merge_r.c
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1 /*<html><pre> -<a href="qh-merge_r.htm#TOC"
2  >-------------------------------</a><a name="TOP">-</a>
3 
4  merge_r.c
5  merges non-convex facets
6 
7  see qh-merge_r.htm and merge_r.h
8 
9  other modules call qh_premerge() and qh_postmerge()
10 
11  the user may call qh_postmerge() to perform additional merges.
12 
13  To remove deleted facets and vertices (qhull() in libqhull_r.c):
14  qh_partitionvisible(qh, !qh_ALL, &numoutside); // visible_list, newfacet_list
15  qh_deletevisible(); // qh.visible_list
16  qh_resetlists(qh, False, qh_RESETvisible); // qh.visible_list newvertex_list newfacet_list
17 
18  assumes qh.CENTERtype= centrum
19 
20  merges occur in qh_mergefacet and in qh_mergecycle
21  vertex->neighbors not set until the first merge occurs
22 
23  Copyright (c) 1993-2015 C.B. Barber.
24  $Id: //main/2015/qhull/src/libqhull_r/merge_r.c#5 $$Change: 2064 $
25  $DateTime: 2016/01/18 12:36:08 $$Author: bbarber $
26 */
27 
28 #include "qhull_ra.h"
29 
30 #ifndef qh_NOmerge
31 
32 /*===== functions(alphabetical after premerge and postmerge) ======*/
33 
34 /*-<a href="qh-merge_r.htm#TOC"
35  >-------------------------------</a><a name="premerge">-</a>
36 
37  qh_premerge(qh, apex, maxcentrum )
38  pre-merge nonconvex facets in qh.newfacet_list for apex
39  maxcentrum defines coplanar and concave (qh_test_appendmerge)
40 
41  returns:
42  deleted facets added to qh.visible_list with facet->visible set
43 
44  notes:
45  uses globals, qh.MERGEexact, qh.PREmerge
46 
47  design:
48  mark duplicate ridges in qh.newfacet_list
49  merge facet cycles in qh.newfacet_list
50  merge duplicate ridges and concave facets in qh.newfacet_list
51  check merged facet cycles for degenerate and redundant facets
52  merge degenerate and redundant facets
53  collect coplanar and concave facets
54  merge concave, coplanar, degenerate, and redundant facets
55 */
56 void qh_premerge(qhT *qh, vertexT *apex, realT maxcentrum, realT maxangle) {
57  boolT othermerge= False;
58  facetT *newfacet;
59 
60  if (qh->ZEROcentrum && qh_checkzero(qh, !qh_ALL))
61  return;
62  trace2((qh, qh->ferr, 2008, "qh_premerge: premerge centrum %2.2g angle %2.2g for apex v%d facetlist f%d\n",
63  maxcentrum, maxangle, apex->id, getid_(qh->newfacet_list)));
64  if (qh->IStracing >= 4 && qh->num_facets < 50)
65  qh_printlists(qh);
66  qh->centrum_radius= maxcentrum;
67  qh->cos_max= maxangle;
68  qh->degen_mergeset= qh_settemp(qh, qh->TEMPsize);
69  qh->facet_mergeset= qh_settemp(qh, qh->TEMPsize);
70  if (qh->hull_dim >=3) {
71  qh_mark_dupridges(qh, qh->newfacet_list); /* facet_mergeset */
72  qh_mergecycle_all(qh, qh->newfacet_list, &othermerge);
73  qh_forcedmerges(qh, &othermerge /* qh->facet_mergeset */);
74  FORALLnew_facets { /* test samecycle merges */
75  if (!newfacet->simplicial && !newfacet->mergeridge)
76  qh_degen_redundant_neighbors(qh, newfacet, NULL);
77  }
78  if (qh_merge_degenredundant(qh))
79  othermerge= True;
80  }else /* qh->hull_dim == 2 */
81  qh_mergecycle_all(qh, qh->newfacet_list, &othermerge);
82  qh_flippedmerges(qh, qh->newfacet_list, &othermerge);
83  if (!qh->MERGEexact || zzval_(Ztotmerge)) {
84  zinc_(Zpremergetot);
85  qh->POSTmerging= False;
86  qh_getmergeset_initial(qh, qh->newfacet_list);
87  qh_all_merges(qh, othermerge, False);
88  }
89  qh_settempfree(qh, &qh->facet_mergeset);
90  qh_settempfree(qh, &qh->degen_mergeset);
91 } /* premerge */
92 
93 /*-<a href="qh-merge_r.htm#TOC"
94  >-------------------------------</a><a name="postmerge">-</a>
95 
96  qh_postmerge(qh, reason, maxcentrum, maxangle, vneighbors )
97  post-merge nonconvex facets as defined by maxcentrum and maxangle
98  'reason' is for reporting progress
99  if vneighbors,
100  calls qh_test_vneighbors at end of qh_all_merge
101  if firstmerge,
102  calls qh_reducevertices before qh_getmergeset
103 
104  returns:
105  if first call (qh.visible_list != qh.facet_list),
106  builds qh.facet_newlist, qh.newvertex_list
107  deleted facets added to qh.visible_list with facet->visible
108  qh.visible_list == qh.facet_list
109 
110  notes:
111 
112 
113  design:
114  if first call
115  set qh.visible_list and qh.newfacet_list to qh.facet_list
116  add all facets to qh.newfacet_list
117  mark non-simplicial facets, facet->newmerge
118  set qh.newvertext_list to qh.vertex_list
119  add all vertices to qh.newvertex_list
120  if a pre-merge occured
121  set vertex->delridge {will retest the ridge}
122  if qh.MERGEexact
123  call qh_reducevertices()
124  if no pre-merging
125  merge flipped facets
126  determine non-convex facets
127  merge all non-convex facets
128 */
129 void qh_postmerge(qhT *qh, const char *reason, realT maxcentrum, realT maxangle,
130  boolT vneighbors) {
131  facetT *newfacet;
132  boolT othermerges= False;
133  vertexT *vertex;
134 
135  if (qh->REPORTfreq || qh->IStracing) {
136  qh_buildtracing(qh, NULL, NULL);
137  qh_printsummary(qh, qh->ferr);
138  if (qh->PRINTstatistics)
139  qh_printallstatistics(qh, qh->ferr, "reason");
140  qh_fprintf(qh, qh->ferr, 8062, "\n%s with 'C%.2g' and 'A%.2g'\n",
141  reason, maxcentrum, maxangle);
142  }
143  trace2((qh, qh->ferr, 2009, "qh_postmerge: postmerge. test vneighbors? %d\n",
144  vneighbors));
145  qh->centrum_radius= maxcentrum;
146  qh->cos_max= maxangle;
147  qh->POSTmerging= True;
148  qh->degen_mergeset= qh_settemp(qh, qh->TEMPsize);
149  qh->facet_mergeset= qh_settemp(qh, qh->TEMPsize);
150  if (qh->visible_list != qh->facet_list) { /* first call */
151  qh->NEWfacets= True;
152  qh->visible_list= qh->newfacet_list= qh->facet_list;
153  FORALLnew_facets {
154  newfacet->newfacet= True;
155  if (!newfacet->simplicial)
156  newfacet->newmerge= True;
157  zinc_(Zpostfacets);
158  }
159  qh->newvertex_list= qh->vertex_list;
160  FORALLvertices
161  vertex->newlist= True;
162  if (qh->VERTEXneighbors) { /* a merge has occurred */
163  FORALLvertices
164  vertex->delridge= True; /* test for redundant, needed? */
165  if (qh->MERGEexact) {
166  if (qh->hull_dim <= qh_DIMreduceBuild)
167  qh_reducevertices(qh); /* was skipped during pre-merging */
168  }
169  }
170  if (!qh->PREmerge && !qh->MERGEexact)
171  qh_flippedmerges(qh, qh->newfacet_list, &othermerges);
172  }
173  qh_getmergeset_initial(qh, qh->newfacet_list);
174  qh_all_merges(qh, False, vneighbors);
175  qh_settempfree(qh, &qh->facet_mergeset);
176  qh_settempfree(qh, &qh->degen_mergeset);
177 } /* post_merge */
178 
179 /*-<a href="qh-merge_r.htm#TOC"
180  >-------------------------------</a><a name="all_merges">-</a>
181 
182  qh_all_merges(qh, othermerge, vneighbors )
183  merge all non-convex facets
184 
185  set othermerge if already merged facets (for qh_reducevertices)
186  if vneighbors
187  tests vertex neighbors for convexity at end
188  qh.facet_mergeset lists the non-convex ridges in qh_newfacet_list
189  qh.degen_mergeset is defined
190  if qh.MERGEexact && !qh.POSTmerging,
191  does not merge coplanar facets
192 
193  returns:
194  deleted facets added to qh.visible_list with facet->visible
195  deleted vertices added qh.delvertex_list with vertex->delvertex
196 
197  notes:
198  unless !qh.MERGEindependent,
199  merges facets in independent sets
200  uses qh.newfacet_list as argument since merges call qh_removefacet()
201 
202  design:
203  while merges occur
204  for each merge in qh.facet_mergeset
205  unless one of the facets was already merged in this pass
206  merge the facets
207  test merged facets for additional merges
208  add merges to qh.facet_mergeset
209  if vertices record neighboring facets
210  rename redundant vertices
211  update qh.facet_mergeset
212  if vneighbors ??
213  tests vertex neighbors for convexity at end
214 */
215 void qh_all_merges(qhT *qh, boolT othermerge, boolT vneighbors) {
216  facetT *facet1, *facet2;
217  mergeT *merge;
218  boolT wasmerge= True, isreduce;
219  void **freelistp; /* used if !qh_NOmem by qh_memfree_() */
220  vertexT *vertex;
221  mergeType mergetype;
222  int numcoplanar=0, numconcave=0, numdegenredun= 0, numnewmerges= 0;
223 
224  trace2((qh, qh->ferr, 2010, "qh_all_merges: starting to merge facets beginning from f%d\n",
225  getid_(qh->newfacet_list)));
226  while (True) {
227  wasmerge= False;
228  while (qh_setsize(qh, qh->facet_mergeset)) {
229  while ((merge= (mergeT*)qh_setdellast(qh->facet_mergeset))) {
230  facet1= merge->facet1;
231  facet2= merge->facet2;
232  mergetype= merge->type;
233  qh_memfree_(qh, merge, (int)sizeof(mergeT), freelistp);
234  if (facet1->visible || facet2->visible) /*deleted facet*/
235  continue;
236  if ((facet1->newfacet && !facet1->tested)
237  || (facet2->newfacet && !facet2->tested)) {
238  if (qh->MERGEindependent && mergetype <= MRGanglecoplanar)
239  continue; /* perform independent sets of merges */
240  }
241  qh_merge_nonconvex(qh, facet1, facet2, mergetype);
242  numdegenredun += qh_merge_degenredundant(qh);
243  numnewmerges++;
244  wasmerge= True;
245  if (mergetype == MRGconcave)
246  numconcave++;
247  else /* MRGcoplanar or MRGanglecoplanar */
248  numcoplanar++;
249  } /* while setdellast */
250  if (qh->POSTmerging && qh->hull_dim <= qh_DIMreduceBuild
251  && numnewmerges > qh_MAXnewmerges) {
252  numnewmerges= 0;
253  qh_reducevertices(qh); /* otherwise large post merges too slow */
254  }
255  qh_getmergeset(qh, qh->newfacet_list); /* facet_mergeset */
256  } /* while mergeset */
257  if (qh->VERTEXneighbors) {
258  isreduce= False;
259  if (qh->hull_dim >=4 && qh->POSTmerging) {
260  FORALLvertices
261  vertex->delridge= True;
262  isreduce= True;
263  }
264  if ((wasmerge || othermerge) && (!qh->MERGEexact || qh->POSTmerging)
265  && qh->hull_dim <= qh_DIMreduceBuild) {
266  othermerge= False;
267  isreduce= True;
268  }
269  if (isreduce) {
270  if (qh_reducevertices(qh)) {
271  qh_getmergeset(qh, qh->newfacet_list); /* facet_mergeset */
272  continue;
273  }
274  }
275  }
276  if (vneighbors && qh_test_vneighbors(qh /* qh->newfacet_list */))
277  continue;
278  break;
279  } /* while (True) */
280  if (qh->CHECKfrequently && !qh->MERGEexact) {
281  qh->old_randomdist= qh->RANDOMdist;
282  qh->RANDOMdist= False;
283  qh_checkconvex(qh, qh->newfacet_list, qh_ALGORITHMfault);
284  /* qh_checkconnect(qh); [this is slow and it changes the facet order] */
285  qh->RANDOMdist= qh->old_randomdist;
286  }
287  trace1((qh, qh->ferr, 1009, "qh_all_merges: merged %d coplanar facets %d concave facets and %d degen or redundant facets.\n",
288  numcoplanar, numconcave, numdegenredun));
289  if (qh->IStracing >= 4 && qh->num_facets < 50)
290  qh_printlists(qh);
291 } /* all_merges */
292 
293 
294 /*-<a href="qh-merge_r.htm#TOC"
295  >-------------------------------</a><a name="appendmergeset">-</a>
296 
297  qh_appendmergeset(qh, facet, neighbor, mergetype, angle )
298  appends an entry to qh.facet_mergeset or qh.degen_mergeset
299 
300  angle ignored if NULL or !qh.ANGLEmerge
301 
302  returns:
303  merge appended to facet_mergeset or degen_mergeset
304  sets ->degenerate or ->redundant if degen_mergeset
305 
306  see:
307  qh_test_appendmerge()
308 
309  design:
310  allocate merge entry
311  if regular merge
312  append to qh.facet_mergeset
313  else if degenerate merge and qh.facet_mergeset is all degenerate
314  append to qh.degen_mergeset
315  else if degenerate merge
316  prepend to qh.degen_mergeset
317  else if redundant merge
318  append to qh.degen_mergeset
319 */
320 void qh_appendmergeset(qhT *qh, facetT *facet, facetT *neighbor, mergeType mergetype, realT *angle) {
321  mergeT *merge, *lastmerge;
322  void **freelistp; /* used if !qh_NOmem by qh_memalloc_() */
323 
324  if (facet->redundant)
325  return;
326  if (facet->degenerate && mergetype == MRGdegen)
327  return;
328  qh_memalloc_(qh, (int)sizeof(mergeT), freelistp, merge, mergeT);
329  merge->facet1= facet;
330  merge->facet2= neighbor;
331  merge->type= mergetype;
332  if (angle && qh->ANGLEmerge)
333  merge->angle= *angle;
334  if (mergetype < MRGdegen)
335  qh_setappend(qh, &(qh->facet_mergeset), merge);
336  else if (mergetype == MRGdegen) {
337  facet->degenerate= True;
338  if (!(lastmerge= (mergeT*)qh_setlast(qh->degen_mergeset))
339  || lastmerge->type == MRGdegen)
340  qh_setappend(qh, &(qh->degen_mergeset), merge);
341  else
342  qh_setaddnth(qh, &(qh->degen_mergeset), 0, merge);
343  }else if (mergetype == MRGredundant) {
344  facet->redundant= True;
345  qh_setappend(qh, &(qh->degen_mergeset), merge);
346  }else /* mergetype == MRGmirror */ {
347  if (facet->redundant || neighbor->redundant) {
348  qh_fprintf(qh, qh->ferr, 6092, "qhull error (qh_appendmergeset): facet f%d or f%d is already a mirrored facet\n",
349  facet->id, neighbor->id);
350  qh_errexit2(qh, qh_ERRqhull, facet, neighbor);
351  }
352  if (!qh_setequal(facet->vertices, neighbor->vertices)) {
353  qh_fprintf(qh, qh->ferr, 6093, "qhull error (qh_appendmergeset): mirrored facets f%d and f%d do not have the same vertices\n",
354  facet->id, neighbor->id);
355  qh_errexit2(qh, qh_ERRqhull, facet, neighbor);
356  }
357  facet->redundant= True;
358  neighbor->redundant= True;
359  qh_setappend(qh, &(qh->degen_mergeset), merge);
360  }
361 } /* appendmergeset */
362 
363 
364 /*-<a href="qh-merge_r.htm#TOC"
365  >-------------------------------</a><a name="basevertices">-</a>
366 
367  qh_basevertices(qh, samecycle )
368  return temporary set of base vertices for samecycle
369  samecycle is first facet in the cycle
370  assumes apex is SETfirst_( samecycle->vertices )
371 
372  returns:
373  vertices(settemp)
374  all ->seen are cleared
375 
376  notes:
377  uses qh_vertex_visit;
378 
379  design:
380  for each facet in samecycle
381  for each unseen vertex in facet->vertices
382  append to result
383 */
384 setT *qh_basevertices(qhT *qh, facetT *samecycle) {
385  facetT *same;
386  vertexT *apex, *vertex, **vertexp;
387  setT *vertices= qh_settemp(qh, qh->TEMPsize);
388 
389  apex= SETfirstt_(samecycle->vertices, vertexT);
390  apex->visitid= ++qh->vertex_visit;
391  FORALLsame_cycle_(samecycle) {
392  if (same->mergeridge)
393  continue;
394  FOREACHvertex_(same->vertices) {
395  if (vertex->visitid != qh->vertex_visit) {
396  qh_setappend(qh, &vertices, vertex);
397  vertex->visitid= qh->vertex_visit;
398  vertex->seen= False;
399  }
400  }
401  }
402  trace4((qh, qh->ferr, 4019, "qh_basevertices: found %d vertices\n",
403  qh_setsize(qh, vertices)));
404  return vertices;
405 } /* basevertices */
406 
407 /*-<a href="qh-merge_r.htm#TOC"
408  >-------------------------------</a><a name="checkconnect">-</a>
409 
410  qh_checkconnect(qh)
411  check that new facets are connected
412  new facets are on qh.newfacet_list
413 
414  notes:
415  this is slow and it changes the order of the facets
416  uses qh.visit_id
417 
418  design:
419  move first new facet to end of qh.facet_list
420  for all newly appended facets
421  append unvisited neighbors to end of qh.facet_list
422  for all new facets
423  report error if unvisited
424 */
425 void qh_checkconnect(qhT *qh /* qh->newfacet_list */) {
426  facetT *facet, *newfacet, *errfacet= NULL, *neighbor, **neighborp;
427 
428  facet= qh->newfacet_list;
429  qh_removefacet(qh, facet);
430  qh_appendfacet(qh, facet);
431  facet->visitid= ++qh->visit_id;
432  FORALLfacet_(facet) {
433  FOREACHneighbor_(facet) {
434  if (neighbor->visitid != qh->visit_id) {
435  qh_removefacet(qh, neighbor);
436  qh_appendfacet(qh, neighbor);
437  neighbor->visitid= qh->visit_id;
438  }
439  }
440  }
441  FORALLnew_facets {
442  if (newfacet->visitid == qh->visit_id)
443  break;
444  qh_fprintf(qh, qh->ferr, 6094, "qhull error: f%d is not attached to the new facets\n",
445  newfacet->id);
446  errfacet= newfacet;
447  }
448  if (errfacet)
449  qh_errexit(qh, qh_ERRqhull, errfacet, NULL);
450 } /* checkconnect */
451 
452 /*-<a href="qh-merge_r.htm#TOC"
453  >-------------------------------</a><a name="checkzero">-</a>
454 
455  qh_checkzero(qh, testall )
456  check that facets are clearly convex for qh.DISTround with qh.MERGEexact
457 
458  if testall,
459  test all facets for qh.MERGEexact post-merging
460  else
461  test qh.newfacet_list
462 
463  if qh.MERGEexact,
464  allows coplanar ridges
465  skips convexity test while qh.ZEROall_ok
466 
467  returns:
468  True if all facets !flipped, !dupridge, normal
469  if all horizon facets are simplicial
470  if all vertices are clearly below neighbor
471  if all opposite vertices of horizon are below
472  clears qh.ZEROall_ok if any problems or coplanar facets
473 
474  notes:
475  uses qh.vertex_visit
476  horizon facets may define multiple new facets
477 
478  design:
479  for all facets in qh.newfacet_list or qh.facet_list
480  check for flagged faults (flipped, etc.)
