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

src/gpu/batches/GrTessellatingPathRenderer.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 "GrTessellatingPathRenderer.h"
 
 #include "GrBatchFlushState.h"
 #include "GrBatchTest.h"
 #include "GrDefaultGeoProcFactory.h"
 #include "GrPathUtils.h"
 #include "GrVertices.h"
 #include "GrResourceCache.h"
 #include "GrResourceProvider.h"
-#include "GrTessellator.h"
+#include "SkChunkAlloc.h"
 #include "SkGeometry.h"
 
 #include "batches/GrVertexBatch.h"
 
 #include <stdio.h>
 
 /*
- * This path renderer tessellates the path into triangles using GrTessellator, uploads the triangles
- * to a vertex buffer, and renders them with a single draw call. It does not currently do 
+ * This path renderer tessellates the path into triangles, uploads the triangles to a
+ * vertex buffer, and renders them with a single draw call. It does not currently do
  * antialiasing, so it must be used in conjunction with multisampling.
+ *
+ * There are six stages to the algorithm:
+ *
+ * 1) Linearize the path contours into piecewise linear segments (path_to_contours()).
+ * 2) Build a mesh of edges connecting the vertices (build_edges()).
+ * 3) Sort the vertices in Y (and secondarily in X) (merge_sort()).
+ * 4) Simplify the mesh by inserting new vertices at intersecting edges (simplify()).
+ * 5) Tessellate the simplified mesh into monotone polygons (tessellate()).
+ * 6) Triangulate the monotone polygons directly into a vertex buffer (polys_to_triangles()).
+ *
+ * The vertex sorting in step (3) is a merge sort, since it plays well with the linked list
+ * of vertices (and the necessity of inserting new vertices on intersection).
+ *
+ * Stages (4) and (5) use an active edge list, which a list of all edges for which the
+ * sweep line has crossed the top vertex, but not the bottom vertex.  It's sorted
+ * left-to-right based on the point where both edges are active (when both top vertices
+ * have been seen, so the "lower" top vertex of the two). If the top vertices are equal
+ * (shared), it's sorted based on the last point where both edges are active, so the
+ * "upper" bottom vertex.
+ *
+ * The most complex step is the simplification (4). It's based on the Bentley-Ottman
+ * line-sweep algorithm, but due to floating point inaccuracy, the intersection points are
+ * not exact and may violate the mesh topology or active edge list ordering. We
+ * accommodate this by adjusting the topology of the mesh and AEL to match the intersection
+ * points. This occurs in three ways:
+ *
+ * A) Intersections may cause a shortened edge to no longer be ordered with respect to its
+ *    neighbouring edges at the top or bottom vertex. This is handled by merging the
+ *    edges (merge_collinear_edges()).
+ * B) Intersections may cause an edge to violate the left-to-right ordering of the
+ *    active edge list. This is handled by splitting the neighbour edge on the
+ *    intersected vertex (cleanup_active_edges()).
+ * C) Shortening an edge may cause an active edge to become inactive or an inactive edge
+ *    to become active. This is handled by removing or inserting the edge in the active
+ *    edge list (fix_active_state()).
+ *
+ * The tessellation steps (5) and (6) are based on "Triangulating Simple Polygons and
+ * Equivalent Problems" (Fournier and Montuno); also a line-sweep algorithm. Note that it
+ * currently uses a linked list for the active edge list, rather than a 2-3 tree as the
+ * paper describes. The 2-3 tree gives O(lg N) lookups, but insertion and removal also
+ * become O(lg N). In all the test cases, it was found that the cost of frequent O(lg N)
+ * insertions and removals was greater than the cost of infrequent O(N) lookups with the
+ * linked list implementation. With the latter, all removals are O(1), and most insertions
+ * are O(1), since we know the adjacent edge in the active edge list based on the topology.
+ * Only type 2 vertices (see paper) require the O(N) lookups, and these are much less
+ * frequent. There may be other data structures worth investigating, however.
+ *
+ * Note that the orientation of the line sweep algorithms is determined by the aspect ratio of the
+ * path bounds. When the path is taller than it is wide, we sort vertices based on increasing Y
+ * coordinate, and secondarily by increasing X coordinate. When the path is wider than it is tall,
+ * we sort by increasing X coordinate, but secondarily by *decreasing* Y coordinate. This is so
+ * that the "left" and "right" orientation in the code remains correct (edges to the left are
+ * increasing in Y; edges to the right are decreasing in Y). That is, the setting rotates 90
+ * degrees counterclockwise, rather that transposing.
  */
+#define LOGGING_ENABLED 0
+#define WIREFRAME 0
+
+#if LOGGING_ENABLED
+#define LOG printf
+#else
+#define LOG(...)
+#endif
+
+#define ALLOC_NEW(Type, args, alloc) 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, Comparator& c, SkChunkAlloc& alloc) {
+#if LOGGING_ENABLED
+    for (int i = 0; i < contourCnt; ++i) {
+        Vertex* v = contours[i];
+        SkASSERT(v);
+        LOG("path.moveTo(%20.20g, %20.20g);\n", v->fPoint.fX, v->fPoint.fY);
+        for (v = v->fNext; v != contours[i]; v = v->fNext) {
+            LOG("path.lineTo(%20.20g, %20.20g);\n", v->fPoint.fX, v->fPoint.fY);
+        }
+    }
+#endif
+    sanitize_contours(contours, contourCnt);
+    Vertex* vertices = build_edges(contours, contourCnt, c, alloc);
+    if (!vertices) {
+        return 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);
+}
+
+// Stage 6: Triangulate the monotone polygons into a vertex buffer.
+
+SkPoint* polys_to_triangles(Poly* polys, SkPath::FillType fillType, SkPoint* data) {
+    SkPoint* d = data;
+    for (Poly* poly = polys; poly; poly = poly->fNext) {
+        if (apply_fill_type(fillType, poly->fWinding)) {
+            d = poly->emit(d);
+        }
+    }
+    return d;
+}
+
 struct TessInfo {
     SkScalar  fTolerance;
     int       fCount;
 };
 
