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
1001
1002
1003
1004
1005
1006
1007
1008
1009
1010
1011
1012
1013
1014
1015
1016
1017
1018
1019
1020
1021
1022
1023
1024
1025
1026
1027
1028
1029
1030
1031
1032
1033
1034
1035
1036
1037
1038
1039
1040
1041
1042
1043
1044
1045
1046
1047
1048
1049
1050
1051
1052
1053
1054
1055
1056
1057
1058
1059
1060
1061
1062
1063
1064
1065
1066
1067
1068
1069
1070
1071
1072
1073
1074
1075
1076
1077
1078
1079
1080
1081
1082
1083
1084
1085
1086
1087
1088
1089
1090
1091
1092
1093
1094
1095
1096
1097
1098
1099
1100
1101
1102
1103
1104
1105
1106
1107
1108
1109
1110
1111
1112
1113
1114
1115
1116
1117
1118
1119
1120
1121
1122
1123
1124
1125
1126
1127
1128
1129
1130
1131
1132
1133
1134
1135
1136
1137
1138
1139
1140
1141
1142
1143
1144
1145
1146
1147
1148
1149
1150
1151
1152
1153
1154
1155
1156
1157
1158
1159
1160
1161
1162
1163
1164
1165
1166
1167
1168
1169
1170
1171
1172
1173
1174
1175
1176
1177
1178
1179
1180
1181
1182
1183
1184
1185
1186
1187
1188
1189
1190
1191
1192
1193
1194
1195
1196
1197
1198
1199
1200
1201
1202
1203
1204
1205
1206
1207
1208
1209
1210
1211
1212
1213
1214
1215
1216
1217
1218
1219
1220
1221
1222
1223
1224
1225
1226
1227
1228
1229
1230
1231
1232
1233
1234
1235
1236
1237
1238
1239
1240
1241
1242
1243
1244
1245
1246
1247
1248
1249
1250
1251
1252
1253
1254
1255
1256
1257
1258
1259
1260
1261
1262
1263
1264
1265
1266
1267
1268
1269
1270
1271
1272
1273
1274
1275
1276
1277
1278
1279
1280
1281
1282
1283
1284
1285
1286
1287
1288
1289
1290
1291
1292
1293
1294
1295
1296
1297
1298
1299
1300
1301
1302
1303
1304
1305
1306
1307
1308
1309
1310
1311
1312
1313
1314
1315
1316
1317
1318
1319
1320
1321
1322
1323
1324
1325
1326
1327
1328
1329
1330
1331
1332
1333
1334
1335
1336
1337
1338
1339
1340
1341
1342
1343
1344
1345
1346
1347
1348
1349
1350
1351
1352
1353
1354
1355
1356
1357
1358
1359
1360
1361
1362
1363
1364
1365
1366
1367
1368
1369
1370
1371
1372
1373
1374
1375
1376
1377
1378
1379
1380
1381
1382
1383
1384
1385
1386
1387
1388
1389
1390
1391
1392
1393
1394
1395
1396
1397
1398
1399
1400
1401
1402
1403
1404
1405
1406
1407
1408
1409
1410
1411
1412
1413
1414
1415
1416
1417
1418
1419
1420
1421
1422
1423
1424
1425
1426
1427
1428
1429
1430
1431
1432
1433
1434
1435
1436
1437
1438
1439
1440
1441
1442
1443
1444
1445
1446
1447
1448
1449
1450
1451
1452
1453
1454
1455
1456
1457
1458
1459
1460
1461
1462
1463
1464
1465
1466
1467
1468
1469
1470
1471
1472
1473
1474
1475
1476
1477
1478
1479
1480
1481
1482
1483
1484
1485
1486
1487
1488
1489
1490
1491
1492
1493
1494
1495
1496
1497
1498
1499
1500
1501
1502
1503
1504
1505
1506
1507
1508
1509
1510
1511
1512
1513
1514
1515
1516
1517
1518
1519
1520
1521
1522
1523
1524
1525
1526
1527
1528
1529
1530
1531
1532
1533
1534
1535
1536
1537
1538
1539
1540
1541
1542
1543
1544
1545
1546
1547
1548
1549
1550
1551
1552
1553
1554
1555
1556
1557
1558
1559
1560
1561
1562
1563
1564
1565
1566
1567
1568
1569
1570
1571
1572
1573
1574
1575
1576
1577
1578
1579
1580
1581
1582
1583
1584
1585
1586
1587
1588
1589
1590
1591
1592
1593
1594
1595
1596
1597
1598
1599
1600
1601
1602
1603
1604
1605
1606
1607
1608
1609
1610
1611
1612
1613
1614
1615
1616
1617
1618
1619
1620
1621
1622
1623
1624
1625
1626
1627
1628
1629
1630
1631
1632
1633
1634
1635
1636
1637
1638
1639
1640
1641
1642
1643
1644
1645
1646
1647
1648
1649
1650
1651
1652
1653
1654
1655
1656
1657
1658
1659
1660
|
/*
* Copyright 2015 Google Inc.
*
* Use of this source code is governed by a BSD-style license that can be
* found in the LICENSE file.
*/
#include "GrTessellatingPathRenderer.h"
#include "GrBatchTarget.h"
#include "GrBatchTest.h"
#include "GrDefaultGeoProcFactory.h"
#include "GrPathUtils.h"
#include "GrVertices.h"
#include "GrResourceCache.h"
#include "GrResourceProvider.h"
#include "SkChunkAlloc.h"
#include "SkGeometry.h"
#include "batches/GrBatch.h"
#include <stdio.h>
/*
* This path renderer tessellates the path into triangles, uploads the triangles to a
* vertex buffer, and renders them with a single draw call. It does not currently do
* antialiasing, so it must be used in conjunction with multisampling.
*
* There are six stages to the algorithm:
*
* 1) Linearize the path contours into piecewise linear segments (path_to_contours()).
* 2) Build a mesh of edges connecting the vertices (build_edges()).
* 3) Sort the vertices in Y (and secondarily in X) (merge_sort()).
* 4) Simplify the mesh by inserting new vertices at intersecting edges (simplify()).
* 5) Tessellate the simplified mesh into monotone polygons (tessellate()).
* 6) Triangulate the monotone polygons directly into a vertex buffer (polys_to_triangles()).
*
* The vertex sorting in step (3) is a merge sort, since it plays well with the linked list
* of vertices (and the necessity of inserting new vertices on intersection).
*
* Stages (4) and (5) use an active edge list, which a list of all edges for which the
* sweep line has crossed the top vertex, but not the bottom vertex. It's sorted
* left-to-right based on the point where both edges are active (when both top vertices
* have been seen, so the "lower" top vertex of the two). If the top vertices are equal
* (shared), it's sorted based on the last point where both edges are active, so the
* "upper" bottom vertex.
*
* The most complex step is the simplification (4). It's based on the Bentley-Ottman
* line-sweep algorithm, but due to floating point inaccuracy, the intersection points are
* not exact and may violate the mesh topology or active edge list ordering. We
* accommodate this by adjusting the topology of the mesh and AEL to match the intersection
* points. This occurs in three ways:
*
* A) Intersections may cause a shortened edge to no longer be ordered with respect to its
* neighbouring edges at the top or bottom vertex. This is handled by merging the
* edges (merge_collinear_edges()).
* B) Intersections may cause an edge to violate the left-to-right ordering of the
* active edge list. This is handled by splitting the neighbour edge on the
* intersected vertex (cleanup_active_edges()).
* C) Shortening an edge may cause an active edge to become inactive or an inactive edge
* to become active. This is handled by removing or inserting the edge in the active
* edge list (fix_active_state()).
*
* The tessellation steps (5) and (6) are based on "Triangulating Simple Polygons and
* Equivalent Problems" (Fournier and Montuno); also a line-sweep algorithm. Note that it
* currently uses a linked list for the active edge list, rather than a 2-3 tree as the
* paper describes. The 2-3 tree gives O(lg N) lookups, but insertion and removal also
* become O(lg N). In all the test cases, it was found that the cost of frequent O(lg N)
* insertions and removals was greater than the cost of infrequent O(N) lookups with the
* linked list implementation. With the latter, all removals are O(1), and most insertions
* are O(1), since we know the adjacent edge in the active edge list based on the topology.
* Only type 2 vertices (see paper) require the O(N) lookups, and these are much less
* frequent. There may be other data structures worth investigating, however.
*
* Note that the orientation of the line sweep algorithms is determined by the aspect ratio of the
* path bounds. When the path is taller than it is wide, we sort vertices based on increasing Y
* coordinate, and secondarily by increasing X coordinate. When the path is wider than it is tall,
* we sort by increasing X coordinate, but secondarily by *decreasing* Y coordinate. This is so
* that the "left" and "right" orientation in the code remains correct (edges to the left are
* increasing in Y; edges to the right are decreasing in Y). That is, the setting rotates 90
* degrees counterclockwise, rather that transposing.
