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 "GrTessellator.h"
9
10#include "GrBatchFlushState.h"
11#include "GrBatchTest.h"
12#include "GrDefaultGeoProcFactory.h"
13#include "GrPathUtils.h"
14#include "GrVertices.h"
15#include "GrResourceCache.h"
16#include "GrResourceProvider.h"
17#include "SkGeometry.h"
18#include "SkChunkAlloc.h"
19
20#include "batches/GrVertexBatch.h"
21
22#include <stdio.h>
23
24/*
25 * There are six stages to the algorithm:
26 *
27 * 1) Linearize the path contours into piecewise linear segments (path_to_contours()).
28 * 2) Build a mesh of edges connecting the vertices (build_edges()).
29 * 3) Sort the vertices in Y (and secondarily in X) (merge_sort()).
30 * 4) Simplify the mesh by inserting new vertices at intersecting edges (simplify()).
31 * 5) Tessellate the simplified mesh into monotone polygons (tessellate()).
32 * 6) Triangulate the monotone polygons directly into a vertex buffer (polys_to_triangles()).
33 *
34 * The vertex sorting in step (3) is a merge sort, since it plays well with the linked list
35 * of vertices (and the necessity of inserting new vertices on intersection).
36 *
37 * Stages (4) and (5) use an active edge list, which a list of all edges for which the
38 * sweep line has crossed the top vertex, but not the bottom vertex.  It's sorted
39 * left-to-right based on the point where both edges are active (when both top vertices
40 * have been seen, so the "lower" top vertex of the two). If the top vertices are equal
41 * (shared), it's sorted based on the last point where both edges are active, so the
42 * "upper" bottom vertex.
43 *
44 * The most complex step is the simplification (4). It's based on the Bentley-Ottman
45 * line-sweep algorithm, but due to floating point inaccuracy, the intersection points are
46 * not exact and may violate the mesh topology or active edge list ordering. We
47 * accommodate this by adjusting the topology of the mesh and AEL to match the intersection
48 * points. This occurs in three ways:
49 *
50 * A) Intersections may cause a shortened edge to no longer be ordered with respect to its
51 *    neighbouring edges at the top or bottom vertex. This is handled by merging the
52 *    edges (merge_collinear_edges()).
53 * B) Intersections may cause an edge to violate the left-to-right ordering of the
54 *    active edge list. This is handled by splitting the neighbour edge on the
55 *    intersected vertex (cleanup_active_edges()).
56 * C) Shortening an edge may cause an active edge to become inactive or an inactive edge
57 *    to become active. This is handled by removing or inserting the edge in the active
58 *    edge list (fix_active_state()).
59 *
60 * The tessellation steps (5) and (6) are based on "Triangulating Simple Polygons and
61 * Equivalent Problems" (Fournier and Montuno); also a line-sweep algorithm. Note that it
62 * currently uses a linked list for the active edge list, rather than a 2-3 tree as the
63 * paper describes. The 2-3 tree gives O(lg N) lookups, but insertion and removal also
64 * become O(lg N). In all the test cases, it was found that the cost of frequent O(lg N)
65 * insertions and removals was greater than the cost of infrequent O(N) lookups with the
66 * linked list implementation. With the latter, all removals are O(1), and most insertions
67 * are O(1), since we know the adjacent edge in the active edge list based on the topology.
68 * Only type 2 vertices (see paper) require the O(N) lookups, and these are much less
69 * frequent. There may be other data structures worth investigating, however.
70 *
71 * Note that the orientation of the line sweep algorithms is determined by the aspect ratio of the
72 * path bounds. When the path is taller than it is wide, we sort vertices based on increasing Y
73 * coordinate, and secondarily by increasing X coordinate. When the path is wider than it is tall,
74 * we sort by increasing X coordinate, but secondarily by *decreasing* Y coordinate. This is so
75 * that the "left" and "right" orientation in the code remains correct (edges to the left are
76 * increasing in Y; edges to the right are decreasing in Y). That is, the setting rotates 90
77 * degrees counterclockwise, rather that transposing.
78 */
79
80#define LOGGING_ENABLED 0
81
82#if LOGGING_ENABLED
83#define LOG printf
84#else
85#define LOG(...)
86#endif
87
88#define ALLOC_NEW(Type, args, alloc) new (alloc.allocThrow(sizeof(Type))) Type args
89
90namespace {
91
92struct Vertex;
93struct Edge;
94struct Poly;
95
96template <class T, T* T::*Prev, T* T::*Next>
97void insert(T* t, T* prev, T* next, T** head, T** tail) {
98    t->*Prev = prev;
99    t->*Next = next;
100    if (prev) {
101        prev->*Next = t;
102    } else if (head) {
103        *head = t;
104    }
105    if (next) {
106        next->*Prev = t;
107    } else if (tail) {
108        *tail = t;
109    }
110}
111
112template <class T, T* T::*Prev, T* T::*Next>
113void remove(T* t, T** head, T** tail) {
114    if (t->*Prev) {
115        t->*Prev->*Next = t->*Next;
116    } else if (head) {
117        *head = t->*Next;
118    }
119    if (t->*Next) {
120        t->*Next->*Prev = t->*Prev;
121    } else if (tail) {
122        *tail = t->*Prev;
123    }
124    t->*Prev = t->*Next = nullptr;
125}
126
127/**
128 * Vertices are used in three ways: first, the path contours are converted into a
129 * circularly-linked list of Vertices for each contour. After edge construction, the same Vertices
130 * are re-ordered by the merge sort according to the sweep_lt comparator (usually, increasing
131 * in Y) using the same fPrev/fNext pointers that were used for the contours, to avoid
132 * reallocation. Finally, MonotonePolys are built containing a circularly-linked list of
133 * Vertices. (Currently, those Vertices are newly-allocated for the MonotonePolys, since
134 * an individual Vertex from the path mesh may belong to multiple
135 * MonotonePolys, so the original Vertices cannot be re-used.
136 */
137
138struct Vertex {
139  Vertex(const SkPoint& point)
140    : fPoint(point), fPrev(nullptr), fNext(nullptr)
141    , fFirstEdgeAbove(nullptr), fLastEdgeAbove(nullptr)
142    , fFirstEdgeBelow(nullptr), fLastEdgeBelow(nullptr)
143    , fProcessed(false)
144#if LOGGING_ENABLED
145    , fID (-1.0f)
146#endif
147    {}
148    SkPoint fPoint;           // Vertex position
149    Vertex* fPrev;            // Linked list of contours, then Y-sorted vertices.
150    Vertex* fNext;            // "
151    Edge*   fFirstEdgeAbove;  // Linked list of edges above this vertex.
152    Edge*   fLastEdgeAbove;   // "
153    Edge*   fFirstEdgeBelow;  // Linked list of edges below this vertex.
154    Edge*   fLastEdgeBelow;   // "
155    bool    fProcessed;       // Has this vertex been seen in simplify()?
156#if LOGGING_ENABLED
157    float   fID;              // Identifier used for logging.
158#endif
159};
160
161/***************************************************************************************/
162
163typedef bool (*CompareFunc)(const SkPoint& a, const SkPoint& b);
164
165struct Comparator {
166    CompareFunc sweep_lt;
167    CompareFunc sweep_gt;
168};
169
170bool sweep_lt_horiz(const SkPoint& a, const SkPoint& b) {
171    return a.fX == b.fX ? a.fY > b.fY : a.fX < b.fX;
172}
173
174bool sweep_lt_vert(const SkPoint& a, const SkPoint& b) {
175    return a.fY == b.fY ? a.fX < b.fX : a.fY < b.fY;
176}
177
178bool sweep_gt_horiz(const SkPoint& a, const SkPoint& b) {
179    return a.fX == b.fX ? a.fY < b.fY : a.fX > b.fX;
180}
181
182bool sweep_gt_vert(const SkPoint& a, const SkPoint& b) {
183    return a.fY == b.fY ? a.fX > b.fX : a.fY > b.fY;
184}
185
186inline SkPoint* emit_vertex(Vertex* v, SkPoint* data) {
187    *data++ = v->fPoint;
188    return data;
189}
190
191SkPoint* emit_triangle(Vertex* v0, Vertex* v1, Vertex* v2, SkPoint* data) {
192#if WIREFRAME
193    data = emit_vertex(v0, data);
194    data = emit_vertex(v1, data);
195    data = emit_vertex(v1, data);
196    data = emit_vertex(v2, data);
197    data = emit_vertex(v2, data);
198    data = emit_vertex(v0, data);
199#else
200    data = emit_vertex(v0, data);
201    data = emit_vertex(v1, data);
202    data = emit_vertex(v2, data);
203#endif
204    return data;
205}
206
207struct EdgeList {
208    EdgeList() : fHead(nullptr), fTail(nullptr) {}
209    Edge* fHead;
210    Edge* fTail;
211};
212
213/**
214 * An Edge joins a top Vertex to a bottom Vertex. Edge ordering for the list of "edges above" and
215 * "edge below" a vertex as well as for the active edge list is handled by isLeftOf()/isRightOf().
