Revert of Broke GrTessellatingPathRenderer's tessellator out into a separate file.

src/gpu/GrTessellator.cpp

-/*
- * Copyright 2015 Google Inc.
- *
- * Use of this source code is governed by a BSD-style license that can be
- * found in the LICENSE file.
- */
-
-#include "GrTessellator.h"
-
-#include "GrBatchFlushState.h"
-#include "GrBatchTest.h"
-#include "GrDefaultGeoProcFactory.h"
-#include "GrPathUtils.h"
-#include "GrVertices.h"
-#include "GrResourceCache.h"
-#include "GrResourceProvider.h"
-#include "SkGeometry.h"
-#include "SkChunkAlloc.h"
-
-#include "batches/GrVertexBatch.h"
-
-#include <stdio.h>
-
-/*
- * There are six stages to the algorithm:
- *
- * 1) Linearize the path contours into piecewise linear segments (path_to_contours()).
- * 2) Build a mesh of edges connecting the vertices (build_edges()).
- * 3) Sort the vertices in Y (and secondarily in X) (merge_sort()).
- * 4) Simplify the mesh by inserting new vertices at intersecting edges (simplify()).
- * 5) Tessellate the simplified mesh into monotone polygons (tessellate()).
- * 6) Triangulate the monotone polygons directly into a vertex buffer (polys_to_triangles()).
- *
- * The vertex sorting in step (3) is a merge sort, since it plays well with the linked list
- * of vertices (and the necessity of inserting new vertices on intersection).
- *
- * Stages (4) and (5) use an active edge list, which a list of all edges for which the
- * sweep line has crossed the top vertex, but not the bottom vertex.  It's sorted
- * left-to-right based on the point where both edges are active (when both top vertices
- * have been seen, so the "lower" top vertex of the two). If the top vertices are equal
- * (shared), it's sorted based on the last point where both edges are active, so the
- * "upper" bottom vertex.
- *
- * The most complex step is the simplification (4). It's based on the Bentley-Ottman
- * line-sweep algorithm, but due to floating point inaccuracy, the intersection points are
- * not exact and may violate the mesh topology or active edge list ordering. We
- * accommodate this by adjusting the topology of the mesh and AEL to match the intersection
- * points. This occurs in three ways:
- *
- * A) Intersections may cause a shortened edge to no longer be ordered with respect to its
- *    neighbouring edges at the top or bottom vertex. This is handled by merging the
- *    edges (merge_collinear_edges()).
- * B) Intersections may cause an edge to violate the left-to-right ordering of the
- *    active edge list. This is handled by splitting the neighbour edge on the
- *    intersected vertex (cleanup_active_edges()).
- * C) Shortening an edge may cause an active edge to become inactive or an inactive edge
- *    to become active. This is handled by removing or inserting the edge in the active
- *    edge list (fix_active_state()).
- *
- * The tessellation steps (5) and (6) are based on "Triangulating Simple Polygons and
- * Equivalent Problems" (Fournier and Montuno); also a line-sweep algorithm. Note that it
- * currently uses a linked list for the active edge list, rather than a 2-3 tree as the
- * paper describes. The 2-3 tree gives O(lg N) lookups, but insertion and removal also
- * become O(lg N). In all the test cases, it was found that the cost of frequent O(lg N)
- * insertions and removals was greater than the cost of infrequent O(N) lookups with the
- * linked list implementation. With the latter, all removals are O(1), and most insertions
- * are O(1), since we know the adjacent edge in the active edge list based on the topology.
- * Only type 2 vertices (see paper) require the O(N) lookups, and these are much less
- * frequent. There may be other data structures worth investigating, however.
- *
- * Note that the orientation of the line sweep algorithms is determined by the aspect ratio of the
- * path bounds. When the path is taller than it is wide, we sort vertices based on increasing Y
- * coordinate, and secondarily by increasing X coordinate. When the path is wider than it is tall,
- * we sort by increasing X coordinate, but secondarily by *decreasing* Y coordinate. This is so
- * that the "left" and "right" orientation in the code remains correct (edges to the left are
- * increasing in Y; edges to the right are decreasing in Y). That is, the setting rotates 90
- * degrees counterclockwise, rather that transposing.
- */
-
-#define LOGGING_ENABLED 0
-
-#if LOGGING_ENABLED
-#define LOG printf
-#else
-#define LOG(...)
-#endif
-
-#define ALLOC_NEW(Type, args, alloc) new (alloc.allocThrow(sizeof(Type))) Type args
-
-namespace {
-
-struct Vertex;
-struct Edge;
-struct Poly;
-
-template <class T, T* T::*Prev, T* T::*Next>
-void insert(T* t, T* prev, T* next, T** head, T** tail) {
-    t->*Prev = prev;
-    t->*Next = next;
-    if (prev) {
-        prev->*Next = t;
-    } else if (head) {
-        *head = t;
-    }
-    if (next) {
-        next->*Prev = t;
-    } else if (tail) {
-        *tail = t;
-    }
-}
-
-template <class T, T* T::*Prev, T* T::*Next>
-void remove(T* t, T** head, T** tail) {
-    if (t->*Prev) {
-        t->*Prev->*Next = t->*Next;
-    } else if (head) {
-        *head = t->*Next;
-    }
-    if (t->*Next) {
-        t->*Next->*Prev = t->*Prev;
-    } else if (tail) {
-        *tail = t->*Prev;
-    }
-    t->*Prev = t->*Next = nullptr;
-}
-
-/**
- * Vertices are used in three ways: first, the path contours are converted into a
- * circularly-linked list of Vertices for each contour. After edge construction, the same Vertices
- * are re-ordered by the merge sort according to the sweep_lt comparator (usually, increasing
- * in Y) using the same fPrev/fNext pointers that were used for the contours, to avoid
- * reallocation. Finally, MonotonePolys are built containing a circularly-linked list of
- * Vertices. (Currently, those Vertices are newly-allocated for the MonotonePolys, since
- * an individual Vertex from the path mesh may belong to multiple
- * MonotonePolys, so the original Vertices cannot be re-used.
- */
-
-struct Vertex {
-  Vertex(const SkPoint& point)
-    : fPoint(point), fPrev(nullptr), fNext(nullptr)
-    , fFirstEdgeAbove(nullptr), fLastEdgeAbove(nullptr)
-    , fFirstEdgeBelow(nullptr), fLastEdgeBelow(nullptr)
-    , fProcessed(false)
-#if LOGGING_ENABLED
-    , fID (-1.0f)
-#endif
-    {}
-    SkPoint fPoint;           // Vertex position
-    Vertex* fPrev;            // Linked list of contours, then Y-sorted vertices.
-    Vertex* fNext;            // "
-    Edge*   fFirstEdgeAbove;  // Linked list of edges above this vertex.
-    Edge*   fLastEdgeAbove;   // "
-    Edge*   fFirstEdgeBelow;  // Linked list of edges below this vertex.
-    Edge*   fLastEdgeBelow;   // "
-    bool    fProcessed;       // Has this vertex been seen in simplify()?
-#if LOGGING_ENABLED
-    float   fID;              // Identifier used for logging.
-#endif
-};
-
-/***************************************************************************************/
-
-typedef bool (*CompareFunc)(const SkPoint& a, const SkPoint& b);
-
-struct Comparator {
-    CompareFunc sweep_lt;
-    CompareFunc sweep_gt;
-};
-
-bool sweep_lt_horiz(const SkPoint& a, const SkPoint& b) {
-    return a.fX == b.fX ? a.fY > b.fY : a.fX < b.fX;
-}
-
-bool sweep_lt_vert(const SkPoint& a, const SkPoint& b) {
-    return a.fY == b.fY ? a.fX < b.fX : a.fY < b.fY;
-}
-
-bool sweep_gt_horiz(const SkPoint& a, const SkPoint& b) {
-    return a.fX == b.fX ? a.fY < b.fY : a.fX > b.fX;
-}
-
-bool sweep_gt_vert(const SkPoint& a, const SkPoint& b) {
-    return a.fY == b.fY ? a.fX > b.fX : a.fY > b.fY;
-}
-
-inline SkPoint* emit_vertex(Vertex* v, SkPoint* data) {
-    *data++ = v->fPoint;
-    return data;
-}
-
-SkPoint* emit_triangle(Vertex* v0, Vertex* v1, Vertex* v2, SkPoint* data) {
-#if WIREFRAME
-    data = emit_vertex(v0, data);
-    data = emit_vertex(v1, data);
-    data = emit_vertex(v1, data);
-    data = emit_vertex(v2, data);
-    data = emit_vertex(v2, data);
-    data = emit_vertex(v0, data);
-#else
-    data = emit_vertex(v0, data);
-    data = emit_vertex(v1, data);
-    data = emit_vertex(v2, data);
-#endif
-    return data;
-}
-
-struct EdgeList {
-    EdgeList() : fHead(nullptr), fTail(nullptr) {}
-    Edge* fHead;
-    Edge* fTail;
-};
-
-/**
- * An Edge joins a top Vertex to a bottom Vertex. Edge ordering for the list of "edges above" and
- * "edge below" a vertex as well as for the active edge list is handled by isLeftOf()/isRightOf().
