1/*
2 * Copyright 2015 Google Inc.
3 *
4 * Use of this source code is governed by a BSD-style license that can be
5 * found in the LICENSE file.
6 */
7
8#include "src/gpu/GrTriangulator.h"
9
10#include "src/gpu/GrEagerVertexAllocator.h"
11#include "src/gpu/GrVertexWriter.h"
12#include "src/gpu/geometry/GrPathUtils.h"
13
14#include "include/core/SkPath.h"
15#include "src/core/SkArenaAlloc.h"
16#include "src/core/SkGeometry.h"
17#include "src/core/SkPointPriv.h"
18
19#include <algorithm>
20#include <cstdio>
21#include <queue>
22#include <unordered_map>
23#include <utility>
24
25/*
26 * There are six stages to the basic algorithm:
27 *
28 * 1) Linearize the path contours into piecewise linear segments (path_to_contours()).
29 * 2) Build a mesh of edges connecting the vertices (build_edges()).
30 * 3) Sort the vertices in Y (and secondarily in X) (merge_sort()).
31 * 4) Simplify the mesh by inserting new vertices at intersecting edges (simplify()).
32 * 5) Tessellate the simplified mesh into monotone polygons (tessellate()).
33 * 6) Triangulate the monotone polygons directly into a vertex buffer (polys_to_triangles()).
34 *
35 * For screenspace antialiasing, the algorithm is modified as follows:
36 *
37 * Run steps 1-5 above to produce polygons.
38 * 5b) Apply fill rules to extract boundary contours from the polygons (extract_boundaries()).
39 * 5c) Simplify boundaries to remove "pointy" vertices that cause inversions (simplify_boundary()).
40 * 5d) Displace edges by half a pixel inward and outward along their normals. Intersect to find
41 * new vertices, and set zero alpha on the exterior and one alpha on the interior. Build a new
42 * antialiased mesh from those vertices (stroke_boundary()).
43 * Run steps 3-6 above on the new mesh, and produce antialiased triangles.
44 *
45 * The vertex sorting in step (3) is a merge sort, since it plays well with the linked list
46 * of vertices (and the necessity of inserting new vertices on intersection).
47 *
48 * Stages (4) and (5) use an active edge list -- a list of all edges for which the
49 * sweep line has crossed the top vertex, but not the bottom vertex. It's sorted
50 * left-to-right based on the point where both edges are active (when both top vertices
51 * have been seen, so the "lower" top vertex of the two). If the top vertices are equal
52 * (shared), it's sorted based on the last point where both edges are active, so the
53 * "upper" bottom vertex.
54 *
55 * The most complex step is the simplification (4). It's based on the Bentley-Ottman
56 * line-sweep algorithm, but due to floating point inaccuracy, the intersection points are
57 * not exact and may violate the mesh topology or active edge list ordering. We
58 * accommodate this by adjusting the topology of the mesh and AEL to match the intersection
59 * points. This occurs in two ways:
60 *
61 * A) Intersections may cause a shortened edge to no longer be ordered with respect to its
62 * neighbouring edges at the top or bottom vertex. This is handled by merging the
63 * edges (merge_collinear_edges()).
64 * B) Intersections may cause an edge to violate the left-to-right ordering of the
65 * active edge list. This is handled by detecting potential violations and rewinding
66 * the active edge list to the vertex before they occur (rewind() during merging,
67 * rewind_if_necessary() during splitting).
68 *
69 * The tessellation steps (5) and (6) are based on "Triangulating Simple Polygons and
70 * Equivalent Problems" (Fournier and Montuno); also a line-sweep algorithm. Note that it
71 * currently uses a linked list for the active edge list, rather than a 2-3 tree as the
72 * paper describes. The 2-3 tree gives O(lg N) lookups, but insertion and removal also
73 * become O(lg N). In all the test cases, it was found that the cost of frequent O(lg N)
74 * insertions and removals was greater than the cost of infrequent O(N) lookups with the
75 * linked list implementation. With the latter, all removals are O(1), and most insertions
76 * are O(1), since we know the adjacent edge in the active edge list based on the topology.
77 * Only type 2 vertices (see paper) require the O(N) lookups, and these are much less
78 * frequent. There may be other data structures worth investigating, however.
79 *
80 * Note that the orientation of the line sweep algorithms is determined by the aspect ratio of the
81 * path bounds. When the path is taller than it is wide, we sort vertices based on increasing Y
82 * coordinate, and secondarily by increasing X coordinate. When the path is wider than it is tall,
83 * we sort by increasing X coordinate, but secondarily by *decreasing* Y coordinate. This is so
84 * that the "left" and "right" orientation in the code remains correct (edges to the left are
85 * increasing in Y; edges to the right are decreasing in Y). That is, the setting rotates 90
86 * degrees counterclockwise, rather that transposing.
87 */
88
89#define LOGGING_ENABLED 0
90
91#if LOGGING_ENABLED
92#define TESS_LOG printf
93#else
94#define TESS_LOG(...)
95#endif
96
97namespace {
98
99using GrTriangulator::Mode;
100
101const int kArenaChunkSize = 16 * 1024;
102const float kCosMiterAngle = 0.97f; // Corresponds to an angle of ~14 degrees.
103
104struct Vertex;
105struct Edge;
106struct Event;
107struct Poly;
108
109template <class T, T* T::*Prev, T* T::*Next>
110void list_insert(T* t, T* prev, T* next, T** head, T** tail) {
111 t->*Prev = prev;
112 t->*Next = next;
113 if (prev) {
114 prev->*Next = t;
115 } else if (head) {
116 *head = t;
117 }
118 if (next) {
119 next->*Prev = t;
120 } else if (tail) {
121 *tail = t;
122 }
123}
124
125template <class T, T* T::*Prev, T* T::*Next>
126void list_remove(T* t, T** head, T** tail) {
127 if (t->*Prev) {
128 t->*Prev->*Next = t->*Next;
129 } else if (head) {
130 *head = t->*Next;
131 }
132 if (t->*Next) {
133 t->*Next->*Prev = t->*Prev;
134 } else if (tail) {
135 *tail = t->*Prev;
136 }
137 t->*Prev = t->*Next = nullptr;
138}
139
140/**
141 * Vertices are used in three ways: first, the path contours are converted into a
142 * circularly-linked list of Vertices for each contour. After edge construction, the same Vertices
143 * are re-ordered by the merge sort according to the sweep_lt comparator (usually, increasing
144 * in Y) using the same fPrev/fNext pointers that were used for the contours, to avoid
145 * reallocation. Finally, MonotonePolys are built containing a circularly-linked list of
146 * Vertices. (Currently, those Vertices are newly-allocated for the MonotonePolys, since
147 * an individual Vertex from the path mesh may belong to multiple
148 * MonotonePolys, so the original Vertices cannot be re-used.
149 */
150
151struct Vertex {
152 Vertex(const SkPoint& point, uint8_t alpha)
153 : fPoint(point), fPrev(nullptr), fNext(nullptr)
154 , fFirstEdgeAbove(nullptr), fLastEdgeAbove(nullptr)
155 , fFirstEdgeBelow(nullptr), fLastEdgeBelow(nullptr)
156 , fLeftEnclosingEdge(nullptr), fRightEnclosingEdge(nullptr)
157 , fPartner(nullptr)
158 , fAlpha(alpha)
159 , fSynthetic(false)
160#if LOGGING_ENABLED
161 , fID (-1.0f)
162#endif
163 {}
164 SkPoint fPoint; // Vertex position
165 Vertex* fPrev; // Linked list of contours, then Y-sorted vertices.
166 Vertex* fNext; // "
167 Edge* fFirstEdgeAbove; // Linked list of edges above this vertex.
168 Edge* fLastEdgeAbove; // "
169 Edge* fFirstEdgeBelow; // Linked list of edges below this vertex.
170 Edge* fLastEdgeBelow; // "
171 Edge* fLeftEnclosingEdge; // Nearest edge in the AEL left of this vertex.
172 Edge* fRightEnclosingEdge; // Nearest edge in the AEL right of this vertex.
173 Vertex* fPartner; // Corresponding inner or outer vertex (for AA).
174 uint8_t fAlpha;
175 bool fSynthetic; // Is this a synthetic vertex?
176#if LOGGING_ENABLED
177 float fID; // Identifier used for logging.
178#endif
179};
180
181/***************************************************************************************/
182
183typedef bool (*CompareFunc)(const SkPoint& a, const SkPoint& b);
184
185bool sweep_lt_horiz(const SkPoint& a, const SkPoint& b) {
186 return a.fX < b.fX || (a.fX == b.fX && a.fY > b.fY);
187}
188
189bool sweep_lt_vert(const SkPoint& a, const SkPoint& b) {
190 return a.fY < b.fY || (a.fY == b.fY && a.fX < b.fX);
191}
192
193struct Comparator {
194 enum class Direction { kVertical, kHorizontal };
195 Comparator(Direction direction) : fDirection(direction) {}
196 bool sweep_lt(const SkPoint& a, const SkPoint& b) const {
197 return fDirection == Direction::kHorizontal ? sweep_lt_horiz(a, b) : sweep_lt_vert(a, b);
198 }
199 Direction fDirection;
200};
201
202inline void* emit_vertex(Vertex* v, bool emitCoverage, void* data) {
203 GrVertexWriter verts{data};
204 verts.write(v->fPoint);
205
206 if (emitCoverage) {
207 verts.write(GrNormalizeByteToFloat(v->fAlpha));
208 }
209
210 return verts.fPtr;
211}
212
213void* emit_triangle(Vertex* v0, Vertex* v1, Vertex* v2, bool emitCoverage, void* data) {
214 TESS_LOG("emit_triangle %g (%g, %g) %d\n", v0->fID, v0->fPoint.fX, v0->fPoint.fY, v0->fAlpha);
215 TESS_LOG(" %g (%g, %g) %d\n", v1->fID, v1->fPoint.fX, v1->fPoint.fY, v1->fAlpha);
216 TESS_LOG(" %g (%g, %g) %d\n", v2->fID, v2->fPoint.fX, v2->fPoint.fY, v2->fAlpha);
217#if TESSELLATOR_WIREFRAME
218 data = emit_vertex(v0, emitCoverage, data);
219 data = emit_vertex(v1, emitCoverage, data);
220 data = emit_vertex(v1, emitCoverage, data);
221 data = emit_vertex(v2, emitCoverage, data);
222 data = emit_vertex(v2, emitCoverage, data);
223 data = emit_vertex(v0, emitCoverage, data);
224#else
225 data = emit_vertex(v0, emitCoverage, data);
226 data = emit_vertex(v1, emitCoverage, data);
227 data = emit_vertex(v2, emitCoverage, data);
228#endif
229 return data;
230}
231
232struct VertexList {
233 VertexList() : fHead(nullptr), fTail(nullptr) {}
234 VertexList(Vertex* head, Vertex* tail) : fHead(head), fTail(tail) {}
235 Vertex* fHead;
236 Vertex* fTail;
237 void insert(Vertex* v, Vertex* prev, Vertex* next) {
238 list_insert<Vertex, &Vertex::fPrev, &Vertex::fNext>(v, prev, next, &fHead, &fTail);
239 }
240 void append(Vertex* v) {
241 insert(v, fTail, nullptr);
242 }
243 void append(const VertexList& list) {
244 if (!list.fHead) {
245 return;
246 }
247 if (fTail) {
248 fTail->fNext = list.fHead;
249 list.fHead->fPrev = fTail;
250 } else {
251 fHead = list.fHead;
252 }
253 fTail = list.fTail;
254 }
255 void prepend(Vertex* v) {
256 insert(v, nullptr, fHead);
257 }
258 void remove(Vertex* v) {
259 list_remove<Vertex, &Vertex::fPrev, &Vertex::fNext>(v, &fHead, &fTail);
260 }
261 void close() {
262 if (fHead && fTail) {
263 fTail->fNext = fHead;
264 fHead->fPrev = fTail;
265 }
266 }
267};
268
269// Round to nearest quarter-pixel. This is used for screenspace tessellation.
270
271inline void round(SkPoint* p) {
272 p->fX = SkScalarRoundToScalar(p->fX * SkFloatToScalar(4.0f)) * SkFloatToScalar(0.25f);
273 p->fY = SkScalarRoundToScalar(p->fY * SkFloatToScalar(4.0f)) * SkFloatToScalar(0.25f);
274}
275
276inline SkScalar double_to_clamped_scalar(double d) {
277 return SkDoubleToScalar(std::min((double) SK_ScalarMax, std::max(d, (double) -SK_ScalarMax)));
278}
279
280// A line equation in implicit form. fA * x + fB * y + fC = 0, for all points (x, y) on the line.
281struct Line {
282 Line(double a, double b, double c) : fA(a), fB(b), fC(c) {}
283 Line(Vertex* p, Vertex* q) : Line(p->fPoint, q->fPoint) {}
284 Line(const SkPoint& p, const SkPoint& q)
285 : fA(static_cast<double>(q.fY) - p.fY) // a = dY
286 , fB(static_cast<double>(p.fX) - q.fX) // b = -dX
287 , fC(static_cast<double>(p.fY) * q.fX - // c = cross(q, p)
288 static_cast<double>(p.fX) * q.fY) {}
289 double dist(const SkPoint& p) const {
290 return fA * p.fX + fB * p.fY + fC;
291 }
292 Line operator*(double v) const {
293 return Line(fA * v, fB * v, fC * v);
294 }
295 double magSq() const {
296 return fA * fA + fB * fB;
297 }
298 void normalize() {
299 double len = sqrt(this->magSq());
300 if (len == 0.0) {
301 return;
302 }
303 double scale = 1.0f / len;
304 fA *= scale;
305 fB *= scale;
306 fC *= scale;
307 }
308 bool nearParallel(const Line& o) const {
309 return fabs(o.fA - fA) < 0.00001 && fabs(o.fB - fB) < 0.00001;
310 }
311
312 // Compute the intersection of two (infinite) Lines.
313 bool intersect(const Line& other, SkPoint* point) const {
314 double denom = fA * other.fB - fB * other.fA;
315 if (denom == 0.0) {
316 return false;
317 }
318 double scale = 1.0 / denom;
319 point->fX = double_to_clamped_scalar((fB * other.fC - other.fB * fC) * scale);
320 point->fY = double_to_clamped_scalar((other.fA * fC - fA * other.fC) * scale);
321 round(point);
322 return point->isFinite();
323 }
324 double fA, fB, fC;
325};
326
327/**
328 * An Edge joins a top Vertex to a bottom Vertex. Edge ordering for the list of "edges above" and
329 * "edge below" a vertex as well as for the active edge list is handled by isLeftOf()/isRightOf().
