src/QuickHull/poly.h

/*<html><pre>  -<a                             href="qh-poly.htm"
  >-------------------------------</a><a name="TOP">-</a>

   poly.h 
   header file for poly.c and poly2.c

   see qh-poly.htm, qhull.h and poly.c

   copyright (c) 1993-2003, The Geometry Center
*/

#ifndef qhDEFpoly
#define qhDEFpoly 1

/*===============   constants ========================== */

/*-<a                             href="qh-geom.htm#TOC"
  >--------------------------------</a><a name="ALGORITHMfault">-</a>
  
  ALGORITHMfault   use as argument to checkconvex() to report errors during buildhull
*/
#define qh_ALGORITHMfault 0

/*-<a                             href="qh-poly.htm#TOC"
  >--------------------------------</a><a name="DATAfault">-</a>
  
  DATAfault        use as argument to checkconvex() to report errors during initialhull
*/
#define qh_DATAfault 1

/*-<a                             href="qh-poly.htm#TOC"
  >--------------------------------</a><a name="DUPLICATEridge">-</a>
  
  DUPLICATEridge
    special value for facet->neighbor to indicate a duplicate ridge
  
  notes:
    set by matchneighbor, used by matchmatch and mark_dupridge
*/
#define qh_DUPLICATEridge ( facetT * ) 1L

/*-<a                             href="qh-poly.htm#TOC"
  >--------------------------------</a><a name="MERGEridge">-</a>
  
  MERGEridge       flag in facet
    special value for facet->neighbor to indicate a merged ridge
  
  notes:
    set by matchneighbor, used by matchmatch and mark_dupridge
*/
#define qh_MERGEridge ( facetT * ) 2L


/*============ -structures- ====================*/

/*=========== -macros- =========================*/

/*-<a                             href="qh-poly.htm#TOC"
  >--------------------------------</a><a name="FORALLfacet_">-</a>
  
  FORALLfacet_( facetlist ) { ... }
    assign 'facet' to each facet in facetlist
    
  notes:
    uses 'facetT *facet;'
    assumes last facet is a sentinel
    
  see:
    FORALLfacets
*/
#define FORALLfacet_( facetlist ) if ( facetlist ) for( facet=( facetlist );facet && facet->next;facet=facet->next )

/*-<a                             href="qh-poly.htm#TOC"
  >--------------------------------</a><a name="FORALLnew_facets">-</a>
  
  FORALLnew_facets { ... } 
    assign 'newfacet' to each facet in qh.newfacet_list
    
  notes:
    uses 'facetT *newfacet;'
    at exit, newfacet==NULL
*/
#define FORALLnew_facets for( newfacet=qh newfacet_list;newfacet && newfacet->next;newfacet=newfacet->next )

/*-<a                             href="qh-poly.htm#TOC"
  >--------------------------------</a><a name="FORALLvertex_">-</a>
  
  FORALLvertex_( vertexlist ) { ... }
    assign 'vertex' to each vertex in vertexlist
    
  notes:
    uses 'vertexT *vertex;'
    at exit, vertex==NULL
*/
#define FORALLvertex_( vertexlist ) for ( vertex=( vertexlist );vertex && vertex->next;vertex= vertex->next )

/*-<a                             href="qh-poly.htm#TOC"
  >--------------------------------</a><a name="FORALLvisible_facets">-</a>
  
  FORALLvisible_facets { ... }
    assign 'visible' to each visible facet in qh.visible_list
    
  notes:
    uses 'vacetT *visible;'
    at exit, visible==NULL
*/
#define FORALLvisible_facets for (visible=qh visible_list; visible && visible->visible; visible= visible->next)

/*-<a                             href="qh-poly.htm#TOC"
  >--------------------------------</a><a name="FORALLsame_">-</a>
  
  FORALLsame_( newfacet ) { ... } 
    assign 'same' to each facet in newfacet->f.samecycle
    
  notes:
    uses 'facetT *same;'
    stops when it returns to newfacet
*/
#define FORALLsame_(newfacet) for (same= newfacet->f.samecycle; same != newfacet; same= same->f.samecycle)

/*-<a                             href="qh-poly.htm#TOC"
  >--------------------------------</a><a name="FORALLsame_cycle_">-</a>
  
