forked from vectorgraphics/asymptote
-
Notifications
You must be signed in to change notification settings - Fork 0
/
bezierpatch.cc
1117 lines (948 loc) · 31.3 KB
/
bezierpatch.cc
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
/*****
* bezierpatch.cc
* Authors: John C. Bowman and Jesse Frohlich
*
* Render Bezier patches and triangles.
*****/
#include "bezierpatch.h"
#include "predicates.h"
namespace camp {
using ::orient2d;
using ::orient3d;
#ifdef HAVE_GL
int MaterialIndex;
//std::vector<GLuint>& I=transparentData.Indices;
//std::vector<VertexData>& V=transparentData.Vertices;
bool colors;
std::vector<GLfloat> zbuffer;
std::vector<GLfloat> xbuffer;
std::vector<GLfloat> ybuffer;
//std::vector<GLfloat> xmin,ymin,zmin;
//std::vector<GLfloat> xmax,ymax,zmax;
std::vector<GLfloat> zsum;
inline double min(double a, double b, double c)
{
return min(min(a,b),c);
}
inline double max(double a, double b, double c)
{
return max(max(a,b),c);
}
struct iz {
unsigned i;
double z;
iz() {}
void minimum(unsigned i, const std::vector<GLuint>& I) {
this->i=i;
unsigned i3=3*i;
z=min(zbuffer[I[i3]],zbuffer[I[i3+1]],zbuffer[I[i3+2]]);
}
};
std::vector<iz> IZ;
const double FillFactor=0.1;
inline int sgn1(double x)
{
return x >= 0.0 ? 1 : -1;
}
inline int sgn(double x)
{
return (x > 0.0 ? 1 : (x < 0.0 ? -1 : 0));
}
bool sameside(const double *a, const double *b, int s0, const double *A,
const double *B, const double *C)
{
if(sgn(orient2d(a,b,A)) == s0) return true;
if(sgn(orient2d(a,b,B)) == s0) return true;
if(sgn(orient2d(a,b,C)) == s0) return true;
return false;
}
// returns true iff 2D triangles abc and ABC intersect
bool intersect2D(const double *a, const double *b, const double *c,
const double *A, const double *B, const double *C)
{
int s0=sgn(orient2d(a,b,c)); // Optimize away
int S0=sgn(orient2d(A,B,C)); // Optimize away
return
sameside(a,b,s0,A,B,C) &&
sameside(b,c,s0,A,B,C) &&
sameside(c,a,s0,A,B,C) &&
sameside(A,B,S0,a,b,c) &&
sameside(B,C,S0,a,b,c) &&
sameside(C,A,S0,a,b,c);
}
// returns true iff triangle abc is pierced by line segment AB.
bool pierce(const double *a, const double *b, const double *c, const double *A, const double *B)
{
int sa=sgn(orient3d(A,b,c,B));
int sb=sgn(orient3d(A,c,a,B));
int sc=sgn(orient3d(A,a,b,B));
return sa == sb && sb == sc;
}
// returns true iff triangle abc is pierced by an edge of triangle ABC
bool intersect0(const double *a, const double *b, const double *c,
const double *A, const double *B, const double *C,
int sA, int sB, int sC)
{
if(sA != sB) {
if(pierce(a,b,c,A,B)) return true;
if(sC != sA) {
if(pierce(a,b,c,C,A)) return true;
} else {
if(pierce(a,b,c,B,C)) return true;
}
} else {
if(pierce(a,b,c,B,C)) return true;
if(pierce(a,b,c,C,A)) return true;
}
return false;
}
// returns true iff triangle abc intersects triangle ABC
bool intersect3D(const double *a, const double *b, const double *c,
const double *A, const double *B, const double *C)
{
int sA=sgn(orient3d(a,b,c,A));
int sB=sgn(orient3d(a,b,c,B));
int sC=sgn(orient3d(a,b,c,C));
if(sA == sB && sB == sC) return false;
int sa=sgn(orient3d(A,B,C,a));
int sb=sgn(orient3d(A,B,C,b));
int sc=sgn(orient3d(A,B,C,c));
if(sa == sb && sb == sc) return false;
return intersect0(a,b,c,A,B,C,sA,sB,sC) || intersect0(A,B,C,a,b,c,sa,sb,sc);
}
// Return the intersection time of the extension of the line segment PQ
// with the plane perpendicular to n and passing through Z.
