src/core/SkPathBuilder.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 "include/core/SkPathBuilder.h"

#include "include/core/SkMatrix.h"
#include "include/core/SkPath.h"
#include "include/core/SkPathTypes.h"
#include "include/core/SkRRect.h"
#include "include/core/SkTypes.h"
#include "include/private/SkPathRef.h"
#include "include/private/base/SkAssert.h" // IWYU pragma: keep
#include "include/private/base/SkFloatingPoint.h"
#include "include/private/base/SkSafe32.h"
#include "include/private/base/SkTArray.h"
#include "include/private/base/SkTo.h"
#include "src/base/SkVx.h"
#include "src/core/SkGeometry.h"
#include "src/core/SkMatrixPriv.h"
#include "src/core/SkPathEnums.h"
#include "src/core/SkPathPriv.h"
#include "src/core/SkPathRawShapes.h"

#include <algorithm>
#include <cmath>
#include <cstdint>
#include <cstring>
#include <utility>

namespace {

void subdivide_cubic_to(SkPathBuilder* path, const SkPoint pts[4], int level = 2) {
    if (--level >= 0) {
        SkPoint tmp[7];

        SkChopCubicAtHalf(pts, tmp);
        subdivide_cubic_to(path, &tmp[0], level);
        subdivide_cubic_to(path, &tmp[3], level);
    } else {
        path->cubicTo(pts[1], pts[2], pts[3]);
    }
}

}  // namespace

SkPathBuilder::SkPathBuilder() {
    this->reset();
}

SkPathBuilder::SkPathBuilder(SkPathFillType ft) {
    this->reset();
    fFillType = ft;
}

SkPathBuilder::SkPathBuilder(const SkPath& src) {
    *this = src;
}

SkPathBuilder::~SkPathBuilder() {
}

SkPathBuilder& SkPathBuilder::reset() {
    fPts.clear();
    fVerbs.clear();
    fConicWeights.clear();
    fFillType = SkPathFillType::kDefault;
    fIsVolatile = false;

    // these are internal state

    fSegmentMask = 0;
    fLastMovePoint = {0, 0};
    fLastMoveIndex = -1;        // illegal
    fNeedsMoveVerb = true;

    fIsA = kIsA_JustMoves;
    fConvexity = SkPathConvexity::kUnknown;

    return *this;
}

SkPathBuilder& SkPathBuilder::operator=(const SkPath& src) {
    this->reset().setFillType(src.getFillType());
    this->setIsVolatile(src.isVolatile());

    auto is_a = [](const sk_sp<SkPathRef>& p) -> IsA {
        if (p->fVerbs.empty()) {
            return IsA::kIsA_JustMoves;
        }
        switch (p->fType) {
            case SkPathRef::PathType::kGeneral: return IsA::kIsA_MoreThanMoves;
            case SkPathRef::PathType::kOval:    return IsA::kIsA_Oval;
            case SkPathRef::PathType::kRRect:   return IsA::kIsA_RRect;
            case SkPathRef::PathType::kArc:     return IsA::kIsA_MoreThanMoves;  // TODO: isArc
        }
        SkUNREACHABLE;
    };

    const sk_sp<SkPathRef>& ref = src.fPathRef;
    fVerbs        = ref->fVerbs;
    fPts          = ref->fPoints;
    fConicWeights = ref->fConicWeights;

    fSegmentMask   = ref->fSegmentMask;
    fLastMoveIndex = src.fLastMoveToIndex < 0 ? ~src.fLastMoveToIndex : src.fLastMoveToIndex;
    fLastMovePoint = fPts.empty() ? SkPoint{0, 0} : fPts[fLastMoveIndex];
    fNeedsMoveVerb = src.fLastMoveToIndex < 0;

    fIsA      = is_a(ref);
    fIsAStart = ref->fRRectOrOvalStartIdx;
    fIsACCW   = ref->fRRectOrOvalIsCCW;

    fConvexity = src.getConvexityOrUnknown();

    return *this;
}

void SkPathBuilder::incReserve(int extraPtCount, int extraVbCount) {
    fPts.reserve_exact(Sk32_sat_add(fPts.size(), extraPtCount));
    fVerbs.reserve_exact(Sk32_sat_add(fVerbs.size(), extraVbCount));
}

std::tuple<SkPoint*, SkScalar*> SkPathBuilder::growForVerbsInPath(const SkPathRef& path) {
    fSegmentMask |= path.fSegmentMask;

    if (int numVerbs = path.countVerbs()) {
         // TODO(borenet): If the current builder is empty or JustMoves, we can use the type of the
         // path. If the path is empty, we can keep the current type.
        fIsA = SkPathBuilder::IsA::kIsA_MoreThanMoves;
        memcpy(fVerbs.push_back_n(numVerbs), path.fVerbs.begin(), numVerbs * sizeof(fVerbs[0]));
    }

    SkPoint* pts = nullptr;
    if (int numPts = path.countPoints()) {
        pts = fPts.push_back_n(numPts);
    }

    SkScalar* weights = nullptr;
    if (int numConics = path.countWeights()) {
        weights = fConicWeights.push_back_n(numConics);
    }

    return {pts, weights};
}

SkRect SkPathBuilder::computeBounds() const {
    return SkRect::BoundsOrEmpty(fPts);
}

