forked from OSGeo/gdal
-
Notifications
You must be signed in to change notification settings - Fork 0
/
geom_r.c
1284 lines (1164 loc) · 45.3 KB
/
geom_r.c
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
/*<html><pre> -<a href="qh-geom_r.htm"
>-------------------------------</a><a name="TOP">-</a>
geom_r.c
geometric routines of qhull
see qh-geom_r.htm and geom_r.h
Copyright (c) 1993-2020 The Geometry Center.
$Id: //main/2019/qhull/src/libqhull_r/geom_r.c#5 $$Change: 2953 $
$DateTime: 2020/05/21 22:05:32 $$Author: bbarber $
infrequent code goes into geom2_r.c
*/
#include "qhull_ra.h"
/*-<a href="qh-geom_r.htm#TOC"
>-------------------------------</a><a name="distplane">-</a>
qh_distplane(qh, point, facet, dist )
return distance from point to facet
returns:
dist
if qh.RANDOMdist, joggles result
notes:
dist > 0 if point is above facet (i.e., outside)
does not error (for qh_sortfacets, qh_outerinner)
for nearly coplanar points, the returned values may be duplicates
for example pairs of nearly incident points, rbox 175 C1,2e-13 t1538759579 | qhull d T4
622 qh_distplane: e-014 # count of two or more duplicate values for unique calls
258 qh_distplane: e-015
38 qh_distplane: e-016
40 qh_distplane: e-017
6 qh_distplane: e-018
5 qh_distplane: -e-018
33 qh_distplane: -e-017
3153 qh_distplane: -2.775557561562891e-017 # duplicated value for 3153 unique calls
42 qh_distplane: -e-016
307 qh_distplane: -e-015
1271 qh_distplane: -e-014
13 qh_distplane: -e-013
see:
qh_distnorm in geom2_r.c
qh_distplane [geom_r.c], QhullFacet::distance, and QhullHyperplane::distance are copies
*/
void qh_distplane(qhT *qh, pointT *point, facetT *facet, realT *dist) {
coordT *normal= facet->normal, *coordp, randr;
int k;
switch (qh->hull_dim){
case 2:
*dist= facet->offset + point[0] * normal[0] + point[1] * normal[1];
break;
case 3:
*dist= facet->offset + point[0] * normal[0] + point[1] * normal[1] + point[2] * normal[2];
break;
case 4:
*dist= facet->offset+point[0]*normal[0]+point[1]*normal[1]+point[2]*normal[2]+point[3]*normal[3];
break;
case 5:
*dist= facet->offset+point[0]*normal[0]+point[1]*normal[1]+point[2]*normal[2]+point[3]*normal[3]+point[4]*normal[4];
break;
case 6:
*dist= facet->offset+point[0]*normal[0]+point[1]*normal[1]+point[2]*normal[2]+point[3]*normal[3]+point[4]*normal[4]+point[5]*normal[5];
break;
case 7:
*dist= facet->offset+point[0]*normal[0]+point[1]*normal[1]+point[2]*normal[2]+point[3]*normal[3]+point[4]*normal[4]+point[5]*normal[5]+point[6]*normal[6];
break;
case 8:
*dist= facet->offset+point[0]*normal[0]+point[1]*normal[1]+point[2]*normal[2]+point[3]*normal[3]+point[4]*normal[4]+point[5]*normal[5]+point[6]*normal[6]+point[7]*normal[7];
break;
default:
*dist= facet->offset;
coordp= point;
for (k=qh->hull_dim; k--; )
*dist += *coordp++ * *normal++;
break;
}
zzinc_(Zdistplane);
if (!qh->RANDOMdist && qh->IStracing < 4)
return;
if (qh->RANDOMdist) {
randr= qh_RANDOMint;
*dist += (2.0 * randr / qh_RANDOMmax - 1.0) *
qh->RANDOMfactor * qh->MAXabs_coord;
}
#ifndef qh_NOtrace
if (qh->IStracing >= 4) {
qh_fprintf(qh, qh->ferr, 8001, "qh_distplane: ");
qh_fprintf(qh, qh->ferr, 8002, qh_REAL_1, *dist);
qh_fprintf(qh, qh->ferr, 8003, "from p%d to f%d\n", qh_pointid(qh, point), facet->id);
}
#endif
return;
} /* distplane */
/*-<a href="qh-geom_r.htm#TOC"
>-------------------------------</a><a name="findbest">-</a>
qh_findbest(qh, point, startfacet, bestoutside, qh_ISnewfacets, qh_NOupper, dist, isoutside, numpart )
find facet that is furthest below a point
for upperDelaunay facets
returns facet only if !qh_NOupper and clearly above
input:
starts search at 'startfacet' (can not be flipped)
if !bestoutside(qh_ALL), stops at qh.MINoutside
returns:
best facet (reports error if NULL)
early out if isoutside defined and bestdist > qh.MINoutside
dist is distance to facet
isoutside is true if point is outside of facet
numpart counts the number of distance tests
see also:
qh_findbestnew()
notes:
If merging (testhorizon), searches horizon facets of coplanar best facets because
after qh_distplane, this and qh_partitionpoint are the most expensive in 3-d
avoid calls to distplane, function calls, and real number operations.
caller traces result
Optimized for outside points. Tried recording a search set for qh_findhorizon.
