/* ---------------------------------
libqhull.c
Quickhull algorithm for convex hulls
qhull() and top-level routines
see qh-qhull.htm, libqhull.h, unix.c
see qhull_a.h for internal functions
Copyright (c) 1993-2020 The Geometry Center.
$Id: //main/2019/qhull/src/libqhull/libqhull.c#13 $$Change: 2953 $
$DateTime: 2020/05/21 22:05:32 $$Author: bbarber $
*/
#include "qhull_a.h"
/*============= functions in alphabetic order after qhull() =======*/
/*---------------------------------
qh_qhull( )
compute DIM3 convex hull of qh.num_points starting at qh.first_point
qh contains all global options and variables
returns:
returns polyhedron
qh.facet_list, qh.num_facets, qh.vertex_list, qh.num_vertices,
returns global variables
qh.hulltime, qh.max_outside, qh.interior_point, qh.max_vertex, qh.min_vertex
returns precision constants
qh.ANGLEround, centrum_radius, cos_max, DISTround, MAXabs_coord, ONEmerge
notes:
unless needed for output
qh.max_vertex and qh.min_vertex are max/min due to merges
see:
to add individual points to either qh.num_points
use qh_addpoint()
if qh.GETarea
qh_produceoutput() returns qh.totarea and qh.totvol via qh_getarea()
design:
record starting time
initialize hull and partition points
build convex hull
unless early termination
update facet->maxoutside for vertices, coplanar, and near-inside points
error if temporary sets exist
record end time
*/
void qh_qhull(void) {
int numoutside;
qh hulltime= qh_CPUclock;
if (qh RERUN || qh JOGGLEmax < REALmax/2)
qh_build_withrestart();
else {
qh_initbuild();
qh_buildhull();
}
if (!qh STOPadd && !qh STOPcone && !qh STOPpoint) {
if (qh ZEROall_ok && !qh TESTvneighbors && qh MERGEexact)
qh_checkzero(qh_ALL);
if (qh ZEROall_ok && !qh TESTvneighbors && !qh WAScoplanar) {
trace2((qh ferr, 2055, "qh_qhull: all facets are clearly convex and no coplanar points. Post-merging and check of maxout not needed.\n"));
qh DOcheckmax= False;
}else {
qh_initmergesets(/* qh.facet_mergeset,degen_mergeset,vertex_mergeset */);
if (qh MERGEexact || (qh hull_dim > qh_DIMreduceBuild && qh PREmerge))
qh_postmerge("First post-merge", qh premerge_centrum, qh premerge_cos,
(qh POSTmerge ? False : qh TESTvneighbors)); /* calls qh_reducevertices */
else if (!qh POSTmerge && qh TESTvneighbors)
qh_postmerge("For testing vertex neighbors", qh premerge_centrum,
qh premerge_cos, True); /* calls qh_test_vneighbors */
if (qh POSTmerge)
qh_postmerge("For post-merging", qh postmerge_centrum,
qh postmerge_cos, qh TESTvneighbors);
if (qh visible_list == qh facet_list) { /* qh_postmerge was called */
qh findbestnew= True;
qh_partitionvisible(!qh_ALL, &numoutside /* qh.visible_list */);
qh findbestnew= False;
qh_deletevisible(/* qh.visible_list */); /* stops at first !f.visible */
qh_resetlists(False, qh_RESETvisible /* qh.visible_list newvertex_list qh.newfacet_list */);
}
qh_all_vertexmerges(-1, NULL, NULL);
qh_freemergesets();
}
if (qh TRACEpoint == qh_IDunknown && qh TRACElevel > qh IStracing) {
qh IStracing= qh TRACElevel;
qh_fprintf(qh ferr, 2112, "qh_qhull: finished qh_buildhull and qh_postmerge, start tracing (TP-1)\n");
}
if (qh DOcheckmax){
if (qh REPORTfreq) {
qh_buildtracing(NULL, NULL);
qh_fprintf(qh ferr, 8115, "\nTesting all coplanar points.\n");
}
qh_check_maxout();
}
if (qh KEEPnearinside && !qh maxoutdone)
qh_nearcoplanar();
}
if (qh_setsize(qhmem.tempstack) != 0) {
qh_fprintf(qh ferr, 6164, "qhull internal error (qh_qhull): temporary sets not empty(%d) at end of Qhull\n",
qh_setsize(qhmem.tempstack));
qh_errexit(qh_ERRqhull, NULL, NULL);
}
qh hulltime= qh_CPUclock - qh hulltime;
qh QHULLfinished= True;
trace1((qh ferr, 1036, "Qhull: algorithm completed\n"));
} /* qhull */
/*---------------------------------
qh_addpoint( furthest, facet, checkdist )
add point (usually furthest point) above facet to hull
if checkdist,
check that point is above facet.
if point is not outside of the hull, uses qh_partitioncoplanar()
assumes that facet is defined by qh_findbestfacet()
else if facet specified,
assumes that point is above facet (major damage if below)
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 False if user requested an early termination
qh.visible_list, newfacet_list, delvertex_list, NEWfacets may be defined
updates qh.facet_list, qh.num_facets, qh.vertex_list, qh.num_vertices
clear qh.maxoutdone (will need to call qh_check_maxout() for facet->maxoutside)
if unknown point, adds a pointer to qh.other_points
do not deallocate the point's coordinates
notes:
called from qh_initbuild, qh_buildhull, and qh_addpoint
tail recursive call if merged a pinchedvertex due to a duplicated ridge
no more than qh.num_vertices calls (QH6296)
assumes point is near its best facet and not at a local minimum of a lens
distributions. Use qh_findbestfacet to avoid this case.
uses qh.visible_list, qh.newfacet_list, qh.delvertex_list, qh.NEWfacets
if called from a user application after qh_qhull and 'QJ' (joggle),
facet merging for precision problems is disabled by default
design:
exit if qh.STOPadd vertices 'TAn'
add point to other_points if needed
if checkdist
if point not above facet
partition coplanar point
exit
exit if pre STOPpoint requested
find horizon and visible facets for point
build cone of new facets to the horizon
exit if build cone fails due to qh.ONLYgood
tail recursive call if build cone fails due to pinched vertices
exit if STOPcone requested
merge non-convex new facets
if merge found, many merges, or 'Qf'
use qh_findbestnew() instead of qh_findbest()
partition outside points from visible facets
delete visible facets
check polyhedron if requested
exit if post STOPpoint requested
reset working lists of facets and vertices
*/
boolT qh_addpoint(pointT *furthest, facetT *facet, boolT checkdist) {
realT dist, pbalance;
facetT *replacefacet, *newfacet;
vertexT *apex;
boolT isoutside= False;
int numpart, numpoints, goodvisible, goodhorizon, apexpointid;
qh maxoutdone= False;
if (qh_pointid(furthest) == qh_IDunknown)
qh_setappend(&qh other_points, furthest);
if (!facet) {
qh_fprintf(qh ferr, 6213, "qhull internal error (qh_addpoint): NULL facet. Need to call qh_findbestfacet first\n");
qh_errexit(qh_ERRqhull, NULL, NULL);
}
qh_detmaxoutside();
if (checkdist) {
facet= qh_findbest(furthest, facet, !qh_ALL, !qh_ISnewfacets, !qh_NOupper,
&dist, &isoutside, &numpart);
zzadd_(Zpartition, numpart);
if (!isoutside) {
zinc_(Znotmax); /* last point of outsideset is no longer furthest. */
facet->notfurthest= True;
qh_partitioncoplanar(furthest, facet, &dist, qh findbestnew);
return True;
}
}
qh_buildtracing(furthest, facet);
if (qh STOPpoint < 0 && qh furthest_id == -qh STOPpoint-1) {
facet->notfurthest= True;
return False;
}
qh_findhorizon(furthest, facet, &goodvisible, &goodhorizon);
if (qh ONLYgood && !qh GOODclosest && !(goodvisible+goodhorizon)) {
zinc_(Znotgood);
facet->notfurthest= True;
/* last point of outsideset is no longer furthest. This is ok
since all points of the outside are likely to be bad */
qh_resetlists(False, qh_RESETvisible /* qh.visible_list newvertex_list qh.newfacet_list */);
return True;
}
apex= qh_buildcone(furthest, facet, goodhorizon, &replacefacet);
/* qh.newfacet_list, visible_list, newvertex_list */
if (!apex) {
if (qh ONLYgood)
return True; /* ignore this furthest point, a good new facet was not found */
if (replacefacet) {
if (qh retry_addpoint++ >= qh num_vertices) {
qh_fprintf(qh ferr, 6296, "qhull internal error (qh_addpoint): infinite loop (%d retries) of merging pinched vertices due to dupridge for point p%d, facet f%d, and %d vertices\n",
qh retry_addpoint, qh_pointid(furthest), facet->id, qh num_vertices);