/*
 *  Some old behavior in SkPath -- should we keep it?
 *
 *  After each edit (i.e. adding a verb)
        this->setConvexityType(SkPathConvexity::kUnknown);
        this->setFirstDirection(SkPathPriv::kUnknown_FirstDirection);
 */

SkPathBuilder& SkPathBuilder::moveTo(SkPoint pt) {
    // only needed while SkPath is mutable
    fLastMoveIndex = SkToInt(fPts.size());

    fPts.push_back(pt);
    fVerbs.push_back(SkPathVerb::kMove);

    fLastMovePoint = pt;
    fNeedsMoveVerb = false;

    if (fIsA == kIsA_Oval || fIsA == kIsA_RRect) {
        fIsA = kIsA_MoreThanMoves;
    }
    fConvexity = SkPathConvexity::kUnknown;

    return *this;
}

SkPathBuilder& SkPathBuilder::lineTo(SkPoint pt) {
    this->ensureMove();

    fPts.push_back(pt);
    fVerbs.push_back(SkPathVerb::kLine);

    fSegmentMask |= kLine_SkPathSegmentMask;
    return *this;
}

SkPathBuilder& SkPathBuilder::quadTo(SkPoint pt1, SkPoint pt2) {
    this->ensureMove();

    SkPoint* p = fPts.push_back_n(2);
    p[0] = pt1;
    p[1] = pt2;
    fVerbs.push_back(SkPathVerb::kQuad);

    fSegmentMask |= kQuad_SkPathSegmentMask;
    return *this;
}

SkPathBuilder& SkPathBuilder::conicTo(SkPoint pt1, SkPoint pt2, SkScalar w) {
    this->ensureMove();

    SkPoint* p = fPts.push_back_n(2);
    p[0] = pt1;
    p[1] = pt2;
    fVerbs.push_back(SkPathVerb::kConic);
    fConicWeights.push_back(w);

    fSegmentMask |= kConic_SkPathSegmentMask;
    return *this;
}

SkPathBuilder& SkPathBuilder::cubicTo(SkPoint pt1, SkPoint pt2, SkPoint pt3) {
    this->ensureMove();

    SkPoint* p = fPts.push_back_n(3);
    p[0] = pt1;
    p[1] = pt2;
    p[2] = pt3;
    fVerbs.push_back(SkPathVerb::kCubic);

    fSegmentMask |= kCubic_SkPathSegmentMask;
    return *this;
}

SkPathBuilder& SkPathBuilder::close() {
    // If this is a 2nd 'close', we just ignore it
    if (!fVerbs.empty() && fVerbs.back() != SkPathVerb::kClose) {
        this->ensureMove();

        fVerbs.push_back(SkPathVerb::kClose);

        // fLastMovePoint stays where it is -- the previous moveTo
        fNeedsMoveVerb = true;
    }
    return *this;
}

///////////////////////////////////////////////////////////////////////////////////////////

SkPathBuilder& SkPathBuilder::rMoveTo(SkPoint pt) {
    SkPoint lastPt = {0,0};
    int count = fPts.size();
    if (count > 0) {
        if (!fNeedsMoveVerb) {
            lastPt = fPts[count - 1];
        } else {
            lastPt = fPts[fLastMoveIndex];
        }
    }
    return this->moveTo(lastPt.fX + pt.fX, lastPt.fY + pt.fY);
}

SkPathBuilder& SkPathBuilder::rLineTo(SkPoint p1) {
    this->ensureMove();
    return this->lineTo(fPts.back() + p1);
}

SkPathBuilder& SkPathBuilder::rQuadTo(SkPoint p1, SkPoint p2) {
    this->ensureMove();
    SkPoint base = fPts.back();
    return this->quadTo(base + p1, base + p2);
}

SkPathBuilder& SkPathBuilder::rConicTo(SkPoint p1, SkPoint p2, SkScalar w) {
    this->ensureMove();
    SkPoint base = fPts.back();
    return this->conicTo(base + p1, base + p2, w);
}

SkPathBuilder& SkPathBuilder::rCubicTo(SkPoint p1, SkPoint p2, SkPoint p3) {
    this->ensureMove();
    SkPoint base = fPts.back();
    return this->cubicTo(base + p1, base + p2, base + p3);
}

///////////////////////////////////////////////////////////////////////////////////////////

SkPath SkPathBuilder::make(sk_sp<SkPathRef> pr) const {
    SkPathFirstDirection dir = SkPathFirstDirection::kUnknown;

    switch (fIsA) {
        case kIsA_Oval:
            pr->setIsOval(fIsACCW, fIsAStart);
            dir = fIsACCW ? SkPathFirstDirection::kCCW : SkPathFirstDirection::kCW;
            SkASSERT(fConvexity == SkPathConvexity::kConvex);
            break;
        case kIsA_RRect:
            pr->setIsRRect(fIsACCW, fIsAStart);
            dir = fIsACCW ? SkPathFirstDirection::kCCW : SkPathFirstDirection::kCW;
            SkASSERT(fConvexity == SkPathConvexity::kConvex);
            break;
        default: break;
    }