330 * Note that an Edge will give occasionally dist() != 0 for its own endpoints (because floating
331 * point). For speed, that case is only tested by the callers that require it (e.g.,
332 * rewind_if_necessary()). Edges also handle checking for intersection with other edges.
333 * Currently, this converts the edges to the parametric form, in order to avoid doing a division
334 * until an intersection has been confirmed. This is slightly slower in the "found" case, but
335 * a lot faster in the "not found" case.
336 *
337 * The coefficients of the line equation stored in double precision to avoid catastrphic
338 * cancellation in the isLeftOf() and isRightOf() checks. Using doubles ensures that the result is
339 * correct in float, since it's a polynomial of degree 2. The intersect() function, being
340 * degree 5, is still subject to catastrophic cancellation. We deal with that by assuming its
341 * output may be incorrect, and adjusting the mesh topology to match (see comment at the top of
342 * this file).
343 */
344
345struct Edge {
346 enum class Type { kInner, kOuter, kConnector };
347 Edge(Vertex* top, Vertex* bottom, int winding, Type type)
348 : fWinding(winding)
349 , fTop(top)
350 , fBottom(bottom)
351 , fType(type)
352 , fLeft(nullptr)
353 , fRight(nullptr)
354 , fPrevEdgeAbove(nullptr)
355 , fNextEdgeAbove(nullptr)
356 , fPrevEdgeBelow(nullptr)
357 , fNextEdgeBelow(nullptr)
358 , fLeftPoly(nullptr)
359 , fRightPoly(nullptr)
360 , fLeftPolyPrev(nullptr)
361 , fLeftPolyNext(nullptr)
362 , fRightPolyPrev(nullptr)
363 , fRightPolyNext(nullptr)
364 , fUsedInLeftPoly(false)
365 , fUsedInRightPoly(false)
366 , fLine(top, bottom) {
367 }
368 int fWinding; // 1 == edge goes downward; -1 = edge goes upward.
369 Vertex* fTop; // The top vertex in vertex-sort-order (sweep_lt).
370 Vertex* fBottom; // The bottom vertex in vertex-sort-order.
371 Type fType;
372 Edge* fLeft; // The linked list of edges in the active edge list.
373 Edge* fRight; // "
374 Edge* fPrevEdgeAbove; // The linked list of edges in the bottom Vertex's "edges above".
375 Edge* fNextEdgeAbove; // "
376 Edge* fPrevEdgeBelow; // The linked list of edges in the top Vertex's "edges below".
377 Edge* fNextEdgeBelow; // "
378 Poly* fLeftPoly; // The Poly to the left of this edge, if any.
379 Poly* fRightPoly; // The Poly to the right of this edge, if any.
380 Edge* fLeftPolyPrev;
381 Edge* fLeftPolyNext;
382 Edge* fRightPolyPrev;
383 Edge* fRightPolyNext;
384 bool fUsedInLeftPoly;
385 bool fUsedInRightPoly;
386 Line fLine;
387 double dist(const SkPoint& p) const {
388 return fLine.dist(p);
389 }
390 bool isRightOf(Vertex* v) const {
391 return fLine.dist(v->fPoint) < 0.0;
392 }
393 bool isLeftOf(Vertex* v) const {
394 return fLine.dist(v->fPoint) > 0.0;
395 }
396 void recompute() {
397 fLine = Line(fTop, fBottom);
398 }
399 bool intersect(const Edge& other, SkPoint* p, uint8_t* alpha = nullptr) const {
400 TESS_LOG("intersecting %g -> %g with %g -> %g\n",
401 fTop->fID, fBottom->fID, other.fTop->fID, other.fBottom->fID);
402 if (fTop == other.fTop || fBottom == other.fBottom) {
403 return false;
404 }
405 double denom = fLine.fA * other.fLine.fB - fLine.fB * other.fLine.fA;
406 if (denom == 0.0) {
407 return false;
408 }
409 double dx = static_cast<double>(other.fTop->fPoint.fX) - fTop->fPoint.fX;
410 double dy = static_cast<double>(other.fTop->fPoint.fY) - fTop->fPoint.fY;
411 double sNumer = dy * other.fLine.fB + dx * other.fLine.fA;
412 double tNumer = dy * fLine.fB + dx * fLine.fA;
413 // If (sNumer / denom) or (tNumer / denom) is not in [0..1], exit early.
414 // This saves us doing the divide below unless absolutely necessary.
415 if (denom > 0.0 ? (sNumer < 0.0 || sNumer > denom || tNumer < 0.0 || tNumer > denom)
416 : (sNumer > 0.0 || sNumer < denom || tNumer > 0.0 || tNumer < denom)) {
417 return false;
418 }
419 double s = sNumer / denom;
420 SkASSERT(s >= 0.0 && s <= 1.0);
421 p->fX = SkDoubleToScalar(fTop->fPoint.fX - s * fLine.fB);
422 p->fY = SkDoubleToScalar(fTop->fPoint.fY + s * fLine.fA);
423 if (alpha) {
424 if (fType == Type::kConnector) {
425 *alpha = (1.0 - s) * fTop->fAlpha + s * fBottom->fAlpha;
426 } else if (other.fType == Type::kConnector) {
427 double t = tNumer / denom;
428 *alpha = (1.0 - t) * other.fTop->fAlpha + t * other.fBottom->fAlpha;
429 } else if (fType == Type::kOuter && other.fType == Type::kOuter) {
430 *alpha = 0;
431 } else {
432 *alpha = 255;
433 }
434 }
435 return true;
436 }
437};
438
439struct SSEdge;
440
441struct SSVertex {
442 SSVertex(Vertex* v) : fVertex(v), fPrev(nullptr), fNext(nullptr) {}
443 Vertex* fVertex;
444 SSEdge* fPrev;
445 SSEdge* fNext;
446};
447
448struct SSEdge {
449 SSEdge(Edge* edge, SSVertex* prev, SSVertex* next)
450 : fEdge(edge), fEvent(nullptr), fPrev(prev), fNext(next) {
451 }
452 Edge* fEdge;
453 Event* fEvent;
454 SSVertex* fPrev;
455 SSVertex* fNext;
456};
457
458typedef std::unordered_map<Vertex*, SSVertex*> SSVertexMap;
459typedef std::vector<SSEdge*> SSEdgeList;
460
461struct EdgeList {
462 EdgeList() : fHead(nullptr), fTail(nullptr) {}
463 Edge* fHead;
464 Edge* fTail;
465 void insert(Edge* edge, Edge* prev, Edge* next) {
466 list_insert<Edge, &Edge::fLeft, &Edge::fRight>(edge, prev, next, &fHead, &fTail);
467 }
468 void append(Edge* e) {
469 insert(e, fTail, nullptr);
470 }
471 void remove(Edge* edge) {
472 list_remove<Edge, &Edge::fLeft, &Edge::fRight>(edge, &fHead, &fTail);
473 }
474 void removeAll() {
475 while (fHead) {
476 this->remove(fHead);
477 }
478 }
479 void close() {
480 if (fHead && fTail) {
481 fTail->fRight = fHead;
482 fHead->fLeft = fTail;
483 }
484 }
485 bool contains(Edge* edge) const {
486 return edge->fLeft || edge->fRight || fHead == edge;
487 }
488};
489
490struct EventList;
491
492struct Event {
493 Event(SSEdge* edge, const SkPoint& point, uint8_t alpha)
494 : fEdge(edge), fPoint(point), fAlpha(alpha) {
495 }
496 SSEdge* fEdge;
497 SkPoint fPoint;
498 uint8_t fAlpha;
499 void apply(VertexList* mesh, Comparator& c, EventList* events, SkArenaAlloc& alloc);
500};
501
502struct EventComparator {
503 enum class Op { kLessThan, kGreaterThan };
504 EventComparator(Op op) : fOp(op) {}
505 bool operator() (Event* const &e1, Event* const &e2) {
506 return fOp == Op::kLessThan ? e1->fAlpha < e2->fAlpha
507 : e1->fAlpha > e2->fAlpha;
508 }
509 Op fOp;
510};
511
512typedef std::priority_queue<Event*, std::vector<Event*>, EventComparator> EventPQ;
513
514struct EventList : EventPQ {
515 EventList(EventComparator comparison) : EventPQ(comparison) {
516 }
517};
518
519void create_event(SSEdge* e, EventList* events, SkArenaAlloc& alloc) {
520 Vertex* prev = e->fPrev->fVertex;
521 Vertex* next = e->fNext->fVertex;
522 if (prev == next || !prev->fPartner || !next->fPartner) {
523 return;
524 }
525 Edge bisector1(prev, prev->fPartner, 1, Edge::Type::kConnector);
526 Edge bisector2(next, next->fPartner, 1, Edge::Type::kConnector);
527 SkPoint p;
528 uint8_t alpha;
529 if (bisector1.intersect(bisector2, &p, &alpha)) {
530 TESS_LOG("found edge event for %g, %g (original %g -> %g), "
531 "will collapse to %g,%g alpha %d\n",
532 prev->fID, next->fID, e->fEdge->fTop->fID, e->fEdge->fBottom->fID, p.fX, p.fY,
533 alpha);
534 e->fEvent = alloc.make<Event>(e, p, alpha);
535 events->push(e->fEvent);
536 }
537}
538
539void create_event(SSEdge* edge, Vertex* v, SSEdge* other, Vertex* dest, EventList* events,
540 Comparator& c, SkArenaAlloc& alloc) {
541 if (!v->fPartner) {
542 return;
543 }
544 Vertex* top = edge->fEdge->fTop;
545 Vertex* bottom = edge->fEdge->fBottom;
546 if (!top || !bottom ) {
547 return;
548 }
549 Line line = edge->fEdge->fLine;
550 line.fC = -(dest->fPoint.fX * line.fA + dest->fPoint.fY * line.fB);
551 Edge bisector(v, v->fPartner, 1, Edge::Type::kConnector);
552 SkPoint p;
553 uint8_t alpha = dest->fAlpha;
554 if (line.intersect(bisector.fLine, &p) && !c.sweep_lt(p, top->fPoint) &&
555 c.sweep_lt(p, bottom->fPoint)) {
556 TESS_LOG("found p edge event for %g, %g (original %g -> %g), "
557 "will collapse to %g,%g alpha %d\n",
558 dest->fID, v->fID, top->fID, bottom->fID, p.fX, p.fY, alpha);
559 edge->fEvent = alloc.make<Event>(edge, p, alpha);
560 events->push(edge->fEvent);
561 }
562}
563
564/***************************************************************************************/
565
566struct Poly {
567 Poly(Vertex* v, int winding)
568 : fFirstVertex(v)
569 , fWinding(winding)
570 , fHead(nullptr)
571 , fTail(nullptr)
572 , fNext(nullptr)
573 , fPartner(nullptr)
574 , fCount(0)
575 {
576#if LOGGING_ENABLED
577 static int gID = 0;
578 fID = gID++;
579 TESS_LOG("*** created Poly %d\n", fID);
580#endif
581 }
582 typedef enum { kLeft_Side, kRight_Side } Side;
583 struct MonotonePoly {
584 MonotonePoly(Edge* edge, Side side, int winding)
585 : fSide(side)
586 , fFirstEdge(nullptr)
587 , fLastEdge(nullptr)
588 , fPrev(nullptr)
589 , fNext(nullptr)
590 , fWinding(winding) {
591 this->addEdge(edge);
592 }
593 Side fSide;
594 Edge* fFirstEdge;
595 Edge* fLastEdge;
596 MonotonePoly* fPrev;
597 MonotonePoly* fNext;
598 int fWinding;
599 void addEdge(Edge* edge) {
600 if (fSide == kRight_Side) {
601 SkASSERT(!edge->fUsedInRightPoly);
602 list_insert<Edge, &Edge::fRightPolyPrev, &Edge::fRightPolyNext>(
603 edge, fLastEdge, nullptr, &fFirstEdge, &fLastEdge);
604 edge->fUsedInRightPoly = true;
605 } else {
606 SkASSERT(!edge->fUsedInLeftPoly);
607 list_insert<Edge, &Edge::fLeftPolyPrev, &Edge::fLeftPolyNext>(
608 edge, fLastEdge, nullptr, &fFirstEdge, &fLastEdge);
609 edge->fUsedInLeftPoly = true;
610 }
611 }
612
613 void* emit(bool emitCoverage, void* data) {
614 Edge* e = fFirstEdge;
615 VertexList vertices;
616 vertices.append(e->fTop);
617 int count = 1;
618 while (e != nullptr) {
619 if (kRight_Side == fSide) {
620 vertices.append(e->fBottom);
621 e = e->fRightPolyNext;
622 } else {
623 vertices.prepend(e->fBottom);
624 e = e->fLeftPolyNext;
625 }
626 count++;
627 }
628 Vertex* first = vertices.fHead;
629 Vertex* v = first->fNext;
630 while (v != vertices.fTail) {
631 SkASSERT(v && v->fPrev && v->fNext);
632 Vertex* prev = v->fPrev;
633 Vertex* curr = v;
634 Vertex* next = v->fNext;
635 if (count == 3) {
636 return this->emitTriangle(prev, curr, next, emitCoverage, data);
637 }
638 double ax = static_cast<double>(curr->fPoint.fX) - prev->fPoint.fX;
639 double ay = static_cast<double>(curr->fPoint.fY) - prev->fPoint.fY;
640 double bx = static_cast<double>(next->fPoint.fX) - curr->fPoint.fX;
641 double by = static_cast<double>(next->fPoint.fY) - curr->fPoint.fY;
642 if (ax * by - ay * bx >= 0.0) {
643 data = this->emitTriangle(prev, curr, next, emitCoverage, data);
644 v->fPrev->fNext = v->fNext;
645 v->fNext->fPrev = v->fPrev;
646 count--;
647 if (v->fPrev == first) {
648 v = v->fNext;
649 } else {
650 v = v->fPrev;
651 }
652 } else {
653 v = v->fNext;
654 }
655 }
656 return data;
657 }
658 void* emitTriangle(Vertex* prev, Vertex* curr, Vertex* next, bool emitCoverage,
659 void* data) const {
660 if (fWinding < 0) {
661 // Ensure our triangles always wind in the same direction as if the path had been
662 // triangulated as a simple fan (a la red book).
