forked from laristra/r3d
-
Notifications
You must be signed in to change notification settings - Fork 0
/
Copy pathr3d.c
1305 lines (1135 loc) · 38.6 KB
/
r3d.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
/*
*
* r3d.c
*
* See r3d.h for usage.
*
* Devon Powell 31 August 2015
*
* This program was prepared by Los Alamos National Security, LLC
* at Los Alamos National Laboratory (LANL) under contract No. DE-AC52-06NA25396
* with the U.S. Department of Energy (DOE). All rights in the
* program are reserved by the DOE and Los Alamos National Security, LLC.
* Permission is granted to the public to copy and use this software without
* charge, provided that this Notice and any statement of authorship are
* reproduced on all copies. Neither the U.S. Government nor LANS makes any
* warranty, express or implied, or assumes any liability or responsibility for
* the use of this software.
*
*/
#include "r3d.h"
#include <math.h>
#include <stdio.h>
#include <string.h>
// useful macros
#define ONE_THIRD 0.333333333333333333333333333333333333333333333333333333
#define ONE_SIXTH 0.16666666666666666666666666666666666666666666666666666667
#define dot(va, vb) (va.x * vb.x + va.y * vb.y + va.z * vb.z)
#define wav(va, wa, vb, wb, vr) \
{ \
vr.x = (wa * va.x + wb * vb.x) / (wa + wb); \
vr.y = (wa * va.y + wb * vb.y) / (wa + wb); \
vr.z = (wa * va.z + wb * vb.z) / (wa + wb); \
}
#define norm(v) \
{ \
r3d_real tmplen = sqrt(dot(v, v)); \
v.x /= (tmplen + 1.0e-299); \
v.y /= (tmplen + 1.0e-299); \
v.z /= (tmplen + 1.0e-299); \
}
void r3d_clip(r3d_poly *poly, r3d_plane *planes, r3d_int nplanes) {
// direct access to vertex buffer
r3d_vertex *vertbuffer = poly->verts;
r3d_int *nverts = &poly->nverts;
if (*nverts <= 0) return;
// variable declarations
r3d_int v, p, np, onv, vcur, vnext, vstart, pnext, numunclipped;
// signed distances to the clipping plane
r3d_real sdists[R3D_MAX_VERTS];
r3d_real smin, smax;
// for marking clipped vertices
r3d_int clipped[R3D_MAX_VERTS];
// loop over each clip plane
for (p = 0; p < nplanes; ++p) {
// calculate signed distances to the clip plane
onv = *nverts;
smin = 1.0e30;
smax = -1.0e30;
memset(&clipped, 0, sizeof(clipped));
for (v = 0; v < onv; ++v) {
sdists[v] = planes[p].d + dot(vertbuffer[v].pos, planes[p].n);
if (sdists[v] < smin) smin = sdists[v];
if (sdists[v] > smax) smax = sdists[v];
if (sdists[v] < 0.0) clipped[v] = 1;
}
// skip this face if the poly lies entirely on one side of it
if (smin >= 0.0) continue;
if (smax <= 0.0) {
*nverts = 0;
return;
}
// check all edges and insert new vertices on the bisected edges
for (vcur = 0; vcur < onv; ++vcur) {
if (clipped[vcur]) continue;
for (np = 0; np < 3; ++np) {
vnext = vertbuffer[vcur].pnbrs[np];
if (!clipped[vnext]) continue;
vertbuffer[*nverts].pnbrs[0] = vcur;
vertbuffer[vcur].pnbrs[np] = *nverts;
wav(vertbuffer[vcur].pos, -sdists[vnext], vertbuffer[vnext].pos,
sdists[vcur], vertbuffer[*nverts].pos);
(*nverts)++;
}
}
// for each new vert, search around the faces for its new neighbors and
// doubly-link everything
for (vstart = onv; vstart < *nverts; ++vstart) {
vcur = vstart;
vnext = vertbuffer[vcur].pnbrs[0];
do {
for (np = 0; np < 3; ++np)
if (vertbuffer[vnext].pnbrs[np] == vcur) break;
vcur = vnext;
pnext = (np + 1) % 3;
vnext = vertbuffer[vcur].pnbrs[pnext];
} while (vcur < onv);
vertbuffer[vstart].pnbrs[2] = vcur;
vertbuffer[vcur].pnbrs[1] = vstart;
}
// go through and compress the vertex list, removing clipped verts and
// re-indexing accordingly (reusing `clipped` to re-index everything)
numunclipped = 0;
