/* ---------------------------------
poly2.c
implements polygons and simplices
see qh-poly.htm, poly.h and qhull.h
frequently used code is in poly.c
copyright (c) 1993-2001, The Geometry Center
*/
#include "qhull_a.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, unsigned 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()
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:
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 (void) {
boolT waserror= False, isoutside, unassigned;
facetT *facet, *bestfacet, *errfacet1= NULL, *errfacet2= NULL;
facetT *facetlist;
realT dist, maxoutside, maxdist= -REALmax;
pointT *point;
int numpart, facet_i, facet_n, notgood= 0, notverified= 0;
setT *facets;
trace1((qh ferr, "qh_check_bestdist: check points below nearest facet. Facet_list f%d\n",
qh facet_list->id));
maxoutside= qh_maxouter();
maxoutside += qh DISTround;
/* one more qh.DISTround for check computation */
trace1((qh ferr, "qh_check_bestdist: check that all points are within %2.2g of best facet\n", maxoutside));
facets= qh_pointfacet (/*qh facet_list*/);
if (!qh_QUICKhelp && qh PRINTprecision)
fprintf (qh ferr, "\n\
qhull output completed. Verifying that %d points are\n\
below %2.2g of the nearest %sfacet.\n",
qh_setsize(facets), maxoutside, (qh ONLYgood ? "good " : ""));
FOREACHfacet_i_(facets) { /* for each point with facet assignment */
if (facet)
unassigned= False;
else {
unassigned= True;
facet= qh facet_list;
}
point= qh_point(facet_i);
if (point == qh GOODpointp)
continue;
bestfacet= qh_findbest (point, facet, qh_ALL, False, !qh_NOupper,
&dist, &isoutside, &numpart);
/* occurs after statistics reported */
maximize_(maxdist, dist);
if (dist > maxoutside) {
if (qh ONLYgood && !bestfacet->good
&& !((bestfacet= qh_findgooddist (point, bestfacet, &dist, &facetlist))
&& dist > maxoutside))
notgood++;
else {
waserror= True;
fprintf(qh ferr, "qhull precision error: point p%d is outside facet f%d, distance= %6.8g maxoutside= %6.8g\n",
facet_i, bestfacet->id, dist, maxoutside);
errfacet2= errfacet1;
errfacet1= bestfacet;
}
}else if (unassigned && dist < -qh MAXcoplanar)
notverified++;
}
qh_settempfree (&facets);
if (notverified && !qh DELAUNAY && !qh_QUICKhelp && qh PRINTprecision)
fprintf(qh ferr, "\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) {
fprintf( qh ferr, "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_ERRprec, errfacet1, errfacet2);
}else if (waserror && qh outside_err > REALmax/2)
qh_errexit2 (qh_ERRprec, errfacet1, errfacet2);
else if (waserror)
; /* the error was logged to qh_errlog() but does not effect the output */
trace0((qh ferr, "qh_check_bestdist: max distance outside %2.2g\n", maxdist));
} /* check_bestdist */
/*---------------------------------
qh_check_maxout()
updates qh.max_outside by checking all points against bestfacet
if qh.ONLYgood, ignores !good facets
returns:
updates facet->maxoutside via qh_findbest()
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 (void) {
facetT *facet, *bestfacet, *neighbor, **neighborp, *facetlist;
realT dist, maxoutside, minvertex;
pointT *point;
int numpart, facet_i, facet_n, notgood= 0;
setT *facets, *vertices;
vertexT *vertex;
trace1((qh ferr, "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 ferr, "qh_check_maxout: determine actual maxoutside and minvertex\n"));
vertices= qh_pointvertex (/*qh facet_list*/);
FORALLvertices {
FOREACHneighbor_(vertex) {
zinc_(Zdistvertex); /* distance also computed by main loop below */
qh_distplane (vertex->point, neighbor, &dist);
minimize_(minvertex, dist);
if (-dist > qh TRACEdist || dist > qh TRACEdist
|| neighbor == qh tracefacet || vertex == qh tracevertex)
fprintf (qh ferr, "qh_check_maxout: p%d (v%d) is %.2g from f%d\n",
qh_pointid (vertex->point), vertex->id, dist, neighbor->id);
}
}
if (qh MERGING) {
wmin_(Wminvertex, qh min_vertex);
}
qh min_vertex= minvertex;
qh_settempfree (&vertices);
}
facets= qh_pointfacet (/*qh facet_list*/);
FOREACHfacet_i_(facets) { /* for each point with facet assignment */
if (facet) {
point= qh_point(facet_i);
if (point == qh GOODpointp)
continue;
zinc_(Ztotcheck);
bestfacet= qh_findbest (point, facet, qh_ALL, False, !qh_NOupper,
&dist, NULL, &numpart);
zadd_(Zcheckpart, numpart);
if (bestfacet && dist > maxoutside) {
if (qh ONLYgood && !bestfacet->good
&& !((bestfacet= qh_findgooddist (point, bestfacet, &dist, &facetlist))
&& dist > maxoutside))
notgood++;
else
maxoutside= dist;
}
if (dist > qh TRACEdist || (bestfacet && bestfacet == qh tracefacet))
fprintf (qh ferr, "qh_check_maxout: p%d is %.2g above f%d\n",
qh_pointid (point), dist, bestfacet->id);
}
}
qh_settempfree (&facets);
wval_(Wmaxout)= maxoutside - qh max_outside;
wmax_(Wmaxoutside, qh max_outside);
qh max_outside= maxoutside;
qh_nearcoplanar (/*qh.facet_list*/);
qh maxoutdone= True;
trace1((qh ferr, "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 (void) {
}
#endif
/*---------------------------------
qh_check_output()
performs the checks at the end of qhull algorithm
*/
void qh_check_output (void) {
int i;
if (qh STOPcone)
return;
if (qh VERIFYoutput | qh IStracing | qh CHECKfrequently) {
qh_checkpolygon (qh facet_list);
qh_checkflipped_all (qh facet_list);
qh_checkconvex (qh facet_list, qh_ALGORITHMfault);
}else if (!qh MERGING && qh_newstats (qhstat precision, &i)) {
qh_checkflipped_all (qh facet_list);
qh_checkconvex (qh facet_list, qh_ALGORITHMfault);
}
} /* check_output */
/*---------------------------------
qh_check_point( point, facet, maxoutside, maxdist, errfacet1, errfacet2 )
check that point is less than maxoutside from facet
*/
void qh_check_point (pointT *point, facetT *facet, realT *maxoutside, realT *maxdist, facetT **errfacet1, facetT **errfacet2) {