inline double intersect(const double *P, const double *Q, const double *n,
const double *Z)
{
double d=n[0]*Z[0]+n[1]*Z[1]+n[2]*Z[2];
double denom=n[0]*(Q[0]-P[0])+n[1]*(Q[1]-P[1])+n[2]*(Q[2]-P[2]);
return denom == 0 ? DBL_MAX : (d-n[0]*P[0]-n[1]*P[1]-n[2]*P[2])/denom;
}
inline triple interp(const double *a, const double *b, double t)
{
return triple(a[0]+t*(b[0]-a[0]),a[1]+t*(b[1]-a[1]),a[2]+t*(b[2]-a[2]));
}
inline void interp(GLfloat *dest,
const GLfloat *a, const GLfloat *b, double t)
{
double onemt=1.0-t;
for(size_t i=0; i < 4; ++i)
dest[i]=onemt*a[i]+t*b[i];
}
inline triple interp(const triple& a, const triple& b, double t)
{
return a+(b-a)*t;
}
unsigned n;
unsigned int count;
// Sort nonintersecting triangles by depth.
int compare(const void *p, const void *P)
{
unsigned Ia=((GLuint *) p)[0];
unsigned Ib=((GLuint *) p)[1];
unsigned Ic=((GLuint *) p)[2];
unsigned IA=((GLuint *) P)[0];
unsigned IB=((GLuint *) P)[1];
unsigned IC=((GLuint *) P)[2];
return zbuffer[Ia]+zbuffer[Ib]+zbuffer[Ic] <
zbuffer[IA]+zbuffer[IB]+zbuffer[IC] ? -1 : 1;
/*
double a[]={xbuffer[Ia],ybuffer[Ia],zbuffer[Ia]};
double b[]={xbuffer[Ib],ybuffer[Ib],zbuffer[Ib]};
double c[]={xbuffer[Ic],ybuffer[Ic],zbuffer[Ic]};
double A[]={xbuffer[IA],ybuffer[IA],zbuffer[IA]};
double B[]={xbuffer[IB],ybuffer[IB],zbuffer[IB]};
double C[]={xbuffer[IC],ybuffer[IC],zbuffer[IC]};
double viewpoint[]={0,0,100000};
double sa=-orient3d(A,B,C,a);
double sb=-orient3d(A,B,C,b);
double sc=-orient3d(A,B,C,c);
double s=min(sa,sb,sc);
double S=max(sa,sb,sc);
double eps=1000;
if(s < -eps && S > eps) { //swap
double sA=-orient3d(a,b,c,A);
double sB=-orient3d(a,b,c,B);
double sC=-orient3d(a,b,c,C);
double s=min(sA,sB,sC);
double S=max(sA,sB,sC);
if(S < -s) S=s;
int sz=sgn1(orient3d(a,b,c,viewpoint));
if(S < -eps) return -sz;
if(S > eps) return sz;
}
if(S < -s) S=s;
int sz=sgn1(orient3d(A,B,C,viewpoint));
if(S < -eps) return sz;
if(S > eps) return -sz;
return a[2]+b[2]+c[2] < A[2]+B[2]+C[2] ? -1 : 1;
*/
}
#if 0
void split(unsigned i3, GLuint ia, GLuint ib, GLuint ic,
double *a, double *b, double *c, double *N, double *A) {
double td=intersect(a,b,N,A);
double te=intersect(a,c,N,A);
triple d=interp(a,b,td);
triple e=interp(a,c,te);
GLuint Ia=tstride*ia;
GLuint Ib=tstride*ib;
GLuint Ic=tstride*ic;
triple na=triple(V[Ia+3],V[Ia+4],V[Ia+5]);
triple nb=triple(V[Ib+3],V[Ib+4],V[Ib+5]);
triple nc=triple(V[Ic+3],V[Ic+4],V[Ic+5]);
triple nd=interp(na,nb,td);
triple ne=interp(na,nc,te);
GLuint id,ie;
if(colors) {
GLfloat *ca=&V[Ia+6];
GLfloat *cb=&V[Ib+6];
GLfloat *cc=&V[Ic+6];
GLfloat cd[4],ce[4];
interp(cd,ca,cb,td);
interp(ce,ca,cc,te);
id=data.Vertex(d,nd,cd);
ie=data.Vertex(e,ne,ce);
} else {
id=data.Vertex(d,nd);
ie=data.Vertex(e,ne);
}
I[i3]=ia;
I[i3+1]=id;
I[i3+2]=ie;
I.push_back(id);
I.push_back(ib);
I.push_back(ie);
I.push_back(ie);
I.push_back(ib);
I.push_back(ic);
}
#endif
void BezierPatch::init(double res)
{
res2=res*res;
Epsilon=FillFactor*res;
MaterialIndex=transparent ?
