At %02d:%02d:%02d & %2.5g CPU secs, qhull has created %d facets and merged %d.\n\ The current hull contains %d facets and %d vertices.  Last point was p%d\n",      tp->tm_hour, tp->tm_min, tp->tm_sec, cpu, qh facet_id -1,      total, qh num_facets, qh num_vertices, qh furthest_id);    return;  }  furthestid= qh_pointid (furthest);  if (qh TRACEpoint == furthestid) {    qh IStracing= qh TRACElevel;    qhmem.IStracing= qh TRACElevel;  }  if (qh REPORTfreq && (qh facet_id-1 > qh lastreport+qh REPORTfreq)) {    qh lastreport= qh facet_id-1;    time (&timedata);    tp= localtime (&timedata);    cpu= (unsigned)clock() - qh hulltime;    cpu /= qh_SECticks;    total= zzval_(Ztotmerge) - zzval_(Zcyclehorizon) + zzval_(Zcyclefacettot);    zinc_(Zdistio);    qh_distplane (furthest, facet, &dist);    fprintf (qh ferr, "\n\At %02d:%02d:%02d & %2.5g CPU secs, qhull has created %d facets and merged %d.\n\ The current hull contains %d facets and %d vertices.  There are %d\n\ outside points.  Next is point p%d (v%d), %2.2g above f%d.\n",      tp->tm_hour, tp->tm_min, tp->tm_sec, cpu, qh facet_id -1,      total, qh num_facets, qh num_vertices, qh num_outside+1,      furthestid, qh vertex_id, dist, getid_(facet));  }else if (qh IStracing >=1) {    cpu= (unsigned)clock() - qh hulltime;    cpu /= qh_SECticks;    qh_distplane (furthest, facet, &dist);    fprintf (qh ferr, "qh_buildhull: add p%d (v%d) to hull of %d facets (%2.2g above f%d) and %d outside at %4.4g CPU secs.  Previous was p%d.\n",      furthestid, qh vertex_id, qh num_facets, dist,      getid_(facet), qh num_outside+1, cpu, qh furthest_id);  }  if (qh visit_id > (unsigned) INT_MAX) {    qh visit_id= 0;    FORALLfacets      facet->visitid= qh visit_id;  }  if (qh vertex_visit > (unsigned) INT_MAX) {    qh vertex_visit= 0;    FORALLvertices      vertex->visitid= qh vertex_visit;  }  qh furthest_id= furthestid;} /* buildtracing *//*--------------------------------------------errexit2- return exitcode to system after an error  assumes exitcode non-zero  for two facets, see qh_errexit() in user.c*/void qh_errexit2(int exitcode, facetT *facet, facetT *otherfacet) {    qh_errprint("ERRONEOUS", facet, otherfacet, NULL, NULL);  qh_errexit (exitcode, NULL, NULL);} /* errexit2 *//*--------------------------------------------------findhorizon- given a visible facet, find the point's horizon and visible facetsreturns:  qh visible_list to all visible facets     marks visible facets with ->visible     goodvisible counts visible->good    initializes num_visiblenotes:  similar to delpoint()*/void qh_findhorizon(pointT *point, facetT *facet, int *goodvisible, int *goodhorizon) {  facetT *neighbor, **neighborp, *visible;  int numhorizon= 0, coplanar= 0;  realT dist;    trace1((qh ferr,"qh_findhorizon: find horizon for point p%d facet f%d\n",qh_pointid(point),facet->id));  *goodvisible= *goodhorizon= 0;  zinc_(Ztotvisible);  qh_removefacet(facet);  /* visible_list at end of qh facet_list */  qh_appendfacet(facet);  qh num_visible= 1;  if (facet->good)    (*goodvisible)++;  qh visible_list= facet;  facet->visible= True;  facet->f.replace= NULL;  if (qh IStracing >=4)    qh_errprint ("visible", facet, NULL, NULL, NULL);  qh visit_id++;  FORALLvisible_facets {    visible->visitid= qh visit_id;    FOREACHneighbor_(visible) {      if (neighbor->visitid == qh visit_id)         continue;      neighbor->visitid= qh visit_id;      zzinc_(Znumvisibility);      