663 std::swap(prev, next);
664 }
665 return emit_triangle(next, curr, prev, emitCoverage, data);
666 }
667 };
668 Poly* addEdge(Edge* e, Side side, SkArenaAlloc& alloc) {
669 TESS_LOG("addEdge (%g -> %g) to poly %d, %s side\n",
670 e->fTop->fID, e->fBottom->fID, fID, side == kLeft_Side ? "left" : "right");
671 Poly* partner = fPartner;
672 Poly* poly = this;
673 if (side == kRight_Side) {
674 if (e->fUsedInRightPoly) {
675 return this;
676 }
677 } else {
678 if (e->fUsedInLeftPoly) {
679 return this;
680 }
681 }
682 if (partner) {
683 fPartner = partner->fPartner = nullptr;
684 }
685 if (!fTail) {
686 fHead = fTail = alloc.make<MonotonePoly>(e, side, fWinding);
687 fCount += 2;
688 } else if (e->fBottom == fTail->fLastEdge->fBottom) {
689 return poly;
690 } else if (side == fTail->fSide) {
691 fTail->addEdge(e);
692 fCount++;
693 } else {
694 e = alloc.make<Edge>(fTail->fLastEdge->fBottom, e->fBottom, 1, Edge::Type::kInner);
695 fTail->addEdge(e);
696 fCount++;
697 if (partner) {
698 partner->addEdge(e, side, alloc);
699 poly = partner;
700 } else {
701 MonotonePoly* m = alloc.make<MonotonePoly>(e, side, fWinding);
702 m->fPrev = fTail;
703 fTail->fNext = m;
704 fTail = m;
705 }
706 }
707 return poly;
708 }
709 void* emit(bool emitCoverage, void *data) {
710 if (fCount < 3) {
711 return data;
712 }
713 TESS_LOG("emit() %d, size %d\n", fID, fCount);
714 for (MonotonePoly* m = fHead; m != nullptr; m = m->fNext) {
715 data = m->emit(emitCoverage, data);
716 }
717 return data;
718 }
719 Vertex* lastVertex() const { return fTail ? fTail->fLastEdge->fBottom : fFirstVertex; }
720 Vertex* fFirstVertex;
721 int fWinding;
722 MonotonePoly* fHead;
723 MonotonePoly* fTail;
724 Poly* fNext;
725 Poly* fPartner;
726 int fCount;
727#if LOGGING_ENABLED
728 int fID;
729#endif
730};
731
732/***************************************************************************************/
733
734bool coincident(const SkPoint& a, const SkPoint& b) {
735 return a == b;
736}
737
738Poly* new_poly(Poly** head, Vertex* v, int winding, SkArenaAlloc& alloc) {
739 Poly* poly = alloc.make<Poly>(v, winding);
740 poly->fNext = *head;
741 *head = poly;
742 return poly;
743}
744
745void append_point_to_contour(const SkPoint& p, VertexList* contour, SkArenaAlloc& alloc) {
746 Vertex* v = alloc.make<Vertex>(p, 255);
747#if LOGGING_ENABLED
748 static float gID = 0.0f;
749 v->fID = gID++;
750#endif
751 contour->append(v);
752}
753
754SkScalar quad_error_at(const SkPoint pts[3], SkScalar t, SkScalar u) {
755 SkQuadCoeff quad(pts);
756 SkPoint p0 = to_point(quad.eval(t - 0.5f * u));
757 SkPoint mid = to_point(quad.eval(t));
758 SkPoint p1 = to_point(quad.eval(t + 0.5f * u));
759 if (!p0.isFinite() || !mid.isFinite() || !p1.isFinite()) {
760 return 0;
761 }
762 return SkPointPriv::DistanceToLineSegmentBetweenSqd(mid, p0, p1);
763}
764
765void append_quadratic_to_contour(const SkPoint pts[3], SkScalar toleranceSqd, VertexList* contour,
766 SkArenaAlloc& alloc) {
767 SkQuadCoeff quad(pts);
768 Sk2s aa = quad.fA * quad.fA;
769 SkScalar denom = 2.0f * (aa[0] + aa[1]);
770 Sk2s ab = quad.fA * quad.fB;
771 SkScalar t = denom ? (-ab[0] - ab[1]) / denom : 0.0f;
772 int nPoints = 1;
773 SkScalar u = 1.0f;
774 // Test possible subdivision values only at the point of maximum curvature.
775 // If it passes the flatness metric there, it'll pass everywhere.
776 while (nPoints < GrPathUtils::kMaxPointsPerCurve) {
777 u = 1.0f / nPoints;
778 if (quad_error_at(pts, t, u) < toleranceSqd) {
779 break;
780 }
781 nPoints++;
782 }
783 for (int j = 1; j <= nPoints; j++) {
784 append_point_to_contour(to_point(quad.eval(j * u)), contour, alloc);
785 }
786}
787
788void generate_cubic_points(const SkPoint& p0,
789 const SkPoint& p1,
790 const SkPoint& p2,
791 const SkPoint& p3,
792 SkScalar tolSqd,
793 VertexList* contour,
794 int pointsLeft,
795 SkArenaAlloc& alloc) {
796 SkScalar d1 = SkPointPriv::DistanceToLineSegmentBetweenSqd(p1, p0, p3);
797 SkScalar d2 = SkPointPriv::DistanceToLineSegmentBetweenSqd(p2, p0, p3);
798 if (pointsLeft < 2 || (d1 < tolSqd && d2 < tolSqd) ||
799 !SkScalarIsFinite(d1) || !SkScalarIsFinite(d2)) {
800 append_point_to_contour(p3, contour, alloc);
801 return;
802 }
803 const SkPoint q[] = {
804 { SkScalarAve(p0.fX, p1.fX), SkScalarAve(p0.fY, p1.fY) },
805 { SkScalarAve(p1.fX, p2.fX), SkScalarAve(p1.fY, p2.fY) },
806 { SkScalarAve(p2.fX, p3.fX), SkScalarAve(p2.fY, p3.fY) }
807 };
808 const SkPoint r[] = {
809 { SkScalarAve(q[0].fX, q[1].fX), SkScalarAve(q[0].fY, q[1].fY) },
810 { SkScalarAve(q[1].fX, q[2].fX), SkScalarAve(q[1].fY, q[2].fY) }
811 };
812 const SkPoint s = { SkScalarAve(r[0].fX, r[1].fX), SkScalarAve(r[0].fY, r[1].fY) };
813 pointsLeft >>= 1;
814 generate_cubic_points(p0, q[0], r[0], s, tolSqd, contour, pointsLeft, alloc);
815 generate_cubic_points(s, r[1], q[2], p3, tolSqd, contour, pointsLeft, alloc);
816}
817
818// Stage 1: convert the input path to a set of linear contours (linked list of Vertices).
819
820void path_to_contours(const SkPath& path, SkScalar tolerance, const SkRect& clipBounds,
821 VertexList* contours, SkArenaAlloc& alloc, Mode mode, bool *isLinear) {
822 SkScalar toleranceSqd = tolerance * tolerance;
823 bool innerPolygons = (Mode::kSimpleInnerPolygons == mode);
824
825 SkPoint pts[4];
826 *isLinear = true;
827 VertexList* contour = contours;
828 SkPath::Iter iter(path, false);
829 if (path.isInverseFillType()) {
830 SkPoint quad[4];
831 clipBounds.toQuad(quad);
832 for (int i = 3; i >= 0; i--) {
833 append_point_to_contour(quad[i], contours, alloc);
834 }
835 contour++;
836 }
837 SkAutoConicToQuads converter;
838 SkPath::Verb verb;
839 while ((verb = iter.next(pts)) != SkPath::kDone_Verb) {
840 switch (verb) {
841 case SkPath::kConic_Verb: {
842 *isLinear = false;
843 if (innerPolygons) {
844 append_point_to_contour(pts[2], contour, alloc);
845 break;
846 }
847 SkScalar weight = iter.conicWeight();
848 const SkPoint* quadPts = converter.computeQuads(pts, weight, toleranceSqd);
849 for (int i = 0; i < converter.countQuads(); ++i) {
850 append_quadratic_to_contour(quadPts, toleranceSqd, contour, alloc);
851 quadPts += 2;
852 }
853 break;
854 }
855 case SkPath::kMove_Verb:
856 if (contour->fHead) {
857 contour++;
858 }
859 append_point_to_contour(pts[0], contour, alloc);
860 break;
861 case SkPath::kLine_Verb: {
862 append_point_to_contour(pts[1], contour, alloc);
863 break;
864 }
865 case SkPath::kQuad_Verb: {
866 *isLinear = false;
867 if (innerPolygons) {
868 append_point_to_contour(pts[2], contour, alloc);
869 break;
870 }
871 append_quadratic_to_contour(pts, toleranceSqd, contour, alloc);
872 break;
873 }
874 case SkPath::kCubic_Verb: {
875 *isLinear = false;
876 if (innerPolygons) {
877 append_point_to_contour(pts[3], contour, alloc);
878 break;
879 }
880 int pointsLeft = GrPathUtils::cubicPointCount(pts, tolerance);
881 generate_cubic_points(pts[0], pts[1], pts[2], pts[3], toleranceSqd, contour,
882 pointsLeft, alloc);
883 break;
884 }
885 case SkPath::kClose_Verb:
886 case SkPath::kDone_Verb:
887 break;
888 }
889 }
890}
891
892inline bool apply_fill_type(SkPathFillType fillType, int winding) {
893 switch (fillType) {
894 case SkPathFillType::kWinding:
895 return winding != 0;
896 case SkPathFillType::kEvenOdd:
897 return (winding & 1) != 0;
898 case SkPathFillType::kInverseWinding:
899 return winding == 1;
900 case SkPathFillType::kInverseEvenOdd:
901 return (winding & 1) == 1;
902 default:
903 SkASSERT(false);
904 return false;
905 }
906}
907
908inline bool apply_fill_type(SkPathFillType fillType, Poly* poly) {
909 return poly && apply_fill_type(fillType, poly->fWinding);
910}
911
912Edge* new_edge(Vertex* prev, Vertex* next, Edge::Type type, Comparator& c, SkArenaAlloc& alloc) {
913 int winding = c.sweep_lt(prev->fPoint, next->fPoint) ? 1 : -1;
914 Vertex* top = winding < 0 ? next : prev;
915 Vertex* bottom = winding < 0 ? prev : next;
916 return alloc.make<Edge>(top, bottom, winding, type);
917}
918
919void remove_edge(Edge* edge, EdgeList* edges) {
920 TESS_LOG("removing edge %g -> %g\n", edge->fTop->fID, edge->fBottom->fID);
921 SkASSERT(edges->contains(edge));
922 edges->remove(edge);
923}
924
925void insert_edge(Edge* edge, Edge* prev, EdgeList* edges) {
926 TESS_LOG("inserting edge %g -> %g\n", edge->fTop->fID, edge->fBottom->fID);
927 SkASSERT(!edges->contains(edge));
928 Edge* next = prev ? prev->fRight : edges->fHead;
929 edges->insert(edge, prev, next);
930}
931
932void find_enclosing_edges(Vertex* v, EdgeList* edges, Edge** left, Edge** right) {
933 if (v->fFirstEdgeAbove && v->fLastEdgeAbove) {
934 *left = v->fFirstEdgeAbove->fLeft;
935 *right = v->fLastEdgeAbove->fRight;
936 return;
937 }
938 Edge* next = nullptr;
939 Edge* prev;
940 for (prev = edges->fTail; prev != nullptr; prev = prev->fLeft) {
941 if (prev->isLeftOf(v)) {
942 break;
943 }
944 next = prev;
945 }
946 *left = prev;
947 *right = next;
948}
949
950void insert_edge_above(Edge* edge, Vertex* v, Comparator& c) {
951 if (edge->fTop->fPoint == edge->fBottom->fPoint ||
952 c.sweep_lt(edge->fBottom->fPoint, edge->fTop->fPoint)) {
953 return;
954 }
955 TESS_LOG("insert edge (%g -> %g) above vertex %g\n",
956 edge->fTop->fID, edge->fBottom->fID, v->fID);
957 Edge* prev = nullptr;
958 Edge* next;
959 for (next = v->fFirstEdgeAbove; next; next = next->fNextEdgeAbove) {
960 if (next->isRightOf(edge->fTop)) {
961 break;
962 }
963 prev = next;
964 }
965 list_insert<Edge, &Edge::fPrevEdgeAbove, &Edge::fNextEdgeAbove>(
966 edge, prev, next, &v->fFirstEdgeAbove, &v->fLastEdgeAbove);
967}
968
969void insert_edge_below(Edge* edge, Vertex* v, Comparator& c) {
970 if (edge->fTop->fPoint == edge->fBottom->fPoint ||
971 c.sweep_lt(edge->fBottom->fPoint, edge->fTop->fPoint)) {
972 return;
973 }
974 TESS_LOG("insert edge (%g -> %g) below vertex %g\n",
975 edge->fTop->fID, edge->fBottom->fID, v->fID);
976 Edge* prev = nullptr;
977 Edge* next;
978 for (next = v->fFirstEdgeBelow; next; next = next->fNextEdgeBelow) {
979 if (next->isRightOf(edge->fBottom)) {
980 break;
981 }
982 prev = next;
983 }
984 list_insert<Edge, &Edge::fPrevEdgeBelow, &Edge::fNextEdgeBelow>(
985 edge, prev, next, &v->fFirstEdgeBelow, &v->fLastEdgeBelow);
986}
987
988void remove_edge_above(Edge* edge) {
989 SkASSERT(edge->fTop && edge->fBottom);
990 TESS_LOG("removing edge (%g -> %g) above vertex %g\n", edge->fTop->fID, edge->fBottom->fID,
991 edge->fBottom->fID);
992 list_remove<Edge, &Edge::fPrevEdgeAbove, &Edge::fNextEdgeAbove>(
993 edge, &edge->fBottom->fFirstEdgeAbove, &edge->fBottom->fLastEdgeAbove);
994}
995
996void remove_edge_below(Edge* edge) {
997 SkASSERT(edge->fTop && edge->fBottom);
998 TESS_LOG("removing edge (%g -> %g) below vertex %g\n",
999 edge->fTop->fID, edge->fBottom->fID, edge->fTop->fID);
1000 list_remove<Edge, &Edge::fPrevEdgeBelow, &Edge::fNextEdgeBelow>(
1001 edge, &edge->fTop->fFirstEdgeBelow, &edge->fTop->fLastEdgeBelow);
1002}
1003
1004void disconnect(Edge* edge)
1005{
1006 remove_edge_above(edge);
1007 remove_edge_below(edge);
1008}
1009
1010void merge_collinear_edges(Edge* edge, EdgeList* activeEdges, Vertex** current, Comparator& c);
1011
1012void rewind(EdgeList* activeEdges, Vertex** current, Vertex* dst, Comparator& c) {