*/
#define LOGGING_ENABLED 0
#define WIREFRAME 0
#if LOGGING_ENABLED
#define LOG printf
#else
#define LOG(...)
#endif
#define ALLOC_NEW(Type, args, alloc) \
SkNEW_PLACEMENT_ARGS(alloc.allocThrow(sizeof(Type)), Type, args)
namespace {
struct Vertex;
struct Edge;
struct Poly;
template <class T, T* T::*Prev, T* T::*Next>
void insert(T* t, T* prev, T* next, T** head, T** tail) {
t->*Prev = prev;
t->*Next = next;
if (prev) {
prev->*Next = t;
} else if (head) {
*head = t;
}
if (next) {
next->*Prev = t;
} else if (tail) {
*tail = t;
}
}
template <class T, T* T::*Prev, T* T::*Next>
void remove(T* t, T** head, T** tail) {
if (t->*Prev) {
t->*Prev->*Next = t->*Next;
} else if (head) {
*head = t->*Next;
}
if (t->*Next) {
t->*Next->*Prev = t->*Prev;
} else if (tail) {
*tail = t->*Prev;
}
t->*Prev = t->*Next = NULL;
}
/**
* Vertices are used in three ways: first, the path contours are converted into a
* circularly-linked list of Vertices for each contour. After edge construction, the same Vertices
* are re-ordered by the merge sort according to the sweep_lt comparator (usually, increasing
* in Y) using the same fPrev/fNext pointers that were used for the contours, to avoid
* reallocation. Finally, MonotonePolys are built containing a circularly-linked list of
* Vertices. (Currently, those Vertices are newly-allocated for the MonotonePolys, since
* an individual Vertex from the path mesh may belong to multiple
* MonotonePolys, so the original Vertices cannot be re-used.
*/
struct Vertex {
Vertex(const SkPoint& point)
: fPoint(point), fPrev(NULL), fNext(NULL)
, fFirstEdgeAbove(NULL), fLastEdgeAbove(NULL)
, fFirstEdgeBelow(NULL), fLastEdgeBelow(NULL)
, fProcessed(false)
#if LOGGING_ENABLED
, fID (-1.0f)
#endif
{}
SkPoint fPoint; // Vertex position
Vertex* fPrev; // Linked list of contours, then Y-sorted vertices.
Vertex* fNext; // "
Edge* fFirstEdgeAbove; // Linked list of edges above this vertex.
Edge* fLastEdgeAbove; // "
Edge* fFirstEdgeBelow; // Linked list of edges below this vertex.
Edge* fLastEdgeBelow; // "
bool fProcessed; // Has this vertex been seen in simplify()?
#if LOGGING_ENABLED
float fID; // Identifier used for logging.
#endif
};
/***************************************************************************************/
typedef bool (*CompareFunc)(const SkPoint& a, const SkPoint& b);
struct Comparator {
CompareFunc sweep_lt;
CompareFunc sweep_gt;
};
bool sweep_lt_horiz(const SkPoint& a, const SkPoint& b) {
return a.fX == b.fX ? a.fY > b.fY : a.fX < b.fX;
}
bool sweep_lt_vert(const SkPoint& a, const SkPoint& b) {
return a.fY == b.fY ? a.fX < b.fX : a.fY < b.fY;
}
bool sweep_gt_horiz(const SkPoint& a, const SkPoint& b) {
return a.fX == b.fX ? a.fY < b.fY : a.fX > b.fX;
}
bool sweep_gt_vert(const SkPoint& a, const SkPoint& b) {
return a.fY == b.fY ? a.fX > b.fX : a.fY > b.fY;
}
inline SkPoint* emit_vertex(Vertex* v, SkPoint* data) {
*data++ = v->fPoint;
return data;
}
SkPoint* emit_triangle(Vertex* v0, Vertex* v1, Vertex* v2, SkPoint* data) {
#if WIREFRAME
data = emit_vertex(v0, data);
data = emit_vertex(v1, data);
data = emit_vertex(v1, data);
data = emit_vertex(v2, data);
data = emit_vertex(v2, data);
data = emit_vertex(v0, data);
#else
data = emit_vertex(v0, data);
data = emit_vertex(v1, data);
data = emit_vertex(v2, data);
#endif
return data;
}
struct EdgeList {
EdgeList() : fHead(NULL), fTail(NULL) {}
Edge* fHead;
Edge* fTail;
};
/**
* An Edge joins a top Vertex to a bottom Vertex. Edge ordering for the list of "edges above" and
* "edge below" a vertex as well as for the active edge list is handled by isLeftOf()/isRightOf().
* Note that an Edge will give occasionally dist() != 0 for its own endpoints (because floating
* point). For speed, that case is only tested by the callers which require it (e.g.,
* cleanup_active_edges()). Edges also handle checking for intersection with other edges.
* Currently, this converts the edges to the parametric form, in order to avoid doing a division
* until an intersection has been confirmed. This is slightly slower in the "found" case, but
* a lot faster in the "not found" case.
*
* The coefficients of the line equation stored in double precision to avoid catastrphic
* cancellation in the isLeftOf() and isRightOf() checks. Using doubles ensures that the result is
* correct in float, since it's a polynomial of degree 2. The intersect() function, being
* degree 5, is still subject to catastrophic cancellation. We deal with that by assuming its
* output may be incorrect, and adjusting the mesh topology to match (see comment at the top of
* this file).
*/
struct Edge {
Edge(Vertex* top, Vertex* bottom, int winding)
: fWinding(winding)
, fTop(top)
, fBottom(bottom)
, fLeft(NULL)
, fRight(NULL)
, fPrevEdgeAbove(NULL)
, fNextEdgeAbove(NULL)
, fPrevEdgeBelow(NULL)
, fNextEdgeBelow(NULL)
, fLeftPoly(NULL)
, fRightPoly(NULL) {
recompute();
}
int fWinding; // 1 == edge goes downward; -1 = edge goes upward.
Vertex* fTop; // The top vertex in vertex-sort-order (sweep_lt).
Vertex* fBottom; // The bottom vertex in vertex-sort-order.
Edge* fLeft; // The linked list of edges in the active edge list.
Edge* fRight; // "
Edge* fPrevEdgeAbove; // The linked list of edges in the bottom Vertex's "edges above".
Edge* fNextEdgeAbove; // "
Edge* fPrevEdgeBelow; // The linked list of edges in the top Vertex's "edges below".
Edge* fNextEdgeBelow; // "
Poly* fLeftPoly; // The Poly to the left of this edge, if any.
Poly* fRightPoly; // The Poly to the right of this edge, if any.
double fDX; // The line equation for this edge, in implicit form.
double fDY; // fDY * x + fDX * y + fC = 0, for point (x, y) on the line.
double fC;
double dist(const SkPoint& p) const {
return fDY * p.fX - fDX * p.fY + fC;
}
bool isRightOf(Vertex* v) const {
return dist(v->fPoint) < 0.0;
}
bool isLeftOf(Vertex* v) const {
return dist(v->fPoint) > 0.0;
}
void recompute() {
fDX = static_cast<double>(fBottom->fPoint.fX) - fTop->fPoint.fX;
fDY = static_cast<double>(fBottom->fPoint.fY) - fTop->fPoint.fY;
fC = static_cast<double>(fTop->fPoint.fY) * fBottom->fPoint.fX -
static_cast<double>(fTop->fPoint.fX) * fBottom->fPoint.fY;
}
bool intersect(const Edge& other, SkPoint* p) {
LOG("intersecting %g -> %g with %g -> %g\n",
fTop->fID, fBottom->fID,
other.fTop->fID, other.fBottom->fID);
if (fTop == other.fTop || fBottom == other.fBottom) {
return false;
}
double denom = fDX * other.fDY - fDY * other.fDX;
if (denom == 0.0) {
return false;
}
double dx = static_cast<double>(fTop->fPoint.fX) - other.fTop->fPoint.fX;
double dy = static_cast<double>(fTop->fPoint.fY) - other.fTop->fPoint.fY;
double sNumer = dy * other.fDX - dx * other.fDY;
double tNumer = dy * fDX - dx * fDY;
// If (sNumer / denom) or (tNumer / denom) is not in [0..1], exit early.