  FORALLsame_cycle_( newfacet ) { ... } 
    assign 'same' to each facet in newfacet->f.samecycle
    
  notes:
    uses 'facetT *same;'
    at exit, same == NULL
*/
#define FORALLsame_cycle_(newfacet) \
     for (same= newfacet->f.samecycle; \
         same; same= (same == newfacet ?  NULL : same->f.samecycle))

/*-<a                             href="qh-poly.htm#TOC"
  >--------------------------------</a><a name="FOREACHneighborA_">-</a>
  
  FOREACHneighborA_( facet ) { ... }
    assign 'neighborA' to each neighbor in facet->neighbors
  
  FOREACHneighborA_( vertex ) { ... }
    assign 'neighborA' to each neighbor in vertex->neighbors
  
  declare:
    facetT *neighborA, **neighborAp;

  see:
    <a href="qset.h#FOREACHsetelement_">FOREACHsetelement_</a>
*/
#define FOREACHneighborA_(facet)  FOREACHsetelement_(facetT, facet->neighbors, neighborA)

/*-<a                             href="qh-poly.htm#TOC"
  >--------------------------------</a><a name="FOREACHvisible_">-</a>
  
  FOREACHvisible_( facets ) { ... } 
    assign 'visible' to each facet in facets
    
  notes:
    uses 'facetT *facet, *facetp;'
    see <a href="qset.h#FOREACHsetelement_">FOREACHsetelement_</a>
*/
#define FOREACHvisible_(facets) FOREACHsetelement_(facetT, facets, visible)

/*-<a                             href="qh-poly.htm#TOC"
  >--------------------------------</a><a name="FOREACHnewfacet_">-</a>
  
  FOREACHnewfacet_( facets ) { ... } 
    assign 'newfacet' to each facet in facets
    
  notes:
    uses 'facetT *newfacet, *newfacetp;'
    see <a href="qset.h#FOREACHsetelement_">FOREACHsetelement_</a>
*/
#define FOREACHnewfacet_(facets) FOREACHsetelement_(facetT, facets, newfacet)

/*-<a                             href="qh-poly.htm#TOC"
  >--------------------------------</a><a name="FOREACHvertexA_">-</a>
  
  FOREACHvertexA_( vertices ) { ... } 
    assign 'vertexA' to each vertex in vertices
    
  notes:
    uses 'vertexT *vertexA, *vertexAp;'
    see <a href="qset.h#FOREACHsetelement_">FOREACHsetelement_</a>
*/
#define FOREACHvertexA_(vertices) FOREACHsetelement_(vertexT, vertices, vertexA)

/*-<a                             href="qh-poly.htm#TOC"
  >--------------------------------</a><a name="FOREACHvertexreverse12_">-</a>
  
  FOREACHvertexreverse12_( vertices ) { ... } 
    assign 'vertex' to each vertex in vertices
    reverse order of first two vertices
    
  notes:
    uses 'vertexT *vertex, *vertexp;'
    see <a href="qset.h#FOREACHsetelement_">FOREACHsetelement_</a>
*/
#define FOREACHvertexreverse12_(vertices) FOREACHsetelementreverse12_(vertexT, vertices, vertex)


/*=============== prototypes poly.c in alphabetical order ================*/

void    qh_appendfacet(facetT *facet);
void    qh_appendvertex(vertexT *vertex);
void    qh_attachnewfacets (void);
boolT   qh_checkflipped (facetT *facet, realT *dist, boolT allerror);
void    qh_delfacet(facetT *facet);
void    qh_deletevisible(void /*qh visible_list, qh horizon_list*/);
setT   *qh_facetintersect (facetT *facetA, facetT *facetB, int *skipAp,int *skipBp, int extra);
unsigned qh_gethash (int hashsize, setT *set, int size, int firstindex, void *skipelem);
facetT *qh_makenewfacet(setT *vertices, boolT toporient, facetT *facet);
void    qh_makenewplanes ( void /* newfacet_list */);
facetT *qh_makenew_nonsimplicial (facetT *visible, vertexT *apex, int *numnew);
facetT *qh_makenew_simplicial (facetT *visible, vertexT *apex, int *numnew);
void    qh_matchneighbor (facetT *newfacet, int newskip, int hashsize,
                          int *hashcount);
void    qh_matchnewfacets (void);
boolT   qh_matchvertices (int firstindex, setT *verticesA, int skipA, 
                          setT *verticesB, int *skipB, boolT *same);
facetT *qh_newfacet(void);
ridgeT *qh_newridge(void);
int     qh_pointid (pointT *point);
void    qh_removefacet(facetT *facet);
void    qh_removevertex(vertexT *vertex);
void    qh_updatevertices (void);