for (v = 0; v < *nverts; ++v) {
if (!clipped[v]) {
vertbuffer[numunclipped] = vertbuffer[v];
clipped[v] = numunclipped++;
}
}
*nverts = numunclipped;
for (v = 0; v < *nverts; ++v)
for (np = 0; np < 3; ++np)
vertbuffer[v].pnbrs[np] = clipped[vertbuffer[v].pnbrs[np]];
}
}
void r3d_split(r3d_poly *inpolys, r3d_int npolys, r3d_plane plane,
r3d_poly *out_pos, r3d_poly *out_neg) {
// direct access to vertex buffer
r3d_int v, np, npnxt, onv, vcur, vnext, vstart, pnext, nright, cside, p;
r3d_rvec3 newpos;
r3d_int side[R3D_MAX_VERTS];
r3d_real sdists[R3D_MAX_VERTS];
r3d_int *nverts;
r3d_vertex *vertbuffer;
r3d_poly *outpolys[2];
for (p = 0; p < npolys; ++p) {
nverts = &inpolys[p].nverts;
vertbuffer = inpolys[p].verts;
outpolys[0] = &out_pos[p];
outpolys[1] = &out_neg[p];
if (*nverts <= 0) {
memset(&out_pos[p], 0, sizeof(r3d_poly));
memset(&out_neg[p], 0, sizeof(r3d_poly));
continue;
}
// calculate signed distances to the clip plane
nright = 0;
memset(&side, 0, sizeof(side));
for (v = 0; v < *nverts; ++v) {
sdists[v] = plane.d + dot(vertbuffer[v].pos, plane.n);
if (sdists[v] < 0.0) {
side[v] = 1;
nright++;
}
}
// return if the poly lies entirely on one side of it
if (nright == 0) {
out_pos[p] = inpolys[p];
memset(&out_neg[p], 0, sizeof(r3d_poly));
continue;
}
if (nright == *nverts) {
out_neg[p] = inpolys[p];
memset(&out_pos[p], 0, sizeof(r3d_poly));
continue;
}
// check all edges and insert new vertices on the bisected edges
onv = *nverts;
for (vcur = 0; vcur < onv; ++vcur) {
if (side[vcur]) continue;
for (np = 0; np < 3; ++np) {
vnext = vertbuffer[vcur].pnbrs[np];
if (!side[vnext]) continue;
wav(vertbuffer[vcur].pos, -sdists[vnext], vertbuffer[vnext].pos,
sdists[vcur], newpos);
vertbuffer[*nverts].pos = newpos;
vertbuffer[*nverts].pnbrs[0] = vcur;
vertbuffer[vcur].pnbrs[np] = *nverts;
(*nverts)++;
vertbuffer[*nverts].pos = newpos;
side[*nverts] = 1;
vertbuffer[*nverts].pnbrs[0] = vnext;
for (npnxt = 0; npnxt < 3; ++npnxt)
if (vertbuffer[vnext].pnbrs[npnxt] == vcur) break;
vertbuffer[vnext].pnbrs[npnxt] = *nverts;
(*nverts)++;
}
}
// for each new vert, search around the faces for its new neighbors and
// doubly-link everything
for (vstart = onv; vstart < *nverts; ++vstart) {
vcur = vstart;
vnext = vertbuffer[vcur].pnbrs[0];
do {
for (np = 0; np < 3; ++np)
if (vertbuffer[vnext].pnbrs[np] == vcur) break;
vcur = vnext;
pnext = (np + 1) % 3;
vnext = vertbuffer[vcur].pnbrs[pnext];
} while (vcur < onv);
vertbuffer[vstart].pnbrs[2] = vcur;
vertbuffer[vcur].pnbrs[1] = vstart;
}
// copy and compress vertices into their new buffers reusing side[] for
// reindexing
onv = *nverts;
outpolys[0]->nverts = 0;
outpolys[1]->nverts = 0;
for (v = 0; v < onv; ++v) {
cside = side[v];
outpolys[cside]->verts[outpolys[cside]->nverts] = vertbuffer[v];
side[v] = (outpolys[cside]->nverts)++;
}
for (v = 0; v < outpolys[0]->nverts; ++v)
for (np = 0; np < 3; ++np)
outpolys[0]->verts[v].pnbrs[np] = side[outpolys[0]->verts[v].pnbrs[np]];
for (v = 0; v < outpolys[1]->nverts; ++v)
for (np = 0; np < 3; ++np)
outpolys[1]->verts[v].pnbrs[np] = side[outpolys[1]->verts[v].pnbrs[np]];
}
}
void r3d_reduce(r3d_poly *poly, r3d_real *moments, r3d_int polyorder) {
// var declarations
r3d_real sixv;
r3d_int np, m, i, j, k, corder;
r3d_int vstart, pstart, vcur, vnext, pnext;
r3d_rvec3 v0, v1, v2, vc;
// direct access to vertex buffer
r3d_vertex *vertbuffer = poly->verts;
r3d_int *nverts = &poly->nverts;
// zero the moments
for (m = 0; m < R3D_NUM_MOMENTS(polyorder); ++m) moments[m] = 0.0;
if (*nverts <= 0) return;