Made code more complicated.
when called by qh_partitionvisible():
indicated by qh_ISnewfacets
qh.newfacet_list is list of simplicial, new facets
qh_findbestnew set if qh_sharpnewfacets returns True (to use qh_findbestnew)
qh.bestfacet_notsharp set if qh_sharpnewfacets returns False
when called by qh_findfacet(), qh_partitionpoint(), qh_partitioncoplanar(),
qh_check_bestdist(), qh_addpoint()
indicated by !qh_ISnewfacets
returns best facet in neighborhood of given facet
this is best facet overall if dist >= -qh.MAXcoplanar
or hull has at least a "spherical" curvature
design:
initialize and test for early exit
repeat while there are better facets
for each neighbor of facet
exit if outside facet found
test for better facet
if point is inside and partitioning
test for new facets with a "sharp" intersection
if so, future calls go to qh_findbestnew()
test horizon facets
*/
facetT *qh_findbest(qhT *qh, pointT *point, facetT *startfacet,
boolT bestoutside, boolT isnewfacets, boolT noupper,
realT *dist, boolT *isoutside, int *numpart) {
realT bestdist= -REALmax/2 /* avoid underflow */;
facetT *facet, *neighbor, **neighborp;
facetT *bestfacet= NULL, *lastfacet= NULL;
int oldtrace= qh->IStracing;
unsigned int visitid= ++qh->visit_id;
int numpartnew=0;
boolT testhorizon= True; /* needed if precise, e.g., rbox c D6 | qhull Q0 Tv */
zinc_(Zfindbest);
#ifndef qh_NOtrace
if (qh->IStracing >= 4 || (qh->TRACElevel && qh->TRACEpoint >= 0 && qh->TRACEpoint == qh_pointid(qh, point))) {
if (qh->TRACElevel > qh->IStracing)
qh->IStracing= qh->TRACElevel;
qh_fprintf(qh, qh->ferr, 8004, "qh_findbest: point p%d starting at f%d isnewfacets? %d, unless %d exit if > %2.2g,",
qh_pointid(qh, point), startfacet->id, isnewfacets, bestoutside, qh->MINoutside);
qh_fprintf(qh, qh->ferr, 8005, " testhorizon? %d, noupper? %d,", testhorizon, noupper);
qh_fprintf(qh, qh->ferr, 8006, " Last qh_addpoint p%d,", qh->furthest_id);
qh_fprintf(qh, qh->ferr, 8007, " Last merge #%d, max_outside %2.2g\n", zzval_(Ztotmerge), qh->max_outside);
}
#endif
if (isoutside)
*isoutside= True;
if (!startfacet->flipped) { /* test startfacet before testing its neighbors */
*numpart= 1;
qh_distplane(qh, point, startfacet, dist); /* this code is duplicated below */
if (!bestoutside && *dist >= qh->MINoutside
&& (!startfacet->upperdelaunay || !noupper)) {
bestfacet= startfacet;
goto LABELreturn_best;
}
bestdist= *dist;
if (!startfacet->upperdelaunay) {
bestfacet= startfacet;
}
}else
*numpart= 0;
startfacet->visitid= visitid;
facet= startfacet;
while (facet) {
trace4((qh, qh->ferr, 4001, "qh_findbest: neighbors of f%d, bestdist %2.2g f%d\n",
facet->id, bestdist, getid_(bestfacet)));
lastfacet= facet;
FOREACHneighbor_(facet) {
if (!neighbor->newfacet && isnewfacets)
continue;
if (neighbor->visitid == visitid)
continue;
neighbor->visitid= visitid;
if (!neighbor->flipped) { /* code duplicated above */
(*numpart)++;
qh_distplane(qh, point, neighbor, dist);
if (*dist > bestdist) {
if (!bestoutside && *dist >= qh->MINoutside
&& (!neighbor->upperdelaunay || !noupper)) {
bestfacet= neighbor;
goto LABELreturn_best;
}
if (!neighbor->upperdelaunay) {
bestfacet= neighbor;
bestdist= *dist;
break; /* switch to neighbor */
}else if (!bestfacet) {
bestdist= *dist;
break; /* switch to neighbor */
}
} /* end of *dist>bestdist */
} /* end of !flipped */
} /* end of FOREACHneighbor */
facet= neighbor; /* non-NULL only if *dist>bestdist */
} /* end of while facet (directed search) */
if (isnewfacets) {
if (!bestfacet) { /* startfacet is upperdelaunay (or flipped) w/o !flipped newfacet neighbors */
bestdist= -REALmax/2;
bestfacet= qh_findbestnew(qh, point, qh->newfacet_list, &bestdist, bestoutside, isoutside, &numpartnew);
testhorizon= False; /* qh_findbestnew calls qh_findbesthorizon */
