libqhull.c
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1 /*<html><pre> -<a href="qh-qhull.htm"
2  >-------------------------------</a><a name="TOP">-</a>
3 
4  libqhull.c
5  Quickhull algorithm for convex hulls
6 
7  qhull() and top-level routines
8 
9  see qh-qhull.htm, libqhull.h, unix.c
10 
11  see qhull_a.h for internal functions
12 
13  Copyright (c) 1993-2015 The Geometry Center.
14  $Id: //main/2015/qhull/src/libqhull/libqhull.c#3 $$Change: 2047 $
15  $DateTime: 2016/01/04 22:03:18 $$Author: bbarber $
16 */
17 
18 #include "qhull_a.h"
19 
20 /*============= functions in alphabetic order after qhull() =======*/
21 
22 /*-<a href="qh-qhull.htm#TOC"
23  >-------------------------------</a><a name="qhull">-</a>
24 
25  qh_qhull()
26  compute DIM3 convex hull of qh.num_points starting at qh.first_point
27  qh contains all global options and variables
28 
29  returns:
30  returns polyhedron
31  qh.facet_list, qh.num_facets, qh.vertex_list, qh.num_vertices,
32 
33  returns global variables
34  qh.hulltime, qh.max_outside, qh.interior_point, qh.max_vertex, qh.min_vertex
35 
36  returns precision constants
37  qh.ANGLEround, centrum_radius, cos_max, DISTround, MAXabs_coord, ONEmerge
38 
39  notes:
40  unless needed for output
41  qh.max_vertex and qh.min_vertex are max/min due to merges
42 
43  see:
44  to add individual points to either qh.num_points
45  use qh_addpoint()
46 
47  if qh.GETarea
48  qh_produceoutput() returns qh.totarea and qh.totvol via qh_getarea()
49 
50  design:
51  record starting time
52  initialize hull and partition points
53  build convex hull
54  unless early termination
55  update facet->maxoutside for vertices, coplanar, and near-inside points
56  error if temporary sets exist
57  record end time
58 */
59 
60 void qh_qhull(void) {
61  int numoutside;
62 
63  qh hulltime= qh_CPUclock;
64  if (qh RERUN || qh JOGGLEmax < REALmax/2)
65  qh_build_withrestart();
66  else {
67  qh_initbuild();
68  qh_buildhull();
69  }
70  if (!qh STOPpoint && !qh STOPcone) {
71  if (qh ZEROall_ok && !qh TESTvneighbors && qh MERGEexact)
72  qh_checkzero( qh_ALL);
73  if (qh ZEROall_ok && !qh TESTvneighbors && !qh WAScoplanar) {
74  trace2((qh ferr, 2055, "qh_qhull: all facets are clearly convex and no coplanar points. Post-merging and check of maxout not needed.\n"));
75  qh DOcheckmax= False;
76  }else {
77  if (qh MERGEexact || (qh hull_dim > qh_DIMreduceBuild && qh PREmerge))
78  qh_postmerge("First post-merge", qh premerge_centrum, qh premerge_cos,
79  (qh POSTmerge ? False : qh TESTvneighbors));
80  else if (!qh POSTmerge && qh TESTvneighbors)
81  qh_postmerge("For testing vertex neighbors", qh premerge_centrum,
82  qh premerge_cos, True);
83  if (qh POSTmerge)
84  qh_postmerge("For post-merging", qh postmerge_centrum,
85  qh postmerge_cos, qh TESTvneighbors);
86  if (qh visible_list == qh facet_list) { /* i.e., merging done */
87  qh findbestnew= True;
88  qh_partitionvisible(/*qh.visible_list*/ !qh_ALL, &numoutside);
89  qh findbestnew= False;
90  qh_deletevisible(/*qh.visible_list*/);
91  qh_resetlists(False, qh_RESETvisible /*qh.visible_list newvertex_list newfacet_list */);
92  }
93  }
94  if (qh DOcheckmax){
95  if (qh REPORTfreq) {
96  qh_buildtracing(NULL, NULL);
97  qh_fprintf(qh ferr, 8115, "\nTesting all coplanar points.\n");
98  }
99  qh_check_maxout();
100  }
101  if (qh KEEPnearinside && !qh maxoutdone)
102  qh_nearcoplanar();
103  }
104  if (qh_setsize(qhmem.tempstack) != 0) {
105  qh_fprintf(qh ferr, 6164, "qhull internal error (qh_qhull): temporary sets not empty(%d)\n",
106  qh_setsize(qhmem.tempstack));
107  qh_errexit(qh_ERRqhull, NULL, NULL);
108  }
109  qh hulltime= qh_CPUclock - qh hulltime;
110  qh QHULLfinished= True;
111  trace1((qh ferr, 1036, "Qhull: algorithm completed\n"));
112 } /* qhull */
113 
114 /*-<a href="qh-qhull.htm#TOC"
115  >-------------------------------</a><a name="addpoint">-</a>
116 
117  qh_addpoint( furthest, facet, checkdist )
118  add point (usually furthest point) above facet to hull
119  if checkdist,
120  check that point is above facet.
121  if point is not outside of the hull, uses qh_partitioncoplanar()
122  assumes that facet is defined by qh_findbestfacet()
123  else if facet specified,
124  assumes that point is above facet (major damage if below)
125  for Delaunay triangulations,
126  Use qh_setdelaunay() to lift point to paraboloid and scale by 'Qbb' if needed
127  Do not use options 'Qbk', 'QBk', or 'QbB' since they scale the coordinates.
128 
129  returns:
130  returns False if user requested an early termination
131  qh.visible_list, newfacet_list, delvertex_list, NEWfacets may be defined
132  updates qh.facet_list, qh.num_facets, qh.vertex_list, qh.num_vertices
133  clear qh.maxoutdone (will need to call qh_check_maxout() for facet->maxoutside)
134  if unknown point, adds a pointer to qh.other_points
135  do not deallocate the point's coordinates
136 
137  notes:
138  assumes point is near its best facet and not at a local minimum of a lens
139  distributions. Use qh_findbestfacet to avoid this case.
