src/gpu/GrDistanceFieldGenFromVector.cpp

/*
 * Copyright 2017 ARM Ltd.
 *
 * Use of this source code is governed by a BSD-style license that can be
 * found in the LICENSE file.
 */

#include "src/core/SkDistanceFieldGen.h"
#include "src/gpu/GrDistanceFieldGenFromVector.h"

#include "include/core/SkMatrix.h"
#include "include/gpu/GrConfig.h"
#include "include/pathops/SkPathOps.h"
#include "src/core/SkAutoMalloc.h"
#include "src/core/SkGeometry.h"
#include "src/core/SkPointPriv.h"
#include "src/core/SkRectPriv.h"
#include "src/gpu/geometry/GrPathUtils.h"

#include "src/pathops/SkPathOpsPoint.h"

/**
 * If a scanline (a row of texel) cross from the kRight_SegSide
 * of a segment to the kLeft_SegSide, the winding score should
 * add 1.
 * And winding score should subtract 1 if the scanline cross
 * from kLeft_SegSide to kRight_SegSide.
 * Always return kNA_SegSide if the scanline does not cross over
 * the segment. Winding score should be zero in this case.
 * You can get the winding number for each texel of the scanline
 * by adding the winding score from left to right.
 * Assuming we always start from outside, so the winding number
 * should always start from zero.
 *      ________         ________
 *     |        |       |        |
 * ...R|L......L|R.....L|R......R|L..... <= Scanline & side of segment
 *     |+1      |-1     |-1      |+1     <= Winding score
 *   0 |   1    ^   0   ^  -1    |0      <= Winding number
 *     |________|       |________|
 *
 * .......NA................NA..........
 *         0                 0
 */
enum SegSide {
    kLeft_SegSide  = -1,
    kOn_SegSide    =  0,
    kRight_SegSide =  1,
    kNA_SegSide    =  2,
};

struct DFData {
    float fDistSq;            // distance squared to nearest (so far) edge
    int   fDeltaWindingScore; // +1 or -1 whenever a scanline cross over a segment
};

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

/*
 * Type definition for double precision DAffineMatrix
 */

// Matrix with double precision for affine transformation.
// We don't store row 3 because its always (0, 0, 1).
class DAffineMatrix {
public:
    double operator[](int index) const {
        SkASSERT((unsigned)index < 6);
        return fMat[index];
    }

    double& operator[](int index) {
        SkASSERT((unsigned)index < 6);
        return fMat[index];
    }

    void setAffine(double m11, double m12, double m13,
                   double m21, double m22, double m23) {
        fMat[0] = m11;
        fMat[1] = m12;
        fMat[2] = m13;
        fMat[3] = m21;
        fMat[4] = m22;
        fMat[5] = m23;
    }

    /** Set the matrix to identity
    */
    void reset() {
        fMat[0] = fMat[4] = 1.0;
        fMat[1] = fMat[3] =
        fMat[2] = fMat[5] = 0.0;
    }

    // alias for reset()
    void setIdentity() { this->reset(); }

    SkDPoint mapPoint(const SkPoint& src) const {
        SkDPoint pt = {src.fX, src.fY};
        return this->mapPoint(pt);
    }

    SkDPoint mapPoint(const SkDPoint& src) const {
        return { fMat[0] * src.fX + fMat[1] * src.fY + fMat[2],
                 fMat[3] * src.fX + fMat[4] * src.fY + fMat[5] };
    }
private:
    double fMat[6];
};

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

static const double kClose = (SK_Scalar1 / 16.0);
static const double kCloseSqd = kClose * kClose;
static const double kNearlyZero = (SK_Scalar1 / (1 << 18));
static const double kTangentTolerance = (SK_Scalar1 / (1 << 11));
static const float  kConicTolerance = 0.25f;

// returns true if a >= min(b,c) && a < max(b,c)
static inline bool between_closed_open(double a, double b, double c,
                                       double tolerance = 0.0,
                                       bool xformToleranceToX = false) {
    SkASSERT(tolerance >= 0.0);
    double tolB = tolerance;
    double tolC = tolerance;

    if (xformToleranceToX) {
        // Canonical space is y = x^2 and the derivative of x^2 is 2x.
        // So the slope of the tangent line at point (x, x^2) is 2x.
        //
        //                          /|
        //  sqrt(2x * 2x + 1 * 1)  / | 2x
        //                        /__|
        //                         1
        tolB = tolerance / sqrt(4.0 * b * b + 1.0);
        tolC = tolerance / sqrt(4.0 * c * c + 1.0);
    }
    return b < c ? (a >= b - tolB && a < c - tolC) :
                   (a >= c - tolC && a < b - tolB);
}