1013 if (!current || *current == dst || c.sweep_lt((*current)->fPoint, dst->fPoint)) {
1014 return;
1015 }
1016 Vertex* v = *current;
1017 TESS_LOG("rewinding active edges from vertex %g to vertex %g\n", v->fID, dst->fID);
1018 while (v != dst) {
1019 v = v->fPrev;
1020 for (Edge* e = v->fFirstEdgeBelow; e; e = e->fNextEdgeBelow) {
1021 remove_edge(e, activeEdges);
1022 }
1023 Edge* leftEdge = v->fLeftEnclosingEdge;
1024 for (Edge* e = v->fFirstEdgeAbove; e; e = e->fNextEdgeAbove) {
1025 insert_edge(e, leftEdge, activeEdges);
1026 leftEdge = e;
1027 Vertex* top = e->fTop;
1028 if (c.sweep_lt(top->fPoint, dst->fPoint) &&
1029 ((top->fLeftEnclosingEdge && !top->fLeftEnclosingEdge->isLeftOf(e->fTop)) ||
1030 (top->fRightEnclosingEdge && !top->fRightEnclosingEdge->isRightOf(e->fTop)))) {
1031 dst = top;
1032 }
1033 }
1034 }
1035 *current = v;
1036}
1037
1038void rewind_if_necessary(Edge* edge, EdgeList* activeEdges, Vertex** current, Comparator& c) {
1039 if (!activeEdges || !current) {
1040 return;
1041 }
1042 Vertex* top = edge->fTop;
1043 Vertex* bottom = edge->fBottom;
1044 if (edge->fLeft) {
1045 Vertex* leftTop = edge->fLeft->fTop;
1046 Vertex* leftBottom = edge->fLeft->fBottom;
1047 if (c.sweep_lt(leftTop->fPoint, top->fPoint) && !edge->fLeft->isLeftOf(top)) {
1048 rewind(activeEdges, current, leftTop, c);
1049 } else if (c.sweep_lt(top->fPoint, leftTop->fPoint) && !edge->isRightOf(leftTop)) {
1050 rewind(activeEdges, current, top, c);
1051 } else if (c.sweep_lt(bottom->fPoint, leftBottom->fPoint) &&
1052 !edge->fLeft->isLeftOf(bottom)) {
1053 rewind(activeEdges, current, leftTop, c);
1054 } else if (c.sweep_lt(leftBottom->fPoint, bottom->fPoint) && !edge->isRightOf(leftBottom)) {
1055 rewind(activeEdges, current, top, c);
1056 }
1057 }
1058 if (edge->fRight) {
1059 Vertex* rightTop = edge->fRight->fTop;
1060 Vertex* rightBottom = edge->fRight->fBottom;
1061 if (c.sweep_lt(rightTop->fPoint, top->fPoint) && !edge->fRight->isRightOf(top)) {
1062 rewind(activeEdges, current, rightTop, c);
1063 } else if (c.sweep_lt(top->fPoint, rightTop->fPoint) && !edge->isLeftOf(rightTop)) {
1064 rewind(activeEdges, current, top, c);
1065 } else if (c.sweep_lt(bottom->fPoint, rightBottom->fPoint) &&
1066 !edge->fRight->isRightOf(bottom)) {
1067 rewind(activeEdges, current, rightTop, c);
1068 } else if (c.sweep_lt(rightBottom->fPoint, bottom->fPoint) &&
1069 !edge->isLeftOf(rightBottom)) {
1070 rewind(activeEdges, current, top, c);
1071 }
1072 }
1073}
1074
1075void set_top(Edge* edge, Vertex* v, EdgeList* activeEdges, Vertex** current, Comparator& c) {
1076 remove_edge_below(edge);
1077 edge->fTop = v;
1078 edge->recompute();
1079 insert_edge_below(edge, v, c);
1080 rewind_if_necessary(edge, activeEdges, current, c);
1081 merge_collinear_edges(edge, activeEdges, current, c);
1082}
1083
1084void set_bottom(Edge* edge, Vertex* v, EdgeList* activeEdges, Vertex** current, Comparator& c) {
1085 remove_edge_above(edge);
1086 edge->fBottom = v;
1087 edge->recompute();
1088 insert_edge_above(edge, v, c);
1089 rewind_if_necessary(edge, activeEdges, current, c);
1090 merge_collinear_edges(edge, activeEdges, current, c);
1091}
1092
1093void merge_edges_above(Edge* edge, Edge* other, EdgeList* activeEdges, Vertex** current,
1094 Comparator& c) {
1095 if (coincident(edge->fTop->fPoint, other->fTop->fPoint)) {
1096 TESS_LOG("merging coincident above edges (%g, %g) -> (%g, %g)\n",
1097 edge->fTop->fPoint.fX, edge->fTop->fPoint.fY,
1098 edge->fBottom->fPoint.fX, edge->fBottom->fPoint.fY);
1099 rewind(activeEdges, current, edge->fTop, c);
1100 other->fWinding += edge->fWinding;
1101 disconnect(edge);
1102 edge->fTop = edge->fBottom = nullptr;
1103 } else if (c.sweep_lt(edge->fTop->fPoint, other->fTop->fPoint)) {
1104 rewind(activeEdges, current, edge->fTop, c);
1105 other->fWinding += edge->fWinding;
1106 set_bottom(edge, other->fTop, activeEdges, current, c);
1107 } else {
1108 rewind(activeEdges, current, other->fTop, c);
1109 edge->fWinding += other->fWinding;
1110 set_bottom(other, edge->fTop, activeEdges, current, c);
1111 }
1112}
1113
1114void merge_edges_below(Edge* edge, Edge* other, EdgeList* activeEdges, Vertex** current,
1115 Comparator& c) {
1116 if (coincident(edge->fBottom->fPoint, other->fBottom->fPoint)) {
1117 TESS_LOG("merging coincident below edges (%g, %g) -> (%g, %g)\n",
1118 edge->fTop->fPoint.fX, edge->fTop->fPoint.fY,
1119 edge->fBottom->fPoint.fX, edge->fBottom->fPoint.fY);
1120 rewind(activeEdges, current, edge->fTop, c);
1121 other->fWinding += edge->fWinding;
1122 disconnect(edge);
1123 edge->fTop = edge->fBottom = nullptr;
1124 } else if (c.sweep_lt(edge->fBottom->fPoint, other->fBottom->fPoint)) {
1125 rewind(activeEdges, current, other->fTop, c);
1126 edge->fWinding += other->fWinding;
1127 set_top(other, edge->fBottom, activeEdges, current, c);
1128 } else {
1129 rewind(activeEdges, current, edge->fTop, c);
1130 other->fWinding += edge->fWinding;
1131 set_top(edge, other->fBottom, activeEdges, current, c);
1132 }
1133}
1134
1135bool top_collinear(Edge* left, Edge* right) {
1136 if (!left || !right) {
1137 return false;
1138 }
1139 return left->fTop->fPoint == right->fTop->fPoint ||
1140 !left->isLeftOf(right->fTop) || !right->isRightOf(left->fTop);
1141}
1142
1143bool bottom_collinear(Edge* left, Edge* right) {
1144 if (!left || !right) {
1145 return false;
1146 }
1147 return left->fBottom->fPoint == right->fBottom->fPoint ||
1148 !left->isLeftOf(right->fBottom) || !right->isRightOf(left->fBottom);
1149}
1150
1151void merge_collinear_edges(Edge* edge, EdgeList* activeEdges, Vertex** current, Comparator& c) {
1152 for (;;) {
1153 if (top_collinear(edge->fPrevEdgeAbove, edge)) {
1154 merge_edges_above(edge->fPrevEdgeAbove, edge, activeEdges, current, c);
1155 } else if (top_collinear(edge, edge->fNextEdgeAbove)) {
1156 merge_edges_above(edge->fNextEdgeAbove, edge, activeEdges, current, c);
1157 } else if (bottom_collinear(edge->fPrevEdgeBelow, edge)) {
1158 merge_edges_below(edge->fPrevEdgeBelow, edge, activeEdges, current, c);
1159 } else if (bottom_collinear(edge, edge->fNextEdgeBelow)) {
1160 merge_edges_below(edge->fNextEdgeBelow, edge, activeEdges, current, c);
1161 } else {
1162 break;
1163 }
1164 }
1165 SkASSERT(!top_collinear(edge->fPrevEdgeAbove, edge));
1166 SkASSERT(!top_collinear(edge, edge->fNextEdgeAbove));
1167 SkASSERT(!bottom_collinear(edge->fPrevEdgeBelow, edge));
1168 SkASSERT(!bottom_collinear(edge, edge->fNextEdgeBelow));
1169}
1170
1171bool split_edge(Edge* edge, Vertex* v, EdgeList* activeEdges, Vertex** current, Comparator& c,
1172 SkArenaAlloc& alloc) {
1173 if (!edge->fTop || !edge->fBottom || v == edge->fTop || v == edge->fBottom) {
1174 return false;
1175 }
1176 TESS_LOG("splitting edge (%g -> %g) at vertex %g (%g, %g)\n",
1177 edge->fTop->fID, edge->fBottom->fID, v->fID, v->fPoint.fX, v->fPoint.fY);
1178 Vertex* top;
1179 Vertex* bottom;
1180 int winding = edge->fWinding;
1181 if (c.sweep_lt(v->fPoint, edge->fTop->fPoint)) {
1182 top = v;
1183 bottom = edge->fTop;
1184 set_top(edge, v, activeEdges, current, c);
1185 } else if (c.sweep_lt(edge->fBottom->fPoint, v->fPoint)) {
1186 top = edge->fBottom;
1187 bottom = v;
1188 set_bottom(edge, v, activeEdges, current, c);
1189 } else {
1190 top = v;
1191 bottom = edge->fBottom;
1192 set_bottom(edge, v, activeEdges, current, c);
1193 }
1194 Edge* newEdge = alloc.make<Edge>(top, bottom, winding, edge->fType);
1195 insert_edge_below(newEdge, top, c);
1196 insert_edge_above(newEdge, bottom, c);
1197 merge_collinear_edges(newEdge, activeEdges, current, c);
1198 return true;
1199}
1200
1201bool intersect_edge_pair(Edge* left, Edge* right, EdgeList* activeEdges, Vertex** current, Comparator& c, SkArenaAlloc& alloc) {
1202 if (!left->fTop || !left->fBottom || !right->fTop || !right->fBottom) {
1203 return false;
1204 }
1205 if (left->fTop == right->fTop || left->fBottom == right->fBottom) {
1206 return false;
1207 }
1208 if (c.sweep_lt(left->fTop->fPoint, right->fTop->fPoint)) {
1209 if (!left->isLeftOf(right->fTop)) {
1210 rewind(activeEdges, current, right->fTop, c);
1211 return split_edge(left, right->fTop, activeEdges, current, c, alloc);
1212 }
1213 } else {
1214 if (!right->isRightOf(left->fTop)) {
1215 rewind(activeEdges, current, left->fTop, c);
1216 return split_edge(right, left->fTop, activeEdges, current, c, alloc);
1217 }
1218 }
1219 if (c.sweep_lt(right->fBottom->fPoint, left->fBottom->fPoint)) {
1220 if (!left->isLeftOf(right->fBottom)) {
1221 rewind(activeEdges, current, right->fBottom, c);
1222 return split_edge(left, right->fBottom, activeEdges, current, c, alloc);
1223 }
1224 } else {
1225 if (!right->isRightOf(left->fBottom)) {
1226 rewind(activeEdges, current, left->fBottom, c);
1227 return split_edge(right, left->fBottom, activeEdges, current, c, alloc);
1228 }
1229 }
1230 return false;
1231}
1232
1233Edge* connect(Vertex* prev, Vertex* next, Edge::Type type, Comparator& c, SkArenaAlloc& alloc,
1234 int winding_scale = 1) {
1235 if (!prev || !next || prev->fPoint == next->fPoint) {
1236 return nullptr;
1237 }
1238 Edge* edge = new_edge(prev, next, type, c, alloc);
1239 insert_edge_below(edge, edge->fTop, c);
1240 insert_edge_above(edge, edge->fBottom, c);
1241 edge->fWinding *= winding_scale;
1242 merge_collinear_edges(edge, nullptr, nullptr, c);
1243 return edge;
1244}
1245
1246void merge_vertices(Vertex* src, Vertex* dst, VertexList* mesh, Comparator& c,
1247 SkArenaAlloc& alloc) {
1248 TESS_LOG("found coincident verts at %g, %g; merging %g into %g\n",
1249 src->fPoint.fX, src->fPoint.fY, src->fID, dst->fID);
1250 dst->fAlpha = std::max(src->fAlpha, dst->fAlpha);
1251 if (src->fPartner) {
1252 src->fPartner->fPartner = dst;
1253 }
1254 while (Edge* edge = src->fFirstEdgeAbove) {
1255 set_bottom(edge, dst, nullptr, nullptr, c);
1256 }
1257 while (Edge* edge = src->fFirstEdgeBelow) {
1258 set_top(edge, dst, nullptr, nullptr, c);
1259 }
1260 mesh->remove(src);
1261 dst->fSynthetic = true;
1262}
1263
1264Vertex* create_sorted_vertex(const SkPoint& p, uint8_t alpha, VertexList* mesh,
1265 Vertex* reference, Comparator& c, SkArenaAlloc& alloc) {
1266 Vertex* prevV = reference;
1267 while (prevV && c.sweep_lt(p, prevV->fPoint)) {
1268 prevV = prevV->fPrev;
1269 }
1270 Vertex* nextV = prevV ? prevV->fNext : mesh->fHead;
1271 while (nextV && c.sweep_lt(nextV->fPoint, p)) {
1272 prevV = nextV;
1273 nextV = nextV->fNext;
1274 }
1275 Vertex* v;
1276 if (prevV && coincident(prevV->fPoint, p)) {
1277 v = prevV;
1278 } else if (nextV && coincident(nextV->fPoint, p)) {
1279 v = nextV;
1280 } else {
1281 v = alloc.make<Vertex>(p, alpha);
1282#if LOGGING_ENABLED
1283 if (!prevV) {
1284 v->fID = mesh->fHead->fID - 1.0f;
1285 } else if (!nextV) {
1286 v->fID = mesh->fTail->fID + 1.0f;
1287 } else {
1288 v->fID = (prevV->fID + nextV->fID) * 0.5f;
1289 }
1290#endif
1291 mesh->insert(v, prevV, nextV);
1292 }
1293 return v;
1294}
1295
1296// If an edge's top and bottom points differ only by 1/2 machine epsilon in the primary
1297// sort criterion, it may not be possible to split correctly, since there is no point which is
1298// below the top and above the bottom. This function detects that case.
