コード例 #1
0
DEF_TEST(PathOpsAngleFindQuadEpsilon, reporter) {
    if (gDisableAngleTests) {
        return;
    }
    SkRandom ran;
    int maxEpsilon = 0;
    double maxAngle = 0;
    for (int index = 0; index < 100000; ++index) {
        SkDLine line = {{{0, 0}, {ran.nextRangeF(0.0001f, 1000), ran.nextRangeF(0.0001f, 1000)}}};
        float t = ran.nextRangeF(0.0001f, 1);
        SkDPoint dPt = line.ptAtT(t);
        float t2 = ran.nextRangeF(0.0001f, 1);
        SkDPoint qPt = line.ptAtT(t2);
        float t3 = ran.nextRangeF(0.0001f, 1);
        SkDPoint qPt2 = line.ptAtT(t3);
        qPt.fX += qPt2.fY;
        qPt.fY -= qPt2.fX;
        QuadPts q = {{line[0], dPt, qPt}};
        SkDQuad quad;
        quad.debugSet(q.fPts);
        // binary search for maximum movement of quad[1] towards test that still has 1 intersection
        double moveT = 0.5f;
        double deltaT = moveT / 2;
        SkDPoint last;
        do {
            last = quad[1];
            quad[1].fX = dPt.fX - line[1].fY * moveT;
            quad[1].fY = dPt.fY + line[1].fX * moveT;
            SkIntersections i;
            i.intersect(quad, line);
            REPORTER_ASSERT(reporter, i.used() > 0);
            if (i.used() == 1) {
                moveT += deltaT;
            } else {
                moveT -= deltaT;
            }
            deltaT /= 2;
        } while (last.asSkPoint() != quad[1].asSkPoint());
        float p1 = SkDoubleToScalar(line[1].fX * last.fY);
        float p2 = SkDoubleToScalar(line[1].fY * last.fX);
        int p1Bits = SkFloatAs2sCompliment(p1);
        int p2Bits = SkFloatAs2sCompliment(p2);
        int epsilon = SkTAbs(p1Bits - p2Bits);
        if (maxEpsilon < epsilon) {
            SkDebugf("line={{0, 0}, {%1.7g, %1.7g}} t=%1.7g/%1.7g/%1.7g moveT=%1.7g"
                    " pt={%1.7g, %1.7g} epsilon=%d\n",
                    line[1].fX, line[1].fY, t, t2, t3, moveT, last.fX, last.fY, epsilon);
            maxEpsilon = epsilon;
        }
        double a1 = atan2(line[1].fY, line[1].fX);
        double a2 = atan2(last.fY, last.fX);
        double angle = fabs(a1 - a2);
        if (maxAngle < angle) {
            SkDebugf("line={{0, 0}, {%1.7g, %1.7g}} t=%1.7g/%1.7g/%1.7g moveT=%1.7g"
                    " pt={%1.7g, %1.7g} angle=%1.7g\n",
                    line[1].fX, line[1].fY, t, t2, t3, moveT, last.fX, last.fY, angle);
            maxAngle = angle;
        }
    }
}
コード例 #2
0
// from http://blog.gludion.com/2009/08/distance-to-quadratic-bezier-curve.html
// (currently only used by testing)
double SkDQuad::nearestT(const SkDPoint& pt) const {
    SkDVector pos = fPts[0] - pt;
    // search points P of bezier curve with PM.(dP / dt) = 0
    // a calculus leads to a 3d degree equation :
    SkDVector A = fPts[1] - fPts[0];
    SkDVector B = fPts[2] - fPts[1];
    B -= A;
    double a = B.dot(B);
    double b = 3 * A.dot(B);
    double c = 2 * A.dot(A) + pos.dot(B);
