/* ---------------------------------
poly2_r.c
implements polygons and simplicies
see qh-poly_r.htm, poly_r.h and libqhull_r.h
frequently used code is in poly_r.c
Copyright (c) 1993-2015 The Geometry Center.
$Id: //main/2015/qhull/src/libqhull_r/poly2_r.c#10 $$Change: 2069 $
$DateTime: 2016/01/18 22:05:03 $$Author: bbarber $
*/
#include "qhull_ra.h"
/*======== functions in alphabetical order ==========*/
/*---------------------------------
qh_addhash( newelem, hashtable, hashsize, hash )
add newelem to linear hash table at hash if not already there
*/
void qh_addhash(void *newelem, setT *hashtable, int hashsize, int hash) {
int scan;
void *elem;
for (scan= (int)hash; (elem= SETelem_(hashtable, scan));
scan= (++scan >= hashsize ? 0 : scan)) {
if (elem == newelem)
break;
}
/* loop terminates because qh_HASHfactor >= 1.1 by qh_initbuffers */
if (!elem)
SETelem_(hashtable, scan)= newelem;
} /* addhash */
/*---------------------------------
qh_check_bestdist(qh)
check that all points are within max_outside of the nearest facet
if qh.ONLYgood,
ignores !good facets
see:
qh_check_maxout(), qh_outerinner()
notes:
only called from qh_check_points()
seldom used since qh.MERGING is almost always set
if notverified>0 at end of routine
some points were well inside the hull. If the hull contains
a lens-shaped component, these points were not verified. Use
options 'Qi Tv' to verify all points. (Exhaustive check also verifies)
design:
determine facet for each point (if any)
for each point
start with the assigned facet or with the first facet
find the best facet for the point and check all coplanar facets
error if point is outside of facet
*/
void qh_check_bestdist(qhT *qh) {
boolT waserror= False, unassigned;
facetT *facet, *bestfacet, *errfacet1= NULL, *errfacet2= NULL;
facetT *facetlist;
realT dist, maxoutside, maxdist= -REALmax;
pointT *point;
int numpart= 0, facet_i, facet_n, notgood= 0, notverified= 0;
setT *facets;
trace1((qh, qh->ferr, 1020, "qh_check_bestdist: check points below nearest facet. Facet_list f%d\n",
qh->facet_list->id));
maxoutside= qh_maxouter(qh);
maxoutside += qh->DISTround;
/* one more qh.DISTround for check computation */
trace1((qh, qh->ferr, 1021, "qh_check_bestdist: check that all points are within %2.2g of best facet\n", maxoutside));
facets= qh_pointfacet(qh /*qh.facet_list*/);
if (!qh_QUICKhelp && qh->PRINTprecision)
qh_fprintf(qh, qh->ferr, 8091, "\n\
qhull output completed. Verifying that %d points are\n\
below %2.2g of the nearest %sfacet.\n",
qh_setsize(qh, facets), maxoutside, (qh->ONLYgood ? "good " : ""));
FOREACHfacet_i_(qh, facets) { /* for each point with facet assignment */
if (facet)
unassigned= False;
else {
unassigned= True;
facet= qh->facet_list;
}
point= qh_point(qh, facet_i);
if (point == qh->GOODpointp)
continue;
qh_distplane(qh, point, facet, &dist);
numpart++;
bestfacet= qh_findbesthorizon(qh, !qh_IScheckmax, point, facet, qh_NOupper, &dist, &numpart);
/* occurs after statistics reported */
maximize_(maxdist, dist);
if (dist > maxoutside) {
if (qh->ONLYgood && !bestfacet->good
&& !((bestfacet= qh_findgooddist(qh, point, bestfacet, &dist, &facetlist))
&& dist > maxoutside))
notgood++;
else {
waserror= True;
qh_fprintf(qh, qh->ferr, 6109, "qhull precision error: point p%d is outside facet f%d, distance= %6.8g maxoutside= %6.8g\n",
facet_i, bestfacet->id, dist, maxoutside);
if (errfacet1 != bestfacet) {
errfacet2= errfacet1;
errfacet1= bestfacet;
}
}
}else if (unassigned && dist < -qh->MAXcoplanar)
notverified++;
}
qh_settempfree(qh, &facets);
if (notverified && !qh->DELAUNAY && !qh_QUICKhelp && qh->PRINTprecision)
qh_fprintf(qh, qh->ferr, 8092, "\n%d points were well inside the hull. If the hull contains\n\
a lens-shaped component, these points were not verified. Use\n\
options 'Qci Tv' to verify all points.\n", notverified);
if (maxdist > qh->outside_err) {
qh_fprintf(qh, qh->ferr, 6110, "qhull precision error (qh_check_bestdist): a coplanar point is %6.2g from convex hull. The maximum value(qh.outside_err) is %6.2g\n",
maxdist, qh->outside_err);
qh_errexit2(qh, qh_ERRprec, errfacet1, errfacet2);
}else if (waserror && qh->outside_err > REALmax/2)
qh_errexit2(qh, qh_ERRprec, errfacet1, errfacet2);
/* else if waserror, the error was logged to qh.ferr but does not effect the output */
trace0((qh, qh->ferr, 20, "qh_check_bestdist: max distance outside %2.2g\n", maxdist));
} /* check_bestdist */
/*---------------------------------
qh_check_dupridge(qh, facet1, dist1, facet2, dist2)
Check duplicate ridge between facet1 and facet2 for wide merge
dist1 is the maximum distance of facet1's vertices to facet2
dist2 is the maximum distance of facet2's vertices to facet1
Returns
Level 1 log of the duplicate ridge with the minimum distance between vertices
Throws error if the merge will increase the maximum facet width by qh_WIDEduplicate (100x)
called from:
qh_forcedmerges()
*/
#ifndef qh_NOmerge
void qh_check_dupridge(qhT *qh, facetT *facet1, realT dist1, facetT *facet2, realT dist2) {
vertexT *vertex, **vertexp, *vertexA, **vertexAp;
realT dist, innerplane, mergedist, outerplane, prevdist, ratio;
realT minvertex= REALmax;
mergedist= fmin_(dist1, dist2);
qh_outerinner(qh, NULL, &outerplane, &innerplane); /* ratio from qh_printsummary */
prevdist= fmax_(outerplane, innerplane);
maximize_(prevdist, qh->ONEmerge + qh->DISTround);
maximize_(prevdist, qh->MINoutside + qh->DISTround);
ratio= mergedist/prevdist;
FOREACHvertex_(facet1->vertices) { /* The duplicate ridge is between facet1 and facet2, so either facet can be tested */
FOREACHvertexA_(facet1->vertices) {
if (vertex > vertexA){ /* Test each pair once */
dist= qh_pointdist(vertex->point, vertexA->point, qh->hull_dim);
minimize_(minvertex, dist);
}
}
}
trace0((qh, qh->ferr, 16, "qh_check_dupridge: duplicate ridge between f%d and f%d due to nearly-coincident vertices (%2.2g), dist %2.2g, reverse dist %2.2g, ratio %2.2g while processing p%d\n",
facet1->id, facet2->id, minvertex, dist1, dist2, ratio, qh->furthest_id));
if (ratio > qh_WIDEduplicate) {
qh_fprintf(qh, qh->ferr, 6271, "qhull precision error (qh_check_dupridge): wide merge (%.0f times wider) due to duplicate ridge with nearly coincident points (%2.2g) between f%d and f%d, merge dist %2.2g, while processing p%d\n- Ignore error with option 'Q12'\n- To be fixed in a later version of Qhull\n",
ratio, minvertex, facet1->id, facet2->id, mergedist, qh->furthest_id);
if (qh->DELAUNAY)
qh_fprintf(qh, qh->ferr, 8145, "- A bounding box for the input sites may alleviate this error.\n");
if(minvertex > qh_WIDEduplicate*prevdist)
qh_fprintf(qh, qh->ferr, 8146, "- Vertex distance %2.2g is greater than %d times maximum distance %2.2g\n Please report to bradb@shore.net with steps to reproduce and all output\n",
minvertex, qh_WIDEduplicate, prevdist);
if (!qh->NOwide)
qh_errexit2(qh, qh_ERRqhull, facet1, facet2);
}
} /* check_dupridge */
#endif
/*---------------------------------
qh_check_maxout(qh)
updates qh.max_outside by checking all points against bestfacet
if qh.ONLYgood, ignores !good facets
returns:
updates facet->maxoutside via qh_findbesthorizon()
sets qh.maxoutdone
if printing qh.min_vertex (qh_outerinner),
it is updated to the current vertices
removes inside/coplanar points from coplanarset as needed
notes:
defines coplanar as min_vertex instead of MAXcoplanar
may not need to check near-inside points because of qh.MAXcoplanar
and qh.KEEPnearinside (before it was -DISTround)
see also:
qh_check_bestdist()
design:
if qh.min_vertex is needed
for all neighbors of all vertices
test distance from vertex to neighbor
determine facet for each point (if any)
for each point with an assigned facet
find the best facet for the point and check all coplanar facets
(updates outer planes)
remove near-inside points from coplanar sets
*/
#ifndef qh_NOmerge
void qh_check_maxout(qhT *qh) {
facetT *facet, *bestfacet, *neighbor, **neighborp, *facetlist;
realT dist, maxoutside, minvertex, old_maxoutside;
pointT *point;
int numpart= 0, facet_i, facet_n, notgood= 0;
setT *facets, *vertices;
vertexT *vertex;
trace1((qh, qh->ferr, 1022, "qh_check_maxout: check and update maxoutside for each facet.\n"));
maxoutside= minvertex= 0;
if (qh->VERTEXneighbors
&& (qh->PRINTsummary || qh->KEEPinside || qh->KEEPcoplanar
|| qh->TRACElevel || qh->PRINTstatistics
|| qh->PRINTout[0] == qh_PRINTsummary || qh->PRINTout[0] == qh_PRINTnone)) {
trace1((qh, qh->ferr, 1023, "qh_check_maxout: determine actual maxoutside and minvertex\n"));
vertices= qh_pointvertex(qh /*qh.facet_list*/);
FORALLvertices {
FOREACHneighbor_(vertex) {
zinc_(Zdistvertex); /* distance also computed by main loop below */
qh_distplane(qh, vertex->point, neighbor, &dist);
minimize_(minvertex, dist);
if (-dist > qh->TRACEdist || dist > qh->TRACEdist
|| neighbor == qh->tracefacet || vertex == qh->tracevertex)
qh_fprintf(qh, qh->ferr, 8093, "qh_check_maxout: p%d(v%d) is %.2g from f%d\n",
qh_pointid(qh, vertex->point), vertex->id, dist, neighbor->id);
}
}
if (qh->MERGING) {
wmin_(Wminvertex, qh->min_vertex);
}
qh->min_vertex= minvertex;
qh_settempfree(qh, &vertices);
}
facets= qh_pointfacet(qh /*qh.facet_list*/);
do {
old_maxoutside= fmax_(qh->max_outside, maxoutside);
FOREACHfacet_i_(qh, facets) { /* for each point with facet assignment */
if (facet) {
point= qh_point(qh, facet_i);
if (point == qh->GOODpointp)
continue;
zzinc_(Ztotcheck);
qh_distplane(qh, point, facet, &dist);
numpart++;
bestfacet= qh_findbesthorizon(qh, qh_IScheckmax, point, facet, !qh_NOupper, &dist, &numpart);
if (bestfacet && dist > maxoutside) {
if (qh->ONLYgood && !bestfacet->good
&& !((bestfacet= qh_findgooddist(qh, point, bestfacet, &dist, &facetlist))
&& dist > maxoutside))
notgood++;
else
maxoutside= dist;
}
if (dist > qh->TRACEdist || (bestfacet && bestfacet == qh->tracefacet))
qh_fprintf(qh, qh->ferr, 8094, "qh_check_maxout: p%d is %.2g above f%d\n",
qh_pointid(qh, point), dist, (bestfacet ? bestfacet->id : UINT_MAX));
}
}
}while
(maxoutside > 2*old_maxoutside);
/* if qh.maxoutside increases substantially, qh_SEARCHdist is not valid
e.g., RBOX 5000 s Z1 G1e-13 t1001200614 | qhull */
zzadd_(Zcheckpart, numpart);
qh_settempfree(qh, &facets);
wval_(Wmaxout)= maxoutside - qh->max_outside;
wmax_(Wmaxoutside, qh->max_outside);
qh->max_outside= maxoutside;
qh_nearcoplanar(qh /*qh.facet_list*/);
qh->maxoutdone= True;
trace1((qh, qh->ferr, 1024, "qh_check_maxout: maxoutside %2.2g, min_vertex %2.2g, outside of not good %d\n",
maxoutside, qh->min_vertex, notgood));
} /* check_maxout */
#else /* qh_NOmerge */
void qh_check_maxout(qhT *qh) {
}
#endif
/*---------------------------------
qh_check_output(qh)
performs the checks at the end of qhull algorithm
Maybe called after voronoi output. Will recompute otherwise centrums are Voronoi centers instead
*/
void qh_check_output(qhT *qh) {
int i;
if (qh->STOPcone)
return;
if (qh->VERIFYoutput | qh->IStracing | qh->CHECKfrequently) {
qh_checkpolygon(qh, qh->facet_list);
qh_checkflipped_all(qh, qh->facet_list);
qh_checkconvex(qh, qh->facet_list, qh_ALGORITHMfault);
}else if (!qh->MERGING && qh_newstats(qh, qh->qhstat.precision, &i)) {
qh_checkflipped_all(qh, qh->facet_list);
qh_checkconvex(qh, qh->facet_list, qh_ALGORITHMfault);
}
} /* check_output */
/*---------------------------------
qh_check_point(qh, point, facet, maxoutside, maxdist, errfacet1, errfacet2 )
check that point is less than maxoutside from facet
*/
void qh_check_point(qhT *qh, pointT *point, facetT *facet, realT *maxoutside, realT *maxdist, facetT **errfacet1, facetT **errfacet2) {
realT dist;
/* occurs after statistics reported */
qh_distplane(qh, point, facet, &dist);
if (dist > *maxoutside) {
if (*errfacet1 != facet) {
*errfacet2= *errfacet1;
*errfacet1= facet;
}
qh_fprintf(qh, qh->ferr, 6111, "qhull precision error: point p%d is outside facet f%d, distance= %6.8g maxoutside= %6.8g\n",
qh_pointid(qh, point), facet->id, dist, *maxoutside);
}
maximize_(*maxdist, dist);
} /* qh_check_point */
/*---------------------------------
qh_check_points(qh)
checks that all points are inside all facets
notes:
if many points and qh_check_maxout not called (i.e., !qh.MERGING),
calls qh_findbesthorizon (seldom done).
