-
Notifications
You must be signed in to change notification settings - Fork 0
/
IDelaunay2D.java
1118 lines (937 loc) · 37.1 KB
/
IDelaunay2D.java
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
/*---
iGeo - http://igeo.jp
Copyright (c) 2002-2013 Satoru Sugihara
This file is part of iGeo.
iGeo is free software: you can redistribute it and/or modify
it under the terms of the GNU Lesser General Public License as
published by the Free Software Foundation, version 3.
iGeo is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with iGeo. If not, see <http://www.gnu.org/licenses/>.
---*/
package igeo;
import java.util.*;
import igeo.gui.*;
/**
Class to calculate Delaunay triangulation out of 2D points.
@author Satoru Sugihara
*/
public class IDelaunay2D {
public static double maxDistToCheck = -1;
/**
Calculates Delaunay triangles out of array of 2D points
@param innerPts points inside edges defined by edgePts
@param edgePts points on the edge (the edge should be naked having only one triangle touching); order of edge points needs to be counter clockwise for outer trim loop, clockwise for inner hole trim loop.
@return array of triangles, which consist of array of 3 points of IVec2
*/
public static IVec2[][] getTriangles(IVec2[] innerPts, IVec2[][] edgePts){
int innerPtsNum = 0;
int edgePtsNum = 0;
if(innerPts!=null) innerPtsNum=innerPts.length;
if(edgePts!=null){
for(int i=0; i<edgePts.length; i++) edgePtsNum+=edgePts[i].length;
}
IVec2[] pts = new IVec2[innerPtsNum+edgePtsNum];
if(innerPts!=null){
for(int i=0; i<innerPts.length; i++){
pts[i] = innerPts[i];
//IOut.p("pts["+i+"] is innerPts "+innerPts[i]); //
}
}
int[][] edgePtIdx = null;
if(edgePts!=null){
edgePtIdx = new int[edgePts.length][];
int ptIdx = innerPtsNum;
for(int i=0; i<edgePts.length; i++){
edgePtIdx[i] = new int[edgePts[i].length];
for(int j=0; j<edgePts[i].length; j++){
//IOut.p("ptIdx="+ptIdx+" / pts.length="+pts.length); //
//IOut.p("pts["+ptIdx+"] is edgePts "+edgePts[i][j]); //
pts[ptIdx] = edgePts[i][j];
edgePtIdx[i][j] = ptIdx;
ptIdx++;
}
}
}
if(pts.length==3){
if(isClockwise(pts[0],pts[1],pts[2]))
return new IVec2[][]{ new IVec2[]{ pts[0],pts[2],pts[1] } };
return new IVec2[][]{ new IVec2[]{ pts[0],pts[1],pts[2] } };
}
ArrayList<IVec2[]> triangles = new ArrayList<IVec2[]>();
ArrayList<FaceIndex> triangleIndex = new ArrayList<FaceIndex>();
//IOut.p("pts.length = "+pts.length); //
//for(int i=0; i<pts.length; i++) IOut.p("pts["+i+"] = "+ pts[i]); //
EdgeCounter edgeCount = new EdgeCounter(pts.length);
for(int i=0; i<edgePtIdx.length; i++){
for(int j=0; j<edgePtIdx[i].length; j++){
edgeCount.addEdge(edgePtIdx[i][j],edgePtIdx[i][(j+1)%edgePtIdx[i].length]);
}
}
// in case a point on edges are on other loop's edge
for(int i=0; i<edgePtIdx.length; i++){
for(int j=0; j<edgePtIdx[i].length; j++){
int ept1 = edgePtIdx[i][j];
int ept2 = edgePtIdx[i][(j+1)%edgePtIdx[i].length];
for(int k=0; k<edgePtIdx.length; k++){
if(k!=i){
for(int l=0; l<edgePtIdx[k].length; l++){
if(pts[edgePtIdx[k][l]].isStraight(pts[ept1],pts[ept2]) &&
pts[edgePtIdx[k][l]].isBetween(pts[ept1],pts[ept2])){
edgeCount.addEdge(ept1, edgePtIdx[k][l]);
edgeCount.addEdge(ept2, edgePtIdx[k][l]);
}
}
}
}
}
}
for(int i=0; i<pts.length-2; i++){
//IOut.p((i+1)+"/"+(pts.length-2)); //
for(int j=i+1; j<pts.length-1; j++){
for(int k=j+1; k<pts.length && edgeCount.isEdgeOpen(i,j); k++){
boolean anyInside=false;
//IOut.p("<"+i+","+j+","+k+">"); //
//IOut.p("isFaceCrossing = "+ isFaceCrossing(pts, edgeCount, i, j, k));
//IOut.p("checkDirectionOnEdgePoints = "+checkDirectionOnEdgePoints(pts,edgePts,i,j,k,innerPtsNum) );
//IOut.p("isStraight = "+pts[i].isStraight(pts[j],pts[k])); //
if(edgeCount.isEdgeOpen(i,k) && edgeCount.isEdgeOpen(j,k)
&& !isFaceCrossing(pts, edgeCount, i, j, k)
//&& checkFaceDirection(pts, edgeCount, i, j, k)
&& checkDirectionOnEdgePoints(pts,edgePts,i,j,k,innerPtsNum) // added
&& !pts[i].isStraight(pts[j],pts[k]) // added
){
for(int l=0; l<pts.length && !anyInside; l++)
if(l!=i && l!=j && l!=k){
