xref: /aosp_15_r20/external/skia/src/gpu/ganesh/geometry/GrTriangulator.cpp (revision c8dee2aa9b3f27cf6c858bd81872bdeb2c07ed17)

/*
 * 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 "src/gpu/ganesh/geometry/GrTriangulator.h"

#include "include/core/SkPathTypes.h"
#include "include/core/SkRect.h"
#include "include/private/base/SkDebug.h"
#include "include/private/base/SkFloatingPoint.h"
#include "include/private/base/SkMath.h"
#include "include/private/base/SkTPin.h"
#include "src/base/SkVx.h"
#include "src/core/SkGeometry.h"
#include "src/core/SkPointPriv.h"
#include "src/gpu/BufferWriter.h"
#include "src/gpu/ganesh/GrColor.h"
#include "src/gpu/ganesh/GrEagerVertexAllocator.h"
#include "src/gpu/ganesh/geometry/GrPathUtils.h"

#include <algorithm>
#include <cstddef>
#include <limits>
#include <memory>
#include <tuple>
#include <utility>

#if !defined(SK_ENABLE_OPTIMIZE_SIZE)

#if TRIANGULATOR_LOGGING
#define TESS_LOG printf
#define DUMP_MESH(M) (M).dump()
#else
#define TESS_LOG(...)
#define DUMP_MESH(M)
#endif

using EdgeType = GrTriangulator::EdgeType;
using Vertex = GrTriangulator::Vertex;
using VertexList = GrTriangulator::VertexList;
using Line = GrTriangulator::Line;
using Edge = GrTriangulator::Edge;
using EdgeList = GrTriangulator::EdgeList;
using Poly = GrTriangulator::Poly;
using MonotonePoly = GrTriangulator::MonotonePoly;
using Comparator = GrTriangulator::Comparator;

template <class T, T* T::*Prev, T* T::*Next>
static void list_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>
static void list_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;
}

typedef bool (*CompareFunc)(const SkPoint& a, const SkPoint& b);

static bool sweep_lt_horiz(const SkPoint& a, const SkPoint& b) {
    return a.fX < b.fX || (a.fX == b.fX && a.fY > b.fY);
}

static bool sweep_lt_vert(const SkPoint& a, const SkPoint& b) {
    return a.fY < b.fY || (a.fY == b.fY && a.fX < b.fX);
}

bool GrTriangulator::Comparator::sweep_lt(const SkPoint& a, const SkPoint& b) const {
    return fDirection == Direction::kHorizontal ? sweep_lt_horiz(a, b) : sweep_lt_vert(a, b);
}

static inline skgpu::VertexWriter emit_vertex(Vertex* v,
                                              bool emitCoverage,
                                              skgpu::VertexWriter data) {
    data << v->fPoint;

    if (emitCoverage) {
        data << GrNormalizeByteToFloat(v->fAlpha);
    }

    return data;
}

static skgpu::VertexWriter emit_triangle(Vertex* v0, Vertex* v1, Vertex* v2,
                                         bool emitCoverage, skgpu::VertexWriter data) {
    TESS_LOG("emit_triangle %g (%g, %g) %d\n", v0->fID, v0->fPoint.fX, v0->fPoint.fY, v0->fAlpha);
    TESS_LOG("              %g (%g, %g) %d\n", v1->fID, v1->fPoint.fX, v1->fPoint.fY, v1->fAlpha);
    TESS_LOG("              %g (%g, %g) %d\n", v2->fID, v2->fPoint.fX, v2->fPoint.fY, v2->fAlpha);
#if TRIANGULATOR_WIREFRAME
    data = emit_vertex(v0, emitCoverage, std::move(data));
    data = emit_vertex(v1, emitCoverage, std::move(data));
    data = emit_vertex(v1, emitCoverage, std::move(data));
    data = emit_vertex(v2, emitCoverage, std::move(data));
    data = emit_vertex(v2, emitCoverage, std::move(data));
    data = emit_vertex(v0, emitCoverage, std::move(data));
#else
    data = emit_vertex(v0, emitCoverage, std::move(data));
    data = emit_vertex(v1, emitCoverage, std::move(data));
    data = emit_vertex(v2, emitCoverage, std::move(data));
#endif
    return data;
}

void GrTriangulator::VertexList::insert(Vertex* v, Vertex* prev, Vertex* next) {
    list_insert<Vertex, &Vertex::fPrev, &Vertex::fNext>(v, prev, next, &fHead, &fTail);
}

void GrTriangulator::VertexList::remove(Vertex* v) {
    list_remove<Vertex, &Vertex::fPrev, &Vertex::fNext>(v, &fHead, &fTail);
}

// Round to nearest quarter-pixel. This is used for screenspace tessellation.

static inline void round(SkPoint* p) {
    p->fX = SkScalarRoundToScalar(p->fX * 4.0f) * 0.25f;
    p->fY = SkScalarRoundToScalar(p->fY * 4.0f) * 0.25f;
}

static inline SkScalar double_to_clamped_scalar(double d) {
    // Clamps large values to what's finitely representable when cast back to a float.
    static const double kMaxLimit = (double) SK_ScalarMax;
    // It's not perfect, but a using a value larger than float_min helps protect from denormalized
    // values and ill-conditions in intermediate calculations on coordinates.
    static const double kNearZeroLimit = 16 * (double) std::numeric_limits<float>::min();
    if (std::abs(d) < kNearZeroLimit) {
        d = 0.f;
    }
    return SkDoubleToScalar(std::max(-kMaxLimit, std::min(d, kMaxLimit)));
}

bool GrTriangulator::Line::intersect(const Line& other, SkPoint* point) const {
    double denom = fA * other.fB - fB * other.fA;
    if (denom == 0.0) {
        return false;
    }
    double scale = 1.0 / denom;
    point->fX = double_to_clamped_scalar((fB * other.fC - other.fB * fC) * scale);
    point->fY = double_to_clamped_scalar((other.fA * fC - fA * other.fC) * scale);
     round(point);
    return point->isFinite();
}

// If the edge's vertices differ by many orders of magnitude, the computed line equation can have
// significant error in its distance and intersection tests. To avoid this, we recursively subdivide
// long edges and effectively perform a binary search to perform a more accurate intersection test.
static bool edge_line_needs_recursion(const SkPoint& p0, const SkPoint& p1) {
    // ilogbf(0) returns an implementation-defined constant, but we are choosing to saturate
    // negative exponents to 0 for comparisons sake. We're only trying to recurse on lines with
    // very large coordinates.
    int expDiffX = std::abs((std::abs(p0.fX) < 1.f ? 0 : std::ilogbf(p0.fX)) -
                            (std::abs(p1.fX) < 1.f ? 0 : std::ilogbf(p1.fX)));
    int expDiffY = std::abs((std::abs(p0.fY) < 1.f ? 0 : std::ilogbf(p0.fY)) -
                            (std::abs(p1.fY) < 1.f ? 0 : std::ilogbf(p1.fY)));
    // Differ by more than 2^20, or roughly a factor of one million.
    return expDiffX > 20 || expDiffY > 20;
}

static bool recursive_edge_intersect(const Line& u, SkPoint u0, SkPoint u1,
                                     const Line& v, SkPoint v0, SkPoint v1,
                                     SkPoint* p, double* s, double* t) {
    // First check if the bounding boxes of [u0,u1] intersects [v0,v1]. If they do not, then the
    // two line segments cannot intersect in their domain (even if the lines themselves might).
    // - don't use SkRect::intersect since the vertices aren't sorted and horiz/vertical lines
    //   appear as empty rects, which then never "intersect" according to SkRect.
    if (std::min(u0.fX, u1.fX) > std::max(v0.fX, v1.fX) ||
        std::max(u0.fX, u1.fX) < std::min(v0.fX, v1.fX) ||
        std::min(u0.fY, u1.fY) > std::max(v0.fY, v1.fY) ||
        std::max(u0.fY, u1.fY) < std::min(v0.fY, v1.fY)) {
        return false;
    }

    // Compute intersection based on current segment vertices; if an intersection is found but the
    // vertices differ too much in magnitude, we recurse using the midpoint of the segment to
    // reject false positives. We don't currently try to avoid false negatives (e.g. large magnitude
    // line reports no intersection but there is one).
    double denom = u.fA * v.fB - u.fB * v.fA;
    if (denom == 0.0) {
        return false;
    }
    double dx = static_cast<double>(v0.fX) - u0.fX;
    double dy = static_cast<double>(v0.fY) - u0.fY;
    double sNumer = dy * v.fB + dx * v.fA;
    double tNumer = dy * u.fB + dx * u.fA;
    // 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;
    }

