1 /*<html><pre> -<a href="qh-user_r.htm"
2 >-------------------------------</a><a name="TOP">-</a>
3
4 user.c
5 user redefinable functions
6
7 see user2_r.c for qh_fprintf, qh_malloc, qh_free
8
9 see README.txt see COPYING.txt for copyright information.
10
11 see libqhull_r.h for data structures, macros, and user-callable functions.
12
13 see user_eg.c, user_eg2.c, and unix.c for examples.
14
15 see user.h for user-definable constants
16
17 use qh_NOmem in mem_r.h to turn off memory management
18 use qh_NOmerge in user.h to turn off facet merging
19 set qh_KEEPstatistics in user.h to 0 to turn off statistics
20
21 This is unsupported software. You're welcome to make changes,
22 but you're on your own if something goes wrong. Use 'Tc' to
23 check frequently. Usually qhull will report an error if
24 a data structure becomes inconsistent. If so, it also reports
25 the last point added to the hull, e.g., 102. You can then trace
26 the execution of qhull with "T4P102".
27
28 Please report any errors that you fix to qhull@qhull.org
29
30 Qhull-template is a template for calling qhull from within your application
31
32 if you recompile and load this module, then user.o will not be loaded
33 from qhull.a
34
35 you can add additional quick allocation sizes in qh_user_memsizes
36
37 if the other functions here are redefined to not use qh_print...,
38 then io.o will not be loaded from qhull.a. See user_eg_r.c for an
39 example. We recommend keeping io.o for the extra debugging
40 information it supplies.
41 */
42
43 #include "qhull_ra.h"
44
45 #include <stdarg.h>
46
47 /*-<a href="qh-user_r.htm#TOC"
48 >-------------------------------</a><a name="qhull_template">-</a>
49
50 Qhull-template
51 Template for calling qhull from inside your program
52
53 returns:
54 exit code(see qh_ERR... in libqhull_r.h)
55 all memory freed
56
57 notes:
58 This can be called any number of times.
59
60 */
61 #if 0
62 {
63 int dim; /* dimension of points */
64 int numpoints; /* number of points */
65 coordT *points; /* array of coordinates for each point */
66 boolT ismalloc; /* True if qhull should free points in qh_freeqhull() or reallocation */
67 char flags[]= "qhull Tv"; /* option flags for qhull, see qh_opt.htm */
68 FILE *outfile= stdout; /* output from qh_produce_output(qh)
69 use NULL to skip qh_produce_output(qh) */
70 FILE *errfile= stderr; /* error messages from qhull code */
71 int exitcode; /* 0 if no error from qhull */
72 facetT *facet; /* set by FORALLfacets */
73 int curlong, totlong; /* memory remaining after qh_memfreeshort */
74
75 qhT qh_qh; /* Qhull's data structure. First argument of most calls */
76 qhT *qh= &qh_qh; /* Alternatively -- qhT *qh= (qhT*)malloc(sizeof(qhT)) */
77
78 QHULL_LIB_CHECK /* Check for compatible library */
79
80 qh_zero(qh, errfile);
81
82 /* initialize dim, numpoints, points[], ismalloc here */
83 exitcode= qh_new_qhull(qh, dim, numpoints, points, ismalloc,
84 flags, outfile, errfile);
85 if (!exitcode) { /* if no error */
86 /* 'qh->facet_list' contains the convex hull */
87 FORALLfacets {
88 /* ... your code ... */
89 }
90 }
91 qh_freeqhull(qh, !qh_ALL);
92 qh_memfreeshort(qh, &curlong, &totlong);
93 if (curlong || totlong)
94 qh_fprintf(qh, errfile, 7068, "qhull internal warning (main): did not free %d bytes of long memory(%d pieces)\n", totlong, curlong);
95 }
96 #endif
97
98 /*-<a href="qh-user_r.htm#TOC"
99 >-------------------------------</a><a name="new_qhull">-</a>
100
101 qh_new_qhull(qh, dim, numpoints, points, ismalloc, qhull_cmd, outfile, errfile )
102 Run qhull and return results in qh.
103 Returns exitcode (0 if no errors).
104 Before first call, either call qh_zero(qh, errfile), or set qh to all zero.
105
106 notes:
107 do not modify points until finished with results.
108 The qhull data structure contains pointers into the points array.
109 do not call qhull functions before qh_new_qhull().