qh_errexit(qh_ERRqhull, facet, NULL);
}
/* retry qh_addpoint after resolving a dupridge via qh_merge_pinchedvertices */
return qh_addpoint(furthest, replacefacet, True /* checkdisk */);
}
qh retry_addpoint= 0;
return True; /* ignore this furthest point, resolved a dupridge by making furthest a coplanar point */
}
if (qh retry_addpoint) {
zinc_(Zretryadd);
zadd_(Zretryaddtot, qh retry_addpoint);
zmax_(Zretryaddmax, qh retry_addpoint);
qh retry_addpoint= 0;
}
apexpointid= qh_pointid(apex->point);
zzinc_(Zprocessed);
if (qh STOPcone && qh furthest_id == qh STOPcone-1) {
facet->notfurthest= True;
return False; /* visible_list etc. still defined */
}
qh findbestnew= False;
if (qh PREmerge || qh MERGEexact) {
qh_initmergesets(/* qh.facet_mergeset,degen_mergeset,vertex_mergeset */);
qh_premerge(apexpointid, qh premerge_centrum, qh premerge_cos /* qh.newfacet_list */);
if (qh_USEfindbestnew)
qh findbestnew= True;
else {
FORALLnew_facets {
if (!newfacet->simplicial) {
qh findbestnew= True; /* use qh_findbestnew instead of qh_findbest*/
break;
}
}
}
}else if (qh BESToutside)
qh findbestnew= True;
if (qh IStracing >= 4)
qh_checkpolygon(qh visible_list);
qh_partitionvisible(!qh_ALL, &numpoints /* qh.visible_list */);
qh findbestnew= False;
qh findbest_notsharp= False;
zinc_(Zpbalance);
pbalance= numpoints - (realT) qh hull_dim /* assumes all points extreme */
* (qh num_points - qh num_vertices)/qh num_vertices;
wadd_(Wpbalance, pbalance);
wadd_(Wpbalance2, pbalance * pbalance);
qh_deletevisible(/* qh.visible_list */);
zmax_(Zmaxvertex, qh num_vertices);
qh NEWfacets= False;
if (qh IStracing >= 4) {
if (qh num_facets < 200)
qh_printlists();
qh_printfacetlist(qh newfacet_list, NULL, True);
qh_checkpolygon(qh facet_list);
}else if (qh CHECKfrequently) {
if (qh num_facets < 1000)
qh_checkpolygon(qh facet_list);
else
qh_checkpolygon(qh newfacet_list);
}
if (qh STOPpoint > 0 && qh furthest_id == qh STOPpoint-1 && qh_setsize(qh vertex_mergeset) > 0)
return False;
qh_resetlists(True, qh_RESETvisible /* qh.visible_list newvertex_list qh.newfacet_list */);
if (qh facet_mergeset) {
/* vertex merges occur after facet merges (qh_premerge) and qh_resetlists */
qh_all_vertexmerges(apexpointid, NULL, NULL);
qh_freemergesets();
}
/* qh_triangulate(); to test qh.TRInormals */
if (qh STOPpoint > 0 && qh furthest_id == qh STOPpoint-1)
return False;
trace2((qh ferr, 2056, "qh_addpoint: added p%d to convex hull with point balance %2.2g\n",
qh_pointid(furthest), pbalance));
return True;
} /* addpoint */
/*---------------------------------
qh_build_withrestart( )
allow restarts due to qh.JOGGLEmax while calling qh_buildhull()
qh_errexit always undoes qh_build_withrestart()
qh.FIRSTpoint/qh.NUMpoints is point array
it may be moved by qh_joggleinput
*/
void qh_build_withrestart(void) {
int restart;
vertexT *vertex, **vertexp;
qh ALLOWrestart= True;
while (True) {
restart= setjmp(qh restartexit); /* simple statement for CRAY J916 */
if (restart) { /* only from qh_joggle_restart() */
qh last_errcode= qh_ERRnone;
zzinc_(Zretry);
wmax_(Wretrymax, qh JOGGLEmax);
/* QH7078 warns about using 'TCn' with 'QJn' */
qh STOPcone= qh_IDunknown; /* if break from joggle, prevents normal output */
FOREACHvertex_(qh del_vertices) {
if (vertex->point && !vertex->partitioned)
vertex->partitioned= True; /* avoid error in qh_freebuild -> qh_delvertex */
}
}
if (!qh RERUN && qh JOGGLEmax < REALmax/2) {
if (qh build_cnt > qh_JOGGLEmaxretry) {
qh_fprintf(qh ferr, 6229, "qhull input error: %d attempts to construct a convex hull with joggled input. Increase joggle above 'QJ%2.2g' or modify qh_JOGGLE... parameters in user.h\n",
qh build_cnt, qh JOGGLEmax);
qh_errexit(qh_ERRinput, NULL, NULL);
}
if (qh build_cnt && !restart)
break;
}else if (qh build_cnt && qh build_cnt >= qh RERUN)
break;
qh STOPcone= 0;
qh_freebuild(True); /* first call is a nop */
qh build_cnt++;
if (!qh qhull_optionsiz)
qh qhull_optionsiz= (int)strlen(qh qhull_options); /* WARN64 */
else {
qh qhull_options[qh qhull_optionsiz]= '\0';
qh qhull_optionlen= qh_OPTIONline; /* starts a new line */
}
qh_option("_run", &qh build_cnt, NULL);
if (qh build_cnt == qh RERUN) {
qh IStracing= qh TRACElastrun; /* duplicated from qh_initqhull_globals */
if (qh TRACEpoint != qh_IDnone || qh TRACEdist < REALmax/2 || qh TRACEmerge) {
qh TRACElevel= (qh IStracing? qh IStracing : 3);
qh IStracing= 0;
}
qhmem.IStracing= qh IStracing;
}
if (qh JOGGLEmax < REALmax/2)
qh_joggleinput();
qh_initbuild();
qh_buildhull();
if (qh JOGGLEmax < REALmax/2 && !qh MERGING)
qh_checkconvex(qh facet_list, qh_ALGORITHMfault);
}
qh ALLOWrestart= False;
} /* qh_build_withrestart */
/*---------------------------------
qh_buildcone( furthest, facet, goodhorizon, &replacefacet )
build cone of new facets from furthest to the horizon
goodhorizon is count of good, horizon facets from qh_find_horizon
returns:
returns apex of cone with qh.newfacet_list and qh.first_newfacet (f.id)
returns NULL if qh.ONLYgood and no good facets
returns NULL and retryfacet if merging pinched vertices will resolve a dupridge
a horizon vertex was nearly adjacent to another vertex
will retry qh_addpoint
returns NULL if resolve a dupridge by making furthest a coplanar point
furthest was nearly adjacent to an existing vertex
updates qh.degen_mergeset (MRGridge) if resolve a dupridge by merging facets
updates qh.newfacet_list, visible_list, newvertex_list
updates qh.facet_list, vertex_list, num_facets, num_vertices
notes:
called by qh_addpoint
see qh_triangulate, it triangulates non-simplicial facets in post-processing
design:
make new facets for point to horizon
compute balance statistics
make hyperplanes for point
exit if qh.ONLYgood and not good (qh_buildcone_onlygood)
match neighboring new facets
if dupridges
exit if !qh.IGNOREpinched and dupridge resolved by coplanar furthest
retry qh_buildcone if !qh.IGNOREpinched and dupridge resolved by qh_buildcone_mergepinched
otherwise dupridges resolved by merging facets
update vertex neighbors and delete interior vertices
*/
vertexT *qh_buildcone(pointT *furthest, facetT *facet, int goodhorizon, facetT **retryfacet) {
vertexT *apex;
realT newbalance;
int numnew;
*retryfacet= NULL;
qh first_newfacet= qh facet_id;
qh NEWtentative= (qh MERGEpinched || qh ONLYgood); /* cleared by qh_attachnewfacets or qh_resetlists */
apex= qh_makenewfacets(furthest /* qh.newfacet_list visible_list, attaches new facets if !qh.NEWtentative */);
numnew= (int)(qh facet_id - qh first_newfacet);
newbalance= numnew - (realT)(qh num_facets - qh num_visible) * qh hull_dim / qh num_vertices;
/* newbalance statistics updated below if the new facets are accepted */
if (qh ONLYgood) { /* qh.MERGEpinched is false by QH6362 */
if (!qh_buildcone_onlygood(apex, goodhorizon /* qh.newfacet_list */)) {
facet->notfurthest= True;
return NULL;
}
}else if(qh MERGEpinched) {
#ifndef qh_NOmerge
if (qh_buildcone_mergepinched(apex, facet, retryfacet /* qh.newfacet_list */))
return NULL;
#else
qh_fprintf(qh ferr, 6375, "qhull option error (qh_buildcone): option 'Q14' (qh.MERGEpinched) is not available due to qh_NOmerge\n");
qh_errexit(qh_ERRinput, NULL, NULL);
#endif
}else {
/* qh_makenewfacets attached new facets to the horizon */
qh_matchnewfacets(); /* ignore returned value. qh_forcedmerges will merge dupridges if any */
qh_makenewplanes(/* qh.newfacet_list */);
qh_update_vertexneighbors_cone();
}
wadd_(Wnewbalance, newbalance);
wadd_(Wnewbalance2, newbalance * newbalance);
trace2((qh ferr, 2067, "qh_buildcone: created %d newfacets for p%d(v%d) new facet balance %2.2g\n",