ignores flipped facets
maxoutside includes 2 qh.DISTrounds
one qh.DISTround for the computed distances in qh_check_points
qh_printafacet and qh_printsummary needs only one qh.DISTround
the computation for qh.VERIFYdirect does not account for qh.other_points
design:
if many points
use qh_check_bestdist()
else
for all facets
for all points
check that point is inside facet
*/
void qh_check_points(qhT *qh) {
facetT *facet, *errfacet1= NULL, *errfacet2= NULL;
realT total, maxoutside, maxdist= -REALmax;
pointT *point, **pointp, *pointtemp;
boolT testouter;
maxoutside= qh_maxouter(qh);
maxoutside += qh->DISTround;
/* one more qh.DISTround for check computation */
trace1((qh, qh->ferr, 1025, "qh_check_points: check all points below %2.2g of all facet planes\n",
maxoutside));
if (qh->num_good) /* miss counts other_points and !good facets */
total= (float)qh->num_good * (float)qh->num_points;
else
total= (float)qh->num_facets * (float)qh->num_points;
if (total >= qh_VERIFYdirect && !qh->maxoutdone) {
if (!qh_QUICKhelp && qh->SKIPcheckmax && qh->MERGING)
qh_fprintf(qh, qh->ferr, 7075, "qhull input warning: merging without checking outer planes('Q5' or 'Po').\n\
Verify may report that a point is outside of a facet.\n");
qh_check_bestdist(qh);
}else {
if (qh_MAXoutside && qh->maxoutdone)
testouter= True;
else
testouter= False;
if (!qh_QUICKhelp) {
if (qh->MERGEexact)
qh_fprintf(qh, qh->ferr, 7076, "qhull input warning: exact merge ('Qx'). Verify may report that a point\n\
is outside of a facet. See qh-optq.htm#Qx\n");
else if (qh->SKIPcheckmax || qh->NOnearinside)
qh_fprintf(qh, qh->ferr, 7077, "qhull input warning: no outer plane check ('Q5') or no processing of\n\
near-inside points ('Q8'). Verify may report that a point is outside\n\
of a facet.\n");
}
if (qh->PRINTprecision) {
if (testouter)
qh_fprintf(qh, qh->ferr, 8098, "\n\
Output completed. Verifying that all points are below outer planes of\n\
all %sfacets. Will make %2.0f distance computations.\n",
(qh->ONLYgood ? "good " : ""), total);
else
qh_fprintf(qh, qh->ferr, 8099, "\n\
Output completed. Verifying that all points are below %2.2g of\n\
all %sfacets. Will make %2.0f distance computations.\n",
maxoutside, (qh->ONLYgood ? "good " : ""), total);
}
FORALLfacets {
if (!facet->good && qh->ONLYgood)
continue;
if (facet->flipped)
continue;
if (!facet->normal) {
qh_fprintf(qh, qh->ferr, 7061, "qhull warning (qh_check_points): missing normal for facet f%d\n", facet->id);
continue;
}
if (testouter) {
#if qh_MAXoutside
maxoutside= facet->maxoutside + 2* qh->DISTround;
/* one DISTround to actual point and another to computed point */
#endif
}
FORALLpoints {
if (point != qh->GOODpointp)
qh_check_point(qh, point, facet, &maxoutside, &maxdist, &errfacet1, &errfacet2);
}
FOREACHpoint_(qh->other_points) {
if (point != qh->GOODpointp)
qh_check_point(qh, point, facet, &maxoutside, &maxdist, &errfacet1, &errfacet2);
}
}
if (maxdist > qh->outside_err) {
qh_fprintf(qh, qh->ferr, 6112, "qhull precision error (qh_check_points): a coplanar point is %6.2g from convex hull. The maximum value(qh.outside_err) is %6.2g\n",
maxdist, qh->outside_err );
qh_errexit2(qh, qh_ERRprec, errfacet1, errfacet2 );
}else if (errfacet1 && qh->outside_err > REALmax/2)
qh_errexit2(qh, qh_ERRprec, errfacet1, errfacet2 );
/* else if errfacet1, the error was logged to qh.ferr but does not effect the output */
trace0((qh, qh->ferr, 21, "qh_check_points: max distance outside %2.2g\n", maxdist));
}
} /* check_points */
/*---------------------------------
qh_checkconvex(qh, facetlist, fault )
check that each ridge in facetlist is convex
fault = qh_DATAfault if reporting errors
= qh_ALGORITHMfault otherwise
returns:
counts Zconcaveridges and Zcoplanarridges
errors if concaveridge or if merging an coplanar ridge
note:
if not merging,
tests vertices for neighboring simplicial facets
else if ZEROcentrum,
tests vertices for neighboring simplicial facets
else
tests centrums of neighboring facets
design:
for all facets
report flipped facets
if ZEROcentrum and simplicial neighbors
test vertices for neighboring simplicial facets
else
test centrum against all neighbors
*/
void qh_checkconvex(qhT *qh, facetT *facetlist, int fault) {
facetT *facet, *neighbor, **neighborp, *errfacet1=NULL, *errfacet2=NULL;
vertexT *vertex;
realT dist;
pointT *centrum;
boolT waserror= False, centrum_warning= False, tempcentrum= False, allsimplicial;
int neighbor_i;
trace1((qh, qh->ferr, 1026, "qh_checkconvex: check all ridges are convex\n"));
if (!qh->RERUN) {
zzval_(Zconcaveridges)= 0;
zzval_(Zcoplanarridges)= 0;
}
FORALLfacet_(facetlist) {
if (facet->flipped) {
qh_precision(qh, "flipped facet");
qh_fprintf(qh, qh->ferr, 6113, "qhull precision error: f%d is flipped(interior point is outside)\n",
facet->id);
errfacet1= facet;
waserror= True;
continue;
}
if (qh->MERGING && (!qh->ZEROcentrum || !facet->simplicial || facet->tricoplanar))
allsimplicial= False;
else {
allsimplicial= True;
neighbor_i= 0;
FOREACHneighbor_(facet) {
vertex= SETelemt_(facet->vertices, neighbor_i++, vertexT);
if (!neighbor->simplicial || neighbor->tricoplanar) {
allsimplicial= False;
continue;
}
qh_distplane(qh, vertex->point, neighbor, &dist);
if (dist > -qh->DISTround) {
if (fault == qh_DATAfault) {
qh_precision(qh, "coplanar or concave ridge");
qh_fprintf(qh, qh->ferr, 6114, "qhull precision error: initial simplex is not convex. Distance=%.2g\n", dist);
qh_errexit(qh, qh_ERRsingular, NULL, NULL);
}
if (dist > qh->DISTround) {
zzinc_(Zconcaveridges);
qh_precision(qh, "concave ridge");
qh_fprintf(qh, qh->ferr, 6115, "qhull precision error: f%d is concave to f%d, since p%d(v%d) is %6.4g above\n",
facet->id, neighbor->id, qh_pointid(qh, vertex->point), vertex->id, dist);
errfacet1= facet;
errfacet2= neighbor;
waserror= True;
}else if (qh->ZEROcentrum) {
if (dist > 0) { /* qh_checkzero checks that dist < - qh->DISTround */
zzinc_(Zcoplanarridges);
qh_precision(qh, "coplanar ridge");
qh_fprintf(qh, qh->ferr, 6116, "qhull precision error: f%d is clearly not convex to f%d, since p%d(v%d) is %6.4g above\n",
facet->id, neighbor->id, qh_pointid(qh, vertex->point), vertex->id, dist);
errfacet1= facet;
errfacet2= neighbor;
waserror= True;
}
}else {
zzinc_(Zcoplanarridges);
qh_precision(qh, "coplanar ridge");
trace0((qh, qh->ferr, 22, "qhull precision error: f%d may be coplanar to f%d, since p%d(v%d) is within %6.4g during p%d\n",
facet->id, neighbor->id, qh_pointid(qh, vertex->point), vertex->id, dist, qh->furthest_id));
}
}
}
}
if (!allsimplicial) {
if (qh->CENTERtype == qh_AScentrum) {
if (!facet->center)
facet->center= qh_getcentrum(qh, facet);
centrum= facet->center;
}else {
if (!centrum_warning && (!facet->simplicial || facet->tricoplanar)) {
centrum_warning= True;
qh_fprintf(qh, qh->ferr, 7062, "qhull warning: recomputing centrums for convexity test. This may lead to false, precision errors.\n");
}
centrum= qh_getcentrum(qh, facet);
tempcentrum= True;
}
FOREACHneighbor_(facet) {
if (qh->ZEROcentrum && facet->simplicial && neighbor->simplicial)
continue;
if (facet->tricoplanar || neighbor->tricoplanar)
continue;
zzinc_(Zdistconvex);
qh_distplane(qh, centrum, neighbor, &dist);
if (dist > qh->DISTround) {
zzinc_(Zconcaveridges);
qh_precision(qh, "concave ridge");
qh_fprintf(qh, qh->ferr, 6117, "qhull precision error: f%d is concave to f%d. Centrum of f%d is %6.4g above f%d\n",
facet->id, neighbor->id, facet->id, dist, neighbor->id);
errfacet1= facet;
errfacet2= neighbor;
waserror= True;
}else if (dist >= 0.0) { /* if arithmetic always rounds the same,
can test against centrum radius instead */
zzinc_(Zcoplanarridges);
qh_precision(qh, "coplanar ridge");
qh_fprintf(qh, qh->ferr, 6118, "qhull precision error: f%d is coplanar or concave to f%d. Centrum of f%d is %6.4g above f%d\n",
facet->id, neighbor->id, facet->id, dist, neighbor->id);
errfacet1= facet;
errfacet2= neighbor;
waserror= True;
}
}
if (tempcentrum)
qh_memfree(qh, centrum, qh->normal_size);
}
}
if (waserror && !qh->FORCEoutput)
qh_errexit2(qh, qh_ERRprec, errfacet1, errfacet2);
} /* checkconvex */
/*---------------------------------
qh_checkfacet(qh, facet, newmerge, waserror )
checks for consistency errors in facet
newmerge set if from merge_r.c
returns:
sets waserror if any error occurs
checks:
vertex ids are inverse sorted
unless newmerge, at least hull_dim neighbors and vertices (exactly if simplicial)
if non-simplicial, at least as many ridges as neighbors
neighbors are not duplicated
ridges are not duplicated
in 3-d, ridges=verticies
(qh.hull_dim-1) ridge vertices
neighbors are reciprocated
ridge neighbors are facet neighbors and a ridge for every neighbor
simplicial neighbors match facetintersect
vertex intersection matches vertices of common ridges
vertex neighbors and facet vertices agree
all ridges have distinct vertex sets
notes:
uses neighbor->seen
design:
check sets
check vertices
check sizes of neighbors and vertices
check for qh_MERGEridge and qh_DUPLICATEridge flags
check neighbor set
check ridge set
check ridges, neighbors, and vertices
*/
void qh_checkfacet(qhT *qh, facetT *facet, boolT newmerge, boolT *waserrorp) {
facetT *neighbor, **neighborp, *errother=NULL;
ridgeT *ridge, **ridgep, *errridge= NULL, *ridge2;
vertexT *vertex, **vertexp;
unsigned previousid= INT_MAX;
int numneighbors, numvertices, numridges=0, numRvertices=0;
boolT waserror= False;
int skipA, skipB, ridge_i, ridge_n, i;
setT *intersection;
if (facet->visible) {
qh_fprintf(qh, qh->ferr, 6119, "qhull internal error (qh_checkfacet): facet f%d is on the visible_list\n",
facet->id);
qh_errexit(qh, qh_ERRqhull, facet, NULL);
}
if (!facet->normal) {
qh_fprintf(qh, qh->ferr, 6120, "qhull internal error (qh_checkfacet): facet f%d does not have a normal\n",
facet->id);
waserror= True;
}
qh_setcheck(qh, facet->vertices, "vertices for f", facet->id);
qh_setcheck(qh, facet->ridges, "ridges for f", facet->id);
qh_setcheck(qh, facet->outsideset, "outsideset for f", facet->id);
qh_setcheck(qh, facet->coplanarset, "coplanarset for f", facet->id);
qh_setcheck(qh, facet->neighbors, "neighbors for f", facet->id);
FOREACHvertex_(facet->vertices) {
if (vertex->deleted) {
qh_fprintf(qh, qh->ferr, 6121, "qhull internal error (qh_checkfacet): deleted vertex v%d in f%d\n", vertex->id, facet->id);
qh_errprint(qh, "ERRONEOUS", NULL, NULL, NULL, vertex);
waserror= True;
}
if (vertex->id >= previousid) {
qh_fprintf(qh, qh->ferr, 6122, "qhull internal error (qh_checkfacet): vertices of f%d are not in descending id order at v%d\n", facet->id, vertex->id);
waserror= True;
break;
}
previousid= vertex->id;
}
numneighbors= qh_setsize(qh, facet->neighbors);
numvertices= qh_setsize(qh, facet->vertices);
numridges= qh_setsize(qh, facet->ridges);
if (facet->simplicial) {
if (numvertices+numneighbors != 2*qh->hull_dim
&& !facet->degenerate && !facet->redundant) {
qh_fprintf(qh, qh->ferr, 6123, "qhull internal error (qh_checkfacet): for simplicial facet f%d, #vertices %d + #neighbors %d != 2*qh->hull_dim\n",
facet->id, numvertices, numneighbors);
qh_setprint(qh, qh->ferr, "", facet->neighbors);
waserror= True;
}
}else { /* non-simplicial */
if (!newmerge
&&(numvertices < qh->hull_dim || numneighbors < qh->hull_dim)
&& !facet->degenerate && !facet->redundant) {
qh_fprintf(qh, qh->ferr, 6124, "qhull internal error (qh_checkfacet): for facet f%d, #vertices %d or #neighbors %d < qh->hull_dim\n",
facet->id, numvertices, numneighbors);
waserror= True;
}
/* in 3-d, can get a vertex twice in an edge list, e.g., RBOX 1000 s W1e-13 t995849315 D2 | QHULL d Tc Tv TP624 TW1e-13 T4 */
if (numridges < numneighbors
||(qh->hull_dim == 3 && numvertices > numridges && !qh->NEWfacets)
||(qh->hull_dim == 2 && numridges + numvertices + numneighbors != 6)) {
if (!facet->degenerate && !facet->redundant) {
qh_fprintf(qh, qh->ferr, 6125, "qhull internal error (qh_checkfacet): for facet f%d, #ridges %d < #neighbors %d or(3-d) > #vertices %d or(2-d) not all 2\n",
facet->id, numridges, numneighbors, numvertices);
waserror= True;
}
}
}
FOREACHneighbor_(facet) {
if (neighbor == qh_MERGEridge || neighbor == qh_DUPLICATEridge) {
qh_fprintf(qh, qh->ferr, 6126, "qhull internal error (qh_checkfacet): facet f%d still has a MERGE or DUP neighbor\n", facet->id);
qh_errexit(qh, qh_ERRqhull, facet, NULL);
}
neighbor->seen= True;
}
FOREACHneighbor_(facet) {
if (!qh_setin(neighbor->neighbors, facet)) {
qh_fprintf(qh, qh->ferr, 6127, "qhull internal error (qh_checkfacet): facet f%d has neighbor f%d, but f%d does not have neighbor f%d\n",
facet->id, neighbor->id, neighbor->id, facet->id);
errother= neighbor;
waserror= True;
}
if (!neighbor->seen) {
qh_fprintf(qh, qh->ferr, 6128, "qhull internal error (qh_checkfacet): facet f%d has a duplicate neighbor f%d\n",
facet->id, neighbor->id);
errother= neighbor;
waserror= True;
}
neighbor->seen= False;
}
FOREACHridge_(facet->ridges) {
qh_setcheck(qh, ridge->vertices, "vertices for r", ridge->id);
ridge->seen= False;
}
FOREACHridge_(facet->ridges) {
if (ridge->seen) {
qh_fprintf(qh, qh->ferr, 6129, "qhull internal error (qh_checkfacet): facet f%d has a duplicate ridge r%d\n",
facet->id, ridge->id);
errridge= ridge;
waserror= True;
}
ridge->seen= True;
numRvertices= qh_setsize(qh, ridge->vertices);
if (numRvertices != qh->hull_dim - 1) {
qh_fprintf(qh, qh->ferr, 6130, "qhull internal error (qh_checkfacet): ridge between f%d and f%d has %d vertices\n",
ridge->top->id, ridge->bottom->id, numRvertices);
errridge= ridge;
waserror= True;
}
neighbor= otherfacet_(ridge, facet);
neighbor->seen= True;
if (!qh_setin(facet->neighbors, neighbor)) {
qh_fprintf(qh, qh->ferr, 6131, "qhull internal error (qh_checkfacet): for facet f%d, neighbor f%d of ridge r%d not in facet\n",
facet->id, neighbor->id, ridge->id);
errridge= ridge;
waserror= True;