110 The qhull data structure is not initialized until qh_new_qhull().
111 do not call qh_init_A (global_r.c)
112
113 Default errfile is stderr, outfile may be null
114 qhull_cmd must start with "qhull "
115 projects points to a new point array for Delaunay triangulations ('d' and 'v')
116 transforms points into a new point array for halfspace intersection ('H')
117
118 see:
119 Qhull-template at the beginning of this file.
120 An example of using qh_new_qhull is user_eg_r.c
121 */
qh_new_qhull(qhT * qh,int dim,int numpoints,coordT * points,boolT ismalloc,char * qhull_cmd,FILE * outfile,FILE * errfile)122 int qh_new_qhull(qhT *qh, int dim, int numpoints, coordT *points, boolT ismalloc,
123 char *qhull_cmd, FILE *outfile, FILE *errfile) {
124 /* gcc may issue a "might be clobbered" warning for dim, points, and ismalloc [-Wclobbered].
125 These parameters are not referenced after a longjmp() and hence not clobbered.
126 See http://stackoverflow.com/questions/7721854/what-sense-do-these-clobbered-variable-warnings-make */
127 int exitcode, hulldim;
128 boolT new_ismalloc;
129 coordT *new_points;
130
131 if(!errfile){
132 errfile= stderr;
133 }
134 if (!qh->qhmem.ferr) {
135 qh_meminit(qh, errfile);
136 } else {
137 qh_memcheck(qh);
138 }
139 if (strncmp(qhull_cmd, "qhull ", (size_t)6)) {
140 qh_fprintf(qh, errfile, 6186, "qhull error (qh_new_qhull): start qhull_cmd argument with \"qhull \"\n");
141 return qh_ERRinput;
142 }
143 qh_initqhull_start(qh, NULL, outfile, errfile);
144 trace1((qh, qh->ferr, 1044, "qh_new_qhull: build new Qhull for %d %d-d points with %s\n", numpoints, dim, qhull_cmd));
145 exitcode = setjmp(qh->errexit);
146 if (!exitcode)
147 {
148 qh->NOerrexit = False;
149 qh_initflags(qh, qhull_cmd);
150 if (qh->DELAUNAY)
151 qh->PROJECTdelaunay= True;
152 if (qh->HALFspace) {
153 /* points is an array of halfspaces,
154 the last coordinate of each halfspace is its offset */
155 hulldim= dim-1;
156 qh_setfeasible(qh, hulldim);
157 new_points= qh_sethalfspace_all(qh, dim, numpoints, points, qh->feasible_point);
158 new_ismalloc= True;
159 if (ismalloc)
160 qh_free(points);
161 }else {
162 hulldim= dim;
163 new_points= points;
164 new_ismalloc= ismalloc;
165 }
166 qh_init_B(qh, new_points, numpoints, hulldim, new_ismalloc);
167 qh_qhull(qh);
168 qh_check_output(qh);
169 if (outfile) {
170 qh_produce_output(qh);
171 }else {
172 qh_prepare_output(qh);
173 }
174 if (qh->VERIFYoutput && !qh->STOPpoint && !qh->STOPcone)
175 qh_check_points(qh);
176 }
177 qh->NOerrexit = True;
178 return exitcode;
179 } /* new_qhull */
180
181 /*-<a href="qh-user_r.htm#TOC"
182 >-------------------------------</a><a name="errexit">-</a>
183
184 qh_errexit(qh, exitcode, facet, ridge )
185 report and exit from an error
186 report facet and ridge if non-NULL
187 reports useful information such as last point processed
188 set qh.FORCEoutput to print neighborhood of facet
189
190 see:
191 qh_errexit2() in libqhull_r.c for printing 2 facets
192
193 design:
194 check for error within error processing
195 compute qh.hulltime
196 print facet and ridge (if any)
197 report commandString, options, qh.furthest_id
198 print summary and statistics (including precision statistics)
199 if qh_ERRsingular
200 print help text for singular data set
201 exit program via long jump (if defined) or exit()
202 */
qh_errexit(qhT * qh,int exitcode,facetT * facet,ridgeT * ridge)203 void qh_errexit(qhT *qh, int exitcode, facetT *facet, ridgeT *ridge) {