1299bool nearly_flat(Comparator& c, Edge* edge) {
1300 SkPoint diff = edge->fBottom->fPoint - edge->fTop->fPoint;
1301 float primaryDiff = c.fDirection == Comparator::Direction::kHorizontal ? diff.fX : diff.fY;
1302 return fabs(primaryDiff) < std::numeric_limits<float>::epsilon() && primaryDiff != 0.0f;
1303}
1304
1305SkPoint clamp(SkPoint p, SkPoint min, SkPoint max, Comparator& c) {
1306 if (c.sweep_lt(p, min)) {
1307 return min;
1308 } else if (c.sweep_lt(max, p)) {
1309 return max;
1310 } else {
1311 return p;
1312 }
1313}
1314
1315void compute_bisector(Edge* edge1, Edge* edge2, Vertex* v, SkArenaAlloc& alloc) {
1316 Line line1 = edge1->fLine;
1317 Line line2 = edge2->fLine;
1318 line1.normalize();
1319 line2.normalize();
1320 double cosAngle = line1.fA * line2.fA + line1.fB * line2.fB;
1321 if (cosAngle > 0.999) {
1322 return;
1323 }
1324 line1.fC += edge1->fWinding > 0 ? -1 : 1;
1325 line2.fC += edge2->fWinding > 0 ? -1 : 1;
1326 SkPoint p;
1327 if (line1.intersect(line2, &p)) {
1328 uint8_t alpha = edge1->fType == Edge::Type::kOuter ? 255 : 0;
1329 v->fPartner = alloc.make<Vertex>(p, alpha);
1330 TESS_LOG("computed bisector (%g,%g) alpha %d for vertex %g\n", p.fX, p.fY, alpha, v->fID);
1331 }
1332}
1333
1334bool check_for_intersection(Edge* left, Edge* right, EdgeList* activeEdges, Vertex** current,
1335 VertexList* mesh, Comparator& c, SkArenaAlloc& alloc) {
1336 if (!left || !right) {
1337 return false;
1338 }
1339 SkPoint p;
1340 uint8_t alpha;
1341 if (left->intersect(*right, &p, &alpha) && p.isFinite()) {
1342 Vertex* v;
1343 TESS_LOG("found intersection, pt is %g, %g\n", p.fX, p.fY);
1344 Vertex* top = *current;
1345 // If the intersection point is above the current vertex, rewind to the vertex above the
1346 // intersection.
1347 while (top && c.sweep_lt(p, top->fPoint)) {
1348 top = top->fPrev;
1349 }
1350 if (!nearly_flat(c, left)) {
1351 p = clamp(p, left->fTop->fPoint, left->fBottom->fPoint, c);
1352 }
1353 if (!nearly_flat(c, right)) {
1354 p = clamp(p, right->fTop->fPoint, right->fBottom->fPoint, c);
1355 }
1356 if (p == left->fTop->fPoint) {
1357 v = left->fTop;
1358 } else if (p == left->fBottom->fPoint) {
1359 v = left->fBottom;
1360 } else if (p == right->fTop->fPoint) {
1361 v = right->fTop;
1362 } else if (p == right->fBottom->fPoint) {
1363 v = right->fBottom;
1364 } else {
1365 v = create_sorted_vertex(p, alpha, mesh, top, c, alloc);
1366 if (left->fTop->fPartner) {
1367 v->fSynthetic = true;
1368 compute_bisector(left, right, v, alloc);
1369 }
1370 }
1371 rewind(activeEdges, current, top ? top : v, c);
1372 split_edge(left, v, activeEdges, current, c, alloc);
1373 split_edge(right, v, activeEdges, current, c, alloc);
1374 v->fAlpha = std::max(v->fAlpha, alpha);
1375 return true;
1376 }
1377 return intersect_edge_pair(left, right, activeEdges, current, c, alloc);
1378}
1379
1380void sanitize_contours(VertexList* contours, int contourCnt, Mode mode) {
1381 bool approximate = (Mode::kEdgeAntialias == mode);
1382 bool removeCollinearVertices = (Mode::kSimpleInnerPolygons != mode);
1383 for (VertexList* contour = contours; contourCnt > 0; --contourCnt, ++contour) {
1384 SkASSERT(contour->fHead);
1385 Vertex* prev = contour->fTail;
1386 if (approximate) {
1387 round(&prev->fPoint);
1388 }
1389 for (Vertex* v = contour->fHead; v;) {
1390 if (approximate) {
1391 round(&v->fPoint);
1392 }
1393 Vertex* next = v->fNext;
1394 Vertex* nextWrap = next ? next : contour->fHead;
1395 if (coincident(prev->fPoint, v->fPoint)) {
1396 TESS_LOG("vertex %g,%g coincident; removing\n", v->fPoint.fX, v->fPoint.fY);
1397 contour->remove(v);
1398 } else if (!v->fPoint.isFinite()) {
1399 TESS_LOG("vertex %g,%g non-finite; removing\n", v->fPoint.fX, v->fPoint.fY);
1400 contour->remove(v);
1401 } else if (removeCollinearVertices &&
1402 Line(prev->fPoint, nextWrap->fPoint).dist(v->fPoint) == 0.0) {
1403 TESS_LOG("vertex %g,%g collinear; removing\n", v->fPoint.fX, v->fPoint.fY);
1404 contour->remove(v);
1405 } else {
1406 prev = v;
1407 }
1408 v = next;
1409 }
1410 }
1411}
1412
1413bool merge_coincident_vertices(VertexList* mesh, Comparator& c, SkArenaAlloc& alloc) {
1414 if (!mesh->fHead) {
1415 return false;
1416 }
1417 bool merged = false;
1418 for (Vertex* v = mesh->fHead->fNext; v;) {
1419 Vertex* next = v->fNext;
1420 if (c.sweep_lt(v->fPoint, v->fPrev->fPoint)) {
1421 v->fPoint = v->fPrev->fPoint;
1422 }
1423 if (coincident(v->fPrev->fPoint, v->fPoint)) {
1424 merge_vertices(v, v->fPrev, mesh, c, alloc);
1425 merged = true;
1426 }
1427 v = next;
1428 }
1429 return merged;
1430}
1431
1432// Stage 2: convert the contours to a mesh of edges connecting the vertices.
1433
1434void build_edges(VertexList* contours, int contourCnt, VertexList* mesh, Comparator& c,
1435 SkArenaAlloc& alloc) {
1436 for (VertexList* contour = contours; contourCnt > 0; --contourCnt, ++contour) {
1437 Vertex* prev = contour->fTail;
1438 for (Vertex* v = contour->fHead; v;) {
1439 Vertex* next = v->fNext;
1440 connect(prev, v, Edge::Type::kInner, c, alloc);
1441 mesh->append(v);
1442 prev = v;
1443 v = next;
1444 }
1445 }
1446}
1447
1448void connect_partners(VertexList* mesh, Comparator& c, SkArenaAlloc& alloc) {
1449 for (Vertex* outer = mesh->fHead; outer; outer = outer->fNext) {
1450 if (Vertex* inner = outer->fPartner) {
1451 if ((inner->fPrev || inner->fNext) && (outer->fPrev || outer->fNext)) {
1452 // Connector edges get zero winding, since they're only structural (i.e., to ensure
1453 // no 0-0-0 alpha triangles are produced), and shouldn't affect the poly winding
1454 // number.
1455 connect(outer, inner, Edge::Type::kConnector, c, alloc, 0);
1456 inner->fPartner = outer->fPartner = nullptr;
1457 }
1458 }
1459 }
1460}
1461
1462template <CompareFunc sweep_lt>
1463void sorted_merge(VertexList* front, VertexList* back, VertexList* result) {
1464 Vertex* a = front->fHead;
1465 Vertex* b = back->fHead;
1466 while (a && b) {
1467 if (sweep_lt(a->fPoint, b->fPoint)) {
1468 front->remove(a);
1469 result->append(a);
1470 a = front->fHead;
1471 } else {
1472 back->remove(b);
1473 result->append(b);
1474 b = back->fHead;
1475 }
1476 }
1477 result->append(*front);
1478 result->append(*back);
1479}
1480
1481void sorted_merge(VertexList* front, VertexList* back, VertexList* result, Comparator& c) {
1482 if (c.fDirection == Comparator::Direction::kHorizontal) {
1483 sorted_merge<sweep_lt_horiz>(front, back, result);
1484 } else {
1485 sorted_merge<sweep_lt_vert>(front, back, result);
1486 }
1487#if LOGGING_ENABLED
1488 float id = 0.0f;
1489 for (Vertex* v = result->fHead; v; v = v->fNext) {
1490 v->fID = id++;
1491 }
1492#endif
1493}
1494
1495// Stage 3: sort the vertices by increasing sweep direction.
1496
1497template <CompareFunc sweep_lt>
1498void merge_sort(VertexList* vertices) {
1499 Vertex* slow = vertices->fHead;
1500 if (!slow) {
1501 return;
1502 }
1503 Vertex* fast = slow->fNext;
1504 if (!fast) {
1505 return;
1506 }
1507 do {
1508 fast = fast->fNext;
1509 if (fast) {
1510 fast = fast->fNext;
1511 slow = slow->fNext;
1512 }
1513 } while (fast);
1514 VertexList front(vertices->fHead, slow);
1515 VertexList back(slow->fNext, vertices->fTail);
1516 front.fTail->fNext = back.fHead->fPrev = nullptr;
1517
1518 merge_sort<sweep_lt>(&front);
1519 merge_sort<sweep_lt>(&back);
1520
1521 vertices->fHead = vertices->fTail = nullptr;
1522 sorted_merge<sweep_lt>(&front, &back, vertices);
1523}
1524
1525void dump_mesh(const VertexList& mesh) {
1526#if LOGGING_ENABLED
1527 for (Vertex* v = mesh.fHead; v; v = v->fNext) {
1528 TESS_LOG("vertex %g (%g, %g) alpha %d", v->fID, v->fPoint.fX, v->fPoint.fY, v->fAlpha);
1529 if (Vertex* p = v->fPartner) {
1530 TESS_LOG(", partner %g (%g, %g) alpha %d\n",
1531 p->fID, p->fPoint.fX, p->fPoint.fY, p->fAlpha);
1532 } else {
1533 TESS_LOG(", null partner\n");
1534 }
1535 for (Edge* e = v->fFirstEdgeAbove; e; e = e->fNextEdgeAbove) {
1536 TESS_LOG(" edge %g -> %g, winding %d\n", e->fTop->fID, e->fBottom->fID, e->fWinding);
1537 }
1538 for (Edge* e = v->fFirstEdgeBelow; e; e = e->fNextEdgeBelow) {
1539 TESS_LOG(" edge %g -> %g, winding %d\n", e->fTop->fID, e->fBottom->fID, e->fWinding);
1540 }
1541 }
1542#endif
1543}
1544
1545void dump_skel(const SSEdgeList& ssEdges) {
1546#if LOGGING_ENABLED
1547 for (SSEdge* edge : ssEdges) {
1548 if (edge->fEdge) {
1549 TESS_LOG("skel edge %g -> %g",
1550 edge->fPrev->fVertex->fID,
1551 edge->fNext->fVertex->fID);
1552 if (edge->fEdge->fTop && edge->fEdge->fBottom) {
1553 TESS_LOG(" (original %g -> %g)\n",
1554 edge->fEdge->fTop->fID,
1555 edge->fEdge->fBottom->fID);
1556 } else {
1557 TESS_LOG("\n");
1558 }
1559 }
1560 }
1561#endif
1562}
1563
1564#ifdef SK_DEBUG
1565void validate_edge_pair(Edge* left, Edge* right, Comparator& c) {
1566 if (!left || !right) {
1567 return;
1568 }
1569 if (left->fTop == right->fTop) {
1570 SkASSERT(left->isLeftOf(right->fBottom));
1571 SkASSERT(right->isRightOf(left->fBottom));
1572 } else if (c.sweep_lt(left->fTop->fPoint, right->fTop->fPoint)) {
1573 SkASSERT(left->isLeftOf(right->fTop));
1574 } else {
1575 SkASSERT(right->isRightOf(left->fTop));
1576 }
1577 if (left->fBottom == right->fBottom) {
1578 SkASSERT(left->isLeftOf(right->fTop));
1579 SkASSERT(right->isRightOf(left->fTop));
1580 } else if (c.sweep_lt(right->fBottom->fPoint, left->fBottom->fPoint)) {
1581 SkASSERT(left->isLeftOf(right->fBottom));
1582 } else {
1583 SkASSERT(right->isRightOf(left->fBottom));
1584 }
1585}
1586
1587void validate_edge_list(EdgeList* edges, Comparator& c) {
1588 Edge* left = edges->fHead;
1589 if (!left) {
1590 return;
1591 }
1592 for (Edge* right = left->fRight; right; right = right->fRight) {
1593 validate_edge_pair(left, right, c);
1594 left = right;
1595 }
1596}
1597#endif
1598
1599// Stage 4: Simplify the mesh by inserting new vertices at intersecting edges.
1600
1601bool connected(Vertex* v) {
1602 return v->fFirstEdgeAbove || v->fFirstEdgeBelow;
1603}
1604
1605enum class SimplifyResult {
1606 kAlreadySimple,
1607 kFoundSelfIntersection,
1608 kAbort
1609};
1610
1611SimplifyResult simplify(Mode mode, VertexList* mesh, Comparator& c, SkArenaAlloc& alloc) {
1612 TESS_LOG("simplifying complex polygons\n");
1613 EdgeList activeEdges;
1614 auto result = SimplifyResult::kAlreadySimple;
1615 for (Vertex* v = mesh->fHead; v != nullptr; v = v->fNext) {
1616 if (!connected(v)) {
1617 continue;
1618 }
1619 Edge* leftEnclosingEdge;
1620 Edge* rightEnclosingEdge;
1621 bool restartChecks;
1622 do {
1623 TESS_LOG("\nvertex %g: (%g,%g), alpha %d\n",
1624 v->fID, v->fPoint.fX, v->fPoint.fY, v->fAlpha);
1625 restartChecks = false;
1626 find_enclosing_edges(v, &activeEdges, &leftEnclosingEdge, &rightEnclosingEdge);
1627 v->fLeftEnclosingEdge = leftEnclosingEdge;
1628 v->fRightEnclosingEdge = rightEnclosingEdge;
1629 if (v->fFirstEdgeBelow) {
1630 for (Edge* edge = v->fFirstEdgeBelow; edge; edge = edge->fNextEdgeBelow) {
1631 if (check_for_intersection(
1632 leftEnclosingEdge, edge, &activeEdges, &v, mesh, c, alloc) ||
1633 check_for_intersection(
1634 edge, rightEnclosingEdge, &activeEdges, &v, mesh, c, alloc)) {
1635 if (Mode::kSimpleInnerPolygons == mode) {
1636 return SimplifyResult::kAbort;
1637 }
1638 result = SimplifyResult::kFoundSelfIntersection;
1639 restartChecks = true;
1640 break;
1641 }
1642 }
1643 } else {
1644 if (check_for_intersection(leftEnclosingEdge, rightEnclosingEdge,
1645 &activeEdges, &v, mesh, c, alloc)) {
1646 if (Mode::kSimpleInnerPolygons == mode) {
1647 return SimplifyResult::kAbort;
1648 }
1649 result = SimplifyResult::kFoundSelfIntersection;
1650 restartChecks = true;
1651 }
1652
1653 }
1654 } while (restartChecks);
1655#ifdef SK_DEBUG
1656 validate_edge_list(&activeEdges, c);
1657#endif
1658 for (Edge* e = v->fFirstEdgeAbove; e; e = e->fNextEdgeAbove) {
1659 remove_edge(e, &activeEdges);
1660 }
1661 Edge* leftEdge = leftEnclosingEdge;
1662 for (Edge* e = v->fFirstEdgeBelow; e; e = e->fNextEdgeBelow) {
1663 insert_edge(e, leftEdge, &activeEdges);
1664 leftEdge = e;
1665 }
1666 }
1667 SkASSERT(!activeEdges.fHead && !activeEdges.fTail);
1668 return result;
1669}
1670
1671// Stage 5: Tessellate the simplified mesh into monotone polygons.
