qhmem is defined in mem.h and qhstat is defined in stat.h   access to qh_qh is via the "qh" macro.  See qh_QHpointer in user.h*/typedef struct qhT qhT;    #if qh_QHpointer#define qh qh_qh->extern qhT *qh_qh;     /* allocated in global.c */#else#define qh qh_qh.extern qhT qh_qh;#endifextern char qh_version[];  /* defined in unix.c */struct qhT {  /*-user flags */  boolT ALLpoints;        /* true 'Qi' if search all points for initial simplex */  boolT ANGLEmerge;	  /* true 'Qa' if sort potential merges by angle */  boolT APPROXhull;       /* true 'Wn' if MINoutside set */  realT MINoutside;       /*   'Wn' min. distance for an outside point */  boolT ATinfinity;       /* true 'd' if point num_points-1 is "at-infinity"                             false 'Qu' if upper hull (no point at-infinity) */  boolT AVOIDold;         /* true 'Q4' if avoid old->new merges */  boolT BESToutside;      /* true 'Qf' if partition points into best outsideset */  boolT CDDinput;         /* true 'Pc' if input uses CDD format (1.0/offset first) */  boolT CDDoutput;        /* true 'PC' if print normals in CDD format (offset first) */  boolT CHECKfrequently;  /* true 'Tc' if checking frequently */  realT premerge_cos;     /*   'A-n'   cos_max when pre merging */  realT postmerge_cos;    /*   'An'    cos_max when post merging */  boolT DELAUNAY;         /* true 'd' if computing DELAUNAY triangulation */  boolT DOintersections;  /* true 'Gh' if print hyperplane intersections */  int   DROPdim;          /* drops dim 'GDn' for 4-d -> 3-d output */  boolT FORCEoutput;      /* true 'Po' if forcing output despite degeneracies */  int   GOODpoint;        /* 1+n for 'QGn', good facet if visible/not(-) from point n*/  pointT *GOODpointp;     /*   the actual point */  boolT GOODthreshold;    /* true if qh lower_threshold/upper_threshold defined   			     false if qh SPLITthreshold */  int   GOODvertex;       /* 1+n, good facet if vertex for point n */  pointT *GOODvertexp;     /*   the actual point */  boolT HALFspace;        /* true 'Hn,n,n' if half-space intersection */  int   IStracing;        /* trace execution, 0=none, 1=least, 4=most, -1=events */  int   KEEParea;         /* 'PAn' number of largest facets to keep */  boolT KEEPcoplanar;     /* true if keeping nearest facet for coplanar points */  boolT KEEPinside;       /* true if keeping nearest facet for inside points */  int   KEEPmerge;         /* 'PMn' number of facets to keep with most merges */  realT KEEPminArea;      /* 'PFn' minimum facet area to keep */  boolT MERGEexact;	  /* true 'Qx' if exact merges (coplanar, degen, dupridge, flipped) */  boolT MERGEindependent; /* true 'Q2' if merging independent sets */  boolT MERGING;          /* true if exact-, pre- or post-merging, with angle and centrum tests */  realT   premerge_centrum;  /*   'C-n' centrum_radius when pre merging */  realT   postmerge_centrum; /*   'Cn' centrum_radius when post merging */  boolT MERGEvertices;	  /* true 'Q3' if merging redundant vertices */  realT MAXcoplanar;      /* 'Un' max distance below a facet to be coplanar*/  realT MINvisible;       /* 'Vn' min. distance for a facet to be visible */  boolT NOnearinside;     /* true 'Q8' if ignore near-inside points when partitioning */  boolT ONLYgood; 	  /* true 'Qg' if process points with good visible or horizon facets */  boolT ONLYmax; 	  /* true 'Qm' if only process points that increase max_outside */  boolT POINTSmalloc;     /* true if qh first_point/num_points allocated */  boolT POSTmerge;        /* true if merging after buildhull (Cn or An) */  boolT PREmerge;         /* true if merging during buildhull (C-n or A-n) */  			/* NOTE: some of these names are similar to qh_PRINT names */  boolT PRINTcentrums;	  /* true 'Gc' if printing centrums */  boolT PRINTcoplanar;    /* true 'Gp' if printing coplanar points */  int	PRINTdim;      	  /* print dimension for Geomview output */  boolT PRINTdots;        /* true 'Ga' if printing all points as dots */  boolT PRINTgood;        /* true 'Pg' if printing good facets */  boolT PRINTinner;	  /* true 'Gi' if printing inner planes */  boolT PRINTneighbors;	  /* true 'PG' if printing neighbors of good facets */  boolT PRINTnoplanes;	  /* true 'Gn' if printing no planes */  boolT PRINToptions1st;  /* true 'FO' if printing options to stderr */  boolT PRINTouter;	  /* true 'Go' if printing outer planes */  boolT PRINTprecision;   /* false 'Pp' if not reporting precision problems */  qh_PRINT PRINTout[qh_PRINTEND]; /* list of output formats to print */  boolT PRINTridges;      /* true 'Gr' if print ridges */  boolT PRINTspheres;     /* true 'Gv' if print vertices as spheres */  boolT PRINTstatistics;  /* true 'Ts' if printing statistics to stderr */  boolT PRINTsummary;     /* true 