n
+qh_addhash
+qh_addpoint
+qh_all_merges
+qh_allstatA
+qh_allstatB
+qh_allstatC
+qh_allstatD
+qh_allstatE
+qh_allstatE2
+qh_allstatF
+qh_allstatG
+qh_allstatH
+qh_allstatI
+qh_allstatistics
+qh_appendfacet
+qh_appendmergeset
+qh_appendprint
+qh_appendvertex
+qh_argv_to_command
+qh_argv_to_command_size
+qh_attachnewfacets
+qh_backnormal
+qh_basevertices
+qh_build_withrestart
+qh_buildhull
+qh_buildtracing
+qh_check_bestdist
+qh_check_maxout
+qh_check_output
+qh_check_point
+qh_check_points
+qh_checkconnect
+qh_checkconvex
+qh_checkfacet
+qh_checkflags
+qh_checkflipped
+qh_checkflipped_all
+qh_checkpolygon
+qh_checkvertex
+qh_checkzero
+qh_clear_outputflags
+qh_clearcenters
+qh_clock
+qh_collectstatistics
+qh_compare_facetarea
+qh_compare_facetmerge
+qh_compare_facetvisit
+qh_compare_vertexpoint
+qh_compareangle
+qh_comparemerge
+qh_comparevisit
+qh_copyfilename
+qh_copynonconvex
+qh_copypoints
+qh_countfacets
+qh_createsimplex
+qh_crossproduct
+qh_degen_redundant_facet
+qh_degen_redundant_neighbors
+qh_deletevisible
+qh_delfacet
+qh_delridge
+qh_delvertex
+qh_determinant
+qh_detjoggle
+qh_detroundoff
+qh_detsimplex
+qh_detvnorm
+qh_detvridge
+qh_detvridge3
+qh_distnorm
+qh_distplane
+qh_distround
+qh_divzero
+qh_eachvoronoi
+qh_eachvoronoi_all
+qh_errexit
+qh_errexit2
+qh_errexit_rbox
+qh_errprint
+qh_exit
+qh_facet2point
+qh_facet3vertex
+qh_facetarea
+qh_facetarea_simplex
+qh_facetcenter
+qh_facetintersect
+qh_facetvertices
+qh_find_newvertex
+qh_findbest
+qh_findbest_test
+qh_findbestfacet
+qh_findbesthorizon
+qh_findbestlower
+qh_findbestneighbor
+qh_findbestnew
+qh_findfacet_all
+qh_findgood
+qh_findgood_all
+qh_findgooddist
+qh_findhorizon
+qh_flippedmerges
+qh_forcedmerges
+qh_fprintf
+qh_fprintf_rbox
+qh_free
+qh_freebuffers
+qh_freebuild
+qh_freeqhull
+qh_freeqhull2
+qh_freestatistics
+qh_furthestnext
+qh_furthestout
+qh_gausselim
+qh_geomplanes
+qh_getangle
+qh_getarea
+qh_getcenter
+qh_getcentrum
+qh_getdistance
+qh_gethash
+qh_getmergeset
+qh_getmergeset_initial
+qh_gram_schmidt
+qh_hashridge
+qh_hashridge_find
+qh_infiniteloop
+qh_init_A
+qh_init_B
+qh_init_qhull_command
+qh_initbuild
+qh_initflags
+qh_initialhull
+qh_initialvertices
+qh_initqhull_buffers
+qh_initqhull_globals
+qh_initqhull_mem
+qh_initqhull_outputflags
+qh_initqhull_start
+qh_initqhull_start2
+qh_initstatistics
+qh_initthresholds
+qh_inthresholds
+qh_isvertex
+qh_joggleinput
+qh_makenew_nonsimplicial
+qh_makenew_simplicial
+qh_makenewfacet
+qh_makenewfacets
+qh_makenewplanes
+qh_makeridges
+qh_malloc
+qh_mark_dupridges
+qh_markkeep
+qh_markvoronoi
+qh_matchduplicates
+qh_matchneighbor
+qh_matchnewfacets
+qh_matchvertices
+qh_maxabsval
+qh_maxmin
+qh_maxouter
+qh_maxsimplex
+qh_maydropneighbor
+qh_memalloc
+qh_memfree
+qh_memfreeshort
+qh_meminit
+qh_meminitbuffers
+qh_memsetup
+qh_memsize
+qh_memstatistics
+qh_memtotal
+qh_merge_degenredundant
+qh_merge_nonconvex
+qh_mergecycle
+qh_mergecycle_all
+qh_mergecycle_facets
+qh_mergecycle_neighbors
+qh_mergecycle_ridges
+qh_mergecycle_vneighbors
+qh_mergefacet
+qh_mergefacet2d
+qh_mergeneighbors
+qh_mergeridges
+qh_mergesimplex
+qh_mergevertex_del
+qh_mergevertex_neighbors
+qh_mergevertices
+qh_minabsval
+qh_mindiff
+qh_nearcoplanar
+qh_nearvertex
+qh_neighbor_intersections
+qh_new_qhull
+qh_newfacet
+qh_newhashtable
+qh_newridge
+qh_newstats
+qh_newvertex
+qh_newvertices
+qh_nextfurthest
+qh_nextridge3d
+qh_normalize
+qh_normalize2
+qh_nostatistic
+qh_option
+qh_order_vertexneighbors
+qh_orientoutside
+qh_outcoplanar
+qh_outerinner
+qh_partitionall
+qh_partitioncoplanar
+qh_partitionpoint
+qh_partitionvisible
+qh_point
+qh_point_add
+qh_pointdist
+qh_pointfacet
+qh_pointid
+qh_pointvertex
+qh_postmerge
+qh_precision
+qh_premerge
+qh_prepare_output
+qh_prependfacet
+qh_printafacet
+qh_printallstatistics
+qh_printbegin
+qh_printcenter
+qh_printcentrum
+qh_printend
+qh_printend4geom
+qh_printextremes
+qh_printextremes_2d
+qh_printextremes_d
+qh_printfacet
+qh_printfacet2geom
+qh_printfacet2geom_points
+qh_printfacet2math
+qh_printfacet3geom_nonsimplicial
+qh_printfacet3geom_points
+qh_printfacet3geom_simplicial
+qh_printfacet3math
+qh_printfacet3vertex
+qh_printfacet4geom_nonsimplicial
+qh_printfacet4geom_simplicial
+qh_printfacetNvertex_nonsimplicial
+qh_printfacetNvertex_simplicial
+qh_printfacetheader
+qh_printfacetlist
+qh_printfacetridges
+qh_printfacets
+qh_printhashtable
+qh_printhelp_degenerate
+qh_printhelp_narrowhull
+qh_printhelp_singular
+qh_printhyperplaneintersection
+qh_printline3geom
+qh_printlists
+qh_printmatrix
+qh_printneighborhood
+qh_printpoint
+qh_printpoint3
+qh_printpointid
+qh_printpoints
+qh_printpoints_out
+qh_printpointvect
+qh_printpointvect2
+qh_printridge
+qh_printspheres
+qh_printstatistics
+qh_printstatlevel
+qh_printstats
+qh_printsummary
+qh_printvdiagram
+qh_printvdiagram2
+qh_printvertex
+qh_printvertexlist
+qh_printvertices
+qh_printvneighbors
+qh_printvnorm
+qh_printvoronoi
+qh_printvridge
+qh_produce_output
+qh_produce_output2
+qh_projectdim3
+qh_projectinput
+qh_projectpoint
+qh_projectpoints
+; Mark as DATA, otherwise links a separate qh_qh.  Requires __dcelspec
+qh_qh               DATA
+qh_qhstat           DATA
+qh_qhull
+qh_rand
+qh_rand_seed
+qh_randomfactor
+qh_randommatrix
+qh_rboxpoints
+qh_readfeasible
+qh_readpoints
+qh_reducevertices
+qh_redundant_vertex
+qh_remove_extravertices
+qh_removefacet
+qh_removevertex
+qh_rename_sharedvertex
+qh_renameridgevertex
+qh_renamevertex
+qh_resetlists
+qh_rotateinput
+qh_rotatepoints
+qh_scaleinput
+qh_scalelast
+qh_scalepoints
+qh_setaddnth
+qh_setaddsorted
+qh_setappend
+qh_setappend2ndlast
+qh_setappend_set
+qh_setcheck
+qh_setcompact
+qh_setcopy
+qh_setdel
+qh_setdelaunay
+qh_setdellast
+qh_setdelnth
+qh_setdelnthsorted
+qh_setdelsorted
+qh_setduplicate
+qh_setequal
+qh_setequal_except
+qh_setequal_skip
+qh_setfacetplane
+qh_setfeasible
+qh_setfree
+qh_setfree2
+qh_setfreelong
+qh_sethalfspace
+qh_sethalfspace_all
+qh_sethyperplane_det
+qh_sethyperplane_gauss
+qh_setin
+qh_setindex
+qh_setlarger
+qh_setlast
+qh_setnew
+qh_setnew_delnthsorted
+qh_setprint
+qh_setreplace
+qh_setsize
+qh_settemp
+qh_settempfree
+qh_settempfree_all
+qh_settemppop
+qh_settemppush
+qh_settruncate
+qh_setunique
+qh_setvoronoi_all
+qh_setzero
+qh_sharpnewfacets
+qh_skipfacet
+qh_skipfilename
+qh_srand
+qh_stddev
+qh_strtod
+qh_strtol
+qh_test_appendmerge
+qh_test_vneighbors
+qh_tracemerge
+qh_tracemerging
+qh_triangulate
+qh_triangulate_facet
+qh_triangulate_link
+qh_triangulate_mirror
+qh_triangulate_null
+qh_updatetested
+qh_updatevertices
+qh_user_memsizes
+qh_version
+qh_vertexintersect
+qh_vertexintersect_new
+qh_vertexneighbors
+qh_vertexridges
+qh_vertexridges_facet
+qh_vertexsubset
+qh_voronoi_center
+qh_willdelete
+; Mark as DATA, otherwise links a separate qhmem.  Requires __dcelspec
+qhmem                   DATA
+qhull_inuse             DATA
+rbox
+rbox_inuse              DATA
+roundi
diff --git a/src/libqhullr/qhull_a_r.h b/src/libqhullr/qhull_a_r.h
new file mode 100644
index 0000000..207dba9
--- /dev/null
+++ b/src/libqhullr/qhull_a_r.h
@@ -0,0 +1,151 @@
+/*
  ---------------------------------
+
+   qhull_a.h
+   all header files for compiling qhull
+
+   see qh-qhull.htm
+
+   see libqhull.h for user-level definitions
+
+   see user.h for user-defineable constants
+
+   defines internal functions for libqhull.c global.c
+
+   Copyright (c) 1993-2012 The Geometry Center.
+   $Id: //main/2011/qhull/src/libqhullr/qhull_a_r.h#1 $$Change: 1640 $
+   $DateTime: 2014/01/15 09:12:08 $$Author: bbarber $
+
+   Notes:  grep for ((" and (" to catch fprintf("lkasdjf");
+           full parens around (x?y:z)
+           use '#include qhull/qhull_a.h' to avoid name clashes
+*/
+
+#ifndef qhDEFqhulla
+#define qhDEFqhulla 1
+
+#include "libqhull.h"  /* Defines data types */
+
+#include "stat.h"
+#include "random.h"
+#include "mem.h"
+#include "qset.h"
+#include "geom.h"
+#include "merge.h"
+#include "poly.h"
+#include "io.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 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(void);
+boolT   qh_addpoint(pointT *furthest, facetT *facet, boolT checkdist);
+void    qh_buildhull(void);
+void    qh_buildtracing(pointT *furthest, facetT *facet);
+void    qh_build_withrestart(void);
+void    qh_errexit2(int exitcode, facetT *facet, facetT *otherfacet);
+void    qh_findhorizon(pointT *point, facetT *facet, int *goodvisible,int *goodhorizon);
+pointT *qh_nextfurthest(facetT **visible);
+void    qh_partitionall(setT *vertices, pointT *points,int npoints);
+void    qh_partitioncoplanar(pointT *point, facetT *facet, realT *dist);
+void    qh_partitionpoint(pointT *point, facetT *facet);
+void    qh_partitionvisible(boolT allpoints, int *numpoints);
+void    qh_precision(const char *reason);
+void    qh_printsummary(FILE *fp);
+
+/***** -global.c internal prototypes (alphabetical) ***********************/
+
+void    qh_appendprint(qh_PRINT format);
+void    qh_freebuild(boolT allmem);
+void    qh_freebuffers(void);
+void    qh_initbuffers(coordT *points, int numpoints, int dim, boolT ismalloc);
+
+/***** -stat.c internal prototypes (alphabetical) ***********************/
+
+void    qh_allstatA(void);
+void    qh_allstatB(void);
+void    qh_allstatC(void);
+void    qh_allstatD(void);
+void    qh_allstatE(void);
+void    qh_allstatE2 (void);
+void    qh_allstatF(void);
+void    qh_allstatG(void);
+void    qh_allstatH(void);
+void    qh_freebuffers(void);
+void    qh_initbuffers(coordT *points, int numpoints, int dim, boolT ismalloc);
+
+#endif /* qhDEFqhulla */
diff --git a/src/libqhullr/qset_r.c b/src/libqhullr/qset_r.c
new file mode 100644
index 0000000..3064b6b
--- /dev/null
+++ b/src/libqhullr/qset_r.c
@@ -0,0 +1,1339 @@
+/*
  ---------------------------------
+
+   qset.c
+   implements set manipulations needed for quickhull
+
+   see qh-set.htm and qset.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) 1993-2012 The Geometry Center.
+   $Id: //main/2011/qhull/src/libqhullr/qset_r.c#1 $$Change: 1640 $
+   $DateTime: 2014/01/15 09:12:08 $$Author: bbarber $
+*/
+
+#include "qset.h"
+#include "mem.h"
+#include 
+#include 
+/*** uncomment here and qhull_a.h
+     if string.h does not define memcpy()
+#include 
+*/
+
+#ifndef qhDEFlibqhull
+typedef struct ridgeT ridgeT;
+typedef struct facetT facetT;
+void    qh_errexit(int exitcode, facetT *, ridgeT *);
+void    qh_fprintf(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( 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(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(setp);
+    sizep= SETsizeaddr_(*setp);
+  }
+  oldsize= sizep->i - 1;
+  if (nth < 0 || nth > oldsize) {
+    qh_fprintf(qhmem.ferr, 6171, "qhull internal error (qh_setaddnth): nth %d is out-of-bounds for set:\n", nth);
+    qh_setprint(qhmem.ferr, "", *setp);
+    qh_errexit(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(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(setp, newindex, newelem);
+} /* setaddsorted */
+
+
+/*---------------------------------
+
+  qh_setappend( 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(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(setp);
+    sizep= SETsizeaddr_(*setp);
+  }
+  count= (sizep->i)++ - 1;
+  endp= (setelemT *)SETelemaddr_(*setp, count, void);
+  (endp++)->p= newelem;
+  endp->p= NULL;
+} /* setappend */
+
+/*---------------------------------
+
+  qh_setappend_set( 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(setT **setp, setT *setA) {
+  int sizeA, size;
+  setT *oldset;
+  setelemT *sizep;
+
+  if (!setA)
+    return;
+  SETreturnsize_(setA, sizeA);
+  if (!*setp)
+    *setp= qh_setnew(sizeA);
+  sizep= SETsizeaddr_(*setp);
+  if (!(size= sizep->i))
+    size= (*setp)->maxsize;
+  else
+    size--;
+  if (size + sizeA > (*setp)->maxsize) {
+    oldset= *setp;
+    *setp= qh_setcopy(oldset, sizeA);
+    qh_setfree(&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( 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(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(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( 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(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(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(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(qhmem.ferr, "ERRONEOUS", set);
+    qh_errexit(qhmem_ERRqhull, NULL, NULL);
+  }
+} /* setcheck */
+
+
+/*---------------------------------
+
+  qh_setcompact( 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(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(set, (int)(destp-firstp));   /* WARN64 */
+} /* setcompact */
+
+
+/*---------------------------------
+
+  qh_setcopy( 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(setT *set, int extra) {
+  setT *newset;
+  int size;
+
+  if (extra < 0)
+    extra= 0;
+  SETreturnsize_(set, size);
+  newset= qh_setnew(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( 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(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(qhmem.ferr, 6174, "qhull internal error (qh_setdelnth): nth %d is out-of-bounds for set:\n", nth);
+    qh_setprint(qhmem.ferr, "", set);
+    qh_errexit(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( 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(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(qhmem.ferr, 6175, "qhull internal error (qh_setdelnthsorted): nth %d is out-of-bounds for set:\n", nth);
+    qh_setprint(qhmem.ferr, "", set);
+    qh_errexit(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( 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(setT *set, int elemsize) {
+  void          *elem, **elemp, *newElem;
+  setT          *newSet;
+  int           size;
+
+  if (!(size= qh_setsize(set)))
+    return NULL;
+  newSet= qh_setnew(size);
+  FOREACHelem_(set) {
+    newElem= qh_memalloc(elemsize);
+    memcpy(newElem, elem, (size_t)elemsize);
+    qh_setappend(&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(  )
+    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( 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(setT **setp) {
+  int size;
+  void **freelistp;  /* used !qh_NOmem */
+
+  if (*setp) {
+    size= sizeof(setT) + ((*setp)->maxsize)*SETelemsize;
+    if (size <= qhmem.LASTsize) {
+      qh_memfree_(*setp, size, freelistp);
+    }else
+      qh_memfree(*setp, size);
+    *setp= NULL;
+  }
+} /* setfree */
+
+
+/*---------------------------------
+
+  qh_setfree2( 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 (setT **setp, int elemsize) {
+  void          *elem, **elemp;
+
+  FOREACHelem_(*setp)
+    qh_memfree(elem, elemsize);
+  qh_setfree(setp);
+} /* setfree2 */
+
+
+
+/*---------------------------------
+
+  qh_setfreelong( 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(setT **setp) {
+  int size;
+
+  if (*setp) {
+    size= sizeof(setT) + ((*setp)->maxsize)*SETelemsize;
+    if (size > qhmem.LASTsize) {
+      qh_memfree(*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( oldsetp )
+    returns a larger set that contains all elements of *oldsetp
+
+  notes:
+    the set is at least twice as large
+    if temp set, updates 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(setT **oldsetp) {
+  int size= 1;
+  setT *newset, *set, **setp, *oldset;
+  setelemT *sizep;
+  setelemT *newp, *oldp;
+
+  if (*oldsetp) {
+    oldset= *oldsetp;
+    SETreturnsize_(oldset, size);
+    qhmem.cntlarger++;
+    qhmem.totlarger += size+1;
+    newset= qh_setnew(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 *)qhmem.tempstack) {
+      if (set == oldset)
+        *(setp-1)= newset;
+    }
+    qh_setfree(oldsetp);
+  }else
+    newset= qh_setnew(3);
+  *oldsetp= newset;
+} /* setlarger */
+
+
+/*---------------------------------
+
+  qh_setlast(  )
+    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( 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(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 <= qhmem.LASTsize) {
+    qh_memalloc_(size, freelistp, set, setT);
+#ifndef qh_NOmem
+    sizereceived= qhmem.sizetable[ qhmem.indextable[size]];
+    if (sizereceived > size)
+      setsize += (sizereceived - size)/SETelemsize;
+#endif
+  }else
+    set= (setT*)qh_memalloc(size);
+  set->maxsize= setsize;
+  set->e[setsize].i= 1;
+  set->e[0].p= NULL;
+  return(set);
+} /* setnew */
+
+
+/*---------------------------------
+
+  qh_setnew_delnthsorted( 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(setT *set, int size, int nth, int prepend) {
+  setT *newset;
+  void **oldp, **newp;
+  int tailsize= size - nth -1, newsize;
+
+  if (tailsize < 0) {
+    qh_fprintf(qhmem.ferr, 6176, "qhull internal error (qh_setnew_delnthsorted): nth %d is out-of-bounds for set:\n", nth);
+    qh_setprint(qhmem.ferr, "", set);
+    qh_errexit(qhmem_ERRqhull, NULL, NULL);
+  }
+  newsize= size-1 + prepend;
+  newset= qh_setnew(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( fp, string, set )
+    print set elements to fp with identifying string
+
+  notes:
+    never errors
+*/
+void qh_setprint(FILE *fp, const char* string, setT *set) {
+  int size, k;
+
+  if (!set)
+    qh_fprintf(fp, 9346, "%s set is null\n", string);
+  else {
+    SETreturnsize_(set, size);
+    qh_fprintf(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(fp, 9348, " %p", set->e[k].p);
+    qh_fprintf(fp, 9349, "\n");
+  }
+} /* setprint */
+
+/*---------------------------------
+
+  qh_setreplace( 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(setT *set, void *oldelem, void *newelem) {
+  void **elemp;
+
+  elemp= SETaddr_(set, void);
+  while (*elemp != oldelem && *elemp)
+    elemp++;
+  if (*elemp)
+    *elemp= newelem;
+  else {
+    qh_fprintf(qhmem.ferr, 6177, "qhull internal error (qh_setreplace): elem %p not found in set\n",
+       oldelem);
+    qh_setprint(qhmem.ferr, "", set);
+    qh_errexit(qhmem_ERRqhull, NULL, NULL);
+  }
+} /* setreplace */
+
+
+/*---------------------------------
+
+  qh_setsize( 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
+
+  design:
+    determine actual size of set from maxsize
+*/
+int qh_setsize(setT *set) {
+  int size;
+  setelemT *sizep;
+
+  if (!set)
+    return(0);
+  sizep= SETsizeaddr_(set);
+  if ((size= sizep->i)) {
+    size--;
+    if (size > set->maxsize) {
+      qh_fprintf(qhmem.ferr, 6178, "qhull internal error (qh_setsize): current set size %d is greater than maximum size %d\n",
+               size, set->maxsize);
+      qh_setprint(qhmem.ferr, "set: ", set);
+      qh_errexit(qhmem_ERRqhull, NULL, NULL);
+    }
+  }else
+    size= set->maxsize;
+  return size;
+} /* setsize */
+
+/*---------------------------------
+
+  qh_settemp( setsize )
+    return a stacked, temporary set of upto setsize elements
+
+  notes:
+    use settempfree or settempfree_all to release from qhmem.tempstack
+    see also qh_setnew
+
+  design:
+    allocate set
+    append to qhmem.tempstack
+
+*/
+setT *qh_settemp(int setsize) {
+  setT *newset;
+
+  newset= qh_setnew(setsize);
+  qh_setappend(&qhmem.tempstack, newset);
+  if (qhmem.IStracing >= 5)
+    qh_fprintf(qhmem.ferr, 8123, "qh_settemp: temp set %p of %d elements, depth %d\n",
+       newset, newset->maxsize, qh_setsize(qhmem.tempstack));
+  return newset;
+} /* settemp */
+
+/*---------------------------------
+
+  qh_settempfree( set )
+    free temporary set at top of 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 qhmem.tempstack
+    free it
+*/
+void qh_settempfree(setT **set) {
+  setT *stackedset;
+
+  if (!*set)
+    return;
+  stackedset= qh_settemppop();
+  if (stackedset != *set) {
+    qh_settemppush(stackedset);
+    qh_fprintf(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(*set), qh_setsize(qhmem.tempstack)+1,
+             stackedset, qh_setsize(stackedset));
+    qh_errexit(qhmem_ERRqhull, NULL, NULL);
+  }
+  qh_setfree(set);
+} /* settempfree */
+
+/*---------------------------------
+
+  qh_settempfree_all(  )
+    free all temporary sets in qhmem.tempstack
+
+  design:
+    for each set in tempstack
+      free set
+    free qhmem.tempstack
+*/
+void qh_settempfree_all(void) {
+  setT *set, **setp;
+
+  FOREACHset_(qhmem.tempstack)
+    qh_setfree(&set);
+  qh_setfree(&qhmem.tempstack);
+} /* settempfree_all */
+
+/*---------------------------------
+
+  qh_settemppop(  )
+    pop and return temporary set from qhmem.tempstack
+
+  notes:
+    the returned set is permanent
+
+  design:
+    pop and check top of qhmem.tempstack
+*/
+setT *qh_settemppop(void) {
+  setT *stackedset;
+
+  stackedset= (setT*)qh_setdellast(qhmem.tempstack);
+  if (!stackedset) {
+    qh_fprintf(qhmem.ferr, 6180, "qhull internal error (qh_settemppop): pop from empty temporary stack\n");
+    qh_errexit(qhmem_ERRqhull, NULL, NULL);
+  }
+  if (qhmem.IStracing >= 5)
+    qh_fprintf(qhmem.ferr, 8124, "qh_settemppop: depth %d temp set %p of %d elements\n",
+       qh_setsize(qhmem.tempstack)+1, stackedset, qh_setsize(stackedset));
+  return stackedset;
+} /* settemppop */
+
+/*---------------------------------
+
+  qh_settemppush( set )
+    push temporary set unto qhmem.tempstack (makes it temporary)
+
+  notes:
+    duplicates settemp() for tracing
+
+  design:
+    append set to tempstack
+*/
+void qh_settemppush(setT *set) {
+    if (!set) {
+        fprintf (qhmem.ferr, "qhull error (qh_settemppush): can not push a NULL temp\n");
+        qh_errexit (qhmem_ERRqhull, NULL, NULL);
+    }
+  qh_setappend(&qhmem.tempstack, set);
+  if (qhmem.IStracing >= 5)
+    qh_fprintf(qhmem.ferr, 8125, "qh_settemppush: depth %d temp set %p of %d elements\n",
+      qh_setsize(qhmem.tempstack), set, qh_setsize(set));
+} /* settemppush */
+
+
+/*---------------------------------
+
+  qh_settruncate( 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(setT *set, int size) {
+
+  if (size < 0 || size > set->maxsize) {
+    qh_fprintf(qhmem.ferr, 6181, "qhull internal error (qh_settruncate): size %d out of bounds for set:\n", size);
+    qh_setprint(qhmem.ferr, "", set);
+    qh_errexit(qhmem_ERRqhull, NULL, NULL);
+  }
+  set->e[set->maxsize].i= size+1;   /* maybe overwritten */
+  set->e[size].p= NULL;
+} /* settruncate */
+
+/*---------------------------------
+
+  qh_setunique( 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(setT **set, void *elem) {
+
+  if (!qh_setin(*set, elem)) {
+    qh_setappend(set, elem);
+    return 1;
+  }
+  return 0;
+} /* setunique */
+
+/*---------------------------------
+
+  qh_setzero( 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(setT *set, int idx, int size) {
+  int count;
+
+  if (idx < 0 || idx >= size || size > set->maxsize) {
+    qh_fprintf(qhmem.ferr, 6182, "qhull internal error (qh_setzero): index %d or size %d out of bounds for set:\n", idx, size);
+    qh_setprint(qhmem.ferr, "", set);
+    qh_errexit(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
new file mode 100644
index 0000000..6212390
--- /dev/null
+++ b/src/libqhullr/qset_r.h
@@ -0,0 +1,488 @@
+/*
  ---------------------------------
+
+   qset.h
+     header file for qset.c that implements set
+
+   see qh-set.htm and qset.c
+
+   only uses mem.c, malloc/free
+
+   for error handling, writes message and calls
+      qh_errexit(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) 1993-2012 The Geometry Center.