(color ? -1-materialIndex : 1+materialIndex) : materialIndex;
pvertex=transparent ? &vertexBuffer::tvertex : &vertexBuffer::vertex;
}
void BezierPatch::render(const triple *p, bool straight, GLfloat *c0)
{
triple p0=p[0];
epsilon=0;
for(unsigned i=1; i < 16; ++i)
epsilon=max(epsilon,abs2(p[i]-p0));
epsilon *= DBL_EPSILON;
triple p3=p[3];
triple p12=p[12];
triple p15=p[15];
triple n0=normal(p3,p[2],p[1],p0,p[4],p[8],p12);
if(abs2(n0) <= epsilon) {
n0=normal(p3,p[2],p[1],p0,p[13],p[14],p15);
if(abs2(n0) <= epsilon) n0=normal(p15,p[11],p[7],p3,p[4],p[8],p12);
}
triple n1=normal(p0,p[4],p[8],p12,p[13],p[14],p15);
if(abs2(n1) <= epsilon) {
n1=normal(p0,p[4],p[8],p12,p[11],p[7],p3);
if(abs2(n1) <= epsilon) n1=normal(p3,p[2],p[1],p0,p[13],p[14],p15);
}
triple n2=normal(p12,p[13],p[14],p15,p[11],p[7],p3);
if(abs2(n2) <= epsilon) {
n2=normal(p12,p[13],p[14],p15,p[2],p[1],p0);
if(abs2(n2) <= epsilon) n2=normal(p0,p[4],p[8],p12,p[11],p[7],p3);
}
triple n3=normal(p15,p[11],p[7],p3,p[2],p[1],p0);
if(abs2(n3) <= epsilon) {
n3=normal(p15,p[11],p[7],p3,p[4],p[8],p12);
if(abs2(n3) <= epsilon) n3=normal(p12,p[13],p[14],p15,p[2],p[1],p0);
}
GLuint i0,i1,i2,i3;
if(color) {
GLfloat *c1=c0+4;
GLfloat *c2=c0+8;
GLfloat *c3=c0+12;
i0=data.Vertex(p0,n0,c0);
i1=data.Vertex(p12,n1,c1);
i2=data.Vertex(p15,n2,c2);
i3=data.Vertex(p3,n3,c3);
if(!straight)
render(p,i0,i1,i2,i3,p0,p12,p15,p3,false,false,false,false,
c0,c1,c2,c3);
} else {
i0=(data.*pvertex)(p0,n0);
i1=(data.*pvertex)(p12,n1);
i2=(data.*pvertex)(p15,n2);
i3=(data.*pvertex)(p3,n3);
if(!straight)
render(p,i0,i1,i2,i3,p0,p12,p15,p3,false,false,false,false);
}
if(straight) {
std::vector<GLuint> &q=data.indices;
triple Pa[]={p0,p12,p15};
if(!offscreen(3,Pa)) {
q.push_back(i0);
q.push_back(i1);
q.push_back(i2);
}
triple Pb[]={p0,p15,p3};
if(!offscreen(3,Pb)) {
q.push_back(i0);
q.push_back(i2);
q.push_back(i3);
}
}
append();
}
// Use a uniform partition to draw a Bezier patch.
// p is an array of 16 triples representing the control points.
// Pi are the (possibly) adjusted vertices indexed by Ii.
// The 'flati' are flatness flags for each boundary.
