Beispiel #1
0
bool intersect(const Quadratic& q1, const Quadratic& q2, Intersections& i) {
    if (implicit_matches(q1, q2)) {
        // FIXME: compute T values
        // compute the intersections of the ends to find the coincident span
        bool useVertical = fabs(q1[0].x - q1[2].x) < fabs(q1[0].y - q1[2].y);
        double t;
        if ((t = axialIntersect(q1, q2[0], useVertical)) >= 0) {
            i.addCoincident(t, 0);
        }
        if ((t = axialIntersect(q1, q2[2], useVertical)) >= 0) {
            i.addCoincident(t, 1);
        }
        useVertical = fabs(q2[0].x - q2[2].x) < fabs(q2[0].y - q2[2].y);
        if ((t = axialIntersect(q2, q1[0], useVertical)) >= 0) {
            i.addCoincident(0, t);
        }
        if ((t = axialIntersect(q2, q1[2], useVertical)) >= 0) {
            i.addCoincident(1, t);
        }
        assert(i.fCoincidentUsed <= 2);
        return i.fCoincidentUsed > 0;
    }
    QuadraticIntersections q(q1, q2, i);
    bool result = q.intersect();
    // FIXME: partial coincidence detection is currently poor. For now, try
    // to fix up the data after the fact. In the future, revisit the error
    // term to try to avoid this kind of result in the first place.
    if (i.fUsed && i.fCoincidentUsed) {
        hackToFixPartialCoincidence(q1, q2, i);
    }
    return result;
}
Beispiel #2
0
bool QTessellatorPrivate::edgeInChain(Intersection i, int edge)
{
    int end = i.edge;
    while (1) {
        if (i.edge == edge)
            return true;
        IntersectionLink l = intersections.value(i);
        if (l.next == end)
            break;
        Q_ASSERT(l.next != -1);
        Q_ASSERT(l.prev != -1);

        Intersection i2 = i;
        i2.edge = l.next;

#ifndef QT_NO_DEBUG
        IntersectionLink l2 = intersections.value(i2);
        Q_ASSERT(l2.next != -1);
        Q_ASSERT(l2.prev != -1);
        Q_ASSERT(l.next == i2.edge);
        Q_ASSERT(l2.prev == i.edge);
#endif
        i = i2;
    }
    return false;
}
Beispiel #3
0
void Scene::cut_segment_plane()
{
    // Build tree (if build fail, exit)
    build_facet_tree();
    if ( m_facet_tree.empty() ) {
        return;
    }

    Plane plane = frame_plane();

    // Compute intersections
    typedef std::vector<Facet_tree::Object_and_primitive_id> Intersections;
    Intersections intersections;
    m_facet_tree.all_intersections(plane, std::back_inserter(intersections));

    // Fill data structure
    m_cut_segments.clear();
    for ( Intersections::iterator it = intersections.begin(),
            end = intersections.end() ; it != end ; ++it )
    {
        const Segment* inter_seg = CGAL::object_cast<Segment>(&(it->first));

        if ( NULL != inter_seg )
        {
            m_cut_segments.push_back(*inter_seg);
        }
    }

    m_cut_plane = CUT_SEGMENTS;
}
Beispiel #4
0
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;
}
Beispiel #5
0
// This method performs intersection testing at the given XY coords, and returns true if
// any intersections were found. It will break after processing the first pickable Window
// it finds.
bool WindowManager::pickAtXY(float x, float y, WidgetList& wl)
{
    Intersections intr;


    osg::Camera* camera = _view->getCamera();
    osgViewer::GraphicsWindow* gw = dynamic_cast<osgViewer::GraphicsWindow*>(camera->getGraphicsContext());
    if (gw)
    {
        _view->computeIntersections(camera, osgUtil::Intersector::WINDOW, x, y, intr, _nodeMask);
    }

    if (!intr.empty())
    {
        // Get the first Window at the XY coordinates; if you want a Window to be
        // non-pickable, set the NodeMask to something else.
        Window* activeWin = 0;

        // Iterate over every picked result and create a list of Widgets that belong
        // to that Window.
        for(Intersections::iterator i = intr.begin(); i != intr.end(); i++) {
            Window* win = dynamic_cast<Window*>(i->nodePath.back()->getParent(0));

            // Make sure that our window is valid, and that our pick is within the
            // "visible area" of the Window.
            if(
                !win ||
                (win->getVisibilityMode() == Window::VM_PARTIAL && !win->isPointerXYWithinVisible(x, y))
            ) {
                continue;
            }

            // Set our activeWin, so that we know when we've got all the Widgets
            // that belong to it.
            if(!activeWin) activeWin = win;

            // If we've found a new Widnow, break out!
            else if(activeWin != win) break;

