C++ Intersections::intersected方法代码示例

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);
            }
        }
    }
}

bool intersect(const Cubic& cubic, Intersections& i) {
    SkTDArray<double> ts;
    double precision = calcPrecision(cubic);
    cubic_to_quadratics(cubic, precision, ts);
    int tsCount = ts.count();
    if (tsCount == 1) {
        return false;
    }
    double t1Start = 0;
    Cubic part;
    for (int idx = 0; idx < tsCount; ++idx) {
        double t1 = ts[idx];
        Quadratic q1;
        sub_divide(cubic, t1Start, t1, part);
        demote_cubic_to_quad(part, q1);
        double t2Start = t1;
        for (int i2 = idx + 1; i2 <= tsCount; ++i2) {
            const double t2 = i2 < tsCount ? ts[i2] : 1;
            Quadratic q2;
            sub_divide(cubic, t2Start, t2, part);
            demote_cubic_to_quad(part, q2);
            Intersections locals;
            intersect2(q1, q2, locals);
            for (int tIdx = 0; tIdx < locals.used(); ++tIdx) {
            // discard intersections at cusp? (maximum curvature)
                double t1sect = locals.fT[0][tIdx];
                double t2sect = locals.fT[1][tIdx];
                if (idx + 1 == i2 && t1sect == 1 && t2sect == 0) {
                    continue;
                }
                double to1 = t1Start + (t1 - t1Start) * t1sect;
                double to2 = t2Start + (t2 - t2Start) * t2sect;
                i.insert(to1, to2);
            }
            t2Start = t2;
        }
        t1Start = t1;
    }
    return i.intersected();
}

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 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();
}