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+/*<html><pre> -<a href="qh-qhull.htm"
+ >-------------------------------</a><a name="TOP">-</a>
+
+ libqhull.h
+ user-level header file for using qhull.a library
+
+ see qh-qhull.htm, qhull_a.h
+
+ Copyright (c) 1993-2015 The Geometry Center.
+ $Id: //main/2015/qhull/src/libqhull/libqhull.h#7 $$Change: 2066 $
+ $DateTime: 2016/01/18 19:29:17 $$Author: bbarber $
+
+ NOTE: access to qh_qh is via the 'qh' macro. This allows
+ qh_qh to be either a pointer or a structure. An example
+ of using qh is "qh.DROPdim" which accesses the DROPdim
+ field of qh_qh. Similarly, access to qh_qhstat is via
+ the 'qhstat' macro.
+
+ includes function prototypes for libqhull.c, geom.c, global.c, io.c, user.c
+
+ use mem.h for mem.c
+ use qset.h for qset.c
+
+ see unix.c for an example of using libqhull.h
+
+ recompile qhull if you change this file
+*/
+
+#ifndef qhDEFlibqhull
+#define qhDEFlibqhull 1
+
+/*=========================== -included files ==============*/
+
+/* user_r.h first for QHULL_CRTDBG */
+#include "user.h" /* user definable constants (e.g., qh_QHpointer) */
+
+#include "mem.h" /* Needed qhT in libqhull_r.h. Here for compatibility */
+#include "qset.h" /* Needed for QHULL_LIB_CHECK */
+/* include stat_r.h after defining boolT. Needed for qhT in libqhull_r.h. Here for compatibility and statT */
+
+#include <setjmp.h>
+#include <float.h>
+#include <time.h>
+#include <stdio.h>
+
+#if __MWERKS__ && __POWERPC__
+#include <SIOUX.h>
+#include <Files.h>
+#include <Desk.h>
+#endif
+
+#ifndef __STDC__
+#ifndef __cplusplus
+#if !_MSC_VER
+#error Neither __STDC__ nor __cplusplus is defined. Please use strict ANSI C or C++ to compile
+#error Qhull. You may need to turn off compiler extensions in your project configuration. If
+#error your compiler is a standard C compiler, you can delete this warning from libqhull.h
+#endif
+#endif
+#endif
+
+/*============ constants and basic types ====================*/
+
+extern const char qh_version[]; /* defined in global.c */
+extern const char qh_version2[]; /* defined in global.c */
+
+/*-<a href="qh-geom.htm#TOC"
+ >--------------------------------</a><a name="coordT">-</a>
+
+ coordT
+ coordinates and coefficients are stored as realT (i.e., double)
+
+ notes:
+ Qhull works well if realT is 'float'. If so joggle (QJ) is not effective.
+
+ Could use 'float' for data and 'double' for calculations (realT vs. coordT)
+ This requires many type casts, and adjusted error bounds.
+ Also C compilers may do expressions in double anyway.
+*/
+#define coordT realT
+
+/*-<a href="qh-geom.htm#TOC"
+ >--------------------------------</a><a name="pointT">-</a>
+
+ pointT
+ a point is an array of coordinates, usually qh.hull_dim
+ qh_pointid returns
+ qh_IDnone if point==0 or qh is undefined
+ qh_IDinterior for qh.interior_point
+ qh_IDunknown if point is neither in qh.first_point... nor qh.other_points
+
+ notes:
+ qh.STOPcone and qh.STOPpoint assume that qh_IDunknown==-1 (other negative numbers indicate points)
+ qh_IDunknown is also returned by getid_() for unknown facet, ridge, or vertex
+*/
+#define pointT coordT
+typedef enum
+{
+ qh_IDnone = -3, qh_IDinterior = -2, qh_IDunknown = -1
+}
+qh_pointT;
+
+/*-<a href="qh-qhull.htm#TOC"
+ >--------------------------------</a><a name="flagT">-</a>
+
+ flagT
+ Boolean flag as a bit
+*/
+#define flagT unsigned int
+
+/*-<a href="qh-qhull.htm#TOC"
+ >--------------------------------</a><a name="boolT">-</a>
+
+ boolT
+ boolean value, either True or False
+
+ notes:
+ needed for portability
+ Use qh_False/qh_True as synonyms
+*/
+#define boolT unsigned int
+#ifdef False
+#undef False
+#endif
+#ifdef True
+#undef True
+#endif
+#define False 0
+#define True 1
+#define qh_False 0
+#define qh_True 1
+
+#include "stat.h" /* after define of boolT */
+
+/*-<a href="qh-qhull.htm#TOC"
+ >--------------------------------</a><a name="CENTERtype">-</a>
+
+ qh_CENTER
+ to distinguish facet->center
+*/
+typedef enum
+{
+ qh_ASnone = 0, /* If not MERGING and not VORONOI */
+ qh_ASvoronoi, /* Set by qh_clearcenters on qh_prepare_output, or if not MERGING and VORONOI */
+ qh_AScentrum /* If MERGING (assumed during merging) */
+}
+qh_CENTER;
+
+/*-<a href="qh-qhull.htm#TOC"
+ >--------------------------------</a><a name="qh_PRINT">-</a>
+
+ qh_PRINT
+ output formats for printing (qh.PRINTout).
+ 'Fa' 'FV' 'Fc' 'FC'
+
+
+ notes:
+ some of these names are similar to qhT names. The similar names are only
+ used in switch statements in qh_printbegin() etc.