+   $Id: //main/2011/qhull/src/libqhullr/qset_r.h#1 $$Change: 1640 $
+   $DateTime: 2014/01/15 09:12:08 $$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
+
+/*------------------------------------------
+
+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
+  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] */
+};
+
+struct setT {
+  int 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_(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_( facets ) FOREACHsetelement_i_( 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_(type, set, variable) \
+        if (((variable= NULL), set)) for (\
+          variable##_i= 0, variable= (type *)((set)->e[0].p), \
+                   variable##_n= qh_setsize(set);\
+          variable##_i < variable##_n;\
+          variable= (type *)((set)->e[++variable##_i].p) )
+
+/*----------------------------------------
+
+   FOREACHsetelementreverse_(type, set, variable)-
+     define FOREACH iterator in reverse order
+
+   declare:
+     assumes *variable and **variablep are declared
+     also declare 'int 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_(type, set, variable) \
+        if (((variable= NULL), set)) for (\
+           variable##temp= qh_setsize(set)-1, variable= qh_setlast(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))
+
+/*-----------------------------------------
+
+   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(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(setT **setp, void *elem);
+void  qh_setaddnth(setT **setp, int nth, void *newelem);
+void  qh_setappend(setT **setp, void *elem);
+void  qh_setappend_set(setT **setp, setT *setA);
+void  qh_setappend2ndlast(setT **setp, void *elem);
+void  qh_setcheck(setT *set, const char *tname, unsigned id);
+void  qh_setcompact(setT *set);
+setT *qh_setcopy(setT *set, int extra);
+void *qh_setdel(setT *set, void *elem);
+void *qh_setdellast(setT *set);
+void *qh_setdelnth(setT *set, int nth);
+void *qh_setdelnthsorted(setT *set, int nth);
+void *qh_setdelsorted(setT *set, void *newelem);
+setT *qh_setduplicate( setT *set, int elemsize);
+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_setendpointer(setT *set);
+void  qh_setfree(setT **set);
+void  qh_setfree2( setT **setp, int elemsize);
+void  qh_setfreelong(setT **set);
+int   qh_setin(setT *set, void *setelem);
+int   qh_setindex(setT *set, void *setelem);
+void  qh_setlarger(setT **setp);
+void *qh_setlast(setT *set);
+setT *qh_setnew(int size);
+setT *qh_setnew_delnthsorted(setT *set, int size, int nth, int prepend);
+void  qh_setprint(FILE *fp, const char* string, setT *set);
+void  qh_setreplace(setT *set, void *oldelem, void *newelem);
+int   qh_setsize(setT *set);
+setT *qh_settemp(int setsize);
+void  qh_settempfree(setT **set);
+void  qh_settempfree_all(void);
+setT *qh_settemppop(void);
+void  qh_settemppush(setT *set);
+void  qh_settruncate(setT *set, int size);
+int   qh_setunique(setT **set, void *elem);
+void  qh_setzero(setT *set, int idx, int size);
+
+
+#endif /* qhDEFset */
diff --git a/src/libqhullr/random_r.c b/src/libqhullr/random_r.c
new file mode 100644
index 0000000..d2af5dd
--- /dev/null
+++ b/src/libqhullr/random_r.c
@@ -0,0 +1,243 @@
+/*
  ---------------------------------
+
+   random.c -- utilities
+     Park & Miller's minimimal standard random number generator
+     argc/argv conversion
+
+     Used by rbox.  Do not use 'qh' 
+*/
+
+#include "libqhull.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( 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 */
+
+int qh_rand_seed= 1;  /* define as global variable instead of using qh */
+
+#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( void) {
+    int lo, hi, test;
+    int seed = qh_rand_seed;
+
+    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_rand_seed= seed;
+    /* seed = seed < qh_RANDOMmax/2 ? 0 : qh_RANDOMmax;  for testing */
+    /* seed = qh_RANDOMmax;  for testing */
+    return seed;
+} /* rand */
+
+void qh_srand( int seed) {
+    if (seed < 1)
+        qh_rand_seed= 1;
+    else if (seed >= qh_rand_m)
+        qh_rand_seed= qh_rand_m - 1;
+    else
+        qh_rand_seed= seed;
+} /* qh_srand */
+
+/*---------------------------------
+
+qh_randomfactor( scale, offset )
+return a random factor r * scale + offset
+
+notes:
+qh.RANDOMa/b are defined in global.c
+*/
+realT qh_randomfactor(realT scale, realT offset) {
+    realT randr;
+
+    randr= qh_RANDOMint;
+    return randr * scale + offset;
+} /* randomfactor */
+
+/*---------------------------------
+
+qh_randommatrix( 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
+*/
+void qh_randommatrix(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
new file mode 100644
index 0000000..9b0ac54
--- /dev/null
+++ b/src/libqhullr/random_r.h
@@ -0,0 +1,34 @@
+/*
  ---------------------------------
+
+  random.h
+    header file for random routines
+
+   see qh-geom.htm and random.c
+
+   Copyright (c) 1993-2012 The Geometry Center.
+   $Id: //main/2011/qhull/src/libqhullr/random_r.h#1 $$Change: 1640 $
+   $DateTime: 2014/01/15 09:12:08 $$Author: bbarber $
+*/
+
+#ifndef qhDEFrandom
+#define qhDEFrandom 1
+
+#include "libqhull.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( void);
+void    qh_srand( int seed);
+realT   qh_randomfactor(realT scale, realT offset);
+void    qh_randommatrix(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
new file mode 100644
index 0000000..0fafeec
--- /dev/null
+++ b/src/libqhullr/rboxlib_r.c
@@ -0,0 +1,795 @@
+/*
  ---------------------------------
+
+   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 roundi( double a);
+void out1( double a);
+void out2n( double a, double b);
+void 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() */
+};
+
+
+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)
+        out1( 1.0);
+      while (*++s) {
+        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--; )
+          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)
+        out1( 1.0);
+      for (k=0; k < dim; k++)
+        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))
+          out1( cube);
+        else
+          out1( -cube);
+      }
+      qh_fprintf_rbox(rbox.fout, 9400, "\n");
+    }
+  }
+
+  /* ============= write diamond vertices =============== */
+  if (adddiamond) {
+    for (j=0; j=0; k--) {
+        if (j/2 != k)
+          out1( 0.0);
+        else if (j & 0x1)
+          out1( diamond);
+        else
+          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 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);
+  }
+} /* roundi */
+
+void out1(double a) {
+
+  if (rbox.isinteger)
+    qh_fprintf_rbox(rbox.fout, 9403, "%d ", roundi( a+rbox.out_offset));
+  else
+    qh_fprintf_rbox(rbox.fout, 9404, qh_REAL_1, a+rbox.out_offset);
+} /* out1 */
+
+void out2n( double a, double b) {
+
+  if (rbox.isinteger)
+    qh_fprintf_rbox(rbox.fout, 9405, "%d %d\n", roundi(a+rbox.out_offset), roundi(b+rbox.out_offset));
+  else
+    qh_fprintf_rbox(rbox.fout, 9406, qh_REAL_2n, a+rbox.out_offset, b+rbox.out_offset);
+} /* out2n */
+
+void out3n( double a, double b, double c) {
+
+  if (rbox.isinteger)
+    qh_fprintf_rbox(rbox.fout, 9407, "%d %d %d\n", roundi(a+rbox.out_offset), roundi(b+rbox.out_offset), 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);
+} /* out3n */
+
+void qh_errexit_rbox(int exitcode)
+{
+    longjmp(rbox.errexit, exitcode);
+} /* rbox_errexit */
+
diff --git a/src/libqhullr/stat_r.c b/src/libqhullr/stat_r.c
new file mode 100644
index 0000000..7060460
--- /dev/null
+++ b/src/libqhullr/stat_r.c
@@ -0,0 +1,714 @@
+/*
  ---------------------------------
+
+   stat.c
+   contains all statistics that are collected for qhull
+
+   see qh-stat.htm and stat.h
+
+   Copyright (c) 1993-2012 The Geometry Center.
+   $Id: //main/2011/qhull/src/libqhullr/stat_r.c#1 $$Change: 1640 $
+   $DateTime: 2014/01/15 09:12:08 $$Author: bbarber $
+*/
+
+#include "qhull_a.h"
+
+/*============ global data structure ==========*/
+
+#if qh_QHpointer
+qhstatT *qh_qhstat=NULL;  /* global data structure */
+#else
+qhstatT qh_qhstat;   /* add "={0}" if this causes a compiler error */
+#endif
+
+/*========== 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(void) {
+
+   /* 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);
+
+  qhstat precision= 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(void) {
+  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(void) {
+  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(void) {
+  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(void) {
+  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(void) {
+  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(void) {
+  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(void) {
+  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(void) {
+  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(void) {
+  qhstat vridges= 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(void) {
+  int i;
+
+  for(i=ZEND; i--; )
+    qhstat printed[i]= False;
+} /* allstatistics */
+
+#if qh_KEEPstatistics
+/*---------------------------------
+
+  qh_collectstatistics()
+    collect statistics for qh.facet_list
+
+*/
+void qh_collectstatistics(void) {
+  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 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(facet->vertices);
+    sizneighbors= qh_setsize(facet->neighbors);
+    sizridges= qh_setsize(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(facet->outsideset));
+    if (facet->coplanarset)
+      zadd_(Zmempoints, sizeof(setT) + SETelemsize * qh_setsize(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(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(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(vertex->neighbors);
+      zadd_(Znumvneighbors, sizneighbors);
+      zmax_(Zmaxvneighbors, sizneighbors);
+      zadd_(Zmemvertices, sizeof(vertexT) + SETelemsize * sizneighbors);
+    }
+  }
+  qh RANDOMdist= qh old_randomdist;
+} /* collectstatistics */
+#endif /* qh_KEEPstatistics */
+
+/*---------------------------------
+
+  qh_freestatistics(  )
+    free memory used for statistics
+*/
+void qh_freestatistics(void) {
+
+#if qh_QHpointer
+  qh_free(qh_qhstat);
+  qh_qhstat= NULL;
+#endif
+} /* freestatistics */
+
+/*---------------------------------
+
+  qh_initstatistics(  )
+    allocate and initialize statistics
+
+  notes:
+    uses qh_malloc() instead of qh_memalloc() since mem.c not set up yet
+    NOerrors -- qh_initstatistics can not use qh_errexit().  One first call, qh_memalloc is not initialized.  Also invoked by QhullQh().
+*/
+void qh_initstatistics(void) {
+  int i;
+  realT realx;
+  int intx;
+
+#if qh_QHpointer
+  if(qh_qhstat){  /* qh_initstatistics may be called from Qhull::resetStatistics() */
+      qh_free(qh_qhstat);
+      qh_qhstat= 0;
+  }
+  if (!(qh_qhstat= (qhstatT *)qh_malloc(sizeof(qhstatT)))) {
+    qh_fprintf(qhmem.ferr, 6183, "qhull error (qh_initstatistics): insufficient memory\n");
+    qh_exit(qh_ERRmem);  /* can not use qh_errexit() */
+  }
+#endif
+
+  qhstat next= 0;
+  qh_allstatA();
+  qh_allstatB();
+  qh_allstatC();
+  qh_allstatD();
+  qh_allstatE();
+  qh_allstatE2();
+  qh_allstatF();
+  qh_allstatG();
+  qh_allstatH();
+  qh_allstatI();
+  if (qhstat next > (int)sizeof(qhstat id)) {
+    qh_fprintf(qhmem.ferr, 6184, "qhull error (qh_initstatistics): increase size of qhstat.id[].\n\
+      qhstat.next %d should be <= sizeof(qhstat id) %d\n", qhstat next, (int)sizeof(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 (qhstat id[i] == qhstat id[j]) {
+          qh_fprintf(qhmem.ferr, 6185, "qhull error (qh_initstatistics): duplicated statistic %d at indices %d and %d\n",
+              qhstat id[i], i, j);
+        }
+      }
+    }
+#endif
+    qh_exit(qh_ERRqhull);  /* can not use qh_errexit() */
+  }
+  qhstat init[zinc].i= 0;
+  qhstat init[zadd].i= 0;
+  qhstat init[zmin].i= INT_MAX;
+  qhstat init[zmax].i= INT_MIN;
+  qhstat init[wadd].r= 0;
+  qhstat init[wmin].r= REALmax;
+  qhstat init[wmax].r= -REALmax;
+  for(i=0; i < ZEND; i++) {
+    if (qhstat type[i] > ZTYPEreal) {
+      realx= qhstat init[(unsigned char)(qhstat type[i])].r;
+      qhstat stats[i].r= realx;
+    }else if (qhstat type[i] != zdoc) {
+      intx= qhstat init[(unsigned char)(qhstat type[i])].i;
+      qhstat stats[i].i= intx;
+    }
+  }
+} /* initstatistics */
+
+/*---------------------------------
+
+  qh_newstats(  )
+    returns True if statistics for zdoc
+
+  returns:
+    next zdoc
+*/
+boolT qh_newstats(int idx, int *nextindex) {
+  boolT isnew= False;
+  int start, i;
+
+  if (qhstat type[qhstat id[idx]] == zdoc)
+    start= idx+1;
+  else
+    start= idx;
+  for(i= start; i < qhstat next && qhstat type[qhstat id[i]] != zdoc; i++) {
+    if (!qh_nostatistic(qhstat id[i]) && !qhstat printed[qhstat id[i]])
+        isnew= True;
+  }
+  *nextindex= i;
+  return isnew;
+} /* newstats */
+
+/*---------------------------------
+
+  qh_nostatistic( index )
+    true if no statistic to print
+*/
+boolT qh_nostatistic(int i) {
+
+  if ((qhstat type[i] > ZTYPEreal
+       &&qhstat stats[i].r == qhstat init[(unsigned char)(qhstat type[i])].r)
+      || (qhstat type[i] < ZTYPEreal
+          &&qhstat stats[i].i == qhstat init[(unsigned char)(qhstat type[i])].i))
+    return True;
+  return False;
+} /* nostatistic */
+
+#if qh_KEEPstatistics
+/*---------------------------------
+
+  qh_printallstatistics( fp, string )
+    print all statistics with header 'string'
+*/
+void qh_printallstatistics(FILE *fp, const char *string) {
+
+  qh_allstatistics();
+  qh_collectstatistics();
+  qh_printstatistics(fp, string);
+  qh_memstatistics(fp);
+}
+
+
+/*---------------------------------
+
+  qh_printstatistics( 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(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(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(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(fp, 9352, "\
+ %6.2g max. distance for near-inside points\n", qh NEARinside);
+  if (qh premerge_cos < REALmax/2) qh_fprintf(fp, 9353, "\
+ %6.2g max. cosine for pre-merge angle\n", qh premerge_cos);
+  if (qh PREmerge) qh_fprintf(fp, 9354, "\
+ %6.2g radius of pre-merge centrum\n", qh premerge_centrum);
+  if (qh postmerge_cos < REALmax/2) qh_fprintf(fp, 9355, "\
+ %6.2g max. cosine for post-merge angle\n", qh postmerge_cos);
+  if (qh POSTmerge) qh_fprintf(fp, 9356, "\
+ %6.2g radius of post-merge centrum\n", qh postmerge_centrum);
+  qh_fprintf(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(fp, 9358, "%6.2e ", qh NEARzero[k]);
+  qh_fprintf(fp, 9359, "\n\n");
+  for(i=0 ; i < qhstat next; )
+    qh_printstats(fp, i, &i);
+} /* printstatistics */
+#endif /* qh_KEEPstatistics */
+
+/*---------------------------------
+
+  qh_printstatlevel( fp, id )
+    print level information for a statistic
+
+  notes:
+    nop if id >= ZEND, printed, or same as initial value
+*/
+void qh_printstatlevel(FILE *fp, int id, int start) {
+#define NULLfield "       "
+
+  if (id >= ZEND || qhstat printed[id])
+    return;
+  if (qhstat type[id] == zdoc) {
+    qh_fprintf(fp, 9360, "%s\n", qhstat doc[id]);
+    return;
+  }
+  start= 0; /* not used */
+  if (qh_nostatistic(id) || !qhstat doc[id])
+    return;
+  qhstat printed[id]= True;
+  if (qhstat count[id] != -1
+      && qhstat stats[(unsigned char)(qhstat count[id])].i == 0)
+    qh_fprintf(fp, 9361, " *0 cnt*");
+  else if (qhstat type[id] >= ZTYPEreal && qhstat count[id] == -1)
+    qh_fprintf(fp, 9362, "%7.2g", qhstat stats[id].r);
+  else if (qhstat type[id] >= ZTYPEreal && qhstat count[id] != -1)
+    qh_fprintf(fp, 9363, "%7.2g", qhstat stats[id].r/ qhstat stats[(unsigned char)(qhstat count[id])].i);
+  else if (qhstat type[id] < ZTYPEreal && qhstat count[id] == -1)
+    qh_fprintf(fp, 9364, "%7d", qhstat stats[id].i);
+  else if (qhstat type[id] < ZTYPEreal && qhstat count[id] != -1)
+    qh_fprintf(fp, 9365, "%7.3g", (realT) qhstat stats[id].i / qhstat stats[(unsigned char)(qhstat count[id])].i);
+  qh_fprintf(fp, 9366, " %s\n", qhstat doc[id]);
+} /* printstatlevel */
+
+
+/*---------------------------------
+
+  qh_printstats( fp, index, nextindex )
+    print statistics for a zdoc group
+
+  returns:
+    next zdoc if non-null
+*/
+void qh_printstats(FILE *fp, int idx, int *nextindex) {
+  int j, nexti;
+
+  if (qh_newstats(idx, &nexti)) {
+    qh_fprintf(fp, 9367, "\n");
+    for (j=idx; j--------------------------------
+
+  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(void) {}
+void    qh_printallstatistics(FILE *fp, char *string) {};
+void    qh_printstatistics(FILE *fp, char *string) {}
+#endif
+
diff --git a/src/libqhullr/stat_r.h b/src/libqhullr/stat_r.h
new file mode 100644
index 0000000..8d334d6
--- /dev/null
+++ b/src/libqhullr/stat_r.h
@@ -0,0 +1,541 @@
+/*
  ---------------------------------
+
+   stat.h
+     contains all statistics that are collected for qhull
+
+   see qh-stat.htm and stat.c
+
+   Copyright (c) 1993-2012 The Geometry Center.