    // Wonder if we can combine convexity and dir internally...
    //  unknown, convex_cw, convex_ccw, concave
    // Do we ever have direction w/o convexity, or viceversa (inside path)?
    //
    auto path = SkPath(std::move(pr), fFillType, fIsVolatile, fConvexity, dir);

    // This hopefully can go away in the future when Paths are immutable,
    // but if while they are still editable, we need to correctly set this.
    SkSpan<const SkPathVerb> verbs = path.fPathRef->verbs();
    if (!verbs.empty()) {
        SkASSERT(fLastMoveIndex >= 0);
        // peek at the last verb, to know if our last contour is closed
        const bool isClosed = (verbs.back() == SkPathVerb::kClose);
        path.fLastMoveToIndex = isClosed ? ~fLastMoveIndex : fLastMoveIndex;
    }

    return path;
}

SkPath SkPathBuilder::snapshot() const {
    return this->make(sk_sp<SkPathRef>(new SkPathRef(fPts,
                                                     fVerbs,
                                                     fConicWeights,
                                                     fSegmentMask)));
}

SkPath SkPathBuilder::detach() {
    auto path = this->make(sk_sp<SkPathRef>(new SkPathRef(std::move(fPts),
                                                          std::move(fVerbs),
                                                          std::move(fConicWeights),
                                                          fSegmentMask)));
    this->reset();
    return path;
}

///////////////////////////////////////////////////////////////////////////////////////////////////

static bool arc_is_lone_point(const SkRect& oval, SkScalar startAngle, SkScalar sweepAngle,
                              SkPoint* pt) {
    if (0 == sweepAngle && (0 == startAngle || SkIntToScalar(360) == startAngle)) {
        // Chrome uses this path to move into and out of ovals. If not
        // treated as a special case the moves can distort the oval's
        // bounding box (and break the circle special case).
        pt->set(oval.fRight, oval.centerY());
        return true;
    } else if (0 == oval.width() && 0 == oval.height()) {
        // Chrome will sometimes create 0 radius round rects. Having degenerate
        // quad segments in the path prevents the path from being recognized as
        // a rect.
        // TODO: optimizing the case where only one of width or height is zero
        // should also be considered. This case, however, doesn't seem to be
        // as common as the single point case.
        pt->set(oval.fRight, oval.fTop);
        return true;
    }
    return false;
}

// Return the unit vectors pointing at the start/stop points for the given start/sweep angles
//
static void angles_to_unit_vectors(SkScalar startAngle, SkScalar sweepAngle,
                                   SkVector* startV, SkVector* stopV, SkRotationDirection* dir) {
    SkScalar startRad = SkDegreesToRadians(startAngle),
             stopRad  = SkDegreesToRadians(startAngle + sweepAngle);

    startV->fY = SkScalarSinSnapToZero(startRad);
    startV->fX = SkScalarCosSnapToZero(startRad);
    stopV->fY = SkScalarSinSnapToZero(stopRad);
    stopV->fX = SkScalarCosSnapToZero(stopRad);

    /*  If the sweep angle is nearly (but less than) 360, then due to precision
     loss in radians-conversion and/or sin/cos, we may end up with coincident
     vectors, which will fool SkBuildQuadArc into doing nothing (bad) instead
     of drawing a nearly complete circle (good).
     e.g. canvas.drawArc(0, 359.99, ...)
     -vs- canvas.drawArc(0, 359.9, ...)
     We try to detect this edge case, and tweak the stop vector
     */
    if (*startV == *stopV) {
        SkScalar sw = SkScalarAbs(sweepAngle);
        if (sw < SkIntToScalar(360) && sw > SkIntToScalar(359)) {
            // make a guess at a tiny angle (in radians) to tweak by
            SkScalar deltaRad = SkScalarCopySign(SK_Scalar1/512, sweepAngle);
            // not sure how much will be enough, so we use a loop
            do {
                stopRad -= deltaRad;
                stopV->fY = SkScalarSinSnapToZero(stopRad);
                stopV->fX = SkScalarCosSnapToZero(stopRad);
            } while (*startV == *stopV);
        }
    }
    *dir = sweepAngle > 0 ? kCW_SkRotationDirection : kCCW_SkRotationDirection;
}

/**
 *  If this returns 0, then the caller should just line-to the singlePt, else it should
 *  ignore singlePt and append the specified number of conics.
 */
static int build_arc_conics(const SkRect& oval, const SkVector& start, const SkVector& stop,
                            SkRotationDirection dir, SkConic conics[SkConic::kMaxConicsForArc],
                            SkPoint* singlePt) {
    SkMatrix    matrix;

    matrix.setScale(SkScalarHalf(oval.width()), SkScalarHalf(oval.height()));
    matrix.postTranslate(oval.centerX(), oval.centerY());

    int count = SkConic::BuildUnitArc(start, stop, dir, &matrix, conics);
    if (0 == count) {
        *singlePt = matrix.mapPoint(stop);
    }
    return count;
}

static bool nearly_equal(const SkPoint& a, const SkPoint& b) {
    return SkScalarNearlyEqual(a.fX, b.fX)
        && SkScalarNearlyEqual(a.fY, b.fY);
}