}else if (!qh->findbest_notsharp && bestdist < -qh->DISTround) {
if (qh_sharpnewfacets(qh)) {
/* seldom used, qh_findbestnew will retest all facets */
zinc_(Zfindnewsharp);
bestfacet= qh_findbestnew(qh, point, bestfacet, &bestdist, bestoutside, isoutside, &numpartnew);
testhorizon= False; /* qh_findbestnew calls qh_findbesthorizon */
qh->findbestnew= True;
}else
qh->findbest_notsharp= True;
}
}
if (!bestfacet)
bestfacet= qh_findbestlower(qh, lastfacet, point, &bestdist, numpart); /* lastfacet is non-NULL because startfacet is non-NULL */
if (testhorizon) /* qh_findbestnew not called */
bestfacet= qh_findbesthorizon(qh, !qh_IScheckmax, point, bestfacet, noupper, &bestdist, &numpartnew);
*dist= bestdist;
if (isoutside && bestdist < qh->MINoutside)
*isoutside= False;
LABELreturn_best:
zadd_(Zfindbesttot, *numpart);
zmax_(Zfindbestmax, *numpart);
(*numpart) += numpartnew;
qh->IStracing= oldtrace;
return bestfacet;
} /* findbest */
/*-<a href="qh-geom_r.htm#TOC"
>-------------------------------</a><a name="findbesthorizon">-</a>
qh_findbesthorizon(qh, qh_IScheckmax, point, startfacet, qh_NOupper, &bestdist, &numpart )
search coplanar and better horizon facets from startfacet/bestdist
ischeckmax turns off statistics and minsearch update
all arguments must be initialized, including *bestdist and *numpart
qh.coplanarfacetset used to maintain current search set, reset whenever best facet is substantially better
returns(ischeckmax):
best facet
updates f.maxoutside for neighbors of searched facets (if qh_MAXoutside)
returns(!ischeckmax):
best facet that is not upperdelaunay or newfacet (qh.first_newfacet)
allows upperdelaunay that is clearly outside
returns:
bestdist is distance to bestfacet
numpart -- updates number of distance tests
notes:
called by qh_findbest if point is not outside a facet (directed search)
called by qh_findbestnew if point is not outside a new facet
called by qh_check_maxout for each point in hull
called by qh_check_bestdist for each point in hull (rarely used)
no early out -- use qh_findbest() or qh_findbestnew()
Searches coplanar or better horizon facets
when called by qh_check_maxout() (qh_IScheckmax)
startfacet must be closest to the point
Otherwise, if point is beyond and below startfacet, startfacet may be a local minimum
even though other facets are below the point.
updates facet->maxoutside for good, visited facets
may return NULL
searchdist is qh.max_outside + 2 * DISTround
+ max( MINvisible('Vn'), MAXcoplanar('Un'));
This setting is a guess. It must be at least max_outside + 2*DISTround
because a facet may have a geometric neighbor across a vertex
design:
for each horizon facet of coplanar best facets
continue if clearly inside
unless upperdelaunay or clearly outside
update best facet
*/
facetT *qh_findbesthorizon(qhT *qh, boolT ischeckmax, pointT* point, facetT *startfacet, boolT noupper, realT *bestdist, int *numpart) {
facetT *bestfacet= startfacet;
realT dist;
facetT *neighbor, **neighborp, *facet;
facetT *nextfacet= NULL; /* optimize last facet of coplanarfacetset */
int numpartinit= *numpart, coplanarfacetset_size, numcoplanar= 0, numfacet= 0;
unsigned int visitid= ++qh->visit_id;
boolT newbest= False; /* for tracing */
realT minsearch, searchdist; /* skip facets that are too far from point */
boolT is_5x_minsearch;
if (!ischeckmax) {
zinc_(Zfindhorizon);
}else {
#if qh_MAXoutside
if ((!qh->ONLYgood || startfacet->good) && *bestdist > startfacet->maxoutside)
startfacet->maxoutside= *bestdist;
#endif
}
searchdist= qh_SEARCHdist; /* an expression, a multiple of qh.max_outside and precision constants */
minsearch= *bestdist - searchdist;
if (ischeckmax) {
/* Always check coplanar facets. Needed for RBOX 1000 s Z1 G1e-13 t996564279 | QHULL Tv */