// This saves us doing the divide below unless absolutely necessary.
if (denom > 0.0 ? (sNumer < 0.0 || sNumer > denom || tNumer < 0.0 || tNumer > denom)
: (sNumer > 0.0 || sNumer < denom || tNumer > 0.0 || tNumer < denom)) {
return false;
}
double s = sNumer / denom;
SkASSERT(s >= 0.0 && s <= 1.0);
p->fX = SkDoubleToScalar(fTop->fPoint.fX + s * fDX);
p->fY = SkDoubleToScalar(fTop->fPoint.fY + s * fDY);
return true;
}
bool isActive(EdgeList* activeEdges) const {
return activeEdges && (fLeft || fRight || activeEdges->fHead == this);
}
};
/***************************************************************************************/
struct Poly {
Poly(int winding)
: fWinding(winding)
, fHead(NULL)
, fTail(NULL)
, fActive(NULL)
, fNext(NULL)
, fPartner(NULL)
, fCount(0)
{
#if LOGGING_ENABLED
static int gID = 0;
fID = gID++;
LOG("*** created Poly %d\n", fID);
#endif
}
typedef enum { kNeither_Side, kLeft_Side, kRight_Side } Side;
struct MonotonePoly {
MonotonePoly()
: fSide(kNeither_Side)
, fHead(NULL)
, fTail(NULL)
, fPrev(NULL)
, fNext(NULL) {}
Side fSide;
Vertex* fHead;
Vertex* fTail;
MonotonePoly* fPrev;
MonotonePoly* fNext;
bool addVertex(Vertex* v, Side side, SkChunkAlloc& alloc) {
Vertex* newV = ALLOC_NEW(Vertex, (v->fPoint), alloc);
bool done = false;
if (fSide == kNeither_Side) {
fSide = side;
} else {
done = side != fSide;
}
if (fHead == NULL) {
fHead = fTail = newV;
} else if (fSide == kRight_Side) {
newV->fPrev = fTail;
fTail->fNext = newV;
fTail = newV;
} else {
newV->fNext = fHead;
fHead->fPrev = newV;
fHead = newV;
}
return done;
}
SkPoint* emit(SkPoint* data) {
Vertex* first = fHead;
Vertex* v = first->fNext;
while (v != fTail) {
SkASSERT(v && v->fPrev && v->fNext);
Vertex* prev = v->fPrev;
Vertex* curr = v;
Vertex* next = v->fNext;
double ax = static_cast<double>(curr->fPoint.fX) - prev->fPoint.fX;
double ay = static_cast<double>(curr->fPoint.fY) - prev->fPoint.fY;
double bx = static_cast<double>(next->fPoint.fX) - curr->fPoint.fX;
double by = static_cast<double>(next->fPoint.fY) - curr->fPoint.fY;
if (ax * by - ay * bx >= 0.0) {
data = emit_triangle(prev, curr, next, data);
v->fPrev->fNext = v->fNext;
v->fNext->fPrev = v->fPrev;
if (v->fPrev == first) {
v = v->fNext;
} else {
v = v->fPrev;
}
} else {
v = v->fNext;
}
}
return data;
}
};
Poly* addVertex(Vertex* v, Side side, SkChunkAlloc& alloc) {
LOG("addVertex() to %d at %g (%g, %g), %s side\n", fID, v->fID, v->fPoint.fX, v->fPoint.fY,
side == kLeft_Side ? "left" : side == kRight_Side ? "right" : "neither");
Poly* partner = fPartner;
Poly* poly = this;
if (partner) {
fPartner = partner->fPartner = NULL;
}
if (!fActive) {
fActive = ALLOC_NEW(MonotonePoly, (), alloc);
}
if (fActive->addVertex(v, side, alloc)) {
if (fTail) {
fActive->fPrev = fTail;
fTail->fNext = fActive;
fTail = fActive;
} else {
fHead = fTail = fActive;
}
if (partner) {
partner->addVertex(v, side, alloc);
poly = partner;
} else {
Vertex* prev = fActive->fSide == Poly::kLeft_Side ?
fActive->fHead->fNext : fActive->fTail->fPrev;
fActive = ALLOC_NEW(MonotonePoly, , alloc);
fActive->addVertex(prev, Poly::kNeither_Side, alloc);
fActive->addVertex(v, side, alloc);
}
}
fCount++;
return poly;
}
void end(Vertex* v, SkChunkAlloc& alloc) {
LOG("end() %d at %g, %g\n", fID, v->fPoint.fX, v->fPoint.fY);
if (fPartner) {
fPartner = fPartner->fPartner = NULL;
}
addVertex(v, fActive->fSide == kLeft_Side ? kRight_Side : kLeft_Side, alloc);
}
SkPoint* emit(SkPoint *data) {
if (fCount < 3) {
return data;
}
LOG("emit() %d, size %d\n", fID, fCount);
for (MonotonePoly* m = fHead; m != NULL; m = m->fNext) {
data = m->emit(data);
}
return data;
}
int fWinding;
MonotonePoly* fHead;
MonotonePoly* fTail;
MonotonePoly* fActive;
Poly* fNext;
Poly* fPartner;
int fCount;
#if LOGGING_ENABLED
int fID;
#endif
};
/***************************************************************************************/
bool coincident(const SkPoint& a, const SkPoint& b) {
return a == b;
}
Poly* new_poly(Poly** head, Vertex* v, int winding, SkChunkAlloc& alloc) {
Poly* poly = ALLOC_NEW(Poly, (winding), alloc);
poly->addVertex(v, Poly::kNeither_Side, alloc);
poly->fNext = *head;
*head = poly;
return poly;
}
Vertex* append_point_to_contour(const SkPoint& p, Vertex* prev, Vertex** head,
SkChunkAlloc& alloc) {
Vertex* v = ALLOC_NEW(Vertex, (p), alloc);
#if LOGGING_ENABLED
static float gID = 0.0f;
v->fID = gID++;
#endif
if (prev) {
prev->fNext = v;
v->fPrev = prev;
} else {
*head = v;
}
return v;
}
Vertex* generate_quadratic_points(const SkPoint& p0,
const SkPoint& p1,
const SkPoint& p2,
SkScalar tolSqd,
Vertex* prev,
Vertex** head,
int pointsLeft,
SkChunkAlloc& alloc) {
SkScalar d = p1.distanceToLineSegmentBetweenSqd(p0, p2);
if (pointsLeft < 2 || d < tolSqd || !SkScalarIsFinite(d)) {
return append_point_to_contour(p2, prev, head, alloc);
}
const SkPoint q[] = {
{ SkScalarAve(p0.fX, p1.fX), SkScalarAve(p0.fY, p1.fY) },
{ SkScalarAve(p1.fX, p2.fX), SkScalarAve(p1.fY, p2.fY) },
};
const SkPoint r = { SkScalarAve(q[0].fX, q[1].fX), SkScalarAve(q[0].fY, q[1].fY) };
pointsLeft >>= 1;
prev = generate_quadratic_points(p0, q[0], r, tolSqd, prev, head, pointsLeft, alloc);
prev = generate_quadratic_points(r, q[1], p2, tolSqd, prev, head, pointsLeft, alloc);
return prev;
}
Vertex* generate_cubic_points(const SkPoint& p0,
const SkPoint& p1,
const SkPoint& p2,
const SkPoint& p3,
SkScalar tolSqd,
Vertex* prev,
Vertex** head,
int pointsLeft,
SkChunkAlloc& alloc) {
SkScalar d1 = p1.distanceToLineSegmentBetweenSqd(p0, p3);
SkScalar d2 = p2.distanceToLineSegmentBetweenSqd(p0, p3);
if (pointsLeft < 2 || (d1 < tolSqd && d2 < tolSqd) ||
!SkScalarIsFinite(d1) || !SkScalarIsFinite(d2)) {
return append_point_to_contour(p3, prev, head, alloc);
}
const SkPoint q[] = {
{ SkScalarAve(p0.fX, p1.fX), SkScalarAve(p0.fY, p1.fY) },
{ SkScalarAve(p1.fX, p2.fX), SkScalarAve(p1.fY, p2.fY) },
{ SkScalarAve(p2.fX, p3.fX), SkScalarAve(p2.fY, p3.fY) }
};
const SkPoint r[] = {
{ SkScalarAve(q[0].fX, q[1].fX), SkScalarAve(q[0].fY, q[1].fY) },
{ SkScalarAve(q[1].fX, q[2].fX), SkScalarAve(q[1].fY, q[2].fY) }
};
const SkPoint s = { SkScalarAve(r[0].fX, r[1].fX), SkScalarAve(r[0].fY, r[1].fY) };
pointsLeft >>= 1;
prev = generate_cubic_points(p0, q[0], r[0], s, tolSqd, prev, head, pointsLeft, alloc);
prev = generate_cubic_points(s, r[1], q[2], p3, tolSqd, prev, head, pointsLeft, alloc);
return prev;
}
// Stage 1: convert the input path to a set of linear contours (linked list of Vertices).
