SkPathBuilder.cpp

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/*
 * 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/SkRRect.h"
#include "include/private/SkPathRef.h"
#include "include/private/base/SkFloatingPoint.h"
#include "include/private/base/SkSafe32.h"
#include "src/base/SkVx.h"
#include "src/core/SkGeometry.h"
#include "src/core/SkPathEnums.h"
#include "src/core/SkPathPriv.h"
 
#include <algorithm>
#include <cmath>
#include <cstdint>
#include <cstring>
#include <iterator>
#include <utility>
 
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::kWinding;
    fIsVolatile = false;
 
    // these are internal state
 
    fSegmentMask = 0;
    fLastMovePoint = {0, 0};
    fLastMoveIndex = -1;        // illegal
    fNeedsMoveVerb = true;
 
    return *this;
}
 
SkPathBuilder& SkPathBuilder::operator=(const SkPath& src) {
    this->reset().setFillType(src.getFillType());
 
    for (auto [verb, pts, w] : SkPathPriv::Iterate(src)) {
        switch (verb) {
            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], w[0]); break;
            case SkPathVerb::kCubic: this->cubicTo(pts[1], pts[2], pts[3]); break;
            case SkPathVerb::kClose: this->close(); break;
        }
    }
    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));
}
 
SkRect SkPathBuilder::computeBounds() const {
    SkRect bounds;
    bounds.setBounds(fPts.begin(), fPts.size());
    return bounds;
}
 
/*
 *  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((uint8_t)SkPathVerb::kMove);
 
    fLastMovePoint = pt;
    fNeedsMoveVerb = false;
    return *this;
}
 
SkPathBuilder& SkPathBuilder::lineTo(SkPoint pt) {
    this->ensureMove();
 
    fPts.push_back(pt);
    fVerbs.push_back((uint8_t)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((uint8_t)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((uint8_t)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((uint8_t)SkPathVerb::kCubic);
 
    fSegmentMask |= kCubic_SkPathSegmentMask;
    return *this;
}
 
SkPathBuilder& SkPathBuilder::close() {
    if (!fVerbs.empty()) {
        this->ensureMove();
 
        fVerbs.push_back((uint8_t)SkPathVerb::kClose);
 
        // fLastMovePoint stays where it is -- the previous moveTo
        fNeedsMoveVerb = true;
    }
    return *this;
}
 
///////////////////////////////////////////////////////////////////////////////////////////
 
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 {
    auto convexity = SkPathConvexity::kUnknown;
    SkPathFirstDirection dir = SkPathFirstDirection::kUnknown;
 
    switch (fIsA) {
        case kIsA_Oval:
            pr->setIsOval(fIsACCW, fIsAStart, /*isClosed=*/true);
            convexity = SkPathConvexity::kConvex;
            dir = fIsACCW ? SkPathFirstDirection::kCCW : SkPathFirstDirection::kCW;
            break;
        case kIsA_RRect:
            pr->setIsRRect(fIsACCW, fIsAStart);
            convexity = SkPathConvexity::kConvex;
            dir = fIsACCW ? SkPathFirstDirection::kCCW : SkPathFirstDirection::kCW;
            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, convexity, 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.
    const uint8_t* start = path.fPathRef->verbsBegin();
    const uint8_t* stop  = path.fPathRef->verbsEnd();
    if (start < stop) {
        SkASSERT(fLastMoveIndex >= 0);
        // peek at the last verb, to know if our last contour is closed
        const bool isClosed = (stop[-1] == (uint8_t)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) {
        matrix.mapXY(stop.x(), stop.y(), singlePt);
    }
    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::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();
 
    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.mapPoints(&transformedMidPoint, &midPointDistance, 1);
    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, (int) std::size(unitPts));
    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/9272)
    // 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, (int) std::size(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;
}
 