140  uses qh.visible_list, qh.newfacet_list, qh.delvertex_list, qh.NEWfacets
141 
142  see also:
143  qh_triangulate() -- triangulate non-simplicial facets
144 
145  design:
146  add point to other_points if needed
147  if checkdist
148  if point not above facet
149  partition coplanar point
150  exit
151  exit if pre STOPpoint requested
152  find horizon and visible facets for point
153  make new facets for point to horizon
154  make hyperplanes for point
155  compute balance statistics
156  match neighboring new facets
157  update vertex neighbors and delete interior vertices
158  exit if STOPcone requested
159  merge non-convex new facets
160  if merge found, many merges, or 'Qf'
161  use qh_findbestnew() instead of qh_findbest()
162  partition outside points from visible facets
163  delete visible facets
164  check polyhedron if requested
165  exit if post STOPpoint requested
166  reset working lists of facets and vertices
167 */
168 boolT qh_addpoint(pointT *furthest, facetT *facet, boolT checkdist) {
169  int goodvisible, goodhorizon;
170  vertexT *vertex;
171  facetT *newfacet;
172  realT dist, newbalance, pbalance;
173  boolT isoutside= False;
174  int numpart, numpoints, numnew, firstnew;
175 
176  qh maxoutdone= False;
177  if (qh_pointid(furthest) == qh_IDunknown)
178  qh_setappend(&qh other_points, furthest);
179  if (!facet) {
180  qh_fprintf(qh ferr, 6213, "qhull internal error (qh_addpoint): NULL facet. Need to call qh_findbestfacet first\n");
181  qh_errexit(qh_ERRqhull, NULL, NULL);
182  }
183  if (checkdist) {
184  facet= qh_findbest(furthest, facet, !qh_ALL, !qh_ISnewfacets, !qh_NOupper,
185  &dist, &isoutside, &numpart);
186  zzadd_(Zpartition, numpart);
187  if (!isoutside) {
188  zinc_(Znotmax); /* last point of outsideset is no longer furthest. */
189  facet->notfurthest= True;
190  qh_partitioncoplanar(furthest, facet, &dist);
191  return True;
192  }
193  }
194  qh_buildtracing(furthest, facet);
195  if (qh STOPpoint < 0 && qh furthest_id == -qh STOPpoint-1) {
196  facet->notfurthest= True;
197  return False;
198  }
199  qh_findhorizon(furthest, facet, &goodvisible, &goodhorizon);
200  if (qh ONLYgood && !(goodvisible+goodhorizon) && !qh GOODclosest) {
201  zinc_(Znotgood);
202  facet->notfurthest= True;
203  /* last point of outsideset is no longer furthest. This is ok
204  since all points of the outside are likely to be bad */
205  qh_resetlists(False, qh_RESETvisible /*qh.visible_list newvertex_list newfacet_list */);
206  return True;
207  }
208  zzinc_(Zprocessed);
209  firstnew= qh facet_id;
210  vertex= qh_makenewfacets(furthest /*visible_list, attaches if !ONLYgood */);
211  qh_makenewplanes(/* newfacet_list */);
212  numnew= qh facet_id - firstnew;
213  newbalance= numnew - (realT) (qh num_facets-qh num_visible)
214  * qh hull_dim/qh num_vertices;
215  wadd_(Wnewbalance, newbalance);
216  wadd_(Wnewbalance2, newbalance * newbalance);
217  if (qh ONLYgood
218  && !qh_findgood(qh newfacet_list, goodhorizon) && !qh GOODclosest) {
219  FORALLnew_facets
220  qh_delfacet(newfacet);
221  qh_delvertex(vertex);
222  qh_resetlists(True, qh_RESETvisible /*qh.visible_list newvertex_list newfacet_list */);
223  zinc_(Znotgoodnew);
224  facet->notfurthest= True;
225  return True;
226  }
227  if (qh ONLYgood)
228  qh_attachnewfacets(/*visible_list*/);
229  qh_matchnewfacets();
230  qh_updatevertices();
231  if (qh STOPcone && qh furthest_id == qh STOPcone-1) {
232  facet->notfurthest= True;
233  return False; /* visible_list etc. still defined */
234  }
235  qh findbestnew= False;
236  if (qh PREmerge || qh MERGEexact) {
237  qh_premerge(vertex, qh premerge_centrum, qh premerge_cos);
238  if (qh_USEfindbestnew)
239  qh findbestnew= True;
240  else {
241  FORALLnew_facets {
242  if (!newfacet->simplicial) {
243  qh findbestnew= True; /* use qh_findbestnew instead of qh_findbest*/
244  break;
245  }
246  }
247  }
248  }else if (qh BESToutside)
249  qh findbestnew= True;
250  qh_partitionvisible(/*qh.visible_list*/ !qh_ALL, &numpoints);
251  qh findbestnew= False;
252  qh findbest_notsharp= False;
253  zinc_(Zpbalance);
254  pbalance= numpoints - (realT) qh hull_dim /* assumes all points extreme */
255  * (qh num_points - qh num_vertices)/qh num_vertices;
256  wadd_(Wpbalance, pbalance);
257  wadd_(Wpbalance2, pbalance * pbalance);
258  qh_deletevisible(/*qh.visible_list*/);
259  zmax_(Zmaxvertex, qh num_vertices);
260  qh NEWfacets= False;
261  if (qh IStracing >= 4) {
262  if (qh num_facets < 2000)
263  qh_printlists();
264  qh_printfacetlist(qh newfacet_list, NULL, True);
265  qh_checkpolygon(qh facet_list);
266  }else if (qh CHECKfrequently) {
267  if (qh num_facets < 50)
268  qh_checkpolygon(qh facet_list);
269  else
270  qh_checkpolygon(qh newfacet_list);
271  }
272  if (qh STOPpoint > 0 && qh furthest_id == qh STOPpoint-1)
273  return False;
274  qh_resetlists(True, qh_RESETvisible /*qh.visible_list newvertex_list newfacet_list */);
275  /* qh_triangulate(); to test qh.TRInormals */
276  trace2((qh ferr, 2056, "qh_addpoint: added p%d new facets %d new balance %2.2g point balance %2.2g\n",
277  qh_pointid(furthest), numnew, newbalance, pbalance));
278  return True;
279 } /* addpoint */
280 
281 /*-<a href="qh-qhull.htm#TOC"
282  >-------------------------------</a><a name="build_withrestart">-</a>
283 
284  qh_build_withrestart()
285  allow restarts due to qh.JOGGLEmax while calling qh_buildhull()
286  qh_errexit always undoes qh_build_withrestart()
287  qh.FIRSTpoint/qh.NUMpoints is point array
288  it may be moved by qh_joggleinput()
289 */
290 void qh_build_withrestart(void) {
291  int restart;
292 
293  qh ALLOWrestart= True;
294  while (True) {
295  restart= setjmp(qh restartexit); /* simple statement for CRAY J916 */
296  if (restart) { /* only from qh_precision() */
297  zzinc_(Zretry);
298  wmax_(Wretrymax, qh JOGGLEmax);
299  /* QH7078 warns about using 'TCn' with 'QJn' */
300  qh STOPcone= qh_IDunknown; /* if break from joggle, prevents normal output */
301  }
302  if (!qh RERUN && qh JOGGLEmax < REALmax/2) {
303  if (qh build_cnt > qh_JOGGLEmaxretry) {
304  qh_fprintf(qh ferr, 6229, "qhull precision error: %d attempts to construct a convex hull\n\
305  with joggled input. Increase joggle above 'QJ%2.2g'\n\
306  or modify qh_JOGGLE... parameters in user.h\n",
307  qh build_cnt, qh JOGGLEmax);
308  qh_errexit(qh_ERRqhull, NULL, NULL);
309  }
310  if (qh build_cnt && !restart)
311  break;
312  }else if (qh build_cnt && qh build_cnt >= qh RERUN)
313  break;
314  qh STOPcone= 0;
315  qh_freebuild(True); /* first call is a nop */
316  qh build_cnt++;
317  if (!qh qhull_optionsiz)
318  qh qhull_optionsiz= (int)strlen(qh qhull_options); /* WARN64 */
319  else {
320  qh qhull_options [qh qhull_optionsiz]= '\0';