    double d = pos.dot(A);
    double ts[3];
    int roots = SkDCubic::RootsValidT(a, b, c, d, ts);
    double d0 = pt.distanceSquared(fPts[0]);
    double d2 = pt.distanceSquared(fPts[2]);
    double distMin = SkTMin(d0, d2);
    int bestIndex = -1;
    for (int index = 0; index < roots; ++index) {
        SkDPoint onQuad = ptAtT(ts[index]);
        double dist = pt.distanceSquared(onQuad);
        if (distMin > dist) {
            distMin = dist;
            bestIndex = index;
        }
    }
    if (bestIndex >= 0) {
        return ts[bestIndex];
    }
    return d0 < d2 ? 0 : 1;
}
static void testLineIntersect(skiatest::Reporter* reporter, const SkDQuad& quad,
                              const SkDLine& line, const double x, const double y) {
    char pathStr[1024];
    sk_bzero(pathStr, sizeof(pathStr));
    char* str = pathStr;
    str += sprintf(str, "    path.moveTo(%1.9g, %1.9g);\n", quad[0].fX, quad[0].fY);
    str += sprintf(str, "    path.quadTo(%1.9g, %1.9g, %1.9g, %1.9g);\n", quad[1].fX,
                   quad[1].fY, quad[2].fX, quad[2].fY);
    str += sprintf(str, "    path.moveTo(%1.9g, %1.9g);\n", line[0].fX, line[0].fY);
    str += sprintf(str, "    path.lineTo(%1.9g, %1.9g);\n", line[1].fX, line[1].fY);

    SkIntersections intersections;
    bool flipped = false;
    int result = doIntersect(intersections, quad, line, flipped);
    bool found = false;
    for (int index = 0; index < result; ++index) {
        double quadT = intersections[0][index];
        SkDPoint quadXY = quad.ptAtT(quadT);
        double lineT = intersections[1][index];
        SkDPoint lineXY = line.ptAtT(lineT);
        if (quadXY.approximatelyEqual(lineXY)) {
            found = true;
        }
    }
    REPORTER_ASSERT(reporter, found);
}
コード例 #4
0
double SkDLine::nearPoint(const SkDPoint& xy) const {
    if (!AlmostBetweenUlps(fPts[0].fX, xy.fX, fPts[1].fX)
            || !AlmostBetweenUlps(fPts[0].fY, xy.fY, fPts[1].fY)) {
        return -1;
    }
    // project a perpendicular ray from the point to the line; find the T on the line
    SkDVector len = fPts[1] - fPts[0]; // the x/y magnitudes of the line
    double denom = len.fX * len.fX + len.fY * len.fY;  // see DLine intersectRay
    SkDVector ab0 = xy - fPts[0];
    double numer = len.fX * ab0.fX + ab0.fY * len.fY;
    if (!between(0, numer, denom)) {
        return -1;
    }
    double t = numer / denom;
    SkDPoint realPt = ptAtT(t);
    double dist = realPt.distance(xy);   // OPTIMIZATION: can we compare against distSq instead ?
    // find the ordinal in the original line with the largest unsigned exponent
    double tiniest = SkTMin(SkTMin(SkTMin(fPts[0].fX, fPts[0].fY), fPts[1].fX), fPts[1].fY);
    double largest = SkTMax(SkTMax(SkTMax(fPts[0].fX, fPts[0].fY), fPts[1].fX), fPts[1].fY);
    largest = SkTMax(largest, -tiniest);
    if (!AlmostEqualUlps(largest, largest + dist)) { // is the dist within ULPS tolerance?