// returns true if a >= min(b,c) && a <= max(b,c)
static inline bool between_closed(double a, double b, double c,
                                  double tolerance = 0.0,
                                  bool xformToleranceToX = false) {
    SkASSERT(tolerance >= 0.0);
    double tolB = tolerance;
    double tolC = tolerance;

    if (xformToleranceToX) {
        tolB = tolerance / sqrt(4.0 * b * b + 1.0);
        tolC = tolerance / sqrt(4.0 * c * c + 1.0);
    }
    return b < c ? (a >= b - tolB && a <= c + tolC) :
                   (a >= c - tolC && a <= b + tolB);
}

static inline bool nearly_zero(double x, double tolerance = kNearlyZero) {
    SkASSERT(tolerance >= 0.0);
    return fabs(x) <= tolerance;
}

static inline bool nearly_equal(double x, double y,
                                double tolerance = kNearlyZero,
                                bool xformToleranceToX = false) {
    SkASSERT(tolerance >= 0.0);
    if (xformToleranceToX) {
        tolerance = tolerance / sqrt(4.0 * y * y + 1.0);
    }
    return fabs(x - y) <= tolerance;
}

static inline double sign_of(const double &val) {
    return std::copysign(1, val);
}

static bool is_colinear(const SkPoint pts[3]) {
    return nearly_zero((pts[1].fY - pts[0].fY) * (pts[1].fX - pts[2].fX) -
                       (pts[1].fY - pts[2].fY) * (pts[1].fX - pts[0].fX), kCloseSqd);
}

class PathSegment {
public:
    enum {
        // These enum values are assumed in member functions below.
        kLine = 0,
        kQuad = 1,
    } fType;

    // line uses 2 pts, quad uses 3 pts
    SkPoint fPts[3];

    SkDPoint  fP0T, fP2T;
    DAffineMatrix fXformMatrix;  // transforms the segment into canonical space
    double fScalingFactor;
    double fScalingFactorSqd;
    double fNearlyZeroScaled;
    double fTangentTolScaledSqd;
    SkRect  fBoundingBox;

    void init();

    int countPoints() {
        static_assert(0 == kLine && 1 == kQuad);
        return fType + 2;
    }

    const SkPoint& endPt() const {
        static_assert(0 == kLine && 1 == kQuad);
        return fPts[fType + 1];
    }
};

typedef SkTArray<PathSegment, true> PathSegmentArray;

void PathSegment::init() {
    const SkDPoint p0 = { fPts[0].fX, fPts[0].fY };
    const SkDPoint p2 = { this->endPt().fX, this->endPt().fY };
    const double p0x = p0.fX;
    const double p0y = p0.fY;
    const double p2x = p2.fX;
    const double p2y = p2.fY;

    fBoundingBox.set(fPts[0], this->endPt());

    if (fType == PathSegment::kLine) {
        fScalingFactorSqd = fScalingFactor = 1.0;
        double hypotenuse = p0.distance(p2);

        const double cosTheta = (p2x - p0x) / hypotenuse;
        const double sinTheta = (p2y - p0y) / hypotenuse;

        // rotates the segment to the x-axis, with p0 at the origin
        fXformMatrix.setAffine(
            cosTheta, sinTheta, -(cosTheta * p0x) - (sinTheta * p0y),
            -sinTheta, cosTheta, (sinTheta * p0x) - (cosTheta * p0y)
        );
    } else {
        SkASSERT(fType == PathSegment::kQuad);