481  for all facets in qh.newfacet_list or qh.facet_list
482  for each neighbor of facet
483  skip horizon facets for qh.newfacet_list
484  test the opposite vertex
485  if qh.newfacet_list
486  test the other vertices in the facet's horizon facet
487 */
488 boolT qh_checkzero(qhT *qh, boolT testall) {
489  facetT *facet, *neighbor, **neighborp;
490  facetT *horizon, *facetlist;
491  int neighbor_i;
492  vertexT *vertex, **vertexp;
493  realT dist;
494 
495  if (testall)
496  facetlist= qh->facet_list;
497  else {
498  facetlist= qh->newfacet_list;
499  FORALLfacet_(facetlist) {
500  horizon= SETfirstt_(facet->neighbors, facetT);
501  if (!horizon->simplicial)
502  goto LABELproblem;
503  if (facet->flipped || facet->dupridge || !facet->normal)
504  goto LABELproblem;
505  }
506  if (qh->MERGEexact && qh->ZEROall_ok) {
507  trace2((qh, qh->ferr, 2011, "qh_checkzero: skip convexity check until first pre-merge\n"));
508  return True;
509  }
510  }
511  FORALLfacet_(facetlist) {
512  qh->vertex_visit++;
513  neighbor_i= 0;
514  horizon= NULL;
515  FOREACHneighbor_(facet) {
516  if (!neighbor_i && !testall) {
517  horizon= neighbor;
518  neighbor_i++;
519  continue; /* horizon facet tested in qh_findhorizon */
520  }
521  vertex= SETelemt_(facet->vertices, neighbor_i++, vertexT);
522  vertex->visitid= qh->vertex_visit;
523  zzinc_(Zdistzero);
524  qh_distplane(qh, vertex->point, neighbor, &dist);
525  if (dist >= -qh->DISTround) {
526  qh->ZEROall_ok= False;
527  if (!qh->MERGEexact || testall || dist > qh->DISTround)
528  goto LABELnonconvex;
529  }
530  }
531  if (!testall && horizon) {
532  FOREACHvertex_(horizon->vertices) {
533  if (vertex->visitid != qh->vertex_visit) {
534  zzinc_(Zdistzero);
535  qh_distplane(qh, vertex->point, facet, &dist);
536  if (dist >= -qh->DISTround) {
537  qh->ZEROall_ok= False;
538  if (!qh->MERGEexact || dist > qh->DISTround)
539  goto LABELnonconvex;
540  }
541  break;
542  }
543  }
544  }
545  }
546  trace2((qh, qh->ferr, 2012, "qh_checkzero: testall %d, facets are %s\n", testall,
547  (qh->MERGEexact && !testall) ?
548  "not concave, flipped, or duplicate ridged" : "clearly convex"));
549  return True;
550 
551  LABELproblem:
552  qh->ZEROall_ok= False;
553  trace2((qh, qh->ferr, 2013, "qh_checkzero: facet f%d needs pre-merging\n",
554  facet->id));
555  return False;
556 
557  LABELnonconvex:
558  trace2((qh, qh->ferr, 2014, "qh_checkzero: facet f%d and f%d are not clearly convex. v%d dist %.2g\n",
559  facet->id, neighbor->id, vertex->id, dist));
560  return False;
561 } /* checkzero */
562 
563 /*-<a href="qh-merge_r.htm#TOC"
564  >-------------------------------</a><a name="compareangle">-</a>
565 
566  qh_compareangle(angle1, angle2 )
567  used by qsort() to order merges by angle
568 */
569 int qh_compareangle(const void *p1, const void *p2) {
570  const mergeT *a= *((mergeT *const*)p1), *b= *((mergeT *const*)p2);
571 
572  return((a->angle > b->angle) ? 1 : -1);
573 } /* compareangle */
574 
575 /*-<a href="qh-merge_r.htm#TOC"
576  >-------------------------------</a><a name="comparemerge">-</a>
577 
578  qh_comparemerge(merge1, merge2 )
579  used by qsort() to order merges
580 */
581 int qh_comparemerge(const void *p1, const void *p2) {
582  const mergeT *a= *((mergeT *const*)p1), *b= *((mergeT *const*)p2);
583 
584  return(a->type - b->type);
585 } /* comparemerge */
586 
587 /*-<a href="qh-merge_r.htm#TOC"
588  >-------------------------------</a><a name="comparevisit">-</a>
589 
590  qh_comparevisit(vertex1, vertex2 )
591  used by qsort() to order vertices by their visitid
592 */
593 int qh_comparevisit(const void *p1, const void *p2) {
594  const vertexT *a= *((vertexT *const*)p1), *b= *((vertexT *const*)p2);
595 
596  return(a->visitid - b->visitid);
597 } /* comparevisit */
598 
599 /*-<a href="qh-merge_r.htm#TOC"
600  >-------------------------------</a><a name="copynonconvex">-</a>
601 
602  qh_copynonconvex(qh, atridge )
603  set non-convex flag on other ridges (if any) between same neighbors
604 
605  notes:
606  may be faster if use smaller ridge set
607 
608  design:
609  for each ridge of atridge's top facet
610  if ridge shares the same neighbor
611  set nonconvex flag
612 */
613 void qh_copynonconvex(qhT *qh, ridgeT *atridge) {
614  facetT *facet, *otherfacet;
615  ridgeT *ridge, **ridgep;
616 
617  facet= atridge->top;
618  otherfacet= atridge->bottom;
619  FOREACHridge_(facet->ridges) {
620  if (otherfacet == otherfacet_(ridge, facet) && ridge != atridge) {
621  ridge->nonconvex= True;
622  trace4((qh, qh->ferr, 4020, "qh_copynonconvex: moved nonconvex flag from r%d to r%d\n",
623  atridge->id, ridge->id));
624  break;
625  }
626  }
627 } /* copynonconvex */
628 
629 /*-<a href="qh-merge_r.htm#TOC"
630  >-------------------------------</a><a name="degen_redundant_facet">-</a>
631 
632  qh_degen_redundant_facet(qh, facet )
633  check facet for degen. or redundancy
634 
635  notes:
636  bumps vertex_visit
637  called if a facet was redundant but no longer is (qh_merge_degenredundant)
638  qh_appendmergeset() only appends first reference to facet (i.e., redundant)
639 
640  see:
641  qh_degen_redundant_neighbors()
642 
643  design:
644  test for redundant neighbor
645  test for degenerate facet
646 */
647 void qh_degen_redundant_facet(qhT *qh, facetT *facet) {
648  vertexT *vertex, **vertexp;
649  facetT *neighbor, **neighborp;
650 
651  trace4((qh, qh->ferr, 4021, "qh_degen_redundant_facet: test facet f%d for degen/redundant\n",
652  facet->id));
653  FOREACHneighbor_(facet) {
654  qh->vertex_visit++;
655  FOREACHvertex_(neighbor->vertices)
656  vertex->visitid= qh->vertex_visit;
657  FOREACHvertex_(facet->vertices) {
658  if (vertex->visitid != qh->vertex_visit)
659  break;
660  }
661  if (!vertex) {
662  qh_appendmergeset(qh, facet, neighbor, MRGredundant, NULL);
663  trace2((qh, qh->ferr, 2015, "qh_degen_redundant_facet: f%d is contained in f%d. merge\n", facet->id, neighbor->id));
664  return;
665  }
666  }
667  if (qh_setsize(qh, facet->neighbors) < qh->hull_dim) {
668  qh_appendmergeset(qh, facet, facet, MRGdegen, NULL);
669  trace2((qh, qh->ferr, 2016, "qh_degen_redundant_neighbors: f%d is degenerate.\n", facet->id));
670  }
671 } /* degen_redundant_facet */
672 
673 
674 /*-<a href="qh-merge_r.htm#TOC"
675  >-------------------------------</a><a name="degen_redundant_neighbors">-</a>
676 
677  qh_degen_redundant_neighbors(qh, facet, delfacet, )
678  append degenerate and redundant neighbors to facet_mergeset
679  if delfacet,
680  only checks neighbors of both delfacet and facet
681  also checks current facet for degeneracy
682 
683  notes:
684  bumps vertex_visit
685  called for each qh_mergefacet() and qh_mergecycle()
686  merge and statistics occur in merge_nonconvex
687  qh_appendmergeset() only appends first reference to facet (i.e., redundant)
688  it appends redundant facets after degenerate ones
689 
690  a degenerate facet has fewer than hull_dim neighbors
691  a redundant facet's vertices is a subset of its neighbor's vertices
692  tests for redundant merges first (appendmergeset is nop for others)
693  in a merge, only needs to test neighbors of merged facet
694 
695  see:
696  qh_merge_degenredundant() and qh_degen_redundant_facet()
697 
698  design:
699  test for degenerate facet
700  test for redundant neighbor
701  test for degenerate neighbor
702 */
703 void qh_degen_redundant_neighbors(qhT *qh, facetT *facet, facetT *delfacet) {
704  vertexT *vertex, **vertexp;
705  facetT *neighbor, **neighborp;
706  int size;
707 
708  trace4((qh, qh->ferr, 4022, "qh_degen_redundant_neighbors: test neighbors of f%d with delfacet f%d\n",
709  facet->id, getid_(delfacet)));
710  if ((size= qh_setsize(qh, facet->neighbors)) < qh->hull_dim) {
711  qh_appendmergeset(qh, facet, facet, MRGdegen, NULL);
712  trace2((qh, qh->ferr, 2017, "qh_degen_redundant_neighbors: f%d is degenerate with %d neighbors.\n", facet->id, size));
713  }
714  if (!delfacet)
715  delfacet= facet;
716  qh->vertex_visit++;
717  FOREACHvertex_(facet->vertices)
718  vertex->visitid= qh->vertex_visit;
719  FOREACHneighbor_(delfacet) {
720  /* uses early out instead of checking vertex count */
721  if (neighbor == facet)
722  continue;
723  FOREACHvertex_(neighbor->vertices) {
724  if (vertex->visitid != qh->vertex_visit)
725  break;
726  }
727  if (!vertex) {
728  qh_appendmergeset(qh, neighbor, facet, MRGredundant, NULL);
729  trace2((qh, qh->ferr, 2018, "qh_degen_redundant_neighbors: f%d is contained in f%d. merge\n", neighbor->id, facet->id));
730  }
731  }
732  FOREACHneighbor_(delfacet) { /* redundant merges occur first */
733  if (neighbor == facet)
734  continue;
735  if ((size= qh_setsize(qh, neighbor->neighbors)) < qh->hull_dim) {
736  qh_appendmergeset(qh, neighbor, neighbor, MRGdegen, NULL);
737  trace2((qh, qh->ferr, 2019, "qh_degen_redundant_neighbors: f%d is degenerate with %d neighbors. Neighbor of f%d.\n", neighbor->id, size, facet->id));
738  }
739  }
740 } /* degen_redundant_neighbors */
741 
742 
743 /*-<a href="qh-merge_r.htm#TOC"
744  >-------------------------------</a><a name="find_newvertex">-</a>
745 
746  qh_find_newvertex(qh, oldvertex, vertices, ridges )
747  locate new vertex for renaming old vertex
748  vertices is a set of possible new vertices
749  vertices sorted by number of deleted ridges
750 
751  returns:
752  newvertex or NULL
753  each ridge includes both vertex and oldvertex
754  vertices sorted by number of deleted ridges
755 
756  notes:
757  modifies vertex->visitid
758  new vertex is in one of the ridges
759  renaming will not cause a duplicate ridge
760  renaming will minimize the number of deleted ridges
761  newvertex may not be adjacent in the dual (though unlikely)
762 
763  design:
764  for each vertex in vertices
765  set vertex->visitid to number of references in ridges
766  remove unvisited vertices
767  set qh.vertex_visit above all possible values
768  sort vertices by number of references in ridges
769  add each ridge to qh.hash_table
770  for each vertex in vertices
771  look for a vertex that would not cause a duplicate ridge after a rename
772 */
773 vertexT *qh_find_newvertex(qhT *qh, vertexT *oldvertex, setT *vertices, setT *ridges) {
774  vertexT *vertex, **vertexp;
775  setT *newridges;
776  ridgeT *ridge, **ridgep;
777  int size, hashsize;
778  int hash;
779 
780 #ifndef qh_NOtrace
781  if (qh->IStracing >= 4) {
782  qh_fprintf(qh, qh->ferr, 8063, "qh_find_newvertex: find new vertex for v%d from ",
783  oldvertex->id);
784  FOREACHvertex_(vertices)
785  qh_fprintf(qh, qh->ferr, 8064, "v%d ", vertex->id);
786  FOREACHridge_(ridges)
787  qh_fprintf(qh, qh->ferr, 8065, "r%d ", ridge->id);
788  qh_fprintf(qh, qh->ferr, 8066, "\n");
789  }
790 #endif
791  FOREACHvertex_(vertices)
792  vertex->visitid= 0;
793  FOREACHridge_(ridges) {
794  FOREACHvertex_(ridge->vertices)
795  vertex->visitid++;
796  }
797  FOREACHvertex_(vertices) {
798  if (!vertex->visitid) {
799  qh_setdelnth(qh, vertices, SETindex_(vertices,vertex));
800  vertexp--; /* repeat since deleted this vertex */
801  }
802  }
803  qh->vertex_visit += (unsigned int)qh_setsize(qh, ridges);
804  if (!qh_setsize(qh, vertices)) {
805  trace4((qh, qh->ferr, 4023, "qh_find_newvertex: vertices not in ridges for v%d\n",
806  oldvertex->id));
807  return NULL;
808  }
809  qsort(SETaddr_(vertices, vertexT), (size_t)qh_setsize(qh, vertices),
810  sizeof(vertexT *), qh_comparevisit);
811  /* can now use qh->vertex_visit */
812  if (qh->PRINTstatistics) {
813  size= qh_setsize(qh, vertices);
814  zinc_(Zintersect);
815  zadd_(Zintersecttot, size);
816  zmax_(Zintersectmax, size);
817  }
818  hashsize= qh_newhashtable(qh, qh_setsize(qh, ridges));
819  FOREACHridge_(ridges)
820  qh_hashridge(qh, qh->hash_table, hashsize, ridge, oldvertex);
821  FOREACHvertex_(vertices) {
822  newridges= qh_vertexridges(qh, vertex);
823  FOREACHridge_(newridges) {
824  if (qh_hashridge_find(qh, qh->hash_table, hashsize, ridge, vertex, oldvertex, &hash)) {
825  zinc_(Zdupridge);
826  break;
827  }
828  }
829  qh_settempfree(qh, &newridges);
830  if (!ridge)
831  break; /* found a rename */
832  }
833  if (vertex) {
834  /* counted in qh_renamevertex */
835  trace2((qh, qh->ferr, 2020, "qh_find_newvertex: found v%d for old v%d from %d vertices and %d ridges.\n",
836  vertex->id, oldvertex->id, qh_setsize(qh, vertices), qh_setsize(qh, ridges)));
837  }else {
838  zinc_(Zfindfail);
839  trace0((qh, qh->ferr, 14, "qh_find_newvertex: no vertex for renaming v%d(all duplicated ridges) during p%d\n",
840  oldvertex->id, qh->furthest_id));
841  }
842  qh_setfree(qh, &qh->hash_table);
843  return vertex;
844 } /* find_newvertex */
845 
846 /*-<a href="qh-merge_r.htm#TOC"
847  >-------------------------------</a><a name="findbest_test">-</a>
848 
849  qh_findbest_test(qh, testcentrum, facet, neighbor, bestfacet, dist, mindist, maxdist )
850  test neighbor of facet for qh_findbestneighbor()
851  if testcentrum,
852  tests centrum (assumes it is defined)
853  else
854  tests vertices
855 
856  returns:
857  if a better facet (i.e., vertices/centrum of facet closer to neighbor)
858  updates bestfacet, dist, mindist, and maxdist
859 */
860 void qh_findbest_test(qhT *qh, boolT testcentrum, facetT *facet, facetT *neighbor,
861  facetT **bestfacet, realT *distp, realT *mindistp, realT *maxdistp) {
862  realT dist, mindist, maxdist;
863 
864  if (testcentrum) {
865  zzinc_(Zbestdist);
866  qh_distplane(qh, facet->center, neighbor, &dist);
867  dist *= qh->hull_dim; /* estimate furthest vertex */
868  if (dist < 0) {
869  maxdist= 0;
870  mindist= dist;
871  dist= -dist;
872  }else {
873  mindist= 0;
874  maxdist= dist;
875  }
876  }else
877  dist= qh_getdistance(qh, facet, neighbor, &mindist, &maxdist);
878  if (dist < *distp) {
879  *bestfacet= neighbor;
880  *mindistp= mindist;
881  *maxdistp= maxdist;
882  *distp= dist;
883  }
884 } /* findbest_test */
885 
886 /*-<a href="qh-merge_r.htm#TOC"
887  >-------------------------------</a><a name="findbestneighbor">-</a>
888 
889  qh_findbestneighbor(qh, facet, dist, mindist, maxdist )
890  finds best neighbor (least dist) of a facet for merging
891 
892  returns:
893  returns min and max distances and their max absolute value
894 
895  notes:
896  error if qh_ASvoronoi
897  avoids merging old into new
898  assumes ridge->nonconvex only set on one ridge between a pair of facets
899  could use an early out predicate but not worth it
900 
901  design:
902  if a large facet
903  will test centrum
904  else
905  will test vertices
906  if a large facet
907  test nonconvex neighbors for best merge
908  else
909  test all neighbors for the best merge
910  if testing centrum
911  get distance information
912 */
913 facetT *qh_findbestneighbor(qhT *qh, facetT *facet, realT *distp, realT *mindistp, realT *maxdistp) {
914  facetT *neighbor, **neighborp, *bestfacet= NULL;
915  ridgeT *ridge, **ridgep;
916  boolT nonconvex= True, testcentrum= False;
917  int size= qh_setsize(qh, facet->vertices);
918 
919  if(qh->CENTERtype==qh_ASvoronoi){
920  qh_fprintf(qh, qh->ferr, 6272, "qhull error: cannot call qh_findbestneighor for f%d while qh.CENTERtype is qh_ASvoronoi\n", facet->id);
921  qh_errexit(qh, qh_ERRqhull, facet, NULL);
922  }
923  *distp= REALmax;
924  if (size > qh_BESTcentrum2 * qh->hull_dim + qh_BESTcentrum) {
925  testcentrum= True;
926  zinc_(Zbestcentrum);
927  if (!facet->center)
928  facet->center= qh_getcentrum(qh, facet);
929  }
930  if (size > qh->hull_dim + qh_BESTnonconvex) {
931  FOREACHridge_(facet->ridges) {
932  if (ridge->nonconvex) {
933  neighbor= otherfacet_(ridge, facet);
934  qh_findbest_test(qh, testcentrum, facet, neighbor,
935  &bestfacet, distp, mindistp, maxdistp);
936  }
937  }
938  }
939  if (!bestfacet) {
940  nonconvex= False;
941  FOREACHneighbor_(facet)
942  qh_findbest_test(qh, testcentrum, facet, neighbor,
943  &bestfacet, distp, mindistp, maxdistp);
944  }
945  if (!bestfacet) {
946  qh_fprintf(qh, qh->ferr, 6095, "qhull internal error (qh_findbestneighbor): no neighbors for f%d\n", facet->id);
947  qh_errexit(qh, qh_ERRqhull, facet, NULL);
948  }
949  if (testcentrum)
950  qh_getdistance(qh, facet, bestfacet, mindistp, maxdistp);
951  trace3((qh, qh->ferr, 3002, "qh_findbestneighbor: f%d is best neighbor for f%d testcentrum? %d nonconvex? %d dist %2.2g min %2.2g max %2.2g\n",
952  bestfacet->id, facet->id, testcentrum, nonconvex, *distp, *mindistp, *maxdistp));
953  return(bestfacet);
954 } /* findbestneighbor */
955 
956 
957 /*-<a href="qh-merge_r.htm#TOC"
958  >-------------------------------</a><a name="flippedmerges">-</a>
959 
960  qh_flippedmerges(qh, facetlist, wasmerge )
961  merge flipped facets into best neighbor
962  assumes qh.facet_mergeset at top of temporary stack
963 
964  returns:
965  no flipped facets on facetlist
966  sets wasmerge if merge occurred
967  degen/redundant merges passed through
968 
969  notes:
970  othermerges not needed since qh.facet_mergeset is empty before & after
971  keep it in case of change
972 
973  design:
974  append flipped facets to qh.facetmergeset
975  for each flipped merge
976  find best neighbor
977  merge facet into neighbor
978  merge degenerate and redundant facets
979  remove flipped merges from qh.facet_mergeset
980 */
981 void qh_flippedmerges(qhT *qh, facetT *facetlist, boolT *wasmerge) {
982  facetT *facet, *neighbor, *facet1;
983  realT dist, mindist, maxdist;
984  mergeT *merge, **mergep;
985  setT *othermerges;
986  int nummerge=0;
987 
988  trace4((qh, qh->ferr, 4024, "qh_flippedmerges: begin\n"));
989  FORALLfacet_(facetlist) {
990  if (facet->flipped && !facet->visible)
991  qh_appendmergeset(qh, facet, facet, MRGflip, NULL);
992  }
993  othermerges= qh_settemppop(qh); /* was facet_mergeset */
994  qh->facet_mergeset= qh_settemp(qh, qh->TEMPsize);
995  qh_settemppush(qh, othermerges);
996  FOREACHmerge_(othermerges) {
997  facet1= merge->facet1;
998  if (merge->type != MRGflip || facet1->visible)
999  continue;
1000  if (qh->TRACEmerge-1 == zzval_(Ztotmerge))
1001  qh->qhmem.IStracing= qh->IStracing= qh->TRACElevel;
1002  neighbor= qh_findbestneighbor(qh, facet1, &dist, &mindist, &maxdist);
1003  trace0((qh, qh->ferr, 15, "qh_flippedmerges: merge flipped f%d into f%d dist %2.2g during p%d\n",
1004  facet1->id, neighbor->id, dist, qh->furthest_id));
1005  qh_mergefacet(qh, facet1, neighbor, &mindist, &maxdist, !qh_MERGEapex);
1006  nummerge++;
1007  if (qh->PRINTstatistics) {
1008  zinc_(Zflipped);
1009  wadd_(Wflippedtot, dist);
1010  wmax_(Wflippedmax, dist);
1011  }
1012  qh_merge_degenredundant(qh);
1013  }
1014  FOREACHmerge_(othermerges) {
1015  if (merge->facet1->visible || merge->facet2->visible)
1016  qh_memfree(qh, merge, (int)sizeof(mergeT));
1017  else
1018  qh_setappend(qh, &qh->facet_mergeset, merge);
1019  }
1020  qh_settempfree(qh, &othermerges);
1021  if (nummerge)
1022  *wasmerge= True;
1023  trace1((qh, qh->ferr, 1010, "qh_flippedmerges: merged %d flipped facets into a good neighbor\n", nummerge));
1024 } /* flippedmerges */
1025 
1026 
1027 /*-<a href="qh-merge_r.htm#TOC"
1028  >-------------------------------</a><a name="forcedmerges">-</a>
1029 
1030  qh_forcedmerges(qh, wasmerge )
1031  merge duplicated ridges
1032 
1033  returns:
1034  removes all duplicate ridges on facet_mergeset
1035  wasmerge set if merge
1036  qh.facet_mergeset may include non-forced merges(none for now)
1037  qh.degen_mergeset includes degen/redun merges
1038 
1039  notes:
1040  duplicate ridges occur when the horizon is pinched,
1041  i.e. a subridge occurs in more than two horizon ridges.
