qh_printfacetheader (fp, facet);    break;  case qh_PRINTgeom:  /* either 2 , 3, or 4-d by qh_printbegin */    if (!facet->normal)      break;    for (k= qh hull_dim; k--; ) {      color[k]= (facet->normal[k]+1.0)/2.0;      maximize_(color[k], -1.0);      minimize_(color[k], +1.0);    }    qh_projectdim3 (color, color);    if (qh PRINTdim != qh hull_dim)      qh_normalize2 (color, 3, True, NULL, NULL);    if (qh hull_dim <= 2)      qh_printfacet2geom (fp, facet, color);    else if (qh hull_dim == 3) {      if (facet->simplicial)        qh_printfacet3geom_simplicial (fp, facet, color);      else        qh_printfacet3geom_nonsimplicial (fp, facet, color);    }else {      if (facet->simplicial)        qh_printfacet4geom_simplicial (fp, facet, color);      else        qh_printfacet4geom_nonsimplicial (fp, facet, color);    }    break;  case qh_PRINTids:    fprintf (fp, "%d\n", facet->id);    break;  case qh_PRINToff:  case qh_PRINTincidences:    if (qh hull_dim == 3)       qh_printfacet3vertex (fp, facet, format);    else if (facet->simplicial || qh hull_dim == 2 || format == qh_PRINToff)      qh_printfacetNvertex_simplicial (fp, facet, format);    else      qh_printfacetNvertex_nonsimplicial (fp, facet, qh printoutvar++);    break;  case qh_PRINTinner:    mindist= REALmax;    FOREACHvertex_(facet->vertices) {      qh_distplane (vertex->point, facet, &dist);      minimize_(mindist, dist);    }    offset= facet->offset - mindist - qh DISTround;    goto LABELprintnorm;  case qh_PRINTmerges:    fprintf (fp, "%d\n", facet->nummerge);    break;  case qh_PRINTnormals:    offset= facet->offset;    goto LABELprintnorm;  case qh_PRINTouter:#if qh_MAXoutside    offset= -facet->maxoutside;#endif    if (!qh MERGING || !qh_MAXoutside || qh SKIPcheckmax)      offset= -fmax_(qh max_outside, qh DISTround);    offset -= qh DISTround;      /* agrees with qh_check_points */    /* 1 DISTround to actual point */    offset += facet->offset;  LABELprintnorm:    if (!facet->normal) {      fprintf (fp, "no normal for facet f%d\n", facet->id);      break;    }    if (qh CDDoutput)       fprintf (fp, qh_REAL_1, -offset);    for (k=0; k<qh hull_dim; k++)       fprintf (fp, qh_REAL_1, facet->normal[k]);    if (!qh CDDoutput)       fprintf (fp, qh_REAL_1, offset);    fprintf (fp, "\n");    break;  case qh_PRINTmathematica:  /* either 2 or 3-d by qh_printbegin */    if (qh hull_dim == 2)      qh_printfacet2math (fp, facet, qh printoutvar++);    else       qh_printfacet3math (fp, facet, qh printoutvar++);    break;  case qh_PRINTneighbors:    fprintf (fp, "%d", qh_setsize (facet->neighbors));    FOREACHneighbor_(facet)      fprintf (fp, " %d", 	       neighbor->visitid ? neighbor->visitid - 1: - neighbor->id);    fprintf (fp, "\n");    break;  case qh_PRINTpointintersect:    if (!qh feasible_point) {      fprintf (fp, "qhull input error (qh_printafacet): option 'Fp' needs qh feasible_point\n");      qh_errexit( qh_ERRinput, NULL, NULL);    }    if (facet->offset > 0)      goto LABELprintinfinite;    point= coordp= (coordT*)qh_memalloc (qh normal_size);    normp= facet->normal;    feasiblep= qh feasible_point;    if (facet->offset < -qh MINdenom) {      for (k= qh hull_dim; k--; )        *(coordp++)= (*(normp++) / - facet->offset) + *(feasiblep++);    }else {      for (k= qh hull_dim; k--; ) {        *(coordp++)= qh_divzero (*(normp++), facet->offset, qh