's' if printing summary to stderr */  boolT PROJECTdelaunay;  /* true if DELAUNAY, no readpoints() and			     need projectinput() for Delaunay */  int   PROJECTinput;     /* number of projected dimensions 'bn:0Bn:0' */  boolT QUICKhelp;	  /* true if quick help message for degen input */  boolT RANDOMdist;       /* true if randomly change distplane and setfacetplane */  realT RANDOMfactor;     /*    maximum perturbation */  realT RANDOMa;         /*  qh_randomfactor is randr * RANDOMa + RANDOMb */  realT RANDOMb;  boolT RANDOMoutside;    /* true if select a random outside point */  int	REPORTfreq;       /* buildtracing reports every n facets */  int   REPORTfreq2;	  /* tracemerging reports every REPORTfreq/2 facets */  int	ROTATErandom;	  /* 'QRn' seed, 0 time, >= rotate input */  boolT SCALEinput;       /* true if scaling input, 'Qb' */  boolT SETroundoff;      /* true 'E' if qh DISTround is predefined */  boolT SKIPcheckmax;	  /* true 'Q5' if skip qh_check_maxout */  boolT SKIPconvex;       /* true 'Q6' if skip convexity testing during pre-merge */  boolT SPLITthresholds;  /* true if upper_/lower_threshold defines a region                               used only for printing (not for qh ONLYgood) */  int	STOPcone;         /* 'TCn' 1+n for stopping after cone for point n*/  int	STOPpoint;        /* 'TVn' 'TV-n' 1+n for stopping after/before(-) 			                adding point n */  boolT TESTvneighbors;   /*  true 'Qv' if test vertex neighbors at end */  int   TRACElevel;       /* 'Tn' conditional IStracing level */  int   TRACEpoint;       /* 'TPn' start tracing when point n is a vertex */  realT TRACEdist;        /* 'TWn' start tracing when merge distance too big */  int   TRACEmerge;       /* 'TMn' start tracing before this merge */  boolT VERIFYoutput;     /* true 'Tv' if verify output at end of qhull */  boolT VIRTUALmemory;    /* true 'Q7' if depth-first processing in buildhull */  boolT VORONOI;	  /* true 'v' if computing Voronoi diagram */  /* -input constants */  realT AREAfactor;       /* 1/(hull_dim-1)! for converting det's to area */  boolT DOcheckmax;       /* true if calling qh_check_maxout (qh_initqhull_globals) */  char	*feasible_string;  /* feasible point 'Hn,n,n' for half-space intersection */  coordT *feasible_point;  /*    as coordinates, both malloc'd */  boolT GETarea;          /* true if need to compute facet areas in io.c */  boolT KEEPnearinside;   /* true if near-inside points in coplanarset */  int 	input_dim;	  /* dimension of input, set by initbuffers */  int 	num_points;       /* number of input points */  pointT *first_point;    /* array of input points, malloc'd */  int 	hull_dim;         /* dimension of hull, set by initbuffers */  char 	qhull_command[256];/* command line that invoked this program */  char 	rbox_command[256]; /* command line that produced the input points */  char  qhull_options[512]; /* descriptive list of options */  int   qhull_optionslen; /*    length of line */  boolT VERTEXneighbors;  /* true if maintaining vertex neighbors */  boolT ZEROcentrum;      /* true if 'C-0' or 'C-0 Qx'.  sets ZEROall_ok */  realT *upper_threshold; /* don't print if facet->normal[k]>=upper_threshold[k]                             must set either GOODthreshold or SPLITthreshold  			     if Delaunay, default is 0.0 for upper envelope */  realT *lower_threshold; /* don't print if facet->normal[k] <=lower_threshold[k] */  realT *upper_bound;     /* scale point[k] to new upper bound */  realT *lower_bound;     /* scale point[k] to new lower bound   			     project if both upper_ and lower_bound == 0 */  /* -precision constants, computed in qh_maxmin */    realT ANGLEround;       /* max round off error for angles */  realT centrum_radius;   /* max centrum radius for convexity (roundoff added) */  realT cos_max;	  /* max cosine for convexity (roundoff added) */  realT DISTround;        /* max round off error for distances, 'E' overrides */  realT maxmaxcoord;      /* max coordinate in any dimension */  realT MINdenom_1;       /* min. abs. value for 1/x */  realT MINdenom;         /*    use divzero if denominator < MINdenom */  realT MINdenom_1_2;     /* min. abs. val for 1/x that allows normalization */  realT MINdenom_2;       /*    use divzero if denominator < MINdenom_2 */  realT MINnorm;          /* min. norm for not redoing qh_sethyperplane_det */  realT *NEARzero;        /* hull_dim array for near zero in gausselim */  realT NEARinside;       /* keep points for qh_check_maxout if close to facet */  realT ONEmerge;         /* max distance for merging simplicial facets */  realT WIDEfacet;        /* size of wide facet for skipping ridge in			     area computation and locking centrum */    /* -internal constants */  char qhull[sizeof("qhull")]; /* for