C++ Intersections::used方法代码示例

bool intersect3(const Cubic& c1, const Cubic& c2, Intersections& i) {
    bool result = intersect3(c1, 0, 1, c2, 0, 1, 1, i);
    // FIXME: pass in cached bounds from caller
    _Rect c1Bounds, c2Bounds;
    c1Bounds.setBounds(c1); // OPTIMIZE use setRawBounds ?
    c2Bounds.setBounds(c2);
    result |= intersectEnd(c1, false, c2, c2Bounds, i);
    result |= intersectEnd(c1, true, c2, c2Bounds, i);
    bool selfIntersect = c1 == c2;
    if (!selfIntersect) {
        i.swap();
        result |= intersectEnd(c2, false, c1, c1Bounds, i);
        result |= intersectEnd(c2, true, c1, c1Bounds, i);
        i.swap();
    }
    // If an end point and a second point very close to the end is returned, the second
    // point may have been detected because the approximate quads
    // intersected at the end and close to it. Verify that the second point is valid.
    if (i.used() <= 1 || i.coincidentUsed()) {
        return result;
    }
    _Point pt[2];
    if (closeStart(c1, 0, i, pt[0]) && closeStart(c2, 1, i, pt[1])
            && pt[0].approximatelyEqual(pt[1])) {
        i.removeOne(1);
    }
    if (closeEnd(c1, 0, i, pt[0]) && closeEnd(c2, 1, i, pt[1])
            && pt[0].approximatelyEqual(pt[1])) {
        i.removeOne(i.used() - 2);
    }
    return result;
}

int intersect(const Cubic& c, Intersections& i) {
    // check to see if x or y end points are the extrema. Are other quick rejects possible?
    if (ends_are_extrema_in_x_or_y(c)) {
        return false;
    }
    (void) intersect3(c, c, i);
    if (i.used() > 0) {
        SkASSERT(i.used() == 1);
        if (i.fT[0][0] > i.fT[1][0]) {
            SkTSwap(i.fT[0][0], i.fT[1][0]);
        }
    }
    return i.used();
}

bool intersect(double minT1, double maxT1, double minT2, double maxT2) {
    Cubic sub1, sub2;
    // FIXME: carry last subdivide and reduceOrder result with cubic
    sub_divide(cubic1, minT1, maxT1, sub1);
    sub_divide(cubic2, minT2, maxT2, sub2);
    Intersections i;
    intersect2(sub1, sub2, i);
    if (i.used() == 0) {
        return false;
    }
    double x1, y1, x2, y2;
    t1 = minT1 + i.fT[0][0] * (maxT1 - minT1);
    t2 = minT2 + i.fT[1][0] * (maxT2 - minT2);
    xy_at_t(cubic1, t1, x1, y1);
    xy_at_t(cubic2, t2, x2, y2);
    if (AlmostEqualUlps(x1, x2) && AlmostEqualUlps(y1, y2)) {
        return true;
    }
    double half1 = (minT1 + maxT1) / 2;
    double half2 = (minT2 + maxT2) / 2;
    ++depth;
    bool result;
    if (depth & 1) {
        result = intersect(minT1, half1, minT2, maxT2) || intersect(half1, maxT1, minT2, maxT2)
            || intersect(minT1, maxT1, minT2, half2) || intersect(minT1, maxT1, half2, maxT2);
    } else {
        result = intersect(minT1, maxT1, minT2, half2) || intersect(minT1, maxT1, half2, maxT2)
            || intersect(minT1, half1, minT2, maxT2) || intersect(half1, maxT1, minT2, maxT2);
    }
    --depth;
    return result;
}

static bool closeEnd(const Cubic& cubic, int cubicIndex, Intersections& i, _Point& pt) {
    int last = i.used() - 1;
    if (i.fT[cubicIndex][last] != 1 || i.fT[cubicIndex][last - 1] < 1 - CLOSE_ENOUGH) {
        return false;
    }
    pt = xy_at_t(cubic, (i.fT[cubicIndex][last] + i.fT[cubicIndex][last - 1]) / 2);
    return true;
}

int intersect(const Cubic& cubic, const Quadratic& quad, Intersections& i) {
    SkTDArray<double> ts;
    double precision = calcPrecision(cubic);
    cubic_to_quadratics(cubic, precision, ts);
    double tStart = 0;
    Cubic part;
    int tsCount = ts.count();
    for (int idx = 0; idx <= tsCount; ++idx) {
        double t = idx < tsCount ? ts[idx] : 1;
        Quadratic q1;
        sub_divide(cubic, tStart, t, part);
        demote_cubic_to_quad(part, q1);
        Intersections locals;
        intersect2(q1, quad, locals);
        for (int tIdx = 0; tIdx < locals.used(); ++tIdx) {
            double globalT = tStart + (t - tStart) * locals.fT[0][tIdx];
            i.insertOne(globalT, 0);
            globalT = locals.fT[1][tIdx];
            i.insertOne(globalT, 1);
        }
        tStart = t;
    }
    return i.used();
}