void path_to_contours(const SkPath& path, SkScalar tolerance, const SkRect& clipBounds,
Vertex** contours, SkChunkAlloc& alloc, bool *isLinear) {
SkScalar toleranceSqd = tolerance * tolerance;
SkPoint pts[4];
bool done = false;
*isLinear = true;
SkPath::Iter iter(path, false);
Vertex* prev = NULL;
Vertex* head = NULL;
if (path.isInverseFillType()) {
SkPoint quad[4];
clipBounds.toQuad(quad);
for (int i = 3; i >= 0; i--) {
prev = append_point_to_contour(quad[i], prev, &head, alloc);
}
head->fPrev = prev;
prev->fNext = head;
*contours++ = head;
head = prev = NULL;
}
SkAutoConicToQuads converter;
while (!done) {
SkPath::Verb verb = iter.next(pts);
switch (verb) {
case SkPath::kConic_Verb: {
SkScalar weight = iter.conicWeight();
const SkPoint* quadPts = converter.computeQuads(pts, weight, toleranceSqd);
for (int i = 0; i < converter.countQuads(); ++i) {
int pointsLeft = GrPathUtils::quadraticPointCount(quadPts, tolerance);
prev = generate_quadratic_points(quadPts[0], quadPts[1], quadPts[2],
toleranceSqd, prev, &head, pointsLeft, alloc);
quadPts += 2;
}
*isLinear = false;
break;
}
case SkPath::kMove_Verb:
if (head) {
head->fPrev = prev;
prev->fNext = head;
*contours++ = head;
}
head = prev = NULL;
prev = append_point_to_contour(pts[0], prev, &head, alloc);
break;
case SkPath::kLine_Verb: {
prev = append_point_to_contour(pts[1], prev, &head, alloc);
break;
}
case SkPath::kQuad_Verb: {
int pointsLeft = GrPathUtils::quadraticPointCount(pts, tolerance);
prev = generate_quadratic_points(pts[0], pts[1], pts[2], toleranceSqd, prev,
&head, pointsLeft, alloc);
*isLinear = false;
break;
}
case SkPath::kCubic_Verb: {
int pointsLeft = GrPathUtils::cubicPointCount(pts, tolerance);
prev = generate_cubic_points(pts[0], pts[1], pts[2], pts[3],
toleranceSqd, prev, &head, pointsLeft, alloc);
*isLinear = false;
break;
}
case SkPath::kClose_Verb:
if (head) {
head->fPrev = prev;
prev->fNext = head;
*contours++ = head;
}
head = prev = NULL;
break;
case SkPath::kDone_Verb:
if (head) {
head->fPrev = prev;
prev->fNext = head;
*contours++ = head;
}
done = true;
break;
}
}
}
inline bool apply_fill_type(SkPath::FillType fillType, int winding) {
switch (fillType) {
case SkPath::kWinding_FillType:
return winding != 0;
case SkPath::kEvenOdd_FillType:
return (winding & 1) != 0;
case SkPath::kInverseWinding_FillType:
return winding == 1;
case SkPath::kInverseEvenOdd_FillType:
return (winding & 1) == 1;
default:
SkASSERT(false);
return false;
}
}
Edge* new_edge(Vertex* prev, Vertex* next, SkChunkAlloc& alloc, Comparator& c) {
int winding = c.sweep_lt(prev->fPoint, next->fPoint) ? 1 : -1;
Vertex* top = winding < 0 ? next : prev;
Vertex* bottom = winding < 0 ? prev : next;
return ALLOC_NEW(Edge, (top, bottom, winding), alloc);
}
void remove_edge(Edge* edge, EdgeList* edges) {
LOG("removing edge %g -> %g\n", edge->fTop->fID, edge->fBottom->fID);
SkASSERT(edge->isActive(edges));
remove<Edge, &Edge::fLeft, &Edge::fRight>(edge, &edges->fHead, &edges->fTail);
}
void insert_edge(Edge* edge, Edge* prev, EdgeList* edges) {
LOG("inserting edge %g -> %g\n", edge->fTop->fID, edge->fBottom->fID);
SkASSERT(!edge->isActive(edges));
Edge* next = prev ? prev->fRight : edges->fHead;
insert<Edge, &Edge::fLeft, &Edge::fRight>(edge, prev, next, &edges->fHead, &edges->fTail);
}
void find_enclosing_edges(Vertex* v, EdgeList* edges, Edge** left, Edge** right) {
if (v->fFirstEdgeAbove) {
*left = v->fFirstEdgeAbove->fLeft;
*right = v->fLastEdgeAbove->fRight;
return;
}
Edge* next = NULL;
Edge* prev;
for (prev = edges->fTail; prev != NULL; prev = prev->fLeft) {
if (prev->isLeftOf(v)) {
break;
}
next = prev;
}
*left = prev;
*right = next;
return;
}
void find_enclosing_edges(Edge* edge, EdgeList* edges, Comparator& c, Edge** left, Edge** right) {
Edge* prev = NULL;
Edge* next;
for (next = edges->fHead; next != NULL; next = next->fRight) {
if ((c.sweep_gt(edge->fTop->fPoint, next->fTop->fPoint) && next->isRightOf(edge->fTop)) ||
(c.sweep_gt(next->fTop->fPoint, edge->fTop->fPoint) && edge->isLeftOf(next->fTop)) ||
(c.sweep_lt(edge->fBottom->fPoint, next->fBottom->fPoint) &&
next->isRightOf(edge->fBottom)) ||
(c.sweep_lt(next->fBottom->fPoint, edge->fBottom->fPoint) &&
edge->isLeftOf(next->fBottom))) {
break;
}
prev = next;
}
*left = prev;
*right = next;
return;
}
void fix_active_state(Edge* edge, EdgeList* activeEdges, Comparator& c) {
if (edge->isActive(activeEdges)) {
if (edge->fBottom->fProcessed || !edge->fTop->fProcessed) {
remove_edge(edge, activeEdges);
}
} else if (edge->fTop->fProcessed && !edge->fBottom->fProcessed) {
Edge* left;
Edge* right;
find_enclosing_edges(edge, activeEdges, c, &left, &right);
insert_edge(edge, left, activeEdges);
}
}
void insert_edge_above(Edge* edge, Vertex* v, Comparator& c) {
if (edge->fTop->fPoint == edge->fBottom->fPoint ||
c.sweep_gt(edge->fTop->fPoint, edge->fBottom->fPoint)) {
return;
}
LOG("insert edge (%g -> %g) above vertex %g\n", edge->fTop->fID, edge->fBottom->fID, v->fID);
Edge* prev = NULL;
Edge* next;
for (next = v->fFirstEdgeAbove; next; next = next->fNextEdgeAbove) {
if (next->isRightOf(edge->fTop)) {
break;
}
prev = next;
}
insert<Edge, &Edge::fPrevEdgeAbove, &Edge::fNextEdgeAbove>(
edge, prev, next, &v->fFirstEdgeAbove, &v->fLastEdgeAbove);
}
void insert_edge_below(Edge* edge, Vertex* v, Comparator& c) {
if (edge->fTop->fPoint == edge->fBottom->fPoint ||
c.sweep_gt(edge->fTop->fPoint, edge->fBottom->fPoint)) {
return;
}
LOG("insert edge (%g -> %g) below vertex %g\n", edge->fTop->fID, edge->fBottom->fID, v->fID);
Edge* prev = NULL;
Edge* next;
for (next = v->fFirstEdgeBelow; next; next = next->fNextEdgeBelow) {
if (next->isRightOf(edge->fBottom)) {
break;
}
prev = next;
}
insert<Edge, &Edge::fPrevEdgeBelow, &Edge::fNextEdgeBelow>(
edge, prev, next, &v->fFirstEdgeBelow, &v->fLastEdgeBelow);
}
void remove_edge_above(Edge* edge) {
LOG("removing edge (%g -> %g) above vertex %g\n", edge->fTop->fID, edge->fBottom->fID,
edge->fBottom->fID);
remove<Edge, &Edge::fPrevEdgeAbove, &Edge::fNextEdgeAbove>(
edge, &edge->fBottom->fFirstEdgeAbove, &edge->fBottom->fLastEdgeAbove);
}
void remove_edge_below(Edge* edge) {
LOG("removing edge (%g -> %g) below vertex %g\n", edge->fTop->fID, edge->fBottom->fID,
edge->fTop->fID);
remove<Edge, &Edge::fPrevEdgeBelow, &Edge::fNextEdgeBelow>(
edge, &edge->fTop->fFirstEdgeBelow, &edge->fTop->fLastEdgeBelow);
}
void erase_edge_if_zero_winding(Edge* edge, EdgeList* edges) {
if (edge->fWinding != 0) {
return;
}
LOG("erasing edge (%g -> %g)\n", edge->fTop->fID, edge->fBottom->fID);
remove_edge_above(edge);
remove_edge_below(edge);
if (edge->isActive(edges)) {
remove_edge(edge, edges);
}
}
void merge_collinear_edges(Edge* edge, EdgeList* activeEdges, Comparator& c);
void set_top(Edge* edge, Vertex* v, EdgeList* activeEdges, Comparator& c) {
remove_edge_below(edge);
edge->fTop = v;
edge->recompute();
insert_edge_below(edge, v, c);
fix_active_state(edge, activeEdges, c);
merge_collinear_edges(edge, activeEdges, c);
}
void set_bottom(Edge* edge, Vertex* v, EdgeList* activeEdges, Comparator& c) {
remove_edge_above(edge);
edge->fBottom = v;
edge->recompute();
insert_edge_above(edge, v, c);
fix_active_state(edge, activeEdges, c);
merge_collinear_edges(edge, activeEdges, c);
}
void merge_edges_above(Edge* edge, Edge* other, EdgeList* activeEdges, Comparator& c) {
if (coincident(edge->fTop->fPoint, other->fTop->fPoint)) {
LOG("merging coincident above edges (%g, %g) -> (%g, %g)\n",
edge->fTop->fPoint.fX, edge->fTop->fPoint.fY,
edge->fBottom->fPoint.fX, edge->fBottom->fPoint.fY);
other->fWinding += edge->fWinding;