/*========== -prototypes poly2.c in alphabetical order ===========*/

void    qh_addhash (void* newelem, setT *hashtable, int hashsize, unsigned hash);
void    qh_check_bestdist (void);
void    qh_check_maxout (void);
void    qh_check_output (void);
void    qh_check_point (pointT *point, facetT *facet, realT *maxoutside, realT *maxdist, facetT **errfacet1, facetT **errfacet2);
void    qh_check_points(void);
void    qh_checkconvex(facetT *facetlist, int fault);
void    qh_checkfacet(facetT *facet, boolT newmerge, boolT *waserrorp);
void    qh_checkflipped_all (facetT *facetlist);
void    qh_checkpolygon(facetT *facetlist);
void    qh_checkvertex (vertexT *vertex);
void    qh_clearcenters (qh_CENTER type);
void    qh_createsimplex(setT *vertices);
void    qh_delridge(ridgeT *ridge);
void    qh_delvertex (vertexT *vertex);
setT   *qh_facet3vertex (facetT *facet);
facetT *qh_findbestfacet (pointT *point, boolT bestoutside,
           realT *bestdist, boolT *isoutside);
facetT *qh_findbestlower (facetT *upperfacet, pointT *point, realT *bestdistp, int *numpart);
facetT *qh_findfacet_all (pointT *point, realT *bestdist, boolT *isoutside,
                          int *numpart);
int     qh_findgood (facetT *facetlist, int goodhorizon);
void    qh_findgood_all (facetT *facetlist);
void    qh_furthestnext (void /* qh facet_list */);
void    qh_furthestout (facetT *facet);
void    qh_infiniteloop (facetT *facet);
void    qh_initbuild(void);
void    qh_initialhull(setT *vertices);
setT   *qh_initialvertices(int dim, setT *maxpoints, pointT *points, int numpoints);
vertexT *qh_isvertex (pointT *point, setT *vertices);
vertexT *qh_makenewfacets (pointT *point /*horizon_list, visible_list*/);
void    qh_matchduplicates (facetT *atfacet, int atskip, int hashsize, int *hashcount);
void    qh_nearcoplanar ( void /* qh.facet_list */);
vertexT *qh_nearvertex (facetT *facet, pointT *point, realT *bestdistp);
int     qh_newhashtable(int newsize);
vertexT *qh_newvertex(pointT *point);
ridgeT *qh_nextridge3d (ridgeT *atridge, facetT *facet, vertexT **vertexp);
void    qh_outcoplanar (void /* facet_list */);
pointT *qh_point (int id);
void    qh_point_add (setT *set, pointT *point, void *elem);
setT   *qh_pointfacet (void /*qh facet_list*/);
setT   *qh_pointvertex (void /*qh facet_list*/);
void    qh_prependfacet(facetT *facet, facetT **facetlist);
void    qh_printhashtable(FILE *fp);
void    qh_printlists (void);
void    qh_resetlists (boolT stats, boolT resetVisible /*qh newvertex_list newfacet_list visible_list*/);
void    qh_setvoronoi_all (void);
void    qh_triangulate (void /*qh facet_list*/);
void    qh_triangulate_facet (facetT *facetA, vertexT **first_vertex);
void    qh_triangulate_link (facetT *oldfacetA, facetT *facetA, facetT *oldfacetB, facetT *facetB);
void    qh_triangulate_mirror (facetT *facetA, facetT *facetB);
void    qh_triangulate_null (facetT *facetA);
void    qh_vertexintersect(setT **vertexsetA,setT *vertexsetB);
setT   *qh_vertexintersect_new(setT *vertexsetA,setT *vertexsetB);
void    qh_vertexneighbors (void /*qh facet_list*/);
boolT   qh_vertexsubset(setT *vertexsetA, setT *vertexsetB);


