/*    assume precise calculations in io.c with roundoff covered by qh_GEOMepsilon    mindist may be off by qh DISTround.  Maxoutside is calculated elsewhere    so a DISTround error may have occured.  */  if (qh MERGING) {#if qh_MAXoutside    maxdist= facet->maxoutside+qh PRINTradius+ qh DISTround;#else    maxdist= qh max_outside+qh PRINTradius+ qh DISTround;#endif    if (qh PRINTcoplanar || qh PRINTspheres)      maxdist += qh maxmaxcoord * qh_GEOMepsilon;   }else     maxdist= 0;  if (qh MERGING)    mindist= -qh PRINTradius - qh DISTround;  else    mindist= 0;  if (qh PRINTouter || (!qh PRINTnoplanes && !qh PRINTinner))    qh_printfacet3geom_points(fp, points, facet, maxdist, color);  if (qh PRINTinner || (!qh PRINTnoplanes && !qh PRINTouter &&              maxdist - mindist > 2 * qh maxmaxcoord * qh_GEOMepsilon)) {    for (k= 3; k--; )      color[k]= 1.0 - color[k];    qh_printfacet3geom_points(fp, points, facet, mindist, color);  }  qh_settempfree(&points);  qh_settempfree(&vertices);  if ((qh DOintersections || qh PRINTridges)  && (!facet->visible || !qh NEWfacets)) {    facet->visitid= qh visit_id;    FOREACHneighbor_(facet) {      if (neighbor->visitid != qh visit_id) {	vertices= qh_setnew_delnthsorted (facet->vertices, qh hull_dim,	                  SETindex_(facet->neighbors, neighbor), 0);        if (qh DOintersections)	   qh_printhyperplaneintersection(fp, facet, neighbor, vertices, black);         if (qh PRINTridges) {          vertexA= SETfirst_(vertices);          vertexB= SETsecond_(vertices);          qh_printline3geom (fp, vertexA->point, vertexB->point, green);        }	qh_setfree(&vertices);      }    }  }} /* printfacet3geom_simplicial *//*------------------------------------------printfacet3vertex- print vertex->point for a 3-d facet (may be non-simplicial)  prints number of vertices first if format == qh_PRINToff*/void qh_printfacet3vertex(FILE *fp, facetT *facet, int format) {  vertexT *vertex, **vertexp;  setT *vertices;  vertices= qh_facet3vertex (facet);  if (format == qh_PRINToff)    fprintf (fp, "%d ", qh_setsize (vertices));  FOREACHvertex_(vertices)     fprintf (fp, "%d ", qh_pointid(vertex->point));  fprintf (fp, "\n");  qh_settempfree(&vertices);} /* printfacet3vertex *//*-----------------------------------------printfacet3math- print 3-d Mathematica output for a facet  may be non-simplicial*/void qh_printfacet3math (FILE *fp, facetT *facet, int notfirst) {  vertexT *vertex, **vertexp;  setT *points, *vertices;  pointT *point, **pointp;  boolT firstpoint= True;  realT dist;    if (notfirst)    fprintf(fp, ",\n");  vertices= qh_facet3vertex (facet);  points= qh_settemp (qh_setsize (vertices));  FOREACHvertex_(vertices) {    zinc_(Zdistio);    qh_distplane(vertex->point, facet, &dist);    point= qh_projectpoint(vertex->point, facet, dist);    qh_setappend (&points, point);  }  fprintf(fp, "Polygon[{");  FOREACHpoint_(points) {    if (firstpoint)      firstpoint= False;    else      fprintf(fp, ",\n");    fprintf(fp, "{%10.8g, %10.8g, %10.8g}", point[0], point[1], point[2]);  }  FOREACHpoint_(points)    qh_memfree (point, qh normal_size);  qh_settempfree(&points);  qh_settempfree(&vertices);  fprintf(fp, "}]");} /* printfacet3math *//*------------------------------------------printfacet4geom_nonsimplicial- print Geomview 4OFF file for a 4d nonsimplicial facet  prints all ridges to unvisited neighbors (qh visit_id)    must agree with printend4geom()  prints in OFF format if DROPdim*/void qh_printfacet4geom_nonsimplicial(FILE *fp, facetT *facet, realT color[3]) {  facetT *neighbor;  ridgeT *ridge, **ridgep;  vertexT *vertex, **vertexp;  pointT *point;  int k;  realT dist;    facet->visitid= qh visit_id;  if (qh PRINTnoplanes || (facet->visible && qh NEWfacets))    return;  FOREACHridge_(facet->ridges) {    neighbor= otherfacet_(ridge, facet);    if (neighbor->visitid == qh visit_id)       continue;    if (qh DOintersections)      qh_printhyperplaneintersection(fp, facet, neighbor, ridge->vertices, color);    else {      if (qh DROPdim >= 0) 	fprintf(fp, "OFF 3 1 1 # f%d\n", facet->id);      else {	qh