    *s = sNumer / denom;
    *t = tNumer / denom;
    SkASSERT(*s >= 0.0 && *s <= 1.0 && *t >= 0.0 && *t <= 1.0);

    const bool uNeedsSplit = edge_line_needs_recursion(u0, u1);
    const bool vNeedsSplit = edge_line_needs_recursion(v0, v1);
    if (!uNeedsSplit && !vNeedsSplit) {
        p->fX = double_to_clamped_scalar(u0.fX - (*s) * u.fB);
        p->fY = double_to_clamped_scalar(u0.fY + (*s) * u.fA);
        return true;
    } else {
        double sScale = 1.0, sShift = 0.0;
        double tScale = 1.0, tShift = 0.0;

        if (uNeedsSplit) {
            SkPoint uM = {(float) (0.5 * u0.fX + 0.5 * u1.fX),
                          (float) (0.5 * u0.fY + 0.5 * u1.fY)};
            sScale = 0.5;
            if (*s >= 0.5) {
                u0 = uM;
                sShift = 0.5;
            } else {
                u1 = uM;
            }
        }
        if (vNeedsSplit) {
            SkPoint vM = {(float) (0.5 * v0.fX + 0.5 * v1.fX),
                          (float) (0.5 * v0.fY + 0.5 * v1.fY)};
            tScale = 0.5;
            if (*t >= 0.5) {
                v0 = vM;
                tShift = 0.5;
            } else {
                v1 = vM;
            }
        }

        // Just recompute both lines, even if only one was split; we're already in a slow path.
        if (recursive_edge_intersect(Line(u0, u1), u0, u1, Line(v0, v1), v0, v1, p, s, t)) {
            // Adjust s and t back to full range
            *s = sScale * (*s) + sShift;
            *t = tScale * (*t) + tShift;
            return true;
        } else {
            // False positive
            return false;
        }
    }
}

bool GrTriangulator::Edge::intersect(const Edge& other, SkPoint* p, uint8_t* alpha) const {
    TESS_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 ||
        fTop == other.fBottom || fBottom == other.fTop) {
        // If the two edges share a vertex by construction, they have already been split and
        // shouldn't be considered "intersecting" anymore.
        return false;
    }

    double s, t; // needed to interpolate vertex alpha
    const bool intersects = recursive_edge_intersect(
            fLine, fTop->fPoint, fBottom->fPoint,
            other.fLine, other.fTop->fPoint, other.fBottom->fPoint,
            p, &s, &t);
    if (!intersects) {
        return false;
    }

    if (alpha) {
        if (fType == EdgeType::kInner || other.fType == EdgeType::kInner) {
            // If the intersection is on any interior edge, it needs to stay fully opaque or later
            // triangulation could leech transparency into the inner fill region.
            *alpha = 255;
        } else if (fType == EdgeType::kOuter && other.fType == EdgeType::kOuter) {
            // Trivially, the intersection will be fully transparent since since it is by
            // construction on the outer edge.
            *alpha = 0;
        } else {
            // Could be two connectors crossing, or a connector crossing an outer edge.
            // Take the max interpolated alpha
            SkASSERT(fType == EdgeType::kConnector || other.fType == EdgeType::kConnector);
            *alpha = std::max((1.0 - s) * fTop->fAlpha + s * fBottom->fAlpha,
                              (1.0 - t) * other.fTop->fAlpha + t * other.fBottom->fAlpha);
        }
    }
    return true;
}

void GrTriangulator::EdgeList::insert(Edge* edge, Edge* prev, Edge* next) {
    list_insert<Edge, &Edge::fLeft, &Edge::fRight>(edge, prev, next, &fHead, &fTail);
}

bool GrTriangulator::EdgeList::remove(Edge* edge) {
    TESS_LOG("removing edge %g -> %g\n", edge->fTop->fID, edge->fBottom->fID);
    // SkASSERT(this->contains(edge));  // Leave this here for future debugging.
    if (!this->contains(edge)) {
        return false;
    }
    list_remove<Edge, &Edge::fLeft, &Edge::fRight>(edge, &fHead, &fTail);
    return true;
}

void GrTriangulator::MonotonePoly::addEdge(Edge* edge) {
    if (fSide == Side::kRight) {
        SkASSERT(!edge->fUsedInRightPoly);
        list_insert<Edge, &Edge::fRightPolyPrev, &Edge::fRightPolyNext>(
            edge, fLastEdge, nullptr, &fFirstEdge, &fLastEdge);
        edge->fUsedInRightPoly = true;
    } else {
        SkASSERT(!edge->fUsedInLeftPoly);
        list_insert<Edge, &Edge::fLeftPolyPrev, &Edge::fLeftPolyNext>(
            edge, fLastEdge, nullptr, &fFirstEdge, &fLastEdge);
        edge->fUsedInLeftPoly = true;
    }
}

skgpu::VertexWriter GrTriangulator::emitMonotonePoly(const MonotonePoly* monotonePoly,
                                                     skgpu::VertexWriter data) const {
    SkASSERT(monotonePoly->fWinding != 0);
    Edge* e = monotonePoly->fFirstEdge;
    VertexList vertices;
    vertices.append(e->fTop);
    int count = 1;
    while (e != nullptr) {
        if (Side::kRight == monotonePoly->fSide) {
            vertices.append(e->fBottom);
            e = e->fRightPolyNext;
        } else {
            vertices.prepend(e->fBottom);
            e = e->fLeftPolyNext;
        }
        count++;
    }
    Vertex* first = vertices.fHead;
    Vertex* v = first->fNext;
    while (v != vertices.fTail) {
        SkASSERT(v && v->fPrev && v->fNext);
        Vertex* prev = v->fPrev;
        Vertex* curr = v;
        Vertex* next = v->fNext;
        if (count == 3) {
            return this->emitTriangle(prev, curr, next, monotonePoly->fWinding, std::move(data));
        }
        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 = this->emitTriangle(prev, curr, next, monotonePoly->fWinding, std::move(data));
            v->fPrev->fNext = v->fNext;
            v->fNext->fPrev = v->fPrev;
            count--;
            if (v->fPrev == first) {
                v = v->fNext;
            } else {
                v = v->fPrev;
            }
        } else {
            v = v->fNext;
        }
    }
    return data;
}

skgpu::VertexWriter GrTriangulator::emitTriangle(
        Vertex* prev, Vertex* curr, Vertex* next, int winding, skgpu::VertexWriter data) const {
    if (winding > 0) {
        // Ensure our triangles always wind in the same direction as if the path had been
        // triangulated as a simple fan (a la red book).
        std::swap(prev, next);
    }
    if (fCollectBreadcrumbTriangles && abs(winding) > 1 &&
        fPath.getFillType() == SkPathFillType::kWinding) {
        // The first winding count will come from the actual triangle we emit. The remaining counts
        // come from the breadcrumb triangle.
        fBreadcrumbList.append(fAlloc, prev->fPoint, curr->fPoint, next->fPoint, abs(winding) - 1);
    }
    return emit_triangle(prev, curr, next, fEmitCoverage, std::move(data));
}

GrTriangulator::Poly::Poly(Vertex* v, int winding)
        : fFirstVertex(v)
        , fWinding(winding)
        , fHead(nullptr)
        , fTail(nullptr)
        , fNext(nullptr)
        , fPartner(nullptr)
        , fCount(0)
{
#if TRIANGULATOR_LOGGING
    static int gID = 0;
    fID = gID++;
    TESS_LOG("*** created Poly %d\n", fID);
#endif
}

Poly* GrTriangulator::Poly::addEdge(Edge* e, Side side, GrTriangulator* tri) {
    TESS_LOG("addEdge (%g -> %g) to poly %d, %s side\n",
             e->fTop->fID,
             e->fBottom->fID,
             fID,
             side == Side::kLeft ? "left" : "right");
    Poly* partner = fPartner;
    Poly* poly = this;
    if (side == Side::kRight) {
        if (e->fUsedInRightPoly) {
            return this;
        }
    } else {
        if (e->fUsedInLeftPoly) {
            return this;
        }
    }
    if (partner) {
        fPartner = partner->fPartner = nullptr;
    }
    if (!fTail) {
        fHead = fTail = tri->allocateMonotonePoly(e, side, fWinding);
        fCount += 2;
    } else if (e->fBottom == fTail->fLastEdge->fBottom) {
        return poly;
    } else if (side == fTail->fSide) {
        fTail->addEdge(e);
        fCount++;
    } else {
        e = tri->allocateEdge(fTail->fLastEdge->fBottom, e->fBottom, 1, EdgeType::kInner);
        fTail->addEdge(e);
        fCount++;
        if (partner) {
            partner->addEdge(e, side, tri);
            poly = partner;
        } else {
            MonotonePoly* m = tri->allocateMonotonePoly(e, side, fWinding);
            m->fPrev = fTail;
            fTail->fNext = m;
            fTail = m;
        }
    }
    return poly;
}
skgpu::VertexWriter GrTriangulator::emitPoly(const Poly* poly, skgpu::VertexWriter data) const {
    if (poly->fCount < 3) {
        return data;
    }
    TESS_LOG("emit() %d, size %d\n", poly->fID, poly->fCount);
    for (MonotonePoly* m = poly->fHead; m != nullptr; m = m->fNext) {
        data = this->emitMonotonePoly(m, std::move(data));
    }
    return data;
}

static bool coincident(const SkPoint& a, const SkPoint& b) {
    return a == b;
}