1042  could rename vertices that pinch the horizon
1043  assumes qh_merge_degenredundant() has not be called
1044  othermerges isn't needed since facet_mergeset is empty afterwards
1045  keep it in case of change
1046 
1047  design:
1048  for each duplicate ridge
1049  find current facets by chasing f.replace links
1050  check for wide merge due to duplicate ridge
1051  determine best direction for facet
1052  merge one facet into the other
1053  remove duplicate ridges from qh.facet_mergeset
1054 */
1055 void qh_forcedmerges(qhT *qh, boolT *wasmerge) {
1056  facetT *facet1, *facet2;
1057  mergeT *merge, **mergep;
1058  realT dist1, dist2, mindist1, mindist2, maxdist1, maxdist2;
1059  setT *othermerges;
1060  int nummerge=0, numflip=0;
1061 
1062  if (qh->TRACEmerge-1 == zzval_(Ztotmerge))
1063  qh->qhmem.IStracing= qh->IStracing= qh->TRACElevel;
1064  trace4((qh, qh->ferr, 4025, "qh_forcedmerges: begin\n"));
1065  othermerges= qh_settemppop(qh); /* was facet_mergeset */
1066  qh->facet_mergeset= qh_settemp(qh, qh->TEMPsize);
1067  qh_settemppush(qh, othermerges);
1068  FOREACHmerge_(othermerges) {
1069  if (merge->type != MRGridge)
1070  continue;
1071  if (qh->TRACEmerge-1 == zzval_(Ztotmerge))
1072  qh->qhmem.IStracing= qh->IStracing= qh->TRACElevel;
1073  facet1= merge->facet1;
1074  facet2= merge->facet2;
1075  while (facet1->visible) /* must exist, no qh_merge_degenredunant */
1076  facet1= facet1->f.replace; /* previously merged facet */
1077  while (facet2->visible)
1078  facet2= facet2->f.replace; /* previously merged facet */
1079  if (facet1 == facet2)
1080  continue;
1081  if (!qh_setin(facet2->neighbors, facet1)) {
1082  qh_fprintf(qh, qh->ferr, 6096, "qhull internal error (qh_forcedmerges): f%d and f%d had a duplicate ridge but as f%d and f%d they are no longer neighbors\n",
1083  merge->facet1->id, merge->facet2->id, facet1->id, facet2->id);
1084  qh_errexit2(qh, qh_ERRqhull, facet1, facet2);
1085  }
1086  dist1= qh_getdistance(qh, facet1, facet2, &mindist1, &maxdist1);
1087  dist2= qh_getdistance(qh, facet2, facet1, &mindist2, &maxdist2);
1088  qh_check_dupridge(qh, facet1, dist1, facet2, dist2);
1089  if (dist1 < dist2)
1090  qh_mergefacet(qh, facet1, facet2, &mindist1, &maxdist1, !qh_MERGEapex);
1091  else {
1092  qh_mergefacet(qh, facet2, facet1, &mindist2, &maxdist2, !qh_MERGEapex);
1093  dist1= dist2;
1094  facet1= facet2;
1095  }
1096  if (facet1->flipped) {
1097  zinc_(Zmergeflipdup);
1098  numflip++;
1099  }else
1100  nummerge++;
1101  if (qh->PRINTstatistics) {
1102  zinc_(Zduplicate);
1103  wadd_(Wduplicatetot, dist1);
1104  wmax_(Wduplicatemax, dist1);
1105  }
1106  }
1107  FOREACHmerge_(othermerges) {
1108  if (merge->type == MRGridge)
1109  qh_memfree(qh, merge, (int)sizeof(mergeT));
1110  else
1111  qh_setappend(qh, &qh->facet_mergeset, merge);
1112  }
1113  qh_settempfree(qh, &othermerges);
1114  if (nummerge)
1115  *wasmerge= True;
1116  trace1((qh, qh->ferr, 1011, "qh_forcedmerges: merged %d facets and %d flipped facets across duplicated ridges\n",
1117  nummerge, numflip));
1118 } /* forcedmerges */
1119 
1120 
1121 /*-<a href="qh-merge_r.htm#TOC"
1122  >-------------------------------</a><a name="getmergeset">-</a>
1123 
1124  qh_getmergeset(qh, facetlist )
1125  determines nonconvex facets on facetlist
1126  tests !tested ridges and nonconvex ridges of !tested facets
1127 
1128  returns:
1129  returns sorted qh.facet_mergeset of facet-neighbor pairs to be merged
1130  all ridges tested
1131 
1132  notes:
1133  assumes no nonconvex ridges with both facets tested
1134  uses facet->tested/ridge->tested to prevent duplicate tests
1135  can not limit tests to modified ridges since the centrum changed
1136  uses qh.visit_id
1137 
1138  see:
1139  qh_getmergeset_initial()
1140 
1141  design:
1142  for each facet on facetlist
1143  for each ridge of facet
1144  if untested ridge
1145  test ridge for convexity
1146  if non-convex
1147  append ridge to qh.facet_mergeset
1148  sort qh.facet_mergeset by angle
1149 */
1150 void qh_getmergeset(qhT *qh, facetT *facetlist) {
1151  facetT *facet, *neighbor, **neighborp;
1152  ridgeT *ridge, **ridgep;
1153  int nummerges;
1154 
1155  nummerges= qh_setsize(qh, qh->facet_mergeset);
1156  trace4((qh, qh->ferr, 4026, "qh_getmergeset: started.\n"));
1157  qh->visit_id++;
1158  FORALLfacet_(facetlist) {
1159  if (facet->tested)
1160  continue;
1161  facet->visitid= qh->visit_id;
1162  facet->tested= True; /* must be non-simplicial due to merge */
1163  FOREACHneighbor_(facet)
1164  neighbor->seen= False;
1165  FOREACHridge_(facet->ridges) {
1166  if (ridge->tested && !ridge->nonconvex)
1167  continue;
1168  /* if tested & nonconvex, need to append merge */
1169  neighbor= otherfacet_(ridge, facet);
1170  if (neighbor->seen) {
1171  ridge->tested= True;
1172  ridge->nonconvex= False;
1173  }else if (neighbor->visitid != qh->visit_id) {
1174  ridge->tested= True;
1175  ridge->nonconvex= False;
1176  neighbor->seen= True; /* only one ridge is marked nonconvex */
1177  if (qh_test_appendmerge(qh, facet, neighbor))
1178  ridge->nonconvex= True;
1179  }
1180  }
1181  }
1182  nummerges= qh_setsize(qh, qh->facet_mergeset);
1183  if (qh->ANGLEmerge)
1184  qsort(SETaddr_(qh->facet_mergeset, mergeT), (size_t)nummerges, sizeof(mergeT *), qh_compareangle);
1185  else
1186  qsort(SETaddr_(qh->facet_mergeset, mergeT), (size_t)nummerges, sizeof(mergeT *), qh_comparemerge);
1187  if (qh->POSTmerging) {
1188  zadd_(Zmergesettot2, nummerges);
1189  }else {
1190  zadd_(Zmergesettot, nummerges);
1191  zmax_(Zmergesetmax, nummerges);
1192  }
1193  trace2((qh, qh->ferr, 2021, "qh_getmergeset: %d merges found\n", nummerges));
1194 } /* getmergeset */
1195 
1196 
1197 /*-<a href="qh-merge_r.htm#TOC"
1198  >-------------------------------</a><a name="getmergeset_initial">-</a>
1199 
1200  qh_getmergeset_initial(qh, facetlist )
1201  determine initial qh.facet_mergeset for facets
1202  tests all facet/neighbor pairs on facetlist
1203 
1204  returns:
1205  sorted qh.facet_mergeset with nonconvex ridges
1206  sets facet->tested, ridge->tested, and ridge->nonconvex
1207 
1208  notes:
1209  uses visit_id, assumes ridge->nonconvex is False
1210 
1211  see:
1212  qh_getmergeset()
1213 
1214  design:
1215  for each facet on facetlist
1216  for each untested neighbor of facet
1217  test facet and neighbor for convexity
1218  if non-convex
1219  append merge to qh.facet_mergeset
1220  mark one of the ridges as nonconvex
1221  sort qh.facet_mergeset by angle
1222 */
1223 void qh_getmergeset_initial(qhT *qh, facetT *facetlist) {
1224  facetT *facet, *neighbor, **neighborp;
1225  ridgeT *ridge, **ridgep;
1226  int nummerges;
1227 
1228  qh->visit_id++;
1229  FORALLfacet_(facetlist) {
1230  facet->visitid= qh->visit_id;
1231  facet->tested= True;
1232  FOREACHneighbor_(facet) {
1233  if (neighbor->visitid != qh->visit_id) {
1234  if (qh_test_appendmerge(qh, facet, neighbor)) {
1235  FOREACHridge_(neighbor->ridges) {
1236  if (facet == otherfacet_(ridge, neighbor)) {
1237  ridge->nonconvex= True;
1238  break; /* only one ridge is marked nonconvex */
1239  }
1240  }
1241  }
1242  }
1243  }
1244  FOREACHridge_(facet->ridges)
1245  ridge->tested= True;
1246  }
1247  nummerges= qh_setsize(qh, qh->facet_mergeset);
1248  if (qh->ANGLEmerge)
1249  qsort(SETaddr_(qh->facet_mergeset, mergeT), (size_t)nummerges, sizeof(mergeT *), qh_compareangle);
1250  else
1251  qsort(SETaddr_(qh->facet_mergeset, mergeT), (size_t)nummerges, sizeof(mergeT *), qh_comparemerge);
1252  if (qh->POSTmerging) {
1253  zadd_(Zmergeinittot2, nummerges);
1254  }else {
1255  zadd_(Zmergeinittot, nummerges);
1256  zmax_(Zmergeinitmax, nummerges);
1257  }
1258  trace2((qh, qh->ferr, 2022, "qh_getmergeset_initial: %d merges found\n", nummerges));
1259 } /* getmergeset_initial */
1260 
1261 
1262 /*-<a href="qh-merge_r.htm#TOC"
1263  >-------------------------------</a><a name="hashridge">-</a>
1264 
1265  qh_hashridge(qh, hashtable, hashsize, ridge, oldvertex )
1266  add ridge to hashtable without oldvertex
1267 
1268  notes:
1269  assumes hashtable is large enough
1270 
1271  design:
1272  determine hash value for ridge without oldvertex
1273  find next empty slot for ridge
1274 */
1275 void qh_hashridge(qhT *qh, setT *hashtable, int hashsize, ridgeT *ridge, vertexT *oldvertex) {
1276  int hash;
1277  ridgeT *ridgeA;
1278 
1279  hash= qh_gethash(qh, hashsize, ridge->vertices, qh->hull_dim-1, 0, oldvertex);
1280  while (True) {
1281  if (!(ridgeA= SETelemt_(hashtable, hash, ridgeT))) {
1282  SETelem_(hashtable, hash)= ridge;
1283  break;
1284  }else if (ridgeA == ridge)
1285  break;
1286  if (++hash == hashsize)
1287  hash= 0;
1288  }
1289 } /* hashridge */
1290 
1291 
1292 /*-<a href="qh-merge_r.htm#TOC"
1293  >-------------------------------</a><a name="hashridge_find">-</a>
1294 
1295  qh_hashridge_find(qh, hashtable, hashsize, ridge, vertex, oldvertex, hashslot )
1296  returns matching ridge without oldvertex in hashtable
1297  for ridge without vertex
1298  if oldvertex is NULL
1299  matches with any one skip
1300 
1301  returns:
1302  matching ridge or NULL
1303  if no match,
1304  if ridge already in table
1305  hashslot= -1
1306  else
1307  hashslot= next NULL index
1308 
1309  notes:
1310  assumes hashtable is large enough
1311  can't match ridge to itself
1312 
1313  design:
1314  get hash value for ridge without vertex
1315  for each hashslot
1316  return match if ridge matches ridgeA without oldvertex
1317 */
1318 ridgeT *qh_hashridge_find(qhT *qh, setT *hashtable, int hashsize, ridgeT *ridge,
1319  vertexT *vertex, vertexT *oldvertex, int *hashslot) {
1320  int hash;
1321  ridgeT *ridgeA;
1322 
1323  *hashslot= 0;
1324  zinc_(Zhashridge);
1325  hash= qh_gethash(qh, hashsize, ridge->vertices, qh->hull_dim-1, 0, vertex);
1326  while ((ridgeA= SETelemt_(hashtable, hash, ridgeT))) {
1327  if (ridgeA == ridge)
1328  *hashslot= -1;
1329  else {
1330  zinc_(Zhashridgetest);
1331  if (qh_setequal_except(ridge->vertices, vertex, ridgeA->vertices, oldvertex))
1332  return ridgeA;
1333  }
1334  if (++hash == hashsize)
1335  hash= 0;
1336  }
1337  if (!*hashslot)
1338  *hashslot= hash;
1339  return NULL;
1340 } /* hashridge_find */
1341 
1342 
1343 /*-<a href="qh-merge_r.htm#TOC"
1344  >-------------------------------</a><a name="makeridges">-</a>
1345 
1346  qh_makeridges(qh, facet )
1347  creates explicit ridges between simplicial facets
1348 
1349  returns:
1350  facet with ridges and without qh_MERGEridge
1351  ->simplicial is False
1352 
1353  notes:
1354  allows qh_MERGEridge flag
1355  uses existing ridges
1356  duplicate neighbors ok if ridges already exist (qh_mergecycle_ridges)
1357 
1358  see:
1359  qh_mergecycle_ridges()
1360 
1361  design:
1362  look for qh_MERGEridge neighbors
1363  mark neighbors that already have ridges
1364  for each unprocessed neighbor of facet
1365  create a ridge for neighbor and facet
1366  if any qh_MERGEridge neighbors
1367  delete qh_MERGEridge flags (already handled by qh_mark_dupridges)
1368 */
1369 void qh_makeridges(qhT *qh, facetT *facet) {
1370  facetT *neighbor, **neighborp;
1371  ridgeT *ridge, **ridgep;
1372  int neighbor_i, neighbor_n;
1373  boolT toporient, mergeridge= False;
1374 
1375  if (!facet->simplicial)
1376  return;
1377  trace4((qh, qh->ferr, 4027, "qh_makeridges: make ridges for f%d\n", facet->id));
1378  facet->simplicial= False;
1379  FOREACHneighbor_(facet) {
1380  if (neighbor == qh_MERGEridge)
1381  mergeridge= True;
1382  else
1383  neighbor->seen= False;
1384  }
1385  FOREACHridge_(facet->ridges)
1386  otherfacet_(ridge, facet)->seen= True;
1387  FOREACHneighbor_i_(qh, facet) {
1388  if (neighbor == qh_MERGEridge)
1389  continue; /* fixed by qh_mark_dupridges */
1390  else if (!neighbor->seen) { /* no current ridges */
1391  ridge= qh_newridge(qh);
1392  ridge->vertices= qh_setnew_delnthsorted(qh, facet->vertices, qh->hull_dim,
1393  neighbor_i, 0);
1394  toporient= facet->toporient ^ (neighbor_i & 0x1);
1395  if (toporient) {
1396  ridge->top= facet;
1397  ridge->bottom= neighbor;
1398  }else {
1399  ridge->top= neighbor;
1400  ridge->bottom= facet;
1401  }
1402 #if 0 /* this also works */
1403  flip= (facet->toporient ^ neighbor->toporient)^(skip1 & 0x1) ^ (skip2 & 0x1);
1404  if (facet->toporient ^ (skip1 & 0x1) ^ flip) {
1405  ridge->top= neighbor;
1406  ridge->bottom= facet;
1407  }else {
1408  ridge->top= facet;
1409  ridge->bottom= neighbor;
1410  }
1411 #endif
1412  qh_setappend(qh, &(facet->ridges), ridge);
1413  qh_setappend(qh, &(neighbor->ridges), ridge);
1414  }
1415  }
1416  if (mergeridge) {
1417  while (qh_setdel(facet->neighbors, qh_MERGEridge))
1418  ; /* delete each one */
1419  }
1420 } /* makeridges */
1421 
1422 
1423 /*-<a href="qh-merge_r.htm#TOC"
1424  >-------------------------------</a><a name="mark_dupridges">-</a>
1425 
1426  qh_mark_dupridges(qh, facetlist )
1427  add duplicated ridges to qh.facet_mergeset
1428  facet->dupridge is true
1429 
1430  returns:
1431  duplicate ridges on qh.facet_mergeset
1432  ->mergeridge/->mergeridge2 set
1433  duplicate ridges marked by qh_MERGEridge and both sides facet->dupridge
1434  no MERGEridges in neighbor sets
1435 
1436  notes:
1437  duplicate ridges occur when the horizon is pinched,
1438  i.e. a subridge occurs in more than two horizon ridges.
