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+/*<html><pre> -<a href="qh-user_r.htm"
+ >-------------------------------</a><a name="TOP">-</a>
+
+ user.c
+ user redefinable functions
+
+ see user2_r.c for qh_fprintf, qh_malloc, qh_free
+
+ see README.txt see COPYING.txt for copyright information.
+
+ see libqhull_r.h for data structures, macros, and user-callable functions.
+
+ see user_eg.c, user_eg2.c, and unix.c for examples.
+
+ see user.h for user-definable constants
+
+ use qh_NOmem in mem_r.h to turn off memory management
+ use qh_NOmerge in user.h to turn off facet merging
+ set qh_KEEPstatistics in user.h to 0 to turn off statistics
+
+ This is unsupported software. You're welcome to make changes,
+ but you're on your own if something goes wrong. Use 'Tc' to
+ check frequently. Usually qhull will report an error if
+ a data structure becomes inconsistent. If so, it also reports
+ the last point added to the hull, e.g., 102. You can then trace
+ the execution of qhull with "T4P102".
+
+ Please report any errors that you fix to qhull@qhull.org
+
+ Qhull-template is a template for calling qhull from within your application
+
+ if you recompile and load this module, then user.o will not be loaded
+ from qhull.a
+
+ you can add additional quick allocation sizes in qh_user_memsizes
+
+ if the other functions here are redefined to not use qh_print...,
+ then io.o will not be loaded from qhull.a. See user_eg_r.c for an
+ example. We recommend keeping io.o for the extra debugging
+ information it supplies.
+*/
+
+#include "qhull_ra.h"
+
+#include <stdarg.h>
+
+/*-<a href="qh-user_r.htm#TOC"
+ >-------------------------------</a><a name="qhull_template">-</a>
+
+ Qhull-template
+ Template for calling qhull from inside your program
+
+ returns:
+ exit code(see qh_ERR... in libqhull_r.h)
+ all memory freed
+
+ notes:
+ This can be called any number of times.
+
+*/
+#if 0
+{
+ int dim; /* dimension of points */
+ int numpoints; /* number of points */
+ coordT *points; /* array of coordinates for each point */
+ boolT ismalloc; /* True if qhull should free points in qh_freeqhull() or reallocation */
+ char flags[]= "qhull Tv"; /* option flags for qhull, see qh_opt.htm */
+ FILE *outfile= stdout; /* output from qh_produce_output(qh)
+ use NULL to skip qh_produce_output(qh) */
+ FILE *errfile= stderr; /* error messages from qhull code */
+ int exitcode; /* 0 if no error from qhull */
+ facetT *facet; /* set by FORALLfacets */
+ int curlong, totlong; /* memory remaining after qh_memfreeshort */
+
+ qhT qh_qh; /* Qhull's data structure. First argument of most calls */
+ qhT *qh= &qh_qh; /* Alternatively -- qhT *qh= (qhT*)malloc(sizeof(qhT)) */
+
+ QHULL_LIB_CHECK /* Check for compatible library */
+
+ qh_zero(qh, errfile);
+
+ /* initialize dim, numpoints, points[], ismalloc here */
+ exitcode= qh_new_qhull(qh, dim, numpoints, points, ismalloc,
+ flags, outfile, errfile);
+ if (!exitcode) { /* if no error */
+ /* 'qh->facet_list' contains the convex hull */
+ FORALLfacets {
+ /* ... your code ... */
+ }
+ }
+ qh_freeqhull(qh, !qh_ALL);
+ qh_memfreeshort(qh, &curlong, &totlong);
+ if (curlong || totlong)
+ qh_fprintf(qh, errfile, 7068, "qhull internal warning (main): did not free %d bytes of long memory(%d pieces)\n", totlong, curlong);
+}
+#endif
+
+/*-<a href="qh-user_r.htm#TOC"
+ >-------------------------------</a><a name="new_qhull">-</a>
+
+ qh_new_qhull(qh, dim, numpoints, points, ismalloc, qhull_cmd, outfile, errfile )
+ Run qhull and return results in qh.
+ Returns exitcode (0 if no errors).
+ Before first call, either call qh_zero(qh, errfile), or set qh to all zero.