numnew, qh_pointid(furthest), apex->id, newbalance));
return apex;
} /* buildcone */
#ifndef qh_NOmerge
/*---------------------------------
qh_buildcone_mergepinched( apex, facet, maxdupdist, &retryfacet )
build cone of new facets from furthest to the horizon
maxdupdist>0.0 for merging dupridges (qh_matchdupridge)
returns:
returns True if merged a pinched vertex and deleted the cone of new facets
if retryfacet is set
a dupridge was resolved by qh_merge_pinchedvertices
retry qh_addpoint
otherwise
apex/furthest was partitioned as a coplanar point
ignore this furthest point
returns False if no dupridges or if dupridges will be resolved by MRGridge
updates qh.facet_list, qh.num_facets, qh.vertex_list, qh.num_vertices
notes:
only called from qh_buildcone with qh.MERGEpinched
design:
match neighboring new facets
if matching detected dupridges with a wide merge (qh_RATIOtrypinched)
if pinched vertices (i.e., nearly adjacent)
delete the cone of new facets
delete the apex and reset the facet lists
if coplanar, pinched apex
partition the apex as a coplanar point
else
repeatedly merge the nearest pair of pinched vertices and subsequent facet merges
return True
otherwise
MRGridge are better than vertex merge, but may report an error
attach new facets
make hyperplanes for point
update vertex neighbors and delete interior vertices
*/
boolT qh_buildcone_mergepinched(vertexT *apex, facetT *facet, facetT **retryfacet) {
facetT *newfacet, *nextfacet;
pointT *apexpoint;
coordT maxdupdist;
int apexpointid;
boolT iscoplanar;
*retryfacet= NULL;
maxdupdist= qh_matchnewfacets();
if (maxdupdist > qh_RATIOtrypinched * qh ONEmerge) { /* one or more dupridges with a wide merge */
if (qh IStracing >= 4 && qh num_facets < 1000)
qh_printlists();
qh_initmergesets(/* qh.facet_mergeset,degen_mergeset,vertex_mergeset */);
if (qh_getpinchedmerges(apex, maxdupdist, &iscoplanar /* qh.newfacet_list, qh.vertex_mergeset */)) {
for (newfacet=qh newfacet_list; newfacet && newfacet->next; newfacet= nextfacet) {
nextfacet= newfacet->next;
qh_delfacet(newfacet);
}
apexpoint= apex->point;
apexpointid= qh_pointid(apexpoint);
qh_delvertex(apex);
qh_resetlists(False, qh_RESETvisible /* qh.visible_list newvertex_list qh.newfacet_list */);
if (iscoplanar) {
zinc_(Zpinchedapex);
facet->notfurthest= True;
qh_partitioncoplanar(apexpoint, facet, NULL, qh findbestnew);
}else {
qh_all_vertexmerges(apexpointid, facet, retryfacet);
}
qh_freemergesets(); /* errors if not empty */
return True;
}
/* MRGridge are better than vertex merge, but may report an error */
qh_freemergesets();
}
qh_attachnewfacets(/* qh.visible_list */);
qh_makenewplanes(/* qh.newfacet_list */);
qh_update_vertexneighbors_cone();
return False;
} /* buildcone_mergepinched */
#endif /* !qh_NOmerge */
/*---------------------------------
qh_buildcone_onlygood( apex, goodhorizon )
build cone of good, new facets from apex and its qh.newfacet_list to the horizon
goodhorizon is count of good, horizon facets from qh_find_horizon
returns:
False if a f.good facet or a qh.GOODclosest facet is not found
updates qh.facet_list, qh.num_facets, qh.vertex_list, qh.num_vertices
notes:
called from qh_buildcone
QH11030 FIX: Review effect of qh.GOODclosest on qh_buildcone_onlygood ('Qg'). qh_findgood preserves old value if didn't find a good facet. See qh_findgood_all for disabling
design:
make hyperplanes for point
if qh_findgood fails to find a f.good facet or a qh.GOODclosest facet
delete cone of new facets
return NULL (ignores apex)
else
attach cone to horizon
match neighboring new facets
*/
boolT qh_buildcone_onlygood(vertexT *apex, int goodhorizon) {
facetT *newfacet, *nextfacet;
qh_makenewplanes(/* qh.newfacet_list */);
if(qh_findgood(qh newfacet_list, goodhorizon) == 0) {
if (!qh GOODclosest) {
for (newfacet=qh newfacet_list; newfacet && newfacet->next; newfacet= nextfacet) {
nextfacet= newfacet->next;
qh_delfacet(newfacet);
}
qh_delvertex(apex);
qh_resetlists(False /*no stats*/, qh_RESETvisible /* qh.visible_list newvertex_list qh.newfacet_list */);
zinc_(Znotgoodnew);
/* !good outside points dropped from hull */
return False;
}
}
qh_attachnewfacets(/* qh.visible_list */);
qh_matchnewfacets(); /* ignore returned value. qh_forcedmerges will merge dupridges if any */
qh_update_vertexneighbors_cone();
return True;
} /* buildcone_onlygood */
/*---------------------------------
qh_buildhull( )
construct a convex hull by adding outside points one at a time
returns:
notes:
may be called multiple times
checks facet and vertex lists for incorrect flags
to recover from STOPcone, call qh_deletevisible and qh_resetlists
design:
check visible facet and newfacet flags
check newfacet vertex flags and qh.STOPcone/STOPpoint
for each facet with a furthest outside point
add point to facet
exit if qh.STOPcone or qh.STOPpoint requested
if qh.NARROWhull for initial simplex
partition remaining outside points to coplanar sets
*/
void qh_buildhull(void) {
facetT *facet;
pointT *furthest;
vertexT *vertex;
int id;
trace1((qh ferr, 1037, "qh_buildhull: start build hull\n"));
FORALLfacets {
if (facet->visible || facet->newfacet) {
qh_fprintf(qh ferr, 6165, "qhull internal error (qh_buildhull): visible or new facet f%d in facet list\n",
facet->id);
qh_errexit(qh_ERRqhull, facet, NULL);
}
}
FORALLvertices {
if (vertex->newfacet) {
qh_fprintf(qh ferr, 6166, "qhull internal error (qh_buildhull): new vertex f%d in vertex list\n",
vertex->id);
qh_errprint("ERRONEOUS", NULL, NULL, NULL, vertex);
qh_errexit(qh_ERRqhull, NULL, NULL);
}
id= qh_pointid(vertex->point);
if ((qh STOPpoint>0 && id == qh STOPpoint-1) ||
(qh STOPpoint<0 && id == -qh STOPpoint-1) ||
(qh STOPcone>0 && id == qh STOPcone-1)) {
trace1((qh ferr, 1038,"qh_buildhull: stop point or cone P%d in initial hull\n", id));
return;
}
}
qh facet_next= qh facet_list; /* advance facet when processed */
while ((furthest= qh_nextfurthest(&facet))) {
qh num_outside--; /* if ONLYmax, furthest may not be outside */
if (qh STOPadd>0 && (qh num_vertices - qh hull_dim - 1 >= qh STOPadd - 1)) {
trace1((qh ferr, 1059, "qh_buildhull: stop after adding %d vertices\n", qh STOPadd-1));
return;
}
if (!qh_addpoint(furthest, facet, qh ONLYmax))
break;
}
if (qh NARROWhull) /* move points from outsideset to coplanarset */
qh_outcoplanar(/* facet_list */ );
if (qh num_outside && !furthest) {
qh_fprintf(qh ferr, 6167, "qhull internal error (qh_buildhull): %d outside points were never processed.\n", qh num_outside);
qh_errexit(qh_ERRqhull, NULL, NULL);
}
trace1((qh ferr, 1039, "qh_buildhull: completed the hull construction\n"));
} /* buildhull */
/*---------------------------------
qh_buildtracing( furthest, facet )
trace an iteration of qh_buildhull() for furthest point and facet
if !furthest, prints progress message
returns:
tracks progress with qh.lastreport, lastcpu, lastfacets, lastmerges, lastplanes, lastdist
updates qh.furthest_id (-3 if furthest is NULL)
also resets visit_id, vertext_visit on wrap around
see:
qh_tracemerging()
design:
if !furthest
print progress message
exit
if 'TFn' iteration
print progress message
else if tracing
trace furthest point and facet
reset qh.visit_id and qh.vertex_visit if overflow may occur
set qh.furthest_id for tracing
*/
void qh_buildtracing(pointT *furthest, facetT *facet) {
realT dist= 0;
double cpu;
int total, furthestid;
time_t timedata;
struct tm *tp;
vertexT *vertex;
qh old_randomdist= qh RANDOMdist;
qh RANDOMdist= False;
if (!furthest) {
time(&timedata);
tp= localtime(&timedata);
cpu= (double)qh_CPUclock - (double)qh hulltime;
cpu /= (double)qh_SECticks;