realT dist;
/* occurs after statistics reported */
qh_distplane(point, facet, &dist);
if (dist > *maxoutside) {
*errfacet2= *errfacet1;
*errfacet1= facet;
fprintf(qh ferr, "qhull precision error: point p%d is outside facet f%d, distance= %6.8g maxoutside= %6.8g\n",
qh_pointid(point), facet->id, dist, *maxoutside);
}
maximize_(*maxdist, dist);
} /* qh_check_point */
/*---------------------------------
qh_check_points()
checks that all points are inside all facets
notes:
uses qh_findbest if lots of points
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 (void) {
facetT *facet, *errfacet1= NULL, *errfacet2= NULL;
realT total, maxoutside, maxdist= -REALmax;
pointT *point, **pointp, *pointtemp;
boolT testouter;
maxoutside= qh_maxouter();
maxoutside += qh DISTround;
/* one more qh.DISTround for check computation */
trace1((qh ferr, "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 * qh num_points;
else
total= (float) qh num_facets * qh num_points;
if (total >= qh_VERIFYdirect && !qh maxoutdone) {
if (!qh_QUICKhelp && qh SKIPcheckmax && qh MERGING)
fprintf (qh ferr, "\n\
qhull input warning: merging without checking outer planes ('Q5').\n\
Verify may report that a point is outside of a facet.\n");
qh_check_bestdist();
}else {
if (qh_MAXoutside && qh maxoutdone)
testouter= True;
else
testouter= False;
if (!qh_QUICKhelp) {
if (qh MERGEexact)
fprintf (qh ferr, "\n\
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)
fprintf (qh ferr, "\n\
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)
fprintf (qh ferr, "\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
fprintf (qh ferr, "\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 (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 (point, facet, &maxoutside, &maxdist, &errfacet1, &errfacet2);
}
FOREACHpoint_(qh other_points) {
if (point != qh GOODpointp)
qh_check_point (point, facet, &maxoutside, &maxdist, &errfacet1, &errfacet2);
}
}
if (maxdist > qh outside_err) {
fprintf( qh ferr, "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_ERRprec, errfacet1, errfacet2 );
}else if (errfacet1 && qh outside_err > REALmax/2)
qh_errexit2( qh_ERRprec, errfacet1, errfacet2 );
else if (errfacet1)
; /* the error was logged to qh.ferr but does not effect the output */
trace0((qh ferr, "qh_check_points: max distance outside %2.2g\n", maxdist));
}
} /* check_points */
/*---------------------------------
qh_checkconvex( 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(facetT *facetlist, int fault) {
facetT *facet, *neighbor, **neighborp, *errfacet1=NULL, *errfacet2=NULL;
vertexT *vertex;
realT dist;
pointT *centrum;
boolT waserror= False, tempcentrum= False, allsimplicial;
int neighbor_i;
trace1((qh ferr, "qh_checkconvex: check all ridges are convex\n"));
if (!qh RERUN) {
zzval_(Zconcaveridges)= 0;
zzval_(Zcoplanarridges)= 0;
}
FORALLfacet_(facetlist) {
if (facet->flipped) {
qh_precision ("flipped facet");
fprintf (qh ferr, "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))
allsimplicial= False;
else {
allsimplicial= True;
neighbor_i= 0;
FOREACHneighbor_(facet) {
vertex= SETelemt_(facet->vertices, neighbor_i++, vertexT);
if (!neighbor->simplicial) {
allsimplicial= False;
continue;
}
qh_distplane (vertex->point, neighbor, &dist);
if (dist > -qh DISTround) {
if (fault == qh_DATAfault) {
qh_precision ("coplanar or concave ridge");
fprintf (qh ferr, "qhull precision error: initial simplex is not convex. Distance=%.2g\n", dist);
qh_errexit(qh_ERRsingular, NULL, NULL);
}
if (dist > qh DISTround) {
zzinc_(Zconcaveridges);
qh_precision ("concave ridge");
fprintf (qh ferr, "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(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 ("coplanar ridge");
fprintf (qh ferr, "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(vertex->point), vertex->id, dist);
errfacet1= facet;
errfacet2= neighbor;
waserror= True;
}
}else {
zzinc_(Zcoplanarridges);
qh_precision ("coplanar ridge");
trace0((qh ferr, "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(vertex->point), vertex->id, dist, qh furthest_id));
}
}
}
}
if (!allsimplicial) {
if (qh CENTERtype == qh_AScentrum) {
if (!facet->center)
facet->center= qh_getcentrum (facet);
centrum= facet->center;
}else {
centrum= qh_getcentrum(facet);
tempcentrum= True;
}
FOREACHneighbor_(facet) {
if (qh ZEROcentrum && facet->simplicial && neighbor->simplicial)
continue;
zzinc_(Zdistconvex);
qh_distplane (centrum, neighbor, &dist);
if (dist > qh DISTround) {
zzinc_(Zconcaveridges);
qh_precision ("concave ridge");
fprintf (qh ferr, "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 ("coplanar ridge");
fprintf (qh ferr, "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(centrum, qh normal_size);
}
}
if (waserror && !qh FORCEoutput)
qh_errexit2 (qh_ERRprec, errfacet1, errfacet2);
} /* checkconvex */
/*---------------------------------
qh_checkfacet( facet, newmerge, waserror )
checks for consistency errors in facet
newmerge set if from merge.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(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) {
fprintf (qh ferr, "qhull internal error (qh_checkfacet): facet f%d is on the visible_list\n",
facet->id);
qh_errexit (qh_ERRqhull, facet, NULL);
}
if (!facet->normal) {
fprintf (qh ferr, "qhull internal error (qh_checkfacet): facet f%d does not have a normal\n",
facet->id);
waserror= True;
}
qh_setcheck (facet->vertices, "vertices for f", facet->id);
qh_setcheck (facet->ridges, "ridges for f", facet->id);
qh_setcheck (facet->outsideset, "outsideset for f", facet->id);
qh_setcheck (facet->coplanarset, "coplanarset for f", facet->id);
qh_setcheck (facet->neighbors, "neighbors for f", facet->id);