1439  could rename vertices that pinch the horizon (thus removing subridge)
1440  uses qh.visit_id
1441 
1442  design:
1443  for all facets on facetlist
1444  if facet contains a duplicate ridge
1445  for each neighbor of facet
1446  if neighbor marked qh_MERGEridge (one side of the merge)
1447  set facet->mergeridge
1448  else
1449  if neighbor contains a duplicate ridge
1450  and the back link is qh_MERGEridge
1451  append duplicate ridge to qh.facet_mergeset
1452  for each duplicate ridge
1453  make ridge sets in preparation for merging
1454  remove qh_MERGEridge from neighbor set
1455  for each duplicate ridge
1456  restore the missing neighbor from the neighbor set that was qh_MERGEridge
1457  add the missing ridge for this neighbor
1458 */
1459 void qh_mark_dupridges(qhT *qh, facetT *facetlist) {
1460  facetT *facet, *neighbor, **neighborp;
1461  int nummerge=0;
1462  mergeT *merge, **mergep;
1463 
1464 
1465  trace4((qh, qh->ferr, 4028, "qh_mark_dupridges: identify duplicate ridges\n"));
1466  FORALLfacet_(facetlist) {
1467  if (facet->dupridge) {
1468  FOREACHneighbor_(facet) {
1469  if (neighbor == qh_MERGEridge) {
1470  facet->mergeridge= True;
1471  continue;
1472  }
1473  if (neighbor->dupridge
1474  && !qh_setin(neighbor->neighbors, facet)) { /* qh_MERGEridge */
1475  qh_appendmergeset(qh, facet, neighbor, MRGridge, NULL);
1476  facet->mergeridge2= True;
1477  facet->mergeridge= True;
1478  nummerge++;
1479  }
1480  }
1481  }
1482  }
1483  if (!nummerge)
1484  return;
1485  FORALLfacet_(facetlist) { /* gets rid of qh_MERGEridge */
1486  if (facet->mergeridge && !facet->mergeridge2)
1487  qh_makeridges(qh, facet);
1488  }
1489  FOREACHmerge_(qh->facet_mergeset) { /* restore the missing neighbors */
1490  if (merge->type == MRGridge) {
1491  qh_setappend(qh, &merge->facet2->neighbors, merge->facet1);
1492  qh_makeridges(qh, merge->facet1); /* and the missing ridges */
1493  }
1494  }
1495  trace1((qh, qh->ferr, 1012, "qh_mark_dupridges: found %d duplicated ridges\n",
1496  nummerge));
1497 } /* mark_dupridges */
1498 
1499 /*-<a href="qh-merge_r.htm#TOC"
1500  >-------------------------------</a><a name="maydropneighbor">-</a>
1501 
1502  qh_maydropneighbor(qh, facet )
1503  drop neighbor relationship if no ridge between facet and neighbor
1504 
1505  returns:
1506  neighbor sets updated
1507  appends degenerate facets to qh.facet_mergeset
1508 
1509  notes:
1510  won't cause redundant facets since vertex inclusion is the same
1511  may drop vertex and neighbor if no ridge
1512  uses qh.visit_id
1513 
1514  design:
1515  visit all neighbors with ridges
1516  for each unvisited neighbor of facet
1517  delete neighbor and facet from the neighbor sets
1518  if neighbor becomes degenerate
1519  append neighbor to qh.degen_mergeset
1520  if facet is degenerate
1521  append facet to qh.degen_mergeset
1522 */
1523 void qh_maydropneighbor(qhT *qh, facetT *facet) {
1524  ridgeT *ridge, **ridgep;
1525  realT angledegen= qh_ANGLEdegen;
1526  facetT *neighbor, **neighborp;
1527 
1528  qh->visit_id++;
1529  trace4((qh, qh->ferr, 4029, "qh_maydropneighbor: test f%d for no ridges to a neighbor\n",
1530  facet->id));
1531  FOREACHridge_(facet->ridges) {
1532  ridge->top->visitid= qh->visit_id;
1533  ridge->bottom->visitid= qh->visit_id;
1534  }
1535  FOREACHneighbor_(facet) {
1536  if (neighbor->visitid != qh->visit_id) {
1537  trace0((qh, qh->ferr, 17, "qh_maydropneighbor: facets f%d and f%d are no longer neighbors during p%d\n",
1538  facet->id, neighbor->id, qh->furthest_id));
1539  zinc_(Zdropneighbor);
1540  qh_setdel(facet->neighbors, neighbor);
1541  neighborp--; /* repeat, deleted a neighbor */
1542  qh_setdel(neighbor->neighbors, facet);
1543  if (qh_setsize(qh, neighbor->neighbors) < qh->hull_dim) {
1544  zinc_(Zdropdegen);
1545  qh_appendmergeset(qh, neighbor, neighbor, MRGdegen, &angledegen);
1546  trace2((qh, qh->ferr, 2023, "qh_maydropneighbors: f%d is degenerate.\n", neighbor->id));
1547  }
1548  }
1549  }
1550  if (qh_setsize(qh, facet->neighbors) < qh->hull_dim) {
1551  zinc_(Zdropdegen);
1552  qh_appendmergeset(qh, facet, facet, MRGdegen, &angledegen);
1553  trace2((qh, qh->ferr, 2024, "qh_maydropneighbors: f%d is degenerate.\n", facet->id));
1554  }
1555 } /* maydropneighbor */
1556 
1557 
1558 /*-<a href="qh-merge_r.htm#TOC"
1559  >-------------------------------</a><a name="merge_degenredundant">-</a>
1560 
1561  qh_merge_degenredundant(qh)
1562  merge all degenerate and redundant facets
1563  qh.degen_mergeset contains merges from qh_degen_redundant_neighbors()
1564 
1565  returns:
1566  number of merges performed
1567  resets facet->degenerate/redundant
1568  if deleted (visible) facet has no neighbors
1569  sets ->f.replace to NULL
1570 
1571  notes:
1572  redundant merges happen before degenerate ones
1573  merging and renaming vertices can result in degen/redundant facets
1574 
1575  design:
1576  for each merge on qh.degen_mergeset
1577  if redundant merge
1578  if non-redundant facet merged into redundant facet
1579  recheck facet for redundancy
1580  else
1581  merge redundant facet into other facet
1582 */
1583 int qh_merge_degenredundant(qhT *qh) {
1584  int size;
1585  mergeT *merge;
1586  facetT *bestneighbor, *facet1, *facet2;
1587  realT dist, mindist, maxdist;
1588  vertexT *vertex, **vertexp;
1589  int nummerges= 0;
1590  mergeType mergetype;
1591 
1592  while ((merge= (mergeT*)qh_setdellast(qh->degen_mergeset))) {
1593  facet1= merge->facet1;
1594  facet2= merge->facet2;
1595  mergetype= merge->type;
1596  qh_memfree(qh, merge, (int)sizeof(mergeT));
1597  if (facet1->visible)
1598  continue;
1599  facet1->degenerate= False;
1600  facet1->redundant= False;
1601  if (qh->TRACEmerge-1 == zzval_(Ztotmerge))
1602  qh->qhmem.IStracing= qh->IStracing= qh->TRACElevel;
1603  if (mergetype == MRGredundant) {
1604  zinc_(Zneighbor);
1605  while (facet2->visible) {
1606  if (!facet2->f.replace) {
1607  qh_fprintf(qh, qh->ferr, 6097, "qhull internal error (qh_merge_degenredunant): f%d redundant but f%d has no replacement\n",
1608  facet1->id, facet2->id);
1609  qh_errexit2(qh, qh_ERRqhull, facet1, facet2);
1610  }
1611  facet2= facet2->f.replace;
1612  }
1613  if (facet1 == facet2) {
1614  qh_degen_redundant_facet(qh, facet1); /* in case of others */
1615  continue;
1616  }
1617  trace2((qh, qh->ferr, 2025, "qh_merge_degenredundant: facet f%d is contained in f%d, will merge\n",
1618  facet1->id, facet2->id));
1619  qh_mergefacet(qh, facet1, facet2, NULL, NULL, !qh_MERGEapex);
1620  /* merge distance is already accounted for */
1621  nummerges++;
1622  }else { /* mergetype == MRGdegen, other merges may have fixed */
1623  if (!(size= qh_setsize(qh, facet1->neighbors))) {
1624  zinc_(Zdelfacetdup);
1625  trace2((qh, qh->ferr, 2026, "qh_merge_degenredundant: facet f%d has no neighbors. Deleted\n", facet1->id));
1626  qh_willdelete(qh, facet1, NULL);
1627  FOREACHvertex_(facet1->vertices) {
1628  qh_setdel(vertex->neighbors, facet1);
1629  if (!SETfirst_(vertex->neighbors)) {
1630  zinc_(Zdegenvertex);
1631  trace2((qh, qh->ferr, 2027, "qh_merge_degenredundant: deleted v%d because f%d has no neighbors\n",
1632  vertex->id, facet1->id));
1633  vertex->deleted= True;
1634  qh_setappend(qh, &qh->del_vertices, vertex);
1635  }
1636  }
1637  nummerges++;
1638  }else if (size < qh->hull_dim) {
1639  bestneighbor= qh_findbestneighbor(qh, facet1, &dist, &mindist, &maxdist);
1640  trace2((qh, qh->ferr, 2028, "qh_merge_degenredundant: facet f%d has %d neighbors, merge into f%d dist %2.2g\n",
1641  facet1->id, size, bestneighbor->id, dist));
1642  qh_mergefacet(qh, facet1, bestneighbor, &mindist, &maxdist, !qh_MERGEapex);
1643  nummerges++;
1644  if (qh->PRINTstatistics) {
1645  zinc_(Zdegen);
1646  wadd_(Wdegentot, dist);
1647  wmax_(Wdegenmax, dist);
1648  }
1649  } /* else, another merge fixed the degeneracy and redundancy tested */
1650  }
1651  }
1652  return nummerges;
1653 } /* merge_degenredundant */
1654 
1655 /*-<a href="qh-merge_r.htm#TOC"
1656  >-------------------------------</a><a name="merge_nonconvex">-</a>
1657 
1658  qh_merge_nonconvex(qh, facet1, facet2, mergetype )
1659  remove non-convex ridge between facet1 into facet2
1660  mergetype gives why the facet's are non-convex
1661 
1662  returns:
1663  merges one of the facets into the best neighbor
1664 
1665  design:
1666  if one of the facets is a new facet
1667  prefer merging new facet into old facet
1668  find best neighbors for both facets
1669  merge the nearest facet into its best neighbor
1670  update the statistics
1671 */
1672 void qh_merge_nonconvex(qhT *qh, facetT *facet1, facetT *facet2, mergeType mergetype) {
1673  facetT *bestfacet, *bestneighbor, *neighbor;
1674  realT dist, dist2, mindist, mindist2, maxdist, maxdist2;
1675 
1676  if (qh->TRACEmerge-1 == zzval_(Ztotmerge))
1677  qh->qhmem.IStracing= qh->IStracing= qh->TRACElevel;
1678  trace3((qh, qh->ferr, 3003, "qh_merge_nonconvex: merge #%d for f%d and f%d type %d\n",
1679  zzval_(Ztotmerge) + 1, facet1->id, facet2->id, mergetype));
1680  /* concave or coplanar */
1681  if (!facet1->newfacet) {
1682  bestfacet= facet2; /* avoid merging old facet if new is ok */
1683  facet2= facet1;
1684  facet1= bestfacet;
1685  }else
1686  bestfacet= facet1;
1687  bestneighbor= qh_findbestneighbor(qh, bestfacet, &dist, &mindist, &maxdist);
1688  neighbor= qh_findbestneighbor(qh, facet2, &dist2, &mindist2, &maxdist2);
1689  if (dist < dist2) {
1690  qh_mergefacet(qh, bestfacet, bestneighbor, &mindist, &maxdist, !qh_MERGEapex);
1691  }else if (qh->AVOIDold && !facet2->newfacet
1692  && ((mindist >= -qh->MAXcoplanar && maxdist <= qh->max_outside)
1693  || dist * 1.5 < dist2)) {
1694  zinc_(Zavoidold);
1695  wadd_(Wavoidoldtot, dist);
1696  wmax_(Wavoidoldmax, dist);
1697  trace2((qh, qh->ferr, 2029, "qh_merge_nonconvex: avoid merging old facet f%d dist %2.2g. Use f%d dist %2.2g instead\n",
1698  facet2->id, dist2, facet1->id, dist2));
1699  qh_mergefacet(qh, bestfacet, bestneighbor, &mindist, &maxdist, !qh_MERGEapex);
1700  }else {
1701  qh_mergefacet(qh, facet2, neighbor, &mindist2, &maxdist2, !qh_MERGEapex);
1702  dist= dist2;
1703  }
1704  if (qh->PRINTstatistics) {
1705  if (mergetype == MRGanglecoplanar) {
1706  zinc_(Zacoplanar);
1707  wadd_(Wacoplanartot, dist);
1708  wmax_(Wacoplanarmax, dist);
1709  }else if (mergetype == MRGconcave) {
1710  zinc_(Zconcave);
1711  wadd_(Wconcavetot, dist);
1712  wmax_(Wconcavemax, dist);
1713  }else { /* MRGcoplanar */
1714  zinc_(Zcoplanar);
1715  wadd_(Wcoplanartot, dist);
1716  wmax_(Wcoplanarmax, dist);
1717  }
1718  }
1719 } /* merge_nonconvex */
1720 
1721 /*-<a href="qh-merge_r.htm#TOC"
1722  >-------------------------------</a><a name="mergecycle">-</a>
1723 
1724  qh_mergecycle(qh, samecycle, newfacet )
1725  merge a cycle of facets starting at samecycle into a newfacet
1726  newfacet is a horizon facet with ->normal
1727  samecycle facets are simplicial from an apex
1728 
1729  returns:
1730  initializes vertex neighbors on first merge
1731  samecycle deleted (placed on qh.visible_list)
1732  newfacet at end of qh.facet_list
1733  deleted vertices on qh.del_vertices
1734 
1735  see:
1736  qh_mergefacet()
1737  called by qh_mergecycle_all() for multiple, same cycle facets
1738 
1739  design:
1740  make vertex neighbors if necessary
1741  make ridges for newfacet
1742  merge neighbor sets of samecycle into newfacet
1743  merge ridges of samecycle into newfacet
1744  merge vertex neighbors of samecycle into newfacet
1745  make apex of samecycle the apex of newfacet
1746  if newfacet wasn't a new facet
1747  add its vertices to qh.newvertex_list
1748  delete samecycle facets a make newfacet a newfacet
1749 */
1750 void qh_mergecycle(qhT *qh, facetT *samecycle, facetT *newfacet) {
1751  int traceonce= False, tracerestore= 0;
1752  vertexT *apex;
1753 #ifndef qh_NOtrace
1754  facetT *same;
1755 #endif
1756 
1757  if (newfacet->tricoplanar) {
1758  if (!qh->TRInormals) {
1759  qh_fprintf(qh, qh->ferr, 6224, "Qhull internal error (qh_mergecycle): does not work for tricoplanar facets. Use option 'Q11'\n");
1760  qh_errexit(qh, qh_ERRqhull, newfacet, NULL);
1761  }
1762  newfacet->tricoplanar= False;
1763  newfacet->keepcentrum= False;
1764  }
1765  if (!qh->VERTEXneighbors)
1766  qh_vertexneighbors(qh);
1767  zzinc_(Ztotmerge);
1768  if (qh->REPORTfreq2 && qh->POSTmerging) {
1769  if (zzval_(Ztotmerge) > qh->mergereport + qh->REPORTfreq2)
1770  qh_tracemerging(qh);
1771  }
1772 #ifndef qh_NOtrace
1773  if (qh->TRACEmerge == zzval_(Ztotmerge))
1774  qh->qhmem.IStracing= qh->IStracing= qh->TRACElevel;
1775  trace2((qh, qh->ferr, 2030, "qh_mergecycle: merge #%d for facets from cycle f%d into coplanar horizon f%d\n",
1776  zzval_(Ztotmerge), samecycle->id, newfacet->id));
1777  if (newfacet == qh->tracefacet) {
1778  tracerestore= qh->IStracing;
1779  qh->IStracing= 4;
1780  qh_fprintf(qh, qh->ferr, 8068, "qh_mergecycle: ========= trace merge %d of samecycle %d into trace f%d, furthest is p%d\n",
1781  zzval_(Ztotmerge), samecycle->id, newfacet->id, qh->furthest_id);
1782  traceonce= True;
1783  }
1784  if (qh->IStracing >=4) {
1785  qh_fprintf(qh, qh->ferr, 8069, " same cycle:");
1786  FORALLsame_cycle_(samecycle)
1787  qh_fprintf(qh, qh->ferr, 8070, " f%d", same->id);
1788  qh_fprintf(qh, qh->ferr, 8071, "\n");
1789  }
1790  if (qh->IStracing >=4)
1791  qh_errprint(qh, "MERGING CYCLE", samecycle, newfacet, NULL, NULL);
1792 #endif /* !qh_NOtrace */
1793  apex= SETfirstt_(samecycle->vertices, vertexT);
1794  qh_makeridges(qh, newfacet);
1795  qh_mergecycle_neighbors(qh, samecycle, newfacet);
1796  qh_mergecycle_ridges(qh, samecycle, newfacet);
1797  qh_mergecycle_vneighbors(qh, samecycle, newfacet);
1798  if (SETfirstt_(newfacet->vertices, vertexT) != apex)
1799  qh_setaddnth(qh, &newfacet->vertices, 0, apex); /* apex has last id */
1800  if (!newfacet->newfacet)
1801  qh_newvertices(qh, newfacet->vertices);
1802  qh_mergecycle_facets(qh, samecycle, newfacet);
1803  qh_tracemerge(qh, samecycle, newfacet);
1804  /* check for degen_redundant_neighbors after qh_forcedmerges() */
1805  if (traceonce) {
1806  qh_fprintf(qh, qh->ferr, 8072, "qh_mergecycle: end of trace facet\n");
1807  qh->IStracing= tracerestore;
1808  }
1809 } /* mergecycle */
1810 
1811 /*-<a href="qh-merge_r.htm#TOC"
1812  >-------------------------------</a><a name="mergecycle_all">-</a>
1813 
1814  qh_mergecycle_all(qh, facetlist, wasmerge )
1815  merge all samecycles of coplanar facets into horizon
1816  don't merge facets with ->mergeridge (these already have ->normal)
1817  all facets are simplicial from apex
1818  all facet->cycledone == False
1819 
1820  returns:
1821  all newfacets merged into coplanar horizon facets
1822  deleted vertices on qh.del_vertices
1823  sets wasmerge if any merge
1824 
1825  see:
1826  calls qh_mergecycle for multiple, same cycle facets
1827 
1828  design:
1829  for each facet on facetlist
1830  skip facets with duplicate ridges and normals
1831  check that facet is in a samecycle (->mergehorizon)