Poly* GrTriangulator::makePoly(Poly** head, Vertex* v, int winding) const {
    Poly* poly = fAlloc->make<Poly>(v, winding);
    poly->fNext = *head;
    *head = poly;
    return poly;
}

void GrTriangulator::appendPointToContour(const SkPoint& p, VertexList* contour) const {
    Vertex* v = fAlloc->make<Vertex>(p, 255);
#if TRIANGULATOR_LOGGING
    static float gID = 0.0f;
    v->fID = gID++;
#endif
    contour->append(v);
}

static SkScalar quad_error_at(const SkPoint pts[3], SkScalar t, SkScalar u) {
    SkQuadCoeff quad(pts);
    SkPoint p0 = to_point(quad.eval(t - 0.5f * u));
    SkPoint mid = to_point(quad.eval(t));
    SkPoint p1 = to_point(quad.eval(t + 0.5f * u));
    if (!p0.isFinite() || !mid.isFinite() || !p1.isFinite()) {
        return 0;
    }
    return SkPointPriv::DistanceToLineSegmentBetweenSqd(mid, p0, p1);
}

void GrTriangulator::appendQuadraticToContour(const SkPoint pts[3], SkScalar toleranceSqd,
                                              VertexList* contour) const {
    SkQuadCoeff quad(pts);
    skvx::float2 aa = quad.fA * quad.fA;
    SkScalar denom = 2.0f * (aa[0] + aa[1]);
    skvx::float2 ab = quad.fA * quad.fB;
    SkScalar t = denom ? (-ab[0] - ab[1]) / denom : 0.0f;
    int nPoints = 1;
    SkScalar u = 1.0f;
    // Test possible subdivision values only at the point of maximum curvature.
    // If it passes the flatness metric there, it'll pass everywhere.
    while (nPoints < GrPathUtils::kMaxPointsPerCurve) {
        u = 1.0f / nPoints;
        if (quad_error_at(pts, t, u) < toleranceSqd) {
            break;
        }
        nPoints++;
    }
    for (int j = 1; j <= nPoints; j++) {
        this->appendPointToContour(to_point(quad.eval(j * u)), contour);
    }
}

void GrTriangulator::generateCubicPoints(const SkPoint& p0, const SkPoint& p1, const SkPoint& p2,
                                         const SkPoint& p3, SkScalar tolSqd, VertexList* contour,
                                         int pointsLeft) const {
    SkScalar d1 = SkPointPriv::DistanceToLineSegmentBetweenSqd(p1, p0, p3);
    SkScalar d2 = SkPointPriv::DistanceToLineSegmentBetweenSqd(p2, p0, p3);
    if (pointsLeft < 2 || (d1 < tolSqd && d2 < tolSqd) || !SkIsFinite(d1, d2)) {
        this->appendPointToContour(p3, contour);
        return;
    }
    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;
    this->generateCubicPoints(p0, q[0], r[0], s, tolSqd, contour, pointsLeft);
    this->generateCubicPoints(s, r[1], q[2], p3, tolSqd, contour, pointsLeft);
}

// Stage 1: convert the input path to a set of linear contours (linked list of Vertices).

void GrTriangulator::pathToContours(float tolerance, const SkRect& clipBounds,
                                    VertexList* contours, bool* isLinear) const {
    SkScalar toleranceSqd = tolerance * tolerance;
    SkPoint pts[4];
    *isLinear = true;
    VertexList* contour = contours;
    SkPath::Iter iter(fPath, false);
    if (fPath.isInverseFillType()) {
        SkPoint quad[4];
        clipBounds.toQuad(quad);
        for (int i = 3; i >= 0; i--) {
            this->appendPointToContour(quad[i], contours);
        }
        contour++;
    }
    SkAutoConicToQuads converter;
    SkPath::Verb verb;
    while ((verb = iter.next(pts)) != SkPath::kDone_Verb) {
        switch (verb) {
            case SkPath::kConic_Verb: {
                *isLinear = false;
                if (toleranceSqd == 0) {
                    this->appendPointToContour(pts[2], contour);
                    break;
                }
                SkScalar weight = iter.conicWeight();
                const SkPoint* quadPts = converter.computeQuads(pts, weight, toleranceSqd);
                for (int i = 0; i < converter.countQuads(); ++i) {
                    this->appendQuadraticToContour(quadPts, toleranceSqd, contour);
                    quadPts += 2;
                }
                break;
            }
            case SkPath::kMove_Verb:
                if (contour->fHead) {
                    contour++;
                }
                this->appendPointToContour(pts[0], contour);
                break;
            case SkPath::kLine_Verb: {
                this->appendPointToContour(pts[1], contour);
                break;
            }
            case SkPath::kQuad_Verb: {
                *isLinear = false;
                if (toleranceSqd == 0) {
                    this->appendPointToContour(pts[2], contour);
                    break;
                }
                this->appendQuadraticToContour(pts, toleranceSqd, contour);
                break;
            }
            case SkPath::kCubic_Verb: {
                *isLinear = false;
                if (toleranceSqd == 0) {
                    this->appendPointToContour(pts[3], contour);
                    break;
                }
                int pointsLeft = GrPathUtils::cubicPointCount(pts, tolerance);
                this->generateCubicPoints(pts[0], pts[1], pts[2], pts[3], toleranceSqd, contour,
                                          pointsLeft);
                break;
            }
            case SkPath::kClose_Verb:
            case SkPath::kDone_Verb:
                break;
        }
    }
}

static inline bool apply_fill_type(SkPathFillType fillType, int winding) {
    switch (fillType) {
        case SkPathFillType::kWinding:
            return winding != 0;
        case SkPathFillType::kEvenOdd:
            return (winding & 1) != 0;
        case SkPathFillType::kInverseWinding:
            return winding == 1;
        case SkPathFillType::kInverseEvenOdd:
            return (winding & 1) == 1;
        default:
            SkASSERT(false);
            return false;
    }
}

bool GrTriangulator::applyFillType(int winding) const {
    return apply_fill_type(fPath.getFillType(), winding);
}

static inline bool apply_fill_type(SkPathFillType fillType, Poly* poly) {
    return poly && apply_fill_type(fillType, poly->fWinding);
}

MonotonePoly* GrTriangulator::allocateMonotonePoly(Edge* edge, Side side, int winding) {
    ++fNumMonotonePolys;
    return fAlloc->make<MonotonePoly>(edge, side, winding);
}

Edge* GrTriangulator::allocateEdge(Vertex* top, Vertex* bottom, int winding, EdgeType type) {
    ++fNumEdges;
    return fAlloc->make<Edge>(top, bottom, winding, type);
}

Edge* GrTriangulator::makeEdge(Vertex* prev, Vertex* next, EdgeType type,
                               const Comparator& c) {
    SkASSERT(prev->fPoint != next->fPoint);
    int winding = c.sweep_lt(prev->fPoint, next->fPoint) ? 1 : -1;
    Vertex* top = winding < 0 ? next : prev;
    Vertex* bottom = winding < 0 ? prev : next;
    return this->allocateEdge(top, bottom, winding, type);
}

bool EdgeList::insert(Edge* edge, Edge* prev) {
    TESS_LOG("inserting edge %g -> %g\n", edge->fTop->fID, edge->fBottom->fID);
    // SkASSERT(!this->contains(edge));  // Leave this here for debugging.
    if (this->contains(edge)) {
        return false;
    }
    Edge* next = prev ? prev->fRight : fHead;
    this->insert(edge, prev, next);
    return true;
}

void GrTriangulator::FindEnclosingEdges(const Vertex& v,
                                        const EdgeList& edges,
                                        Edge** left, Edge**right) {
    if (v.fFirstEdgeAbove && v.fLastEdgeAbove) {
        *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;
}

void GrTriangulator::Edge::insertAbove(Vertex* v, const Comparator& c) {
    if (fTop->fPoint == fBottom->fPoint ||
        c.sweep_lt(fBottom->fPoint, fTop->fPoint)) {
        return;
    }
    TESS_LOG("insert edge (%g -> %g) above vertex %g\n", fTop->fID, fBottom->fID, v->fID);
    Edge* prev = nullptr;
    Edge* next;
    for (next = v->fFirstEdgeAbove; next; next = next->fNextEdgeAbove) {
        if (next->isRightOf(*fTop)) {
            break;
        }
        prev = next;
    }
    list_insert<Edge, &Edge::fPrevEdgeAbove, &Edge::fNextEdgeAbove>(
        this, prev, next, &v->fFirstEdgeAbove, &v->fLastEdgeAbove);
}