216 * Note that an Edge will give occasionally dist() != 0 for its own endpoints (because floating
217 * point). For speed, that case is only tested by the callers which require it (e.g.,
218 * cleanup_active_edges()). Edges also handle checking for intersection with other edges.
219 * Currently, this converts the edges to the parametric form, in order to avoid doing a division
220 * until an intersection has been confirmed. This is slightly slower in the "found" case, but
221 * a lot faster in the "not found" case.
222 *
223 * The coefficients of the line equation stored in double precision to avoid catastrphic
224 * cancellation in the isLeftOf() and isRightOf() checks. Using doubles ensures that the result is
225 * correct in float, since it's a polynomial of degree 2. The intersect() function, being
226 * degree 5, is still subject to catastrophic cancellation. We deal with that by assuming its
227 * output may be incorrect, and adjusting the mesh topology to match (see comment at the top of
228 * this file).
229 */
230
231struct Edge {
232    Edge(Vertex* top, Vertex* bottom, int winding)
233        : fWinding(winding)
234        , fTop(top)
235        , fBottom(bottom)
236        , fLeft(nullptr)
237        , fRight(nullptr)
238        , fPrevEdgeAbove(nullptr)
239        , fNextEdgeAbove(nullptr)
240        , fPrevEdgeBelow(nullptr)
241        , fNextEdgeBelow(nullptr)
242        , fLeftPoly(nullptr)
243        , fRightPoly(nullptr) {
244            recompute();
245        }
246    int      fWinding;          // 1 == edge goes downward; -1 = edge goes upward.
247    Vertex*  fTop;              // The top vertex in vertex-sort-order (sweep_lt).
248    Vertex*  fBottom;           // The bottom vertex in vertex-sort-order.
249    Edge*    fLeft;             // The linked list of edges in the active edge list.
250    Edge*    fRight;            // "
251    Edge*    fPrevEdgeAbove;    // The linked list of edges in the bottom Vertex's "edges above".
252    Edge*    fNextEdgeAbove;    // "
253    Edge*    fPrevEdgeBelow;    // The linked list of edges in the top Vertex's "edges below".
254    Edge*    fNextEdgeBelow;    // "
255    Poly*    fLeftPoly;         // The Poly to the left of this edge, if any.
256    Poly*    fRightPoly;        // The Poly to the right of this edge, if any.
257    double   fDX;               // The line equation for this edge, in implicit form.
258    double   fDY;               // fDY * x + fDX * y + fC = 0, for point (x, y) on the line.
259    double   fC;
260    double dist(const SkPoint& p) const {
261        return fDY * p.fX - fDX * p.fY + fC;
262    }
263    bool isRightOf(Vertex* v) const {
264        return dist(v->fPoint) < 0.0;
265    }
266    bool isLeftOf(Vertex* v) const {
267        return dist(v->fPoint) > 0.0;
268    }
269    void recompute() {
270        fDX = static_cast<double>(fBottom->fPoint.fX) - fTop->fPoint.fX;
271        fDY = static_cast<double>(fBottom->fPoint.fY) - fTop->fPoint.fY;
272        fC = static_cast<double>(fTop->fPoint.fY) * fBottom->fPoint.fX -
273             static_cast<double>(fTop->fPoint.fX) * fBottom->fPoint.fY;
274    }
275    bool intersect(const Edge& other, SkPoint* p) {
276        LOG("intersecting %g -> %g with %g -> %g\n",
277               fTop->fID, fBottom->fID,
278               other.fTop->fID, other.fBottom->fID);
279        if (fTop == other.fTop || fBottom == other.fBottom) {
280            return false;
281        }
282        double denom = fDX * other.fDY - fDY * other.fDX;
283        if (denom == 0.0) {
284            return false;
285        }
286        double dx = static_cast<double>(fTop->fPoint.fX) - other.fTop->fPoint.fX;
287        double dy = static_cast<double>(fTop->fPoint.fY) - other.fTop->fPoint.fY;
288        double sNumer = dy * other.fDX - dx * other.fDY;
289        double tNumer = dy * fDX - dx * fDY;
290        // If (sNumer / denom) or (tNumer / denom) is not in [0..1], exit early.
291        // This saves us doing the divide below unless absolutely necessary.
292        if (denom > 0.0 ? (sNumer < 0.0 || sNumer > denom || tNumer < 0.0 || tNumer > denom)
293                        : (sNumer > 0.0 || sNumer < denom || tNumer > 0.0 || tNumer < denom)) {
294            return false;
295        }
296        double s = sNumer / denom;
297        SkASSERT(s >= 0.0 && s <= 1.0);
298        p->fX = SkDoubleToScalar(fTop->fPoint.fX + s * fDX);
299        p->fY = SkDoubleToScalar(fTop->fPoint.fY + s * fDY);
300        return true;
301    }
302    bool isActive(EdgeList* activeEdges) const {
303        return activeEdges && (fLeft || fRight || activeEdges->fHead == this);
304    }
305};
306
307/***************************************************************************************/
308
309struct Poly {
310    Poly(int winding)
311        : fWinding(winding)
312        , fHead(nullptr)
313        , fTail(nullptr)
314        , fActive(nullptr)
315        , fNext(nullptr)
316        , fPartner(nullptr)
317        , fCount(0)
318    {
319#if LOGGING_ENABLED
320        static int gID = 0;
321        fID = gID++;
322        LOG("*** created Poly %d\n", fID);
323#endif
324    }
325    typedef enum { kNeither_Side, kLeft_Side, kRight_Side } Side;
326    struct MonotonePoly {
327        MonotonePoly()
328            : fSide(kNeither_Side)
329            , fHead(nullptr)
330            , fTail(nullptr)
331            , fPrev(nullptr)
332            , fNext(nullptr) {}
333        Side          fSide;
334        Vertex*       fHead;
335        Vertex*       fTail;
336        MonotonePoly* fPrev;
337        MonotonePoly* fNext;
338        bool addVertex(Vertex* v, Side side, SkChunkAlloc& alloc) {
339            Vertex* newV = ALLOC_NEW(Vertex, (v->fPoint), alloc);
340            bool done = false;
341            if (fSide == kNeither_Side) {
342                fSide = side;
343            } else {
344                done = side != fSide;
345            }
346            if (fHead == nullptr) {
347                fHead = fTail = newV;
348            } else if (fSide == kRight_Side) {
349                newV->fPrev = fTail;
350                fTail->fNext = newV;
351                fTail = newV;
352            } else {
353                newV->fNext = fHead;
354                fHead->fPrev = newV;
355                fHead = newV;
356            }
357            return done;
358        }
359
360        SkPoint* emit(SkPoint* data) {
361            Vertex* first = fHead;
362            Vertex* v = first->fNext;
363            while (v != fTail) {
364                SkASSERT(v && v->fPrev && v->fNext);
365                Vertex* prev = v->fPrev;
366                Vertex* curr = v;
367                Vertex* next = v->fNext;
368                double ax = static_cast<double>(curr->fPoint.fX) - prev->fPoint.fX;
369                double ay = static_cast<double>(curr->fPoint.fY) - prev->fPoint.fY;
370                double bx = static_cast<double>(next->fPoint.fX) - curr->fPoint.fX;
371                double by = static_cast<double>(next->fPoint.fY) - curr->fPoint.fY;
372                if (ax * by - ay * bx >= 0.0) {
373                    data = emit_triangle(prev, curr, next, data);
374                    v->fPrev->fNext = v->fNext;
375                    v->fNext->fPrev = v->fPrev;
376                    if (v->fPrev == first) {
377                        v = v->fNext;
378                    } else {
379                        v = v->fPrev;
380                    }
381                } else {
382                    v = v->fNext;
383                }
384            }
385            return data;
386        }
387    };
388    Poly* addVertex(Vertex* v, Side side, SkChunkAlloc& alloc) {
389        LOG("addVertex() to %d at %g (%g, %g), %s side\n", fID, v->fID, v->fPoint.fX, v->fPoint.fY,
390               side == kLeft_Side ? "left" : side == kRight_Side ? "right" : "neither");
391        Poly* partner = fPartner;
392        Poly* poly = this;
393        if (partner) {
394            fPartner = partner->fPartner = nullptr;
395        }
396        if (!fActive) {
397            fActive = ALLOC_NEW(MonotonePoly, (), alloc);
398        }
399        if (fActive->addVertex(v, side, alloc)) {
400            if (fTail) {
401                fActive->fPrev = fTail;
402                fTail->fNext = fActive;
403                fTail = fActive;
404            } else {
405                fHead = fTail = fActive;
406            }
407            if (partner) {
408                partner->addVertex(v, side, alloc);
409                poly = partner;