#endif /* qhDEFpoly */
Revision:	1138
Committed:	Tue May 29 22:51:00 2007 UTC (18 years, 5 months ago) by chuckv
Content type:	text/plain
File size:	10826 byte(s)
Log Message:	Addded QuickHull to cvs.
#	User	Rev	Content
1	chuckv	1138	/*<html><pre> -<a href="qh-poly.htm"
2			>-------------------------------</a><a name="TOP">-</a>
3
4			poly.h
5			header file for poly.c and poly2.c
6
7			see qh-poly.htm, qhull.h and poly.c
8
9			copyright (c) 1993-2003, The Geometry Center
10			*/
11
12			#ifndef qhDEFpoly
13			#define qhDEFpoly 1
14
15			/=============== constants ========================== /
16
17			/*-<a href="qh-geom.htm#TOC"
18			>--------------------------------</a><a name="ALGORITHMfault">-</a>
19
20			ALGORITHMfault use as argument to checkconvex() to report errors during buildhull
21			*/
22			#define qh_ALGORITHMfault 0
23
24			/*-<a href="qh-poly.htm#TOC"
25			>--------------------------------</a><a name="DATAfault">-</a>
26
27			DATAfault use as argument to checkconvex() to report errors during initialhull
28			*/
29			#define qh_DATAfault 1
30
31			/*-<a href="qh-poly.htm#TOC"
32			>--------------------------------</a><a name="DUPLICATEridge">-</a>
33
34			DUPLICATEridge
35			special value for facet->neighbor to indicate a duplicate ridge
36
37			notes:
38			set by matchneighbor, used by matchmatch and mark_dupridge
39			*/
40			#define qh_DUPLICATEridge ( facetT * ) 1L
41
42			/*-<a href="qh-poly.htm#TOC"
43			>--------------------------------</a><a name="MERGEridge">-</a>
44
45			MERGEridge flag in facet
46			special value for facet->neighbor to indicate a merged ridge
47
48			notes:
49			set by matchneighbor, used by matchmatch and mark_dupridge
50			*/
51			#define qh_MERGEridge ( facetT * ) 2L
52
53
54			/============ -structures- ====================/
55
56			/=========== -macros- =========================/
57
58			/*-<a href="qh-poly.htm#TOC"
59			>--------------------------------</a><a name="FORALLfacet_">-</a>
60
61			FORALLfacet_( facetlist ) { ... }
62			assign 'facet' to each facet in facetlist
63
64			notes:
65			uses 'facetT *facet;'
66			assumes last facet is a sentinel
67
68			see:
69			FORALLfacets
70			*/
71			#define FORALLfacet_( facetlist ) if ( facetlist ) for( facet=( facetlist );facet && facet->next;facet=facet->next )
72
73			/*-<a href="qh-poly.htm#TOC"
74			>--------------------------------</a><a name="FORALLnew_facets">-</a>
75
76			FORALLnew_facets { ... }
77			assign 'newfacet' to each facet in qh.newfacet_list
78
79			notes:
80			uses 'facetT *newfacet;'
81			at exit, newfacet==NULL
82			*/
83			#define FORALLnew_facets for( newfacet=qh newfacet_list;newfacet && newfacet->next;newfacet=newfacet->next )
84
85			/*-<a href="qh-poly.htm#TOC"
86			>--------------------------------</a><a name="FORALLvertex_">-</a>
87
88			FORALLvertex_( vertexlist ) { ... }
89			assign 'vertex' to each vertex in vertexlist
90
91			notes:
92			uses 'vertexT *vertex;'
93			at exit, vertex==NULL
94			*/
95			#define FORALLvertex_( vertexlist ) for ( vertex=( vertexlist );vertex && vertex->next;vertex= vertex->next )
96
97			/*-<a href="qh-poly.htm#TOC"
98			>--------------------------------</a><a name="FORALLvisible_facets">-</a>
99
100			FORALLvisible_facets { ... }
101			assign 'visible' to each visible facet in qh.visible_list
102
103			notes:
104			uses 'vacetT *visible;'
105			at exit, visible==NULL
106			*/
107			#define FORALLvisible_facets for (visible=qh visible_list; visible && visible->visible; visible= visible->next)
108
109			/*-<a href="qh-poly.htm#TOC"
110			>--------------------------------</a><a name="FORALLsame_">-</a>
111
112			FORALLsame_( newfacet ) { ... }
113			assign 'same' to each facet in newfacet->f.samecycle
114
115			notes:
116			uses 'facetT *same;'
117			stops when it returns to newfacet