void GrTriangulator::Edge::insertBelow(Vertex* v, const Comparator& c) {
    if (fTop->fPoint == fBottom->fPoint ||
        c.sweep_lt(fBottom->fPoint, fTop->fPoint)) {
        return;
    }
    TESS_LOG("insert edge (%g -> %g) below vertex %g\n", fTop->fID, fBottom->fID, v->fID);
    Edge* prev = nullptr;
    Edge* next;
    for (next = v->fFirstEdgeBelow; next; next = next->fNextEdgeBelow) {
        if (next->isRightOf(*fBottom)) {
            break;
        }
        prev = next;
    }
    list_insert<Edge, &Edge::fPrevEdgeBelow, &Edge::fNextEdgeBelow>(
        this, prev, next, &v->fFirstEdgeBelow, &v->fLastEdgeBelow);
}

static void remove_edge_above(Edge* edge) {
    SkASSERT(edge->fTop && edge->fBottom);
    TESS_LOG("removing edge (%g -> %g) above vertex %g\n", edge->fTop->fID, edge->fBottom->fID,
             edge->fBottom->fID);
    list_remove<Edge, &Edge::fPrevEdgeAbove, &Edge::fNextEdgeAbove>(
        edge, &edge->fBottom->fFirstEdgeAbove, &edge->fBottom->fLastEdgeAbove);
}

static void remove_edge_below(Edge* edge) {
    SkASSERT(edge->fTop && edge->fBottom);
    TESS_LOG("removing edge (%g -> %g) below vertex %g\n",
             edge->fTop->fID, edge->fBottom->fID, edge->fTop->fID);
    list_remove<Edge, &Edge::fPrevEdgeBelow, &Edge::fNextEdgeBelow>(
        edge, &edge->fTop->fFirstEdgeBelow, &edge->fTop->fLastEdgeBelow);
}

void GrTriangulator::Edge::disconnect() {
    remove_edge_above(this);
    remove_edge_below(this);
}

static bool rewind(EdgeList* activeEdges, Vertex** current, Vertex* dst, const Comparator& c) {
    if (!current || *current == dst || c.sweep_lt((*current)->fPoint, dst->fPoint)) {
        return true;
    }
    Vertex* v = *current;
    TESS_LOG("rewinding active edges from vertex %g to vertex %g\n", v->fID, dst->fID);
    while (v != dst) {
        v = v->fPrev;
        for (Edge* e = v->fFirstEdgeBelow; e; e = e->fNextEdgeBelow) {
            if (!activeEdges->remove(e)) {
                return false;
            }
        }
        Edge* leftEdge = v->fLeftEnclosingEdge;
        for (Edge* e = v->fFirstEdgeAbove; e; e = e->fNextEdgeAbove) {
            if (!activeEdges->insert(e, leftEdge)) {
                return false;
            }
            leftEdge = e;
            Vertex* top = e->fTop;
            if (c.sweep_lt(top->fPoint, dst->fPoint) &&
                ((top->fLeftEnclosingEdge && !top->fLeftEnclosingEdge->isLeftOf(*e->fTop)) ||
                 (top->fRightEnclosingEdge && !top->fRightEnclosingEdge->isRightOf(*e->fTop)))) {
                dst = top;
            }
        }
    }
    *current = v;
    return true;
}

static bool rewind_if_necessary(Edge* edge, EdgeList* activeEdges, Vertex** current,
                                const Comparator& c) {
    if (!activeEdges || !current) {
        return true;
    }
    if (!edge) {
        return false;
    }
    Vertex* top = edge->fTop;
    Vertex* bottom = edge->fBottom;
    if (edge->fLeft) {
        Vertex* leftTop = edge->fLeft->fTop;
        Vertex* leftBottom = edge->fLeft->fBottom;
        if (leftTop && leftBottom) {
            if (c.sweep_lt(leftTop->fPoint, top->fPoint) && !edge->fLeft->isLeftOf(*top)) {
                if (!rewind(activeEdges, current, leftTop, c)) {
                    return false;
                }
            } else if (c.sweep_lt(top->fPoint, leftTop->fPoint) && !edge->isRightOf(*leftTop)) {
                if (!rewind(activeEdges, current, top, c)) {
                    return false;
                }
            } else if (c.sweep_lt(bottom->fPoint, leftBottom->fPoint) &&
                       !edge->fLeft->isLeftOf(*bottom)) {
                if (!rewind(activeEdges, current, leftTop, c)) {
                    return false;
                }
            } else if (c.sweep_lt(leftBottom->fPoint, bottom->fPoint) &&
                       !edge->isRightOf(*leftBottom)) {
                if (!rewind(activeEdges, current, top, c)) {
                    return false;
                }
            }
        }
    }
    if (edge->fRight) {
        Vertex* rightTop = edge->fRight->fTop;
        Vertex* rightBottom = edge->fRight->fBottom;
        if (rightTop && rightBottom) {
            if (c.sweep_lt(rightTop->fPoint, top->fPoint) && !edge->fRight->isRightOf(*top)) {
                if (!rewind(activeEdges, current, rightTop, c)) {
                    return false;
                }
            } else if (c.sweep_lt(top->fPoint, rightTop->fPoint) && !edge->isLeftOf(*rightTop)) {
                if (!rewind(activeEdges, current, top, c)) {
                    return false;
                }
            } else if (c.sweep_lt(bottom->fPoint, rightBottom->fPoint) &&
                       !edge->fRight->isRightOf(*bottom)) {
                if (!rewind(activeEdges, current, rightTop, c)) {
                    return false;
                }
            } else if (c.sweep_lt(rightBottom->fPoint, bottom->fPoint) &&
                       !edge->isLeftOf(*rightBottom)) {
                if (!rewind(activeEdges, current, top, c)) {
                    return false;
                }
            }
        }
    }
    return true;
}

bool GrTriangulator::setTop(Edge* edge, Vertex* v, EdgeList* activeEdges, Vertex** current,
                            const Comparator& c) const {
    remove_edge_below(edge);
    if (fCollectBreadcrumbTriangles) {
        fBreadcrumbList.append(fAlloc, edge->fTop->fPoint, edge->fBottom->fPoint, v->fPoint,
                               edge->fWinding);
    }
    edge->fTop = v;
    edge->recompute();
    edge->insertBelow(v, c);
    if (!rewind_if_necessary(edge, activeEdges, current, c)) {
        return false;
    }
    return this->mergeCollinearEdges(edge, activeEdges, current, c);
}

bool GrTriangulator::setBottom(Edge* edge, Vertex* v, EdgeList* activeEdges, Vertex** current,
                               const Comparator& c) const {
    remove_edge_above(edge);
    if (fCollectBreadcrumbTriangles) {
        fBreadcrumbList.append(fAlloc, edge->fTop->fPoint, edge->fBottom->fPoint, v->fPoint,
                               edge->fWinding);
    }
    edge->fBottom = v;
    edge->recompute();
    edge->insertAbove(v, c);
    if (!rewind_if_necessary(edge, activeEdges, current, c)) {
        return false;
    }
    return this->mergeCollinearEdges(edge, activeEdges, current, c);
}

bool GrTriangulator::mergeEdgesAbove(Edge* edge, Edge* other, EdgeList* activeEdges,
                                     Vertex** current, const Comparator& c) const {
    if (!edge || !other) {
        return false;
    }
    if (coincident(edge->fTop->fPoint, other->fTop->fPoint)) {
        TESS_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);
        if (!rewind(activeEdges, current, edge->fTop, c)) {
            return false;
        }
        other->fWinding += edge->fWinding;
        edge->disconnect();
        edge->fTop = edge->fBottom = nullptr;
    } else if (c.sweep_lt(edge->fTop->fPoint, other->fTop->fPoint)) {
        if (!rewind(activeEdges, current, edge->fTop, c)) {
            return false;
        }
        other->fWinding += edge->fWinding;
        if (!this->setBottom(edge, other->fTop, activeEdges, current, c)) {
            return false;
        }
    } else {
        if (!rewind(activeEdges, current, other->fTop, c)) {
            return false;
        }
        edge->fWinding += other->fWinding;
        if (!this->setBottom(other, edge->fTop, activeEdges, current, c)) {
            return false;
        }
    }
    return true;
}