204
205 if (qh->ERREXITcalled) {
206 qh_fprintf(qh, qh->ferr, 8126, "\nqhull error while processing previous error. Exit program\n");
207 qh_exit(qh_ERRqhull);
208 }
209 qh->ERREXITcalled= True;
210 if (!qh->QHULLfinished)
211 qh->hulltime= qh_CPUclock - qh->hulltime;
212 qh_errprint(qh, "ERRONEOUS", facet, NULL, ridge, NULL);
213 qh_fprintf(qh, qh->ferr, 8127, "\nWhile executing: %s | %s\n", qh->rbox_command, qh->qhull_command);
214 qh_fprintf(qh, qh->ferr, 8128, "Options selected for Qhull %s:\n%s\n", qh_version, qh->qhull_options);
215 if (qh->furthest_id >= 0) {
216 qh_fprintf(qh, qh->ferr, 8129, "Last point added to hull was p%d.", qh->furthest_id);
217 if (zzval_(Ztotmerge))
218 qh_fprintf(qh, qh->ferr, 8130, " Last merge was #%d.", zzval_(Ztotmerge));
219 if (qh->QHULLfinished)
220 qh_fprintf(qh, qh->ferr, 8131, "\nQhull has finished constructing the hull.");
221 else if (qh->POSTmerging)
222 qh_fprintf(qh, qh->ferr, 8132, "\nQhull has started post-merging.");
223 qh_fprintf(qh, qh->ferr, 8133, "\n");
224 }
225 if (qh->FORCEoutput && (qh->QHULLfinished || (!facet && !ridge)))
226 qh_produce_output(qh);
227 else if (exitcode != qh_ERRinput) {
228 if (exitcode != qh_ERRsingular && zzval_(Zsetplane) > qh->hull_dim+1) {
229 qh_fprintf(qh, qh->ferr, 8134, "\nAt error exit:\n");
230 qh_printsummary(qh, qh->ferr);
231 if (qh->PRINTstatistics) {
232 qh_collectstatistics(qh);
233 qh_printstatistics(qh, qh->ferr, "at error exit");
234 qh_memstatistics(qh, qh->ferr);
235 }
236 }
237 if (qh->PRINTprecision)
238 qh_printstats(qh, qh->ferr, qh->qhstat.precision, NULL);
239 }
240 if (!exitcode)
241 exitcode= qh_ERRqhull;
242 else if (exitcode == qh_ERRsingular)
243 qh_printhelp_singular(qh, qh->ferr);
244 else if (exitcode == qh_ERRprec && !qh->PREmerge)
245 qh_printhelp_degenerate(qh, qh->ferr);
246 if (qh->NOerrexit) {
247 qh_fprintf(qh, qh->ferr, 6187, "qhull error while ending program, or qh->NOerrexit not cleared after setjmp(). Exit program with error.\n");
248 qh_exit(qh_ERRqhull);
249 }
250 qh->ERREXITcalled= False;
251 qh->NOerrexit= True;
252 qh->ALLOWrestart= False; /* longjmp will undo qh_build_withrestart */
253 longjmp(qh->errexit, exitcode);
254 } /* errexit */
255
256
257 /*-<a href="qh-user_r.htm#TOC"
258 >-------------------------------</a><a name="errprint">-</a>
259
260 qh_errprint(qh, fp, string, atfacet, otherfacet, atridge, atvertex )
261 prints out the information of facets and ridges to fp
262 also prints neighbors and geomview output
263
264 notes:
265 except for string, any parameter may be NULL
266 */
qh_errprint(qhT * qh,const char * string,facetT * atfacet,facetT * otherfacet,ridgeT * atridge,vertexT * atvertex)267 void qh_errprint(qhT *qh, const char *string, facetT *atfacet, facetT *otherfacet, ridgeT *atridge, vertexT *atvertex) {
268 int i;
269
270 if (atfacet) {
271 qh_fprintf(qh, qh->ferr, 8135, "%s FACET:\n", string);
272 qh_printfacet(qh, qh->ferr, atfacet);
273 }
274 if (otherfacet) {
275 qh_fprintf(qh, qh->ferr, 8136, "%s OTHER FACET:\n", string);
276 qh_printfacet(qh, qh->ferr, otherfacet);
277 }
278 if (atridge) {
279 qh_fprintf(qh, qh->ferr, 8137, "%s RIDGE:\n", string);
280 qh_printridge(qh, qh->ferr, atridge);
281 if (atridge->top && atridge->top != atfacet && atridge->top != otherfacet)
282 qh_printfacet(qh, qh->ferr, atridge->top);
283 if (atridge->bottom
284 && atridge->bottom != atfacet && atridge->bottom != otherfacet)