total= zzval_(Ztotmerge) - zzval_(Zcyclehorizon) + zzval_(Zcyclefacettot);
qh_fprintf(qh ferr, 8118, "\n\
At %02d:%02d:%02d & %2.5g CPU secs, qhull has created %d facets and merged %d.\n\
The current hull contains %d facets and %d vertices. Last point was p%d\n",
tp->tm_hour, tp->tm_min, tp->tm_sec, cpu, qh facet_id -1,
total, qh num_facets, qh num_vertices, qh furthest_id);
return;
}
furthestid= qh_pointid(furthest);
#ifndef qh_NOtrace
if (qh TRACEpoint == furthestid) {
trace1((qh ferr, 1053, "qh_buildtracing: start trace T%d for point TP%d above facet f%d\n", qh TRACElevel, furthestid, facet->id));
qh IStracing= qh TRACElevel;
qhmem.IStracing= qh TRACElevel;
}else if (qh TRACEpoint != qh_IDnone && qh TRACEdist < REALmax/2) {
qh IStracing= 0;
qhmem.IStracing= 0;
}
#endif
if (qh REPORTfreq && (qh facet_id-1 > qh lastreport + (unsigned int)qh REPORTfreq)) {
qh lastreport= qh facet_id-1;
time(&timedata);
tp= localtime(&timedata);
cpu= (double)qh_CPUclock - (double)qh hulltime;
cpu /= (double)qh_SECticks;
total= zzval_(Ztotmerge) - zzval_(Zcyclehorizon) + zzval_(Zcyclefacettot);
zinc_(Zdistio);
qh_distplane(furthest, facet, &dist);
qh_fprintf(qh ferr, 8119, "\n\
At %02d:%02d:%02d & %2.5g CPU secs, qhull has created %d facets and merged %d.\n\
The current hull contains %d facets and %d vertices. There are %d\n\
outside points. Next is point p%d(v%d), %2.2g above f%d.\n",
tp->tm_hour, tp->tm_min, tp->tm_sec, cpu, qh facet_id -1,
total, qh num_facets, qh num_vertices, qh num_outside+1,
furthestid, qh vertex_id, dist, getid_(facet));
}else if (qh IStracing >=1) {
cpu= (double)qh_CPUclock - (double)qh hulltime;
cpu /= (double)qh_SECticks;
qh_distplane(furthest, facet, &dist);
qh_fprintf(qh ferr, 1049, "qh_addpoint: add p%d(v%d) %2.2g above f%d to hull of %d facets, %d merges, %d outside at %4.4g CPU secs. Previous p%d(v%d) delta %4.4g CPU, %d facets, %d merges, %d hyperplanes, %d distplanes, %d retries\n",
furthestid, qh vertex_id, dist, getid_(facet), qh num_facets, zzval_(Ztotmerge), qh num_outside+1, cpu, qh furthest_id, qh vertex_id - 1,
cpu - qh lastcpu, qh num_facets - qh lastfacets, zzval_(Ztotmerge) - qh lastmerges, zzval_(Zsetplane) - qh lastplanes, zzval_(Zdistplane) - qh lastdist, qh retry_addpoint);
qh lastcpu= cpu;
qh lastfacets= qh num_facets;
qh lastmerges= zzval_(Ztotmerge);
qh lastplanes= zzval_(Zsetplane);
qh lastdist= zzval_(Zdistplane);
}
zmax_(Zvisit2max, (int)qh visit_id/2);
if (qh visit_id > (unsigned int) INT_MAX) { /* 31 bits */
zinc_(Zvisit);
if (!qh_checklists(qh facet_list)) {
qh_fprintf(qh ferr, 6370, "qhull internal error: qh_checklists failed on reset of qh.visit_id %u\n", qh visit_id);
qh_errexit(qh_ERRqhull, NULL, NULL);
}
qh visit_id= 0;
FORALLfacets
facet->visitid= 0;
}
zmax_(Zvvisit2max, (int)qh vertex_visit/2);
if (qh vertex_visit > (unsigned int) INT_MAX) { /* 31 bits */
zinc_(Zvvisit);
if (qh visit_id && !qh_checklists(qh facet_list)) {
qh_fprintf(qh ferr, 6371, "qhull internal error: qh_checklists failed on reset of qh.vertex_visit %u\n", qh vertex_visit);
qh_errexit(qh_ERRqhull, NULL, NULL);
}
qh vertex_visit= 0;
FORALLvertices
vertex->visitid= 0;
}
qh furthest_id= furthestid;
qh RANDOMdist= qh old_randomdist;
} /* buildtracing */
/*---------------------------------
qh_errexit2( exitcode, facet, otherfacet )
return exitcode to system after an error
report two facets
returns:
assumes exitcode non-zero
see:
normally use qh_errexit() in user.c(reports a facet and a ridge)
*/
void qh_errexit2(int exitcode, facetT *facet, facetT *otherfacet) {
qh tracefacet= NULL; /* avoid infinite recursion through qh_fprintf */
qh traceridge= NULL;
qh tracevertex= NULL;
qh_errprint("ERRONEOUS", facet, otherfacet, NULL, NULL);
qh_errexit(exitcode, NULL, NULL);
} /* errexit2 */
/*---------------------------------
qh_findhorizon( point, facet, goodvisible, goodhorizon )
given a visible facet, find the point's horizon and visible facets
for all facets, !facet-visible
returns:
returns qh.visible_list/num_visible with all visible facets
marks visible facets with ->visible
updates count of good visible and good horizon facets
updates qh.max_outside, qh.max_vertex, facet->maxoutside
see:
similar to qh_delpoint()
design:
move facet to qh.visible_list at end of qh.facet_list
for all visible facets
for each unvisited neighbor of a visible facet
compute distance of point to neighbor
if point above neighbor
move neighbor to end of qh.visible_list
else if point is coplanar with neighbor
update qh.max_outside, qh.max_vertex, neighbor->maxoutside
mark neighbor coplanar (will create a samecycle later)
update horizon statistics
*/
void qh_findhorizon(pointT *point, facetT *facet, int *goodvisible, int *goodhorizon) {
facetT *neighbor, **neighborp, *visible;
int numhorizon= 0, coplanar= 0;
realT dist;
trace1((qh ferr, 1040, "qh_findhorizon: find horizon for point p%d facet f%d\n",qh_pointid(point),facet->id));
*goodvisible= *goodhorizon= 0;
zinc_(Ztotvisible);
qh_removefacet(facet); /* visible_list at end of qh facet_list */
qh_appendfacet(facet);
qh num_visible= 1;
if (facet->good)
(*goodvisible)++;
qh visible_list= facet;
facet->visible= True;
facet->f.replace= NULL;
if (qh IStracing >=4)
qh_errprint("visible", facet, NULL, NULL, NULL);
qh visit_id++;
FORALLvisible_facets {
if (visible->tricoplanar && !qh TRInormals) {
qh_fprintf(qh ferr, 6230, "qhull internal error (qh_findhorizon): does not work for tricoplanar facets. Use option 'Q11'\n");
qh_errexit(qh_ERRqhull, visible, NULL);
}
if (qh_setsize(visible->neighbors) == 0) {
qh_fprintf(qh ferr, 6295, "qhull internal error (qh_findhorizon): visible facet f%d does not have neighbors\n", visible->id);
qh_errexit(qh_ERRqhull, visible, NULL);
}
visible->visitid= qh visit_id;
FOREACHneighbor_(visible) {
if (neighbor->visitid == qh visit_id)
continue;
neighbor->visitid= qh visit_id;
zzinc_(Znumvisibility);
qh_distplane(point, neighbor, &dist);
if (dist > qh MINvisible) {
zinc_(Ztotvisible);
qh_removefacet(neighbor); /* append to end of qh visible_list */
qh_appendfacet(neighbor);
neighbor->visible= True;
neighbor->f.replace= NULL;
qh num_visible++;
if (neighbor->good)
(*goodvisible)++;
if (qh IStracing >=4)
qh_errprint("visible", neighbor, NULL, NULL, NULL);
}else {
if (dist >= -qh MAXcoplanar) {
neighbor->coplanarhorizon= True;
zzinc_(Zcoplanarhorizon);
qh_joggle_restart("coplanar horizon");
coplanar++;
if (qh MERGING) {
if (dist > 0) {
maximize_(qh max_outside, dist);
maximize_(qh max_vertex, dist);
#if qh_MAXoutside
maximize_(neighbor->maxoutside, dist);
#endif
}else
minimize_(qh min_vertex, dist); /* due to merge later */
}
trace2((qh ferr, 2057, "qh_findhorizon: point p%d is coplanar to horizon f%d, dist=%2.7g < qh MINvisible(%2.7g)\n",
qh_pointid(point), neighbor->id, dist, qh MINvisible));
}else
neighbor->coplanarhorizon= False;
zinc_(Ztothorizon);
numhorizon++;
if (neighbor->good)
(*goodhorizon)++;
if (qh IStracing >=4)
qh_errprint("horizon", neighbor, NULL, NULL, NULL);
}
}
}
if (!numhorizon) {
qh_joggle_restart("empty horizon");
qh_fprintf(qh ferr, 6168, "qhull topology error (qh_findhorizon): empty horizon for p%d. It was above all facets.\n", qh_pointid(point));
if (qh num_facets < 100) {
qh_printfacetlist(qh facet_list, NULL, True);
}
qh_errexit(qh_ERRtopology, NULL, NULL);
}
trace1((qh ferr, 1041, "qh_findhorizon: %d horizon facets(good %d), %d visible(good %d), %d coplanar\n",
numhorizon, *goodhorizon, qh num_visible, *goodvisible, coplanar));
if (qh IStracing >= 4 && qh num_facets < 100)
qh_printlists();
} /* findhorizon */
/*---------------------------------