void CubicIntersection_Test() {
    for (size_t index = firstCubicIntersectionTest; index < tests_count; ++index) {
        const Cubic& cubic1 = tests[index][0];
        const Cubic& cubic2 = tests[index][1];
        Cubic reduce1, reduce2;
        int order1 = reduceOrder(cubic1, reduce1, kReduceOrder_NoQuadraticsAllowed);
        int order2 = reduceOrder(cubic2, reduce2, kReduceOrder_NoQuadraticsAllowed);
        if (order1 < 4) {
            printf("%s [%d] cubic1 order=%d\n", __FUNCTION__, (int) index, order1);
            continue;
        }
        if (order2 < 4) {
            printf("%s [%d] cubic2 order=%d\n", __FUNCTION__, (int) index, order2);
            continue;
        }
        if (implicit_matches(reduce1, reduce2)) {
            printf("%s [%d] coincident\n", __FUNCTION__, (int) index);
            continue;
        }
        Intersections tIntersections;
        intersect(reduce1, reduce2, tIntersections);
        if (!tIntersections.intersected()) {
            printf("%s [%d] no intersection\n", __FUNCTION__, (int) index);
            continue;
        }
        for (int pt = 0; pt < tIntersections.used(); ++pt) {
            double tt1 = tIntersections.fT[0][pt];
            double tx1, ty1;
            xy_at_t(cubic1, tt1, tx1, ty1);
            double tt2 = tIntersections.fT[1][pt];
            double tx2, ty2;
            xy_at_t(cubic2, tt2, tx2, ty2);
            if (!AlmostEqualUlps(tx1, tx2)) {
                printf("%s [%d,%d] x!= t1=%g (%g,%g) t2=%g (%g,%g)\n",
                    __FUNCTION__, (int)index, pt, tt1, tx1, ty1, tt2, tx2, ty2);
            }
            if (!AlmostEqualUlps(ty1, ty2)) {
                printf("%s [%d,%d] y!= t1=%g (%g,%g) t2=%g (%g,%g)\n",
                    __FUNCTION__, (int)index, pt, tt1, tx1, ty1, tt2, tx2, ty2);
            }
        }
    }
}

static void standardTestCases() {
    for (size_t index = firstQuadIntersectionTest; index < quadraticTests_count; ++index) {
        const Quadratic& quad1 = quadraticTests[index][0];
        const Quadratic& quad2 = quadraticTests[index][1];
        Quadratic reduce1, reduce2;
        int order1 = reduceOrder(quad1, reduce1, kReduceOrder_TreatAsFill);
        int order2 = reduceOrder(quad2, reduce2, kReduceOrder_TreatAsFill);
        if (order1 < 3) {
            printf("[%d] quad1 order=%d\n", (int) index, order1);
        }
        if (order2 < 3) {
            printf("[%d] quad2 order=%d\n", (int) index, order2);
        }
        if (order1 == 3 && order2 == 3) {
            Intersections intersections;
            intersect2(reduce1, reduce2, intersections);
            if (intersections.intersected()) {
                for (int pt = 0; pt < intersections.used(); ++pt) {
                    double tt1 = intersections.fT[0][pt];
                    double tx1, ty1;
                    xy_at_t(quad1, tt1, tx1, ty1);
                    double tt2 = intersections.fT[1][pt];
                    double tx2, ty2;
                    xy_at_t(quad2, tt2, tx2, ty2);
                    if (!approximately_equal(tx1, tx2)) {
                        printf("%s [%d,%d] x!= t1=%g (%g,%g) t2=%g (%g,%g)\n",
                            __FUNCTION__, (int)index, pt, tt1, tx1, ty1, tt2, tx2, ty2);
                    }
                    if (!approximately_equal(ty1, ty2)) {
                        printf("%s [%d,%d] y!= t1=%g (%g,%g) t2=%g (%g,%g)\n",
                            __FUNCTION__, (int)index, pt, tt1, tx1, ty1, tt2, tx2, ty2);
                    }
                }
            }
        }
    }
}