minimize_(minsearch, -searchdist);
}
coplanarfacetset_size= 0;
startfacet->visitid= visitid;
facet= startfacet;
while (True) {
numfacet++;
is_5x_minsearch= (ischeckmax && facet->nummerge > 10 && qh_setsize(qh, facet->neighbors) > 100); /* QH11033 FIX: qh_findbesthorizon: many tests for facets with many merges and neighbors. Can hide coplanar facets, e.g., 'rbox 1000 s Z1 G1e-13' with 4400+ neighbors */
trace4((qh, qh->ferr, 4002, "qh_findbesthorizon: test neighbors of f%d bestdist %2.2g f%d ischeckmax? %d noupper? %d minsearch %2.2g is_5x? %d searchdist %2.2g\n",
facet->id, *bestdist, getid_(bestfacet), ischeckmax, noupper,
minsearch, is_5x_minsearch, searchdist));
FOREACHneighbor_(facet) {
if (neighbor->visitid == visitid)
continue;
neighbor->visitid= visitid;
if (!neighbor->flipped) { /* neighbors of flipped facets always searched via nextfacet */
qh_distplane(qh, point, neighbor, &dist); /* duplicate qh_distpane for new facets, they may be coplanar */
(*numpart)++;
if (dist > *bestdist) {
if (!neighbor->upperdelaunay || ischeckmax || (!noupper && dist >= qh->MINoutside)) {
if (!ischeckmax) {
minsearch= dist - searchdist;
if (dist > *bestdist + searchdist) {
zinc_(Zfindjump); /* everything in qh.coplanarfacetset at least searchdist below */
coplanarfacetset_size= 0;
}
}
bestfacet= neighbor;
*bestdist= dist;
newbest= True;
}
}else if (is_5x_minsearch) {
if (dist < 5 * minsearch)
continue; /* skip this neighbor, do not set nextfacet. dist is negative */
}else if (dist < minsearch)
continue; /* skip this neighbor, do not set nextfacet. If ischeckmax, dist can't be positive */
#if qh_MAXoutside
if (ischeckmax && dist > neighbor->maxoutside)
neighbor->maxoutside= dist;
#endif
} /* end of !flipped, need to search neighbor */
if (nextfacet) {
numcoplanar++;
if (!coplanarfacetset_size++) {
SETfirst_(qh->coplanarfacetset)= nextfacet;
SETtruncate_(qh->coplanarfacetset, 1);
}else
qh_setappend(qh, &qh->coplanarfacetset, nextfacet); /* Was needed for RBOX 1000 s W1e-13 P0 t996547055 | QHULL d Qbb Qc Tv
and RBOX 1000 s Z1 G1e-13 t996564279 | qhull Tv */
}
nextfacet= neighbor;
} /* end of EACHneighbor */
facet= nextfacet;
if (facet)
nextfacet= NULL;
else if (!coplanarfacetset_size)
break;
else if (!--coplanarfacetset_size) {
facet= SETfirstt_(qh->coplanarfacetset, facetT);
SETtruncate_(qh->coplanarfacetset, 0);
}else
facet= (facetT *)qh_setdellast(qh->coplanarfacetset);
} /* while True, i.e., "for each facet in qh.coplanarfacetset" */
if (!ischeckmax) {
zadd_(Zfindhorizontot, *numpart - numpartinit);
zmax_(Zfindhorizonmax, *numpart - numpartinit);
if (newbest)
zinc_(Znewbesthorizon);
}
trace4((qh, qh->ferr, 4003, "qh_findbesthorizon: p%d, newbest? %d, bestfacet f%d, bestdist %2.2g, numfacet %d, coplanarfacets %d, numdist %d\n",
qh_pointid(qh, point), newbest, getid_(bestfacet), *bestdist, numfacet, numcoplanar, *numpart - numpartinit));
return bestfacet;
} /* findbesthorizon */
/*-<a href="qh-geom_r.htm#TOC"
>-------------------------------</a><a name="findbestnew">-</a>
qh_findbestnew(qh, point, startfacet, dist, isoutside, numpart )
find best newfacet for point
searches all of qh.newfacet_list starting at startfacet
searches horizon facets of coplanar best newfacets
searches all facets if startfacet == qh.facet_list
returns:
best new or horizon facet that is not upperdelaunay
early out if isoutside and not 'Qf'
dist is distance to facet
isoutside is true if point is outside of facet
numpart is number of distance tests
notes:
Always used for merged new facets (see qh_USEfindbestnew)
Avoids upperdelaunay facet unless (isoutside and outside)
Uses qh.visit_id, qh.coplanarfacetset.
If share visit_id with qh_findbest, coplanarfacetset is incorrect.