- * Note that an Edge will give occasionally dist() != 0 for its own endpoints (because floating
- * point). For speed, that case is only tested by the callers which require it (e.g.,
- * cleanup_active_edges()). Edges also handle checking for intersection with other edges.
- * Currently, this converts the edges to the parametric form, in order to avoid doing a division
- * until an intersection has been confirmed. This is slightly slower in the "found" case, but
- * a lot faster in the "not found" case.
- *
- * The coefficients of the line equation stored in double precision to avoid catastrphic
- * cancellation in the isLeftOf() and isRightOf() checks. Using doubles ensures that the result is
- * correct in float, since it's a polynomial of degree 2. The intersect() function, being
- * degree 5, is still subject to catastrophic cancellation. We deal with that by assuming its
- * output may be incorrect, and adjusting the mesh topology to match (see comment at the top of
- * this file).
- */
-
-struct Edge {
-    Edge(Vertex* top, Vertex* bottom, int winding)
-        : fWinding(winding)
-        , fTop(top)
-        , fBottom(bottom)
-        , fLeft(nullptr)
-        , fRight(nullptr)
-        , fPrevEdgeAbove(nullptr)
-        , fNextEdgeAbove(nullptr)
-        , fPrevEdgeBelow(nullptr)
-        , fNextEdgeBelow(nullptr)
-        , fLeftPoly(nullptr)
-        , fRightPoly(nullptr) {
-            recompute();
-        }
-    int      fWinding;          // 1 == edge goes downward; -1 = edge goes upward.
-    Vertex*  fTop;              // The top vertex in vertex-sort-order (sweep_lt).
-    Vertex*  fBottom;           // The bottom vertex in vertex-sort-order.
-    Edge*    fLeft;             // The linked list of edges in the active edge list.
-    Edge*    fRight;            // "
-    Edge*    fPrevEdgeAbove;    // The linked list of edges in the bottom Vertex's "edges above".
-    Edge*    fNextEdgeAbove;    // "
-    Edge*    fPrevEdgeBelow;    // The linked list of edges in the top Vertex's "edges below".
-    Edge*    fNextEdgeBelow;    // "
-    Poly*    fLeftPoly;         // The Poly to the left of this edge, if any.
-    Poly*    fRightPoly;        // The Poly to the right of this edge, if any.
-    double   fDX;               // The line equation for this edge, in implicit form.
-    double   fDY;               // fDY * x + fDX * y + fC = 0, for point (x, y) on the line.
-    double   fC;
-    double dist(const SkPoint& p) const {
-        return fDY * p.fX - fDX * p.fY + fC;
-    }
-    bool isRightOf(Vertex* v) const {
-        return dist(v->fPoint) < 0.0;
-    }
-    bool isLeftOf(Vertex* v) const {
-        return dist(v->fPoint) > 0.0;
-    }
-    void recompute() {
-        fDX = static_cast<double>(fBottom->fPoint.fX) - fTop->fPoint.fX;
-        fDY = static_cast<double>(fBottom->fPoint.fY) - fTop->fPoint.fY;
-        fC = static_cast<double>(fTop->fPoint.fY) * fBottom->fPoint.fX -
-             static_cast<double>(fTop->fPoint.fX) * fBottom->fPoint.fY;
-    }
-    bool intersect(const Edge& other, SkPoint* p) {
-        LOG("intersecting %g -> %g with %g -> %g\n",
-               fTop->fID, fBottom->fID,
-               other.fTop->fID, other.fBottom->fID);
-        if (fTop == other.fTop || fBottom == other.fBottom) {
-            return false;
-        }
-        double denom = fDX * other.fDY - fDY * other.fDX;
-        if (denom == 0.0) {
-            return false;
-        }
-        double dx = static_cast<double>(fTop->fPoint.fX) - other.fTop->fPoint.fX;
-        double dy = static_cast<double>(fTop->fPoint.fY) - other.fTop->fPoint.fY;
-        double sNumer = dy * other.fDX - dx * other.fDY;
-        double tNumer = dy * fDX - dx * fDY;
-        // If (sNumer / denom) or (tNumer / denom) is not in [0..1], exit early.
-        // This saves us doing the divide below unless absolutely necessary.
-        if (denom > 0.0 ? (sNumer < 0.0 || sNumer > denom || tNumer < 0.0 || tNumer > denom)
-                        : (sNumer > 0.0 || sNumer < denom || tNumer > 0.0 || tNumer < denom)) {
-            return false;
-        }
-        double s = sNumer / denom;
-        SkASSERT(s >= 0.0 && s <= 1.0);
-        p->fX = SkDoubleToScalar(fTop->fPoint.fX + s * fDX);
-        p->fY = SkDoubleToScalar(fTop->fPoint.fY + s * fDY);
-        return true;
-    }
-    bool isActive(EdgeList* activeEdges) const {
-        return activeEdges && (fLeft || fRight || activeEdges->fHead == this);
-    }
-};
-
-/***************************************************************************************/
-
-struct Poly {
-    Poly(int winding)
-        : fWinding(winding)
-        , fHead(nullptr)
-        , fTail(nullptr)
-        , fActive(nullptr)
-        , fNext(nullptr)
-        , fPartner(nullptr)
-        , fCount(0)
-    {
-#if LOGGING_ENABLED
-        static int gID = 0;
-        fID = gID++;
-        LOG("*** created Poly %d\n", fID);
-#endif
-    }
-    typedef enum { kNeither_Side, kLeft_Side, kRight_Side } Side;
-    struct MonotonePoly {
-        MonotonePoly()
-            : fSide(kNeither_Side)
-            , fHead(nullptr)
-            , fTail(nullptr)
-            , fPrev(nullptr)
-            , fNext(nullptr) {}
-        Side          fSide;
-        Vertex*       fHead;
-        Vertex*       fTail;
-        MonotonePoly* fPrev;
-        MonotonePoly* fNext;
-        bool addVertex(Vertex* v, Side side, SkChunkAlloc& alloc) {
-            Vertex* newV = ALLOC_NEW(Vertex, (v->fPoint), alloc);
-            bool done = false;
-            if (fSide == kNeither_Side) {
-                fSide = side;
-            } else {
-                done = side != fSide;
-            }
-            if (fHead == nullptr) {
-                fHead = fTail = newV;
-            } else if (fSide == kRight_Side) {
-                newV->fPrev = fTail;
-                fTail->fNext = newV;
-                fTail = newV;
-            } else {
-                newV->fNext = fHead;
-                fHead->fPrev = newV;
-                fHead = newV;
-            }
-            return done;
-        }
-
-        SkPoint* emit(SkPoint* data) {
-            Vertex* first = fHead;
-            Vertex* v = first->fNext;
-            while (v != fTail) {
-                SkASSERT(v && v->fPrev && v->fNext);
-                Vertex* prev = v->fPrev;
-                Vertex* curr = v;
-                Vertex* next = v->fNext;
-                double ax = static_cast<double>(curr->fPoint.fX) - prev->fPoint.fX;
-                double ay = static_cast<double>(curr->fPoint.fY) - prev->fPoint.fY;
-                double bx = static_cast<double>(next->fPoint.fX) - curr->fPoint.fX;
-                double by = static_cast<double>(next->fPoint.fY) - curr->fPoint.fY;
-                if (ax * by - ay * bx >= 0.0) {
-                    data = emit_triangle(prev, curr, next, data);
-                    v->fPrev->fNext = v->fNext;
-                    v->fNext->fPrev = v->fPrev;
-                    if (v->fPrev == first) {
-                        v = v->fNext;
-                    } else {
-                        v = v->fPrev;
-                    }
-                } else {
-                    v = v->fNext;
-                }
-            }
-            return data;
-        }
-    };
-    Poly* addVertex(Vertex* v, Side side, SkChunkAlloc& alloc) {
-        LOG("addVertex() to %d at %g (%g, %g), %s side\n", fID, v->fID, v->fPoint.fX, v->fPoint.fY,
-               side == kLeft_Side ? "left" : side == kRight_Side ? "right" : "neither");
-        Poly* partner = fPartner;
-        Poly* poly = this;
-        if (partner) {
-            fPartner = partner->fPartner = nullptr;
-        }
-        if (!fActive) {
-            fActive = ALLOC_NEW(MonotonePoly, (), alloc);
-        }
-        if (fActive->addVertex(v, side, alloc)) {
-            if (fTail) {
-                fActive->fPrev = fTail;
-                fTail->fNext = fActive;
-                fTail = fActive;
-            } else {
-                fHead = fTail = fActive;
-            }
-            if (partner) {
-                partner->addVertex(v, side, alloc);
-                poly = partner;
-            } else {
-                Vertex* prev = fActive->fSide == Poly::kLeft_Side ?