erase_edge_if_zero_winding(other, activeEdges);
edge->fWinding = 0;
erase_edge_if_zero_winding(edge, activeEdges);
} else if (c.sweep_lt(edge->fTop->fPoint, other->fTop->fPoint)) {
other->fWinding += edge->fWinding;
erase_edge_if_zero_winding(other, activeEdges);
set_bottom(edge, other->fTop, activeEdges, c);
} else {
edge->fWinding += other->fWinding;
erase_edge_if_zero_winding(edge, activeEdges);
set_bottom(other, edge->fTop, activeEdges, c);
}
}
void merge_edges_below(Edge* edge, Edge* other, EdgeList* activeEdges, Comparator& c) {
if (coincident(edge->fBottom->fPoint, other->fBottom->fPoint)) {
LOG("merging coincident below edges (%g, %g) -> (%g, %g)\n",
edge->fTop->fPoint.fX, edge->fTop->fPoint.fY,
edge->fBottom->fPoint.fX, edge->fBottom->fPoint.fY);
other->fWinding += edge->fWinding;
erase_edge_if_zero_winding(other, activeEdges);
edge->fWinding = 0;
erase_edge_if_zero_winding(edge, activeEdges);
} else if (c.sweep_lt(edge->fBottom->fPoint, other->fBottom->fPoint)) {
edge->fWinding += other->fWinding;
erase_edge_if_zero_winding(edge, activeEdges);
set_top(other, edge->fBottom, activeEdges, c);
} else {
other->fWinding += edge->fWinding;
erase_edge_if_zero_winding(other, activeEdges);
set_top(edge, other->fBottom, activeEdges, c);
}
}
void merge_collinear_edges(Edge* edge, EdgeList* activeEdges, Comparator& c) {
if (edge->fPrevEdgeAbove && (edge->fTop == edge->fPrevEdgeAbove->fTop ||
!edge->fPrevEdgeAbove->isLeftOf(edge->fTop))) {
merge_edges_above(edge, edge->fPrevEdgeAbove, activeEdges, c);
} else if (edge->fNextEdgeAbove && (edge->fTop == edge->fNextEdgeAbove->fTop ||
!edge->isLeftOf(edge->fNextEdgeAbove->fTop))) {
merge_edges_above(edge, edge->fNextEdgeAbove, activeEdges, c);
}
if (edge->fPrevEdgeBelow && (edge->fBottom == edge->fPrevEdgeBelow->fBottom ||
!edge->fPrevEdgeBelow->isLeftOf(edge->fBottom))) {
merge_edges_below(edge, edge->fPrevEdgeBelow, activeEdges, c);
} else if (edge->fNextEdgeBelow && (edge->fBottom == edge->fNextEdgeBelow->fBottom ||
!edge->isLeftOf(edge->fNextEdgeBelow->fBottom))) {
merge_edges_below(edge, edge->fNextEdgeBelow, activeEdges, c);
}
}
void split_edge(Edge* edge, Vertex* v, EdgeList* activeEdges, Comparator& c, SkChunkAlloc& alloc);
void cleanup_active_edges(Edge* edge, EdgeList* activeEdges, Comparator& c, SkChunkAlloc& alloc) {
Vertex* top = edge->fTop;
Vertex* bottom = edge->fBottom;
if (edge->fLeft) {
Vertex* leftTop = edge->fLeft->fTop;
Vertex* leftBottom = edge->fLeft->fBottom;
if (c.sweep_gt(top->fPoint, leftTop->fPoint) && !edge->fLeft->isLeftOf(top)) {
split_edge(edge->fLeft, edge->fTop, activeEdges, c, alloc);
} else if (c.sweep_gt(leftTop->fPoint, top->fPoint) && !edge->isRightOf(leftTop)) {
split_edge(edge, leftTop, activeEdges, c, alloc);
} else if (c.sweep_lt(bottom->fPoint, leftBottom->fPoint) &&
!edge->fLeft->isLeftOf(bottom)) {
split_edge(edge->fLeft, bottom, activeEdges, c, alloc);
} else if (c.sweep_lt(leftBottom->fPoint, bottom->fPoint) && !edge->isRightOf(leftBottom)) {
split_edge(edge, leftBottom, activeEdges, c, alloc);
}
}
if (edge->fRight) {
Vertex* rightTop = edge->fRight->fTop;
Vertex* rightBottom = edge->fRight->fBottom;
if (c.sweep_gt(top->fPoint, rightTop->fPoint) && !edge->fRight->isRightOf(top)) {
split_edge(edge->fRight, top, activeEdges, c, alloc);
} else if (c.sweep_gt(rightTop->fPoint, top->fPoint) && !edge->isLeftOf(rightTop)) {
split_edge(edge, rightTop, activeEdges, c, alloc);
} else if (c.sweep_lt(bottom->fPoint, rightBottom->fPoint) &&
!edge->fRight->isRightOf(bottom)) {
split_edge(edge->fRight, bottom, activeEdges, c, alloc);
} else if (c.sweep_lt(rightBottom->fPoint, bottom->fPoint) &&
!edge->isLeftOf(rightBottom)) {
split_edge(edge, rightBottom, activeEdges, c, alloc);
}
}
}
void split_edge(Edge* edge, Vertex* v, EdgeList* activeEdges, Comparator& c, SkChunkAlloc& alloc) {
LOG("splitting edge (%g -> %g) at vertex %g (%g, %g)\n",
edge->fTop->fID, edge->fBottom->fID,
v->fID, v->fPoint.fX, v->fPoint.fY);
if (c.sweep_lt(v->fPoint, edge->fTop->fPoint)) {
set_top(edge, v, activeEdges, c);
} else if (c.sweep_gt(v->fPoint, edge->fBottom->fPoint)) {
set_bottom(edge, v, activeEdges, c);
} else {
Edge* newEdge = ALLOC_NEW(Edge, (v, edge->fBottom, edge->fWinding), alloc);
insert_edge_below(newEdge, v, c);
insert_edge_above(newEdge, edge->fBottom, c);
set_bottom(edge, v, activeEdges, c);
cleanup_active_edges(edge, activeEdges, c, alloc);
fix_active_state(newEdge, activeEdges, c);
merge_collinear_edges(newEdge, activeEdges, c);
}
}
void merge_vertices(Vertex* src, Vertex* dst, Vertex** head, Comparator& c, SkChunkAlloc& alloc) {
LOG("found coincident verts at %g, %g; merging %g into %g\n", src->fPoint.fX, src->fPoint.fY,
src->fID, dst->fID);
for (Edge* edge = src->fFirstEdgeAbove; edge;) {
Edge* next = edge->fNextEdgeAbove;
set_bottom(edge, dst, NULL, c);
edge = next;
}
for (Edge* edge = src->fFirstEdgeBelow; edge;) {
Edge* next = edge->fNextEdgeBelow;
set_top(edge, dst, NULL, c);
edge = next;
}
remove<Vertex, &Vertex::fPrev, &Vertex::fNext>(src, head, NULL);
}
Vertex* check_for_intersection(Edge* edge, Edge* other, EdgeList* activeEdges, Comparator& c,
SkChunkAlloc& alloc) {
SkPoint p;
if (!edge || !other) {
return NULL;
}
if (edge->intersect(*other, &p)) {
Vertex* v;
LOG("found intersection, pt is %g, %g\n", p.fX, p.fY);
if (p == edge->fTop->fPoint || c.sweep_lt(p, edge->fTop->fPoint)) {
split_edge(other, edge->fTop, activeEdges, c, alloc);
v = edge->fTop;
} else if (p == edge->fBottom->fPoint || c.sweep_gt(p, edge->fBottom->fPoint)) {
split_edge(other, edge->fBottom, activeEdges, c, alloc);
v = edge->fBottom;
} else if (p == other->fTop->fPoint || c.sweep_lt(p, other->fTop->fPoint)) {
split_edge(edge, other->fTop, activeEdges, c, alloc);
v = other->fTop;
} else if (p == other->fBottom->fPoint || c.sweep_gt(p, other->fBottom->fPoint)) {
split_edge(edge, other->fBottom, activeEdges, c, alloc);
v = other->fBottom;
} else {
Vertex* nextV = edge->fTop;
while (c.sweep_lt(p, nextV->fPoint)) {
nextV = nextV->fPrev;
}
while (c.sweep_lt(nextV->fPoint, p)) {
nextV = nextV->fNext;
}
Vertex* prevV = nextV->fPrev;
if (coincident(prevV->fPoint, p)) {
v = prevV;
} else if (coincident(nextV->fPoint, p)) {
v = nextV;
} else {
v = ALLOC_NEW(Vertex, (p), alloc);
LOG("inserting between %g (%g, %g) and %g (%g, %g)\n",
prevV->fID, prevV->fPoint.fX, prevV->fPoint.fY,
nextV->fID, nextV->fPoint.fX, nextV->fPoint.fY);
#if LOGGING_ENABLED
v->fID = (nextV->fID + prevV->fID) * 0.5f;
#endif
v->fPrev = prevV;
v->fNext = nextV;
prevV->fNext = v;
nextV->fPrev = v;
}
split_edge(edge, v, activeEdges, c, alloc);
split_edge(other, v, activeEdges, c, alloc);
}
return v;
}
return NULL;
}
void sanitize_contours(Vertex** contours, int contourCnt) {
for (int i = 0; i < contourCnt; ++i) {
SkASSERT(contours[i]);
for (Vertex* v = contours[i];;) {
if (coincident(v->fPrev->fPoint, v->fPoint)) {
LOG("vertex %g,%g coincident; removing\n", v->fPoint.fX, v->fPoint.fY);
if (v->fPrev == v) {
contours[i] = NULL;
break;
}
v->fPrev->fNext = v->fNext;
v->fNext->fPrev = v->fPrev;
if (contours[i] == v) {
contours[i] = v->fNext;
}
v = v->fPrev;
} else {
v = v->fNext;
if (v == contours[i]) break;
}
}
}
}
void merge_coincident_vertices(Vertex** vertices, Comparator& c, SkChunkAlloc& alloc) {
for (Vertex* v = (*vertices)->fNext; v != NULL; v = v->fNext) {
if (c.sweep_lt(v->fPoint, v->fPrev->fPoint)) {
v->fPoint = v->fPrev->fPoint;
}
if (coincident(v->fPrev->fPoint, v->fPoint)) {
merge_vertices(v->fPrev, v, vertices, c, alloc);
}
}
}
// Stage 2: convert the contours to a mesh of edges connecting the vertices.