If merging (testhorizon), searches horizon facets of coplanar best facets because
a point maybe coplanar to the bestfacet, below its horizon facet,
and above a horizon facet of a coplanar newfacet. For example,
rbox 1000 s Z1 G1e-13 | qhull
rbox 1000 s W1e-13 P0 t992110337 | QHULL d Qbb Qc
qh_findbestnew() used if
qh_sharpnewfacets -- newfacets contains a sharp angle
if many merges, qh_premerge found a merge, or 'Qf' (qh.findbestnew)
see also:
qh_partitionall() and qh_findbest()
design:
for each new facet starting from startfacet
test distance from point to facet
return facet if clearly outside
unless upperdelaunay and a lowerdelaunay exists
update best facet
test horizon facets
*/
facetT *qh_findbestnew(qhT *qh, pointT *point, facetT *startfacet,
realT *dist, boolT bestoutside, boolT *isoutside, int *numpart) {
realT bestdist= -REALmax/2;
facetT *bestfacet= NULL, *facet;
int oldtrace= qh->IStracing, i;
unsigned int visitid= ++qh->visit_id;
realT distoutside= 0.0;
boolT isdistoutside; /* True if distoutside is defined */
/* boolT testhorizon= True; */ /* needed if precise, e.g., rbox c D6 | qhull Q0 Tv */
if (!startfacet || !startfacet->next) {
if (qh->MERGING) {
qh_fprintf(qh, qh->ferr, 6001, "qhull topology error (qh_findbestnew): merging has formed and deleted a cone of new facets. Can not continue.\n");
qh_errexit(qh, qh_ERRtopology, NULL, NULL);
}else {
qh_fprintf(qh, qh->ferr, 6002, "qhull internal error (qh_findbestnew): no new facets for point p%d\n",
qh->furthest_id);
qh_errexit(qh, qh_ERRqhull, NULL, NULL);
}
}
zinc_(Zfindnew);
if (qh->BESToutside || bestoutside)
isdistoutside= False;
else {
isdistoutside= True;
distoutside= qh_DISToutside; /* multiple of qh.MINoutside & qh.max_outside, see user_r.h */
}
if (isoutside)
*isoutside= True;
*numpart= 0;
#ifndef qh_NOtrace
if (qh->IStracing >= 4 || (qh->TRACElevel && qh->TRACEpoint >= 0 && qh->TRACEpoint == qh_pointid(qh, point))) {
if (qh->TRACElevel > qh->IStracing)
qh->IStracing= qh->TRACElevel;
qh_fprintf(qh, qh->ferr, 8008, "qh_findbestnew: point p%d facet f%d. Stop? %d if dist > %2.2g,",
qh_pointid(qh, point), startfacet->id, isdistoutside, distoutside);
qh_fprintf(qh, qh->ferr, 8009, " Last qh_addpoint p%d, qh.visit_id %d, vertex_visit %d,", qh->furthest_id, visitid, qh->vertex_visit);
qh_fprintf(qh, qh->ferr, 8010, " Last merge #%d\n", zzval_(Ztotmerge));
}
#endif
/* visit all new facets starting with startfacet, maybe qh->facet_list */
for (i=0, facet=startfacet; i < 2; i++, facet= qh->newfacet_list) {
FORALLfacet_(facet) {
if (facet == startfacet && i)
break;
facet->visitid= visitid;
if (!facet->flipped) {
qh_distplane(qh, point, facet, dist);
(*numpart)++;
if (*dist > bestdist) {
if (!facet->upperdelaunay || *dist >= qh->MINoutside) {
bestfacet= facet;
if (isdistoutside && *dist >= distoutside)
goto LABELreturn_bestnew;
bestdist= *dist;
}
}
} /* end of !flipped */
} /* FORALLfacet from startfacet or qh->newfacet_list */
}
/* if (testhorizon || !bestfacet) */ /* testhorizon is always True. Keep the same code as qh_findbest */
bestfacet= qh_findbesthorizon(qh, !qh_IScheckmax, point, bestfacet ? bestfacet : startfacet,
!qh_NOupper, &bestdist, numpart);
*dist= bestdist;
if (isoutside && *dist < qh->MINoutside)
*isoutside= False;
LABELreturn_bestnew:
zadd_(Zfindnewtot, *numpart);
zmax_(Zfindnewmax, *numpart);
trace4((qh, qh->ferr, 4004, "qh_findbestnew: bestfacet f%d bestdist %2.2g for p%d f%d bestoutside? %d \n",
getid_(bestfacet), *dist, qh_pointid(qh, point), startfacet->id, bestoutside));
qh->IStracing= oldtrace;
return bestfacet;
} /* findbestnew */
/* ============ hyperplane functions -- keep code together [?] ============ */
/*-<a href="qh-geom_r.htm#TOC"
>-------------------------------</a><a name="backnormal">-</a>
qh_backnormal(qh, rows, numrow, numcol, sign, normal, nearzero )
given an upper-triangular rows array and a sign,
solve for normal equation x using back substitution over rows U
returns:
normal= x
if will not be able to divzero() when normalized(qh.MINdenom_2 and qh.MINdenom_1_2),
if fails on last row
this means that the hyperplane intersects [0,..,1]
sets last coordinate of normal to sign
otherwise
sets tail of normal to [...,sign,0,...], i.e., solves for b= [0...0]
sets nearzero
notes:
assumes numrow == numcol-1
see Golub & van Loan, 1983, Eq. 4.4-9 for "Gaussian elimination with complete pivoting"
solves Ux=b where Ax=b and PA=LU
b= [0,...,0,sign or 0] (sign is either -1 or +1)
last row of A= [0,...,0,1]
1) Ly=Pb == y=b since P only permutes the 0's of b
design:
for each row from end
perform back substitution
if near zero
use qh_divzero for division
if zero divide and not last row
set tail of normal to 0
*/
void qh_backnormal(qhT *qh, realT **rows, int numrow, int numcol, boolT sign,
coordT *normal, boolT *nearzero) {
int i, j;
coordT *normalp, *normal_tail, *ai, *ak;
realT diagonal;
boolT waszero;
int zerocol= -1;
normalp= normal + numcol - 1;
*normalp--= (sign ? -1.0 : 1.0);
for (i=numrow; i--; ) {
*normalp= 0.0;
ai= rows[i] + i + 1;
ak= normalp+1;
for (j=i+1; j < numcol; j++)
*normalp -= *ai++ * *ak++;
diagonal= (rows[i])[i];
if (fabs_(diagonal) > qh->MINdenom_2)
*(normalp--) /= diagonal;
else {
waszero= False;
*normalp= qh_divzero(*normalp, diagonal, qh->MINdenom_1_2, &waszero);
if (waszero) {
zerocol= i;
*(normalp--)= (sign ? -1.0 : 1.0);
for (normal_tail= normalp+2; normal_tail < normal + numcol; normal_tail++)
*normal_tail= 0.0;
}else
normalp--;
}
}
if (zerocol != -1) {
*nearzero= True;
trace4((qh, qh->ferr, 4005, "qh_backnormal: zero diagonal at column %d.\n", i));
zzinc_(Zback0);
qh_joggle_restart(qh, "zero diagonal on back substitution");
}
} /* backnormal */
/*-<a href="qh-geom_r.htm#TOC"
>-------------------------------</a><a name="gausselim">-</a>
qh_gausselim(qh, rows, numrow, numcol, sign )
Gaussian elimination with partial pivoting
returns:
rows is upper triangular (includes row exchanges)
flips sign for each row exchange
sets nearzero if pivot[k] < qh.NEARzero[k], else clears it
notes:
if nearzero, the determinant's sign may be incorrect.
assumes numrow <= numcol
design:
for each row
determine pivot and exchange rows if necessary
test for near zero
perform gaussian elimination step
*/
void qh_gausselim(qhT *qh, realT **rows, int numrow, int numcol, boolT *sign, boolT *nearzero) {
realT *ai, *ak, *rowp, *pivotrow;
realT n, pivot, pivot_abs= 0.0, temp;
int i, j, k, pivoti, flip=0;
*nearzero= False;
for (k=0; k < numrow; k++) {
pivot_abs= fabs_((rows[k])[k]);
pivoti= k;
for (i=k+1; i < numrow; i++) {
if ((temp= fabs_((rows[i])[k])) > pivot_abs) {
pivot_abs= temp;
pivoti= i;
}
}
if (pivoti != k) {
rowp= rows[pivoti];
rows[pivoti]= rows[k];
rows[k]= rowp;
*sign ^= 1;
flip ^= 1;
}
if (pivot_abs <= qh->NEARzero[k]) {
*nearzero= True;
if (pivot_abs == 0.0) { /* remainder of column == 0 */
#ifndef qh_NOtrace
if (qh->IStracing >= 4) {
qh_fprintf(qh, qh->ferr, 8011, "qh_gausselim: 0 pivot at column %d. (%2.2g < %2.2g)\n", k, pivot_abs, qh->DISTround);
qh_printmatrix(qh, qh->ferr, "Matrix:", rows, numrow, numcol);
}
#endif
zzinc_(Zgauss0);
qh_joggle_restart(qh, "zero pivot for Gaussian elimination");
goto LABELnextcol;
}
}
pivotrow= rows[k] + k;
pivot= *pivotrow++; /* signed value of pivot, and remainder of row */
for (i=k+1; i < numrow; i++) {
ai= rows[i] + k;
ak= pivotrow;
n= (*ai++)/pivot; /* divzero() not needed since |pivot| >= |*ai| */
for (j= numcol - (k+1); j--; )
*ai++ -= n * *ak++;
}
LABELnextcol:
;
}
wmin_(Wmindenom, pivot_abs); /* last pivot element */
if (qh->IStracing >= 5)
qh_printmatrix(qh, qh->ferr, "qh_gausselem: result", rows, numrow, numcol);
} /* gausselim */
/*-<a href="qh-geom_r.htm#TOC"
>-------------------------------</a><a name="getangle">-</a>
qh_getangle(qh, vect1, vect2 )
returns the dot product of two vectors
if qh.RANDOMdist, joggles result
notes:
the angle may be > 1.0 or < -1.0 because of roundoff errors
*/