+   $Id: //main/2011/qhull/src/libqhullr/stat_r.h#1 $$Change: 1640 $
+   $DateTime: 2014/01/15 09:12:08 $$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
+
+#include "libqhull.h"
+
+/*---------------------------------
+
+  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
+      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 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 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) qhstat id[qhstat next++]=name; \
+   qhstat doc[name]= string; qhstat count[name]= cnt; qhstat type[name]= stype
+#if qh_KEEPstatistics
+#define zdef_(stype,name,string,cnt) qhstat id[qhstat next++]=name; \
+   qhstat doc[name]= string; qhstat count[name]= cnt; qhstat type[name]= stype
+#else
+#define zdef_(type,name,doc,count)
+#endif
+
+/*----------------------------------
+
+  zzinc_( name ), zinc_( name)
+    increment an integer statistic
+*/
+#define zzinc_(id) {MAYdebugx; qhstat stats[id].i++;}
+#if qh_KEEPstatistics
+#define zinc_(id) {MAYdebugx; 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; qhstat stats[id].i += (val);}
+#define wwadd_(id, val) {MAYdebugx; qhstat stats[id].r += (val);}
+#if qh_KEEPstatistics
+#define zadd_(id, val) {MAYdebugx; qhstat stats[id].i += (val);}
+#define wadd_(id, val) {MAYdebugx; 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) ((qhstat stats[id]).i)
+#define wwval_(id) ((qhstat stats[id]).r)
+#if qh_KEEPstatistics
+#define zval_(id) ((qhstat stats[id]).i)
+#define wval_(id) ((qhstat stats[id]).r)
+#else
+#define zval_(id) qhstat tempi
+#define wval_(id) qhstat tempr
+#endif
+
+/*----------------------------------
+
+  zmax_( id, val ), wmax_( id, value )
+    maximize id with val
+*/
+#define wwmax_(id, val) {MAYdebugx; maximize_(qhstat stats[id].r,(val));}
+#if qh_KEEPstatistics
+#define zmax_(id, val) {MAYdebugx; maximize_(qhstat stats[id].i,(val));}
+#define wmax_(id, val) {MAYdebugx; maximize_(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_(qhstat stats[id].i,(val));}
+#define wmin_(id, val) {MAYdebugx; minimize_(qhstat stats[id].r,(val));}
+#else
+#define zmin_(id, val) {}
+#define wmin_(id, val) {}
+#endif
+
+/*================== stat.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
+    global data structure for statistics, similar to qh and qhrbox
+
+  notes:
+   access to qh_qhstat is via the "qhstat" macro.  There are two choices
+   qh_QHpointer = 1     access globals via a pointer
+                        enables qh_saveqhull() and qh_restoreqhull()
+                = 0     qh_qhstat is a static data structure
+                        only one instance of qhull() can be active at a time
+                        default value
+   qh_QHpointer is defined in libqhull.h
+   qh_QHpointer_dllimport and qh_dllimport define qh_qh as __declspec(dllimport) [libqhull.h]
+
+   allocated in stat.c using qh_malloc()
+*/
+#ifndef DEFqhstatT
+#define DEFqhstatT 1
+typedef struct qhstatT qhstatT;
+#endif
+
+#if qh_QHpointer_dllimport
+#define qhstat qh_qhstat->
+__declspec(dllimport) extern qhstatT *qh_qhstat;
+#elif qh_QHpointer
+#define qhstat qh_qhstat->
+extern qhstatT *qh_qhstat;
+#elif qh_dllimport
+#define qhstat qh_qhstat.
+__declspec(dllimport) extern qhstatT qh_qhstat;
+#else
+#define qhstat qh_qhstat.
+extern qhstatT qh_qhstat;
+#endif
+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(void);
+void    qh_allstatB(void);
+void    qh_allstatC(void);
+void    qh_allstatD(void);
+void    qh_allstatE(void);
+void    qh_allstatE2(void);
+void    qh_allstatF(void);
+void    qh_allstatG(void);
+void    qh_allstatH(void);
+void    qh_allstatI(void);
+void    qh_allstatistics(void);
+void    qh_collectstatistics(void);
+void    qh_freestatistics(void);
+void    qh_initstatistics(void);
+boolT   qh_newstats(int idx, int *nextindex);
+boolT   qh_nostatistic(int i);
+void    qh_printallstatistics(FILE *fp, const char *string);
+void    qh_printstatistics(FILE *fp, const char *string);
+void    qh_printstatlevel(FILE *fp, int id, int start);
+void    qh_printstats(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
new file mode 100644
index 0000000..653c5a4
--- /dev/null
+++ b/src/libqhullr/user_r.c
@@ -0,0 +1,527 @@
+/*
  ---------------------------------
+
+   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;
+  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/libqhullr/user_r.h b/src/libqhullr/user_r.h
new file mode 100644
index 0000000..a3322aa
--- /dev/null
+++ b/src/libqhullr/user_r.h
@@ -0,0 +1,858 @@
+/*
  ---------------------------------
+
+   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.
+
+  def counters =  [27, 1047, 2059, 3025, 4068, 5003,
+     6241, 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_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
+              #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/libqhullr/usermem_r.c b/src/libqhullr/usermem_r.c
new file mode 100644
index 0000000..8cb6ba4
--- /dev/null
+++ b/src/libqhullr/usermem_r.c
@@ -0,0 +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
+
+   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/libqhullr/userprintf_r.c b/src/libqhullr/userprintf_r.c
new file mode 100644
index 0000000..88ead2f
--- /dev/null
+++ b/src/libqhullr/userprintf_r.c
@@ -0,0 +1,63 @@
+/*
  ---------------------------------
+
+   userprintf.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
+   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 Qhull.cpp and RboxPoints.cpp for examples.
+
+   Please report any errors that you fix to qhull@qhull.org
+*/
+
+#include "libqhull.h"
+
+#include 
+#include 
+#include 
+
+/*---------------------------------
+
+   qh_fprintf(fp, msgcode, format, list of args )
+     print arguments to *fp according to format
+     Use qh_fprintf_rbox() for rboxlib.c
+
+   notes:
+     same as fprintf()
+     fgets() is not trapped like fprintf()
+     exit qh_fprintf via qh_errexit()
+*/
+
+void qh_fprintf(FILE *fp, int msgcode, const char *fmt, ... ) {
+    va_list args;
+
+    if (!fp) {
+        fprintf(stderr, "QH6232 Qhull internal error (userprintf.c): fp is 0.  Wrong qh_fprintf called.\n");
+        qh_errexit(6232, NULL, NULL);
+    }
+    va_start(args, fmt);
+#if qh_QHpointer
+    if (qh_qh && qh ANNOTATEoutput) {
+#else
+    if (qh ANNOTATEoutput) {
+#endif
+      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
new file mode 100644
index 0000000..92c3572
--- /dev/null
+++ b/src/libqhullr/userprintf_rbox_r.c
@@ -0,0 +1,53 @@
+/*
  ---------------------------------
+
+   userprintf_rbox.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
+   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 Qhull.cpp and RboxPoints.cpp for examples.
+
+   Please report any errors that you fix to qhull@qhull.org
+*/
+
+#include "libqhull.h"
+
+#include 
+#include 
+#include 
+
+/*---------------------------------
+
+   qh_fprintf_rbox(fp, msgcode, format, list of args )
+     print arguments to *fp according to format
+     Use qh_fprintf_rbox() for rboxlib.c
+
+   notes:
+     same as fprintf()
+     fgets() is not trapped like fprintf()
+     exit qh_fprintf_rbox via qh_errexit_rbox()
+*/
+
+void qh_fprintf_rbox(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");
+        qh_errexit_rbox(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/libqhullrcpp/Coordinates.cpp b/src/libqhullrcpp/Coordinates.cpp
new file mode 100644
index 0000000..72b8557
--- /dev/null
+++ b/src/libqhullrcpp/Coordinates.cpp
@@ -0,0 +1,184 @@
+/****************************************************************************
+**
+** Copyright (c) 2009-2012 C.B. Barber. All rights reserved.
+** $Id: //main/2011/qhull/src/libqhullrcpp/Coordinates.cpp#1 $$Change: 1640 $
+** $DateTime: 2014/01/15 09:12:08 $$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
+{
+    int 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
+{
+    return ((idx < 0 || idx >= count()) ? defaultValue : (*this)[idx]);
+}//value
+
+#//Operator
+
+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)
+{
+    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)
+{
+    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::
+count(const coordT &t) const
+{
+    CoordinatesIterator i(*this);
+    int result= 0;
+    while(i.findNext(t)){
+        ++result;
+    }
+    return result;
+}//count
+
+int Coordinates::
+indexOf(const coordT &t, int from) const
+{
+    if(from<0){
+        from += count();
+        if(from<0){
+            from= 0;
+        }
+    }
+    if(from(i-begin())); // WARN64
+            }
+            ++i;
+        }
+    }
+    return -1;
+}//indexOf
+
+int Coordinates::
+lastIndexOf(const coordT &t, int 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
+            }
+        }
+    }
+    return -1;
+}//lastIndexOf
+
+void Coordinates::
+removeAll(const coordT &t)
+{
+    MutableCoordinatesIterator i(*this);
+    while(i.findNext(t)){
+        i.remove();
+    }
+}//removeAll
+
+}//namespace orgQhull
+
+#//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--; ){
+        os << *c++ << " ";
+    }
+    return os;
+}//operator<<
+
diff --git a/src/libqhullrcpp/Coordinates.h b/src/libqhullrcpp/Coordinates.h
new file mode 100644
index 0000000..7713bc0
--- /dev/null
+++ b/src/libqhullrcpp/Coordinates.h
@@ -0,0 +1,311 @@
+/****************************************************************************
+**
+** Copyright (c) 2009-2012 C.B. Barber. All rights reserved.
+** $Id: //main/2011/qhull/src/libqhullrcpp/Coordinates.h#1 $$Change: 1640 $
+** $DateTime: 2014/01/15 09:12:08 $$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
+    //! an allocated vector of point coordinates
+    //!  Used by PointCoordinates for RboxPoints
+    //!  A QhullPoint refers to previously allocated coordinates
+    class  Coordinates;
+    class  MutableCoordinatesIterator;
+
+
+class Coordinates {
+
+private:
+#//Fields
+    std::vector coordinate_array;
+
+public:
+#//Subtypes
+
+    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 ptrdiff_t           difference_type;
+    typedef int                 size_type;
+
+#//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
+
+    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
+    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
+    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
+    Coordinates         operator+(const Coordinates &other) const;
+
+#//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; }
+    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
+    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
+    // before const_iterator for conversion with comparison operators
+    class iterator {
+
+    private:
+        std::vector::iterator i;
+        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; }
+        std::vector::iterator &base() { return i; }
+                        // No operator-> for base types
+        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
+    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]; }
+
+        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
+
+std::ostream &operator<<(std::ostream &os, const orgQhull::Coordinates &c);
+
+#endif // QHCOORDINATES_H
diff --git a/src/libqhullrcpp/PointCoordinates.cpp b/src/libqhullrcpp/PointCoordinates.cpp
new file mode 100644
index 0000000..52a68ac
--- /dev/null
+++ b/src/libqhullrcpp/PointCoordinates.cpp
@@ -0,0 +1,294 @@
+/****************************************************************************
+**
+** Copyright (c) 2009-2012 C.B. Barber. All rights reserved.
+** $Id: //main/2011/qhull/src/libqhullrcpp/PointCoordinates.cpp#1 $$Change: 1640 $
+** $DateTime: 2014/01/15 09:12:08 $$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)
+{
+    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
+    //! Zero or more points with Coordinates, count, and dimension
+    class PointCoordinates;
+
+class PointCoordinates : public QhullPoints {
+
+private:
+#//Field
+    Coordinates         point_coordinates;      //! array of point coordinates
+                                                //! may have extraCoordinates()
+    std::string         point_comment;          //! 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
+                        //! Use append() and appendPoints() for Coordinates and vector
+                        PointCoordinates(const PointCoordinates &other);
+    PointCoordinates   &operator=(const PointCoordinates &other);
+    ~PointCoordinates();
+
+#//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
+    //! 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; }
+    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
+    //! See QhullPoints for at, back, first, front, last, mid, [], value
+
+#//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
+    //! See QhullPoints for contains, count, indexOf, lastIndexOf
+
+#//Read-only
+    PointCoordinates    operator+(const PointCoordinates &other) const;
+
+#//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; }
+    // reserve() is non-const
+    void                reserveCoordinates(int newCoordinates);
+
+#//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
+
+std::ostream           &operator<<(std::ostream &os, const orgQhull::PointCoordinates &p);
+
+#endif // QHPOINTCOORDINATES_H
diff --git a/src/libqhullrcpp/Qhull.cpp b/src/libqhullrcpp/Qhull.cpp
new file mode 100644
index 0000000..00cbcbe
--- /dev/null
+++ b/src/libqhullrcpp/Qhull.cpp
@@ -0,0 +1,543 @@
+/****************************************************************************
+**
+** Copyright (c) 2008-2012 C.B. Barber. All rights reserved.
+** $Id: //main/2011/qhull/src/libqhullrcpp/Qhull.cpp#1 $$Change: 1640 $
+** $DateTime: 2014/01/15 09:12:08 $$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();
+}//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();
+    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();
+    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();
+}//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()
+{
+    #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
+
+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/libqhullrcpp/Qhull.h b/src/libqhullrcpp/Qhull.h
new file mode 100644
index 0000000..5025191
--- /dev/null
+++ b/src/libqhullrcpp/Qhull.h
@@ -0,0 +1,147 @@
+/****************************************************************************
+**
+** Copyright (c) 2008-2012 C.B. Barber. All rights reserved.
+** $Id: //main/2011/qhull/src/libqhullrcpp/Qhull.h#1 $$Change: 1640 $
+** $DateTime: 2014/01/15 09:12:08 $$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;
+
+    //Defined elsewhere
+    class QhullFacetList;
+    class RboxPoints;
+
+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)
+    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
+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
+                        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();
+private:
+    void                initializeQhull();
+
+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); }
+    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; }
+    QhullVertexList     vertexList() const;
+
+#//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
+    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/libqhullrcpp/QhullError.h b/src/libqhullrcpp/QhullError.h
new file mode 100644
index 0000000..6019247
--- /dev/null
+++ b/src/libqhullrcpp/QhullError.h
@@ -0,0 +1,64 @@
+/****************************************************************************
+**
+** Copyright (c) 2008-2012 C.B. Barber. All rights reserved.
+** $Id: //main/2011/qhull/src/libqhullrcpp/QhullError.h#1 $$Change: 1640 $
+** $DateTime: 2014/01/15 09:12:08 $$Author: bbarber $
+**
+****************************************************************************/
+
+#ifndef QHULLERROR_H
+#define QHULLERROR_H
+
+#include "RoadError.h"
+
+#include 
+#include 
+#include 
+
+namespace orgQhull {
+
+#//Types
+    //! QhullError -- std::exception class for Qhull
+    class QhullError;
+
+class QhullError : public RoadError {
+
+public:
+#//Constants
+    enum {
+        QHULLfirstError= 10000, //MSG_QHULL_ERROR in Qhull's user.h
+        QHULLlastError= 10070,
+        NOthrow= 1 //! For flag to UsingLibQhull()
+    };
+
+#//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
+
+inline std::ostream &operator<<(std::ostream &os, const orgQhull::QhullError &e) { return os << e.what(); }
+
+#endif // QHULLERROR_H
diff --git a/src/libqhullrcpp/QhullFacet.cpp b/src/libqhullrcpp/QhullFacet.cpp
new file mode 100644
index 0000000..fdd6468
--- /dev/null
+++ b/src/libqhullrcpp/QhullFacet.cpp
@@ -0,0 +1,524 @@
+/****************************************************************************
+**
+** Copyright (c) 2008-2012 C.B. Barber. All rights reserved.
+** $Id: //main/2011/qhull/src/libqhullrcpp/QhullFacet.cpp#1 $$Change: 1640 $
+** $DateTime: 2014/01/15 09:12:08 $$Author: bbarber $
+**
+****************************************************************************/
+
+#//! QhullFacet -- Qhull's facet structure, facetT, as a C++ class
+
+#include "QhullError.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
+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
+{
+    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
+
+//! Return voronoi center or facet centrum.  Derived from qh_printcenter [io.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
+QhullPoint QhullFacet::
+getCenter(int qhRunId, qh_PRINT printFormat)
+{
+    UsingLibQhull q(qhRunId);
+
+    if(qh CENTERtype==qh_ASvoronoi){
+        if(!qh_facet->normal || !qh_facet->upperdelaunay || !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);
+                }
+                q.maybeThrowQhullMessage(exitCode);
+            }
+            return QhullPoint(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){
+            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());
+            }
+            q.maybeThrowQhullMessage(exitCode);
+        }
+        return QhullPoint(numCoords, qh_facet->center);
+    }
+    return QhullPoint();
+ }//getCenter
+
+//! Return innerplane clearly below the vertices
+//! from io.c[qh_PRINTinner]
+QhullHyperplane QhullFacet::
+innerplane(int qhRunId) const{
+    UsingLibQhull q(qhRunId);
+    realT inner;
+    // Does not error
+    qh_outerinner(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]
+QhullHyperplane QhullFacet::
+outerplane(int qhRunId) const{
+    UsingLibQhull q(qhRunId);
+    realT outer;
+    // Does not error
+    qh_outerinner(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 0; // FIXUP QH11009 Should false be the NULL facet or empty facet
+}//tricoplanarOwner
+
+QhullPoint QhullFacet::
+voronoiVertex(int qhRunId)
+{
+    if(
+#if qh_QHpointer
+      !qh_qh ||
+#endif
+      qh CENTERtype!=qh_ASvoronoi){
+          throw QhullError(10052, "Error: QhullFacet.voronoiVertex() requires option 'v' (qh_ASvoronoi)");
+    }
+    return getCenter(qhRunId);
+}//voronoiVertex
+
+#//Value
+
+//! Disables tricoplanarOwner()
+double QhullFacet::
+facetArea(int qhRunId)
+{
+    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_facet->isarea= True;
+        }
+        q.maybeThrowQhullMessage(exitCode);
+    }
+    return qh_facet->f.area;
+}//facetArea
+
+#//Foreach
+
+QhullPointSet QhullFacet::
+coplanarPoints() const
+{
+    return QhullPointSet(dimension(), qh_facet->coplanarset);
+}//coplanarPoints
+
+QhullFacetSet QhullFacet::
+neighborFacets() const
+{
+    return QhullFacetSet(qh_facet->neighbors);
+}//neighborFacets
+
+QhullPointSet QhullFacet::
+outsidePoints() const
+{
+    return QhullPointSet(dimension(), qh_facet->outsideset);
+}//outsidePoints
+
+QhullRidgeSet QhullFacet::
+ridges() const
+{
+    return QhullRidgeSet(qh_facet->ridges);
+}//ridges
+
+QhullVertexSet QhullFacet::
+vertices() const
+{
+    return QhullVertexSet(qh_facet->vertices);
+}//vertices
+
+
+}//namespace orgQhull
+
+#//operator<<
+
+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);
+    if(!f.ridges().isEmpty()){
+        os << f.printRidges(pr.run_id);
+    }
+    return os;
+}//operator<< PrintFacet
+
+//! Print Voronoi center or facet centrum to stream.  Same as qh_printcenter [io.c]
+//! 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){
+        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(!f->center){
+                f->center= qh_facetcenter(f->vertices);
+            }
+            for(int k=0; kcenter[k] << " "; // FIXUP QH11010 qh_REAL_1
+            }
+        }else{
+            for(int k=0; kcenter){
+            f->center= qh_getcentrum(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]
+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]
+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){
+        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 qh_MAXoutside
+    if(f->maxoutside > 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;
+            for(QhullPointSet::iterator i=ps.begin(); i!=ps.end(); ++i){
+                QhullPoint p= *i;
+                os << p.print(pr.run_id, "     ");
+            }
+        }else if(ps.size()<21){
+            os << ps.print(pr.run_id, "    - outside set:");
+        }else{
+            os << "    - outside set:  " << ps.size() << " points.";
+            os << furthest.print(pr.run_id, "  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;
+            for(QhullPointSet::iterator i=cs.begin(); i!=cs.end(); ++i){
+                QhullPoint p= *i;
+                os << p.print(pr.run_id, "     ");
+            }
+        }else if(cs.size()<21){
+            os << cs.print(pr.run_id, "    - coplanar set:");
+        }else{
+            os << "    - coplanar set:  " << cs.size() << " points.";
+            os << furthest.print(pr.run_id, "  Furthest");
+        }
+        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:");
+    }
+    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
+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;
+            }
+        }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);
+                ++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);
+                        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);
+            }
+        }
+    }
+    return os;
+}//operator<< PrintRidges
+
+// "No conversion" error if defined inline
+ostream &
+operator<<(ostream &os, QhullFacet &f)
+{
+    os << f.print(UsingLibQhull::NOqhRunId);
+    return os;
+}//<< QhullFacet
diff --git a/src/libqhullrcpp/QhullFacet.h b/src/libqhullrcpp/QhullFacet.h
new file mode 100644
index 0000000..c310db0
--- /dev/null
+++ b/src/libqhullrcpp/QhullFacet.h
@@ -0,0 +1,155 @@
+/****************************************************************************
+**
+** Copyright (c) 2008-2012 C.B. Barber. All rights reserved.
+** $Id: //main/2011/qhull/src/libqhullrcpp/QhullFacet.h#1 $$Change: 1640 $
+** $DateTime: 2014/01/15 09:12:08 $$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
+    class QhullFacetSet;
+    class QhullRidge;
+    typedef QhullSet  QhullRidgeSet;
+    class QhullVertex;
+    class QhullVertexSet;
+
+#//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()
+
+#//Class objects
+    static facetT       s_empty_facet; // needed for shallow copy
+
+public:
+#//Constants
+
+#//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() {}
+
+#//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; }
+
+#//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;
+    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
+    //! 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
+    // Can not inline.  Otherwise circular reference
+    QhullPointSet       coplanarPoints() const;
+    QhullFacetSet       neighborFacets() const;
+    QhullPointSet       outsidePoints() const;
+    QhullRidgeSet       ridges() const;
+    QhullVertexSet      vertices() const;
+
+#//IO
+    struct PrintCenter{
+        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()
+        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;
+                        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) {}
+    };//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
+
+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/libqhullrcpp/QhullFacetList.cpp b/src/libqhullrcpp/QhullFacetList.cpp
new file mode 100644
index 0000000..05f2422
--- /dev/null
+++ b/src/libqhullrcpp/QhullFacetList.cpp
@@ -0,0 +1,164 @@
+/****************************************************************************
+**
+** Copyright (c) 2008-2012 C.B. Barber. All rights reserved.