-                               fActive->fHead->fNext : fActive->fTail->fPrev;
-                fActive = ALLOC_NEW(MonotonePoly, , alloc);
-                fActive->addVertex(prev, Poly::kNeither_Side, alloc);
-                fActive->addVertex(v, side, alloc);
-            }
-        }
-        fCount++;
-        return poly;
-    }
-    void end(Vertex* v, SkChunkAlloc& alloc) {
-        LOG("end() %d at %g, %g\n", fID, v->fPoint.fX, v->fPoint.fY);
-        if (fPartner) {
-            fPartner = fPartner->fPartner = nullptr;
-        }
-        addVertex(v, fActive->fSide == kLeft_Side ? kRight_Side : kLeft_Side, alloc);
-    }
-    SkPoint* emit(SkPoint *data) {
-        if (fCount < 3) {
-            return data;
-        }
-        LOG("emit() %d, size %d\n", fID, fCount);
-        for (MonotonePoly* m = fHead; m != nullptr; m = m->fNext) {
-            data = m->emit(data);
-        }
-        return data;
-    }
-    int fWinding;
-    MonotonePoly* fHead;
-    MonotonePoly* fTail;
-    MonotonePoly* fActive;
-    Poly* fNext;
-    Poly* fPartner;
-    int fCount;
-#if LOGGING_ENABLED
-    int fID;
-#endif
-};
-
-/***************************************************************************************/
-
-bool coincident(const SkPoint& a, const SkPoint& b) {
-    return a == b;
-}
-
-Poly* new_poly(Poly** head, Vertex* v, int winding, SkChunkAlloc& alloc) {
-    Poly* poly = ALLOC_NEW(Poly, (winding), alloc);
-    poly->addVertex(v, Poly::kNeither_Side, alloc);
-    poly->fNext = *head;
-    *head = poly;
-    return poly;
-}
-
-Vertex* append_point_to_contour(const SkPoint& p, Vertex* prev, Vertex** head,
-                                SkChunkAlloc& alloc) {
-    Vertex* v = ALLOC_NEW(Vertex, (p), alloc);
-#if LOGGING_ENABLED
-    static float gID = 0.0f;
-    v->fID = gID++;
-#endif
-    if (prev) {
-        prev->fNext = v;
-        v->fPrev = prev;
-    } else {
-        *head = v;
-    }
-    return v;
-}
-
-Vertex* generate_quadratic_points(const SkPoint& p0,
-                                  const SkPoint& p1,
-                                  const SkPoint& p2,
-                                  SkScalar tolSqd,
-                                  Vertex* prev,
-                                  Vertex** head,
-                                  int pointsLeft,
-                                  SkChunkAlloc& alloc) {
-    SkScalar d = p1.distanceToLineSegmentBetweenSqd(p0, p2);
-    if (pointsLeft < 2 || d < tolSqd || !SkScalarIsFinite(d)) {
-        return append_point_to_contour(p2, prev, head, alloc);
-    }
-
-    const SkPoint q[] = {
-        { SkScalarAve(p0.fX, p1.fX), SkScalarAve(p0.fY, p1.fY) },
-        { SkScalarAve(p1.fX, p2.fX), SkScalarAve(p1.fY, p2.fY) },
-    };
-    const SkPoint r = { SkScalarAve(q[0].fX, q[1].fX), SkScalarAve(q[0].fY, q[1].fY) };
-
-    pointsLeft >>= 1;
-    prev = generate_quadratic_points(p0, q[0], r, tolSqd, prev, head, pointsLeft, alloc);
-    prev = generate_quadratic_points(r, q[1], p2, tolSqd, prev, head, pointsLeft, alloc);
-    return prev;
-}
-
-Vertex* generate_cubic_points(const SkPoint& p0,
-                              const SkPoint& p1,
-                              const SkPoint& p2,
-                              const SkPoint& p3,
-                              SkScalar tolSqd,
-                              Vertex* prev,
-                              Vertex** head,
-                              int pointsLeft,
-                              SkChunkAlloc& alloc) {
-    SkScalar d1 = p1.distanceToLineSegmentBetweenSqd(p0, p3);
-    SkScalar d2 = p2.distanceToLineSegmentBetweenSqd(p0, p3);
-    if (pointsLeft < 2 || (d1 < tolSqd && d2 < tolSqd) ||
-        !SkScalarIsFinite(d1) || !SkScalarIsFinite(d2)) {
-        return append_point_to_contour(p3, prev, head, alloc);
-    }
-    const SkPoint q[] = {
-        { SkScalarAve(p0.fX, p1.fX), SkScalarAve(p0.fY, p1.fY) },
-        { SkScalarAve(p1.fX, p2.fX), SkScalarAve(p1.fY, p2.fY) },
-        { SkScalarAve(p2.fX, p3.fX), SkScalarAve(p2.fY, p3.fY) }
-    };
-    const SkPoint r[] = {
-        { SkScalarAve(q[0].fX, q[1].fX), SkScalarAve(q[0].fY, q[1].fY) },
-        { SkScalarAve(q[1].fX, q[2].fX), SkScalarAve(q[1].fY, q[2].fY) }
-    };
-    const SkPoint s = { SkScalarAve(r[0].fX, r[1].fX), SkScalarAve(r[0].fY, r[1].fY) };
-    pointsLeft >>= 1;
-    prev = generate_cubic_points(p0, q[0], r[0], s, tolSqd, prev, head, pointsLeft, alloc);
-    prev = generate_cubic_points(s, r[1], q[2], p3, tolSqd, prev, head, pointsLeft, alloc);
-    return prev;
-}
-
-// Stage 1: convert the input path to a set of linear contours (linked list of Vertices).