321  qh qhull_optionlen= qh_OPTIONline; /* starts a new line */
322  }
323  qh_option("_run", &qh build_cnt, NULL);
324  if (qh build_cnt == qh RERUN) {
325  qh IStracing= qh TRACElastrun; /* duplicated from qh_initqhull_globals */
326  if (qh TRACEpoint != qh_IDunknown || qh TRACEdist < REALmax/2 || qh TRACEmerge) {
327  qh TRACElevel= (qh IStracing? qh IStracing : 3);
328  qh IStracing= 0;
329  }
330  qhmem.IStracing= qh IStracing;
331  }
332  if (qh JOGGLEmax < REALmax/2)
333  qh_joggleinput();
334  qh_initbuild();
335  qh_buildhull();
336  if (qh JOGGLEmax < REALmax/2 && !qh MERGING)
337  qh_checkconvex(qh facet_list, qh_ALGORITHMfault);
338  }
339  qh ALLOWrestart= False;
340 } /* qh_build_withrestart */
341 
342 /*-<a href="qh-qhull.htm#TOC"
343  >-------------------------------</a><a name="buildhull">-</a>
344 
345  qh_buildhull()
346  construct a convex hull by adding outside points one at a time
347 
348  returns:
349 
350  notes:
351  may be called multiple times
352  checks facet and vertex lists for incorrect flags
353  to recover from STOPcone, call qh_deletevisible and qh_resetlists
354 
355  design:
356  check visible facet and newfacet flags
357  check newlist vertex flags and qh.STOPcone/STOPpoint
358  for each facet with a furthest outside point
359  add point to facet
360  exit if qh.STOPcone or qh.STOPpoint requested
361  if qh.NARROWhull for initial simplex
362  partition remaining outside points to coplanar sets
363 */
364 void qh_buildhull(void) {
365  facetT *facet;
366  pointT *furthest;
367  vertexT *vertex;
368  int id;
369 
370  trace1((qh ferr, 1037, "qh_buildhull: start build hull\n"));
371  FORALLfacets {
372  if (facet->visible || facet->newfacet) {
373  qh_fprintf(qh ferr, 6165, "qhull internal error (qh_buildhull): visible or new facet f%d in facet list\n",
374  facet->id);
375  qh_errexit(qh_ERRqhull, facet, NULL);
376  }
377  }
378  FORALLvertices {
379  if (vertex->newlist) {
380  qh_fprintf(qh ferr, 6166, "qhull internal error (qh_buildhull): new vertex f%d in vertex list\n",
381  vertex->id);
382  qh_errprint("ERRONEOUS", NULL, NULL, NULL, vertex);
383  qh_errexit(qh_ERRqhull, NULL, NULL);
384  }
385  id= qh_pointid(vertex->point);
386  if ((qh STOPpoint>0 && id == qh STOPpoint-1) ||
387  (qh STOPpoint<0 && id == -qh STOPpoint-1) ||
388  (qh STOPcone>0 && id == qh STOPcone-1)) {
389  trace1((qh ferr, 1038,"qh_buildhull: stop point or cone P%d in initial hull\n", id));
390  return;
391  }
392  }
393  qh facet_next= qh facet_list; /* advance facet when processed */
394  while ((furthest= qh_nextfurthest(&facet))) {
395  qh num_outside--; /* if ONLYmax, furthest may not be outside */
396  if (!qh_addpoint(furthest, facet, qh ONLYmax))
397  break;
398  }
399  if (qh NARROWhull) /* move points from outsideset to coplanarset */
400  qh_outcoplanar( /* facet_list */ );
401  if (qh num_outside && !furthest) {
402  qh_fprintf(qh ferr, 6167, "qhull internal error (qh_buildhull): %d outside points were never processed.\n", qh num_outside);
403  qh_errexit(qh_ERRqhull, NULL, NULL);
404  }
405  trace1((qh ferr, 1039, "qh_buildhull: completed the hull construction\n"));
406 } /* buildhull */
407 
408 
409 /*-<a href="qh-qhull.htm#TOC"
410  >-------------------------------</a><a name="buildtracing">-</a>
411 
412  qh_buildtracing( furthest, facet )
413  trace an iteration of qh_buildhull() for furthest point and facet
414  if !furthest, prints progress message
415 
416  returns:
417  tracks progress with qh.lastreport
418  updates qh.furthest_id (-3 if furthest is NULL)
419  also resets visit_id, vertext_visit on wrap around
420 
421  see:
422  qh_tracemerging()
423 
424  design:
425  if !furthest
426  print progress message
427  exit
428  if 'TFn' iteration
429  print progress message
430  else if tracing
431  trace furthest point and facet
432  reset qh.visit_id and qh.vertex_visit if overflow may occur
433  set qh.furthest_id for tracing
434 */
435 void qh_buildtracing(pointT *furthest, facetT *facet) {
436  realT dist= 0;
437  float cpu;
438  int total, furthestid;
439  time_t timedata;
440  struct tm *tp;
441  vertexT *vertex;
442 
443  qh old_randomdist= qh RANDOMdist;
444  qh RANDOMdist= False;
445  if (!furthest) {
446  time(&timedata);
447  tp= localtime(&timedata);
448  cpu= (float)qh_CPUclock - (float)qh hulltime;
449  cpu /= (float)qh_SECticks;
450  total= zzval_(Ztotmerge) - zzval_(Zcyclehorizon) + zzval_(Zcyclefacettot);
451  qh_fprintf(qh ferr, 8118, "\n\
452 At %02d:%02d:%02d & %2.5g CPU secs, qhull has created %d facets and merged %d.\n\
453  The current hull contains %d facets and %d vertices. Last point was p%d\n",
454  tp->tm_hour, tp->tm_min, tp->tm_sec, cpu, qh facet_id -1,
455  total, qh num_facets, qh num_vertices, qh furthest_id);
456  return;
457  }
458  furthestid= qh_pointid(furthest);
459  if (qh TRACEpoint == furthestid) {
460  qh IStracing= qh TRACElevel;
461  qhmem.IStracing= qh TRACElevel;
462  }else if (qh TRACEpoint != qh_IDunknown && qh TRACEdist < REALmax/2) {
463  qh IStracing= 0;
464  qhmem.IStracing= 0;
465  }
466  if (qh REPORTfreq && (qh facet_id-1 > qh lastreport+qh REPORTfreq)) {
467  qh lastreport= qh facet_id-1;
468  time(&timedata);
469  tp= localtime(&timedata);
470  cpu= (float)qh_CPUclock - (float)qh hulltime;
471  cpu /= (float)qh_SECticks;
472  total= zzval_(Ztotmerge) - zzval_(Zcyclehorizon) + zzval_(Zcyclefacettot);
473  zinc_(Zdistio);
474  qh_distplane(furthest, facet, &dist);
475  qh_fprintf(qh ferr, 8119, "\n\
476 At %02d:%02d:%02d & %2.5g CPU secs, qhull has created %d facets and merged %d.\n\
477  The current hull contains %d facets and %d vertices. There are %d\n\
478  outside points. Next is point p%d(v%d), %2.2g above f%d.\n",
479  tp->tm_hour, tp->tm_min, tp->tm_sec, cpu, qh facet_id -1,
480  total, qh num_facets, qh num_vertices, qh num_outside+1,
481  furthestid, qh vertex_id, dist, getid_(facet));
482  }else if (qh IStracing >=1) {
483  cpu= (float)qh_CPUclock - (float)qh hulltime;
484  cpu /= (float)qh_SECticks;
485  qh_distplane(furthest, facet, &dist);
486  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",
487  furthestid, qh vertex_id, qh num_facets, dist,
488  getid_(facet), qh num_outside+1, cpu, qh furthest_id);
489  }
490  zmax_(Zvisit2max, (int)qh visit_id/2);
491  if (qh visit_id > (unsigned) INT_MAX) { /* 31 bits */
492  zinc_(Zvisit);
493  qh visit_id= 0;
494  FORALLfacets
495  facet->visitid= 0;
496  }
497  zmax_(Zvvisit2max, (int)qh vertex_visit/2);
498  if (qh vertex_visit > (unsigned) INT_MAX) { /* 31 bits */
499  zinc_(Zvvisit);
500  qh vertex_visit= 0;
501  FORALLvertices
502  vertex->visitid= 0;
503  }
504  qh furthest_id= furthestid;
505  qh RANDOMdist= qh old_randomdist;
506 } /* buildtracing */