bool GrTriangulator::mergeEdgesBelow(Edge* edge, Edge* other, EdgeList* activeEdges,
                                     Vertex** current, const Comparator& c) const {
    if (!edge || !other) {
        return false;
    }
    if (coincident(edge->fBottom->fPoint, other->fBottom->fPoint)) {
        TESS_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);
        if (!rewind(activeEdges, current, edge->fTop, c)) {
            return false;
        }
        other->fWinding += edge->fWinding;
        edge->disconnect();
        edge->fTop = edge->fBottom = nullptr;
    } else if (c.sweep_lt(edge->fBottom->fPoint, other->fBottom->fPoint)) {
        if (!rewind(activeEdges, current, other->fTop, c)) {
            return false;
        }
        edge->fWinding += other->fWinding;
        if (!this->setTop(other, edge->fBottom, activeEdges, current, c)) {
            return false;
        }
    } else {
        if (!rewind(activeEdges, current, edge->fTop, c)) {
            return false;
        }
        other->fWinding += edge->fWinding;
        if (!this->setTop(edge, other->fBottom, activeEdges, current, c)) {
            return false;
        }
    }
    return true;
}

static bool top_collinear(Edge* left, Edge* right) {
    if (!left || !right) {
        return false;
    }
    return left->fTop->fPoint == right->fTop->fPoint ||
           !left->isLeftOf(*right->fTop) || !right->isRightOf(*left->fTop);
}

static bool bottom_collinear(Edge* left, Edge* right) {
    if (!left || !right) {
        return false;
    }
    return left->fBottom->fPoint == right->fBottom->fPoint ||
           !left->isLeftOf(*right->fBottom) || !right->isRightOf(*left->fBottom);
}

bool GrTriangulator::mergeCollinearEdges(Edge* edge, EdgeList* activeEdges, Vertex** current,
                                         const Comparator& c) const {
    for (;;) {
        if (top_collinear(edge->fPrevEdgeAbove, edge)) {
            if (!this->mergeEdgesAbove(edge->fPrevEdgeAbove, edge, activeEdges, current, c)) {
                return false;
            }
        } else if (top_collinear(edge, edge->fNextEdgeAbove)) {
            if (!this->mergeEdgesAbove(edge->fNextEdgeAbove, edge, activeEdges, current, c)) {
                return false;
            }
        } else if (bottom_collinear(edge->fPrevEdgeBelow, edge)) {
            if (!this->mergeEdgesBelow(edge->fPrevEdgeBelow, edge, activeEdges, current, c)) {
                return false;
            }
        } else if (bottom_collinear(edge, edge->fNextEdgeBelow)) {
            if (!this->mergeEdgesBelow(edge->fNextEdgeBelow, edge, activeEdges, current, c)) {
                return false;
            }
        } else {
            break;
        }
    }
    SkASSERT(!top_collinear(edge->fPrevEdgeAbove, edge));
    SkASSERT(!top_collinear(edge, edge->fNextEdgeAbove));
    SkASSERT(!bottom_collinear(edge->fPrevEdgeBelow, edge));
    SkASSERT(!bottom_collinear(edge, edge->fNextEdgeBelow));
    return true;
}

GrTriangulator::BoolFail GrTriangulator::splitEdge(
        Edge* edge, Vertex* v, EdgeList* activeEdges, Vertex** current, const Comparator& c) {
    if (!edge->fTop || !edge->fBottom || v == edge->fTop || v == edge->fBottom) {
        return BoolFail::kFalse;
    }
    TESS_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);
    Vertex* top;
    Vertex* bottom;
    int winding = edge->fWinding;
    // Theoretically, and ideally, the edge betwee p0 and p1 is being split by v, and v is "between"
    // the segment end points according to c. This is equivalent to p0 < v < p1.  Unfortunately, if
    // v was clamped/rounded this relation doesn't always hold.
    if (c.sweep_lt(v->fPoint, edge->fTop->fPoint)) {
        // Actually "v < p0 < p1": update 'edge' to be v->p1 and add v->p0. We flip the winding on
        // the new edge so that it winds as if it were p0->v.
        top = v;
        bottom = edge->fTop;
        winding *= -1;
        if (!this->setTop(edge, v, activeEdges, current, c)) {
            return BoolFail::kFail;
        }
    } else if (c.sweep_lt(edge->fBottom->fPoint, v->fPoint)) {
        // Actually "p0 < p1 < v": update 'edge' to be p0->v and add p1->v. We flip the winding on
        // the new edge so that it winds as if it were v->p1.
        top = edge->fBottom;
        bottom = v;
        winding *= -1;
        if (!this->setBottom(edge, v, activeEdges, current, c)) {
            return BoolFail::kFail;
        }
    } else {
        // The ideal case, "p0 < v < p1": update 'edge' to be p0->v and add v->p1. Original winding
        // is valid for both edges.
        top = v;
        bottom = edge->fBottom;
        if (!this->setBottom(edge, v, activeEdges, current, c)) {
            return BoolFail::kFail;
        }
    }
    Edge* newEdge = this->allocateEdge(top, bottom, winding, edge->fType);
    newEdge->insertBelow(top, c);
    newEdge->insertAbove(bottom, c);
    if (!this->mergeCollinearEdges(newEdge, activeEdges, current, c)) {
        return BoolFail::kFail;
    }
    return BoolFail::kTrue;
}

GrTriangulator::BoolFail GrTriangulator::intersectEdgePair(
        Edge* left, Edge* right, EdgeList* activeEdges, Vertex** current, const Comparator& c) {
    if (!left->fTop || !left->fBottom || !right->fTop || !right->fBottom) {
        return BoolFail::kFalse;
    }
    if (left->fTop == right->fTop || left->fBottom == right->fBottom) {
        return BoolFail::kFalse;
    }

    // Check if the lines intersect as determined by isLeftOf and isRightOf, since that is the
    // source of ground truth. It may suggest an intersection even if Edge::intersect() did not have
    // the precision to check it. In this case we are explicitly correcting the edge topology to
    // match the sided-ness checks.
    Edge* split = nullptr;
    Vertex* splitAt = nullptr;
    if (c.sweep_lt(left->fTop->fPoint, right->fTop->fPoint)) {
        if (!left->isLeftOf(*right->fTop)) {
            split = left;
            splitAt = right->fTop;
        }
    } else {
        if (!right->isRightOf(*left->fTop)) {
            split = right;
            splitAt = left->fTop;
        }
    }
    if (c.sweep_lt(right->fBottom->fPoint, left->fBottom->fPoint)) {
        if (!left->isLeftOf(*right->fBottom)) {
            split = left;
            splitAt = right->fBottom;
        }
    } else {
        if (!right->isRightOf(*left->fBottom)) {
            split = right;
            splitAt = left->fBottom;
        }
    }

    if (!split) {
        return BoolFail::kFalse;
    }

    // Rewind to the top of the edge that is "moving" since this topology correction can change the
    // geometry of the split edge.
    if (!rewind(activeEdges, current, split->fTop, c)) {
        return BoolFail::kFail;
    }
    return this->splitEdge(split, splitAt, activeEdges, current, c);
}

Edge* GrTriangulator::makeConnectingEdge(Vertex* prev, Vertex* next, EdgeType type,
                                         const Comparator& c, int windingScale) {
    if (!prev || !next || prev->fPoint == next->fPoint) {
        return nullptr;
    }
    Edge* edge = this->makeEdge(prev, next, type, c);
    edge->insertBelow(edge->fTop, c);
    edge->insertAbove(edge->fBottom, c);
    edge->fWinding *= windingScale;
    this->mergeCollinearEdges(edge, nullptr, nullptr, c);
    return edge;
}

void GrTriangulator::mergeVertices(Vertex* src, Vertex* dst, VertexList* mesh,
                                   const Comparator& c) const {
    TESS_LOG("found coincident verts at %g, %g; merging %g into %g\n",
             src->fPoint.fX, src->fPoint.fY, src->fID, dst->fID);
    dst->fAlpha = std::max(src->fAlpha, dst->fAlpha);
    if (src->fPartner) {
        src->fPartner->fPartner = dst;
    }
    while (Edge* edge = src->fFirstEdgeAbove) {
        std::ignore = this->setBottom(edge, dst, nullptr, nullptr, c);
    }
    while (Edge* edge = src->fFirstEdgeBelow) {
        std::ignore = this->setTop(edge, dst, nullptr, nullptr, c);
    }
    mesh->remove(src);
    dst->fSynthetic = true;
}

Vertex* GrTriangulator::makeSortedVertex(const SkPoint& p, uint8_t alpha, VertexList* mesh,
                                         Vertex* reference, const Comparator& c) const {
    Vertex* prevV = reference;
    while (prevV && c.sweep_lt(p, prevV->fPoint)) {
        prevV = prevV->fPrev;
    }
    Vertex* nextV = prevV ? prevV->fNext : mesh->fHead;
    while (nextV && c.sweep_lt(nextV->fPoint, p)) {
        prevV = nextV;
        nextV = nextV->fNext;
    }
    Vertex* v;
    if (prevV && coincident(prevV->fPoint, p)) {
        v = prevV;
    } else if (nextV && coincident(nextV->fPoint, p)) {
        v = nextV;
    } else {
        v = fAlloc->make<Vertex>(p, alpha);
#if TRIANGULATOR_LOGGING
        if (!prevV) {
            v->fID = mesh->fHead->fID - 1.0f;
        } else if (!nextV) {
            v->fID = mesh->fTail->fID + 1.0f;
        } else {
            v->fID = (prevV->fID + nextV->fID) * 0.5f;
        }
#endif
        mesh->insert(v, prevV, nextV);
    }
    return v;
}