-
-void path_to_contours(const SkPath& path, SkScalar tolerance, const SkRect& clipBounds,
-                      Vertex** contours, SkChunkAlloc& alloc, bool *isLinear) {
-    SkScalar toleranceSqd = tolerance * tolerance;
-
-    SkPoint pts[4];
-    bool done = false;
-    *isLinear = true;
-    SkPath::Iter iter(path, false);
-    Vertex* prev = nullptr;
-    Vertex* head = nullptr;
-    if (path.isInverseFillType()) {
-        SkPoint quad[4];
-        clipBounds.toQuad(quad);
-        for (int i = 3; i >= 0; i--) {
-            prev = append_point_to_contour(quad[i], prev, &head, alloc);
-        }
-        head->fPrev = prev;
-        prev->fNext = head;
-        *contours++ = head;
-        head = prev = nullptr;
-    }
-    SkAutoConicToQuads converter;
-    while (!done) {
-        SkPath::Verb verb = iter.next(pts);
-        switch (verb) {
-            case SkPath::kConic_Verb: {
-                SkScalar weight = iter.conicWeight();
-                const SkPoint* quadPts = converter.computeQuads(pts, weight, toleranceSqd);
-                for (int i = 0; i < converter.countQuads(); ++i) {
-                    int pointsLeft = GrPathUtils::quadraticPointCount(quadPts, tolerance);
-                    prev = generate_quadratic_points(quadPts[0], quadPts[1], quadPts[2],
-                                                     toleranceSqd, prev, &head, pointsLeft, alloc);
-                    quadPts += 2;
-                }
-                *isLinear = false;
-                break;
-            }
-            case SkPath::kMove_Verb:
-                if (head) {
-                    head->fPrev = prev;
-                    prev->fNext = head;
-                    *contours++ = head;
-                }
-                head = prev = nullptr;
-                prev = append_point_to_contour(pts[0], prev, &head, alloc);
-                break;
-            case SkPath::kLine_Verb: {
-                prev = append_point_to_contour(pts[1], prev, &head, alloc);
-                break;
-            }
-            case SkPath::kQuad_Verb: {
-                int pointsLeft = GrPathUtils::quadraticPointCount(pts, tolerance);
-                prev = generate_quadratic_points(pts[0], pts[1], pts[2], toleranceSqd, prev,
-                                                 &head, pointsLeft, alloc);
-                *isLinear = false;
-                break;
-            }
-            case SkPath::kCubic_Verb: {
-                int pointsLeft = GrPathUtils::cubicPointCount(pts, tolerance);
-                prev = generate_cubic_points(pts[0], pts[1], pts[2], pts[3],
-                                toleranceSqd, prev, &head, pointsLeft, alloc);
-                *isLinear = false;
-                break;
-            }
-            case SkPath::kClose_Verb:
-                if (head) {
-                    head->fPrev = prev;
-                    prev->fNext = head;
-                    *contours++ = head;
-                }
-                head = prev = nullptr;
-                break;
-            case SkPath::kDone_Verb:
-                if (head) {
-                    head->fPrev = prev;
-                    prev->fNext = head;
-                    *contours++ = head;
-                }
-                done = true;
-                break;
-        }
-    }
-}
-
-inline bool apply_fill_type(SkPath::FillType fillType, int winding) {
-    switch (fillType) {
-        case SkPath::kWinding_FillType:
-            return winding != 0;
-        case SkPath::kEvenOdd_FillType:
-            return (winding & 1) != 0;
-        case SkPath::kInverseWinding_FillType:
-            return winding == 1;
-        case SkPath::kInverseEvenOdd_FillType:
-            return (winding & 1) == 1;
-        default:
-            SkASSERT(false);
-            return false;
-    }
-}
-
-Edge* new_edge(Vertex* prev, Vertex* next, SkChunkAlloc& alloc, Comparator& c) {
-    int winding = c.sweep_lt(prev->fPoint, next->fPoint) ? 1 : -1;
-    Vertex* top = winding < 0 ? next : prev;
-    Vertex* bottom = winding < 0 ? prev : next;
-    return ALLOC_NEW(Edge, (top, bottom, winding), alloc);
-}
-
-void remove_edge(Edge* edge, EdgeList* edges) {
-    LOG("removing edge %g -> %g\n", edge->fTop->fID, edge->fBottom->fID);
-    SkASSERT(edge->isActive(edges));
-    remove<Edge, &Edge::fLeft, &Edge::fRight>(edge, &edges->fHead, &edges->fTail);
-}
-
-void insert_edge(Edge* edge, Edge* prev, EdgeList* edges) {
-    LOG("inserting edge %g -> %g\n", edge->fTop->fID, edge->fBottom->fID);
-    SkASSERT(!edge->isActive(edges));
-    Edge* next = prev ? prev->fRight : edges->fHead;
-    insert<Edge, &Edge::fLeft, &Edge::fRight>(edge, prev, next, &edges->fHead, &edges->fTail);
-}
-
-void find_enclosing_edges(Vertex* v, EdgeList* edges, Edge** left, Edge** right) {
-    if (v->fFirstEdgeAbove) {
-        *left = v->fFirstEdgeAbove->fLeft;
-        *right = v->fLastEdgeAbove->fRight;
-        return;
-    }
-    Edge* next = nullptr;
-    Edge* prev;
-    for (prev = edges->fTail; prev != nullptr; prev = prev->fLeft) {
-        if (prev->isLeftOf(v)) {
-            break;
-        }
-        next = prev;
-    }
-    *left = prev;
-    *right = next;
-    return;
-}
-
-void find_enclosing_edges(Edge* edge, EdgeList* edges, Comparator& c, Edge** left, Edge** right) {
-    Edge* prev = nullptr;
-    Edge* next;
-    for (next = edges->fHead; next != nullptr; next = next->fRight) {
-        if ((c.sweep_gt(edge->fTop->fPoint, next->fTop->fPoint) && next->isRightOf(edge->fTop)) ||
-            (c.sweep_gt(next->fTop->fPoint, edge->fTop->fPoint) && edge->isLeftOf(next->fTop)) ||
-            (c.sweep_lt(edge->fBottom->fPoint, next->fBottom->fPoint) &&
-             next->isRightOf(edge->fBottom)) ||
-            (c.sweep_lt(next->fBottom->fPoint, edge->fBottom->fPoint) &&
-             edge->isLeftOf(next->fBottom))) {
-            break;
-        }
-        prev = next;
-    }
-    *left = prev;
-    *right = next;
-    return;
-}
-
-void fix_active_state(Edge* edge, EdgeList* activeEdges, Comparator& c) {
-    if (edge->isActive(activeEdges)) {
-        if (edge->fBottom->fProcessed || !edge->fTop->fProcessed) {
-            remove_edge(edge, activeEdges);
-        }
-    } else if (edge->fTop->fProcessed && !edge->fBottom->fProcessed) {
-        Edge* left;
-        Edge* right;
-        find_enclosing_edges(edge, activeEdges, c, &left, &right);
-        insert_edge(edge, left, activeEdges);
-    }
-}
-
-void insert_edge_above(Edge* edge, Vertex* v, Comparator& c) {
-    if (edge->fTop->fPoint == edge->fBottom->fPoint ||
-        c.sweep_gt(edge->fTop->fPoint, edge->fBottom->fPoint)) {
-        return;
-    }
-    LOG("insert edge (%g -> %g) above vertex %g\n", edge->fTop->fID, edge->fBottom->fID, v->fID);
-    Edge* prev = nullptr;
-    Edge* next;
-    for (next = v->fFirstEdgeAbove; next; next = next->fNextEdgeAbove) {
-        if (next->isRightOf(edge->fTop)) {
-            break;
-        }
-        prev = next;
-    }
-    insert<Edge, &Edge::fPrevEdgeAbove, &Edge::fNextEdgeAbove>(
-        edge, prev, next, &v->fFirstEdgeAbove, &v->fLastEdgeAbove);
-}
-
-void insert_edge_below(Edge* edge, Vertex* v, Comparator& c) {
-    if (edge->fTop->fPoint == edge->fBottom->fPoint ||
-        c.sweep_gt(edge->fTop->fPoint, edge->fBottom->fPoint)) {
-        return;
-    }
-    LOG("insert edge (%g -> %g) below vertex %g\n", edge->fTop->fID, edge->fBottom->fID, v->fID);
-    Edge* prev = nullptr;
-    Edge* next;