507 
508 /*-<a href="qh-qhull.htm#TOC"
509  >-------------------------------</a><a name="errexit2">-</a>
510 
511  qh_errexit2( exitcode, facet, otherfacet )
512  return exitcode to system after an error
513  report two facets
514 
515  returns:
516  assumes exitcode non-zero
517 
518  see:
519  normally use qh_errexit() in user.c(reports a facet and a ridge)
520 */
521 void qh_errexit2(int exitcode, facetT *facet, facetT *otherfacet) {
522 
523  qh_errprint("ERRONEOUS", facet, otherfacet, NULL, NULL);
524  qh_errexit(exitcode, NULL, NULL);
525 } /* errexit2 */
526 
527 
528 /*-<a href="qh-qhull.htm#TOC"
529  >-------------------------------</a><a name="findhorizon">-</a>
530 
531  qh_findhorizon( point, facet, goodvisible, goodhorizon )
532  given a visible facet, find the point's horizon and visible facets
533  for all facets, !facet-visible
534 
535  returns:
536  returns qh.visible_list/num_visible with all visible facets
537  marks visible facets with ->visible
538  updates count of good visible and good horizon facets
539  updates qh.max_outside, qh.max_vertex, facet->maxoutside
540 
541  see:
542  similar to qh_delpoint()
543 
544  design:
545  move facet to qh.visible_list at end of qh.facet_list
546  for all visible facets
547  for each unvisited neighbor of a visible facet
548  compute distance of point to neighbor
549  if point above neighbor
550  move neighbor to end of qh.visible_list
551  else if point is coplanar with neighbor
552  update qh.max_outside, qh.max_vertex, neighbor->maxoutside
553  mark neighbor coplanar (will create a samecycle later)
554  update horizon statistics
555 */
556 void qh_findhorizon(pointT *point, facetT *facet, int *goodvisible, int *goodhorizon) {
557  facetT *neighbor, **neighborp, *visible;
558  int numhorizon= 0, coplanar= 0;
559  realT dist;
560 
561  trace1((qh ferr, 1040,"qh_findhorizon: find horizon for point p%d facet f%d\n",qh_pointid(point),facet->id));
562  *goodvisible= *goodhorizon= 0;
563  zinc_(Ztotvisible);
564  qh_removefacet(facet); /* visible_list at end of qh facet_list */
565  qh_appendfacet(facet);
566  qh num_visible= 1;
567  if (facet->good)
568  (*goodvisible)++;
569  qh visible_list= facet;
570  facet->visible= True;
571  facet->f.replace= NULL;
572  if (qh IStracing >=4)
573  qh_errprint("visible", facet, NULL, NULL, NULL);
574  qh visit_id++;
575  FORALLvisible_facets {
576  if (visible->tricoplanar && !qh TRInormals) {
577  qh_fprintf(qh ferr, 6230, "Qhull internal error (qh_findhorizon): does not work for tricoplanar facets. Use option 'Q11'\n");
578  qh_errexit(qh_ERRqhull, visible, NULL);
579  }
580  visible->visitid= qh visit_id;
581  FOREACHneighbor_(visible) {
582  if (neighbor->visitid == qh visit_id)
583  continue;
584  neighbor->visitid= qh visit_id;
585  zzinc_(Znumvisibility);
586  qh_distplane(point, neighbor, &dist);
587  if (dist > qh MINvisible) {
588  zinc_(Ztotvisible);
589  qh_removefacet(neighbor); /* append to end of qh visible_list */
590  qh_appendfacet(neighbor);
591  neighbor->visible= True;
592  neighbor->f.replace= NULL;
593  qh num_visible++;
594  if (neighbor->good)
595  (*goodvisible)++;
596  if (qh IStracing >=4)
597  qh_errprint("visible", neighbor, NULL, NULL, NULL);
598  }else {
599  if (dist > - qh MAXcoplanar) {
600  neighbor->coplanar= True;
601  zzinc_(Zcoplanarhorizon);
602  qh_precision("coplanar horizon");
603  coplanar++;
604  if (qh MERGING) {
605  if (dist > 0) {
606  maximize_(qh max_outside, dist);
607  maximize_(qh max_vertex, dist);
608 #if qh_MAXoutside
609  maximize_(neighbor->maxoutside, dist);
610 #endif
611  }else
612  minimize_(qh min_vertex, dist); /* due to merge later */
613  }
614  trace2((qh ferr, 2057, "qh_findhorizon: point p%d is coplanar to horizon f%d, dist=%2.7g < qh MINvisible(%2.7g)\n",
615  qh_pointid(point), neighbor->id, dist, qh MINvisible));
616  }else
617  neighbor->coplanar= False;
618  zinc_(Ztothorizon);
619  numhorizon++;
620  if (neighbor->good)
621  (*goodhorizon)++;
622  if (qh IStracing >=4)
623  qh_errprint("horizon", neighbor, NULL, NULL, NULL);
624  }
625  }
626  }
627  if (!numhorizon) {
628  qh_precision("empty horizon");
629  qh_fprintf(qh ferr, 6168, "qhull precision error (qh_findhorizon): empty horizon\n\
630 QhullPoint p%d was above all facets.\n", qh_pointid(point));
631  qh_printfacetlist(qh facet_list, NULL, True);
632  qh_errexit(qh_ERRprec, NULL, NULL);
633  }
634  trace1((qh ferr, 1041, "qh_findhorizon: %d horizon facets(good %d), %d visible(good %d), %d coplanar\n",
635  numhorizon, *goodhorizon, qh num_visible, *goodvisible, coplanar));
636  if (qh IStracing >= 4 && qh num_facets < 50)
637  qh_printlists();
638 } /* findhorizon */
639 
640 /*-<a href="qh-qhull.htm#TOC"
641  >-------------------------------</a><a name="nextfurthest">-</a>
642 
643  qh_nextfurthest( visible )
644  returns next furthest point and visible facet for qh_addpoint()
645  starts search at qh.facet_next
646 
647  returns:
648  removes furthest point from outside set
649  NULL if none available
650  advances qh.facet_next over facets with empty outside sets
651 
652  design:
653  for each facet from qh.facet_next
654  if empty outside set
655  advance qh.facet_next
656  else if qh.NARROWhull
657  determine furthest outside point
658  if furthest point is not outside
659  advance qh.facet_next(point will be coplanar)
660  remove furthest point from outside set
661 */
662 pointT *qh_nextfurthest(facetT **visible) {
663  facetT *facet;
664  int size, idx;
665  realT randr, dist;
666  pointT *furthest;
667 
668  while ((facet= qh facet_next) != qh facet_tail) {
669  if (!facet->outsideset) {
670  qh facet_next= facet->next;
671  continue;
672  }
673  SETreturnsize_(facet->outsideset, size);
674  if (!size) {
675  qh_setfree(&facet->outsideset);
676  qh facet_next= facet->next;
677  continue;
678  }
679  if (qh NARROWhull) {
680  if (facet->notfurthest)
681  qh_furthestout(facet);
682  furthest= (pointT*)qh_setlast(facet->outsideset);
683 #if qh_COMPUTEfurthest
684  qh_distplane(furthest, facet, &dist);
685  zinc_(Zcomputefurthest);
686 #else
687  dist= facet->furthestdist;
688 #endif
689  if (dist < qh MINoutside) { /* remainder of outside set is coplanar for qh_outcoplanar */
690  qh facet_next= facet->next;
691  continue;
692  }
693  }
694  if (!qh RANDOMoutside && !qh VIRTUALmemory) {
695  if (qh PICKfurthest) {
696  qh_furthestnext(/* qh.facet_list */);
697  facet= qh facet_next;
698  }
699  *visible= facet;
700  return((pointT*)qh_setdellast(facet->outsideset));
701  }
702  if (qh RANDOMoutside) {
703  int outcoplanar = 0;
704  if (qh NARROWhull) {
705  FORALLfacets {
706  if (facet == qh facet_next)
707  break;
708  if (facet->outsideset)
709  outcoplanar += qh_setsize( facet->outsideset);