}
}
if (!facet->simplicial) {
FOREACHneighbor_(facet) {
if (!neighbor->seen) {
qh_fprintf(qh, qh->ferr, 6132, "qhull internal error (qh_checkfacet): facet f%d does not have a ridge for neighbor f%d\n",
facet->id, neighbor->id);
errother= neighbor;
waserror= True;
}
intersection= qh_vertexintersect_new(qh, facet->vertices, neighbor->vertices);
qh_settemppush(qh, intersection);
FOREACHvertex_(facet->vertices) {
vertex->seen= False;
vertex->seen2= False;
}
FOREACHvertex_(intersection)
vertex->seen= True;
FOREACHridge_(facet->ridges) {
if (neighbor != otherfacet_(ridge, facet))
continue;
FOREACHvertex_(ridge->vertices) {
if (!vertex->seen) {
qh_fprintf(qh, qh->ferr, 6133, "qhull internal error (qh_checkfacet): vertex v%d in r%d not in f%d intersect f%d\n",
vertex->id, ridge->id, facet->id, neighbor->id);
qh_errexit(qh, qh_ERRqhull, facet, ridge);
}
vertex->seen2= True;
}
}
if (!newmerge) {
FOREACHvertex_(intersection) {
if (!vertex->seen2) {
if (qh->IStracing >=3 || !qh->MERGING) {
qh_fprintf(qh, qh->ferr, 6134, "qhull precision error (qh_checkfacet): vertex v%d in f%d intersect f%d but\n\
not in a ridge. This is ok under merging. Last point was p%d\n",
vertex->id, facet->id, neighbor->id, qh->furthest_id);
if (!qh->FORCEoutput && !qh->MERGING) {
qh_errprint(qh, "ERRONEOUS", facet, neighbor, NULL, vertex);
if (!qh->MERGING)
qh_errexit(qh, qh_ERRqhull, NULL, NULL);
}
}
}
}
}
qh_settempfree(qh, &intersection);
}
}else { /* simplicial */
FOREACHneighbor_(facet) {
if (neighbor->simplicial) {
skipA= SETindex_(facet->neighbors, neighbor);
skipB= qh_setindex(neighbor->neighbors, facet);
if (skipA<0 || skipB<0 || !qh_setequal_skip(facet->vertices, skipA, neighbor->vertices, skipB)) {
qh_fprintf(qh, qh->ferr, 6135, "qhull internal error (qh_checkfacet): facet f%d skip %d and neighbor f%d skip %d do not match \n",
facet->id, skipA, neighbor->id, skipB);
errother= neighbor;
waserror= True;
}
}
}
}
if (qh->hull_dim < 5 && (qh->IStracing > 2 || qh->CHECKfrequently)) {
FOREACHridge_i_(qh, facet->ridges) { /* expensive */
for (i=ridge_i+1; i < ridge_n; i++) {
ridge2= SETelemt_(facet->ridges, i, ridgeT);
if (qh_setequal(ridge->vertices, ridge2->vertices)) {
qh_fprintf(qh, qh->ferr, 6227, "Qhull internal error (qh_checkfacet): ridges r%d and r%d have the same vertices\n",
ridge->id, ridge2->id);
errridge= ridge;
waserror= True;
}
}
}
}
if (waserror) {
qh_errprint(qh, "ERRONEOUS", facet, errother, errridge, NULL);
*waserrorp= True;
}
} /* checkfacet */
/*---------------------------------
qh_checkflipped_all(qh, facetlist )
checks orientation of facets in list against interior point
*/
void qh_checkflipped_all(qhT *qh, facetT *facetlist) {
facetT *facet;
boolT waserror= False;
realT dist;
if (facetlist == qh->facet_list)
zzval_(Zflippedfacets)= 0;
FORALLfacet_(facetlist) {
if (facet->normal && !qh_checkflipped(qh, facet, &dist, !qh_ALL)) {
qh_fprintf(qh, qh->ferr, 6136, "qhull precision error: facet f%d is flipped, distance= %6.12g\n",
facet->id, dist);
if (!qh->FORCEoutput) {
qh_errprint(qh, "ERRONEOUS", facet, NULL, NULL, NULL);
waserror= True;
}
}
}
if (waserror) {
qh_fprintf(qh, qh->ferr, 8101, "\n\
A flipped facet occurs when its distance to the interior point is\n\
greater than %2.2g, the maximum roundoff error.\n", -qh->DISTround);
qh_errexit(qh, qh_ERRprec, NULL, NULL);
}
} /* checkflipped_all */
/*---------------------------------
qh_checkpolygon(qh, facetlist )
checks the correctness of the structure
notes:
call with either qh.facet_list or qh.newfacet_list
checks num_facets and num_vertices if qh.facet_list
design:
for each facet
checks facet and outside set
initializes vertexlist
for each facet
checks vertex set
if checking all facets(qh.facetlist)
check facet count
if qh.VERTEXneighbors
check vertex neighbors and count
check vertex count
*/
void qh_checkpolygon(qhT *qh, facetT *facetlist) {
facetT *facet;
vertexT *vertex, **vertexp, *vertexlist;
int numfacets= 0, numvertices= 0, numridges= 0;
int totvneighbors= 0, totvertices= 0;
boolT waserror= False, nextseen= False, visibleseen= False;
trace1((qh, qh->ferr, 1027, "qh_checkpolygon: check all facets from f%d\n", facetlist->id));
if (facetlist != qh->facet_list || qh->ONLYgood)
nextseen= True;
FORALLfacet_(facetlist) {
if (facet == qh->visible_list)
visibleseen= True;
if (!facet->visible) {
if (!nextseen) {
if (facet == qh->facet_next)
nextseen= True;
else if (qh_setsize(qh, facet->outsideset)) {
if (!qh->NARROWhull
#if !qh_COMPUTEfurthest
|| facet->furthestdist >= qh->MINoutside
#endif
) {
qh_fprintf(qh, qh->ferr, 6137, "qhull internal error (qh_checkpolygon): f%d has outside points before qh->facet_next\n",
facet->id);
qh_errexit(qh, qh_ERRqhull, facet, NULL);
}
}
}
numfacets++;
qh_checkfacet(qh, facet, False, &waserror);
}
}
if (qh->visible_list && !visibleseen && facetlist == qh->facet_list) {
qh_fprintf(qh, qh->ferr, 6138, "qhull internal error (qh_checkpolygon): visible list f%d no longer on facet list\n", qh->visible_list->id);
qh_printlists(qh);
qh_errexit(qh, qh_ERRqhull, qh->visible_list, NULL);
}
if (facetlist == qh->facet_list)
vertexlist= qh->vertex_list;
else if (facetlist == qh->newfacet_list)
vertexlist= qh->newvertex_list;
else
vertexlist= NULL;
FORALLvertex_(vertexlist) {
vertex->seen= False;
vertex->visitid= 0;
}
FORALLfacet_(facetlist) {
if (facet->visible)
continue;
if (facet->simplicial)
numridges += qh->hull_dim;
else
numridges += qh_setsize(qh, facet->ridges);
FOREACHvertex_(facet->vertices) {
vertex->visitid++;
if (!vertex->seen) {
vertex->seen= True;
numvertices++;
if (qh_pointid(qh, vertex->point) == qh_IDunknown) {
qh_fprintf(qh, qh->ferr, 6139, "qhull internal error (qh_checkpolygon): unknown point %p for vertex v%d first_point %p\n",
vertex->point, vertex->id, qh->first_point);
waserror= True;
}
}
}
}
qh->vertex_visit += (unsigned int)numfacets;
if (facetlist == qh->facet_list) {
if (numfacets != qh->num_facets - qh->num_visible) {
qh_fprintf(qh, qh->ferr, 6140, "qhull internal error (qh_checkpolygon): actual number of facets is %d, cumulative facet count is %d - %d visible facets\n",
numfacets, qh->num_facets, qh->num_visible);
waserror= True;
}
qh->vertex_visit++;
if (qh->VERTEXneighbors) {
FORALLvertices {
qh_setcheck(qh, vertex->neighbors, "neighbors for v", vertex->id);
if (vertex->deleted)
continue;
totvneighbors += qh_setsize(qh, vertex->neighbors);
}
FORALLfacet_(facetlist)
totvertices += qh_setsize(qh, facet->vertices);
if (totvneighbors != totvertices) {
qh_fprintf(qh, qh->ferr, 6141, "qhull internal error (qh_checkpolygon): vertex neighbors inconsistent. Totvneighbors %d, totvertices %d\n",
totvneighbors, totvertices);
waserror= True;
}
}
if (numvertices != qh->num_vertices - qh_setsize(qh, qh->del_vertices)) {
qh_fprintf(qh, qh->ferr, 6142, "qhull internal error (qh_checkpolygon): actual number of vertices is %d, cumulative vertex count is %d\n",
numvertices, qh->num_vertices - qh_setsize(qh, qh->del_vertices));
waserror= True;
}
if (qh->hull_dim == 2 && numvertices != numfacets) {
qh_fprintf(qh, qh->ferr, 6143, "qhull internal error (qh_checkpolygon): #vertices %d != #facets %d\n",
numvertices, numfacets);
waserror= True;
}
if (qh->hull_dim == 3 && numvertices + numfacets - numridges/2 != 2) {
qh_fprintf(qh, qh->ferr, 7063, "qhull warning: #vertices %d + #facets %d - #edges %d != 2\n\
A vertex appears twice in a edge list. May occur during merging.",
numvertices, numfacets, numridges/2);
/* occurs if lots of merging and a vertex ends up twice in an edge list. e.g., RBOX 1000 s W1e-13 t995849315 D2 | QHULL d Tc Tv */
}
}
if (waserror)
qh_errexit(qh, qh_ERRqhull, NULL, NULL);
} /* checkpolygon */
/*---------------------------------
qh_checkvertex(qh, vertex )
check vertex for consistency
checks vertex->neighbors
notes:
neighbors checked efficiently in checkpolygon
*/
void qh_checkvertex(qhT *qh, vertexT *vertex) {
boolT waserror= False;
facetT *neighbor, **neighborp, *errfacet=NULL;
if (qh_pointid(qh, vertex->point) == qh_IDunknown) {
qh_fprintf(qh, qh->ferr, 6144, "qhull internal error (qh_checkvertex): unknown point id %p\n", vertex->point);
waserror= True;
}
if (vertex->id >= qh->vertex_id) {
qh_fprintf(qh, qh->ferr, 6145, "qhull internal error (qh_checkvertex): unknown vertex id %d\n", vertex->id);
waserror= True;
}
if (!waserror && !vertex->deleted) {
if (qh_setsize(qh, vertex->neighbors)) {
FOREACHneighbor_(vertex) {
if (!qh_setin(neighbor->vertices, vertex)) {
qh_fprintf(qh, qh->ferr, 6146, "qhull internal error (qh_checkvertex): neighbor f%d does not contain v%d\n", neighbor->id, vertex->id);
errfacet= neighbor;
waserror= True;
}
}
}
}
if (waserror) {
qh_errprint(qh, "ERRONEOUS", NULL, NULL, NULL, vertex);
qh_errexit(qh, qh_ERRqhull, errfacet, NULL);
}
} /* checkvertex */
/*---------------------------------
qh_clearcenters(qh, type )
clear old data from facet->center
notes:
sets new centertype
nop if CENTERtype is the same
*/
void qh_clearcenters(qhT *qh, qh_CENTER type) {
facetT *facet;
if (qh->CENTERtype != type) {
FORALLfacets {
if (facet->tricoplanar && !facet->keepcentrum)
facet->center= NULL; /* center is owned by the ->keepcentrum facet */
else if (qh->CENTERtype == qh_ASvoronoi){
if (facet->center) {
qh_memfree(qh, facet->center, qh->center_size);
facet->center= NULL;
}
}else /* qh->CENTERtype == qh_AScentrum */ {
if (facet->center) {
qh_memfree(qh, facet->center, qh->normal_size);
facet->center= NULL;
}
}
}
qh->CENTERtype= type;
}
trace2((qh, qh->ferr, 2043, "qh_clearcenters: switched to center type %d\n", type));
} /* clearcenters */
/*---------------------------------
qh_createsimplex(qh, vertices )
creates a simplex from a set of vertices
returns:
initializes qh.facet_list to the simplex
initializes qh.newfacet_list, .facet_tail
initializes qh.vertex_list, .newvertex_list, .vertex_tail
design:
initializes lists
for each vertex
create a new facet
for each new facet
create its neighbor set
*/
void qh_createsimplex(qhT *qh, setT *vertices) {
facetT *facet= NULL, *newfacet;
boolT toporient= True;
int vertex_i, vertex_n, nth;
setT *newfacets= qh_settemp(qh, qh->hull_dim+1);
vertexT *vertex;
qh->facet_list= qh->newfacet_list= qh->facet_tail= qh_newfacet(qh);
qh->num_facets= qh->num_vertices= qh->num_visible= 0;
qh->vertex_list= qh->newvertex_list= qh->vertex_tail= qh_newvertex(qh, NULL);
FOREACHvertex_i_(qh, vertices) {
newfacet= qh_newfacet(qh);
newfacet->vertices= qh_setnew_delnthsorted(qh, vertices, vertex_n,
vertex_i, 0);
newfacet->toporient= (unsigned char)toporient;
qh_appendfacet(qh, newfacet);
newfacet->newfacet= True;
qh_appendvertex(qh, vertex);
qh_setappend(qh, &newfacets, newfacet);
toporient ^= True;
}
FORALLnew_facets {
nth= 0;
FORALLfacet_(qh->newfacet_list) {
if (facet != newfacet)
SETelem_(newfacet->neighbors, nth++)= facet;
}
qh_settruncate(qh, newfacet->neighbors, qh->hull_dim);
}
qh_settempfree(qh, &newfacets);
trace1((qh, qh->ferr, 1028, "qh_createsimplex: created simplex\n"));
} /* createsimplex */
/*---------------------------------
qh_delridge(qh, ridge )
deletes ridge from data structures it belongs to
frees up its memory
notes:
in merge_r.c, caller sets vertex->delridge for each vertex
ridges also freed in qh_freeqhull
*/
void qh_delridge(qhT *qh, ridgeT *ridge) {
void **freelistp; /* used if !qh_NOmem by qh_memfree_() */
qh_setdel(ridge->top->ridges, ridge);
qh_setdel(ridge->bottom->ridges, ridge);
qh_setfree(qh, &(ridge->vertices));
qh_memfree_(qh, ridge, (int)sizeof(ridgeT), freelistp);
} /* delridge */
/*---------------------------------
qh_delvertex(qh, vertex )
deletes a vertex and frees its memory
notes:
assumes vertex->adjacencies have been updated if needed
unlinks from vertex_list
*/
void qh_delvertex(qhT *qh, vertexT *vertex) {
if (vertex == qh->tracevertex)
qh->tracevertex= NULL;
qh_removevertex(qh, vertex);
qh_setfree(qh, &vertex->neighbors);
qh_memfree(qh, vertex, (int)sizeof(vertexT));
} /* delvertex */
/*---------------------------------
qh_facet3vertex(qh, )
return temporary set of 3-d vertices in qh_ORIENTclock order
design:
if simplicial facet
build set from facet->vertices with facet->toporient
else
for each ridge in order
build set from ridge's vertices
*/
setT *qh_facet3vertex(qhT *qh, facetT *facet) {
ridgeT *ridge, *firstridge;
vertexT *vertex;
int cntvertices, cntprojected=0;
setT *vertices;
cntvertices= qh_setsize(qh, facet->vertices);
vertices= qh_settemp(qh, cntvertices);
if (facet->simplicial) {
if (cntvertices != 3) {
qh_fprintf(qh, qh->ferr, 6147, "qhull internal error (qh_facet3vertex): only %d vertices for simplicial facet f%d\n",
cntvertices, facet->id);
qh_errexit(qh, qh_ERRqhull, facet, NULL);
}
qh_setappend(qh, &vertices, SETfirst_(facet->vertices));
if (facet->toporient ^ qh_ORIENTclock)
qh_setappend(qh, &vertices, SETsecond_(facet->vertices));
else
qh_setaddnth(qh, &vertices, 0, SETsecond_(facet->vertices));
qh_setappend(qh, &vertices, SETelem_(facet->vertices, 2));
}else {
ridge= firstridge= SETfirstt_(facet->ridges, ridgeT); /* no infinite */
while ((ridge= qh_nextridge3d(ridge, facet, &vertex))) {
qh_setappend(qh, &vertices, vertex);
if (++cntprojected > cntvertices || ridge == firstridge)
break;
}
if (!ridge || cntprojected != cntvertices) {
qh_fprintf(qh, qh->ferr, 6148, "qhull internal error (qh_facet3vertex): ridges for facet %d don't match up. got at least %d\n",
facet->id, cntprojected);
qh_errexit(qh, qh_ERRqhull, facet, ridge);
}
}
return vertices;
} /* facet3vertex */
/*---------------------------------
qh_findbestfacet(qh, point, bestoutside, bestdist, isoutside )
find facet that is furthest below a point
for Delaunay triangulations,
Use qh_setdelaunay() to lift point to paraboloid and scale by 'Qbb' if needed
Do not use options 'Qbk', 'QBk', or 'QbB' since they scale the coordinates.