///////////////////////////////////////////////////////////////////////////////////////////
 
namespace {
    template <unsigned N> class PointIterator {
    public:
        PointIterator(SkPathDirection dir, unsigned startIndex)
            : fCurrent(startIndex % N)
            , fAdvance(dir == SkPathDirection::kCW ? 1 : N - 1)
        {}
 
        const SkPoint& current() const {
            SkASSERT(fCurrent < N);
            return fPts[fCurrent];
        }
 
        const SkPoint& next() {
            fCurrent = (fCurrent + fAdvance) % N;
            return this->current();
        }
 
    protected:
        SkPoint fPts[N];
 
    private:
        unsigned fCurrent;
        unsigned fAdvance;
    };
 
    class RectPointIterator : public PointIterator<4> {
    public:
        RectPointIterator(const SkRect& rect, SkPathDirection dir, unsigned startIndex)
        : PointIterator(dir, startIndex) {
 
            fPts[0] = SkPoint::Make(rect.fLeft, rect.fTop);
            fPts[1] = SkPoint::Make(rect.fRight, rect.fTop);
            fPts[2] = SkPoint::Make(rect.fRight, rect.fBottom);
            fPts[3] = SkPoint::Make(rect.fLeft, rect.fBottom);
        }
    };
 
    class OvalPointIterator : public PointIterator<4> {
    public:
        OvalPointIterator(const SkRect& oval, SkPathDirection dir, unsigned startIndex)
        : PointIterator(dir, startIndex) {
 
            const SkScalar cx = oval.centerX();
            const SkScalar cy = oval.centerY();
 
            fPts[0] = SkPoint::Make(cx, oval.fTop);
            fPts[1] = SkPoint::Make(oval.fRight, cy);
            fPts[2] = SkPoint::Make(cx, oval.fBottom);
            fPts[3] = SkPoint::Make(oval.fLeft, cy);
        }
    };
 
    class RRectPointIterator : public PointIterator<8> {
    public:
        RRectPointIterator(const SkRRect& rrect, SkPathDirection dir, unsigned startIndex)
            : PointIterator(dir, startIndex)
        {
            const SkRect& bounds = rrect.getBounds();
            const SkScalar L = bounds.fLeft;
            const SkScalar T = bounds.fTop;
            const SkScalar R = bounds.fRight;
            const SkScalar B = bounds.fBottom;
 
            fPts[0] = SkPoint::Make(L + rrect.radii(SkRRect::kUpperLeft_Corner).fX, T);
            fPts[1] = SkPoint::Make(R - rrect.radii(SkRRect::kUpperRight_Corner).fX, T);
            fPts[2] = SkPoint::Make(R, T + rrect.radii(SkRRect::kUpperRight_Corner).fY);
            fPts[3] = SkPoint::Make(R, B - rrect.radii(SkRRect::kLowerRight_Corner).fY);
            fPts[4] = SkPoint::Make(R - rrect.radii(SkRRect::kLowerRight_Corner).fX, B);
            fPts[5] = SkPoint::Make(L + rrect.radii(SkRRect::kLowerLeft_Corner).fX, B);
            fPts[6] = SkPoint::Make(L, B - rrect.radii(SkRRect::kLowerLeft_Corner).fY);
            fPts[7] = SkPoint::Make(L, T + rrect.radii(SkRRect::kUpperLeft_Corner).fY);
        }
    };
} // anonymous namespace
 
 
SkPathBuilder& SkPathBuilder::addRect(const SkRect& rect, SkPathDirection dir, unsigned index) {
    const int kPts   = 4;   // moveTo + 3 lines
    const int kVerbs = 5;   // moveTo + 3 lines + close
    this->incReserve(kPts, kVerbs);
 
    RectPointIterator iter(rect, dir, index);
 
    this->moveTo(iter.current());
    this->lineTo(iter.next());
    this->lineTo(iter.next());
    this->lineTo(iter.next());
    return this->close();
}
 
SkPathBuilder& SkPathBuilder::addOval(const SkRect& oval, SkPathDirection dir, unsigned index) {
    const IsA prevIsA = fIsA;
 
    const int kPts   = 9;   // moveTo + 4 conics(2 pts each)
    const int kVerbs = 6;   // moveTo + 4 conics + close
    this->incReserve(kPts, kVerbs);
 