1672
1673Poly* tessellate(SkPathFillType fillType, Mode mode, const VertexList& vertices,
1674 SkArenaAlloc& alloc) {
1675 TESS_LOG("\ntessellating simple polygons\n");
1676 int maxWindMagnitude = std::numeric_limits<int>::max();
1677 if (Mode::kSimpleInnerPolygons == mode && !SkPathFillType_IsEvenOdd(fillType)) {
1678 maxWindMagnitude = 1;
1679 }
1680 EdgeList activeEdges;
1681 Poly* polys = nullptr;
1682 for (Vertex* v = vertices.fHead; v != nullptr; v = v->fNext) {
1683 if (!connected(v)) {
1684 continue;
1685 }
1686#if LOGGING_ENABLED
1687 TESS_LOG("\nvertex %g: (%g,%g), alpha %d\n", v->fID, v->fPoint.fX, v->fPoint.fY, v->fAlpha);
1688#endif
1689 Edge* leftEnclosingEdge;
1690 Edge* rightEnclosingEdge;
1691 find_enclosing_edges(v, &activeEdges, &leftEnclosingEdge, &rightEnclosingEdge);
1692 Poly* leftPoly;
1693 Poly* rightPoly;
1694 if (v->fFirstEdgeAbove) {
1695 leftPoly = v->fFirstEdgeAbove->fLeftPoly;
1696 rightPoly = v->fLastEdgeAbove->fRightPoly;
1697 } else {
1698 leftPoly = leftEnclosingEdge ? leftEnclosingEdge->fRightPoly : nullptr;
1699 rightPoly = rightEnclosingEdge ? rightEnclosingEdge->fLeftPoly : nullptr;
1700 }
1701#if LOGGING_ENABLED
1702 TESS_LOG("edges above:\n");
1703 for (Edge* e = v->fFirstEdgeAbove; e; e = e->fNextEdgeAbove) {
1704 TESS_LOG("%g -> %g, lpoly %d, rpoly %d\n",
1705 e->fTop->fID, e->fBottom->fID,
1706 e->fLeftPoly ? e->fLeftPoly->fID : -1,
1707 e->fRightPoly ? e->fRightPoly->fID : -1);
1708 }
1709 TESS_LOG("edges below:\n");
1710 for (Edge* e = v->fFirstEdgeBelow; e; e = e->fNextEdgeBelow) {
1711 TESS_LOG("%g -> %g, lpoly %d, rpoly %d\n",
1712 e->fTop->fID, e->fBottom->fID,
1713 e->fLeftPoly ? e->fLeftPoly->fID : -1,
1714 e->fRightPoly ? e->fRightPoly->fID : -1);
1715 }
1716#endif
1717 if (v->fFirstEdgeAbove) {
1718 if (leftPoly) {
1719 leftPoly = leftPoly->addEdge(v->fFirstEdgeAbove, Poly::kRight_Side, alloc);
1720 }
1721 if (rightPoly) {
1722 rightPoly = rightPoly->addEdge(v->fLastEdgeAbove, Poly::kLeft_Side, alloc);
1723 }
1724 for (Edge* e = v->fFirstEdgeAbove; e != v->fLastEdgeAbove; e = e->fNextEdgeAbove) {
1725 Edge* rightEdge = e->fNextEdgeAbove;
1726 remove_edge(e, &activeEdges);
1727 if (e->fRightPoly) {
1728 e->fRightPoly->addEdge(e, Poly::kLeft_Side, alloc);
1729 }
1730 if (rightEdge->fLeftPoly && rightEdge->fLeftPoly != e->fRightPoly) {
1731 rightEdge->fLeftPoly->addEdge(e, Poly::kRight_Side, alloc);
1732 }
1733 }
1734 remove_edge(v->fLastEdgeAbove, &activeEdges);
1735 if (!v->fFirstEdgeBelow) {
1736 if (leftPoly && rightPoly && leftPoly != rightPoly) {
1737 SkASSERT(leftPoly->fPartner == nullptr && rightPoly->fPartner == nullptr);
1738 rightPoly->fPartner = leftPoly;
1739 leftPoly->fPartner = rightPoly;
1740 }
1741 }
1742 }
1743 if (v->fFirstEdgeBelow) {
1744 if (!v->fFirstEdgeAbove) {
1745 if (leftPoly && rightPoly) {
1746 if (leftPoly == rightPoly) {
1747 if (leftPoly->fTail && leftPoly->fTail->fSide == Poly::kLeft_Side) {
1748 leftPoly = new_poly(&polys, leftPoly->lastVertex(),
1749 leftPoly->fWinding, alloc);
1750 leftEnclosingEdge->fRightPoly = leftPoly;
1751 } else {
1752 rightPoly = new_poly(&polys, rightPoly->lastVertex(),
1753 rightPoly->fWinding, alloc);
1754 rightEnclosingEdge->fLeftPoly = rightPoly;
1755 }
1756 }
1757 Edge* join = alloc.make<Edge>(leftPoly->lastVertex(), v, 1, Edge::Type::kInner);
1758 leftPoly = leftPoly->addEdge(join, Poly::kRight_Side, alloc);
1759 rightPoly = rightPoly->addEdge(join, Poly::kLeft_Side, alloc);
1760 }
1761 }
1762 Edge* leftEdge = v->fFirstEdgeBelow;
1763 leftEdge->fLeftPoly = leftPoly;
1764 insert_edge(leftEdge, leftEnclosingEdge, &activeEdges);
1765 for (Edge* rightEdge = leftEdge->fNextEdgeBelow; rightEdge;
1766 rightEdge = rightEdge->fNextEdgeBelow) {
1767 insert_edge(rightEdge, leftEdge, &activeEdges);
1768 int winding = leftEdge->fLeftPoly ? leftEdge->fLeftPoly->fWinding : 0;
1769 winding += leftEdge->fWinding;
1770 if (winding != 0) {
1771 if (abs(winding) > maxWindMagnitude) {
1772 return nullptr; // We can't have weighted wind in kSimpleInnerPolygons mode
1773 }
1774 Poly* poly = new_poly(&polys, v, winding, alloc);
1775 leftEdge->fRightPoly = rightEdge->fLeftPoly = poly;
1776 }
1777 leftEdge = rightEdge;
1778 }
1779 v->fLastEdgeBelow->fRightPoly = rightPoly;
1780 }
1781#if LOGGING_ENABLED
1782 TESS_LOG("\nactive edges:\n");
1783 for (Edge* e = activeEdges.fHead; e != nullptr; e = e->fRight) {
1784 TESS_LOG("%g -> %g, lpoly %d, rpoly %d\n",
1785 e->fTop->fID, e->fBottom->fID,
1786 e->fLeftPoly ? e->fLeftPoly->fID : -1,
1787 e->fRightPoly ? e->fRightPoly->fID : -1);
1788 }
1789#endif
1790 }
1791 return polys;
1792}
1793
1794void remove_non_boundary_edges(const VertexList& mesh, SkPathFillType fillType,
1795 SkArenaAlloc& alloc) {
1796 TESS_LOG("removing non-boundary edges\n");
1797 EdgeList activeEdges;
1798 for (Vertex* v = mesh.fHead; v != nullptr; v = v->fNext) {
1799 if (!connected(v)) {
1800 continue;
1801 }
1802 Edge* leftEnclosingEdge;
1803 Edge* rightEnclosingEdge;
1804 find_enclosing_edges(v, &activeEdges, &leftEnclosingEdge, &rightEnclosingEdge);
1805 bool prevFilled = leftEnclosingEdge &&
1806 apply_fill_type(fillType, leftEnclosingEdge->fWinding);
1807 for (Edge* e = v->fFirstEdgeAbove; e;) {
1808 Edge* next = e->fNextEdgeAbove;
1809 remove_edge(e, &activeEdges);
1810 bool filled = apply_fill_type(fillType, e->fWinding);
1811 if (filled == prevFilled) {
1812 disconnect(e);
1813 }
1814 prevFilled = filled;
1815 e = next;
1816 }
1817 Edge* prev = leftEnclosingEdge;
1818 for (Edge* e = v->fFirstEdgeBelow; e; e = e->fNextEdgeBelow) {
1819 if (prev) {
1820 e->fWinding += prev->fWinding;
1821 }
1822 insert_edge(e, prev, &activeEdges);
1823 prev = e;
1824 }
1825 }
1826}
1827
1828// Note: this is the normal to the edge, but not necessarily unit length.
1829void get_edge_normal(const Edge* e, SkVector* normal) {
1830 normal->set(SkDoubleToScalar(e->fLine.fA),
1831 SkDoubleToScalar(e->fLine.fB));
1832}
1833
1834// Stage 5c: detect and remove "pointy" vertices whose edge normals point in opposite directions
1835// and whose adjacent vertices are less than a quarter pixel from an edge. These are guaranteed to
1836// invert on stroking.
1837
1838void simplify_boundary(EdgeList* boundary, Comparator& c, SkArenaAlloc& alloc) {
1839 Edge* prevEdge = boundary->fTail;
1840 SkVector prevNormal;
1841 get_edge_normal(prevEdge, &prevNormal);
1842 for (Edge* e = boundary->fHead; e != nullptr;) {
1843 Vertex* prev = prevEdge->fWinding == 1 ? prevEdge->fTop : prevEdge->fBottom;
1844 Vertex* next = e->fWinding == 1 ? e->fBottom : e->fTop;
1845 double distPrev = e->dist(prev->fPoint);
1846 double distNext = prevEdge->dist(next->fPoint);
1847 SkVector normal;
1848 get_edge_normal(e, &normal);
1849 constexpr double kQuarterPixelSq = 0.25f * 0.25f;
1850 if (prev == next) {
1851 remove_edge(prevEdge, boundary);
1852 remove_edge(e, boundary);
1853 prevEdge = boundary->fTail;
1854 e = boundary->fHead;
1855 if (prevEdge) {
1856 get_edge_normal(prevEdge, &prevNormal);
1857 }
1858 } else if (prevNormal.dot(normal) < 0.0 &&
1859 (distPrev * distPrev <= kQuarterPixelSq || distNext * distNext <= kQuarterPixelSq)) {
1860 Edge* join = new_edge(prev, next, Edge::Type::kInner, c, alloc);
1861 if (prev->fPoint != next->fPoint) {
1862 join->fLine.normalize();
1863 join->fLine = join->fLine * join->fWinding;
1864 }
1865 insert_edge(join, e, boundary);
1866 remove_edge(prevEdge, boundary);
1867 remove_edge(e, boundary);
1868 if (join->fLeft && join->fRight) {
1869 prevEdge = join->fLeft;
1870 e = join;
1871 } else {
1872 prevEdge = boundary->fTail;
1873 e = boundary->fHead; // join->fLeft ? join->fLeft : join;
1874 }
1875 get_edge_normal(prevEdge, &prevNormal);
1876 } else {
1877 prevEdge = e;
1878 prevNormal = normal;
1879 e = e->fRight;
1880 }
1881 }
1882}
1883
1884void ss_connect(Vertex* v, Vertex* dest, Comparator& c, SkArenaAlloc& alloc) {
1885 if (v == dest) {
1886 return;
1887 }
1888 TESS_LOG("ss_connecting vertex %g to vertex %g\n", v->fID, dest->fID);
1889 if (v->fSynthetic) {
1890 connect(v, dest, Edge::Type::kConnector, c, alloc, 0);
1891 } else if (v->fPartner) {
1892 TESS_LOG("setting %g's partner to %g ", v->fPartner->fID, dest->fID);
1893 TESS_LOG("and %g's partner to null\n", v->fID);
1894 v->fPartner->fPartner = dest;
1895 v->fPartner = nullptr;
1896 }
1897}
1898
1899void Event::apply(VertexList* mesh, Comparator& c, EventList* events, SkArenaAlloc& alloc) {
1900 if (!fEdge) {
1901 return;
1902 }
1903 Vertex* prev = fEdge->fPrev->fVertex;
1904 Vertex* next = fEdge->fNext->fVertex;
1905 SSEdge* prevEdge = fEdge->fPrev->fPrev;
1906 SSEdge* nextEdge = fEdge->fNext->fNext;
1907 if (!prevEdge || !nextEdge || !prevEdge->fEdge || !nextEdge->fEdge) {
1908 return;
1909 }
1910 Vertex* dest = create_sorted_vertex(fPoint, fAlpha, mesh, prev, c, alloc);
1911 dest->fSynthetic = true;
1912 SSVertex* ssv = alloc.make<SSVertex>(dest);
1913 TESS_LOG("collapsing %g, %g (original edge %g -> %g) to %g (%g, %g) alpha %d\n",
1914 prev->fID, next->fID, fEdge->fEdge->fTop->fID, fEdge->fEdge->fBottom->fID, dest->fID,
1915 fPoint.fX, fPoint.fY, fAlpha);
1916 fEdge->fEdge = nullptr;
1917
1918 ss_connect(prev, dest, c, alloc);
1919 ss_connect(next, dest, c, alloc);
1920
1921 prevEdge->fNext = nextEdge->fPrev = ssv;
1922 ssv->fPrev = prevEdge;
1923 ssv->fNext = nextEdge;
1924 if (!prevEdge->fEdge || !nextEdge->fEdge) {
1925 return;
1926 }
1927 if (prevEdge->fEvent) {
1928 prevEdge->fEvent->fEdge = nullptr;
1929 }
1930 if (nextEdge->fEvent) {
1931 nextEdge->fEvent->fEdge = nullptr;
1932 }
1933 if (prevEdge->fPrev == nextEdge->fNext) {
1934 ss_connect(prevEdge->fPrev->fVertex, dest, c, alloc);
1935 prevEdge->fEdge = nextEdge->fEdge = nullptr;
1936 } else {
1937 compute_bisector(prevEdge->fEdge, nextEdge->fEdge, dest, alloc);
1938 SkASSERT(prevEdge != fEdge && nextEdge != fEdge);
1939 if (dest->fPartner) {
1940 create_event(prevEdge, events, alloc);
1941 create_event(nextEdge, events, alloc);
1942 } else {
1943 create_event(prevEdge, prevEdge->fPrev->fVertex, nextEdge, dest, events, c, alloc);
1944 create_event(nextEdge, nextEdge->fNext->fVertex, prevEdge, dest, events, c, alloc);
1945 }
1946 }
1947}
1948
1949bool is_overlap_edge(Edge* e) {
1950 if (e->fType == Edge::Type::kOuter) {
1951 return e->fWinding != 0 && e->fWinding != 1;
1952 } else if (e->fType == Edge::Type::kInner) {
1953 return e->fWinding != 0 && e->fWinding != -2;
1954 } else {
1955 return false;
1956 }
1957}
1958
1959// This is a stripped-down version of tessellate() which computes edges which
1960// join two filled regions, which represent overlap regions, and collapses them.