+*/
+typedef enum {qh_PRINTnone= 0,
+ qh_PRINTarea, qh_PRINTaverage, /* 'Fa' 'FV' 'Fc' 'FC' */
+ qh_PRINTcoplanars, qh_PRINTcentrums,
+ qh_PRINTfacets, qh_PRINTfacets_xridge, /* 'f' 'FF' 'G' 'FI' 'Fi' 'Fn' */
+ qh_PRINTgeom, qh_PRINTids, qh_PRINTinner, qh_PRINTneighbors,
+ qh_PRINTnormals, qh_PRINTouter, qh_PRINTmaple, /* 'n' 'Fo' 'i' 'm' 'Fm' 'FM', 'o' */
+ qh_PRINTincidences, qh_PRINTmathematica, qh_PRINTmerges, qh_PRINToff,
+ qh_PRINToptions, qh_PRINTpointintersect, /* 'FO' 'Fp' 'FP' 'p' 'FQ' 'FS' */
+ qh_PRINTpointnearest, qh_PRINTpoints, qh_PRINTqhull, qh_PRINTsize,
+ qh_PRINTsummary, qh_PRINTtriangles, /* 'Fs' 'Ft' 'Fv' 'FN' 'Fx' */
+ qh_PRINTvertices, qh_PRINTvneighbors, qh_PRINTextremes,
+ qh_PRINTEND} qh_PRINT;
+
+/*-<a href="qh-qhull.htm#TOC"
+ >--------------------------------</a><a name="qh_ALL">-</a>
+
+ qh_ALL
+ argument flag for selecting everything
+*/
+#define qh_ALL True
+#define qh_NOupper True /* argument for qh_findbest */
+#define qh_IScheckmax True /* argument for qh_findbesthorizon */
+#define qh_ISnewfacets True /* argument for qh_findbest */
+#define qh_RESETvisible True /* argument for qh_resetlists */
+
+/*-<a href="qh-qhull.htm#TOC"
+ >--------------------------------</a><a name="qh_ERR">-</a>
+
+ qh_ERR
+ Qhull exit codes, for indicating errors
+ See: MSG_ERROR and MSG_WARNING [user.h]
+*/
+#define qh_ERRnone 0 /* no error occurred during qhull */
+#define qh_ERRinput 1 /* input inconsistency */
+#define qh_ERRsingular 2 /* singular input data */
+#define qh_ERRprec 3 /* precision error */
+#define qh_ERRmem 4 /* insufficient memory, matches mem.h */
+#define qh_ERRqhull 5 /* internal error detected, matches mem.h */
+
+/*-<a href="qh-qhull.htm#TOC"
+>--------------------------------</a><a name="qh_FILEstderr">-</a>
+
+qh_FILEstderr
+Fake stderr to distinguish error output from normal output
+For C++ interface. Must redefine qh_fprintf_qhull
+*/
+#define qh_FILEstderr ((FILE*)1)
+
+/* ============ -structures- ====================
+ each of the following structures is defined by a typedef
+ all realT and coordT fields occur at the beginning of a structure
+ (otherwise space may be wasted due to alignment)
+ define all flags together and pack into 32-bit number
+ DEFsetT is likewise defined in
+ mem.h and qset.h
+*/
+
+typedef struct vertexT vertexT;
+typedef struct ridgeT ridgeT;
+typedef struct facetT facetT;
+#ifndef DEFsetT
+#define DEFsetT 1
+typedef struct setT setT; /* defined in qset.h */
+#endif
+
+/*-<a href="qh-poly.htm#TOC"
+ >--------------------------------</a><a name="facetT">-</a>
+
+ facetT
+ defines a facet
+
+ notes:
+ qhull() generates the hull as a list of facets.
+
+ topological information:
+ f.previous,next doubly-linked list of facets
+ f.vertices set of vertices
+ f.ridges set of ridges
+ f.neighbors set of neighbors
+ f.toporient True if facet has top-orientation (else bottom)
+
+ geometric information:
+ f.offset,normal hyperplane equation
+ f.maxoutside offset to outer plane -- all points inside
+ f.center centrum for testing convexity
+ f.simplicial True if facet is simplicial
+ f.flipped True if facet does not include qh.interior_point
+
+ for constructing hull:
+ f.visible True if facet on list of visible facets (will be deleted)
+ f.newfacet True if facet on list of newly created facets
+ f.coplanarset set of points coplanar with this facet
+ (includes near-inside points for later testing)
+ f.outsideset set of points outside of this facet
+ f.furthestdist distance to furthest point of outside set
+ f.visitid marks visited facets during a loop
+ f.replace replacement facet for to-be-deleted, visible facets
+ f.samecycle,newcycle cycle of facets for merging into horizon facet
+
+ see below for other flags and fields
+*/
+struct facetT {
+#if !qh_COMPUTEfurthest
+ coordT furthestdist;/* distance to furthest point of outsideset */
+#endif
+#if qh_MAXoutside
+ coordT maxoutside; /* max computed distance of point to facet
+ Before QHULLfinished this is an approximation
+ since maxdist not always set for mergefacet
+ Actual outer plane is +DISTround and
+ computed outer plane is +2*DISTround */
+#endif
+ coordT offset; /* exact offset of hyperplane from origin */
+ coordT *normal; /* normal of hyperplane, hull_dim coefficients */
+ /* if tricoplanar, shared with a neighbor */
+ union { /* in order of testing */
+ realT area; /* area of facet, only in io.c if ->isarea */
+ facetT *replace; /* replacement facet if ->visible and NEWfacets
+ is NULL only if qh_mergedegen_redundant or interior */
+ facetT *samecycle; /* cycle of facets from the same visible/horizon intersection,
+ if ->newfacet */
+ facetT *newcycle; /* in horizon facet, current samecycle of new facets */
+ facetT *trivisible; /* visible facet for ->tricoplanar facets during qh_triangulate() */
+ facetT *triowner; /* owner facet for ->tricoplanar, !isarea facets w/ ->keepcentrum */
+ }f;
+ coordT *center; /* set according to qh.CENTERtype */
+ /* qh_ASnone: no center (not MERGING) */
+ /* qh_AScentrum: centrum for testing convexity (qh_getcentrum) */
+ /* assumed qh_AScentrum while merging */
+ /* qh_ASvoronoi: Voronoi center (qh_facetcenter) */
+ /* after constructing the hull, it may be changed (qh_clearcenter) */
+ /* if tricoplanar and !keepcentrum, shared with a neighbor */
+ facetT *previous; /* previous facet in the facet_list */
+ facetT *next; /* next facet in the facet_list */
+ setT *vertices; /* vertices for this facet, inverse sorted by ID
+ if simplicial, 1st vertex was apex/furthest */
+ setT *ridges; /* explicit ridges for nonsimplicial facets.