//IOut.p("<"+i+","+j+","+k+","+l+">"); //
if(isInsideCircumcircle(pts[l],pts[i],pts[j],pts[k])){
// check if case pts[l] is crossing edge of trim lines
if(checkDirectionOfInnerCircumcirclePoint(pts,edgePts,
i,j,k,l,
innerPtsNum)){
anyInside=true;
//IOut.p(pts[l] + " is inside <"+pts[i]+", "+pts[j]+", "+pts[k]+">"); //
//IOut.p("pt["+l+"] is INside pt["+i+"], pt["+j+"], pt["+k+"]"); //
}
//else; // when pts[l] is crossing the edge of trim
}
else{
//IOut.p(pts[l] + " is outside <"+pts[i]+", "+pts[j]+", "+pts[k]+">"); //
//IOut.p("pt["+l+"] is OUTside pt["+i+"], pt["+j+"], pt["+k+"]"); //
}
}
if(!anyInside){ // nothing is inside
//IOut.p("<"+i+","+j+","+k+">: triangle is added at "+triangles.size()); //
if(isClockwise(pts[i],pts[j],pts[k])){
triangles.add(new IVec2[]{ pts[i], pts[k], pts[j] });
triangleIndex.add(new FaceIndex(i,k,j));
}
else{
triangles.add(new IVec2[]{ pts[i], pts[j], pts[k] });
triangleIndex.add(new FaceIndex(i,j,k));
}
/*
if(i==0&&j==1&&k==4){
new IGCurve(new IVec[]{ new IVec(pts[i]),
new IVec(pts[j]),
new IVec(pts[k])});
}
*/
edgeCount.addFace(i,j,k);
//IOut.p("edgeCount.isEdgeOnOutline("+i+","+j+") = "+edgeCount.isEdgeOnOutline(i,j));
//IOut.p("edgeCount.getEdgeNum("+i+","+j+") = "+edgeCount.getEdgeNum(i,j));
//IOut.p("edgeCount.getFaceVertexIndex("+i+","+j+") = "+edgeCount.getFaceVertexIndex(i,j));
//edgeCount.addEdge(i,j);
//edgeCount.addEdge(i,k);
//edgeCount.addEdge(j,k);
}
//else IOut.p("pt out"); //
}
}
}
}
// filling holes
checkNakedEdge(pts, triangleIndex, triangles, edgeCount);
//IOut.p("trinangles.size()="+triangles.size()); //
return triangles.toArray(new IVec2[triangles.size()][]);
}
/**
Getting delaunay triangles out of array of 3D points interpreted as 2D points on XY plane.
@return array of triangles, which consist of array of 3 points of IVec2
*/
public static IVecI[][] getTriangles(IVecI[] pts){
return getTriangles(pts, null);
}
/**
Getting delaunay triangles out of array of 3D points interpreted as 2D points on a projected plane.
@return array of triangles, which consist of array of 3 points of IVec2
*/
public static IVecI[][] getTriangles(IVecI[] pts, IVecI projectionDir){
IVec2[] pts2 = new IVec2[pts.length];
for(int i=0; i<pts2.length; i++){
if(projectionDir!=null){ pts2[i] = pts[i].get().to2d(projectionDir); }
else{ pts2[i] = pts[i].get().to2d(); }
}
IVec2[][] ret2 = getTriangles(pts2);
IVecI[][] ret = new IVecI[ret2.length][];
List<IVec2> pts2list = Arrays.asList(pts2);
for(int i=0; i<ret2.length; i++){
ret[i] = new IVecI[ret2[i].length];
for(int j=0; j<ret2[i].length; j++){
int idx = pts2list.indexOf(ret2[i][j]);
if(idx>=0){ ret[i][j] = pts[idx]; }
}
}
return ret;
}
/**
Getting delaunay triangles out of array of 3D points interpreted as 2D points on a specified plane.
@return array of triangles, which consist of array of 3 points of IVec2
*/
public static IVecI[][] getTriangles(IVecI[] pts, IVecI planeDir, IVecI planePt){
IVec2[] pts2 = new IVec2[pts.length];
IVec planeZ = planeDir.get().cp();
IVec planeY = IG.zaxis.cross(planeZ);
if(planeY.len2()==0){
planeY = planeZ.cross(IG.xaxis);
}
IVec planeX = planeY.cross(planeZ);
for(int i=0; i<pts2.length; i++){
IMatrix4 conv = IMatrix4.convertCoordinates(planeX, planeY, planeZ, planePt.get(), IG.xaxis, IG.yaxis, IG.zaxis, IG.origin);
pts2[i] = pts[i].get().cp().transform(conv).to2d();
}
IVec2[][] ret2 = getTriangles(pts2);
IVecI[][] ret = new IVecI[ret2.length][];
List<IVec2> pts2list = Arrays.asList(pts2);
for(int i=0; i<ret2.length; i++){
ret[i] = new IVecI[ret2[i].length];
for(int j=0; j<ret2[i].length; j++){
int idx = pts2list.indexOf(ret2[i][j]);
if(idx>=0){ ret[i][j] = pts[idx]; }
}
}
return ret;
}
/**
Getting delaunay triangles out of array of 3D points interpreted as 2D points on XY plane.
@return array of triangles, which consist of array of 3 points of IVec2
*/
public static IVec[][] getTriangles(IVec[] pts){
return getTriangles(pts, null);
}
/**
Getting delaunay triangles out of array of 3D points interpreted as 2D points on a projected plane.