FOREACHvertex_(facet->vertices) {
if (vertex->deleted) {
fprintf(qh ferr, "qhull internal error (qh_checkfacet): deleted vertex v%d in f%d\n", vertex->id, facet->id);
qh_errprint ("ERRONEOUS", NULL, NULL, NULL, vertex);
waserror= True;
}
if (vertex->id >= previousid) {
fprintf(qh ferr, "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(facet->neighbors);
numvertices= qh_setsize(facet->vertices);
numridges= qh_setsize(facet->ridges);
if (facet->simplicial) {
if (numvertices+numneighbors != 2*qh hull_dim
&& !facet->degenerate && !facet->redundant) {
fprintf(qh ferr, "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 ferr, "", facet->neighbors);
waserror= True;
}
}else { /* non-simplicial */
if (!newmerge
&&(numvertices < qh hull_dim || numneighbors < qh hull_dim)
&& !facet->degenerate && !facet->redundant) {
fprintf(qh ferr, "qhull internal error (qh_checkfacet): for facet f%d, #vertices %d or #neighbors %d < qh hull_dim\n",
facet->id, numvertices, numneighbors);
waserror= True;
}
if (numridges < numneighbors
||(qh hull_dim == 3 && numvertices != numridges && !qh NEWfacets)
||(qh hull_dim == 2 && numridges + numvertices + numneighbors != 6)) {
if (!facet->degenerate && !facet->redundant) {
fprintf(qh ferr, "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) {
fprintf(qh ferr, "qhull internal error (qh_checkfacet): facet f%d still has a MERGE or DUP neighbor\n", facet->id);
qh_errexit (qh_ERRqhull, facet, NULL);
}
neighbor->seen= True;
}
FOREACHneighbor_(facet) {
if (!qh_setin(neighbor->neighbors, facet)) {
fprintf(qh ferr, "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) {
fprintf(qh ferr, "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 (ridge->vertices, "vertices for r", ridge->id);
ridge->seen= False;
}
FOREACHridge_(facet->ridges) {
if (ridge->seen) {
fprintf(qh ferr, "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(ridge->vertices);
if (numRvertices != qh hull_dim - 1) {
fprintf(qh ferr, "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)) {
fprintf(qh ferr, "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) {
fprintf(qh ferr, "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(facet->vertices, neighbor->vertices);
qh_settemppush (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) {
fprintf (qh ferr, "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_ERRqhull, facet, ridge);
}
vertex->seen2= True;
}
}
if (!newmerge) {
FOREACHvertex_(intersection) {
if (!vertex->seen2) {
if (qh IStracing >=3 || !qh MERGING) {
fprintf (qh ferr, "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 ("ERRONEOUS", facet, neighbor, NULL, vertex);
if (!qh MERGING)
qh_errexit (qh_ERRqhull, NULL, NULL);
}
}
}
}
}
qh_settempfree (&intersection);
}
}else { /* simplicial */
FOREACHneighbor_(facet) {
if (neighbor->simplicial) {
skipA= SETindex_(facet->neighbors, neighbor);
skipB= qh_setindex (neighbor->neighbors, facet);
if (!qh_setequal_skip (facet->vertices, skipA, neighbor->vertices, skipB)) {
fprintf (qh ferr, "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_(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)) {
fprintf (qh ferr, "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("ERRONEOUS", facet, errother, errridge, NULL);
*waserrorp= True;
}
} /* checkfacet */
/*---------------------------------
qh_checkflipped_all( facetlist )
checks orientation of facets in list against interior point
*/
void qh_checkflipped_all (facetT *facetlist) {
facetT *facet;
boolT waserror= False;
realT dist;
if (facetlist == qh facet_list)
zzval_(Zflippedfacets)= 0;
FORALLfacet_(facetlist) {
if (facet->normal && !qh_checkflipped (facet, &dist, !qh_ALL)) {
fprintf(qh ferr, "qhull precision error: facet f%d is flipped, distance= %6.12g\n",
facet->id, dist);
if (!qh FORCEoutput) {
qh_errprint("ERRONEOUS", facet, NULL, NULL, NULL);
waserror= True;
}
}
}
if (waserror) {
fprintf (qh ferr, "\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_ERRprec, NULL, NULL);
}
} /* checkflipped_all */
/*---------------------------------
qh_checkpolygon( 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(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 ferr, "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 (facet->outsideset)
&& !(qh NARROWhull && qh CHECKfrequently)) {
fprintf (qh ferr, "qhull internal error (qh_checkpolygon): f%d has outside set before qh facet_next\n",
facet->id);
qh_errexit (qh_ERRqhull, facet, NULL);
}
}
numfacets++;
qh_checkfacet(facet, False, &waserror);
}
}
if (qh visible_list && !visibleseen && facetlist == qh facet_list) {
fprintf (qh ferr, "qhull internal error (qh_checkpolygon): visible list f%d no longer on facet list\n", qh visible_list->id);
qh_printlists();
qh_errexit (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 (facet->ridges);
FOREACHvertex_(facet->vertices) {
vertex->visitid++;
if (!vertex->seen) {
vertex->seen= True;
numvertices++;
if (qh_pointid (vertex->point) == -1) {
fprintf (qh ferr, "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 += numfacets;
if (facetlist == qh facet_list) {
if (numfacets != qh num_facets - qh num_visible) {
fprintf(qh ferr, "qhull internal error (qh_checkpolygon): actual number of facets is %d, cumulative facet count is %d\n",
numfacets, qh num_facets- qh num_visible);
waserror= True;
}
qh vertex_visit++;
if (qh VERTEXneighbors) {
FORALLvertices {
qh_setcheck (vertex->neighbors, "neighbors for v", vertex->id);
if (vertex->deleted)
continue;
totvneighbors += qh_setsize (vertex->neighbors);
}
FORALLfacet_(facetlist)
totvertices += qh_setsize (facet->vertices);
if (totvneighbors != totvertices) {
fprintf(qh ferr, "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 del_vertices)) {