qh_distplane(point, neighbor, &dist);      if (dist > qh MINvisible) {        zinc_(Ztotvisible);	qh_removefacet(neighbor);  /* append to end of qh visible_list */	qh_appendfacet(neighbor);	neighbor->visible= True;        neighbor->f.replace= NULL;	qh num_visible++;	if (neighbor->good)	  (*goodvisible)++;        if (qh IStracing >=4)          qh_errprint ("visible", neighbor, NULL, NULL, NULL);      }else { 	if (dist > - qh MAXcoplanar) {    	  neighbor->coplanar= True;          zzinc_(Zcoplanarhorizon);	  coplanar++;	  if (qh MERGING) {	    if (dist > 0) {	      maximize_(qh max_outside, dist);	      maximize_(qh max_vertex, dist);#if qh_MAXoutside	      maximize_(neighbor->maxoutside, dist);#endif	    }else	      minimize_(qh min_vertex, dist);  /* due to merge later */	  }      	  trace2((qh ferr, "qh_findhorizon: point p%d is coplanar to horizon f%d, dist=%2.7g < qh MINvisible (%2.7g)\n",	      qh_pointid(point), neighbor->id, dist, qh MINvisible));	}else    	  neighbor->coplanar= False;    	zinc_(Ztothorizon);        numhorizon++;	if (neighbor->good)	  (*goodhorizon)++;        if (qh IStracing >=4)          qh_errprint ("horizon", neighbor, NULL, NULL, NULL);      }    }  }  if (!numhorizon) {    fprintf(qh ferr, "qhull precision error (qh_findhorizon): empty horizon\n\Point p%d was above all facets.\n", qh_pointid(point));    qh_printfacetlist (qh facet_list, NULL, True);    qh_errexit(qh_ERRprec, NULL, NULL);  }  trace1((qh ferr, "qh_findhorizon: %d horizon facets (good %d), %d visible (good %d), %d coplanar\n",        numhorizon, *goodhorizon, qh num_visible, *goodvisible, coplanar));  if (qh IStracing >= 4 && qh num_facets < 50)     qh_printlists ();} /* findhorizon *//*-------------------------------------------------nextfurthest- returns next furthest point for processingreturns:  NULL if none available  visible facet for furthest  removes empty outside sets  */pointT *qh_nextfurthest (facetT **visible) {  facetT *facet;  int size, index;  realT randr;  pointT *furthest;  while ((facet= qh facet_next) != qh facet_tail) {    if (!facet->outsideset) {      qh facet_next= facet->next;      continue;    }    SETreturnsize_(facet->outsideset, size);    if (!size) {      qh_setfree (&facet->outsideset);      qh facet_next= facet->next;      continue;    }    if (!qh RANDOMoutside && !qh VIRTUALmemory) {      *visible= facet;      return ((pointT*)qh_setdellast (facet->outsideset));    }    if (qh RANDOMoutside) {      randr= qh_RANDOMint;      randr= randr/(qh_RANDOMmax+1);      index= floor(qh num_outside * randr);      FORALLfacet_(qh facet_next) {        if (facet->outsideset) {          SETreturnsize_(facet->outsideset, size);          if (!size)            qh_setfree (&facet->outsideset);          else if (size > index) {            *visible= facet;            return ((pointT*)qh_setdelnth (facet->outsideset, index));          }else            index -= size;        }      }      fprintf (qh ferr, "qhull internal error (qh_nextfurthest): num_outside %d incorrect or random %2.2g >= 1.0\n",              qh num_outside, randr);      qh_errexit (qh_ERRqhull, NULL, NULL);    }else { /* VIRTUALmemory */      facet= qh facet_tail->previous;      if (!