SkPathBuilder& SkPathBuilder::arcTo(const SkRect& oval, SkScalar startAngle, SkScalar sweepAngle,
                                    bool forceMoveTo) {
    if (oval.width() < 0 || oval.height() < 0) {
        return *this;
    }

    if (fVerbs.empty()) {
        forceMoveTo = true;
    }

    SkPoint lonePt;
    if (arc_is_lone_point(oval, startAngle, sweepAngle, &lonePt)) {
        return forceMoveTo ? this->moveTo(lonePt) : this->lineTo(lonePt);
    }

    SkVector startV, stopV;
    SkRotationDirection dir;
    angles_to_unit_vectors(startAngle, sweepAngle, &startV, &stopV, &dir);

    SkPoint singlePt;

    // Adds a move-to to 'pt' if forceMoveTo is true. Otherwise a lineTo unless we're sufficiently
    // close to 'pt' currently. This prevents spurious lineTos when adding a series of contiguous
    // arcs from the same oval.
    auto addPt = [forceMoveTo, this](const SkPoint& pt) {
        if (forceMoveTo) {
            this->moveTo(pt);
        } else if (!nearly_equal(fPts.back(), pt)) {
            this->lineTo(pt);
        }
    };

    // At this point, we know that the arc is not a lone point, but startV == stopV
    // indicates that the sweepAngle is too small such that angles_to_unit_vectors
    // cannot handle it.
    if (startV == stopV) {
        SkScalar endAngle = SkDegreesToRadians(startAngle + sweepAngle);
        SkScalar radiusX = oval.width() / 2;
        SkScalar radiusY = oval.height() / 2;
        // We do not use SkScalar[Sin|Cos]SnapToZero here. When sin(startAngle) is 0 and sweepAngle
        // is very small and radius is huge, the expected behavior here is to draw a line. But
        // calling SkScalarSinSnapToZero will make sin(endAngle) be 0 which will then draw a dot.
        singlePt.set(oval.centerX() + radiusX * SkScalarCos(endAngle),
                     oval.centerY() + radiusY * SkScalarSin(endAngle));
        addPt(singlePt);
        return *this;
    }

    SkConic conics[SkConic::kMaxConicsForArc];
    int count = build_arc_conics(oval, startV, stopV, dir, conics, &singlePt);
    if (count) {
        this->incReserve(count * 2 + 1);
        const SkPoint& pt = conics[0].fPts[0];
        addPt(pt);
        for (int i = 0; i < count; ++i) {
            this->conicTo(conics[i].fPts[1], conics[i].fPts[2], conics[i].fW);
        }
    } else {
        addPt(singlePt);
    }
    return *this;
}

SkPathBuilder& SkPathBuilder::rArcTo(SkScalar rx, SkScalar ry, SkScalar xAxisRotate,
                                     SkPathBuilder::ArcSize largeArc,
                                     SkPathDirection sweep, SkScalar dx, SkScalar dy) {
    const SkPoint currentPoint = this->getLastPt().value_or(SkPoint{0, 0});
    return this->arcTo({rx, ry}, xAxisRotate, largeArc, sweep,
                       {currentPoint.fX + dx, currentPoint.fY + dy});
}

SkPathBuilder& SkPathBuilder::addArc(const SkRect& oval, SkScalar startAngle, SkScalar sweepAngle) {
    if (oval.isEmpty() || 0 == sweepAngle) {
        return *this;
    }

    const SkScalar kFullCircleAngle = SkIntToScalar(360);

    if (sweepAngle >= kFullCircleAngle || sweepAngle <= -kFullCircleAngle) {
        // We can treat the arc as an oval if it begins at one of our legal starting positions.
        // See SkPath::addOval() docs.
        SkScalar startOver90 = startAngle / 90.f;
        SkScalar startOver90I = SkScalarRoundToScalar(startOver90);
        SkScalar error = startOver90 - startOver90I;
        if (SkScalarNearlyEqual(error, 0)) {
            // Index 1 is at startAngle == 0.
            SkScalar startIndex = std::fmod(startOver90I + 1.f, 4.f);
            startIndex = startIndex < 0 ? startIndex + 4.f : startIndex;
            return this->addOval(oval, sweepAngle > 0 ? SkPathDirection::kCW : SkPathDirection::kCCW,
                                 (unsigned) startIndex);
        }
    }
    return this->arcTo(oval, startAngle, sweepAngle, true);
}

SkPathBuilder& SkPathBuilder::arcTo(SkPoint p1, SkPoint p2, SkScalar radius) {
    this->ensureMove();

    if (radius == 0) {
        return this->lineTo(p1);
    }

    // need to know our prev pt so we can construct tangent vectors
    SkPoint start = fPts.back();

    // need double precision for these calcs.
    skvx::double2 befored = normalize(skvx::double2{p1.fX - start.fX, p1.fY - start.fY});
    skvx::double2 afterd = normalize(skvx::double2{p2.fX - p1.fX, p2.fY - p1.fY});
    double cosh = dot(befored, afterd);
    double sinh = cross(befored, afterd);

    // If the previous point equals the first point, befored will be denormalized.
    // If the two points equal, afterd will be denormalized.
    // If the second point equals the first point, sinh will be zero.
    // In all these cases, we cannot construct an arc, so we construct a line to the first point.
    if (!isfinite(befored) || !isfinite(afterd) || SkScalarNearlyZero(SkDoubleToScalar(sinh))) {
        return this->lineTo(p1);
    }