returns:
if bestoutside is set (e.g., qh_ALL)
returns best facet that is not upperdelaunay
if Delaunay and inside, point is outside circumsphere of bestfacet
else
returns first facet below point
if point is inside, returns nearest, !upperdelaunay facet
distance to facet
isoutside set if outside of facet
notes:
For tricoplanar facets, this finds one of the tricoplanar facets closest
to the point. For Delaunay triangulations, the point may be inside a
different tricoplanar facet. See locate a facet with qh_findbestfacet()
If inside, qh_findbestfacet performs an exhaustive search
this may be too conservative. Sometimes it is clearly required.
qh_findbestfacet is not used by qhull.
uses qh.visit_id and qh.coplanarset
see:
qh_findbest
*/
facetT *qh_findbestfacet(qhT *qh, pointT *point, boolT bestoutside,
realT *bestdist, boolT *isoutside) {
facetT *bestfacet= NULL;
int numpart, totpart= 0;
bestfacet= qh_findbest(qh, point, qh->facet_list,
bestoutside, !qh_ISnewfacets, bestoutside /* qh_NOupper */,
bestdist, isoutside, &totpart);
if (*bestdist < -qh->DISTround) {
bestfacet= qh_findfacet_all(qh, point, bestdist, isoutside, &numpart);
totpart += numpart;
if ((isoutside && *isoutside && bestoutside)
|| (isoutside && !*isoutside && bestfacet->upperdelaunay)) {
bestfacet= qh_findbest(qh, point, bestfacet,
bestoutside, False, bestoutside,
bestdist, isoutside, &totpart);
totpart += numpart;
}
}
trace3((qh, qh->ferr, 3014, "qh_findbestfacet: f%d dist %2.2g isoutside %d totpart %d\n",
bestfacet->id, *bestdist, (isoutside ? *isoutside : UINT_MAX), totpart));
return bestfacet;
} /* findbestfacet */
/*---------------------------------
qh_findbestlower(qh, facet, point, bestdist, numpart )
returns best non-upper, non-flipped neighbor of facet for point
if needed, searches vertex neighbors
returns:
returns bestdist and updates numpart
notes:
if Delaunay and inside, point is outside of circumsphere of bestfacet
called by qh_findbest() for points above an upperdelaunay facet
*/
facetT *qh_findbestlower(qhT *qh, facetT *upperfacet, pointT *point, realT *bestdistp, int *numpart) {
facetT *neighbor, **neighborp, *bestfacet= NULL;
realT bestdist= -REALmax/2 /* avoid underflow */;
realT dist;
vertexT *vertex;
boolT isoutside= False; /* not used */
zinc_(Zbestlower);
FOREACHneighbor_(upperfacet) {
if (neighbor->upperdelaunay || neighbor->flipped)
continue;
(*numpart)++;
qh_distplane(qh, point, neighbor, &dist);
if (dist > bestdist) {
bestfacet= neighbor;
bestdist= dist;
}
}
if (!bestfacet) {
zinc_(Zbestlowerv);
/* rarely called, numpart does not count nearvertex computations */
vertex= qh_nearvertex(qh, upperfacet, point, &dist);
qh_vertexneighbors(qh);
FOREACHneighbor_(vertex) {
if (neighbor->upperdelaunay || neighbor->flipped)
continue;
(*numpart)++;
qh_distplane(qh, point, neighbor, &dist);
if (dist > bestdist) {
bestfacet= neighbor;
bestdist= dist;
}
}
}
if (!bestfacet) {
zinc_(Zbestlowerall); /* invoked once per point in outsideset */
zmax_(Zbestloweralln, qh->num_facets);
/* [dec'15] Previously reported as QH6228 */
trace3((qh, qh->ferr, 3025, "qh_findbestlower: all neighbors of facet %d are flipped or upper Delaunay. Search all facets\n",
upperfacet->id));
/* rarely called */
bestfacet= qh_findfacet_all(qh, point, &bestdist, &isoutside, numpart);
}
*bestdistp= bestdist;
trace3((qh, qh->ferr, 3015, "qh_findbestlower: f%d dist %2.2g for f%d p%d\n",
bestfacet->id, bestdist, upperfacet->id, qh_pointid(qh, point)));
return bestfacet;
} /* findbestlower */
/*---------------------------------
qh_findfacet_all(qh, point, bestdist, isoutside, numpart )
exhaustive search for facet below a point
for Delaunay triangulations,
Use qh_setdelaunay() to lift point to paraboloid and scale by 'Qbb' if needed
Do not use options 'Qbk', 'QBk', or 'QbB' since they scale the coordinates.
returns:
returns first facet below point
if point is inside,
returns nearest facet
distance to facet
isoutside if point is outside of the hull
number of distance tests
notes:
primarily for library users, rarely used by Qhull
*/
facetT *qh_findfacet_all(qhT *qh, pointT *point, realT *bestdist, boolT *isoutside,
int *numpart) {
facetT *bestfacet= NULL, *facet;
realT dist;
int totpart= 0;
*bestdist= -REALmax;
*isoutside= False;
FORALLfacets {
if (facet->flipped || !facet->normal)
continue;
totpart++;
qh_distplane(qh, point, facet, &dist);
if (dist > *bestdist) {
*bestdist= dist;
bestfacet= facet;
if (dist > qh->MINoutside) {
*isoutside= True;
break;
}
}
}
*numpart= totpart;
trace3((qh, qh->ferr, 3016, "qh_findfacet_all: f%d dist %2.2g isoutside %d totpart %d\n",
getid_(bestfacet), *bestdist, *isoutside, totpart));
return bestfacet;
} /* findfacet_all */
/*---------------------------------
qh_findgood(qh, facetlist, goodhorizon )
identify good facets for qh.PRINTgood
if qh.GOODvertex>0
facet includes point as vertex
if !match, returns goodhorizon
inactive if qh.MERGING
if qh.GOODpoint
facet is visible or coplanar (>0) or not visible (<0)
if qh.GOODthreshold
facet->normal matches threshold
if !goodhorizon and !match,
selects facet with closest angle
sets GOODclosest
returns:
number of new, good facets found
determines facet->good
may update qh.GOODclosest
notes:
qh_findgood_all further reduces the good region
design:
count good facets
mark good facets for qh.GOODpoint
mark good facets for qh.GOODthreshold
if necessary
update qh.GOODclosest
*/
int qh_findgood(qhT *qh, facetT *facetlist, int goodhorizon) {
facetT *facet, *bestfacet= NULL;
realT angle, bestangle= REALmax, dist;
int numgood=0;
FORALLfacet_(facetlist) {
if (facet->good)
numgood++;
}
if (qh->GOODvertex>0 && !qh->MERGING) {
FORALLfacet_(facetlist) {
if (!qh_isvertex(qh->GOODvertexp, facet->vertices)) {
facet->good= False;
numgood--;
}
}
}
if (qh->GOODpoint && numgood) {
FORALLfacet_(facetlist) {
if (facet->good && facet->normal) {
zinc_(Zdistgood);
qh_distplane(qh, qh->GOODpointp, facet, &dist);
if ((qh->GOODpoint > 0) ^ (dist > 0.0)) {
facet->good= False;
numgood--;
}
}
}
}
if (qh->GOODthreshold && (numgood || goodhorizon || qh->GOODclosest)) {
FORALLfacet_(facetlist) {
if (facet->good && facet->normal) {
if (!qh_inthresholds(qh, facet->normal, &angle)) {
facet->good= False;
numgood--;
if (angle < bestangle) {
bestangle= angle;
bestfacet= facet;
}
}
}
}
if (!numgood && (!goodhorizon || qh->GOODclosest)) {
if (qh->GOODclosest) {
if (qh->GOODclosest->visible)
qh->GOODclosest= NULL;
else {
qh_inthresholds(qh, qh->GOODclosest->normal, &angle);
if (angle < bestangle)
bestfacet= qh->GOODclosest;
}
}
if (bestfacet && bestfacet != qh->GOODclosest) {
if (qh->GOODclosest)
qh->GOODclosest->good= False;
qh->GOODclosest= bestfacet;
bestfacet->good= True;
numgood++;
trace2((qh, qh->ferr, 2044, "qh_findgood: f%d is closest(%2.2g) to thresholds\n",
bestfacet->id, bestangle));
return numgood;
}
}else if (qh->GOODclosest) { /* numgood > 0 */
qh->GOODclosest->good= False;
qh->GOODclosest= NULL;
}
}
zadd_(Zgoodfacet, numgood);
trace2((qh, qh->ferr, 2045, "qh_findgood: found %d good facets with %d good horizon\n",
numgood, goodhorizon));
if (!numgood && qh->GOODvertex>0 && !qh->MERGING)
return goodhorizon;
return numgood;
} /* findgood */
/*---------------------------------
qh_findgood_all(qh, facetlist )
apply other constraints for good facets (used by qh.PRINTgood)
if qh.GOODvertex
facet includes (>0) or doesn't include (<0) point as vertex
if last good facet and ONLYgood, prints warning and continues
if qh.SPLITthresholds
facet->normal matches threshold, or if none, the closest one
calls qh_findgood
nop if good not used
returns:
clears facet->good if not good
sets qh.num_good
notes:
this is like qh_findgood but more restrictive
design:
uses qh_findgood to mark good facets
marks facets for qh.GOODvertex
marks facets for qh.SPLITthreholds
*/
void qh_findgood_all(qhT *qh, facetT *facetlist) {
facetT *facet, *bestfacet=NULL;
realT angle, bestangle= REALmax;
int numgood=0, startgood;
if (!qh->GOODvertex && !qh->GOODthreshold && !qh->GOODpoint
&& !qh->SPLITthresholds)
return;
if (!qh->ONLYgood)
qh_findgood(qh, qh->facet_list, 0);
FORALLfacet_(facetlist) {
if (facet->good)
numgood++;
}
if (qh->GOODvertex <0 || (qh->GOODvertex > 0 && qh->MERGING)) {
FORALLfacet_(facetlist) {
if (facet->good && ((qh->GOODvertex > 0) ^ !!qh_isvertex(qh->GOODvertexp, facet->vertices))) {
if (!--numgood) {
if (qh->ONLYgood) {
qh_fprintf(qh, qh->ferr, 7064, "qhull warning: good vertex p%d does not match last good facet f%d. Ignored.\n",
qh_pointid(qh, qh->GOODvertexp), facet->id);
return;
}else if (qh->GOODvertex > 0)
qh_fprintf(qh, qh->ferr, 7065, "qhull warning: point p%d is not a vertex('QV%d').\n",
qh->GOODvertex-1, qh->GOODvertex-1);
else
qh_fprintf(qh, qh->ferr, 7066, "qhull warning: point p%d is a vertex for every facet('QV-%d').\n",
-qh->GOODvertex - 1, -qh->GOODvertex - 1);
}
facet->good= False;
}
}
}
startgood= numgood;
if (qh->SPLITthresholds) {
FORALLfacet_(facetlist) {
if (facet->good) {
if (!qh_inthresholds(qh, facet->normal, &angle)) {
facet->good= False;
numgood--;
if (angle < bestangle) {
bestangle= angle;
bestfacet= facet;
}
}
}
}
if (!numgood && bestfacet) {
bestfacet->good= True;
numgood++;
trace0((qh, qh->ferr, 23, "qh_findgood_all: f%d is closest(%2.2g) to thresholds\n",
bestfacet->id, bestangle));
return;
}
}
qh->num_good= numgood;
trace0((qh, qh->ferr, 24, "qh_findgood_all: %d good facets remain out of %d facets\n",
numgood, startgood));
} /* findgood_all */
/*---------------------------------
qh_furthestnext()
set qh.facet_next to facet with furthest of all furthest points
searches all facets on qh.facet_list
notes:
this may help avoid precision problems
*/
void qh_furthestnext(qhT *qh /* qh->facet_list */) {
facetT *facet, *bestfacet= NULL;
realT dist, bestdist= -REALmax;
FORALLfacets {
if (facet->outsideset) {
#if qh_COMPUTEfurthest
pointT *furthest;
furthest= (pointT*)qh_setlast(facet->outsideset);
zinc_(Zcomputefurthest);
qh_distplane(qh, furthest, facet, &dist);
#else
dist= facet->furthestdist;
#endif
if (dist > bestdist) {
bestfacet= facet;
bestdist= dist;
}
}
}
if (bestfacet) {
qh_removefacet(qh, bestfacet);
qh_prependfacet(qh, bestfacet, &qh->facet_next);
trace1((qh, qh->ferr, 1029, "qh_furthestnext: made f%d next facet(dist %.2g)\n",
bestfacet->id, bestdist));
}
} /* furthestnext */
/*---------------------------------
qh_furthestout(qh, facet )
make furthest outside point the last point of outsideset
returns:
updates facet->outsideset
clears facet->notfurthest
sets facet->furthestdist
design:
determine best point of outsideset
make it the last point of outsideset
*/
void qh_furthestout(qhT *qh, facetT *facet) {
pointT *point, **pointp, *bestpoint= NULL;
realT dist, bestdist= -REALmax;
FOREACHpoint_(facet->outsideset) {
qh_distplane(qh, point, facet, &dist);
zinc_(Zcomputefurthest);
if (dist > bestdist) {
bestpoint= point;
bestdist= dist;
}
}
if (bestpoint) {
qh_setdel(facet->outsideset, point);
qh_setappend(qh, &facet->outsideset, point);
#if !qh_COMPUTEfurthest
facet->furthestdist= bestdist;
#endif
}
facet->notfurthest= False;
trace3((qh, qh->ferr, 3017, "qh_furthestout: p%d is furthest outside point of f%d\n",
qh_pointid(qh, point), facet->id));
} /* furthestout */
/*---------------------------------
qh_infiniteloop(qh, facet )
report infinite loop error due to facet
*/
void qh_infiniteloop(qhT *qh, facetT *facet) {
qh_fprintf(qh, qh->ferr, 6149, "qhull internal error (qh_infiniteloop): potential infinite loop detected\n");
qh_errexit(qh, qh_ERRqhull, facet, NULL);
} /* qh_infiniteloop */