285 qh_printfacet(qh, qh->ferr, atridge->bottom);
286 if (!atfacet)
287 atfacet= atridge->top;
288 if (!otherfacet)
289 otherfacet= otherfacet_(atridge, atfacet);
290 }
291 if (atvertex) {
292 qh_fprintf(qh, qh->ferr, 8138, "%s VERTEX:\n", string);
293 qh_printvertex(qh, qh->ferr, atvertex);
294 }
295 if (qh->fout && qh->FORCEoutput && atfacet && !qh->QHULLfinished && !qh->IStracing) {
296 qh_fprintf(qh, qh->ferr, 8139, "ERRONEOUS and NEIGHBORING FACETS to output\n");
297 for (i=0; i < qh_PRINTEND; i++) /* use fout for geomview output */
298 qh_printneighborhood(qh, qh->fout, qh->PRINTout[i], atfacet, otherfacet,
299 !qh_ALL);
300 }
301 } /* errprint */
302
303
304 /*-<a href="qh-user_r.htm#TOC"
305 >-------------------------------</a><a name="printfacetlist">-</a>
306
307 qh_printfacetlist(qh, fp, facetlist, facets, printall )
308 print all fields for a facet list and/or set of facets to fp
309 if !printall,
310 only prints good facets
311
312 notes:
313 also prints all vertices
314 */
qh_printfacetlist(qhT * qh,facetT * facetlist,setT * facets,boolT printall)315 void qh_printfacetlist(qhT *qh, facetT *facetlist, setT *facets, boolT printall) {
316 facetT *facet, **facetp;
317
318 qh_printbegin(qh, qh->ferr, qh_PRINTfacets, facetlist, facets, printall);
319 FORALLfacet_(facetlist)
320 qh_printafacet(qh, qh->ferr, qh_PRINTfacets, facet, printall);
321 FOREACHfacet_(facets)
322 qh_printafacet(qh, qh->ferr, qh_PRINTfacets, facet, printall);
323 qh_printend(qh, qh->ferr, qh_PRINTfacets, facetlist, facets, printall);
324 } /* printfacetlist */
325
326
327 /*-<a href="qh-io_r.htm#TOC"
328 >-------------------------------</a><a name="printhelp_degenerate">-</a>
329
330 qh_printhelp_degenerate(qh, fp )
331 prints descriptive message for precision error
332
333 notes:
334 no message if qh_QUICKhelp
335 */
qh_printhelp_degenerate(qhT * qh,FILE * fp)336 void qh_printhelp_degenerate(qhT *qh, FILE *fp) {
337
338 if (qh->MERGEexact || qh->PREmerge || qh->JOGGLEmax < REALmax/2)
339 qh_fprintf(qh, fp, 9368, "\n\
340 A Qhull error has occurred. Qhull should have corrected the above\n\
341 precision error. Please send the input and all of the output to\n\
342 qhull_bug@qhull.org\n");
343 else if (!qh_QUICKhelp) {
344 qh_fprintf(qh, fp, 9369, "\n\
345 Precision problems were detected during construction of the convex hull.\n\
346 This occurs because convex hull algorithms assume that calculations are\n\
347 exact, but floating-point arithmetic has roundoff errors.\n\
348 \n\
349 To correct for precision problems, do not use 'Q0'. By default, Qhull\n\
350 selects 'C-0' or 'Qx' and merges non-convex facets. With option 'QJ',\n\
351 Qhull joggles the input to prevent precision problems. See \"Imprecision\n\
352 in Qhull\" (qh-impre.htm).\n\
353 \n\
354 If you use 'Q0', the output may include\n\
355 coplanar ridges, concave ridges, and flipped facets. In 4-d and higher,\n\
356 Qhull may produce a ridge with four neighbors or two facets with the same \n\
357 vertices. Qhull reports these events when they occur. It stops when a\n\
358 concave ridge, flipped facet, or duplicate facet occurs.\n");
359 #if REALfloat
360 qh_fprintf(qh, fp, 9370, "\
361 \n\
362 Qhull is currently using single precision arithmetic. The following\n\
363 will probably remove the precision problems:\n\
364 - recompile qhull for realT precision(#define REALfloat 0 in user.h).\n");
365 #endif
366 if (qh->DELAUNAY && !qh->SCALElast && qh->MAXabs_coord > 1e4)