void BezierPatch::render(const triple *p,
GLuint I0, GLuint I1, GLuint I2, GLuint I3,
triple P0, triple P1, triple P2, triple P3,
bool flat0, bool flat1, bool flat2, bool flat3,
GLfloat *C0, GLfloat *C1, GLfloat *C2, GLfloat *C3)
{
pair d=Distance(p);
if(d.getx() < res2 && d.gety() < res2) { // Bezier patch is flat
triple Pa[]={P0,P1,P2};
std::vector<GLuint> &q=data.indices;
if(!offscreen(3,Pa)) {
q.push_back(I0);
q.push_back(I1);
q.push_back(I2);
}
triple Pb[]={P0,P2,P3};
if(!offscreen(3,Pb)) {
q.push_back(I0);
q.push_back(I2);
q.push_back(I3);
}
} else { // Patch is not flat
if(offscreen(16,p)) return;
/* Control points are indexed as follows:
Coordinate
+-----
Index
03 13 23 33
+-----+-----+-----+
|3 |7 |11 |15
| | | |
|02 |12 |22 |32
+-----+-----+-----+
|2 |6 |10 |14
| | | |
|01 |11 |21 |31
+-----+-----+-----+
|1 |5 |9 |13
| | | |
|00 |10 |20 |30
+-----+-----+-----+
0 4 8 12
*/
triple p0=p[0];
triple p3=p[3];
triple p12=p[12];
triple p15=p[15];
if(d.getx() < res2) { // flat in horizontal direction; split vertically
/*
P refers to a corner
m refers to a midpoint
s refers to a subpatch
+--------+--------+
|P3 P2|
| |
| s1 |
| |
| |
m1 +-----------------+ m0
| |
| |
| s0 |
| |
|P0 P1|
+-----------------+
*/
Split3 c0(p0,p[1],p[2],p3);
Split3 c1(p[4],p[5],p[6],p[7]);
Split3 c2(p[8],p[9],p[10],p[11]);
Split3 c3(p12,p[13],p[14],p15);
triple s0[]={p0 ,c0.m0,c0.m3,c0.m5,
p[4],c1.m0,c1.m3,c1.m5,
p[8],c2.m0,c2.m3,c2.m5,
p12 ,c3.m0,c3.m3,c3.m5};
triple s1[]={c0.m5,c0.m4,c0.m2,p3,
c1.m5,c1.m4,c1.m2,p[7],
c2.m5,c2.m4,c2.m2,p[11],
c3.m5,c3.m4,c3.m2,p15};
triple n0=normal(s0[12],s0[13],s0[14],s0[15],s0[11],s0[7],s0[3]);
if(abs2(n0) <= epsilon) {
n0=normal(s0[12],s0[13],s0[14],s0[15],s0[2],s0[1],s0[0]);
if(abs2(n0) <= epsilon)
n0=normal(s0[0],s0[4],s0[8],s0[12],s0[11],s0[7],s0[3]);
}
triple n1=normal(s1[3],s1[2],s1[1],s1[0],s1[4],s1[8],s1[12]);
if(abs2(n1) <= epsilon) {
n1=normal(s1[3],s1[2],s1[1],s1[0],s1[13],s1[14],s1[15]);
if(abs2(n1) <= epsilon)
n1=normal(s1[15],s1[11],s1[7],s1[3],s1[4],s1[8],s1[12]);
}
// A kludge to remove subdivision cracks, only applied the first time
// an edge is found to be flat before the rest of the subpatch is.
triple m0=0.5*(P1+P2);
if(!flat1) {
if((flat1=Straightness(p12,p[13],p[14],p15) < res2))
m0 -= Epsilon*unit(differential(s1[12],s1[8],s1[4],s1[0]));
else m0=s0[15];
}
triple m1=0.5*(P3+P0);
if(!flat3) {
if((flat3=Straightness(p0,p[1],p[2],p3) < res2))
m1 -= Epsilon*unit(differential(s0[3],s0[7],s0[11],s0[15]));
else m1=s1[0];
}
if(color) {
GLfloat c0[4],c1[4];
for(size_t i=0; i < 4; ++i) {
c0[i]=0.5*(C1[i]+C2[i]);
c1[i]=0.5*(C3[i]+C0[i]);
}
GLuint i0=data.Vertex(m0,n0,c0);
GLuint i1=data.Vertex(m1,n1,c1);
render(s0,I0,I1,i0,i1,P0,P1,m0,m1,flat0,flat1,false,flat3,C0,C1,c0,c1);
render(s1,i1,i0,I2,I3,m1,m0,P2,P3,false,flat1,flat2,flat3,c1,c0,C2,C3);
} else {
GLuint i0=(data.*pvertex)(m0,n0);
GLuint i1=(data.*pvertex)(m1,n1);
render(s0,I0,I1,i0,i1,P0,P1,m0,m1,flat0,flat1,false,flat3);
render(s1,i1,i0,I2,I3,m1,m0,P2,P3,false,flat1,flat2,flat3);
}
return;
}
if(d.gety() < res2) { // flat in vertical direction; split horizontally
/*
P refers to a corner
m refers to a midpoint
s refers to a subpatch
m1
+--------+--------+
|P3 | P2|
| | |
| | |
| | |
| | |
| s0 | s1 |
| | |
| | |
| | |
| | |
|P0 | P1|
+--------+--------+
m0
*/
Split3 c0(p0,p[4],p[8],p12);
Split3 c1(p[1],p[5],p[9],p[13]);
Split3 c2(p[2],p[6],p[10],p[14]);
Split3 c3(p3,p[7],p[11],p15);
triple s0[]={p0,p[1],p[2],p3,
c0.m0,c1.m0,c2.m0,c3.m0,
c0.m3,c1.m3,c2.m3,c3.m3,
c0.m5,c1.m5,c2.m5,c3.m5};
triple s1[]={c0.m5,c1.m5,c2.m5,c3.m5,
c0.m4,c1.m4,c2.m4,c3.m4,
c0.m2,c1.m2,c2.m2,c3.m2,
p12,p[13],p[14],p15};
triple n0=normal(s0[0],s0[4],s0[8],s0[12],s0[13],s0[14],s0[15]);
if(abs2(n0) <= epsilon) {
n0=normal(s0[0],s0[4],s0[8],s0[12],s0[11],s0[7],s0[3]);
if(abs2(n0) <= epsilon)
n0=normal(s0[3],s0[2],s0[1],s0[0],s0[13],s0[14],s0[15]);
}
triple n1=normal(s1[15],s1[11],s1[7],s1[3],s1[2],s1[1],s1[0]);
if(abs2(n1) <= epsilon) {
n1=normal(s1[15],s1[11],s1[7],s1[3],s1[4],s1[8],s1[12]);
if(abs2(n1) <= epsilon)
n1=normal(s1[12],s1[13],s1[14],s1[15],s1[2],s1[1],s1[0]);
}
// A kludge to remove subdivision cracks, only applied the first time
// an edge is found to be flat before the rest of the subpatch is.