+** $Id: //main/2011/qhull/src/libqhullrcpp/QhullFacetList.cpp#1 $$Change: 1640 $
+** $DateTime: 2014/01/15 09:12:08 $$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
+
+// 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
+{
+    std::vector vs;
+    QhullVertexSet qvs(qhRunId, first().getFacetT(), NULL, 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
+
+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
+
+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);
+    return os;
+}//operator<<
+
+//! Print facet list to stream.  From qh_printafacet [io.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);
+        }
+    }
+    return os;
+}//printFacets
+
+//! Print vertices of good faces in facet list to stream.  From qh_printvertexlist [io.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());
+    for(QhullVertexSet::iterator i=vs.begin(); i!=vs.end(); ++i){
+        QhullVertex v= *i;
+        os << v.print(pr.run_id);
+    }
+    return os;
+}//printVertices
+
+std::ostream &
+operator<<(ostream &os, const QhullFacetList &fs)
+{
+    os << fs.printFacets(UsingLibQhull::NOqhRunId);
+    return os;
+}//QhullFacetList
+
diff --git a/src/libqhullrcpp/QhullFacetList.h b/src/libqhullrcpp/QhullFacetList.h
new file mode 100644
index 0000000..1c1d9fb
--- /dev/null
+++ b/src/libqhullrcpp/QhullFacetList.h
@@ -0,0 +1,102 @@
+/****************************************************************************
+**
+** Copyright (c) 2008-2012 C.B. Barber. All rights reserved.
+** $Id: //main/2011/qhull/src/libqhullrcpp/QhullFacetList.h#1 $$Change: 1640 $
+** $DateTime: 2014/01/15 09:12:08 $$Author: bbarber $
+**
+****************************************************************************/
+
+#ifndef QHULLFACETLIST_H
+#define QHULLFACETLIST_H
+
+#include "QhullLinkedList.h"
+#include "QhullFacet.h"
+
+#include 
+
+namespace orgQhull {
+
+#//ClassRef
+    class               QhullFacet;
+
+#//Types
+    //! QhullFacetList -- List of Qhull facets, as a C++ class.  See QhullFacetSet.h
+    class               QhullFacetList;
+    //! QhullFacetListIterator -- if(f.isGood()){ ... }
+    typedef QhullLinkedListIterator
+                        QhullFacetListIterator;
+
+class QhullFacetList : public QhullLinkedList {
+
+#// Fields
+private:
+    bool                select_all;   //! True if include bad facets.  Default is false.
+
+#//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() {}
+
+private:
+                        //!Disable default constructor and copy assignment.  See QhullLinkedList
+                        QhullFacetList();
+    QhullFacetList     &operator=(const QhullFacetList &);
+public:
+
+#//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
+    bool                isSelectAll() const { return select_all; }
+    void                selectAll() { select_all= true; }
+    void                selectGood() { select_all= false; }
+
+#//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
+    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 =========================================
+
+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/libqhullrcpp/QhullFacetSet.cpp b/src/libqhullrcpp/QhullFacetSet.cpp
new file mode 100644
index 0000000..2dd843b
--- /dev/null
+++ b/src/libqhullrcpp/QhullFacetSet.cpp
@@ -0,0 +1,145 @@
+/****************************************************************************
+**
+** Copyright (c) 2008-2012 C.B. Barber. All rights reserved.
+** $Id: //main/2011/qhull/src/libqhullrcpp/QhullFacetSet.cpp#1 $$Change: 1640 $
+** $DateTime: 2014/01/15 09:12:08 $$Author: bbarber $
+**
+****************************************************************************/
+
+#//! QhullFacetSet -- Qhull's linked facets, as a C++ class
+
+#include "QhullFacet.h"
+#include "QhullFacetSet.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
+
+// 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
+
+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
+
+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, "");
+    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;
+
+#//Types
+    //! QhullFacetSet -- a set of Qhull facets, as a C++ class.  See QhullFacetList.h
+    class               QhullFacetSet;
+    typedef QhullSetIterator
+                        QhullFacetSetIterator;
+
+class QhullFacetSet : public QhullSet {
+
+private:
+#//Fields
+    bool                select_all;   //! True if include bad facets.  Default is false.
+
+public:
+#//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 &);
+public:
+
+#//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
+                        //! 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
+    // 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) {}
+    };//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;
+                        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 =========================================
+
+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/libqhullrcpp/QhullHyperplane.cpp b/src/libqhullrcpp/QhullHyperplane.cpp
new file mode 100644
index 0000000..4cba3c3
--- /dev/null
+++ b/src/libqhullrcpp/QhullHyperplane.cpp
@@ -0,0 +1,166 @@
+/****************************************************************************
+**
+** Copyright (c) 2009-2012 C.B. Barber. All rights reserved.
+** $Id: //main/2011/qhull/src/libqhullrcpp/QhullHyperplane.cpp#1 $$Change: 1640 $
+** $DateTime: 2014/01/15 09:12:08 $$Author: bbarber $
+**
+****************************************************************************/
+
+#include "QhullHyperplane.h"
+#include "QhullPoint.h"
+
+#include 
+
+
+#ifdef _MSC_VER  // Microsoft Visual C++ -- warning level 4
+#endif
+
+namespace orgQhull {
+
+#//Conversion
+
+// 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
+
+//! 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
+//    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
+
+using std::ostream;
+using orgQhull::QhullHyperplane;
+using orgQhull::UsingLibQhull;
+
+#//operator<<
+
+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;
+    }
+    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/libqhullrcpp/QhullHyperplane.h b/src/libqhullrcpp/QhullHyperplane.h
new file mode 100644
index 0000000..99b4871
--- /dev/null
+++ b/src/libqhullrcpp/QhullHyperplane.h
@@ -0,0 +1,122 @@
+/****************************************************************************
+**
+** Copyright (c) 2009-2012 C.B. Barber. All rights reserved.
+** $Id: //main/2011/qhull/src/libqhullrcpp/QhullHyperplane.h#1 $$Change: 1640 $
+** $DateTime: 2014/01/15 09:12:08 $$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
+    class QhullPoint;
+
+#//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
+    int                 hyperplane_dimension;
+    coordT              hyperplane_offset;
+
+public:
+#//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) {}
+                        // 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() {}
+
+#//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
+public:
+    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
+    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
+    double              distance(const QhullPoint &p) const;
+    double              norm() const;
+
+#//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
+    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
+#include 
+#include 
+//! Avoid dependence on 
+namespace std { struct bidirectional_iterator_tag; struct random_access_iterator_tag; }
+
+namespace orgQhull {
+
+#//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/libqhullrcpp/QhullLinkedList.h b/src/libqhullrcpp/QhullLinkedList.h
new file mode 100644
index 0000000..d3627ff
--- /dev/null
+++ b/src/libqhullrcpp/QhullLinkedList.h
@@ -0,0 +1,377 @@
+/****************************************************************************
+**
+** Copyright (c) 2008-2012 C.B. Barber. All rights reserved.
+** $Id: //main/2011/qhull/src/libqhullrcpp/QhullLinkedList.h#1 $$Change: 1640 $
+** $DateTime: 2014/01/15 09:12:08 $$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
+    //! 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
+    T                   begin_node;
+    T                   end_node;     //! Sentinel node at end of list
+
+public:
+#//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
+                        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() {}
+
+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
+#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(); }
+    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
+    //! 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.
+
+#//Search
+    bool                contains(const T &t) const;
+    int                 count(const T &t) const;
+
+#//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;
+
+    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; }
+
+        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++(int) { iterator o= i; i= i.next(); return o; }
+        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; }
+    };//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
+
+#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
+
+template 
+int QhullLinkedList::
+count() const
+{
+    const_iterator i= begin_node;
+    int c= 0;
+    while(i != end_node){
+        c++;
+        i++;
+    }
+    return c;
+}//count
+
+#//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
+
+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
+
+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
+
+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/libqhullrcpp/QhullPoint.cpp b/src/libqhullrcpp/QhullPoint.cpp
new file mode 100644
index 0000000..77a4e76
--- /dev/null
+++ b/src/libqhullrcpp/QhullPoint.cpp
@@ -0,0 +1,177 @@
+/****************************************************************************
+**
+** Copyright (c) 2009-2012 C.B. Barber. All rights reserved.
+** $Id: //main/2011/qhull/src/libqhullrcpp/QhullPoint.cpp#1 $$Change: 1640 $
+** $DateTime: 2014/01/15 09:12:08 $$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
+
+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==
+
+
+#//Value
+
+//! Return distance betweeen 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; 
+    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/libqhullrcpp/QhullPoint.h b/src/libqhullrcpp/QhullPoint.h
new file mode 100644
index 0000000..d733cc2
--- /dev/null
+++ b/src/libqhullrcpp/QhullPoint.h
@@ -0,0 +1,130 @@
+/****************************************************************************
+**
+** Copyright (c) 2009-2012 C.B. Barber. All rights reserved.
+** $Id: //main/2011/qhull/src/libqhullrcpp/QhullPoint.h#1 $$Change: 1640 $
+** $DateTime: 2014/01/15 09:12:08 $$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
+    //! 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
+    int                 point_dimension;
+
+public:
+#//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
+    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
+                        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() {}
+
+#//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
+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; }
+    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
+    double              distance(const QhullPoint &p) const;
+
+#//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
+    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
+#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 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
+//! Derived from QhullSet::value
+QhullPoint QhullPointSet::
+value(int idx) const
+{
+    // Avoid call to 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
+
+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;
+
+#//Classref
+    class               QhullPoint;
+
+class QhullPointSet : public QhullSet {
+
+private:
+#//Field
+    int                 point_dimension;
+
+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
+                        //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() {}
+
+//Default constructor and copy assignment disabled since p= p2 is ambiguous (coord* vs coord)
+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
+    struct PrintIdentifiers{
+        const QhullPointSet *point_set;
+        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;
+        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
+
+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/libqhullrcpp/QhullPoints.cpp b/src/libqhullrcpp/QhullPoints.cpp
new file mode 100644
index 0000000..6402964
--- /dev/null
+++ b/src/libqhullrcpp/QhullPoints.cpp
@@ -0,0 +1,235 @@
+/****************************************************************************
+**
+** Copyright (c) 2009-2012 C.B. Barber. All rights reserved.
+** $Id: //main/2011/qhull/src/libqhullrcpp/QhullPoints.cpp#1 $$Change: 1640 $
+** $DateTime: 2014/01/15 09:12:08 $$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
+
+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
+    //! 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
+    int                 point_dimension;  // >= 0
+
+public:
+#//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() {}
+
+//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(); }
+#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; }
+    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
+    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; }
+        // 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++(int) { iterator n= *this; operator++(); return iterator(n); }
+        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(); }
+    };//QhullPoints::iterator
+
+#//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 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[](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
+    struct PrintPoints{
+        const QhullPoints  *points;
+        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
+    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
+
+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/libqhullrcpp/QhullQh.cpp b/src/libqhullrcpp/QhullQh.cpp
new file mode 100644
index 0000000..f108f5c
--- /dev/null
+++ b/src/libqhullrcpp/QhullQh.cpp
@@ -0,0 +1,104 @@
+/****************************************************************************
+**
+** Copyright (c) 2008-2012 C.B. Barber. All rights reserved.
+** $Id: //main/2011/qhull/src/libqhullrcpp/QhullQh.cpp#1 $$Change: 1640 $
+** $DateTime: 2014/01/15 09:12:08 $$Author: bbarber $
+**
+****************************************************************************/
+
+#//! QhullQh -- Qhull's global data structure, qhT, as a C++ class
+
+
+
+#include "QhullError.h"
+#include "QhullQh.h"
+#include "QhullStat.h"
+
+#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
+
+#//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()
+{
+    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();
+    // NOerrors -- Does not call qh_errexit()
+    qh_initqhull_start2(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();
+    }else{
+        qh_freeqhull2(qh_ALL); // sets qh.NOerrexit.  Clears struct *qh_qh including run_id, but not qh_qh itself
+    }
+#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);
+        e.logError();
+    }else{
+        qh_freeqhull2(qh_ALL); // sets qh.NOerrexit.  Clears struct *qh_qh including run_id, but not qh_qh itself
+    }
+#endif
+}//~QhullQh
+
+#//Parallel Access
+
+}//namespace orgQhull
+
diff --git a/src/libqhullrcpp/QhullQh.h b/src/libqhullrcpp/QhullQh.h
new file mode 100644
index 0000000..bb0439a
--- /dev/null
+++ b/src/libqhullrcpp/QhullQh.h
@@ -0,0 +1,51 @@
+/****************************************************************************
+**
+** Copyright (c) 2008-2012 C.B. Barber. All rights reserved.
+** $Id: //main/2011/qhull/src/libqhullrcpp/QhullQh.h#1 $$Change: 1640 $
+** $DateTime: 2014/01/15 09:12:08 $$Author: bbarber $
+**
+****************************************************************************/
+
+#ifndef QHULLQH_H
+#define QHULLQH_H
+
+extern "C" {
+    #include "libqhull/qhull_a.h"
+}
+
+#include 
+#include 
+
+namespace orgQhull {
+
+#//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
+    // 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
+
+public:
+#//constructor, assignment, destructor, invariant
+    QhullQh();
+    ~QhullQh();
+
+private:
+    //!disable copy constructor and assignment
+                        QhullQh(const QhullQh &);
+    QhullQh            &operator=(const QhullQh &);
+
+};//class QhullQh
+
+}//namespace orgQhull
+
+#endif // QHULLQH_H
diff --git a/src/libqhullrcpp/QhullRidge.cpp b/src/libqhullrcpp/QhullRidge.cpp
new file mode 100644
index 0000000..139bc2b
--- /dev/null
+++ b/src/libqhullrcpp/QhullRidge.cpp
@@ -0,0 +1,102 @@
+/****************************************************************************
+**
+** Copyright (c) 2008-2012 C.B. Barber. All rights reserved.
+** $Id: //main/2011/qhull/src/libqhullrcpp/QhullRidge.cpp#1 $$Change: 1640 $
+** $DateTime: 2014/01/15 09:12:08 $$Author: bbarber $
+**
+****************************************************************************/
+
+#//! QhullRidge -- Qhull's ridge structure, ridgeT, as a C++ class
+
+#include "QhullSets.h"
+#include "QhullVertex.h"
+#include "QhullRidge.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
+ridgeT QhullRidge::
+s_empty_ridge= {0,0,0,0,0,
+                0,0};
+
+#//Constructor, destructor, etc.
+
+#//Accessors
+
+//! Return True if nextRidge3d
+//! Simplicial facets may have incomplete ridgeSets
+//! Does not use qh_qh or qh_errexit()
+bool QhullRidge::
+hasNextRidge3d(const QhullFacet f) const
+{
+    vertexT *v= 0;
+    ridgeT *ridge= qh_nextridge3d(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()
+QhullRidge QhullRidge::
+nextRidge3d(const QhullFacet f, QhullVertex *nextVertex) const
+{
+    vertexT *v= 0;
+    ridgeT *ridge= qh_nextridge3d(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);
+    }
+    return QhullRidge(ridge);
+}//nextRidge3d
+
+
+}//namespace orgQhull
+
+#//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);
+    return os;
+}//<< QhullRidge
+
+//! Duplicate of qh_printridge [io.c]
+//!  if pr.run_id==UsingLibQhull::NOqhRunId, no access to qh [needed for QhullVertex/QhullPoint]
+ostream &
+operator<<(ostream &os, const QhullRidge::PrintRidge &pr)
+{
+    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:");
+    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/libqhullrcpp/QhullRidge.h b/src/libqhullrcpp/QhullRidge.h
new file mode 100644
index 0000000..111e678
--- /dev/null
+++ b/src/libqhullrcpp/QhullRidge.h
@@ -0,0 +1,110 @@
+/****************************************************************************
+**
+** Copyright (c) 2008-2012 C.B. Barber. All rights reserved.
+** $Id: //main/2011/qhull/src/libqhullrcpp/QhullRidge.h#1 $$Change: 1640 $
+** $DateTime: 2014/01/15 09:12:08 $$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
+    class QhullVertex;
+    class QhullVertexSet;
+    class QhullFacet;
+
+#//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;
+
+#//Class objects
+    static ridgeT       s_empty_ridge;
+
+public:
+#//Constants
+
+#//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() {}
+
+#//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; }
+    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
+    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
+
+    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/libqhullrcpp/QhullSet.cpp b/src/libqhullrcpp/QhullSet.cpp
new file mode 100644
index 0000000..d7965ef
--- /dev/null
+++ b/src/libqhullrcpp/QhullSet.cpp
@@ -0,0 +1,47 @@
+/****************************************************************************
+**
+** Copyright (c) 2008-2012 C.B. Barber. All rights reserved.
+** $Id: //main/2011/qhull/src/libqhullrcpp/QhullSet.cpp#1 $$Change: 1640 $
+** $DateTime: 2014/01/15 09:12:08 $$Author: bbarber $
+**
+****************************************************************************/
+
+#//! QhullSet -- Qhull's facet structure, facetT, as a C++ class
+
+#include "QhullError.h"
+#include "QhullSet.h"
+
+#ifdef _MSC_VER  // Microsoft Visual C++ -- warning level 4
+#endif
+
+namespace orgQhull {
+
+#//static members
+
+setT QhullSetBase::
+s_empty_set;
+
+// Same code for qh_setsize [qset.c] and QhullSetBase::count
+int QhullSetBase::count(const setT *set)
+{
+    int size;
+    const setelemT *sizep;
+
+    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
+        size= set->maxsize;
+    return size;
+}
+
+
+}//namespace orgQhull
+
diff --git a/src/libqhullrcpp/QhullSet.h b/src/libqhullrcpp/QhullSet.h
new file mode 100644
index 0000000..0559274
--- /dev/null
+++ b/src/libqhullrcpp/QhullSet.h
@@ -0,0 +1,360 @@
+/****************************************************************************
+**
+** Copyright (c) 2008-2012 C.B. Barber. All rights reserved.
+** $Id: //main/2011/qhull/src/libqhullrcpp/QhullSet.h#1 $$Change: 1640 $
+** $DateTime: 2014/01/15 09:12:08 $$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
+    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;
+
+#//Class objects
+    static setT         s_empty_set;  //! Workaround for no setT allocator.  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
+                        //! 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() {}
+
+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
+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); }
+                        //! Always points to 0
+    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
+
+#//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;
+    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) {}
+                        //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() {}
+
+private:
+                        //!Disable default constructor and copy assignment.  See QhullSetBase
+                        QhullSet();
+    QhullSet        &operator=(const QhullSet &);
+public:
+
+#//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()
+    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(); }
+    //! 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); }
+    // 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
+    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
+    typedef typename QhullSet::const_iterator const_iterator;
+
+private:
+#//Fields
+    const_iterator      i;
+    const_iterator      begin_i;
+    const_iterator      end_i;
+
+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; }
+
+#//ReadOnly
+    int                 countRemaining() { return (int)(end_i-begin_i); } // WARN64
+
+#//Search
+    bool                findNext(const T &t);
+    bool                findPrevious(const T &t);
+
+#//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
+
+#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
+
+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
+
+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 =========================================
+
+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/libqhullrcpp/QhullSets.h b/src/libqhullrcpp/QhullSets.h
new file mode 100644
index 0000000..d3c61f8
--- /dev/null
+++ b/src/libqhullrcpp/QhullSets.h
@@ -0,0 +1,27 @@
+/****************************************************************************
+**
+** Copyright (c) 2008-2012 C.B. Barber. All rights reserved.
+** $Id: //main/2011/qhull/src/libqhullrcpp/QhullSets.h#1 $$Change: 1640 $
+** $DateTime: 2014/01/15 09:12:08 $$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/libqhullrcpp/QhullStat.cpp b/src/libqhullrcpp/QhullStat.cpp
new file mode 100644
index 0000000..d806f7e
--- /dev/null
+++ b/src/libqhullrcpp/QhullStat.cpp
@@ -0,0 +1,42 @@
+/****************************************************************************
+**
+** Copyright (c) 2008-2012 C.B. Barber. All rights reserved.
+** $Id: //main/2011/qhull/src/libqhullrcpp/QhullStat.cpp#1 $$Change: 1640 $
+** $DateTime: 2014/01/15 09:12:08 $$Author: bbarber $
+**
+****************************************************************************/
+
+#//! QhullStat -- Qhull's global data structure, statT, as a C++ class
+
+
+#include "QhullError.h"
+#include "QhullStat.h"
+
+#include 
+#include 
+
+using std::cerr;
+using std::string;
+using std::vector;
+using std::ostream;
+
+#ifdef _MSC_VER  // Microsoft Visual C++ -- warning level 4
+#endif
+
+namespace orgQhull {
+
+#//Constructor, destructor, etc.
+
+//! If qh_QHpointer==0, invoke with placement new on qh_stat;
+QhullStat::
+QhullStat()
+{
+}//QhullStat
+
+QhullStat::
+~QhullStat()
+{
+}//~QhullStat
+
+}//namespace orgQhull
+
diff --git a/src/libqhullrcpp/QhullStat.h b/src/libqhullrcpp/QhullStat.h
new file mode 100644
index 0000000..ba213dc
--- /dev/null
+++ b/src/libqhullrcpp/QhullStat.h
@@ -0,0 +1,52 @@
+/****************************************************************************
+**
+** Copyright (c) 2008-2012 C.B. Barber. All rights reserved.
+** $Id: //main/2011/qhull/src/libqhullrcpp/QhullStat.h#1 $$Change: 1640 $
+** $DateTime: 2014/01/15 09:12:08 $$Author: bbarber $
+**
+****************************************************************************/
+
+#ifndef QHULLSTAT_H
+#define QHULLSTAT_H
+
+extern "C" {
+    #include "libqhull/qhull_a.h"
+}
+
+#include 
+#include 
+
+namespace orgQhull {
+
+#//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
+
+public:
+#//Constants
+
+#//class methods
+    static void         clearStatistics();
+
+#//constructor, assignment, destructor, invariant
+                        QhullStat();
+                       ~QhullStat();
+
+private:
+    //!disable copy constructor and assignment
+                        QhullStat(const QhullStat &);
+    QhullStat          &operator=(const QhullStat &);
+public:
+
+#//Access
+};//class QhullStat
+
+}//namespace orgQhull
+
+#endif // QHULLSTAT_H
diff --git a/src/libqhullrcpp/QhullVertex.cpp b/src/libqhullrcpp/QhullVertex.cpp
new file mode 100644
index 0000000..f5583a5
--- /dev/null
+++ b/src/libqhullrcpp/QhullVertex.cpp
@@ -0,0 +1,94 @@
+/****************************************************************************
+**
+** Copyright (c) 2008-2012 C.B. Barber. All rights reserved.
