C++ SkDQuad类代码示例

// returns false if there's more than one intercept or the intercept doesn't match the point
// returns true if the intercept was successfully added or if the
// original quads need to be subdivided
static bool add_intercept(const SkDQuad& q1, const SkDQuad& q2, double tMin, double tMax,
                          SkIntersections* i, bool* subDivide) {
    double tMid = (tMin + tMax) / 2;
    SkDPoint mid = q2.ptAtT(tMid);
    SkDLine line;
    line[0] = line[1] = mid;
    SkDVector dxdy = q2.dxdyAtT(tMid);
    line[0] -= dxdy;
    line[1] += dxdy;
    SkIntersections rootTs;
    rootTs.allowNear(false);
    int roots = rootTs.intersect(q1, line);
    if (roots == 0) {
        if (subDivide) {
            *subDivide = true;
        }
        return true;
    }
    if (roots == 2) {
        return false;
    }
    SkDPoint pt2 = q1.ptAtT(rootTs[0][0]);
    if (!pt2.approximatelyEqualHalf(mid)) {
        return false;
    }
    i->insertSwap(rootTs[0][0], tMid, pt2);
    return true;
}

static bool checkParallel(skiatest::Reporter* reporter, const SkDQuad& quad1, const SkDQuad& quad2) {
    SkDVector sweep[2], tweep[2];
    setQuadHullSweep(quad1, sweep);
    setQuadHullSweep(quad2, tweep);
    // if the ctrl tangents are not nearly parallel, use them
    // solve for opposite direction displacement scale factor == m
    // initial dir = v1.cross(v2) == v2.x * v1.y - v2.y * v1.x
    // displacement of q1[1] : dq1 = { -m * v1.y, m * v1.x } + q1[1]
    // straight angle when : v2.x * (dq1.y - q1[0].y) == v2.y * (dq1.x - q1[0].x)
    //                       v2.x * (m * v1.x + v1.y) == v2.y * (-m * v1.y + v1.x)
    // - m * (v2.x * v1.x + v2.y * v1.y) == v2.x * v1.y - v2.y * v1.x
    // m = (v2.y * v1.x - v2.x * v1.y) / (v2.x * v1.x + v2.y * v1.y)
    // m = v1.cross(v2) / v1.dot(v2)
    double s0dt0 = sweep[0].dot(tweep[0]);
    REPORTER_ASSERT(reporter, s0dt0 != 0);
    double s0xt0 = sweep[0].crossCheck(tweep[0]);
    double m = s0xt0 / s0dt0;
    double sDist = sweep[0].length() * m;
    double tDist = tweep[0].length() * m;
    bool useS = fabs(sDist) < fabs(tDist);
    double mFactor = fabs(useS ? distEndRatio(sDist, quad1) : distEndRatio(tDist, quad2));
    if (mFactor < 5000) {  // empirically found limit
        return s0xt0 < 0;
    }
    SkDVector m0 = quad1.ptAtT(0.5) - quad1[0];
    SkDVector m1 = quad2.ptAtT(0.5) - quad2[0];
    return m0.crossCheck(m1) < 0;
}

static void oneOffTest(skiatest::Reporter* reporter) {
    for (size_t index = 0; index < testSetCount; ++index) {
        const QuadPts& q = testSet[index];
        SkDQuad quad;
        quad.debugSet(q.fPts);
        SkReduceOrder reducer;
        SkDEBUGCODE(int result = ) reducer.reduce(quad);
        SkASSERT(result == 3);
    }
}

void SkGlyphCache::AddQuad(const SkPoint pts[2], SkScalar axis, bool yAxis,
                     SkGlyph::Intercept* intercept) {
    SkDQuad quad;
    quad.set(pts);
    double roots[2];
    int count = yAxis ? quad.verticalIntersect(axis, roots)
            : quad.horizontalIntersect(axis, roots);
    while (--count >= 0) {
        SkPoint pt = quad.ptAtT(roots[count]).asSkPoint();
        AddInterval(*(&pt.fX + yAxis), intercept);
    }
}

SkPath::Verb SkReduceOrder::Quad(const SkPoint a[3], SkPoint* reducePts) {
    SkDQuad quad;
    quad.set(a);
    SkReduceOrder reducer;
    int order = reducer.reduce(quad);
    if (order == 2) {  // quad became line
        for (int index = 0; index < order; ++index) {
            *reducePts++ = reducer.fLine[index].asSkPoint();
        }
    }
    return SkPathOpsPointsToVerb(order - 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);
}