        return -1;
    }
    t = SkPinT(t);
    SkASSERT(between(0, t, 1));
    return t;
}
コード例 #5
0
DEF_TEST(PathOpsAngleFindCrossEpsilon, reporter) {
    if (gDisableAngleTests) {
        return;
    }
    SkRandom ran;
    int maxEpsilon = 0;
    for (int index = 0; index < 10000000; ++index) {
        SkDLine line = {{{0, 0}, {ran.nextRangeF(0.0001f, 1000), ran.nextRangeF(0.0001f, 1000)}}};
        for (int inner = 0; inner < 10; ++inner) {
            float t = ran.nextRangeF(0.0001f, 1);
            SkDPoint dPt = line.ptAtT(t);
            SkPoint pt = dPt.asSkPoint();
            float xs[3] = { prev(pt.fX), pt.fX, next(pt.fX) };
            float ys[3] = { prev(pt.fY), pt.fY, next(pt.fY) };
            for (int xIdx = 0; xIdx < 3; ++xIdx) {
                for (int yIdx = 0; yIdx < 3; ++yIdx) {
                    SkPoint test = { xs[xIdx], ys[yIdx] };
                    float p1 = SkDoubleToScalar(line[1].fX * test.fY);
                    float p2 = SkDoubleToScalar(line[1].fY * test.fX);
                    int p1Bits = SkFloatAs2sCompliment(p1);
                    int p2Bits = SkFloatAs2sCompliment(p2);
                    int epsilon = SkTAbs(p1Bits - p2Bits);
                    if (maxEpsilon < epsilon) {
                        SkDebugf("line={{0, 0}, {%1.7g, %1.7g}} t=%1.7g pt={%1.7g, %1.7g}"
                            " epsilon=%d\n",
                            line[1].fX, line[1].fY, t, test.fX, test.fY, epsilon);
                        maxEpsilon = epsilon;
                    }
                }
            }
        }
    }
}
コード例 #6
0
ファイル: PathOpsDebug.cpp プロジェクト: llluiop/skia
void SkOpSegment::dumpDPts() const {
    int count = SkPathOpsVerbToPoints(fVerb);
    SkDebugf("((SkOpSegment*) 0x%p) [%d] {{", this, debugID());
    int index = 0;
    do {
        SkDPoint dPt = {fPts[index].fX, fPts[index].fY};
        dPt.dump();
        if (index != count) {
            SkDebugf(", ");
        }
    } while (++index <= count);
    SkDebugf("}}\n");
}
コード例 #7
0
bool SkDLine::nearRay(const SkDPoint& xy) const {
    // project a perpendicular ray from the point to the line; find the T on the line
    SkDVector len = fPts[1] - fPts[0]; // the x/y magnitudes of the line
    double denom = len.fX * len.fX + len.fY * len.fY;  // see DLine intersectRay
    SkDVector ab0 = xy - fPts[0];
    double numer = len.fX * ab0.fX + ab0.fY * len.fY;
    double t = numer / denom;
    SkDPoint realPt = ptAtT(t);
    double dist = realPt.distance(xy);   // OPTIMIZATION: can we compare against distSq instead ?
    // find the ordinal in the original line with the largest unsigned exponent
    double tiniest = SkTMin(SkTMin(SkTMin(fPts[0].fX, fPts[0].fY), fPts[1].fX), fPts[1].fY);
    double largest = SkTMax(SkTMax(SkTMax(fPts[0].fX, fPts[0].fY), fPts[1].fX), fPts[1].fY);
    largest = SkTMax(largest, -tiniest);
    return RoughlyEqualUlps(largest, largest + dist); // is the dist within ULPS tolerance?