fprintf(qh ferr, "qhull internal error (qh_checkpolygon): actual number of vertices is %d, cumulative vertex count is %d\n",
numvertices, qh num_vertices - qh_setsize(qh del_vertices));
waserror= True;
}
if (qh hull_dim == 2 && numvertices != numfacets) {
fprintf (qh ferr, "qhull internal error (qh_checkpolygon): #vertices %d != #facets %d\n",
numvertices, numfacets);
waserror= True;
}
if (qh hull_dim == 3 && numvertices + numfacets - numridges/2 != 2) {
fprintf (qh ferr, "qhull internal error (qh_checkpolygon): #vertices %d + #facets %d - #edges %d != 2\n",
numvertices, numfacets, numridges/2);
waserror= True;
}
}
if (waserror)
qh_errexit(qh_ERRqhull, NULL, NULL);
} /* checkpolygon */
/*---------------------------------
qh_checkvertex( vertex )
check vertex for consistency
checks vertex->neighbors
notes:
neighbors checked efficiently in checkpolygon
*/
void qh_checkvertex (vertexT *vertex) {
boolT waserror= False;
facetT *neighbor, **neighborp, *errfacet=NULL;
if (qh_pointid (vertex->point) == -1) {
fprintf (qh ferr, "qhull internal error (qh_checkvertex): unknown point id %p\n", vertex->point);
waserror= True;
}
if (vertex->id >= qh vertex_id) {
fprintf (qh ferr, "qhull internal error (qh_checkvertex): unknown vertex id %d\n", vertex->id);
waserror= True;
}
if (!waserror && !vertex->deleted) {
if (qh_setsize (vertex->neighbors)) {
FOREACHneighbor_(vertex) {
if (!qh_setin (neighbor->vertices, vertex)) {
fprintf (qh ferr, "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 ("ERRONEOUS", NULL, NULL, NULL, vertex);
qh_errexit (qh_ERRqhull, errfacet, NULL);
}
} /* checkvertex */
/*---------------------------------
qh_clearcenters( type )
clear old data from facet->center
notes:
sets new centertype
nop if CENTERtype is the same
*/
void qh_clearcenters (qh_CENTER type) {
facetT *facet;
if (qh CENTERtype != type) {
FORALLfacets {
if (qh CENTERtype == qh_ASvoronoi){
if (facet->center) {
qh_memfree (facet->center, qh center_size);
facet->center= NULL;
}
}else /* qh CENTERtype == qh_AScentrum */ {
if (facet->center) {
qh_memfree (facet->center, qh normal_size);
facet->center= NULL;
}
}
}
qh CENTERtype= type;
}
trace2((qh ferr, "qh_clearcenters: switched to center type %d\n", type));
} /* clearcenters */
/*---------------------------------
qh_createsimplex( 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(setT *vertices) {
facetT *facet= NULL, *newfacet;
boolT toporient= True;
int vertex_i, vertex_n, nth;
setT *newfacets= qh_settemp (qh hull_dim+1);
vertexT *vertex;
qh facet_list= qh newfacet_list= qh facet_tail= qh_newfacet();
qh num_facets= qh num_vertices= 0;
qh vertex_list= qh newvertex_list= qh vertex_tail= qh_newvertex(NULL);
FOREACHvertex_i_(vertices) {
newfacet= qh_newfacet();
newfacet->vertices= qh_setnew_delnthsorted (vertices, vertex_n,
vertex_i, 0);
newfacet->toporient= toporient;
qh_appendfacet(newfacet);
newfacet->newfacet= True;
qh_appendvertex (vertex);
qh_setappend (&newfacets, newfacet);
toporient ^= True;
}
FORALLnew_facets {
nth= 0;
FORALLfacet_(qh newfacet_list) {
if (facet != newfacet)
SETelem_(newfacet->neighbors, nth++)= facet;
}
qh_settruncate (newfacet->neighbors, qh hull_dim);
}
qh_settempfree (&newfacets);
trace1((qh ferr, "qh_createsimplex: created simplex\n"));
} /* createsimplex */
/*---------------------------------
qh_delridge( ridge )
deletes ridge from data structures it belongs to
frees up its memory
notes:
in merge.c, caller sets vertex->delridge for each vertex
ridges also freed in qh_freeqhull
*/
void qh_delridge(ridgeT *ridge) {
void **freelistp; /* used !qh_NOmem */
qh_setdel(ridge->top->ridges, ridge);
qh_setdel(ridge->bottom->ridges, ridge);
qh_setfree(&(ridge->vertices));
qh_memfree_(ridge, sizeof(ridgeT), freelistp);
} /* delridge */
/*---------------------------------
qh_delvertex( vertex )
deletes a vertex and frees its memory
notes:
assumes vertex->adjacencies have been updated if needed
unlinks from vertex_list
*/
void qh_delvertex (vertexT *vertex) {
if (vertex == qh tracevertex)
qh tracevertex= NULL;
qh_removevertex (vertex);
qh_setfree (&vertex->neighbors);
qh_memfree(vertex, sizeof(vertexT));
} /* delvertex */
/*---------------------------------
qh_facet3vertex( )
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 (facetT *facet) {
ridgeT *ridge, *firstridge;
vertexT *vertex;
int cntvertices, cntprojected=0;
setT *vertices;
cntvertices= qh_setsize(facet->vertices);
vertices= qh_settemp (cntvertices);
if (facet->simplicial) {
if (cntvertices != 3) {
fprintf (qh ferr, "qhull internal error (qh_facet3vertex): only %d vertices for simplicial facet f%d\n",
cntvertices, facet->id);
qh_errexit(qh_ERRqhull, facet, NULL);
}
qh_setappend (&vertices, SETfirst_(facet->vertices));
if (facet->toporient ^ qh_ORIENTclock)
qh_setappend (&vertices, SETsecond_(facet->vertices));
else
qh_setaddnth (&vertices, 0, SETsecond_(facet->vertices));
qh_setappend (&vertices, SETelem_(facet->vertices, 2));
}else {
ridge= firstridge= SETfirstt_(facet->ridges, ridgeT); /* no infinite */
while ((ridge= qh_nextridge3d (ridge, facet, &vertex))) {
qh_setappend (&vertices, vertex);
if (++cntprojected > cntvertices || ridge == firstridge)
break;
}
if (!ridge || cntprojected != cntvertices) {
fprintf (qh ferr, "qhull internal error (qh_facet3vertex): ridges for facet %d don't match up. got at least %d\n",
facet->id, cntprojected);
qh_errexit(qh_ERRqhull, facet, ridge);
}
}
return vertices;
} /* facet3vertex */
/*---------------------------------
qh_findbestfacet( 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:
this works for all distributions
if inside, qh_findbestfacet performed an exhaustive search
qh_findbestfacet is not used by qhull.