+ for simplicial facets, neighbors define the ridges */
+ setT *neighbors; /* neighbors of the facet. If simplicial, the kth
+ neighbor is opposite the kth vertex, and the first
+ neighbor is the horizon facet for the first vertex*/
+ setT *outsideset; /* set of points outside this facet
+ if non-empty, last point is furthest
+ if NARROWhull, includes coplanars for partitioning*/
+ setT *coplanarset; /* set of points coplanar with this facet
+ > qh.min_vertex and <= facet->max_outside
+ a point is assigned to the furthest facet
+ if non-empty, last point is furthest away */
+ unsigned visitid; /* visit_id, for visiting all neighbors,
+ all uses are independent */
+ unsigned id; /* unique identifier from qh.facet_id */
+ unsigned nummerge:9; /* number of merges */
+#define qh_MAXnummerge 511 /* 2^9-1, 32 flags total, see "flags:" in io.c */
+ flagT tricoplanar:1; /* True if TRIangulate and simplicial and coplanar with a neighbor */
+ /* all tricoplanars share the same apex */
+ /* all tricoplanars share the same ->center, ->normal, ->offset, ->maxoutside */
+ /* ->keepcentrum is true for the owner. It has the ->coplanareset */
+ /* if ->degenerate, does not span facet (one logical ridge) */
+ /* during qh_triangulate, f.trivisible points to original facet */
+ flagT newfacet:1; /* True if facet on qh.newfacet_list (new or merged) */
+ flagT visible:1; /* True if visible facet (will be deleted) */
+ flagT toporient:1; /* True if created with top orientation
+ after merging, use ridge orientation */
+ flagT simplicial:1;/* True if simplicial facet, ->ridges may be implicit */
+ flagT seen:1; /* used to perform operations only once, like visitid */
+ flagT seen2:1; /* used to perform operations only once, like visitid */
+ flagT flipped:1; /* True if facet is flipped */
+ flagT upperdelaunay:1; /* True if facet is upper envelope of Delaunay triangulation */
+ flagT notfurthest:1; /* True if last point of outsideset is not furthest*/
+
+/*-------- flags primarily for output ---------*/
+ flagT good:1; /* True if a facet marked good for output */
+ flagT isarea:1; /* True if facet->f.area is defined */
+
+/*-------- flags for merging ------------------*/
+ flagT dupridge:1; /* True if duplicate ridge in facet */
+ flagT mergeridge:1; /* True if facet or neighbor contains a qh_MERGEridge
+ ->normal defined (also defined for mergeridge2) */
+ flagT mergeridge2:1; /* True if neighbor contains a qh_MERGEridge (mark_dupridges */
+ flagT coplanar:1; /* True if horizon facet is coplanar at last use */
+ flagT mergehorizon:1; /* True if will merge into horizon (->coplanar) */
+ flagT cycledone:1;/* True if mergecycle_all already done */
+ flagT tested:1; /* True if facet convexity has been tested (false after merge */
+ flagT keepcentrum:1; /* True if keep old centrum after a merge, or marks owner for ->tricoplanar */
+ flagT newmerge:1; /* True if facet is newly merged for reducevertices */
+ flagT degenerate:1; /* True if facet is degenerate (degen_mergeset or ->tricoplanar) */
+ flagT redundant:1; /* True if facet is redundant (degen_mergeset) */
+};
+
+
+/*-<a href="qh-poly.htm#TOC"
+ >--------------------------------</a><a name="ridgeT">-</a>
+
+ ridgeT
+ defines a ridge
+
+ notes:
+ a ridge is hull_dim-1 simplex between two neighboring facets. If the
+ facets are non-simplicial, there may be more than one ridge between
+ two facets. E.G. a 4-d hypercube has two triangles between each pair
+ of neighboring facets.
+
+ topological information:
+ vertices a set of vertices
+ top,bottom neighboring facets with orientation
+
+ geometric information:
+ tested True if ridge is clearly convex
+ nonconvex True if ridge is non-convex
+*/
+struct ridgeT {
+ setT *vertices; /* vertices belonging to this ridge, inverse sorted by ID
+ NULL if a degen ridge (matchsame) */
+ facetT *top; /* top facet this ridge is part of */
+ facetT *bottom; /* bottom facet this ridge is part of */
+ unsigned id; /* unique identifier. Same size as vertex_id and ridge_id */
+ flagT seen:1; /* used to perform operations only once */
+ flagT tested:1; /* True when ridge is tested for convexity */
+ flagT nonconvex:1; /* True if getmergeset detected a non-convex neighbor
+ only one ridge between neighbors may have nonconvex */
+};
+
+/*-<a href="qh-poly.htm#TOC"
+ >--------------------------------</a><a name="vertexT">-</a>
+
+ vertexT
+ defines a vertex
+
+ topological information:
+ next,previous doubly-linked list of all vertices
+ neighbors set of adjacent facets (only if qh.VERTEXneighbors)
+
+ geometric information:
+ point array of DIM3 coordinates
+*/
+struct vertexT {
+ vertexT *next; /* next vertex in vertex_list */
+ vertexT *previous; /* previous vertex in vertex_list */
+ pointT *point; /* hull_dim coordinates (coordT) */
+ setT *neighbors; /* neighboring facets of vertex, qh_vertexneighbors()
+ inits in io.c or after first merge */
+ unsigned id; /* unique identifier. Same size as qh.vertex_id and qh.ridge_id */
+ unsigned visitid; /* for use with qh.vertex_visit, size must match */
+ flagT seen:1; /* used to perform operations only once */
+ flagT seen2:1; /* another seen flag */
+ flagT delridge:1; /* vertex was part of a deleted ridge */
+ flagT deleted:1; /* true if vertex on qh.del_vertices */
+ flagT newlist:1; /* true if vertex on qh.newvertex_list */
+};
+
+/*======= -global variables -qh ============================*/
+
+/*-<a href="qh-globa.htm#TOC"
+ >--------------------------------</a><a name="qh">-</a>
+
+ qh
+ all global variables for qhull are in qh, qhmem, and qhstat
+
+ notes:
+ qhmem is defined in mem.h, qhstat is defined in stat.h, qhrbox is defined in rboxpoints.h
+ Access to qh_qh is via the "qh" macro. See qh_QHpointer in user.h
+
+ All global variables for qhull are in qh, qhmem, and qhstat
+ qh must be unique for each instance of qhull
+ qhstat may be shared between qhull instances.