printoutvar++;	fprintf (fp, "# r%d between f%d f%d\n", ridge->id, facet->id, neighbor->id);      }      FOREACHvertex_(ridge->vertices) {	zinc_(Zdistio);	qh_distplane(vertex->point,facet, &dist);	point=qh_projectpoint(vertex->point,facet, dist);	for(k= 0; k < qh hull_dim; k++) {	  if (k != qh DROPdim)  	    fprintf(fp, "%8.4g ", point[k]);  	}	fprintf (fp, "\n");	qh_memfree (point, qh normal_size);      }      if (qh DROPdim >= 0)        fprintf(fp, "3 0 1 2 %8.4g %8.4g %8.4g\n", color[0], color[1], color[2]);    }  }} /* printfacet4geom_nonsimplicial *//*------------------------------------------printfacet4geom_simplicial- print Geomview 4OFF file for a 4d simplicial facet  prints triangles for unvisited neighbors (qh visit_id)    must agree with printend4geom()*/void qh_printfacet4geom_simplicial(FILE *fp, facetT *facet, realT color[3]) {  setT *vertices;  facetT *neighbor, **neighborp;  vertexT *vertex, **vertexp;  int k;    facet->visitid= qh visit_id;  if (qh PRINTnoplanes || (facet->visible && qh NEWfacets))    return;  FOREACHneighbor_(facet) {    if (neighbor->visitid == qh visit_id)      continue;    vertices= qh_setnew_delnthsorted (facet->vertices, qh hull_dim,	                  SETindex_(facet->neighbors, neighbor), 0);    if (qh DOintersections)      qh_printhyperplaneintersection(fp, facet, neighbor, vertices, color);    else {      if (qh DROPdim >= 0) 	fprintf(fp, "OFF 3 1 1 # ridge between f%d f%d\n",		facet->id, neighbor->id);      else {	qh printoutvar++;	fprintf (fp, "# ridge between f%d f%d\n", facet->id, neighbor->id);      }      FOREACHvertex_(vertices) {	for(k= 0; k < qh hull_dim; k++) {	  if (k != qh DROPdim)  	    fprintf(fp, "%8.4g ", vertex->point[k]);  	}	fprintf (fp, "\n");      }      if (qh DROPdim >= 0)         fprintf(fp, "3 0 1 2 %8.4g %8.4g %8.4g\n", color[0], color[1], color[2]);    }    qh_setfree(&vertices);  }} /* printfacet4geom_simplicial *//*------------------------------------------printfacetNvertex_nonsimplicial- print vertices for an N-d non-simplicial facet  triangulates each ridge to the id*/void qh_printfacetNvertex_nonsimplicial(FILE *fp, facetT *facet, int id) {  vertexT *vertex, **vertexp;  ridgeT *ridge, **ridgep;  if (facet->visible && qh NEWfacets)    return;  FOREACHridge_(facet->ridges) {    fprintf(fp, "%d ", id);    if ((ridge->top == facet) ^ qh_ORIENTclock) {      FOREACHvertex_(ridge->vertices)        fprintf(fp, "%d ", qh_pointid(vertex->point));    }else {      FOREACHvertexreverse12_(ridge->vertices)        fprintf(fp, "%d ", qh_pointid(vertex->point));    }    fprintf(fp, "\n");  }} /* printfacetNvertex_nonsimplicial *//*------------------------------------------printfacetNvertex_simplicial- print vertices for an N-d simplicial facet  also prints PRINToff format for non-simplicial facets*/void qh_printfacetNvertex_simplicial(FILE *fp, facetT *facet, int format) {  vertexT *vertex, **vertexp;  if (format == qh_PRINToff)    fprintf (fp, "%d ", qh_setsize (facet->vertices));  if ((facet->toporient ^ qh_ORIENTclock) || !facet->simplicial) {    FOREACHvertex_(facet->vertices)      fprintf(fp, "%d ", qh_pointid(vertex->point));  }else {    FOREACHvertexreverse12_(facet->vertices)      fprintf(fp, "%d ", qh_pointid(vertex->point));  }  fprintf(fp, "\n");} /* printfacetNvertex_simplicial *//*------------------------------------------printfacetheader- prints header fields of a facet to fp*/void qh_printfacetheader(FILE *fp, facetT *facet) {  pointT *point, **pointp, *furthest;  facetT *neighbor, **neighborp;  realT dist;  if (facet == qh_MERGEridge) {    fprintf (fp, " MERGEridge\n");    return;  }else if (facet == qh_DUPLICATEridge) {    fprintf (fp, " DUPLICATEridge\n");    return;  }else if (!facet) {    fprintf (fp, " NULLfacet\n");    return;  }  fprintf(fp, "- f%d\n", facet->id);  fprintf(fp, "    - flags:");  if (facet->toporient)     fprintf(fp, " top");  else    fprintf(fp, " bottom");  if (facet->simplicial)    fprintf(fp, " simplicial");  if (facet->upperdelaunay)    fprintf(fp, " upperDelaunay");  if (facet->visible)    fprintf(fp, " visible");  if (facet->newfacet)    