qh_joggle_restart( reason )
if joggle ('QJn') and not merging, restart on precision and topology errors
*/
void qh_joggle_restart(const char *reason) {
if (qh JOGGLEmax < REALmax/2) {
if (qh ALLOWrestart && !qh PREmerge && !qh MERGEexact) {
trace0((qh ferr, 26, "qh_joggle_restart: qhull restart because of %s\n", reason));
/* May be called repeatedly if qh ALLOWrestart */
longjmp(qh restartexit, qh_ERRprec);
}
}
} /* qh_joggle_restart */
/*---------------------------------
qh_nextfurthest( visible )
returns next furthest point and visible facet for qh_addpoint()
starts search at qh.facet_next
returns:
removes furthest point from outside set
NULL if none available
advances qh.facet_next over facets with empty outside sets
design:
for each facet from qh.facet_next
if empty outside set
advance qh.facet_next
else if qh.NARROWhull
determine furthest outside point
if furthest point is not outside
advance qh.facet_next(point will be coplanar)
remove furthest point from outside set
*/
pointT *qh_nextfurthest(facetT **visible) {
facetT *facet;
int size, idx, loopcount= 0;
realT randr, dist;
pointT *furthest;
while ((facet= qh facet_next) != qh facet_tail) {
if (!facet || loopcount++ > qh num_facets) {
qh_fprintf(qh ferr, 6406, "qhull internal error (qh_nextfurthest): null facet or infinite loop detected for qh.facet_next f%d facet_tail f%d\n",
getid_(facet), getid_(qh facet_tail));
qh_printlists();
qh_errexit2(qh_ERRqhull, facet, qh facet_tail);
}
if (!facet->outsideset) {
qh facet_next= facet->next;
continue;
}
SETreturnsize_(facet->outsideset, size);
if (!size) {
qh_setfree(&facet->outsideset);
qh facet_next= facet->next;
continue;
}
if (qh NARROWhull) {
if (facet->notfurthest)
qh_furthestout(facet);
furthest= (pointT *)qh_setlast(facet->outsideset);
#if qh_COMPUTEfurthest
qh_distplane(furthest, facet, &dist);
zinc_(Zcomputefurthest);
#else
dist= facet->furthestdist;
#endif
if (dist < qh MINoutside) { /* remainder of outside set is coplanar for qh_outcoplanar */
qh facet_next= facet->next;
continue;
}
}
if (!qh RANDOMoutside && !qh VIRTUALmemory) {
if (qh PICKfurthest) {
qh_furthestnext(/* qh.facet_list */);
facet= qh facet_next;
}
*visible= facet;
return ((pointT *)qh_setdellast(facet->outsideset));
}
if (qh RANDOMoutside) {
int outcoplanar= 0;
if (qh NARROWhull) {
FORALLfacets {
if (facet == qh facet_next)
break;
if (facet->outsideset)
outcoplanar += qh_setsize(facet->outsideset);
}
}
randr= qh_RANDOMint;
randr= randr/(qh_RANDOMmax+1);
randr= floor((qh num_outside - outcoplanar) * randr);
idx= (int)randr;
FORALLfacet_(qh facet_next) {
if (facet->outsideset) {
SETreturnsize_(facet->outsideset, size);
if (!size)
qh_setfree(&facet->outsideset);
else if (size > idx) {
*visible= facet;
return ((pointT *)qh_setdelnth(facet->outsideset, idx));
}else
idx -= size;
}
}
qh_fprintf(qh ferr, 6169, "qhull internal error (qh_nextfurthest): num_outside %d is too low\nby at least %d, or a random real %g >= 1.0\n",
qh num_outside, idx+1, randr);
qh_errexit(qh_ERRqhull, NULL, NULL);
}else { /* VIRTUALmemory */
facet= qh facet_tail->previous;
if (!(furthest= (pointT *)qh_setdellast(facet->outsideset))) {
if (facet->outsideset)
qh_setfree(&facet->outsideset);
qh_removefacet(facet);
qh_prependfacet(facet, &qh facet_list);
continue;
}
*visible= facet;
return furthest;
}
}
return NULL;
} /* nextfurthest */
/*---------------------------------
qh_partitionall( vertices, points, numpoints )
partitions all points in points/numpoints to the outsidesets of facets
vertices= vertices in qh.facet_list(!partitioned)
returns:
builds facet->outsideset
does not partition qh.GOODpoint
if qh.ONLYgood && !qh.MERGING,
does not partition qh.GOODvertex
notes:
faster if qh.facet_list sorted by anticipated size of outside set
design:
initialize pointset with all points
remove vertices from pointset
remove qh.GOODpointp from pointset (unless it's qh.STOPcone or qh.STOPpoint)
for all facets
for all remaining points in pointset
compute distance from point to facet
if point is outside facet
remove point from pointset (by not reappending)
update bestpoint
append point or old bestpoint to facet's outside set
append bestpoint to facet's outside set (furthest)
for all points remaining in pointset
partition point into facets' outside sets and coplanar sets
*/
void qh_partitionall(setT *vertices, pointT *points, int numpoints){
setT *pointset;
vertexT *vertex, **vertexp;
pointT *point, **pointp, *bestpoint;
int size, point_i, point_n, point_end, remaining, i, id;
facetT *facet;
realT bestdist= -REALmax, dist, distoutside;
trace1((qh ferr, 1042, "qh_partitionall: partition all points into outside sets\n"));
pointset= qh_settemp(numpoints);
qh num_outside= 0;
pointp= SETaddr_(pointset, pointT);
for (i=numpoints, point= points; i--; point += qh hull_dim)
*(pointp++)= point;
qh_settruncate(pointset, numpoints);
FOREACHvertex_(vertices) {
if ((id= qh_pointid(vertex->point)) >= 0)
SETelem_(pointset, id)= NULL;
}
id= qh_pointid(qh GOODpointp);
if (id >=0 && qh STOPcone-1 != id && -qh STOPpoint-1 != id)
SETelem_(pointset, id)= NULL;
if (qh GOODvertexp && qh ONLYgood && !qh MERGING) { /* matches qhull()*/
if ((id= qh_pointid(qh GOODvertexp)) >= 0)
SETelem_(pointset, id)= NULL;
}
if (!qh BESToutside) { /* matches conditional for qh_partitionpoint below */
distoutside= qh_DISToutside; /* multiple of qh.MINoutside & qh.max_outside, see user.h */
zval_(Ztotpartition)= qh num_points - qh hull_dim - 1; /*misses GOOD... */
remaining= qh num_facets;
point_end= numpoints;
FORALLfacets {
size= point_end/(remaining--) + 100;
facet->outsideset= qh_setnew(size);
bestpoint= NULL;
point_end= 0;
FOREACHpoint_i_(pointset) {
if (point) {
zzinc_(Zpartitionall);
qh_distplane(point, facet, &dist);
if (dist < distoutside)
SETelem_(pointset, point_end++)= point;
else {
qh num_outside++;
if (!bestpoint) {
bestpoint= point;
bestdist= dist;
}else if (dist > bestdist) {
qh_setappend(&facet->outsideset, bestpoint);
bestpoint= point;
bestdist= dist;
}else
qh_setappend(&facet->outsideset, point);
}
}
}
if (bestpoint) {
qh_setappend(&facet->outsideset, bestpoint);
#if !qh_COMPUTEfurthest
facet->furthestdist= bestdist;
#endif
}else
qh_setfree(&facet->outsideset);
qh_settruncate(pointset, point_end);
}
}
/* if !qh BESToutside, pointset contains points not assigned to outsideset */
if (qh BESToutside || qh MERGING || qh KEEPcoplanar || qh KEEPinside || qh KEEPnearinside) {
qh findbestnew= True;
FOREACHpoint_i_(pointset) {
if (point)
qh_partitionpoint(point, qh facet_list);
}
qh findbestnew= False;
}
zzadd_(Zpartitionall, zzval_(Zpartition));
zzval_(Zpartition)= 0;
qh_settempfree(&pointset);
if (qh IStracing >= 4)
qh_printfacetlist(qh facet_list, NULL, True);
} /* partitionall */
/*---------------------------------
qh_partitioncoplanar( point, facet, dist, allnew )
partition coplanar point to a facet
dist is distance from point to facet
if dist NULL,
searches for bestfacet and does nothing if inside
if allnew (qh.findbestnew)
searches new facets instead of using qh_findbest()
returns:
qh.max_ouside updated
if qh.KEEPcoplanar or qh.KEEPinside
point assigned to best coplanarset
qh.repart_facetid==0 (for detecting infinite recursion via qh_partitionpoint)
notes:
facet->maxoutside is updated at end by qh_check_maxout
design:
if dist undefined
find best facet for point
if point sufficiently below facet (depends on qh.NEARinside and qh.KEEPinside)
exit
if keeping coplanar/nearinside/inside points
if point is above furthest coplanar point
append point to coplanar set (it is the new furthest)
update qh.max_outside
else