-    for (next = v->fFirstEdgeBelow; next; next = next->fNextEdgeBelow) {
-        if (next->isRightOf(edge->fBottom)) {
-            break;
-        }
-        prev = next;
-    }
-    insert<Edge, &Edge::fPrevEdgeBelow, &Edge::fNextEdgeBelow>(
-        edge, prev, next, &v->fFirstEdgeBelow, &v->fLastEdgeBelow);
-}
-
-void remove_edge_above(Edge* edge) {
-    LOG("removing edge (%g -> %g) above vertex %g\n", edge->fTop->fID, edge->fBottom->fID,
-        edge->fBottom->fID);
-    remove<Edge, &Edge::fPrevEdgeAbove, &Edge::fNextEdgeAbove>(
-        edge, &edge->fBottom->fFirstEdgeAbove, &edge->fBottom->fLastEdgeAbove);
-}
-
-void remove_edge_below(Edge* edge) {
-    LOG("removing edge (%g -> %g) below vertex %g\n", edge->fTop->fID, edge->fBottom->fID,
-        edge->fTop->fID);
-    remove<Edge, &Edge::fPrevEdgeBelow, &Edge::fNextEdgeBelow>(
-        edge, &edge->fTop->fFirstEdgeBelow, &edge->fTop->fLastEdgeBelow);
-}
-
-void erase_edge_if_zero_winding(Edge* edge, EdgeList* edges) {
-    if (edge->fWinding != 0) {
-        return;
-    }
-    LOG("erasing edge (%g -> %g)\n", edge->fTop->fID, edge->fBottom->fID);
-    remove_edge_above(edge);
-    remove_edge_below(edge);
-    if (edge->isActive(edges)) {
-        remove_edge(edge, edges);
-    }
-}
-
-void merge_collinear_edges(Edge* edge, EdgeList* activeEdges, Comparator& c);
-
-void set_top(Edge* edge, Vertex* v, EdgeList* activeEdges, Comparator& c) {
-    remove_edge_below(edge);
-    edge->fTop = v;
-    edge->recompute();
-    insert_edge_below(edge, v, c);
-    fix_active_state(edge, activeEdges, c);
-    merge_collinear_edges(edge, activeEdges, c);
-}
-
-void set_bottom(Edge* edge, Vertex* v, EdgeList* activeEdges, Comparator& c) {
-    remove_edge_above(edge);
-    edge->fBottom = v;
-    edge->recompute();
-    insert_edge_above(edge, v, c);
-    fix_active_state(edge, activeEdges, c);
-    merge_collinear_edges(edge, activeEdges, c);
-}
-
-void merge_edges_above(Edge* edge, Edge* other, EdgeList* activeEdges, Comparator& c) {
-    if (coincident(edge->fTop->fPoint, other->fTop->fPoint)) {
-        LOG("merging coincident above edges (%g, %g) -> (%g, %g)\n",
-            edge->fTop->fPoint.fX, edge->fTop->fPoint.fY,
-            edge->fBottom->fPoint.fX, edge->fBottom->fPoint.fY);
-        other->fWinding += edge->fWinding;
-        erase_edge_if_zero_winding(other, activeEdges);
-        edge->fWinding = 0;
-        erase_edge_if_zero_winding(edge, activeEdges);
-    } else if (c.sweep_lt(edge->fTop->fPoint, other->fTop->fPoint)) {
-        other->fWinding += edge->fWinding;
-        erase_edge_if_zero_winding(other, activeEdges);
-        set_bottom(edge, other->fTop, activeEdges, c);
-    } else {
-        edge->fWinding += other->fWinding;
-        erase_edge_if_zero_winding(edge, activeEdges);
-        set_bottom(other, edge->fTop, activeEdges, c);
-    }
-}
-
-void merge_edges_below(Edge* edge, Edge* other, EdgeList* activeEdges, Comparator& c) {
-    if (coincident(edge->fBottom->fPoint, other->fBottom->fPoint)) {
-        LOG("merging coincident below edges (%g, %g) -> (%g, %g)\n",
-            edge->fTop->fPoint.fX, edge->fTop->fPoint.fY,
-            edge->fBottom->fPoint.fX, edge->fBottom->fPoint.fY);
-        other->fWinding += edge->fWinding;
-        erase_edge_if_zero_winding(other, activeEdges);
-        edge->fWinding = 0;
-        erase_edge_if_zero_winding(edge, activeEdges);
-    } else if (c.sweep_lt(edge->fBottom->fPoint, other->fBottom->fPoint)) {
-        edge->fWinding += other->fWinding;
-        erase_edge_if_zero_winding(edge, activeEdges);
-        set_top(other, edge->fBottom, activeEdges, c);
-    } else {
-        other->fWinding += edge->fWinding;
-        erase_edge_if_zero_winding(other, activeEdges);
-        set_top(edge, other->fBottom, activeEdges, c);
-    }
-}
-
-void merge_collinear_edges(Edge* edge, EdgeList* activeEdges, Comparator& c) {
-    if (edge->fPrevEdgeAbove && (edge->fTop == edge->fPrevEdgeAbove->fTop ||
-                                 !edge->fPrevEdgeAbove->isLeftOf(edge->fTop))) {
-        merge_edges_above(edge, edge->fPrevEdgeAbove, activeEdges, c);
-    } else if (edge->fNextEdgeAbove && (edge->fTop == edge->fNextEdgeAbove->fTop ||
-                                        !edge->isLeftOf(edge->fNextEdgeAbove->fTop))) {
-        merge_edges_above(edge, edge->fNextEdgeAbove, activeEdges, c);
-    }
-    if (edge->fPrevEdgeBelow && (edge->fBottom == edge->fPrevEdgeBelow->fBottom ||
-                                 !edge->fPrevEdgeBelow->isLeftOf(edge->fBottom))) {
-        merge_edges_below(edge, edge->fPrevEdgeBelow, activeEdges, c);
-    } else if (edge->fNextEdgeBelow && (edge->fBottom == edge->fNextEdgeBelow->fBottom ||
-                                        !edge->isLeftOf(edge->fNextEdgeBelow->fBottom))) {
-        merge_edges_below(edge, edge->fNextEdgeBelow, activeEdges, c);
-    }
-}
-
-void split_edge(Edge* edge, Vertex* v, EdgeList* activeEdges, Comparator& c, SkChunkAlloc& alloc);
-
-void cleanup_active_edges(Edge* edge, EdgeList* activeEdges, Comparator& c, SkChunkAlloc& alloc) {
-    Vertex* top = edge->fTop;
-    Vertex* bottom = edge->fBottom;
-    if (edge->fLeft) {
-        Vertex* leftTop = edge->fLeft->fTop;
-        Vertex* leftBottom = edge->fLeft->fBottom;
-        if (c.sweep_gt(top->fPoint, leftTop->fPoint) && !edge->fLeft->isLeftOf(top)) {
-            split_edge(edge->fLeft, edge->fTop, activeEdges, c, alloc);
-        } else if (c.sweep_gt(leftTop->fPoint, top->fPoint) && !edge->isRightOf(leftTop)) {
-            split_edge(edge, leftTop, activeEdges, c, alloc);
-        } else if (c.sweep_lt(bottom->fPoint, leftBottom->fPoint) &&
-                   !edge->fLeft->isLeftOf(bottom)) {
-            split_edge(edge->fLeft, bottom, activeEdges, c, alloc);
-        } else if (c.sweep_lt(leftBottom->fPoint, bottom->fPoint) && !edge->isRightOf(leftBottom)) {
-            split_edge(edge, leftBottom, activeEdges, c, alloc);
-        }
-    }
-    if (edge->fRight) {
-        Vertex* rightTop = edge->fRight->fTop;
-        Vertex* rightBottom = edge->fRight->fBottom;
-        if (c.sweep_gt(top->fPoint, rightTop->fPoint) && !edge->fRight->isRightOf(top)) {
-            split_edge(edge->fRight, top, activeEdges, c, alloc);
-        } else if (c.sweep_gt(rightTop->fPoint, top->fPoint) && !edge->isLeftOf(rightTop)) {
-            split_edge(edge, rightTop, activeEdges, c, alloc);
-        } else if (c.sweep_lt(bottom->fPoint, rightBottom->fPoint) &&
-                   !edge->fRight->isRightOf(bottom)) {
-            split_edge(edge->fRight, bottom, activeEdges, c, alloc);
-        } else if (c.sweep_lt(rightBottom->fPoint, bottom->fPoint) &&
-                   !edge->isLeftOf(rightBottom)) {
-            split_edge(edge, rightBottom, activeEdges, c, alloc);
-        }
-    }
-}
-
-void split_edge(Edge* edge, Vertex* v, EdgeList* activeEdges, Comparator& c, SkChunkAlloc& alloc) {
-    LOG("splitting edge (%g -> %g) at vertex %g (%g, %g)\n",
-        edge->fTop->fID, edge->fBottom->fID,
-        v->fID, v->fPoint.fX, v->fPoint.fY);
-    if (c.sweep_lt(v->fPoint, edge->fTop->fPoint)) {
-        set_top(edge, v, activeEdges, c);
-    } else if (c.sweep_gt(v->fPoint, edge->fBottom->fPoint)) {
-        set_bottom(edge, v, activeEdges, c);
-    } else {
-        Edge* newEdge = ALLOC_NEW(Edge, (v, edge->fBottom, edge->fWinding), alloc);
-        insert_edge_below(newEdge, v, c);
-        insert_edge_above(newEdge, edge->fBottom, c);