+ qhmem may be shared across multiple instances of Qhull.
+ Rbox uses global variables rbox_inuse and rbox, but does not persist data across calls.
+
+ Qhull is not multi-threaded. Global state could be stored in thread-local storage.
+
+ QHULL_LIB_CHECK checks that a program and the corresponding
+ qhull library were built with the same type of header files.
+*/
+
+typedef struct qhT qhT;
+
+#define QHULL_NON_REENTRANT 0
+#define QHULL_QH_POINTER 1
+#define QHULL_REENTRANT 2
+
+#if qh_QHpointer_dllimport
+#define qh qh_qh->
+__declspec(dllimport) extern qhT *qh_qh; /* allocated in global.c */
+#define QHULL_LIB_TYPE QHULL_QH_POINTER
+
+#elif qh_QHpointer
+#define qh qh_qh->
+extern qhT *qh_qh; /* allocated in global.c */
+#define QHULL_LIB_TYPE QHULL_QH_POINTER
+
+#elif qh_dllimport
+#define qh qh_qh.
+__declspec(dllimport) extern qhT qh_qh; /* allocated in global.c */
+#define QHULL_LIB_TYPE QHULL_NON_REENTRANT
+
+#else
+#define qh qh_qh.
+extern qhT qh_qh;
+#define QHULL_LIB_TYPE QHULL_NON_REENTRANT
+#endif
+
+#define QHULL_LIB_CHECK qh_lib_check(QHULL_LIB_TYPE, sizeof(qhT), sizeof(vertexT), sizeof(ridgeT), sizeof(facetT), sizeof(setT), sizeof(qhmemT));
+#define QHULL_LIB_CHECK_RBOX qh_lib_check(QHULL_LIB_TYPE, sizeof(qhT), sizeof(vertexT), sizeof(ridgeT), sizeof(facetT), 0, 0);
+
+struct qhT {
+
+/*-<a href="qh-globa.htm#TOC"
+ >--------------------------------</a><a name="qh-const">-</a>
+
+ qh constants
+ configuration flags and constants for Qhull
+
+ notes:
+ The user configures Qhull by defining flags. They are
+ copied into qh by qh_setflags(). qh-quick.htm#options defines the flags.
+*/
+ boolT ALLpoints; /* true 'Qs' 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 ANNOTATEoutput; /* true 'Ta' if annotate output with message codes */
+ boolT ATinfinity; /* true 'Qz' if point num_points-1 is "at-infinity"
+ for improving precision in Delaunay triangulations */
+ 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 halfspace intersection */
+ boolT ISqhullQh; /* Set by Qhull.cpp on initialization */
+ int IStracing; /* trace execution, 0=none, 1=least, 4=most, -1=events */
+ int KEEParea; /* 'PAn' number of largest facets to keep */
+ boolT KEEPcoplanar; /* true 'Qc' if keeping nearest facet for coplanar points */
+ boolT KEEPinside; /* true 'Qi' if keeping nearest facet for inside points
+ set automatically if 'd Qc' */
+ int KEEPmerge; /* 'PMn' number of facets to keep with most merges */
+ realT KEEPminArea; /* 'PFn' minimum facet area to keep */
+ realT MAXcoplanar; /* 'Un' max distance below a facet to be coplanar*/
+ 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. Default is round-off */
+ realT postmerge_centrum; /* 'Cn' centrum_radius when post merging. Default is round-off */
+ boolT MERGEvertices; /* true 'Q3' if merging redundant vertices */
+ realT MINvisible; /* 'Vn' min. distance for a facet to be visible */
+ boolT NOnarrow; /* true 'Q10' if no special processing for narrow distributions */
+ boolT NOnearinside; /* true 'Q8' if ignore near-inside points when partitioning */
+ boolT NOpremerge; /* true 'Q0' if no defaults for C-0 or Qx */
+ boolT NOwide; /* true 'Q12' if no error on wide merge due to duplicate ridge */
+ 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 PICKfurthest; /* true 'Q9' if process furthest of furthest points*/
+ 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 PRINTtransparent; /* true 'Gt' if print transparent outer ridges */
+ boolT PROJECTdelaunay; /* true if DELAUNAY, no readpoints() and
+ need projectinput() for Delaunay in qh_init_B */
+ 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 random 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 RERUN; /* 'TRn' rerun qhull n times (qh.build_cnt) */
+ int ROTATErandom; /* 'QRn' seed, 0 time, >= rotate input */
+ boolT SCALEinput; /* true 'Qbk' if scaling input */
+ boolT SCALElast; /* true 'Qbb' if scale last coord to max prev coord */
+ 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 (!for qh.ONLYgood) */
+ int STOPcone; /* 'TCn' 1+n for stopping after cone for point n */
+ /* also used by qh_build_withresart for err exit*/
+ int STOPpoint; /* 'TVn' 'TV-n' 1+n for stopping after/before(-)
+ adding point n */
+ int TESTpoints; /* 'QTn' num of test points after qh.num_points. Test points always coplanar. */
+ boolT TESTvneighbors; /* true 'Qv' if test vertex neighbors at end */
+ int TRACElevel; /* 'Tn' conditional IStracing level */
+ int TRACElastrun; /* qh.TRACElevel applies to last qh.RERUN */
+ 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 TRIangulate; /* true 'Qt' if triangulate non-simplicial facets */
+ boolT TRInormals; /* true 'Q11' if triangulate duplicates ->normal and ->center (sets Qt) */
+ boolT UPPERdelaunay; /* true 'Qu' if computing furthest-site Delaunay */
+ boolT USEstdout; /* true 'Tz' if using stdout instead of stderr */