+
+ notes:
+ do not modify points until finished with results.
+ The qhull data structure contains pointers into the points array.
+ do not call qhull functions before qh_new_qhull().
+ The qhull data structure is not initialized until qh_new_qhull().
+ do not call qh_init_A (global_r.c)
+
+ Default errfile is stderr, outfile may be null
+ qhull_cmd must start with "qhull "
+ projects points to a new point array for Delaunay triangulations ('d' and 'v')
+ transforms points into a new point array for halfspace intersection ('H')
+
+ see:
+ Qhull-template at the beginning of this file.
+ An example of using qh_new_qhull is user_eg_r.c
+*/
+int qh_new_qhull(qhT *qh, int dim, int numpoints, coordT *points, boolT ismalloc,
+ char *qhull_cmd, FILE *outfile, FILE *errfile) {
+ /* gcc may issue a "might be clobbered" warning for dim, points, and ismalloc [-Wclobbered].
+ These parameters are not referenced after a longjmp() and hence not clobbered.
+ See http://stackoverflow.com/questions/7721854/what-sense-do-these-clobbered-variable-warnings-make */
+ int exitcode, hulldim;
+ boolT new_ismalloc;
+ coordT *new_points;
+
+ if(!errfile){
+ errfile= stderr;
+ }
+ if (!qh->qhmem.ferr) {
+ qh_meminit(qh, errfile);
+ } else {
+ qh_memcheck(qh);
+ }
+ if (strncmp(qhull_cmd, "qhull ", (size_t)6)) {
+ qh_fprintf(qh, errfile, 6186, "qhull error (qh_new_qhull): start qhull_cmd argument with \"qhull \"\n");
+ return qh_ERRinput;
+ }
+ qh_initqhull_start(qh, NULL, outfile, errfile);
+ trace1((qh, qh->ferr, 1044, "qh_new_qhull: build new Qhull for %d %d-d points with %s\n", numpoints, dim, qhull_cmd));
+ exitcode = setjmp(qh->errexit);
+ if (!exitcode)
+ {
+ qh->NOerrexit = False;
+ qh_initflags(qh, qhull_cmd);
+ if (qh->DELAUNAY)
+ qh->PROJECTdelaunay= True;
+ if (qh->HALFspace) {
+ /* points is an array of halfspaces,
+ the last coordinate of each halfspace is its offset */
+ hulldim= dim-1;
+ qh_setfeasible(qh, hulldim);
+ new_points= qh_sethalfspace_all(qh, dim, numpoints, points, qh->feasible_point);
+ new_ismalloc= True;
+ if (ismalloc)
+ qh_free(points);
+ }else {
+ hulldim= dim;
+ new_points= points;
+ new_ismalloc= ismalloc;
+ }
+ qh_init_B(qh, new_points, numpoints, hulldim, new_ismalloc);
+ qh_qhull(qh);
+ qh_check_output(qh);
+ if (outfile) {
+ qh_produce_output(qh);
+ }else {
+ qh_prepare_output(qh);
+ }
+ if (qh->VERIFYoutput && !qh->STOPpoint && !qh->STOPcone)
+ qh_check_points(qh);
+ }
+ qh->NOerrexit = True;
+ return exitcode;
+} /* new_qhull */
+
+/*-<a href="qh-user_r.htm#TOC"
+ >-------------------------------</a><a name="errexit">-</a>
+
+ qh_errexit(qh, exitcode, facet, ridge )
+ report and exit from an error
+ report facet and ridge if non-NULL
+ reports useful information such as last point processed
+ set qh.FORCEoutput to print neighborhood of facet
+
+ see:
+ qh_errexit2() in libqhull_r.c for printing 2 facets
+
+ design:
+ check for error within error processing
+ compute qh.hulltime
+ print facet and ridge (if any)
+ report commandString, options, qh.furthest_id
+ print summary and statistics (including precision statistics)
+ if qh_ERRsingular
+ print help text for singular data set
+ exit program via long jump (if defined) or exit()