410            } else {
411                Vertex* prev = fActive->fSide == Poly::kLeft_Side ?
412                               fActive->fHead->fNext : fActive->fTail->fPrev;
413                fActive = ALLOC_NEW(MonotonePoly, , alloc);
414                fActive->addVertex(prev, Poly::kNeither_Side, alloc);
415                fActive->addVertex(v, side, alloc);
416            }
417        }
418        fCount++;
419        return poly;
420    }
421    void end(Vertex* v, SkChunkAlloc& alloc) {
422        LOG("end() %d at %g, %g\n", fID, v->fPoint.fX, v->fPoint.fY);
423        if (fPartner) {
424            fPartner = fPartner->fPartner = nullptr;
425        }
426        addVertex(v, fActive->fSide == kLeft_Side ? kRight_Side : kLeft_Side, alloc);
427    }
428    SkPoint* emit(SkPoint *data) {
429        if (fCount < 3) {
430            return data;
431        }
432        LOG("emit() %d, size %d\n", fID, fCount);
433        for (MonotonePoly* m = fHead; m != nullptr; m = m->fNext) {
434            data = m->emit(data);
435        }
436        return data;
437    }
438    int fWinding;
439    MonotonePoly* fHead;
440    MonotonePoly* fTail;
441    MonotonePoly* fActive;
442    Poly* fNext;
443    Poly* fPartner;
444    int fCount;
445#if LOGGING_ENABLED
446    int fID;
447#endif
448};
449
450/***************************************************************************************/
451
452bool coincident(const SkPoint& a, const SkPoint& b) {
453    return a == b;
454}
455
456Poly* new_poly(Poly** head, Vertex* v, int winding, SkChunkAlloc& alloc) {
457    Poly* poly = ALLOC_NEW(Poly, (winding), alloc);
458    poly->addVertex(v, Poly::kNeither_Side, alloc);
459    poly->fNext = *head;
460    *head = poly;
461    return poly;
462}
463
464Vertex* append_point_to_contour(const SkPoint& p, Vertex* prev, Vertex** head,
465                                SkChunkAlloc& alloc) {
466    Vertex* v = ALLOC_NEW(Vertex, (p), alloc);
467#if LOGGING_ENABLED
468    static float gID = 0.0f;
469    v->fID = gID++;
470#endif
471    if (prev) {
472        prev->fNext = v;
473        v->fPrev = prev;
474    } else {
475        *head = v;
476    }
477    return v;
478}
479
480Vertex* generate_quadratic_points(const SkPoint& p0,
481                                  const SkPoint& p1,
482                                  const SkPoint& p2,
483                                  SkScalar tolSqd,
484                                  Vertex* prev,
485                                  Vertex** head,
486                                  int pointsLeft,
487                                  SkChunkAlloc& alloc) {
488    SkScalar d = p1.distanceToLineSegmentBetweenSqd(p0, p2);
489    if (pointsLeft < 2 || d < tolSqd || !SkScalarIsFinite(d)) {
490        return append_point_to_contour(p2, prev, head, alloc);
491    }
492
493    const SkPoint q[] = {
494        { SkScalarAve(p0.fX, p1.fX), SkScalarAve(p0.fY, p1.fY) },
495        { SkScalarAve(p1.fX, p2.fX), SkScalarAve(p1.fY, p2.fY) },
496    };
497    const SkPoint r = { SkScalarAve(q[0].fX, q[1].fX), SkScalarAve(q[0].fY, q[1].fY) };
498
499    pointsLeft >>= 1;
500    prev = generate_quadratic_points(p0, q[0], r, tolSqd, prev, head, pointsLeft, alloc);
501    prev = generate_quadratic_points(r, q[1], p2, tolSqd, prev, head, pointsLeft, alloc);
502    return prev;
503}
504
505Vertex* generate_cubic_points(const SkPoint& p0,
506                              const SkPoint& p1,
507                              const SkPoint& p2,
508                              const SkPoint& p3,
509                              SkScalar tolSqd,
510                              Vertex* prev,
511                              Vertex** head,
512                              int pointsLeft,
513                              SkChunkAlloc& alloc) {
514    SkScalar d1 = p1.distanceToLineSegmentBetweenSqd(p0, p3);
515    SkScalar d2 = p2.distanceToLineSegmentBetweenSqd(p0, p3);
516    if (pointsLeft < 2 || (d1 < tolSqd && d2 < tolSqd) ||
517        !SkScalarIsFinite(d1) || !SkScalarIsFinite(d2)) {
518        return append_point_to_contour(p3, prev, head, alloc);
519    }
520    const SkPoint q[] = {
521        { SkScalarAve(p0.fX, p1.fX), SkScalarAve(p0.fY, p1.fY) },
522        { SkScalarAve(p1.fX, p2.fX), SkScalarAve(p1.fY, p2.fY) },
523        { SkScalarAve(p2.fX, p3.fX), SkScalarAve(p2.fY, p3.fY) }
524    };
525    const SkPoint r[] = {
526        { SkScalarAve(q[0].fX, q[1].fX), SkScalarAve(q[0].fY, q[1].fY) },
527        { SkScalarAve(q[1].fX, q[2].fX), SkScalarAve(q[1].fY, q[2].fY) }
528    };
529    const SkPoint s = { SkScalarAve(r[0].fX, r[1].fX), SkScalarAve(r[0].fY, r[1].fY) };
530    pointsLeft >>= 1;
531    prev = generate_cubic_points(p0, q[0], r[0], s, tolSqd, prev, head, pointsLeft, alloc);
532    prev = generate_cubic_points(s, r[1], q[2], p3, tolSqd, prev, head, pointsLeft, alloc);
533    return prev;
534}
535
536// Stage 1: convert the input path to a set of linear contours (linked list of Vertices).