/* returns
   -1 if overlaps
    0 if no overlap cw
    1 if no overlap ccw
*/
static int quadHullsOverlap(skiatest::Reporter* reporter, const SkDQuad& quad1,
        const SkDQuad& quad2) {
    SkDVector sweep[2], tweep[2];
    setQuadHullSweep(quad1, sweep);
    setQuadHullSweep(quad2, tweep);
    double s0xs1 = sweep[0].crossCheck(sweep[1]);
    double s0xt0 = sweep[0].crossCheck(tweep[0]);
    double s1xt0 = sweep[1].crossCheck(tweep[0]);
    bool tBetweenS = s0xs1 > 0 ? s0xt0 > 0 && s1xt0 < 0 : s0xt0 < 0 && s1xt0 > 0;
    double s0xt1 = sweep[0].crossCheck(tweep[1]);
    double s1xt1 = sweep[1].crossCheck(tweep[1]);
    tBetweenS |= s0xs1 > 0 ? s0xt1 > 0 && s1xt1 < 0 : s0xt1 < 0 && s1xt1 > 0;
    double t0xt1 = tweep[0].crossCheck(tweep[1]);
    if (tBetweenS) {
        return -1;
    }
    if ((s0xt0 == 0 && s1xt1 == 0) || (s1xt0 == 0 && s0xt1 == 0)) {  // s0 to s1 equals t0 to t1
        return -1;
    }
    bool sBetweenT = t0xt1 > 0 ? s0xt0 < 0 && s0xt1 > 0 : s0xt0 > 0 && s0xt1 < 0;
    sBetweenT |= t0xt1 > 0 ? s1xt0 < 0 && s1xt1 > 0 : s1xt0 > 0 && s1xt1 < 0;
    if (sBetweenT) {
        return -1;
    }
    // if all of the sweeps are in the same half plane, then the order of any pair is enough
    if (s0xt0 >= 0 && s0xt1 >= 0 && s1xt0 >= 0 && s1xt1 >= 0) {
        return 0;
    }
    if (s0xt0 <= 0 && s0xt1 <= 0 && s1xt0 <= 0 && s1xt1 <= 0) {
        return 1;
    }
    // if the outside sweeps are greater than 180 degress:
        // first assume the inital tangents are the ordering
        // if the midpoint direction matches the inital order, that is enough
    SkDVector m0 = quad1.ptAtT(0.5) - quad1[0];
    SkDVector m1 = quad2.ptAtT(0.5) - quad2[0];
    double m0xm1 = m0.crossCheck(m1);
    if (s0xt0 > 0 && m0xm1 > 0) {
        return 0;
    }
    if (s0xt0 < 0 && m0xm1 < 0) {
        return 1;
    }
    REPORTER_ASSERT(reporter, s0xt0 != 0);
    return checkParallel(reporter, quad1, quad2);
}

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");
}

static int check_linear(const SkDQuad& quad,
        int minX, int maxX, int minY, int maxY, SkDQuad& reduction) {
    if (!quad.isLinear(0, 2)) {
        return 0;
    }
    // four are colinear: return line formed by outside
    reduction[0] = quad[0];
    reduction[1] = quad[2];
    return reductionLineCount(reduction);
}

// find a point on a quad by choosing a t from 0 to 1
// create a vertical span above and below the point
// verify that intersecting the vertical span and the quad returns t
// verify that a vertical span starting at quad[0] intersects at t=0
// verify that a vertical span starting at quad[2] intersects at t=1
static void testQuadLineIntersectMain(PathOpsThreadState* data)
{
    PathOpsThreadState& state = *data;
    REPORTER_ASSERT(state.fReporter, data);
    int ax = state.fA & 0x03;
    int ay = state.fA >> 2;
    int bx = state.fB & 0x03;
    int by = state.fB >> 2;
    int cx = state.fC & 0x03;
    int cy = state.fC >> 2;
    SkDQuad quad = {{{(double) ax, (double) ay}, {(double) bx, (double) by},
            {(double) cx, (double) cy}
        }
    };
    SkReduceOrder reducer;
    int order = reducer.reduce(quad);
    if (order < 3) {
        return;
    }
    for (int tIndex = 0; tIndex <= 4; ++tIndex) {
        SkDPoint xy = quad.ptAtT(tIndex / 4.0);
        for (int h = -2; h <= 2; ++h) {
            for (int v = -2; v <= 2; ++v) {
                if (h == v && abs(h) != 1) {
                    continue;
                }
                double x = xy.fX;
                double y = xy.fY;
                SkDLine line = {{{x - h, y - v}, {x, y}}};
                testLineIntersect(state.fReporter, quad, line, x, y);
                state.fReporter->bumpTestCount();
                SkDLine line2 = {{{x, y}, {x + h, y + v}}};
                testLineIntersect(state.fReporter, quad, line2, x, y);
                state.fReporter->bumpTestCount();
                SkDLine line3 = {{{x - h, y - v}, {x + h, y + v}}};
                testLineIntersect(state.fReporter, quad, line3, x, y);
                state.fReporter->bumpTestCount();
            }
        }
    }
}