// flag to translate a polyhedron to the origin for increased accuracy
// (this will increase computational cost, in particular for higher moments)
r3d_int shift_poly = 1;
if(shift_poly) vc = r3d_poly_center(poly);
// for keeping track of which edges have been visited
r3d_int emarks[*nverts][3];
memset(&emarks, 0, sizeof(emarks));
// Storage for coefficients keep two layers of the pyramid of coefficients
// Note: Uses twice as much space as needed, but indexing is faster this way
r3d_int prevlayer = 0;
r3d_int curlayer = 1;
r3d_real S[polyorder + 1][polyorder + 1][2];
r3d_real D[polyorder + 1][polyorder + 1][2];
r3d_real C[polyorder + 1][polyorder + 1][2];
// loop over all vertices to find the starting point for each face
for (vstart = 0; vstart < *nverts; ++vstart)
for (pstart = 0; pstart < 3; ++pstart) {
// skip this face if we have marked it
if (emarks[vstart][pstart]) continue;
// initialize face looping
pnext = pstart;
vcur = vstart;
emarks[vcur][pnext] = 1;
vnext = vertbuffer[vcur].pnbrs[pnext];
v0 = vertbuffer[vcur].pos;
if(shift_poly) {
v0.x = v0.x - vc.x;
v0.y = v0.y - vc.y;
v0.z = v0.z - vc.z;
}
// move to the second edge
for (np = 0; np < 3; ++np)
if (vertbuffer[vnext].pnbrs[np] == vcur) break;
vcur = vnext;
pnext = (np + 1) % 3;
emarks[vcur][pnext] = 1;
vnext = vertbuffer[vcur].pnbrs[pnext];
// make a triangle fan using edges and first vertex
while (vnext != vstart) {
v2 = vertbuffer[vcur].pos;
v1 = vertbuffer[vnext].pos;
if(shift_poly) {
v2.x = v2.x - vc.x;
v2.y = v2.y - vc.y;
v2.z = v2.z - vc.z;
v1.x = v1.x - vc.x;
v1.y = v1.y - vc.y;
v1.z = v1.z - vc.z;
}
sixv = (-v2.x * v1.y * v0.z + v1.x * v2.y * v0.z + v2.x * v0.y * v1.z -
v0.x * v2.y * v1.z - v1.x * v0.y * v2.z + v0.x * v1.y * v2.z);
// calculate the moments using the fast recursive method of Koehl (2012)
// essentially building a set of trinomial pyramids, one layer at a time
// base case
S[0][0][prevlayer] = 1.0;
D[0][0][prevlayer] = 1.0;
C[0][0][prevlayer] = 1.0;
moments[0] += ONE_SIXTH * sixv;
// build up successive polynomial orders
for (corder = 1, m = 1; corder <= polyorder; ++corder) {
for (i = corder; i >= 0; --i)
for (j = corder - i; j >= 0; --j, ++m) {
k = corder - i - j;
C[i][j][curlayer] = 0;
D[i][j][curlayer] = 0;
S[i][j][curlayer] = 0;
if (i > 0) {
C[i][j][curlayer] += v2.x * C[i - 1][j][prevlayer];
D[i][j][curlayer] += v1.x * D[i - 1][j][prevlayer];
S[i][j][curlayer] += v0.x * S[i - 1][j][prevlayer];
}
if (j > 0) {
C[i][j][curlayer] += v2.y * C[i][j - 1][prevlayer];
D[i][j][curlayer] += v1.y * D[i][j - 1][prevlayer];
S[i][j][curlayer] += v0.y * S[i][j - 1][prevlayer];
}
if (k > 0) {
C[i][j][curlayer] += v2.z * C[i][j][prevlayer];
D[i][j][curlayer] += v1.z * D[i][j][prevlayer];
S[i][j][curlayer] += v0.z * S[i][j][prevlayer];
}
D[i][j][curlayer] += C[i][j][curlayer];
S[i][j][curlayer] += D[i][j][curlayer];
moments[m] += sixv * S[i][j][curlayer];
}
curlayer = 1 - curlayer;
prevlayer = 1 - prevlayer;
}
// move to the next edge
for (np = 0; np < 3; ++np)
if (vertbuffer[vnext].pnbrs[np] == vcur) break;
vcur = vnext;
pnext = (np + 1) % 3;
emarks[vcur][pnext] = 1;
vnext = vertbuffer[vcur].pnbrs[pnext];
}
}
// reuse C to recursively compute the leading multinomial coefficients
C[0][0][prevlayer] = 1.0;
for (corder = 1, m = 1; corder <= polyorder; ++corder) {
for (i = corder; i >= 0; --i)
for (j = corder - i; j >= 0; --j, ++m) {
k = corder - i - j;
C[i][j][curlayer] = 0.0;
if (i > 0) C[i][j][curlayer] += C[i - 1][j][prevlayer];
if (j > 0) C[i][j][curlayer] += C[i][j - 1][prevlayer];
if (k > 0) C[i][j][curlayer] += C[i][j][prevlayer];