1832  if facet only member of samecycle
1833  sets vertex->delridge for all vertices except apex
1834  merge facet into horizon
1835  else
1836  mark all facets in samecycle
1837  remove facets with duplicate ridges from samecycle
1838  merge samecycle into horizon (deletes facets from facetlist)
1839 */
1840 void qh_mergecycle_all(qhT *qh, facetT *facetlist, boolT *wasmerge) {
1841  facetT *facet, *same, *prev, *horizon;
1842  facetT *samecycle= NULL, *nextfacet, *nextsame;
1843  vertexT *apex, *vertex, **vertexp;
1844  int cycles=0, total=0, facets, nummerge;
1845 
1846  trace2((qh, qh->ferr, 2031, "qh_mergecycle_all: begin\n"));
1847  for (facet= facetlist; facet && (nextfacet= facet->next); facet= nextfacet) {
1848  if (facet->normal)
1849  continue;
1850  if (!facet->mergehorizon) {
1851  qh_fprintf(qh, qh->ferr, 6225, "Qhull internal error (qh_mergecycle_all): f%d without normal\n", facet->id);
1852  qh_errexit(qh, qh_ERRqhull, facet, NULL);
1853  }
1854  horizon= SETfirstt_(facet->neighbors, facetT);
1855  if (facet->f.samecycle == facet) {
1856  zinc_(Zonehorizon);
1857  /* merge distance done in qh_findhorizon */
1858  apex= SETfirstt_(facet->vertices, vertexT);
1859  FOREACHvertex_(facet->vertices) {
1860  if (vertex != apex)
1861  vertex->delridge= True;
1862  }
1863  horizon->f.newcycle= NULL;
1864  qh_mergefacet(qh, facet, horizon, NULL, NULL, qh_MERGEapex);
1865  }else {
1866  samecycle= facet;
1867  facets= 0;
1868  prev= facet;
1869  for (same= facet->f.samecycle; same; /* FORALLsame_cycle_(facet) */
1870  same= (same == facet ? NULL :nextsame)) { /* ends at facet */
1871  nextsame= same->f.samecycle;
1872  if (same->cycledone || same->visible)
1873  qh_infiniteloop(qh, same);
1874  same->cycledone= True;
1875  if (same->normal) {
1876  prev->f.samecycle= same->f.samecycle; /* unlink ->mergeridge */
1877  same->f.samecycle= NULL;
1878  }else {
1879  prev= same;
1880  facets++;
1881  }
1882  }
1883  while (nextfacet && nextfacet->cycledone) /* will delete samecycle */
1884  nextfacet= nextfacet->next;
1885  horizon->f.newcycle= NULL;
1886  qh_mergecycle(qh, samecycle, horizon);
1887  nummerge= horizon->nummerge + facets;
1888  if (nummerge > qh_MAXnummerge)
1889  horizon->nummerge= qh_MAXnummerge;
1890  else
1891  horizon->nummerge= (short unsigned int)nummerge;
1892  zzinc_(Zcyclehorizon);
1893  total += facets;
1894  zzadd_(Zcyclefacettot, facets);
1895  zmax_(Zcyclefacetmax, facets);
1896  }
1897  cycles++;
1898  }
1899  if (cycles)
1900  *wasmerge= True;
1901  trace1((qh, qh->ferr, 1013, "qh_mergecycle_all: merged %d same cycles or facets into coplanar horizons\n", cycles));
1902 } /* mergecycle_all */
1903 
1904 /*-<a href="qh-merge_r.htm#TOC"
1905  >-------------------------------</a><a name="mergecycle_facets">-</a>
1906 
1907  qh_mergecycle_facets(qh, samecycle, newfacet )
1908  finish merge of samecycle into newfacet
1909 
1910  returns:
1911  samecycle prepended to visible_list for later deletion and partitioning
1912  each facet->f.replace == newfacet
1913 
1914  newfacet moved to end of qh.facet_list
1915  makes newfacet a newfacet (get's facet1->id if it was old)
1916  sets newfacet->newmerge
1917  clears newfacet->center (unless merging into a large facet)
1918  clears newfacet->tested and ridge->tested for facet1
1919 
1920  adds neighboring facets to facet_mergeset if redundant or degenerate
1921 
1922  design:
1923  make newfacet a new facet and set its flags
1924  move samecycle facets to qh.visible_list for later deletion
1925  unless newfacet is large
1926  remove its centrum
1927 */
1928 void qh_mergecycle_facets(qhT *qh, facetT *samecycle, facetT *newfacet) {
1929  facetT *same, *next;
1930 
1931  trace4((qh, qh->ferr, 4030, "qh_mergecycle_facets: make newfacet new and samecycle deleted\n"));
1932  qh_removefacet(qh, newfacet); /* append as a newfacet to end of qh->facet_list */
1933  qh_appendfacet(qh, newfacet);
1934  newfacet->newfacet= True;
1935  newfacet->simplicial= False;
1936  newfacet->newmerge= True;
1937 
1938  for (same= samecycle->f.samecycle; same; same= (same == samecycle ? NULL : next)) {
1939  next= same->f.samecycle; /* reused by willdelete */
1940  qh_willdelete(qh, same, newfacet);
1941  }
1942  if (newfacet->center
1943  && qh_setsize(qh, newfacet->vertices) <= qh->hull_dim + qh_MAXnewcentrum) {
1944  qh_memfree(qh, newfacet->center, qh->normal_size);
1945  newfacet->center= NULL;
1946  }
1947  trace3((qh, qh->ferr, 3004, "qh_mergecycle_facets: merged facets from cycle f%d into f%d\n",
1948  samecycle->id, newfacet->id));
1949 } /* mergecycle_facets */
1950 
1951 /*-<a href="qh-merge_r.htm#TOC"
1952  >-------------------------------</a><a name="mergecycle_neighbors">-</a>
1953 
1954  qh_mergecycle_neighbors(qh, samecycle, newfacet )
1955  add neighbors for samecycle facets to newfacet
1956 
1957  returns:
1958  newfacet with updated neighbors and vice-versa
1959  newfacet has ridges
1960  all neighbors of newfacet marked with qh.visit_id
1961  samecycle facets marked with qh.visit_id-1
1962  ridges updated for simplicial neighbors of samecycle with a ridge
1963 
1964  notes:
1965  assumes newfacet not in samecycle
1966  usually, samecycle facets are new, simplicial facets without internal ridges
1967  not so if horizon facet is coplanar to two different samecycles
1968 
1969  see:
1970  qh_mergeneighbors()
1971 
1972  design:
1973  check samecycle
1974  delete neighbors from newfacet that are also in samecycle
1975  for each neighbor of a facet in samecycle
1976  if neighbor is simplicial
1977  if first visit
1978  move the neighbor relation to newfacet
1979  update facet links for its ridges
1980  else
1981  make ridges for neighbor
1982  remove samecycle reference
1983  else
1984  update neighbor sets
1985 */
1986 void qh_mergecycle_neighbors(qhT *qh, facetT *samecycle, facetT *newfacet) {
1987  facetT *same, *neighbor, **neighborp;
1988  int delneighbors= 0, newneighbors= 0;
1989  unsigned int samevisitid;
1990  ridgeT *ridge, **ridgep;
1991 
1992  samevisitid= ++qh->visit_id;
1993  FORALLsame_cycle_(samecycle) {
1994  if (same->visitid == samevisitid || same->visible)
1995  qh_infiniteloop(qh, samecycle);
1996  same->visitid= samevisitid;
1997  }
1998  newfacet->visitid= ++qh->visit_id;
1999  trace4((qh, qh->ferr, 4031, "qh_mergecycle_neighbors: delete shared neighbors from newfacet\n"));
2000  FOREACHneighbor_(newfacet) {
2001  if (neighbor->visitid == samevisitid) {
2002  SETref_(neighbor)= NULL; /* samecycle neighbors deleted */
2003  delneighbors++;
2004  }else
2005  neighbor->visitid= qh->visit_id;
2006  }
2007  qh_setcompact(qh, newfacet->neighbors);
2008 
2009  trace4((qh, qh->ferr, 4032, "qh_mergecycle_neighbors: update neighbors\n"));
2010  FORALLsame_cycle_(samecycle) {
2011  FOREACHneighbor_(same) {
2012  if (neighbor->visitid == samevisitid)
2013  continue;
2014  if (neighbor->simplicial) {
2015  if (neighbor->visitid != qh->visit_id) {
2016  qh_setappend(qh, &newfacet->neighbors, neighbor);
2017  qh_setreplace(qh, neighbor->neighbors, same, newfacet);
2018  newneighbors++;
2019  neighbor->visitid= qh->visit_id;
2020  FOREACHridge_(neighbor->ridges) { /* update ridge in case of qh_makeridges */
2021  if (ridge->top == same) {
2022  ridge->top= newfacet;
2023  break;
2024  }else if (ridge->bottom == same) {
2025  ridge->bottom= newfacet;
2026  break;
2027  }
2028  }
2029  }else {
2030  qh_makeridges(qh, neighbor);
2031  qh_setdel(neighbor->neighbors, same);
2032  /* same can't be horizon facet for neighbor */
2033  }
2034  }else { /* non-simplicial neighbor */
2035  qh_setdel(neighbor->neighbors, same);
2036  if (neighbor->visitid != qh->visit_id) {
2037  qh_setappend(qh, &neighbor->neighbors, newfacet);
2038  qh_setappend(qh, &newfacet->neighbors, neighbor);
2039  neighbor->visitid= qh->visit_id;
2040  newneighbors++;
2041  }
2042  }
2043  }
2044  }
2045  trace2((qh, qh->ferr, 2032, "qh_mergecycle_neighbors: deleted %d neighbors and added %d\n",
2046  delneighbors, newneighbors));
2047 } /* mergecycle_neighbors */
2048 
2049 /*-<a href="qh-merge_r.htm#TOC"
2050  >-------------------------------</a><a name="mergecycle_ridges">-</a>
2051 
2052  qh_mergecycle_ridges(qh, samecycle, newfacet )
2053  add ridges/neighbors for facets in samecycle to newfacet
2054  all new/old neighbors of newfacet marked with qh.visit_id
2055  facets in samecycle marked with qh.visit_id-1
2056  newfacet marked with qh.visit_id
2057 
2058  returns:
2059  newfacet has merged ridges
2060 
2061  notes:
2062  ridge already updated for simplicial neighbors of samecycle with a ridge
2063 
2064  see:
2065  qh_mergeridges()
2066  qh_makeridges()
2067 
2068  design:
2069  remove ridges between newfacet and samecycle
2070  for each facet in samecycle
2071  for each ridge in facet
2072  update facet pointers in ridge
2073  skip ridges processed in qh_mergecycle_neighors
2074  free ridges between newfacet and samecycle
2075  free ridges between facets of samecycle (on 2nd visit)
2076  append remaining ridges to newfacet
2077  if simpilicial facet
2078  for each neighbor of facet
2079  if simplicial facet
2080  and not samecycle facet or newfacet
2081  make ridge between neighbor and newfacet
2082 */
2083 void qh_mergecycle_ridges(qhT *qh, facetT *samecycle, facetT *newfacet) {
2084  facetT *same, *neighbor= NULL;
2085  int numold=0, numnew=0;
2086  int neighbor_i, neighbor_n;
2087  unsigned int samevisitid;
2088  ridgeT *ridge, **ridgep;
2089  boolT toporient;
2090  void **freelistp; /* used if !qh_NOmem by qh_memfree_() */
2091 
2092  trace4((qh, qh->ferr, 4033, "qh_mergecycle_ridges: delete shared ridges from newfacet\n"));
2093  samevisitid= qh->visit_id -1;
2094  FOREACHridge_(newfacet->ridges) {
2095  neighbor= otherfacet_(ridge, newfacet);
2096  if (neighbor->visitid == samevisitid)
2097  SETref_(ridge)= NULL; /* ridge free'd below */
2098  }
2099  qh_setcompact(qh, newfacet->ridges);
2100 
2101  trace4((qh, qh->ferr, 4034, "qh_mergecycle_ridges: add ridges to newfacet\n"));
2102  FORALLsame_cycle_(samecycle) {
2103  FOREACHridge_(same->ridges) {
2104  if (ridge->top == same) {
2105  ridge->top= newfacet;
2106  neighbor= ridge->bottom;
2107  }else if (ridge->bottom == same) {
2108  ridge->bottom= newfacet;
2109  neighbor= ridge->top;
2110  }else if (ridge->top == newfacet || ridge->bottom == newfacet) {
2111  qh_setappend(qh, &newfacet->ridges, ridge);
2112  numold++; /* already set by qh_mergecycle_neighbors */
2113  continue;
2114  }else {
2115  qh_fprintf(qh, qh->ferr, 6098, "qhull internal error (qh_mergecycle_ridges): bad ridge r%d\n", ridge->id);
2116  qh_errexit(qh, qh_ERRqhull, NULL, ridge);
2117  }
2118  if (neighbor == newfacet) {
2119  qh_setfree(qh, &(ridge->vertices));
2120  qh_memfree_(qh, ridge, (int)sizeof(ridgeT), freelistp);
2121  numold++;
2122  }else if (neighbor->visitid == samevisitid) {
2123  qh_setdel(neighbor->ridges, ridge);
2124  qh_setfree(qh, &(ridge->vertices));
2125  qh_memfree_(qh, ridge, (int)sizeof(ridgeT), freelistp);
2126  numold++;
2127  }else {
2128  qh_setappend(qh, &newfacet->ridges, ridge);
2129  numold++;
2130  }
2131  }
2132  if (same->ridges)
2133  qh_settruncate(qh, same->ridges, 0);
2134  if (!same->simplicial)
2135  continue;
2136  FOREACHneighbor_i_(qh, same) { /* note: !newfact->simplicial */
2137  if (neighbor->visitid != samevisitid && neighbor->simplicial) {
2138  ridge= qh_newridge(qh);
2139  ridge->vertices= qh_setnew_delnthsorted(qh, same->vertices, qh->hull_dim,
2140  neighbor_i, 0);
2141  toporient= same->toporient ^ (neighbor_i & 0x1);
2142  if (toporient) {
2143  ridge->top= newfacet;
2144  ridge->bottom= neighbor;
2145  }else {
2146  ridge->top= neighbor;
2147  ridge->bottom= newfacet;
2148  }
2149  qh_setappend(qh, &(newfacet->ridges), ridge);
2150  qh_setappend(qh, &(neighbor->ridges), ridge);
2151  numnew++;
2152  }
2153  }
2154  }
2155 
2156  trace2((qh, qh->ferr, 2033, "qh_mergecycle_ridges: found %d old ridges and %d new ones\n",
2157  numold, numnew));
2158 } /* mergecycle_ridges */
2159 
2160 /*-<a href="qh-merge_r.htm#TOC"
2161  >-------------------------------</a><a name="mergecycle_vneighbors">-</a>
2162 
2163  qh_mergecycle_vneighbors(qh, samecycle, newfacet )
2164  create vertex neighbors for newfacet from vertices of facets in samecycle
2165  samecycle marked with visitid == qh.visit_id - 1
2166 
2167  returns:
2168  newfacet vertices with updated neighbors
2169  marks newfacet with qh.visit_id-1
2170  deletes vertices that are merged away
2171  sets delridge on all vertices (faster here than in mergecycle_ridges)
2172 
2173  see:
2174  qh_mergevertex_neighbors()
2175 
2176  design:
2177  for each vertex of samecycle facet
2178  set vertex->delridge
2179  delete samecycle facets from vertex neighbors
2180  append newfacet to vertex neighbors
2181  if vertex only in newfacet
2182  delete it from newfacet
2183  add it to qh.del_vertices for later deletion
2184 */
2185 void qh_mergecycle_vneighbors(qhT *qh, facetT *samecycle, facetT *newfacet) {
2186  facetT *neighbor, **neighborp;
2187  unsigned int mergeid;
2188  vertexT *vertex, **vertexp, *apex;
2189  setT *vertices;
2190 
2191  trace4((qh, qh->ferr, 4035, "qh_mergecycle_vneighbors: update vertex neighbors for newfacet\n"));
2192  mergeid= qh->visit_id - 1;
2193  newfacet->visitid= mergeid;
2194  vertices= qh_basevertices(qh, samecycle); /* temp */
2195  apex= SETfirstt_(samecycle->vertices, vertexT);
2196  qh_setappend(qh, &vertices, apex);
2197  FOREACHvertex_(vertices) {
2198  vertex->delridge= True;
2199  FOREACHneighbor_(vertex) {
2200  if (neighbor->visitid == mergeid)
2201  SETref_(neighbor)= NULL;
2202  }
2203  qh_setcompact(qh, vertex->neighbors);
2204  qh_setappend(qh, &vertex->neighbors, newfacet);
2205  if (!SETsecond_(vertex->neighbors)) {
2206  zinc_(Zcyclevertex);
2207  trace2((qh, qh->ferr, 2034, "qh_mergecycle_vneighbors: deleted v%d when merging cycle f%d into f%d\n",
2208  vertex->id, samecycle->id, newfacet->id));
2209  qh_setdelsorted(newfacet->vertices, vertex);
2210  vertex->deleted= True;
2211  qh_setappend(qh, &qh->del_vertices, vertex);
2212  }
2213  }
2214  qh_settempfree(qh, &vertices);
2215  trace3((qh, qh->ferr, 3005, "qh_mergecycle_vneighbors: merged vertices from cycle f%d into f%d\n",
2216  samecycle->id, newfacet->id));
2217 } /* mergecycle_vneighbors */
2218 
2219 /*-<a href="qh-merge_r.htm#TOC"
2220  >-------------------------------</a><a name="mergefacet">-</a>
2221 
2222  qh_mergefacet(qh, facet1, facet2, mindist, maxdist, mergeapex )
2223  merges facet1 into facet2
2224  mergeapex==qh_MERGEapex if merging new facet into coplanar horizon
2225 
2226  returns:
2227  qh.max_outside and qh.min_vertex updated
2228  initializes vertex neighbors on first merge
2229 
2230  returns:
2231  facet2 contains facet1's vertices, neighbors, and ridges
2232  facet2 moved to end of qh.facet_list
2233  makes facet2 a newfacet
2234  sets facet2->newmerge set
2235  clears facet2->center (unless merging into a large facet)
2236  clears facet2->tested and ridge->tested for facet1
2237 