@return array of triangles, which consist of array of 3 points of IVec2
*/
public static IVec[][] getTriangles(IVec[] pts, IVecI projectionDir){
IVec2[] pts2 = new IVec2[pts.length];
for(int i=0; i<pts2.length; i++){
if(projectionDir!=null){ pts2[i] = pts[i].to2d(projectionDir); }
else{ pts2[i] = pts[i].to2d(); }
}
IVec2[][] ret2 = getTriangles(pts2);
IVec[][] ret = new IVec[ret2.length][];
List<IVec2> pts2list = Arrays.asList(pts2);
for(int i=0; i<ret2.length; i++){
ret[i] = new IVec[ret2[i].length];
for(int j=0; j<ret2[i].length; j++){
int idx = pts2list.indexOf(ret2[i][j]);
if(idx>=0){ ret[i][j] = pts[idx]; }
}
}
return ret;
}
/**
Getting delaunay triangles out of array of 2D points
@return array of triangles, which consist of array of 3 points of IVec2
*/
public static IVec2[][] getTriangles(IVec2[] pts){
if(pts.length==3){
if(isClockwise(pts[0],pts[1],pts[2]))
return new IVec2[][]{ new IVec2[]{ pts[0],pts[2],pts[1] } };
return new IVec2[][]{ new IVec2[]{ pts[0],pts[1],pts[2] } };
}
ArrayList<IVec2[]> triangles = new ArrayList<IVec2[]>();
//IOut.p("pts.length = "+pts.length); //
//for(int i=0; i<pts.length; i++) IOut.p("pts["+i+"] = "+ pts[i]); //
//int[] edgeCount = createEdgeCounter(pts.length);
for(int i=0; i<pts.length-2; i++){
//IOut.p((i+1)+"/"+(pts.length-2)); //
IOut.debug(40, (i+1)+"/"+(pts.length-2)); //
for(int j=i+1; j<pts.length-1; j++){
if(maxDistToCheck < 0 ||
maxDistToCheck >= 0 && pts[i].dist(pts[j]) <= maxDistToCheck){
for(int k=j+1; k<pts.length; k++){
if(maxDistToCheck < 0 ||
maxDistToCheck >= 0 && pts[i].dist(pts[k]) <= maxDistToCheck){
boolean anyInside=false;
for(int l=0; l<pts.length && !anyInside; l++)
if(l!=i && l!=j && l!=k){
//IOut.p("<"+i+","+j+","+k+","+l+">"); //
if(isInsideCircumcircle(pts[l],pts[i],pts[j],pts[k])){
anyInside=true;
//IOut.p(pts[l] + " is inside <"+pts[i]+", "+pts[j]+", "+pts[k]+">"); //
//IOut.p("pt["+l+"] is INside pt["+i+"], pt["+j+"], pt["+k+"]"); //
}
else{
//IOut.p(pts[l] + " is outside <"+pts[i]+", "+pts[j]+", "+pts[k]+">"); //
//IOut.p("pt["+l+"] is OUTside pt["+i+"], pt["+j+"], pt["+k+"]"); //
}
}
if(!anyInside){ // nothing is inside
//IOut.p("<"+i+","+j+","+k+">: triangle is added"); //
if(isClockwise(pts[i],pts[j],pts[k]))
triangles.add(new IVec2[]{ pts[i], pts[k], pts[j] });
else
triangles.add(new IVec2[]{ pts[i], pts[j], pts[k] });
}
//else IOut.p("pt out"); //
}
}
}
}
}
//IOut.p("trinangles.size()="+triangles.size()); //
return triangles.toArray(new IVec2[triangles.size()][]);
}
/**
Getting delaunay triangles out of array of 3D points interpreted as 2D points on XY plane.
@return a mesh.
*/
public static IMesh getMesh(IVecI[] pts){
IVertex[] vtx = new IVertex[pts.length];
for(int i=0; i<pts.length; i++){
vtx[i] = new IVertex(pts[i]);
}
IVecI[][] tri = getTriangles(vtx);
IFace[] faces = new IFace[tri.length];
for(int i=0; i<tri.length; i++){
IVertex v1 = (IVertex)tri[i][0];
IVertex v2 = (IVertex)tri[i][1];
IVertex v3 = (IVertex)tri[i][2];
faces[i] = new IFace(v1,v2,v3);
}
return new IMesh(faces);
}
/**
Getting edges of delaunay triangles out of array of 2D points
@return array of triangles, which consist of array of 3 points of IVec2
*/
public static IVec2[][] getEdges(IVec2[] pts){
IVec2[][] tri = getTriangles(pts);
ArrayList<IVec2[]> pairs = new ArrayList<IVec2[]>();
for(int i=0; i<tri.length; i++){
for(int j=0; j<tri[i].length; j++){
boolean exists=false;
for(int k=0; k<pairs.size()&&!exists; k++){
if(pairs.get(k)[0] == tri[i][j] &&
pairs.get(k)[1] == tri[i][(j+1)%tri[i].length] ||
pairs.get(k)[1] == tri[i][j] &&
pairs.get(k)[0] == tri[i][(j+1)%tri[i].length]){
exists=true;
}
}
if(!exists){
pairs.add(new IVec2[]{ tri[i][j], tri[i][(j+1)%tri[i].length] });
}
}
}
return pairs.toArray(new IVec2[pairs.size()][]);
}
/**
Getting edges of 2D delaunay triangles out of array of 3D points and projection vector.
@return array of triangles, which consist of array of 3 points of IVec2
*/
public static IVecI[][] getEdges(IVecI[] pts){ return getEdges(pts,null); }
/**
Getting edges of 2D delaunay triangles out of array of 3D points and projection vector.