uses qh.visit_id, qh.searchset
see:
qh_findbest
*/
facetT *qh_findbestfacet (pointT *point, boolT bestoutside,
realT *bestdist, boolT *isoutside) {
facetT *bestfacet= NULL;
int numpart, totpart= 0;
bestfacet= qh_findbest (point, qh facet_list,
bestoutside, False, bestoutside,
bestdist, isoutside, &totpart);
if (!bestfacet) {
fprintf (qh ferr, "qh_findbestfacet: all facets are flipped or upper Delaunay\n");
qh_errexit (qh_ERRqhull, NULL, NULL);
}
if (*bestdist < -qh DISTround) {
bestfacet= qh_findfacet_all (point, bestdist, isoutside, &numpart);
totpart += numpart;
if ((isoutside && bestoutside)
|| (!isoutside && bestfacet->upperdelaunay)) {
bestfacet= qh_findbest (point, bestfacet,
bestoutside, False, bestoutside,
bestdist, isoutside, &totpart);
totpart += numpart;
}
}
trace3((qh ferr, "qh_findbestfacet: f%d dist %2.2g isoutside %d totpart %d\n",
bestfacet->id, *bestdist, *isoutside, totpart));
return bestfacet;
} /* findbestfacet */
/*---------------------------------
qh_findfacet_all( 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
*/
facetT *qh_findfacet_all (pointT *point, realT *bestdist, boolT *isoutside,
int *numpart) {
facetT *bestfacet= NULL, *facet;
realT dist;
int totpart= 0;
*bestdist= REALmin;
*isoutside= False;
FORALLfacets {
if (facet->flipped || !facet->normal)
continue;
totpart++;
qh_distplane (point, facet, &dist);
if (dist > *bestdist) {
*bestdist= dist;
bestfacet= facet;
if (dist > qh MINoutside) {
*isoutside= True;
break;
}
}
}
*numpart= totpart;
trace3((qh ferr, "qh_findfacet_all: f%d dist %2.2g isoutside %d totpart %d\n",
getid_(bestfacet), *bestdist, *isoutside, totpart));
return bestfacet;
} /* findfacet_all */
/*---------------------------------
qh_findgood( 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 (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 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 (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 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 ferr, "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 ferr, "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( 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 (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 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) {
fprintf (qh ferr, "qhull warning: good vertex p%d does not match last good facet f%d. Ignored.\n",
qh_pointid(qh GOODvertexp), facet->id);
return;
}else if (qh GOODvertex > 0)
fprintf (qh ferr, "qhull warning: point p%d is not a vertex ('QV%d').\n",
qh GOODvertex-1, qh GOODvertex-1);
else
fprintf (qh ferr, "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 (facet->normal, &angle)) {
facet->good= False;
numgood--;
if (angle < bestangle) {
bestangle= angle;
bestfacet= facet;
}
}
}
}
if (!numgood && bestfacet) {
bestfacet->good= True;
numgood++;
trace0((qh ferr, "qh_findgood_all: f%d is closest (%2.2g) to thresholds\n",
bestfacet->id, bestangle));
return;
}
}
qh num_good= numgood;
trace0((qh ferr, "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 (void /* 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 (furthest, facet, &dist);
#else
dist= facet->furthestdist;
#endif
if (dist > bestdist) {
bestfacet= facet;
bestdist= dist;
}
}
}
if (bestfacet) {
qh_removefacet (bestfacet);
qh_prependfacet (bestfacet, &qh facet_next);
trace1((qh ferr, "qh_furthestnext: made f%d next facet (dist %.2g)\n",
bestfacet->id, bestdist));
}
} /* furthestnext */
/*---------------------------------
qh_furthestout( 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 (facetT *facet) {
pointT *point, **pointp, *bestpoint= NULL;
realT dist, bestdist= -REALmax;
FOREACHpoint_(facet->outsideset) {
qh_distplane (point, facet, &dist);
zinc_(Zcomputefurthest);
if (dist > bestdist) {
bestpoint= point;
bestdist= dist;
}
}
if (bestpoint) {
qh_setdel (facet->outsideset, point);
qh_setappend (&facet->outsideset, point);
#if !qh_COMPUTEfurthest
facet->furthestdist= bestdist;
#endif
}
facet->notfurthest= False;
trace3((qh ferr, "qh_furthestout: p%d is furthest outside point of f%d\n",
qh_pointid (point), facet->id));
} /* furthestout */
/*---------------------------------
qh_infiniteloop( facet )
report infinite loop error due to facet
*/
void qh_infiniteloop (facetT *facet) {
fprintf (qh ferr, "qhull internal error (qh_infiniteloop): potential infinite loop detected\n");
qh_errexit (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( void) {
setT *maxpoints, *vertices;
facetT *facet;
int i, numpart;
realT dist;
boolT isoutside;
qh furthest_id= -1;
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 GOODpoint-1);
else if (qh GOODpoint < 0)
qh GOODpointp= qh_point (-qh GOODpoint-1);
if (qh GOODvertex > 0)
qh GOODvertexp= qh_point (qh GOODvertex-1);
else if (qh GOODvertex < 0)
qh GOODvertexp= qh_point (-qh GOODvertex-1);
if ((qh GOODpoint
&& (qh GOODpointp < qh first_point /* also catches !GOODpointp */
|| qh GOODpointp > qh_point (qh num_points-1)))
|| (qh GOODvertex
&& (qh GOODvertexp < qh first_point /* also catches !GOODvertexp */
|| qh GOODvertexp > qh_point (qh num_points-1)))) {
fprintf (qh ferr, "qhull input error: either QGn or QVn point is > p%d\n",
qh num_points-1);
qh_errexit (qh_ERRinput, NULL, NULL);
}
maxpoints= qh_maxmin(qh first_point, qh num_points, qh hull_dim);
if (qh SCALElast)
qh_scalelast (qh first_point, qh num_points, qh hull_dim,
qh MINlastcoord, qh MAXlastcoord, qh MAXwidth);
qh_detroundoff();
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 hull_dim, maxpoints, qh first_point, qh num_points);
qh_initialhull (vertices); /* initial qh facet_list */
qh_partitionall (vertices, qh first_point, qh num_points);
if (qh PRINToptions1st || qh TRACElevel || qh IStracing) {
if (qh TRACElevel || qh IStracing)
fprintf (qh ferr, "\nTrace level %d for %s | %s\n",
qh IStracing ? qh IStracing : qh TRACElevel, qh rbox_command, qh qhull_command);
fprintf (qh ferr, "Options selected for Qhull %s:\n%s\n", qh_version, qh qhull_options);
}