MINdenom_1,				 &zerodiv) + *(feasiblep++);        if (zerodiv) {          qh_memfree (point, qh normal_size);          goto LABELprintinfinite;        }      }    }    qh_printpoint (fp, NULL, point);    qh_memfree (point, qh normal_size);    break;  LABELprintinfinite:    for (k= qh hull_dim; k--; )      fprintf (fp, qh_REAL_1, qh_INFINITE);    fprintf (fp, "\n");       break;  case qh_PRINTpointnearest:    FOREACHpoint_(facet->coplanarset) {      int id, id2;      vertex= qh_nearvertex (facet, point, &dist);      id= qh_pointid (vertex->point);      id2= qh_pointid (point);      fprintf (fp, "%d %d %d " qh_REAL_1 "\n", id, id2, facet->id, dist);    }    break;  case qh_PRINTpoints:  /* VORONOI only by qh_printbegin */    if (qh CDDoutput)      fprintf (fp, "1 ");    qh_printcenter (fp, format, NULL, facet);    break;  case qh_PRINTvertices:    fprintf (fp, "%d", qh_setsize (facet->vertices));    FOREACHvertex_(facet->vertices)      fprintf (fp, " %d", qh_pointid (vertex->point));    fprintf (fp, "\n");    break;  }} /* printafacet *//*------------------------------------------printbegin- prints header for all output formats  checks for valid format  uses qh visit_id for 3/4off  changes qh interior_point if printing centrums*/void qh_printbegin (FILE *fp, int format, facetT *facetlist, setT *facets, boolT printall) {  int numfacets, numsimplicial, numridges, totneighbors, numcoplanars;  int i, num;  facetT *facet, **facetp;  vertexT *vertex, **vertexp;  setT *vertices;  pointT *point, **pointp, *pointtemp;  qh printoutnum= 0;  qh_countfacets (facetlist, facets, printall, &numfacets, &numsimplicial,       &totneighbors, &numridges, &numcoplanars);  switch (format) {  case qh_PRINTnone:    break;  case qh_PRINTarea:    fprintf (fp, "%d\n", numfacets);    break;  case qh_PRINTcoplanars:    fprintf (fp, "%d\n", numfacets);    break;  case qh_PRINTcentrums:    if (qh CENTERtype == qh_ASnone)      qh_clearcenters (qh_AScentrum);    fprintf (fp, "%d\n%d\n", qh hull_dim, numfacets);    break;  case qh_PRINTfacets:  case qh_PRINTfacets_xridge:    if (facetlist)      qh_printvertexlist (fp, "Vertices and facets:\n", facetlist, facets, printall);    break;  case qh_PRINTgeom:     if (qh hull_dim > 4)  /* qh_initqhull_globals also checks */      goto LABELnoformat;    if (qh VORONOI && qh hull_dim > 3)  /* PRINTdim == DROPdim == hull_dim-1 */      goto LABELnoformat;    if (qh hull_dim == 2 && (qh PRINTridges || qh DOintersections))      fprintf (qh ferr, "qhull warning: output for ridges and intersections not implemented in 2-d\n");    if (qh hull_dim == 4 && (qh PRINTinner || qh PRINTouter ||			     (qh PRINTdim == 4 && qh PRINTcentrums)))      fprintf (qh ferr, "qhull warning: output for outer/inner planes and centrums not implemented in 4-d\n");    if (qh PRINTdim == 4 && (qh PRINTspheres))      fprintf (qh ferr, "qhull warning: output for vertices not implemented in 4-d\n");    if (qh PRINTdim == 4 && qh DOintersections && qh PRINTnoplanes)      fprintf (qh ferr, "qhull warning: 'Gnh' generates no output in 4-d\n");    if (qh PRINTdim == 2) {      fprintf(fp, "{appearance {linewidth 3} LIST # %s | %s\n",	      qh rbox_command, qh qhull_command);    }else if (qh PRINTdim == 3) {      fprintf(fp, "{appearance {+edge -evert linewidth 2} LIST # %s | %s\n",	      qh rbox_command, qh qhull_command);    }else if (qh