+** $Id: //main/2011/qhull/src/libqhullrcpp/QhullVertex.cpp#1 $$Change: 1640 $
+** $DateTime: 2014/01/15 09:12:08 $$Author: bbarber $
+**
+****************************************************************************/
+
+#//! QhullVertex -- Qhull's vertex structure, vertexT, as a C++ class
+
+#include "UsingLibQhull.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
+vertexT QhullVertex::
+s_empty_vertex= {0,0,0,0,0,
+                 0,0,0,0,0,
+                 0,0};
+
+#//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);
+}//neighborFacets
+
+}//namespace orgQhull
+
+#//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]
+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() << "): ";
+    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;
+            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/libqhullrcpp/QhullVertex.h b/src/libqhullrcpp/QhullVertex.h
new file mode 100644
index 0000000..22b29ae
--- /dev/null
+++ b/src/libqhullrcpp/QhullVertex.h
@@ -0,0 +1,103 @@
+/****************************************************************************
+**
+** Copyright (c) 2008-2012 C.B. Barber. All rights reserved.
+** $Id: //main/2011/qhull/src/libqhullrcpp/QhullVertex.h#1 $$Change: 1640 $
+** $DateTime: 2014/01/15 09:12:08 $$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
+    class QhullFacetSet;
+
+#//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;
+
+#//Class objects
+    static vertexT      s_empty_vertex;  // needed for shallow copy
+
+public:
+#//Constants
+
+#//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() {}
+
+#//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; }
+    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
+    //See also QhullVertexList
+    QhullFacetSet       neighborFacets() const;
+
+#//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
+
+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/libqhullrcpp/QhullVertexSet.cpp b/src/libqhullrcpp/QhullVertexSet.cpp
new file mode 100644
index 0000000..e03c661
--- /dev/null
+++ b/src/libqhullrcpp/QhullVertexSet.cpp
@@ -0,0 +1,110 @@
+/****************************************************************************
+**
+** Copyright (c) 2009-2012 C.B. Barber. All rights reserved.
+** $Id: //main/2011/qhull/src/libqhullrcpp/QhullVertexSet.cpp#1 $$Change: 1640 $
+** $DateTime: 2014/01/15 09:12:08 $$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"
+
+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)
+, 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);
+        defineAs(vertices);
+        qhsettemp_qhull= s_qhull_output;
+        qhsettemp_defined= true;
+    }
+    q.maybeThrowQhullMessage(exitCode);
+}//QhullVertexSet facetlist facetset
+
+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);
+        }
+    }
+}//freeQhSetTemp
+
+QhullVertexSet::
+~QhullVertexSet()
+{
+    freeQhSetTemp();
+}//~QhullVertexSet
+
+}//namespace orgQhull
+
+#//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]
+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){
+        const QhullVertex v= *i;
+        os << " v" << v.id();
+    }
+    os << endl;
+    return os;
+}//<
+
+namespace orgQhull {
+
+#//ClassRef
+    class               QhullVertex;
+
+#//Types
+    //! QhullVertexSet -- a set of Qhull Vertices, as a C++ class.
+    //! See Qhull
+    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()
+
+public:
+#//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();
+
+private:
+                        //!Disable default constructor and copy assignment.  See QhullSetBase
+                        QhullVertexSet();
+    QhullVertexSet      &operator=(const QhullVertexSet &);
+public:
+
+#//Constructor, destructor
+    void                freeQhSetTemp();
+
+#//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) {}
+    };//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;
+                        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 =========================================
+
+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/libqhullrcpp/RboxPoints.cpp b/src/libqhullrcpp/RboxPoints.cpp
new file mode 100644
index 0000000..fd69940
--- /dev/null
+++ b/src/libqhullrcpp/RboxPoints.cpp
@@ -0,0 +1,219 @@
+/****************************************************************************
+**
+** Copyright (c) 2008-2012 C.B. Barber. All rights reserved.
+** $Id: //main/2011/qhull/src/libqhullrcpp/RboxPoints.cpp#1 $$Change: 1640 $
+** $DateTime: 2014/01/15 09:12:08 $$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")
+, rbox_new_count(0)
+, rbox_status(qh_ERRnone)
+, rbox_message()
+{
+    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;
+
+    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/libqhullrcpp/RboxPoints.h b/src/libqhullrcpp/RboxPoints.h
new file mode 100644
index 0000000..424454f
--- /dev/null
+++ b/src/libqhullrcpp/RboxPoints.h
@@ -0,0 +1,66 @@
+/****************************************************************************
+**
+** Copyright (c) 2008-2012 C.B. Barber. All rights reserved.
+** $Id: //main/2011/qhull/src/libqhullrcpp/RboxPoints.h#1 $$Change: 1640 $
+** $DateTime: 2014/01/15 09:12:08 $$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
+    //! RboxPoints -- generate random PointCoordinates for Qhull
+    class RboxPoints;
+
+    class RboxPoints : public PointCoordinates {
+
+private:
+#//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
+                        RboxPoints();
+    explicit            RboxPoints(const char *rboxCommand);
+                        RboxPoints(const RboxPoints &other);
+                        RboxPoints &operator=(const RboxPoints &other);
+                       ~RboxPoints();
+
+public:
+#//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
+    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/libqhullrcpp/RoadError.cpp b/src/libqhullrcpp/RoadError.cpp
new file mode 100644
index 0000000..d0b6212
--- /dev/null
+++ b/src/libqhullrcpp/RoadError.cpp
@@ -0,0 +1,156 @@
+/****************************************************************************
+**
+** Copyright (c) 2008-2012 C.B. Barber. All rights reserved.
+** $Id: //main/2011/qhull/src/libqhullrcpp/RoadError.cpp#1 $$Change: 1640 $
+** $DateTime: 2014/01/15 09:12:08 $$Author: bbarber $
+**
+****************************************************************************/
+
+#//! RoadError -- All exceptions thrown by Qhull are RoadErrors
+#//! Do not throw RoadError's from destructors.  Use e.logError() instead.
+
+#include "RoadError.h"
+
+#include 
+#include 
+#include 
+
+using std::cerr;
+using std::cout;
+using std::string;
+
+#ifdef _MSC_VER  // Microsoft Visual C++ -- warning level 4
+#endif
+
+namespace orgQhull {
+
+#//Class fields
+
+//! Identifies error messages from Qhull and Road for web searches.
+//! See QhullError.h#QHULLlastError and user.h#MSG_ERROR
+const char * RoadError::
+ROADtag= "QH";
+
+std::ostringstream RoadError::
+global_log;
+
+#//Constructor
+
+RoadError::
+RoadError()
+: error_code(0)
+, log_event()
+, error_message()
+{ }
+
+RoadError::
+RoadError(const RoadError &other)
+: error_code(other.error_code)
+, log_event(other.log_event)
+, error_message(other.error_message)
+{
+}//copy construct
+
+RoadError::
+RoadError(int code, const std::string &message)
+: error_code(code)
+, log_event(message.c_str())
+, error_message(log_event.toString(ROADtag, error_code))
+{
+    log_event.cstr_1= error_message.c_str(); // overwrites initial value
+}
+
+RoadError::
+RoadError(int code, const char *fmt)
+: error_code(code)
+, log_event(fmt)
+, error_message()
+{ }
+
+RoadError::
+RoadError(int code, const char *fmt, int d)
+: error_code(code)
+, log_event(fmt, d)
+, error_message()
+{ }
+
+RoadError::
+RoadError(int code, const char *fmt, int d, int d2)
+: error_code(code)
+, log_event(fmt, d, d2)
+, error_message()
+{ }
+
+RoadError::
+RoadError(int code, const char *fmt, int d, int d2, float f)
+: error_code(code)
+, log_event(fmt, d, d2, f)
+, error_message()
+{ }
+
+RoadError::
+RoadError(int code, const char *fmt, int d, int d2, float f, const char *s)
+: error_code(code)
+, log_event(fmt, d, d2, f, s)
+, error_message(log_event.toString(ROADtag, code)) // char * may go out of scope
+{ }
+
+RoadError::
+RoadError(int code, const char *fmt, int d, int d2, float f, const void *x)
+: error_code(code)
+, log_event(fmt, d, d2, f, x)
+, error_message()
+{ }
+
+RoadError::
+RoadError(int code, const char *fmt, int d, int d2, float f, int i)
+: error_code(code)
+, log_event(fmt, d, d2, f, i)
+, error_message()
+{ }
+
+RoadError::
+RoadError(int code, const char *fmt, int d, int d2, float f, long long i)
+: error_code(code)
+, log_event(fmt, d, d2, f, i)
+, error_message()
+{ }
+
+RoadError::
+RoadError(int code, const char *fmt, int d, int d2, float f, double e)
+: error_code(code)
+, log_event(fmt, d, d2, f, e)
+, error_message()
+{ }
+
+RoadError & RoadError::
+operator=(const RoadError &other)
+{
+    error_code= other.error_code;
+    error_message= other.error_message;
+    log_event= other.log_event;
+    return *this;
+}//operator=
+
+#//Virtual
+const char * RoadError::
+what() const throw()
+{
+    if(error_message.empty()){
+        error_message= log_event.toString(ROADtag, error_code);
+    }
+    return error_message.c_str();
+}//what
+
+#//Updates
+
+//! Log error instead of throwing it.
+void RoadError::
+logError() const
+{
+    global_log << what() << endl;
+}//logError
+
+
+}//namespace orgQhull
+
diff --git a/src/libqhullrcpp/RoadError.h b/src/libqhullrcpp/RoadError.h
new file mode 100644
index 0000000..f9c1239
--- /dev/null
+++ b/src/libqhullrcpp/RoadError.h
@@ -0,0 +1,86 @@
+/****************************************************************************
+**
+** Copyright (c) 2008-2012 C.B. Barber. All rights reserved.
+** $Id: //main/2011/qhull/src/libqhullrcpp/RoadError.h#1 $$Change: 1640 $
+** $DateTime: 2014/01/15 09:12:08 $$Author: bbarber $
+**
+****************************************************************************/
+
+#ifndef ROADERROR_H
+#define ROADERROR_H
+
+#include "RoadLogEvent.h"
+
+#include 
+#include 
+#include 
+#include 
+
+using std::endl;
+
+namespace orgQhull {
+
+#//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
+    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;
+    static std::ostringstream  global_log; //! May be replaced with any ostream object
+
+public:
+#//Constants
+
+#//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() {};
+
+#//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
+    virtual const char *what() const throw();
+
+#//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
+    void                logError() const;
+};//class RoadError
+
+}//namespace orgQhull
+
+#//Global functions
+
+inline std::ostream    &operator<<(std::ostream &os, const orgQhull::RoadError &e) { return os << e.what(); }
+
+#endif // ROADERROR_H
diff --git a/src/libqhullrcpp/RoadLogEvent.cpp b/src/libqhullrcpp/RoadLogEvent.cpp
new file mode 100644
index 0000000..4a0d479
--- /dev/null
+++ b/src/libqhullrcpp/RoadLogEvent.cpp
@@ -0,0 +1,122 @@
+/****************************************************************************
+**
+** Copyright (c) 2008-2012 C.B. Barber. All rights reserved.
+** $Id: //main/2011/qhull/src/libqhullrcpp/RoadLogEvent.cpp#1 $$Change: 1640 $
+** $Date: 2014/01/15 $$Author: bbarber $
+**
+****************************************************************************/
+
+#//! RoadError -- All exceptions thrown by Qhull are RoadErrors
+
+#include "RoadError.h"
+
+#include 
+#include 
+#include 
+
+using std::cout;
+using std::endl;
+using std::ostringstream;
+using std::string;
+
+#ifdef _MSC_VER  // Microsoft Visual C++ -- warning level 4
+#endif
+
+namespace orgQhull {
+
+#//!\name Conversion
+string RoadLogEvent::
+toString(const char *tag, int code) const
+{
+    ostringstream os;
+    if(tag && code){
+        os << tag << code;
+        if(format_string){
+            os << " ";
+        }
+    }
+    if(!format_string){
+        return os.str();
+    }
+    const char *s= format_string;
+    int dCount= 0;  // Count of %d
+    int fCount= 0;  // Count of %f
+    char extraCode= '\0';
+    while(*s){
+        if(*s!='%'){
+            os << *s++;
+        }else{
+            char c= *++s;
+            s++;
+            switch(c){
+            case 'd':
+                if(++dCount>2){
+                    os << " ERROR_three_%d_in_format ";
+                }else if(dCount==2){
+                    os << int_2;
+                }else{
+                    os << int_1;
+                }
+                break;
+            case 'e':
+                if(firstExtraCode(os, c, &extraCode)){
+                    os << double_1;
+                }
+                break;
+            case 'f':
+                if(++fCount>1){
+                    os << " ERROR_two_%f_in_format ";
+                }else{
+                    os << float_1;
+                }
+                break;
+            case 'i':
+                if(firstExtraCode(os, c, &extraCode)){
+                    os << int64_1;
+                }
+                break;
+            case 's':
+                if(firstExtraCode(os, c, &extraCode)){
+                    os << cstr_1;
+                }
+                break;
+            case 'u':
+                if(firstExtraCode(os, c, &extraCode)){
+                    os << "0x" << std::hex << int64_1 << std::dec;
+                }
+                break;
+            case 'x':
+                if(firstExtraCode(os, c, &extraCode)){
+                    os << void_1;
+                }
+                break;
+            case '%':
+                os << c;
+                break;
+            default:
+                os << " ERROR_%" << c << "_not_defined_in_format";
+                break;
+            }
+        }
+    }
+    if(s[-1]!='\n'){
+        os << endl;
+    }
+    return os.str();
+}//toString
+
+#//Class helpers (static)
+
+//! True if this char is the first extra code
+bool RoadLogEvent::
+firstExtraCode(std::ostream &os, char c, char *extraCode){
+    if(*extraCode){
+        os << " ERROR_%" << *extraCode << "_and_%" << c << "_in_format ";
+        return false;
+    }
+    *extraCode= c;
+    return true;
+}//firstExtraCode
+
+}//namespace orgQhull
+
diff --git a/src/libqhullrcpp/RoadLogEvent.h b/src/libqhullrcpp/RoadLogEvent.h
new file mode 100644
index 0000000..3f6d2be
--- /dev/null
+++ b/src/libqhullrcpp/RoadLogEvent.h
@@ -0,0 +1,77 @@
+/****************************************************************************
+**
+** Copyright (c) 2008-2012 C.B. Barber. All rights reserved.
+** $Id: //main/2011/qhull/src/libqhullrcpp/RoadLogEvent.h#1 $$Change: 1640 $
+** $DateTime: 2014/01/15 09:12:08 $$Author: bbarber $
+**
+****************************************************************************/
+
+#ifndef ROADLOGEVENT_H
+#define ROADLOGEVENT_H
+
+#include 
+#include 
+#include 
+
+namespace orgQhull {
+
+#//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)
+    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
+
+#//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
+    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; };
+    long long           int64() const { return int64_1; };
+    double              double1() const { return double_1; };
+
+#//Conversion
+
+    std::string        toString(const char* tag, int code) const;
+
+private:
+#//Class helpers
+    static bool         firstExtraCode(std::ostream &os, char c, char *extraCode);
+
+
+};//class RoadLogEvent
+
+}//namespace orgQhull
+
+#endif // ROADLOGEVENT_H
diff --git a/src/libqhullrcpp/functionObjects.h b/src/libqhullrcpp/functionObjects.h
new file mode 100644
index 0000000..ad6647a
--- /dev/null
+++ b/src/libqhullrcpp/functionObjects.h
@@ -0,0 +1,66 @@
+/****************************************************************************
+**
+** Copyright (c) 2008-2012 C.B. Barber. All rights reserved.
+** $Id: //main/2011/qhull/src/libqhullrcpp/functionObjects.h#1 $$Change: 1640 $
+** $DateTime: 2014/01/15 09:12:08 $$Author: bbarber $
+**
+****************************************************************************/
+
+#ifndef QHFUNCTIONOBJECTS_H
+#define QHFUNCTIONOBJECTS_H
+
+#include 
+#include 
+
+namespace orgQhull {
+#//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
+
+//! 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/libqhullrcpp/libqhullrcpp.pro b/src/libqhullrcpp/libqhullrcpp.pro
new file mode 100644
index 0000000..f91d1cc
--- /dev/null
+++ b/src/libqhullrcpp/libqhullrcpp.pro
@@ -0,0 +1,71 @@
+# -------------------------------------------------
+# 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
+
+DEFINES += qh_QHpointer # libqhull/user.h
+
+INCLUDEPATH += ../../src
+INCLUDEPATH += $$PWD # for MOC_DIR
+
+CONFIG += qhull_warn_shadow qhull_warn_conversion
+
+SOURCES += Coordinates.cpp
+SOURCES += PointCoordinates.cpp
+SOURCES += Qhull.cpp
+SOURCES += QhullFacet.cpp
+SOURCES += QhullFacetList.cpp
+SOURCES += QhullFacetSet.cpp
+SOURCES += QhullHyperplane.cpp
+SOURCES += QhullPoint.cpp
+SOURCES += QhullPoints.cpp
+SOURCES += QhullPointSet.cpp
+SOURCES += QhullQh.cpp
+SOURCES += QhullRidge.cpp
+SOURCES += QhullSet.cpp
+SOURCES += QhullStat.cpp
+SOURCES += QhullVertex.cpp
+SOURCES += QhullVertexSet.cpp
+SOURCES += RboxPoints.cpp
+SOURCES += RoadError.cpp
+SOURCES += RoadLogEvent.cpp
+SOURCES += UsingLibQhull.cpp
+
+HEADERS += Coordinates.h
+HEADERS += functionObjects.h
+HEADERS += PointCoordinates.h
+HEADERS += Qhull.h
+HEADERS += QhullError.h
+HEADERS += QhullFacet.h
+HEADERS += QhullFacetList.h
+HEADERS += QhullFacetSet.h
+HEADERS += QhullHyperplane.h
+HEADERS += QhullIterator.h
+HEADERS += QhullLinkedList.h
+HEADERS += QhullPoint.h
+HEADERS += QhullPoints.h
+HEADERS += QhullPointSet.h
+HEADERS += QhullQh.h
+HEADERS += QhullRidge.h
+HEADERS += QhullSet.h
+HEADERS += QhullSets.h
+HEADERS += QhullStat.h
+HEADERS += QhullVertex.h
+HEADERS += RboxPoints.h
+HEADERS += RoadError.h
+HEADERS += RoadLogEvent.h
+HEADERS += UsingLibQhull.h
diff --git a/src/libqhullrcpp/qt-qhullr.cpp b/src/libqhullrcpp/qt-qhullr.cpp
new file mode 100644
index 0000000..bb91e12
--- /dev/null
+++ b/src/libqhullrcpp/qt-qhullr.cpp
@@ -0,0 +1,129 @@
+/****************************************************************************
+**
+** Copyright (c) 2009-2012 C.B. Barber. All rights reserved.
+** $Id: //main/2011/qhull/src/libqhullrcpp/qt-qhullr.cpp#1 $$Change: 1640 $
+** $DateTime: 2014/01/15 09:12:08 $$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
+{
+    QList vs;
+    QhullVertexSet qvs(qhRunId, 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/qhullr/qhullr.pro b/src/qhullr/qhullr.pro
new file mode 100644
index 0000000..e70d146
--- /dev/null
+++ b/src/qhullr/qhullr.pro
@@ -0,0 +1,9 @@
+# -------------------------------------------------
+# qhull.pro -- Qt project file for qhull.exe
+# -------------------------------------------------
+
+include(../qhull-app-c.pri)
+
+TARGET = qhull
+
+SOURCES += unix.c
diff --git a/src/qhullr/unix_r.c b/src/qhullr/unix_r.c
new file mode 100644
index 0000000..4bb34b7
--- /dev/null
+++ b/src/qhullr/unix_r.c
@@ -0,0 +1,382 @@
+/*
  ---------------------------------
+
+   unix.c
+     command line interface to qhull
+         includes SIOUX interface for Macintoshes
+
+   see qh-qhull.htm
+
+   Copyright (c) 1993-2012 The Geometry Center.