// this flavor centers potential intersections recursively. In contrast, '2' may inadvertently
// chase intersections near quadratic ends, requiring odd hacks to find them.
static bool intersect3(const Cubic& cubic1, double t1s, double t1e, const Cubic& cubic2,
        double t2s, double t2e, double precisionScale, Intersections& i) {
    i.upDepth();
    bool result = false;
    Cubic c1, c2;
    sub_divide(cubic1, t1s, t1e, c1);
    sub_divide(cubic2, t2s, t2e, c2);
    SkTDArray<double> ts1;
    // OPTIMIZE: if c1 == c2, call once (happens when detecting self-intersection)
    cubic_to_quadratics(c1, calcPrecision(c1) * precisionScale, ts1);
    SkTDArray<double> ts2;
    cubic_to_quadratics(c2, calcPrecision(c2) * precisionScale, ts2);
    double t1Start = t1s;
    int ts1Count = ts1.count();
    for (int i1 = 0; i1 <= ts1Count; ++i1) {
        const double tEnd1 = i1 < ts1Count ? ts1[i1] : 1;
        const double t1 = t1s + (t1e - t1s) * tEnd1;
        Quadratic s1;
        int o1 = quadPart(cubic1, t1Start, t1, s1);
        double t2Start = t2s;
        int ts2Count = ts2.count();
        for (int i2 = 0; i2 <= ts2Count; ++i2) {
            const double tEnd2 = i2 < ts2Count ? ts2[i2] : 1;
            const double t2 = t2s + (t2e - t2s) * tEnd2;
            if (cubic1 == cubic2 && t1Start >= t2Start) {
                t2Start = t2;
                continue;
            }
            Quadratic s2;
            int o2 = quadPart(cubic2, t2Start, t2, s2);
        #if ONE_OFF_DEBUG
            char tab[] = "                  ";
            if (tLimits1[0][0] >= t1Start && tLimits1[0][1] <= t1
                    && tLimits1[1][0] >= t2Start && tLimits1[1][1] <= t2) {
                Cubic cSub1, cSub2;
                sub_divide(cubic1, t1Start, t1, cSub1);
                sub_divide(cubic2, t2Start, t2, cSub2);
                SkDebugf("%.*s %s t1=(%1.9g,%1.9g) t2=(%1.9g,%1.9g)", i.depth()*2, tab, __FUNCTION__,
                        t1Start, t1, t2Start, t2);
                Intersections xlocals;
                intersectWithOrder(s1, o1, s2, o2, xlocals);
                SkDebugf(" xlocals.fUsed=%d\n", xlocals.used());
            }
        #endif
            Intersections locals;
            intersectWithOrder(s1, o1, s2, o2, locals);
            double coStart[2] = { -1 };
            _Point coPoint;
            int tCount = locals.used();
            for (int tIdx = 0; tIdx < tCount; ++tIdx) {
                double to1 = t1Start + (t1 - t1Start) * locals.fT[0][tIdx];
                double to2 = t2Start + (t2 - t2Start) * locals.fT[1][tIdx];
    // if the computed t is not sufficiently precise, iterate
                _Point p1 = xy_at_t(cubic1, to1);
                _Point p2 = xy_at_t(cubic2, to2);
                if (p1.approximatelyEqual(p2)) {
                    if (locals.fIsCoincident[0] & 1 << tIdx) {
                        if (coStart[0] < 0) {
                            coStart[0] = to1;
                            coStart[1] = to2;
                            coPoint = p1;
                        } else {
                            i.insertCoincidentPair(coStart[0], to1, coStart[1], to2, coPoint, p1);
                            coStart[0] = -1;
                        }
                        result = true;
                    } else if (cubic1 != cubic2 || !approximately_equal(to1, to2)) {
                        if (i.swapped()) { // FIXME: insert should respect swap
                            i.insert(to2, to1, p1);
                        } else {
                            i.insert(to1, to2, p1);
                        }
                        result = true;
                    }
                } else {
                    double offset = precisionScale / 16; // FIME: const is arbitrary -- test & refine
#if 1
                    double c1Bottom = tIdx == 0 ? 0 :
                            (t1Start + (t1 - t1Start) * locals.fT[0][tIdx - 1] + to1) / 2;
                    double c1Min = SkTMax(c1Bottom, to1 - offset);
                    double c1Top = tIdx == tCount - 1 ? 1 :
                            (t1Start + (t1 - t1Start) * locals.fT[0][tIdx + 1] + to1) / 2;
                    double c1Max = SkTMin(c1Top, to1 + offset);
                    double c2Min = SkTMax(0., to2 - offset);
                    double c2Max = SkTMin(1., to2 + offset);
                #if ONE_OFF_DEBUG
                    SkDebugf("%.*s %s 1 contains1=%d/%d contains2=%d/%d\n", i.depth()*2, tab, __FUNCTION__,
                            c1Min <= tLimits1[0][1] && tLimits1[0][0] <= c1Max
                         && c2Min <= tLimits1[1][1] && tLimits1[1][0] <= c2Max,
                            to1 - offset <= tLimits1[0][1] && tLimits1[0][0] <= to1 + offset
                         && to2 - offset <= tLimits1[1][1] && tLimits1[1][0] <= to2 + offset,
                            c1Min <= tLimits2[0][1] && tLimits2[0][0] <= c1Max
                         && c2Min <= tLimits2[1][1] && tLimits2[1][0] <= c2Max,
                            to1 - offset <= tLimits2[0][1] && tLimits2[0][0] <= to1 + offset
                         && to2 - offset <= tLimits2[1][1] && tLimits2[1][0] <= to2 + offset);
                    SkDebugf("%.*s %s 1 c1Bottom=%1.9g c1Top=%1.9g c2Bottom=%1.9g c2Top=%1.9g"
                            " 1-o=%1.9g 1+o=%1.9g 2-o=%1.9g 2+o=%1.9g offset=%1.9g\n",
                            i.depth()*2, tab, __FUNCTION__, c1Bottom, c1Top, 0., 1.,
//.........这里部分代码省略.........