    // safe to convert back to floats now
    SkScalar dist = SkScalarAbs(SkDoubleToScalar(radius * (1 - cosh) / sinh));
    SkScalar xx = p1.fX - dist * befored[0];
    SkScalar yy = p1.fY - dist * befored[1];

    SkVector after = SkVector::Make(afterd[0], afterd[1]);
    after.setLength(dist);
    this->lineTo(xx, yy);
    SkScalar weight = SkScalarSqrt(SkDoubleToScalar(SK_ScalarHalf + cosh * 0.5));
    return this->conicTo(p1, p1 + after, weight);
}

// This converts the SVG arc to conics.
// Partly adapted from Niko's code in kdelibs/kdecore/svgicons.
// Then transcribed from webkit/chrome's SVGPathNormalizer::decomposeArcToCubic()
// See also SVG implementation notes:
// http://www.w3.org/TR/SVG/implnote.html#ArcConversionEndpointToCenter
// Note that arcSweep bool value is flipped from the original implementation.
SkPathBuilder& SkPathBuilder::arcTo(SkPoint rad, SkScalar angle, SkPathBuilder::ArcSize arcLarge,
                                    SkPathDirection arcSweep, SkPoint endPt) {
    this->ensureMove();

    const SkPoint srcPts[2] = { fPts.back(), endPt };

    // If rx = 0 or ry = 0 then this arc is treated as a straight line segment (a "lineto")
    // joining the endpoints.
    // http://www.w3.org/TR/SVG/implnote.html#ArcOutOfRangeParameters
    if (!rad.fX || !rad.fY) {
        return this->lineTo(endPt);
    }
    // If the current point and target point for the arc are identical, it should be treated as a
    // zero length path. This ensures continuity in animations.
    if (srcPts[0] == srcPts[1]) {
        return this->lineTo(endPt);
    }
    SkScalar rx = SkScalarAbs(rad.fX);
    SkScalar ry = SkScalarAbs(rad.fY);
    SkVector midPointDistance = srcPts[0] - srcPts[1];
    midPointDistance *= 0.5f;

    SkMatrix pointTransform;
    pointTransform.setRotate(-angle);

    SkPoint transformedMidPoint = pointTransform.mapPoint(midPointDistance);
    SkScalar squareRx = rx * rx;
    SkScalar squareRy = ry * ry;
    SkScalar squareX = transformedMidPoint.fX * transformedMidPoint.fX;
    SkScalar squareY = transformedMidPoint.fY * transformedMidPoint.fY;

    // Check if the radii are big enough to draw the arc, scale radii if not.
    // http://www.w3.org/TR/SVG/implnote.html#ArcCorrectionOutOfRangeRadii
    SkScalar radiiScale = squareX / squareRx + squareY / squareRy;
    if (radiiScale > 1) {
        radiiScale = SkScalarSqrt(radiiScale);
        rx *= radiiScale;
        ry *= radiiScale;
    }

    pointTransform.setScale(1 / rx, 1 / ry);
    pointTransform.preRotate(-angle);

    SkPoint unitPts[2];
    pointTransform.mapPoints(unitPts, srcPts);
    SkVector delta = unitPts[1] - unitPts[0];

    SkScalar d = delta.fX * delta.fX + delta.fY * delta.fY;
    SkScalar scaleFactorSquared = std::max(1 / d - 0.25f, 0.f);

    SkScalar scaleFactor = SkScalarSqrt(scaleFactorSquared);
    if ((arcSweep == SkPathDirection::kCCW) != SkToBool(arcLarge)) {  // flipped from the original implementation
        scaleFactor = -scaleFactor;
    }
    delta.scale(scaleFactor);
    SkPoint centerPoint = unitPts[0] + unitPts[1];
    centerPoint *= 0.5f;
    centerPoint.offset(-delta.fY, delta.fX);
    unitPts[0] -= centerPoint;
    unitPts[1] -= centerPoint;
    SkScalar theta1 = SkScalarATan2(unitPts[0].fY, unitPts[0].fX);
    SkScalar theta2 = SkScalarATan2(unitPts[1].fY, unitPts[1].fX);
    SkScalar thetaArc = theta2 - theta1;
    if (thetaArc < 0 && (arcSweep == SkPathDirection::kCW)) {  // arcSweep flipped from the original implementation
        thetaArc += SK_ScalarPI * 2;
    } else if (thetaArc > 0 && (arcSweep != SkPathDirection::kCW)) {  // arcSweep flipped from the original implementation
        thetaArc -= SK_ScalarPI * 2;
    }

    // Very tiny angles cause our subsequent math to go wonky (skbug.com/40040578)
    // so we do a quick check here. The precise tolerance amount is just made up.
    // PI/million happens to fix the bug in 9272, but a larger value is probably
    // ok too.
    if (SkScalarAbs(thetaArc) < (SK_ScalarPI / (1000 * 1000))) {
        return this->lineTo(endPt);
    }

    pointTransform.setRotate(angle);
    pointTransform.preScale(rx, ry);