710  }
711  }
712  randr= qh_RANDOMint;
713  randr= randr/(qh_RANDOMmax+1);
714  idx= (int)floor((qh num_outside - outcoplanar) * randr);
715  FORALLfacet_(qh facet_next) {
716  if (facet->outsideset) {
717  SETreturnsize_(facet->outsideset, size);
718  if (!size)
719  qh_setfree(&facet->outsideset);
720  else if (size > idx) {
721  *visible= facet;
722  return((pointT*)qh_setdelnth(facet->outsideset, idx));
723  }else
724  idx -= size;
725  }
726  }
727  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",
728  qh num_outside, idx+1, randr);
729  qh_errexit(qh_ERRqhull, NULL, NULL);
730  }else { /* VIRTUALmemory */
731  facet= qh facet_tail->previous;
732  if (!(furthest= (pointT*)qh_setdellast(facet->outsideset))) {
733  if (facet->outsideset)
734  qh_setfree(&facet->outsideset);
735  qh_removefacet(facet);
736  qh_prependfacet(facet, &qh facet_list);
737  continue;
738  }
739  *visible= facet;
740  return furthest;
741  }
742  }
743  return NULL;
744 } /* nextfurthest */
745 
746 /*-<a href="qh-qhull.htm#TOC"
747  >-------------------------------</a><a name="partitionall">-</a>
748 
749  qh_partitionall( vertices, points, numpoints )
750  partitions all points in points/numpoints to the outsidesets of facets
751  vertices= vertices in qh.facet_list(!partitioned)
752 
753  returns:
754  builds facet->outsideset
755  does not partition qh.GOODpoint
756  if qh.ONLYgood && !qh.MERGING,
757  does not partition qh.GOODvertex
758 
759  notes:
760  faster if qh.facet_list sorted by anticipated size of outside set
761 
762  design:
763  initialize pointset with all points
764  remove vertices from pointset
765  remove qh.GOODpointp from pointset (unless it's qh.STOPcone or qh.STOPpoint)
766  for all facets
767  for all remaining points in pointset
768  compute distance from point to facet
769  if point is outside facet
770  remove point from pointset (by not reappending)
771  update bestpoint
772  append point or old bestpoint to facet's outside set
773  append bestpoint to facet's outside set (furthest)
774  for all points remaining in pointset
775  partition point into facets' outside sets and coplanar sets
776 */
777 void qh_partitionall(setT *vertices, pointT *points, int numpoints){
778  setT *pointset;
779  vertexT *vertex, **vertexp;
780  pointT *point, **pointp, *bestpoint;
781  int size, point_i, point_n, point_end, remaining, i, id;
782  facetT *facet;
783  realT bestdist= -REALmax, dist, distoutside;
784 
785  trace1((qh ferr, 1042, "qh_partitionall: partition all points into outside sets\n"));
786  pointset= qh_settemp(numpoints);
787  qh num_outside= 0;
788  pointp= SETaddr_(pointset, pointT);
789  for (i=numpoints, point= points; i--; point += qh hull_dim)
790  *(pointp++)= point;
791  qh_settruncate(pointset, numpoints);
792  FOREACHvertex_(vertices) {
793  if ((id= qh_pointid(vertex->point)) >= 0)
794  SETelem_(pointset, id)= NULL;
795  }
796  id= qh_pointid(qh GOODpointp);
797  if (id >=0 && qh STOPcone-1 != id && -qh STOPpoint-1 != id)
798  SETelem_(pointset, id)= NULL;
799  if (qh GOODvertexp && qh ONLYgood && !qh MERGING) { /* matches qhull()*/
800  if ((id= qh_pointid(qh GOODvertexp)) >= 0)
801  SETelem_(pointset, id)= NULL;
802  }
803  if (!qh BESToutside) { /* matches conditional for qh_partitionpoint below */
804  distoutside= qh_DISToutside; /* multiple of qh.MINoutside & qh.max_outside, see user.h */
805  zval_(Ztotpartition)= qh num_points - qh hull_dim - 1; /*misses GOOD... */
806  remaining= qh num_facets;
807  point_end= numpoints;
808  FORALLfacets {
809  size= point_end/(remaining--) + 100;
810  facet->outsideset= qh_setnew(size);
811  bestpoint= NULL;
812  point_end= 0;
813  FOREACHpoint_i_(pointset) {
814  if (point) {
815  zzinc_(Zpartitionall);
816  qh_distplane(point, facet, &dist);
817  if (dist < distoutside)
818  SETelem_(pointset, point_end++)= point;
819  else {
820  qh num_outside++;
821  if (!bestpoint) {
822  bestpoint= point;
823  bestdist= dist;
824  }else if (dist > bestdist) {
825  qh_setappend(&facet->outsideset, bestpoint);
826  bestpoint= point;
827  bestdist= dist;
828  }else
829  qh_setappend(&facet->outsideset, point);
830  }
831  }
832  }
833  if (bestpoint) {
834  qh_setappend(&facet->outsideset, bestpoint);
835 #if !qh_COMPUTEfurthest
836  facet->furthestdist= bestdist;
837 #endif
838  }else
839  qh_setfree(&facet->outsideset);
840  qh_settruncate(pointset, point_end);
841  }
842  }
843  /* if !qh BESToutside, pointset contains points not assigned to outsideset */
844  if (qh BESToutside || qh MERGING || qh KEEPcoplanar || qh KEEPinside) {
845  qh findbestnew= True;
846  FOREACHpoint_i_(pointset) {
847  if (point)
848  qh_partitionpoint(point, qh facet_list);
849  }
850  qh findbestnew= False;
851  }
852  zzadd_(Zpartitionall, zzval_(Zpartition));
853  zzval_(Zpartition)= 0;
854  qh_settempfree(&pointset);
855  if (qh IStracing >= 4)
856  qh_printfacetlist(qh facet_list, NULL, True);
857 } /* partitionall */
858 
859 
860 /*-<a href="qh-qhull.htm#TOC"
861  >-------------------------------</a><a name="partitioncoplanar">-</a>
862 
863  qh_partitioncoplanar( point, facet, dist )
864  partition coplanar point to a facet
865  dist is distance from point to facet
866  if dist NULL,
867  searches for bestfacet and does nothing if inside
868  if qh.findbestnew set,
869  searches new facets instead of using qh_findbest()
870 
871  returns:
872  qh.max_ouside updated
873  if qh.KEEPcoplanar or qh.KEEPinside
874  point assigned to best coplanarset
875 
876  notes:
877  facet->maxoutside is updated at end by qh_check_maxout
878 
879  design:
880  if dist undefined
881  find best facet for point
882  if point sufficiently below facet (depends on qh.NEARinside and qh.KEEPinside)
883  exit
884  if keeping coplanar/nearinside/inside points
885  if point is above furthest coplanar point
886  append point to coplanar set (it is the new furthest)
887  update qh.max_outside
888  else
889  append point one before end of coplanar set
890  else if point is clearly outside of qh.max_outside and bestfacet->coplanarset
891  and bestfacet is more than perpendicular to facet
892  repartition the point using qh_findbest() -- it may be put on an outsideset
893  else
894  update qh.max_outside
895 */
896 void qh_partitioncoplanar(pointT *point, facetT *facet, realT *dist) {
897  facetT *bestfacet;
898  pointT *oldfurthest;
899  realT bestdist, dist2= 0, angle;
900  int numpart= 0, oldfindbest;
901  boolT isoutside;
902 
903  qh WAScoplanar= True;
904  if (!dist) {
905  if (qh findbestnew)
906  bestfacet= qh_findbestnew(point, facet, &bestdist, qh_ALL, &isoutside, &numpart);
907  else
908  bestfacet= qh_findbest(point, facet, qh_ALL, !qh_ISnewfacets, qh DELAUNAY,