1961bool collapse_overlap_regions(VertexList* mesh, Comparator& c, SkArenaAlloc& alloc,
1962 EventComparator comp) {
1963 TESS_LOG("\nfinding overlap regions\n");
1964 EdgeList activeEdges;
1965 EventList events(comp);
1966 SSVertexMap ssVertices;
1967 SSEdgeList ssEdges;
1968 for (Vertex* v = mesh->fHead; v != nullptr; v = v->fNext) {
1969 if (!connected(v)) {
1970 continue;
1971 }
1972 Edge* leftEnclosingEdge;
1973 Edge* rightEnclosingEdge;
1974 find_enclosing_edges(v, &activeEdges, &leftEnclosingEdge, &rightEnclosingEdge);
1975 for (Edge* e = v->fLastEdgeAbove; e && e != leftEnclosingEdge;) {
1976 Edge* prev = e->fPrevEdgeAbove ? e->fPrevEdgeAbove : leftEnclosingEdge;
1977 remove_edge(e, &activeEdges);
1978 bool leftOverlap = prev && is_overlap_edge(prev);
1979 bool rightOverlap = is_overlap_edge(e);
1980 bool isOuterBoundary = e->fType == Edge::Type::kOuter &&
1981 (!prev || prev->fWinding == 0 || e->fWinding == 0);
1982 if (prev) {
1983 e->fWinding -= prev->fWinding;
1984 }
1985 if (leftOverlap && rightOverlap) {
1986 TESS_LOG("found interior overlap edge %g -> %g, disconnecting\n",
1987 e->fTop->fID, e->fBottom->fID);
1988 disconnect(e);
1989 } else if (leftOverlap || rightOverlap) {
1990 TESS_LOG("found overlap edge %g -> %g%s\n",
1991 e->fTop->fID, e->fBottom->fID,
1992 isOuterBoundary ? ", is outer boundary" : "");
1993 Vertex* prevVertex = e->fWinding < 0 ? e->fBottom : e->fTop;
1994 Vertex* nextVertex = e->fWinding < 0 ? e->fTop : e->fBottom;
1995 SSVertex* ssPrev = ssVertices[prevVertex];
1996 if (!ssPrev) {
1997 ssPrev = ssVertices[prevVertex] = alloc.make<SSVertex>(prevVertex);
1998 }
1999 SSVertex* ssNext = ssVertices[nextVertex];
2000 if (!ssNext) {
2001 ssNext = ssVertices[nextVertex] = alloc.make<SSVertex>(nextVertex);
2002 }
2003 SSEdge* ssEdge = alloc.make<SSEdge>(e, ssPrev, ssNext);
2004 ssEdges.push_back(ssEdge);
2005// SkASSERT(!ssPrev->fNext && !ssNext->fPrev);
2006 ssPrev->fNext = ssNext->fPrev = ssEdge;
2007 create_event(ssEdge, &events, alloc);
2008 if (!isOuterBoundary) {
2009 disconnect(e);
2010 }
2011 }
2012 e = prev;
2013 }
2014 Edge* prev = leftEnclosingEdge;
2015 for (Edge* e = v->fFirstEdgeBelow; e; e = e->fNextEdgeBelow) {
2016 if (prev) {
2017 e->fWinding += prev->fWinding;
2018 }
2019 insert_edge(e, prev, &activeEdges);
2020 prev = e;
2021 }
2022 }
2023 bool complex = events.size() > 0;
2024
2025 TESS_LOG("\ncollapsing overlap regions\n");
2026 TESS_LOG("skeleton before:\n");
2027 dump_skel(ssEdges);
2028 while (events.size() > 0) {
2029 Event* event = events.top();
2030 events.pop();
2031 event->apply(mesh, c, &events, alloc);
2032 }
2033 TESS_LOG("skeleton after:\n");
2034 dump_skel(ssEdges);
2035 for (SSEdge* edge : ssEdges) {
2036 if (Edge* e = edge->fEdge) {
2037 connect(edge->fPrev->fVertex, edge->fNext->fVertex, e->fType, c, alloc, 0);
2038 }
2039 }
2040 return complex;
2041}
2042
2043bool inversion(Vertex* prev, Vertex* next, Edge* origEdge, Comparator& c) {
2044 if (!prev || !next) {
2045 return true;
2046 }
2047 int winding = c.sweep_lt(prev->fPoint, next->fPoint) ? 1 : -1;
2048 return winding != origEdge->fWinding;
2049}
2050
2051// Stage 5d: Displace edges by half a pixel inward and outward along their normals. Intersect to
2052// find new vertices, and set zero alpha on the exterior and one alpha on the interior. Build a
2053// new antialiased mesh from those vertices.
2054
2055void stroke_boundary(EdgeList* boundary, VertexList* innerMesh, VertexList* outerMesh,
2056 Comparator& c, SkArenaAlloc& alloc) {
2057 TESS_LOG("\nstroking boundary\n");
2058 // A boundary with fewer than 3 edges is degenerate.
2059 if (!boundary->fHead || !boundary->fHead->fRight || !boundary->fHead->fRight->fRight) {
2060 return;
2061 }
2062 Edge* prevEdge = boundary->fTail;
2063 Vertex* prevV = prevEdge->fWinding > 0 ? prevEdge->fTop : prevEdge->fBottom;
2064 SkVector prevNormal;
2065 get_edge_normal(prevEdge, &prevNormal);
2066 double radius = 0.5;
2067 Line prevInner(prevEdge->fLine);
2068 prevInner.fC -= radius;
2069 Line prevOuter(prevEdge->fLine);
2070 prevOuter.fC += radius;
2071 VertexList innerVertices;
2072 VertexList outerVertices;
2073 bool innerInversion = true;
2074 bool outerInversion = true;
2075 for (Edge* e = boundary->fHead; e != nullptr; e = e->fRight) {
2076 Vertex* v = e->fWinding > 0 ? e->fTop : e->fBottom;
2077 SkVector normal;
2078 get_edge_normal(e, &normal);
2079 Line inner(e->fLine);
2080 inner.fC -= radius;
2081 Line outer(e->fLine);
2082 outer.fC += radius;
2083 SkPoint innerPoint, outerPoint;
2084 TESS_LOG("stroking vertex %g (%g, %g)\n", v->fID, v->fPoint.fX, v->fPoint.fY);
2085 if (!prevEdge->fLine.nearParallel(e->fLine) && prevInner.intersect(inner, &innerPoint) &&
2086 prevOuter.intersect(outer, &outerPoint)) {
2087 float cosAngle = normal.dot(prevNormal);
2088 if (cosAngle < -kCosMiterAngle) {
2089 Vertex* nextV = e->fWinding > 0 ? e->fBottom : e->fTop;
2090
2091 // This is a pointy vertex whose angle is smaller than the threshold; miter it.
2092 Line bisector(innerPoint, outerPoint);
2093 Line tangent(v->fPoint, v->fPoint + SkPoint::Make(bisector.fA, bisector.fB));
2094 if (tangent.fA == 0 && tangent.fB == 0) {
2095 continue;
2096 }
2097 tangent.normalize();
2098 Line innerTangent(tangent);
2099 Line outerTangent(tangent);
2100 innerTangent.fC -= 0.5;
2101 outerTangent.fC += 0.5;
2102 SkPoint innerPoint1, innerPoint2, outerPoint1, outerPoint2;
2103 if (prevNormal.cross(normal) > 0) {
2104 // Miter inner points
2105 if (!innerTangent.intersect(prevInner, &innerPoint1) ||
2106 !innerTangent.intersect(inner, &innerPoint2) ||
2107 !outerTangent.intersect(bisector, &outerPoint)) {
2108 continue;
2109 }
2110 Line prevTangent(prevV->fPoint,
2111 prevV->fPoint + SkVector::Make(prevOuter.fA, prevOuter.fB));
2112 Line nextTangent(nextV->fPoint,
2113 nextV->fPoint + SkVector::Make(outer.fA, outer.fB));
2114 if (prevTangent.dist(outerPoint) > 0) {
2115 bisector.intersect(prevTangent, &outerPoint);
2116 }
2117 if (nextTangent.dist(outerPoint) < 0) {
2118 bisector.intersect(nextTangent, &outerPoint);
2119 }
2120 outerPoint1 = outerPoint2 = outerPoint;
2121 } else {
2122 // Miter outer points
2123 if (!outerTangent.intersect(prevOuter, &outerPoint1) ||
2124 !outerTangent.intersect(outer, &outerPoint2)) {
2125 continue;
2126 }
2127 Line prevTangent(prevV->fPoint,
2128 prevV->fPoint + SkVector::Make(prevInner.fA, prevInner.fB));
2129 Line nextTangent(nextV->fPoint,
2130 nextV->fPoint + SkVector::Make(inner.fA, inner.fB));
2131 if (prevTangent.dist(innerPoint) > 0) {
2132 bisector.intersect(prevTangent, &innerPoint);
2133 }
2134 if (nextTangent.dist(innerPoint) < 0) {
2135 bisector.intersect(nextTangent, &innerPoint);
2136 }
2137 innerPoint1 = innerPoint2 = innerPoint;
2138 }
2139 if (!innerPoint1.isFinite() || !innerPoint2.isFinite() ||
2140 !outerPoint1.isFinite() || !outerPoint2.isFinite()) {
2141 continue;
2142 }
2143 TESS_LOG("inner (%g, %g), (%g, %g), ",
2144 innerPoint1.fX, innerPoint1.fY, innerPoint2.fX, innerPoint2.fY);
2145 TESS_LOG("outer (%g, %g), (%g, %g)\n",
2146 outerPoint1.fX, outerPoint1.fY, outerPoint2.fX, outerPoint2.fY);
2147 Vertex* innerVertex1 = alloc.make<Vertex>(innerPoint1, 255);
2148 Vertex* innerVertex2 = alloc.make<Vertex>(innerPoint2, 255);
2149 Vertex* outerVertex1 = alloc.make<Vertex>(outerPoint1, 0);
2150 Vertex* outerVertex2 = alloc.make<Vertex>(outerPoint2, 0);
2151 innerVertex1->fPartner = outerVertex1;
2152 innerVertex2->fPartner = outerVertex2;
2153 outerVertex1->fPartner = innerVertex1;
2154 outerVertex2->fPartner = innerVertex2;
2155 if (!inversion(innerVertices.fTail, innerVertex1, prevEdge, c)) {
2156 innerInversion = false;
2157 }
2158 if (!inversion(outerVertices.fTail, outerVertex1, prevEdge, c)) {
2159 outerInversion = false;
2160 }
2161 innerVertices.append(innerVertex1);
2162 innerVertices.append(innerVertex2);
2163 outerVertices.append(outerVertex1);
2164 outerVertices.append(outerVertex2);
2165 } else {
2166 TESS_LOG("inner (%g, %g), ", innerPoint.fX, innerPoint.fY);
2167 TESS_LOG("outer (%g, %g)\n", outerPoint.fX, outerPoint.fY);
2168 Vertex* innerVertex = alloc.make<Vertex>(innerPoint, 255);
2169 Vertex* outerVertex = alloc.make<Vertex>(outerPoint, 0);
2170 innerVertex->fPartner = outerVertex;
2171 outerVertex->fPartner = innerVertex;
2172 if (!inversion(innerVertices.fTail, innerVertex, prevEdge, c)) {
2173 innerInversion = false;
2174 }
2175 if (!inversion(outerVertices.fTail, outerVertex, prevEdge, c)) {
2176 outerInversion = false;
2177 }
2178 innerVertices.append(innerVertex);
2179 outerVertices.append(outerVertex);
2180 }
2181 }
2182 prevInner = inner;
2183 prevOuter = outer;
2184 prevV = v;
2185 prevEdge = e;
2186 prevNormal = normal;
2187 }
2188 if (!inversion(innerVertices.fTail, innerVertices.fHead, prevEdge, c)) {
2189 innerInversion = false;
2190 }
2191 if (!inversion(outerVertices.fTail, outerVertices.fHead, prevEdge, c)) {
2192 outerInversion = false;
2193 }
2194 // Outer edges get 1 winding, and inner edges get -2 winding. This ensures that the interior
2195 // is always filled (1 + -2 = -1 for normal cases, 1 + 2 = 3 for thin features where the
2196 // interior inverts).
2197 // For total inversion cases, the shape has now reversed handedness, so invert the winding
2198 // so it will be detected during collapse_overlap_regions().
2199 int innerWinding = innerInversion ? 2 : -2;
2200 int outerWinding = outerInversion ? -1 : 1;
2201 for (Vertex* v = innerVertices.fHead; v && v->fNext; v = v->fNext) {
2202 connect(v, v->fNext, Edge::Type::kInner, c, alloc, innerWinding);
2203 }
2204 connect(innerVertices.fTail, innerVertices.fHead, Edge::Type::kInner, c, alloc, innerWinding);
2205 for (Vertex* v = outerVertices.fHead; v && v->fNext; v = v->fNext) {
2206 connect(v, v->fNext, Edge::Type::kOuter, c, alloc, outerWinding);
2207 }
2208 connect(outerVertices.fTail, outerVertices.fHead, Edge::Type::kOuter, c, alloc, outerWinding);
2209 innerMesh->append(innerVertices);
2210 outerMesh->append(outerVertices);
2211}
2212
2213void extract_boundary(EdgeList* boundary, Edge* e, SkPathFillType fillType, SkArenaAlloc& alloc) {
2214 TESS_LOG("\nextracting boundary\n");
2215 bool down = apply_fill_type(fillType, e->fWinding);
2216 Vertex* start = down ? e->fTop : e->fBottom;
2217 do {
2218 e->fWinding = down ? 1 : -1;
2219 Edge* next;
2220 e->fLine.normalize();
2221 e->fLine = e->fLine * e->fWinding;
2222 boundary->append(e);
2223 if (down) {
2224 // Find outgoing edge, in clockwise order.