@return array of triangles, which consist of array of 3 points of IVec2
*/
public static IVecI[][] getEdges(IVecI[] pts, IVecI projectionDir){
IVec2[] pts2 = new IVec2[pts.length];
for(int i=0; i<pts2.length; i++){
if(projectionDir!=null){ pts2[i] = pts[i].get().to2d(projectionDir); }
else{ pts2[i] = pts[i].get().to2d(); }
}
IVec2[][] ret2 = getEdges(pts2);
IVecI[][] ret = new IVecI[ret2.length][];
List<IVec2> pts2list = Arrays.asList(pts2);
for(int i=0; i<ret2.length; i++){
ret[i] = new IVecI[ret2[i].length];
for(int j=0; j<ret2[i].length; j++){
int idx = pts2list.indexOf(ret2[i][j]);
if(idx>=0){ ret[i][j] = pts[idx]; }
}
}
return ret;
}
/**
Getting edges of 2D delaunay triangles out of array of 3D points and projection vector.
@return array of triangles, which consist of array of 3 points of IVec2
*/
public static IVec[][] getEdges(IVec[] pts){ return getEdges(pts,null); }
/**
Getting edges of 2D delaunay triangles out of array of 3D points and projection vector.
@return array of triangles, which consist of array of 3 points of IVec2
*/
public static IVec[][] getEdges(IVec[] pts, IVecI projectionDir){
IVec2[] pts2 = new IVec2[pts.length];
for(int i=0; i<pts2.length; i++){
if(projectionDir!=null){ pts2[i] = pts[i].to2d(projectionDir); }
else{ pts2[i] = pts[i].to2d(); }
}
IVec2[][] ret2 = getEdges(pts2);
IVec[][] ret = new IVec[ret2.length][];
List<IVec2> pts2list = Arrays.asList(pts2);
for(int i=0; i<ret2.length; i++){
ret[i] = new IVec[ret2[i].length];
for(int j=0; j<ret2[i].length; j++){
int idx = pts2list.indexOf(ret2[i][j]);
if(idx>=0){ ret[i][j] = pts[idx]; }
}
}
return ret;
}
public static boolean isInsideCircumcircle(IVec2 pt, IVec2 trianglePt1,
IVec2 trianglePt2, IVec2 trianglePt3){
IVec2 tpt1=null,tpt2=null,tpt3=null;
if(isClockwise(trianglePt1, trianglePt2, trianglePt3)){
tpt1 = trianglePt1; tpt2 = trianglePt3; tpt3 = trianglePt2;
}
else{ tpt1 = trianglePt1; tpt2 = trianglePt2; tpt3 = trianglePt3; }
double det =
determinant(tpt1.x - pt.x, tpt1.y - pt.y,
(tpt1.x*tpt1.x - pt.x*pt.x) + (tpt1.y*tpt1.y - pt.y*pt.y),
tpt2.x - pt.x, tpt2.y - pt.y,
(tpt2.x*tpt2.x - pt.x*pt.x) + (tpt2.y*tpt2.y - pt.y*pt.y),
tpt3.x - pt.x, tpt3.y - pt.y,
(tpt3.x*tpt3.x - pt.x*pt.x) + (tpt3.y*tpt3.y - pt.y*pt.y) );
//IOut.p("determinant = "+det); //
//return det > 0;
//final double minDeterminant = 0.000001; // is this number valid?
final double minDeterminant = 0; //
return det > minDeterminant;
/*
// triangle points needs to be counter clockwise
if(isClockwise(trianglePt1, trianglePt2, trianglePt3)){
IVec2 tmp = trianglePt2;
trianglePt2 = trianglePt3;
trianglePt3 = tmp;
}
return determinant(trianglePt1.x - pt.x, trianglePt1.y - pt.y,
(trianglePt1.x*trianglePt1.x - pt.x*pt.x) -
(trianglePt1.y*trianglePt1.y - pt.y*pt.y),
trianglePt2.x - pt.x, trianglePt2.y - pt.y,
(trianglePt2.x*trianglePt2.x - pt.x*pt.x) -
(trianglePt2.y*trianglePt2.y - pt.y*pt.y),
trianglePt3.x - pt.x, trianglePt3.y - pt.y,
(trianglePt3.x*trianglePt3.x - pt.x*pt.x) -
(trianglePt3.y*trianglePt3.y - pt.y*pt.y) ) >= 0; // > or >=?
*/
}
public static boolean isClockwise(IVec2 pt1, IVec2 pt2, IVec2 pt3){
return pt2.diff(pt1).cross(pt3.diff(pt2)).z < 0;
}
public static double determinant(double v11, double v12, double v13,
double v21, double v22, double v23,
double v31, double v32, double v33){
/*
IOut.p("[["+v11+","+v12+","+v13+"],["+
v21+","+v22+","+v23+"],["+
v31+","+v32+","+v33+"]]"); //
IOut.p("v11*v22*v33 = "+v11*v22*v33); //
IOut.p("v12*v23*v31 = "+v12*v23*v31); //
IOut.p("v13*v21*v32 = "+v13*v21*v32); //
IOut.p("v11*v23*v32 = "+v11*v23*v32); //
IOut.p("v12*v21*v33 = "+v12*v21*v33); //
IOut.p("v13*v22*v31 = "+v13*v22*v31); //
IOut.p("first term = "+(v11*v22*v33 + v12*v23*v31 + v13*v21*v32));
IOut.p("second term = "+(- v11*v23*v32 - v12*v21*v33 - v13*v22*v31));
*/
return v11*v22*v33 + v12*v23*v31 + v13*v21*v32
- v11*v23*v32 - v12*v21*v33 - v13*v22*v31;
}
public static boolean isFaceCrossing(IVec2[] pts, EdgeCounter edgeCount,
int ptIdx1, int ptIdx2, int ptIdx3){
if(edgeCount.hasOneFace(ptIdx1, ptIdx2)){
if(isVertexOnSameSide(pts[ptIdx1],pts[ptIdx2],pts[ptIdx3],
pts[edgeCount.getFaceVertexIndex(ptIdx1,ptIdx2)]))
return true;
}
if(edgeCount.hasOneFace(ptIdx1, ptIdx3)){
if(isVertexOnSameSide(pts[ptIdx1],pts[ptIdx3],pts[ptIdx2],
pts[edgeCount.getFaceVertexIndex(ptIdx1,ptIdx3)]))
return true;
}
if(edgeCount.hasOneFace(ptIdx2, ptIdx3)){
if(isVertexOnSameSide(pts[ptIdx2],pts[ptIdx3],pts[ptIdx1],
pts[edgeCount.getFaceVertexIndex(ptIdx2,ptIdx3)]))
return true;
}
return false;
}
public static boolean isVertexOnSameSide(IVec2 edgePt1, IVec2 edgePt2,
IVec2 vertexPt1, IVec2 vertexPt2){
IVec2 diff = edgePt2.diff(edgePt1);
return diff.cross(vertexPt1.diff(edgePt1)).z*diff.cross(vertexPt2.diff(edgePt1)).z>=0;
}
public static boolean isFaceDirectionOnEdgeCorrect(IVec2 edgePt1, IVec2 edgePt2,
IVec2 vertexPt){
// this is under assumption of outer trim loop goes counter-clockwise and
// inner trim hole loop goes clockwise always.