909  &bestdist, &isoutside, &numpart);
910  zinc_(Ztotpartcoplanar);
911  zzadd_(Zpartcoplanar, numpart);
912  if (!qh DELAUNAY && !qh KEEPinside) { /* for 'd', bestdist skips upperDelaunay facets */
913  if (qh KEEPnearinside) {
914  if (bestdist < -qh NEARinside) {
915  zinc_(Zcoplanarinside);
916  trace4((qh ferr, 4062, "qh_partitioncoplanar: point p%d is more than near-inside facet f%d dist %2.2g findbestnew %d\n",
917  qh_pointid(point), bestfacet->id, bestdist, qh findbestnew));
918  return;
919  }
920  }else if (bestdist < -qh MAXcoplanar) {
921  trace4((qh ferr, 4063, "qh_partitioncoplanar: point p%d is inside facet f%d dist %2.2g findbestnew %d\n",
922  qh_pointid(point), bestfacet->id, bestdist, qh findbestnew));
923  zinc_(Zcoplanarinside);
924  return;
925  }
926  }
927  }else {
928  bestfacet= facet;
929  bestdist= *dist;
930  }
931  if (bestdist > qh max_outside) {
932  if (!dist && facet != bestfacet) {
933  zinc_(Zpartangle);
934  angle= qh_getangle(facet->normal, bestfacet->normal);
935  if (angle < 0) {
936  /* typically due to deleted vertex and coplanar facets, e.g.,
937  RBOX 1000 s Z1 G1e-13 t1001185205 | QHULL Tv */
938  zinc_(Zpartflip);
939  trace2((qh ferr, 2058, "qh_partitioncoplanar: repartition point p%d from f%d. It is above flipped facet f%d dist %2.2g\n",
940  qh_pointid(point), facet->id, bestfacet->id, bestdist));
941  oldfindbest= qh findbestnew;
942  qh findbestnew= False;
943  qh_partitionpoint(point, bestfacet);
944  qh findbestnew= oldfindbest;
945  return;
946  }
947  }
948  qh max_outside= bestdist;
949  if (bestdist > qh TRACEdist) {
950  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",
951  qh_pointid(point), facet->id, bestdist, bestfacet->id, qh furthest_id);
952  qh_errprint("DISTANT", facet, bestfacet, NULL, NULL);
953  }
954  }
955  if (qh KEEPcoplanar + qh KEEPinside + qh KEEPnearinside) {
956  oldfurthest= (pointT*)qh_setlast(bestfacet->coplanarset);
957  if (oldfurthest) {
958  zinc_(Zcomputefurthest);
959  qh_distplane(oldfurthest, bestfacet, &dist2);
960  }
961  if (!oldfurthest || dist2 < bestdist)
962  qh_setappend(&bestfacet->coplanarset, point);
963  else
964  qh_setappend2ndlast(&bestfacet->coplanarset, point);
965  }
966  trace4((qh ferr, 4064, "qh_partitioncoplanar: point p%d is coplanar with facet f%d(or inside) dist %2.2g\n",
967  qh_pointid(point), bestfacet->id, bestdist));
968 } /* partitioncoplanar */
969 
970 /*-<a href="qh-qhull.htm#TOC"
971  >-------------------------------</a><a name="partitionpoint">-</a>
972 
973  qh_partitionpoint( point, facet )
974  assigns point to an outside set, coplanar set, or inside set (i.e., dropt)
975  if qh.findbestnew
976  uses qh_findbestnew() to search all new facets
977  else
978  uses qh_findbest()
979 
980  notes:
981  after qh_distplane(), this and qh_findbest() are most expensive in 3-d
982 
983  design:
984  find best facet for point
985  (either exhaustive search of new facets or directed search from facet)
986  if qh.NARROWhull
987  retain coplanar and nearinside points as outside points
988  if point is outside bestfacet
989  if point above furthest point for bestfacet
990  append point to outside set (it becomes the new furthest)
991  if outside set was empty
992  move bestfacet to end of qh.facet_list (i.e., after qh.facet_next)
993  update bestfacet->furthestdist
994  else
995  append point one before end of outside set
996  else if point is coplanar to bestfacet
997  if keeping coplanar points or need to update qh.max_outside
998  partition coplanar point into bestfacet
999  else if near-inside point
1000  partition as coplanar point into bestfacet
1001  else is an inside point
1002  if keeping inside points
1003  partition as coplanar point into bestfacet
1004 */
1005 void qh_partitionpoint(pointT *point, facetT *facet) {
1006  realT bestdist;
1007  boolT isoutside;
1008  facetT *bestfacet;
1009  int numpart;
1010 #if qh_COMPUTEfurthest
1011  realT dist;
1012 #endif
1013 
1014  if (qh findbestnew)
1015  bestfacet= qh_findbestnew(point, facet, &bestdist, qh BESToutside, &isoutside, &numpart);
1016  else
1017  bestfacet= qh_findbest(point, facet, qh BESToutside, qh_ISnewfacets, !qh_NOupper,
1018  &bestdist, &isoutside, &numpart);
1019  zinc_(Ztotpartition);
1020  zzadd_(Zpartition, numpart);
1021  if (qh NARROWhull) {
1022  if (qh DELAUNAY && !isoutside && bestdist >= -qh MAXcoplanar)
1023  qh_precision("nearly incident point(narrow hull)");
1024  if (qh KEEPnearinside) {
1025  if (bestdist >= -qh NEARinside)
1026  isoutside= True;
1027  }else if (bestdist >= -qh MAXcoplanar)
1028  isoutside= True;
1029  }
1030 
1031  if (isoutside) {
1032  if (!bestfacet->outsideset
1033  || !qh_setlast(bestfacet->outsideset)) {
1034  qh_setappend(&(bestfacet->outsideset), point);
1035  if (!bestfacet->newfacet) {
1036  qh_removefacet(bestfacet); /* make sure it's after qh facet_next */
1037  qh_appendfacet(bestfacet);
1038  }
1039 #if !qh_COMPUTEfurthest
1040  bestfacet->furthestdist= bestdist;
1041 #endif
1042  }else {
1043 #if qh_COMPUTEfurthest
1044  zinc_(Zcomputefurthest);
1045  qh_distplane(oldfurthest, bestfacet, &dist);
1046  if (dist < bestdist)
1047  qh_setappend(&(bestfacet->outsideset), point);
1048  else
1049  qh_setappend2ndlast(&(bestfacet->outsideset), point);
1050 #else
1051  if (bestfacet->furthestdist < bestdist) {
1052  qh_setappend(&(bestfacet->outsideset), point);
1053  bestfacet->furthestdist= bestdist;
1054  }else
1055  qh_setappend2ndlast(&(bestfacet->outsideset), point);
1056 #endif
1057  }
1058  qh num_outside++;
1059  trace4((qh ferr, 4065, "qh_partitionpoint: point p%d is outside facet f%d new? %d (or narrowhull)\n",
1060  qh_pointid(point), bestfacet->id, bestfacet->newfacet));
1061  }else if (qh DELAUNAY || bestdist >= -qh MAXcoplanar) { /* for 'd', bestdist skips upperDelaunay facets */
1062  zzinc_(Zcoplanarpart);
1063  if (qh DELAUNAY)
1064  qh_precision("nearly incident point");
1065  if ((qh KEEPcoplanar + qh KEEPnearinside) || bestdist > qh max_outside)
1066  qh_partitioncoplanar(point, bestfacet, &bestdist);
1067  else {
1068  trace4((qh ferr, 4066, "qh_partitionpoint: point p%d is coplanar to facet f%d (dropped)\n",
1069  qh_pointid(point), bestfacet->id));
1070  }
1071  }else if (qh KEEPnearinside && bestdist > -qh NEARinside) {
1072  zinc_(Zpartnear);
1073  qh_partitioncoplanar(point, bestfacet, &bestdist);
1074  }else {
1075  zinc_(Zpartinside);
1076  trace4((qh ferr, 4067, "qh_partitionpoint: point p%d is inside all facets, closest to f%d dist %2.2g\n",
1077  qh_pointid(point), bestfacet->id, bestdist));
1078  if (qh KEEPinside)
1079  qh_partitioncoplanar(point, bestfacet, &bestdist);
1080  }
1081 } /* partitionpoint */
1082 
1083 /*-<a href="qh-qhull.htm#TOC"