+   $Id: //main/2011/qhull/src/qhullr/unix_r.c#1 $$Change: 1640 $
+   $DateTime: 2014/01/15 09:12:08 $$Author: bbarber $
+*/
+
+#include "mem.h"
+#include "qset.h"
+#include "libqhull.h"
+
+#include 
+#include 
+#include 
+#include 
+#include 
+
+#if __MWERKS__ && __POWERPC__
+#include 
+#include 
+#include 
+#include 
+
+#elif __cplusplus
+extern "C" {
+  int isatty(int);
+}
+
+#elif _MSC_VER
+#include 
+#define isatty _isatty
+int _isatty(int);
+
+#else
+int isatty(int);  /* returns 1 if stdin is a tty
+                   if "Undefined symbol" this can be deleted along with call in main() */
+#endif
+
+/*---------------------------------
+
+  qh_prompt
+    long prompt for qhull
+
+  see:
+    concise prompt below
+*/
+char qh_prompta[]= "\n\
+qhull- compute convex hulls and related structures.\n\
+    http://www.qhull.org  %s\n\
+\n\
+input (stdin):\n\
+    first lines: dimension and number of points (or vice-versa).\n\
+    other lines: point coordinates, best if one point per line\n\
+    comments:    start with a non-numeric character\n\
+    halfspaces:  use dim plus one and put offset after coefficients.\n\
+                 May be preceeded by a single interior point ('H').\n\
+\n\
+options:\n\
+    d    - Delaunay triangulation by lifting points to a paraboloid\n\
+    d Qu - furthest-site Delaunay triangulation (upper convex hull)\n\
+    v    - Voronoi diagram (dual of the Delaunay triangulation)\n\
+    v Qu - furthest-site Voronoi diagram\n\
+    Hn,n,... - halfspace intersection about point [n,n,0,...]\n\
+    Qt   - triangulated output\n\
+    QJ   - joggled input instead of merged facets\n\
+    Qc   - keep coplanar points with nearest facet\n\
+    Qi   - keep interior points with nearest facet\n\
+\n\
+Qhull control options:\n\
+    Qbk:n   - scale coord k so that low bound is n\n\
+      QBk:n - scale coord k so that upper bound is n (QBk is %2.2g)\n\
+    QbB  - scale input to unit cube centered at the origin\n\
+    Qbb  - scale last coordinate to [0,m] for Delaunay triangulations\n\
+    Qbk:0Bk:0 - remove k-th coordinate from input\n\
+    QJn  - randomly joggle input in range [-n,n]\n\
+    QRn  - random rotation (n=seed, n=0 time, n=-1 time/no rotate)\n\
+%s%s%s%s";  /* split up qh_prompt for Visual C++ */
+char qh_promptb[]= "\
+    Qf   - partition point to furthest outside facet\n\
+    Qg   - only build good facets (needs 'QGn', 'QVn', or 'PdD')\n\
+    Qm   - only process points that would increase max_outside\n\
+    Qr   - process random outside points instead of furthest ones\n\
+    Qs   - search all points for the initial simplex\n\
+    Qu   - for 'd' or 'v', compute upper hull without point at-infinity\n\
+              returns furthest-site Delaunay triangulation\n\
+    Qv   - test vertex neighbors for convexity\n\
+    Qx   - exact pre-merges (skips coplanar and angle-coplanar facets)\n\
+    Qz   - add point-at-infinity to Delaunay triangulation\n\
+    QGn  - good facet if visible from point n, -n for not visible\n\
+    QVn  - good facet if it includes point n, -n if not\n\
+    Q0   - turn off default premerge with 'C-0'/'Qx'\n\
+    Q1     - sort merges by type instead of angle\n\
+    Q2   - merge all non-convex at once instead of independent sets\n\
+    Q3   - do not merge redundant vertices\n\
+    Q4   - avoid old->new merges\n\
+    Q5   - do not correct outer planes at end of qhull\n\
+    Q6   - do not pre-merge concave or coplanar facets\n\
+    Q7   - depth-first processing instead of breadth-first\n\
+    Q8   - do not process near-inside points\n\
+    Q9   - process furthest of furthest points\n\
+    Q10  - no special processing for narrow distributions\n\
+    Q11  - copy normals and recompute centrums for tricoplanar facets\n\
+\n\
+";
+char qh_promptc[]= "\
+Topts- Trace options:\n\
+    T4   - trace at level n, 4=all, 5=mem/gauss, -1= events\n\
+    Ta   - annotate output with message codes\n\
+    Tc   - check frequently during execution\n\
+    Ts   - print statistics\n\
+    Tv   - verify result: structure, convexity, and point inclusion\n\
+    Tz   - send all output to stdout\n\
+    TFn  - report summary when n or more facets created\n\
+    TI file - input data from file, no spaces or single quotes\n\
+    TO file - output results to file, may be enclosed in single quotes\n\
+    TPn  - turn on tracing when point n added to hull\n\
+     TMn - turn on tracing at merge n\n\
+     TWn - trace merge facets when width > n\n\
+    TRn  - rerun qhull n times.  Use with 'QJn'\n\
+    TVn  - stop qhull after adding point n, -n for before (see TCn)\n\
+     TCn - stop qhull after building cone for point n (see TVn)\n\
+\n\
+Precision options:\n\
+    Cn   - radius of centrum (roundoff added).  Merge facets if non-convex\n\
+     An  - cosine of maximum angle.  Merge facets if cosine > n or non-convex\n\
+           C-0 roundoff, A-0.99/C-0.01 pre-merge, A0.99/C0.01 post-merge\n\
+    En   - max roundoff error for distance computation\n\
+    Rn   - randomly perturb computations by a factor of [1-n,1+n]\n\
+    Vn   - min distance above plane for a visible facet (default 3C-n or En)\n\
+    Un   - max distance below plane for a new, coplanar point (default Vn)\n\
+    Wn   - min facet width for outside point (before roundoff, default 2Vn)\n\
+\n\
+Output formats (may be combined; if none, produces a summary to stdout):\n\
+    f    - facet dump\n\
+    G    - Geomview output (see below)\n\
+    i    - vertices incident to each facet\n\
+    m    - Mathematica output (2-d and 3-d)\n\
+    o    - OFF format (dim, points and facets; Voronoi regions)\n\
+    n    - normals with offsets\n\
+    p    - vertex coordinates or Voronoi vertices (coplanar points if 'Qc')\n\
+    s    - summary (stderr)\n\
+\n\
+";
+char qh_promptd[]= "\
+More formats:\n\
+    Fa   - area for each facet\n\
+    FA   - compute total area and volume for option 's'\n\
+    Fc   - count plus coplanar points for each facet\n\
+           use 'Qc' (default) for coplanar and 'Qi' for interior\n\
+    FC   - centrum or Voronoi center for each facet\n\
+    Fd   - use cdd format for input (homogeneous with offset first)\n\
+    FD   - use cdd format for numeric output (offset first)\n\
+    FF   - facet dump without ridges\n\
+    Fi   - inner plane for each facet\n\
+           for 'v', separating hyperplanes for bounded Voronoi regions\n\
+    FI   - ID of each facet\n\
+    Fm   - merge count for each facet (511 max)\n\
+    FM   - Maple output (2-d and 3-d)\n\
+    Fn   - count plus neighboring facets for each facet\n\
+    FN   - count plus neighboring facets for each point\n\
+    Fo   - outer plane (or max_outside) for each facet\n\
+           for 'v', separating hyperplanes for unbounded Voronoi regions\n\
+    FO   - options and precision constants\n\
+    Fp   - dim, count, and intersection coordinates (halfspace only)\n\
+    FP   - nearest vertex and distance for each coplanar point\n\
+    FQ   - command used for qhull\n\
+    Fs   - summary: #int (8), dimension, #points, tot vertices, tot facets,\n\
+                      output: #vertices, #facets, #coplanars, #nonsimplicial\n\
+                    #real (2), max outer plane, min vertex\n\
+    FS   - sizes:   #int (0)\n\
+                    #real (2) tot area, tot volume\n\
+    Ft   - triangulation with centrums for non-simplicial facets (OFF format)\n\
+    Fv   - count plus vertices for each facet\n\
+           for 'v', Voronoi diagram as Voronoi vertices for pairs of sites\n\
+    FV   - average of vertices (a feasible point for 'H')\n\
+    Fx   - extreme points (in order for 2-d)\n\
+\n\
+";
+char qh_prompte[]= "\
+Geomview options (2-d, 3-d, and 4-d; 2-d Voronoi)\n\
+    Ga   - all points as dots\n\
+     Gp  -  coplanar points and vertices as radii\n\
+     Gv  -  vertices as spheres\n\
+    Gi   - inner planes only\n\
+     Gn  -  no planes\n\
+     Go  -  outer planes only\n\
+    Gc   - centrums\n\
+    Gh   - hyperplane intersections\n\
+    Gr   - ridges\n\
+    GDn  - drop dimension n in 3-d and 4-d output\n\
+    Gt   - for 3-d 'd', transparent outer ridges\n\
+\n\
+Print options:\n\
+    PAn  - keep n largest facets by area\n\
+    Pdk:n - drop facet if normal[k] <= n (default 0.0)\n\
+    PDk:n - drop facet if normal[k] >= n\n\
+    Pg   - print good facets (needs 'QGn' or 'QVn')\n\
+    PFn  - keep facets whose area is at least n\n\
+    PG   - print neighbors of good facets\n\
+    PMn  - keep n facets with most merges\n\
+    Po   - force output.  If error, output neighborhood of facet\n\
+    Pp   - do not report precision problems\n\
+\n\
+    .    - list of all options\n\
+    -    - one line descriptions of all options\n\
+";
+/* for opts, don't assign 'e' or 'E' to a flag (already used for exponent) */
+
+/*---------------------------------
+
+  qh_prompt2
+    synopsis for qhull
+*/
+char qh_prompt2[]= "\n\
+qhull- compute convex hulls and related structures.  Qhull %s\n\
+    input (stdin): dimension, n, point coordinates\n\
+    comments start with a non-numeric character\n\
+    halfspace: use dim+1 and put offsets after coefficients\n\
+\n\
+options (qh-quick.htm):\n\
+    d    - Delaunay triangulation by lifting points to a paraboloid\n\
+    d Qu - furthest-site Delaunay triangulation (upper convex hull)\n\
+    v    - Voronoi diagram as the dual of the Delaunay triangulation\n\
+    v Qu - furthest-site Voronoi diagram\n\
+    H1,1 - Halfspace intersection about [1,1,0,...] via polar duality\n\
+    Qt   - triangulated output\n\
+    QJ   - joggled input instead of merged facets\n\
+    Tv   - verify result: structure, convexity, and point inclusion\n\
+    .    - concise list of all options\n\
+    -    - one-line description of each option\n\
+\n\
+Output options (subset):\n\
+    s    - summary of results (default)\n\
+    i    - vertices incident to each facet\n\
+    n    - normals with offsets\n\
+    p    - vertex coordinates (if 'Qc', includes coplanar points)\n\
+           if 'v', Voronoi vertices\n\
+    Fp   - halfspace intersections\n\
+    Fx   - extreme points (convex hull vertices)\n\
+    FA   - compute total area and volume\n\
+    o    - OFF format (if 'v', outputs Voronoi regions)\n\
+    G    - Geomview output (2-d, 3-d and 4-d)\n\
+    m    - Mathematica output (2-d and 3-d)\n\
+    QVn  - print facets that include point n, -n if not\n\
+    TO file- output results to file, may be enclosed in single quotes\n\
+\n\
+examples:\n\
+    rbox c d D2 | qhull Qc s f Fx | more      rbox 1000 s | qhull Tv s FA\n\
+    rbox 10 D2 | qhull d QJ s i TO result     rbox 10 D2 | qhull v Qbb Qt p\n\
+    rbox 10 D2 | qhull d Qu QJ m              rbox 10 D2 | qhull v Qu QJ o\n\
+    rbox c | qhull n                          rbox c | qhull FV n | qhull H Fp\n\
+    rbox d D12 | qhull QR0 FA                 rbox c D7 | qhull FA TF1000\n\
+    rbox y 1000 W0 | qhull                    rbox 10 | qhull v QJ o Fv\n\
+\n\
+";
+/* for opts, don't assign 'e' or 'E' to a flag (already used for exponent) */
+
+/*---------------------------------
+
+  qh_prompt3
+    concise prompt for qhull
+*/
+char qh_prompt3[]= "\n\
+Qhull %s.\n\
+Except for 'F.' and 'PG', upper-case options take an argument.\n\
+\n\
+ delaunay       voronoi        Geomview       Halfspace      facet_dump\n\
+ incidences     mathematica    normals        OFF_format     points\n\
+ summary\n\
+\n\
+ Farea          FArea-total    Fcoplanars     FCentrums      Fd-cdd-in\n\
+ FD-cdd-out     FF-dump-xridge Finner         FIDs           Fmerges\n\
+ Fneighbors     FNeigh-vertex  Fouter         FOptions       Fpoint-intersect\n\
+ FPoint_near    FQhull         Fsummary       FSize          Ftriangles\n\
+ Fvertices      Fvoronoi       FVertex-ave    Fxtremes       FMaple\n\
+\n\
+ Gvertices      Gpoints        Gall_points    Gno_planes     Ginner\n\
+ Gcentrums      Ghyperplanes   Gridges        Gouter         GDrop_dim\n\
+ Gtransparent\n\
+\n\
+ PArea-keep     Pdrop d0:0D0   Pgood          PFacet_area_keep\n\
+ PGood_neighbors PMerge-keep   Poutput_forced Pprecision_not\n\
+\n\
+ QbBound 0:0.5  Qbk:0Bk:0_drop QbB-scale-box  Qbb-scale-last Qcoplanar\n\
+ Qfurthest      Qgood_only     QGood_point    Qinterior      Qmax_out\n\
+ QJoggle        Qrandom        QRotate        Qsearch_1st    Qtriangulate\n\
+ QupperDelaunay QVertex_good   Qvneighbors    Qxact_merge    Qzinfinite\n\
+\n\
+ Q0_no_premerge Q1_no_angle    Q2_no_independ Q3_no_redundant Q4_no_old\n\
+ Q5_no_check_out Q6_no_concave Q7_depth_first Q8_no_near_in  Q9_pick_furthest\n\
+ Q10_no_narrow  Q11_trinormals\n\
+\n\
+ T4_trace       Tannotate      Tcheck_often   Tstatistics    Tverify\n\
+ Tz_stdout      TFacet_log     TInput_file    TPoint_trace   TMerge_trace\n\
+ TOutput_file   TRerun         TWide_trace    TVertex_stop   TCone_stop\n\
+\n\
+ Angle_max      Centrum_size   Error_round    Random_dist    Visible_min\n\
+ Ucoplanar_max  Wide_outside\n\
+";
+
+/*---------------------------------
+
+  main( argc, argv )
+    processes the command line, calls qhull() to do the work, and exits
+
+  design:
+    initializes data structures
+    reads points
+    finishes initialization
+    computes convex hull and other structures
+    checks the result
+    writes the output
+    frees memory
+*/
+int main(int argc, char *argv[]) {
+  int curlong, totlong; /* used !qh_NOmem */
+  int exitcode, numpoints, dim;
+  coordT *points;
+  boolT ismalloc;
+
+#if __MWERKS__ && __POWERPC__
+  char inBuf[BUFSIZ], outBuf[BUFSIZ], errBuf[BUFSIZ];
+  SIOUXSettings.showstatusline= false;
+  SIOUXSettings.tabspaces= 1;
+  SIOUXSettings.rows= 40;
+  if (setvbuf(stdin, inBuf, _IOFBF, sizeof(inBuf)) < 0   /* w/o, SIOUX I/O is slow*/
+  || setvbuf(stdout, outBuf, _IOFBF, sizeof(outBuf)) < 0
+  || (stdout != stderr && setvbuf(stderr, errBuf, _IOFBF, sizeof(errBuf)) < 0))
+    fprintf(stderr, "qhull internal warning (main): could not change stdio to fully buffered.\n");
+  argc= ccommand(&argv);
+#endif
+
+  if ((argc == 1) && isatty( 0 /*stdin*/)) {
+    fprintf(stdout, qh_prompt2, qh_version);
+    exit(qh_ERRnone);
+  }
+  if (argc > 1 && *argv[1] == '-' && !*(argv[1]+1)) {
+    fprintf(stdout, qh_prompta, qh_version, qh_DEFAULTbox,
+                qh_promptb, qh_promptc, qh_promptd, qh_prompte);
+    exit(qh_ERRnone);
+  }
+  if (argc >1 && *argv[1] == '.' && !*(argv[1]+1)) {
+    fprintf(stdout, qh_prompt3, qh_version);
+    exit(qh_ERRnone);
+  }
+  qh_init_A(stdin, stdout, stderr, argc, argv);  /* sets qh qhull_command */
+  exitcode= setjmp(qh errexit); /* simple statement for CRAY J916 */
+  if (!exitcode) {
+    qh_initflags(qh qhull_command);
+    points= qh_readpoints(&numpoints, &dim, &ismalloc);
+    qh_init_B(points, numpoints, dim, ismalloc);
+    qh_qhull();
+    qh_check_output();
+    qh_produce_output();
+    if (qh VERIFYoutput && !qh FORCEoutput && !qh STOPpoint && !qh STOPcone)
+      qh_check_points();
+    exitcode= qh_ERRnone;
+  }
+  qh NOerrexit= True;  /* no more setjmp */
+#ifdef qh_NOmem
+  qh_freeqhull( True);
+#else
+  qh_freeqhull( False);
+  qh_memfreeshort(&curlong, &totlong);
+  if (curlong || totlong)
+    fprintf(stderr, "qhull internal warning (main): did not free %d bytes of long memory(%d pieces)\n",
+       totlong, curlong);
+#endif
+  return exitcode;
+} /* main */
+
diff --git a/src/qhullrtest/Coordinates_test.cpp b/src/qhullrtest/Coordinates_test.cpp
new file mode 100644
index 0000000..54717c9
--- /dev/null
+++ b/src/qhullrtest/Coordinates_test.cpp
@@ -0,0 +1,534 @@
+/****************************************************************************
+**
+** Copyright (c) 2009-2012 C.B. Barber. All rights reserved.