// Clamps x and y coordinates independently, so the returned point will lie within the bounding
// box formed by the corners of 'min' and 'max' (although min/max here refer to the ordering
// imposed by 'c').
static SkPoint clamp(SkPoint p, SkPoint min, SkPoint max, const Comparator& c) {
    if (c.fDirection == Comparator::Direction::kHorizontal) {
        // With horizontal sorting, we know min.x <= max.x, but there's no relation between
        // Y components unless min.x == max.x.
        return {SkTPin(p.fX, min.fX, max.fX),
                min.fY < max.fY ? SkTPin(p.fY, min.fY, max.fY)
                                : SkTPin(p.fY, max.fY, min.fY)};
    } else {
        // And with vertical sorting, we know Y's relation but not necessarily X's.
        return {min.fX < max.fX ? SkTPin(p.fX, min.fX, max.fX)
                                : SkTPin(p.fX, max.fX, min.fX),
                SkTPin(p.fY, min.fY, max.fY)};
    }
}

void GrTriangulator::computeBisector(Edge* edge1, Edge* edge2, Vertex* v) const {
    SkASSERT(fEmitCoverage);  // Edge-AA only!
    Line line1 = edge1->fLine;
    Line line2 = edge2->fLine;
    line1.normalize();
    line2.normalize();
    double cosAngle = line1.fA * line2.fA + line1.fB * line2.fB;
    if (cosAngle > 0.999) {
        return;
    }
    line1.fC += edge1->fWinding > 0 ? -1 : 1;
    line2.fC += edge2->fWinding > 0 ? -1 : 1;
    SkPoint p;
    if (line1.intersect(line2, &p)) {
        uint8_t alpha = edge1->fType == EdgeType::kOuter ? 255 : 0;
        v->fPartner = fAlloc->make<Vertex>(p, alpha);
        TESS_LOG("computed bisector (%g,%g) alpha %d for vertex %g\n", p.fX, p.fY, alpha, v->fID);
    }
}

GrTriangulator::BoolFail GrTriangulator::checkForIntersection(
        Edge* left, Edge* right, EdgeList* activeEdges,
        Vertex** current, VertexList* mesh,
        const Comparator& c) {
    if (!left || !right) {
        return BoolFail::kFalse;
    }
    SkPoint p;
    uint8_t alpha;
    // If we are going to call intersect, then there must be tops and bottoms.
    if (!left->fTop || !left->fBottom || !right->fTop || !right->fBottom) {
        return BoolFail::kFail;
    }
    if (left->intersect(*right, &p, &alpha) && p.isFinite()) {
        Vertex* v;
        TESS_LOG("found intersection, pt is %g, %g\n", p.fX, p.fY);
        Vertex* top = *current;
        // If the intersection point is above the current vertex, rewind to the vertex above the
        // intersection.
        while (top && c.sweep_lt(p, top->fPoint)) {
            top = top->fPrev;
        }

        // Always clamp the intersection to lie between the vertices of each segment, since
        // in theory that's where the intersection is, but in reality, floating point error may
        // have computed an intersection beyond a vertex's component(s).
        p = clamp(p, left->fTop->fPoint, left->fBottom->fPoint, c);
        p = clamp(p, right->fTop->fPoint, right->fBottom->fPoint, c);

        if (coincident(p, left->fTop->fPoint)) {
            v = left->fTop;
        } else if (coincident(p, left->fBottom->fPoint)) {
            v = left->fBottom;
        } else if (coincident(p, right->fTop->fPoint)) {
            v = right->fTop;
        } else if (coincident(p, right->fBottom->fPoint)) {
            v = right->fBottom;
        } else {
            v = this->makeSortedVertex(p, alpha, mesh, top, c);
            if (left->fTop->fPartner) {
                SkASSERT(fEmitCoverage);  // Edge-AA only!
                v->fSynthetic = true;
                this->computeBisector(left, right, v);
            }
        }
        if (!rewind(activeEdges, current, top ? top : v, c)) {
            return BoolFail::kFail;
        }
        if (this->splitEdge(left, v, activeEdges, current, c) == BoolFail::kFail) {
            return BoolFail::kFail;
        }
        if (this->splitEdge(right, v, activeEdges, current, c) == BoolFail::kFail) {
            return BoolFail::kFail;
        }
        v->fAlpha = std::max(v->fAlpha, alpha);
        return BoolFail::kTrue;
    }
    return this->intersectEdgePair(left, right, activeEdges, current, c);
}

void GrTriangulator::sanitizeContours(VertexList* contours, int contourCnt) const {
    for (VertexList* contour = contours; contourCnt > 0; --contourCnt, ++contour) {
        SkASSERT(contour->fHead);
        Vertex* prev = contour->fTail;
        prev->fPoint.fX = double_to_clamped_scalar((double) prev->fPoint.fX);
        prev->fPoint.fY = double_to_clamped_scalar((double) prev->fPoint.fY);
        if (fRoundVerticesToQuarterPixel) {
            round(&prev->fPoint);
        }
        for (Vertex* v = contour->fHead; v;) {
            v->fPoint.fX = double_to_clamped_scalar((double) v->fPoint.fX);
            v->fPoint.fY = double_to_clamped_scalar((double) v->fPoint.fY);
            if (fRoundVerticesToQuarterPixel) {
                round(&v->fPoint);
            }
            Vertex* next = v->fNext;
            Vertex* nextWrap = next ? next : contour->fHead;
            if (coincident(prev->fPoint, v->fPoint)) {
                TESS_LOG("vertex %g,%g coincident; removing\n", v->fPoint.fX, v->fPoint.fY);
                contour->remove(v);
            } else if (!v->fPoint.isFinite()) {
                TESS_LOG("vertex %g,%g non-finite; removing\n", v->fPoint.fX, v->fPoint.fY);
                contour->remove(v);
            } else if (!fPreserveCollinearVertices &&
                       Line(prev->fPoint, nextWrap->fPoint).dist(v->fPoint) == 0.0) {
                TESS_LOG("vertex %g,%g collinear; removing\n", v->fPoint.fX, v->fPoint.fY);
                contour->remove(v);
            } else {
                prev = v;
            }
            v = next;
        }
    }
}

bool GrTriangulator::mergeCoincidentVertices(VertexList* mesh, const Comparator& c) const {
    if (!mesh->fHead) {
        return false;
    }
    bool merged = false;
    for (Vertex* v = mesh->fHead->fNext; v;) {
        Vertex* next = v->fNext;
        if (c.sweep_lt(v->fPoint, v->fPrev->fPoint)) {
            v->fPoint = v->fPrev->fPoint;
        }
        if (coincident(v->fPrev->fPoint, v->fPoint)) {
            this->mergeVertices(v, v->fPrev, mesh, c);
            merged = true;
        }
        v = next;
    }
    return merged;
}

// Stage 2: convert the contours to a mesh of edges connecting the vertices.

void GrTriangulator::buildEdges(VertexList* contours, int contourCnt, VertexList* mesh,
                                const Comparator& c) {
    for (VertexList* contour = contours; contourCnt > 0; --contourCnt, ++contour) {
        Vertex* prev = contour->fTail;
        for (Vertex* v = contour->fHead; v;) {
            Vertex* next = v->fNext;
            this->makeConnectingEdge(prev, v, EdgeType::kInner, c);
            mesh->append(v);
            prev = v;
            v = next;
        }
    }
}

template <CompareFunc sweep_lt>
static void sorted_merge(VertexList* front, VertexList* back, VertexList* result) {
    Vertex* a = front->fHead;
    Vertex* b = back->fHead;
    while (a && b) {
        if (sweep_lt(a->fPoint, b->fPoint)) {
            front->remove(a);
            result->append(a);
            a = front->fHead;
        } else {
            back->remove(b);
            result->append(b);
            b = back->fHead;
        }
    }
    result->append(*front);
    result->append(*back);
}

void GrTriangulator::SortedMerge(VertexList* front, VertexList* back, VertexList* result,
                                 const Comparator& c) {
    if (c.fDirection == Comparator::Direction::kHorizontal) {
        sorted_merge<sweep_lt_horiz>(front, back, result);
    } else {
        sorted_merge<sweep_lt_vert>(front, back, result);
    }
#if TRIANGULATOR_LOGGING
    float id = 0.0f;
    for (Vertex* v = result->fHead; v; v = v->fNext) {
        v->fID = id++;
    }
#endif
}

// Stage 3: sort the vertices by increasing sweep direction.

