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user.h

/*<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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