append point one before end of coplanar set
else if point is clearly outside of qh.max_outside and bestfacet->coplanarset
and bestfacet is more than perpendicular to facet
repartition the point using qh_findbest() -- it may be put on an outsideset
else
update qh.max_outside
*/
void qh_partitioncoplanar(pointT *point, facetT *facet, realT *dist, boolT allnew) {
facetT *bestfacet;
pointT *oldfurthest;
realT bestdist, angle, nearest, dist2= 0.0;
int numpart= 0;
boolT isoutside, oldfindbest, repartition= False;
trace4((qh ferr, 4090, "qh_partitioncoplanar: partition coplanar point p%d starting with f%d dist? %2.2g, allnew? %d, gh.repart_facetid f%d\n",
qh_pointid(point), facet->id, (dist ? *dist : 0.0), allnew, qh repart_facetid));
qh WAScoplanar= True;
if (!dist) {
if (allnew)
bestfacet= qh_findbestnew(point, facet, &bestdist, qh_ALL, &isoutside, &numpart);
else
bestfacet= qh_findbest(point, facet, qh_ALL, !qh_ISnewfacets, qh DELAUNAY,
&bestdist, &isoutside, &numpart);
zinc_(Ztotpartcoplanar);
zzadd_(Zpartcoplanar, numpart);
if (!qh DELAUNAY && !qh KEEPinside) { /* for 'd', bestdist skips upperDelaunay facets */
if (qh KEEPnearinside) {
if (bestdist < -qh NEARinside) {
zinc_(Zcoplanarinside);
trace4((qh ferr, 4062, "qh_partitioncoplanar: point p%d is more than near-inside facet f%d dist %2.2g allnew? %d\n",
qh_pointid(point), bestfacet->id, bestdist, allnew));
qh repart_facetid= 0;
return;
}
}else if (bestdist < -qh MAXcoplanar) {
trace4((qh ferr, 4063, "qh_partitioncoplanar: point p%d is inside facet f%d dist %2.2g allnew? %d\n",
qh_pointid(point), bestfacet->id, bestdist, allnew));
zinc_(Zcoplanarinside);
qh repart_facetid= 0;
return;
}
}
}else {
bestfacet= facet;
bestdist= *dist;
}
if(bestfacet->visible){
qh_fprintf(qh ferr, 6405, "qhull internal error (qh_partitioncoplanar): cannot partition coplanar p%d of f%d into visible facet f%d\n",
qh_pointid(point), facet->id, bestfacet->id);
qh_errexit2(qh_ERRqhull, facet, bestfacet);
}
if (bestdist > qh max_outside) {
if (!dist && facet != bestfacet) { /* can't be recursive from qh_partitionpoint since facet != bestfacet */
zinc_(Zpartangle);
angle= qh_getangle(facet->normal, bestfacet->normal);
if (angle < 0) {
nearest= qh_vertex_bestdist(bestfacet->vertices);
/* typically due to deleted vertex and coplanar facets, e.g.,
RBOX 1000 s Z1 G1e-13 t1001185205 | QHULL Tv */
zinc_(Zpartcorner);
trace2((qh ferr, 2058, "qh_partitioncoplanar: repartition coplanar point p%d from f%d as an outside point above corner facet f%d dist %2.2g with angle %2.2g\n",
qh_pointid(point), facet->id, bestfacet->id, bestdist, angle));
repartition= True;
}
}
if (!repartition) {
if (bestdist > qh MAXoutside * qh_RATIOcoplanaroutside) {
nearest= qh_vertex_bestdist(bestfacet->vertices);
if (facet->id == bestfacet->id) {
if (facet->id == qh repart_facetid) {
qh_fprintf(qh ferr, 6404, "Qhull internal error (qh_partitioncoplanar): infinite loop due to recursive call to qh_partitionpoint. Repartition point p%d from f%d as a outside point dist %2.2g nearest vertices %2.2g\n",
qh_pointid(point), facet->id, bestdist, nearest);
qh_errexit(qh_ERRqhull, facet, NULL);
}
qh repart_facetid= facet->id; /* reset after call to qh_partitionpoint */
}
if (point == qh coplanar_apex) {
/* otherwise may loop indefinitely, the point is well above a facet, yet near a vertex */
qh_fprintf(qh ferr, 6425, "Qhull topology error (qh_partitioncoplanar): can not repartition coplanar point p%d from f%d as outside point above f%d. It previously failed to form a cone of facets, dist %2.2g, nearest vertices %2.2g\n",
qh_pointid(point), facet->id, bestfacet->id, bestdist, nearest);
qh_errexit(qh_ERRtopology, facet, NULL);
}
if (nearest < 2 * qh MAXoutside * qh_RATIOcoplanaroutside) {
zinc_(Zparttwisted);
qh_fprintf(qh ferr, 7085, "Qhull precision warning: repartition coplanar point p%d from f%d as an outside point above twisted facet f%d dist %2.2g nearest vertices %2.2g\n",
qh_pointid(point), facet->id, bestfacet->id, bestdist, nearest);
}else {
zinc_(Zparthidden);
qh_fprintf(qh ferr, 7086, "Qhull precision warning: repartition coplanar point p%d from f%d as an outside point above hidden facet f%d dist %2.2g nearest vertices %2.2g\n",
qh_pointid(point), facet->id, bestfacet->id, bestdist, nearest);
}
repartition= True;
}
}
if (repartition) {
oldfindbest= qh findbestnew;
qh findbestnew= False;
qh_partitionpoint(point, bestfacet);
qh findbestnew= oldfindbest;
qh repart_facetid= 0;
return;
}
qh repart_facetid= 0;
qh max_outside= bestdist;
if (bestdist > qh TRACEdist || qh IStracing >= 3) {
qh_fprintf(qh ferr, 3041, "qh_partitioncoplanar: == p%d from f%d increases qh.max_outside to %2.2g of f%d last p%d\n",
qh_pointid(point), facet->id, bestdist, bestfacet->id, qh furthest_id);
qh_errprint("DISTANT", facet, bestfacet, NULL, NULL);
}
}
if (qh KEEPcoplanar + qh KEEPinside + qh KEEPnearinside) {
oldfurthest= (pointT *)qh_setlast(bestfacet->coplanarset);
if (oldfurthest) {
zinc_(Zcomputefurthest);
qh_distplane(oldfurthest, bestfacet, &dist2);
}
if (!oldfurthest || dist2 < bestdist)
qh_setappend(&bestfacet->coplanarset, point);
else
qh_setappend2ndlast(&bestfacet->coplanarset, point);
}
trace4((qh ferr, 4064, "qh_partitioncoplanar: point p%d is coplanar with facet f%d (or inside) dist %2.2g\n",
qh_pointid(point), bestfacet->id, bestdist));
} /* partitioncoplanar */
/*---------------------------------
qh_partitionpoint( point, facet )
assigns point to an outside set, coplanar set, or inside set (i.e., dropt)
if qh.findbestnew
uses qh_findbestnew() to search all new facets
else
uses qh_findbest()
notes:
after qh_distplane(), this and qh_findbest() are most expensive in 3-d
design:
find best facet for point
(either exhaustive search of new facets or directed search from facet)
if qh.NARROWhull
retain coplanar and nearinside points as outside points
if point is outside bestfacet
if point above furthest point for bestfacet
append point to outside set (it becomes the new furthest)
if outside set was empty
move bestfacet to end of qh.facet_list (i.e., after qh.facet_next)
update bestfacet->furthestdist
else
append point one before end of outside set
else if point is coplanar to bestfacet
if keeping coplanar points or need to update qh.max_outside
partition coplanar point into bestfacet
else if near-inside point
partition as coplanar point into bestfacet
else is an inside point
if keeping inside points
partition as coplanar point into bestfacet
*/
void qh_partitionpoint(pointT *point, facetT *facet) {
realT bestdist, previousdist;
boolT isoutside, isnewoutside= False;
facetT *bestfacet;
int numpart;
if (qh findbestnew)
bestfacet= qh_findbestnew(point, facet, &bestdist, qh BESToutside, &isoutside, &numpart);
else
bestfacet= qh_findbest(point, facet, qh BESToutside, qh_ISnewfacets, !qh_NOupper,
&bestdist, &isoutside, &numpart);
zinc_(Ztotpartition);
zzadd_(Zpartition, numpart);
if(bestfacet->visible){
qh_fprintf(qh ferr, 6293, "qhull internal error (qh_partitionpoint): cannot partition p%d of f%d into visible facet f%d\n",
qh_pointid(point), facet->id, bestfacet->id);
qh_errexit2(qh_ERRqhull, facet, bestfacet);
}
if (qh NARROWhull) {
if (qh DELAUNAY && !isoutside && bestdist >= -qh MAXcoplanar)
qh_joggle_restart("nearly incident point (narrow hull)");
if (qh KEEPnearinside) {
if (bestdist >= -qh NEARinside)
isoutside= True;
}else if (bestdist >= -qh MAXcoplanar)
isoutside= True;
}
if (isoutside) {
if (!bestfacet->outsideset
|| !qh_setlast(bestfacet->outsideset)) { /* empty outside set */
qh_setappend(&(bestfacet->outsideset), point);