-        set_bottom(edge, v, activeEdges, c);
-        cleanup_active_edges(edge, activeEdges, c, alloc);
-        fix_active_state(newEdge, activeEdges, c);
-        merge_collinear_edges(newEdge, activeEdges, c);
-    }
-}
-
-void merge_vertices(Vertex* src, Vertex* dst, Vertex** head, Comparator& c, SkChunkAlloc& alloc) {
-    LOG("found coincident verts at %g, %g; merging %g into %g\n", src->fPoint.fX, src->fPoint.fY,
-        src->fID, dst->fID);
-    for (Edge* edge = src->fFirstEdgeAbove; edge;) {
-        Edge* next = edge->fNextEdgeAbove;
-        set_bottom(edge, dst, nullptr, c);
-        edge = next;
-    }
-    for (Edge* edge = src->fFirstEdgeBelow; edge;) {
-        Edge* next = edge->fNextEdgeBelow;
-        set_top(edge, dst, nullptr, c);
-        edge = next;
-    }
-    remove<Vertex, &Vertex::fPrev, &Vertex::fNext>(src, head, nullptr);
-}
-
-Vertex* check_for_intersection(Edge* edge, Edge* other, EdgeList* activeEdges, Comparator& c,
-                               SkChunkAlloc& alloc) {
-    SkPoint p;
-    if (!edge || !other) {
-        return nullptr;
-    }
-    if (edge->intersect(*other, &p)) {
-        Vertex* v;
-        LOG("found intersection, pt is %g, %g\n", p.fX, p.fY);
-        if (p == edge->fTop->fPoint || c.sweep_lt(p, edge->fTop->fPoint)) {
-            split_edge(other, edge->fTop, activeEdges, c, alloc);
-            v = edge->fTop;
-        } else if (p == edge->fBottom->fPoint || c.sweep_gt(p, edge->fBottom->fPoint)) {
-            split_edge(other, edge->fBottom, activeEdges, c, alloc);
-            v = edge->fBottom;
-        } else if (p == other->fTop->fPoint || c.sweep_lt(p, other->fTop->fPoint)) {
-            split_edge(edge, other->fTop, activeEdges, c, alloc);
-            v = other->fTop;
-        } else if (p == other->fBottom->fPoint || c.sweep_gt(p, other->fBottom->fPoint)) {
-            split_edge(edge, other->fBottom, activeEdges, c, alloc);
-            v = other->fBottom;
-        } else {
-            Vertex* nextV = edge->fTop;
-            while (c.sweep_lt(p, nextV->fPoint)) {
-                nextV = nextV->fPrev;
-            }
-            while (c.sweep_lt(nextV->fPoint, p)) {
-                nextV = nextV->fNext;
-            }
-            Vertex* prevV = nextV->fPrev;
-            if (coincident(prevV->fPoint, p)) {
-                v = prevV;
-            } else if (coincident(nextV->fPoint, p)) {
-                v = nextV;
-            } else {
-                v = ALLOC_NEW(Vertex, (p), alloc);
-                LOG("inserting between %g (%g, %g) and %g (%g, %g)\n",
-                    prevV->fID, prevV->fPoint.fX, prevV->fPoint.fY,
-                    nextV->fID, nextV->fPoint.fX, nextV->fPoint.fY);
-#if LOGGING_ENABLED
-                v->fID = (nextV->fID + prevV->fID) * 0.5f;
-#endif
-                v->fPrev = prevV;
-                v->fNext = nextV;
-                prevV->fNext = v;
-                nextV->fPrev = v;
-            }
-            split_edge(edge, v, activeEdges, c, alloc);
-            split_edge(other, v, activeEdges, c, alloc);
-        }
-        return v;
-    }
-    return nullptr;
-}
-
-void sanitize_contours(Vertex** contours, int contourCnt) {
-    for (int i = 0; i < contourCnt; ++i) {
-        SkASSERT(contours[i]);
-        for (Vertex* v = contours[i];;) {
-            if (coincident(v->fPrev->fPoint, v->fPoint)) {
-                LOG("vertex %g,%g coincident; removing\n", v->fPoint.fX, v->fPoint.fY);
-                if (v->fPrev == v) {
-                    contours[i] = nullptr;
-                    break;
-                }
-                v->fPrev->fNext = v->fNext;
-                v->fNext->fPrev = v->fPrev;
-                if (contours[i] == v) {
-                    contours[i] = v->fNext;
-                }
-                v = v->fPrev;
-            } else {
-                v = v->fNext;
-                if (v == contours[i]) break;
-            }
-        }
-    }
-}
-
-void merge_coincident_vertices(Vertex** vertices, Comparator& c, SkChunkAlloc& alloc) {
-    for (Vertex* v = (*vertices)->fNext; v != nullptr; v = v->fNext) {
-        if (c.sweep_lt(v->fPoint, v->fPrev->fPoint)) {
-            v->fPoint = v->fPrev->fPoint;
-        }
-        if (coincident(v->fPrev->fPoint, v->fPoint)) {
-            merge_vertices(v->fPrev, v, vertices, c, alloc);
-        }
-    }
-}
-
-// Stage 2: convert the contours to a mesh of edges connecting the vertices.
-
-Vertex* build_edges(Vertex** contours, int contourCnt, Comparator& c, SkChunkAlloc& alloc) {
-    Vertex* vertices = nullptr;
-    Vertex* prev = nullptr;
-    for (int i = 0; i < contourCnt; ++i) {
-        for (Vertex* v = contours[i]; v != nullptr;) {
-            Vertex* vNext = v->fNext;
-            Edge* edge = new_edge(v->fPrev, v, alloc, c);
-            if (edge->fWinding > 0) {
-                insert_edge_below(edge, v->fPrev, c);
-                insert_edge_above(edge, v, c);
-            } else {
-                insert_edge_below(edge, v, c);
-                insert_edge_above(edge, v->fPrev, c);
-            }
-            merge_collinear_edges(edge, nullptr, c);
-            if (prev) {
-                prev->fNext = v;
-                v->fPrev = prev;
-            } else {
-                vertices = v;
-            }
-            prev = v;
-            v = vNext;
-            if (v == contours[i]) break;
-        }
-    }
-    if (prev) {
-        prev->fNext = vertices->fPrev = nullptr;
-    }
-    return vertices;
-}
-
-// Stage 3: sort the vertices by increasing sweep direction.
-
-Vertex* sorted_merge(Vertex* a, Vertex* b, Comparator& c);
-
-void front_back_split(Vertex* v, Vertex** pFront, Vertex** pBack) {
-    Vertex* fast;
-    Vertex* slow;
-    if (!v || !v->fNext) {
-        *pFront = v;
-        *pBack = nullptr;
-    } else {
-        slow = v;
-        fast = v->fNext;
-
-        while (fast != nullptr) {
-            fast = fast->fNext;
-            if (fast != nullptr) {
-                slow = slow->fNext;
-                fast = fast->fNext;
-            }
-        }
-
-        *pFront = v;
-        *pBack = slow->fNext;
-        slow->fNext->fPrev = nullptr;
-        slow->fNext = nullptr;
-    }
-}
-
-void merge_sort(Vertex** head, Comparator& c) {
-    if (!*head || !(*head)->fNext) {
-        return;
-    }
-
-    Vertex* a;
-    Vertex* b;
-    front_back_split(*head, &a, &b);
-
-    merge_sort(&a, c);
-    merge_sort(&b, c);
-
-    *head = sorted_merge(a, b, c);
-}
-
-inline void append_vertex(Vertex* v, Vertex** head, Vertex** tail) {
-    insert<Vertex, &Vertex::fPrev, &Vertex::fNext>(v, *tail, nullptr, head, tail);
-}
-
-inline void append_vertex_list(Vertex* v, Vertex** head, Vertex** tail) {
-    insert<Vertex, &Vertex::fPrev, &Vertex::fNext>(v, *tail, v->fNext, head, tail);
-}
-
-Vertex* sorted_merge(Vertex* a, Vertex* b, Comparator& c) {
-    Vertex* head = nullptr;
-    Vertex* tail = nullptr;
-
-    while (a && b) {
-        if (c.sweep_lt(a->fPoint, b->fPoint)) {
-            Vertex* next = a->fNext;
-            append_vertex(a, &head, &tail);
-            a = next;
-        } else {
-            Vertex* next = b->fNext;
-            append_vertex(b, &head, &tail);
-            b = next;
-        }
-    }
-    if (a) {
-        append_vertex_list(a, &head, &tail);
-    }
-    if (b) {
-        append_vertex_list(b, &head, &tail);
-    }
-    return head;
-}
-
-// Stage 4: Simplify the mesh by inserting new vertices at intersecting edges.