template <CompareFunc sweep_lt>
static void merge_sort(VertexList* vertices) {
    Vertex* slow = vertices->fHead;
    if (!slow) {
        return;
    }
    Vertex* fast = slow->fNext;
    if (!fast) {
        return;
    }
    do {
        fast = fast->fNext;
        if (fast) {
            fast = fast->fNext;
            slow = slow->fNext;
        }
    } while (fast);
    VertexList front(vertices->fHead, slow);
    VertexList back(slow->fNext, vertices->fTail);
    front.fTail->fNext = back.fHead->fPrev = nullptr;

    merge_sort<sweep_lt>(&front);
    merge_sort<sweep_lt>(&back);

    vertices->fHead = vertices->fTail = nullptr;
    sorted_merge<sweep_lt>(&front, &back, vertices);
}

#if TRIANGULATOR_LOGGING
void VertexList::dump() const {
    for (Vertex* v = fHead; v; v = v->fNext) {
        TESS_LOG("vertex %g (%g, %g) alpha %d", v->fID, v->fPoint.fX, v->fPoint.fY, v->fAlpha);
        if (Vertex* p = v->fPartner) {
            TESS_LOG(", partner %g (%g, %g) alpha %d\n",
                    p->fID, p->fPoint.fX, p->fPoint.fY, p->fAlpha);
        } else {
            TESS_LOG(", null partner\n");
        }
        for (Edge* e = v->fFirstEdgeAbove; e; e = e->fNextEdgeAbove) {
            TESS_LOG("  edge %g -> %g, winding %d\n", e->fTop->fID, e->fBottom->fID, e->fWinding);
        }
        for (Edge* e = v->fFirstEdgeBelow; e; e = e->fNextEdgeBelow) {
            TESS_LOG("  edge %g -> %g, winding %d\n", e->fTop->fID, e->fBottom->fID, e->fWinding);
        }
    }
}
#endif

#ifdef SK_DEBUG
static void validate_edge_pair(Edge* left, Edge* right, const Comparator& c) {
    if (!left || !right) {
        return;
    }
    if (left->fTop == right->fTop) {
        SkASSERT(left->isLeftOf(*right->fBottom));
        SkASSERT(right->isRightOf(*left->fBottom));
    } else if (c.sweep_lt(left->fTop->fPoint, right->fTop->fPoint)) {
        SkASSERT(left->isLeftOf(*right->fTop));
    } else {
        SkASSERT(right->isRightOf(*left->fTop));
    }
    if (left->fBottom == right->fBottom) {
        SkASSERT(left->isLeftOf(*right->fTop));
        SkASSERT(right->isRightOf(*left->fTop));
    } else if (c.sweep_lt(right->fBottom->fPoint, left->fBottom->fPoint)) {
        SkASSERT(left->isLeftOf(*right->fBottom));
    } else {
        SkASSERT(right->isRightOf(*left->fBottom));
    }
}

static void validate_edge_list(EdgeList* edges, const Comparator& c) {
    Edge* left = edges->fHead;
    if (!left) {
        return;
    }
    for (Edge* right = left->fRight; right; right = right->fRight) {
        validate_edge_pair(left, right, c);
        left = right;
    }
}
#endif

// Stage 4: Simplify the mesh by inserting new vertices at intersecting edges.

GrTriangulator::SimplifyResult GrTriangulator::simplify(VertexList* mesh,
                                                        const Comparator& c) {
    TESS_LOG("simplifying complex polygons\n");

    int initialNumEdges = fNumEdges;
    int initialNumVertices = 0;
    for (Vertex* v = mesh->fHead; v != nullptr; v = v->fNext) {
        ++initialNumVertices;
    }
    int numSelfIntersections = 0;

    EdgeList activeEdges;
    auto result = SimplifyResult::kAlreadySimple;
    int numVisitedVertices = 0;
    for (Vertex* v = mesh->fHead; v != nullptr; v = v->fNext) {
        ++numVisitedVertices;
        if (!v->isConnected()) {
            continue;
        }

        // The max increase across all skps, svgs and gms with only the triangulating and SW path
        // renderers enabled and with the triangulator's maxVerbCount set to the Chrome value is
        // 17x.
        if (fNumEdges > 170*initialNumEdges) {
            return SimplifyResult::kFailed;
        }

        if (numVisitedVertices > 170*initialNumVertices) {
            return SimplifyResult::kFailed;
        }

        Edge* leftEnclosingEdge;
        Edge* rightEnclosingEdge;
        bool restartChecks;
        do {
            TESS_LOG("\nvertex %g: (%g,%g), alpha %d\n",
                     v->fID, v->fPoint.fX, v->fPoint.fY, v->fAlpha);
            restartChecks = false;
            FindEnclosingEdges(*v, activeEdges, &leftEnclosingEdge, &rightEnclosingEdge);
            v->fLeftEnclosingEdge = leftEnclosingEdge;
            v->fRightEnclosingEdge = rightEnclosingEdge;
            if (v->fFirstEdgeBelow) {
                for (Edge* edge = v->fFirstEdgeBelow; edge; edge = edge->fNextEdgeBelow) {
                    BoolFail l = this->checkForIntersection(
                            leftEnclosingEdge, edge, &activeEdges, &v, mesh, c);
                    if (l == BoolFail::kFail) {
                        return SimplifyResult::kFailed;
                    }
                    if (l == BoolFail::kFalse) {
                        BoolFail r = this->checkForIntersection(
                                edge, rightEnclosingEdge, &activeEdges, &v, mesh, c);
                        if (r == BoolFail::kFail) {
                            return SimplifyResult::kFailed;
                        }
                        if (r == BoolFail::kFalse) {
                            // Neither l and r are both false.
                            continue;
                        }
                    }

                    // Either l or r are true.
                    result = SimplifyResult::kFoundSelfIntersection;
                    restartChecks = true;
                    ++numSelfIntersections;
                    break;
                }  // for
            } else {
                BoolFail bf = this->checkForIntersection(
                        leftEnclosingEdge, rightEnclosingEdge, &activeEdges, &v, mesh, c);
                if (bf == BoolFail::kFail) {
                    return SimplifyResult::kFailed;
                }
                if (bf == BoolFail::kTrue) {
                    result = SimplifyResult::kFoundSelfIntersection;
                    restartChecks = true;
                    ++numSelfIntersections;
                }
            }

            // In pathological cases, a path can intersect itself millions of times. After 500,000
            // self-intersections are found, reject the path.
            if (numSelfIntersections > 500000) {
                return SimplifyResult::kFailed;
            }
        } while (restartChecks);
#ifdef SK_DEBUG
        validate_edge_list(&activeEdges, c);
#endif
        for (Edge* e = v->fFirstEdgeAbove; e; e = e->fNextEdgeAbove) {
            if (!activeEdges.remove(e)) {
                return SimplifyResult::kFailed;
            }
        }
        Edge* leftEdge = leftEnclosingEdge;
        for (Edge* e = v->fFirstEdgeBelow; e; e = e->fNextEdgeBelow) {
            activeEdges.insert(e, leftEdge);
            leftEdge = e;
        }
    }
    SkASSERT(!activeEdges.fHead && !activeEdges.fTail);
    return result;
}

// Stage 5: Tessellate the simplified mesh into monotone polygons.