2238  facet1 prepended to visible_list for later deletion and partitioning
2239  facet1->f.replace == facet2
2240 
2241  adds neighboring facets to facet_mergeset if redundant or degenerate
2242 
2243  notes:
2244  mindist/maxdist may be NULL (only if both NULL)
2245  traces merge if fmax_(maxdist,-mindist) > TRACEdist
2246 
2247  see:
2248  qh_mergecycle()
2249 
2250  design:
2251  trace merge and check for degenerate simplex
2252  make ridges for both facets
2253  update qh.max_outside, qh.max_vertex, qh.min_vertex
2254  update facet2->maxoutside and keepcentrum
2255  update facet2->nummerge
2256  update tested flags for facet2
2257  if facet1 is simplicial
2258  merge facet1 into facet2
2259  else
2260  merge facet1's neighbors into facet2
2261  merge facet1's ridges into facet2
2262  merge facet1's vertices into facet2
2263  merge facet1's vertex neighbors into facet2
2264  add facet2's vertices to qh.new_vertexlist
2265  unless qh_MERGEapex
2266  test facet2 for degenerate or redundant neighbors
2267  move facet1 to qh.visible_list for later deletion
2268  move facet2 to end of qh.newfacet_list
2269 */
2270 void qh_mergefacet(qhT *qh, facetT *facet1, facetT *facet2, realT *mindist, realT *maxdist, boolT mergeapex) {
2271  boolT traceonce= False;
2272  vertexT *vertex, **vertexp;
2273  int tracerestore=0, nummerge;
2274 
2275  if (facet1->tricoplanar || facet2->tricoplanar) {
2276  if (!qh->TRInormals) {
2277  qh_fprintf(qh, qh->ferr, 6226, "Qhull internal error (qh_mergefacet): does not work for tricoplanar facets. Use option 'Q11'\n");
2278  qh_errexit2(qh, qh_ERRqhull, facet1, facet2);
2279  }
2280  if (facet2->tricoplanar) {
2281  facet2->tricoplanar= False;
2282  facet2->keepcentrum= False;
2283  }
2284  }
2285  zzinc_(Ztotmerge);
2286  if (qh->REPORTfreq2 && qh->POSTmerging) {
2287  if (zzval_(Ztotmerge) > qh->mergereport + qh->REPORTfreq2)
2288  qh_tracemerging(qh);
2289  }
2290 #ifndef qh_NOtrace
2291  if (qh->build_cnt >= qh->RERUN) {
2292  if (mindist && (-*mindist > qh->TRACEdist || *maxdist > qh->TRACEdist)) {
2293  tracerestore= 0;
2294  qh->IStracing= qh->TRACElevel;
2295  traceonce= True;
2296  qh_fprintf(qh, qh->ferr, 8075, "qh_mergefacet: ========= trace wide merge #%d(%2.2g) for f%d into f%d, last point was p%d\n", zzval_(Ztotmerge),
2297  fmax_(-*mindist, *maxdist), facet1->id, facet2->id, qh->furthest_id);
2298  }else if (facet1 == qh->tracefacet || facet2 == qh->tracefacet) {
2299  tracerestore= qh->IStracing;
2300  qh->IStracing= 4;
2301  traceonce= True;
2302  qh_fprintf(qh, qh->ferr, 8076, "qh_mergefacet: ========= trace merge #%d involving f%d, furthest is p%d\n",
2303  zzval_(Ztotmerge), qh->tracefacet_id, qh->furthest_id);
2304  }
2305  }
2306  if (qh->IStracing >= 2) {
2307  realT mergemin= -2;
2308  realT mergemax= -2;
2309 
2310  if (mindist) {
2311  mergemin= *mindist;
2312  mergemax= *maxdist;
2313  }
2314  qh_fprintf(qh, qh->ferr, 8077, "qh_mergefacet: #%d merge f%d into f%d, mindist= %2.2g, maxdist= %2.2g\n",
2315  zzval_(Ztotmerge), facet1->id, facet2->id, mergemin, mergemax);
2316  }
2317 #endif /* !qh_NOtrace */
2318  if (facet1 == facet2 || facet1->visible || facet2->visible) {
2319  qh_fprintf(qh, qh->ferr, 6099, "qhull internal error (qh_mergefacet): either f%d and f%d are the same or one is a visible facet\n",
2320  facet1->id, facet2->id);
2321  qh_errexit2(qh, qh_ERRqhull, facet1, facet2);
2322  }
2323  if (qh->num_facets - qh->num_visible <= qh->hull_dim + 1) {
2324  qh_fprintf(qh, qh->ferr, 6227, "\n\
2325 qhull precision error: Only %d facets remain. Can not merge another\n\
2326 pair. The input is too degenerate or the convexity constraints are\n\
2327 too strong.\n", qh->hull_dim+1);
2328  if (qh->hull_dim >= 5 && !qh->MERGEexact)
2329  qh_fprintf(qh, qh->ferr, 8079, "Option 'Qx' may avoid this problem.\n");
2330  qh_errexit(qh, qh_ERRprec, NULL, NULL);
2331  }
2332  if (!qh->VERTEXneighbors)
2333  qh_vertexneighbors(qh);
2334  qh_makeridges(qh, facet1);
2335  qh_makeridges(qh, facet2);
2336  if (qh->IStracing >=4)
2337  qh_errprint(qh, "MERGING", facet1, facet2, NULL, NULL);
2338  if (mindist) {
2339  maximize_(qh->max_outside, *maxdist);
2340  maximize_(qh->max_vertex, *maxdist);
2341 #if qh_MAXoutside
2342  maximize_(facet2->maxoutside, *maxdist);
2343 #endif
2344  minimize_(qh->min_vertex, *mindist);
2345  if (!facet2->keepcentrum
2346  && (*maxdist > qh->WIDEfacet || *mindist < -qh->WIDEfacet)) {
2347  facet2->keepcentrum= True;
2348  zinc_(Zwidefacet);
2349  }
2350  }
2351  nummerge= facet1->nummerge + facet2->nummerge + 1;
2352  if (nummerge >= qh_MAXnummerge)
2353  facet2->nummerge= qh_MAXnummerge;
2354  else
2355  facet2->nummerge= (short unsigned int)nummerge;
2356  facet2->newmerge= True;
2357  facet2->dupridge= False;
2358  qh_updatetested(qh, facet1, facet2);
2359  if (qh->hull_dim > 2 && qh_setsize(qh, facet1->vertices) == qh->hull_dim)
2360  qh_mergesimplex(qh, facet1, facet2, mergeapex);
2361  else {
2362  qh->vertex_visit++;
2363  FOREACHvertex_(facet2->vertices)
2364  vertex->visitid= qh->vertex_visit;
2365  if (qh->hull_dim == 2)
2366  qh_mergefacet2d(qh, facet1, facet2);
2367  else {
2368  qh_mergeneighbors(qh, facet1, facet2);
2369  qh_mergevertices(qh, facet1->vertices, &facet2->vertices);
2370  }
2371  qh_mergeridges(qh, facet1, facet2);
2372  qh_mergevertex_neighbors(qh, facet1, facet2);
2373  if (!facet2->newfacet)
2374  qh_newvertices(qh, facet2->vertices);
2375  }
2376  if (!mergeapex)
2377  qh_degen_redundant_neighbors(qh, facet2, facet1);
2378  if (facet2->coplanar || !facet2->newfacet) {
2379  zinc_(Zmergeintohorizon);
2380  }else if (!facet1->newfacet && facet2->newfacet) {
2381  zinc_(Zmergehorizon);
2382  }else {
2383  zinc_(Zmergenew);
2384  }
2385  qh_willdelete(qh, facet1, facet2);
2386  qh_removefacet(qh, facet2); /* append as a newfacet to end of qh->facet_list */
2387  qh_appendfacet(qh, facet2);
2388  facet2->newfacet= True;
2389  facet2->tested= False;
2390  qh_tracemerge(qh, facet1, facet2);
2391  if (traceonce) {
2392  qh_fprintf(qh, qh->ferr, 8080, "qh_mergefacet: end of wide tracing\n");
2393  qh->IStracing= tracerestore;
2394  }
2395 } /* mergefacet */
2396 
2397 
2398 /*-<a href="qh-merge_r.htm#TOC"
2399  >-------------------------------</a><a name="mergefacet2d">-</a>
2400 
2401  qh_mergefacet2d(qh, facet1, facet2 )
2402  in 2d, merges neighbors and vertices of facet1 into facet2
2403 
2404  returns:
2405  build ridges for neighbors if necessary
2406  facet2 looks like a simplicial facet except for centrum, ridges
2407  neighbors are opposite the corresponding vertex
2408  maintains orientation of facet2
2409 
2410  notes:
2411  qh_mergefacet() retains non-simplicial structures
2412  they are not needed in 2d, but later routines may use them
2413  preserves qh.vertex_visit for qh_mergevertex_neighbors()
2414 
2415  design:
2416  get vertices and neighbors
2417  determine new vertices and neighbors
2418  set new vertices and neighbors and adjust orientation
2419  make ridges for new neighbor if needed
2420 */
2421 void qh_mergefacet2d(qhT *qh, facetT *facet1, facetT *facet2) {
2422  vertexT *vertex1A, *vertex1B, *vertex2A, *vertex2B, *vertexA, *vertexB;
2423  facetT *neighbor1A, *neighbor1B, *neighbor2A, *neighbor2B, *neighborA, *neighborB;
2424 
2425  vertex1A= SETfirstt_(facet1->vertices, vertexT);
2426  vertex1B= SETsecondt_(facet1->vertices, vertexT);
2427  vertex2A= SETfirstt_(facet2->vertices, vertexT);
2428  vertex2B= SETsecondt_(facet2->vertices, vertexT);
2429  neighbor1A= SETfirstt_(facet1->neighbors, facetT);
2430  neighbor1B= SETsecondt_(facet1->neighbors, facetT);
2431  neighbor2A= SETfirstt_(facet2->neighbors, facetT);
2432  neighbor2B= SETsecondt_(facet2->neighbors, facetT);
2433  if (vertex1A == vertex2A) {
2434  vertexA= vertex1B;
2435  vertexB= vertex2B;
2436  neighborA= neighbor2A;
2437  neighborB= neighbor1A;
2438  }else if (vertex1A == vertex2B) {
2439  vertexA= vertex1B;
2440  vertexB= vertex2A;
2441  neighborA= neighbor2B;
2442  neighborB= neighbor1A;
2443  }else if (vertex1B == vertex2A) {
2444  vertexA= vertex1A;
2445  vertexB= vertex2B;
2446  neighborA= neighbor2A;
2447  neighborB= neighbor1B;
2448  }else { /* 1B == 2B */
2449  vertexA= vertex1A;
2450  vertexB= vertex2A;
2451  neighborA= neighbor2B;
2452  neighborB= neighbor1B;
2453  }
2454  /* vertexB always from facet2, neighborB always from facet1 */
2455  if (vertexA->id > vertexB->id) {
2456  SETfirst_(facet2->vertices)= vertexA;
2457  SETsecond_(facet2->vertices)= vertexB;
2458  if (vertexB == vertex2A)
2459  facet2->toporient= !facet2->toporient;
2460  SETfirst_(facet2->neighbors)= neighborA;
2461  SETsecond_(facet2->neighbors)= neighborB;
2462  }else {
2463  SETfirst_(facet2->vertices)= vertexB;
2464  SETsecond_(facet2->vertices)= vertexA;
2465  if (vertexB == vertex2B)
2466  facet2->toporient= !facet2->toporient;
2467  SETfirst_(facet2->neighbors)= neighborB;
2468  SETsecond_(facet2->neighbors)= neighborA;
2469  }
2470  qh_makeridges(qh, neighborB);
2471  qh_setreplace(qh, neighborB->neighbors, facet1, facet2);
2472  trace4((qh, qh->ferr, 4036, "qh_mergefacet2d: merged v%d and neighbor f%d of f%d into f%d\n",
2473  vertexA->id, neighborB->id, facet1->id, facet2->id));
2474 } /* mergefacet2d */
2475 
2476 
2477 /*-<a href="qh-merge_r.htm#TOC"
2478  >-------------------------------</a><a name="mergeneighbors">-</a>
2479 
2480  qh_mergeneighbors(qh, facet1, facet2 )
2481  merges the neighbors of facet1 into facet2
2482 
2483  see:
2484  qh_mergecycle_neighbors()
2485 
2486  design:
2487  for each neighbor of facet1
2488  if neighbor is also a neighbor of facet2
2489  if neighbor is simpilicial
2490  make ridges for later deletion as a degenerate facet
2491  update its neighbor set
2492  else
2493  move the neighbor relation to facet2
2494  remove the neighbor relation for facet1 and facet2
2495 */
2496 void qh_mergeneighbors(qhT *qh, facetT *facet1, facetT *facet2) {
2497  facetT *neighbor, **neighborp;
2498 
2499  trace4((qh, qh->ferr, 4037, "qh_mergeneighbors: merge neighbors of f%d and f%d\n",
2500  facet1->id, facet2->id));
2501  qh->visit_id++;
2502  FOREACHneighbor_(facet2) {
2503  neighbor->visitid= qh->visit_id;
2504  }
2505  FOREACHneighbor_(facet1) {
2506  if (neighbor->visitid == qh->visit_id) {
2507  if (neighbor->simplicial) /* is degen, needs ridges */
2508  qh_makeridges(qh, neighbor);
2509  if (SETfirstt_(neighbor->neighbors, facetT) != facet1) /*keep newfacet->horizon*/
2510  qh_setdel(neighbor->neighbors, facet1);
2511  else {
2512  qh_setdel(neighbor->neighbors, facet2);
2513  qh_setreplace(qh, neighbor->neighbors, facet1, facet2);
2514  }
2515  }else if (neighbor != facet2) {
2516  qh_setappend(qh, &(facet2->neighbors), neighbor);
2517  qh_setreplace(qh, neighbor->neighbors, facet1, facet2);
2518  }
2519  }
2520  qh_setdel(facet1->neighbors, facet2); /* here for makeridges */
2521  qh_setdel(facet2->neighbors, facet1);
2522 } /* mergeneighbors */
2523 
2524 
2525 /*-<a href="qh-merge_r.htm#TOC"
2526  >-------------------------------</a><a name="mergeridges">-</a>
2527 
2528  qh_mergeridges(qh, facet1, facet2 )
2529  merges the ridge set of facet1 into facet2
2530 
2531  returns:
2532  may delete all ridges for a vertex
2533  sets vertex->delridge on deleted ridges
2534 
2535  see:
2536  qh_mergecycle_ridges()
2537 
2538  design:
2539  delete ridges between facet1 and facet2
2540  mark (delridge) vertices on these ridges for later testing
2541  for each remaining ridge
2542  rename facet1 to facet2
2543 */
2544 void qh_mergeridges(qhT *qh, facetT *facet1, facetT *facet2) {
2545  ridgeT *ridge, **ridgep;
2546  vertexT *vertex, **vertexp;
2547 
2548  trace4((qh, qh->ferr, 4038, "qh_mergeridges: merge ridges of f%d and f%d\n",
2549  facet1->id, facet2->id));
2550  FOREACHridge_(facet2->ridges) {
2551  if ((ridge->top == facet1) || (ridge->bottom == facet1)) {
2552  FOREACHvertex_(ridge->vertices)
2553  vertex->delridge= True;
2554  qh_delridge(qh, ridge); /* expensive in high-d, could rebuild */
2555  ridgep--; /*repeat*/
2556  }
2557  }
2558  FOREACHridge_(facet1->ridges) {
2559  if (ridge->top == facet1)
2560  ridge->top= facet2;
2561  else
2562  ridge->bottom= facet2;
2563  qh_setappend(qh, &(facet2->ridges), ridge);
2564  }
2565 } /* mergeridges */
2566 
2567 
2568 /*-<a href="qh-merge_r.htm#TOC"
2569  >-------------------------------</a><a name="mergesimplex">-</a>
2570 
2571  qh_mergesimplex(qh, facet1, facet2, mergeapex )
2572  merge simplicial facet1 into facet2
2573  mergeapex==qh_MERGEapex if merging samecycle into horizon facet
2574  vertex id is latest (most recently created)
2575  facet1 may be contained in facet2
2576  ridges exist for both facets
2577 
2578  returns:
2579  facet2 with updated vertices, ridges, neighbors
2580  updated neighbors for facet1's vertices
2581  facet1 not deleted
2582  sets vertex->delridge on deleted ridges
2583 
2584  notes:
2585  special case code since this is the most common merge
2586  called from qh_mergefacet()
2587 
2588  design:
2589  if qh_MERGEapex
2590  add vertices of facet2 to qh.new_vertexlist if necessary
2591  add apex to facet2
2592  else
2593  for each ridge between facet1 and facet2
2594  set vertex->delridge
2595  determine the apex for facet1 (i.e., vertex to be merged)
2596  unless apex already in facet2
2597  insert apex into vertices for facet2
2598  add vertices of facet2 to qh.new_vertexlist if necessary
2599  add apex to qh.new_vertexlist if necessary
2600  for each vertex of facet1
2601  if apex
2602  rename facet1 to facet2 in its vertex neighbors
2603  else
2604  delete facet1 from vertex neighors
2605  if only in facet2
2606  add vertex to qh.del_vertices for later deletion
2607  for each ridge of facet1
2608  delete ridges between facet1 and facet2
2609  append other ridges to facet2 after renaming facet to facet2
2610 */
2611 void qh_mergesimplex(qhT *qh, facetT *facet1, facetT *facet2, boolT mergeapex) {
2612  vertexT *vertex, **vertexp, *apex;
2613  ridgeT *ridge, **ridgep;
2614  boolT issubset= False;
2615  int vertex_i= -1, vertex_n;
2616  facetT *neighbor, **neighborp, *otherfacet;
2617 
2618  if (mergeapex) {
2619  if (!facet2->newfacet)
2620  qh_newvertices(qh, facet2->vertices); /* apex is new */
2621  apex= SETfirstt_(facet1->vertices, vertexT);
2622  if (SETfirstt_(facet2->vertices, vertexT) != apex)
2623  qh_setaddnth(qh, &facet2->vertices, 0, apex); /* apex has last id */
2624  else
2625  issubset= True;
2626  }else {
2627  zinc_(Zmergesimplex);
2628  FOREACHvertex_(facet1->vertices)
2629  vertex->seen= False;
2630  FOREACHridge_(facet1->ridges) {
2631  if (otherfacet_(ridge, facet1) == facet2) {
2632  FOREACHvertex_(ridge->vertices) {
2633  vertex->seen= True;
2634  vertex->delridge= True;
2635  }
2636  break;
2637  }
2638  }
2639  FOREACHvertex_(facet1->vertices) {
2640  if (!vertex->seen)
2641  break; /* must occur */
2642  }
2643  apex= vertex;
2644  trace4((qh, qh->ferr, 4039, "qh_mergesimplex: merge apex v%d of f%d into facet f%d\n",
2645  apex->id, facet1->id, facet2->id));
2646  FOREACHvertex_i_(qh, facet2->vertices) {