triple m0=0.5*(P0+P1);
if(!flat0) {
if((flat0=Straightness(p0,p[4],p[8],p12) < res2))
m0 -= Epsilon*unit(differential(s1[0],s1[1],s1[2],s1[3]));
else m0=s0[12];
}
triple m1=0.5*(P2+P3);
if(!flat2) {
if((flat2=Straightness(p15,p[11],p[7],p3) < res2))
m1 -= Epsilon*unit(differential(s0[15],s0[14],s0[13],s0[12]));
else m1=s1[3];
}
if(color) {
GLfloat c0[4],c1[4];
for(size_t i=0; i < 4; ++i) {
c0[i]=0.5*(C0[i]+C1[i]);
c1[i]=0.5*(C2[i]+C3[i]);
}
GLuint i0=data.Vertex(m0,n0,c0);
GLuint i1=data.Vertex(m1,n1,c1);
render(s0,I0,i0,i1,I3,P0,m0,m1,P3,flat0,false,flat2,flat3,C0,c0,c1,C3);
render(s1,i0,I1,I2,i1,m0,P1,P2,m1,flat0,flat1,flat2,false,c0,C1,C2,c1);
} else {
GLuint i0=(data.*pvertex)(m0,n0);
GLuint i1=(data.*pvertex)(m1,n1);
render(s0,I0,i0,i1,I3,P0,m0,m1,P3,flat0,false,flat2,flat3);
render(s1,i0,I1,I2,i1,m0,P1,P2,m1,flat0,flat1,flat2,false);
}
return;
}
/*
Horizontal and vertical subdivision:
P refers to a corner
m refers to a midpoint
s refers to a subpatch
m2
+--------+--------+
|P3 | P2|
| | |
| s3 | s2 |
| | |
| | m4 |
m3 +--------+--------+ m1
| | |
| | |
| s0 | s1 |
| | |
|P0 | P1|
+--------+--------+
m0
*/
// Subdivide patch:
Split3 c0(p0,p[1],p[2],p3);
Split3 c1(p[4],p[5],p[6],p[7]);
Split3 c2(p[8],p[9],p[10],p[11]);
Split3 c3(p12,p[13],p[14],p15);
Split3 c4(p0,p[4],p[8],p12);
Split3 c5(c0.m0,c1.m0,c2.m0,c3.m0);
Split3 c6(c0.m3,c1.m3,c2.m3,c3.m3);
Split3 c7(c0.m5,c1.m5,c2.m5,c3.m5);
Split3 c8(c0.m4,c1.m4,c2.m4,c3.m4);
Split3 c9(c0.m2,c1.m2,c2.m2,c3.m2);
Split3 c10(p3,p[7],p[11],p15);
triple s0[]={p0,c0.m0,c0.m3,c0.m5,c4.m0,c5.m0,c6.m0,c7.m0,
c4.m3,c5.m3,c6.m3,c7.m3,c4.m5,c5.m5,c6.m5,c7.m5};
triple s1[]={c4.m5,c5.m5,c6.m5,c7.m5,c4.m4,c5.m4,c6.m4,c7.m4,
c4.m2,c5.m2,c6.m2,c7.m2,p12,c3.m0,c3.m3,c3.m5};
triple s2[]={c7.m5,c8.m5,c9.m5,c10.m5,c7.m4,c8.m4,c9.m4,c10.m4,
c7.m2,c8.m2,c9.m2,c10.m2,c3.m5,c3.m4,c3.m2,p15};
triple s3[]={c0.m5,c0.m4,c0.m2,p3,c7.m0,c8.m0,c9.m0,c10.m0,
c7.m3,c8.m3,c9.m3,c10.m3,c7.m5,c8.m5,c9.m5,c10.m5};
triple m4=s0[15];
triple n0=normal(s0[0],s0[4],s0[8],s0[12],s0[13],s0[14],s0[15]);
if(abs2(n0) <= epsilon) {
n0=normal(s0[0],s0[4],s0[8],s0[12],s0[11],s0[7],s0[3]);
if(abs2(n0) <= epsilon)
n0=normal(s0[3],s0[2],s0[1],s0[0],s0[13],s0[14],s0[15]);
}
triple n1=normal(s1[12],s1[13],s1[14],s1[15],s1[11],s1[7],s1[3]);
if(abs2(n1) <= epsilon) {
n1=normal(s1[12],s1[13],s1[14],s1[15],s1[2],s1[1],s1[0]);
if(abs2(n1) <= epsilon)
n1=normal(s1[0],s1[4],s1[8],s1[12],s1[11],s1[7],s1[3]);
}
triple n2=normal(s2[15],s2[11],s2[7],s2[3],s2[2],s2[1],s2[0]);
if(abs2(n2) <= epsilon) {
n2=normal(s2[15],s2[11],s2[7],s2[3],s2[4],s2[8],s2[12]);
if(abs2(n2) <= epsilon)