static void standardTestCases(skiatest::Reporter* reporter) {
    size_t index;
    SkReduceOrder reducer;
    int order;
    enum {
        RunAll,
        RunQuadraticLines,
        RunQuadraticModLines,
        RunNone
    } run = RunAll;
    int firstTestIndex = 0;
#if 0
    run = RunQuadraticLines;
    firstTestIndex = 1;
#endif
    int firstQuadraticLineTest = run == RunAll ? 0 : run == RunQuadraticLines ? firstTestIndex
            : SK_MaxS32;
    int firstQuadraticModLineTest = run == RunAll ? 0 : run == RunQuadraticModLines ? firstTestIndex
            : SK_MaxS32;

    for (index = firstQuadraticLineTest; index < quadraticLines_count; ++index) {
        const QuadPts& q = quadraticLines[index];
        SkDQuad quad;
        quad.debugSet(q.fPts);
        order = reducer.reduce(quad);
        if (order != 2) {
            SkDebugf("[%d] line quad order=%d\n", (int) index, order);
        }
    }
    for (index = firstQuadraticModLineTest; index < quadraticModEpsilonLines_count; ++index) {
        const QuadPts& q = quadraticModEpsilonLines[index];
        SkDQuad quad;
        quad.debugSet(q.fPts);
        order = reducer.reduce(quad);
        if (order != 2 && order != 3) {  // FIXME: data probably is not good
            SkDebugf("[%d] line mod quad order=%d\n", (int) index, order);
        }
    }
}

void SkDRect::setBounds(const SkDQuad& quad) {
    set(quad[0]);
    add(quad[2]);
    double tValues[2];
    int roots = 0;
    if (!between(quad[0].fX, quad[1].fX, quad[2].fX)) {
        roots = SkDQuad::FindExtrema(quad[0].fX, quad[1].fX, quad[2].fX, tValues);
    }
    if (!between(quad[0].fY, quad[1].fY, quad[2].fY)) {
        roots += SkDQuad::FindExtrema(quad[0].fY, quad[1].fY, quad[2].fY, &tValues[roots]);
    }
    for (int x = 0; x < roots; ++x) {
        add(quad.ptAtT(tValues[x]));
    }
}

static int check_linear(const SkDQuad& quad,
        int minX, int maxX, int minY, int maxY, SkDQuad& reduction) {
    int startIndex = 0;
    int endIndex = 2;
    while (quad[startIndex].approximatelyEqual(quad[endIndex])) {
        --endIndex;
        if (endIndex == 0) {
            SkDebugf("%s shouldn't get here if all four points are about equal", __FUNCTION__);
            SkASSERT(0);
        }
    }
    if (!quad.isLinear(startIndex, endIndex)) {
        return 0;
    }
    // four are colinear: return line formed by outside
    reduction[0] = quad[0];
    reduction[1] = quad[2];
    return reductionLineCount(reduction);
}

static int findRoots(const SkDQuadImplicit& i, const SkDQuad& quad, double roots[4],
        bool oneHint, bool flip, int firstCubicRoot) {
    SkDQuad flipped;
    const SkDQuad& q = flip ? (flipped = quad.flip()) : quad;
    double a, b, c;
    SkDQuad::SetABC(&q[0].fX, &a, &b, &c);
    double d, e, f;
    SkDQuad::SetABC(&q[0].fY, &d, &e, &f);
    const double t4 =     i.x2() *  a * a
                    +     i.xy() *  a * d
                    +     i.y2() *  d * d;
    const double t3 = 2 * i.x2() *  a * b
                    +     i.xy() * (a * e +     b * d)
                    + 2 * i.y2() *  d * e;
    const double t2 =     i.x2() * (b * b + 2 * a * c)
                    +     i.xy() * (c * d +     b * e + a * f)
                    +     i.y2() * (e * e + 2 * d * f)
                    +     i.x()  *  a
                    +     i.y()  *  d;
    const double t1 = 2 * i.x2() *  b * c
                    +     i.xy() * (c * e + b * f)
                    + 2 * i.y2() *  e * f
                    +     i.x()  *  b
                    +     i.y()  *  e;
    const double t0 =     i.x2() *  c * c
                    +     i.xy() *  c * f
                    +     i.y2() *  f * f
                    +     i.x()  *  c
                    +     i.y()  *  f
                    +     i.c();
    int rootCount = SkReducedQuarticRoots(t4, t3, t2, t1, t0, oneHint, roots);
    if (rootCount < 0) {
        rootCount = SkQuarticRootsReal(firstCubicRoot, t4, t3, t2, t1, t0, roots);
    }
    if (flip) {
        for (int index = 0; index < rootCount; ++index) {
            roots[index] = 1 - roots[index];
        }
    }
    return rootCount;
}

// Up promote the quad to a cubic.
// OPTIMIZATION If this is a common use case, optimize by duplicating
// the intersect 3 loop to avoid the promotion  / demotion code
int SkIntersections::intersect(const SkDCubic& cubic, const SkDQuad& quad) {
    SkDCubic up = quad.toCubic();
    (void) intersect(cubic, up);
    return used();
}