        // Calculate bounding box
        const SkPoint _P1mP0 = fPts[1] - fPts[0];
        SkPoint t = _P1mP0 - fPts[2] + fPts[1];
        t.fX = _P1mP0.fX / t.fX;
        t.fY = _P1mP0.fY / t.fY;
        t.fX = SkTPin(t.fX, 0.0f, 1.0f);
        t.fY = SkTPin(t.fY, 0.0f, 1.0f);
        t.fX = _P1mP0.fX * t.fX;
        t.fY = _P1mP0.fY * t.fY;
        const SkPoint m = fPts[0] + t;
        SkRectPriv::GrowToInclude(&fBoundingBox, m);

        const double p1x = fPts[1].fX;
        const double p1y = fPts[1].fY;

        const double p0xSqd = p0x * p0x;
        const double p0ySqd = p0y * p0y;
        const double p2xSqd = p2x * p2x;
        const double p2ySqd = p2y * p2y;
        const double p1xSqd = p1x * p1x;
        const double p1ySqd = p1y * p1y;

        const double p01xProd = p0x * p1x;
        const double p02xProd = p0x * p2x;
        const double b12xProd = p1x * p2x;
        const double p01yProd = p0y * p1y;
        const double p02yProd = p0y * p2y;
        const double b12yProd = p1y * p2y;

        // calculate quadratic params
        const double sqrtA = p0y - (2.0 * p1y) + p2y;
        const double a = sqrtA * sqrtA;
        const double h = -1.0 * (p0y - (2.0 * p1y) + p2y) * (p0x - (2.0 * p1x) + p2x);
        const double sqrtB = p0x - (2.0 * p1x) + p2x;
        const double b = sqrtB * sqrtB;
        const double c = (p0xSqd * p2ySqd) - (4.0 * p01xProd * b12yProd)
                - (2.0 * p02xProd * p02yProd) + (4.0 * p02xProd * p1ySqd)
                + (4.0 * p1xSqd * p02yProd) - (4.0 * b12xProd * p01yProd)
                + (p2xSqd * p0ySqd);
        const double g = (p0x * p02yProd) - (2.0 * p0x * p1ySqd)
                + (2.0 * p0x * b12yProd) - (p0x * p2ySqd)
                + (2.0 * p1x * p01yProd) - (4.0 * p1x * p02yProd)
                + (2.0 * p1x * b12yProd) - (p2x * p0ySqd)
                + (2.0 * p2x * p01yProd) + (p2x * p02yProd)
                - (2.0 * p2x * p1ySqd);
        const double f = -((p0xSqd * p2y) - (2.0 * p01xProd * p1y)
                - (2.0 * p01xProd * p2y) - (p02xProd * p0y)
                + (4.0 * p02xProd * p1y) - (p02xProd * p2y)
                + (2.0 * p1xSqd * p0y) + (2.0 * p1xSqd * p2y)
                - (2.0 * b12xProd * p0y) - (2.0 * b12xProd * p1y)
                + (p2xSqd * p0y));

        const double cosTheta = sqrt(a / (a + b));
        const double sinTheta = -1.0 * sign_of((a + b) * h) * sqrt(b / (a + b));

        const double gDef = cosTheta * g - sinTheta * f;
        const double fDef = sinTheta * g + cosTheta * f;


        const double x0 = gDef / (a + b);
        const double y0 = (1.0 / (2.0 * fDef)) * (c - (gDef * gDef / (a + b)));


        const double lambda = -1.0 * ((a + b) / (2.0 * fDef));
        fScalingFactor = fabs(1.0 / lambda);
        fScalingFactorSqd = fScalingFactor * fScalingFactor;

        const double lambda_cosTheta = lambda * cosTheta;
        const double lambda_sinTheta = lambda * sinTheta;

        // transforms to lie on a canonical y = x^2 parabola
        fXformMatrix.setAffine(
            lambda_cosTheta, -lambda_sinTheta, lambda * x0,
            lambda_sinTheta, lambda_cosTheta, lambda * y0
        );
    }

    fNearlyZeroScaled = kNearlyZero / fScalingFactor;
    fTangentTolScaledSqd = kTangentTolerance * kTangentTolerance / fScalingFactorSqd;

    fP0T = fXformMatrix.mapPoint(p0);
    fP2T = fXformMatrix.mapPoint(p2);
}

static void init_distances(DFData* data, int size) {
    DFData* currData = data;

    for (int i = 0; i < size; ++i) {
        // init distance to "far away"
        currData->fDistSq = SK_DistanceFieldMagnitude * SK_DistanceFieldMagnitude;
        currData->fDeltaWindingScore = 0;
        ++currData;
    }
}

