ridgeT *ridge, **ridgep;  samevisitid= ++qh visit_id;  FORALLsame_cycle_(samecycle) {    if (same->visitid == samevisitid || same->visible)      qh_infiniteloop (samecycle);    same->visitid= samevisitid;  }  newfacet->visitid= ++qh visit_id;  trace4((qh ferr, "qh_mergecycle_neighbors: delete shared neighbors from newfacet\n"));    FOREACHneighbor_(newfacet) {    if (neighbor->visitid == samevisitid) {      SETref_(neighbor)= NULL;  /* samecycle neighbors deleted */      delneighbors++;    }else      neighbor->visitid= qh visit_id;  }  qh_setcompact (newfacet->neighbors);  trace4((qh ferr, "qh_mergecycle_neighbors: update neighbors\n"));    FORALLsame_cycle_(samecycle) {    FOREACHneighbor_(same) {      if (neighbor->visitid == samevisitid)	continue;      if (neighbor->simplicial) {	if (neighbor->visitid != qh visit_id) {	  qh_setappend (&newfacet->neighbors, neighbor);	  qh_setreplace (neighbor->neighbors, same, newfacet);	  newneighbors++;	  neighbor->visitid= qh visit_id;	  FOREACHridge_(neighbor->ridges) { /* update ridge in case of qh_makeridges */	    if (ridge->top == same) {	      ridge->top= newfacet;	      break;	    }else if (ridge->bottom == same) {	      ridge->bottom= newfacet;	      break;	    }	  }	}else {	  qh_makeridges (neighbor);	  qh_setdel (neighbor->neighbors, same);	  /* same can't be horizon facet for neighbor */	}      }else { /* non-simplicial neighbor */        qh_setdel (neighbor->neighbors, same);        if (neighbor->visitid != qh visit_id) {          qh_setappend (&neighbor->neighbors, newfacet);          qh_setappend (&newfacet->neighbors, neighbor);          neighbor->visitid= qh visit_id;          newneighbors++;        }       }    }  }  trace2((qh ferr, "qh_mergecycle_neighbors: deleted %d neighbors and added %d\n",              delneighbors, newneighbors));} /* mergecycle_neighbors *//*--------------------------------------------------mergecycle_ridges- add ridges/neighbors for ->f.samecycle to newfacet  all new/old neighbors of newfacet marked with qh visit_id    cycle marked with qh visit_id-1    newfacet marked with qh visit_id  newfacet has ridges  ridge already updated for simplicial neighbors of samecycle with a ridgereturns:  newfacet has merged ridgesnotes:  similar to mergeridges, and makeridges*/void qh_mergecycle_ridges(facetT *samecycle, facetT *newfacet) {  facetT *same, *neighbor= NULL;  int numold=0, numnew=0;  int neighbor_i, neighbor_n, samevisitid;  ridgeT *ridge, **ridgep;  boolT toporient;  void **freelistp;  trace4((qh ferr, "qh_mergecycle_ridges: delete shared ridges from newfacet\n"));    samevisitid= qh visit_id -1;  FOREACHridge_(newfacet->ridges) {    neighbor= otherfacet_(ridge, newfacet);    if (neighbor->visitid == samevisitid)      SETref_(ridge)= NULL; /* ridge free'd below */    }  qh_setcompact (newfacet->ridges);    trace4((qh ferr, "qh_mergecycle_ridges: add ridges to newfacet\n"));    FORALLsame_cycle_(samecycle) {    FOREACHridge_(same->ridges) {      if (ridge->top == same) {        ridge->top= newfacet;	neighbor= ridge->bottom;      }else if (ridge->bottom == same) {	ridge->bottom= newfacet;	neighbor= ridge->top;      }else if (ridge->top == newfacet || ridge->bottom == newfacet) {        qh_setappend (&newfacet->ridges, ridge);        numold++;  /* already set by qh_mergecycle_neighbors */	continue;        }else {	fprintf (qh ferr, "qhull internal error (qh_mergecycle_ridges): bad ridge r%d\n", ridge->id);	qh_errexit (qh_ERRqhull, NULL, ridge);      }      if (neighbor == newfacet) {        qh_setfree(&(ridge->vertices));         qh_memfree_(ridge, sizeof(ridgeT), freelistp);        numold++;      }else if (neighbor->visitid == samevisitid) {	qh_setdel (neighbor->ridges, ridge);	qh_setfree(&(ridge->vertices)); 	qh_memfree_(ridge, sizeof(ridgeT), freelistp);	numold++;      }else {        qh_setappend (&newfacet->ridges, ridge);        numold++;      }    }    if (same->ridges)      qh_settruncate (same->ridges, 0);    if (!same->simplicial)      continue;    FOREACHneighbor_i_(same) {       /* note: !newfact->simplicial */      if (neighbor->visitid != samevisitid && neighbor->simplicial) {        ridge= qh_newridge();        ridge->vertices= qh_setnew_delnthsorted (same->vertices, qh hull_dim,  					                  neighbor_i, 0);        toporient= same->toporient ^ (neighbor_i & 0x1);        if (toporient) {          ridge->top= newfacet;          ridge->bottom= neighbor;        }else {          ridge->top= neighbor;          ridge->bottom= newfacet;        }        qh_setappend(&(newfacet->ridges), ridge);        qh_setappend(&(neighbor->ridges), ridge);        numnew++;      }    }  }  trace2((qh ferr, "qh_mergecycle_ridges: found %d old ridges and %d new ones\n",              numold, numnew));} /* mergecycle_ridges *//*--------------------------------------------------mergecycle_vneighbors- create vertex neighbors for newfacet  samecycle with ->visitid == qh visit_id - 1returns:  newfacet vertices with updated neighbors  deletes vertices that are merged away  sets delridge on all vertices (faster than in mergecycle_ridges)notes:  same function as mergevertex_neighbors*/void qh_mergecycle_vneighbors (facetT *samecycle, facetT *newfacet) {  facetT *neighbor, **neighborp;  int mergeid;  vertexT *vertex, **vertexp, *apex;  setT *vertices;    trace4((qh ferr, "qh_mergecycle_vneighbors: update vertex neighbors for newfacet\n"));    mergeid= qh visit_id - 1;  newfacet->visitid= mergeid;  vertices= qh_basevertices (samecycle); /* temp */  apex= SETfirst_(samecycle->vertices);  qh_setappend (&vertices, apex);  FOREACHvertex_(vertices) {    vertex->delridge= True;    FOREACHneighbor_(vertex) {      if (neighbor->visitid == mergeid)        SETref_(neighbor)= NULL;    }    qh_setcompact (vertex->neighbors);    qh_setappend (&vertex->neighbors, newfacet);    if (!SETsecond_(vertex->neighbors)) {      zinc_(Zcyclevertex);      trace2((qh ferr, "qh_mergecycle_vneighbors: deleted v%d when merging cycle f%d into f%d\n",        vertex->id, samecycle->id, newfacet->id));      qh_setdelsorted (newfacet->vertices, vertex);      vertex->deleted= True;      qh_setappend (&qh del_vertices, vertex);    }  }  qh_settempfree (&vertices);  trace3((qh ferr, "qh_mergecycle_vneighbors: merged vertices from cycle f%d into f%d\n",              samecycle->id, newfacet->id));} /* mergecycle_vneighbors *//*--------------------------------------------------mergefacet- merges facet1 into facet2  traces merge if fmax_(maxdist,-mindist) > TRACEdist  mindist/maxdist may be NULL  max_outside and min_vertex updated  qh_MERGEapex if new facet into coplanar horizon  initializes vertex neighbors on first mergereturns:  facet1 prepended to visible_list for later deletion and partitioning     facet1->f.replace == facet2  facet2 moved to end of qh facet_list    makes facet2 a newfacet    sets facet2->newmerge set    clears facet2->center (unless merging into a large facet)    clears facet2->tested and ridge->tested for facet1  adds neighboring facets to facet_mergeset if redundant or degeneratenotes:   similar to mergecycle*/void qh_mergefacet(facetT *facet1, facetT *facet2, realT *mindist, realT *maxdist, boolT mergeapex) {  boolT traceonce= False;  vertexT *vertex, **vertexp;  int tracerestore=0, nummerge;  if (!qh VERTEXneighbors)    qh_vertexneighbors();  zzinc_(Ztotmerge);  if (qh POSTmerging && zzval_(Ztotmerge) > qh mergereport + qh REPORTfreq2)    qh_tracemerging();#ifndef qh_NOtrace   if (mindist && (-*mindist > qh TRACEdist || *maxdist > qh TRACEdist)) {    tracerestore= 0;    qh IStracing= qh TRACElevel;    traceonce= True;    fprintf (qh ferr, "qh_mergefacet: ========= trace wide merge #%d (%2.2g) for f%d into f%d, last point was p%d\n", zzval_(Ztotmerge),           fmax_(-*mindist, *maxdist), facet1->id, facet2->id, qh furthest_id);  }else if (facet1 == qh tracefacet || facet2 == qh tracefacet) {    tracerestore= qh IStracing;    qh IStracing= 4;    traceonce= True;    fprintf (qh ferr, "qh_mergefacet: ========= trace merge #%d involving f%d, furthest is p%d\n",	       zzval_(Ztotmerge), qh tracefacet_id,  qh furthest_id);  }  if (qh IStracing >= 2) {    realT mergemin= -2;    realT mergemax= -2;        if (mindist) {      mergemin= *mindist;      mergemax= *maxdist;    }    fprintf (qh ferr, "qh_mergefacet: #%d merge f%d into f%d, mindist= %2.2g, maxdist= %2.2g\n",     zzval_(Ztotmerge), facet1->id, facet2->id, mergemin, mergemax);  }#endif /* !qh_NOtrace */  if (facet1 == facet2 || facet1->visible || facet2->visible) {    fprintf (qh ferr, "qhull internal error (qh_mergefacet): either f%d and f%d are the same or one is a visible facet\n",	     facet1->id, facet2->id);    qh_errexit2 (qh_ERRqhull, facet1, facet2);  }  if (qh num_facets - qh num_visible <= qh hull_dim + 1) {    fprintf(qh ferr, "\n\qhull precision error: Only %d facets remain.  