2225 if ((next = e->fNextEdgeAbove)) {
2226 down = false;
2227 } else if ((next = e->fBottom->fLastEdgeBelow)) {
2228 down = true;
2229 } else if ((next = e->fPrevEdgeAbove)) {
2230 down = false;
2231 }
2232 } else {
2233 // Find outgoing edge, in counter-clockwise order.
2234 if ((next = e->fPrevEdgeBelow)) {
2235 down = true;
2236 } else if ((next = e->fTop->fFirstEdgeAbove)) {
2237 down = false;
2238 } else if ((next = e->fNextEdgeBelow)) {
2239 down = true;
2240 }
2241 }
2242 disconnect(e);
2243 e = next;
2244 } while (e && (down ? e->fTop : e->fBottom) != start);
2245}
2246
2247// Stage 5b: Extract boundaries from mesh, simplify and stroke them into a new mesh.
2248
2249void extract_boundaries(const VertexList& inMesh, VertexList* innerVertices,
2250 VertexList* outerVertices, SkPathFillType fillType,
2251 Comparator& c, SkArenaAlloc& alloc) {
2252 remove_non_boundary_edges(inMesh, fillType, alloc);
2253 for (Vertex* v = inMesh.fHead; v; v = v->fNext) {
2254 while (v->fFirstEdgeBelow) {
2255 EdgeList boundary;
2256 extract_boundary(&boundary, v->fFirstEdgeBelow, fillType, alloc);
2257 simplify_boundary(&boundary, c, alloc);
2258 stroke_boundary(&boundary, innerVertices, outerVertices, c, alloc);
2259 }
2260 }
2261}
2262
2263// This is a driver function that calls stages 2-5 in turn.
2264
2265void contours_to_mesh(VertexList* contours, int contourCnt, Mode mode,
2266 VertexList* mesh, Comparator& c, SkArenaAlloc& alloc) {
2267#if LOGGING_ENABLED
2268 for (int i = 0; i < contourCnt; ++i) {
2269 Vertex* v = contours[i].fHead;
2270 SkASSERT(v);
2271 TESS_LOG("path.moveTo(%20.20g, %20.20g);\n", v->fPoint.fX, v->fPoint.fY);
2272 for (v = v->fNext; v; v = v->fNext) {
2273 TESS_LOG("path.lineTo(%20.20g, %20.20g);\n", v->fPoint.fX, v->fPoint.fY);
2274 }
2275 }
2276#endif
2277 sanitize_contours(contours, contourCnt, mode);
2278 build_edges(contours, contourCnt, mesh, c, alloc);
2279}
2280
2281void sort_mesh(VertexList* vertices, Comparator& c, SkArenaAlloc& alloc) {
2282 if (!vertices || !vertices->fHead) {
2283 return;
2284 }
2285
2286 // Sort vertices in Y (secondarily in X).
2287 if (c.fDirection == Comparator::Direction::kHorizontal) {
2288 merge_sort<sweep_lt_horiz>(vertices);
2289 } else {
2290 merge_sort<sweep_lt_vert>(vertices);
2291 }
2292#if LOGGING_ENABLED
2293 for (Vertex* v = vertices->fHead; v != nullptr; v = v->fNext) {
2294 static float gID = 0.0f;
2295 v->fID = gID++;
2296 }
2297#endif
2298}
2299
2300Poly* contours_to_polys(VertexList* contours, int contourCnt, SkPathFillType fillType,
2301 const SkRect& pathBounds, Mode mode, VertexList* outerMesh,
2302 SkArenaAlloc& alloc) {
2303 Comparator c(pathBounds.width() > pathBounds.height() ? Comparator::Direction::kHorizontal
2304 : Comparator::Direction::kVertical);
2305 VertexList mesh;
2306 contours_to_mesh(contours, contourCnt, mode, &mesh, c, alloc);
2307 sort_mesh(&mesh, c, alloc);
2308 merge_coincident_vertices(&mesh, c, alloc);
2309 if (SimplifyResult::kAbort == simplify(mode, &mesh, c, alloc)) {
2310 return nullptr;
2311 }
2312 TESS_LOG("\nsimplified mesh:\n");
2313 dump_mesh(mesh);
2314 if (Mode::kEdgeAntialias == mode) {
2315 VertexList innerMesh;
2316 extract_boundaries(mesh, &innerMesh, outerMesh, fillType, c, alloc);
2317 sort_mesh(&innerMesh, c, alloc);
2318 sort_mesh(outerMesh, c, alloc);
2319 merge_coincident_vertices(&innerMesh, c, alloc);
2320 bool was_complex = merge_coincident_vertices(outerMesh, c, alloc);
2321 auto result = simplify(mode, &innerMesh, c, alloc);
2322 SkASSERT(SimplifyResult::kAbort != result);
2323 was_complex = (SimplifyResult::kFoundSelfIntersection == result) || was_complex;
2324 result = simplify(mode, outerMesh, c, alloc);
2325 SkASSERT(SimplifyResult::kAbort != result);
2326 was_complex = (SimplifyResult::kFoundSelfIntersection == result) || was_complex;
2327 TESS_LOG("\ninner mesh before:\n");
2328 dump_mesh(innerMesh);
2329 TESS_LOG("\nouter mesh before:\n");
2330 dump_mesh(*outerMesh);
2331 EventComparator eventLT(EventComparator::Op::kLessThan);
2332 EventComparator eventGT(EventComparator::Op::kGreaterThan);
2333 was_complex = collapse_overlap_regions(&innerMesh, c, alloc, eventLT) || was_complex;
2334 was_complex = collapse_overlap_regions(outerMesh, c, alloc, eventGT) || was_complex;
2335 if (was_complex) {
2336 TESS_LOG("found complex mesh; taking slow path\n");
2337 VertexList aaMesh;
2338 TESS_LOG("\ninner mesh after:\n");
2339 dump_mesh(innerMesh);
2340 TESS_LOG("\nouter mesh after:\n");
2341 dump_mesh(*outerMesh);
2342 connect_partners(outerMesh, c, alloc);
2343 connect_partners(&innerMesh, c, alloc);
2344 sorted_merge(&innerMesh, outerMesh, &aaMesh, c);
2345 merge_coincident_vertices(&aaMesh, c, alloc);
2346 result = simplify(mode, &aaMesh, c, alloc);
2347 SkASSERT(SimplifyResult::kAbort != result);
2348 TESS_LOG("combined and simplified mesh:\n");
2349 dump_mesh(aaMesh);
2350 outerMesh->fHead = outerMesh->fTail = nullptr;
2351 return tessellate(fillType, mode, aaMesh, alloc);
2352 } else {
2353 TESS_LOG("no complex polygons; taking fast path\n");
2354 return tessellate(fillType, mode, innerMesh, alloc);
2355 }
2356 } else {
2357 return tessellate(fillType, mode, mesh, alloc);
2358 }
2359}
2360
2361// Stage 6: Triangulate the monotone polygons into a vertex buffer.
2362void* polys_to_triangles(Poly* polys, SkPathFillType fillType, Mode mode, void* data) {
2363 bool emitCoverage = (Mode::kEdgeAntialias == mode);
2364 for (Poly* poly = polys; poly; poly = poly->fNext) {
2365 if (apply_fill_type(fillType, poly)) {
2366 data = poly->emit(emitCoverage, data);
2367 }
2368 }
2369 return data;
2370}
2371
2372Poly* path_to_polys(const SkPath& path, SkScalar tolerance, const SkRect& clipBounds,
2373 int contourCnt, SkArenaAlloc& alloc, Mode mode, bool* isLinear,
2374 VertexList* outerMesh) {
2375 SkPathFillType fillType = path.getFillType();
2376 if (SkPathFillType_IsInverse(fillType)) {
2377 contourCnt++;
2378 }
2379 std::unique_ptr<VertexList[]> contours(new VertexList[contourCnt]);
2380
2381 path_to_contours(path, tolerance, clipBounds, contours.get(), alloc, mode, isLinear);
2382 return contours_to_polys(contours.get(), contourCnt, path.getFillType(), path.getBounds(),
2383 mode, outerMesh, alloc);
2384}
2385
2386int get_contour_count(const SkPath& path, SkScalar tolerance) {
2387 // We could theoretically be more aggressive about not counting empty contours, but we need to
2388 // actually match the exact number of contour linked lists the tessellator will create later on.
2389 int contourCnt = 1;
2390 bool hasPoints = false;
2391
2392 SkPath::Iter iter(path, false);
2393 SkPath::Verb verb;
2394 SkPoint pts[4];
2395 bool first = true;
2396 while ((verb = iter.next(pts)) != SkPath::kDone_Verb) {
2397 switch (verb) {
2398 case SkPath::kMove_Verb:
2399 if (!first) {
2400 ++contourCnt;
2401 }
2402 // fallthru.
2403 case SkPath::kLine_Verb:
2404 case SkPath::kConic_Verb:
2405 case SkPath::kQuad_Verb:
2406 case SkPath::kCubic_Verb:
2407 hasPoints = true;
2408 // fallthru to break.
2409 default:
2410 break;
2411 }
2412 first = false;
2413 }
2414 if (!hasPoints) {
2415 return 0;
2416 }
2417 return contourCnt;
2418}
2419
2420int64_t count_points(Poly* polys, SkPathFillType fillType) {
2421 int64_t count = 0;
2422 for (Poly* poly = polys; poly; poly = poly->fNext) {
2423 if (apply_fill_type(fillType, poly) && poly->fCount >= 3) {
2424 count += (poly->fCount - 2) * (TRIANGULATOR_WIREFRAME ? 6 : 3);
2425 }
2426 }
2427 return count;
2428}
2429
2430int64_t count_outer_mesh_points(const VertexList& outerMesh) {
2431 int64_t count = 0;
2432 for (Vertex* v = outerMesh.fHead; v; v = v->fNext) {
2433 for (Edge* e = v->fFirstEdgeBelow; e; e = e->fNextEdgeBelow) {
2434 count += TRIANGULATOR_WIREFRAME ? 12 : 6;
2435 }
2436 }
2437 return count;
2438}
2439
2440void* outer_mesh_to_triangles(const VertexList& outerMesh, bool emitCoverage, void* data) {
2441 for (Vertex* v = outerMesh.fHead; v; v = v->fNext) {
2442 for (Edge* e = v->fFirstEdgeBelow; e; e = e->fNextEdgeBelow) {
2443 Vertex* v0 = e->fTop;
2444 Vertex* v1 = e->fBottom;
2445 Vertex* v2 = e->fBottom->fPartner;
2446 Vertex* v3 = e->fTop->fPartner;
2447 data = emit_triangle(v0, v1, v2, emitCoverage, data);
2448 data = emit_triangle(v0, v2, v3, emitCoverage, data);
2449 }
2450 }
2451 return data;
2452}
2453
2454} // namespace
2455
2456namespace GrTriangulator {
2457
2458// Stage 6: Triangulate the monotone polygons into a vertex buffer.
2459
2460int PathToTriangles(const SkPath& path, SkScalar tolerance, const SkRect& clipBounds,
2461 GrEagerVertexAllocator* vertexAllocator, Mode mode, bool* isLinear) {
2462 int contourCnt = get_contour_count(path, tolerance);
2463 if (contourCnt <= 0) {
2464 *isLinear = true;
2465 return 0;
2466 }
2467 SkArenaAlloc alloc(kArenaChunkSize);
2468 VertexList outerMesh;
2469 Poly* polys = path_to_polys(path, tolerance, clipBounds, contourCnt, alloc, mode,
2470 isLinear, &outerMesh);
2471 SkPathFillType fillType = (Mode::kEdgeAntialias == mode) ?
2472 SkPathFillType::kWinding : path.getFillType();
2473 int64_t count64 = count_points(polys, fillType);
2474 if (Mode::kEdgeAntialias == mode) {
2475 count64 += count_outer_mesh_points(outerMesh);
2476 }
2477 if (0 == count64 || count64 > SK_MaxS32) {
2478 return 0;
2479 }
2480 int count = count64;
2481
2482 size_t vertexStride = GetVertexStride(mode);
2483 void* verts = vertexAllocator->lock(vertexStride, count);
2484 if (!verts) {
2485 SkDebugf("Could not allocate vertices\n");
2486 return 0;
2487 }
2488
2489 TESS_LOG("emitting %d verts\n", count);
2490 void* end = polys_to_triangles(polys, fillType, mode, verts);
2491 end = outer_mesh_to_triangles(outerMesh, true, end);
2492
2493 int actualCount = static_cast<int>((static_cast<uint8_t*>(end) - static_cast<uint8_t*>(verts))
2494 / vertexStride);
2495 SkASSERT(actualCount <= count);
2496 vertexAllocator->unlock(actualCount);
2497 return actualCount;
2498}
2499
2500int PathToVertices(const SkPath& path, SkScalar tolerance, const SkRect& clipBounds,
2501 WindingVertex** verts) {
2502 int contourCnt = get_contour_count(path, tolerance);
2503 if (contourCnt <= 0) {
2504 *verts = nullptr;
2505 return 0;
2506 }
2507 SkArenaAlloc alloc(kArenaChunkSize);
2508 bool isLinear;
2509 Poly* polys = path_to_polys(path, tolerance, clipBounds, contourCnt, alloc, Mode::kNormal,
2510 &isLinear, nullptr);
2511 SkPathFillType fillType = path.getFillType();
2512 int64_t count64 = count_points(polys, fillType);
2513 if (0 == count64 || count64 > SK_MaxS32) {
2514 *verts = nullptr;
2515 return 0;
2516 }
2517 int count = count64;
2518
2519 *verts = new WindingVertex[count];
2520 WindingVertex* vertsEnd = *verts;
2521 SkPoint* points = new SkPoint[count];
2522 SkPoint* pointsEnd = points;
2523 for (Poly* poly = polys; poly; poly = poly->fNext) {
2524 if (apply_fill_type(fillType, poly)) {
2525 SkPoint* start = pointsEnd;
2526 pointsEnd = static_cast<SkPoint*>(poly->emit(false, pointsEnd));
2527 while (start != pointsEnd) {
2528 vertsEnd->fPos = *start;
2529 vertsEnd->fWinding = poly->fWinding;
2530 ++start;
2531 ++vertsEnd;
2532 }
2533 }
2534 }
2535 int actualCount = static_cast<int>(vertsEnd - *verts);
2536 SkASSERT(actualCount <= count);
2537 SkASSERT(pointsEnd - points == actualCount);
2538 delete[] points;
2539 return actualCount;
2540}
2541
2542} // namespace
2543