realT qh_getangle(qhT *qh, pointT *vect1, pointT *vect2) {
realT angle= 0, randr;
int k;
for (k=qh->hull_dim; k--; )
angle += *vect1++ * *vect2++;
if (qh->RANDOMdist) {
randr= qh_RANDOMint;
angle += (2.0 * randr / qh_RANDOMmax - 1.0) *
qh->RANDOMfactor;
}
trace4((qh, qh->ferr, 4006, "qh_getangle: %4.4g\n", angle));
return(angle);
} /* getangle */
/*-<a href="qh-geom_r.htm#TOC"
>-------------------------------</a><a name="getcenter">-</a>
qh_getcenter(qh, vertices )
returns arithmetic center of a set of vertices as a new point
notes:
allocates point array for center
*/
pointT *qh_getcenter(qhT *qh, setT *vertices) {
int k;
pointT *center, *coord;
vertexT *vertex, **vertexp;
int count= qh_setsize(qh, vertices);
if (count < 2) {
qh_fprintf(qh, qh->ferr, 6003, "qhull internal error (qh_getcenter): not defined for %d points\n", count);
qh_errexit(qh, qh_ERRqhull, NULL, NULL);
}
center= (pointT *)qh_memalloc(qh, qh->normal_size);
for (k=0; k < qh->hull_dim; k++) {
coord= center+k;
*coord= 0.0;
FOREACHvertex_(vertices)
*coord += vertex->point[k];
*coord /= count; /* count>=2 by QH6003 */
}
return(center);
} /* getcenter */
/*-<a href="qh-geom_r.htm#TOC"
>-------------------------------</a><a name="getcentrum">-</a>
qh_getcentrum(qh, facet )
returns the centrum for a facet as a new point
notes:
allocates the centrum
*/
pointT *qh_getcentrum(qhT *qh, facetT *facet) {
realT dist;
pointT *centrum, *point;
point= qh_getcenter(qh, facet->vertices);
zzinc_(Zcentrumtests);
qh_distplane(qh, point, facet, &dist);
centrum= qh_projectpoint(qh, point, facet, dist);
qh_memfree(qh, point, qh->normal_size);
trace4((qh, qh->ferr, 4007, "qh_getcentrum: for f%d, %d vertices dist= %2.2g\n",
facet->id, qh_setsize(qh, facet->vertices), dist));
return centrum;
} /* getcentrum */
/*-<a href="qh-geom_r.htm#TOC"
>-------------------------------</a><a name="getdistance">-</a>
qh_getdistance(qh, facet, neighbor, mindist, maxdist )
returns the min and max distance to neighbor of non-neighbor vertices in facet
returns:
the max absolute value
design:
for each vertex of facet that is not in neighbor
test the distance from vertex to neighbor
*/
coordT qh_getdistance(qhT *qh, facetT *facet, facetT *neighbor, coordT *mindist, coordT *maxdist) {
vertexT *vertex, **vertexp;
coordT dist, maxd, mind;
FOREACHvertex_(facet->vertices)
vertex->seen= False;
FOREACHvertex_(neighbor->vertices)
vertex->seen= True;
mind= 0.0;
maxd= 0.0;
FOREACHvertex_(facet->vertices) {
if (!vertex->seen) {
zzinc_(Zbestdist);
qh_distplane(qh, vertex->point, neighbor, &dist);
if (dist < mind)
mind= dist;
else if (dist > maxd)
maxd= dist;
}
}
*mindist= mind;
*maxdist= maxd;
mind= -mind;
if (maxd > mind)
return maxd;
else
return mind;
} /* getdistance */
/*-<a href="qh-geom_r.htm#TOC"
>-------------------------------</a><a name="normalize">-</a>
qh_normalize(qh, normal, dim, toporient )
normalize a vector and report if too small
does not use min norm
see:
qh_normalize2
*/
void qh_normalize(qhT *qh, coordT *normal, int dim, boolT toporient) {
qh_normalize2(qh, normal, dim, toporient, NULL, NULL);
} /* normalize */
/*-<a href="qh-geom_r.htm#TOC"
>-------------------------------</a><a name="normalize2">-</a>
qh_normalize2(qh, normal, dim, toporient, minnorm, ismin )
normalize a vector and report if too small
qh.MINdenom/MINdenom1 are the upper limits for divide overflow
returns:
normalized vector
flips sign if !toporient
if minnorm non-NULL,
sets ismin if normal < minnorm
notes:
if zero norm
sets all elements to sqrt(1.0/dim)
if divide by zero (divzero())
sets largest element to +/-1
bumps Znearlysingular
design:
computes norm
test for minnorm
if not near zero
normalizes normal
else if zero norm
sets normal to standard value
else
uses qh_divzero to normalize
if nearzero
sets norm to direction of maximum value
*/
void qh_normalize2(qhT *qh, coordT *normal, int dim, boolT toporient,
realT *minnorm, boolT *ismin) {
int k;
realT *colp, *maxp, norm= 0, temp, *norm1, *norm2, *norm3;