2647  if (vertex->id < apex->id) {
2648  break;
2649  }else if (vertex->id == apex->id) {
2650  issubset= True;
2651  break;
2652  }
2653  }
2654  if (!issubset)
2655  qh_setaddnth(qh, &facet2->vertices, vertex_i, apex);
2656  if (!facet2->newfacet)
2657  qh_newvertices(qh, facet2->vertices);
2658  else if (!apex->newlist) {
2659  qh_removevertex(qh, apex);
2660  qh_appendvertex(qh, apex);
2661  }
2662  }
2663  trace4((qh, qh->ferr, 4040, "qh_mergesimplex: update vertex neighbors of f%d\n",
2664  facet1->id));
2665  FOREACHvertex_(facet1->vertices) {
2666  if (vertex == apex && !issubset)
2667  qh_setreplace(qh, vertex->neighbors, facet1, facet2);
2668  else {
2669  qh_setdel(vertex->neighbors, facet1);
2670  if (!SETsecond_(vertex->neighbors))
2671  qh_mergevertex_del(qh, vertex, facet1, facet2);
2672  }
2673  }
2674  trace4((qh, qh->ferr, 4041, "qh_mergesimplex: merge ridges and neighbors of f%d into f%d\n",
2675  facet1->id, facet2->id));
2676  qh->visit_id++;
2677  FOREACHneighbor_(facet2)
2678  neighbor->visitid= qh->visit_id;
2679  FOREACHridge_(facet1->ridges) {
2680  otherfacet= otherfacet_(ridge, facet1);
2681  if (otherfacet == facet2) {
2682  qh_setdel(facet2->ridges, ridge);
2683  qh_setfree(qh, &(ridge->vertices));
2684  qh_memfree(qh, ridge, (int)sizeof(ridgeT));
2685  qh_setdel(facet2->neighbors, facet1);
2686  }else {
2687  qh_setappend(qh, &facet2->ridges, ridge);
2688  if (otherfacet->visitid != qh->visit_id) {
2689  qh_setappend(qh, &facet2->neighbors, otherfacet);
2690  qh_setreplace(qh, otherfacet->neighbors, facet1, facet2);
2691  otherfacet->visitid= qh->visit_id;
2692  }else {
2693  if (otherfacet->simplicial) /* is degen, needs ridges */
2694  qh_makeridges(qh, otherfacet);
2695  if (SETfirstt_(otherfacet->neighbors, facetT) != facet1)
2696  qh_setdel(otherfacet->neighbors, facet1);
2697  else { /*keep newfacet->neighbors->horizon*/
2698  qh_setdel(otherfacet->neighbors, facet2);
2699  qh_setreplace(qh, otherfacet->neighbors, facet1, facet2);
2700  }
2701  }
2702  if (ridge->top == facet1) /* wait until after qh_makeridges */
2703  ridge->top= facet2;
2704  else
2705  ridge->bottom= facet2;
2706  }
2707  }
2708  SETfirst_(facet1->ridges)= NULL; /* it will be deleted */
2709  trace3((qh, qh->ferr, 3006, "qh_mergesimplex: merged simplex f%d apex v%d into facet f%d\n",
2710  facet1->id, getid_(apex), facet2->id));
2711 } /* mergesimplex */
2712 
2713 /*-<a href="qh-merge_r.htm#TOC"
2714  >-------------------------------</a><a name="mergevertex_del">-</a>
2715 
2716  qh_mergevertex_del(qh, vertex, facet1, facet2 )
2717  delete a vertex because of merging facet1 into facet2
2718 
2719  returns:
2720  deletes vertex from facet2
2721  adds vertex to qh.del_vertices for later deletion
2722 */
2723 void qh_mergevertex_del(qhT *qh, vertexT *vertex, facetT *facet1, facetT *facet2) {
2724 
2725  zinc_(Zmergevertex);
2726  trace2((qh, qh->ferr, 2035, "qh_mergevertex_del: deleted v%d when merging f%d into f%d\n",
2727  vertex->id, facet1->id, facet2->id));
2728  qh_setdelsorted(facet2->vertices, vertex);
2729  vertex->deleted= True;
2730  qh_setappend(qh, &qh->del_vertices, vertex);
2731 } /* mergevertex_del */
2732 
2733 /*-<a href="qh-merge_r.htm#TOC"
2734  >-------------------------------</a><a name="mergevertex_neighbors">-</a>
2735 
2736  qh_mergevertex_neighbors(qh, facet1, facet2 )
2737  merge the vertex neighbors of facet1 to facet2
2738 
2739  returns:
2740  if vertex is current qh.vertex_visit
2741  deletes facet1 from vertex->neighbors
2742  else
2743  renames facet1 to facet2 in vertex->neighbors
2744  deletes vertices if only one neighbor
2745 
2746  notes:
2747  assumes vertex neighbor sets are good
2748 */
2749 void qh_mergevertex_neighbors(qhT *qh, facetT *facet1, facetT *facet2) {
2750  vertexT *vertex, **vertexp;
2751 
2752  trace4((qh, qh->ferr, 4042, "qh_mergevertex_neighbors: merge vertex neighbors of f%d and f%d\n",
2753  facet1->id, facet2->id));
2754  if (qh->tracevertex) {
2755  qh_fprintf(qh, qh->ferr, 8081, "qh_mergevertex_neighbors: of f%d and f%d at furthest p%d f0= %p\n",
2756  facet1->id, facet2->id, qh->furthest_id, qh->tracevertex->neighbors->e[0].p);
2757  qh_errprint(qh, "TRACE", NULL, NULL, NULL, qh->tracevertex);
2758  }
2759  FOREACHvertex_(facet1->vertices) {
2760  if (vertex->visitid != qh->vertex_visit)
2761  qh_setreplace(qh, vertex->neighbors, facet1, facet2);
2762  else {
2763  qh_setdel(vertex->neighbors, facet1);
2764  if (!SETsecond_(vertex->neighbors))
2765  qh_mergevertex_del(qh, vertex, facet1, facet2);
2766  }
2767  }
2768  if (qh->tracevertex)
2769  qh_errprint(qh, "TRACE", NULL, NULL, NULL, qh->tracevertex);
2770 } /* mergevertex_neighbors */
2771 
2772 
2773 /*-<a href="qh-merge_r.htm#TOC"
2774  >-------------------------------</a><a name="mergevertices">-</a>
2775 
2776  qh_mergevertices(qh, vertices1, vertices2 )
2777  merges the vertex set of facet1 into facet2
2778 
2779  returns:
2780  replaces vertices2 with merged set
2781  preserves vertex_visit for qh_mergevertex_neighbors
2782  updates qh.newvertex_list
2783 
2784  design:
2785  create a merged set of both vertices (in inverse id order)
2786 */
2787 void qh_mergevertices(qhT *qh, setT *vertices1, setT **vertices2) {
2788  int newsize= qh_setsize(qh, vertices1)+qh_setsize(qh, *vertices2) - qh->hull_dim + 1;
2789  setT *mergedvertices;
2790  vertexT *vertex, **vertexp, **vertex2= SETaddr_(*vertices2, vertexT);
2791 
2792  mergedvertices= qh_settemp(qh, newsize);
2793  FOREACHvertex_(vertices1) {
2794  if (!*vertex2 || vertex->id > (*vertex2)->id)
2795  qh_setappend(qh, &mergedvertices, vertex);
2796  else {
2797  while (*vertex2 && (*vertex2)->id > vertex->id)
2798  qh_setappend(qh, &mergedvertices, *vertex2++);
2799  if (!*vertex2 || (*vertex2)->id < vertex->id)
2800  qh_setappend(qh, &mergedvertices, vertex);
2801  else
2802  qh_setappend(qh, &mergedvertices, *vertex2++);
2803  }
2804  }
2805  while (*vertex2)
2806  qh_setappend(qh, &mergedvertices, *vertex2++);
2807  if (newsize < qh_setsize(qh, mergedvertices)) {
2808  qh_fprintf(qh, qh->ferr, 6100, "qhull internal error (qh_mergevertices): facets did not share a ridge\n");
2809  qh_errexit(qh, qh_ERRqhull, NULL, NULL);
2810  }
2811  qh_setfree(qh, vertices2);
2812  *vertices2= mergedvertices;
2813  qh_settemppop(qh);
2814 } /* mergevertices */
2815 
2816 
2817 /*-<a href="qh-merge_r.htm#TOC"
2818  >-------------------------------</a><a name="neighbor_intersections">-</a>
2819 
2820  qh_neighbor_intersections(qh, vertex )
2821  return intersection of all vertices in vertex->neighbors except for vertex
2822 
2823  returns:
2824  returns temporary set of vertices
2825  does not include vertex
2826  NULL if a neighbor is simplicial
2827  NULL if empty set
2828 
2829  notes:
2830  used for renaming vertices
2831 
2832  design:
2833  initialize the intersection set with vertices of the first two neighbors
2834  delete vertex from the intersection
2835  for each remaining neighbor
2836  intersect its vertex set with the intersection set
2837  return NULL if empty
2838  return the intersection set
2839 */
2840 setT *qh_neighbor_intersections(qhT *qh, vertexT *vertex) {
2841  facetT *neighbor, **neighborp, *neighborA, *neighborB;
2842  setT *intersect;
2843  int neighbor_i, neighbor_n;
2844 
2845  FOREACHneighbor_(vertex) {
2846  if (neighbor->simplicial)
2847  return NULL;
2848  }
2849  neighborA= SETfirstt_(vertex->neighbors, facetT);
2850  neighborB= SETsecondt_(vertex->neighbors, facetT);
2851  zinc_(Zintersectnum);
2852  if (!neighborA)
2853  return NULL;
2854  if (!neighborB)
2855  intersect= qh_setcopy(qh, neighborA->vertices, 0);
2856  else
2857  intersect= qh_vertexintersect_new(qh, neighborA->vertices, neighborB->vertices);
2858  qh_settemppush(qh, intersect);
2859  qh_setdelsorted(intersect, vertex);
2860  FOREACHneighbor_i_(qh, vertex) {
2861  if (neighbor_i >= 2) {
2862  zinc_(Zintersectnum);
2863  qh_vertexintersect(qh, &intersect, neighbor->vertices);
2864  if (!SETfirst_(intersect)) {
2865  zinc_(Zintersectfail);
2866  qh_settempfree(qh, &intersect);
2867  return NULL;
2868  }
2869  }
2870  }
2871  trace3((qh, qh->ferr, 3007, "qh_neighbor_intersections: %d vertices in neighbor intersection of v%d\n",
2872  qh_setsize(qh, intersect), vertex->id));
2873  return intersect;
2874 } /* neighbor_intersections */
2875 
2876 /*-<a href="qh-merge_r.htm#TOC"
2877  >-------------------------------</a><a name="newvertices">-</a>
2878 
2879  qh_newvertices(qh, vertices )
2880  add vertices to end of qh.vertex_list (marks as new vertices)
2881 
2882  returns:
2883  vertices on qh.newvertex_list
2884  vertex->newlist set
2885 */
2886 void qh_newvertices(qhT *qh, setT *vertices) {
2887  vertexT *vertex, **vertexp;
2888 
2889  FOREACHvertex_(vertices) {
2890  if (!vertex->newlist) {
2891  qh_removevertex(qh, vertex);
2892  qh_appendvertex(qh, vertex);
2893  }
2894  }
2895 } /* newvertices */
2896 
2897 /*-<a href="qh-merge_r.htm#TOC"
2898  >-------------------------------</a><a name="reducevertices">-</a>
2899 
2900  qh_reducevertices(qh)
2901  reduce extra vertices, shared vertices, and redundant vertices
2902  facet->newmerge is set if merged since last call
2903  if !qh.MERGEvertices, only removes extra vertices
2904 
2905  returns:
2906  True if also merged degen_redundant facets
2907  vertices are renamed if possible
2908  clears facet->newmerge and vertex->delridge
2909 
2910  notes:
2911  ignored if 2-d
2912 
2913  design:
2914  merge any degenerate or redundant facets
2915  for each newly merged facet
2916  remove extra vertices
2917  if qh.MERGEvertices
2918  for each newly merged facet
2919  for each vertex
2920  if vertex was on a deleted ridge
2921  rename vertex if it is shared
2922  remove delridge flag from new vertices
2923 */
2924 boolT qh_reducevertices(qhT *qh) {
2925  int numshare=0, numrename= 0;
2926  boolT degenredun= False;
2927  facetT *newfacet;
2928  vertexT *vertex, **vertexp;
2929 
2930  if (qh->hull_dim == 2)
2931  return False;
2932  if (qh_merge_degenredundant(qh))
2933  degenredun= True;
2934  LABELrestart:
2935  FORALLnew_facets {
2936  if (newfacet->newmerge) {
2937  if (!qh->MERGEvertices)
2938  newfacet->newmerge= False;
2939  qh_remove_extravertices(qh, newfacet);
2940  }
2941  }
2942  if (!qh->MERGEvertices)
2943  return False;
2944  FORALLnew_facets {
2945  if (newfacet->newmerge) {
2946  newfacet->newmerge= False;
2947  FOREACHvertex_(newfacet->vertices) {
2948  if (vertex->delridge) {
2949  if (qh_rename_sharedvertex(qh, vertex, newfacet)) {
2950  numshare++;
2951  vertexp--; /* repeat since deleted vertex */
2952  }
2953  }
2954  }
2955  }
2956  }
2957  FORALLvertex_(qh->newvertex_list) {
2958  if (vertex->delridge && !vertex->deleted) {
2959  vertex->delridge= False;
2960  if (qh->hull_dim >= 4 && qh_redundant_vertex(qh, vertex)) {
2961  numrename++;
2962  if (qh_merge_degenredundant(qh)) {
2963  degenredun= True;
2964  goto LABELrestart;
2965  }
2966  }
2967  }
2968  }
2969  trace1((qh, qh->ferr, 1014, "qh_reducevertices: renamed %d shared vertices and %d redundant vertices. Degen? %d\n",
2970  numshare, numrename, degenredun));
2971  return degenredun;
2972 } /* reducevertices */
2973 
2974 /*-<a href="qh-merge_r.htm#TOC"
2975  >-------------------------------</a><a name="redundant_vertex">-</a>
2976 
2977  qh_redundant_vertex(qh, vertex )
2978  detect and rename a redundant vertex
2979  vertices have full vertex->neighbors
2980 
2981  returns:
2982  returns true if find a redundant vertex
2983  deletes vertex(vertex->deleted)
2984 
2985  notes:
2986  only needed if vertex->delridge and hull_dim >= 4
2987  may add degenerate facets to qh.facet_mergeset
2988  doesn't change vertex->neighbors or create redundant facets
2989 
2990  design:
2991  intersect vertices of all facet neighbors of vertex
2992  determine ridges for these vertices
2993  if find a new vertex for vertex amoung these ridges and vertices
2994  rename vertex to the new vertex
2995 */
2996 vertexT *qh_redundant_vertex(qhT *qh, vertexT *vertex) {
2997  vertexT *newvertex= NULL;
2998  setT *vertices, *ridges;
2999 
3000  trace3((qh, qh->ferr, 3008, "qh_redundant_vertex: check if v%d can be renamed\n", vertex->id));
3001  if ((vertices= qh_neighbor_intersections(qh, vertex))) {
3002  ridges= qh_vertexridges(qh, vertex);
3003  if ((newvertex= qh_find_newvertex(qh, vertex, vertices, ridges)))
3004  qh_renamevertex(qh, vertex, newvertex, ridges, NULL, NULL);
3005  qh_settempfree(qh, &ridges);
3006  qh_settempfree(qh, &vertices);
3007  }
3008  return newvertex;
3009 } /* redundant_vertex */
3010 
3011 /*-<a href="qh-merge_r.htm#TOC"
3012  >-------------------------------</a><a name="remove_extravertices">-</a>
3013 
3014  qh_remove_extravertices(qh, facet )
3015  remove extra vertices from non-simplicial facets
3016 
3017  returns:
3018  returns True if it finds them
3019 
3020  design:
3021  for each vertex in facet
3022  if vertex not in a ridge (i.e., no longer used)
3023  delete vertex from facet
3024  delete facet from vertice's neighbors
3025  unless vertex in another facet
3026  add vertex to qh.del_vertices for later deletion
3027 */
3028 boolT qh_remove_extravertices(qhT *qh, facetT *facet) {
3029  ridgeT *ridge, **ridgep;
3030  vertexT *vertex, **vertexp;
3031  boolT foundrem= False;
3032 
3033  trace4((qh, qh->ferr, 4043, "qh_remove_extravertices: test f%d for extra vertices\n",
3034  facet->id));
3035  FOREACHvertex_(facet->vertices)
3036  vertex->seen= False;
3037  FOREACHridge_(facet->ridges) {
3038  FOREACHvertex_(ridge->vertices)
3039  vertex->seen= True;
3040  }
3041  FOREACHvertex_(facet->vertices) {
3042  if (!vertex->seen) {
3043  foundrem= True;
3044  zinc_(Zremvertex);
3045  qh_setdelsorted(facet->vertices, vertex);
3046  qh_setdel(vertex->neighbors, facet);
3047  if (!qh_setsize(qh, vertex->neighbors)) {
3048  vertex->deleted= True;
3049  qh_setappend(qh, &qh->del_vertices, vertex);
3050  zinc_(Zremvertexdel);
3051  trace2((qh, qh->ferr, 2036, "qh_remove_extravertices: v%d deleted because it's lost all ridges\n", vertex->id));
3052  }else
3053  trace3((qh, qh->ferr, 3009, "qh_remove_extravertices: v%d removed from f%d because it's lost all ridges\n", vertex->id, facet->id));
3054  vertexp--; /*repeat*/
3055  }
3056  }
3057  return foundrem;
3058 } /* remove_extravertices */
3059 
3060 /*-<a href="qh-merge_r.htm#TOC"
3061  >-------------------------------</a><a name="rename_sharedvertex">-</a>
3062 
3063  qh_rename_sharedvertex(qh, vertex, facet )
3064  detect and rename if shared vertex in facet
3065  vertices have full ->neighbors
3066 
3067  returns:
3068  newvertex or NULL
3069  the vertex may still exist in other facets (i.e., a neighbor was pinched)
3070  does not change facet->neighbors
3071  updates vertex->neighbors
3072 
3073  notes:
3074  a shared vertex for a facet is only in ridges to one neighbor
3075  this may undo a pinched facet
3076 
3077  it does not catch pinches involving multiple facets. These appear
3078  to be difficult to detect, since an exhaustive search is too expensive.