static inline void add_line(const SkPoint pts[2], PathSegmentArray* segments) {
    segments->push_back();
    segments->back().fType = PathSegment::kLine;
    segments->back().fPts[0] = pts[0];
    segments->back().fPts[1] = pts[1];

    segments->back().init();
}

static inline void add_quad(const SkPoint pts[3], PathSegmentArray* segments) {
    if (SkPointPriv::DistanceToSqd(pts[0], pts[1]) < kCloseSqd ||
        SkPointPriv::DistanceToSqd(pts[1], pts[2]) < kCloseSqd ||
        is_colinear(pts)) {
        if (pts[0] != pts[2]) {
            SkPoint line_pts[2];
            line_pts[0] = pts[0];
            line_pts[1] = pts[2];
            add_line(line_pts, segments);
        }
    } else {
        segments->push_back();
        segments->back().fType = PathSegment::kQuad;
        segments->back().fPts[0] = pts[0];
        segments->back().fPts[1] = pts[1];
        segments->back().fPts[2] = pts[2];

        segments->back().init();
    }
}

static inline void add_cubic(const SkPoint pts[4],
                             PathSegmentArray* segments) {
    SkSTArray<15, SkPoint, true> quads;
    GrPathUtils::convertCubicToQuads(pts, SK_Scalar1, &quads);
    int count = quads.count();
    for (int q = 0; q < count; q += 3) {
        add_quad(&quads[q], segments);
    }
}

static float calculate_nearest_point_for_quad(
                const PathSegment& segment,
                const SkDPoint &xFormPt) {
    static const float kThird = 0.33333333333f;
    static const float kTwentySeventh = 0.037037037f;

    const float a = 0.5f - (float)xFormPt.fY;
    const float b = -0.5f * (float)xFormPt.fX;

    const float a3 = a * a * a;
    const float b2 = b * b;

    const float c = (b2 * 0.25f) + (a3 * kTwentySeventh);

    if (c >= 0.f) {
        const float sqrtC = sqrt(c);
        const float result = (float)cbrt((-b * 0.5f) + sqrtC) + (float)cbrt((-b * 0.5f) - sqrtC);
        return result;
    } else {
        const float cosPhi = (float)sqrt((b2 * 0.25f) * (-27.f / a3)) * ((b > 0) ? -1.f : 1.f);
        const float phi = (float)acos(cosPhi);
        float result;
        if (xFormPt.fX > 0.f) {
            result = 2.f * (float)sqrt(-a * kThird) * (float)cos(phi * kThird);
            if (!between_closed(result, segment.fP0T.fX, segment.fP2T.fX)) {
                result = 2.f * (float)sqrt(-a * kThird) * (float)cos((phi * kThird) + (SK_ScalarPI * 2.f * kThird));
            }
        } else {
            result = 2.f * (float)sqrt(-a * kThird) * (float)cos((phi * kThird) + (SK_ScalarPI * 2.f * kThird));
            if (!between_closed(result, segment.fP0T.fX, segment.fP2T.fX)) {
                result = 2.f * (float)sqrt(-a * kThird) * (float)cos(phi * kThird);
            }
        }
        return result;
    }
}

// This structure contains some intermediate values shared by the same row.
// It is used to calculate segment side of a quadratic bezier.
struct RowData {
    // The intersection type of a scanline and y = x * x parabola in canonical space.
    enum IntersectionType {
        kNoIntersection,
        kVerticalLine,
        kTangentLine,
        kTwoPointsIntersect
    } fIntersectionType;

    // The direction of the quadratic segment/scanline in the canonical space.
    //  1: The quadratic segment/scanline going from negative x-axis to positive x-axis.
    //  0: The scanline is a vertical line in the canonical space.
    // -1: The quadratic segment/scanline going from positive x-axis to negative x-axis.
    int fQuadXDirection;
    int fScanlineXDirection;

    // The y-value(equal to x*x) of intersection point for the kVerticalLine intersection type.
    double fYAtIntersection;