1084  >-------------------------------</a><a name="partitionvisible">-</a>
1085 
1086  qh_partitionvisible( allpoints, numoutside )
1087  partitions points in visible facets to qh.newfacet_list
1088  qh.visible_list= visible facets
1089  for visible facets
1090  1st neighbor (if any) points to a horizon facet or a new facet
1091  if allpoints(!used),
1092  repartitions coplanar points
1093 
1094  returns:
1095  updates outside sets and coplanar sets of qh.newfacet_list
1096  updates qh.num_outside (count of outside points)
1097 
1098  notes:
1099  qh.findbest_notsharp should be clear (extra work if set)
1100 
1101  design:
1102  for all visible facets with outside set or coplanar set
1103  select a newfacet for visible facet
1104  if outside set
1105  partition outside set into new facets
1106  if coplanar set and keeping coplanar/near-inside/inside points
1107  if allpoints
1108  partition coplanar set into new facets, may be assigned outside
1109  else
1110  partition coplanar set into coplanar sets of new facets
1111  for each deleted vertex
1112  if allpoints
1113  partition vertex into new facets, may be assigned outside
1114  else
1115  partition vertex into coplanar sets of new facets
1116 */
1117 void qh_partitionvisible(/*qh.visible_list*/ boolT allpoints, int *numoutside) {
1118  facetT *visible, *newfacet;
1119  pointT *point, **pointp;
1120  int coplanar=0, size;
1121  unsigned count;
1122  vertexT *vertex, **vertexp;
1123 
1124  if (qh ONLYmax)
1125  maximize_(qh MINoutside, qh max_vertex);
1126  *numoutside= 0;
1127  FORALLvisible_facets {
1128  if (!visible->outsideset && !visible->coplanarset)
1129  continue;
1130  newfacet= visible->f.replace;
1131  count= 0;
1132  while (newfacet && newfacet->visible) {
1133  newfacet= newfacet->f.replace;
1134  if (count++ > qh facet_id)
1135  qh_infiniteloop(visible);
1136  }
1137  if (!newfacet)
1138  newfacet= qh newfacet_list;
1139  if (newfacet == qh facet_tail) {
1140  qh_fprintf(qh ferr, 6170, "qhull precision error (qh_partitionvisible): all new facets deleted as\n degenerate facets. Can not continue.\n");
1141  qh_errexit(qh_ERRprec, NULL, NULL);
1142  }
1143  if (visible->outsideset) {
1144  size= qh_setsize(visible->outsideset);
1145  *numoutside += size;
1146  qh num_outside -= size;
1147  FOREACHpoint_(visible->outsideset)
1148  qh_partitionpoint(point, newfacet);
1149  }
1150  if (visible->coplanarset && (qh KEEPcoplanar + qh KEEPinside + qh KEEPnearinside)) {
1151  size= qh_setsize(visible->coplanarset);
1152  coplanar += size;
1153  FOREACHpoint_(visible->coplanarset) {
1154  if (allpoints) /* not used */
1155  qh_partitionpoint(point, newfacet);
1156  else
1157  qh_partitioncoplanar(point, newfacet, NULL);
1158  }
1159  }
1160  }
1161  FOREACHvertex_(qh del_vertices) {
1162  if (vertex->point) {
1163  if (allpoints) /* not used */
1164  qh_partitionpoint(vertex->point, qh newfacet_list);
1165  else
1166  qh_partitioncoplanar(vertex->point, qh newfacet_list, NULL);
1167  }
1168  }
1169  trace1((qh ferr, 1043,"qh_partitionvisible: partitioned %d points from outsidesets and %d points from coplanarsets\n", *numoutside, coplanar));
1170 } /* partitionvisible */
1171 
1172 
1173 
1174 /*-<a href="qh-qhull.htm#TOC"
1175  >-------------------------------</a><a name="precision">-</a>
1176 
1177  qh_precision( reason )
1178  restart on precision errors if not merging and if 'QJn'
1179 */
1180 void qh_precision(const char *reason) {
1181 
1182  if (qh ALLOWrestart && !qh PREmerge && !qh MERGEexact) {
1183  if (qh JOGGLEmax < REALmax/2) {
1184  trace0((qh ferr, 26, "qh_precision: qhull restart because of %s\n", reason));
1185  /* May be called repeatedly if qh->ALLOWrestart */
1186  longjmp(qh restartexit, qh_ERRprec);
1187  }
1188  }
1189 } /* qh_precision */
1190 
1191 /*-<a href="qh-qhull.htm#TOC"
1192  >-------------------------------</a><a name="printsummary">-</a>
1193 
1194  qh_printsummary( fp )
1195  prints summary to fp
1196 
1197  notes:
1198  not in io.c so that user_eg.c can prevent io.c from loading
1199  qh_printsummary and qh_countfacets must match counts
1200 
1201  design:
1202  determine number of points, vertices, and coplanar points
1203  print summary
1204 */
1205 void qh_printsummary(FILE *fp) {
1206  realT ratio, outerplane, innerplane;
1207  float cpu;
1208  int size, id, nummerged, numvertices, numcoplanars= 0, nonsimplicial=0;
1209  int goodused;
1210  facetT *facet;
1211  const char *s;
1212  int numdel= zzval_(Zdelvertextot);
1213  int numtricoplanars= 0;
1214 
1215  size= qh num_points + qh_setsize(qh other_points);
1216  numvertices= qh num_vertices - qh_setsize(qh del_vertices);
1217  id= qh_pointid(qh GOODpointp);
1218  FORALLfacets {
1219  if (facet->coplanarset)
1220  numcoplanars += qh_setsize( facet->coplanarset);
1221  if (facet->good) {
1222  if (facet->simplicial) {
1223  if (facet->keepcentrum && facet->tricoplanar)
1224  numtricoplanars++;
1225  }else if (qh_setsize(facet->vertices) != qh hull_dim)
1226  nonsimplicial++;
1227  }
1228  }
1229  if (id >=0 && qh STOPcone-1 != id && -qh STOPpoint-1 != id)
1230  size--;
1231  if (qh STOPcone || qh STOPpoint)
1232  qh_fprintf(fp, 9288, "\nAt a premature exit due to 'TVn', 'TCn', 'TRn', or precision error with 'QJn'.");
1233  if (qh UPPERdelaunay)
1234  goodused= qh GOODvertex + qh GOODpoint + qh SPLITthresholds;
1235  else if (qh DELAUNAY)
1236  goodused= qh GOODvertex + qh GOODpoint + qh GOODthreshold;
1237  else
1238  goodused= qh num_good;
1239  nummerged= zzval_(Ztotmerge) - zzval_(Zcyclehorizon) + zzval_(Zcyclefacettot);
1240  if (qh VORONOI) {
1241  if (qh UPPERdelaunay)
1242  qh_fprintf(fp, 9289, "\n\
1243 Furthest-site Voronoi vertices by the convex hull of %d points in %d-d:\n\n", size, qh hull_dim);
1244  else
1245  qh_fprintf(fp, 9290, "\n\
1246 Voronoi diagram by the convex hull of %d points in %d-d:\n\n", size, qh hull_dim);
1247  qh_fprintf(fp, 9291, " Number of Voronoi regions%s: %d\n",
1248  qh ATinfinity ? " and at-infinity" : "", numvertices);
1249  if (numdel)
1250  qh_fprintf(fp, 9292, " Total number of deleted points due to merging: %d\n", numdel);
1251  if (numcoplanars - numdel > 0)
1252  qh_fprintf(fp, 9293, " Number of nearly incident points: %d\n", numcoplanars - numdel);
1253  else if (size - numvertices - numdel > 0)
1254  qh_fprintf(fp, 9294, " Total number of nearly incident points: %d\n", size - numvertices - numdel);
1255  qh_fprintf(fp, 9295, " Number of%s Voronoi vertices: %d\n",
1256  goodused ? " 'good'" : "", qh num_good);
1257  if (nonsimplicial)
1258  qh_fprintf(fp, 9296, " Number of%s non-simplicial Voronoi vertices: %d\n",
1259  goodused ? " 'good'" : "", nonsimplicial);
1260  }else if (qh DELAUNAY) {
1261  if (qh UPPERdelaunay)
1262  qh_fprintf(fp, 9297, "\n\