}
コード例 #8
0
static void chopCompare(const SkConic chopped[2], const SkDConic dChopped[2]) {
    SkASSERT(roughly_equal(chopped[0].fW, dChopped[0].fWeight));
    SkASSERT(roughly_equal(chopped[1].fW, dChopped[1].fWeight));
    for (int cIndex = 0; cIndex < 2; ++cIndex) {
        for (int pIndex = 0; pIndex < 3; ++pIndex) {
            SkDPoint up;
            up.set(chopped[cIndex].fPts[pIndex]);
            SkASSERT(dChopped[cIndex].fPts[pIndex].approximatelyEqual(up));
        }
    }
#if DEBUG_VISUALIZE_CONICS
    dChopped[0].dump();
    dChopped[1].dump();
#endif
}
コード例 #9
0
static void testOneOffs(skiatest::Reporter* reporter) {
    SkIntersections intersections;
    bool flipped = false;
    for (size_t index = 0; index < oneOffs_count; ++index) {
        const SkDQuad& quad = oneOffs[index].quad;
        const SkDLine& line = oneOffs[index].line;
        int result = doIntersect(intersections, quad, line, flipped);
        for (int inner = 0; inner < result; ++inner) {
            double quadT = intersections[0][inner];
            SkDPoint quadXY = quad.xyAtT(quadT);
            double lineT = intersections[1][inner];
            SkDPoint lineXY = line.xyAtT(lineT);
            REPORTER_ASSERT(reporter, quadXY.approximatelyEqual(lineXY));
        }
    }
}
コード例 #10
0
static void pointFinder(const SkDQuad& q1, const SkDQuad& q2) {
    for (int index = 0; index < 3; ++index) {
        double t = q1.nearestT(q2[index]);
        SkDPoint onQuad = q1.ptAtT(t);
        SkDebugf("%s t=%1.9g (%1.9g,%1.9g) dist=%1.9g\n", __FUNCTION__, t, onQuad.fX, onQuad.fY,
                onQuad.distance(q2[index]));
        double left[3];
        left[0] = ((const SkDLine&) q1[0]).isLeft(q2[index]);
        left[1] = ((const SkDLine&) q1[1]).isLeft(q2[index]);
        SkDLine diag = {{q1[0], q1[2]}};
        left[2] = diag.isLeft(q2[index]);
        SkDebugf("%s left=(%d, %d, %d) inHull=%s\n", __FUNCTION__, floatSign(left[0]),
                floatSign(left[1]), floatSign(left[2]),
                q1.pointInHull(q2[index]) ? "true" : "false");
    }
    SkDebugf("\n");
}
コード例 #11
0
ファイル: SkIntersections.cpp プロジェクト: Arternis/skia
int SkIntersections::insert(double one, double two, const SkDPoint& pt) {
    if (fIsCoincident[0] == 3 && between(fT[0][0], one, fT[0][1])) {
        // For now, don't allow a mix of coincident and non-coincident intersections
        return -1;
    }
    SkASSERT(fUsed <= 1 || fT[0][0] <= fT[0][1]);
    int index;
    for (index = 0; index < fUsed; ++index) {
        double oldOne = fT[0][index];
        double oldTwo = fT[1][index];
        if (one == oldOne && two == oldTwo) {
            return -1;
        }
        if (more_roughly_equal(oldOne, one) && more_roughly_equal(oldTwo, two)) {
            if ((precisely_zero(one) && !precisely_zero(oldOne))
                    || (precisely_equal(one, 1) && !precisely_equal(oldOne, 1))
                    || (precisely_zero(two) && !precisely_zero(oldTwo))
                    || (precisely_equal(two, 1) && !precisely_equal(oldTwo, 1))) {
                SkASSERT(one >= 0 && one <= 1);
                SkASSERT(two >= 0 && two <= 1);
                fT[0][index] = one;
                fT[1][index] = two;
                fPt[index] = pt;
            }
            return -1;
        }
    #if ONE_OFF_DEBUG
        if (pt.roughlyEqual(fPt[index])) {
            SkDebugf("%s t=%1.9g pts roughly equal\n", __FUNCTION__, one);
        }
    #endif
        if (fT[0][index] > one) {
            break;
        }
    }
    if (fUsed >= fMax) {
        SkASSERT(0);  // FIXME : this error, if it is to be handled at runtime in release, must
                      // be propagated all the way back down to the caller, and return failure.