    // The x-value for two intersection points.
    double fXAtIntersection1;
    double fXAtIntersection2;
};

void precomputation_for_row(RowData *rowData, const PathSegment& segment,
                            const SkPoint& pointLeft, const SkPoint& pointRight) {
    if (segment.fType != PathSegment::kQuad) {
        return;
    }

    const SkDPoint& xFormPtLeft = segment.fXformMatrix.mapPoint(pointLeft);
    const SkDPoint& xFormPtRight = segment.fXformMatrix.mapPoint(pointRight);

    rowData->fQuadXDirection = (int)sign_of(segment.fP2T.fX - segment.fP0T.fX);
    rowData->fScanlineXDirection = (int)sign_of(xFormPtRight.fX - xFormPtLeft.fX);

    const double x1 = xFormPtLeft.fX;
    const double y1 = xFormPtLeft.fY;
    const double x2 = xFormPtRight.fX;
    const double y2 = xFormPtRight.fY;

    if (nearly_equal(x1, x2, segment.fNearlyZeroScaled, true)) {
        rowData->fIntersectionType = RowData::kVerticalLine;
        rowData->fYAtIntersection = x1 * x1;
        rowData->fScanlineXDirection = 0;
        return;
    }

    // Line y = mx + b
    const double m = (y2 - y1) / (x2 - x1);
    const double b = -m * x1 + y1;

    const double m2 = m * m;
    const double c = m2 + 4.0 * b;

    const double tol = 4.0 * segment.fTangentTolScaledSqd / (m2 + 1.0);

    // Check if the scanline is the tangent line of the curve,
    // and the curve start or end at the same y-coordinate of the scanline
    if ((rowData->fScanlineXDirection == 1 &&
         (segment.fPts[0].fY == pointLeft.fY ||
         segment.fPts[2].fY == pointLeft.fY)) &&
         nearly_zero(c, tol)) {
        rowData->fIntersectionType = RowData::kTangentLine;
        rowData->fXAtIntersection1 = m / 2.0;
        rowData->fXAtIntersection2 = m / 2.0;
    } else if (c <= 0.0) {
        rowData->fIntersectionType = RowData::kNoIntersection;
        return;
    } else {
        rowData->fIntersectionType = RowData::kTwoPointsIntersect;
        const double d = sqrt(c);
        rowData->fXAtIntersection1 = (m + d) / 2.0;
        rowData->fXAtIntersection2 = (m - d) / 2.0;
    }
}

SegSide calculate_side_of_quad(
            const PathSegment& segment,
            const SkPoint& point,
            const SkDPoint& xFormPt,
            const RowData& rowData) {
    SegSide side = kNA_SegSide;

    if (RowData::kVerticalLine == rowData.fIntersectionType) {
        side = (SegSide)(int)(sign_of(xFormPt.fY - rowData.fYAtIntersection) * rowData.fQuadXDirection);
    }
    else if (RowData::kTwoPointsIntersect == rowData.fIntersectionType) {
        const double p1 = rowData.fXAtIntersection1;
        const double p2 = rowData.fXAtIntersection2;

        int signP1 = (int)sign_of(p1 - xFormPt.fX);
        bool includeP1 = true;
        bool includeP2 = true;

        if (rowData.fScanlineXDirection == 1) {
            if ((rowData.fQuadXDirection == -1 && segment.fPts[0].fY <= point.fY &&
                 nearly_equal(segment.fP0T.fX, p1, segment.fNearlyZeroScaled, true)) ||
                 (rowData.fQuadXDirection == 1 && segment.fPts[2].fY <= point.fY &&
                 nearly_equal(segment.fP2T.fX, p1, segment.fNearlyZeroScaled, true))) {
                includeP1 = false;
            }
            if ((rowData.fQuadXDirection == -1 && segment.fPts[2].fY <= point.fY &&
                 nearly_equal(segment.fP2T.fX, p2, segment.fNearlyZeroScaled, true)) ||
                 (rowData.fQuadXDirection == 1 && segment.fPts[0].fY <= point.fY &&
                 nearly_equal(segment.fP0T.fX, p2, segment.fNearlyZeroScaled, true))) {
                includeP2 = false;
            }
        }

        if (includeP1 && between_closed(p1, segment.fP0T.fX, segment.fP2T.fX,
                                        segment.fNearlyZeroScaled, true)) {
            side = (SegSide)(signP1 * rowData.fQuadXDirection);
        }
        if (includeP2 && between_closed(p2, segment.fP0T.fX, segment.fP2T.fX,
                                        segment.fNearlyZeroScaled, true)) {
            int signP2 = (int)sign_of(p2 - xFormPt.fX);
            if (side == kNA_SegSide || signP2 == 1) {
                side = (SegSide)(-signP2 * rowData.fQuadXDirection);
            }
        }
    } else if (RowData::kTangentLine == rowData.fIntersectionType) {
        // The scanline is the tangent line of current quadratic segment.