-
-void simplify(Vertex* vertices, Comparator& c, SkChunkAlloc& alloc) {
-    LOG("simplifying complex polygons\n");
-    EdgeList activeEdges;
-    for (Vertex* v = vertices; v != nullptr; v = v->fNext) {
-        if (!v->fFirstEdgeAbove && !v->fFirstEdgeBelow) {
-            continue;
-        }
-#if LOGGING_ENABLED
-        LOG("\nvertex %g: (%g,%g)\n", v->fID, v->fPoint.fX, v->fPoint.fY);
-#endif
-        Edge* leftEnclosingEdge = nullptr;
-        Edge* rightEnclosingEdge = nullptr;
-        bool restartChecks;
-        do {
-            restartChecks = false;
-            find_enclosing_edges(v, &activeEdges, &leftEnclosingEdge, &rightEnclosingEdge);
-            if (v->fFirstEdgeBelow) {
-                for (Edge* edge = v->fFirstEdgeBelow; edge != nullptr; edge = edge->fNextEdgeBelow) {
-                    if (check_for_intersection(edge, leftEnclosingEdge, &activeEdges, c, alloc)) {
-                        restartChecks = true;
-                        break;
-                    }
-                    if (check_for_intersection(edge, rightEnclosingEdge, &activeEdges, c, alloc)) {
-                        restartChecks = true;
-                        break;
-                    }
-                }
-            } else {
-                if (Vertex* pv = check_for_intersection(leftEnclosingEdge, rightEnclosingEdge,
-                                                        &activeEdges, c, alloc)) {
-                    if (c.sweep_lt(pv->fPoint, v->fPoint)) {
-                        v = pv;
-                    }
-                    restartChecks = true;
-                }
-
-            }
-        } while (restartChecks);
-        for (Edge* e = v->fFirstEdgeAbove; e; e = e->fNextEdgeAbove) {
-            remove_edge(e, &activeEdges);
-        }
-        Edge* leftEdge = leftEnclosingEdge;
-        for (Edge* e = v->fFirstEdgeBelow; e; e = e->fNextEdgeBelow) {
-            insert_edge(e, leftEdge, &activeEdges);
-            leftEdge = e;
-        }
-        v->fProcessed = true;
-    }
-}
-
-// Stage 5: Tessellate the simplified mesh into monotone polygons.
-
-Poly* tessellate(Vertex* vertices, SkChunkAlloc& alloc) {
-    LOG("tessellating simple polygons\n");
-    EdgeList activeEdges;
-    Poly* polys = nullptr;
-    for (Vertex* v = vertices; v != nullptr; v = v->fNext) {
-        if (!v->fFirstEdgeAbove && !v->fFirstEdgeBelow) {
-            continue;
-        }
-#if LOGGING_ENABLED
-        LOG("\nvertex %g: (%g,%g)\n", v->fID, v->fPoint.fX, v->fPoint.fY);
-#endif
-        Edge* leftEnclosingEdge = nullptr;
-        Edge* rightEnclosingEdge = nullptr;
-        find_enclosing_edges(v, &activeEdges, &leftEnclosingEdge, &rightEnclosingEdge);
-        Poly* leftPoly = nullptr;
-        Poly* rightPoly = nullptr;
-        if (v->fFirstEdgeAbove) {
-            leftPoly = v->fFirstEdgeAbove->fLeftPoly;
-            rightPoly = v->fLastEdgeAbove->fRightPoly;
-        } else {
-            leftPoly = leftEnclosingEdge ? leftEnclosingEdge->fRightPoly : nullptr;
-            rightPoly = rightEnclosingEdge ? rightEnclosingEdge->fLeftPoly : nullptr;
-        }
-#if LOGGING_ENABLED
-        LOG("edges above:\n");
-        for (Edge* e = v->fFirstEdgeAbove; e; e = e->fNextEdgeAbove) {
-            LOG("%g -> %g, lpoly %d, rpoly %d\n", e->fTop->fID, e->fBottom->fID,
-                e->fLeftPoly ? e->fLeftPoly->fID : -1, e->fRightPoly ? e->fRightPoly->fID : -1);
-        }
-        LOG("edges below:\n");
-        for (Edge* e = v->fFirstEdgeBelow; e; e = e->fNextEdgeBelow) {
-            LOG("%g -> %g, lpoly %d, rpoly %d\n", e->fTop->fID, e->fBottom->fID,
-                e->fLeftPoly ? e->fLeftPoly->fID : -1, e->fRightPoly ? e->fRightPoly->fID : -1);
-        }
-#endif
-        if (v->fFirstEdgeAbove) {
-            if (leftPoly) {
-                leftPoly = leftPoly->addVertex(v, Poly::kRight_Side, alloc);
-            }
-            if (rightPoly) {
-                rightPoly = rightPoly->addVertex(v, Poly::kLeft_Side, alloc);
-            }
-            for (Edge* e = v->fFirstEdgeAbove; e != v->fLastEdgeAbove; e = e->fNextEdgeAbove) {
-                Edge* leftEdge = e;
-                Edge* rightEdge = e->fNextEdgeAbove;
-                SkASSERT(rightEdge->isRightOf(leftEdge->fTop));
-                remove_edge(leftEdge, &activeEdges);
-                if (leftEdge->fRightPoly) {
-                    leftEdge->fRightPoly->end(v, alloc);
-                }
-                if (rightEdge->fLeftPoly && rightEdge->fLeftPoly != leftEdge->fRightPoly) {
-                    rightEdge->fLeftPoly->end(v, alloc);
-                }
-            }
-            remove_edge(v->fLastEdgeAbove, &activeEdges);
-            if (!v->fFirstEdgeBelow) {
-                if (leftPoly && rightPoly && leftPoly != rightPoly) {
-                    SkASSERT(leftPoly->fPartner == nullptr && rightPoly->fPartner == nullptr);
-                    rightPoly->fPartner = leftPoly;
-                    leftPoly->fPartner = rightPoly;
-                }
-            }
-        }
-        if (v->fFirstEdgeBelow) {
-            if (!v->fFirstEdgeAbove) {
-                if (leftPoly && leftPoly == rightPoly) {
-                    // Split the poly.
-                    if (leftPoly->fActive->fSide == Poly::kLeft_Side) {
-                        leftPoly = new_poly(&polys, leftEnclosingEdge->fTop, leftPoly->fWinding,
-                                            alloc);
-                        leftPoly->addVertex(v, Poly::kRight_Side, alloc);
-                        rightPoly->addVertex(v, Poly::kLeft_Side, alloc);
-                        leftEnclosingEdge->fRightPoly = leftPoly;
-                    } else {
-                        rightPoly = new_poly(&polys, rightEnclosingEdge->fTop, rightPoly->fWinding,
-                                             alloc);
-                        rightPoly->addVertex(v, Poly::kLeft_Side, alloc);
-                        leftPoly->addVertex(v, Poly::kRight_Side, alloc);
-                        rightEnclosingEdge->fLeftPoly = rightPoly;
-                    }
-                } else {
-                    if (leftPoly) {
-                        leftPoly = leftPoly->addVertex(v, Poly::kRight_Side, alloc);
-                    }
-                    if (rightPoly) {
-                        rightPoly = rightPoly->addVertex(v, Poly::kLeft_Side, alloc);
-                    }
-                }
-            }
-            Edge* leftEdge = v->fFirstEdgeBelow;
-            leftEdge->fLeftPoly = leftPoly;
-            insert_edge(leftEdge, leftEnclosingEdge, &activeEdges);
-            for (Edge* rightEdge = leftEdge->fNextEdgeBelow; rightEdge;
-                 rightEdge = rightEdge->fNextEdgeBelow) {
-                insert_edge(rightEdge, leftEdge, &activeEdges);
-                int winding = leftEdge->fLeftPoly ? leftEdge->fLeftPoly->fWinding : 0;
-                winding += leftEdge->fWinding;
-                if (winding != 0) {
-                    Poly* poly = new_poly(&polys, v, winding, alloc);
-                    leftEdge->fRightPoly = rightEdge->fLeftPoly = poly;
-                }
-                leftEdge = rightEdge;
-            }
-            v->fLastEdgeBelow->fRightPoly = rightPoly;
-        }
-#if LOGGING_ENABLED
-        LOG("\nactive edges:\n");
-        for (Edge* e = activeEdges.fHead; e != nullptr; e = e->fRight) {
-            LOG("%g -> %g, lpoly %d, rpoly %d\n", e->fTop->fID, e->fBottom->fID,
-                e->fLeftPoly ? e->fLeftPoly->fID : -1, e->fRightPoly ? e->fRightPoly->fID : -1);
-        }
-#endif
-    }
-    return polys;
-}
-
-// This is a driver function which calls stages 2-5 in turn.