            Widget* widget = dynamic_cast<Widget*>(i->drawable.get());

            if(!widget) continue;

            // We need to return a list of every Widget that was picked, so
            // that the handler can operate on it accordingly.
            else wl.push_back(widget);
        }

        if(wl.size()) {
            // Potentially VERY expensive; only to be used for debugging. :)
            if(_flags & WM_PICK_DEBUG) _updatePickWindow(&wl, x, y);

            return true;
        }
    }

    if(_flags & WM_PICK_DEBUG) _updatePickWindow(0, x, y);

    return false;
}
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 Widget::computeIntersections(osgGA::EventVisitor* ev, osgGA::GUIEventAdapter* event, Intersections& intersections, osg::Node::NodeMask traversalMask) const
{
    osgGA::GUIActionAdapter* aa = ev ? ev->getActionAdapter() : 0;
    osgUtil::LineSegmentIntersector::Intersections source_intersections;
    if (aa && aa->computeIntersections(*event, ev->getNodePath(), source_intersections, traversalMask))
    {
        typedef std::vector<const osgUtil::LineSegmentIntersector::Intersection*> IntersectionPointerList;
        IntersectionPointerList intersectionsToSort;

        // populate the temporay vector of poiners to the original intersection pointers.
        for(osgUtil::LineSegmentIntersector::Intersections::iterator itr = source_intersections.begin();
            itr != source_intersections.end();
            ++itr)
        {
            if (itr->drawable->getName()!="DepthSetPanel")
            {
                intersectionsToSort.push_back(&(*itr));
            }
        }

        // sort the pointer list into order based on child traversal order, to be consistent with osgUI rendering order.
        std::sort(intersectionsToSort.begin(), intersectionsToSort.end(), SortTraversalOrder());

        // copy the pointers to final Intersection container
        for(IntersectionPointerList::iterator itr = intersectionsToSort.begin();
            itr != intersectionsToSort.end();
            ++itr)
        {
            intersections.push_back(*(*itr));
        }
        return true;
    }
    return false;
}
Beispiel #8
0
void QTessellatorPrivate::addIntersections()
{
    if (scanline.size) {
        QDEBUG() << "INTERSECTIONS";
        // check marked edges for intersections
#ifdef DEBUG
        for (int i = 0; i < scanline.size; ++i) {
            Edge *e = scanline.edges[i];
            QDEBUG() << "    " << i << e->edge << "isect=(" << e->intersect_left << e->intersect_right
                     << ')';
        }
#endif

        for (int i = 0; i < scanline.size - 1; ++i) {
            Edge *e1 = scanline.edges[i];
            Edge *e2 = scanline.edges[i + 1];
            // check for intersection
            if (e1->intersect_right || e2->intersect_left)
                addIntersection(e1, e2);
        }
    }
#if 0
    if (intersections.constBegin().key().y == y) {
        QDEBUG() << "----------------> intersection on same line";
        scanline.clearMarks();
        scanline.processIntersections(y, &intersections);
        goto redo;
    }
#endif
}
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;
}
Beispiel #10
0
// FIXME: add intersection of convex null on cubics' ends with the opposite cubic. The hull line
// segments can be constructed to be only as long as the calculated precision suggests. If the hull
// line segments intersect the cubic, then use the intersections to construct a subdivision for
// quadratic curve fitting.
bool intersect2(const Cubic& c1, const Cubic& c2, Intersections& i) {
#if SK_DEBUG
    debugDepth = 0;
#endif
    bool result = intersect2(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);
    i.swap();
    result |= intersectEnd(c2, false, c1, c1Bounds, i);
    result |= intersectEnd(c2, true, c1, c1Bounds, i);
    i.swap();
    return result;
}
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;
}
Beispiel #12
0
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);
            }
        }
    }
}
Beispiel #13
0
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);
                    }
                }
            }
        }
    }
}
Beispiel #15
0
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();
}
static void addValidRoots(const double roots[4], const int count, const int side, Intersections& i) {
    int index;
    for (index = 0; index < count; ++index) {
        if (!approximately_zero_or_more(roots[index]) || !approximately_one_or_less(roots[index])) {
            continue;
        }
        double t = 1 - roots[index];
        if (approximately_less_than_zero(t)) {
            t = 0;
        } else if (approximately_greater_than_one(t)) {
            t = 1;
        }
        i.insertOne(t, side);
    }
}
// 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 intersect(const Cubic& cubic, const Quadratic& quad, Intersections& i) {
    Cubic up;
    toCubic(quad, up);
    (void) intersect3(cubic, up, i);
    return i.used();
}
Beispiel #18
0
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);
        i.fCoincidentUsed -= 2;
        int remaining = i.fCoincidentUsed - cIndex;
        if (remaining > 0) {
            memmove(&i.fCoincidentT[0][cIndex], &i.fCoincidentT[0][cIndex + 2], sizeof(i.fCoincidentT[0][0]) * remaining);
            memmove(&i.fCoincidentT[1][cIndex], &i.fCoincidentT[1][cIndex + 2], sizeof(i.fCoincidentT[1][0]) * remaining);
        }
    }
}
// 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.,
                            to1 - offset, to1 + offset, to2 - offset, to2 + offset, offset);
                    SkDebugf("%.*s %s 1 to1=%1.9g to2=%1.9g c1Min=%1.9g c1Max=%1.9g c2Min=%1.9g"
                            " c2Max=%1.9g\n", i.depth()*2, tab, __FUNCTION__, to1, to2, c1Min, c1Max, c2Min, c2Max);
                #endif
                    intersect3(cubic1, c1Min, c1Max, cubic2, c2Min, c2Max, offset, i);
                #if ONE_OFF_DEBUG
                    SkDebugf("%.*s %s 1 i.used=%d t=%1.9g\n", i.depth()*2, tab, __FUNCTION__, i.used(),
                            i.used() > 0 ? i.fT[0][i.used() - 1] : -1);
                #endif
                    if (tCount > 1) {
                        c1Min = SkTMax(0., to1 - offset);
                        c1Max = SkTMin(1., to1 + offset);
                        double c2Bottom = tIdx == 0 ? to2 :
                                (t2Start + (t2 - t2Start) * locals.fT[1][tIdx - 1] + to2) / 2;
                        double c2Top = tIdx == tCount - 1 ? to2 :
                                (t2Start + (t2 - t2Start) * locals.fT[1][tIdx + 1] + to2) / 2;
                        if (c2Bottom > c2Top) {
                            SkTSwap(c2Bottom, c2Top);
                        }
                        if (c2Bottom == to2) {
                            c2Bottom = 0;
                        }
                        if (c2Top == to2) {
                            c2Top = 1;
                        }
                        c2Min = SkTMax(c2Bottom, to2 - offset);
                        c2Max = SkTMin(c2Top, to2 + offset);
                    #if ONE_OFF_DEBUG
                        SkDebugf("%.*s %s 2 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 2 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__, 0., 1., c2Bottom, c2Top,
                                to1 - offset, to1 + offset, to2 - offset, to2 + offset, offset);
                        SkDebugf("%.*s %s 2 to1=%1.9g to2=%1.9g c1Min=%1.9g c1Max=%1.9g c2Min=%1.9g"
                                " c2Max=%1.9g\n", i.depth()*2, tab, __FUNCTION__, to1, to2, c1Min, c1Max, c2Min, c2Max);
                    #endif
                        intersect3(cubic1, c1Min, c1Max, cubic2, c2Min, c2Max, offset, i);
                #if ONE_OFF_DEBUG
                    SkDebugf("%.*s %s 2 i.used=%d t=%1.9g\n", i.depth()*2, tab, __FUNCTION__, i.used(),
                            i.used() > 0 ? i.fT[0][i.used() - 1] : -1);
                #endif
                        c1Min = SkTMax(c1Bottom, to1 - offset);
                        c1Max = SkTMin(c1Top, to1 + offset);
                    #if ONE_OFF_DEBUG
                        SkDebugf("%.*s %s 3 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 3 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__, 0., 1., c2Bottom, c2Top,
                                to1 - offset, to1 + offset, to2 - offset, to2 + offset, offset);
                        SkDebugf("%.*s %s 3 to1=%1.9g to2=%1.9g c1Min=%1.9g c1Max=%1.9g c2Min=%1.9g"
                                " c2Max=%1.9g\n", i.depth()*2, tab, __FUNCTION__, to1, to2, c1Min, c1Max, c2Min, c2Max);
                    #endif
                        intersect3(cubic1, c1Min, c1Max, cubic2, c2Min, c2Max, offset, i);
                #if ONE_OFF_DEBUG
                    SkDebugf("%.*s %s 3 i.used=%d t=%1.9g\n", i.depth()*2, tab, __FUNCTION__, i.used(),
                            i.used() > 0 ? i.fT[0][i.used() - 1] : -1);
                #endif
                    }
#else
                    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 c2Bottom = tIdx == 0 ? to2 :
                            (t2Start + (t2 - t2Start) * locals.fT[1][tIdx - 1] + to2) / 2;
                    double c2Top = tIdx == tCount - 1 ? to2 :
                            (t2Start + (t2 - t2Start) * locals.fT[1][tIdx + 1] + to2) / 2;
                    if (c2Bottom > c2Top) {
                        SkTSwap(c2Bottom, c2Top);
                    }
                    if (c2Bottom == to2) {
                        c2Bottom = 0;
                    }
                    if (c2Top == to2) {
                        c2Top = 1;
                    }
                    double c2Min = SkTMax(c2Bottom, to2 - offset);
                    double c2Max = SkTMin(c2Top, to2 + offset);
                #if ONE_OFF_DEBUG
                    SkDebugf("%s contains1=%d/%d contains2=%d/%d\n", __FUNCTION__,
                            c1Min <= 0.210357794 && 0.210357794 <= c1Max
                         && c2Min <= 0.223476406 && 0.223476406 <= c2Max,
                            to1 - offset <= 0.210357794 && 0.210357794 <= to1 + offset
                         && to2 - offset <= 0.223476406 && 0.223476406 <= to2 + offset,
                            c1Min <= 0.211324707 && 0.211324707 <= c1Max
                         && c2Min <= 0.211327209 && 0.211327209 <= c2Max,
                            to1 - offset <= 0.211324707 && 0.211324707 <= to1 + offset
                         && to2 - offset <= 0.211327209 && 0.211327209 <= to2 + offset);
                    SkDebugf("%s 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",
                            __FUNCTION__, c1Bottom, c1Top, c2Bottom, c2Top,
                            to1 - offset, to1 + offset, to2 - offset, to2 + offset, offset);
                    SkDebugf("%s to1=%1.9g to2=%1.9g c1Min=%1.9g c1Max=%1.9g c2Min=%1.9g"
                            " c2Max=%1.9g\n", __FUNCTION__, to1, to2, c1Min, c1Max, c2Min, c2Max);
                #endif
#endif
                    intersect3(cubic1, c1Min, c1Max, cubic2, c2Min, c2Max, offset, i);
                    // TODO: if no intersection is found, either quadratics intersected where
                    // cubics did not, or the intersection was missed. In the former case, expect
                    // the quadratics to be nearly parallel at the point of intersection, and check
                    // for that.
                }
            }
            SkASSERT(coStart[0] == -1);
            t2Start = t2;
        }
        t1Start = t1;
    }
    i.downDepth();
    return result;
}
Beispiel #20
0
void QTessellatorPrivate::processIntersections()
{
    QDEBUG() << "PROCESS INTERSECTIONS";
    // process intersections
    while (!intersections.isEmpty()) {
        Intersections::iterator it = intersections.begin();
        if (it.key().y != y)
            break;

        // swap edges
        QDEBUG() << "    swapping intersecting edges ";
        int min = scanline.size;
        int max = 0;
        Q27Dot5 xmin = INT_MAX;
        Q27Dot5 xmax = INT_MIN;
        int num = 0;
        while (1) {
            const Intersection &i = it.key();
            int next = it->next;

            int edgePos = scanline.findEdge(i.edge);
            if (edgePos >= 0) {
                ++num;
                min = qMin(edgePos, min);
                max = qMax(edgePos, max);
                Edge *edge = scanline.edges[edgePos];
                xmin = qMin(xmin, edge->positionAt(y));
                xmax = qMax(xmax, edge->positionAt(y));
            }
            Intersection key;
            key.y = y;
            key.edge = next;
            it = intersections.find(key);
            intersections.remove(i);
            if (it == intersections.end())
                break;
        }
        if (num < 2)
            continue;

        Q_ASSERT(min != max);
        QDEBUG() << "sorting between" << min << "and" << max << "xpos=" << xmin << xmax;
        while (min > 0 && scanline.edges[min - 1]->positionAt(y) >= xmin) {
            QDEBUG() << "    adding edge on left";
            --min;
        }
        while (max + 1 < scanline.size && scanline.edges[max + 1]->positionAt(y) <=  xmax) {
            QDEBUG() << "    adding edge on right";
            ++max;
        }

        qSort(scanline.edges + min, scanline.edges + max + 1, EdgeSorter(y));
#ifdef DEBUG
        for (int i = min; i <= max; ++i)
            QDEBUG() << "        " << scanline.edges[i]->edge << "at pos" << i;
#endif
        for (int i = min; i <= max; ++i) {
            Edge *edge = scanline.edges[i];
            edge->intersect_left = true;
            edge->intersect_right = true;
            edge->mark = true;
        }
    }
}
// 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;
}
Beispiel #22
0
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);
    }
    intersections.insert(i1, link1);
    intersections.insert(i2, link2);
#ifdef DEBUG
    checkLinkChain(intersections, i1);
    checkLinkChain(intersections, i2);
    Q_ASSERT(edgeInChain(i1, i2.edge));
#endif
    return;

}
Beispiel #23
0
// 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();
}