        const double p = rowData.fXAtIntersection1;
        int signP = (int)sign_of(p - xFormPt.fX);
        if (rowData.fScanlineXDirection == 1) {
            // The path start or end at the tangent point.
            if (segment.fPts[0].fY == point.fY) {
                side = (SegSide)(signP);
            } else if (segment.fPts[2].fY == point.fY) {
                side = (SegSide)(-signP);
            }
        }
    }

    return side;
}

static float distance_to_segment(const SkPoint& point,
                                 const PathSegment& segment,
                                 const RowData& rowData,
                                 SegSide* side) {
    SkASSERT(side);

    const SkDPoint xformPt = segment.fXformMatrix.mapPoint(point);

    if (segment.fType == PathSegment::kLine) {
        float result = SK_DistanceFieldPad * SK_DistanceFieldPad;

        if (between_closed(xformPt.fX, segment.fP0T.fX, segment.fP2T.fX)) {
            result = (float)(xformPt.fY * xformPt.fY);
        } else if (xformPt.fX < segment.fP0T.fX) {
            result = (float)(xformPt.fX * xformPt.fX + xformPt.fY * xformPt.fY);
        } else {
            result = (float)((xformPt.fX - segment.fP2T.fX) * (xformPt.fX - segment.fP2T.fX)
                     + xformPt.fY * xformPt.fY);
        }

        if (between_closed_open(point.fY, segment.fBoundingBox.fTop,
                                segment.fBoundingBox.fBottom)) {
            *side = (SegSide)(int)sign_of(xformPt.fY);
        } else {
            *side = kNA_SegSide;
        }
        return result;
    } else {
        SkASSERT(segment.fType == PathSegment::kQuad);

        const float nearestPoint = calculate_nearest_point_for_quad(segment, xformPt);

        float dist;

        if (between_closed(nearestPoint, segment.fP0T.fX, segment.fP2T.fX)) {
            SkDPoint x = { nearestPoint, nearestPoint * nearestPoint };
            dist = (float)xformPt.distanceSquared(x);
        } else {
            const float distToB0T = (float)xformPt.distanceSquared(segment.fP0T);
            const float distToB2T = (float)xformPt.distanceSquared(segment.fP2T);

            if (distToB0T < distToB2T) {
                dist = distToB0T;
            } else {
                dist = distToB2T;
            }
        }

        if (between_closed_open(point.fY, segment.fBoundingBox.fTop,
                                segment.fBoundingBox.fBottom)) {
            *side = calculate_side_of_quad(segment, point, xformPt, rowData);
        } else {
            *side = kNA_SegSide;
        }

        return (float)(dist * segment.fScalingFactorSqd);
    }
}

static void calculate_distance_field_data(PathSegmentArray* segments,
                                          DFData* dataPtr,
                                          int width, int height) {
    int count = segments->count();
    // for each segment
    for (int a = 0; a < count; ++a) {
        PathSegment& segment = (*segments)[a];
        const SkRect& segBB = segment.fBoundingBox;
        // get the bounding box, outset by distance field pad, and clip to total bounds
        const SkRect& paddedBB = segBB.makeOutset(SK_DistanceFieldPad, SK_DistanceFieldPad);
        int startColumn = (int)paddedBB.fLeft;
        int endColumn = SkScalarCeilToInt(paddedBB.fRight);

        int startRow = (int)paddedBB.fTop;
        int endRow = SkScalarCeilToInt(paddedBB.fBottom);

        SkASSERT((startColumn >= 0) && "StartColumn < 0!");
        SkASSERT((endColumn <= width) && "endColumn > width!");
        SkASSERT((startRow >= 0) && "StartRow < 0!");
        SkASSERT((endRow <= height) && "EndRow > height!");