n2=normal(s2[12],s2[13],s2[14],s2[15],s2[2],s2[1],s2[0]);
}
triple n3=normal(s3[3],s3[2],s3[1],s3[0],s3[4],s3[8],s3[12]);
if(abs2(n3) <= epsilon) {
n3=normal(s3[3],s3[2],s3[1],s3[0],s3[13],s3[14],s3[15]);
if(abs2(n3) <= epsilon)
n3=normal(s3[15],s3[11],s3[7],s3[3],s3[4],s3[8],s3[12]);
}
triple n4=normal(s2[3],s2[2],s2[1],m4,s2[4],s2[8],s2[12]);
// A kludge to remove subdivision cracks, only applied the first time
// an edge is found to be flat before the rest of the subpatch is.
triple m0=0.5*(P0+P1);
if(!flat0) {
if((flat0=Straightness(p0,p[4],p[8],p12) < res2))
m0 -= Epsilon*unit(differential(s1[0],s1[1],s1[2],s1[3]));
else m0=s0[12];
}
triple m1=0.5*(P1+P2);
if(!flat1) {
if((flat1=Straightness(p12,p[13],p[14],p15) < res2))
m1 -= Epsilon*unit(differential(s2[12],s2[8],s2[4],s2[0]));
else m1=s1[15];
}
triple m2=0.5*(P2+P3);
if(!flat2) {
if((flat2=Straightness(p15,p[11],p[7],p3) < res2))
m2 -= Epsilon*unit(differential(s3[15],s3[14],s3[13],s3[12]));
else m2=s2[3];
}
triple m3=0.5*(P3+P0);
if(!flat3) {
if((flat3=Straightness(p0,p[1],p[2],p3) < res2))
m3 -= Epsilon*unit(differential(s0[3],s0[7],s0[11],s0[15]));
else m3=s3[0];
}
if(color) {
GLfloat c0[4],c1[4],c2[4],c3[4],c4[4];
for(size_t i=0; i < 4; ++i) {
c0[i]=0.5*(C0[i]+C1[i]);
c1[i]=0.5*(C1[i]+C2[i]);
c2[i]=0.5*(C2[i]+C3[i]);
c3[i]=0.5*(C3[i]+C0[i]);
c4[i]=0.5*(c0[i]+c2[i]);
}
GLuint i0=data.Vertex(m0,n0,c0);
GLuint i1=data.Vertex(m1,n1,c1);
GLuint i2=data.Vertex(m2,n2,c2);
GLuint i3=data.Vertex(m3,n3,c3);
GLuint i4=data.Vertex(m4,n4,c4);
render(s0,I0,i0,i4,i3,P0,m0,m4,m3,flat0,false,false,flat3,C0,c0,c4,c3);
render(s1,i0,I1,i1,i4,m0,P1,m1,m4,flat0,flat1,false,false,c0,C1,c1,c4);
render(s2,i4,i1,I2,i2,m4,m1,P2,m2,false,flat1,flat2,false,c4,c1,C2,c2);
render(s3,i3,i4,i2,I3,m3,m4,m2,P3,false,false,flat2,flat3,c3,c4,c2,C3);
} else {
GLuint i0=(data.*pvertex)(m0,n0);
GLuint i1=(data.*pvertex)(m1,n1);
GLuint i2=(data.*pvertex)(m2,n2);
GLuint i3=(data.*pvertex)(m3,n3);
GLuint i4=(data.*pvertex)(m4,n4);
render(s0,I0,i0,i4,i3,P0,m0,m4,m3,flat0,false,false,flat3);
render(s1,i0,I1,i1,i4,m0,P1,m1,m4,flat0,flat1,false,false);
render(s2,i4,i1,I2,i2,m4,m1,P2,m2,false,flat1,flat2,false);
render(s3,i3,i4,i2,I3,m3,m4,m2,P3,false,false,flat2,flat3);
}
}
}
void BezierTriangle::render(const triple *p, bool straight, GLfloat *c0)
{
triple p0=p[0];
epsilon=0;
for(int i=1; i < 10; ++i)
epsilon=max(epsilon,abs2(p[i]-p0));
epsilon *= DBL_EPSILON;
triple p6=p[6];
triple p9=p[9];
triple n0=normal(p9,p[5],p[2],p0,p[1],p[3],p6);
triple n1=normal(p0,p[1],p[3],p6,p[7],p[8],p9);
triple n2=normal(p6,p[7],p[8],p9,p[5],p[2],p0);
GLuint i0,i1,i2;
if(color) {
GLfloat *c1=c0+4;
GLfloat *c2=c0+8;