(furthest= (pointT*)qh_setdellast(facet->outsideset))) {        if (facet->outsideset)          qh_setfree (&facet->outsideset);        qh_removefacet (facet);        qh_prependfacet (facet, &qh facet_list);        continue;      }      *visible= facet;      return furthest;    }  }  return NULL;} /* nextfurthest *//*--------------------------------------------------partitionall- partitions all points into the outsidesets of facets   vertices= set of vertices used by qh facet_list     does not partition qh GOODpoint     if ONLYgood && !MERGING, does not partition GOODvertex   all facets have ->newfacet for qh_findbestnew in qh_partitionpointnotes:   faster if qh facet_list sorted by anticipated size of outside set*/void qh_partitionall(setT *vertices, pointT *points, int numpoints){  setT *pointset;  vertexT *vertex, **vertexp;  pointT *point, **pointp, *bestpoint;  int size, point_i, point_n, point_end, remaining, i, id;  facetT *facet;  realT bestdist= -REALmax, dist, distoutside;      trace1((qh ferr, "qh_partitionall: partition all points into outside sets\n"));  pointset= qh_settemp (numpoints);  pointp= SETaddr_(pointset, pointT);  for (i=numpoints, point= points; i--; point += qh hull_dim)    *(pointp++)= point;  qh_settruncate (pointset, numpoints);  FOREACHvertex_(vertices) {    if ((id= qh_pointid(vertex->point)) >= 0)      SETelem_(pointset, id)= NULL;  }  id= qh_pointid (qh GOODpointp);  if (id >=0 && qh STOPcone-1 != id && -qh STOPpoint-1 != id)    SETelem_(pointset, id)= NULL;  if (qh GOODvertexp && qh ONLYgood && !qh MERGING) { /* matches qhull()*/    if ((id= qh_pointid(qh GOODvertexp)) >= 0)      SETelem_(pointset, id)= NULL;  }  if (!qh BESToutside) {  /* matches conditional for qh_partitionpoint below */    if (qh MERGING)      distoutside= qh_DISToutside; /* defined in user.h */    else      distoutside= qh MINoutside;    zval_(Ztotpartition)= qh num_points - qh hull_dim - 1; /*misses GOOD... */    remaining= qh num_facets;    point_end= numpoints;    FORALLfacets {      size= point_end/(remaining--) + 100;      facet->outsideset= qh_setnew (size);      bestpoint= NULL;      point_end= 0;      FOREACHpoint_i_(pointset) {        if (point) {          zzinc_(Zpartitionall);          qh_distplane (point, facet, &dist);          if (dist < distoutside)            SETelem_(pointset, point_end++)= point;          else {	    qh num_outside++;            if (!bestpoint) {              bestpoint= point;              bestdist= dist;            }else if (dist > bestdist) {              qh_setappend (&facet->outsideset, bestpoint);              bestpoint= point;              bestdist= dist;            }else               qh_setappend (&facet->outsideset, point);          }        }      }      if (bestpoint) {        qh_setappend (&facet->outsideset, bestpoint);#if !qh_COMPUTEfurthest	facet->furthestdist= bestdist;#endif      }else        qh_setfree (&facet->outsideset);      qh_settruncate (pointset, point_end);    }  }  if (qh BESToutside || qh MERGING || qh KEEPcoplanar || qh KEEPinside) {    qh findbestnew= True;    FOREACHpoint_i_(pointset) {       if (point)        qh_partitionpoint(point, qh facet_list);    }    qh findbestnew= False;  }  zzadd_(Zpartitionall, zzval_(Zpartition));  zzval_(Zpartition)= 0;  qh_settempfree(&pointset);  if (qh IStracing >= 4)    qh_printfacetlist (qh facet_list, NULL, True);} /* partitionall *//*--------------------------------------------------partitioncoplanar- partition coplanar point to a facet  if dist NULL, searches for bestfacet, and does nothing if inside      if qh findbestnew, searches new facets instead of findbestreturns: