C++ Intersections::insert方法代码示例

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();
}

void QTessellatorPrivate::addIntersection(const Edge *e1, const Edge *e2)
{
    const IntersectionLink emptyLink = {-1, -1};

    int next = vertices.nextPos(vertices[e1->edge]);
    if (e2->edge == next)
        return;
    int prev = vertices.prevPos(vertices[e1->edge]);
    if (e2->edge == prev)
        return;

    Q27Dot5 yi;
    bool det_positive;
    bool isect = e1->intersect(*e2, &yi, &det_positive);
    QDEBUG("checking edges %d and %d", e1->edge, e2->edge);
    if (!isect) {
        QDEBUG() << "    no intersection";
        return;
    }

    // don't emit an intersection if it's at the start of a line segment or above us
    if (yi <= y) {
        if (!det_positive)
            return;
        QDEBUG() << "        ----->>>>>> WRONG ORDER!";
        yi = y;
    }
    QDEBUG() << "   between edges " << e1->edge << "and" << e2->edge << "at point ("
             << Q27Dot5ToDouble(yi) << ')';

    Intersection i1;
    i1.y = yi;
    i1.edge = e1->edge;
    IntersectionLink link1 = intersections.value(i1, emptyLink);
    Intersection i2;
    i2.y = yi;
    i2.edge = e2->edge;
    IntersectionLink link2 = intersections.value(i2, emptyLink);

    // new pair of edges
    if (link1.next == -1 && link2.next == -1) {
        link1.next = link1.prev = i2.edge;
        link2.next = link2.prev = i1.edge;
    } else if (link1.next == i2.edge || link1.prev == i2.edge
               || link2.next == i1.edge || link2.prev == i1.edge) {
#ifdef DEBUG
        checkLinkChain(intersections, i1);
        checkLinkChain(intersections, i2);
        Q_ASSERT(edgeInChain(i1, i2.edge));
#endif
        return;
    } else if (link1.next == -1 || link2.next == -1) {
        if (link2.next == -1) {
            qSwap(i1, i2);
            qSwap(link1, link2);
        }
        Q_ASSERT(link1.next == -1);
#ifdef DEBUG
        checkLinkChain(intersections, i2);
#endif
        // only i2 in list
        link1.next = i2.edge;
        link1.prev = link2.prev;
        link2.prev = i1.edge;
        Intersection other;
        other.y = yi;
        other.edge = link1.prev;
        IntersectionLink link = intersections.value(other, emptyLink);
        Q_ASSERT(link.next == i2.edge);
        Q_ASSERT(link.prev != -1);
        link.next = i1.edge;
        intersections.insert(other, link);
    } else {
        bool connected = edgeInChain(i1, i2.edge);
        if (connected)
            return;
#ifdef DEBUG
        checkLinkChain(intersections, i1);
        checkLinkChain(intersections, i2);
#endif
        // both already in some list. Have to make sure they are connected
        // this can be done by cutting open the ring(s) after the two eges and
        // connecting them again
        Intersection other1;
        other1.y = yi;
        other1.edge = link1.next;
        IntersectionLink linko1 = intersections.value(other1, emptyLink);
        Intersection other2;
        other2.y = yi;
        other2.edge = link2.next;
        IntersectionLink linko2 = intersections.value(other2, emptyLink);

        linko1.prev = i2.edge;
        link2.next = other1.edge;

        linko2.prev = i1.edge;
        link1.next = other2.edge;
        intersections.insert(other1, linko1);
        intersections.insert(other2, linko2);
    }
//.........这里部分代码省略.........

static void hackToFixPartialCoincidence(const Quadratic& q1, const Quadratic& q2, Intersections& i) {
    // look to see if non-coincident data basically has unsortable tangents

    // look to see if a point between non-coincident data is on the curve
    int cIndex;
    for (int uIndex = 0; uIndex < i.fUsed; ) {
        double bestDist1 = 1;
        double bestDist2 = 1;
        int closest1 = -1;
        int closest2 = -1;
        for (cIndex = 0; cIndex < i.fCoincidentUsed; ++cIndex) {
            double dist = fabs(i.fT[0][uIndex] - i.fCoincidentT[0][cIndex]);
            if (bestDist1 > dist) {
                bestDist1 = dist;
                closest1 = cIndex;
            }
            dist = fabs(i.fT[1][uIndex] - i.fCoincidentT[1][cIndex]);
            if (bestDist2 > dist) {
                bestDist2 = dist;
                closest2 = cIndex;
            }
        }
        _Line ends;
        _Point mid;
        double t1 = i.fT[0][uIndex];
        xy_at_t(q1, t1, ends[0].x, ends[0].y);
        xy_at_t(q1, i.fCoincidentT[0][closest1], ends[1].x, ends[1].y);
        double midT = (t1 + i.fCoincidentT[0][closest1]) / 2;
        xy_at_t(q1, midT, mid.x, mid.y);
        LineParameters params;
        params.lineEndPoints(ends);
        double midDist = params.pointDistance(mid);
        // Note that we prefer to always measure t error, which does not scale,
        // instead of point error, which is scale dependent. FIXME
        if (!approximately_zero(midDist)) {
            ++uIndex;
            continue;
        }
        double t2 = i.fT[1][uIndex];
        xy_at_t(q2, t2, ends[0].x, ends[0].y);
        xy_at_t(q2, i.fCoincidentT[1][closest2], ends[1].x, ends[1].y);
        midT = (t2 + i.fCoincidentT[1][closest2]) / 2;
        xy_at_t(q2, midT, mid.x, mid.y);
        params.lineEndPoints(ends);
        midDist = params.pointDistance(mid);
        if (!approximately_zero(midDist)) {
            ++uIndex;
            continue;
        }
        // if both midpoints are close to the line, lengthen coincident span
        int cEnd = closest1 ^ 1; // assume coincidence always travels in pairs
        if (!between(i.fCoincidentT[0][cEnd], t1, i.fCoincidentT[0][closest1])) {
            i.fCoincidentT[0][closest1] = t1;
        }
        cEnd = closest2 ^ 1;
        if (!between(i.fCoincidentT[0][cEnd], t2, i.fCoincidentT[0][closest2])) {
            i.fCoincidentT[0][closest2] = t2;
        }
        int remaining = --i.fUsed - uIndex;
        if (remaining > 0) {
            memmove(&i.fT[0][uIndex], &i.fT[0][uIndex + 1], sizeof(i.fT[0][0]) * remaining);
            memmove(&i.fT[1][uIndex], &i.fT[1][uIndex + 1], sizeof(i.fT[1][0]) * remaining);
        }
    }
    // if coincident data is subjectively a tiny span, replace it with a single point
    for (cIndex = 0; cIndex < i.fCoincidentUsed; ) {
        double start1 = i.fCoincidentT[0][cIndex];
        double end1 = i.fCoincidentT[0][cIndex + 1];
        _Line ends1;
        xy_at_t(q1, start1, ends1[0].x, ends1[0].y);
        xy_at_t(q1, end1, ends1[1].x, ends1[1].y);
        if (!AlmostEqualUlps(ends1[0].x, ends1[1].x) || AlmostEqualUlps(ends1[0].y, ends1[1].y)) {
            cIndex += 2;
            continue;
        }
        double start2 = i.fCoincidentT[1][cIndex];
        double end2 = i.fCoincidentT[1][cIndex + 1];
        _Line ends2;
        xy_at_t(q2, start2, ends2[0].x, ends2[0].y);
        xy_at_t(q2, end2, ends2[1].x, ends2[1].y);
        // again, approximately should be used with T values, not points FIXME
        if (!AlmostEqualUlps(ends2[0].x, ends2[1].x) || AlmostEqualUlps(ends2[0].y, ends2[1].y)) {
            cIndex += 2;
            continue;
        }
        if (approximately_less_than_zero(start1) || approximately_less_than_zero(end1)) {
            start1 = 0;
        } else if (approximately_greater_than_one(start1) || approximately_greater_than_one(end1)) {
            start1 = 1;
        } else {
            start1 = (start1 + end1) / 2;
        }
        if (approximately_less_than_zero(start2) || approximately_less_than_zero(end2)) {
            start2 = 0;
        } else if (approximately_greater_than_one(start2) || approximately_greater_than_one(end2)) {
            start2 = 1;
        } else {
            start2 = (start2 + end2) / 2;
        }
        i.insert(start1, start2);
//.........这里部分代码省略.........

// 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();
}