    OvalPointIterator ovalIter(oval, dir, index);
    RectPointIterator rectIter(oval, dir, index + (dir == SkPathDirection::kCW ? 0 : 1));
 
    // The corner iterator pts are tracking "behind" the oval/radii pts.
 
    this->moveTo(ovalIter.current());
    for (unsigned i = 0; i < 4; ++i) {
        this->conicTo(rectIter.next(), ovalIter.next(), SK_ScalarRoot2Over2);
    }
    this->close();
 
    if (prevIsA == kIsA_JustMoves) {
        fIsA      = kIsA_Oval;
        fIsACCW   = (dir == SkPathDirection::kCCW);
        fIsAStart = index % 4;
    }
    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 {
        // we start with a conic on odd indices when moving CW vs. even indices when moving CCW
        const bool startsWithConic = ((index & 1) == (dir == SkPathDirection::kCW));
        const SkScalar weight = SK_ScalarRoot2Over2;
 
        const int kVerbs = startsWithConic
            ? 9   // moveTo + 4x conicTo + 3x lineTo + close
            : 10; // moveTo + 4x lineTo + 4x conicTo + close
        this->incReserve(kVerbs);
 
        RRectPointIterator rrectIter(rrect, dir, index);
        // Corner iterator indices follow the collapsed radii model,
        // adjusted such that the start pt is "behind" the radii start pt.
        const unsigned rectStartIndex = index / 2 + (dir == SkPathDirection::kCW ? 0 : 1);
        RectPointIterator rectIter(bounds, dir, rectStartIndex);
 
        this->moveTo(rrectIter.current());
        if (startsWithConic) {
            for (unsigned i = 0; i < 3; ++i) {
                this->conicTo(rectIter.next(), rrectIter.next(), weight);
                this->lineTo(rrectIter.next());
            }
            this->conicTo(rectIter.next(), rrectIter.next(), weight);
            // final lineTo handled by close().
        } else {
            for (unsigned i = 0; i < 4; ++i) {
                this->lineTo(rrectIter.next());
                this->conicTo(rectIter.next(), rrectIter.next(), weight);
            }
        }
        this->close();
    }
 
    if (prevIsA == kIsA_JustMoves) {
        fIsA      = kIsA_RRect;
        fIsACCW   = (dir == SkPathDirection::kCCW);
        fIsAStart = index % 8;
    }
    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(const SkPoint pts[], int count, bool isClosed) {
    if (count <= 0) {
        return *this;
    }
 
    this->moveTo(pts[0]);
    this->polylineTo(&pts[1], count - 1);
    if (isClosed) {
        this->close();
    }
    return *this;
}
 
SkPathBuilder& SkPathBuilder::polylineTo(const SkPoint pts[], int count) {
    if (count > 0) {
        this->ensureMove();
 
        this->incReserve(count, count);
        memcpy(fPts.push_back_n(count), pts, 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& src) {
    SkPath::RawIter iter(src);
    SkPoint pts[4];
    SkPath::Verb verb;
 
    while ((verb = iter.next(pts)) != SkPath::kDone_Verb) {
        switch (verb) {
            case SkPath::kMove_Verb:  this->moveTo (pts[0]); break;
            case SkPath::kLine_Verb:  this->lineTo (pts[1]); break;
            case SkPath::kQuad_Verb:  this->quadTo (pts[1], pts[2]); break;
            case SkPath::kCubic_Verb: this->cubicTo(pts[1], pts[2], pts[3]); break;
            case SkPath::kConic_Verb: this->conicTo(pts[1], pts[2], iter.conicWeight()); break;
            case SkPath::kClose_Verb: this->close(); break;
            case SkPath::kDone_Verb: SkUNREACHABLE;
        }
    }
 
    return *this;
}
 
SkPathBuilder& SkPathBuilder::privateReverseAddPath(const SkPath& src) {
 
    const uint8_t* verbsBegin = src.fPathRef->verbsBegin();
    const uint8_t* 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) {
        uint8_t 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;
            default:
                SkDEBUGFAIL("unexpected verb");
        }
    }
    return *this;
}