/*---------------------------------
qh_initbuild()
initialize hull and outside sets with point array
qh.FIRSTpoint/qh.NUMpoints is point array
if qh.GOODpoint
adds qh.GOODpoint to initial hull
returns:
qh_facetlist with initial hull
points partioned into outside sets, coplanar sets, or inside
initializes qh.GOODpointp, qh.GOODvertexp,
design:
initialize global variables used during qh_buildhull
determine precision constants and points with max/min coordinate values
if qh.SCALElast, scale last coordinate(for 'd')
build initial simplex
partition input points into facets of initial simplex
set up lists
if qh.ONLYgood
check consistency
add qh.GOODvertex if defined
*/
void qh_initbuild(qhT *qh) {
setT *maxpoints, *vertices;
facetT *facet;
int i, numpart;
realT dist;
boolT isoutside;
qh->furthest_id= qh_IDunknown;
qh->lastreport= 0;
qh->facet_id= qh->vertex_id= qh->ridge_id= 0;
qh->visit_id= qh->vertex_visit= 0;
qh->maxoutdone= False;
if (qh->GOODpoint > 0)
qh->GOODpointp= qh_point(qh, qh->GOODpoint-1);
else if (qh->GOODpoint < 0)
qh->GOODpointp= qh_point(qh, -qh->GOODpoint-1);
if (qh->GOODvertex > 0)
qh->GOODvertexp= qh_point(qh, qh->GOODvertex-1);
else if (qh->GOODvertex < 0)
qh->GOODvertexp= qh_point(qh, -qh->GOODvertex-1);
if ((qh->GOODpoint
&& (qh->GOODpointp < qh->first_point /* also catches !GOODpointp */
|| qh->GOODpointp > qh_point(qh, qh->num_points-1)))
|| (qh->GOODvertex
&& (qh->GOODvertexp < qh->first_point /* also catches !GOODvertexp */
|| qh->GOODvertexp > qh_point(qh, qh->num_points-1)))) {
qh_fprintf(qh, qh->ferr, 6150, "qhull input error: either QGn or QVn point is > p%d\n",
qh->num_points-1);
qh_errexit(qh, qh_ERRinput, NULL, NULL);
}
maxpoints= qh_maxmin(qh, qh->first_point, qh->num_points, qh->hull_dim);
if (qh->SCALElast)
qh_scalelast(qh, qh->first_point, qh->num_points, qh->hull_dim,
qh->MINlastcoord, qh->MAXlastcoord, qh->MAXwidth);
qh_detroundoff(qh);
if (qh->DELAUNAY && qh->upper_threshold[qh->hull_dim-1] > REALmax/2
&& qh->lower_threshold[qh->hull_dim-1] < -REALmax/2) {
for (i=qh_PRINTEND; i--; ) {
if (qh->PRINTout[i] == qh_PRINTgeom && qh->DROPdim < 0
&& !qh->GOODthreshold && !qh->SPLITthresholds)
break; /* in this case, don't set upper_threshold */
}
if (i < 0) {
if (qh->UPPERdelaunay) { /* matches qh.upperdelaunay in qh_setfacetplane */
qh->lower_threshold[qh->hull_dim-1]= qh->ANGLEround * qh_ZEROdelaunay;
qh->GOODthreshold= True;
}else {
qh->upper_threshold[qh->hull_dim-1]= -qh->ANGLEround * qh_ZEROdelaunay;
if (!qh->GOODthreshold)
qh->SPLITthresholds= True; /* build upper-convex hull even if Qg */
/* qh_initqhull_globals errors if Qg without Pdk/etc. */
}
}
}
vertices= qh_initialvertices(qh, qh->hull_dim, maxpoints, qh->first_point, qh->num_points);
qh_initialhull(qh, vertices); /* initial qh->facet_list */
qh_partitionall(qh, vertices, qh->first_point, qh->num_points);
if (qh->PRINToptions1st || qh->TRACElevel || qh->IStracing) {
if (qh->TRACElevel || qh->IStracing)
qh_fprintf(qh, qh->ferr, 8103, "\nTrace level %d for %s | %s\n",
qh->IStracing ? qh->IStracing : qh->TRACElevel, qh->rbox_command, qh->qhull_command);
qh_fprintf(qh, qh->ferr, 8104, "Options selected for Qhull %s:\n%s\n", qh_version, qh->qhull_options);
}
qh_resetlists(qh, False, qh_RESETvisible /*qh.visible_list newvertex_list newfacet_list */);
qh->facet_next= qh->facet_list;
qh_furthestnext(qh /* qh->facet_list */);
if (qh->PREmerge) {
qh->cos_max= qh->premerge_cos;
qh->centrum_radius= qh->premerge_centrum;
}
if (qh->ONLYgood) {
if (qh->GOODvertex > 0 && qh->MERGING) {
qh_fprintf(qh, qh->ferr, 6151, "qhull input error: 'Qg QVn' (only good vertex) does not work with merging.\nUse 'QJ' to joggle the input or 'Q0' to turn off merging.\n");
qh_errexit(qh, qh_ERRinput, NULL, NULL);
}
if (!(qh->GOODthreshold || qh->GOODpoint
|| (!qh->MERGEexact && !qh->PREmerge && qh->GOODvertexp))) {
qh_fprintf(qh, qh->ferr, 6152, "qhull input error: 'Qg' (ONLYgood) needs a good threshold('Pd0D0'), a\n\
good point(QGn or QG-n), or a good vertex with 'QJ' or 'Q0' (QVn).\n");
qh_errexit(qh, qh_ERRinput, NULL, NULL);
}
if (qh->GOODvertex > 0 && !qh->MERGING /* matches qh_partitionall */
&& !qh_isvertex(qh->GOODvertexp, vertices)) {
facet= qh_findbestnew(qh, qh->GOODvertexp, qh->facet_list,
&dist, !qh_ALL, &isoutside, &numpart);
zadd_(Zdistgood, numpart);
if (!isoutside) {
qh_fprintf(qh, qh->ferr, 6153, "qhull input error: point for QV%d is inside initial simplex. It can not be made a vertex.\n",
qh_pointid(qh, qh->GOODvertexp));
qh_errexit(qh, qh_ERRinput, NULL, NULL);
}
if (!qh_addpoint(qh, qh->GOODvertexp, facet, False)) {
qh_settempfree(qh, &vertices);
qh_settempfree(qh, &maxpoints);
return;
}
}
qh_findgood(qh, qh->facet_list, 0);
}
qh_settempfree(qh, &vertices);
qh_settempfree(qh, &maxpoints);
trace1((qh, qh->ferr, 1030, "qh_initbuild: initial hull created and points partitioned\n"));
} /* initbuild */
/*---------------------------------
qh_initialhull(qh, vertices )
constructs the initial hull as a DIM3 simplex of vertices
design:
creates a simplex (initializes lists)
determines orientation of simplex
sets hyperplanes for facets
doubles checks orientation (in case of axis-parallel facets with Gaussian elimination)
checks for flipped facets and qh.NARROWhull
checks the result
*/
void qh_initialhull(qhT *qh, setT *vertices) {
facetT *facet, *firstfacet, *neighbor, **neighborp;
realT dist, angle, minangle= REALmax;
#ifndef qh_NOtrace
int k;
#endif
qh_createsimplex(qh, vertices); /* qh->facet_list */
qh_resetlists(qh, False, qh_RESETvisible);
qh->facet_next= qh->facet_list; /* advance facet when processed */
qh->interior_point= qh_getcenter(qh, vertices);
firstfacet= qh->facet_list;
qh_setfacetplane(qh, firstfacet);
zinc_(Znumvisibility); /* needs to be in printsummary */
qh_distplane(qh, qh->interior_point, firstfacet, &dist);
if (dist > 0) {
FORALLfacets
facet->toporient ^= (unsigned char)True;
}
FORALLfacets
qh_setfacetplane(qh, facet);
FORALLfacets {
if (!qh_checkflipped(qh, facet, NULL, qh_ALL)) {/* due to axis-parallel facet */
trace1((qh, qh->ferr, 1031, "qh_initialhull: initial orientation incorrect. Correct all facets\n"));
facet->flipped= False;
FORALLfacets {
facet->toporient ^= (unsigned char)True;
qh_orientoutside(qh, facet);
}
break;
}
}
FORALLfacets {
if (!qh_checkflipped(qh, facet, NULL, !qh_ALL)) { /* can happen with 'R0.1' */
if (qh->DELAUNAY && ! qh->ATinfinity) {
if (qh->UPPERdelaunay)
qh_fprintf(qh, qh->ferr, 6240, "Qhull precision error: Initial simplex is cocircular or cospherical. Option 'Qs' searches all points. Can not compute the upper Delaunay triangulation or upper Voronoi diagram of cocircular/cospherical points.\n");
else
qh_fprintf(qh, qh->ferr, 6239, "Qhull precision error: Initial simplex is cocircular or cospherical. Use option 'Qz' for the Delaunay triangulation or Voronoi diagram of cocircular/cospherical points. Option 'Qz' adds a point \"at infinity\". Use option 'Qs' to search all points for the initial simplex.\n");
qh_errexit(qh, qh_ERRinput, NULL, NULL);
}
qh_precision(qh, "initial simplex is flat");
qh_fprintf(qh, qh->ferr, 6154, "Qhull precision error: Initial simplex is flat (facet %d is coplanar with the interior point)\n",
facet->id);
qh_errexit(qh, qh_ERRsingular, NULL, NULL); /* calls qh_printhelp_singular */
}
FOREACHneighbor_(facet) {
angle= qh_getangle(qh, facet->normal, neighbor->normal);
minimize_( minangle, angle);
}
}
if (minangle < qh_MAXnarrow && !qh->NOnarrow) {
realT diff= 1.0 + minangle;
qh->NARROWhull= True;
qh_option(qh, "_narrow-hull", NULL, &diff);
if (minangle < qh_WARNnarrow && !qh->RERUN && qh->PRINTprecision)
qh_printhelp_narrowhull(qh, qh->ferr, minangle);
}
zzval_(Zprocessed)= qh->hull_dim+1;
qh_checkpolygon(qh, qh->facet_list);
qh_checkconvex(qh, qh->facet_list, qh_DATAfault);
#ifndef qh_NOtrace
if (qh->IStracing >= 1) {
qh_fprintf(qh, qh->ferr, 8105, "qh_initialhull: simplex constructed, interior point:");
for (k=0; k < qh->hull_dim; k++)
qh_fprintf(qh, qh->ferr, 8106, " %6.4g", qh->interior_point[k]);
qh_fprintf(qh, qh->ferr, 8107, "\n");
}
#endif
} /* initialhull */
/*---------------------------------
qh_initialvertices(qh, dim, maxpoints, points, numpoints )
determines a non-singular set of initial vertices
maxpoints may include duplicate points
returns:
temporary set of dim+1 vertices in descending order by vertex id
if qh.RANDOMoutside && !qh.ALLpoints
picks random points
if dim >= qh_INITIALmax,
uses min/max x and max points with non-zero determinants
notes:
unless qh.ALLpoints,
uses maxpoints as long as determinate is non-zero
*/
setT *qh_initialvertices(qhT *qh, int dim, setT *maxpoints, pointT *points, int numpoints) {
pointT *point, **pointp;
setT *vertices, *simplex, *tested;
realT randr;
int idx, point_i, point_n, k;
boolT nearzero= False;
vertices= qh_settemp(qh, dim + 1);
simplex= qh_settemp(qh, dim+1);
if (qh->ALLpoints)
qh_maxsimplex(qh, dim, NULL, points, numpoints, &simplex);
else if (qh->RANDOMoutside) {
while (qh_setsize(qh, simplex) != dim+1) {
randr= qh_RANDOMint;
randr= randr/(qh_RANDOMmax+1);
idx= (int)floor(qh->num_points * randr);
while (qh_setin(simplex, qh_point(qh, idx))) {
idx++; /* in case qh_RANDOMint always returns the same value */
idx= idx < qh->num_points ? idx : 0;
}
qh_setappend(qh, &simplex, qh_point(qh, idx));
}
}else if (qh->hull_dim >= qh_INITIALmax) {
tested= qh_settemp(qh, dim+1);
qh_setappend(qh, &simplex, SETfirst_(maxpoints)); /* max and min X coord */
qh_setappend(qh, &simplex, SETsecond_(maxpoints));
qh_maxsimplex(qh, fmin_(qh_INITIALsearch, dim), maxpoints, points, numpoints, &simplex);
k= qh_setsize(qh, simplex);
FOREACHpoint_i_(qh, maxpoints) {
if (point_i & 0x1) { /* first pick up max. coord. points */
if (!qh_setin(simplex, point) && !qh_setin(tested, point)){
qh_detsimplex(qh, point, simplex, k, &nearzero);
if (nearzero)
qh_setappend(qh, &tested, point);
else {
qh_setappend(qh, &simplex, point);
if (++k == dim) /* use search for last point */
break;
}
}
}
}
while (k != dim && (point= (pointT*)qh_setdellast(maxpoints))) {
if (!qh_setin(simplex, point) && !qh_setin(tested, point)){
qh_detsimplex(qh, point, simplex, k, &nearzero);
if (nearzero)
qh_setappend(qh, &tested, point);
else {
qh_setappend(qh, &simplex, point);
k++;
}
}
}
idx= 0;
while (k != dim && (point= qh_point(qh, idx++))) {
if (!qh_setin(simplex, point) && !qh_setin(tested, point)){
qh_detsimplex(qh, point, simplex, k, &nearzero);
if (!nearzero){
qh_setappend(qh, &simplex, point);
k++;
}
}
}
qh_settempfree(qh, &tested);
qh_maxsimplex(qh, dim, maxpoints, points, numpoints, &simplex);
}else
qh_maxsimplex(qh, dim, maxpoints, points, numpoints, &simplex);
FOREACHpoint_(simplex)
qh_setaddnth(qh, &vertices, 0, qh_newvertex(qh, point)); /* descending order */
qh_settempfree(qh, &simplex);
return vertices;
} /* initialvertices */
/*---------------------------------
qh_isvertex( point, vertices )
returns vertex if point is in vertex set, else returns NULL
notes:
for qh.GOODvertex
*/
vertexT *qh_isvertex(pointT *point, setT *vertices) {
vertexT *vertex, **vertexp;
FOREACHvertex_(vertices) {
if (vertex->point == point)
return vertex;
}
return NULL;
} /* isvertex */
/*---------------------------------
qh_makenewfacets(qh, point )
make new facets from point and qh.visible_list
returns:
qh.newfacet_list= list of new facets with hyperplanes and ->newfacet
qh.newvertex_list= list of vertices in new facets with ->newlist set
if (qh.ONLYgood)
newfacets reference horizon facets, but not vice versa