//return edgePt2.diff(edgePt1).cross(vertexPt.diff(edgePt1)).z > 0;
double z = edgePt2.diff(edgePt1).cross(vertexPt.diff(edgePt1)).z;
//IOut.p("edge1 = "+edgePt1 +", edge2 = "+edgePt2+", vertexPt = "+vertexPt);
//if(z>0) IOut.p("correct direction"); //
//else IOut.p("wrong direction"); //
//return z > 0;
return z >= 0; // changed 2011/07/11
}
public static boolean isFaceDirectionOnEdgeCorrect(IVec2[][] edgePts,
IVec2 pt,
IVec2 vertexPt1, IVec2 vertexPt2){
IVec2[] adjacentPts = getAdjacentPointsOnEdgeLoop(edgePts, pt);
if(adjacentPts==null) return false; // ERROR
if(adjacentPts[0]==vertexPt1)
return isFaceDirectionOnEdgeCorrect(vertexPt1, pt, vertexPt2);
if(adjacentPts[0]==vertexPt2)
return isFaceDirectionOnEdgeCorrect(vertexPt2, pt, vertexPt1);
if(adjacentPts[1]==vertexPt1)
return isFaceDirectionOnEdgeCorrect(pt, vertexPt1, vertexPt2);
if(adjacentPts[1]==vertexPt2)
return isFaceDirectionOnEdgeCorrect(pt, vertexPt2, vertexPt1);
/*
if(!isFaceDirectionOnEdgeCorrect(adjacentPts[0], pt, vertexPt1) &&
!isFaceDirectionOnEdgeCorrect(pt, adjacentPts[1], vertexPt1)) return false;
if(!isFaceDirectionOnEdgeCorrect(adjacentPts[0], pt, vertexPt2) &&
!isFaceDirectionOnEdgeCorrect(pt, adjacentPts[1], vertexPt2)) return false;
*/
if(!isPointInsideEdge(vertexPt1, adjacentPts[0], pt, adjacentPts[1])) return false;
if(!isPointInsideEdge(vertexPt2, adjacentPts[0], pt, adjacentPts[1])) return false;
if(isPointsIntersectiongWithEdge(vertexPt1, vertexPt2,
adjacentPts[0], pt, adjacentPts[1])) return false;
/*
IVec2 vertexPtMid = vertexPt1.mid(vertexPt2);
if(!isFaceDirectionOnEdgeCorrect(adjacentPts[0], pt, vertexPtMid)&&
!isFaceDirectionOnEdgeCorrect(pt, adjacentPts[1], vertexPtMid)) return false;
*/
return true;
}
public static boolean isPointsIntersectiongWithEdge(IVec2 pt1, IVec2 pt2,
IVec2 edgePt1, IVec2 edgePt2,
IVec2 edgePt3){
IVec2 diff1 = edgePt2.diff(edgePt1);
IVec2 diff2 = edgePt3.diff(edgePt2);
// edge bent inward; no intersection
if(diff1.cross(diff2).z >= 0) return false;
// edge bent outward
if(isFaceDirectionOnEdgeCorrect(edgePt1,edgePt2,pt1)&&
isFaceDirectionOnEdgeCorrect(edgePt1,edgePt2,pt2)) return false;
if(isFaceDirectionOnEdgeCorrect(edgePt2,edgePt3,pt1)&&
isFaceDirectionOnEdgeCorrect(edgePt2,edgePt3,pt2)) return false;
IVec2 bisector1 = diff1.neg().bisect(diff2);
IVec2 bisector2 = pt1.diff(edgePt2).bisect(pt2.diff(edgePt2));
if(bisector1.dot(bisector2)>0) return true;
return false;
}
public static boolean isPointInsideEdge(IVec2 pt,
IVec2 edgePt1, IVec2 edgePt2, IVec2 edgePt3){
// inside of edge is left side of the edge formed by edgePt1, edgePt2, edgePt3
IVec2 diff1 = edgePt2.diff(edgePt1);
IVec2 diff2 = edgePt3.diff(edgePt2);
// edge bent inward
if(diff1.cross(diff2).z >= 0){
if(!isFaceDirectionOnEdgeCorrect(edgePt1, edgePt2, pt) ||
!isFaceDirectionOnEdgeCorrect(edgePt2, edgePt3, pt)) return false;
return true;
}
if(!isFaceDirectionOnEdgeCorrect(edgePt1, edgePt2, pt) &&
!isFaceDirectionOnEdgeCorrect(edgePt2, edgePt3, pt)) return false;
return true;
}
public static boolean checkFaceDirection(IVec2[] pts, EdgeCounter edgeCount,
int ptIdx1, int ptIdx2, int ptIdx3){
//IOut.p("<"+ptIdx1+", "+ptIdx2+", "+ptIdx3+">"); //
if(edgeCount.isEdgeOnOutline(ptIdx1, ptIdx2)){
if(ptIdx2-ptIdx1 != 1){
// to be sequential difference should be 1, if not, it's closing poitn of loop