std::tuple<Poly*, bool> GrTriangulator::tessellate(const VertexList& vertices, const Comparator&) {
    TESS_LOG("\ntessellating simple polygons\n");
    EdgeList activeEdges;
    Poly* polys = nullptr;
    for (Vertex* v = vertices.fHead; v != nullptr; v = v->fNext) {
        if (!v->isConnected()) {
            continue;
        }
#if TRIANGULATOR_LOGGING
        TESS_LOG("\nvertex %g: (%g,%g), alpha %d\n", v->fID, v->fPoint.fX, v->fPoint.fY, v->fAlpha);
#endif
        Edge* leftEnclosingEdge;
        Edge* rightEnclosingEdge;
        FindEnclosingEdges(*v, activeEdges, &leftEnclosingEdge, &rightEnclosingEdge);
        Poly* leftPoly;
        Poly* rightPoly;
        if (v->fFirstEdgeAbove) {
            leftPoly = v->fFirstEdgeAbove->fLeftPoly;
            rightPoly = v->fLastEdgeAbove->fRightPoly;
        } else {
            leftPoly = leftEnclosingEdge ? leftEnclosingEdge->fRightPoly : nullptr;
            rightPoly = rightEnclosingEdge ? rightEnclosingEdge->fLeftPoly : nullptr;
        }
#if TRIANGULATOR_LOGGING
        TESS_LOG("edges above:\n");
        for (Edge* e = v->fFirstEdgeAbove; e; e = e->fNextEdgeAbove) {
            TESS_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);
        }
        TESS_LOG("edges below:\n");
        for (Edge* e = v->fFirstEdgeBelow; e; e = e->fNextEdgeBelow) {
            TESS_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->addEdge(v->fFirstEdgeAbove, Side::kRight, this);
            }
            if (rightPoly) {
                rightPoly = rightPoly->addEdge(v->fLastEdgeAbove, Side::kLeft, this);
            }
            for (Edge* e = v->fFirstEdgeAbove; e != v->fLastEdgeAbove; e = e->fNextEdgeAbove) {
                Edge* rightEdge = e->fNextEdgeAbove;
                activeEdges.remove(e);
                if (e->fRightPoly) {
                    e->fRightPoly->addEdge(e, Side::kLeft, this);
                }
                if (rightEdge->fLeftPoly && rightEdge->fLeftPoly != e->fRightPoly) {
                    rightEdge->fLeftPoly->addEdge(e, Side::kRight, this);
                }
            }
            activeEdges.remove(v->fLastEdgeAbove);
            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 && rightPoly) {
                    if (leftPoly == rightPoly) {
                        if (leftPoly->fTail && leftPoly->fTail->fSide == Side::kLeft) {
                            leftPoly = this->makePoly(&polys, leftPoly->lastVertex(),
                                                      leftPoly->fWinding);
                            leftEnclosingEdge->fRightPoly = leftPoly;
                        } else {
                            rightPoly = this->makePoly(&polys, rightPoly->lastVertex(),
                                                       rightPoly->fWinding);
                            rightEnclosingEdge->fLeftPoly = rightPoly;
                        }
                    }
                    Edge* join = this->allocateEdge(leftPoly->lastVertex(), v, 1, EdgeType::kInner);
                    leftPoly = leftPoly->addEdge(join, Side::kRight, this);
                    rightPoly = rightPoly->addEdge(join, Side::kLeft, this);
                }
            }
            Edge* leftEdge = v->fFirstEdgeBelow;
            leftEdge->fLeftPoly = leftPoly;
            activeEdges.insert(leftEdge, leftEnclosingEdge);
            for (Edge* rightEdge = leftEdge->fNextEdgeBelow; rightEdge;
                 rightEdge = rightEdge->fNextEdgeBelow) {
                activeEdges.insert(rightEdge, leftEdge);
                int winding = leftEdge->fLeftPoly ? leftEdge->fLeftPoly->fWinding : 0;
                winding += leftEdge->fWinding;
                if (winding != 0) {
                    Poly* poly = this->makePoly(&polys, v, winding);
                    leftEdge->fRightPoly = rightEdge->fLeftPoly = poly;
                }
                leftEdge = rightEdge;
            }
            v->fLastEdgeBelow->fRightPoly = rightPoly;
        }
#if TRIANGULATOR_LOGGING
        TESS_LOG("\nactive edges:\n");
        for (Edge* e = activeEdges.fHead; e != nullptr; e = e->fRight) {
            TESS_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, true };
}

// This is a driver function that calls stages 2-5 in turn.

void GrTriangulator::contoursToMesh(VertexList* contours, int contourCnt, VertexList* mesh,
                                    const Comparator& c) {
#if TRIANGULATOR_LOGGING
    for (int i = 0; i < contourCnt; ++i) {
        Vertex* v = contours[i].fHead;
        SkASSERT(v);
        TESS_LOG("path.moveTo(%20.20g, %20.20g);\n", v->fPoint.fX, v->fPoint.fY);
        for (v = v->fNext; v; v = v->fNext) {
            TESS_LOG("path.lineTo(%20.20g, %20.20g);\n", v->fPoint.fX, v->fPoint.fY);
        }
    }
#endif
    this->sanitizeContours(contours, contourCnt);
    this->buildEdges(contours, contourCnt, mesh, c);
}

void GrTriangulator::SortMesh(VertexList* vertices, const Comparator& c) {
    if (!vertices || !vertices->fHead) {
        return;
    }

    // Sort vertices in Y (secondarily in X).
    if (c.fDirection == Comparator::Direction::kHorizontal) {
        merge_sort<sweep_lt_horiz>(vertices);
    } else {
        merge_sort<sweep_lt_vert>(vertices);
    }
#if TRIANGULATOR_LOGGING
    for (Vertex* v = vertices->fHead; v != nullptr; v = v->fNext) {
        static float gID = 0.0f;
        v->fID = gID++;
    }
#endif
}

std::tuple<Poly*, bool> GrTriangulator::contoursToPolys(VertexList* contours, int contourCnt) {
    const SkRect& pathBounds = fPath.getBounds();
    Comparator c(pathBounds.width() > pathBounds.height() ? Comparator::Direction::kHorizontal
                                                          : Comparator::Direction::kVertical);
    VertexList mesh;
    this->contoursToMesh(contours, contourCnt, &mesh, c);
    TESS_LOG("\ninitial mesh:\n");
    DUMP_MESH(mesh);
    SortMesh(&mesh, c);
    TESS_LOG("\nsorted mesh:\n");
    DUMP_MESH(mesh);
    this->mergeCoincidentVertices(&mesh, c);
    TESS_LOG("\nsorted+merged mesh:\n");
    DUMP_MESH(mesh);
    auto result = this->simplify(&mesh, c);
    if (result == SimplifyResult::kFailed) {
        return { nullptr, false };
    }
    TESS_LOG("\nsimplified mesh:\n");
    DUMP_MESH(mesh);
    return this->tessellate(mesh, c);
}

// Stage 6: Triangulate the monotone polygons into a vertex buffer.
skgpu::VertexWriter GrTriangulator::polysToTriangles(Poly* polys,
                                                     SkPathFillType overrideFillType,
                                                     skgpu::VertexWriter data) const {
    for (Poly* poly = polys; poly; poly = poly->fNext) {
        if (apply_fill_type(overrideFillType, poly)) {
            data = this->emitPoly(poly, std::move(data));
        }
    }
    return data;
}

static int get_contour_count(const SkPath& path, SkScalar tolerance) {
    // We could theoretically be more aggressive about not counting empty contours, but we need to
    // actually match the exact number of contour linked lists the tessellator will create later on.
    int contourCnt = 1;
    bool hasPoints = false;

    SkPath::Iter iter(path, false);
    SkPath::Verb verb;
    SkPoint pts[4];
    bool first = true;
    while ((verb = iter.next(pts)) != SkPath::kDone_Verb) {
        switch (verb) {
            case SkPath::kMove_Verb:
                if (!first) {
                    ++contourCnt;
                }
                [[fallthrough]];
            case SkPath::kLine_Verb:
            case SkPath::kConic_Verb:
            case SkPath::kQuad_Verb:
            case SkPath::kCubic_Verb:
                hasPoints = true;
                break;
            default:
                break;
        }
        first = false;
    }
    if (!hasPoints) {
        return 0;
    }
    return contourCnt;
}

std::tuple<Poly*, bool> GrTriangulator::pathToPolys(float tolerance, const SkRect& clipBounds, bool* isLinear) {
    int contourCnt = get_contour_count(fPath, tolerance);
    if (contourCnt <= 0) {
        *isLinear = true;
        return { nullptr, true };
    }

    if (SkPathFillType_IsInverse(fPath.getFillType())) {
        contourCnt++;
    }
    std::unique_ptr<VertexList[]> contours(new VertexList[contourCnt]);

    this->pathToContours(tolerance, clipBounds, contours.get(), isLinear);
    return this->contoursToPolys(contours.get(), contourCnt);
}

int64_t GrTriangulator::CountPoints(Poly* polys, SkPathFillType overrideFillType) {
    int64_t count = 0;
    for (Poly* poly = polys; poly; poly = poly->fNext) {
        if (apply_fill_type(overrideFillType, poly) && poly->fCount >= 3) {
            count += (poly->fCount - 2) * (TRIANGULATOR_WIREFRAME ? 6 : 3);
        }
    }
    return count;
}

// Stage 6: Triangulate the monotone polygons into a vertex buffer.

int GrTriangulator::polysToTriangles(Poly* polys, GrEagerVertexAllocator* vertexAllocator) const {
    int64_t count64 = CountPoints(polys, fPath.getFillType());
    if (0 == count64 || count64 > SK_MaxS32) {
        return 0;
    }
    int count = count64;

    size_t vertexStride = sizeof(SkPoint);
    if (fEmitCoverage) {
        vertexStride += sizeof(float);
    }
    skgpu::VertexWriter verts = vertexAllocator->lockWriter(vertexStride, count);
    if (!verts) {
        SkDebugf("Could not allocate vertices\n");
        return 0;
    }

    TESS_LOG("emitting %d verts\n", count);

    skgpu::BufferWriter::Mark start = verts.mark();
    verts = this->polysToTriangles(polys, fPath.getFillType(), std::move(verts));

    int actualCount = static_cast<int>((verts.mark() - start) / vertexStride);
    SkASSERT(actualCount <= count);
    vertexAllocator->unlock(actualCount);
    return actualCount;
}

#endif // SK_ENABLE_OPTIMIZE_SIZE