+ 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 halfspace intersection */
+ coordT *feasible_point; /* as coordinates, both malloc'd */
+ boolT GETarea; /* true 'Fa', 'FA', 'FS', 'PAn', 'PFn' if compute facet area/Voronoi volume in io.c */
+ boolT KEEPnearinside; /* true if near-inside points in coplanarset */
+ int hull_dim; /* dimension of hull, set by initbuffers */
+ int input_dim; /* dimension of input, set by initbuffers */
+ int num_points; /* number of input points */
+ pointT *first_point; /* array of input points, see POINTSmalloc */
+ boolT POINTSmalloc; /* true if qh.first_point/num_points allocated */
+ pointT *input_points; /* copy of original qh.first_point for input points for qh_joggleinput */
+ boolT input_malloc; /* true if qh.input_points malloc'd */
+ char qhull_command[256];/* command line that invoked this program */
+ int qhull_commandsiz2; /* size of qhull_command at qh_clear_outputflags */
+ char rbox_command[256]; /* command line that produced the input points */
+ char qhull_options[512];/* descriptive list of options */
+ int qhull_optionlen; /* length of last line */
+ int qhull_optionsiz; /* size of qhull_options at qh_build_withrestart */
+ int qhull_optionsiz2; /* size of qhull_options at qh_clear_outputflags */
+ int run_id; /* non-zero, random identifier for this instance of qhull */
+ 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 */
+
+/*-<a href="qh-globa.htm#TOC"
+ >--------------------------------</a><a name="qh-prec">-</a>
+
+ qh precision constants
+ precision constants for Qhull
+
+ notes:
+ qh_detroundoff() computes the maximum roundoff error for distance
+ and other computations. It also sets default values for the
+ qh constants above.
+*/
+ 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 qh_distround() */
+ realT MAXabs_coord; /* max absolute coordinate */
+ realT MAXlastcoord; /* max last coordinate for qh_scalelast */
+ realT MAXsumcoord; /* max sum of coordinates */
+ realT MAXwidth; /* max rectilinear width of point coordinates */
+ 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 MINlastcoord; /* min. last coordinate for qh_scalelast */
+ boolT NARROWhull; /* set in qh_initialhull if angle < qh_MAXnarrow */
+ 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 outside_err; /* application's epsilon for coplanar points
+ qh_check_bestdist() qh_check_points() reports error if point outside */
+ realT WIDEfacet; /* size of wide facet for skipping ridge in
+ area computation and locking centrum */
+
+/*-<a href="qh-globa.htm#TOC"
+ >--------------------------------</a><a name="qh-codetern">-</a>
+
+ qh internal constants
+ internal constants for Qhull
+*/
+ char qhull[sizeof("qhull")]; /* "qhull" for checking ownership while debugging */
+ jmp_buf errexit; /* exit label for qh_errexit, defined by setjmp() and NOerrexit */
+ char jmpXtra[40]; /* extra bytes in case jmp_buf is defined wrong by compiler */
+ jmp_buf restartexit; /* restart label for qh_errexit, defined by setjmp() and ALLOWrestart */
+ char jmpXtra2[40]; /* extra bytes in case jmp_buf is defined wrong by compiler*/
+ FILE *fin; /* pointer to input file, init by qh_initqhull_start2 */
+ 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) */
+
+/*-<a href="qh-globa.htm#TOC"
+ >--------------------------------</a><a name="qh-lists">-</a>
+
+ qh facet and vertex lists
+ defines lists of facets, new facets, visible facets, vertices, and
+ new vertices. Includes counts, next ids, and trace ids.
+ see:
+ qh_resetlists()
+*/
+ facetT *facet_list; /* first facet */
+ facetT *facet_tail; /* end of facet_list (dummy facet) */
+ facetT *facet_next; /* next facet for buildhull()
+ previous facets do not have outside sets
+ NARROWhull: previous facets may have coplanar outside sets for qh_outcoplanar */
+ facetT *newfacet_list; /* list of new facets to end of facet_list */
+ facetT *visible_list; /* list of visible facets preceding 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; /* end of vertex_list (dummy vertex) */
+ 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 visible faces (num_visible) */
+ int num_vertices; /* number of vertices in facet_list */
+ int num_outside; /* number of points in outsidesets (for tracing and RANDOMoutside)
+ includes coplanar outsideset points for NARROWhull/qh_outcoplanar() */
+ int num_good; /* number of good facets (after findgood_all) */
+ unsigned facet_id; /* ID of next, new facet from newfacet() */
+ unsigned ridge_id; /* ID of next, new ridge from newridge() */
+ unsigned vertex_id; /* ID of next, new vertex from newvertex() */
+
+/*-<a href="qh-globa.htm#TOC"
+ >--------------------------------</a><a name="qh-var">-</a>
+
+ qh global variables
+ defines minimum and maximum distances, next visit ids, several flags,
+ and other global variables.