118			*/
119			#define FORALLsame_(newfacet) for (same= newfacet->f.samecycle; same != newfacet; same= same->f.samecycle)
120
121			/*-<a href="qh-poly.htm#TOC"
122			>--------------------------------</a><a name="FORALLsame_cycle_">-</a>
123
124			FORALLsame_cycle_( newfacet ) { ... }
125			assign 'same' to each facet in newfacet->f.samecycle
126
127			notes:
128			uses 'facetT *same;'
129			at exit, same == NULL
130			*/
131			#define FORALLsame_cycle_(newfacet) \
132			for (same= newfacet->f.samecycle; \
133			same; same= (same == newfacet ? NULL : same->f.samecycle))
134
135			/*-<a href="qh-poly.htm#TOC"
136			>--------------------------------</a><a name="FOREACHneighborA_">-</a>
137
138			FOREACHneighborA_( facet ) { ... }
139			assign 'neighborA' to each neighbor in facet->neighbors
140
141			FOREACHneighborA_( vertex ) { ... }
142			assign 'neighborA' to each neighbor in vertex->neighbors
143
144			declare:
145			facetT neighborA, *neighborAp;
146
147			see:
148			<a href="qset.h#FOREACHsetelement_">FOREACHsetelement_</a>
149			*/
150			#define FOREACHneighborA_(facet) FOREACHsetelement_(facetT, facet->neighbors, neighborA)
151
152			/*-<a href="qh-poly.htm#TOC"
153			>--------------------------------</a><a name="FOREACHvisible_">-</a>
154
155			FOREACHvisible_( facets ) { ... }
156			assign 'visible' to each facet in facets
157
158			notes:
159			uses 'facetT facet, facetp;'
160			see <a href="qset.h#FOREACHsetelement_">FOREACHsetelement_</a>
161			*/
162			#define FOREACHvisible_(facets) FOREACHsetelement_(facetT, facets, visible)
163
164			/*-<a href="qh-poly.htm#TOC"
165			>--------------------------------</a><a name="FOREACHnewfacet_">-</a>
166
167			FOREACHnewfacet_( facets ) { ... }
168			assign 'newfacet' to each facet in facets
169
170			notes:
171			uses 'facetT newfacet, newfacetp;'
172			see <a href="qset.h#FOREACHsetelement_">FOREACHsetelement_</a>
173			*/
174			#define FOREACHnewfacet_(facets) FOREACHsetelement_(facetT, facets, newfacet)
175
176			/*-<a href="qh-poly.htm#TOC"
177			>--------------------------------</a><a name="FOREACHvertexA_">-</a>
178
179			FOREACHvertexA_( vertices ) { ... }
180			assign 'vertexA' to each vertex in vertices
181
182			notes:
183			uses 'vertexT vertexA, vertexAp;'
184			see <a href="qset.h#FOREACHsetelement_">FOREACHsetelement_</a>
185			*/
186			#define FOREACHvertexA_(vertices) FOREACHsetelement_(vertexT, vertices, vertexA)
187
188			/*-<a href="qh-poly.htm#TOC"
189			>--------------------------------</a><a name="FOREACHvertexreverse12_">-</a>
190
191			FOREACHvertexreverse12_( vertices ) { ... }
192			assign 'vertex' to each vertex in vertices
193			reverse order of first two vertices
194
195			notes:
196			uses 'vertexT vertex, vertexp;'
197			see <a href="qset.h#FOREACHsetelement_">FOREACHsetelement_</a>
198			*/
199			#define FOREACHvertexreverse12_(vertices) FOREACHsetelementreverse12_(vertexT, vertices, vertex)
200
201
202			/=============== prototypes poly.c in alphabetical order ================/
203
204			void qh_appendfacet(facetT *facet);
205			void qh_appendvertex(vertexT *vertex);
206			void qh_attachnewfacets (void);
207			boolT qh_checkflipped (facetT facet, realT dist, boolT allerror);
208			void qh_delfacet(facetT *facet);
209			void qh_deletevisible(void /qh visible_list, qh horizon_list/);
210			setT qh_facetintersect (facetT facetA, facetT facetB, int skipAp,int *skipBp, int extra);
211			unsigned qh_gethash (int hashsize, setT set, int size, int firstindex, void skipelem);
212			facetT qh_makenewfacet(setT vertices, boolT toporient, facetT *facet);
213			void qh_makenewplanes ( void /* newfacet_list */);
214			facetT qh_makenew_nonsimplicial (facetT visible, vertexT apex, int numnew);
215			facetT qh_makenew_simplicial (facetT visible, vertexT apex, int numnew);