537
538void path_to_contours(const SkPath& path, SkScalar tolerance, const SkRect& clipBounds,
539                      Vertex** contours, SkChunkAlloc& alloc, bool *isLinear) {
540    SkScalar toleranceSqd = tolerance * tolerance;
541
542    SkPoint pts[4];
543    bool done = false;
544    *isLinear = true;
545    SkPath::Iter iter(path, false);
546    Vertex* prev = nullptr;
547    Vertex* head = nullptr;
548    if (path.isInverseFillType()) {
549        SkPoint quad[4];
550        clipBounds.toQuad(quad);
551        for (int i = 3; i >= 0; i--) {
552            prev = append_point_to_contour(quad[i], prev, &head, alloc);
553        }
554        head->fPrev = prev;
555        prev->fNext = head;
556        *contours++ = head;
557        head = prev = nullptr;
558    }
559    SkAutoConicToQuads converter;
560    while (!done) {
561        SkPath::Verb verb = iter.next(pts);
562        switch (verb) {
563            case SkPath::kConic_Verb: {
564                SkScalar weight = iter.conicWeight();
565                const SkPoint* quadPts = converter.computeQuads(pts, weight, toleranceSqd);
566                for (int i = 0; i < converter.countQuads(); ++i) {
567                    int pointsLeft = GrPathUtils::quadraticPointCount(quadPts, tolerance);
568                    prev = generate_quadratic_points(quadPts[0], quadPts[1], quadPts[2],
569                                                     toleranceSqd, prev, &head, pointsLeft, alloc);
570                    quadPts += 2;
571                }
572                *isLinear = false;
573                break;
574            }
575            case SkPath::kMove_Verb:
576                if (head) {
577                    head->fPrev = prev;
578                    prev->fNext = head;
579                    *contours++ = head;
580                }
581                head = prev = nullptr;
582                prev = append_point_to_contour(pts[0], prev, &head, alloc);
583                break;
584            case SkPath::kLine_Verb: {
585                prev = append_point_to_contour(pts[1], prev, &head, alloc);
586                break;
587            }
588            case SkPath::kQuad_Verb: {
589                int pointsLeft = GrPathUtils::quadraticPointCount(pts, tolerance);
590                prev = generate_quadratic_points(pts[0], pts[1], pts[2], toleranceSqd, prev,
591                                                 &head, pointsLeft, alloc);
592                *isLinear = false;
593                break;
594            }
595            case SkPath::kCubic_Verb: {
596                int pointsLeft = GrPathUtils::cubicPointCount(pts, tolerance);
597                prev = generate_cubic_points(pts[0], pts[1], pts[2], pts[3],
598                                toleranceSqd, prev, &head, pointsLeft, alloc);
599                *isLinear = false;
600                break;
601            }
602            case SkPath::kClose_Verb:
603                if (head) {
604                    head->fPrev = prev;
605                    prev->fNext = head;
606                    *contours++ = head;
607                }
608                head = prev = nullptr;
609                break;
610            case SkPath::kDone_Verb:
611                if (head) {
612                    head->fPrev = prev;
613                    prev->fNext = head;
614                    *contours++ = head;
615                }
616                done = true;
617                break;
618        }
619    }
620}
621
622inline bool apply_fill_type(SkPath::FillType fillType, int winding) {
623    switch (fillType) {
624        case SkPath::kWinding_FillType:
625            return winding != 0;
626        case SkPath::kEvenOdd_FillType:
627            return (winding & 1) != 0;
628        case SkPath::kInverseWinding_FillType:
629            return winding == 1;
630        case SkPath::kInverseEvenOdd_FillType:
631            return (winding & 1) == 1;
632        default:
633            SkASSERT(false);
634            return false;
635    }
636}
637
638Edge* new_edge(Vertex* prev, Vertex* next, SkChunkAlloc& alloc, Comparator& c) {
639    int winding = c.sweep_lt(prev->fPoint, next->fPoint) ? 1 : -1;
640    Vertex* top = winding < 0 ? next : prev;
641    Vertex* bottom = winding < 0 ? prev : next;
642    return ALLOC_NEW(Edge, (top, bottom, winding), alloc);
643}
644
645void remove_edge(Edge* edge, EdgeList* edges) {
646    LOG("removing edge %g -> %g\n", edge->fTop->fID, edge->fBottom->fID);
647    SkASSERT(edge->isActive(edges));
648    remove<Edge, &Edge::fLeft, &Edge::fRight>(edge, &edges->fHead, &edges->fTail);
649}
650
651void insert_edge(Edge* edge, Edge* prev, EdgeList* edges) {
652    LOG("inserting edge %g -> %g\n", edge->fTop->fID, edge->fBottom->fID);
653    SkASSERT(!edge->isActive(edges));
654    Edge* next = prev ? prev->fRight : edges->fHead;
655    insert<Edge, &Edge::fLeft, &Edge::fRight>(edge, prev, next, &edges->fHead, &edges->fTail);
656}
657
658void find_enclosing_edges(Vertex* v, EdgeList* edges, Edge** left, Edge** right) {
659    if (v->fFirstEdgeAbove) {
660        *left = v->fFirstEdgeAbove->fLeft;
661        *right = v->fLastEdgeAbove->fRight;
662        return;
663    }
664    Edge* next = nullptr;
665    Edge* prev;
666    for (prev = edges->fTail; prev != nullptr; prev = prev->fLeft) {
667        if (prev->isLeftOf(v)) {
668            break;
669        }
670        next = prev;
671    }
672    *left = prev;
673    *right = next;
674    return;
675}
676
677void find_enclosing_edges(Edge* edge, EdgeList* edges, Comparator& c, Edge** left, Edge** right) {
678    Edge* prev = nullptr;
679    Edge* next;
680    for (next = edges->fHead; next != nullptr; next = next->fRight) {
681        if ((c.sweep_gt(edge->fTop->fPoint, next->fTop->fPoint) && next->isRightOf(edge->fTop)) ||
682            (c.sweep_gt(next->fTop->fPoint, edge->fTop->fPoint) && edge->isLeftOf(next->fTop)) ||
683            (c.sweep_lt(edge->fBottom->fPoint, next->fBottom->fPoint) &&
684             next->isRightOf(edge->fBottom)) ||
685            (c.sweep_lt(next->fBottom->fPoint, edge->fBottom->fPoint) &&
686             edge->isLeftOf(next->fBottom))) {
687            break;
688        }
689        prev = next;
690    }
691    *left = prev;
692    *right = next;
693    return;
694}
695
696void fix_active_state(Edge* edge, EdgeList* activeEdges, Comparator& c) {
697    if (edge->isActive(activeEdges)) {
698        if (edge->fBottom->fProcessed || !edge->fTop->fProcessed) {
699            remove_edge(edge, activeEdges);
700        }
701    } else if (edge->fTop->fProcessed && !edge->fBottom->fProcessed) {
702        Edge* left;
703        Edge* right;
704        find_enclosing_edges(edge, activeEdges, c, &left, &right);
705        insert_edge(edge, left, activeEdges);
706    }
707}
708
709void insert_edge_above(Edge* edge, Vertex* v, Comparator& c) {
710    if (edge->fTop->fPoint == edge->fBottom->fPoint ||
711        c.sweep_gt(edge->fTop->fPoint, edge->fBottom->fPoint)) {
712        return;
713    }
714    LOG("insert edge (%g -> %g) above vertex %g\n", edge->fTop->fID, edge->fBottom->fID, v->fID);
715    Edge* prev = nullptr;
716    Edge* next;
717    for (next = v->fFirstEdgeAbove; next; next = next->fNextEdgeAbove) {
718        if (next->isRightOf(edge->fTop)) {
719            break;
720        }
721        prev = next;
722    }
723    insert<Edge, &Edge::fPrevEdgeAbove, &Edge::fNextEdgeAbove>(
724        edge, prev, next, &v->fFirstEdgeAbove, &v->fLastEdgeAbove);
725}
726
727void insert_edge_below(Edge* edge, Vertex* v, Comparator& c) {
728    if (edge->fTop->fPoint == edge->fBottom->fPoint ||
729        c.sweep_gt(edge->fTop->fPoint, edge->fBottom->fPoint)) {
730        return;
731    }
732    LOG("insert edge (%g -> %g) below vertex %g\n", edge->fTop->fID, edge->fBottom->fID, v->fID);
733    Edge* prev = nullptr;
734    Edge* next;
735    for (next = v->fFirstEdgeBelow; next; next = next->fNextEdgeBelow) {