        fUsed = 0;
        return 0;
    }
    int remaining = fUsed - index;
    if (remaining > 0) {
        memmove(&fPt[index + 1], &fPt[index], sizeof(fPt[0]) * remaining);
        memmove(&fT[0][index + 1], &fT[0][index], sizeof(fT[0][0]) * remaining);
        memmove(&fT[1][index + 1], &fT[1][index], sizeof(fT[1][0]) * remaining);
        int clearMask = ~((1 << index) - 1);
        fIsCoincident[0] += fIsCoincident[0] & clearMask;
        fIsCoincident[1] += fIsCoincident[1] & clearMask;
    }
    fPt[index] = pt;
    SkASSERT(one >= 0 && one <= 1);
    SkASSERT(two >= 0 && two <= 1);
    fT[0][index] = one;
    fT[1][index] = two;
    ++fUsed;
    return index;
}
コード例 #12
0
ファイル: PathOpsDPointTest.cpp プロジェクト: ROM-PacMe/skia
DEF_TEST(PathOpsDPoint, reporter) {
    for (size_t index = 0; index < tests_count; ++index) {
        const SkDPoint& pt = tests[index];
        SkASSERT(ValidPoint(pt));
        SkDPoint p = pt;
        REPORTER_ASSERT(reporter, p == pt);
        REPORTER_ASSERT(reporter, !(pt != pt));
        SkDVector v = p - pt;
        p += v;
        REPORTER_ASSERT(reporter, p == pt);
        p -= v;
        REPORTER_ASSERT(reporter, p == pt);
        REPORTER_ASSERT(reporter, p.approximatelyEqual(pt));
        SkPoint sPt = pt.asSkPoint();
        p.set(sPt);
        REPORTER_ASSERT(reporter, p == pt);
        REPORTER_ASSERT(reporter, p.approximatelyEqual(sPt));
        REPORTER_ASSERT(reporter, p.roughlyEqual(pt));
        p.fX = p.fY = 0;
        REPORTER_ASSERT(reporter, p.fX == 0 && p.fY == 0);
        REPORTER_ASSERT(reporter, p.approximatelyZero());
        REPORTER_ASSERT(reporter, pt.distanceSquared(p) == pt.fX * pt.fX + pt.fY * pt.fY);
        REPORTER_ASSERT(reporter, approximately_equal(pt.distance(p),
                        sqrt(pt.fX * pt.fX + pt.fY * pt.fY)));
    }
}
コード例 #13
0
void SkIntersections::cubicInsert(double one, double two, const SkDPoint& pt,
        const SkDCubic& cubic1, const SkDCubic& cubic2) {
    for (int index = 0; index < fUsed; ++index) {
        if (fT[0][index] == one) {
            double oldTwo = fT[1][index];
            if (oldTwo == two) {
                return;
            }
            SkDPoint mid = cubic2.ptAtT((oldTwo + two) / 2);
            if (mid.approximatelyEqual(fPt[index])) {
                return;
            }
        }
        if (fT[1][index] == two) {
            SkDPoint mid = cubic1.ptAtT((fT[0][index] + two) / 2);
            if (mid.approximatelyEqual(fPt[index])) {
                return;
            }
        }
    }
    insert(one, two, pt);
}
コード例 #14
0
static void testOneOffs(skiatest::Reporter* reporter) {
    bool flipped = false;
    for (size_t index = 0; index < oneOffs_count; ++index) {
        const SkDConic& conic = oneOffs[index].conic;
        SkASSERT(ValidConic(conic));
        const SkDLine& line = oneOffs[index].line;
        SkASSERT(ValidLine(line));
        SkIntersections intersections;
        int result = doIntersect(intersections, conic, line, flipped);
        for (int inner = 0; inner < result; ++inner) {
            double conicT = intersections[0][inner];
            SkDPoint conicXY = conic.ptAtT(conicT);
            double lineT = intersections[1][inner];
            SkDPoint lineXY = line.ptAtT(lineT);
            if (!conicXY.approximatelyEqual(lineXY)) {
                conicXY.approximatelyEqual(lineXY);
                SkDebugf("");
            }
            REPORTER_ASSERT(reporter, conicXY.approximatelyEqual(lineXY));
        }
    }
}
コード例 #15
0
        bool uniqueAnswer(double cubicT, const SkDPoint& pt) {