        // Clip inside the distance field to avoid overflow
        startColumn = std::max(startColumn, 0);
        endColumn   = std::min(endColumn,   width);
        startRow    = std::max(startRow,    0);
        endRow      = std::min(endRow,      height);

        // for each row in the padded bounding box
        for (int row = startRow; row < endRow; ++row) {
            SegSide prevSide = kNA_SegSide;   // track side for winding count
            const float pY = row + 0.5f;      // offset by 1/2? why?
            RowData rowData;

            const SkPoint pointLeft = SkPoint::Make((SkScalar)startColumn, pY);
            const SkPoint pointRight = SkPoint::Make((SkScalar)endColumn, pY);

            // if this is a row inside the original segment bounding box
            if (between_closed_open(pY, segBB.fTop, segBB.fBottom)) {
                // compute intersections with the row
                precomputation_for_row(&rowData, segment, pointLeft, pointRight);
            }

            // adjust distances and windings in each column based on the row calculation
            for (int col = startColumn; col < endColumn; ++col) {
                int idx = (row * width) + col;

                const float pX = col + 0.5f;
                const SkPoint point = SkPoint::Make(pX, pY);

                const float distSq = dataPtr[idx].fDistSq;

                 // Optimization for not calculating some points.
                int dilation = distSq < 1.5f * 1.5f ? 1 :
                               distSq < 2.5f * 2.5f ? 2 :
                               distSq < 3.5f * 3.5f ? 3 : SK_DistanceFieldPad;
                if (dilation < SK_DistanceFieldPad &&
                    !segBB.roundOut().makeOutset(dilation, dilation).contains(col, row)) {
                    continue;
                }

                SegSide side = kNA_SegSide;
                int     deltaWindingScore = 0;
                float   currDistSq = distance_to_segment(point, segment, rowData, &side);
                if (prevSide == kLeft_SegSide && side == kRight_SegSide) {
                    deltaWindingScore = -1;
                } else if (prevSide == kRight_SegSide && side == kLeft_SegSide) {
                    deltaWindingScore = 1;
                }

                prevSide = side;

                if (currDistSq < distSq) {
                    dataPtr[idx].fDistSq = currDistSq;
                }

                dataPtr[idx].fDeltaWindingScore += deltaWindingScore;
            }
        }
    }
}

template <int distanceMagnitude>
static unsigned char pack_distance_field_val(float dist) {
    // The distance field is constructed as unsigned char values, so that the zero value is at 128,
    // Beside 128, we have 128 values in range [0, 128), but only 127 values in range (128, 255].
    // So we multiply distanceMagnitude by 127/128 at the latter range to avoid overflow.
    dist = SkTPin<float>(-dist, -distanceMagnitude, distanceMagnitude * 127.0f / 128.0f);

    // Scale into the positive range for unsigned distance.
    dist += distanceMagnitude;

    // Scale into unsigned char range.
    // Round to place negative and positive values as equally as possible around 128
    // (which represents zero).
    return (unsigned char)SkScalarRoundToInt(dist / (2 * distanceMagnitude) * 256.0f);
}

bool GrGenerateDistanceFieldFromPath(unsigned char* distanceField,
                                     const SkPath& path, const SkMatrix& drawMatrix,
                                     int width, int height, size_t rowBytes) {
    SkASSERT(distanceField);

    // transform to device space, then:
    // translate path to offset (SK_DistanceFieldPad, SK_DistanceFieldPad)
    SkMatrix dfMatrix(drawMatrix);
    dfMatrix.postTranslate(SK_DistanceFieldPad, SK_DistanceFieldPad);

#ifdef SK_DEBUG
    SkPath xformPath;
    path.transform(dfMatrix, &xformPath);
    SkIRect pathBounds = xformPath.getBounds().roundOut();
    SkIRect expectPathBounds = SkIRect::MakeWH(width, height);
#endif

    SkASSERT(expectPathBounds.isEmpty() ||
             expectPathBounds.contains(pathBounds.fLeft, pathBounds.fTop));
    SkASSERT(expectPathBounds.isEmpty() || pathBounds.isEmpty() ||
             expectPathBounds.contains(pathBounds));