boolT zerodiv;
norm1= normal+1;
norm2= normal+2;
norm3= normal+3;
if (dim == 2)
norm= sqrt((*normal)*(*normal) + (*norm1)*(*norm1));
else if (dim == 3)
norm= sqrt((*normal)*(*normal) + (*norm1)*(*norm1) + (*norm2)*(*norm2));
else if (dim == 4) {
norm= sqrt((*normal)*(*normal) + (*norm1)*(*norm1) + (*norm2)*(*norm2)
+ (*norm3)*(*norm3));
}else if (dim > 4) {
norm= (*normal)*(*normal) + (*norm1)*(*norm1) + (*norm2)*(*norm2)
+ (*norm3)*(*norm3);
for (k=dim-4, colp=normal+4; k--; colp++)
norm += (*colp) * (*colp);
norm= sqrt(norm);
}
if (minnorm) {
if (norm < *minnorm)
*ismin= True;
else
*ismin= False;
}
wmin_(Wmindenom, norm);
if (norm > qh->MINdenom) {
if (!toporient)
norm= -norm;
*normal /= norm;
*norm1 /= norm;
if (dim == 2)
; /* all done */
else if (dim == 3)
*norm2 /= norm;
else if (dim == 4) {
*norm2 /= norm;
*norm3 /= norm;
}else if (dim >4) {
*norm2 /= norm;
*norm3 /= norm;
for (k=dim-4, colp=normal+4; k--; )
*colp++ /= norm;
}
}else if (norm == 0.0) {
temp= sqrt(1.0/dim);
for (k=dim, colp=normal; k--; )
*colp++= temp;
}else {
if (!toporient)
norm= -norm;
for (k=dim, colp=normal; k--; colp++) { /* k used below */
temp= qh_divzero(*colp, norm, qh->MINdenom_1, &zerodiv);
if (!zerodiv)
*colp= temp;
else {
maxp= qh_maxabsval(normal, dim);
temp= ((*maxp * norm >= 0.0) ? 1.0 : -1.0);
for (k=dim, colp=normal; k--; colp++)
*colp= 0.0;
*maxp= temp;
zzinc_(Znearlysingular);
/* qh_joggle_restart ignored for Znearlysingular, normal part of qh_sethyperplane_gauss */
trace0((qh, qh->ferr, 1, "qh_normalize: norm=%2.2g too small during p%d\n",
norm, qh->furthest_id));
return;
}
}
}
} /* normalize */
/*-<a href="qh-geom_r.htm#TOC"
>-------------------------------</a><a name="projectpoint">-</a>
qh_projectpoint(qh, point, facet, dist )
project point onto a facet by dist
returns:
returns a new point
notes:
if dist= distplane(point,facet)
this projects point to hyperplane
assumes qh_memfree_() is valid for normal_size
*/
pointT *qh_projectpoint(qhT *qh, pointT *point, facetT *facet, realT dist) {
pointT *newpoint, *np, *normal;
int normsize= qh->normal_size;
int k;
void **freelistp; /* used if !qh_NOmem by qh_memalloc_() */
qh_memalloc_(qh, normsize, freelistp, newpoint, pointT);
np= newpoint;
normal= facet->normal;
for (k=qh->hull_dim; k--; )
*(np++)= *point++ - dist * *normal++;
return(newpoint);
} /* projectpoint */
/*-<a href="qh-geom_r.htm#TOC"
>-------------------------------</a><a name="setfacetplane">-</a>
qh_setfacetplane(qh, facet )
sets the hyperplane for a facet
if qh.RANDOMdist, joggles hyperplane
notes:
uses global buffers qh.gm_matrix and qh.gm_row
overwrites facet->normal if already defined
updates Wnewvertex if PRINTstatistics
sets facet->upperdelaunay if upper envelope of Delaunay triangulation
design:
copy vertex coordinates to qh.gm_matrix/gm_row
compute determinate
if nearzero
recompute determinate with gaussian elimination
if nearzero
force outside orientation by testing interior point
*/
void qh_setfacetplane(qhT *qh, facetT *facet) {
pointT *point;
vertexT *vertex, **vertexp;
int normsize= qh->normal_size;
int k,i, oldtrace= 0;
realT dist;
void **freelistp; /* used if !qh_NOmem by qh_memalloc_() */
coordT *coord, *gmcoord;
pointT *point0= SETfirstt_(facet->vertices, vertexT)->point;
boolT nearzero= False;
zzinc_(Zsetplane);
if (!facet->normal)
qh_memalloc_(qh, normsize, freelistp, facet->normal, coordT);
#ifndef qh_NOtrace
if (facet == qh->tracefacet) {
oldtrace= qh->IStracing;
qh->IStracing= 5;
qh_fprintf(qh, qh->ferr, 8012, "qh_setfacetplane: facet f%d created.\n", facet->id);
qh_fprintf(qh, qh->ferr, 8013, " Last point added to hull was p%d.", qh->furthest_id);
if (zzval_(Ztotmerge))
qh_fprintf(qh, qh->ferr, 8014, " Last merge was #%d.", zzval_(Ztotmerge));
qh_fprintf(qh, qh->ferr, 8015, "\n\nCurrent summary is:\n");
qh_printsummary(qh, qh->ferr);
}
#endif
if (qh->hull_dim <= 4) {
i= 0;
if (qh->RANDOMdist) {
gmcoord= qh->gm_matrix;