---------------------------------
poly2.c
implements polygons and simplices
see qh-poly.htm, poly.h and qhull.h
frequently used code is in poly.c
copyright (c) 1993-2003, 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:
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 (void) {
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 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;
qh_distplane(point, facet, &dist);
numpart++;
bestfacet= qh_findbesthorizon (!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 (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);
if (errfacet1 != bestfacet) {
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.ferr 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_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 (void) {
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 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*/);
do {
old_maxoutside= fmax_(qh max_outside, maxoutside);
FOREACHfacet_i_(facets) { /* for each point with facet assignment */
if (facet) {
point= qh_point(facet_i);
if (point == qh GOODpointp)
continue;
zinc_(Ztotcheck);
qh_distplane(point, facet, &dist);
numpart++;
bestfacet= qh_findbesthorizon (qh_IScheckmax, point, facet, !qh_NOupper, &dist, &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);
}
}
}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 (&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
Maybe called after voronoi output. Will recompute otherwise centrums are Voronoi centers instead
*/
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) {
if (*errfacet1 != facet) {
*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:
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 (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' or 'Po').\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 (!facet->normal) {
fprintf( qh ferr, "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 (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, centrum_warning= 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 || 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 (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 {
if (!centrum_warning && (!facet->simplicial || facet->tricoplanar)) {
centrum_warning= True;
fprintf (qh ferr, "qhull note: recomputing centrums for convexity test. This may lead to false, precision errors.\n");
}
centrum= qh_getcentrum(facet);
tempcentrum= True;
}
FOREACHneighbor_(facet) {
if (qh ZEROcentrum && facet->simplicial && neighbor->simplicial)
continue;
if (facet->tricoplanar || neighbor->tricoplanar)
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;
}
/* 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) {
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)) {
if (!qh NARROWhull
#if !qh_COMPUTEfurthest
|| facet->furthestdist >= qh MINoutside
#endif
) {
fprintf (qh ferr, "qhull internal error (qh_checkpolygon): f%d has outside points 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 - %d visible facets\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 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_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= qh num_visible= 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:
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 (pointT *point, boolT bestoutside,
realT *bestdist, boolT *isoutside) {
facetT *bestfacet= NULL;
int numpart, totpart= 0;
bestfacet= qh_findbest (point, qh facet_list,
bestoutside, !qh_ISnewfacets, bestoutside /* qh_NOupper */,
bestdist, isoutside, &totpart);
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_findbestlower( 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 (facetT *upperfacet, pointT *point, realT *bestdistp, int *numpart) {
facetT *neighbor, **neighborp, *bestfacet= NULL;
realT bestdist= -REALmax/2 /* avoid underflow */;
realT dist;
vertexT *vertex;
zinc_(Zbestlower);
FOREACHneighbor_(upperfacet) {
if (neighbor->upperdelaunay || neighbor->flipped)
continue;
(*numpart)++;
qh_distplane (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 (upperfacet, point, &dist);
qh_vertexneighbors();
FOREACHneighbor_(vertex) {
if (neighbor->upperdelaunay || neighbor->flipped)
continue;
(*numpart)++;
qh_distplane (point, neighbor, &dist);
if (dist > bestdist) {
bestfacet= neighbor;
bestdist= dist;
}
}
}
if (!bestfacet) {
fprintf(qh ferr, "\n\
qh_findbestlower: all neighbors of facet %d are flipped or upper Delaunay.\n\
Please report this error to qhull_bug@qhull.org with the input and all of the output.\n",
upperfacet->id);
qh_errexit (qh_ERRqhull, upperfacet, NULL);
}
*bestdistp= bestdist;
trace3((qh ferr, "qh_findbestlower: f%d dist %2.2g for f%d p%d\n",
bestfacet->id, bestdist, upperfacet->id, qh_pointid(point)));
return bestfacet;
} /* findbestlower */
/*---------------------------------
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 GOODthresholdpri href="qh-poly.htm#TOC"
>--------------------------------
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:
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 (pointT *point, boolT bestoutside,
