max_ouside updated  facet->maxoutside's updated at end by qh_check_maxout  if KEEPcoplanar or KEEPinside    point assigned to best coplanarset*/void qh_partitioncoplanar (pointT *point, facetT *facet, realT *dist) {  facetT *bestfacet;  pointT *oldfurthest;  realT bestdist, dist2;  int numpart= 0;  boolT isoutside, istrace= False;  if (!dist) {    if (qh findbestnew)      bestfacet= qh_findbestnew (point, facet, 			  &bestdist, NULL, &numpart);    else      bestfacet= qh_findbest (point, facet, qh_ALL, False,                           &bestdist, &isoutside, &numpart);    zinc_(Ztotpartcoplanar);    zzadd_(Zpartcoplanar, numpart);    if (qh KEEPnearinside) {      if (bestdist < -qh NEARinside) {         zinc_(Zcoplanarinside);        return;      }    }else if (!qh KEEPinside && bestdist < -qh MAXcoplanar) {      zinc_(Zcoplanarinside);      return;    }  }else {    bestfacet= facet;    bestdist= *dist;  }  if (qh KEEPcoplanar + qh KEEPinside + qh KEEPnearinside) {    oldfurthest= (pointT*)qh_setlast (bestfacet->coplanarset);    if (oldfurthest) {      zinc_(Zcomputefurthest);      qh_distplane (oldfurthest, bestfacet, &dist2);    }    if (!oldfurthest || dist2 < bestdist) {      qh_setappend(&bestfacet->coplanarset, point);      if (bestdist > qh max_outside) {	qh max_outside= bestdist;	if (bestdist > qh TRACEdist)	  istrace= True;      }    }else      qh_setappend2ndlast(&bestfacet->coplanarset, point);  }else { /* !KEEPcoplanar && !KEEPinside */    if (bestdist > qh max_outside) {      qh max_outside= bestdist;      if (bestdist > qh TRACEdist) 	istrace= True;    }  }  if (istrace) {    fprintf (qh ferr, "qh_partitioncoplanar: ====== p%d increases max_outside to %2.2g of f%d last p%d\n",		   qh_pointid(point), bestdist, bestfacet->id, qh furthest_id);    qh_errprint ("DISTANT", bestfacet, NULL, NULL, NULL);  }  trace4((qh ferr, "qh_partitioncoplanar: point p%d is coplanar with facet f%d (or inside) dist %2.2g\n",	  qh_pointid(point), bestfacet->id, bestdist));} /* partitioncoplanar *//*--------------------------------------------------partitionpoint- assigns point to a visible facet  uses qh_findbest with qh BESToutside and newfacets  qh findbestnew if search new facets instead of findbest()notes:  after qh_distplane, this and qh_findbest are most expensive in 3-d*/void qh_partitionpoint (pointT *point, facetT *facet) {  realT bestdist;  pointT *oldfurthest;  boolT isoutside;  facetT *bestfacet;  int numpart;#if qh_COMPUTEfurthest  realT dist;#endif  if (qh findbestnew)    bestfacet= qh_findbestnew (point, facet,			  &bestdist, &isoutside, &numpart);  else    bestfacet= qh_findbest (point, facet, qh BESToutside, True,			  &bestdist, &isoutside, &numpart);  zinc_(Ztotpartition);  zzadd_(Zpartition, numpart);  if (isoutside) {    if (!bestfacet->outsideset     || !(oldfurthest= (pointT*)qh_setlast (bestfacet->outsideset))) {      qh_setappend(&(bestfacet->outsideset), point);      if (!bestfacet->newfacet) {        qh_removefacet (bestfacet);  /* make sure it's after qh facet_next */        qh_appendfacet (bestfacet);      }#if !qh_COMPUTEfurthest      bestfacet->furthestdist= bestdist;#endif    }else {#if qh_COMPUTEfurthest      zinc_(Zcomputefurthest);      qh_distplane (oldfurthest, bestfacet, &dist);      if (dist < bestdist) 	qh_setappend(&(bestfacet->outsideset), point);      else	qh_setappend2ndlast(&(bestfacet->outsideset), point);#else      if (bestfacet->furthestdist < bestdist) {	qh_setappend(&(bestfacet->outsideset), point);	bestfacet->furthestdist= bestdist;      }else	qh_setappend2ndlast(&(bestfacet->outsideset), point);#endif    }    qh num_outside++;    trace4((qh ferr, "qh_partitionpoint: point p%d is outside facet f%d\n",	  qh_pointid(point), bestfacet->id));  }else if (bestdist >= -qh MAXcoplanar) {    zzinc_(Zcoplanarpart);    if (qh KEEPcoplanar + qh KEEPnearinside || bestdist > qh max_outside)       qh_partitioncoplanar (point, bestfacet, &bestdist);  }else if (qh KEEPnearinside && bestdist > -qh NEARinside) {    zinc_(Zpartnear);    qh_partitioncoplanar (point, bestfacet, &bestdist);  }else {    zinc_(Zpartinside);    trace4((qh ferr, "qh_partitionpoint: point p%d is inside all facets, closest to f%d dist %2.2g\n",	  qh_pointid(point), bestfacet->id, bestdist));    if (qh KEEPinside)	        qh_partitioncoplanar (point, bestfacet, &bestdist);  }} /* partitionpoint *//*--------------------------------------------------partitionvisible- partitions points in visible_list to newfacet_list  1st neighbor (if any) points to a horizon facet or a new facet  repartitions coplanar points if allpoints (not used)  qh findbestnew if search new facets instead of findbest()  qh findbest_notsharp should be clear*/void qh_partitionvisible(/*visible_list*/ boolT allpoints, int *numoutside) {  facetT *visible, *newfacet;  pointT *point, **pointp;  int coplanar=0, size, count;  vertexT *vertex, **vertexp;    if (qh ONLYmax)    maximize_(qh MINoutside, qh max_vertex);  *numoutside= 0;  FORALLvisible_facets {    if (!visible->outsideset && !visible->coplanarset)      continue;    newfacet= visible->f.replace;    count= 0;    while (newfacet && newfacet->visible) {      newfacet= newfacet->f.replace;      if (count++ > qh facet_id)	qh_infiniteloop (visible);    }    if (!newfacet)      newfacet= qh newfacet_list;    if (visible->outsideset) {      size= qh_setsize (visible->outsideset);      *numoutside += size;      qh num_outside -= size;      FOREACHpoint_(visible->outsideset)         qh_partitionpoint (point, newfacet);    }    if (visible->coplanarset && (qh KEEPcoplanar + qh KEEPinside + qh KEEPnearinside)) {      size= qh_setsize (visible->coplanarset);      coplanar += size;      FOREACHpoint_(visible->coplanarset) {        if (allpoints)          qh_partitionpoint (point, newfacet);        else          qh_partitioncoplanar (point, newfacet, NULL);      }    }  }  FOREACHvertex_(qh del_vertices) {    if (vertex->point) {      if (allpoints)        qh_partitionpoint (vertex->point, qh newfacet_list);      else        qh_partitioncoplanar (vertex->point, qh newfacet_list, NULL);    }  }  trace1((qh ferr,"qh_partitionvisible: partitioned %d points from outsidesets and %d points from coplanarsets\n", *numoutside, coplanar));} /* partitionvisible *//*-----------------------------------------printsummary- prints the summary about the computation  not in io.c so that user_eg.c can prevent io.c from loading*/void qh_printsummary(FILE *fp) {  realT ratio, dist;  float cpu;  int size, id, total, numvertices, numcoplanars= 0;  facetT *facet;  size= qh num_points + qh_setsize (qh other_points);  numvertices= qh num_vertices - qh_setsize (qh del_vertices);  id= qh_pointid (qh GOODpointp);  if (qh DELAUNAY)     numcoplanars= size - numvertices;  else {    FORALLfacets {      if (facet->coplanarset)	numcoplanars += qh_setsize( facet->coplanarset);    }  }  if (id >=0 && qh STOPcone-1 != id && -qh STOPpoint-1 != id)    size--;  if (qh VORONOI)    fprintf (fp, "\nVoronoi diagram by the convex");  else if (qh DELAUNAY)    