qh_resetlists (False /*qh visible_list newvertex_list newfacet_list */);
qh facet_next= qh facet_list;
qh_furthestnext (/* 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) {
fprintf (qh ferr, "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_ERRinput, NULL, NULL);
}
if (!(qh GOODthreshold || qh GOODpoint
|| (!qh MERGEexact && !qh PREmerge && qh GOODvertexp))) {
fprintf (qh ferr, "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_ERRinput, NULL, NULL);
}
if (qh GOODvertex > 0 && !qh MERGING /* matches qh_partitionall */
&& !qh_isvertex (qh GOODvertexp, vertices)) {
facet= qh_findbestnew (qh GOODvertexp, qh facet_list,
&dist, &isoutside, &numpart);
zadd_(Zdistgood, numpart);
if (!isoutside) {
fprintf (qh ferr, "qhull input error: point for QV%d is inside initial simplex. It can not be made a vertex.\n",
qh_pointid(qh GOODvertexp));
qh_errexit (qh_ERRinput, NULL, NULL);
}
if (!qh_addpoint (qh GOODvertexp, facet, False)) {
qh_settempfree(&vertices);
qh_settempfree(&maxpoints);
return;
}
}
qh_findgood (qh facet_list, 0);
}
qh_settempfree(&vertices);
qh_settempfree(&maxpoints);
trace1((qh ferr, "qh_initbuild: initial hull created and points partitioned\n"));
} /* initbuild */
/*---------------------------------
qh_initialhull( 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(setT *vertices) {
facetT *facet, *firstfacet, *neighbor, **neighborp;
realT dist, angle, minangle= REALmax;
#ifndef qh_NOtrace
int k;
#endif
qh_createsimplex(vertices); /* qh facet_list */
qh_resetlists (False);
qh facet_next= qh facet_list; /* advance facet when processed */
qh interior_point= qh_getcenter(vertices);
firstfacet= qh facet_list;
qh_setfacetplane(firstfacet);
zinc_(Znumvisibility); /* needs to be in printsummary */
qh_distplane(qh interior_point, firstfacet, &dist);
if (dist > 0) {
FORALLfacets
facet->toporient ^= True;
}
FORALLfacets
qh_setfacetplane(facet);
FORALLfacets {
if (!qh_checkflipped (facet, NULL, qh_ALL)) {/* due to axis-parallel facet */
trace1((qh ferr, "qh_initialhull: initial orientation incorrect. Correct all facets\n"));
facet->flipped= False;
FORALLfacets {
facet->toporient ^= True;
qh_orientoutside (facet);
}
break;
}
}
FORALLfacets {
if (!qh_checkflipped (facet, NULL, !qh_ALL)) { /* can happen with 'R0.1' */
qh_precision ("initial facet is coplanar with interior point");
fprintf (qh ferr, "qhull precision error: initial facet %d is coplanar with the interior point\n",
facet->id);
qh_errexit (qh_ERRsingular, facet, NULL);
}
FOREACHneighbor_(facet) {
angle= qh_getangle (facet->normal, neighbor->normal);
minimize_( minangle, angle);
}
}
if (minangle < qh_MAXnarrow) {
realT diff= 1.0 + minangle;
qh NARROWhull= True;
qh_option ("_narrow-hull", NULL, &diff);
if (minangle < qh_WARNnarrow && !qh RERUN && qh PRINTprecision)
fprintf (qh ferr, "qhull precision warning: \n\
The initial hull is narrow (the cosine of the minimum angle is %.9g).\n\
A coplanar point may lead to a wide facet. Options 'Qs' (search for best\n\
initial hull), 'QbB' (scale to unit box), or 'Qbb' (scale last coordinate)\n\
may remove this warning. Use 'Pp' to ignore this warning.\n\
See 'Limitations' in qh-impre.htm.\n",
-minangle); /* convert from angle between normals to angle between facets */
}
zzval_(Zprocessed)= qh hull_dim+1;
qh_checkpolygon (qh facet_list);
qh_checkconvex(qh facet_list, qh_DATAfault);
#ifndef qh_NOtrace
if (qh IStracing >= 1) {
fprintf(qh ferr, "qh_initialhull: simplex constructed, interior point:");
for (k=0; k < qh hull_dim; k++)
fprintf (qh ferr, " %6.4g", qh interior_point[k]);
fprintf (qh ferr, "\n");
}
#endif
} /* initialhull */
/*---------------------------------
qh_initialvertices( 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(int dim, setT *maxpoints, pointT *points, int numpoints) {
pointT *point, **pointp;
setT *vertices, *simplex, *tested;
realT randr;
int index, point_i, point_n, k;
boolT nearzero= False;
vertices= qh_settemp (dim + 1);
simplex= qh_settemp (dim+1);
if (qh ALLpoints)
qh_maxsimplex (dim, NULL, points, numpoints, &simplex);
else if (qh RANDOMoutside) {
while (qh_setsize (simplex) != dim+1) {
randr= qh_RANDOMint;
randr= randr/(qh_RANDOMmax+1);
index= (int)floor(qh num_points * randr);
while (qh_setin (simplex, qh_point (index))) {
index++; /* in case qh_RANDOMint always returns the same value */
index= index < qh num_points ? index : 0;
}
qh_setappend (&simplex, qh_point (index));
}
}else if (qh hull_dim >= qh_INITIALmax) {
tested= qh_settemp (dim+1);
qh_setappend (&simplex, SETfirst_(maxpoints)); /* max and min X coord */
qh_setappend (&simplex, SETsecond_(maxpoints));
qh_maxsimplex (fmin_(qh_INITIALsearch, dim), maxpoints, points, numpoints, &simplex);
k= qh_setsize (simplex);
FOREACHpoint_i_(maxpoints) {
if (point_i & 0x1) { /* first pick up max. coord. points */
if (!qh_setin (simplex, point) && !qh_setin (tested, point)){
qh_detsimplex(point, simplex, k, &nearzero);
if (nearzero)
qh_setappend (&tested, point);
else {
qh_setappend (&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 (point, simplex, k, &nearzero);
if (nearzero)
qh_setappend (&tested, point);
else {
qh_setappend (&simplex, point);
k++;
}
}
}
index= 0;
while (k != dim && (point= qh_point (index++))) {
if (!qh_setin (simplex, point) && !qh_setin (tested, point)){
qh_detsimplex (point, simplex, k, &nearzero);
if (!nearzero){
qh_setappend (&simplex, point);
k++;
}
}
}
qh_settempfree (&tested);
qh_maxsimplex (dim, maxpoints, points, numpoints, &simplex);
}else
qh_maxsimplex (dim, maxpoints, points, numpoints, &simplex);
FOREACHpoint_(simplex)
qh_setaddnth (&vertices, 0, qh_newvertex(point)); /* descending order */
qh_settempfree (&simplex);
return vertices;
} /* initialvertices */
/*---------------------------------
qh_isvertex( )
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( 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
design:
for each visible facet
make new facets to its horizon facets
update its f.replace
clear its neighbor set
*/
vertexT *qh_makenewfacets (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(point);