ridges reference non-simplicial horizon ridges, but not vice versa
does not change existing facets
else
sets qh.NEWfacets
new facets attached to horizon facets and ridges
for visible facets,
visible->r.replace is corresponding new facet
see also:
qh_makenewplanes() -- make hyperplanes for facets
qh_attachnewfacets() -- attachnewfacets if not done here(qh->ONLYgood)
qh_matchnewfacets() -- match up neighbors
qh_updatevertices() -- update vertex neighbors and delvertices
qh_deletevisible() -- delete visible facets
qh_checkpolygon() --check the result
qh_triangulate() -- triangulate a non-simplicial facet
design:
for each visible facet
make new facets to its horizon facets
update its f.replace
clear its neighbor set
*/
vertexT *qh_makenewfacets(qhT *qh, pointT *point /*visible_list*/) {
facetT *visible, *newfacet= NULL, *newfacet2= NULL, *neighbor, **neighborp;
vertexT *apex;
int numnew=0;
qh->newfacet_list= qh->facet_tail;
qh->newvertex_list= qh->vertex_tail;
apex= qh_newvertex(qh, point);
qh_appendvertex(qh, apex);
qh->visit_id++;
if (!qh->ONLYgood)
qh->NEWfacets= True;
FORALLvisible_facets {
FOREACHneighbor_(visible)
neighbor->seen= False;
if (visible->ridges) {
visible->visitid= qh->visit_id;
newfacet2= qh_makenew_nonsimplicial(qh, visible, apex, &numnew);
}
if (visible->simplicial)
newfacet= qh_makenew_simplicial(qh, visible, apex, &numnew);
if (!qh->ONLYgood) {
if (newfacet2) /* newfacet is null if all ridges defined */
newfacet= newfacet2;
if (newfacet)
visible->f.replace= newfacet;
else
zinc_(Zinsidevisible);
SETfirst_(visible->neighbors)= NULL;
}
}
trace1((qh, qh->ferr, 1032, "qh_makenewfacets: created %d new facets from point p%d to horizon\n",
numnew, qh_pointid(qh, point)));
if (qh->IStracing >= 4)
qh_printfacetlist(qh, qh->newfacet_list, NULL, qh_ALL);
return apex;
} /* makenewfacets */
/*---------------------------------
qh_matchduplicates(qh, atfacet, atskip, hashsize, hashcount )
match duplicate ridges in qh.hash_table for atfacet/atskip
duplicates marked with ->dupridge and qh_DUPLICATEridge
returns:
picks match with worst merge (min distance apart)
updates hashcount
see also:
qh_matchneighbor
notes:
design:
compute hash value for atfacet and atskip
repeat twice -- once to make best matches, once to match the rest
for each possible facet in qh.hash_table
if it is a matching facet and pass 2
make match
unless tricoplanar, mark match for merging (qh_MERGEridge)
[e.g., tricoplanar RBOX s 1000 t993602376 | QHULL C-1e-3 d Qbb FA Qt]
if it is a matching facet and pass 1
test if this is a better match
if pass 1,
make best match (it will not be merged)
*/
#ifndef qh_NOmerge
void qh_matchduplicates(qhT *qh, facetT *atfacet, int atskip, int hashsize, int *hashcount) {
boolT same, ismatch;
int hash, scan;
facetT *facet, *newfacet, *maxmatch= NULL, *maxmatch2= NULL, *nextfacet;
int skip, newskip, nextskip= 0, maxskip= 0, maxskip2= 0, makematch;
realT maxdist= -REALmax, mindist, dist2, low, high;
hash= qh_gethash(qh, hashsize, atfacet->vertices, qh->hull_dim, 1,
SETelem_(atfacet->vertices, atskip));
trace2((qh, qh->ferr, 2046, "qh_matchduplicates: find duplicate matches for f%d skip %d hash %d hashcount %d\n",
atfacet->id, atskip, hash, *hashcount));
for (makematch= 0; makematch < 2; makematch++) {
qh->visit_id++;
for (newfacet= atfacet, newskip= atskip; newfacet; newfacet= nextfacet, newskip= nextskip) {
zinc_(Zhashlookup);
nextfacet= NULL;
newfacet->visitid= qh->visit_id;
for (scan= hash; (facet= SETelemt_(qh->hash_table, scan, facetT));
scan= (++scan >= hashsize ? 0 : scan)) {
if (!facet->dupridge || facet->visitid == qh->visit_id)
continue;
zinc_(Zhashtests);
if (qh_matchvertices(qh, 1, newfacet->vertices, newskip, facet->vertices, &skip, &same)) {
ismatch= (same == (boolT)(newfacet->toporient ^ facet->toporient));
if (SETelemt_(facet->neighbors, skip, facetT) != qh_DUPLICATEridge) {
if (!makematch) {
qh_fprintf(qh, qh->ferr, 6155, "qhull internal error (qh_matchduplicates): missing dupridge at f%d skip %d for new f%d skip %d hash %d\n",
facet->id, skip, newfacet->id, newskip, hash);
qh_errexit2(qh, qh_ERRqhull, facet, newfacet);
}
}else if (ismatch && makematch) {
if (SETelemt_(newfacet->neighbors, newskip, facetT) == qh_DUPLICATEridge) {
SETelem_(facet->neighbors, skip)= newfacet;
if (newfacet->tricoplanar)
SETelem_(newfacet->neighbors, newskip)= facet;
else
SETelem_(newfacet->neighbors, newskip)= qh_MERGEridge;
*hashcount -= 2; /* removed two unmatched facets */
trace4((qh, qh->ferr, 4059, "qh_matchduplicates: duplicate f%d skip %d matched with new f%d skip %d merge\n",
facet->id, skip, newfacet->id, newskip));
}
}else if (ismatch) {
mindist= qh_getdistance(qh, facet, newfacet, &low, &high);
dist2= qh_getdistance(qh, newfacet, facet, &low, &high);
minimize_(mindist, dist2);
if (mindist > maxdist) {
maxdist= mindist;
maxmatch= facet;
maxskip= skip;
maxmatch2= newfacet;
maxskip2= newskip;
}
trace3((qh, qh->ferr, 3018, "qh_matchduplicates: duplicate f%d skip %d new f%d skip %d at dist %2.2g, max is now f%d f%d\n",
facet->id, skip, newfacet->id, newskip, mindist,
maxmatch->id, maxmatch2->id));
}else { /* !ismatch */
nextfacet= facet;
nextskip= skip;
}
}
if (makematch && !facet
&& SETelemt_(facet->neighbors, skip, facetT) == qh_DUPLICATEridge) {
qh_fprintf(qh, qh->ferr, 6156, "qhull internal error (qh_matchduplicates): no MERGEridge match for duplicate f%d skip %d at hash %d\n",
newfacet->id, newskip, hash);
qh_errexit(qh, qh_ERRqhull, newfacet, NULL);
}
}
} /* end of for each new facet at hash */
if (!makematch) {
if (!maxmatch) {
qh_fprintf(qh, qh->ferr, 6157, "qhull internal error (qh_matchduplicates): no maximum match at duplicate f%d skip %d at hash %d\n",
atfacet->id, atskip, hash);
qh_errexit(qh, qh_ERRqhull, atfacet, NULL);
}
SETelem_(maxmatch->neighbors, maxskip)= maxmatch2; /* maxmatch!=0 by QH6157 */
SETelem_(maxmatch2->neighbors, maxskip2)= maxmatch;
*hashcount -= 2; /* removed two unmatched facets */
zzinc_(Zmultiridge);
trace0((qh, qh->ferr, 25, "qh_matchduplicates: duplicate f%d skip %d matched with new f%d skip %d keep\n",
maxmatch->id, maxskip, maxmatch2->id, maxskip2));
qh_precision(qh, "ridge with multiple neighbors");
if (qh->IStracing >= 4)
qh_errprint(qh, "DUPLICATED/MATCH", maxmatch, maxmatch2, NULL, NULL);
}
}
} /* matchduplicates */
/*---------------------------------
qh_nearcoplanar()
for all facets, remove near-inside points from facet->coplanarset
coplanar points defined by innerplane from qh_outerinner()
returns:
if qh->KEEPcoplanar && !qh->KEEPinside
facet->coplanarset only contains coplanar points
if qh.JOGGLEmax
drops inner plane by another qh.JOGGLEmax diagonal since a
vertex could shift out while a coplanar point shifts in
notes:
used for qh.PREmerge and qh.JOGGLEmax
must agree with computation of qh.NEARcoplanar in qh_detroundoff(qh)
design:
if not keeping coplanar or inside points
free all coplanar sets
else if not keeping both coplanar and inside points
remove !coplanar or !inside points from coplanar sets
*/
void qh_nearcoplanar(qhT *qh /* qh.facet_list */) {
facetT *facet;
pointT *point, **pointp;
int numpart;
realT dist, innerplane;
if (!qh->KEEPcoplanar && !qh->KEEPinside) {
FORALLfacets {
if (facet->coplanarset)
qh_setfree(qh, &facet->coplanarset);
}
}else if (!qh->KEEPcoplanar || !qh->KEEPinside) {
qh_outerinner(qh, NULL, NULL, &innerplane);
if (qh->JOGGLEmax < REALmax/2)
innerplane -= qh->JOGGLEmax * sqrt((realT)qh->hull_dim);
numpart= 0;
FORALLfacets {
if (facet->coplanarset) {
FOREACHpoint_(facet->coplanarset) {
numpart++;
qh_distplane(qh, point, facet, &dist);
if (dist < innerplane) {
if (!qh->KEEPinside)
SETref_(point)= NULL;
}else if (!qh->KEEPcoplanar)
SETref_(point)= NULL;
}
qh_setcompact(qh, facet->coplanarset);
}
}
zzadd_(Zcheckpart, numpart);
}
} /* nearcoplanar */
/*---------------------------------
qh_nearvertex(qh, facet, point, bestdist )
return nearest vertex in facet to point
returns:
vertex and its distance
notes:
if qh.DELAUNAY
distance is measured in the input set
searches neighboring tricoplanar facets (requires vertexneighbors)
Slow implementation. Recomputes vertex set for each point.
The vertex set could be stored in the qh.keepcentrum facet.
*/
vertexT *qh_nearvertex(qhT *qh, facetT *facet, pointT *point, realT *bestdistp) {
realT bestdist= REALmax, dist;
vertexT *bestvertex= NULL, *vertex, **vertexp, *apex;
coordT *center;
facetT *neighbor, **neighborp;
setT *vertices;
int dim= qh->hull_dim;
if (qh->DELAUNAY)
dim--;
if (facet->tricoplanar) {
if (!qh->VERTEXneighbors || !facet->center) {
qh_fprintf(qh, qh->ferr, 6158, "qhull internal error (qh_nearvertex): qh.VERTEXneighbors and facet->center required for tricoplanar facets\n");
qh_errexit(qh, qh_ERRqhull, facet, NULL);
}
vertices= qh_settemp(qh, qh->TEMPsize);
apex= SETfirstt_(facet->vertices, vertexT);
center= facet->center;
FOREACHneighbor_(apex) {
if (neighbor->center == center) {
FOREACHvertex_(neighbor->vertices)
qh_setappend(qh, &vertices, vertex);
}
}
}else
vertices= facet->vertices;
FOREACHvertex_(vertices) {
dist= qh_pointdist(vertex->point, point, -dim);
if (dist < bestdist) {
bestdist= dist;
bestvertex= vertex;
}
}
if (facet->tricoplanar)
qh_settempfree(qh, &vertices);
*bestdistp= sqrt(bestdist);
if (!bestvertex) {
qh_fprintf(qh, qh->ferr, 6261, "qhull internal error (qh_nearvertex): did not find bestvertex for f%d p%d\n", facet->id, qh_pointid(qh, point));
qh_errexit(qh, qh_ERRqhull, facet, NULL);
}
trace3((qh, qh->ferr, 3019, "qh_nearvertex: v%d dist %2.2g for f%d p%d\n",
bestvertex->id, *bestdistp, facet->id, qh_pointid(qh, point))); /* bestvertex!=0 by QH2161 */
return bestvertex;
} /* nearvertex */
/*---------------------------------
qh_newhashtable(qh, newsize )
returns size of qh.hash_table of at least newsize slots
notes:
assumes qh.hash_table is NULL
qh_HASHfactor determines the number of extra slots
size is not divisible by 2, 3, or 5
*/
int qh_newhashtable(qhT *qh, int newsize) {
int size;
size= ((newsize+1)*qh_HASHfactor) | 0x1; /* odd number */
while (True) {
if (newsize<0 || size<0) {
qh_fprintf(qh, qh->qhmem.ferr, 6236, "qhull error (qh_newhashtable): negative request (%d) or size (%d). Did int overflow due to high-D?\n", newsize, size); /* WARN64 */
qh_errexit(qh, qhmem_ERRmem, NULL, NULL);
}
if ((size%3) && (size%5))
break;
size += 2;
/* loop terminates because there is an infinite number of primes */
}
qh->hash_table= qh_setnew(qh, size);
qh_setzero(qh, qh->hash_table, 0, size);
return size;
} /* newhashtable */
/*---------------------------------
qh_newvertex(qh, point )
returns a new vertex for point
*/
vertexT *qh_newvertex(qhT *qh, pointT *point) {
vertexT *vertex;
zinc_(Ztotvertices);
vertex= (vertexT *)qh_memalloc(qh, (int)sizeof(vertexT));
memset((char *) vertex, (size_t)0, sizeof(vertexT));
if (qh->vertex_id == UINT_MAX) {
qh_memfree(qh, vertex, (int)sizeof(vertexT));
qh_fprintf(qh, qh->ferr, 6159, "qhull error: more than 2^32 vertices. vertexT.id field overflows. Vertices would not be sorted correctly.\n");
qh_errexit(qh, qh_ERRqhull, NULL, NULL);
}
if (qh->vertex_id == qh->tracevertex_id)
qh->tracevertex= vertex;
vertex->id= qh->vertex_id++;
vertex->point= point;
trace4((qh, qh->ferr, 4060, "qh_newvertex: vertex p%d(v%d) created\n", qh_pointid(qh, vertex->point),
vertex->id));
return(vertex);
} /* newvertex */
/*---------------------------------
qh_nextridge3d( atridge, facet, vertex )
return next ridge and vertex for a 3d facet
returns NULL on error
[for QhullFacet::nextRidge3d] Does not call qh_errexit nor access qhT.