+ initialize in qh_initbuild or qh_maxmin if used in qh_buildhull
+*/
+ unsigned long hulltime; /* ignore time to set up input and randomize */
+ /* use unsigned to avoid wrap-around errors */
+ boolT ALLOWrestart; /* true if qh_precision can use qh.restartexit */
+ int build_cnt; /* number of calls to qh_initbuild */
+ 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 */
+ boolT hasAreaVolume; /* true if totarea, totvol was defined by qh_getarea */
+ boolT hasTriangulation; /* true if triangulation created by qh_triangulate */
+ realT JOGGLEmax; /* set 'QJn' if randomly joggle input */
+ boolT maxoutdone; /* set qh_check_maxout(), cleared by qh_addpoint() */
+ 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, due to a merge */
+ realT min_vertex; /* minimum distance (<0) from vertex to a facet,
+ before roundoff, due to a merge
+ if qh.JOGGLEmax, qh_makenewplanes sets it
+ recomputed if qh.DOcheckmax, default -qh.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, cleared after setjmp */
+ 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; /* 'FA': total facet area computed by qh_getarea, hasAreaVolume */
+ realT totvol; /* 'FA': total volume computed by qh_getarea, hasAreaVolume */
+ unsigned int visit_id; /* unique ID for searching neighborhoods, */
+ unsigned int vertex_visit; /* unique ID for searching vertices, reset with qh_buildtracing */
+ boolT ZEROall_ok; /* True if qh_checkzero always succeeds */
+ boolT WAScoplanar; /* True if qh_partitioncoplanar (qh_check_maxout) */
+
+/*-<a href="qh-globa.htm#TOC"
+ >--------------------------------</a><a name="qh-set">-</a>
+
+ qh global sets
+ defines sets for merging, initial simplex, hashing, extra input points,
+ and deleted vertices
+*/
+ setT *facet_mergeset; /* temporary set of merges to be done */
+ setT *degen_mergeset; /* temporary set of degenerate and redundant merges */
+ setT *hash_table; /* hash table for matching ridges in qh_matchfacets
+ size is setsize() */
+ setT *other_points; /* additional points */
+ setT *del_vertices; /* vertices to partition and delete with visible
+ facets. Have deleted set for checkfacet */
+
+/*-<a href="qh-globa.htm#TOC"
+ >--------------------------------</a><a name="qh-buf">-</a>
+
+ qh global buffers
+ defines buffers for maxtrix operations, input, and error messages
+*/
+ coordT *gm_matrix; /* (dim+1)Xdim matrix for geom.c */
+ coordT **gm_row; /* array of gm_matrix rows */
+ char* line; /* malloc'd input line of maxline+1 chars */
+ int maxline;
+ coordT *half_space; /* malloc'd input array for halfspace (qh normal_size+coordT) */
+ coordT *temp_malloc; /* malloc'd input array for points */
+
+/*-<a href="qh-globa.htm#TOC"
+ >--------------------------------</a><a name="qh-static">-</a>
+
+ qh static variables
+ defines static variables for individual functions
+
+ notes:
+ do not use 'static' within a function. Multiple instances of qhull
+ may exist.
+
+ do not assume zero initialization, 'QPn' may cause a restart
+*/
+ boolT ERREXITcalled; /* true during qh_errexit (prevents duplicate calls */
+ boolT firstcentrum; /* for qh_printcentrum */
+ boolT old_randomdist; /* save RANDOMdist flag during io, tracing, or statistics */
+ setT *coplanarfacetset; /* set of coplanar facets for searching qh_findbesthorizon() */
+ realT last_low; /* qh_scalelast parameters for qh_setdelaunay */
+ realT last_high;
+ realT last_newhigh;
+ unsigned lastreport; /* for qh_buildtracing */
+ int mergereport; /* for qh_tracemerging */
+ qhstatT *old_qhstat; /* for saving qh_qhstat in save_qhull() and UsingLibQhull. Free with qh_free() */
+ setT *old_tempstack; /* for saving qhmem.tempstack in save_qhull */
+ int ridgeoutnum; /* number of ridges for 4OFF output (qh_printbegin,etc) */
+};
+
+/*=========== -macros- =========================*/
+
+/*-<a href="qh-poly.htm#TOC"
+ >--------------------------------</a><a name="otherfacet_">-</a>
+
+ otherfacet_(ridge, facet)
+ return neighboring facet for a ridge in facet
+*/
+#define otherfacet_(ridge, facet) \
+ (((ridge)->top == (facet)) ? (ridge)->bottom : (ridge)->top)
+
+/*-<a href="qh-poly.htm#TOC"
+ >--------------------------------</a><a name="getid_">-</a>
+
+ getid_(p)
+ return int ID for facet, ridge, or vertex
+ return qh_IDunknown(-1) if NULL
+*/
+#define getid_(p) ((p) ? (int)((p)->id) : qh_IDunknown)
+
+/*============== FORALL macros ===================*/
+
+/*-<a href="qh-poly.htm#TOC"
+ >--------------------------------</a><a name="FORALLfacets">-</a>
+
+ FORALLfacets { ... }
+ assign 'facet' to each facet in qh.facet_list
+
+ notes:
+ uses 'facetT *facet;'
+ assumes last facet is a sentinel
+
+ see:
+ FORALLfacet_( facetlist )
+*/
+#define FORALLfacets for (facet=qh facet_list;facet && facet->next;facet=facet->next)
+
+/*-<a href="qh-poly.htm#TOC"
+ >--------------------------------</a><a name="FORALLpoints">-</a>
+
+ FORALLpoints { ... }
+ assign 'point' to each point in qh.first_point, qh.num_points
+
+ declare:
+ coordT *point, *pointtemp;
+*/
+#define FORALLpoints FORALLpoint_(qh first_point, qh num_points)
+
+/*-<a href="qh-poly.htm#TOC"
+ >--------------------------------</a><a name="FORALLpoint_">-</a>
+
+ FORALLpoint_( points, num) { ... }
+ assign 'point' to each point in points array of num points
+
+ declare:
+ coordT *point, *pointtemp;
+*/
+#define FORALLpoint_(points, num) for (point= (points), \
+ pointtemp= (points)+qh hull_dim*(num); point < pointtemp; point += qh hull_dim)
+
+/*-<a href="qh-poly.htm#TOC"
+ >--------------------------------</a><a name="FORALLvertices">-</a>
+
+ FORALLvertices { ... }
+ assign 'vertex' to each vertex in qh.vertex_list
+
+ declare:
+ vertexT *vertex;
+
+ notes:
+ assumes qh.vertex_list terminated with a sentinel
+*/
+#define FORALLvertices for (vertex=qh vertex_list;vertex && vertex->next;vertex= vertex->next)
+
+/*-<a href="qh-poly.htm#TOC"
+ >--------------------------------</a><a name="FOREACHfacet_">-</a>
+
+ FOREACHfacet_( facets ) { ... }
+ assign 'facet' to each facet in facets
+
+ declare:
+ facetT *facet, **facetp;
+
+ see:
+ <a href="qset.h#FOREACHsetelement_">FOREACHsetelement_</a>
+*/
+#define FOREACHfacet_(facets) FOREACHsetelement_(facetT, facets, facet)
+
+/*-<a href="qh-poly.htm#TOC"
+ >--------------------------------</a><a name="FOREACHneighbor_">-</a>
+
+ FOREACHneighbor_( facet ) { ... }
+ assign 'neighbor' to each neighbor in facet->neighbors
+
+ FOREACHneighbor_( vertex ) { ... }
+ assign 'neighbor' to each neighbor in vertex->neighbors
+
+ declare:
+ facetT *neighbor, **neighborp;
+
+ see:
+ <a href="qset.h#FOREACHsetelement_">FOREACHsetelement_</a>
+*/
+#define FOREACHneighbor_(facet) FOREACHsetelement_(facetT, facet->neighbors, neighbor)
+
+/*-<a href="qh-poly.htm#TOC"
+ >--------------------------------</a><a name="FOREACHpoint_">-</a>
+
+ FOREACHpoint_( points ) { ... }
+ assign 'point' to each point in points set
+
+ declare:
+ pointT *point, **pointp;
+
+ see:
+ <a href="qset.h#FOREACHsetelement_">FOREACHsetelement_</a>
+*/
+#define FOREACHpoint_(points) FOREACHsetelement_(pointT, points, point)
+
+/*-<a href="qh-poly.htm#TOC"
+ >--------------------------------</a><a name="FOREACHridge_">-</a>
+
+ FOREACHridge_( ridges ) { ... }
+ assign 'ridge' to each ridge in ridges set
+
+ declare:
+ ridgeT *ridge, **ridgep;
+
+ see:
+ <a href="qset.h#FOREACHsetelement_">FOREACHsetelement_</a>
+*/
+#define FOREACHridge_(ridges) FOREACHsetelement_(ridgeT, ridges, ridge)
+
+/*-<a href="qh-poly.htm#TOC"
+ >--------------------------------</a><a name="FOREACHvertex_">-</a>
+
+ FOREACHvertex_( vertices ) { ... }
+ assign 'vertex' to each vertex in vertices set
+
+ declare:
+ vertexT *vertex, **vertexp;
+
+ see:
+ <a href="qset.h#FOREACHsetelement_">FOREACHsetelement_</a>
+*/
+#define FOREACHvertex_(vertices) FOREACHsetelement_(vertexT, vertices,vertex)
+
+/*-<a href="qh-poly.htm#TOC"
+ >--------------------------------</a><a name="FOREACHfacet_i_">-</a>
+
+ FOREACHfacet_i_( facets ) { ... }
+ assign 'facet' and 'facet_i' for each facet in facets set
+
+ declare:
+ facetT *facet;
+ int facet_n, facet_i;
+
+ see:
+ <a href="qset.h#FOREACHsetelement_i_">FOREACHsetelement_i_</a>
+*/
+#define FOREACHfacet_i_(facets) FOREACHsetelement_i_(facetT, facets, facet)
+
+/*-<a href="qh-poly.htm#TOC"
+ >--------------------------------</a><a name="FOREACHneighbor_i_">-</a>
+
+ FOREACHneighbor_i_( facet ) { ... }
+ assign 'neighbor' and 'neighbor_i' for each neighbor in facet->neighbors
+
+ FOREACHneighbor_i_( vertex ) { ... }
+ assign 'neighbor' and 'neighbor_i' for each neighbor in vertex->neighbors
+
+ declare:
+ facetT *neighbor;
+ int neighbor_n, neighbor_i;
+
+ see:
+ <a href="qset.h#FOREACHsetelement_i_">FOREACHsetelement_i_</a>
+*/
+#define FOREACHneighbor_i_(facet) FOREACHsetelement_i_(facetT, facet->neighbors, neighbor)
+
+/*-<a href="qh-poly.htm#TOC"
+ >--------------------------------</a><a name="FOREACHpoint_i_">-</a>
+
+ FOREACHpoint_i_( points ) { ... }
+ assign 'point' and 'point_i' for each point in points set
+
+ declare:
+ pointT *point;
+ int point_n, point_i;
+
+ see:
+ <a href="qset.h#FOREACHsetelement_i_">FOREACHsetelement_i_</a>
+*/
+#define FOREACHpoint_i_(points) FOREACHsetelement_i_(pointT, points, point)
+
+/*-<a href="qh-poly.htm#TOC"
+ >--------------------------------</a><a name="FOREACHridge_i_">-</a>
+
+ FOREACHridge_i_( ridges ) { ... }
+ assign 'ridge' and 'ridge_i' for each ridge in ridges set
+
+ declare:
+ ridgeT *ridge;
+ int ridge_n, ridge_i;
+
+ see:
+ <a href="qset.h#FOREACHsetelement_i_">FOREACHsetelement_i_</a>
+*/
+#define FOREACHridge_i_(ridges) FOREACHsetelement_i_(ridgeT, ridges, ridge)
+
+/*-<a href="qh-poly.htm#TOC"
+ >--------------------------------</a><a name="FOREACHvertex_i_">-</a>
+
+ FOREACHvertex_i_( vertices ) { ... }
+ assign 'vertex' and 'vertex_i' for each vertex in vertices set
+
+ declare:
+ vertexT *vertex;
+ int vertex_n, vertex_i;
+
+ see:
+ <a href="qset.h#FOREACHsetelement_i_">FOREACHsetelement_i_</a>