            for (int inner = 0; inner < fIntersections->used(); ++inner) {
                if (fIntersections->pt(inner) != pt) {
                    continue;
                }
                double existingCubicT = (*fIntersections)[0][inner];
                if (cubicT == existingCubicT) {
                    return false;
                }
                // check if midway on cubic is also same point. If so, discard this
                double cubicMidT = (existingCubicT + cubicT) / 2;
                SkDPoint cubicMidPt = fCubic.ptAtT(cubicMidT);
                if (cubicMidPt.approximatelyEqual(pt)) {
                    return false;
                }
            }
#if ONE_OFF_DEBUG
            SkDPoint cPt = fCubic.ptAtT(cubicT);
            SkDebugf("%s pt=(%1.9g,%1.9g) cPt=(%1.9g,%1.9g)\n", __FUNCTION__, pt.fX, pt.fY,
                    cPt.fX, cPt.fY);
#endif
            return true;
        }
コード例 #16
0
static void testOneOffs(skiatest::Reporter* reporter) {
    bool flipped = false;
    for (size_t index = 0; index < oneOffs_count; ++index) {
        const QuadPts& q = oneOffs[index].quad;
        SkDQuad quad;
        quad.debugSet(q.fPts);
        SkASSERT(ValidQuad(quad));
        const SkDLine& line = oneOffs[index].line;
        SkASSERT(ValidLine(line));
        SkIntersections intersections;
        int result = doIntersect(intersections, quad, line, flipped);
        for (int inner = 0; inner < result; ++inner) {
            double quadT = intersections[0][inner];
            SkDPoint quadXY = quad.ptAtT(quadT);
            double lineT = intersections[1][inner];
            SkDPoint lineXY = line.ptAtT(lineT);
            if (!quadXY.approximatelyEqual(lineXY)) {
                quadXY.approximatelyEqual(lineXY);
                SkDebugf("");
            }
            REPORTER_ASSERT(reporter, quadXY.approximatelyEqual(lineXY));
        }
    }
}
コード例 #17
0
ファイル: SkIntersections.cpp プロジェクト: Arternis/skia
int SkIntersections::closestTo(double rangeStart, double rangeEnd, const SkDPoint& testPt,
        double* closestDist) const {
    int closest = -1;
    *closestDist = SK_ScalarMax;
    for (int index = 0; index < fUsed; ++index) {
        if (!between(rangeStart, fT[0][index], rangeEnd)) {
            continue;
        }
        const SkDPoint& iPt = fPt[index];
        double dist = testPt.distanceSquared(iPt);
        if (*closestDist > dist) {
            *closestDist = dist;
            closest = index;
        }
    }
    return closest;
}
コード例 #18
0
ファイル: SkOpAngle.cpp プロジェクト: venkatarajasekhar/Qt
bool SkOpAngle::endsIntersect(const SkOpAngle& rh) const {
    SkPath::Verb lVerb = fSegment->verb();
    SkPath::Verb rVerb = rh.fSegment->verb();
    int lPts = SkPathOpsVerbToPoints(lVerb);
    int rPts = SkPathOpsVerbToPoints(rVerb);
    SkDLine rays[] = {{{fCurvePart[0], rh.fCurvePart[rPts]}},
            {{fCurvePart[0], fCurvePart[lPts]}}};
    if (rays[0][1] == rays[1][1]) {
        return checkParallel(rh);
    }
    double smallTs[2] = {-1, -1};
    bool limited[2] = {false, false};
    for (int index = 0; index < 2; ++index) {
        const SkOpSegment& segment = index ? *rh.fSegment : *fSegment;
        SkIntersections i;
        (*CurveIntersectRay[index ? rPts : lPts])(segment.pts(), rays[index], &i);
//      SkASSERT(i.used() >= 1);
//        if (i.used() <= 1) {
//            continue;
//        }
        double tStart = segment.t(index ? rh.fStart : fStart);
        double tEnd = segment.t(index ? rh.fComputedEnd : fComputedEnd);
        bool testAscends = index ? rh.fStart < rh.fComputedEnd : fStart < fComputedEnd;