int tmp = ptIdx2; ptIdx2 = ptIdx1; ptIdx1 = tmp;
}
if(!isFaceDirectionOnEdgeCorrect(pts[ptIdx1],pts[ptIdx2],pts[ptIdx3]))
return false;
}
if(edgeCount.isEdgeOnOutline(ptIdx1, ptIdx3)){
if(ptIdx3-ptIdx1 != 1){
// to be sequential difference should be 1, if not, it's closing poitn of loop
int tmp = ptIdx1; ptIdx1 = ptIdx3; ptIdx3 = tmp;
}
if(!isFaceDirectionOnEdgeCorrect(pts[ptIdx1],pts[ptIdx3],pts[ptIdx2]))
return false;
}
if(edgeCount.isEdgeOnOutline(ptIdx2, ptIdx3)){
if(ptIdx3-ptIdx2 != 1){
// to be sequential difference should be 1, if not, it's closing poitn of loop
int tmp = ptIdx3; ptIdx3 = ptIdx2; ptIdx2 = tmp;
}
if(!isFaceDirectionOnEdgeCorrect(pts[ptIdx2],pts[ptIdx3],pts[ptIdx1]))
return false;
}
return true;
}
static public boolean checkDirectionOnEdgePoints(IVec2[] pts,
IVec2[][] edgePts,
int ptIdx1,
int ptIdx2,
int ptIdx3,
int innerPtNum){
if(ptIdx1>=innerPtNum){ // on the edgePts
if(!isFaceDirectionOnEdgeCorrect(edgePts,pts[ptIdx1],pts[ptIdx2],pts[ptIdx3])){
return false;
}
}
if(ptIdx2>=innerPtNum){ // on the edgePts
if(!isFaceDirectionOnEdgeCorrect(edgePts,pts[ptIdx2],pts[ptIdx1],pts[ptIdx3])){
return false;
}
}
if(ptIdx3>=innerPtNum){ // on the edgePts
if(!isFaceDirectionOnEdgeCorrect(edgePts,pts[ptIdx3],pts[ptIdx1],pts[ptIdx2])){
return false;
}
}
return true;
}
static public IVec2[] getAdjacentPointsOnEdgeLoop(IVec2[][] edgePts, IVec2 pt){
for(int i=0; i<edgePts.length; i++){
for(int j=0; j<edgePts[i].length; j++){
if(edgePts[i][j] == pt){
return new IVec2[]{edgePts[i][(j-1+edgePts[i].length)%edgePts[i].length],
edgePts[i][(j+1)%edgePts[i].length]};
}
}
}
IOut.err("no point found in edgePts : pt = "+pt);
return null;
}
static public boolean checkDirectionOfInnerCircumcirclePoint(IVec2[] pts,
IVec2[][] edgePts,
int ptIdx1,
int ptIdx2,
int ptIdx3,
int ptIdx4,
int innerPtNum){
IVec2[] adjacentPts1 = null;
if(ptIdx1>=innerPtNum && ptIdx2>=innerPtNum){
adjacentPts1 = getAdjacentPointsOnEdgeLoop(edgePts,pts[ptIdx1]);
if( adjacentPts1[1]==pts[ptIdx2] &&
!isFaceDirectionOnEdgeCorrect(pts[ptIdx1], pts[ptIdx2], pts[ptIdx4]) ||
adjacentPts1[0]==pts[ptIdx2] &&
!isFaceDirectionOnEdgeCorrect(pts[ptIdx2], pts[ptIdx1], pts[ptIdx4]) ){
return false;
}
}
if(ptIdx1>=innerPtNum && ptIdx3>=innerPtNum){
if(adjacentPts1==null)
adjacentPts1 = getAdjacentPointsOnEdgeLoop(edgePts,pts[ptIdx1]);
if( adjacentPts1[1]==pts[ptIdx3] &&
!isFaceDirectionOnEdgeCorrect(pts[ptIdx1], pts[ptIdx3], pts[ptIdx4]) ||
adjacentPts1[0]==pts[ptIdx3] &&
!isFaceDirectionOnEdgeCorrect(pts[ptIdx3], pts[ptIdx1], pts[ptIdx4])){
return false;
}
}
if(ptIdx2>=innerPtNum && ptIdx3>=innerPtNum){
IVec2[] adjacentPts2 = getAdjacentPointsOnEdgeLoop(edgePts,pts[ptIdx2]);
if( adjacentPts2[1]==pts[ptIdx3] &&
!isFaceDirectionOnEdgeCorrect(pts[ptIdx2], pts[ptIdx3], pts[ptIdx4]) ||
adjacentPts2[0]==pts[ptIdx3] &&
!isFaceDirectionOnEdgeCorrect(pts[ptIdx3], pts[ptIdx2], pts[ptIdx4]) ){
return false;
}
}
return true;
}
static public void checkNakedEdge(IVec2[] pts,
ArrayList<FaceIndex> faceIdx,
ArrayList<IVec2[]> triangles,
EdgeCounter edgeCount){
for(int i=0; i<pts.length-1; i++){
//IOut.p(i+"/"+pts.length); //
for(int j=i+1; j<pts.length; j++){
if(edgeCount.getEdgeNum(i,j)==1){
boolean added=false;
//for(int k=j+1; k<pts.length && !added; k++){
for(int k=0; k<pts.length && !added; k++){
// fill triangle at the edge or, fill triangle in an obvious triangular hole