+*/
+#define FOREACHvertex_i_(vertices) FOREACHsetelement_i_(vertexT, vertices,vertex)
+
+/********* -libqhull.c prototypes (duplicated from qhull_a.h) **********************/
+
+void qh_qhull(void);
+boolT qh_addpoint(pointT *furthest, facetT *facet, boolT checkdist);
+void qh_printsummary(FILE *fp);
+
+/********* -user.c prototypes (alphabetical) **********************/
+
+void qh_errexit(int exitcode, facetT *facet, ridgeT *ridge);
+void qh_errprint(const char* string, facetT *atfacet, facetT *otherfacet, ridgeT *atridge, vertexT *atvertex);
+int qh_new_qhull(int dim, int numpoints, coordT *points, boolT ismalloc,
+ char *qhull_cmd, FILE *outfile, FILE *errfile);
+void qh_printfacetlist(facetT *facetlist, setT *facets, boolT printall);
+void qh_printhelp_degenerate(FILE *fp);
+void qh_printhelp_narrowhull(FILE *fp, realT minangle);
+void qh_printhelp_singular(FILE *fp);
+void qh_user_memsizes(void);
+
+/********* -usermem.c prototypes (alphabetical) **********************/
+void qh_exit(int exitcode);
+void qh_fprintf_stderr(int msgcode, const char *fmt, ... );
+void qh_free(void *mem);
+void *qh_malloc(size_t size);
+
+/********* -userprintf.c and userprintf_rbox.c prototypes **********************/
+void qh_fprintf(FILE *fp, int msgcode, const char *fmt, ... );
+void qh_fprintf_rbox(FILE *fp, int msgcode, const char *fmt, ... );
+
+/***** -geom.c/geom2.c/random.c prototypes (duplicated from geom.h, random.h) ****************/
+
+facetT *qh_findbest(pointT *point, facetT *startfacet,
+ boolT bestoutside, boolT newfacets, boolT noupper,
+ realT *dist, boolT *isoutside, int *numpart);
+facetT *qh_findbestnew(pointT *point, facetT *startfacet,
+ realT *dist, boolT bestoutside, boolT *isoutside, int *numpart);
+boolT qh_gram_schmidt(int dim, realT **rows);
+void qh_outerinner(facetT *facet, realT *outerplane, realT *innerplane);
+void qh_printsummary(FILE *fp);
+void qh_projectinput(void);
+void qh_randommatrix(realT *buffer, int dim, realT **row);
+void qh_rotateinput(realT **rows);
+void qh_scaleinput(void);
+void qh_setdelaunay(int dim, int count, pointT *points);
+coordT *qh_sethalfspace_all(int dim, int count, coordT *halfspaces, pointT *feasible);
+
+/***** -global.c prototypes (alphabetical) ***********************/
+
+unsigned long qh_clock(void);
+void qh_checkflags(char *command, char *hiddenflags);
+void qh_clear_outputflags(void);
+void qh_freebuffers(void);
+void qh_freeqhull(boolT allmem);
+void qh_freeqhull2(boolT allmem);
+void qh_init_A(FILE *infile, FILE *outfile, FILE *errfile, int argc, char *argv[]);
+void qh_init_B(coordT *points, int numpoints, int dim, boolT ismalloc);
+void qh_init_qhull_command(int argc, char *argv[]);
+void qh_initbuffers(coordT *points, int numpoints, int dim, boolT ismalloc);
+void qh_initflags(char *command);
+void qh_initqhull_buffers(void);
+void qh_initqhull_globals(coordT *points, int numpoints, int dim, boolT ismalloc);
+void qh_initqhull_mem(void);
+void qh_initqhull_outputflags(void);
+void qh_initqhull_start(FILE *infile, FILE *outfile, FILE *errfile);
+void qh_initqhull_start2(FILE *infile, FILE *outfile, FILE *errfile);
+void qh_initthresholds(char *command);
+void qh_lib_check(int qhullLibraryType, int qhTsize, int vertexTsize, int ridgeTsize, int facetTsize, int setTsize, int qhmemTsize);
+void qh_option(const char *option, int *i, realT *r);
+#if qh_QHpointer
+void qh_restore_qhull(qhT **oldqh);
+qhT *qh_save_qhull(void);
+#endif
+
+/***** -io.c prototypes (duplicated from io.h) ***********************/
+
+void qh_dfacet(unsigned id);
+void qh_dvertex(unsigned id);
+void qh_printneighborhood(FILE *fp, qh_PRINT format, facetT *facetA, facetT *facetB, boolT printall);
+void qh_produce_output(void);
+coordT *qh_readpoints(int *numpoints, int *dimension, boolT *ismalloc);
+
+
+/********* -mem.c prototypes (duplicated from mem.h) **********************/
+
+void qh_meminit(FILE *ferr);
+void qh_memfreeshort(int *curlong, int *totlong);
+
+/********* -poly.c/poly2.c prototypes (duplicated from poly.h) **********************/
+
+void qh_check_output(void);
+void qh_check_points(void);
+setT *qh_facetvertices(facetT *facetlist, setT *facets, boolT allfacets);
+facetT *qh_findbestfacet(pointT *point, boolT bestoutside,
+ realT *bestdist, boolT *isoutside);
+vertexT *qh_nearvertex(facetT *facet, pointT *point, realT *bestdistp);
+pointT *qh_point(int id);
+setT *qh_pointfacet(void /*qh.facet_list*/);
+int qh_pointid(pointT *point);
+setT *qh_pointvertex(void /*qh.facet_list*/);
+void qh_setvoronoi_all(void);
+void qh_triangulate(void /*qh.facet_list*/);
+
+/********* -rboxlib.c prototypes **********************/
+int qh_rboxpoints(FILE* fout, FILE* ferr, char* rbox_command);
+void qh_errexit_rbox(int exitcode);
+
+/********* -stat.c prototypes (duplicated from stat.h) **********************/
+
+void qh_collectstatistics(void);
+void qh_printallstatistics(FILE *fp, const char *string);
+
+#endif /* qhDEFlibqhull */