+*/
+void qh_errexit(qhT *qh, int exitcode, facetT *facet, ridgeT *ridge) {
+
+ if (qh->ERREXITcalled) {
+ qh_fprintf(qh, qh->ferr, 8126, "\nqhull error while processing previous error. Exit program\n");
+ qh_exit(qh_ERRqhull);
+ }
+ qh->ERREXITcalled= True;
+ if (!qh->QHULLfinished)
+ qh->hulltime= qh_CPUclock - qh->hulltime;
+ qh_errprint(qh, "ERRONEOUS", facet, NULL, ridge, NULL);
+ qh_fprintf(qh, qh->ferr, 8127, "\nWhile executing: %s | %s\n", qh->rbox_command, qh->qhull_command);
+ qh_fprintf(qh, qh->ferr, 8128, "Options selected for Qhull %s:\n%s\n", qh_version, qh->qhull_options);
+ if (qh->furthest_id >= 0) {
+ qh_fprintf(qh, qh->ferr, 8129, "Last point added to hull was p%d.", qh->furthest_id);
+ if (zzval_(Ztotmerge))
+ qh_fprintf(qh, qh->ferr, 8130, " Last merge was #%d.", zzval_(Ztotmerge));
+ if (qh->QHULLfinished)
+ qh_fprintf(qh, qh->ferr, 8131, "\nQhull has finished constructing the hull.");
+ else if (qh->POSTmerging)
+ qh_fprintf(qh, qh->ferr, 8132, "\nQhull has started post-merging.");
+ qh_fprintf(qh, qh->ferr, 8133, "\n");
+ }
+ if (qh->FORCEoutput && (qh->QHULLfinished || (!facet && !ridge)))
+ qh_produce_output(qh);
+ else if (exitcode != qh_ERRinput) {
+ if (exitcode != qh_ERRsingular && zzval_(Zsetplane) > qh->hull_dim+1) {
+ qh_fprintf(qh, qh->ferr, 8134, "\nAt error exit:\n");
+ qh_printsummary(qh, qh->ferr);
+ if (qh->PRINTstatistics) {
+ qh_collectstatistics(qh);
+ qh_printstatistics(qh, qh->ferr, "at error exit");
+ qh_memstatistics(qh, qh->ferr);
+ }
+ }
+ if (qh->PRINTprecision)
+ qh_printstats(qh, qh->ferr, qh->qhstat.precision, NULL);
+ }
+ if (!exitcode)
+ exitcode= qh_ERRqhull;
+ else if (exitcode == qh_ERRsingular)
+ qh_printhelp_singular(qh, qh->ferr);
+ else if (exitcode == qh_ERRprec && !qh->PREmerge)
+ qh_printhelp_degenerate(qh, qh->ferr);
+ if (qh->NOerrexit) {
+ qh_fprintf(qh, qh->ferr, 6187, "qhull error while ending program, or qh->NOerrexit not cleared after setjmp(). Exit program with error.\n");
+ qh_exit(qh_ERRqhull);
+ }
+ qh->ERREXITcalled= False;
+ qh->NOerrexit= True;
+ qh->ALLOWrestart= False; /* longjmp will undo qh_build_withrestart */
+ longjmp(qh->errexit, exitcode);
+} /* errexit */
+
+
+/*-<a href="qh-user_r.htm#TOC"
+ >-------------------------------</a><a name="errprint">-</a>
+
+ qh_errprint(qh, fp, string, atfacet, otherfacet, atridge, atvertex )
+ prints out the information of facets and ridges to fp
+ also prints neighbors and geomview output
+
+ notes:
+ except for string, any parameter may be NULL
+*/
+void qh_errprint(qhT *qh, const char *string, facetT *atfacet, facetT *otherfacet, ridgeT *atridge, vertexT *atvertex) {
+ int i;
+
+ if (atfacet) {
+ qh_fprintf(qh, qh->ferr, 8135, "%s FACET:\n", string);
+ qh_printfacet(qh, qh->ferr, atfacet);
+ }
+ if (otherfacet) {
+ qh_fprintf(qh, qh->ferr, 8136, "%s OTHER FACET:\n", string);
+ qh_printfacet(qh, qh->ferr, otherfacet);
+ }
+ if (atridge) {
+ qh_fprintf(qh, qh->ferr, 8137, "%s RIDGE:\n", string);
+ qh_printridge(qh, qh->ferr, atridge);
+ if (atridge->top && atridge->top != atfacet && atridge->top != otherfacet)
+ qh_printfacet(qh, qh->ferr, atridge->top);
+ if (atridge->bottom
+ && atridge->bottom != atfacet && atridge->bottom != otherfacet)