736        if (next->isRightOf(edge->fBottom)) {
737            break;
738        }
739        prev = next;
740    }
741    insert<Edge, &Edge::fPrevEdgeBelow, &Edge::fNextEdgeBelow>(
742        edge, prev, next, &v->fFirstEdgeBelow, &v->fLastEdgeBelow);
743}
744
745void remove_edge_above(Edge* edge) {
746    LOG("removing edge (%g -> %g) above vertex %g\n", edge->fTop->fID, edge->fBottom->fID,
747        edge->fBottom->fID);
748    remove<Edge, &Edge::fPrevEdgeAbove, &Edge::fNextEdgeAbove>(
749        edge, &edge->fBottom->fFirstEdgeAbove, &edge->fBottom->fLastEdgeAbove);
750}
751
752void remove_edge_below(Edge* edge) {
753    LOG("removing edge (%g -> %g) below vertex %g\n", edge->fTop->fID, edge->fBottom->fID,
754        edge->fTop->fID);
755    remove<Edge, &Edge::fPrevEdgeBelow, &Edge::fNextEdgeBelow>(
756        edge, &edge->fTop->fFirstEdgeBelow, &edge->fTop->fLastEdgeBelow);
757}
758
759void erase_edge_if_zero_winding(Edge* edge, EdgeList* edges) {
760    if (edge->fWinding != 0) {
761        return;
762    }
763    LOG("erasing edge (%g -> %g)\n", edge->fTop->fID, edge->fBottom->fID);
764    remove_edge_above(edge);
765    remove_edge_below(edge);
766    if (edge->isActive(edges)) {
767        remove_edge(edge, edges);
768    }
769}
770
771void merge_collinear_edges(Edge* edge, EdgeList* activeEdges, Comparator& c);
772
773void set_top(Edge* edge, Vertex* v, EdgeList* activeEdges, Comparator& c) {
774    remove_edge_below(edge);
775    edge->fTop = v;
776    edge->recompute();
777    insert_edge_below(edge, v, c);
778    fix_active_state(edge, activeEdges, c);
779    merge_collinear_edges(edge, activeEdges, c);
780}
781
782void set_bottom(Edge* edge, Vertex* v, EdgeList* activeEdges, Comparator& c) {
783    remove_edge_above(edge);
784    edge->fBottom = v;
785    edge->recompute();
786    insert_edge_above(edge, v, c);
787    fix_active_state(edge, activeEdges, c);
788    merge_collinear_edges(edge, activeEdges, c);
789}
790
791void merge_edges_above(Edge* edge, Edge* other, EdgeList* activeEdges, Comparator& c) {
792    if (coincident(edge->fTop->fPoint, other->fTop->fPoint)) {
793        LOG("merging coincident above edges (%g, %g) -> (%g, %g)\n",
794            edge->fTop->fPoint.fX, edge->fTop->fPoint.fY,
795            edge->fBottom->fPoint.fX, edge->fBottom->fPoint.fY);
796        other->fWinding += edge->fWinding;
797        erase_edge_if_zero_winding(other, activeEdges);
798        edge->fWinding = 0;
799        erase_edge_if_zero_winding(edge, activeEdges);
800    } else if (c.sweep_lt(edge->fTop->fPoint, other->fTop->fPoint)) {
801        other->fWinding += edge->fWinding;
802        erase_edge_if_zero_winding(other, activeEdges);
803        set_bottom(edge, other->fTop, activeEdges, c);
804    } else {
805        edge->fWinding += other->fWinding;
806        erase_edge_if_zero_winding(edge, activeEdges);
807        set_bottom(other, edge->fTop, activeEdges, c);
808    }
809}
810
811void merge_edges_below(Edge* edge, Edge* other, EdgeList* activeEdges, Comparator& c) {
812    if (coincident(edge->fBottom->fPoint, other->fBottom->fPoint)) {
813        LOG("merging coincident below edges (%g, %g) -> (%g, %g)\n",
814            edge->fTop->fPoint.fX, edge->fTop->fPoint.fY,
815            edge->fBottom->fPoint.fX, edge->fBottom->fPoint.fY);
816        other->fWinding += edge->fWinding;
817        erase_edge_if_zero_winding(other, activeEdges);
818        edge->fWinding = 0;
819        erase_edge_if_zero_winding(edge, activeEdges);
820    } else if (c.sweep_lt(edge->fBottom->fPoint, other->fBottom->fPoint)) {
821        edge->fWinding += other->fWinding;
822        erase_edge_if_zero_winding(edge, activeEdges);
823        set_top(other, edge->fBottom, activeEdges, c);
824    } else {
825        other->fWinding += edge->fWinding;
826        erase_edge_if_zero_winding(other, activeEdges);
827        set_top(edge, other->fBottom, activeEdges, c);
828    }
829}
830
831void merge_collinear_edges(Edge* edge, EdgeList* activeEdges, Comparator& c) {
832    if (edge->fPrevEdgeAbove && (edge->fTop == edge->fPrevEdgeAbove->fTop ||
833                                 !edge->fPrevEdgeAbove->isLeftOf(edge->fTop))) {
834        merge_edges_above(edge, edge->fPrevEdgeAbove, activeEdges, c);
835    } else if (edge->fNextEdgeAbove && (edge->fTop == edge->fNextEdgeAbove->fTop ||
836                                        !edge->isLeftOf(edge->fNextEdgeAbove->fTop))) {
837        merge_edges_above(edge, edge->fNextEdgeAbove, activeEdges, c);
838    }
839    if (edge->fPrevEdgeBelow && (edge->fBottom == edge->fPrevEdgeBelow->fBottom ||
840                                 !edge->fPrevEdgeBelow->isLeftOf(edge->fBottom))) {
841        merge_edges_below(edge, edge->fPrevEdgeBelow, activeEdges, c);
842    } else if (edge->fNextEdgeBelow && (edge->fBottom == edge->fNextEdgeBelow->fBottom ||
843                                        !edge->isLeftOf(edge->fNextEdgeBelow->fBottom))) {
844        merge_edges_below(edge, edge->fNextEdgeBelow, activeEdges, c);
845    }
846}
847
848void split_edge(Edge* edge, Vertex* v, EdgeList* activeEdges, Comparator& c, SkChunkAlloc& alloc);
849
850void cleanup_active_edges(Edge* edge, EdgeList* activeEdges, Comparator& c, SkChunkAlloc& alloc) {
851    Vertex* top = edge->fTop;
852    Vertex* bottom = edge->fBottom;
853    if (edge->fLeft) {
854        Vertex* leftTop = edge->fLeft->fTop;
855        Vertex* leftBottom = edge->fLeft->fBottom;
856        if (c.sweep_gt(top->fPoint, leftTop->fPoint) && !edge->fLeft->isLeftOf(top)) {
857            split_edge(edge->fLeft, edge->fTop, activeEdges, c, alloc);
858        } else if (c.sweep_gt(leftTop->fPoint, top->fPoint) && !edge->isRightOf(leftTop)) {
859            split_edge(edge, leftTop, activeEdges, c, alloc);
860        } else if (c.sweep_lt(bottom->fPoint, leftBottom->fPoint) &&
861                   !edge->fLeft->isLeftOf(bottom)) {
862            split_edge(edge->fLeft, bottom, activeEdges, c, alloc);
863        } else if (c.sweep_lt(leftBottom->fPoint, bottom->fPoint) && !edge->isRightOf(leftBottom)) {
864            split_edge(edge, leftBottom, activeEdges, c, alloc);
865        }
866    }
867    if (edge->fRight) {
868        Vertex* rightTop = edge->fRight->fTop;
869        Vertex* rightBottom = edge->fRight->fBottom;
870        if (c.sweep_gt(top->fPoint, rightTop->fPoint) && !edge->fRight->isRightOf(top)) {
871            split_edge(edge->fRight, top, activeEdges, c, alloc);
872        } else if (c.sweep_gt(rightTop->fPoint, top->fPoint) && !edge->isLeftOf(rightTop)) {
873            split_edge(edge, rightTop, activeEdges, c, alloc);
874        } else if (c.sweep_lt(bottom->fPoint, rightBottom->fPoint) &&
875                   !edge->fRight->isRightOf(bottom)) {
876            split_edge(edge->fRight, bottom, activeEdges, c, alloc);
877        } else if (c.sweep_lt(rightBottom->fPoint, bottom->fPoint) &&
878                   !edge->isLeftOf(rightBottom)) {
879            split_edge(edge, rightBottom, activeEdges, c, alloc);
880        }
881    }
882}
883
884void split_edge(Edge* edge, Vertex* v, EdgeList* activeEdges, Comparator& c, SkChunkAlloc& alloc) {
885    LOG("splitting edge (%g -> %g) at vertex %g (%g, %g)\n",
886        edge->fTop->fID, edge->fBottom->fID,
887        v->fID, v->fPoint.fX, v->fPoint.fY);
888    if (c.sweep_lt(v->fPoint, edge->fTop->fPoint)) {
889        set_top(edge, v, activeEdges, c);
890    } else if (c.sweep_gt(v->fPoint, edge->fBottom->fPoint)) {
891        set_bottom(edge, v, activeEdges, c);
892    } else {
893        Edge* newEdge = ALLOC_NEW(Edge, (v, edge->fBottom, edge->fWinding), alloc);
894        insert_edge_below(newEdge, v, c);
895        insert_edge_above(newEdge, edge->fBottom, c);
896        set_bottom(edge, v, activeEdges, c);
897        cleanup_active_edges(edge, activeEdges, c, alloc);
898        fix_active_state(newEdge, activeEdges, c);