Can not merge another\n\pair.  The convexity constraints may be too strong.  Reduce the\n\magnitude of 'Cn' or increase the magnitude of 'An'.  For example,\n\try 'C-0.001' instead of 'C-0.1' or 'A-0.999' instead of 'A-0.9'.\n",                  qh hull_dim+1);    if (qh hull_dim >= 5 && !qh MERGEexact)      fprintf(qh ferr, "Option 'Qx' may avoid this problem.\n");    qh_errexit(qh_ERRinput, NULL, NULL);  }  qh_makeridges(facet1);  qh_makeridges(facet2);  if (qh IStracing >=4)    qh_errprint ("MERGING", facet1, facet2, NULL, NULL);  if (mindist) {    maximize_(qh max_outside, *maxdist);    maximize_(qh max_vertex, *maxdist);#if qh_MAXoutside    maximize_(facet2->maxoutside, *maxdist);#endif    minimize_(qh min_vertex, *mindist);    if (!facet2->keepcentrum     && (*maxdist > qh WIDEfacet || *mindist < -qh WIDEfacet)) {      facet2->keepcentrum= True;      zinc_(Zwidefacet);    }  }  nummerge= facet1->nummerge + facet2->nummerge + 1;  if (nummerge >= qh_MAXnummerge)     facet2->nummerge= qh_MAXnummerge;  else    facet2->nummerge= nummerge;  facet2->newmerge= True;  facet2->dupridge= False;  qh_updatetested  (facet1, facet2);  if (qh_setsize (facet1->vertices) == qh hull_dim)    qh_mergesimplex (facet1, facet2, mergeapex);  else {    qh_mergeneighbors(facet1, facet2);    qh_mergeridges(facet1, facet2);    qh vertex_visit++;    FOREACHvertex_(facet2->vertices)      vertex->visitid= qh vertex_visit;    if (qh hull_dim == 2)       /* qh_mergevertices2d(facet1->vertices, facet2->vertices);      RS950202: changes the coordinates of one of the old vertices      to retain consistency with the existing edges */      qh_mungevertices2d(facet1, facet2);    else       qh_mergevertices(facet1->vertices, &facet2->vertices);    qh_mergevertex_neighbors(facet1, facet2);    if (!facet2->newfacet)      qh_newvertices (facet2->vertices);  }  if (!mergeapex)    qh_degen_redundant_neighbors (facet2, facet1);  if (facet2->coplanar || !facet2->newfacet) {    zinc_(Zmergeintohorizon);  }else if (!facet1->newfacet && facet2->newfacet) {    zinc_(Zmergehorizon);  }else {    zinc_(Zmergenew);  }  qh_willdelete (facet1, facet2);  qh_removefacet(facet2);  /* append as a newfacet to end of qh facet_list */  qh_appendfacet(facet2);  facet2->newfacet= True;  facet2->tested= False;  qh_tracemerge (facet1, facet2);  if (traceonce) {    fprintf (qh ferr, "qh_mergefacet: end of wide tracing\n");    qh IStracing= tracerestore;  }} /* mergefacet *//*--------------------------------------------------mergeneighbors- merges the neighbors of facet1 into facet2notes:  similar to mergecycle_neighbors*/void qh_mergeneighbors(facetT *facet1, facetT *facet2) {  facetT *neighbor, **neighborp;  trace4((qh ferr, "qh_mergeneighbors: merge neighbors of f%d and f%d\n",	  facet1->id, facet2->id));  qh visit_id++;  FOREACHneighbor_(facet2) {    neighbor->visitid= qh visit_id;  }  FOREACHneighbor_(facet1) {    if (neighbor->visitid == qh visit_id) {      if (neighbor->simplicial)    /* is degen, needs ridges */	qh_makeridges (neighbor);      if (SETfirst_(neighbor->neighbors) != facet1) /*keep newfacet->horizon*/	qh_setdel (neighbor->neighbors, facet1);      else {        qh_setdel(neighbor->neighbors, facet2);        qh_setreplace(neighbor->neighbors, facet1, facet2);      }    }else if (neighbor != facet2) {      qh_setappend(&(facet2->neighbors), neighbor);      qh_setreplace(neighbor->neighbors, facet1, facet2);    }  }  qh_setdel(facet1->neighbors, facet2);  /* here for makeridges */  qh_setdel(facet2->neighbors, facet1);} /* mergeneighbors *//*--------------------------------------------------mergeridges- merges the ridge set of facet1 into facet2  may delete all ridges for a vertexreturns:  sets vertex->delridge on deleted ridgesnotes:  similar to mergecycle_ridges*/void qh_mergeridges(facetT *facet1, facetT *facet2) {  ridgeT *ridge, **ridgep;  vertexT *vertex, **vertexp;  trace4((qh ferr, "qh_mergeridges: merge ridges of f%d and f%d\n",	  facet1->id, facet2->id));  FOREACHridge_(facet2->ridges) {    if ((ridge->top == facet1) || (ridge->bottom == facet1))