// not filling when 3 edges already form a triangle
FaceIndex fidx=null;
boolean addFace=false;
if(k!=i && k!=j){
int idx1=i;
int idx2=j;
int idx3=k;
// re-order
if(k<i){ idx1=k; idx2=i; idx3=j; }
else if(k<j){ idx1=i; idx2=k; idx3=j; }
/*
IOut.p("checking <"+i+","+j+","+k+">"); //
IOut.p("isEdgeOnOutline("+idx1+","+idx2+") = "+
edgeCount.isEdgeOnOutline(idx1,idx2));
IOut.p("isEdgeOnOutline("+idx1+","+idx3+") = "+
edgeCount.isEdgeOnOutline(idx1,idx3));
IOut.p("isEdgeOnOutline("+idx2+","+idx3+") = "+
edgeCount.isEdgeOnOutline(idx2,idx3));
IOut.p("isFaceDirectionOnEdgeCorrect("+idx1+","+idx2+","+idx3+") = "+
isFaceDirectionOnEdgeCorrect(pts[idx1],pts[idx2],pts[idx3]));
IOut.p("isFaceDirectionOnEdgeCorrect("+idx1+","+idx3+","+idx2+") = "+
isFaceDirectionOnEdgeCorrect(pts[idx1],pts[idx3],pts[idx2]));
IOut.p("isFaceDirectionOnEdgeCorrect("+idx2+","+idx3+","+idx1+") = "+
isFaceDirectionOnEdgeCorrect(pts[idx2],pts[idx3],pts[idx1]));
IOut.p("isEdgeOpen("+idx1+","+idx2+") = "+
edgeCount.isEdgeOpen(idx1,idx2));
IOut.p("isEdgeOpen("+idx1+","+idx3+") = "+
edgeCount.isEdgeOpen(idx1,idx3));
IOut.p("isEdgeOpen("+idx2+","+idx3+") = "+
edgeCount.isEdgeOpen(idx2,idx3));
*/
if(edgeCount.isEdgeOnOutline(idx1,idx2) &&
edgeCount.isEdgeOnOutline(idx2,idx3) &&
edgeCount.hasOneFace(idx1,idx3) &&
//isFaceDirectionOnEdgeCorrect(pts[idx1],pts[idx2],pts[idx3])){
// if idx1==0, idx2 is last point on outline and order should be idx2->idx1
isFaceDirectionOnEdgeCorrect(pts[idx1==0?idx2:idx1],pts[idx1==0?idx1:idx2],pts[idx3])){
//IOut.p("addFace 4"); //
addFace=true;
}
else if(edgeCount.isEdgeOnOutline(idx1,idx3) &&
edgeCount.isEdgeOnOutline(idx2,idx3) &&
edgeCount.hasOneFace(idx1,idx2) &&
//isFaceDirectionOnEdgeCorrect(pts[idx1],pts[idx3],pts[idx2])){
isFaceDirectionOnEdgeCorrect(pts[idx1==0?idx3:idx1],pts[idx1==0?idx1:idx3],pts[idx2])){
//IOut.p("addFace 5"); //
addFace=true;
}
else if(edgeCount.isEdgeOnOutline(idx1,idx3) &&
edgeCount.isEdgeOnOutline(idx1,idx2) &&
edgeCount.hasOneFace(idx2,idx3) &&
//isFaceDirectionOnEdgeCorrect(pts[idx2],pts[idx3],pts[idx1])){
isFaceDirectionOnEdgeCorrect(pts[idx2==0?idx3:idx2],pts[idx2==0?idx2:idx3],pts[idx1])){
//IOut.p("addFace 6"); //
addFace=true;
}
else if(edgeCount.isEdgeOnOutline(idx1,idx2) &&
//(edgeCount.isEdgeOpen(idx1,idx3) || edgeCount.isEdgeOpen(idx2,idx3))){
edgeCount.isEdgeOpen(idx1,idx3) && edgeCount.isEdgeOpen(idx2,idx3)){
if(isFaceDirectionOnEdgeCorrect(pts[idx1==0?idx2:idx1],pts[idx1==0?idx1:idx2],pts[idx3])
&& !isFaceCrossing(pts, edgeCount, idx1, idx2, idx3)){
//IOut.p("addFace 1"); //
addFace=true;
}
}
else if(edgeCount.isEdgeOnOutline(idx1,idx3) &&
//(edgeCount.isEdgeOpen(idx1,idx2)||edgeCount.isEdgeOpen(idx2,idx3))){
edgeCount.isEdgeOpen(idx1,idx2)&&edgeCount.isEdgeOpen(idx2,idx3)){
if(isFaceDirectionOnEdgeCorrect(pts[idx1==0?idx3:idx1],pts[idx1==0?idx1:idx3],pts[idx2])
&& !isFaceCrossing(pts, edgeCount, idx1, idx2, idx3)){
//IOut.p("addFace 2"); //
addFace=true;
}
}
else if(edgeCount.isEdgeOnOutline(idx2,idx3) &&
//(edgeCount.isEdgeOpen(idx1,idx2)||edgeCount.isEdgeOpen(idx1,idx3))){
edgeCount.isEdgeOpen(idx1,idx2)&&edgeCount.isEdgeOpen(idx1,idx3)){
//IOut.p("isFaceCrossing("+idx1+","+idx2+","+idx3+") = "+isFaceCrossing(pts, edgeCount, idx1, idx2, idx3)); //
if(isFaceDirectionOnEdgeCorrect(pts[idx2==0?idx3:idx2],pts[idx2==0?idx2:idx3],pts[idx1])