1263 Furthest-site Delaunay triangulation by the convex hull of %d points in %d-d:\n\n", size, qh hull_dim);
1264  else
1265  qh_fprintf(fp, 9298, "\n\
1266 Delaunay triangulation by the convex hull of %d points in %d-d:\n\n", size, qh hull_dim);
1267  qh_fprintf(fp, 9299, " Number of input sites%s: %d\n",
1268  qh ATinfinity ? " and at-infinity" : "", numvertices);
1269  if (numdel)
1270  qh_fprintf(fp, 9300, " Total number of deleted points due to merging: %d\n", numdel);
1271  if (numcoplanars - numdel > 0)
1272  qh_fprintf(fp, 9301, " Number of nearly incident points: %d\n", numcoplanars - numdel);
1273  else if (size - numvertices - numdel > 0)
1274  qh_fprintf(fp, 9302, " Total number of nearly incident points: %d\n", size - numvertices - numdel);
1275  qh_fprintf(fp, 9303, " Number of%s Delaunay regions: %d\n",
1276  goodused ? " 'good'" : "", qh num_good);
1277  if (nonsimplicial)
1278  qh_fprintf(fp, 9304, " Number of%s non-simplicial Delaunay regions: %d\n",
1279  goodused ? " 'good'" : "", nonsimplicial);
1280  }else if (qh HALFspace) {
1281  qh_fprintf(fp, 9305, "\n\
1282 Halfspace intersection by the convex hull of %d points in %d-d:\n\n", size, qh hull_dim);
1283  qh_fprintf(fp, 9306, " Number of halfspaces: %d\n", size);
1284  qh_fprintf(fp, 9307, " Number of non-redundant halfspaces: %d\n", numvertices);
1285  if (numcoplanars) {
1286  if (qh KEEPinside && qh KEEPcoplanar)
1287  s= "similar and redundant";
1288  else if (qh KEEPinside)
1289  s= "redundant";
1290  else
1291  s= "similar";
1292  qh_fprintf(fp, 9308, " Number of %s halfspaces: %d\n", s, numcoplanars);
1293  }
1294  qh_fprintf(fp, 9309, " Number of intersection points: %d\n", qh num_facets - qh num_visible);
1295  if (goodused)
1296  qh_fprintf(fp, 9310, " Number of 'good' intersection points: %d\n", qh num_good);
1297  if (nonsimplicial)
1298  qh_fprintf(fp, 9311, " Number of%s non-simplicial intersection points: %d\n",
1299  goodused ? " 'good'" : "", nonsimplicial);
1300  }else {
1301  qh_fprintf(fp, 9312, "\n\
1302 Convex hull of %d points in %d-d:\n\n", size, qh hull_dim);
1303  qh_fprintf(fp, 9313, " Number of vertices: %d\n", numvertices);
1304  if (numcoplanars) {
1305  if (qh KEEPinside && qh KEEPcoplanar)
1306  s= "coplanar and interior";
1307  else if (qh KEEPinside)
1308  s= "interior";
1309  else
1310  s= "coplanar";
1311  qh_fprintf(fp, 9314, " Number of %s points: %d\n", s, numcoplanars);
1312  }
1313  qh_fprintf(fp, 9315, " Number of facets: %d\n", qh num_facets - qh num_visible);
1314  if (goodused)
1315  qh_fprintf(fp, 9316, " Number of 'good' facets: %d\n", qh num_good);
1316  if (nonsimplicial)
1317  qh_fprintf(fp, 9317, " Number of%s non-simplicial facets: %d\n",
1318  goodused ? " 'good'" : "", nonsimplicial);
1319  }
1320  if (numtricoplanars)
1321  qh_fprintf(fp, 9318, " Number of triangulated facets: %d\n", numtricoplanars);
1322  qh_fprintf(fp, 9319, "\nStatistics for: %s | %s",
1323  qh rbox_command, qh qhull_command);
1324  if (qh ROTATErandom != INT_MIN)
1325  qh_fprintf(fp, 9320, " QR%d\n\n", qh ROTATErandom);
1326  else
1327  qh_fprintf(fp, 9321, "\n\n");
1328  qh_fprintf(fp, 9322, " Number of points processed: %d\n", zzval_(Zprocessed));
1329  qh_fprintf(fp, 9323, " Number of hyperplanes created: %d\n", zzval_(Zsetplane));
1330  if (qh DELAUNAY)
1331  qh_fprintf(fp, 9324, " Number of facets in hull: %d\n", qh num_facets - qh num_visible);
1332  qh_fprintf(fp, 9325, " Number of distance tests for qhull: %d\n", zzval_(Zpartition)+
1333  zzval_(Zpartitionall)+zzval_(Znumvisibility)+zzval_(Zpartcoplanar));
1334 #if 0 /* NOTE: must print before printstatistics() */
1335  {realT stddev, ave;
1336  qh_fprintf(fp, 9326, " average new facet balance: %2.2g\n",
1337  wval_(Wnewbalance)/zval_(Zprocessed));
1338  stddev= qh_stddev(zval_(Zprocessed), wval_(Wnewbalance),
1339  wval_(Wnewbalance2), &ave);
1340  qh_fprintf(fp, 9327, " new facet standard deviation: %2.2g\n", stddev);
1341  qh_fprintf(fp, 9328, " average partition balance: %2.2g\n",
1342  wval_(Wpbalance)/zval_(Zpbalance));
1343  stddev= qh_stddev(zval_(Zpbalance), wval_(Wpbalance),
1344  wval_(Wpbalance2), &ave);
1345  qh_fprintf(fp, 9329, " partition standard deviation: %2.2g\n", stddev);
1346  }
1347 #endif
1348  if (nummerged) {
1349  qh_fprintf(fp, 9330," Number of distance tests for merging: %d\n",zzval_(Zbestdist)+
1350  zzval_(Zcentrumtests)+zzval_(Zdistconvex)+zzval_(Zdistcheck)+
1351  zzval_(Zdistzero));
1352  qh_fprintf(fp, 9331," Number of distance tests for checking: %d\n",zzval_(Zcheckpart));
1353  qh_fprintf(fp, 9332," Number of merged facets: %d\n", nummerged);
1354  }
1355  if (!qh RANDOMoutside && qh QHULLfinished) {
1356  cpu= (float)qh hulltime;
1357  cpu /= (float)qh_SECticks;
1358  wval_(Wcpu)= cpu;
1359  qh_fprintf(fp, 9333, " CPU seconds to compute hull (after input): %2.4g\n", cpu);
1360  }
1361  if (qh RERUN) {
1362  if (!qh PREmerge && !qh MERGEexact)
1363  qh_fprintf(fp, 9334, " Percentage of runs with precision errors: %4.1f\n",
1364  zzval_(Zretry)*100.0/qh build_cnt); /* careful of order */
1365  }else if (qh JOGGLEmax < REALmax/2) {
1366  if (zzval_(Zretry))
1367  qh_fprintf(fp, 9335, " After %d retries, input joggled by: %2.2g\n",
1368  zzval_(Zretry), qh JOGGLEmax);
1369  else
1370  qh_fprintf(fp, 9336, " Input joggled by: %2.2g\n", qh JOGGLEmax);
1371  }
1372  if (qh totarea != 0.0)
1373  qh_fprintf(fp, 9337, " %s facet area: %2.8g\n",
1374  zzval_(Ztotmerge) ? "Approximate" : "Total", qh totarea);
1375  if (qh totvol != 0.0)
1376  qh_fprintf(fp, 9338, " %s volume: %2.8g\n",
1377  zzval_(Ztotmerge) ? "Approximate" : "Total", qh totvol);
1378  if (qh MERGING) {
1379  qh_outerinner(NULL, &outerplane, &innerplane);
1380  if (outerplane > 2 * qh DISTround) {
1381  qh_fprintf(fp, 9339, " Maximum distance of %spoint above facet: %2.2g",
1382  (qh QHULLfinished ? "" : "merged "), outerplane);
1383  ratio= outerplane/(qh ONEmerge + qh DISTround);
1384  /* don't report ratio if MINoutside is large */
1385  if (ratio > 0.05 && 2* qh ONEmerge > qh MINoutside && qh JOGGLEmax > REALmax/2)
1386  qh_fprintf(fp, 9340, " (%.1fx)\n", ratio);
1387  else
1388  qh_fprintf(fp, 9341, "\n");
1389  }
1390  if (innerplane < -2 * qh DISTround) {
1391  qh_fprintf(fp, 9342, " Maximum distance of %svertex below facet: %2.2g",
1392  (qh QHULLfinished ? "" : "merged "), innerplane);
1393  ratio= -innerplane/(qh ONEmerge+qh DISTround);
1394  if (ratio > 0.05 && qh JOGGLEmax > REALmax/2)
1395  qh_fprintf(fp, 9343, " (%.1fx)\n", ratio);
1396  else
1397  qh_fprintf(fp, 9344, "\n");
1398  }
1399  }
1400  qh_fprintf(fp, 9345, "\n");
1401 } /* printsummary */
1402 
1403 
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autogenerated on Fri Jun 2 2023 02:39:01