    // the arc may be slightly bigger than 1/4 circle, so allow up to 1/3rd
    int segments = SkScalarCeilToInt(SkScalarAbs(thetaArc / (2 * SK_ScalarPI / 3)));
    SkScalar thetaWidth = thetaArc / segments;
    SkScalar t = SkScalarTan(0.5f * thetaWidth);
    if (!SkIsFinite(t)) {
        return *this;
    }
    SkScalar startTheta = theta1;
    SkScalar w = SkScalarSqrt(SK_ScalarHalf + SkScalarCos(thetaWidth) * SK_ScalarHalf);
    auto scalar_is_integer = [](SkScalar scalar) -> bool {
        return scalar == SkScalarFloorToScalar(scalar);
    };
    bool expectIntegers = SkScalarNearlyZero(SK_ScalarPI/2 - SkScalarAbs(thetaWidth)) &&
        scalar_is_integer(rx) && scalar_is_integer(ry) &&
        scalar_is_integer(endPt.fX) && scalar_is_integer(endPt.fY);

    for (int i = 0; i < segments; ++i) {
        SkScalar endTheta    = startTheta + thetaWidth,
                 sinEndTheta = SkScalarSinSnapToZero(endTheta),
                 cosEndTheta = SkScalarCosSnapToZero(endTheta);

        unitPts[1].set(cosEndTheta, sinEndTheta);
        unitPts[1] += centerPoint;
        unitPts[0] = unitPts[1];
        unitPts[0].offset(t * sinEndTheta, -t * cosEndTheta);
        SkPoint mapped[2];
        pointTransform.mapPoints(mapped, unitPts);
        /*
        Computing the arc width introduces rounding errors that cause arcs to start
        outside their marks. A round rect may lose convexity as a result. If the input
        values are on integers, place the conic on integers as well.
         */
        if (expectIntegers) {
            for (SkPoint& point : mapped) {
                point.fX = SkScalarRoundToScalar(point.fX);
                point.fY = SkScalarRoundToScalar(point.fY);
            }
        }
        this->conicTo(mapped[0], mapped[1], w);
        startTheta = endTheta;
    }

    // The final point should match the input point (by definition); replace it to
    // ensure that rounding errors in the above math don't cause any problems.
    fPts.back() = endPt;
    return *this;
}

///////////////////////////////////////////////////////////////////////////////////////////

SkPathBuilder& SkPathBuilder::addRaw(const SkPathRaw& raw) {
    this->incReserve(raw.points().size(), raw.verbs().size());

    for (auto iter = raw.iter(); auto rec = iter.next();) {
        const auto pts = rec->pts;
        switch (rec->vrb) {
            case SkPathVerb::kMove:  this->moveTo( pts[0]); break;
            case SkPathVerb::kLine:  this->lineTo( pts[1]); break;
            case SkPathVerb::kQuad:  this->quadTo( pts[1], pts[2]); break;
            case SkPathVerb::kConic: this->conicTo(pts[1], pts[2], rec->w); break;
            case SkPathVerb::kCubic: this->cubicTo(pts[1], pts[2], pts[3]); break;
            case SkPathVerb::kClose: this->close(); break;
        }
    }
    return *this;
}

SkPathBuilder& SkPathBuilder::addRect(const SkRect& rect, SkPathDirection dir, unsigned index) {
    const IsA prevIsA = fIsA;

    this->addRaw(SkPathRawShapes::Rect(rect, dir, index));

    if (prevIsA == kIsA_JustMoves) {
        fConvexity = SkPathConvexity::kConvex;
    }
    return *this;
}

SkPathBuilder& SkPathBuilder::addOval(const SkRect& oval, SkPathDirection dir, unsigned index) {
    const IsA prevIsA = fIsA;

    this->addRaw(SkPathRawShapes::Oval(oval, dir, index));

    if (prevIsA == kIsA_JustMoves) {
        fIsA      = kIsA_Oval;
        fIsACCW   = (dir == SkPathDirection::kCCW);
        fIsAStart = index % 4;
        fConvexity = SkPathConvexity::kConvex;
    }

    return *this;
}

SkPathBuilder& SkPathBuilder::addRRect(const SkRRect& rrect, SkPathDirection dir, unsigned index) {
    const IsA prevIsA = fIsA;

    const SkRect& bounds = rrect.getBounds();

    if (rrect.isRect() || rrect.isEmpty()) {
        // degenerate(rect) => radii points are collapsing
        this->addRect(bounds, dir, (index + 1) / 2);
    } else if (rrect.isOval()) {
        // degenerate(oval) => line points are collapsing
        this->addOval(bounds, dir, index / 2);
    } else {
        this->addRaw(SkPathRawShapes::RRect(rrect, dir, index));
    }

    if (prevIsA == kIsA_JustMoves) {
        fIsA      = kIsA_RRect;
        fIsACCW   = (dir == SkPathDirection::kCCW);
        fIsAStart = index % 8;
        fConvexity = SkPathConvexity::kConvex;
    }
    return *this;
}

SkPathBuilder& SkPathBuilder::addCircle(SkScalar x, SkScalar y, SkScalar r, SkPathDirection dir) {
    if (r >= 0) {
        this->addOval(SkRect::MakeLTRB(x - r, y - r, x + r, y + r), dir);
    }
    return *this;
}