realT *bestdist, boolT *isoutside) {
facetT *bestfacet= NULL;
int numpart, totpart= 0;
bestfacet= qh_findbest (point, qh facet_list,
bestoutside, !qh_ISnewfacets, bestoutside /* qh_NOupper */,
bestdist, isoutside, &totpart);
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_findbestlower( 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 (facetT *upperfacet, pointT *point, realT *bestdistp, int *numpart) {
facetT *neighbor, **neighborp, *bestfacet= NULL;
realT bestdist= -REALmax/2 /* avoid underflow */;
realT dist;
vertexT *vertex;
zinc_(Zbestlower);
FOREACHneighbor_(upperfacet) {
if (neighbor->upperdelaunay || neighbor->flipped)
continue;
(*numpart)++;
qh_distplane (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 (upperfacet, point, &dist);
qh_vertexneighbors();
FOREACHneighbor_(vertex) {
if (neighbor->upperdelaunay || neighbor->flipped)
continue;
(*numpart)++;
qh_distplane (point, neighbor, &dist);
if (dist > bestdist) {
bestfacet= neighbor;
bestdist= dist;
}
}
}
if (!bestfacet) {
fprintf(qh ferr, "\n\
qh_findbestlower: all neighbors of facet %d are flipped or upper Delaunay.\n\
Please report this error to qhull_bug@qhull.org with the input and all of the output.\n",
upperfacet->id);
qh_errexit (qh_ERRqhull, upperfacet, NULL);
}
*bestdistp= bestdist;
trace3((qh ferr, "qh_findbestlower: f%d dist %2.2g for f%d p%d\n",
bestfacet->id, bestdist, upperfacet->id, qh_pointid(point)));
return bestfacet;
} /* findbestlower */
/*---------------------------------
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 GOODthresholdpri href="qh-poly.htm#TOC"
>--------------------------------
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:
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 (pointT *point, boolT bestoutside,
realT *bestdist, boolT *isoutside) {
facetT *bestfacet= NULL;
int numpart, totpart= 0;
bestfacet= qh_findbest (point, qh facet_list,
bestoutside, !qh_ISnewfacets, bestoutside /* qh_NOupper */,
bestdist, isoutside, &totpart);
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_findbestlower( 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 (facetT *upperfacet, pointT *point, realT *bestdistp, int *numpart) {
facetT *neighbor, **neighborp, *bestfacet= NULL;
realT bestdist= -REALmax/2 /* avoid underflow */;
realT dist;
vertexT *vertex;
zinc_(Zbestlower);
FOREACHneighbor_(upperfacet) {
if (neighbor->upperdelaunay || neighbor->flipped)
continue;
(*numpart)++;
qh_distplane (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 (upperfacet, point, &dist);
qh_vertexneighbors();
FOREACHneighbor_(vertex) {
if (neighbor->upperdelaunay || neighbor->flipped)
continue;
(*numpart)++;
qh_distplane (point, neighbor, &dist);
if (dist > bestdist) {
bestfacet= neighbor;
bestdist= dist;
}
}
}
if (!bestfacet) {
fprintf(qh ferr, "\n\
qh_findbestlower: all neighbors of facet %d are flipped or upper Delaunay.\n\
Please report this error to qhull_bug@qhull.org with the input and all of the output.\n",
upperfacet->id);
qh_errexit (qh_ERRqhull, upperfacet, NULL);
}
*bestdistp= bestdist;
trace3((qh ferr, "qh_findbestlower: f%d dist %2.2g for f%d p%d\n",
bestfacet->id, bestdist, upperfacet->id, qh_pointid(point)));
return bestfacet;
} /* findbestlower */
/*---------------------------------
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 GOODthresholdpri href="qh-poly.htm#TOC"
>--------------------------------
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:
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 (pointT *point, boolT bestoutside,
realT *bestdist, boolT *isoutside) {
facetT *bestfacet= NULL;
int numpart, totpart= 0;
bestfacet= qh_findbest (point, qh facet_list,
bestoutside, !qh_ISnewfacets, bestoutside /* qh_NOupper */,
bestdist, isoutside, &totpart);
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_findbestlower( 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 (facetT *upperfacet, pointT *point, realT *bestdistp, int *numpart) {
facetT *neighbor, **neighborp, *bestfacet= NULL;
realT bestdist= -REALmax/2 /* avoid underflow */;
realT dist;
vertexT *vertex;
zinc_(Zbestlower);
FOREACHneighbor_(upperfacet) {
if (neighbor->upperdelaunay || neighbor->flipped)
continue;
(*numpart)++;
qh_distplane (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 (upperfacet, point, &dist);
qh_vertexneighbors();
FOREACHneighbor_(vertex) {
if (neighbor->upperdelaunay || neighbor->flipped)
continue;
(*numpart)++;
qh_distplane (point, neighbor, &dist);
if (dist > bestdist) {
bestfacet= neighbor;
bestdist= dist;
}
}
}
if (!bestfacet) {
fprintf(qh ferr, "\n\
qh_findbestlower: all neighbors of facet %d are flipped or upper Delaunay.\n\
Please report this error to qhull_bug@qhull.org with the input and all of the output.\n",
upperfacet->id);
qh_errexit (qh_ERRqhull, upperfacet, NULL);
}
*bestdistp= bestdist;
trace3((qh ferr, "qh_findbestlower: f%d dist %2.2g for f%d p%d\n",
bestfacet->id, bestdist, upperfacet->id, qh_pointid(point)));
return bestfacet;
} /* findbestlower */
/*---------------------------------
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 *