moments[m] /=
C[i][j][curlayer] * (corder + 1) * (corder + 2) * (corder + 3);
}
curlayer = 1 - curlayer;
prevlayer = 1 - prevlayer;
}
if(shift_poly) r3d_shift_moments(moments, polyorder, vc);
}
void r3d_shift_moments(r3d_real* moments, r3d_int polyorder, r3d_rvec3 vc) {
// var declarations
r3d_int m, i, j, k, corder;
r3d_int mm, mi, mj, mk, mcorder;
// store moments of a shifted polygon
r3d_real moments2[R3D_NUM_MOMENTS(polyorder)];
for (m = 0; m < R3D_NUM_MOMENTS(polyorder); ++m) moments2[m] = 0.0;
// calculate and save Pascal's triangle
r3d_real B[polyorder+1][polyorder+1];
B[0][0] = 1.0;
for(corder = 1, m = 1; corder <= polyorder; ++corder) {
for(i = corder; i >= 0; --i, ++m) {
j = corder - i;
B[i][corder] = 1.0;
if(i > 0 && j > 0) B[i][corder] = B[i][corder-1] + B[i-1][corder-1];
}
}
// shift moments back to the original position using
// \int_\Omega x^i y^j z^k d\vec r =
// \int_\omega (x+\xi)^i (y+\eta)^j (z+\zeta)^k d\vec r =
// \sum_{a,b,c=0}^{i,j,k} \binom{i}{a} \binom{j}{b} \binom{k}{c}
// \xi^{i-a} \eta^{j-b} \zeta^{k-c} \int_\omega x^a y^b z^c d\vec r
for (corder = 1, m = 1; corder <= polyorder; ++corder) {
for (i = corder; i >= 0; --i)
for (j = corder - i; j >= 0; --j, ++m) {
k = corder - i - j;
for (mcorder = 0, mm = 0; mcorder <= corder; ++mcorder) {
for (mi = mcorder; mi >= 0; --mi)
for (mj = mcorder - mi; mj >= 0; --mj, ++mm) {
mk = mcorder - mi - mj;
if (mi <= i && mj <= j && mk <= k ) {
moments2[m] += B[mi][i] * B[mj][j] * B[mk][k] * pow(vc.x,(i-mi)) *
pow(vc.y,(j-mj)) * pow(vc.z,(k-mk)) * moments[mm];
}
}
}
}
}
// assign shifted moments
for(m = 1; m < R3D_NUM_MOMENTS(polyorder); ++m)
moments[m] = moments2[m];
}
r3d_rvec3 r3d_poly_center(r3d_poly* poly) {
// var declarations
r3d_int vcur;
r3d_rvec3 vc;
// direct access to vertex buffer
r3d_vertex* vertbuffer = poly->verts;
r3d_int* nverts = &poly->nverts;
vc.x = 0.0;
vc.y = 0.0;
vc.z = 0.0;
for(vcur = 0; vcur < *nverts; ++vcur) {
vc.x += vertbuffer[vcur].pos.x;
vc.y += vertbuffer[vcur].pos.y;
vc.z += vertbuffer[vcur].pos.z;
}
vc.x /= *nverts;
vc.y /= *nverts;
vc.z /= *nverts;
return vc;
}
r3d_int r3d_is_good(r3d_poly *poly) {
r3d_int v, np, rcur;
r3d_int nvstack;
r3d_int va, vb, vc;
r3d_int vct[R3D_MAX_VERTS];
r3d_int stack[R3D_MAX_VERTS];
r3d_int regions[R3D_MAX_VERTS];
// direct access to vertex buffer
r3d_vertex *vertbuffer = poly->verts;
r3d_int *nverts = &poly->nverts;
// consistency check
memset(&vct, 0, sizeof(vct));
for (v = 0; v < *nverts; ++v) {
// return false if two vertices are connected by more than one edge or if
// any edges are obviously invalid
for (np = 0; np < 3; ++np) {
if (vertbuffer[v].pnbrs[np] == vertbuffer[v].pnbrs[(np + 1) % 3]) {
printf("Double edge.\n");
return 0;
}
if (vertbuffer[v].pnbrs[np] >= *nverts) {
printf("Bad pointer.\n");
return 0;
}
}
vct[vertbuffer[v].pnbrs[0]]++;
vct[vertbuffer[v].pnbrs[1]]++;
vct[vertbuffer[v].pnbrs[2]]++;
}
// return false if any vertices are pointed to by more or fewer than three
// other vertices
for (v = 0; v < *nverts; ++v)
if (vct[v] != 3) {
printf("Bad edge count: count[%d] = %d.\n", v, vct[v]);
return 0;
}
// check for 3-vertex-connectedness this is O(nverts^2)
// handle multiply-connected polyhedra by testing each component separately.
// Flood-fill starting from each vertex to give each connected region a unique
// ID.
rcur = 1;
memset(®ions, 0, sizeof(regions));
for (v = 0; v < *nverts; ++v) {
if (regions[v]) continue;
nvstack = 0;
stack[nvstack++] = v;
while (nvstack > 0) {
vc = stack[--nvstack];
if (regions[vc]) continue;
regions[vc] = rcur;