+bool cache_match(GrVertexBuffer* vertexBuffer, SkScalar tol, int* actualCount) {
+    if (!vertexBuffer) {
+        return false;
+    }
+    const SkData* data = vertexBuffer->getUniqueKey().getCustomData();
+    SkASSERT(data);
+    const TessInfo* info = static_cast<const TessInfo*>(data->data());
+    if (info->fTolerance == 0 || info->fTolerance < 3.0f * tol) {
+        *actualCount = info->fCount;
+        return true;
+    }
+    return false;
+}
+
+};
+
+GrTessellatingPathRenderer::GrTessellatingPathRenderer() {
+}
+
+namespace {
+
 // When the SkPathRef genID changes, invalidate a corresponding GrResource described by key.
 class PathInvalidator : public SkPathRef::GenIDChangeListener {
 public:
     explicit PathInvalidator(const GrUniqueKey& key) : fMsg(key) {}
 private:
     GrUniqueKeyInvalidatedMessage fMsg;
 
     void onChange() override {
         SkMessageBus<GrUniqueKeyInvalidatedMessage>::Post(fMsg);
     }
 };
 
-bool cache_match(GrVertexBuffer* vertexBuffer, SkScalar tol, int* actualCount) {
-    if (!vertexBuffer) {
-        return false;
-    }
-    const SkData* data = vertexBuffer->getUniqueKey().getCustomData();
-    SkASSERT(data);
-    const TessInfo* info = static_cast<const TessInfo*>(data->data());
-    if (info->fTolerance == 0 || info->fTolerance < 3.0f * tol) {
-        *actualCount = info->fCount;
-        return true;
-    }
-    return false;
-}
-
 }  // namespace
 
-GrTessellatingPathRenderer::GrTessellatingPathRenderer() {
-}
-
 bool GrTessellatingPathRenderer::onCanDrawPath(const CanDrawPathArgs& args) const {
     // This path renderer can draw all fill styles, all stroke styles except hairlines, but does
     // not do antialiasing. It can do convex and concave paths, but we'll leave the convex ones to
     // simpler algorithms.
     return !IsStrokeHairlineOrEquivalent(*args.fStroke, *args.fViewMatrix, nullptr) &&
            !args.fAntiAlias && !args.fPath->isConvex();
 }
 
 class TessellatingPathBatch : public GrVertexBatch {
 public:
@@ skipping 40 matching lines @@
         } else {
             path = fPath;
         }
         if (!stroke.isFillStyle()) {
             stroke.setResScale(SkScalarAbs(fViewMatrix.getMaxScale()));
             if (!stroke.applyToPath(&path, path)) {
                 return 0;
             }
             stroke.setFillStyle();
         }
+        SkRect pathBounds = path.getBounds();
+        Comparator c;
+        if (pathBounds.width() > pathBounds.height()) {
+            c.sweep_lt = sweep_lt_horiz;
+            c.sweep_gt = sweep_gt_horiz;
+        } else {
+            c.sweep_lt = sweep_lt_vert;
+            c.sweep_gt = sweep_gt_vert;
+        }
         SkScalar screenSpaceTol = GrPathUtils::kDefaultTolerance;
-        SkRect pathBounds = path.getBounds();
         SkScalar tol = GrPathUtils::scaleToleranceToSrc(screenSpaceTol, fViewMatrix, pathBounds);
+        int contourCnt;
+        int maxPts = GrPathUtils::worstCasePointCount(path, &contourCnt, tol);
+        if (maxPts <= 0) {
+            return 0;
+        }
+        if (maxPts > ((int)SK_MaxU16 + 1)) {
+            SkDebugf("Path not rendered, too many verts (%d)\n", maxPts);
+            return 0;
+        }
+        SkPath::FillType fillType = path.getFillType();
+        if (SkPath::IsInverseFillType(fillType)) {
+            contourCnt++;
+        }
 
