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user.h
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/*<html><pre> -<a href="qh-user.htm"
>-------------------------------</a><a name="TOP">-</a>
user.h
user redefinable constants
see qh-user.htm. see COPYING for copyright information.
before reading any code, review qhull.h for data structure definitions and
the "qh" macro.
*/
#ifndef qhDEFuser
#define qhDEFuser 1
/*============= data types and configuration macros ==========*/
/*-<a href="qh-user.htm#TOC"
>--------------------------------</a><a name="realT">-</a>
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
help 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
/*-<a href="qh-user.htm#TOC"
>--------------------------------</a><a name="CPUclock">-</a>
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.
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
/*-<a href="qh-user.htm#TOC"
>--------------------------------</a><a name="RANDOM">-</a>
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
/*-<a href="qh-user.htm#TOC"
>--------------------------------</a><a name="ORIENTclock">-</a>
qh_ORIENTclock
0 for inward pointing normals by Geomview convention
*/
#define qh_ORIENTclock 0
/*========= performance related constants =========*/
/*-<a href="qh-user.htm#TOC"
>--------------------------------</a><a name="HASHfactor">-</a>
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
/*-<a href="qh-user.htm#TOC"
>--------------------------------</a><a name="VERIFYdirect">-</a>
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
/*-<a href="qh-user.htm#TOC"
>--------------------------------</a><a name="INITIALsearch">-</a>
qh_INITIALsearch
if qh_INITIALmax, search points up to this dimension
*/
#define qh_INITIALsearch 6
/*-<a href="qh-user.htm#TOC"
>--------------------------------</a><a name="INITIALmax">-</a>
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
/*-<a href="qh-user.htm#TOC"
>--------------------------------</a><a name="JOGGLEdefault">-</a>
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
/*-<a href="qh-user.htm#TOC"
>--------------------------------</a><a name="JOGGLEincrease">-</a>
qh_JOGGLEincrease
factor to increase qh.JOGGLEmax on qh_JOGGLEretry or qh_JOGGLEagain
*/
#define qh_JOGGLEincrease 10.0
/*-<a href="qh-user.htm#TOC"
>--------------------------------</a><a name="JOGGLEretry">-</a>
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
/*-<a href="qh-user.htm#TOC"
>--------------------------------</a><a name="JOGGLEagain">-</a>
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
/*-<a href="qh-user.htm#TOC"
>--------------------------------</a><a name="JOGGLEmaxincrease">-</a>
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
/*-<a href="qh-user.htm#TOC"
>--------------------------------</a><a name="JOGGLEmaxretry">-</a>
qh_JOGGLEmaxretry
stop after qh_JOGGLEmaxretry attempts
*/
#define qh_JOGGLEmaxretry 100
/*========= memory constants =========*/
/*-<a href="qh-user.htm#TOC"
>--------------------------------</a><a name="MEMalign">-</a>
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 fmax_(sizeof(realT), sizeof(void *))
/*-<a href="qh-user.htm#TOC"
>--------------------------------</a><a name="MEMbufsize">-</a>
qh_MEMbufsize
size of additional memory buffers
notes:
used for qh_meminitbuffers() in global.c
*/
#define qh_MEMbufsize 0x10000 /* allocate 64K memory buffers */
/*-<a href="qh-user.htm#TOC"
>--------------------------------</a><a name="MEMinitbuf">-</a>
qh_MEMinitbuf
size of initial memory buffer
notes:
use for qh_meminitbuffers() in global.c
*/
#define qh_MEMinitbuf 0x20000 /* initially allocate 128K buffer */
/*-<a href="qh-user.htm#TOC"
>--------------------------------</a><a name="INFINITE">-</a>
qh_INFINITE
on output, indicates Voronoi center at infinity
*/
#define qh_INFINITE -10.101
/*-<a href="qh-user.htm#TOC"
>--------------------------------</a><a name="DEFAULTbox">-</a>
qh_DEFAULTbox
default box size (Geomview expects 0.5)
*/
#define qh_DEFAULTbox 0.5
/*======= conditional compilation ============================*/
/*-<a href="qh-user.htm#TOC"
>--------------------------------</a><a name="compiler">-</a>
__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
*/
/*-<a href="qh-user.htm#TOC"
>--------------------------------</a><a name="COMPUTEfurthest">-</a>
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
/*-<a href="qh-user.htm#TOC"
>--------------------------------</a><a name="KEEPstatistics">-</a>
qh_KEEPstatistics
=0 removes most of statistic gathering and reporting
notes:
if 0, code size is reduced by about 4%.