stack[nvstack++] = vertbuffer[vc].pnbrs[0];
stack[nvstack++] = vertbuffer[vc].pnbrs[1];
stack[nvstack++] = vertbuffer[vc].pnbrs[2];
}
++rcur;
}
// loop over unique pairs of verts
for (va = 0; va < *nverts; ++va) {
rcur = regions[va];
for (vb = va + 1; vb < *nverts; ++vb) {
// make sure va and vb are in the same connected component
if (regions[vb] != rcur) continue;
// pick vc != va && vc != vb and in the same connected component as va and
// vb
for (vc = 0; vc < *nverts; ++vc)
if (regions[vc] == rcur && vc != va && vc != vb) break;
// use vct to mark visited verts mask out va and vb
memset(&vct, 0, sizeof(vct));
vct[va] = 1;
vct[vb] = 1;
// flood-fill from vc to make sure the graph is still connected when va
// and vb are masked
nvstack = 0;
stack[nvstack++] = vc;
while (nvstack > 0) {
vc = stack[--nvstack];
if (vct[vc]) continue;
vct[vc] = 1;
stack[nvstack++] = vertbuffer[vc].pnbrs[0];
stack[nvstack++] = vertbuffer[vc].pnbrs[1];
stack[nvstack++] = vertbuffer[vc].pnbrs[2];
}
// if any verts in the region rcur were untouched, the graph is only
// 2-vertex-connected and hence an invalid polyhedron
for (v = 0; v < *nverts; ++v)
if (regions[v] == rcur && !vct[v]) {
printf("Not 3-vertex-connected.\n");
return 0;
}
}
}
return 1;
}
void r3d_rotate(r3d_poly *poly, r3d_real theta, r3d_int axis) {
r3d_int v;
r3d_rvec3 tmp;
r3d_real sine = sin(theta);
r3d_real cosine = cos(theta);
for (v = 0; v < poly->nverts; ++v) {
tmp = poly->verts[v].pos;
poly->verts[v].pos.xyz[(axis + 1) % 3] =
cosine * tmp.xyz[(axis + 1) % 3] - sine * tmp.xyz[(axis + 2) % 3];
poly->verts[v].pos.xyz[(axis + 2) % 3] =
sine * tmp.xyz[(axis + 1) % 3] + cosine * tmp.xyz[(axis + 2) % 3];
}
}
void r3d_translate(r3d_poly *poly, r3d_rvec3 shift) {
r3d_int v;
for (v = 0; v < poly->nverts; ++v) {
poly->verts[v].pos.x += shift.x;
poly->verts[v].pos.y += shift.y;
poly->verts[v].pos.z += shift.z;
}
}
void r3d_scale(r3d_poly *poly, r3d_real scale) {
r3d_int v;
for (v = 0; v < poly->nverts; ++v) {
poly->verts[v].pos.x *= scale;
poly->verts[v].pos.y *= scale;
poly->verts[v].pos.z *= scale;
}
}
void r3d_shear(r3d_poly *poly, r3d_real shear, r3d_int axb, r3d_int axs) {
r3d_int v;
for (v = 0; v < poly->nverts; ++v) {
poly->verts[v].pos.xyz[axb] += shear * poly->verts[v].pos.xyz[axs];
}
}
void r3d_affine(r3d_poly *poly, r3d_real mat[4][4]) {
r3d_int v;
r3d_rvec3 tmp;
r3d_real w;
for (v = 0; v < poly->nverts; ++v) {
tmp = poly->verts[v].pos;
// affine transformation
poly->verts[v].pos.x =
tmp.x * mat[0][0] + tmp.y * mat[0][1] + tmp.z * mat[0][2] + mat[0][3];
poly->verts[v].pos.y =
tmp.x * mat[1][0] + tmp.y * mat[1][1] + tmp.z * mat[1][2] + mat[1][3];
poly->verts[v].pos.z =
tmp.x * mat[2][0] + tmp.y * mat[2][1] + tmp.z * mat[2][2] + mat[2][3];
w = tmp.x * mat[3][0] + tmp.y * mat[3][1] + tmp.z * mat[3][2] + mat[3][3];
// homogeneous divide if w != 1, i.e. in a perspective projection
poly->verts[v].pos.x /= w;
poly->verts[v].pos.y /= w;
poly->verts[v].pos.z /= w;
}
}
void r3d_init_tet(r3d_poly *poly, r3d_rvec3 verts[4]) {
// direct access to vertex buffer
r3d_vertex *vertbuffer = poly->verts;
r3d_int *nverts = &poly->nverts;
// initialize graph connectivity
*nverts = 4;
vertbuffer[0].pnbrs[0] = 1;
vertbuffer[0].pnbrs[1] = 3;
vertbuffer[0].pnbrs[2] = 2;
vertbuffer[1].pnbrs[0] = 2;
vertbuffer[1].pnbrs[1] = 3;
vertbuffer[1].pnbrs[2] = 0;
vertbuffer[2].pnbrs[0] = 0;
vertbuffer[2].pnbrs[1] = 3;
vertbuffer[2].pnbrs[2] = 1;
vertbuffer[3].pnbrs[0] = 1;
vertbuffer[3].pnbrs[1] = 2;
vertbuffer[3].pnbrs[2] = 0;
// copy vertex coordinates
r3d_int v;