Vertex* build_edges(Vertex** contours, int contourCnt, Comparator& c, SkChunkAlloc& alloc) {
Vertex* vertices = NULL;
Vertex* prev = NULL;
for (int i = 0; i < contourCnt; ++i) {
for (Vertex* v = contours[i]; v != NULL;) {
Vertex* vNext = v->fNext;
Edge* edge = new_edge(v->fPrev, v, alloc, c);
if (edge->fWinding > 0) {
insert_edge_below(edge, v->fPrev, c);
insert_edge_above(edge, v, c);
} else {
insert_edge_below(edge, v, c);
insert_edge_above(edge, v->fPrev, c);
}
merge_collinear_edges(edge, NULL, c);
if (prev) {
prev->fNext = v;
v->fPrev = prev;
} else {
vertices = v;
}
prev = v;
v = vNext;
if (v == contours[i]) break;
}
}
if (prev) {
prev->fNext = vertices->fPrev = NULL;
}
return vertices;
}
// Stage 3: sort the vertices by increasing sweep direction.
Vertex* sorted_merge(Vertex* a, Vertex* b, Comparator& c);
void front_back_split(Vertex* v, Vertex** pFront, Vertex** pBack) {
Vertex* fast;
Vertex* slow;
if (!v || !v->fNext) {
*pFront = v;
*pBack = NULL;
} else {
slow = v;
fast = v->fNext;
while (fast != NULL) {
fast = fast->fNext;
if (fast != NULL) {
slow = slow->fNext;
fast = fast->fNext;
}
}
*pFront = v;
*pBack = slow->fNext;
slow->fNext->fPrev = NULL;
slow->fNext = NULL;
}
}
void merge_sort(Vertex** head, Comparator& c) {
if (!*head || !(*head)->fNext) {
return;
}
Vertex* a;
Vertex* b;
front_back_split(*head, &a, &b);
merge_sort(&a, c);
merge_sort(&b, c);
*head = sorted_merge(a, b, c);
}
inline void append_vertex(Vertex* v, Vertex** head, Vertex** tail) {
insert<Vertex, &Vertex::fPrev, &Vertex::fNext>(v, *tail, NULL, head, tail);
}
inline void append_vertex_list(Vertex* v, Vertex** head, Vertex** tail) {
insert<Vertex, &Vertex::fPrev, &Vertex::fNext>(v, *tail, v->fNext, head, tail);
}
Vertex* sorted_merge(Vertex* a, Vertex* b, Comparator& c) {
Vertex* head = NULL;
Vertex* tail = NULL;
while (a && b) {
if (c.sweep_lt(a->fPoint, b->fPoint)) {
Vertex* next = a->fNext;
append_vertex(a, &head, &tail);
a = next;
} else {
Vertex* next = b->fNext;
append_vertex(b, &head, &tail);
b = next;
}
}
if (a) {
append_vertex_list(a, &head, &tail);
}
if (b) {
append_vertex_list(b, &head, &tail);
}
return head;
}
// Stage 4: Simplify the mesh by inserting new vertices at intersecting edges.
void simplify(Vertex* vertices, Comparator& c, SkChunkAlloc& alloc) {
LOG("simplifying complex polygons\n");
EdgeList activeEdges;
for (Vertex* v = vertices; v != NULL; v = v->fNext) {
if (!v->fFirstEdgeAbove && !v->fFirstEdgeBelow) {
continue;
}
#if LOGGING_ENABLED
LOG("\nvertex %g: (%g,%g)\n", v->fID, v->fPoint.fX, v->fPoint.fY);
#endif
Edge* leftEnclosingEdge = NULL;
Edge* rightEnclosingEdge = NULL;
bool restartChecks;
do {
restartChecks = false;
find_enclosing_edges(v, &activeEdges, &leftEnclosingEdge, &rightEnclosingEdge);
if (v->fFirstEdgeBelow) {
for (Edge* edge = v->fFirstEdgeBelow; edge != NULL; edge = edge->fNextEdgeBelow) {
if (check_for_intersection(edge, leftEnclosingEdge, &activeEdges, c, alloc)) {
restartChecks = true;
break;
}
if (check_for_intersection(edge, rightEnclosingEdge, &activeEdges, c, alloc)) {
restartChecks = true;
break;
}
}
} else {
if (Vertex* pv = check_for_intersection(leftEnclosingEdge, rightEnclosingEdge,
&activeEdges, c, alloc)) {
if (c.sweep_lt(pv->fPoint, v->fPoint)) {
v = pv;
}
restartChecks = true;
}
}
} while (restartChecks);
for (Edge* e = v->fFirstEdgeAbove; e; e = e->fNextEdgeAbove) {
remove_edge(e, &activeEdges);
}
Edge* leftEdge = leftEnclosingEdge;
for (Edge* e = v->fFirstEdgeBelow; e; e = e->fNextEdgeBelow) {
insert_edge(e, leftEdge, &activeEdges);
leftEdge = e;
}
v->fProcessed = true;
}
}
// Stage 5: Tessellate the simplified mesh into monotone polygons.