SkPathBuilder& SkPathBuilder::addPolygon(SkSpan<const SkPoint> pts, bool isClosed) {
    if (pts.empty()) {
        return *this;
    }

    this->moveTo(pts[0]);
    this->polylineTo(pts.last(pts.size() - 1));
    if (isClosed) {
        this->close();
    }
    return *this;
}

SkPathBuilder& SkPathBuilder::polylineTo(SkSpan<const SkPoint> pts) {
    if (!pts.empty()) {
        this->ensureMove();

        const auto count = pts.size();
        this->incReserve(count, count);
        memcpy(fPts.push_back_n(count), pts.data(), count * sizeof(SkPoint));
        memset(fVerbs.push_back_n(count), (uint8_t)SkPathVerb::kLine, count);
        fSegmentMask |= kLine_SkPathSegmentMask;
    }
    return *this;
}

//////////////////////////////////////////////////////////////////////////////////////////////////

SkPathBuilder& SkPathBuilder::offset(SkScalar dx, SkScalar dy) {
    for (auto& p : fPts) {
        p += {dx, dy};
    }
    return *this;
}

SkPathBuilder& SkPathBuilder::addPath(const SkPath& path, SkScalar dx, SkScalar dy,
                                      SkPath::AddPathMode mode) {
    SkMatrix matrix = SkMatrix::Translate(dx, dy);
    return this->addPath(path, matrix, mode);
}

SkPathBuilder& SkPathBuilder::addPath(const SkPath& src, const SkMatrix& matrix,
                                      SkPath::AddPathMode mode) {
    if (src.isEmpty()) {
        return *this;
    }

    if (this->isEmpty() && matrix.isIdentity()) {
        const SkPathFillType fillType = fFillType;
        *this = src;
        fFillType = fillType;
        return *this;
    }

    if (SkPath::AddPathMode::kAppend_AddPathMode == mode && !matrix.hasPerspective()) {
        if (src.fLastMoveToIndex >= 0) {
            fLastMoveIndex = src.fLastMoveToIndex + this->countPoints();
            fNeedsMoveVerb = false;
        } else {
            fLastMoveIndex = ~src.fLastMoveToIndex + this->countPoints();
            fNeedsMoveVerb = true;
        }

        auto [newPts, newWeights] = this->growForVerbsInPath(*src.fPathRef);
        const auto count = src.countPoints();
        matrix.mapPoints({newPts, count}, {src.fPathRef->points(), count});
        if (int numWeights = src.fPathRef->countWeights()) {
            memcpy(newWeights, src.fPathRef->conicWeights(), numWeights * sizeof(newWeights[0]));
        }
        fLastMovePoint = fPts.at(fLastMoveIndex);
        return *this;  // TODO(borenet): dirtyAfterEdit sets convexity and firstDirection.
    }

    SkMatrixPriv::MapPtsProc mapPtsProc = SkMatrixPriv::GetMapPtsProc(matrix);
    bool firstVerb = true;
    for (auto [verb, pts, w] : SkPathPriv::Iterate(src)) {
        SkPoint mappedPts[3];
        switch (verb) {
            case SkPathVerb::kMove:
                mapPtsProc(matrix, mappedPts, &pts[0], 1);
                if (firstVerb && mode == SkPath::kExtend_AddPathMode && !isEmpty()) {
                    this->ensureMove(); // In case last contour is closed
                    std::optional<SkPoint> lastPt = this->getLastPt();
                    // don't add lineTo if it is degenerate
                    if (!lastPt.has_value() || lastPt.value() != mappedPts[0]) {
                        this->lineTo(mappedPts[0]);
                    }
                } else {
                    this->moveTo(mappedPts[0]);
                }
                break;
            case SkPathVerb::kLine:
                mapPtsProc(matrix, mappedPts, &pts[1], 1);
                this->lineTo(mappedPts[0]);
                break;
            case SkPathVerb::kQuad:
                mapPtsProc(matrix, mappedPts, &pts[1], 2);
                this->quadTo(mappedPts[0], mappedPts[1]);
                break;
            case SkPathVerb::kConic:
                mapPtsProc(matrix, mappedPts, &pts[1], 2);
                this->conicTo(mappedPts[0], mappedPts[1], *w);
                break;
            case SkPathVerb::kCubic:
                mapPtsProc(matrix, mappedPts, &pts[1], 3);
                this->cubicTo(mappedPts[0], mappedPts[1], mappedPts[2]);
                break;
            case SkPathVerb::kClose:
                this->close();
                break;
        }
        firstVerb = false;
    }
    return *this;
}

// ignore the last point of the 1st contour
SkPathBuilder& SkPathBuilder::privateReversePathTo(const SkPath& path) {
    if (path.fPathRef->fVerbs.empty()) {
        return *this;
    }

    const SkPathVerb* verbs = path.fPathRef->verbsEnd();
    const SkPathVerb* verbsBegin = path.fPathRef->verbsBegin();
    const SkPoint*  pts = path.fPathRef->pointsEnd() - 1;
    const SkScalar* conicWeights = path.fPathRef->conicWeightsEnd();

    while (verbs > verbsBegin) {
        SkPathVerb v = *--verbs;
        pts -= SkPathPriv::PtsInVerb(v);
        switch (v) {
            case SkPathVerb::kMove:
                // if the path has multiple contours, stop after reversing the last
                return *this;
            case SkPathVerb::kLine:
                this->lineTo(pts[0]);
                break;
            case SkPathVerb::kQuad:
                this->quadTo(pts[1], pts[0]);
                break;
            case SkPathVerb::kConic:
                this->conicTo(pts[1], pts[0], *--conicWeights);
                break;
            case SkPathVerb::kCubic:
                this->cubicTo(pts[2], pts[1], pts[0]);
                break;
            case SkPathVerb::kClose:
                break;
        }
    }
    return *this;
}