+        LOG("got %d pts, %d contours\n", maxPts, contourCnt);
+        SkAutoTDeleteArray<Vertex*> contours(new Vertex* [contourCnt]);
+
+        // For the initial size of the chunk allocator, estimate based on the point count:
+        // one vertex per point for the initial passes, plus two for the vertices in the
+        // resulting Polys, since the same point may end up in two Polys.  Assume minimal
+        // connectivity of one Edge per Vertex (will grow for intersections).
+        SkChunkAlloc alloc(maxPts * (3 * sizeof(Vertex) + sizeof(Edge)));
         bool isLinear;
-        int count = GrTessellator::PathToTriangles(path, tol, fClipBounds, resourceProvider, 
-                                                   vertexBuffer, canMapVB, &isLinear);
+        path_to_contours(path, tol, fClipBounds, contours.get(), alloc, &isLinear);
+        Poly* polys;
+        polys = contours_to_polys(contours.get(), contourCnt, c, alloc);
+        int count = 0;
+        for (Poly* poly = polys; poly; poly = poly->fNext) {
+            if (apply_fill_type(fillType, poly->fWinding) && poly->fCount >= 3) {
+                count += (poly->fCount - 2) * (WIREFRAME ? 6 : 3);
+            }
+        }
+        if (0 == count) {
+            return 0;
+        }
+
+        size_t size = count * sizeof(SkPoint);
+        if (!vertexBuffer.get() || vertexBuffer->gpuMemorySize() < size) {
+            vertexBuffer.reset(resourceProvider->createVertexBuffer(
+                size, GrResourceProvider::kStatic_BufferUsage, 0));
+        }
+        if (!vertexBuffer.get()) {
+            SkDebugf("Could not allocate vertices\n");
+            return 0;
+        }
+        SkPoint* verts;
+        if (canMapVB) {
+            verts = static_cast<SkPoint*>(vertexBuffer->map());
+        } else {
+            verts = new SkPoint[count];
+        }
+        SkPoint* end = polys_to_triangles(polys, fillType, verts);
+        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;
+        }
+
+
         if (!fPath.isVolatile()) {
             TessInfo info;
             info.fTolerance = isLinear ? 0 : tol;
-            info.fCount = count;
+            info.fCount = actualCount;
             SkAutoTUnref<SkData> data(SkData::NewWithCopy(&info, sizeof(info)));
             key->setCustomData(data.get());
             resourceProvider->assignUniqueKeyToResource(*key, vertexBuffer.get());
             SkPathPriv::AddGenIDChangeListener(fPath, new PathInvalidator(*key));
         }
-        return count;
+        return actualCount;
     }
 
     void onPrepareDraws(Target* target) const override {
         // construct a cache key from the path's genID and the view matrix
         static const GrUniqueKey::Domain kDomain = GrUniqueKey::GenerateDomain();
         GrUniqueKey key;
         int clipBoundsSize32 =
             fPath.isInverseFillType() ? sizeof(fClipBounds) / sizeof(uint32_t) : 0;
         int strokeDataSize32 = fStroke.computeUniqueKeyFragmentData32Cnt();
         GrUniqueKey::Builder builder(&key, kDomain, 2 + clipBoundsSize32 + strokeDataSize32);
@@ skipping 35 matching lines @@
                 coverageType = Coverage::kNone_Type;
             }
             Coverage coverage(coverageType);
             gp.reset(GrDefaultGeoProcFactory::Create(color, coverage, localCoords,
                                                      fViewMatrix));
         }
 
         target->initDraw(gp, this->pipeline());
         SkASSERT(gp->getVertexStride() == sizeof(SkPoint));
 
-        GrPrimitiveType primitiveType = TESSELLATOR_WIREFRAME ? kLines_GrPrimitiveType
-                                                              : kTriangles_GrPrimitiveType;
+        GrPrimitiveType primitiveType = WIREFRAME ? kLines_GrPrimitiveType
+                                                  : kTriangles_GrPrimitiveType;
         GrVertices vertices;
         vertices.init(primitiveType, vertexBuffer.get(), 0, actualCount);
         target->draw(vertices);
     }
 
     bool onCombineIfPossible(GrBatch*, const GrCaps&) override { return false; }
 
     TessellatingPathBatch(const GrColor& color,
                           const SkPath& path,
                           const GrStrokeInfo& stroke,
@@ skipping 73 matching lines @@
     bool result = viewMatrix.invert(&vmi);
     if (!result) {
         SkFAIL("Cannot invert matrix\n");
     }
     vmi.mapRect(&clipBounds);
     GrStrokeInfo strokeInfo = GrTest::TestStrokeInfo(random);
     return TessellatingPathBatch::Create(color, path, strokeInfo, viewMatrix, clipBounds);
 }
 
 #endif