3079 
3080  design:
3081  if vertex only has two neighbors
3082  determine the ridges that contain the vertex
3083  determine the vertices shared by both neighbors
3084  if can find a new vertex in this set
3085  rename the vertex to the new vertex
3086 */
3087 vertexT *qh_rename_sharedvertex(qhT *qh, vertexT *vertex, facetT *facet) {
3088  facetT *neighbor, **neighborp, *neighborA= NULL;
3089  setT *vertices, *ridges;
3090  vertexT *newvertex;
3091 
3092  if (qh_setsize(qh, vertex->neighbors) == 2) {
3093  neighborA= SETfirstt_(vertex->neighbors, facetT);
3094  if (neighborA == facet)
3095  neighborA= SETsecondt_(vertex->neighbors, facetT);
3096  }else if (qh->hull_dim == 3)
3097  return NULL;
3098  else {
3099  qh->visit_id++;
3100  FOREACHneighbor_(facet)
3101  neighbor->visitid= qh->visit_id;
3102  FOREACHneighbor_(vertex) {
3103  if (neighbor->visitid == qh->visit_id) {
3104  if (neighborA)
3105  return NULL;
3106  neighborA= neighbor;
3107  }
3108  }
3109  if (!neighborA) {
3110  qh_fprintf(qh, qh->ferr, 6101, "qhull internal error (qh_rename_sharedvertex): v%d's neighbors not in f%d\n",
3111  vertex->id, facet->id);
3112  qh_errprint(qh, "ERRONEOUS", facet, NULL, NULL, vertex);
3113  qh_errexit(qh, qh_ERRqhull, NULL, NULL);
3114  }
3115  }
3116  /* the vertex is shared by facet and neighborA */
3117  ridges= qh_settemp(qh, qh->TEMPsize);
3118  neighborA->visitid= ++qh->visit_id;
3119  qh_vertexridges_facet(qh, vertex, facet, &ridges);
3120  trace2((qh, qh->ferr, 2037, "qh_rename_sharedvertex: p%d(v%d) is shared by f%d(%d ridges) and f%d\n",
3121  qh_pointid(qh, vertex->point), vertex->id, facet->id, qh_setsize(qh, ridges), neighborA->id));
3122  zinc_(Zintersectnum);
3123  vertices= qh_vertexintersect_new(qh, facet->vertices, neighborA->vertices);
3124  qh_setdel(vertices, vertex);
3125  qh_settemppush(qh, vertices);
3126  if ((newvertex= qh_find_newvertex(qh, vertex, vertices, ridges)))
3127  qh_renamevertex(qh, vertex, newvertex, ridges, facet, neighborA);
3128  qh_settempfree(qh, &vertices);
3129  qh_settempfree(qh, &ridges);
3130  return newvertex;
3131 } /* rename_sharedvertex */
3132 
3133 /*-<a href="qh-merge_r.htm#TOC"
3134  >-------------------------------</a><a name="renameridgevertex">-</a>
3135 
3136  qh_renameridgevertex(qh, ridge, oldvertex, newvertex )
3137  renames oldvertex as newvertex in ridge
3138 
3139  returns:
3140 
3141  design:
3142  delete oldvertex from ridge
3143  if newvertex already in ridge
3144  copy ridge->noconvex to another ridge if possible
3145  delete the ridge
3146  else
3147  insert newvertex into the ridge
3148  adjust the ridge's orientation
3149 */
3150 void qh_renameridgevertex(qhT *qh, ridgeT *ridge, vertexT *oldvertex, vertexT *newvertex) {
3151  int nth= 0, oldnth;
3152  facetT *temp;
3153  vertexT *vertex, **vertexp;
3154 
3155  oldnth= qh_setindex(ridge->vertices, oldvertex);
3156  qh_setdelnthsorted(qh, ridge->vertices, oldnth);
3157  FOREACHvertex_(ridge->vertices) {
3158  if (vertex == newvertex) {
3159  zinc_(Zdelridge);
3160  if (ridge->nonconvex) /* only one ridge has nonconvex set */
3161  qh_copynonconvex(qh, ridge);
3162  trace2((qh, qh->ferr, 2038, "qh_renameridgevertex: ridge r%d deleted. It contained both v%d and v%d\n",
3163  ridge->id, oldvertex->id, newvertex->id));
3164  qh_delridge(qh, ridge);
3165  return;
3166  }
3167  if (vertex->id < newvertex->id)
3168  break;
3169  nth++;
3170  }
3171  qh_setaddnth(qh, &ridge->vertices, nth, newvertex);
3172  if (abs(oldnth - nth)%2) {
3173  trace3((qh, qh->ferr, 3010, "qh_renameridgevertex: swapped the top and bottom of ridge r%d\n",
3174  ridge->id));
3175  temp= ridge->top;
3176  ridge->top= ridge->bottom;
3177  ridge->bottom= temp;
3178  }
3179 } /* renameridgevertex */
3180 
3181 
3182 /*-<a href="qh-merge_r.htm#TOC"
3183  >-------------------------------</a><a name="renamevertex">-</a>
3184 
3185  qh_renamevertex(qh, oldvertex, newvertex, ridges, oldfacet, neighborA )
3186  renames oldvertex as newvertex in ridges
3187  gives oldfacet/neighborA if oldvertex is shared between two facets
3188 
3189  returns:
3190  oldvertex may still exist afterwards
3191 
3192 
3193  notes:
3194  can not change neighbors of newvertex (since it's a subset)
3195 
3196  design:
3197  for each ridge in ridges
3198  rename oldvertex to newvertex and delete degenerate ridges
3199  if oldfacet not defined
3200  for each neighbor of oldvertex
3201  delete oldvertex from neighbor's vertices
3202  remove extra vertices from neighbor
3203  add oldvertex to qh.del_vertices
3204  else if oldvertex only between oldfacet and neighborA
3205  delete oldvertex from oldfacet and neighborA
3206  add oldvertex to qh.del_vertices
3207  else oldvertex is in oldfacet and neighborA and other facets (i.e., pinched)
3208  delete oldvertex from oldfacet
3209  delete oldfacet from oldvertice's neighbors
3210  remove extra vertices (e.g., oldvertex) from neighborA
3211 */
3212 void qh_renamevertex(qhT *qh, vertexT *oldvertex, vertexT *newvertex, setT *ridges, facetT *oldfacet, facetT *neighborA) {
3213  facetT *neighbor, **neighborp;
3214  ridgeT *ridge, **ridgep;
3215  boolT istrace= False;
3216 
3217  if (qh->IStracing >= 2 || oldvertex->id == qh->tracevertex_id ||
3218  newvertex->id == qh->tracevertex_id)
3219  istrace= True;
3220  FOREACHridge_(ridges)
3221  qh_renameridgevertex(qh, ridge, oldvertex, newvertex);
3222  if (!oldfacet) {
3223  zinc_(Zrenameall);
3224  if (istrace)
3225  qh_fprintf(qh, qh->ferr, 8082, "qh_renamevertex: renamed v%d to v%d in several facets\n",
3226  oldvertex->id, newvertex->id);
3227  FOREACHneighbor_(oldvertex) {
3228  qh_maydropneighbor(qh, neighbor);
3229  qh_setdelsorted(neighbor->vertices, oldvertex);
3230  if (qh_remove_extravertices(qh, neighbor))
3231  neighborp--; /* neighbor may be deleted */
3232  }
3233  if (!oldvertex->deleted) {
3234  oldvertex->deleted= True;
3235  qh_setappend(qh, &qh->del_vertices, oldvertex);
3236  }
3237  }else if (qh_setsize(qh, oldvertex->neighbors) == 2) {
3238  zinc_(Zrenameshare);
3239  if (istrace)
3240  qh_fprintf(qh, qh->ferr, 8083, "qh_renamevertex: renamed v%d to v%d in oldfacet f%d\n",
3241  oldvertex->id, newvertex->id, oldfacet->id);
3242  FOREACHneighbor_(oldvertex)
3243  qh_setdelsorted(neighbor->vertices, oldvertex);
3244  oldvertex->deleted= True;
3245  qh_setappend(qh, &qh->del_vertices, oldvertex);
3246  }else {
3247  zinc_(Zrenamepinch);
3248  if (istrace || qh->IStracing)
3249  qh_fprintf(qh, qh->ferr, 8084, "qh_renamevertex: renamed pinched v%d to v%d between f%d and f%d\n",
3250  oldvertex->id, newvertex->id, oldfacet->id, neighborA->id);
3251  qh_setdelsorted(oldfacet->vertices, oldvertex);
3252  qh_setdel(oldvertex->neighbors, oldfacet);
3253  qh_remove_extravertices(qh, neighborA);
3254  }
3255 } /* renamevertex */
3256 
3257 
3258 /*-<a href="qh-merge_r.htm#TOC"
3259  >-------------------------------</a><a name="test_appendmerge">-</a>
3260 
3261  qh_test_appendmerge(qh, facet, neighbor )
3262  tests facet/neighbor for convexity
3263  appends to mergeset if non-convex
3264  if pre-merging,
3265  nop if qh.SKIPconvex, or qh.MERGEexact and coplanar
3266 
3267  returns:
3268  true if appends facet/neighbor to mergeset
3269  sets facet->center as needed
3270  does not change facet->seen
3271 
3272  design:
3273  if qh.cos_max is defined
3274  if the angle between facet normals is too shallow
3275  append an angle-coplanar merge to qh.mergeset
3276  return True
3277  make facet's centrum if needed
3278  if facet's centrum is above the neighbor
3279  set isconcave
3280  else
3281  if facet's centrum is not below the neighbor
3282  set iscoplanar
3283  make neighbor's centrum if needed
3284  if neighbor's centrum is above the facet
3285  set isconcave
3286  else if neighbor's centrum is not below the facet
3287  set iscoplanar
3288  if isconcave or iscoplanar
3289  get angle if needed
3290  append concave or coplanar merge to qh.mergeset
3291 */
3292 boolT qh_test_appendmerge(qhT *qh, facetT *facet, facetT *neighbor) {
3293  realT dist, dist2= -REALmax, angle= -REALmax;
3294  boolT isconcave= False, iscoplanar= False, okangle= False;
3295 
3296  if (qh->SKIPconvex && !qh->POSTmerging)
3297  return False;
3298  if ((!qh->MERGEexact || qh->POSTmerging) && qh->cos_max < REALmax/2) {
3299  angle= qh_getangle(qh, facet->normal, neighbor->normal);
3300  zinc_(Zangletests);
3301  if (angle > qh->cos_max) {
3302  zinc_(Zcoplanarangle);
3303  qh_appendmergeset(qh, facet, neighbor, MRGanglecoplanar, &angle);
3304  trace2((qh, qh->ferr, 2039, "qh_test_appendmerge: coplanar angle %4.4g between f%d and f%d\n",
3305  angle, facet->id, neighbor->id));
3306  return True;
3307  }else
3308  okangle= True;
3309  }
3310  if (!facet->center)
3311  facet->center= qh_getcentrum(qh, facet);
3312  zzinc_(Zcentrumtests);
3313  qh_distplane(qh, facet->center, neighbor, &dist);
3314  if (dist > qh->centrum_radius)
3315  isconcave= True;
3316  else {
3317  if (dist > -qh->centrum_radius)
3318  iscoplanar= True;
3319  if (!neighbor->center)
3320  neighbor->center= qh_getcentrum(qh, neighbor);
3321  zzinc_(Zcentrumtests);
3322  qh_distplane(qh, neighbor->center, facet, &dist2);
3323  if (dist2 > qh->centrum_radius)
3324  isconcave= True;
3325  else if (!iscoplanar && dist2 > -qh->centrum_radius)
3326  iscoplanar= True;
3327  }
3328  if (!isconcave && (!iscoplanar || (qh->MERGEexact && !qh->POSTmerging)))
3329  return False;
3330  if (!okangle && qh->ANGLEmerge) {
3331  angle= qh_getangle(qh, facet->normal, neighbor->normal);
3332  zinc_(Zangletests);
3333  }
3334  if (isconcave) {
3335  zinc_(Zconcaveridge);
3336  if (qh->ANGLEmerge)
3337  angle += qh_ANGLEconcave + 0.5;
3338  qh_appendmergeset(qh, facet, neighbor, MRGconcave, &angle);
3339  trace0((qh, qh->ferr, 18, "qh_test_appendmerge: concave f%d to f%d dist %4.4g and reverse dist %4.4g angle %4.4g during p%d\n",
3340  facet->id, neighbor->id, dist, dist2, angle, qh->furthest_id));
3341  }else /* iscoplanar */ {
3342  zinc_(Zcoplanarcentrum);
3343  qh_appendmergeset(qh, facet, neighbor, MRGcoplanar, &angle);
3344  trace2((qh, qh->ferr, 2040, "qh_test_appendmerge: coplanar f%d to f%d dist %4.4g, reverse dist %4.4g angle %4.4g\n",
3345  facet->id, neighbor->id, dist, dist2, angle));
3346  }
3347  return True;
3348 } /* test_appendmerge */
3349 
3350 /*-<a href="qh-merge_r.htm#TOC"
3351  >-------------------------------</a><a name="test_vneighbors">-</a>
3352 
3353  qh_test_vneighbors(qh)
3354  test vertex neighbors for convexity
3355  tests all facets on qh.newfacet_list
3356 
3357  returns:
3358  true if non-convex vneighbors appended to qh.facet_mergeset
3359  initializes vertex neighbors if needed
3360 
3361  notes:
3362  assumes all facet neighbors have been tested
3363  this can be expensive
3364  this does not guarantee that a centrum is below all facets
3365  but it is unlikely
3366  uses qh.visit_id
3367 
3368  design:
3369  build vertex neighbors if necessary
3370  for all new facets
3371  for all vertices
3372  for each unvisited facet neighbor of the vertex
3373  test new facet and neighbor for convexity
3374 */
3375 boolT qh_test_vneighbors(qhT *qh /* qh->newfacet_list */) {
3376  facetT *newfacet, *neighbor, **neighborp;
3377  vertexT *vertex, **vertexp;
3378  int nummerges= 0;
3379 
3380  trace1((qh, qh->ferr, 1015, "qh_test_vneighbors: testing vertex neighbors for convexity\n"));
3381  if (!qh->VERTEXneighbors)
3382  qh_vertexneighbors(qh);
3383  FORALLnew_facets
3384  newfacet->seen= False;
3385  FORALLnew_facets {
3386  newfacet->seen= True;
3387  newfacet->visitid= qh->visit_id++;
3388  FOREACHneighbor_(newfacet)
3389  newfacet->visitid= qh->visit_id;
3390  FOREACHvertex_(newfacet->vertices) {
3391  FOREACHneighbor_(vertex) {
3392  if (neighbor->seen || neighbor->visitid == qh->visit_id)
3393  continue;
3394  if (qh_test_appendmerge(qh, newfacet, neighbor))
3395  nummerges++;
3396  }
3397  }
3398  }
3399  zadd_(Ztestvneighbor, nummerges);
3400  trace1((qh, qh->ferr, 1016, "qh_test_vneighbors: found %d non-convex, vertex neighbors\n",
3401  nummerges));
3402  return (nummerges > 0);
3403 } /* test_vneighbors */
3404 
3405 /*-<a href="qh-merge_r.htm#TOC"
3406  >-------------------------------</a><a name="tracemerge">-</a>
3407 
3408  qh_tracemerge(qh, facet1, facet2 )
3409  print trace message after merge
3410 */
3411 void qh_tracemerge(qhT *qh, facetT *facet1, facetT *facet2) {
3412  boolT waserror= False;
3413 
3414 #ifndef qh_NOtrace
3415  if (qh->IStracing >= 4)
3416  qh_errprint(qh, "MERGED", facet2, NULL, NULL, NULL);
3417  if (facet2 == qh->tracefacet || (qh->tracevertex && qh->tracevertex->newlist)) {
3418  qh_fprintf(qh, qh->ferr, 8085, "qh_tracemerge: trace facet and vertex after merge of f%d and f%d, furthest p%d\n", facet1->id, facet2->id, qh->furthest_id);
3419  if (facet2 != qh->tracefacet)
3420  qh_errprint(qh, "TRACE", qh->tracefacet,
3421  (qh->tracevertex && qh->tracevertex->neighbors) ?
3422  SETfirstt_(qh->tracevertex->neighbors, facetT) : NULL,
3423  NULL, qh->tracevertex);
3424  }
3425  if (qh->tracevertex) {
3426  if (qh->tracevertex->deleted)
3427  qh_fprintf(qh, qh->ferr, 8086, "qh_tracemerge: trace vertex deleted at furthest p%d\n",
3428  qh->furthest_id);
3429  else
3430  qh_checkvertex(qh, qh->tracevertex);
3431  }
3432  if (qh->tracefacet) {
3433  qh_checkfacet(qh, qh->tracefacet, True, &waserror);
3434  if (waserror)
3435  qh_errexit(qh, qh_ERRqhull, qh->tracefacet, NULL);
3436  }
3437 #endif /* !qh_NOtrace */
3438  if (qh->CHECKfrequently || qh->IStracing >= 4) { /* can't check polygon here */
3439  qh_checkfacet(qh, facet2, True, &waserror);
3440  if (waserror)
3441  qh_errexit(qh, qh_ERRqhull, NULL, NULL);
3442  }
3443 } /* tracemerge */
3444 
3445 /*-<a href="qh-merge_r.htm#TOC"
3446  >-------------------------------</a><a name="tracemerging">-</a>
3447 
3448  qh_tracemerging(qh)
3449  print trace message during POSTmerging
3450 
3451  returns:
3452  updates qh.mergereport
3453 
3454  notes:
3455  called from qh_mergecycle() and qh_mergefacet()
3456 
3457  see:
3458  qh_buildtracing()
3459 */
3460 void qh_tracemerging(qhT *qh) {
3461  realT cpu;
3462  int total;
3463  time_t timedata;
3464  struct tm *tp;
3465 
3466  qh->mergereport= zzval_(Ztotmerge);
3467  time(&timedata);
3468  tp= localtime(&timedata);
3469  cpu= qh_CPUclock;
3470  cpu /= qh_SECticks;
3471  total= zzval_(Ztotmerge) - zzval_(Zcyclehorizon) + zzval_(Zcyclefacettot);
3472  qh_fprintf(qh, qh->ferr, 8087, "\n\
3473 At %d:%d:%d & %2.5g CPU secs, qhull has merged %d facets. The hull\n\
3474  contains %d facets and %d vertices.\n",
3475  tp->tm_hour, tp->tm_min, tp->tm_sec, cpu,
3476  total, qh->num_facets - qh->num_visible,
3477  qh->num_vertices-qh_setsize(qh, qh->del_vertices));
3478 } /* tracemerging */
3479 
3480 /*-<a href="qh-merge_r.htm#TOC"
3481  >-------------------------------</a><a name="updatetested">-</a>
3482 
3483  qh_updatetested(qh, facet1, facet2 )
3484  clear facet2->tested and facet1->ridge->tested for merge
3485 
3486  returns:
3487  deletes facet2->center unless it's already large
3488  if so, clears facet2->ridge->tested
3489 
3490  design:
3491  clear facet2->tested
3492  clear ridge->tested for facet1's ridges
3493  if facet2 has a centrum
3494  if facet2 is large
3495  set facet2->keepcentrum
3496  else if facet2 has 3 vertices due to many merges, or not large and post merging
3497  clear facet2->keepcentrum
3498  unless facet2->keepcentrum
3499  clear facet2->center to recompute centrum later
3500  clear ridge->tested for facet2's ridges
3501 */
3502 void qh_updatetested(qhT *qh, facetT *facet1, facetT *facet2) {
3503  ridgeT *ridge, **ridgep;
3504  int size;
3505 
3506  facet2->tested= False;
3507  FOREACHridge_(facet1->ridges)
3508  ridge->tested= False;
3509  if (!facet2->center)
3510  return;
3511  size= qh_setsize(qh, facet2->vertices);
3512  if (!facet2->keepcentrum) {
3513  if (size > qh->hull_dim + qh_MAXnewcentrum) {
3514  facet2->keepcentrum= True;
3515  zinc_(Zwidevertices);
3516  }
3517  }else if (size <= qh->hull_dim + qh_MAXnewcentrum) {
3518  /* center and keepcentrum was set */
3519  if (size == qh->hull_dim || qh->POSTmerging)
3520  facet2->keepcentrum= False; /* if many merges need to recompute centrum */
3521  }
3522  if (!facet2->keepcentrum) {
3523  qh_memfree(qh, facet2->center, qh->normal_size);
3524  facet2->center= NULL;
3525  FOREACHridge_(facet2->ridges)
3526  ridge->tested= False;
3527  }
3528 } /* updatetested */
3529 
3530 /*-<a href="qh-merge_r.htm#TOC"
3531  >-------------------------------</a><a name="vertexridges">-</a>
3532 
3533  qh_vertexridges(qh, vertex )
3534  return temporary set of ridges adjacent to a vertex
3535  vertex->neighbors defined
3536 
3537  ntoes:
3538  uses qh.visit_id
3539  does not include implicit ridges for simplicial facets
3540 
3541  design:
3542  for each neighbor of vertex
3543  add ridges that include the vertex to ridges
3544 */
3545 setT *qh_vertexridges(qhT *qh, vertexT *vertex) {
3546  facetT *neighbor, **neighborp;
3547  setT *ridges= qh_settemp(qh, qh->TEMPsize);
3548  int size;
3549 
3550  qh->visit_id++;
3551  FOREACHneighbor_(vertex)
3552  neighbor->visitid= qh->visit_id;
3553  FOREACHneighbor_(vertex) {
3554  if (*neighborp) /* no new ridges in last neighbor */
3555  qh_vertexridges_facet(qh, vertex, neighbor, &ridges);
3556  }
3557  if (qh->PRINTstatistics || qh->IStracing) {
3558  size= qh_setsize(qh, ridges);
3559  zinc_(Zvertexridge);
3560  zadd_(Zvertexridgetot, size);
3561  zmax_(Zvertexridgemax, size);
3562  trace3((qh, qh->ferr, 3011, "qh_vertexridges: found %d ridges for v%d\n",
3563  size, vertex->id));
3564  }
3565  return ridges;
3566 } /* vertexridges */
3567 
3568 /*-<a href="qh-merge_r.htm#TOC"
3569  >-------------------------------</a><a name="vertexridges_facet">-</a>
3570 
3571  qh_vertexridges_facet(qh, vertex, facet, ridges )
3572  add adjacent ridges for vertex in facet
3573  neighbor->visitid==qh.visit_id if it hasn't been visited
3574 
3575  returns:
3576  ridges updated
3577  sets facet->visitid to qh.visit_id-1
3578 
3579  design:
3580  for each ridge of facet
3581  if ridge of visited neighbor (i.e., unprocessed)
3582  if vertex in ridge
3583  append ridge to vertex
3584  mark facet processed
3585 */
3586 void qh_vertexridges_facet(qhT *qh, vertexT *vertex, facetT *facet, setT **ridges) {
3587  ridgeT *ridge, **ridgep;
3588  facetT *neighbor;
3589 
3590  FOREACHridge_(facet->ridges) {
3591  neighbor= otherfacet_(ridge, facet);
3592  if (neighbor->visitid == qh->visit_id
3593  && qh_setin(ridge->vertices, vertex))
3594  qh_setappend(qh, ridges, ridge);
3595  }
3596  facet->visitid= qh->visit_id-1;
3597 } /* vertexridges_facet */
3598 
3599 /*-<a href="qh-merge_r.htm#TOC"
3600  >-------------------------------</a><a name="willdelete">-</a>
3601 
3602  qh_willdelete(qh, facet, replace )
3603  moves facet to visible list
3604  sets facet->f.replace to replace (may be NULL)
3605 
3606  returns:
3607  bumps qh.num_visible
3608 */
3609 void qh_willdelete(qhT *qh, facetT *facet, facetT *replace) {
3610 
3611  qh_removefacet(qh, facet);
3612  qh_prependfacet(qh, facet, &qh->visible_list);
3613  qh->num_visible++;
3614  facet->visible= True;
3615  facet->f.replace= replace;
3616 } /* willdelete */
3617 
3618 #else /* qh_NOmerge */
3619 void qh_premerge(qhT *qh, vertexT *apex, realT maxcentrum, realT maxangle) {
3620 }
3621 void qh_postmerge(qhT *qh, const char *reason, realT maxcentrum, realT maxangle,
3622  boolT vneighbors) {
3623 }
3624 boolT qh_checkzero(qhT *qh, boolT testall) {
3625  }
3626 #endif /* qh_NOmerge */
3627 
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