899        merge_collinear_edges(newEdge, activeEdges, c);
900    }
901}
902
903void merge_vertices(Vertex* src, Vertex* dst, Vertex** head, Comparator& c, SkChunkAlloc& alloc) {
904    LOG("found coincident verts at %g, %g; merging %g into %g\n", src->fPoint.fX, src->fPoint.fY,
905        src->fID, dst->fID);
906    for (Edge* edge = src->fFirstEdgeAbove; edge;) {
907        Edge* next = edge->fNextEdgeAbove;
908        set_bottom(edge, dst, nullptr, c);
909        edge = next;
910    }
911    for (Edge* edge = src->fFirstEdgeBelow; edge;) {
912        Edge* next = edge->fNextEdgeBelow;
913        set_top(edge, dst, nullptr, c);
914        edge = next;
915    }
916    remove<Vertex, &Vertex::fPrev, &Vertex::fNext>(src, head, nullptr);
917}
918
919Vertex* check_for_intersection(Edge* edge, Edge* other, EdgeList* activeEdges, Comparator& c,
920                               SkChunkAlloc& alloc) {
921    SkPoint p;
922    if (!edge || !other) {
923        return nullptr;
924    }
925    if (edge->intersect(*other, &p)) {
926        Vertex* v;
927        LOG("found intersection, pt is %g, %g\n", p.fX, p.fY);
928        if (p == edge->fTop->fPoint || c.sweep_lt(p, edge->fTop->fPoint)) {
929            split_edge(other, edge->fTop, activeEdges, c, alloc);
930            v = edge->fTop;
931        } else if (p == edge->fBottom->fPoint || c.sweep_gt(p, edge->fBottom->fPoint)) {
932            split_edge(other, edge->fBottom, activeEdges, c, alloc);
933            v = edge->fBottom;
934        } else if (p == other->fTop->fPoint || c.sweep_lt(p, other->fTop->fPoint)) {
935            split_edge(edge, other->fTop, activeEdges, c, alloc);
936            v = other->fTop;
937        } else if (p == other->fBottom->fPoint || c.sweep_gt(p, other->fBottom->fPoint)) {
938            split_edge(edge, other->fBottom, activeEdges, c, alloc);
939            v = other->fBottom;
940        } else {
941            Vertex* nextV = edge->fTop;
942            while (c.sweep_lt(p, nextV->fPoint)) {
943                nextV = nextV->fPrev;
944            }
945            while (c.sweep_lt(nextV->fPoint, p)) {
946                nextV = nextV->fNext;
947            }
948            Vertex* prevV = nextV->fPrev;
949            if (coincident(prevV->fPoint, p)) {
950                v = prevV;
951            } else if (coincident(nextV->fPoint, p)) {
952                v = nextV;
953            } else {
954                v = ALLOC_NEW(Vertex, (p), alloc);
955                LOG("inserting between %g (%g, %g) and %g (%g, %g)\n",
956                    prevV->fID, prevV->fPoint.fX, prevV->fPoint.fY,
957                    nextV->fID, nextV->fPoint.fX, nextV->fPoint.fY);
958#if LOGGING_ENABLED
959                v->fID = (nextV->fID + prevV->fID) * 0.5f;
960#endif
961                v->fPrev = prevV;
962                v->fNext = nextV;
963                prevV->fNext = v;
964                nextV->fPrev = v;
965            }
966            split_edge(edge, v, activeEdges, c, alloc);
967            split_edge(other, v, activeEdges, c, alloc);
968        }
969        return v;
970    }
971    return nullptr;
972}
973
974void sanitize_contours(Vertex** contours, int contourCnt) {
975    for (int i = 0; i < contourCnt; ++i) {
976        SkASSERT(contours[i]);
977        for (Vertex* v = contours[i];;) {
978            if (coincident(v->fPrev->fPoint, v->fPoint)) {
979                LOG("vertex %g,%g coincident; removing\n", v->fPoint.fX, v->fPoint.fY);
980                if (v->fPrev == v) {
981                    contours[i] = nullptr;
982                    break;
983                }
984                v->fPrev->fNext = v->fNext;
985                v->fNext->fPrev = v->fPrev;
986                if (contours[i] == v) {
987                    contours[i] = v->fNext;
988                }
989                v = v->fPrev;
990            } else {
991                v = v->fNext;
992                if (v == contours[i]) break;
993            }
994        }
995    }
996}
997
998void merge_coincident_vertices(Vertex** vertices, Comparator& c, SkChunkAlloc& alloc) {
999    for (Vertex* v = (*vertices)->fNext; v != nullptr; v = v->fNext) {
1000        if (c.sweep_lt(v->fPoint, v->fPrev->fPoint)) {
1001            v->fPoint = v->fPrev->fPoint;
1002        }
1003        if (coincident(v->fPrev->fPoint, v->fPoint)) {
1004            merge_vertices(v->fPrev, v, vertices, c, alloc);
1005        }
1006    }
1007}
1008
1009// Stage 2: convert the contours to a mesh of edges connecting the vertices.
1010
1011Vertex* build_edges(Vertex** contours, int contourCnt, Comparator& c, SkChunkAlloc& alloc) {
1012    Vertex* vertices = nullptr;
1013    Vertex* prev = nullptr;
1014    for (int i = 0; i < contourCnt; ++i) {
1015        for (Vertex* v = contours[i]; v != nullptr;) {
1016            Vertex* vNext = v->fNext;
1017            Edge* edge = new_edge(v->fPrev, v, alloc, c);
1018            if (edge->fWinding > 0) {
1019                insert_edge_below(edge, v->fPrev, c);
1020                insert_edge_above(edge, v, c);
1021            } else {
1022                insert_edge_below(edge, v, c);
1023                insert_edge_above(edge, v->fPrev, c);
1024            }
1025            merge_collinear_edges(edge, nullptr, c);
1026            if (prev) {
1027                prev->fNext = v;
1028                v->fPrev = prev;
1029            } else {
1030                vertices = v;
1031            }
1032            prev = v;
1033            v = vNext;
1034            if (v == contours[i]) break;
1035        }
1036    }
1037    if (prev) {
1038        prev->fNext = vertices->fPrev = nullptr;
1039    }
1040    return vertices;
1041}
1042
1043// Stage 3: sort the vertices by increasing sweep direction.
1044
1045Vertex* sorted_merge(Vertex* a, Vertex* b, Comparator& c);
1046
1047void front_back_split(Vertex* v, Vertex** pFront, Vertex** pBack) {
1048    Vertex* fast;
1049    Vertex* slow;
1050    if (!v || !v->fNext) {
1051        *pFront = v;
1052        *pBack = nullptr;
1053    } else {
1054        slow = v;
1055        fast = v->fNext;
1056
1057        while (fast != nullptr) {
1058            fast = fast->fNext;
1059            if (fast != nullptr) {
1060                slow = slow->fNext;
1061                fast = fast->fNext;
1062            }
1063        }
1064
1065        *pFront = v;
1066        *pBack = slow->fNext;
1067        slow->fNext->fPrev = nullptr;
1068        slow->fNext = nullptr;
1069    }
1070}
1071
1072void merge_sort(Vertex** head, Comparator& c) {
1073    if (!*head || !(*head)->fNext) {
1074        return;
1075    }
1076
1077    Vertex* a;
1078    Vertex* b;
1079    front_back_split(*head, &a, &b);
1080
1081    merge_sort(&a, c);
1082    merge_sort(&b, c);
1083
1084    *head = sorted_merge(a, b, c);
1085}
1086
1087inline void append_vertex(Vertex* v, Vertex** head, Vertex** tail) {
1088    insert<Vertex, &Vertex::fPrev, &Vertex::fNext>(v, *tail, nullptr, head, tail);
1089}
1090
1091inline void append_vertex_list(Vertex* v, Vertex** head, Vertex** tail) {
1092    insert<Vertex, &Vertex::fPrev, &Vertex::fNext>(v, *tail, v->fNext, head, tail);
1093}
1094
1095Vertex* sorted_merge(Vertex* a, Vertex* b, Comparator& c) {
1096    Vertex* head = nullptr;
1097    Vertex* tail = nullptr;
1098
1099    while (a && b) {
1100        if (c.sweep_lt(a->fPoint, b->fPoint)) {
1101            Vertex* next = a->fNext;
1102            append_vertex(a, &head, &tail);
1103            a = next;
1104        } else {
1105            Vertex* next = b->fNext;
1106            append_vertex(b, &head, &tail);
1107            b = next;
1108        }
1109    }
1110    if (a) {
1111        append_vertex_list(a, &head, &tail);
1112    }
1113    if (b) {
1114        append_vertex_list(b, &head, &tail);
1115    }
1116    return head;
1117}
1118
1119// Stage 4: Simplify the mesh by inserting new vertices at intersecting edges.