i0=data.Vertex(p0,n0,c0);
i1=data.Vertex(p6,n1,c1);
i2=data.Vertex(p9,n2,c2);
if(!straight)
render(p,i0,i1,i2,p0,p6,p9,false,false,false,c0,c1,c2);
} else {
i0=(data.*pvertex)(p0,n0);
i1=(data.*pvertex)(p6,n1);
i2=(data.*pvertex)(p9,n2);
if(!straight)
render(p,i0,i1,i2,p0,p6,p9,false,false,false);
}
if(straight) {
triple P[]={p0,p6,p9};
if(!offscreen(3,P)) {
std::vector<GLuint> &q=data.indices;
q.push_back(i0);
q.push_back(i1);
q.push_back(i2);
}
}
append();
}
// Use a uniform partition to draw a Bezier triangle.
// p is an array of 10 triples representing the control points.
// Pi are the (possibly) adjusted vertices indexed by Ii.
// The 'flati' are flatness flags for each boundary.
void BezierTriangle::render(const triple *p,
GLuint I0, GLuint I1, GLuint I2,
triple P0, triple P1, triple P2,
bool flat0, bool flat1, bool flat2,
GLfloat *C0, GLfloat *C1, GLfloat *C2)
{
if(Distance(p) < res2) { // Bezier triangle is flat
triple P[]={P0,P1,P2};
if(!offscreen(3,P)) {
std::vector<GLuint> &q=data.indices;
q.push_back(I0);
q.push_back(I1);
q.push_back(I2);
}
} else { // Triangle is not flat
if(offscreen(10,p)) return;
/* Control points are indexed as follows:
Coordinate
Index
030
9
/\
/ \
/ \
/ \
/ \
021 + + 120
5 / \ 8
/ \
/ \
/ \
/ \
012 + + + 210
2 / 111 \ 7
/ 4 \
/ \
/ \
/ \
/__________________________________\
003 102 201 300
0 1 3 6
Subdivision:
P2
030
/\
/ \
/ \
/ \
/ \
/ up \
/ \
/ \
p1 /________________\ p0
/\ / \
/ \ / \
/ \ / \
/ \ center / \
/ \ / \
/ \ / \
/ left \ / right \
/ \ / \
/________________V_________________\
003 p2 300
P0 P1
*/
// Subdivide triangle:
triple l003=p[0];
triple p102=p[1];
triple p012=p[2];
triple p201=p[3];
triple p111=p[4];
triple p021=p[5];
triple r300=p[6];
triple p210=p[7];
triple p120=p[8];
triple u030=p[9];
triple u021=0.5*(u030+p021);
triple u120=0.5*(u030+p120);
triple p033=0.5*(p021+p012);
triple p231=0.5*(p120+p111);
triple p330=0.5*(p120+p210);
triple p123=0.5*(p012+p111);
triple l012=0.5*(p012+l003);
triple p312=0.5*(p111+p201);
triple r210=0.5*(p210+r300);
triple l102=0.5*(l003+p102);
triple p303=0.5*(p102+p201);
triple r201=0.5*(p201+r300);
triple u012=0.5*(u021+p033);
triple u210=0.5*(u120+p330);
triple l021=0.5*(p033+l012);
triple p4xx=0.5*p231+0.25*(p111+p102);
triple r120=0.5*(p330+r210);
triple px4x=0.5*p123+0.25*(p111+p210);
triple pxx4=0.25*(p021+p111)+0.5*p312;
triple l201=0.5*(l102+p303);
triple r102=0.5*(p303+r201);
triple l210=0.5*(px4x+l201); // =c120
triple r012=0.5*(px4x+r102); // =c021
triple l300=0.5*(l201+r102); // =r003=c030
triple r021=0.5*(pxx4+r120); // =c012
triple u201=0.5*(u210+pxx4); // =c102