&& !isFaceCrossing(pts, edgeCount, idx1, idx2, idx3)){
//IOut.p("addFace 3 <"+idx2+","+idx3+","+idx1+">"); //
addFace=true;
}
}
else if((edgeCount.getEdgeNum(idx1,idx2)==1&&
edgeCount.getEdgeNum(idx1,idx3)==1&&
edgeCount.getEdgeNum(idx2,idx3)==1 &&
edgeCount.getFaceVertexIndex(idx1,idx2)!=-1 &&
edgeCount.getFaceVertexIndex(idx1,idx3)!=-1 &&
edgeCount.getFaceVertexIndex(idx2,idx3)!=-1 &&
((fidx=findTriangleIndexWithEdge(faceIdx,idx1,idx2))==null ||
fidx.getOtherIndex(idx1,idx2) != idx3))){
//IOut.p("addFace 7"); //
addFace=true;
}
if(addFace){
//IOut.p("face added at <"+i+","+j+","+k+">"); //
//edgeCount.addFace(i,j,k);
//triangles.add(new IVec2[]{ pts[i],pts[j],pts[k]});
//faceIdx.add(new FaceIndex(i,j,k));
//IOut.p("face added at <"+idx1+","+idx2+","+idx3+">"); //
edgeCount.addFace(idx1,idx2,idx3);
triangles.add(new IVec2[]{ pts[idx1],pts[idx2],pts[idx3]});
faceIdx.add(new FaceIndex(idx1,idx2,idx3));
added=true;
}
}
/*
if((edgeCount.getEdgeNum(i,k)==1&&edgeCount.getEdgeNum(j,k)==1 ||
edgeCount.getEdgeNum(i,k)==1&&edgeCount.getEdgeNum(j,k)==0 ||
edgeCount.getEdgeNum(i,k)==0&&edgeCount.getEdgeNum(j,k)==1 ) &&
(edgeCount.getFaceVertexIndex(i,j)==-1 ||
edgeCount.getFaceVertexIndex(i,k)==-1 ||
edgeCount.getFaceVertexIndex(j,k)==-1 )
||
( edgeCount.getEdgeNum(i,k)==1&&edgeCount.getEdgeNum(j,k)==1 &&
edgeCount.getFaceVertexIndex(i,j)!=-1 &&
edgeCount.getFaceVertexIndex(i,k)!=-1 &&
edgeCount.getFaceVertexIndex(j,k)!=-1 &&
((fidx = findTriangleIndexWithEdge(faceIdx, i, j)) ==null ||
fidx.getOtherIndex(i,j) != k))
){
IOut.p("face added at <"+i+","+j+","+k+">"); //
edgeCount.addFace(i,j,k);
triangles.add(new IVec2[]{ pts[i],pts[j],pts[k]});
faceIdx.add(new FaceIndex(i,j,k));
added=true;
}
*/
}
}
}
}
// remove triangles which have naked edge but not on the outline
// (likely to be inside of inner holes or outside of outer trim
for(int i=0; i<pts.length-1; i++){
for(int j=i+1; j<pts.length; j++){
if(edgeCount.getEdgeNum(i,j)==1 &&
edgeCount.getFaceVertexIndex(i,j)!=-1){
//IOut.p("naked edge found at <"+i+","+j+">"); //
FaceIndex fidx = findTriangleIndexWithEdge(faceIdx, i, j);
if(fidx!=null){
int k = fidx.getOtherIndex(i,j);
IVec2[] tr = findTriangleWithIndex(pts, triangles, i,j,k);
if(tr!=null){
triangles.remove(tr);
//IOut.p("face removed at <"+i+","+j+","+k+">"); //
}
}
}
}
}
}
static public IVec2[] findTriangleWithIndex(IVec2[] pts, ArrayList<IVec2[]> triangles,
int index1, int index2, int index3){
for(int i=0; i<triangles.size(); i++){
if(isSameTriangle(triangles.get(i), pts[index1], pts[index2], pts[index3]))
return triangles.get(i);
}
return null;
}
static public boolean isSameTriangle(IVec2[] triangle, IVec2 pt1, IVec2 pt2, IVec2 pt3){
return triangle[0]==pt1 && triangle[1]==pt2 && triangle[2]==pt3 ||
triangle[0]==pt2 && triangle[1]==pt3 && triangle[2]==pt1 ||
triangle[0]==pt3 && triangle[1]==pt1 && triangle[2]==pt2 ||
triangle[0]==pt1 && triangle[1]==pt3 && triangle[2]==pt2 ||
triangle[0]==pt2 && triangle[1]==pt1 && triangle[2]==pt3 ||
triangle[0]==pt3 && triangle[1]==pt2 && triangle[2]==pt1;
}
/**
@param ptIdx1 requirement: ptIdx1 < ptIdx2
*/
static public FaceIndex findTriangleIndexWithEdge(ArrayList<FaceIndex> faceIdx,
int ptIdx1, int ptIdx2){
for(int i=0; i<faceIdx.size(); i++){
if(faceIdx.get(i).contains(ptIdx1,ptIdx2)) return faceIdx.get(i);