// TODO: restore when Simplify() is working correctly
//       see https://bugs.chromium.org/p/skia/issues/detail?id=9732
//    SkPath simplifiedPath;
    SkPath workingPath;
//    if (Simplify(path, &simplifiedPath)) {
//        workingPath = simplifiedPath;
//    } else {
        workingPath = path;
//    }
    // only even-odd and inverse even-odd supported
    if (!IsDistanceFieldSupportedFillType(workingPath.getFillType())) {
        return false;
    }

    // transform to device space + SDF offset
    workingPath.transform(dfMatrix);

    SkDEBUGCODE(pathBounds = workingPath.getBounds().roundOut());
    SkASSERT(expectPathBounds.isEmpty() ||
             expectPathBounds.contains(pathBounds.fLeft, pathBounds.fTop));
    SkASSERT(expectPathBounds.isEmpty() || pathBounds.isEmpty() ||
             expectPathBounds.contains(pathBounds));

    // create temp data
    size_t dataSize = width * height * sizeof(DFData);
    SkAutoSMalloc<1024> dfStorage(dataSize);
    DFData* dataPtr = (DFData*) dfStorage.get();

    // create initial distance data (init to "far away")
    init_distances(dataPtr, width * height);

    // polygonize path into line and quad segments
    SkPathEdgeIter iter(workingPath);
    SkSTArray<15, PathSegment, true> segments;
    while (auto e = iter.next()) {
        switch (e.fEdge) {
            case SkPathEdgeIter::Edge::kLine: {
                add_line(e.fPts, &segments);
                break;
            }
            case SkPathEdgeIter::Edge::kQuad:
                add_quad(e.fPts, &segments);
                break;
            case SkPathEdgeIter::Edge::kConic: {
                SkScalar weight = iter.conicWeight();
                SkAutoConicToQuads converter;
                const SkPoint* quadPts = converter.computeQuads(e.fPts, weight, kConicTolerance);
                for (int i = 0; i < converter.countQuads(); ++i) {
                    add_quad(quadPts + 2*i, &segments);
                }
                break;
            }
            case SkPathEdgeIter::Edge::kCubic: {
                add_cubic(e.fPts, &segments);
                break;
            }
        }
    }

    // do all the work
    calculate_distance_field_data(&segments, dataPtr, width, height);

    // adjust distance based on winding
    for (int row = 0; row < height; ++row) {
        int windingNumber = 0; // Winding number start from zero for each scanline
        for (int col = 0; col < width; ++col) {
            int idx = (row * width) + col;
            windingNumber += dataPtr[idx].fDeltaWindingScore;

            enum DFSign {
                kInside = -1,
                kOutside = 1
            } dfSign;

            switch (workingPath.getFillType()) {
                case SkPathFillType::kWinding:
                    dfSign = windingNumber ? kInside : kOutside;
                    break;
                case SkPathFillType::kInverseWinding:
                    dfSign = windingNumber ? kOutside : kInside;
                    break;
                case SkPathFillType::kEvenOdd:
                    dfSign = (windingNumber % 2) ? kInside : kOutside;
                    break;
                case SkPathFillType::kInverseEvenOdd:
                    dfSign = (windingNumber % 2) ? kOutside : kInside;
                    break;
            }

            // The winding number at the end of a scanline should be zero.
            SkASSERT(((col != width - 1) || (windingNumber == 0)) &&
                    "Winding number should be zero at the end of a scan line.");
            // Fallback to use SkPath::contains to determine the sign of pixel in release build.
            if (col == width - 1 && windingNumber != 0) {
                for (int col = 0; col < width; ++col) {
                    int idx = (row * width) + col;
                    dfSign = workingPath.contains(col + 0.5, row + 0.5) ? kInside : kOutside;
                    const float miniDist = sqrt(dataPtr[idx].fDistSq);
                    const float dist = dfSign * miniDist;

                    unsigned char pixelVal = pack_distance_field_val<SK_DistanceFieldMagnitude>(dist);

                    distanceField[(row * rowBytes) + col] = pixelVal;
                }
                continue;
            }

            const float miniDist = sqrt(dataPtr[idx].fDistSq);
            const float dist = dfSign * miniDist;

            unsigned char pixelVal = pack_distance_field_val<SK_DistanceFieldMagnitude>(dist);

            distanceField[(row * rowBytes) + col] = pixelVal;
        }
    }
    return true;
}