fprintf (fp, "\nDelaunay triangulation by the convex");  else if (qh HALFspace)    fprintf (fp, "\nHalfspace intersection by the convex");  else    fprintf (fp, "\nConvex");  fprintf(fp, " hull of %d points in %d-d:\n\n", size, qh hull_dim);  fprintf(fp, "  Number of vertices%s: %d\n",	  qh HALFspace ? " (halfspaces)" : "", numvertices);  if (numcoplanars)     fprintf(fp, "  Number of %s points: %d\n", 	    qh DELAUNAY ? "similar" : "coplanar", numcoplanars);   fprintf(fp, "  Number of facets%s: %d\n", 	  qh HALFspace ? " (intersections)" : "",	  qh num_facets - qh num_visible);  if (qh num_good)    fprintf(fp, "  Number of good facets: %d\n", qh num_good);  fprintf(fp, "\nStatistics for: %s | %s",                       qh rbox_command, qh qhull_command);  if (qh ROTATErandom > 0)    fprintf(fp, " QR%d\n\n", qh ROTATErandom);  else    fprintf(fp, "\n\n");  fprintf(fp, "  Number of points processed: %d\n", zzval_(Zprocessed));  fprintf(fp, "  Number of hyperplanes created: %d\n", zzval_(Zsetplane));  fprintf(fp, "  Number of distance tests for qhull: %d\n", zzval_(Zpartition)+  zzval_(Zpartitionall)+zzval_(Znumvisibility)+zzval_(Zpartcoplanar));#if 0  /* NOTE: must print before printstatistics() */  {realT stddev, ave;  fprintf(fp, "  average new facet balance: %2.2g\n",	  wval_(Wnewbalance)/zval_(Zprocessed));  stddev= qh_stddev (zval_(Zprocessed), wval_(Wnewbalance),                                  wval_(Wnewbalance2), &ave);  fprintf(fp, "  new facet standard deviation: %2.2g\n", stddev);  fprintf(fp, "  average partition balance: %2.2g\n",	  wval_(Wpbalance)/zval_(Zpbalance));  stddev= qh_stddev (zval_(Zpbalance), wval_(Wpbalance),                                  wval_(Wpbalance2), &ave);  fprintf(fp, "  partition standard deviation: %2.2g\n", stddev);  }#endif  if (qh MERGING) {    total= zzval_(Ztotmerge) - zzval_(Zcyclehorizon) + zzval_(Zcyclefacettot);    fprintf(fp,"  Number of merged facets: %d\n", total);    fprintf(fp,"  Number of distance tests for merging: %d\n",zzval_(Zbestdist)+          zzval_(Zcentrumtests)+zzval_(Zdistconvex)+zzval_(Zdistcheck)+          zzval_(Zdistzero));  }  if (!qh RANDOMoutside && qh QHULLfinished) {    cpu= qh hulltime;    cpu /= qh_SECticks;    wval_(Wcpu)= cpu;    fprintf (fp, "  CPU seconds to compute hull (after input): %2.4g\n", cpu);  }  if (qh totarea != 0.0) {    fprintf(fp, "  %s facet area:   %2.8g\n", 	    zzval_(Ztotmerge) ? "Approximate" : "Total", qh totarea);    fprintf(fp, "  %s volume:       %2.8g\n", 	    zzval_(Ztotmerge) ? "Approximate" : "Total", qh totvol);  }  if (!qh FORCEoutput && qh max_outside > qh DISTround) {    dist= qh max_outside + qh DISTround;   /* agrees with qh_check_points */    /* 1 DISTround to actual point */    fprintf(fp, "  Maximum distance of %spoint above facet: %2.2g", 	    (qh QHULLfinished ? "" : "merged "), dist);    ratio= dist/(qh ONEmerge+ qh DISTround);    if (qh MERGING && ratio > 0.05 && (qh ONEmerge > qh MINoutside))      fprintf (fp, " (%.1fx)\n", ratio);    else      fprintf (fp, "\n");  }  if (!qh FORCEoutput && qh min_vertex < -qh DISTround) {    dist= qh min_vertex - qh DISTround;   /* agrees with qh_check_points */    /* 1 DISTround to actual point */    fprintf(fp, "  Maximum distance of %svertex below facet: %2.2g", 	    (qh QHULLfinished ? "" : "merged "), dist);    ratio= -dist/(qh ONEmerge+qh DISTround);    if (qh MERGING && ratio > 0.05)       fprintf (fp, " (%.1fx)\n", ratio);    else      fprintf (fp, "\n");  }  fprintf(fp, "\n");} /* printsummary */