// intersect the end of the cubic with the other. Try lines from the end to control and opposite
// end to determine range of t on opposite cubic.
static bool intersectEnd(const Cubic& cubic1, bool start, const Cubic& cubic2, const _Rect& bounds2,
        Intersections& i) {
 //   bool selfIntersect = cubic1 == cubic2;
    _Line line;
    int t1Index = start ? 0 : 3;
    line[0] = cubic1[t1Index];
    // don't bother if the two cubics are connnected
#if 0
    if (!selfIntersect && (line[0].approximatelyEqual(cubic2[0])
            || line[0].approximatelyEqual(cubic2[3]))) {
        return false;
    }
#endif
    bool result = false;
    SkTDArray<double> tVals; // OPTIMIZE: replace with hard-sized array
    for (int index = 0; index < 4; ++index) {
        if (index == t1Index) {
            continue;
        }
        _Vector dxy1 = cubic1[index] - line[0];
        dxy1 /= gPrecisionUnit;
        line[1] = line[0] + dxy1;
        _Rect lineBounds;
        lineBounds.setBounds(line);
        if (!bounds2.intersects(lineBounds)) {
            continue;
        }
        Intersections local;
        if (!intersect(cubic2, line, local)) {
            continue;
        }
        for (int idx2 = 0; idx2 < local.used(); ++idx2) {
            double foundT = local.fT[0][idx2];
            if (approximately_less_than_zero(foundT)
                    || approximately_greater_than_one(foundT)) {
                continue;
            }
            if (local.fPt[idx2].approximatelyEqual(line[0])) {
                if (i.swapped()) { // FIXME: insert should respect swap
                    i.insert(foundT, start ? 0 : 1, line[0]);
                } else {
                    i.insert(start ? 0 : 1, foundT, line[0]);
                }
                result = true;
            } else {
                *tVals.append() = local.fT[0][idx2];
            }
        }
    }
    if (tVals.count() == 0) {
        return result;
    }
    QSort<double>(tVals.begin(), tVals.end() - 1);
    double tMin1 = start ? 0 : 1 - LINE_FRACTION;
    double tMax1 = start ? LINE_FRACTION : 1;
    int tIdx = 0;
    do {
        int tLast = tIdx;
        while (tLast + 1 < tVals.count() && roughly_equal(tVals[tLast + 1], tVals[tIdx])) {
            ++tLast;
        }
        double tMin2 = SkTMax(tVals[tIdx] - LINE_FRACTION, 0.0);
        double tMax2 = SkTMin(tVals[tLast] + LINE_FRACTION, 1.0);
        int lastUsed = i.used();
        result |= intersect3(cubic1, tMin1, tMax1, cubic2, tMin2, tMax2, 1, i);
        if (lastUsed == i.used()) {
            tMin2 = SkTMax(tVals[tIdx] - (1.0 / gPrecisionUnit), 0.0);
            tMax2 = SkTMin(tVals[tLast] + (1.0 / gPrecisionUnit), 1.0);
            result |= intersect3(cubic1, tMin1, tMax1, cubic2, tMin2, tMax2, 1, i);
        }
        tIdx = tLast + 1;
    } while (tIdx < tVals.count());
    return result;
}