PRINTdim == 4) {      qh visit_id++;      num= 0;      FORALLfacet_(facetlist)    /* get number of ridges to be printed */        qh_printend4geom (NULL, facet, &num, printall);      FOREACHfacet_(facets)        qh_printend4geom (NULL, facet, &num, printall);      qh ridgeoutnum= num;      qh printoutvar= 0;  /* counts number of ridges in output */      fprintf (fp, "LIST # %s | %s\n", qh rbox_command, qh qhull_command);    }    if (qh PRINTdots) {      qh printoutnum++;      num= qh num_points + qh_setsize (qh other_points);      if (qh DELAUNAY && qh ATinfinity)	num--;      if (qh PRINTdim == 4)        fprintf (fp, "4VECT %d %d 1\n", num, num);      else	fprintf (fp, "VECT %d %d 1\n", num, num);      for (i= num; i--; ) {        if (i % 20 == 0)          fprintf (fp, "\n");	fprintf (fp, "1 ");      }      fprintf (fp, "# 1 point per line\n1 ");      for (i= num-1; i--; ) {        if (i % 20 == 0)          fprintf (fp, "\n");	fprintf (fp, "0 ");      }      fprintf (fp, "# 1 color for all\n");      FORALLpoints {        if (!qh DELAUNAY || !qh ATinfinity || qh_pointid(point) != qh num_points-1) {	  if (qh PRINTdim == 4)	    qh_printpoint (fp, NULL, point);	  else	    qh_printpoint3 (fp, point);	}      }      FOREACHpoint_(qh other_points) {	if (qh PRINTdim == 4)	  qh_printpoint (fp, NULL, point);	else	  qh_printpoint3 (fp, point);      }      fprintf (fp, "0 1 1 1  # color of points\n");    }    if (qh PRINTdim == 4  && !qh PRINTnoplanes)      /* 4dview loads up multiple 4OFF objects slowly */      fprintf(fp, "4OFF %d %d 1\n", 3*qh ridgeoutnum, qh ridgeoutnum);    qh PRINTcradius= 2 * qh DISTround;  /* include test DISTround */    if (qh PREmerge) {      maximize_(qh PRINTcradius, qh premerge_centrum + qh DISTround);    }else if (qh POSTmerge)      maximize_(qh PRINTcradius, qh postmerge_centrum + qh DISTround);    qh PRINTradius= qh PRINTcradius;    if (qh PRINTspheres + qh PRINTcoplanar)      maximize_(qh PRINTradius, qh maxmaxcoord * qh_MINradius);    if (qh premerge_cos < REALmax/2) {      maximize_(qh PRINTradius, (1- qh premerge_cos) * qh maxmaxcoord);    }else if (!qh PREmerge && qh POSTmerge && qh postmerge_cos < REALmax/2) {      maximize_(qh PRINTradius, (1- qh postmerge_cos) * qh maxmaxcoord);    }    maximize_(qh PRINTradius, qh MINvisible);     if (qh PRINTdim != 4 &&	(qh PRINTcoplanar || qh PRINTspheres || qh PRINTcentrums)) {      vertices= qh_facetvertices (facetlist, facets, printall);      if (qh PRINTspheres && qh PRINTdim <= 3)         qh_printspheres (fp, vertices, qh PRINTradius);      if (qh PRINTcoplanar || qh PRINTcentrums) {        qh firstcentrum= True;        if (qh PRINTcoplanar&& !qh PRINTspheres) {          FOREACHvertex_(vertices)             qh_printpointvect2 (fp, vertex->point, NULL,				qh interior_point, qh PRINTradius);	}        FORALLfacet_(facetlist) {	  if (!printall && qh_skipfacet(facet))	    continue;	  if (!facet->normal)	    continue;          if (qh PRINTcentrums && qh PRINTdim <= 3)            qh_printcentrum (fp, facet, qh PRINTcradius);          FOREACHpoint_(facet->coplanarset)            qh_printpointvect2 (fp, point, facet->normal, NULL, qh PRINTradius);          FOREACHpoint_(facet->outsideset)            qh_printpointvect2 (fp, point, facet->normal, NULL, qh PRINTradius);        }        FOREACHfacet_(facets) {	  if (!printall && qh_skipfacet(facet))	    