+** $Id: //main/2011/qhull/src/qhullrtest/Coordinates_test.cpp#1 $$Change: 1640 $
+** $DateTime: 2014/01/15 09:12:08 $$Author: bbarber $
+**
+****************************************************************************/
+
+//pre-compiled headers
+#include 
+#include "RoadTest.h" // QT_VERSION
+
+#include "Coordinates.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;
+
+namespace orgQhull {
+
+class Coordinates_test : public RoadTest
+{
+    Q_OBJECT
+
+#//Test slots
+private slots:
+    void t_construct();
+    void t_convert();
+    void t_element();
+    void t_readonly();
+    void t_operator();
+    void t_const_iterator();
+    void t_iterator();
+    void t_coord_iterator();
+    void t_mutable_coord_iterator();
+    void t_readwrite();
+    void t_search();
+    void t_io();
+};//Coordinates_test
+
+void
+add_Coordinates_test()
+{
+    new Coordinates_test();
+}
+
+void Coordinates_test::
+t_construct()
+{
+    Coordinates c;
+    QCOMPARE(c.size(), 0U);
+    QVERIFY(c.isEmpty());
+    c << 1.0;
+    QCOMPARE(c.count(), 1);
+    Coordinates c2(c);
+    c2 << 2.0;
+    QCOMPARE(c2.count(), 2);
+    Coordinates c3;
+    c3 = c2;
+    QCOMPARE(c3.count(), 2);
+    QCOMPARE(c3[0]+c3[1], 3.0);
+    QVERIFY(c2==c3);
+    std::vector vc;
+    vc.push_back(3.0);
+    vc.push_back(4.0);
+    Coordinates c4(vc);
+    QCOMPARE(c4[0]+c4[1], 7.0);
+    Coordinates c5(c3);
+    QVERIFY(c5==c3);
+    c5= vc;
+    QVERIFY(c5!=c3);
+    QVERIFY(c5==c4);
+}//t_construct
+
+void Coordinates_test::
+t_convert()
+{
+    Coordinates c;
+    c << 1.0 << 3.0;
+    QCOMPARE(c.data()[1], 3.0);
+    coordT *c2= c.data();
+    const coordT *c3= c.data();
+    QCOMPARE(c2, c3);
+    std::vector vc= c.toStdVector();
+    QCOMPARE(vc.size(), c.size());
+    for(size_t k= vc.size(); k--; ){
+        QCOMPARE(vc[k], c[k]);
+    }
+    QList qc= c.toQList();
+    QCOMPARE(qc.count(), c.count());
+    for(int k= qc.count(); k--; ){
+        QCOMPARE(qc[k], c[k]);
+    }
+    Coordinates c4;
+    c4= std::vector(2, 0.0);
+    QCOMPARE(c4.back(), 0.0);
+    Coordinates c5(std::vector(2, 0.0));
+    QCOMPARE(c4.size(), c5.size());
+    QVERIFY(c4==c5);
+}//t_convert
+
+void Coordinates_test::
+t_element()
+{
+    Coordinates c;
+    c << 1.0 << -2.0;
+    c.at(1)= -3;
+    QCOMPARE(c.at(1), -3.0);
+    QCOMPARE(c.back(), -3.0);
+    QCOMPARE(c.front(), 1.0);
+    c[1]= -2.0;
+    QCOMPARE(c[1],-2.0);
+    QCOMPARE(c.first(), 1.0);
+    c.first()= 2.0;
+    QCOMPARE(c.first(), 2.0);
+    QCOMPARE(c.last(), -2.0);
+    c.last()= 0.0;
+    QCOMPARE(c.first()+c.last(), 2.0);
+    coordT *c4= &c.first();
+    const coordT *c5= &c.first();
+    QCOMPARE(c4, c5);
+    coordT *c6= &c.last();
+    const coordT *c7= &c.last();
+    QCOMPARE(c6, c7);
+    Coordinates c2= c.mid(1);
+    QCOMPARE(c2.count(), 1);
+    c << 3.0;
+    Coordinates c3= c.mid(1,1);
+    QCOMPARE(c2, c3);
+    QCOMPARE(c3.value(-1, -1.0), -1.0);
+    QCOMPARE(c3.value(3, 4.0), 4.0);
+    QCOMPARE(c.value(2, 4.0), 3.0);
+}//t_element
+
+void Coordinates_test::
+t_readonly()
+{
+    Coordinates c;
+    QCOMPARE(c.size(), 0u);
+    QCOMPARE(c.count(), 0);
+    QVERIFY(c.empty());
+    QVERIFY(c.isEmpty());
+    c << 1.0 << -2.0;
+    QCOMPARE(c.size(), 2u);
+    QCOMPARE(c.count(), 2);
+    QVERIFY(!c.empty());
+    QVERIFY(!c.isEmpty());
+}//t_readonly
+
+void Coordinates_test::
+t_operator()
+{
+    Coordinates c;
+    Coordinates c2(c);
+    QVERIFY(c==c2);
+    QVERIFY(!(c!=c2));
+    c << 1.0;
+    QVERIFY(!(c==c2));
+    QVERIFY(c!=c2);
+    c2 << 1.0;
+    QVERIFY(c==c2);
+    QVERIFY(!(c!=c2));
+    c[0]= 0.0;
+    QVERIFY(c!=c2);
+    Coordinates c3= c+c2;
+    QCOMPARE(c3.count(), 2);
+    QCOMPARE(c3[0], 0.0);
+    QCOMPARE(c3[1], 1.0);
+    c3 += c3;
+    QCOMPARE(c3.count(), 4);
+    QCOMPARE(c3[2], 0.0);
+    QCOMPARE(c3[3], 1.0);
+    c3 += c2;
+    QCOMPARE(c3[4], 1.0);
+    c3 += 5.0;
+    QCOMPARE(c3.count(), 6);
+    QCOMPARE(c3[5], 5.0);
+    // << checked above
+}//t_operator
+
+void Coordinates_test::
+t_const_iterator()
+{
+    Coordinates c;
+    QCOMPARE(c.begin(), c.end());
+    // begin and end checked elsewhere
+    c << 1.0 << 3.0;
+    Coordinates::const_iterator i= c.begin();
+    QCOMPARE(*i, 1.0);
+    QCOMPARE(i[1], 3.0);
+    // i[1]= -3.0; // compiler error
+    // operator-> is not applicable to double
+    QCOMPARE(*i++, 1.0);
+    QCOMPARE(*i, 3.0);
+    QCOMPARE(*i--, 3.0);
+    QCOMPARE(*i, 1.0);
+    QCOMPARE(*(i+1), 3.0);
+    QCOMPARE(*++i, 3.0);
+    QCOMPARE(*(i-1), 1.0);
+    QCOMPARE(*--i, 1.0);
+    QVERIFY(i==c.begin());
+    QVERIFY(i==c.constBegin());
+    QVERIFY(i!=c.end());
+    QVERIFY(i!=c.constEnd());
+    QVERIFY(i=c.begin());
+    QVERIFY(i+1<=c.end());
+    QVERIFY(i+1>c.begin());
+    Coordinates::iterator i2= c.begin();
+    Coordinates::const_iterator i3(i2);
+    QCOMPARE(*i3, 1.0);
+    QCOMPARE(i3[1], 3.0);
+}//t_const_iterator
+
+void Coordinates_test::
+t_iterator()
+{
+    Coordinates c;
+    QCOMPARE(c.begin(), c.end());
+    // begin and end checked elsewhere
+    c << 1.0 << 3.0;
+    Coordinates::iterator i= c.begin();
+    QCOMPARE(*i, 1.0);
+    QCOMPARE(i[1], 3.0);
+    *i= -1.0;
+    QCOMPARE(*i, -1.0);
+    i[1]= -3.0;
+    QCOMPARE(i[1], -3.0);
+    *i= 1.0;
+    // operator-> is not applicable to double
+    QCOMPARE(*i++, 1.0);
+    QCOMPARE(*i, -3.0);
+    *i= 3.0;
+    QCOMPARE(*i--, 3.0);
+    QCOMPARE(*i, 1.0);
+    QCOMPARE(*(i+1), 3.0);
+    QCOMPARE(*++i, 3.0);
+    QCOMPARE(*(i-1), 1.0);
+    QCOMPARE(*--i, 1.0);
+    QVERIFY(i==c.begin());
+    QVERIFY(i==c.constBegin());
+    QVERIFY(i!=c.end());
+    QVERIFY(i!=c.constEnd());
+    QVERIFY(i=c.begin());
+    QVERIFY(i+1<=c.end());
+    QVERIFY(i+1>c.begin());
+}//t_iterator
+
+void Coordinates_test::
+t_coord_iterator()
+{
+    Coordinates c;
+    c << 1.0 << 3.0;
+    CoordinatesIterator i(c);
+    CoordinatesIterator i2= c;
+    QVERIFY(i.findNext(1.0));
+    QVERIFY(!i.findNext(2.0));
+    QVERIFY(!i.findNext(3.0));
+    QVERIFY(i.findPrevious(3.0));
+    QVERIFY(!i.findPrevious(2.0));
+    QVERIFY(!i.findPrevious(1.0));
+    QVERIFY(i2.findNext(3.0));
+    QVERIFY(i2.findPrevious(3.0));
+    QVERIFY(i2.findNext(3.0));
+    QVERIFY(i2.findPrevious(1.0));
+    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());
+    Coordinates c2;
+    i2= c2;
+    QVERIFY(!i2.hasNext());
+    QVERIFY(!i2.hasPrevious());
+    i2.toBack();
+    QVERIFY(!i2.hasNext());
+    QVERIFY(!i2.hasPrevious());
+    QCOMPARE(i.peekPrevious(), 3.0);
+    QCOMPARE(i.previous(), 3.0);
+    QCOMPARE(i.previous(), 1.0);
+    QVERIFY(!i.hasPrevious());
+    QCOMPARE(i.peekNext(), 1.0);
+    // i.peekNext()= 1.0; // compiler error
+    QCOMPARE(i.next(), 1.0);
+    QCOMPARE(i.peekNext(), 3.0);
+    QCOMPARE(i.next(), 3.0);
+    QVERIFY(!i.hasNext());
+    i.toFront();
+    QCOMPARE(i.next(), 1.0);
+}//t_coord_iterator
+
+void Coordinates_test::
+t_mutable_coord_iterator()
+{
+    // Same tests as CoordinatesIterator
+    Coordinates c;
+    c << 1.0 << 3.0;
+    MutableCoordinatesIterator i(c);
+    MutableCoordinatesIterator i2= c;
+    QVERIFY(i.findNext(1.0));
+    QVERIFY(!i.findNext(2.0));
+    QVERIFY(!i.findNext(3.0));
+    QVERIFY(i.findPrevious(3.0));
+    QVERIFY(!i.findPrevious(2.0));
+    QVERIFY(!i.findPrevious(1.0));
+    QVERIFY(i2.findNext(3.0));
+    QVERIFY(i2.findPrevious(3.0));
+    QVERIFY(i2.findNext(3.0));
+    QVERIFY(i2.findPrevious(1.0));
+    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());
+    Coordinates c2;
+    i2= c2;
+    QVERIFY(!i2.hasNext());
+    QVERIFY(!i2.hasPrevious());
+    i2.toBack();
+    QVERIFY(!i2.hasNext());
+    QVERIFY(!i2.hasPrevious());
+    QCOMPARE(i.peekPrevious(), 3.0);
+    QCOMPARE(i.peekPrevious(), 3.0);
+    QCOMPARE(i.previous(), 3.0);
+    QCOMPARE(i.previous(), 1.0);
+    QVERIFY(!i.hasPrevious());
+    QCOMPARE(i.peekNext(), 1.0);
+    QCOMPARE(i.next(), 1.0);
+    QCOMPARE(i.peekNext(), 3.0);
+    QCOMPARE(i.next(), 3.0);
+    QVERIFY(!i.hasNext());
+    i.toFront();
+    QCOMPARE(i.next(), 1.0);
+
+    // Mutable tests
+    i.toFront();
+    i.peekNext()= -1.0;
+    QCOMPARE(i.peekNext(), -1.0);
+    QCOMPARE((i.next()= 1.0), 1.0);
+    QCOMPARE(i.peekPrevious(), 1.0);
+    i.remove();
+    QCOMPARE(c.count(), 1);
+    i.remove();
+    QCOMPARE(c.count(), 1);
+    QCOMPARE(i.peekNext(), 3.0);
+    i.insert(1.0);
+    i.insert(2.0);
+    QCOMPARE(c.count(), 3);
+    QCOMPARE(i.peekNext(), 3.0);
+    QCOMPARE(i.peekPrevious(), 2.0);
+    i.peekPrevious()= -2.0;
+    QCOMPARE(i.peekPrevious(), -2.0);
+    QCOMPARE((i.previous()= 2.0), 2.0);
+    QCOMPARE(i.peekNext(), 2.0);
+    i.toBack();
+    i.remove();
+    QCOMPARE(c.count(), 3); // unchanged
+    i.toFront();
+    i.remove();
+    QCOMPARE(c.count(), 3); // unchanged
+    QCOMPARE(i.peekNext(), 1.0);
+    i.remove();
+    QCOMPARE(c.count(), 3); // unchanged
+    i.insert(0.0);
+    QCOMPARE(c.count(), 4);
+    QCOMPARE(i.value(), 0.0);
+    QCOMPARE(i.peekPrevious(), 0.0);
+    i.setValue(-10.0);
+    QCOMPARE(c.count(), 4); // unchanged
+    QCOMPARE(i.peekNext(), 1.0);
+    QCOMPARE(i.peekPrevious(), -10.0);
+    i.findNext(1.0);
+    i.setValue(-1.0);
+    QCOMPARE(i.peekPrevious(), -1.0);
+    i.setValue(1.0);
+    QCOMPARE(i.peekPrevious(), 1.0);
+    QCOMPARE(i.value(), 1.0);
+    i.findPrevious(1.0);
+    i.setValue(-1.0);
+    QCOMPARE(i.peekNext(), -1.0);
+    i.toBack();
+    QCOMPARE(i.previous(), 3.0);
+    i.setValue(-3.0);
+    QCOMPARE(i.peekNext(), -3.0);
+    double d= i.value();
+    QCOMPARE(d, -3.0);
+    QCOMPARE(i.previous(), 2.0);
+}//t_mutable_coord_iterator
+
+void Coordinates_test::
+t_readwrite()
+{
+    Coordinates c;
+    c.clear();
+    QCOMPARE(c.count(), 0);
+    c << 1.0 << 3.0;
+    c.clear();
+    QCOMPARE(c.count(), 0);
+    c << 1.0 << 3.0;
+    c.erase(c.begin(), c.end());
+    QCOMPARE(c.count(), 0);
+    c << 1.0 << 0.0;
+    Coordinates::iterator i= c.erase(c.begin());
+    QCOMPARE(*i, 0.0);
+    i= c.insert(c.end(), 1.0);
+    QCOMPARE(*i, 1.0);
+    QCOMPARE(c.count(), 2);
+    c.pop_back();
+    QCOMPARE(c.count(), 1);   // 0
+    QCOMPARE(c[0], 0.0);
+    c.push_back(2.0);
+    QCOMPARE(c.count(), 2);
+    c.append(3.0);
+    QCOMPARE(c.count(), 3);   // 0, 2, 3
+    QCOMPARE(c[2], 3.0);
+    c.insert(0, 4.0);
+    QCOMPARE(c[0], 4.0);
+    QCOMPARE(c[3], 3.0);
+    c.insert(c.count(), 5.0);
+    QCOMPARE(c.count(), 5);   // 4, 0, 2, 3, 5
+    QCOMPARE(c[4], 5.0);
+    c.move(4, 0);
+    QCOMPARE(c.count(), 5);   // 5, 4, 0, 2, 3
+    QCOMPARE(c[0], 5.0);
+    c.pop_front();
+    QCOMPARE(c.count(), 4);
+    QCOMPARE(c[0], 4.0);
+    c.prepend(6.0);
+    QCOMPARE(c.count(), 5);   // 6, 4, 0, 2, 3
+    QCOMPARE(c[0], 6.0);
+    c.push_front(7.0);
+    QCOMPARE(c.count(), 6);
+    QCOMPARE(c[0], 7.0);
+    c.removeAt(1);
+    QCOMPARE(c.count(), 5);   // 7, 4, 0, 2, 3
+    QCOMPARE(c[1], 4.0);
+    c.removeFirst();
+    QCOMPARE(c.count(), 4);   // 4, 0, 2, 3
+    QCOMPARE(c[0], 4.0);
+    c.removeLast();
+    QCOMPARE(c.count(), 3);
+    QCOMPARE(c.last(), 2.0);
+    c.replace(2, 8.0);
+    QCOMPARE(c.count(), 3);   // 4, 0, 8
+    QCOMPARE(c[2], 8.0);
+    c.swap(0, 2);
+    QCOMPARE(c[2], 4.0);
+    double d= c.takeAt(2);
+    QCOMPARE(c.count(), 2);   // 8, 0
+    QCOMPARE(d, 4.0);
+    double d2= c.takeFirst();
+    QCOMPARE(c.count(), 1);   // 0
+    QCOMPARE(d2, 8.0);
+    double d3= c.takeLast();
+    QVERIFY(c.isEmpty()); \
+    QCOMPARE(d3, 0.0);
+}//t_readwrite
+
+void Coordinates_test::
+t_search()
+{
+    Coordinates c;
+    c << 1.0 << 3.0 << 1.0;
+    QVERIFY(c.contains(1.0));
+    QVERIFY(c.contains(3.0));
+    QVERIFY(!c.contains(0.0));
+    QCOMPARE(c.count(1.0), 2);
+    QCOMPARE(c.count(3.0), 1);
+    QCOMPARE(c.count(0.0), 0);
+    QCOMPARE(c.indexOf(1.0), 0);
+    QCOMPARE(c.indexOf(3.0), 1);
+    QCOMPARE(c.indexOf(1.0, -1), 2);
+    QCOMPARE(c.indexOf(3.0, -1), -1);
+    QCOMPARE(c.indexOf(3.0, -2), 1);
+    QCOMPARE(c.indexOf(1.0, -3), 0);
+    QCOMPARE(c.indexOf(1.0, -4), 0);
+    QCOMPARE(c.indexOf(1.0, 1), 2);
+    QCOMPARE(c.indexOf(3.0, 2), -1);
+    QCOMPARE(c.indexOf(1.0, 2), 2);
+    QCOMPARE(c.indexOf(1.0, 3), -1);
+    QCOMPARE(c.indexOf(1.0, 4), -1);
+    QCOMPARE(c.lastIndexOf(1.0), 2);
+    QCOMPARE(c.lastIndexOf(3.0), 1);
+    QCOMPARE(c.lastIndexOf(1.0, -1), 2);
+    QCOMPARE(c.lastIndexOf(3.0, -1), 1);
+    QCOMPARE(c.lastIndexOf(3.0, -2), 1);
+    QCOMPARE(c.lastIndexOf(1.0, -3), 0);
+    QCOMPARE(c.lastIndexOf(1.0, -4), -1);
+    QCOMPARE(c.lastIndexOf(1.0, 1), 0);
+    QCOMPARE(c.lastIndexOf(3.0, 2), 1);
+    QCOMPARE(c.lastIndexOf(1.0, 2), 2);
+    QCOMPARE(c.lastIndexOf(1.0, 3), 2);
+    QCOMPARE(c.lastIndexOf(1.0, 4), 2);
+    c.removeAll(3.0);
+    QCOMPARE(c.count(), 2);
+    c.removeAll(4.0);
+    QCOMPARE(c.count(), 2);
+    c.removeAll(1.0);
+    QCOMPARE(c.count(), 0);
+    c.removeAll(4.0);
+    QCOMPARE(c.count(), 0);
+}//t_search
+
+void Coordinates_test::
+t_io()
+{
+    Coordinates c;
+    c << 1.0 << 2.0 << 3.0;
+    ostringstream os;
+    os << "Coordinates 1-2-3\n" << c;
+    cout << os.str();
+    QString s= QString::fromStdString(os.str());
+    QCOMPARE(s.count("2"), 2);
+}//t_io
+
+}//orgQhull
+
+#include "moc/Coordinates_test.moc"
diff --git a/src/qhullrtest/PointCoordinates_test.cpp b/src/qhullrtest/PointCoordinates_test.cpp
new file mode 100644
index 0000000..d49d9c9
--- /dev/null
+++ b/src/qhullrtest/PointCoordinates_test.cpp
@@ -0,0 +1,397 @@
+/****************************************************************************
+**
+** Copyright (c) 2009-2012 C.B. Barber. All rights reserved.
+** $Id: //main/2011/qhull/src/qhullrtest/PointCoordinates_test.cpp#1 $$Change: 1640 $
+** $DateTime: 2014/01/15 09:12:08 $$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/qhullrtest/Point_test.cpp b/src/qhullrtest/Point_test.cpp
new file mode 100644
index 0000000..95394a2
--- /dev/null
+++ b/src/qhullrtest/Point_test.cpp
@@ -0,0 +1,238 @@
+/****************************************************************************
+**
+** Copyright (C) 2009-2012 C.B. Barber. All rights reserved.
+** $Id: //main/2011/qhull/src/qhullrtest/Point_test.cpp#1 $$Change: 1640 $
+** $DateTime: 2014/01/15 09:12:08 $$Author: bbarber $
+**
+****************************************************************************/
+
+#include 
+using std::cout;
+using std::endl;
+#include "RoadTest.h" // QT_VERSION
+
+#include "QhullPoint.h"
+
+#include "Qhull.h"
+
+namespace orgQhull {
+
+class Point_test : public RoadTest
+{
+    Q_OBJECT
+
+#//Test slots
+private slots:
+    void initTestCase();
+    void t_construct();
+    void t_getset();
+    void t_operator();
+    void t_const_iterator();
+    void t_iterator();
+    void t_point_iterator();
+    // void t_mutable_point_iterator();
+    // void t_io();
+};//Point_test
+
+void
+add_Point_test()
+{
+    new Point_test();
+}
+
+void Point_test::
+initTestCase(){
+    RboxPoints rcube("c");
+    Qhull q(rcube, "");
+    UsingQhullLib::setGlobals();
+}//initTestCase
+
+void Point_test::
+t_construct()
+{
+    QhullPoint p;
+    QCOMPARE(p.dimension(), 0);
+    coordT c[]= {0.0, 1.0, 2.0};
+    QhullPoint p2;
+    p2.defineAs(3, c);
+    QCOMPARE(p2.dimension(), 3);
+    QCOMPARE(p2.coordinates(), c);
+    coordT c2[]= {0.0, 1.0, 2.0};
+    QhullPoint p3(3, c2);
+    QVERIFY(p3==p2);
+    QhullPoint p5(p3);
+    QVERIFY(p5==p3);
+}//t_construct
+
+void Point_test::
+t_getset()
+{
+    coordT c[]= {0.0, 1.0, 2.0};
+    QhullPoint p(3, c);
+    QCOMPARE(p.coordinates(), c);
+    QCOMPARE(p.dimension(), 3);
+    QCOMPARE(p[2], 2.0);
+    QhullPoint p2(p);
+    p2.defineAs(p);
+    QVERIFY(p2==p);
+    QVERIFY(p2.coordinates()==p.coordinates());
+    QVERIFY(p2.dimension()==p.dimension());
+    p2.setDimension(2);
+    QCOMPARE(p2.dimension(), 2);
+    QVERIFY(p2!=p);
+    coordT c2[]= {0.0, 1.0};
+    p2.setCoordinates(c2);
+    QCOMPARE(p2.coordinates(), c2);
+    p.defineAs(2, c);
+    QVERIFY(p2==p);
+    QCOMPARE(p[1], 1.0);
+}//t_getset
+
+void Point_test::
+t_operator()
+{
+    QhullPoint p;
+    QhullPoint p2(p);
+    QVERIFY(p==p2);
+    QVERIFY(!(p!=p2));
+    coordT c[]= {0.0, 1.0, 2.0};
+    QhullPoint p3(3, c);
+    QVERIFY(p3!=p2);
+    QhullPoint p4(p3);
+    QVERIFY(p4==p3);
+    coordT c5[]= {5.0, 6.0, 7.0};
+    QhullPoint p5(3, c5);
+    QVERIFY(p5!=p3);
+    QCOMPARE(p5[1], 6.0);
+    QCOMPARE(p5[0], 5.0);
+    const coordT *c0= &p5[0];
+    QCOMPARE(*c0, 5.0);
+}//t_operator
+
+void Point_test::
+t_const_iterator()
+{
+    coordT c[]= {1.0, 2.0, 3.0};
+    QhullPoint p(3, c);
+    QhullPoint::const_iterator i(p.coordinates());
+    QhullPoint::const_iterator i2= p.coordinates();
+    QVERIFY(i==i2);
+    QVERIFY(i>=i2);
+    QVERIFY(i<=i2);
+    QCOMPARE(*i, 1.0);
+    QCOMPARE(*(i+1), 2.0);
+    QCOMPARE(*(i+1), i[1]);
+    i= p.end();
+    QVERIFY(i!=i2);
+    i= i2;
+    QVERIFY(i==i2);
+    i= p.end();
+    i= p.begin();
+    QCOMPARE(*i, 1.0);
+    QhullPoint::ConstIterator i3= p.end();
+    QCOMPARE(*(i3-1), 3.0);
+    QCOMPARE(*(i3-1), i3[-1]);
+    QVERIFY(i!=i3);
+    QVERIFY(ii);
+    QVERIFY(i3>=i);
+}//t_const_iterator
+
+
+void Point_test::
+t_iterator()
+{
+    coordT c[]= {1.0, 2.0, 3.0};
+    QhullPoint p(3, c);
+    QhullPoint::Iterator i(p.coordinates());
+    QhullPoint::iterator i2= p.coordinates();
+    QVERIFY(i==i2);
+    QVERIFY(i>=i2);
+    QVERIFY(i<=i2);
+    QCOMPARE(*i, 1.0);
+    QCOMPARE(*(i+1), 2.0);
+    QCOMPARE(*(i+1), i[1]);
+    i= p.end();
+    QVERIFY(i!=i2);
+    i= i2;
+    QVERIFY(i==i2);
+    i= p.end();
+    i= p.begin();
+    QCOMPARE(*i, 1.0);
+    QhullPoint::Iterator i3= p.end();
+    QCOMPARE(*(i3-1), 3.0);
+    QCOMPARE(*(i3-1), i3[-1]);
+    QVERIFY(i!=i3);
+    QVERIFY(ii);
+    QVERIFY(i3>=i);
+    // compiler errors -- QhullPoint is const-only
+    // QCOMPARE((i[0]= -10.0), -10.0);
+    // coordT *c3= &i3[1];
+}//t_iterator
+
+void Point_test::
+t_point_iterator()
+{
+    coordT c[]= {1.0, 3.0, 4.0};
+    QhullPoint p(3, c);
+    QhullPointIterator i(p);
+    QhullPointIterator i2= p;
+    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());
+
+    coordT c2[]= {1.0, 3.0, 4.0};
+    QhullPoint p2(0, c2); // 0-dimensional
+    i2= p2;
+    QVERIFY(!i2.hasNext());
+    QVERIFY(!i2.hasPrevious());
+    i2.toBack();
+    QVERIFY(!i2.hasNext());
+    QVERIFY(!i2.hasPrevious());
+    QCOMPARE(i.peekPrevious(), 4.0);
+    QCOMPARE(i.previous(), 4.0);
+    QCOMPARE(i.previous(), 3.0);
+    QCOMPARE(i.previous(), 1.0);
+    QVERIFY(!i.hasPrevious());
+    QCOMPARE(i.peekNext(), 1.0);
+    // i.peekNext()= 1.0; // compiler error
+    QCOMPARE(i.next(), 1.0);
+    QCOMPARE(i.peekNext(), 3.0);
+    QCOMPARE(i.next(), 3.0);
+    QCOMPARE(i.next(), 4.0);
+    QVERIFY(!i.hasNext());
+    i.toFront();
+    QCOMPARE(i.next(), 1.0);
+}//t_point_iterator
+
+// No MutableQhullPointIterator since QhullPoint is const-only
+
+#if 0
+
+void Point_test::
+t_io()
+{
+    QhullPoint p;
+    cout<< "INFO:     empty point" << p << endl;
+    const coordT c[]= {1.0, 3.0, 4.0};
+    QhullPoint p2(2, c); // 2-dimensional
+    cout<< "INFO:   " << p2 << endl;
+}//t_io
+
+error LNK2019: unresolved external symbol "class std::basic_ostream > & __cdecl operator<<(class std::basic_ostream > &,class orgQhull::QhullPoint &)" (??6@YAAAV?$basic_ostream@DU?$char_traits@D@std@@@std@@AAV01@AAVPoint@orgQhull@@@Z) referenced in function "private: void __thiscall orgQhull::Point_test::t_io(void)" (?t_io@Point_test@orgQhull@@AAEXXZ)
+
+#endif
+
+}//orgQhull
+
+#include "moc/Point_test.moc"
diff --git a/src/qhullrtest/QhullFacetList_test.cpp b/src/qhullrtest/QhullFacetList_test.cpp
new file mode 100644
index 0000000..ce7d34f
--- /dev/null
+++ b/src/qhullrtest/QhullFacetList_test.cpp
@@ -0,0 +1,172 @@
+/****************************************************************************
+**
+** Copyright (c) 2008-2012 C.B. Barber. All rights reserved.