        double t = testAscends ? 0 : 1;
        for (int idx2 = 0; idx2 < i.used(); ++idx2) {
            double testT = i[0][idx2];
            if (!approximately_between_orderable(tStart, testT, tEnd)) {
                continue;
            }
            if (approximately_equal_orderable(tStart, testT)) {
                continue;
            }
            smallTs[index] = t = testAscends ? SkTMax(t, testT) : SkTMin(t, testT);
            limited[index] = approximately_equal_orderable(t, tEnd);
        }
    }
#if 0
    if (smallTs[0] < 0 && smallTs[1] < 0) {  // if neither ray intersects, do endpoint sort
        double m0xm1 = 0;
        if (lVerb == SkPath::kLine_Verb) {
            SkASSERT(rVerb != SkPath::kLine_Verb);
            SkDVector m0 = rays[1][1] - fCurvePart[0];
            SkDPoint endPt;
            endPt.set(rh.fSegment->pts()[rh.fStart < rh.fEnd ? rPts : 0]);
            SkDVector m1 = endPt - fCurvePart[0];
            m0xm1 = m0.crossCheck(m1);
        }
        if (rVerb == SkPath::kLine_Verb) {
            SkDPoint endPt;
            endPt.set(fSegment->pts()[fStart < fEnd ? lPts : 0]);
            SkDVector m0 = endPt - fCurvePart[0];
            SkDVector m1 = rays[0][1] - fCurvePart[0];
            m0xm1 = m0.crossCheck(m1);
        }
        if (m0xm1 != 0) {
            return m0xm1 < 0;
        }
    }
#endif
    bool sRayLonger = false;
    SkDVector sCept = {0, 0};
    double sCeptT = -1;
    int sIndex = -1;
    bool useIntersect = false;
    for (int index = 0; index < 2; ++index) {
        if (smallTs[index] < 0) {
            continue;
        }
        const SkOpSegment& segment = index ? *rh.fSegment : *fSegment;
        const SkDPoint& dPt = segment.dPtAtT(smallTs[index]);
        SkDVector cept = dPt - rays[index][0];
        // If this point is on the curve, it should have been detected earlier by ordinary
        // curve intersection. This may be hard to determine in general, but for lines,
        // the point could be close to or equal to its end, but shouldn't be near the start.
        if ((index ? lPts : rPts) == 1) {
            SkDVector total = rays[index][1] - rays[index][0];
            if (cept.lengthSquared() * 2 < total.lengthSquared()) {
                continue;
            }
        }
        SkDVector end = rays[index][1] - rays[index][0];
        if (cept.fX * end.fX < 0 || cept.fY * end.fY < 0) {
            continue;
        }
        double rayDist = cept.length();
        double endDist = end.length();
        bool rayLonger = rayDist > endDist;
        if (limited[0] && limited[1] && rayLonger) {
            useIntersect = true;
            sRayLonger = rayLonger;
            sCept = cept;
            sCeptT = smallTs[index];
            sIndex = index;
            break;
        }
        double delta = fabs(rayDist - endDist);
        double minX, minY, maxX, maxY;
        minX = minY = SK_ScalarInfinity;
        maxX = maxY = -SK_ScalarInfinity;
        const SkDCubic& curve = index ? rh.fCurvePart : fCurvePart;
        int ptCount = index ? rPts : lPts;
        for (int idx2 = 0; idx2 <= ptCount; ++idx2) {
            minX = SkTMin(minX, curve[idx2].fX);
            minY = SkTMin(minY, curve[idx2].fY);
            maxX = SkTMax(maxX, curve[idx2].fX);
            maxY = SkTMax(maxY, curve[idx2].fY);
        }
        double maxWidth = SkTMax(maxX - minX, maxY - minY);
        delta /= maxWidth;
        if (delta > 1e-4 && (useIntersect ^= true)) {  // FIXME: move this magic number
            sRayLonger = rayLonger;