+ qh_printfacet(qh, qh->ferr, atridge->bottom);
+ if (!atfacet)
+ atfacet= atridge->top;
+ if (!otherfacet)
+ otherfacet= otherfacet_(atridge, atfacet);
+ }
+ if (atvertex) {
+ qh_fprintf(qh, qh->ferr, 8138, "%s VERTEX:\n", string);
+ qh_printvertex(qh, qh->ferr, atvertex);
+ }
+ if (qh->fout && qh->FORCEoutput && atfacet && !qh->QHULLfinished && !qh->IStracing) {
+ qh_fprintf(qh, qh->ferr, 8139, "ERRONEOUS and NEIGHBORING FACETS to output\n");
+ for (i=0; i < qh_PRINTEND; i++) /* use fout for geomview output */
+ qh_printneighborhood(qh, qh->fout, qh->PRINTout[i], atfacet, otherfacet,
+ !qh_ALL);
+ }
+} /* errprint */
+
+
+/*-<a href="qh-user_r.htm#TOC"
+ >-------------------------------</a><a name="printfacetlist">-</a>
+
+ qh_printfacetlist(qh, fp, facetlist, facets, printall )
+ print all fields for a facet list and/or set of facets to fp
+ if !printall,
+ only prints good facets
+
+ notes:
+ also prints all vertices
+*/
+void qh_printfacetlist(qhT *qh, facetT *facetlist, setT *facets, boolT printall) {
+ facetT *facet, **facetp;
+
+ qh_printbegin(qh, qh->ferr, qh_PRINTfacets, facetlist, facets, printall);
+ FORALLfacet_(facetlist)
+ qh_printafacet(qh, qh->ferr, qh_PRINTfacets, facet, printall);
+ FOREACHfacet_(facets)
+ qh_printafacet(qh, qh->ferr, qh_PRINTfacets, facet, printall);
+ qh_printend(qh, qh->ferr, qh_PRINTfacets, facetlist, facets, printall);
+} /* printfacetlist */
+
+
+/*-<a href="qh-io_r.htm#TOC"
+ >-------------------------------</a><a name="printhelp_degenerate">-</a>
+
+ qh_printhelp_degenerate(qh, fp )
+ prints descriptive message for precision error
+
+ notes:
+ no message if qh_QUICKhelp
+*/
+void qh_printhelp_degenerate(qhT *qh, FILE *fp) {
+
+ if (qh->MERGEexact || qh->PREmerge || qh->JOGGLEmax < REALmax/2)
+ qh_fprintf(qh, fp, 9368, "\n\
+A Qhull error has occurred. Qhull should have corrected the above\n\
+precision error. Please send the input and all of the output to\n\
+qhull_bug@qhull.org\n");
+ else if (!qh_QUICKhelp) {
+ qh_fprintf(qh, fp, 9369, "\n\
+Precision problems were detected during construction of the convex hull.\n\
+This occurs because convex hull algorithms assume that calculations are\n\
+exact, but floating-point arithmetic has roundoff errors.\n\
+\n\
+To correct for precision problems, do not use 'Q0'. By default, Qhull\n\
+selects 'C-0' or 'Qx' and merges non-convex facets. With option 'QJ',\n\
+Qhull joggles the input to prevent precision problems. See \"Imprecision\n\
+in Qhull\" (qh-impre.htm).\n\
+\n\
+If you use 'Q0', the output may include\n\
+coplanar ridges, concave ridges, and flipped facets. In 4-d and higher,\n\
+Qhull may produce a ridge with four neighbors or two facets with the same \n\
+vertices. Qhull reports these events when they occur. It stops when a\n\
+concave ridge, flipped facet, or duplicate facet occurs.\n");
+#if REALfloat
+ qh_fprintf(qh, fp, 9370, "\
+\n\
+Qhull is currently using single precision arithmetic. The following\n\
+will probably remove the precision problems:\n\
+ - recompile qhull for realT precision(#define REALfloat 0 in user.h).\n");
+#endif
+ if (qh->DELAUNAY && !qh->SCALElast && qh->MAXabs_coord > 1e4)
+ qh_fprintf(qh, fp, 9371, "\