notes:
in qh_ORIENTclock order
this is a O(n^2) implementation to trace all ridges
be sure to stop on any 2nd visit
same as QhullRidge::nextRidge3d
does not use qhT or qh_errexit [QhullFacet.cpp]
design:
for each ridge
exit if it is the ridge after atridge
*/
ridgeT *qh_nextridge3d(ridgeT *atridge, facetT *facet, vertexT **vertexp) {
vertexT *atvertex, *vertex, *othervertex;
ridgeT *ridge, **ridgep;
if ((atridge->top == facet) ^ qh_ORIENTclock)
atvertex= SETsecondt_(atridge->vertices, vertexT);
else
atvertex= SETfirstt_(atridge->vertices, vertexT);
FOREACHridge_(facet->ridges) {
if (ridge == atridge)
continue;
if ((ridge->top == facet) ^ qh_ORIENTclock) {
othervertex= SETsecondt_(ridge->vertices, vertexT);
vertex= SETfirstt_(ridge->vertices, vertexT);
}else {
vertex= SETsecondt_(ridge->vertices, vertexT);
othervertex= SETfirstt_(ridge->vertices, vertexT);
}
if (vertex == atvertex) {
if (vertexp)
*vertexp= othervertex;
return ridge;
}
}
return NULL;
} /* nextridge3d */
#else /* qh_NOmerge */
void qh_matchduplicates(qhT *qh, facetT *atfacet, int atskip, int hashsize, int *hashcount) {
}
ridgeT *qh_nextridge3d(ridgeT *atridge, facetT *facet, vertexT **vertexp) {
return NULL;
}
#endif /* qh_NOmerge */
/*---------------------------------
qh_outcoplanar()
move points from all facets' outsidesets to their coplanarsets
notes:
for post-processing under qh.NARROWhull
design:
for each facet
for each outside point for facet
partition point into coplanar set
*/
void qh_outcoplanar(qhT *qh /* facet_list */) {
pointT *point, **pointp;
facetT *facet;
realT dist;
trace1((qh, qh->ferr, 1033, "qh_outcoplanar: move outsideset to coplanarset for qh->NARROWhull\n"));
FORALLfacets {
FOREACHpoint_(facet->outsideset) {
qh->num_outside--;
if (qh->KEEPcoplanar || qh->KEEPnearinside) {
qh_distplane(qh, point, facet, &dist);
zinc_(Zpartition);
qh_partitioncoplanar(qh, point, facet, &dist);
}
}
qh_setfree(qh, &facet->outsideset);
}
} /* outcoplanar */
/*---------------------------------
qh_point(qh, id )
return point for a point id, or NULL if unknown
alternative code:
return((pointT *)((unsigned long)qh.first_point
+ (unsigned long)((id)*qh.normal_size)));
*/
pointT *qh_point(qhT *qh, int id) {
if (id < 0)
return NULL;
if (id < qh->num_points)
return qh->first_point + id * qh->hull_dim;
id -= qh->num_points;
if (id < qh_setsize(qh, qh->other_points))
return SETelemt_(qh->other_points, id, pointT);
return NULL;
} /* point */
/*---------------------------------
qh_point_add(qh, set, point, elem )
stores elem at set[point.id]
returns:
access function for qh_pointfacet and qh_pointvertex
notes:
checks point.id
*/
void qh_point_add(qhT *qh, setT *set, pointT *point, void *elem) {
int id, size;
SETreturnsize_(set, size);
if ((id= qh_pointid(qh, point)) < 0)
qh_fprintf(qh, qh->ferr, 7067, "qhull internal warning (point_add): unknown point %p id %d\n",
point, id);
else if (id >= size) {
qh_fprintf(qh, qh->ferr, 6160, "qhull internal errror(point_add): point p%d is out of bounds(%d)\n",
id, size);
qh_errexit(qh, qh_ERRqhull, NULL, NULL);
}else
SETelem_(set, id)= elem;
} /* point_add */
/*---------------------------------
qh_pointfacet()
return temporary set of facet for each point
the set is indexed by point id
notes:
vertices assigned to one of the facets
coplanarset assigned to the facet
outside set assigned to the facet
NULL if no facet for point (inside)
includes qh.GOODpointp
access:
FOREACHfacet_i_(qh, facets) { ... }
SETelem_(facets, i)
design:
for each facet
add each vertex
add each coplanar point
add each outside point
*/
setT *qh_pointfacet(qhT *qh /*qh.facet_list*/) {
int numpoints= qh->num_points + qh_setsize(qh, qh->other_points);
setT *facets;
facetT *facet;
vertexT *vertex, **vertexp;
pointT *point, **pointp;
facets= qh_settemp(qh, numpoints);
qh_setzero(qh, facets, 0, numpoints);
qh->vertex_visit++;
FORALLfacets {
FOREACHvertex_(facet->vertices) {
if (vertex->visitid != qh->vertex_visit) {
vertex->visitid= qh->vertex_visit;
qh_point_add(qh, facets, vertex->point, facet);
}
}
FOREACHpoint_(facet->coplanarset)
qh_point_add(qh, facets, point, facet);
FOREACHpoint_(facet->outsideset)
qh_point_add(qh, facets, point, facet);
}
return facets;
} /* pointfacet */
/*---------------------------------
qh_pointvertex(qh, )
return temporary set of vertices indexed by point id
entry is NULL if no vertex for a point
this will include qh.GOODpointp
access:
FOREACHvertex_i_(qh, vertices) { ... }
SETelem_(vertices, i)
*/
setT *qh_pointvertex(qhT *qh /*qh.facet_list*/) {
int numpoints= qh->num_points + qh_setsize(qh, qh->other_points);
setT *vertices;
vertexT *vertex;
vertices= qh_settemp(qh, numpoints);
qh_setzero(qh, vertices, 0, numpoints);
FORALLvertices
qh_point_add(qh, vertices, vertex->point, vertex);
return vertices;
} /* pointvertex */
/*---------------------------------
qh_prependfacet(qh, facet, facetlist )
prepend facet to the start of a facetlist
returns:
increments qh.numfacets
updates facetlist, qh.facet_list, facet_next
notes:
be careful of prepending since it can lose a pointer.
e.g., can lose _next by deleting and then prepending before _next
*/
void qh_prependfacet(qhT *qh, facetT *facet, facetT **facetlist) {
facetT *prevfacet, *list;
trace4((qh, qh->ferr, 4061, "qh_prependfacet: prepend f%d before f%d\n",
facet->id, getid_(*facetlist)));
if (!*facetlist)
(*facetlist)= qh->facet_tail;
list= *facetlist;
prevfacet= list->previous;
facet->previous= prevfacet;
if (prevfacet)
prevfacet->next= facet;
list->previous= facet;
facet->next= *facetlist;
if (qh->facet_list == list) /* this may change *facetlist */
qh->facet_list= facet;
if (qh->facet_next == list)
qh->facet_next= facet;
*facetlist= facet;
qh->num_facets++;
} /* prependfacet */
/*---------------------------------
qh_printhashtable(qh, fp )
print hash table to fp
notes:
not in I/O to avoid bringing io_r.c in
design:
for each hash entry
if defined
if unmatched or will merge (NULL, qh_MERGEridge, qh_DUPLICATEridge)
print entry and neighbors
*/
void qh_printhashtable(qhT *qh, FILE *fp) {
facetT *facet, *neighbor;
int id, facet_i, facet_n, neighbor_i= 0, neighbor_n= 0;
vertexT *vertex, **vertexp;
FOREACHfacet_i_(qh, qh->hash_table) {
if (facet) {
FOREACHneighbor_i_(qh, facet) {
if (!neighbor || neighbor == qh_MERGEridge || neighbor == qh_DUPLICATEridge)
break;
}
if (neighbor_i == neighbor_n)
continue;
qh_fprintf(qh, fp, 9283, "hash %d f%d ", facet_i, facet->id);
FOREACHvertex_(facet->vertices)
qh_fprintf(qh, fp, 9284, "v%d ", vertex->id);
qh_fprintf(qh, fp, 9285, "\n neighbors:");
FOREACHneighbor_i_(qh, facet) {
if (neighbor == qh_MERGEridge)
id= -3;
else if (neighbor == qh_DUPLICATEridge)
id= -2;
else
id= getid_(neighbor);
qh_fprintf(qh, fp, 9286, " %d", id);
}
qh_fprintf(qh, fp, 9287, "\n");
}
}
} /* printhashtable */
/*---------------------------------
qh_printlists(qh, fp )
print out facet and vertex list for debugging (without 'f/v' tags)
*/
void qh_printlists(qhT *qh) {
facetT *facet;
vertexT *vertex;
int count= 0;
qh_fprintf(qh, qh->ferr, 8108, "qh_printlists: facets:");
FORALLfacets {
if (++count % 100 == 0)
qh_fprintf(qh, qh->ferr, 8109, "\n ");
qh_fprintf(qh, qh->ferr, 8110, " %d", facet->id);
}
qh_fprintf(qh, qh->ferr, 8111, "\n new facets %d visible facets %d next facet for qh_addpoint %d\n vertices(new %d):",
getid_(qh->newfacet_list), getid_(qh->visible_list), getid_(qh->facet_next),
getid_(qh->newvertex_list));
count = 0;
FORALLvertices {
if (++count % 100 == 0)
qh_fprintf(qh, qh->ferr, 8112, "\n ");
qh_fprintf(qh, qh->ferr, 8113, " %d", vertex->id);
}
qh_fprintf(qh, qh->ferr, 8114, "\n");
} /* printlists */
/*---------------------------------
qh_resetlists(qh, stats, qh_RESETvisible )
reset newvertex_list, newfacet_list, visible_list
if stats,
maintains statistics
returns:
visible_list is empty if qh_deletevisible was called
*/
void qh_resetlists(qhT *qh, boolT stats, boolT resetVisible /*qh.newvertex_list newfacet_list visible_list*/) {
vertexT *vertex;
facetT *newfacet, *visible;
int totnew=0, totver=0;
if (stats) {
FORALLvertex_(qh->newvertex_list)
totver++;
FORALLnew_facets
totnew++;
zadd_(Zvisvertextot, totver);
zmax_(Zvisvertexmax, totver);
zadd_(Znewfacettot, totnew);
zmax_(Znewfacetmax, totnew);
}
FORALLvertex_(qh->newvertex_list)
vertex->newlist= False;
qh->newvertex_list= NULL;
FORALLnew_facets
newfacet->newfacet= False;
qh->newfacet_list= NULL;
if (resetVisible) {
FORALLvisible_facets {
visible->f.replace= NULL;
visible->visible= False;
}
qh->num_visible= 0;
}
qh->visible_list= NULL; /* may still have visible facets via qh_triangulate */
qh->NEWfacets= False;
} /* resetlists */
/*---------------------------------
qh_setvoronoi_all(qh)
compute Voronoi centers for all facets
includes upperDelaunay facets if qh.UPPERdelaunay ('Qu')
returns:
facet->center is the Voronoi center
notes:
this is unused/untested code
please email bradb@shore.net if this works ok for you
use:
FORALLvertices {...} to locate the vertex for a point.
FOREACHneighbor_(vertex) {...} to visit the Voronoi centers for a Voronoi cell.
*/
void qh_setvoronoi_all(qhT *qh) {
facetT *facet;
qh_clearcenters(qh, qh_ASvoronoi);
qh_vertexneighbors(qh);
FORALLfacets {
if (!facet->normal || !facet->upperdelaunay || qh->UPPERdelaunay) {
if (!facet->center)
facet->center= qh_facetcenter(qh, facet->vertices);
}
}
} /* setvoronoi_all */
#ifndef qh_NOmerge
/*---------------------------------
qh_triangulate()
triangulate non-simplicial facets on qh.facet_list,
if qh->VORONOI, sets Voronoi centers of non-simplicial facets
nop if hasTriangulation
returns:
all facets simplicial
each tricoplanar facet has ->f.triowner == owner of ->center,normal,etc.