*/
#define qh_KEEPstatistics 1
/*-<a href="qh-user.htm#TOC"
>--------------------------------</a><a name="MAXoutside">-</a>
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
/*-<a href="qh-user.htm#TOC"
>--------------------------------</a><a name="NOmerge">-</a>
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:
<a href="mem.h#NOmem">qh_NOmem</a> in mem.c
see user.c/user_eg.c for removing io.o
*/
/*-<a href="qh-user.htm#TOC"
>--------------------------------</a><a name="NOtrace">-</a>
qh_NOtrace
no tracing if defined
notes:
This saves about 5% space.
#define qh_NOtrace
*/
/*-<a href="qh-user.htm#TOC"
>--------------------------------</a><a name="QHpointer">-</a>
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()
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
notes:
all global variables for qhull are in qh, qhmem, and qhstat
qh is defined in qhull.h
qhmem is defined in mem.h
qhstat is defined in stat.h
see:
user_eg.c for an example
*/
#define qh_QHpointer 0
#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
/*-<a href="qh-user.htm#TOC"
>--------------------------------</a><a name="QUICKhelp">-</a>
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 these. They effect the performance of facet merging.
*/
/*-<a href="qh-user.htm#TOC"
>--------------------------------</a><a name="DIMmergeVertex">-</a>
qh_DIMmergeVertex
max dimension for vertex merging (it is not effective in high-d)
*/
#define qh_DIMmergeVertex 6
/*-<a href="qh-user.htm#TOC"
>--------------------------------</a><a name="DIMreduceBuild">-</a>
qh_DIMreduceBuild
max dimension for vertex reduction during build (slow in high-d)
*/
#define qh_DIMreduceBuild 5
/*-<a href="qh-user.htm#TOC"
>--------------------------------</a><a name="BESTcentrum">-</a>
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
/*-<a href="qh-user.htm#TOC"
>--------------------------------</a><a name="BESTnonconvex">-</a>
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
/*-<a href="qh-user.htm#TOC"
>--------------------------------</a><a name="MAXnewmerges">-</a>
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
/*-<a href="qh-user.htm#TOC"
>--------------------------------</a><a name="MAXnewcentrum">-</a>
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
/*-<a href="qh-user.htm#TOC"
>--------------------------------</a><a name="COPLANARratio">-</a>
qh_COPLANARratio
for 3-d+ merging, qh.MINvisible is n*premerge_centrum
notes:
for non-merging, it's DISTround
*/
#define qh_COPLANARratio 3
/*-<a href="qh-user.htm#TOC"
>--------------------------------</a><a name="DISToutside">-</a>
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))
/*-<a href="qh-user.htm#TOC"
>--------------------------------</a><a name="RATIOnearinside">-</a>
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
/*-<a href="qh-user.htm#TOC"
>--------------------------------</a><a name="SEARCHdist">-</a>
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)));
/*-<a href="qh-user.htm#TOC"
>--------------------------------</a><a name="USEfindbestnew">-</a>
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)
/*-<a href="qh-user.htm#TOC"
>--------------------------------</a><a name="WIDEcoplanar">-</a>
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
/*-<a href="qh-user.htm#TOC"
>--------------------------------</a><a name="MAXnarrow">-</a>
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
/*-<a href="qh-user.htm#TOC"
>--------------------------------</a><a name="WARNnarrow">-</a>
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
/*-<a href="qh-user.htm#TOC"
>--------------------------------</a><a name="ZEROdelaunay">-</a>
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 */

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