+\n\
+When computing the Delaunay triangulation of coordinates > 1.0,\n\
+ - use 'Qbb' to scale the last coordinate to [0,m] (max previous coordinate)\n");
+ if (qh->DELAUNAY && !qh->ATinfinity)
+ qh_fprintf(qh, fp, 9372, "\
+When computing the Delaunay triangulation:\n\
+ - use 'Qz' to add a point at-infinity. This reduces precision problems.\n");
+
+ qh_fprintf(qh, fp, 9373, "\
+\n\
+If you need triangular output:\n\
+ - use option 'Qt' to triangulate the output\n\
+ - use option 'QJ' to joggle the input points and remove precision errors\n\
+ - use option 'Ft'. It triangulates non-simplicial facets with added points.\n\
+\n\
+If you must use 'Q0',\n\
+try one or more of the following options. They can not guarantee an output.\n\
+ - use 'QbB' to scale the input to a cube.\n\
+ - use 'Po' to produce output and prevent partitioning for flipped facets\n\
+ - use 'V0' to set min. distance to visible facet as 0 instead of roundoff\n\
+ - use 'En' to specify a maximum roundoff error less than %2.2g.\n\
+ - options 'Qf', 'Qbb', and 'QR0' may also help\n",
+ qh->DISTround);
+ qh_fprintf(qh, fp, 9374, "\
+\n\
+To guarantee simplicial output:\n\
+ - use option 'Qt' to triangulate the output\n\
+ - use option 'QJ' to joggle the input points and remove precision errors\n\
+ - use option 'Ft' to triangulate the output by adding points\n\
+ - use exact arithmetic (see \"Imprecision in Qhull\", qh-impre.htm)\n\
+");
+ }
+} /* printhelp_degenerate */
+
+
+/*-<a href="qh-globa_r.htm#TOC"
+ >-------------------------------</a><a name="printhelp_narrowhull">-</a>
+
+ qh_printhelp_narrowhull(qh, minangle )
+ Warn about a narrow hull
+
+ notes:
+ Alternatively, reduce qh_WARNnarrow in user.h
+
+*/
+void qh_printhelp_narrowhull(qhT *qh, FILE *fp, realT minangle) {
+
+ qh_fprintf(qh, fp, 9375, "qhull precision warning: \n\
+The initial hull is narrow (cosine of min. angle is %.16f).\n\
+Is the input lower dimensional (e.g., on a plane in 3-d)? Qhull may\n\
+produce a wide facet. Options 'QbB' (scale to unit box) or 'Qbb' (scale\n\
+last coordinate) may remove this warning. Use 'Pp' to skip this warning.\n\
+See 'Limitations' in qh-impre.htm.\n",
+ -minangle); /* convert from angle between normals to angle between facets */
+} /* printhelp_narrowhull */
+
+/*-<a href="qh-io_r.htm#TOC"
+ >-------------------------------</a><a name="printhelp_singular">-</a>
+
+ qh_printhelp_singular(qh, fp )
+ prints descriptive message for singular input
+*/
+void qh_printhelp_singular(qhT *qh, FILE *fp) {
+ facetT *facet;
+ vertexT *vertex, **vertexp;
+ realT min, max, *coord, dist;
+ int i,k;
+
+ qh_fprintf(qh, fp, 9376, "\n\
+The input to qhull appears to be less than %d dimensional, or a\n\
+computation has overflowed.\n\n\
+Qhull could not construct a clearly convex simplex from points:\n",
+ qh->hull_dim);
+ qh_printvertexlist(qh, fp, "", qh->facet_list, NULL, qh_ALL);
+ if (!qh_QUICKhelp)
+ qh_fprintf(qh, fp, 9377, "\n\
+The center point is coplanar with a facet, or a vertex is coplanar\n\
+with a neighboring facet. The maximum round off error for\n\
+computing distances is %2.2g. The center point, facets and distances\n\
+to the center point are as follows:\n\n", qh->DISTround);