notes:
call after qh_check_output since may switch to Voronoi centers
Output may overwrite ->f.triowner with ->f.area
*/
void qh_triangulate(qhT *qh /*qh.facet_list*/) {
facetT *facet, *nextfacet, *owner;
int onlygood= qh->ONLYgood;
facetT *neighbor, *visible= NULL, *facet1, *facet2, *new_facet_list= NULL;
facetT *orig_neighbor= NULL, *otherfacet;
vertexT *new_vertex_list= NULL;
mergeT *merge;
mergeType mergetype;
int neighbor_i, neighbor_n;
if (qh->hasTriangulation)
return;
trace1((qh, qh->ferr, 1034, "qh_triangulate: triangulate non-simplicial facets\n"));
if (qh->hull_dim == 2)
return;
if (qh->VORONOI) { /* otherwise lose Voronoi centers [could rebuild vertex set from tricoplanar] */
qh_clearcenters(qh, qh_ASvoronoi);
qh_vertexneighbors(qh);
}
qh->ONLYgood= False; /* for makenew_nonsimplicial */
qh->visit_id++;
qh->NEWfacets= True;
qh->degen_mergeset= qh_settemp(qh, qh->TEMPsize);
qh->newvertex_list= qh->vertex_tail;
for (facet= qh->facet_list; facet && facet->next; facet= nextfacet) { /* non-simplicial facets moved to end */
nextfacet= facet->next;
if (facet->visible || facet->simplicial)
continue;
/* triangulate all non-simplicial facets, otherwise merging does not work, e.g., RBOX c P-0.1 P+0.1 P+0.1 D3 | QHULL d Qt Tv */
if (!new_facet_list)
new_facet_list= facet; /* will be moved to end */
qh_triangulate_facet(qh, facet, &new_vertex_list);
}
trace2((qh, qh->ferr, 2047, "qh_triangulate: delete null facets from f%d -- apex same as second vertex\n", getid_(new_facet_list)));
for (facet= new_facet_list; facet && facet->next; facet= nextfacet) { /* null facets moved to end */
nextfacet= facet->next;
if (facet->visible)
continue;
if (facet->ridges) {
if (qh_setsize(qh, facet->ridges) > 0) {
qh_fprintf(qh, qh->ferr, 6161, "qhull error (qh_triangulate): ridges still defined for f%d\n", facet->id);
qh_errexit(qh, qh_ERRqhull, facet, NULL);
}
qh_setfree(qh, &facet->ridges);
}
if (SETfirst_(facet->vertices) == SETsecond_(facet->vertices)) {
zinc_(Ztrinull);
qh_triangulate_null(qh, facet);
}
}
trace2((qh, qh->ferr, 2048, "qh_triangulate: delete %d or more mirror facets -- same vertices and neighbors\n", qh_setsize(qh, qh->degen_mergeset)));
qh->visible_list= qh->facet_tail;
while ((merge= (mergeT*)qh_setdellast(qh->degen_mergeset))) {
facet1= merge->facet1;
facet2= merge->facet2;
mergetype= merge->type;
qh_memfree(qh, merge, (int)sizeof(mergeT));
if (mergetype == MRGmirror) {
zinc_(Ztrimirror);
qh_triangulate_mirror(qh, facet1, facet2);
}
}
qh_settempfree(qh, &qh->degen_mergeset);
trace2((qh, qh->ferr, 2049, "qh_triangulate: update neighbor lists for vertices from v%d\n", getid_(new_vertex_list)));
qh->newvertex_list= new_vertex_list; /* all vertices of new facets */
qh->visible_list= NULL;
qh_updatevertices(qh /*qh.newvertex_list, empty newfacet_list and visible_list*/);
qh_resetlists(qh, False, !qh_RESETvisible /*qh.newvertex_list, empty newfacet_list and visible_list*/);
trace2((qh, qh->ferr, 2050, "qh_triangulate: identify degenerate tricoplanar facets from f%d\n", getid_(new_facet_list)));
trace2((qh, qh->ferr, 2051, "qh_triangulate: and replace facet->f.triowner with tricoplanar facets that own center, normal, etc.\n"));
FORALLfacet_(new_facet_list) {
if (facet->tricoplanar && !facet->visible) {
FOREACHneighbor_i_(qh, facet) {
if (neighbor_i == 0) { /* first iteration */
if (neighbor->tricoplanar)
orig_neighbor= neighbor->f.triowner;
else
orig_neighbor= neighbor;
}else {
if (neighbor->tricoplanar)
otherfacet= neighbor->f.triowner;
else
otherfacet= neighbor;
if (orig_neighbor == otherfacet) {
zinc_(Ztridegen);
facet->degenerate= True;
break;
}
}
}
}
}
trace2((qh, qh->ferr, 2052, "qh_triangulate: delete visible facets -- non-simplicial, null, and mirrored facets\n"));
owner= NULL;
visible= NULL;
for (facet= new_facet_list; facet && facet->next; facet= nextfacet) { /* may delete facet */
nextfacet= facet->next;
if (facet->visible) {
if (facet->tricoplanar) { /* a null or mirrored facet */
qh_delfacet(qh, facet);
qh->num_visible--;
}else { /* a non-simplicial facet followed by its tricoplanars */
if (visible && !owner) {
/* RBOX 200 s D5 t1001471447 | QHULL Qt C-0.01 Qx Qc Tv Qt -- f4483 had 6 vertices/neighbors and 8 ridges */
trace2((qh, qh->ferr, 2053, "qh_triangulate: all tricoplanar facets degenerate for non-simplicial facet f%d\n",
visible->id));
qh_delfacet(qh, visible);
qh->num_visible--;
}
visible= facet;
owner= NULL;
}
}else if (facet->tricoplanar) {
if (facet->f.triowner != visible || visible==NULL) {
qh_fprintf(qh, qh->ferr, 6162, "qhull error (qh_triangulate): tricoplanar facet f%d not owned by its visible, non-simplicial facet f%d\n", facet->id, getid_(visible));
qh_errexit2(qh, qh_ERRqhull, facet, visible);
}
if (owner)
facet->f.triowner= owner;
else if (!facet->degenerate) {
owner= facet;
nextfacet= visible->next; /* rescan tricoplanar facets with owner, visible!=0 by QH6162 */
facet->keepcentrum= True; /* one facet owns ->normal, etc. */
facet->coplanarset= visible->coplanarset;
facet->outsideset= visible->outsideset;
visible->coplanarset= NULL;
visible->outsideset= NULL;
if (!qh->TRInormals) { /* center and normal copied to tricoplanar facets */
visible->center= NULL;
visible->normal= NULL;
}
qh_delfacet(qh, visible);
qh->num_visible--;
}
}
}
if (visible && !owner) {
trace2((qh, qh->ferr, 2054, "qh_triangulate: all tricoplanar facets degenerate for last non-simplicial facet f%d\n",
visible->id));
qh_delfacet(qh, visible);
qh->num_visible--;
}
qh->NEWfacets= False;
qh->ONLYgood= onlygood; /* restore value */
if (qh->CHECKfrequently)
qh_checkpolygon(qh, qh->facet_list);
qh->hasTriangulation= True;
} /* triangulate */
/*---------------------------------
qh_triangulate_facet(qh, facetA, &firstVertex )
triangulate a non-simplicial facet
if qh.CENTERtype=qh_ASvoronoi, sets its Voronoi center
returns:
qh.newfacet_list == simplicial facets
facet->tricoplanar set and ->keepcentrum false
facet->degenerate set if duplicated apex
facet->f.trivisible set to facetA
facet->center copied from facetA (created if qh_ASvoronoi)
qh_eachvoronoi, qh_detvridge, qh_detvridge3 assume centers copied
facet->normal,offset,maxoutside copied from facetA
notes:
only called by qh_triangulate
qh_makenew_nonsimplicial uses neighbor->seen for the same
if qh.TRInormals, newfacet->normal will need qh_free
if qh.TRInormals and qh_AScentrum, newfacet->center will need qh_free
keepcentrum is also set on Zwidefacet in qh_mergefacet
freed by qh_clearcenters
see also:
qh_addpoint() -- add a point
qh_makenewfacets() -- construct a cone of facets for a new vertex
design:
if qh_ASvoronoi,
compute Voronoi center (facet->center)
select first vertex (highest ID to preserve ID ordering of ->vertices)
triangulate from vertex to ridges
copy facet->center, normal, offset
update vertex neighbors
*/
void qh_triangulate_facet(qhT *qh, facetT *facetA, vertexT **first_vertex) {
facetT *newfacet;
facetT *neighbor, **neighborp;
vertexT *apex;
int numnew=0;
trace3((qh, qh->ferr, 3020, "qh_triangulate_facet: triangulate facet f%d\n", facetA->id));
if (qh->IStracing >= 4)
qh_printfacet(qh, qh->ferr, facetA);
FOREACHneighbor_(facetA) {
neighbor->seen= False;
neighbor->coplanar= False;
}
if (qh->CENTERtype == qh_ASvoronoi && !facetA->center /* matches upperdelaunay in qh_setfacetplane() */
&& fabs_(facetA->normal[qh->hull_dim -1]) >= qh->ANGLEround * qh_ZEROdelaunay) {
facetA->center= qh_facetcenter(qh, facetA->vertices);
}
qh_willdelete(qh, facetA, NULL);
qh->newfacet_list= qh->facet_tail;
facetA->visitid= qh->visit_id;
apex= SETfirstt_(facetA->vertices, vertexT);
qh_makenew_nonsimplicial(qh, facetA, apex, &numnew);
SETfirst_(facetA->neighbors)= NULL;
FORALLnew_facets {
newfacet->tricoplanar= True;
newfacet->f.trivisible= facetA;
newfacet->degenerate= False;
newfacet->upperdelaunay= facetA->upperdelaunay;
newfacet->good= facetA->good;
if (qh->TRInormals) { /* 'Q11' triangulate duplicates ->normal and ->center */
newfacet->keepcentrum= True;
if(facetA->normal){
newfacet->normal= qh_memalloc(qh, qh->normal_size);
memcpy((char *)newfacet->normal, facetA->normal, qh->normal_size);
}
if (qh->CENTERtype == qh_AScentrum)
newfacet->center= qh_getcentrum(qh, newfacet);
else if (qh->CENTERtype == qh_ASvoronoi && facetA->center){
newfacet->center= qh_memalloc(qh, qh->center_size);
memcpy((char *)newfacet->center, facetA->center, qh->center_size);
}
}else {
newfacet->keepcentrum= False;
/* one facet will have keepcentrum=True at end of qh_triangulate */
newfacet->normal= facetA->normal;
newfacet->center= facetA->center;
}
newfacet->offset= facetA->offset;
#if qh_MAXoutside
newfacet->maxoutside= facetA->maxoutside;
#endif
}
qh_matchnewfacets(qh /*qh.newfacet_list*/);
zinc_(Ztricoplanar);
zadd_(Ztricoplanartot, numnew);
zmax_(Ztricoplanarmax, numnew);
qh->visible_list= NULL;
if (!(*first_vertex))
(*first_vertex)= qh->newvertex_list;
qh->newvertex_list= NULL;
qh_updatevertices(qh /*qh.newfacet_list, qh.empty visible_list and qh.newvertex_list*/);
qh_resetlists(qh, False, !qh_RESETvisible /*qh.newfacet_list, qh.empty visible_list and qh.newvertex_list*/);
} /* triangulate_facet */
/*---------------------------------
qh_triangulate_link(qh, oldfacetA, facetA, oldfacetB, facetB)
relink facetA to facetB via oldfacets
returns:
adds mirror facets to qh->degen_mergeset (4-d and up only)
design:
if they are already neighbors, the opposing neighbors become MRGmirror facets
*/
void qh_triangulate_link(qhT *qh, facetT *oldfacetA, facetT *facetA, facetT *oldfacetB, facetT *facetB) {
int errmirror= False;
trace3((qh, qh->ferr, 3021, "qh_triangulate_link: relink old facets f%d and f%d between neighbors f%d and f%d\n",
oldfacetA->id, oldfacetB->id, facetA->id, facetB->id));
if (qh_setin(facetA->neighbors, facetB)) {
if (!qh_setin(facetB->neighbors, facetA))
errmirror= True;
else
qh_appendmergeset(qh, facetA, facetB, MRGmirror, NULL);
}else if (qh_setin(facetB->neighbors, facetA))
errmirror= True;
if (errmirror) {
qh_fprintf(qh, qh->ferr, 6163, "qhull error (qh_triangulate_link): mirror facets f%d and f%d do not match for old facets f%d and f%d\n",
facetA->id, facetB->id, oldfacetA->id, oldfacetB->id);
qh_errexit2(qh, qh_ERRqhull, facetA, facetB);
}
qh_setreplace(qh, facetB->neighbors, oldfacetB, facetA);
qh_setreplace(qh, facetA->neighbors, oldfacetA, facetB);
} /* triangulate_link */
/*---------------------------------
qh_triangulate_mirror(qh, facetA, facetB)
delete mirrored facets from qh_triangulate_null() and qh_triangulate_mirror
a mirrored facet shares the same vertices of a logical ridge
design:
since a null facet duplicates the first two vertices, the opposing neighbors absorb the null facet
if they are already neighbors, the opposing neighbors become MRGmirror facets
*/
void qh_triangulate_mirror(qhT *qh, facetT *facetA, facetT *facetB) {
facetT *neighbor, *neighborB;
int neighbor_i, neighbor_n;
trace3((qh, qh->ferr, 3022, "qh_triangulate_mirror: delete mirrored facets f%d and f%d\n",
facetA->id, facetB->id));
FOREACHneighbor_i_(qh, facetA) {
neighborB= SETelemt_(facetB->neighbors, neighbor_i, facetT);
if (neighbor == neighborB)
continue; /* occurs twice */
qh_triangulate_link(qh, facetA, neighbor, facetB, neighborB);
}
qh_willdelete(qh, facetA, NULL);
qh_willdelete(qh, facetB, NULL);
} /* triangulate_mirror */
/*---------------------------------
qh_triangulate_null(qh, facetA)
remove null facetA from qh_triangulate_facet()
a null facet has vertex #1 (apex) == vertex #2
returns:
adds facetA to ->visible for deletion after qh_updatevertices
qh->degen_mergeset contains mirror facets (4-d and up only)
design:
since a null facet duplicates the first two vertices, the opposing neighbors absorb the null facet
if they are already neighbors, the opposing neighbors become MRGmirror facets
*/
void qh_triangulate_null(qhT *qh, facetT *facetA) {
facetT *neighbor, *otherfacet;
trace3((qh, qh->ferr, 3023, "qh_triangulate_null: delete null facet f%d\n", facetA->id));
neighbor= SETfirstt_(facetA->neighbors, facetT);
otherfacet= SETsecondt_(facetA->neighbors, facetT);
qh_triangulate_link(qh, facetA, neighbor, facetA, otherfacet);
qh_willdelete(qh, facetA, NULL);
} /* triangulate_null */
#else /* qh_NOmerge */
void qh_triangulate(qhT *qh) {
}
#endif /* qh_NOmerge */
/*---------------------------------
qh_vertexintersect(qh, vertexsetA, vertexsetB )
intersects two vertex sets (inverse id ordered)
vertexsetA is a temporary set at the top of qh->qhmem.tempstack
returns:
replaces vertexsetA with the intersection
notes:
could overwrite vertexsetA if currently too slow
*/
void qh_vertexintersect(qhT *qh, setT **vertexsetA,setT *vertexsetB) {
setT *intersection;
intersection= qh_vertexintersect_new(qh, *vertexsetA, vertexsetB);
qh_settempfree(qh, vertexsetA);
*vertexsetA= intersection;
qh_settemppush(qh, intersection);
} /* vertexintersect */
/*---------------------------------
qh_vertexintersect_new(qh, )
intersects two vertex sets (inverse id ordered)
returns:
a new set
*/
setT *qh_vertexintersect_new(qhT *qh, setT *vertexsetA,setT *vertexsetB) {
setT *intersection= qh_setnew(qh, qh->hull_dim - 1);
vertexT **vertexA= SETaddr_(vertexsetA, vertexT);
vertexT **vertexB= SETaddr_(vertexsetB, vertexT);
while (*vertexA && *vertexB) {
if (*vertexA == *vertexB) {
qh_setappend(qh, &intersection, *vertexA);
vertexA++; vertexB++;
}else {
if ((*vertexA)->id > (*vertexB)->id)
vertexA++;
else
vertexB++;
}
}
return intersection;
} /* vertexintersect_new */
/*---------------------------------
qh_vertexneighbors(qh)
for each vertex in qh.facet_list,
determine its neighboring facets
returns:
sets qh.VERTEXneighbors
nop if qh.VERTEXneighbors already set
qh_addpoint() will maintain them
notes:
assumes all vertex->neighbors are NULL
design:
for each facet
for each vertex
append facet to vertex->neighbors
*/
void qh_vertexneighbors(qhT *qh /*qh.facet_list*/) {
facetT *facet;
vertexT *vertex, **vertexp;
if (qh->VERTEXneighbors)
return;
trace1((qh, qh->ferr, 1035, "qh_vertexneighbors: determining neighboring facets for each vertex\n"));
qh->vertex_visit++;
FORALLfacets {
if (facet->visible)
continue;
FOREACHvertex_(facet->vertices) {
if (vertex->visitid != qh->vertex_visit) {
vertex->visitid= qh->vertex_visit;
vertex->neighbors= qh_setnew(qh, qh->hull_dim);
}
qh_setappend(qh, &vertex->neighbors, facet);
}
}
qh->VERTEXneighbors= True;
} /* vertexneighbors */
/*---------------------------------
qh_vertexsubset( vertexsetA, vertexsetB )
returns True if vertexsetA is a subset of vertexsetB
assumes vertexsets are sorted
note:
empty set is a subset of any other set
*/
boolT qh_vertexsubset(setT *vertexsetA, setT *vertexsetB) {
vertexT **vertexA= (vertexT **) SETaddr_(vertexsetA, vertexT);
vertexT **vertexB= (vertexT **) SETaddr_(vertexsetB, vertexT);
while (True) {
if (!*vertexA)
return True;
if (!*vertexB)
return False;
if ((*vertexA)->id > (*vertexB)->id)
return False;
if (*vertexA == *vertexB)
vertexA++;
vertexB++;
}
return False; /* avoid warnings */
} /* vertexsubset */