continue;	  if (!facet->normal)	    continue;          if (qh PRINTcentrums && qh PRINTdim <= 3)            qh_printcentrum (fp, facet, qh PRINTcradius);          FOREACHpoint_(facet->coplanarset)            qh_printpointvect2 (fp, point, facet->normal, NULL, qh PRINTradius);          FOREACHpoint_(facet->outsideset)            qh_printpointvect2 (fp, point, facet->normal, NULL, qh PRINTradius);        }      }      qh_settempfree (&vertices);    }    qh visit_id++; /* for printing hyperplane intersections */    break;  case qh_PRINTids:    fprintf (fp, "%d\n", numfacets);    break;  case qh_PRINTincidences:    if (qh VORONOI)      fprintf (qh ferr, "qhull warning: writing Delaunay.  Use 'p' or 'o' for Voronoi centers\n");    qh printoutvar= qh vertex_id;  /* centrum id for non-simplicial facets */    if (qh hull_dim <= 3)      fprintf(fp, "%d\n", numfacets);    else      fprintf(fp, "%d\n", numsimplicial+numridges);    break;  case qh_PRINTinner:  case qh_PRINTnormals:  case qh_PRINTouter:    if (qh CDDoutput)      fprintf (fp, "%s | %s\nbegin\n    %d %d real\n", qh rbox_command,               qh qhull_command, numfacets, qh hull_dim+1);    else      fprintf (fp, "%d\n%d\n", qh hull_dim+1, numfacets);    break;  case qh_PRINTmathematica:      if (qh hull_dim > 3)  /* qh_initbuffers also checks */      goto LABELnoformat;    if (qh VORONOI)      fprintf (qh ferr, "qhull warning: output is the Delaunay triangulation\n");    fprintf(fp, "{\n");    qh printoutvar= 0;   /* counts number of facets for notfirst */    break;  case qh_PRINTmerges:    fprintf (fp, "%d\n", numfacets);    break;  case qh_PRINTpointintersect:    fprintf (fp, "%d\n%d\n", qh hull_dim, numfacets);    break;  case qh_PRINTneighbors:    fprintf (fp, "%d\n", numfacets);    break;  case qh_PRINToff:    if (qh VORONOI)      goto LABELnoformat;    fprintf (fp, "%d\n%d %d %d\n", qh hull_dim,      qh num_points+qh_setsize (qh other_points), numfacets, totneighbors/2);    FORALLpoints      qh_printpoint (qh fout, NULL, point);    FOREACHpoint_(qh other_points)      qh_printpoint (qh fout, NULL, point);    break;  case qh_PRINTpointnearest:    fprintf (fp, "%d\n", numcoplanars);    break;  case qh_PRINTpoints:    if (!qh VORONOI)      goto LABELnoformat;    if (qh CDDoutput)      fprintf (fp, "%s | %s\nbegin\n%d %d real\n", qh rbox_command,             qh qhull_command, numfacets, qh hull_dim);    else      fprintf (fp, "%d\n%d\n", qh hull_dim-1, numfacets);    break;  case qh_PRINTvertices:    fprintf (fp, "%d\n", numfacets);    break;  case qh_PRINTsummary:  default:  LABELnoformat:    fprintf (qh ferr, "qhull internal error (qh_printbegin): can not use this format for dimension %d\n",         qh hull_dim);    qh_errexit (qh_ERRqhull, NULL, NULL);  }} /* printbegin *//*------------------------------------------printcenter- print facet center as either centrum or Voronoi center  nop if qh CENTERtype neither CENTERvoronoi nor CENTERcentrum  if upper envelope of Delaunay triangulation and point at-infinity    prints qh_INFINITE instead;  defines facet->center if needed  string may be NULL or include %d for id.  Don't include other '%' codes.  if format=PRINTgeom, adds a 0 if otherwise 2-d*/void qh_printcenter (FILE *fp, int format, char *string, facetT *facet) {  int k, num;    if (qh CENTERtype != qh_ASvoronoi && qh CENTERtype != qh_AScentrum)    return;