Poly* tessellate(Vertex* vertices, SkChunkAlloc& alloc) {
LOG("tessellating simple polygons\n");
EdgeList activeEdges;
Poly* polys = NULL;
for (Vertex* v = vertices; v != NULL; v = v->fNext) {
if (!v->fFirstEdgeAbove && !v->fFirstEdgeBelow) {
continue;
}
#if LOGGING_ENABLED
LOG("\nvertex %g: (%g,%g)\n", v->fID, v->fPoint.fX, v->fPoint.fY);
#endif
Edge* leftEnclosingEdge = NULL;
Edge* rightEnclosingEdge = NULL;
find_enclosing_edges(v, &activeEdges, &leftEnclosingEdge, &rightEnclosingEdge);
Poly* leftPoly = NULL;
Poly* rightPoly = NULL;
if (v->fFirstEdgeAbove) {
leftPoly = v->fFirstEdgeAbove->fLeftPoly;
rightPoly = v->fLastEdgeAbove->fRightPoly;
} else {
leftPoly = leftEnclosingEdge ? leftEnclosingEdge->fRightPoly : NULL;
rightPoly = rightEnclosingEdge ? rightEnclosingEdge->fLeftPoly : NULL;
}
#if LOGGING_ENABLED
LOG("edges above:\n");
for (Edge* e = v->fFirstEdgeAbove; e; e = e->fNextEdgeAbove) {
LOG("%g -> %g, lpoly %d, rpoly %d\n", e->fTop->fID, e->fBottom->fID,
e->fLeftPoly ? e->fLeftPoly->fID : -1, e->fRightPoly ? e->fRightPoly->fID : -1);
}
LOG("edges below:\n");
for (Edge* e = v->fFirstEdgeBelow; e; e = e->fNextEdgeBelow) {
LOG("%g -> %g, lpoly %d, rpoly %d\n", e->fTop->fID, e->fBottom->fID,
e->fLeftPoly ? e->fLeftPoly->fID : -1, e->fRightPoly ? e->fRightPoly->fID : -1);
}
#endif
if (v->fFirstEdgeAbove) {
if (leftPoly) {
leftPoly = leftPoly->addVertex(v, Poly::kRight_Side, alloc);
}
if (rightPoly) {
rightPoly = rightPoly->addVertex(v, Poly::kLeft_Side, alloc);
}
for (Edge* e = v->fFirstEdgeAbove; e != v->fLastEdgeAbove; e = e->fNextEdgeAbove) {
Edge* leftEdge = e;
Edge* rightEdge = e->fNextEdgeAbove;
SkASSERT(rightEdge->isRightOf(leftEdge->fTop));
remove_edge(leftEdge, &activeEdges);
if (leftEdge->fRightPoly) {
leftEdge->fRightPoly->end(v, alloc);
}
if (rightEdge->fLeftPoly && rightEdge->fLeftPoly != leftEdge->fRightPoly) {
rightEdge->fLeftPoly->end(v, alloc);
}
}
remove_edge(v->fLastEdgeAbove, &activeEdges);
if (!v->fFirstEdgeBelow) {
if (leftPoly && rightPoly && leftPoly != rightPoly) {
SkASSERT(leftPoly->fPartner == NULL && rightPoly->fPartner == NULL);
rightPoly->fPartner = leftPoly;
leftPoly->fPartner = rightPoly;
}
}
}
if (v->fFirstEdgeBelow) {
if (!v->fFirstEdgeAbove) {
if (leftPoly && leftPoly == rightPoly) {
// Split the poly.
if (leftPoly->fActive->fSide == Poly::kLeft_Side) {
leftPoly = new_poly(&polys, leftEnclosingEdge->fTop, leftPoly->fWinding,
alloc);
leftPoly->addVertex(v, Poly::kRight_Side, alloc);
rightPoly->addVertex(v, Poly::kLeft_Side, alloc);
leftEnclosingEdge->fRightPoly = leftPoly;
} else {
rightPoly = new_poly(&polys, rightEnclosingEdge->fTop, rightPoly->fWinding,
alloc);
rightPoly->addVertex(v, Poly::kLeft_Side, alloc);
leftPoly->addVertex(v, Poly::kRight_Side, alloc);
rightEnclosingEdge->fLeftPoly = rightPoly;
}
} else {
if (leftPoly) {
leftPoly = leftPoly->addVertex(v, Poly::kRight_Side, alloc);
}
if (rightPoly) {
rightPoly = rightPoly->addVertex(v, Poly::kLeft_Side, alloc);
}
}
}
Edge* leftEdge = v->fFirstEdgeBelow;
leftEdge->fLeftPoly = leftPoly;
insert_edge(leftEdge, leftEnclosingEdge, &activeEdges);
for (Edge* rightEdge = leftEdge->fNextEdgeBelow; rightEdge;
rightEdge = rightEdge->fNextEdgeBelow) {
insert_edge(rightEdge, leftEdge, &activeEdges);
int winding = leftEdge->fLeftPoly ? leftEdge->fLeftPoly->fWinding : 0;
winding += leftEdge->fWinding;
if (winding != 0) {
Poly* poly = new_poly(&polys, v, winding, alloc);
leftEdge->fRightPoly = rightEdge->fLeftPoly = poly;
}
leftEdge = rightEdge;
}
v->fLastEdgeBelow->fRightPoly = rightPoly;
}
#if LOGGING_ENABLED
LOG("\nactive edges:\n");
for (Edge* e = activeEdges.fHead; e != NULL; e = e->fRight) {
LOG("%g -> %g, lpoly %d, rpoly %d\n", e->fTop->fID, e->fBottom->fID,
e->fLeftPoly ? e->fLeftPoly->fID : -1, e->fRightPoly ? e->fRightPoly->fID : -1);
}
#endif
}
return polys;
}
// This is a driver function which calls stages 2-5 in turn.
Poly* contours_to_polys(Vertex** contours, int contourCnt, Comparator& c, SkChunkAlloc& alloc) {
#if LOGGING_ENABLED
for (int i = 0; i < contourCnt; ++i) {
Vertex* v = contours[i];
SkASSERT(v);
LOG("path.moveTo(%20.20g, %20.20g);\n", v->fPoint.fX, v->fPoint.fY);
for (v = v->fNext; v != contours[i]; v = v->fNext) {
LOG("path.lineTo(%20.20g, %20.20g);\n", v->fPoint.fX, v->fPoint.fY);
}
}
#endif
sanitize_contours(contours, contourCnt);
Vertex* vertices = build_edges(contours, contourCnt, c, alloc);
if (!vertices) {
return NULL;
}
// Sort vertices in Y (secondarily in X).
merge_sort(&vertices, c);
merge_coincident_vertices(&vertices, c, alloc);
#if LOGGING_ENABLED
for (Vertex* v = vertices; v != NULL; v = v->fNext) {
static float gID = 0.0f;
v->fID = gID++;
}
#endif
simplify(vertices, c, alloc);
return tessellate(vertices, alloc);
}
// Stage 6: Triangulate the monotone polygons into a vertex buffer.
SkPoint* polys_to_triangles(Poly* polys, SkPath::FillType fillType, SkPoint* data) {
SkPoint* d = data;
for (Poly* poly = polys; poly; poly = poly->fNext) {
if (apply_fill_type(fillType, poly->fWinding)) {
d = poly->emit(d);
}
}
return d;
}
struct TessInfo {
SkScalar fTolerance;
int fCount;
};
bool cache_match(GrVertexBuffer* vertexBuffer, SkScalar tol, int* actualCount) {
if (!vertexBuffer) {
return false;
}
const SkData* data = vertexBuffer->getUniqueKey().getCustomData();
SkASSERT(data);
const TessInfo* info = static_cast<const TessInfo*>(data->data());
if (info->fTolerance == 0 || info->fTolerance < 3.0f * tol) {
*actualCount = info->fCount;
return true;
}
return false;
}
};
GrTessellatingPathRenderer::GrTessellatingPathRenderer() {
}
GrPathRenderer::StencilSupport GrTessellatingPathRenderer::onGetStencilSupport(
const GrDrawTarget*,
const GrPipelineBuilder*,
const SkPath&,
const GrStrokeInfo&) const {
return GrPathRenderer::kNoSupport_StencilSupport;
}
namespace {
// When the SkPathRef genID changes, invalidate a corresponding GrResource described by key.
class PathInvalidator : public SkPathRef::GenIDChangeListener {
public:
explicit PathInvalidator(const GrUniqueKey& key) : fMsg(key) {}
private:
GrUniqueKeyInvalidatedMessage fMsg;
void onChange() override {
SkMessageBus<GrUniqueKeyInvalidatedMessage>::Post(fMsg);
}
};
} // namespace
bool GrTessellatingPathRenderer::onCanDrawPath(const CanDrawPathArgs& args) const {
// This path renderer can draw all fill styles, all stroke styles except hairlines, but does
// not do antialiasing. It can do convex and concave paths, but we'll leave the convex ones to
// simpler algorithms.