367 qh_fprintf(qh, fp, 9371, "\
368 \n\
369 When computing the Delaunay triangulation of coordinates > 1.0,\n\
370 - use 'Qbb' to scale the last coordinate to [0,m] (max previous coordinate)\n");
371 if (qh->DELAUNAY && !qh->ATinfinity)
372 qh_fprintf(qh, fp, 9372, "\
373 When computing the Delaunay triangulation:\n\
374 - use 'Qz' to add a point at-infinity. This reduces precision problems.\n");
375
376 qh_fprintf(qh, fp, 9373, "\
377 \n\
378 If you need triangular output:\n\
379 - use option 'Qt' to triangulate the output\n\
380 - use option 'QJ' to joggle the input points and remove precision errors\n\
381 - use option 'Ft'. It triangulates non-simplicial facets with added points.\n\
382 \n\
383 If you must use 'Q0',\n\
384 try one or more of the following options. They can not guarantee an output.\n\
385 - use 'QbB' to scale the input to a cube.\n\
386 - use 'Po' to produce output and prevent partitioning for flipped facets\n\
387 - use 'V0' to set min. distance to visible facet as 0 instead of roundoff\n\
388 - use 'En' to specify a maximum roundoff error less than %2.2g.\n\
389 - options 'Qf', 'Qbb', and 'QR0' may also help\n",
390 qh->DISTround);
391 qh_fprintf(qh, fp, 9374, "\
392 \n\
393 To guarantee simplicial output:\n\
394 - use option 'Qt' to triangulate the output\n\
395 - use option 'QJ' to joggle the input points and remove precision errors\n\
396 - use option 'Ft' to triangulate the output by adding points\n\
397 - use exact arithmetic (see \"Imprecision in Qhull\", qh-impre.htm)\n\
398 ");
399 }
400 } /* printhelp_degenerate */
401
402
403 /*-<a href="qh-globa_r.htm#TOC"
404 >-------------------------------</a><a name="printhelp_narrowhull">-</a>
405
406 qh_printhelp_narrowhull(qh, minangle )
407 Warn about a narrow hull
408
409 notes:
410 Alternatively, reduce qh_WARNnarrow in user.h
411
412 */
qh_printhelp_narrowhull(qhT * qh,FILE * fp,realT minangle)413 void qh_printhelp_narrowhull(qhT *qh, FILE *fp, realT minangle) {
414
415 qh_fprintf(qh, fp, 9375, "qhull precision warning: \n\
416 The initial hull is narrow (cosine of min. angle is %.16f).\n\
417 Is the input lower dimensional (e.g., on a plane in 3-d)? Qhull may\n\
418 produce a wide facet. Options 'QbB' (scale to unit box) or 'Qbb' (scale\n\
419 last coordinate) may remove this warning. Use 'Pp' to skip this warning.\n\
420 See 'Limitations' in qh-impre.htm.\n",
421 -minangle); /* convert from angle between normals to angle between facets */
422 } /* printhelp_narrowhull */
423
424 /*-<a href="qh-io_r.htm#TOC"
425 >-------------------------------</a><a name="printhelp_singular">-</a>
426
427 qh_printhelp_singular(qh, fp )
428 prints descriptive message for singular input
429 */
qh_printhelp_singular(qhT * qh,FILE * fp)430 void qh_printhelp_singular(qhT *qh, FILE *fp) {
431 facetT *facet;
432 vertexT *vertex, **vertexp;
433 realT min, max, *coord, dist;
434 int i,k;
435
436 qh_fprintf(qh, fp, 9376, "\n\
437 The input to qhull appears to be less than %d dimensional, or a\n\
438 computation has overflowed.\n\n\
439 Qhull could not construct a clearly convex simplex from points:\n",
440 qh->hull_dim);
441 qh_printvertexlist(qh, fp, "", qh->facet_list, NULL, qh_ALL);
442 if (!qh_QUICKhelp)
443 qh_fprintf(qh, fp, 9377, "\n\
444 The center point is coplanar with a facet, or a vertex is coplanar\n\
445 with a neighboring facet. The maximum round off error for\n\
446 computing distances is %2.2g. The center point, facets and distances\n\