qh_appendvertex (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 (visible, apex, &numnew);
}
if (visible->simplicial)
newfacet= qh_makenew_simplicial (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 ferr, "qh_makenewfacets: created %d new facets from point p%d to horizon\n",
numnew, qh_pointid(point)));
if (qh IStracing >= 4)
qh_printfacetlist (qh newfacet_list, NULL, qh_ALL);
return apex;
} /* makenewfacets */
/*---------------------------------
qh_matchduplicates( 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
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 marked for merging (qh_MERGEridge)
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 (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= (int)qh_gethash (hashsize, atfacet->vertices, qh hull_dim, 1,
SETelem_(atfacet->vertices, atskip));
trace2((qh ferr, "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 (1, newfacet->vertices, newskip, facet->vertices, &skip, &same)) {
ismatch= (same == (newfacet->toporient ^ facet->toporient));
if (SETelemt_(facet->neighbors, skip, facetT) != qh_DUPLICATEridge) {
if (!makematch) {
fprintf (qh ferr, "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_ERRqhull, facet, newfacet);
}
}else if (ismatch && makematch) {
if (SETelemt_(newfacet->neighbors, newskip, facetT) == qh_DUPLICATEridge) {
SETelem_(facet->neighbors, skip)= newfacet;
SETelem_(newfacet->neighbors, newskip)= qh_MERGEridge;
*hashcount -= 2; /* removed two unmatched facets */
trace4((qh ferr, "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 (facet, newfacet, &low, &high);
dist2= qh_getdistance (newfacet, facet, &low, &high);
minimize_(mindist, dist2);
if (mindist > maxdist) {
maxdist= mindist;
maxmatch= facet;
maxskip= skip;
maxmatch2= newfacet;
maxskip2= newskip;
}
trace3((qh ferr, "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) {
fprintf (qh ferr, "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_ERRqhull, newfacet, NULL);
}
}
} /* end of for each new facet at hash */
if (!makematch) {
if (!maxmatch) {
fprintf (qh ferr, "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_ERRqhull, atfacet, NULL);
}
SETelem_(maxmatch->neighbors, maxskip)= maxmatch2;
SETelem_(maxmatch2->neighbors, maxskip2)= maxmatch;
*hashcount -= 2; /* removed two unmatched facets */
zzinc_(Zmultiridge);
trace0((qh ferr, "qh_matchduplicates: duplicate f%d skip %d matched with new f%d skip %d keep\n",
maxmatch->id, maxskip, maxmatch2->id, maxskip2));
qh_precision ("ridge with multiple neighbors");
if (qh IStracing >= 4)
qh_errprint ("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()
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 ( void /* qh.facet_list */) {
facetT *facet;
pointT *point, **pointp;
int numpart;
realT dist, innerplane;
if (!qh KEEPcoplanar && !qh KEEPinside) {
FORALLfacets {
if (facet->coplanarset)
qh_setfree( &facet->coplanarset);
}
}else if (!qh KEEPcoplanar || !qh KEEPinside) {
qh_outerinner (NULL, NULL, &innerplane);
if (qh JOGGLEmax < REALmax/2)
innerplane -= qh JOGGLEmax * sqrt (qh hull_dim);
numpart= 0;
FORALLfacets {
if (facet->coplanarset) {
FOREACHpoint_(facet->coplanarset) {
numpart++;
qh_distplane (point, facet, &dist);
if (dist < innerplane) {
if (!qh KEEPinside)
SETref_(point)= NULL;
}else if (!qh KEEPcoplanar)
SETref_(point)= NULL;
}
qh_setcompact (facet->coplanarset);
}
}
zadd_(Zcheckpart, numpart);
}
} /* nearcoplanar */
/*---------------------------------
qh_nearvertex( 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
*/
vertexT *qh_nearvertex (facetT *facet, pointT *point, realT *bestdistp) {
realT bestdist= REALmax, dist;
vertexT *bestvertex= NULL, *vertex, **vertexp;
int dim= qh hull_dim;
if (qh DELAUNAY)
dim--;
FOREACHvertex_(facet->vertices) {
dist= qh_pointdist (vertex->point, point, -dim);
if (dist < bestdist) {
bestdist= dist;
bestvertex= vertex;
}
}
*bestdistp= sqrt (bestdist);
return bestvertex;
} /* nearvertex */
/*---------------------------------
qh_newhashtable( 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(int newsize) {
int size;
size= ((newsize+1)*qh_HASHfactor) | 0x1; /* odd number */
while (True) {
if ((size%3) && (size%5))
break;
size += 2;
/* loop terminates because there is an infinite number of primes */
}
qh hash_table= qh_setnew (size);
qh_setzero (qh hash_table, 0, size);
return size;
} /* newhashtable */
/*---------------------------------
qh_newvertex( point )
returns a new vertex for point
*/
vertexT *qh_newvertex(pointT *point) {
vertexT *vertex;
zinc_(Ztotvertices);
vertex= (vertexT *)qh_memalloc(sizeof(vertexT));
memset ((char *) vertex, 0, sizeof (vertexT));
if (qh vertex_id == 0xFFFFFF) {
fprintf(qh ferr, "qhull input error: more than %d vertices. ID field overflows and two vertices\n\
may have the same identifier. Vertices not sorted correctly.\n", 0xFFFFFF);
qh_errexit(qh_ERRinput, NULL, NULL);
}
if (qh vertex_id == qh tracevertex_id)
qh tracevertex= vertex;
vertex->id= qh vertex_id++;
vertex->point= point;
trace4((qh ferr, "qh_newvertex: vertex p%d (v%d) created\n", qh_pointid(vertex->point),
vertex->id));
return (vertex);
} /* newvertex */
/*---------------------------------
qh_nextridge3d( atridge, facet, vertex )
return next ridge and vertex for a 3d facet
notes:
in qh_ORIENTclock order
this is a O(n^2) implementation to trace all ridges
be sure to stop on any 2nd visit
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 (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 (void /* facet_list */) {
pointT *point, **pointp;
facetT *facet;
realT dist;
trace1((qh ferr, "qh_outcoplanar: move outsideset to coplanarset for qh NARROWhull\n"));
FORALLfacets {
FOREACHpoint_(facet->outsideset) {
qh num_outside--;
if (qh KEEPcoplanar || qh KEEPnearinside) {
qh_distplane (point, facet, &dist);
zinc_(Zpartition);
qh_partitioncoplanar (point, facet, &dist);
}
}
qh_setfree (&facet->outsideset);
}
} /* outcoplanar */
/*---------------------------------