// this flavor approximates the cubics with quads to find the intersecting ts
// OPTIMIZE: if this strategy proves successful, the quad approximations, or the ts used
// to create the approximations, could be stored in the cubic segment
// FIXME: this strategy needs to intersect the convex hull on either end with the opposite to
// account for inset quadratics that cause the endpoint intersection to avoid detection
// the segments can be very short -- the length of the maximum quadratic error (precision)
// FIXME: this needs to recurse on itself, taking a range of T values and computing the new
// t range ala is linear inner. The range can be figured by taking the dx/dy and determining
// the fraction that matches the precision. That fraction is the change in t for the smaller cubic.
static bool intersect2(const Cubic& cubic1, double t1s, double t1e, const Cubic& cubic2,
        double t2s, double t2e, double precisionScale, Intersections& i) {
    Cubic c1, c2;
    sub_divide(cubic1, t1s, t1e, c1);
    sub_divide(cubic2, t2s, t2e, c2);
    SkTDArray<double> ts1;
    cubic_to_quadratics(c1, calcPrecision(c1) * precisionScale, ts1);
    SkTDArray<double> ts2;
    cubic_to_quadratics(c2, calcPrecision(c2) * precisionScale, ts2);
    double t1Start = t1s;
    int ts1Count = ts1.count();
    for (int i1 = 0; i1 <= ts1Count; ++i1) {
        const double tEnd1 = i1 < ts1Count ? ts1[i1] : 1;
        const double t1 = t1s + (t1e - t1s) * tEnd1;
        Cubic part1;
        sub_divide(cubic1, t1Start, t1, part1);
        Quadratic q1;
        demote_cubic_to_quad(part1, q1);
  //      start here;
        // should reduceOrder be looser in this use case if quartic is going to blow up on an
        // extremely shallow quadratic?
        Quadratic s1;
        int o1 = reduceOrder(q1, s1);
        double t2Start = t2s;
        int ts2Count = ts2.count();
        for (int i2 = 0; i2 <= ts2Count; ++i2) {
            const double tEnd2 = i2 < ts2Count ? ts2[i2] : 1;
            const double t2 = t2s + (t2e - t2s) * tEnd2;
            Cubic part2;
            sub_divide(cubic2, t2Start, t2, part2);
            Quadratic q2;
            demote_cubic_to_quad(part2, q2);
            Quadratic s2;
            double o2 = reduceOrder(q2, s2);
            Intersections locals;
            if (o1 == 3 && o2 == 3) {
                intersect2(q1, q2, locals);
            } else if (o1 <= 2 && o2 <= 2) {
                locals.fUsed = intersect((const _Line&) s1, (const _Line&) s2, locals.fT[0],
                        locals.fT[1]);
            } else if (o1 == 3 && o2 <= 2) {
                intersect(q1, (const _Line&) s2, locals);
            } else {
                SkASSERT(o1 <= 2 && o2 == 3);
                intersect(q2, (const _Line&) s1, locals);
                for (int s = 0; s < locals.fUsed; ++s) {
                    SkTSwap(locals.fT[0][s], locals.fT[1][s]);
                }
            }
            for (int tIdx = 0; tIdx < locals.used(); ++tIdx) {
                double to1 = t1Start + (t1 - t1Start) * locals.fT[0][tIdx];
                double to2 = t2Start + (t2 - t2Start) * locals.fT[1][tIdx];
    // if the computed t is not sufficiently precise, iterate
                _Point p1, p2;
                xy_at_t(cubic1, to1, p1.x, p1.y);
                xy_at_t(cubic2, to2, p2.x, p2.y);
                if (p1.approximatelyEqual(p2)) {
                    i.insert(i.swapped() ? to2 : to1, i.swapped() ? to1 : to2);
                } else {
                    double dt1, dt2;
                    computeDelta(cubic1, to1, (t1e - t1s), cubic2, to2, (t2e - t2s), dt1, dt2);
                    double scale = precisionScale;
                    if (dt1 > 0.125 || dt2 > 0.125) {
                        scale /= 2;
                        SkDebugf("%s scale=%1.9g\n", __FUNCTION__, scale);
                    }
#if SK_DEBUG
                    ++debugDepth;
                    assert(debugDepth < 10);
#endif
                    i.swap();
                    intersect2(cubic2, SkTMax(to2 - dt2, 0.), SkTMin(to2 + dt2, 1.),
                            cubic1, SkTMax(to1 - dt1, 0.), SkTMin(to1 + dt1, 1.), scale, i);
                    i.swap();
#if SK_DEBUG
                    --debugDepth;
#endif
                }
            }
            t2Start = t2;
        }
        t1Start = t1;
    }
    return i.intersected();
}