1120
1121void simplify(Vertex* vertices, Comparator& c, SkChunkAlloc& alloc) {
1122    LOG("simplifying complex polygons\n");
1123    EdgeList activeEdges;
1124    for (Vertex* v = vertices; v != nullptr; v = v->fNext) {
1125        if (!v->fFirstEdgeAbove && !v->fFirstEdgeBelow) {
1126            continue;
1127        }
1128#if LOGGING_ENABLED
1129        LOG("\nvertex %g: (%g,%g)\n", v->fID, v->fPoint.fX, v->fPoint.fY);
1130#endif
1131        Edge* leftEnclosingEdge = nullptr;
1132        Edge* rightEnclosingEdge = nullptr;
1133        bool restartChecks;
1134        do {
1135            restartChecks = false;
1136            find_enclosing_edges(v, &activeEdges, &leftEnclosingEdge, &rightEnclosingEdge);
1137            if (v->fFirstEdgeBelow) {
1138                for (Edge* edge = v->fFirstEdgeBelow; edge != nullptr; edge = edge->fNextEdgeBelow) {
1139                    if (check_for_intersection(edge, leftEnclosingEdge, &activeEdges, c, alloc)) {
1140                        restartChecks = true;
1141                        break;
1142                    }
1143                    if (check_for_intersection(edge, rightEnclosingEdge, &activeEdges, c, alloc)) {
1144                        restartChecks = true;
1145                        break;
1146                    }
1147                }
1148            } else {
1149                if (Vertex* pv = check_for_intersection(leftEnclosingEdge, rightEnclosingEdge,
1150                                                        &activeEdges, c, alloc)) {
1151                    if (c.sweep_lt(pv->fPoint, v->fPoint)) {
1152                        v = pv;
1153                    }
1154                    restartChecks = true;
1155                }
1156
1157            }
1158        } while (restartChecks);
1159        for (Edge* e = v->fFirstEdgeAbove; e; e = e->fNextEdgeAbove) {
1160            remove_edge(e, &activeEdges);
1161        }
1162        Edge* leftEdge = leftEnclosingEdge;
1163        for (Edge* e = v->fFirstEdgeBelow; e; e = e->fNextEdgeBelow) {
1164            insert_edge(e, leftEdge, &activeEdges);
1165            leftEdge = e;
1166        }
1167        v->fProcessed = true;
1168    }
1169}
1170
1171// Stage 5: Tessellate the simplified mesh into monotone polygons.
1172
1173Poly* tessellate(Vertex* vertices, SkChunkAlloc& alloc) {
1174    LOG("tessellating simple polygons\n");
1175    EdgeList activeEdges;
1176    Poly* polys = nullptr;
1177    for (Vertex* v = vertices; v != nullptr; v = v->fNext) {
1178        if (!v->fFirstEdgeAbove && !v->fFirstEdgeBelow) {
1179            continue;
1180        }
1181#if LOGGING_ENABLED
1182        LOG("\nvertex %g: (%g,%g)\n", v->fID, v->fPoint.fX, v->fPoint.fY);
1183#endif
1184        Edge* leftEnclosingEdge = nullptr;
1185        Edge* rightEnclosingEdge = nullptr;
1186        find_enclosing_edges(v, &activeEdges, &leftEnclosingEdge, &rightEnclosingEdge);
1187        Poly* leftPoly = nullptr;
1188        Poly* rightPoly = nullptr;
1189        if (v->fFirstEdgeAbove) {
1190            leftPoly = v->fFirstEdgeAbove->fLeftPoly;
1191            rightPoly = v->fLastEdgeAbove->fRightPoly;
1192        } else {
1193            leftPoly = leftEnclosingEdge ? leftEnclosingEdge->fRightPoly : nullptr;
1194            rightPoly = rightEnclosingEdge ? rightEnclosingEdge->fLeftPoly : nullptr;
1195        }
1196#if LOGGING_ENABLED
1197        LOG("edges above:\n");
1198        for (Edge* e = v->fFirstEdgeAbove; e; e = e->fNextEdgeAbove) {
1199            LOG("%g -> %g, lpoly %d, rpoly %d\n", e->fTop->fID, e->fBottom->fID,
1200                e->fLeftPoly ? e->fLeftPoly->fID : -1, e->fRightPoly ? e->fRightPoly->fID : -1);
1201        }
1202        LOG("edges below:\n");
1203        for (Edge* e = v->fFirstEdgeBelow; e; e = e->fNextEdgeBelow) {
1204            LOG("%g -> %g, lpoly %d, rpoly %d\n", e->fTop->fID, e->fBottom->fID,
1205                e->fLeftPoly ? e->fLeftPoly->fID : -1, e->fRightPoly ? e->fRightPoly->fID : -1);
1206        }
1207#endif
1208        if (v->fFirstEdgeAbove) {
1209            if (leftPoly) {
1210                leftPoly = leftPoly->addVertex(v, Poly::kRight_Side, alloc);
1211            }
1212            if (rightPoly) {
1213                rightPoly = rightPoly->addVertex(v, Poly::kLeft_Side, alloc);
1214            }
1215            for (Edge* e = v->fFirstEdgeAbove; e != v->fLastEdgeAbove; e = e->fNextEdgeAbove) {
1216                Edge* leftEdge = e;
1217                Edge* rightEdge = e->fNextEdgeAbove;
1218                SkASSERT(rightEdge->isRightOf(leftEdge->fTop));
1219                remove_edge(leftEdge, &activeEdges);
1220                if (leftEdge->fRightPoly) {
1221                    leftEdge->fRightPoly->end(v, alloc);
1222                }
1223                if (rightEdge->fLeftPoly && rightEdge->fLeftPoly != leftEdge->fRightPoly) {
1224                    rightEdge->fLeftPoly->end(v, alloc);
1225                }
1226            }
1227            remove_edge(v->fLastEdgeAbove, &activeEdges);
1228            if (!v->fFirstEdgeBelow) {
1229                if (leftPoly && rightPoly && leftPoly != rightPoly) {
1230                    SkASSERT(leftPoly->fPartner == nullptr && rightPoly->fPartner == nullptr);
1231                    rightPoly->fPartner = leftPoly;
1232                    leftPoly->fPartner = rightPoly;
1233                }
1234            }
1235        }
1236        if (v->fFirstEdgeBelow) {
1237            if (!v->fFirstEdgeAbove) {
1238                if (leftPoly && leftPoly == rightPoly) {
1239                    // Split the poly.
1240                    if (leftPoly->fActive->fSide == Poly::kLeft_Side) {
1241                        leftPoly = new_poly(&polys, leftEnclosingEdge->fTop, leftPoly->fWinding,
1242                                            alloc);
1243                        leftPoly->addVertex(v, Poly::kRight_Side, alloc);
1244                        rightPoly->addVertex(v, Poly::kLeft_Side, alloc);
1245                        leftEnclosingEdge->fRightPoly = leftPoly;
1246                    } else {
1247                        rightPoly = new_poly(&polys, rightEnclosingEdge->fTop, rightPoly->fWinding,
1248                                             alloc);
1249                        rightPoly->addVertex(v, Poly::kLeft_Side, alloc);
1250                        leftPoly->addVertex(v, Poly::kRight_Side, alloc);
1251                        rightEnclosingEdge->fLeftPoly = rightPoly;
1252                    }
1253                } else {
1254                    if (leftPoly) {
1255                        leftPoly = leftPoly->addVertex(v, Poly::kRight_Side, alloc);
1256                    }
1257                    if (rightPoly) {
1258                        rightPoly = rightPoly->addVertex(v, Poly::kLeft_Side, alloc);
1259                    }
1260                }
1261            }
1262            Edge* leftEdge = v->fFirstEdgeBelow;
1263            leftEdge->fLeftPoly = leftPoly;
1264            insert_edge(leftEdge, leftEnclosingEdge, &activeEdges);
1265            for (Edge* rightEdge = leftEdge->fNextEdgeBelow; rightEdge;
1266                 rightEdge = rightEdge->fNextEdgeBelow) {
1267                insert_edge(rightEdge, leftEdge, &activeEdges);
1268                int winding = leftEdge->fLeftPoly ? leftEdge->fLeftPoly->fWinding : 0;
1269                winding += leftEdge->fWinding;
1270                if (winding != 0) {
1271                    Poly* poly = new_poly(&polys, v, winding, alloc);
1272                    leftEdge->fRightPoly = rightEdge->fLeftPoly = poly;
1273                }
1274                leftEdge = rightEdge;
1275            }
1276            v->fLastEdgeBelow->fRightPoly = rightPoly;
1277        }
1278#if LOGGING_ENABLED
1279        LOG("\nactive edges:\n");
1280        for (Edge* e = activeEdges.fHead; e != nullptr; e = e->fRight) {
1281            LOG("%g -> %g, lpoly %d, rpoly %d\n", e->fTop->fID, e->fBottom->fID,
1282                e->fLeftPoly ? e->fLeftPoly->fID : -1, e->fRightPoly ? e->fRightPoly->fID : -1);
1283        }
1284#endif
1285    }
1286    return polys;
1287}
1288
1289// This is a driver function which calls stages 2-5 in turn.