+** $Id: //main/2011/qhull/src/qhullrtest/QhullFacetList_test.cpp#1 $$Change: 1640 $
+** $DateTime: 2014/01/15 09:12:08 $$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());
+    QCOMPARE(fv5.size(), 7u);
+    QList fv6= fs2.vertices_toQList(q.runId());
+    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());
+    QCOMPARE(fv7.size(), 8u);
+    QList fv8= fs2.vertices_toQList(q.runId());
+    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
+        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/qhullrtest/QhullFacetSet_test.cpp b/src/qhullrtest/QhullFacetSet_test.cpp
new file mode 100644
index 0000000..647a7fa
--- /dev/null
+++ b/src/qhullrtest/QhullFacetSet_test.cpp
@@ -0,0 +1,153 @@
+/****************************************************************************
+**
+** Copyright (c) 2008-2012 C.B. Barber. All rights reserved.
+** $Id: //main/2011/qhull/src/qhullrtest/QhullFacetSet_test.cpp#1 $$Change: 1640 $
+** $DateTime: 2014/01/15 09:12:08 $$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.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/qhullrtest/QhullFacet_test.cpp b/src/qhullrtest/QhullFacet_test.cpp
new file mode 100644
index 0000000..631e340
--- /dev/null
+++ b/src/qhullrtest/QhullFacet_test.cpp
@@ -0,0 +1,264 @@
+/****************************************************************************
+**
+** Copyright (c) 2008-2012 C.B. Barber. All rights reserved.
+** $Id: //main/2011/qhull/src/qhullrtest/QhullFacet_test.cpp#1 $$Change: 1640 $
+** $DateTime: 2014/01/15 09:12:08 $$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());
+            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());
+            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());
+            cout << "Center: " << center << endl;
+            double d= f.distance(center);
+            QVERIFY(d < innerOffset-outerOffset);
+            QhullPoint center2= f.getCenter(q.runId(), 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);
+        QCOMPARE(center3.dimension(), 3);
+        QhullPoint center4= f2.getCenter(q.runId());
+        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());
+            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.printFlags("    - flags:");
+        os << f.printCenter(q.runId(), qh_PRINTfacets, "    - center:");
+        os << f.printRidges(q.runId());
+        cout << os.str();
+        ostringstream os2;
+        os2 << f.print(q.runId());  // 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/qhullrtest/QhullHyperplane_test.cpp b/src/qhullrtest/QhullHyperplane_test.cpp
new file mode 100644
index 0000000..64d8b52
--- /dev/null
+++ b/src/qhullrtest/QhullHyperplane_test.cpp
@@ -0,0 +1,412 @@
+/****************************************************************************
+**
+** Copyright (c) 2009-2012 C.B. Barber. All rights reserved.
+** $Id: //main/2011/qhull/src/qhullrtest/QhullHyperplane_test.cpp#1 $$Change: 1640 $
+** $DateTime: 2014/01/15 09:12:08 $$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 << 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/qhullrtest/QhullLinkedList_test.cpp b/src/qhullrtest/QhullLinkedList_test.cpp
new file mode 100644
index 0000000..512b138
--- /dev/null
+++ b/src/qhullrtest/QhullLinkedList_test.cpp
@@ -0,0 +1,330 @@
+/****************************************************************************
+**
+** Copyright (c) 2009-2012 C.B. Barber. All rights reserved.
+** $Id: //main/2011/qhull/src/qhullrtest/QhullLinkedList_test.cpp#1 $$Change: 1640 $
+** $DateTime: 2014/01/15 09:12:08 $$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()
+{
+    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);
+        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);
+        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
+    }
+    QCOMPARE(coplanarCount, 1000);
+}//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);
+}//t_convert
+
+// readonly tested in t_construct
+//   dimension, 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.first(), p);
+    QCOMPARE(ps.front(), ps.first());
+    QCOMPARE(ps.last(), p2);
+    QCOMPARE(ps.back(), ps.last());
+    QhullPoint p8;
+    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++);
+    }
+}//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, ps[0]);
+    i2--;
+    QhullPoint p2= *i2;
+    QCOMPARE(p2.dimension(), ps.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);
+
+    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
+}//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, ps[0]);
+    i2--;
+    QhullPoint p2= *i2;
+    QCOMPARE(p2.dimension(), ps.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
+}//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);
+    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);
+}//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;
+    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;
+    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.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);
+    QhullPoint p4= i.peekNext();
+    QVERIFY(p4!=p3);
+    QCOMPARE(i.next(), p4);
+    QVERIFY(i.hasNext());
+    i.toFront();
+    QCOMPARE(i.next(), p);
+}//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");
+    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);
+}//t_io
+
+}//orgQhull
+
+#include "moc/QhullPointSet_test.moc"
diff --git a/src/qhullrtest/QhullPoint_test.cpp b/src/qhullrtest/QhullPoint_test.cpp
new file mode 100644
index 0000000..5046170
--- /dev/null
+++ b/src/qhullrtest/QhullPoint_test.cpp
@@ -0,0 +1,397 @@
+/****************************************************************************
+**
+** Copyright (c) 2008-2012 C.B. Barber. All rights reserved.
+** $Id: //main/2011/qhull/src/qhullrtest/QhullPoint_test.cpp#1 $$Change: 1640 $
+** $DateTime: 2014/01/15 09:12:08 $$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_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;
+    QVERIFY(!p.isDefined());
+    QCOMPARE(p.dimension(),0);
+    QCOMPARE(p.coordinates(),static_cast(0));
+    RboxPoints rcube("c");
+    Qhull q(rcube,"Qt QR0");  // triangulation of rotated unit cube
+    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);
+    Coordinates c;
+    c << 0.0 << 0.0 << 0.0;
+    QhullPoint p6(c);
+    QCOMPARE(p6, q.origin());
+    QhullPoint p5= p2; // copy constructor
+    QVERIFY(p5==p2);
+}//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]);
+    }
+}//t_convert
+
+void QhullPoint_test::
+t_readonly()
+{
+    RboxPoints rcube("c");
+    {
+        Qhull q(rcube,"Qt QR0");  // triangulation of rotated unit cube
+        QhullVertexList vs= q.vertexList();
+        QhullVertexListIterator i(vs);
+        while(i.hasNext()){
+            QhullPoint p= i.next().point();
+            int id= p.id(q.runId());
+            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);
+        }
+        QhullPoint p2= vs.first().point();
+        QhullPoint p3= vs.last().point();
+        QVERIFY(p2!=p3);
+        QVERIFY(p3.coordinates()!=p2.coordinates());
+    }
+}//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;
+        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);
+    }
+}//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);
+}//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 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
+    }
+}//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
+    }
+}//t_const_iterator
+
+void QhullPoint_test::
+t_qhullpoint_iterator()
+{
+    QhullPoint p2;
+    QhullPointIterator i= p2;
+    QCOMPARE(p2.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
+    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]);
+}//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 << 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 ");
+        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);
+    }
+}//t_io
+
+}//orgQhull
+
+#include "moc/QhullPoint_test.moc"
diff --git a/src/qhullrtest/QhullPoints_test.cpp b/src/qhullrtest/QhullPoints_test.cpp
new file mode 100644
index 0000000..721a9cc
--- /dev/null
+++ b/src/qhullrtest/QhullPoints_test.cpp
@@ -0,0 +1,481 @@
+/****************************************************************************
+**
+** Copyright (p) 2009-2012 C.B. Barber. All rights reserved.
+** $Id: //main/2011/qhull/src/qhullrtest/QhullPoints_test.cpp#1 $$Change: 1640 $
+** $DateTime: 2014/01/15 09:12:08 $$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
+    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");
+    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/qhullrtest/QhullRidge_test.cpp b/src/qhullrtest/QhullRidge_test.cpp
new file mode 100644
index 0000000..18fd8eb
--- /dev/null
+++ b/src/qhullrtest/QhullRidge_test.cpp
@@ -0,0 +1,163 @@
+/****************************************************************************
+**
+** Copyright (c) 2008-2012 C.B. Barber. All rights reserved.
+** $Id: //main/2011/qhull/src/qhullrtest/QhullRidge_test.cpp#1 $$Change: 1640 $
+** $DateTime: 2014/01/15 09:12:08 $$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());
+        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/qhullrtest/QhullSet_test.cpp b/src/qhullrtest/QhullSet_test.cpp
new file mode 100644
index 0000000..18adc42
--- /dev/null
+++ b/src/qhullrtest/QhullSet_test.cpp
@@ -0,0 +1,435 @@
+/****************************************************************************
+**
+** Copyright (c) 2009-2012 C.B. Barber. All rights reserved.
+** $Id: //main/2011/qhull/src/qhullrtest/QhullSet_test.cpp#1 $$Change: 1640 $
+** $DateTime: 2014/01/15 09:12:08 $$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/qhullrtest/QhullVertexSet_test.cpp b/src/qhullrtest/QhullVertexSet_test.cpp
new file mode 100644
index 0000000..b70fd6b
--- /dev/null
+++ b/src/qhullrtest/QhullVertexSet_test.cpp
@@ -0,0 +1,185 @@
+/****************************************************************************
+**
+** Copyright (c) 2008-2012 C.B. Barber. All rights reserved.
+** $Id: //main/2011/qhull/src/qhullrtest/QhullVertexSet_test.cpp#1 $$Change: 1640 $
+** $DateTime: 2014/01/15 09:12:08 $$Author: bbarber $
+**
+****************************************************************************/
+
+#include 
+#include "../road/RoadTest.h" // FIXUP First for QHULL_USES_QT
+
+#include "Qhull.h"
+#include "QhullError.h"
+#include "QhullFacet.h"
+#include "QhullFacetSet.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();
+    UsingQhullLib::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 q(rcube,"QR0 QV2");  // rotated unit cube
+    QhullFacet f= q.firstFacet();
+    QhullFacetSet fs2= f.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.printIdentifiers("\nFacet identifiers: ");
+        cout<< os.str();
+        QString facets= QString::fromStdString(os.str());
+        QCOMPARE(facets.count(QRegExp(" f[0-9]")), 2+13*2);
+    }
+}//t_io
+
+//FIXUP -- Move conditional, QhullFacetSet code to QhullFacetSet.cpp
+#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
+
+#ifdef QHULL_USES_QT
+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
+#endif //QHULL_USES_QT
+
+}//orgQhull
+
+#include "moc/QhullFacetSet_test.moc"
diff --git a/src/qhullrtest/QhullVertex_test.cpp b/src/qhullrtest/QhullVertex_test.cpp
new file mode 100644
index 0000000..012dd2f
--- /dev/null
+++ b/src/qhullrtest/QhullVertex_test.cpp
@@ -0,0 +1,184 @@
+/****************************************************************************
+**
+** Copyright (c) 2008-2012 C.B. Barber. All rights reserved.
+** $Id: //main/2011/qhull/src/qhullrtest/QhullVertex_test.cpp#1 $$Change: 1640 $
+** $DateTime: 2014/01/15 09:12:08 $$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;
+            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:");
+        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 << 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 << 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/qhullrtest/Qhull_test.cpp b/src/qhullrtest/Qhull_test.cpp
new file mode 100644
index 0000000..8c1f5aa
--- /dev/null
+++ b/src/qhullrtest/Qhull_test.cpp
@@ -0,0 +1,380 @@
+/****************************************************************************
+**
+** Copyright (c) 2008-2012 C.B. Barber. All rights reserved.
+** $Id: //main/2011/qhull/src/qhullrtest/Qhull_test.cpp#1 $$Change: 1640 $
+** $DateTime: 2014/01/15 09:12:08 $$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/qhullrtest/RboxPoints_test.cpp b/src/qhullrtest/RboxPoints_test.cpp
new file mode 100644
index 0000000..fd2c8f3
--- /dev/null
+++ b/src/qhullrtest/RboxPoints_test.cpp
@@ -0,0 +1,216 @@
+/****************************************************************************
+**
+** Copyright (c) 2006-2012 C.B. Barber. All rights reserved.
+** $Id: //main/2011/qhull/src/qhullrtest/RboxPoints_test.cpp#1 $$Change: 1640 $
+** $DateTime: 2014/01/15 09:12:08 $$Author: bbarber $
+**
+****************************************************************************/
+//pre-compiled headers
+#include 
+#include "RoadTest.h" // QT_VERSION
+
+#include "RboxPoints.h"
+#include "QhullError.h"
+
+using std::cout;
+using std::endl;
+using std::ostringstream;
+using std::string;
+using std::stringstream;
+
+namespace orgQhull {
+
+//! Test C++ interface to Rbox
+//! See eg/q_test for tests of rbox commands
+class RboxPoints_test : public RoadTest
+{
+    Q_OBJECT
+
+#//Test slots
+private slots:
+    void t_construct();
+    void t_error();
+    void t_test();
+    void t_getSet();
+    void t_foreach();
+    void t_change();
+    void t_ostream();
+};
+
+void
+add_RboxPoints_test()
+{
+    new RboxPoints_test();
+}
+
+void RboxPoints_test::
+t_construct()
+{
+    RboxPoints rp;
+    QCOMPARE(rp.dimension(), 0);
+    QCOMPARE(rp.count(), 0);
+    QVERIFY(QString::fromStdString(rp.comment()) != QString(""));
+    QVERIFY(rp.isEmpty());
+    QVERIFY(!rp.hasRboxMessage());
+    QCOMPARE(rp.rboxStatus(), qh_ERRnone);
+    QCOMPARE(QString::fromStdString(rp.rboxMessage()), QString("rbox warning: no points generated\n"));
+
+    RboxPoints rp2("c"); // 3-d cube
+    QCOMPARE(rp2.dimension(), 3);
+    QCOMPARE(rp2.count(), 8);
+    QCOMPARE(QString::fromStdString(rp2.comment()), QString("rbox \"c\""));
+    QVERIFY(!rp2.isEmpty());
+    QVERIFY(!rp2.hasRboxMessage());
+    QCOMPARE(rp2.rboxStatus(), qh_ERRnone);
+    QCOMPARE(QString::fromStdString(rp2.rboxMessage()), QString("rbox: OK\n"));
+}//t_construct
+
+void RboxPoints_test::
+t_error()
+{
+    RboxPoints rp;
+    try{
+        rp.appendPoints("D0 c");
+        QFAIL("'D0 c' did not fail.");
+    }catch (const std::exception &e) {
+        const char *s= e.what();
+        cout << "INFO   : Caught " << s;
+        QCOMPARE(QString(s).left(6), QString("QH6189"));
+        QVERIFY(rp.hasRboxMessage());
+        QCOMPARE(QString::fromStdString(rp.rboxMessage()).left(8), QString("rbox err"));
+        QCOMPARE(rp.rboxStatus(), 6189);
+        rp.clearRboxMessage();
+        QVERIFY(!rp.hasRboxMessage());
+    }
+    try{
+        RboxPoints rp2;
+        rp2.setDimension(-1);
+        QFAIL("setDimension(-1) did not fail.");
+    }catch (const RoadError &e) {
+        const char *s= e.what();
+        cout << "INFO   : Caught " << s;
+        QCOMPARE(QString(s).left(7), QString("QH10062"));
+        QCOMPARE(e.errorCode(), 10062);
+        QCOMPARE(QString::fromStdString(e.what()), QString(s));
+        RoadLogEvent logEvent= e.roadLogEvent();
+        QCOMPARE(logEvent.int1(), -1);
+    }
+}//t_error
+
+void RboxPoints_test::
+t_test()
+{
+    // isEmpty -- t_construct
+}//t_test
+
+void RboxPoints_test::
+t_getSet()
+{
+    // comment -- t_construct
+    // count -- t_construct
+    // dimension -- t_construct
+
+    RboxPoints rp;
+    QCOMPARE(rp.dimension(), 0);
+    rp.setDimension(2);
+    QCOMPARE(rp.dimension(), 2);
+    rp.setDimension(2);
+    QCOMPARE(rp.dimension(), 2);
+    try{
+        rp.setDimension(102);
+        QFAIL("setDimension(102) did not fail.");
+    }catch (const std::exception &e) {
+        cout << "INFO   : Caught " << e.what();
+    }
+    QCOMPARE(rp.newCount(), 0);
+    rp.appendPoints("D2 P1 P2");
+    QCOMPARE(rp.count(), 2);
+    QCOMPARE(rp.newCount(), 2); // From previous appendPoints();
+    PointCoordinates pc(2);
+    pc << 1.0 << 0.0 << 2.0 << 0.0;
+    QCOMPARE(pc.dimension(), 2);
+    QCOMPARE(pc.count(), 2);
+    QVERIFY(rp==pc);
+    rp.setNewCount(10);  // Normally only used by appendPoints for rbox processing
+    QCOMPARE(rp.newCount(), 10);
+    rp.reservePoints();
+    QVERIFY(rp==pc);
+}//t_getSet
+
+void RboxPoints_test::
+t_foreach()
+{
+    RboxPoints rp("c");
+    Coordinates::ConstIterator cci= rp.beginCoordinates();
+    orgQhull::Coordinates::Iterator ci= rp.beginCoordinates();
+    QCOMPARE(*cci, -0.5);
+    QCOMPARE(*ci, *cci);
+    int i=1;
+    while(++cci
+#include 
+#include "RoadTest.h"
+
+using std::cout;
+using std::endl;
+
+namespace orgQhull {
+
+#//class variable
+
+QList RoadTest::
+s_testcases;
+
+int RoadTest::
+s_test_count= 0;
+
+int RoadTest::
+s_test_fail= 0;
+
+QStringList RoadTest::
+s_failed_tests;
+
+#//Slot
+
+//! Executed after each test
+void RoadTest::
+cleanup()
+{
+    s_test_count++;
+    if(QTest::currentTestFailed()){
+        recordFailedTest();
+    }
+}//cleanup
+
+#//Helper
+
+void RoadTest::
+recordFailedTest()
+{
+    s_test_fail++;
+    QString className= metaObject()->className();
+    s_failed_tests << className + "::" + QTest::currentTestFunction();
+}
+
+#//class function
+
+int RoadTest::
+runTests(QStringList arguments)
+{
+    int result= 0; // assume success
+
+    foreach(RoadTest *testcase, s_testcases){
+        try{
+            result += QTest::qExec(testcase, arguments);
+        }catch(const std::exception &e){
+            cout << "FAIL!  : Threw error ";
+            cout << e.what() << endl;
+    s_test_count++;
+            testcase->recordFailedTest();
+            // Qt 4.5.2 OK.  In Qt 4.3.3, qtestcase did not clear currentTestObject
+        }
+    }
+    if(s_test_fail){
+        cout << "Failed " << s_test_fail << " of " << s_test_count << " tests.\n";
+        cout << s_failed_tests.join("\n").toLocal8Bit().constData() << std::endl;
+    }else{
+        cout << "Passed " << s_test_count << " tests.\n";
+    }
+    return result;
+}//runTests
+
+}//orgQhull
+
+#include "moc/moc_RoadTest.cpp"
diff --git a/src/qhullrtest/RoadTest.h b/src/qhullrtest/RoadTest.h
new file mode 100644
index 0000000..a234c79
--- /dev/null
+++ b/src/qhullrtest/RoadTest.h
@@ -0,0 +1,101 @@
+/****************************************************************************
+**
+** Copyright (c) 2008-2012 C.B. Barber. All rights reserved.
+** $Id: //main/2011/qhull/src/qhullrtest/RoadTest.h#1 $$Change: 1640 $
+** $Date: 2014/01/15 $$Author: bbarber $
+**
+****************************************************************************/
+
+#ifndef ROADTEST_H
+#define ROADTEST_H
+
+//pre-compiled with RoadTest.h
+#include     // Qt C++ Framework
+#include 
+
+#define QHULL_USES_QT 1
+
+namespace orgQhull {
+
+#//!\name Defined here
+
+    //! RoadTest -- Generic test for Qt's QTest
+    class RoadTest;
+    //! TESTadd_(t) -- Add a RoadTest
+
+/** Test Name objects using Qt's QTestLib
+
+Template:
+
+class Name_test : public RoadTest
+{
+    Q_OBJECT
+#//Test slot
+private slots:
+    void t_name();
+    //Executed before any test
+    void initTestCase();
+    void init();          // Each test
+    //Executed after each test
+    void cleanup(); //RoadTest::cleanup();
+    // Executed after last test
+    void cleanupTestCase();
+};
+
+void
+add_Name_test()
+{
+    new Name_test();
+}
+
+Send additional output to cout
+*/
+
+class RoadTest : public QObject
+{
+    Q_OBJECT
+
+#//!\name Class globals
+protected:
+    static QList
+                        s_testcases; ///! List of testcases to execute.  Initialized via add_...()
+    static int          s_test_count; ///! Total number of tests executed
+    static int          s_test_fail; ///! Number of failed tests
+    static QStringList  s_failed_tests; ///! List of failed tests
+
+#//!\name Test slots
+public slots:
+    void cleanup();
+
+public:
+#//!\name Constructors, etc.
+    RoadTest()  { s_testcases.append(this); }
+    ~RoadTest() { s_testcases.removeAll(this); }
+
+#//Helper
+    void                recordFailedTest();
+
+
+#//!\name Class functions
+    static int          runTests(QStringList arguments);
+
+};//RoadTest
+
+#define TESTadd_(t) extern void t(); t();
+
+
+}//orgQhull
+
+namespace QTest{
+
+template<>
+inline char *
+toString(const std::string &s)
+{
+    return qstrdup(s.c_str());
+}
+
+}//namespace QTest
+
+#endif //ROADTEST_H
+
diff --git a/src/qhullrtest/qhullrtest.cpp b/src/qhullrtest/qhullrtest.cpp
new file mode 100644
index 0000000..935b012
--- /dev/null
+++ b/src/qhullrtest/qhullrtest.cpp
@@ -0,0 +1,86 @@
+/****************************************************************************
+**
+** Copyright (c) 2008-2012 C.B. Barber. All rights reserved.
+** $Id: //main/2011/qhull/src/qhullrtest/qhullrtest.cpp#1 $$Change: 1640 $
+** $DateTime: 2014/01/15 09:12:08 $$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
+
+    if(args.contains("--all")){
+        args.removeAll("--all");
+        // up-to-date
+        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/qhullrtest/qhullrtest.pro b/src/qhullrtest/qhullrtest.pro
new file mode 100644
index 0000000..dce1404
--- /dev/null
+++ b/src/qhullrtest/qhullrtest.pro
@@ -0,0 +1,34 @@
+# -------------------------------------------------
+# qhulltest.pro -- Qt project for qhulltest.exe (QTestLib)
+# -------------------------------------------------
+
+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