if (!qh NARROWhull || bestdist > qh MINoutside)
isnewoutside= True;
#if !qh_COMPUTEfurthest
bestfacet->furthestdist= bestdist;
#endif
}else {
#if qh_COMPUTEfurthest
zinc_(Zcomputefurthest);
qh_distplane(oldfurthest, bestfacet, &previousdist);
if (previousdist < bestdist)
qh_setappend(&(bestfacet->outsideset), point);
else
qh_setappend2ndlast(&(bestfacet->outsideset), point);
#else
previousdist= bestfacet->furthestdist;
if (previousdist < bestdist) {
qh_setappend(&(bestfacet->outsideset), point);
bestfacet->furthestdist= bestdist;
if (qh NARROWhull && previousdist < qh MINoutside && bestdist >= qh MINoutside)
isnewoutside= True;
}else
qh_setappend2ndlast(&(bestfacet->outsideset), point);
#endif
}
if (isnewoutside && qh facet_next != bestfacet) {
if (bestfacet->newfacet) {
if (qh facet_next->newfacet)
qh facet_next= qh newfacet_list; /* make sure it's after qh.facet_next */
}else {
qh_removefacet(bestfacet); /* make sure it's after qh.facet_next */
qh_appendfacet(bestfacet);
if(qh newfacet_list){
bestfacet->newfacet= True;
}
}
}
qh num_outside++;
trace4((qh ferr, 4065, "qh_partitionpoint: point p%d is outside facet f%d newfacet? %d, newoutside? %d (or narrowhull)\n",
qh_pointid(point), bestfacet->id, bestfacet->newfacet, isnewoutside));
}else if (qh DELAUNAY || bestdist >= -qh MAXcoplanar) { /* for 'd', bestdist skips upperDelaunay facets */
if (qh DELAUNAY)
qh_joggle_restart("nearly incident point");
/* allow coplanar points with joggle, may be interior */
zzinc_(Zcoplanarpart);
if ((qh KEEPcoplanar + qh KEEPnearinside) || bestdist > qh max_outside)
qh_partitioncoplanar(point, bestfacet, &bestdist, qh findbestnew);
else {
trace4((qh ferr, 4066, "qh_partitionpoint: point p%d is coplanar to facet f%d (dropped)\n",
qh_pointid(point), bestfacet->id));
}
}else if (qh KEEPnearinside && bestdist >= -qh NEARinside) {
zinc_(Zpartnear);
qh_partitioncoplanar(point, bestfacet, &bestdist, qh findbestnew);
}else {
zinc_(Zpartinside);
trace4((qh ferr, 4067, "qh_partitionpoint: point p%d is inside all facets, closest to f%d dist %2.2g\n",
qh_pointid(point), bestfacet->id, bestdist));
if (qh KEEPinside)
qh_partitioncoplanar(point, bestfacet, &bestdist, qh findbestnew);
}
} /* partitionpoint */
/*---------------------------------
qh_partitionvisible( allpoints, numoutside )
partitions outside points in visible facets (qh.visible_list) to qh.newfacet_list
if keeping coplanar/near-inside/inside points
partitions coplanar points; repartitions if 'allpoints' (not used)
1st neighbor (if any) of visible facets points to a horizon facet or a new facet
returns:
updates outside sets and coplanar sets of qh.newfacet_list
updates qh.num_outside (count of outside points)
does not truncate f.outsideset, f.coplanarset, or qh.del_vertices (see qh_deletevisible)
notes:
called by qh_qhull, qh_addpoint, and qh_all_vertexmerges
qh.findbest_notsharp should be clear (extra work if set)
design:
for all visible facets with outside set or coplanar set
select a newfacet for visible facet
if outside set
partition outside set into new facets
if coplanar set and keeping coplanar/near-inside/inside points
if allpoints
partition coplanar set into new facets, may be assigned outside
else
partition coplanar set into coplanar sets of new facets
for each deleted vertex
if allpoints
partition vertex into new facets, may be assigned outside
else
partition vertex into coplanar sets of new facets
*/
void qh_partitionvisible(boolT allpoints, int *numoutside /* qh.visible_list */) {
facetT *visible, *newfacet;
pointT *point, **pointp;
int delsize, coplanar=0, size;
vertexT *vertex, **vertexp;
trace3((qh ferr, 3042, "qh_partitionvisible: partition outside and coplanar points of visible and merged facets f%d into new facets f%d\n",
qh visible_list->id, qh newfacet_list->id));
if (qh ONLYmax)
maximize_(qh MINoutside, qh max_vertex);
*numoutside= 0;
FORALLvisible_facets {
if (!visible->outsideset && !visible->coplanarset)
continue;
newfacet= qh_getreplacement(visible);
if (!newfacet)
newfacet= qh newfacet_list;
if (!newfacet->next) {
qh_fprintf(qh ferr, 6170, "qhull topology error (qh_partitionvisible): all new facets deleted as\n degenerate facets. Can not continue.\n");
qh_errexit(qh_ERRtopology, NULL, NULL);
}
if (visible->outsideset) {
size= qh_setsize(visible->outsideset);
*numoutside += size;
qh num_outside -= size;
FOREACHpoint_(visible->outsideset)
qh_partitionpoint(point, newfacet);
}
if (visible->coplanarset && (qh KEEPcoplanar + qh KEEPinside + qh KEEPnearinside)) {
size= qh_setsize(visible->coplanarset);
coplanar += size;
FOREACHpoint_(visible->coplanarset) {
if (allpoints) /* not used */
qh_partitionpoint(point, newfacet);
else
qh_partitioncoplanar(point, newfacet, NULL, qh findbestnew);
}
}
}
delsize= qh_setsize(qh del_vertices);
if (delsize > 0) {
trace3((qh ferr, 3049, "qh_partitionvisible: partition %d deleted vertices as coplanar? %d points into new facets f%d\n",
delsize, !allpoints, qh newfacet_list->id));
FOREACHvertex_(qh del_vertices) {
if (vertex->point && !vertex->partitioned) {
if (!qh newfacet_list || qh newfacet_list == qh facet_tail) {
qh_fprintf(qh ferr, 6284, "qhull internal error (qh_partitionvisible): all new facets deleted or none defined. Can not partition deleted v%d.\n", vertex->id);
qh_errexit(qh_ERRqhull, NULL, NULL);
}
if (allpoints) /* not used */
/* [apr'2019] infinite loop if vertex recreates the same facets from the same horizon
e.g., qh_partitionpoint if qh.DELAUNAY with qh.MERGEindependent for all mergetype, ../eg/qtest.sh t427764 '1000 s W1e-13 D3' 'd' */
qh_partitionpoint(vertex->point, qh newfacet_list);
else
qh_partitioncoplanar(vertex->point, qh newfacet_list, NULL, qh_ALL); /* search all new facets */
vertex->partitioned= True;
}
}
}
trace1((qh ferr, 1043,"qh_partitionvisible: partitioned %d points from outsidesets, %d points from coplanarsets, and %d deleted vertices\n", *numoutside, coplanar, delsize));
} /* partitionvisible */
/*---------------------------------
qh_printsummary( fp )
prints summary to fp
notes:
not in io.c so that user_eg.c can prevent io.c from loading
qh_printsummary and qh_countfacets must match counts
updates qh.facet_visit to detect infinite loop
design:
determine number of points, vertices, and coplanar points
print summary
*/
void qh_printsummary(FILE *fp) {
realT ratio, outerplane, innerplane;
double cpu;
int size, id, nummerged, numpinched, numvertices, numcoplanars= 0, nonsimplicial=0, numdelaunay= 0;
facetT *facet;
const char *s;
int numdel= zzval_(Zdelvertextot);
int numtricoplanars= 0;
boolT goodused;
size= qh num_points + qh_setsize(qh other_points);
numvertices= qh num_vertices - qh_setsize(qh del_vertices);
id= qh_pointid(qh GOODpointp);
if (!qh_checklists(qh facet_list) && !qh ERREXITcalled) {
qh_fprintf(fp, 6372, "qhull internal error: qh_checklists failed at qh_printsummary\n");
if (qh num_facets < 4000)
qh_printlists();
qh_errexit(qh_ERRqhull, NULL, NULL);
}
if (qh DELAUNAY && qh ERREXITcalled) {
/* update f.good and determine qh.num_good as in qh_findgood_all */
FORALLfacets {
if (facet->visible)
facet->good= False; /* will be deleted */
else if (facet->good) {
if (facet->normal && !qh_inthresholds(facet->normal, NULL))
facet->good= False;
else
numdelaunay++;
}
}
qh num_good= numdelaunay;
}
FORALLfacets {
if (facet->coplanarset)
numcoplanars += qh_setsize(facet->coplanarset);
if (facet->good) {
if (facet->simplicial) {
if (facet->keepcentrum && facet->tricoplanar)
numtricoplanars++;
}else if (qh_setsize(facet->vertices) != qh hull_dim)
nonsimplicial++;
}
}
if (id >=0 && qh STOPcone-1 != id && -qh STOPpoint-1 != id)