checking ownership */  void *old_stat;         /* pointer to saved qh_qhstat, qh_save_qhull */  jmp_buf errexit;        /* exit label for qh_errexit, defined by setjmp() */  char jmpXtra[40];       /* extra bytes in case jmp_buf is defined wrong */  FILE *fin;              /* pointer to input file, init by qh_meminit */  FILE *fout;             /* pointer to output file */  FILE *ferr;             /* pointer to error file */  pointT *interior_point; /* center point of the initial simplex*/  int   normal_size;      /* size in bytes for facet normals and point coords*/  int   center_size;      /* size in bytes for Voronoi centers */  int   TEMPsize;         /* size for small, temporary sets (in quick mem) */  /* -list of all facets, from facet_list to facet_tail, see qh_appendfacet */   facetT *facet_list;     /* first facet */  facetT  *facet_tail;     /* end of facet_list (dummy facet) */  facetT *facet_next;     /* next facet for buildhull()    			     all previous facets do not have outside sets*/  facetT *newfacet_list;  /* list of new facets to end of facet_list */  facetT *visible_list;   /* list of visible facets preceeding newfacet_list,                             facet->visible set */  int       num_visible;  /* current number of visible facets */  unsigned tracefacet_id;  /* set at init, then can print whenever */  facetT *tracefacet;     /*   set in newfacet/mergefacet, undone in delfacet*/  unsigned tracevertex_id;  /* set at buildtracing, can print whenever */  vertexT *tracevertex;     /*   set in newvertex, undone in delvertex*/  vertexT *vertex_list;   /* list of all vertices, to vertex_tail */  vertexT  *vertex_tail;     vertexT *newvertex_list; /* list of vertices in newfacet_list, to vertex_tail                             all vertices have 'newlist' set */  int 	num_facets;	  /* number of facets in facet_list			     includes visble faces (num_visible) */  int 	num_vertices;     /* number of vertices in facet_list */  int   num_outside;      /* number of points in outsidesets (for tracing) */  int   num_good;         /* number of good facets (after findgood_all) */  int 	facet_id;         /* id of next, new facet from newfacet() */  int 	ridge_id;         /* id of next, new ridge from newridge() */  unsigned vertex_id;        /* id of next, new vertex from newvertex() */  /* -variables */    unsigned hulltime;       /* ignore time to set up input and randomize */  qh_CENTER CENTERtype;       /* current type of facet->center, qh_CENTER */  int 	furthest_id;      /* pointid of furthest point, for tracing */  facetT *GOODclosest;    /* closest facet to GOODthreshold in qh_findgood */  realT max_outside;      /* maximum distance from a point to a facet,			       before roundoff, not simplicial vertices			       actual outer plane is +DISTround and			       computed outer plane is +2*DISTround */  realT max_vertex;       /* maximum distance (>0) from vertex to a facet,			       before roundoff, not simplicial vertices */  realT min_vertex;       /* minimum distance (<0) from vertex to a facet,			       before roundoff, not simplicial vertices 			       actual inner plane is -DISTround and			       computed inner plane is -2*DISTround */  boolT NEWfacets;        /* true while visible facets invalid due to new or merge			      from makecone/attachnewfacets to deletevisible */  boolT findbestnew;	  /* true if partitioning calls qh_findbestnew */  boolT findbest_notsharp; /* true if new facets are at least 90 degrees */  boolT NOerrexit;        /* true if qh_errexit is not available */  realT PRINTcradius;     /* radius for printing centrums */  realT PRINTradius;      /* radius for printing vertex spheres and points */  boolT POSTmerging;      /* true when post merging */  int 	printoutvar;	  /* temporary variable for qh_printbegin, etc. */  int 	printoutnum;	  /* number of facets printed */  boolT QHULLfinished;    /* True after qhull() is finished */  realT totarea;          /* total facet area computed by qh_getarea */  realT totvol;           /* total volume computed by qh_getarea */  int 	visit_id;         /* unique id for searching neighborhoods, */  int 	vertex_visit;     /* unique id for searching vertices */  boolT ZEROall_ok;       /* True if qh_checkzero always succeeds */    /* -sets */  setT *facet_mergeset;   /* temporary set of merges to be done */  setT *degen_mergeset;   /* temporary set of degenerate and redundant merges */  setT *initial_points;   /* initial simplex for buildhull() */  setT *hash_table;	  /* hash table for matching ridges in qh_matchfacets                              size is setsize() */  int   num_hashentries;  /* current number of hashentries */  setT *other_points;     /* additional points (first is qh interior_point) */