            sCept = cept;
            sCeptT = smallTs[index];
            sIndex = index;
        }
    }
    if (useIntersect) {
        const SkDCubic& curve = sIndex ? rh.fCurvePart : fCurvePart;
        const SkOpSegment& segment = sIndex ? *rh.fSegment : *fSegment;
        double tStart = segment.t(sIndex ? rh.fStart : fStart);
        SkDVector mid = segment.dPtAtT(tStart + (sCeptT - tStart) / 2) - curve[0];
        double septDir = mid.crossCheck(sCept);
        if (!septDir) {
            return checkParallel(rh);
        }
        return sRayLonger ^ (sIndex == 0) ^ (septDir < 0);
    } else {
        return checkParallel(rh);
    }
}
static bool is_linear_inner(const SkDQuad& q1, double t1s, double t1e, const SkDQuad& q2,
                            double t2s, double t2e, SkIntersections* i, bool* subDivide) {
    SkDQuad hull = q1.subDivide(t1s, t1e);
    SkDLine line = {{hull[2], hull[0]}};
    const SkDLine* testLines[] = { &line, (const SkDLine*) &hull[0], (const SkDLine*) &hull[1] };
    const size_t kTestCount = SK_ARRAY_COUNT(testLines);
    SkSTArray<kTestCount * 2, double, true> tsFound;
    for (size_t index = 0; index < kTestCount; ++index) {
        SkIntersections rootTs;
        rootTs.allowNear(false);
        int roots = rootTs.intersect(q2, *testLines[index]);
        for (int idx2 = 0; idx2 < roots; ++idx2) {
            double t = rootTs[0][idx2];
#ifdef SK_DEBUG
            SkDPoint qPt = q2.ptAtT(t);
            SkDPoint lPt = testLines[index]->ptAtT(rootTs[1][idx2]);
            SkASSERT(qPt.approximatelyEqual(lPt));
#endif
            if (approximately_negative(t - t2s) || approximately_positive(t - t2e)) {
                continue;
            }
            tsFound.push_back(rootTs[0][idx2]);
        }
    }
    int tCount = tsFound.count();
    if (tCount <= 0) {
        return true;
    }
    double tMin, tMax;
    if (tCount == 1) {
        tMin = tMax = tsFound[0];
    } else {
        SkASSERT(tCount > 1);
        SkTQSort<double>(tsFound.begin(), tsFound.end() - 1);
        tMin = tsFound[0];
        tMax = tsFound[tsFound.count() - 1];
    }
    SkDPoint end = q2.ptAtT(t2s);
    bool startInTriangle = hull.pointInHull(end);
    if (startInTriangle) {
        tMin = t2s;
    }
    end = q2.ptAtT(t2e);
    bool endInTriangle = hull.pointInHull(end);
    if (endInTriangle) {
        tMax = t2e;
    }
    int split = 0;
    SkDVector dxy1, dxy2;
    if (tMin != tMax || tCount > 2) {
        dxy2 = q2.dxdyAtT(tMin);
        for (int index = 1; index < tCount; ++index) {
            dxy1 = dxy2;
            dxy2 = q2.dxdyAtT(tsFound[index]);
            double dot = dxy1.dot(dxy2);
            if (dot < 0) {
                split = index - 1;
                break;
            }
        }
    }
    if (split == 0) {  // there's one point
        if (add_intercept(q1, q2, tMin, tMax, i, subDivide)) {
            return true;
        }
        i->swap();
        return is_linear_inner(q2, tMin, tMax, q1, t1s, t1e, i, subDivide);
    }
    // At this point, we have two ranges of t values -- treat each separately at the split
    bool result;
    if (add_intercept(q1, q2, tMin, tsFound[split - 1], i, subDivide)) {
        result = true;
    } else {
        i->swap();
        result = is_linear_inner(q2, tMin, tsFound[split - 1], q1, t1s, t1e, i, subDivide);
    }
    if (add_intercept(q1, q2, tsFound[split], tMax, i, subDivide)) {
        result = true;
    } else {
        i->swap();
        result |= is_linear_inner(q2, tsFound[split], tMax, q1, t1s, t1e, i, subDivide);
    }
    return result;
}