-
-Poly* contours_to_polys(Vertex** contours, int contourCnt, const SkRect& pathBounds, 
-                        SkChunkAlloc& alloc) {
-    Comparator c;
-    if (pathBounds.width() > pathBounds.height()) {
-        c.sweep_lt = sweep_lt_horiz;
-        c.sweep_gt = sweep_gt_horiz;
-    } else {
-        c.sweep_lt = sweep_lt_vert;
-        c.sweep_gt = sweep_gt_vert;
-    }
-#if LOGGING_ENABLED
-    for (int i = 0; i < contourCnt; ++i) {
-        Vertex* v = contours[i];
-        SkASSERT(v);
-        LOG("path.moveTo(%20.20g, %20.20g);\n", v->fPoint.fX, v->fPoint.fY);
-        for (v = v->fNext; v != contours[i]; v = v->fNext) {
-            LOG("path.lineTo(%20.20g, %20.20g);\n", v->fPoint.fX, v->fPoint.fY);
-        }
-    }
-#endif
-    sanitize_contours(contours, contourCnt);
-    Vertex* vertices = build_edges(contours, contourCnt, c, alloc);
-    if (!vertices) {
-        return nullptr;
-    }
-
-    // Sort vertices in Y (secondarily in X).
-    merge_sort(&vertices, c);
-    merge_coincident_vertices(&vertices, c, alloc);
-#if LOGGING_ENABLED
-    for (Vertex* v = vertices; v != nullptr; v = v->fNext) {
-        static float gID = 0.0f;
-        v->fID = gID++;
-    }
-#endif
-    simplify(vertices, c, alloc);
-    return tessellate(vertices, alloc);
-}
-
-Poly* path_to_polys(const SkPath& path, SkScalar tolerance, const SkRect& clipBounds, 
-                    int contourCnt, SkChunkAlloc& alloc, bool* isLinear) {
-    SkPath::FillType fillType = path.getFillType();
-    if (SkPath::IsInverseFillType(fillType)) {
-        contourCnt++;
-    }
-    SkAutoTDeleteArray<Vertex*> contours(new Vertex* [contourCnt]);
-
-    path_to_contours(path, tolerance, clipBounds, contours.get(), alloc, isLinear);
-    return contours_to_polys(contours.get(), contourCnt, path.getBounds(), alloc);
-}
-
-void get_contour_count_and_size_estimate(const SkPath& path, SkScalar tolerance, int* contourCnt, 
-                                         int* sizeEstimate) {
-    int maxPts = GrPathUtils::worstCasePointCount(path, contourCnt, tolerance);
-    if (maxPts <= 0) {
-        *contourCnt = 0;
-        return;
-    }
-    if (maxPts > ((int)SK_MaxU16 + 1)) {
-        SkDebugf("Path not rendered, too many verts (%d)\n", maxPts);
-        *contourCnt = 0;
-        return;
-    }
-    // For the initial size of the chunk allocator, estimate based on the point count:
-    // one vertex per point for the initial passes, plus two for the vertices in the
-    // resulting Polys, since the same point may end up in two Polys.  Assume minimal
-    // connectivity of one Edge per Vertex (will grow for intersections).
-    *sizeEstimate = maxPts * (3 * sizeof(Vertex) + sizeof(Edge));
-}
-
-int count_points(Poly* polys, SkPath::FillType fillType) {
-    int count = 0;
-    for (Poly* poly = polys; poly; poly = poly->fNext) {
-        if (apply_fill_type(fillType, poly->fWinding) && poly->fCount >= 3) {
-            count += (poly->fCount - 2) * (TESSELLATOR_WIREFRAME ? 6 : 3);
-        }
-    }
-    return count;
-}
-
-} // namespace
-
-namespace GrTessellator {
-
-// Stage 6: Triangulate the monotone polygons into a vertex buffer.
-
-int PathToTriangles(const SkPath& path, SkScalar tolerance, const SkRect& clipBounds, 
-                    GrResourceProvider* resourceProvider, 
-                    SkAutoTUnref<GrVertexBuffer>& vertexBuffer, bool canMapVB, bool* isLinear) {
-    int contourCnt;
-    int sizeEstimate;
-    get_contour_count_and_size_estimate(path, tolerance, &contourCnt, &sizeEstimate);
-    if (contourCnt <= 0) {
-        return 0;
-    }
-    SkChunkAlloc alloc(sizeEstimate);
-    Poly* polys = path_to_polys(path, tolerance, clipBounds, contourCnt, alloc, isLinear);
-    SkPath::FillType fillType = path.getFillType();
-    int count = count_points(polys, fillType);
-    if (0 == count) {
-        return 0;
-    }
-
-    size_t size = count * sizeof(SkPoint);
-    if (!vertexBuffer.get() || vertexBuffer->gpuMemorySize() < size) {
-        vertexBuffer.reset(resourceProvider->createVertexBuffer(
-            size, GrResourceProvider::kStatic_BufferUsage, 0));
-    }
-    if (!vertexBuffer.get()) {
-        SkDebugf("Could not allocate vertices\n");
-        return 0;
-    }
-    SkPoint* verts;
-    if (canMapVB) {
-        verts = static_cast<SkPoint*>(vertexBuffer->map());
-    } else {
-        verts = new SkPoint[count];
-    }
-    SkPoint* end = verts;
-    for (Poly* poly = polys; poly; poly = poly->fNext) {
-        if (apply_fill_type(fillType, poly->fWinding)) {
-            end = poly->emit(end);
-        }
-    }
-    int actualCount = static_cast<int>(end - verts);
-    LOG("actual count: %d\n", actualCount);
-    SkASSERT(actualCount <= count);
-    if (canMapVB) {
-        vertexBuffer->unmap();
-    } else {
-        vertexBuffer->updateData(verts, actualCount * sizeof(SkPoint));
-        delete[] verts;
-    }
-
-    return actualCount;
-}
-
-int PathToVertices(const SkPath& path, SkScalar tolerance, const SkRect& clipBounds, 
-                   GrTessellator::WindingVertex** verts) {
-    int contourCnt;
-    int sizeEstimate;
-    get_contour_count_and_size_estimate(path, tolerance, &contourCnt, &sizeEstimate);
-    if (contourCnt <= 0) {
-        return 0;
-    }
-    SkChunkAlloc alloc(sizeEstimate);
-    bool isLinear;
-    Poly* polys = path_to_polys(path, tolerance, clipBounds, contourCnt, alloc, &isLinear);
-    SkPath::FillType fillType = path.getFillType();
-    int count = count_points(polys, fillType);
-    if (0 == count) {
-        *verts = nullptr;
-        return 0;
-    }
-
-    *verts = new GrTessellator::WindingVertex[count];
-    GrTessellator::WindingVertex* vertsEnd = *verts;
-    SkPoint* points = new SkPoint[count];
-    SkPoint* pointsEnd = points;
-    for (Poly* poly = polys; poly; poly = poly->fNext) {
-        if (apply_fill_type(fillType, poly->fWinding)) {
-            SkPoint* start = pointsEnd;
-            pointsEnd = poly->emit(pointsEnd);
-            while (start != pointsEnd) {
-                vertsEnd->fPos = *start;
-                vertsEnd->fWinding = poly->fWinding;
-                ++start;
-                ++vertsEnd;
-            }
-        }
-    }
-    int actualCount = static_cast<int>(vertsEnd - *verts);
-    SkASSERT(actualCount <= count);
-    SkASSERT(pointsEnd - points == actualCount);
-    delete[] points;
-    return actualCount;
-}
-
-} // namespace