216			void qh_matchneighbor (facetT *newfacet, int newskip, int hashsize,
217			int *hashcount);
218			void qh_matchnewfacets (void);
219			boolT qh_matchvertices (int firstindex, setT *verticesA, int skipA,
220			setT verticesB, int skipB, boolT *same);
221			facetT *qh_newfacet(void);
222			ridgeT *qh_newridge(void);
223			int qh_pointid (pointT *point);
224			void qh_removefacet(facetT *facet);
225			void qh_removevertex(vertexT *vertex);
226			void qh_updatevertices (void);
227
228
229			/========== -prototypes poly2.c in alphabetical order ===========/
230
231			void qh_addhash (void* newelem, setT *hashtable, int hashsize, unsigned hash);
232			void qh_check_bestdist (void);
233			void qh_check_maxout (void);
234			void qh_check_output (void);
235			void qh_check_point (pointT point, facetT facet, realT maxoutside, realT maxdist, facetT errfacet1, facetT errfacet2);
236			void qh_check_points(void);
237			void qh_checkconvex(facetT *facetlist, int fault);
238			void qh_checkfacet(facetT facet, boolT newmerge, boolT waserrorp);
239			void qh_checkflipped_all (facetT *facetlist);
240			void qh_checkpolygon(facetT *facetlist);
241			void qh_checkvertex (vertexT *vertex);
242			void qh_clearcenters (qh_CENTER type);
243			void qh_createsimplex(setT *vertices);
244			void qh_delridge(ridgeT *ridge);
245			void qh_delvertex (vertexT *vertex);
246			setT qh_facet3vertex (facetT facet);
247			facetT qh_findbestfacet (pointT point, boolT bestoutside,
248			realT bestdist, boolT isoutside);
249			facetT qh_findbestlower (facetT upperfacet, pointT point, realT bestdistp, int *numpart);
250			facetT qh_findfacet_all (pointT point, realT bestdist, boolT isoutside,
251			int *numpart);
252			int qh_findgood (facetT *facetlist, int goodhorizon);
253			void qh_findgood_all (facetT *facetlist);
254			void qh_furthestnext (void /* qh facet_list */);
255			void qh_furthestout (facetT *facet);
256			void qh_infiniteloop (facetT *facet);
257			void qh_initbuild(void);
258			void qh_initialhull(setT *vertices);
259			setT qh_initialvertices(int dim, setT maxpoints, pointT *points, int numpoints);
260			vertexT qh_isvertex (pointT point, setT *vertices);
261			vertexT qh_makenewfacets (pointT point /horizon_list, visible_list/);
262			void qh_matchduplicates (facetT atfacet, int atskip, int hashsize, int hashcount);
263			void qh_nearcoplanar ( void /* qh.facet_list */);
264			vertexT qh_nearvertex (facetT facet, pointT point, realT bestdistp);
265			int qh_newhashtable(int newsize);
266			vertexT qh_newvertex(pointT point);
267			ridgeT qh_nextridge3d (ridgeT atridge, facetT facet, vertexT *vertexp);
268			void qh_outcoplanar (void /* facet_list */);
269			pointT *qh_point (int id);
270			void qh_point_add (setT set, pointT point, void *elem);
271			setT qh_pointfacet (void /qh facet_list*/);
272			setT qh_pointvertex (void /qh facet_list*/);
273			void qh_prependfacet(facetT facet, facetT *facetlist);
274			void qh_printhashtable(FILE *fp);
275			void qh_printlists (void);
276			void qh_resetlists (boolT stats, boolT resetVisible /qh newvertex_list newfacet_list visible_list/);
277			void qh_setvoronoi_all (void);
278			void qh_triangulate (void /qh facet_list/);
279			void qh_triangulate_facet (facetT facetA, vertexT *first_vertex);
280			void qh_triangulate_link (facetT oldfacetA, facetT facetA, facetT oldfacetB, facetT facetB);
281			void qh_triangulate_mirror (facetT facetA, facetT facetB);
282			void qh_triangulate_null (facetT *facetA);
283			void qh_vertexintersect(setT *vertexsetA,setT vertexsetB);
284			setT qh_vertexintersect_new(setT vertexsetA,setT *vertexsetB);
285			void qh_vertexneighbors (void /qh facet_list/);
286			boolT qh_vertexsubset(setT vertexsetA, setT vertexsetB);
287
288
289			#endif /* qhDEFpoly */