1290
1291Poly* contours_to_polys(Vertex** contours, int contourCnt, const SkRect& pathBounds,
1292                        SkChunkAlloc& alloc) {
1293    Comparator c;
1294    if (pathBounds.width() > pathBounds.height()) {
1295        c.sweep_lt = sweep_lt_horiz;
1296        c.sweep_gt = sweep_gt_horiz;
1297    } else {
1298        c.sweep_lt = sweep_lt_vert;
1299        c.sweep_gt = sweep_gt_vert;
1300    }
1301#if LOGGING_ENABLED
1302    for (int i = 0; i < contourCnt; ++i) {
1303        Vertex* v = contours[i];
1304        SkASSERT(v);
1305        LOG("path.moveTo(%20.20g, %20.20g);\n", v->fPoint.fX, v->fPoint.fY);
1306        for (v = v->fNext; v != contours[i]; v = v->fNext) {
1307            LOG("path.lineTo(%20.20g, %20.20g);\n", v->fPoint.fX, v->fPoint.fY);
1308        }
1309    }
1310#endif
1311    sanitize_contours(contours, contourCnt);
1312    Vertex* vertices = build_edges(contours, contourCnt, c, alloc);
1313    if (!vertices) {
1314        return nullptr;
1315    }
1316
1317    // Sort vertices in Y (secondarily in X).
1318    merge_sort(&vertices, c);
1319    merge_coincident_vertices(&vertices, c, alloc);
1320#if LOGGING_ENABLED
1321    for (Vertex* v = vertices; v != nullptr; v = v->fNext) {
1322        static float gID = 0.0f;
1323        v->fID = gID++;
1324    }
1325#endif
1326    simplify(vertices, c, alloc);
1327    return tessellate(vertices, alloc);
1328}
1329
1330Poly* path_to_polys(const SkPath& path, SkScalar tolerance, const SkRect& clipBounds,
1331                    int contourCnt, SkChunkAlloc& alloc, bool* isLinear) {
1332    SkPath::FillType fillType = path.getFillType();
1333    if (SkPath::IsInverseFillType(fillType)) {
1334        contourCnt++;
1335    }
1336    SkAutoTDeleteArray<Vertex*> contours(new Vertex* [contourCnt]);
1337
1338    path_to_contours(path, tolerance, clipBounds, contours.get(), alloc, isLinear);
1339    return contours_to_polys(contours.get(), contourCnt, path.getBounds(), alloc);
1340}
1341
1342void get_contour_count_and_size_estimate(const SkPath& path, SkScalar tolerance, int* contourCnt,
1343                                         int* sizeEstimate) {
1344    int maxPts = GrPathUtils::worstCasePointCount(path, contourCnt, tolerance);
1345    if (maxPts <= 0) {
1346        *contourCnt = 0;
1347        return;
1348    }
1349    if (maxPts > ((int)SK_MaxU16 + 1)) {
1350        SkDebugf("Path not rendered, too many verts (%d)\n", maxPts);
1351        *contourCnt = 0;
1352        return;
1353    }
1354    // For the initial size of the chunk allocator, estimate based on the point count:
1355    // one vertex per point for the initial passes, plus two for the vertices in the
1356    // resulting Polys, since the same point may end up in two Polys.  Assume minimal
1357    // connectivity of one Edge per Vertex (will grow for intersections).
1358    *sizeEstimate = maxPts * (3 * sizeof(Vertex) + sizeof(Edge));
1359}
1360
1361int count_points(Poly* polys, SkPath::FillType fillType) {
1362    int count = 0;
1363    for (Poly* poly = polys; poly; poly = poly->fNext) {
1364        if (apply_fill_type(fillType, poly->fWinding) && poly->fCount >= 3) {
1365            count += (poly->fCount - 2) * (TESSELLATOR_WIREFRAME ? 6 : 3);
1366        }
1367    }
1368    return count;
1369}
1370
1371} // namespace
1372
1373namespace GrTessellator {
1374
1375// Stage 6: Triangulate the monotone polygons into a vertex buffer.
1376
1377int PathToTriangles(const SkPath& path, SkScalar tolerance, const SkRect& clipBounds,
1378                    GrResourceProvider* resourceProvider,
1379                    SkAutoTUnref<GrVertexBuffer>& vertexBuffer, bool canMapVB, bool* isLinear) {
1380    int contourCnt;
1381    int sizeEstimate;
1382    get_contour_count_and_size_estimate(path, tolerance, &contourCnt, &sizeEstimate);
1383    if (contourCnt <= 0) {
1384        *isLinear = true;
1385        return 0;
1386    }
1387    SkChunkAlloc alloc(sizeEstimate);
1388    Poly* polys = path_to_polys(path, tolerance, clipBounds, contourCnt, alloc, isLinear);
1389    SkPath::FillType fillType = path.getFillType();
1390    int count = count_points(polys, fillType);
1391    if (0 == count) {
1392        return 0;
1393    }
1394
1395    size_t size = count * sizeof(SkPoint);
1396    if (!vertexBuffer.get() || vertexBuffer->gpuMemorySize() < size) {
1397        vertexBuffer.reset(resourceProvider->createVertexBuffer(
1398            size, GrResourceProvider::kStatic_BufferUsage, 0));
1399    }
1400    if (!vertexBuffer.get()) {
1401        SkDebugf("Could not allocate vertices\n");
1402        return 0;
1403    }
1404    SkPoint* verts;
1405    if (canMapVB) {
1406        verts = static_cast<SkPoint*>(vertexBuffer->map());
1407    } else {
1408        verts = new SkPoint[count];
1409    }
1410    SkPoint* end = verts;
1411    for (Poly* poly = polys; poly; poly = poly->fNext) {
1412        if (apply_fill_type(fillType, poly->fWinding)) {
1413            end = poly->emit(end);
1414        }
1415    }
1416    int actualCount = static_cast<int>(end - verts);
1417    LOG("actual count: %d\n", actualCount);
1418    SkASSERT(actualCount <= count);
1419    if (canMapVB) {
1420        vertexBuffer->unmap();
1421    } else {
1422        vertexBuffer->updateData(verts, actualCount * sizeof(SkPoint));
1423        delete[] verts;
1424    }
1425
1426    return actualCount;
1427}
1428
1429int PathToVertices(const SkPath& path, SkScalar tolerance, const SkRect& clipBounds,
1430                   GrTessellator::WindingVertex** verts) {
1431    int contourCnt;
1432    int sizeEstimate;
1433    get_contour_count_and_size_estimate(path, tolerance, &contourCnt, &sizeEstimate);
1434    if (contourCnt <= 0) {
1435        return 0;
1436    }
1437    SkChunkAlloc alloc(sizeEstimate);
1438    bool isLinear;
1439    Poly* polys = path_to_polys(path, tolerance, clipBounds, contourCnt, alloc, &isLinear);
1440    SkPath::FillType fillType = path.getFillType();
1441    int count = count_points(polys, fillType);
1442    if (0 == count) {
1443        *verts = nullptr;
1444        return 0;
1445    }
1446
1447    *verts = new GrTessellator::WindingVertex[count];
1448    GrTessellator::WindingVertex* vertsEnd = *verts;
1449    SkPoint* points = new SkPoint[count];
1450    SkPoint* pointsEnd = points;
1451    for (Poly* poly = polys; poly; poly = poly->fNext) {
1452        if (apply_fill_type(fillType, poly->fWinding)) {
1453            SkPoint* start = pointsEnd;
1454            pointsEnd = poly->emit(pointsEnd);
1455            while (start != pointsEnd) {
1456                vertsEnd->fPos = *start;
1457                vertsEnd->fWinding = poly->fWinding;
1458                ++start;
1459                ++vertsEnd;
1460            }
1461        }
1462    }
1463    int actualCount = static_cast<int>(vertsEnd - *verts);
1464    SkASSERT(actualCount <= count);
1465    SkASSERT(pointsEnd - points == actualCount);
1466    delete[] points;
1467    return actualCount;
1468}
1469
1470} // namespace
1471