qh_point( 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 (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 other_points))
return SETelemt_(qh other_points, id, pointT);
return NULL;
} /* point */
/*---------------------------------
qh_point_add( 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 (setT *set, pointT *point, void *elem) {
int id, size;
SETreturnsize_(set, size);
if ((id= qh_pointid(point)) < 0)
fprintf (qh ferr, "qhull internal warning (point_add): unknown point %p id %d\n",
point, id);
else if (id >= size) {
fprintf (qh ferr, "qhull internal errror (point_add): point p%d is out of bounds (%d)\n",
id, size);
qh_errexit (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_(facets) { ... }
SETelem_(facets, i)
design:
for each facet
add each vertex
add each coplanar point
add each outside point
*/
setT *qh_pointfacet (void /*qh facet_list*/) {
int numpoints= qh num_points + qh_setsize (qh other_points);
setT *facets;
facetT *facet;
vertexT *vertex, **vertexp;
pointT *point, **pointp;
facets= qh_settemp (numpoints);
qh_setzero (facets, 0, numpoints);
qh vertex_visit++;
FORALLfacets {
FOREACHvertex_(facet->vertices) {
if (vertex->visitid != qh vertex_visit) {
vertex->visitid= qh vertex_visit;
qh_point_add (facets, vertex->point, facet);
}
}
FOREACHpoint_(facet->coplanarset)
qh_point_add (facets, point, facet);
FOREACHpoint_(facet->outsideset)
qh_point_add (facets, point, facet);
}
return facets;
} /* pointfacet */
/*---------------------------------
qh_pointvertex( )
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_(vertices) { ... }
SETelem_(vertices, i)
*/
setT *qh_pointvertex (void /*qh facet_list*/) {
int numpoints= qh num_points + qh_setsize (qh other_points);
setT *vertices;
vertexT *vertex;
vertices= qh_settemp (numpoints);
qh_setzero (vertices, 0, numpoints);
FORALLvertices
qh_point_add (vertices, vertex->point, vertex);
return vertices;
} /* pointvertex */
/*---------------------------------
qh_prependfacet( 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(facetT *facet, facetT **facetlist) {
facetT *prevfacet, *list= *facetlist;
trace4((qh ferr, "qh_prependfacet: prepend f%d before f%d\n",
facet->id, list->id));
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( fp )
print hash table to fp
notes:
not in I/O to avoid bringing io.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(FILE *fp) {
facetT *facet, *neighbor;
int id, facet_i, facet_n, neighbor_i= 0, neighbor_n= 0;
vertexT *vertex, **vertexp;
FOREACHfacet_i_(qh hash_table) {
if (facet) {
FOREACHneighbor_i_(facet) {
if (!neighbor || neighbor == qh_MERGEridge || neighbor == qh_DUPLICATEridge)
break;
}
if (neighbor_i == neighbor_n)
continue;
fprintf (fp, "hash %d f%d ", facet_i, facet->id);
FOREACHvertex_(facet->vertices)
fprintf (fp, "v%d ", vertex->id);
fprintf (fp, "\n neighbors:");
FOREACHneighbor_i_(facet) {
if (neighbor == qh_MERGEridge)
id= -3;
else if (neighbor == qh_DUPLICATEridge)
id= -2;
else
id= getid_(neighbor);
fprintf (fp, " %d", id);
}
fprintf (fp, "\n");
}
}
} /* printhashtable */
/*---------------------------------
qh_printlists( fp )
print out facet and vertex list for debugging (without 'f/v' tags)
*/
void qh_printlists (void) {
facetT *facet;
vertexT *vertex;
fprintf (qh ferr, "qh_printlists: facets:");
FORALLfacets
fprintf (qh ferr, " %d", facet->id);
fprintf (qh ferr, "\n new facets %d visible facets %d next facet for addpoint %d\n vertices (new %d):",
getid_(qh newfacet_list), getid_(qh visible_list), getid_(qh facet_next),
getid_(qh newvertex_list));
FORALLvertices
fprintf (qh ferr, " %d", vertex->id);
fprintf (qh ferr, "\n");
} /* printlists */
/*---------------------------------
qh_resetlists( stats )
reset newvertex_list, newfacet_list, visible_list
if stats,
maintains statistics
returns:
clears num_visible
visible_list is empty if qh_deletevisible was called
*/
void qh_resetlists (boolT stats /*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;
FORALLvisible_facets {
visible->f.replace= NULL;
visible->visible= False;
}
qh visible_list= NULL;
qh num_visible= 0;
qh NEWfacets= False;
} /* resetlists */
/*---------------------------------
qh_setvoronoi_all()
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 (void) {
facetT *facet;
qh_clearcenters (qh_ASvoronoi);
qh_vertexneighbors();
FORALLfacets {
if (!facet->normal || !facet->upperdelaunay || qh UPPERdelaunay) {
if (!facet->center)
facet->center= qh_facetcenter (facet->vertices);
}
}
} /* setvoronoi_all */
/*---------------------------------
qh_vertexintersect( vertexsetA, vertexsetB )
intersects two vertex sets (inverse id ordered)
vertexsetA is a temporary set at the top of qhmem.tempstack
returns:
replaces vertexsetA with the intersection
notes:
could overwrite vertexsetA if currently too slow
*/
void qh_vertexintersect(setT **vertexsetA,setT *vertexsetB) {
setT *intersection;
intersection= qh_vertexintersect_new (*vertexsetA, vertexsetB);
qh_settempfree (vertexsetA);
*vertexsetA= intersection;
qh_settemppush (intersection);
} /* vertexintersect */
/*---------------------------------
qh_vertexintersect_new( )
intersects two vertex sets (inverse id ordered)
returns:
a new set
*/
setT *qh_vertexintersect_new (setT *vertexsetA,setT *vertexsetB) {
setT *intersection= qh_setnew (qh hull_dim - 1);
vertexT **vertexA= SETaddr_(vertexsetA, vertexT);
vertexT **vertexB= SETaddr_(vertexsetB, vertexT);
while (*vertexA && *vertexB) {
if (*vertexA == *vertexB) {
qh_setappend(&intersection, *vertexA);
vertexA++; vertexB++;
}else {
if ((*vertexA)->id > (*vertexB)->id)
vertexA++;
else
vertexB++;
}
}
return intersection;
} /* vertexintersect_new */
/*---------------------------------
qh_vertexneighhbors()
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 (void /*qh facet_list*/) {
facetT *facet;
vertexT *vertex, **vertexp;
if (qh VERTEXneighbors)
return;
trace1((qh ferr, "qh_vertexneighbors: determing 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 hull_dim);
}
qh_setappend (&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 */