for (v = 0; v < 4; ++v) vertbuffer[v].pos = verts[v];
}
void r3d_init_box(r3d_poly *poly, r3d_rvec3 rbounds[2]) {
// direct access to vertex buffer
r3d_vertex *vertbuffer = poly->verts;
r3d_int *nverts = &poly->nverts;
*nverts = 8;
vertbuffer[0].pnbrs[0] = 1;
vertbuffer[0].pnbrs[1] = 4;
vertbuffer[0].pnbrs[2] = 3;
vertbuffer[1].pnbrs[0] = 2;
vertbuffer[1].pnbrs[1] = 5;
vertbuffer[1].pnbrs[2] = 0;
vertbuffer[2].pnbrs[0] = 3;
vertbuffer[2].pnbrs[1] = 6;
vertbuffer[2].pnbrs[2] = 1;
vertbuffer[3].pnbrs[0] = 0;
vertbuffer[3].pnbrs[1] = 7;
vertbuffer[3].pnbrs[2] = 2;
vertbuffer[4].pnbrs[0] = 7;
vertbuffer[4].pnbrs[1] = 0;
vertbuffer[4].pnbrs[2] = 5;
vertbuffer[5].pnbrs[0] = 4;
vertbuffer[5].pnbrs[1] = 1;
vertbuffer[5].pnbrs[2] = 6;
vertbuffer[6].pnbrs[0] = 5;
vertbuffer[6].pnbrs[1] = 2;
vertbuffer[6].pnbrs[2] = 7;
vertbuffer[7].pnbrs[0] = 6;
vertbuffer[7].pnbrs[1] = 3;
vertbuffer[7].pnbrs[2] = 4;
vertbuffer[0].pos.x = rbounds[0].x;
vertbuffer[0].pos.y = rbounds[0].y;
vertbuffer[0].pos.z = rbounds[0].z;
vertbuffer[1].pos.x = rbounds[1].x;
vertbuffer[1].pos.y = rbounds[0].y;
vertbuffer[1].pos.z = rbounds[0].z;
vertbuffer[2].pos.x = rbounds[1].x;
vertbuffer[2].pos.y = rbounds[1].y;
vertbuffer[2].pos.z = rbounds[0].z;
vertbuffer[3].pos.x = rbounds[0].x;
vertbuffer[3].pos.y = rbounds[1].y;
vertbuffer[3].pos.z = rbounds[0].z;
vertbuffer[4].pos.x = rbounds[0].x;
vertbuffer[4].pos.y = rbounds[0].y;
vertbuffer[4].pos.z = rbounds[1].z;
vertbuffer[5].pos.x = rbounds[1].x;
vertbuffer[5].pos.y = rbounds[0].y;
vertbuffer[5].pos.z = rbounds[1].z;
vertbuffer[6].pos.x = rbounds[1].x;
vertbuffer[6].pos.y = rbounds[1].y;
vertbuffer[6].pos.z = rbounds[1].z;
vertbuffer[7].pos.x = rbounds[0].x;
vertbuffer[7].pos.y = rbounds[1].y;
vertbuffer[7].pos.z = rbounds[1].z;
}
void r3d_init_poly(r3d_poly *poly, r3d_rvec3 *vertices, r3d_int numverts,
r3d_int **faceinds, r3d_int *numvertsperface,
r3d_int numfaces) {
// dummy vars
r3d_int v, vprev, vcur, vnext, f, np;
// direct access to vertex buffer
r3d_vertex *vertbuffer = poly->verts;
r3d_int *nverts = &poly->nverts;
// count up the number of faces per vertex and act accordingly
r3d_int eperv[R3D_MAX_VERTS];
r3d_int minvperf = R3D_MAX_VERTS;
r3d_int maxvperf = 0;
memset(&eperv, 0, sizeof(eperv));
for (f = 0; f < numfaces; ++f)
for (v = 0; v < numvertsperface[f]; ++v) ++eperv[faceinds[f][v]];
for (v = 0; v < numverts; ++v) {
if (eperv[v] < minvperf) minvperf = eperv[v];
if (eperv[v] > maxvperf) maxvperf = eperv[v];
}
// clear the poly
*nverts = 0;
// return if we were given an invalid poly
if (minvperf < 3) return;
if (maxvperf == 3) {
// simple case with no need for duplicate vertices
// read in vertex locations
*nverts = numverts;
for (v = 0; v < *nverts; ++v) {
vertbuffer[v].pos = vertices[v];
for (np = 0; np < 3; ++np) vertbuffer[v].pnbrs[np] = R3D_MAX_VERTS;
}
// build graph connectivity by correctly orienting half-edges for each
// vertex
for (f = 0; f < numfaces; ++f) {
for (v = 0; v < numvertsperface[f]; ++v) {
vprev = faceinds[f][v];
vcur = faceinds[f][(v + 1) % numvertsperface[f]];
vnext = faceinds[f][(v + 2) % numvertsperface[f]];
for (np = 0; np < 3; ++np) {
if (vertbuffer[vcur].pnbrs[np] == vprev) {
vertbuffer[vcur].pnbrs[(np + 2) % 3] = vnext;
break;
} else if (vertbuffer[vcur].pnbrs[np] == vnext) {
vertbuffer[vcur].pnbrs[(np + 1) % 3] = vprev;
break;
}
}
if (np == 3) {
vertbuffer[vcur].pnbrs[1] = vprev;
vertbuffer[vcur].pnbrs[0] = vnext;
}
}
}
} else {
// we need to create duplicate, degenerate vertices to account for more than
// three edges per vertex. This is complicated.