+ qh_printpointid(qh, fp, "center point", qh->hull_dim, qh->interior_point, qh_IDunknown);
+ qh_fprintf(qh, fp, 9378, "\n");
+ FORALLfacets {
+ qh_fprintf(qh, fp, 9379, "facet");
+ FOREACHvertex_(facet->vertices)
+ qh_fprintf(qh, fp, 9380, " p%d", qh_pointid(qh, vertex->point));
+ zinc_(Zdistio);
+ qh_distplane(qh, qh->interior_point, facet, &dist);
+ qh_fprintf(qh, fp, 9381, " distance= %4.2g\n", dist);
+ }
+ if (!qh_QUICKhelp) {
+ if (qh->HALFspace)
+ qh_fprintf(qh, fp, 9382, "\n\
+These points are the dual of the given halfspaces. They indicate that\n\
+the intersection is degenerate.\n");
+ qh_fprintf(qh, fp, 9383,"\n\
+These points either have a maximum or minimum x-coordinate, or\n\
+they maximize the determinant for k coordinates. Trial points\n\
+are first selected from points that maximize a coordinate.\n");
+ if (qh->hull_dim >= qh_INITIALmax)
+ qh_fprintf(qh, fp, 9384, "\n\
+Because of the high dimension, the min x-coordinate and max-coordinate\n\
+points are used if the determinant is non-zero. Option 'Qs' will\n\
+do a better, though much slower, job. Instead of 'Qs', you can change\n\
+the points by randomly rotating the input with 'QR0'.\n");
+ }
+ qh_fprintf(qh, fp, 9385, "\nThe min and max coordinates for each dimension are:\n");
+ for (k=0; k < qh->hull_dim; k++) {
+ min= REALmax;
+ max= -REALmin;
+ for (i=qh->num_points, coord= qh->first_point+k; i--; coord += qh->hull_dim) {
+ maximize_(max, *coord);
+ minimize_(min, *coord);
+ }
+ qh_fprintf(qh, fp, 9386, " %d: %8.4g %8.4g difference= %4.4g\n", k, min, max, max-min);
+ }
+ if (!qh_QUICKhelp) {
+ qh_fprintf(qh, fp, 9387, "\n\
+If the input should be full dimensional, you have several options that\n\
+may determine an initial simplex:\n\
+ - use 'QJ' to joggle the input and make it full dimensional\n\
+ - use 'QbB' to scale the points to the unit cube\n\
+ - use 'QR0' to randomly rotate the input for different maximum points\n\
+ - use 'Qs' to search all points for the initial simplex\n\
+ - use 'En' to specify a maximum roundoff error less than %2.2g.\n\
+ - trace execution with 'T3' to see the determinant for each point.\n",
+ qh->DISTround);
+#if REALfloat
+ qh_fprintf(qh, fp, 9388, "\
+ - recompile qhull for realT precision(#define REALfloat 0 in libqhull_r.h).\n");
+#endif
+ qh_fprintf(qh, fp, 9389, "\n\
+If the input is lower dimensional:\n\
+ - use 'QJ' to joggle the input and make it full dimensional\n\
+ - use 'Qbk:0Bk:0' to delete coordinate k from the input. You should\n\
+ pick the coordinate with the least range. The hull will have the\n\
+ correct topology.\n\
+ - determine the flat containing the points, rotate the points\n\
+ into a coordinate plane, and delete the other coordinates.\n\
+ - add one or more points to make the input full dimensional.\n\
+");
+ }
+} /* printhelp_singular */
+
+/*-<a href="qh-globa_r.htm#TOC"
+ >-------------------------------</a><a name="user_memsizes">-</a>
+
+ qh_user_memsizes(qh)
+ allocate up to 10 additional, quick allocation sizes
+
+ notes:
+ increase maximum number of allocations in qh_initqhull_mem()
+*/
+void qh_user_memsizes(qhT *qh) {
+
+ QHULL_UNUSED(qh)
+ /* qh_memsize(qh, size); */
+} /* user_memsizes */
+
+