return !IsStrokeHairlineOrEquivalent(*args.fStroke, *args.fViewMatrix, NULL) &&
!args.fAntiAlias && !args.fPath->isConvex();
}
class TessellatingPathBatch : public GrBatch {
public:
static GrBatch* Create(const GrColor& color,
const SkPath& path,
const GrStrokeInfo& stroke,
const SkMatrix& viewMatrix,
SkRect clipBounds) {
return SkNEW_ARGS(TessellatingPathBatch, (color, path, stroke, viewMatrix, clipBounds));
}
const char* name() const override { return "TessellatingPathBatch"; }
void getInvariantOutputColor(GrInitInvariantOutput* out) const override {
out->setKnownFourComponents(fColor);
}
void getInvariantOutputCoverage(GrInitInvariantOutput* out) const override {
out->setUnknownSingleComponent();
}
void initBatchTracker(const GrPipelineInfo& init) override {
// Handle any color overrides
if (!init.readsColor()) {
fColor = GrColor_ILLEGAL;
}
init.getOverrideColorIfSet(&fColor);
fPipelineInfo = init;
}
int tessellate(GrUniqueKey* key,
GrResourceProvider* resourceProvider,
SkAutoTUnref<GrVertexBuffer>& vertexBuffer) {
SkPath path;
GrStrokeInfo stroke(fStroke);
if (stroke.isDashed()) {
if (!stroke.applyDashToPath(&path, &stroke, fPath)) {
return 0;
}
} else {
path = fPath;
}
if (!stroke.isFillStyle()) {
stroke.setResScale(SkScalarAbs(fViewMatrix.getMaxScale()));
if (!stroke.applyToPath(&path, path)) {
return 0;
}
stroke.setFillStyle();
}
SkRect pathBounds = path.getBounds();
Comparator c;
if (pathBounds.width() > pathBounds.height()) {
c.sweep_lt = sweep_lt_horiz;
c.sweep_gt = sweep_gt_horiz;
} else {
c.sweep_lt = sweep_lt_vert;
c.sweep_gt = sweep_gt_vert;
}
SkScalar screenSpaceTol = GrPathUtils::kDefaultTolerance;
SkScalar tol = GrPathUtils::scaleToleranceToSrc(screenSpaceTol, fViewMatrix, pathBounds);
int contourCnt;
int maxPts = GrPathUtils::worstCasePointCount(path, &contourCnt, tol);
if (maxPts <= 0) {
return 0;
}
if (maxPts > ((int)SK_MaxU16 + 1)) {
SkDebugf("Path not rendered, too many verts (%d)\n", maxPts);
return 0;
}
SkPath::FillType fillType = path.getFillType();
if (SkPath::IsInverseFillType(fillType)) {
contourCnt++;
}
LOG("got %d pts, %d contours\n", maxPts, contourCnt);
SkAutoTDeleteArray<Vertex*> contours(SkNEW_ARRAY(Vertex *, contourCnt));
// For the initial size of the chunk allocator, estimate based on the point count:
// one vertex per point for the initial passes, plus two for the vertices in the
// resulting Polys, since the same point may end up in two Polys. Assume minimal
// connectivity of one Edge per Vertex (will grow for intersections).
SkChunkAlloc alloc(maxPts * (3 * sizeof(Vertex) + sizeof(Edge)));
bool isLinear;
path_to_contours(path, tol, fClipBounds, contours.get(), alloc, &isLinear);
Poly* polys;
polys = contours_to_polys(contours.get(), contourCnt, c, alloc);
int count = 0;
for (Poly* poly = polys; poly; poly = poly->fNext) {
if (apply_fill_type(fillType, poly->fWinding) && poly->fCount >= 3) {
count += (poly->fCount - 2) * (WIREFRAME ? 6 : 3);
}
}
if (0 == count) {
return 0;
}
size_t size = count * sizeof(SkPoint);
if (!vertexBuffer.get() || vertexBuffer->gpuMemorySize() < size) {
vertexBuffer.reset(resourceProvider->createVertexBuffer(
size, GrResourceProvider::kStatic_BufferUsage, 0));
}
if (!vertexBuffer.get()) {
SkDebugf("Could not allocate vertices\n");
return 0;
}
SkPoint* verts = static_cast<SkPoint*>(vertexBuffer->map());
LOG("emitting %d verts\n", count);
SkPoint* end = polys_to_triangles(polys, fillType, verts);
vertexBuffer->unmap();
int actualCount = static_cast<int>(end - verts);
LOG("actual count: %d\n", actualCount);
SkASSERT(actualCount <= count);
if (!fPath.isVolatile()) {
TessInfo info;
info.fTolerance = isLinear ? 0 : tol;
info.fCount = actualCount;
SkAutoTUnref<SkData> data(SkData::NewWithCopy(&info, sizeof(info)));
key->setCustomData(data.get());
resourceProvider->assignUniqueKeyToResource(*key, vertexBuffer.get());
SkPathPriv::AddGenIDChangeListener(fPath, SkNEW(PathInvalidator(*key)));
}
return actualCount;
}
void generateGeometry(GrBatchTarget* batchTarget) override {
// construct a cache key from the path's genID and the view matrix
static const GrUniqueKey::Domain kDomain = GrUniqueKey::GenerateDomain();
GrUniqueKey key;
int clipBoundsSize32 =
fPath.isInverseFillType() ? sizeof(fClipBounds) / sizeof(uint32_t) : 0;
int strokeDataSize32 = fStroke.computeUniqueKeyFragmentData32Cnt();
GrUniqueKey::Builder builder(&key, kDomain, 2 + clipBoundsSize32 + strokeDataSize32);
builder[0] = fPath.getGenerationID();
builder[1] = fPath.getFillType();
// For inverse fills, the tessellation is dependent on clip bounds.
if (fPath.isInverseFillType()) {
memcpy(&builder[2], &fClipBounds, sizeof(fClipBounds));
}
fStroke.asUniqueKeyFragment(&builder[2 + clipBoundsSize32]);
builder.finish();
GrResourceProvider* rp = batchTarget->resourceProvider();
SkAutoTUnref<GrVertexBuffer> vertexBuffer(rp->findAndRefTByUniqueKey<GrVertexBuffer>(key));
int actualCount;
SkScalar screenSpaceTol = GrPathUtils::kDefaultTolerance;
SkScalar tol = GrPathUtils::scaleToleranceToSrc(
screenSpaceTol, fViewMatrix, fPath.getBounds());
if (!cache_match(vertexBuffer.get(), tol, &actualCount)) {
actualCount = tessellate(&key, rp, vertexBuffer);
}
if (actualCount == 0) {
return;
}
SkAutoTUnref<const GrGeometryProcessor> gp;
{
using namespace GrDefaultGeoProcFactory;
Color color(fColor);
LocalCoords localCoords(fPipelineInfo.readsLocalCoords() ?
LocalCoords::kUsePosition_Type :
LocalCoords::kUnused_Type);
Coverage::Type coverageType;
if (fPipelineInfo.readsCoverage()) {
coverageType = Coverage::kSolid_Type;
} else {
coverageType = Coverage::kNone_Type;
}
Coverage coverage(coverageType);
gp.reset(GrDefaultGeoProcFactory::Create(color, coverage, localCoords,
fViewMatrix));
}
batchTarget->initDraw(gp, this->pipeline());
SkASSERT(gp->getVertexStride() == sizeof(SkPoint));
GrPrimitiveType primitiveType = WIREFRAME ? kLines_GrPrimitiveType
: kTriangles_GrPrimitiveType;
GrVertices vertices;
vertices.init(primitiveType, vertexBuffer.get(), 0, actualCount);
batchTarget->draw(vertices);
}
bool onCombineIfPossible(GrBatch*) override {
return false;
}
private:
TessellatingPathBatch(const GrColor& color,
const SkPath& path,
const GrStrokeInfo& stroke,
const SkMatrix& viewMatrix,
const SkRect& clipBounds)
: fColor(color)
, fPath(path)
, fStroke(stroke)
, fViewMatrix(viewMatrix)
, fClipBounds(clipBounds) {
this->initClassID<TessellatingPathBatch>();
fBounds = path.getBounds();
if (!stroke.isFillStyle()) {
SkScalar radius = SkScalarHalf(stroke.getWidth());
if (stroke.getJoin() == SkPaint::kMiter_Join) {
SkScalar scale = stroke.getMiter();
if (scale > SK_Scalar1) {
radius = SkScalarMul(radius, scale);
}
}
fBounds.outset(radius, radius);
}
viewMatrix.mapRect(&fBounds);
}
GrColor fColor;
SkPath fPath;
GrStrokeInfo fStroke;
SkMatrix fViewMatrix;
SkRect fClipBounds; // in source space
GrPipelineInfo fPipelineInfo;
};
bool GrTessellatingPathRenderer::onDrawPath(const DrawPathArgs& args) {
SkASSERT(!args.fAntiAlias);
const GrRenderTarget* rt = args.fPipelineBuilder->getRenderTarget();
if (NULL == rt) {
return false;
}
SkIRect clipBoundsI;
args.fPipelineBuilder->clip().getConservativeBounds(rt, &clipBoundsI);
SkRect clipBounds = SkRect::Make(clipBoundsI);
SkMatrix vmi;
if (!args.fViewMatrix->invert(&vmi)) {
return false;
}
vmi.mapRect(&clipBounds);
SkAutoTUnref<GrBatch> batch(TessellatingPathBatch::Create(args.fColor, *args.fPath,
*args.fStroke, *args.fViewMatrix,
clipBounds));
args.fTarget->drawBatch(*args.fPipelineBuilder, batch);
return true;
}
///////////////////////////////////////////////////////////////////////////////////////////////////
#ifdef GR_TEST_UTILS
BATCH_TEST_DEFINE(TesselatingPathBatch) {
GrColor color = GrRandomColor(random);
SkMatrix viewMatrix = GrTest::TestMatrixInvertible(random);
SkPath path = GrTest::TestPath(random);
SkRect clipBounds = GrTest::TestRect(random);
SkMatrix vmi;
bool result = viewMatrix.invert(&vmi);
if (!result) {
SkFAIL("Cannot invert matrix\n");
}
vmi.mapRect(&clipBounds);
GrStrokeInfo strokeInfo = GrTest::TestStrokeInfo(random);
return TessellatingPathBatch::Create(color, path, strokeInfo, viewMatrix, clipBounds);
}
#endif
|