fprintf(fp, " new");  if (facet->tested)    fprintf(fp, " tested");  if (!facet->good)    fprintf(fp, " notG");  if (facet->seen)    fprintf(fp, " seen");  if (facet->coplanar)    fprintf(fp, " coplanar");  if (facet->mergehorizon)    fprintf(fp, " mergehorizon");  if (facet->keepcentrum)    fprintf(fp, " keepcentrum");  if (facet->dupridge)    fprintf(fp, " dupridge");  if (facet->mergeridge && !facet->mergeridge2)    fprintf(fp, " mergeridge1");  if (facet->mergeridge2)    fprintf(fp, " mergeridge2");  if (facet->newmerge)    fprintf(fp, " newmerge");  if (facet->flipped)     fprintf(fp, " flipped");  if (facet->degenerate)    fprintf(fp, " degenerate");  if (facet->redundant)    fprintf(fp, " redundant");  fprintf(fp, "\n");  if (facet->isarea)    fprintf(fp, "    - area: %2.2g\n", facet->f.area);  else if (qh NEWfacets && facet->visible && facet->f.replace)    fprintf(fp, "    - replacement: f%d\n", facet->f.replace->id);  else if (facet->newfacet) {    if (facet->f.samecycle && facet->f.samecycle != facet)      fprintf(fp, "    - shares same visible/horizon as f%d\n", facet->f.samecycle->id);  }else if (facet->f.newcycle)    fprintf(fp, "    - was horizon to f%d\n", facet->f.newcycle->id);  if (facet->nummerge)    fprintf(fp, "    - merges: %d\n", facet->nummerge);  qh_printpoint(fp, "    - normal: ", facet->normal);  fprintf(fp, "    - offset: %10.7g\n", facet->offset);  if (qh CENTERtype == qh_ASvoronoi || facet->center)    qh_printcenter (fp, qh_PRINTfacets, "    - center: ", facet);#if qh_MAXoutside  if (facet->maxoutside > qh DISTround)    fprintf(fp, "    - maxoutside: %10.7g\n", facet->maxoutside);#endif  if (!SETempty_(facet->outsideset)) {    furthest= (pointT*)qh_setlast(facet->outsideset);    if (qh_setsize (facet->outsideset) < 6) {      fprintf(fp, "    - outside set (furthest p%d):\n", qh_pointid(furthest));      FOREACHpoint_(facet->outsideset)	qh_printpoint(fp, "     ", point);    }else if (qh_setsize (facet->outsideset) < 21) {      qh_printpoints(fp, "    - outside set:", facet->outsideset);    }else {      fprintf(fp, "    - outside set:  %d points.", qh_setsize(facet->outsideset));      qh_printpoint(fp, "  Furthest", furthest);    }#if !qh_COMPUTEfurthest    fprintf(fp, "    - furthest distance= %2.2g\n", facet->furthestdist);#endif  }  if (!SETempty_(facet->coplanarset)) {    furthest= (pointT*)qh_setlast(facet->coplanarset);    if (qh_setsize (facet->coplanarset) < 6) {      fprintf(fp, "    - coplanar set (furthest p%d):\n", qh_pointid(furthest));      FOREACHpoint_(facet->coplanarset)	qh_printpoint(fp, "     ", point);    }else if (qh_setsize (facet->coplanarset) < 21) {      qh_printpoints(fp, "    - coplanar set:", facet->coplanarset);    }else {      fprintf(fp, "    - coplanar set:  %d points.", qh_setsize(facet->coplanarset));      qh_printpoint(fp, "  Furthest", furthest);    }    zinc_(Zdistio);    qh_distplane (furthest, facet, &dist);    fprintf(fp, "      furthest distance= %2.2g\n", dist);  }  qh_printvertices (fp, "    - vertices:", facet->vertices);  fprintf(fp, "    - neighboring facets: ");  FOREACHneighbor_(facet) {    if (neighbor == qh_MERGEridge)      fprintf(fp, " MERGE");    else if (neighbor == qh_DUPLICATEridge)      fprintf(fp, " DUP");    else      fprintf(fp, " f%d", neighbor->id);  }  fprintf(fp, "\n");} /* printfacetheader *//*------------------------------------------printfacetridges- prints ridges of a facet to fp  ridges printed in neighbor order  assumes the ridges exist*/void qh_printfacetridges(FILE *fp, facetT *facet) {  facetT *neighbor, **neighborp;  ridgeT *ridge, **ridgep, *firstridge;  int numridges= 0;  if (facet->visible && qh NEWfacets) {    fprintf(fp, "    - ridges (ids may be garbage):");    FOREACHridge_(facet->ridges)      fprintf(fp, " r%d", ridge->id);    fprintf(fp, "\n");  }else {    fprintf(fp, "    - ridges:\n");    FOREACHridge_(facet->ridges)      ridge->seen= False;    if (qh hull_dim == 3) {      ridge= firstridge= SETfirst_(facet->ridges);      while (ridge && !ridge->seen) {	ridge->seen= True;	qh_printridge(fp, ridge);	numridges++;