SkPathBuilder& SkPathBuilder::privateReverseAddPath(const SkPath& src) {
    const SkPathVerb* verbsBegin = src.fPathRef->verbsBegin();
    const SkPathVerb* verbs = src.fPathRef->verbsEnd();
    const SkPoint* pts = src.fPathRef->pointsEnd();
    const SkScalar* conicWeights = src.fPathRef->conicWeightsEnd();

    bool needMove = true;
    bool needClose = false;
    while (verbs > verbsBegin) {
        SkPathVerb v = *--verbs;
        int n = SkPathPriv::PtsInVerb(v);

        if (needMove) {
            --pts;
            this->moveTo(pts->fX, pts->fY);
            needMove = false;
        }
        pts -= n;
        switch ((SkPathVerb)v) {
            case SkPathVerb::kMove:
                if (needClose) {
                    this->close();
                    needClose = false;
                }
                needMove = true;
                pts += 1;   // so we see the point in "if (needMove)" above
                break;
            case SkPathVerb::kLine:
                this->lineTo(pts[0]);
                break;
            case SkPathVerb::kQuad:
                this->quadTo(pts[1], pts[0]);
                break;
            case SkPathVerb::kConic:
                this->conicTo(pts[1], pts[0], *--conicWeights);
                break;
            case SkPathVerb::kCubic:
                this->cubicTo(pts[2], pts[1], pts[0]);
                break;
            case SkPathVerb::kClose:
                needClose = true;
                break;
        }
    }
    return *this;
}

std::optional<SkPoint> SkPathBuilder::getLastPt() const {
    int count = this->fPts.size();
    if (count > 0) {
        return this->fPts.at(count - 1);
    }
    return std::nullopt;
};

void SkPathBuilder::setLastPt(SkScalar x, SkScalar y) {
    int count = fPts.size();
    if (count == 0) {
        this->moveTo(x, y);
    } else {
        fPts.at(count-1).set(x, y);
    }
}

SkPathBuilder& SkPathBuilder::transform(const SkMatrix& matrix, SkApplyPerspectiveClip pc) {
    if (matrix.isIdentity()) {
        return *this;
    }

    if (matrix.hasPerspective()) {
        SkPath src = this->detach();

        // Apply perspective clip if needed.
        if (pc == SkApplyPerspectiveClip::kYes) {
            SkPath clipped;
            if (SkPathPriv::PerspectiveClip(src, matrix, &clipped)) {
                src = std::move(clipped);
            }
        }

        // Convert to a format more amenable to perspective.
        *this = SkPathBuilder(fFillType);
        for (auto [verb, pts, wt] : SkPathPriv::Iterate(src)) {
            switch (verb) {
                case SkPathVerb::kMove:
                    this->moveTo(pts[0]);
                    break;
                case SkPathVerb::kLine:
                    this->lineTo(pts[1]);
                    break;
                case SkPathVerb::kQuad:
                    // promote the quad to a conic
                    this->conicTo(pts[1], pts[2],
                                  SkConic::TransformW(pts, SK_Scalar1, matrix));
                    break;
                case SkPathVerb::kConic:
                    this->conicTo(pts[1], pts[2],
                                  SkConic::TransformW(pts, wt[0], matrix));
                    break;
                case SkPathVerb::kCubic:
                    subdivide_cubic_to(this, pts);
                    break;
                case SkPathVerb::kClose:
                    this->close();
                    break;
            }
        }
    }

    matrix.mapPoints(fPts);

    const bool isScaleTrans = matrix.isScaleTranslate();

    // this logic is lifted from SkPath::transform()
    if (fConvexity == SkPathConvexity::kConvex &&
        (!isScaleTrans || !SkPathPriv::IsAxisAligned(this->points()))) {
        // Not safe to still assume we're convex...
        fConvexity = SkPathConvexity::kUnknown;
    }

    if (!isScaleTrans && (fIsA == kIsA_Oval || fIsA == kIsA_RRect)) {
        fIsA = kIsA_MoreThanMoves;
    }

    // TODO: handle bounds, and direction when added.

    return *this;
}

bool SkPathBuilder::isFinite() const {
    for (auto p : fPts) {
        if (!p.isFinite()) {
            return false;
        }
    }
    return true;
}

bool SkPathBuilder::isZeroLengthSincePoint(int startPtIndex) const {
    int count = fPts.size() - startPtIndex;
    if (count < 2) {
        return true;
    }
    const SkPoint* pts = fPts.begin() + startPtIndex;
    const SkPoint& first = *pts;
    for (int index = 1; index < count; ++index) {
        if (first != pts[index]) {
            return false;
        }
    }
    return true;
}