size--;
if (qh STOPadd || qh STOPcone || qh STOPpoint)
qh_fprintf(fp, 9288, "\nEarly exit due to 'TAn', 'TVn', 'TCn', 'TRn', or precision error with 'QJn'.");
goodused= False;
if (qh ERREXITcalled)
; /* qh_findgood_all not called */
else if (qh UPPERdelaunay) {
if (qh GOODvertex || qh GOODpoint || qh SPLITthresholds)
goodused= True;
}else if (qh DELAUNAY) {
if (qh GOODvertex || qh GOODpoint || qh GOODthreshold)
goodused= True;
}else if (qh num_good > 0 || qh GOODthreshold)
goodused= True;
nummerged= zzval_(Ztotmerge) - zzval_(Zcyclehorizon) + zzval_(Zcyclefacettot);
if (qh VORONOI) {
if (qh UPPERdelaunay)
qh_fprintf(fp, 9289, "\n\
Furthest-site Voronoi vertices by the convex hull of %d points in %d-d:\n\n", size, qh hull_dim);
else
qh_fprintf(fp, 9290, "\n\
Voronoi diagram by the convex hull of %d points in %d-d:\n\n", size, qh hull_dim);
qh_fprintf(fp, 9291, " Number of Voronoi regions%s: %d\n",
qh ATinfinity ? " and at-infinity" : "", numvertices);
if (numdel)
qh_fprintf(fp, 9292, " Total number of deleted points due to merging: %d\n", numdel);
if (numcoplanars - numdel > 0)
qh_fprintf(fp, 9293, " Number of nearly incident points: %d\n", numcoplanars - numdel);
else if (size - numvertices - numdel > 0)
qh_fprintf(fp, 9294, " Total number of nearly incident points: %d\n", size - numvertices - numdel);
qh_fprintf(fp, 9295, " Number of%s Voronoi vertices: %d\n",
goodused ? " 'good'" : "", qh num_good);
if (nonsimplicial)
qh_fprintf(fp, 9296, " Number of%s non-simplicial Voronoi vertices: %d\n",
goodused ? " 'good'" : "", nonsimplicial);
}else if (qh DELAUNAY) {
if (qh UPPERdelaunay)
qh_fprintf(fp, 9297, "\n\
Furthest-site Delaunay triangulation by the convex hull of %d points in %d-d:\n\n", size, qh hull_dim);
else
qh_fprintf(fp, 9298, "\n\
Delaunay triangulation by the convex hull of %d points in %d-d:\n\n", size, qh hull_dim);
qh_fprintf(fp, 9299, " Number of input sites%s: %d\n",
qh ATinfinity ? " and at-infinity" : "", numvertices);
if (numdel)
qh_fprintf(fp, 9300, " Total number of deleted points due to merging: %d\n", numdel);
if (numcoplanars - numdel > 0)
qh_fprintf(fp, 9301, " Number of nearly incident points: %d\n", numcoplanars - numdel);
else if (size - numvertices - numdel > 0)
qh_fprintf(fp, 9302, " Total number of nearly incident points: %d\n", size - numvertices - numdel);
qh_fprintf(fp, 9303, " Number of%s Delaunay regions: %d\n",
goodused ? " 'good'" : "", qh num_good);
if (nonsimplicial)
qh_fprintf(fp, 9304, " Number of%s non-simplicial Delaunay regions: %d\n",
goodused ? " 'good'" : "", nonsimplicial);
}else if (qh HALFspace) {
qh_fprintf(fp, 9305, "\n\
Halfspace intersection by the convex hull of %d points in %d-d:\n\n", size, qh hull_dim);
qh_fprintf(fp, 9306, " Number of halfspaces: %d\n", size);
qh_fprintf(fp, 9307, " Number of non-redundant halfspaces: %d\n", numvertices);
if (numcoplanars) {
if (qh KEEPinside && qh KEEPcoplanar)
s= "similar and redundant";
else if (qh KEEPinside)
s= "redundant";
else
s= "similar";
qh_fprintf(fp, 9308, " Number of %s halfspaces: %d\n", s, numcoplanars);
}
qh_fprintf(fp, 9309, " Number of intersection points: %d\n", qh num_facets - qh num_visible);
if (goodused)
qh_fprintf(fp, 9310, " Number of 'good' intersection points: %d\n", qh num_good);
if (nonsimplicial)
qh_fprintf(fp, 9311, " Number of%s non-simplicial intersection points: %d\n",
goodused ? " 'good'" : "", nonsimplicial);
}else {
qh_fprintf(fp, 9312, "\n\
Convex hull of %d points in %d-d:\n\n", size, qh hull_dim);
qh_fprintf(fp, 9313, " Number of vertices: %d\n", numvertices);
if (numcoplanars) {
if (qh KEEPinside && qh KEEPcoplanar)
s= "coplanar and interior";
else if (qh KEEPinside)
s= "interior";
else
s= "coplanar";
qh_fprintf(fp, 9314, " Number of %s points: %d\n", s, numcoplanars);
}
qh_fprintf(fp, 9315, " Number of facets: %d\n", qh num_facets - qh num_visible);
if (goodused)
qh_fprintf(fp, 9316, " Number of 'good' facets: %d\n", qh num_good);
if (nonsimplicial)
qh_fprintf(fp, 9317, " Number of%s non-simplicial facets: %d\n",
goodused ? " 'good'" : "", nonsimplicial);
}
if (numtricoplanars)
qh_fprintf(fp, 9318, " Number of triangulated facets: %d\n", numtricoplanars);
qh_fprintf(fp, 9319, "\nStatistics for: %s | %s",
qh rbox_command, qh qhull_command);
if (qh ROTATErandom != INT_MIN)
qh_fprintf(fp, 9320, " QR%d\n\n", qh ROTATErandom);
else
qh_fprintf(fp, 9321, "\n\n");
qh_fprintf(fp, 9322, " Number of points processed: %d\n", zzval_(Zprocessed));
qh_fprintf(fp, 9323, " Number of hyperplanes created: %d\n", zzval_(Zsetplane));
if (qh DELAUNAY)
qh_fprintf(fp, 9324, " Number of facets in hull: %d\n", qh num_facets - qh num_visible);
qh_fprintf(fp, 9325, " Number of distance tests for qhull: %d\n", zzval_(Zpartition)+
zzval_(Zpartitionall)+zzval_(Znumvisibility)+zzval_(Zpartcoplanar));
#if 0 /* NOTE: must print before printstatistics() */
{realT stddev, ave;
qh_fprintf(fp, 9326, " average new facet balance: %2.2g\n",
wval_(Wnewbalance)/zval_(Zprocessed));
stddev= qh_stddev(zval_(Zprocessed), wval_(Wnewbalance),
wval_(Wnewbalance2), &ave);
qh_fprintf(fp, 9327, " new facet standard deviation: %2.2g\n", stddev);
qh_fprintf(fp, 9328, " average partition balance: %2.2g\n",
wval_(Wpbalance)/zval_(Zpbalance));
stddev= qh_stddev(zval_(Zpbalance), wval_(Wpbalance),
wval_(Wpbalance2), &ave);
qh_fprintf(fp, 9329, " partition standard deviation: %2.2g\n", stddev);
}
#endif
if (nummerged) {
qh_fprintf(fp, 9330," Number of distance tests for merging: %d\n",zzval_(Zbestdist)+
zzval_(Zcentrumtests)+zzval_(Zvertextests)+zzval_(Zdistcheck)+zzval_(Zdistzero));
qh_fprintf(fp, 9331," Number of distance tests for checking: %d\n",zzval_(Zcheckpart)+zzval_(Zdistconvex));
qh_fprintf(fp, 9332," Number of merged facets: %d\n", nummerged);
}
numpinched= zzval_(Zpinchduplicate) + zzval_(Zpinchedvertex);
if (numpinched)
qh_fprintf(fp, 9375," Number of merged pinched vertices: %d\n", numpinched);
if (!qh RANDOMoutside && qh QHULLfinished) {
cpu= (double)qh hulltime;
cpu /= (double)qh_SECticks;
wval_(Wcpu)= cpu;
qh_fprintf(fp, 9333, " CPU seconds to compute hull (after input): %2.4g\n", cpu);
}
if (qh RERUN) {
if (!qh PREmerge && !qh MERGEexact)
qh_fprintf(fp, 9334, " Percentage of runs with precision errors: %4.1f\n",
zzval_(Zretry)*100.0/qh build_cnt); /* careful of order */
}else if (qh JOGGLEmax < REALmax/2) {
if (zzval_(Zretry))
qh_fprintf(fp, 9335, " After %d retries, input joggled by: %2.2g\n",
zzval_(Zretry), qh JOGGLEmax);
else
qh_fprintf(fp, 9336, " Input joggled by: %2.2g\n", qh JOGGLEmax);
}
if (qh totarea != 0.0)
qh_fprintf(fp, 9337, " %s facet area: %2.8g\n",
zzval_(Ztotmerge) ? "Approximate" : "Total", qh totarea);
if (qh totvol != 0.0)
qh_fprintf(fp, 9338, " %s volume: %2.8g\n",
zzval_(Ztotmerge) ? "Approximate" : "Total", qh totvol);
if (qh MERGING) {
qh_outerinner(NULL, &outerplane, &innerplane);
if (outerplane > 2 * qh DISTround) {
qh_fprintf(fp, 9339, " Maximum distance of point above facet: %2.2g", outerplane);
ratio= outerplane/(qh ONEmerge + qh DISTround);
/* don't report ratio if MINoutside is large */
if (ratio > 0.05 && 2* qh ONEmerge > qh MINoutside && qh JOGGLEmax > REALmax/2)
qh_fprintf(fp, 9340, " (%.1fx)\n", ratio);
else
qh_fprintf(fp, 9341, "\n");
}
if (innerplane < -2 * qh DISTround) {
qh_fprintf(fp, 9342, " Maximum distance of vertex below facet: %2.2g", innerplane);
ratio= -innerplane/(qh ONEmerge+qh DISTround);
if (ratio > 0.05 && qh JOGGLEmax > REALmax/2)
qh_fprintf(fp, 9343, " (%.1fx)\n", ratio);
else
qh_fprintf(fp, 9344, "\n");
}
}
qh_fprintf(fp, 9345, "\n");
} /* printsummary */