r3d_int tface = 0;
for (v = 0; v < numverts; ++v) tface += eperv[v];
// need more variables
r3d_int v0, v1, v00, v11, numunclipped;
// we need a few extra buffers to handle the necessary operations
r3d_vertex vbtmp[3 * R3D_MAX_VERTS];
r3d_int util[3 * R3D_MAX_VERTS];
r3d_int vstart[R3D_MAX_VERTS];
// build vertex mappings to degenerate duplicates and read in vertex
// locations
*nverts = 0;
for (v = 0; v < numverts; ++v) {
vstart[v] = *nverts;
for (vcur = 0; vcur < eperv[v]; ++vcur) {
vbtmp[*nverts].pos = vertices[v];
for (np = 0; np < 3; ++np) vbtmp[*nverts].pnbrs[np] = R3D_MAX_VERTS;
++(*nverts);
}
}
// fill in connectivity for all duplicates
memset(&util, 0, sizeof(util));
for (f = 0; f < numfaces; ++f) {
for (v = 0; v < numvertsperface[f]; ++v) {
vprev = faceinds[f][v];
vcur = faceinds[f][(v + 1) % numvertsperface[f]];
vnext = faceinds[f][(v + 2) % numvertsperface[f]];
r3d_int vcur_old = vcur;
vcur = vstart[vcur] + util[vcur];
util[vcur_old]++;
vbtmp[vcur].pnbrs[1] = vnext;
vbtmp[vcur].pnbrs[2] = vprev;
}
}
// link degenerate duplicates, putting them in the correct order use util to
// mark and avoid double-processing verts
memset(&util, 0, sizeof(util));
for (v = 0; v < numverts; ++v) {
for (v0 = vstart[v]; v0 < vstart[v] + eperv[v]; ++v0) {
for (v1 = vstart[v]; v1 < vstart[v] + eperv[v]; ++v1) {
if (vbtmp[v0].pnbrs[2] == vbtmp[v1].pnbrs[1] && !util[v0]) {
vbtmp[v0].pnbrs[2] = v1;
vbtmp[v1].pnbrs[0] = v0;
util[v0] = 1;
}
}
}
}
// complete vertex pairs
memset(&util, 0, sizeof(util));
for (v0 = 0; v0 < numverts; ++v0)
for (v1 = v0 + 1; v1 < numverts; ++v1) {
for (v00 = vstart[v0]; v00 < vstart[v0] + eperv[v0]; ++v00)
for (v11 = vstart[v1]; v11 < vstart[v1] + eperv[v1]; ++v11) {
if (vbtmp[v00].pnbrs[1] == v1 && vbtmp[v11].pnbrs[1] == v0 &&
!util[v00] && !util[v11]) {
vbtmp[v00].pnbrs[1] = v11;
vbtmp[v11].pnbrs[1] = v00;
util[v00] = 1;
util[v11] = 1;
}
}
}
// remove unnecessary dummy vertices
memset(&util, 0, sizeof(util));
for (v = 0; v < numverts; ++v) {
v0 = vstart[v];
v1 = vbtmp[v0].pnbrs[0];
v00 = vbtmp[v0].pnbrs[2];
v11 = vbtmp[v1].pnbrs[0];
vbtmp[v00].pnbrs[0] = vbtmp[v0].pnbrs[1];
vbtmp[v11].pnbrs[2] = vbtmp[v1].pnbrs[1];
for (np = 0; np < 3; ++np)
if (vbtmp[vbtmp[v0].pnbrs[1]].pnbrs[np] == v0) break;
vbtmp[vbtmp[v0].pnbrs[1]].pnbrs[np] = v00;
for (np = 0; np < 3; ++np)
if (vbtmp[vbtmp[v1].pnbrs[1]].pnbrs[np] == v1) break;
vbtmp[vbtmp[v1].pnbrs[1]].pnbrs[np] = v11;
util[v0] = 1;
util[v1] = 1;
}
// copy to the real vertbuffer and compress
numunclipped = 0;
for (v = 0; v < *nverts; ++v) {
if (!util[v]) {
vertbuffer[numunclipped] = vbtmp[v];
util[v] = numunclipped++;
}
}
*nverts = numunclipped;
for (v = 0; v < *nverts; ++v)
for (np = 0; np < 3; ++np)
vertbuffer[v].pnbrs[np] = util[vertbuffer[v].pnbrs[np]];
}
}
void r3d_tet_faces_from_verts(r3d_plane *faces, r3d_rvec3 *verts) {
r3d_rvec3 tmpcent;
faces[0].n.x = ((verts[3].y - verts[1].y) * (verts[2].z - verts[1].z) -
(verts[2].y - verts[1].y) * (verts[3].z - verts[1].z));
faces[0].n.y = ((verts[2].x - verts[1].x) * (verts[3].z - verts[1].z) -
(verts[3].x - verts[1].x) * (verts[2].z - verts[1].z));
faces[0].n.z = ((verts[3].x - verts[1].x) * (verts[2].y - verts[1].y) -
(verts[2].x - verts[1].x) * (verts[3].y - verts[1].y));
norm(faces[0].n);
tmpcent.x = ONE_THIRD * (verts[1].x + verts[2].x + verts[3].x);
tmpcent.y = ONE_THIRD * (verts[1].y + verts[2].y + verts[3].y);
tmpcent.z = ONE_THIRD * (verts[1].z + verts[2].z + verts[3].z);
faces[0].d = -dot(faces[0].n, tmpcent);
faces[1].n.x = ((verts[2].y - verts[0].y) * (verts[3].z - verts[2].z) -
(verts[2].y - verts[3].y) * (verts[0].z - verts[2].z));
faces[1].n.y = ((verts[3].x - verts[2].x) * (verts[2].z - verts[0].z) -
(verts[0].x - verts[2].x) * (verts[2].z - verts[3].z));