447 to the center point are as follows:\n\n", qh->DISTround);
448 qh_printpointid(qh, fp, "center point", qh->hull_dim, qh->interior_point, qh_IDunknown);
449 qh_fprintf(qh, fp, 9378, "\n");
450 FORALLfacets {
451 qh_fprintf(qh, fp, 9379, "facet");
452 FOREACHvertex_(facet->vertices)
453 qh_fprintf(qh, fp, 9380, " p%d", qh_pointid(qh, vertex->point));
454 zinc_(Zdistio);
455 qh_distplane(qh, qh->interior_point, facet, &dist);
456 qh_fprintf(qh, fp, 9381, " distance= %4.2g\n", dist);
457 }
458 if (!qh_QUICKhelp) {
459 if (qh->HALFspace)
460 qh_fprintf(qh, fp, 9382, "\n\
461 These points are the dual of the given halfspaces. They indicate that\n\
462 the intersection is degenerate.\n");
463 qh_fprintf(qh, fp, 9383,"\n\
464 These points either have a maximum or minimum x-coordinate, or\n\
465 they maximize the determinant for k coordinates. Trial points\n\
466 are first selected from points that maximize a coordinate.\n");
467 if (qh->hull_dim >= qh_INITIALmax)
468 qh_fprintf(qh, fp, 9384, "\n\
469 Because of the high dimension, the min x-coordinate and max-coordinate\n\
470 points are used if the determinant is non-zero. Option 'Qs' will\n\
471 do a better, though much slower, job. Instead of 'Qs', you can change\n\
472 the points by randomly rotating the input with 'QR0'.\n");
473 }
474 qh_fprintf(qh, fp, 9385, "\nThe min and max coordinates for each dimension are:\n");
475 for (k=0; k < qh->hull_dim; k++) {
476 min= REALmax;
477 max= -REALmin;
478 for (i=qh->num_points, coord= qh->first_point+k; i--; coord += qh->hull_dim) {
479 maximize_(max, *coord);
480 minimize_(min, *coord);
481 }
482 qh_fprintf(qh, fp, 9386, " %d: %8.4g %8.4g difference= %4.4g\n", k, min, max, max-min);
483 }
484 if (!qh_QUICKhelp) {
485 qh_fprintf(qh, fp, 9387, "\n\
486 If the input should be full dimensional, you have several options that\n\
487 may determine an initial simplex:\n\
488 - use 'QJ' to joggle the input and make it full dimensional\n\
489 - use 'QbB' to scale the points to the unit cube\n\
490 - use 'QR0' to randomly rotate the input for different maximum points\n\
491 - use 'Qs' to search all points for the initial simplex\n\
492 - use 'En' to specify a maximum roundoff error less than %2.2g.\n\
493 - trace execution with 'T3' to see the determinant for each point.\n",
494 qh->DISTround);
495 #if REALfloat
496 qh_fprintf(qh, fp, 9388, "\
497 - recompile qhull for realT precision(#define REALfloat 0 in libqhull_r.h).\n");
498 #endif
499 qh_fprintf(qh, fp, 9389, "\n\
500 If the input is lower dimensional:\n\
501 - use 'QJ' to joggle the input and make it full dimensional\n\
502 - use 'Qbk:0Bk:0' to delete coordinate k from the input. You should\n\
503 pick the coordinate with the least range. The hull will have the\n\
504 correct topology.\n\
505 - determine the flat containing the points, rotate the points\n\
506 into a coordinate plane, and delete the other coordinates.\n\
507 - add one or more points to make the input full dimensional.\n\
508 ");
509 }
510 } /* printhelp_singular */
511
512 /*-<a href="qh-globa_r.htm#TOC"
513 >-------------------------------</a><a name="user_memsizes">-</a>
514
515 qh_user_memsizes(qh)
516 allocate up to 10 additional, quick allocation sizes
517
518 notes:
519 increase maximum number of allocations in qh_initqhull_mem()
520 */
qh_user_memsizes(qhT * qh)521 void qh_user_memsizes(qhT *qh) {
522
523 QHULL_UNUSED(qh)
524 /* qh_memsize(qh, size); */
525 } /* user_memsizes */
526
527
528