triple r030=0.5*(u210+r120); // =u300=c003
triple u102=0.5*(u012+p4xx); // =c201
triple l120=0.5*(l021+p4xx); // =c210
triple l030=0.5*(u012+l021); // =u003=c300
triple l111=0.5*(p123+l102);
triple r111=0.5*(p312+r210);
triple u111=0.5*(u021+p231);
triple c111=0.25*(p033+p330+p303+p111);
triple l[]={l003,l102,l012,l201,l111,l021,l300,l210,l120,l030}; // left
triple r[]={l300,r102,r012,r201,r111,r021,r300,r210,r120,r030}; // right
triple u[]={l030,u102,u012,u201,u111,u021,r030,u210,u120,u030}; // up
triple c[]={r030,u201,r021,u102,c111,r012,l030,l120,l210,l300}; // center
triple n0=normal(l300,r012,r021,r030,u201,u102,l030);
triple n1=normal(r030,u201,u102,l030,l120,l210,l300);
triple n2=normal(l030,l120,l210,l300,r012,r021,r030);
// A kludge to remove subdivision cracks, only applied the first time
// an edge is found to be flat before the rest of the subpatch is.
triple m0=0.5*(P1+P2);
if(!flat0) {
if((flat0=Straightness(r300,p210,p120,u030) < res2))
m0 -= Epsilon*unit(differential(c[0],c[2],c[5],c[9])+
differential(c[0],c[1],c[3],c[6]));
else m0=r030;
}
triple m1=0.5*(P2+P0);
if(!flat1) {
if((flat1=Straightness(l003,p012,p021,u030) < res2))
m1 -= Epsilon*unit(differential(c[6],c[3],c[1],c[0])+
differential(c[6],c[7],c[8],c[9]));
else m1=l030;
}
triple m2=0.5*(P0+P1);
if(!flat2) {
if((flat2=Straightness(l003,p102,p201,r300) < res2))
m2 -= Epsilon*unit(differential(c[9],c[8],c[7],c[6])+
differential(c[9],c[5],c[2],c[0]));
else m2=l300;
}
if(color) {
GLfloat c0[4],c1[4],c2[4];
for(int i=0; i < 4; ++i) {
c0[i]=0.5*(C1[i]+C2[i]);
c1[i]=0.5*(C2[i]+C0[i]);
c2[i]=0.5*(C0[i]+C1[i]);
}
GLuint i0=data.Vertex(m0,n0,c0);
GLuint i1=data.Vertex(m1,n1,c1);
GLuint i2=data.Vertex(m2,n2,c2);
render(l,I0,i2,i1,P0,m2,m1,false,flat1,flat2,C0,c2,c1);
render(r,i2,I1,i0,m2,P1,m0,flat0,false,flat2,c2,C1,c0);
render(u,i1,i0,I2,m1,m0,P2,flat0,flat1,false,c1,c0,C2);
render(c,i0,i1,i2,m0,m1,m2,false,false,false,c0,c1,c2);
} else {
GLuint i0=(data.*pvertex)(m0,n0);
GLuint i1=(data.*pvertex)(m1,n1);
GLuint i2=(data.*pvertex)(m2,n2);
render(l,I0,i2,i1,P0,m2,m1,false,flat1,flat2);
render(r,i2,I1,i0,m2,P1,m0,flat0,false,flat2);
render(u,i1,i0,I2,m1,m0,P2,flat0,flat1,false);
render(c,i0,i1,i2,m0,m1,m2,false,false,false);
}
}
}
void transform(const std::vector<VertexData>& b)
{
unsigned n=b.size();
// xbuffer.resize(n);
// ybuffer.resize(n);
zbuffer.resize(n);
double Tz0=gl::dView[2];
double Tz1=gl::dView[6];
double Tz2=gl::dView[10];
for(unsigned i=0; i < n; ++i) {
const GLfloat *v=b[i].position;
zbuffer[i]=Tz0*v[0]+Tz1*v[1]+Tz2*v[2];
}
}
#if 0
// precompute min and max bounds of each triangle
void bounds(const std::vector<GLuint>& I)