faces[1].n.z = ((verts[2].x - verts[0].x) * (verts[3].y - verts[2].y) -
(verts[2].x - verts[3].x) * (verts[0].y - verts[2].y));
norm(faces[1].n);
tmpcent.x = ONE_THIRD * (verts[2].x + verts[3].x + verts[0].x);
tmpcent.y = ONE_THIRD * (verts[2].y + verts[3].y + verts[0].y);
tmpcent.z = ONE_THIRD * (verts[2].z + verts[3].z + verts[0].z);
faces[1].d = -dot(faces[1].n, tmpcent);
faces[2].n.x = ((verts[1].y - verts[3].y) * (verts[0].z - verts[3].z) -
(verts[0].y - verts[3].y) * (verts[1].z - verts[3].z));
faces[2].n.y = ((verts[0].x - verts[3].x) * (verts[1].z - verts[3].z) -
(verts[1].x - verts[3].x) * (verts[0].z - verts[3].z));
faces[2].n.z = ((verts[1].x - verts[3].x) * (verts[0].y - verts[3].y) -
(verts[0].x - verts[3].x) * (verts[1].y - verts[3].y));
norm(faces[2].n);
tmpcent.x = ONE_THIRD * (verts[3].x + verts[0].x + verts[1].x);
tmpcent.y = ONE_THIRD * (verts[3].y + verts[0].y + verts[1].y);
tmpcent.z = ONE_THIRD * (verts[3].z + verts[0].z + verts[1].z);
faces[2].d = -dot(faces[2].n, tmpcent);
faces[3].n.x = ((verts[0].y - verts[2].y) * (verts[1].z - verts[0].z) -
(verts[0].y - verts[1].y) * (verts[2].z - verts[0].z));
faces[3].n.y = ((verts[1].x - verts[0].x) * (verts[0].z - verts[2].z) -
(verts[2].x - verts[0].x) * (verts[0].z - verts[1].z));
faces[3].n.z = ((verts[0].x - verts[2].x) * (verts[1].y - verts[0].y) -
(verts[0].x - verts[1].x) * (verts[2].y - verts[0].y));
norm(faces[3].n);
tmpcent.x = ONE_THIRD * (verts[0].x + verts[1].x + verts[2].x);
tmpcent.y = ONE_THIRD * (verts[0].y + verts[1].y + verts[2].y);
tmpcent.z = ONE_THIRD * (verts[0].z + verts[1].z + verts[2].z);
faces[3].d = -dot(faces[3].n, tmpcent);
}
void r3d_box_faces_from_verts(r3d_plane *faces, r3d_rvec3 *rbounds) {
faces[0].n.x = 0.0;
faces[0].n.y = 0.0;
faces[0].n.z = 1.0;
faces[0].d = -rbounds[0].z;
faces[2].n.x = 0.0;
faces[2].n.y = 1.0;
faces[2].n.z = 0.0;
faces[2].d = -rbounds[0].y;
faces[4].n.x = 1.0;
faces[4].n.y = 0.0;
faces[4].n.z = 0.0;
faces[4].d = -rbounds[0].x;
faces[1].n.x = 0.0;
faces[1].n.y = 0.0;
faces[1].n.z = -1.0;
faces[1].d = rbounds[1].z;
faces[3].n.x = 0.0;
faces[3].n.y = -1.0;
faces[3].n.z = 0.0;
faces[3].d = rbounds[1].y;
faces[5].n.x = -1.0;
faces[5].n.y = 0.0;
faces[5].n.z = 0.0;
faces[5].d = rbounds[1].x;
}
void r3d_poly_faces_from_verts(r3d_plane *faces, r3d_rvec3 *vertices,
r3d_int numverts, r3d_int **faceinds,
r3d_int *numvertsperface, r3d_int numfaces) {
// dummy vars
r3d_int v, f;
r3d_rvec3 p0, p1, p2, centroid;
// calculate a centroid and a unit normal for each face
for (f = 0; f < numfaces; ++f) {
centroid.x = 0.0;
centroid.y = 0.0;
centroid.z = 0.0;
faces[f].n.x = 0.0;
faces[f].n.y = 0.0;
faces[f].n.z = 0.0;
for (v = 0; v < numvertsperface[f]; ++v) {
// add cross product of edges to the total normal
p0 = vertices[faceinds[f][v]];
p1 = vertices[faceinds[f][(v + 1) % numvertsperface[f]]];
p2 = vertices[faceinds[f][(v + 2) % numvertsperface[f]]];
faces[f].n.x +=
(p1.y - p0.y) * (p2.z - p0.z) - (p1.z - p0.z) * (p2.y - p0.y);
faces[f].n.y +=
(p1.z - p0.z) * (p2.x - p0.x) - (p1.x - p0.x) * (p2.z - p0.z);
faces[f].n.z +=
(p1.x - p0.x) * (p2.y - p0.y) - (p1.y - p0.y) * (p2.x - p0.x);
// add the vertex position to the centroid
centroid.x += p0.x;
centroid.y += p0.y;
centroid.z += p0.z;
}
// normalize the normals and set the signed distance to origin
centroid.x /= numvertsperface[f];
centroid.y /= numvertsperface[f];
centroid.z /= numvertsperface[f];
norm(faces[f].n);
faces[f].d = -dot(faces[f].n, centroid);
}
}
r3d_real r3d_orient(r3d_rvec3 *verts) {
r3d_real adx, bdx, cdx;
r3d_real ady, bdy, cdy;
r3d_real adz, bdz, cdz;
adx = verts[0].x - verts[3].x;
bdx = verts[1].x - verts[3].x;
cdx = verts[2].x - verts[3].x;
ady = verts[0].y - verts[3].y;
bdy = verts[1].y - verts[3].y;
cdy = verts[2].y - verts[3].y;