qpathclipper.cpp

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// Copyright (C) 2016 The Qt Company Ltd.
// SPDX-License-Identifier: LicenseRef-Qt-Commercial OR LGPL-3.0-only OR GPL-2.0-only OR GPL-3.0-only
 
#include "qpathclipper_p.h"
 
#include <private/qbezier_p.h>
#include <private/qdatabuffer_p.h>
#include <private/qnumeric_p.h>
#include <qmath.h>
#include <algorithm>
 
/**
  The algorithm is as follows:
 
  1. Find all intersections between the two paths (including self-intersections),
     and build a winged edge structure of non-intersecting parts.
  2. While there are more unhandled edges:
    3. Pick a y-coordinate from an unhandled edge.
    4. Intersect the horizontal line at y-coordinate with all edges.
    5. Traverse intersections left to right deciding whether each subpath should be added or not.
    6. If the subpath should be added, traverse the winged-edge structure and add the edges to
       a separate winged edge structure.
    7. Mark all edges in subpaths crossing the horizontal line as handled.
 8. (Optional) Simplify the resulting winged edge structure by merging shared edges.
 9. Convert the resulting winged edge structure to a painter path.
 */
 
#include <qdebug.h>
 
QT_BEGIN_NAMESPACE
 
static inline bool fuzzyIsNull(qreal d)
{
    if (sizeof(qreal) == sizeof(double))
        return qAbs(d) <= 1e-12;
    else
        return qAbs(d) <= 1e-5f;
}
 
static inline bool comparePoints(const QPointF &a, const QPointF &b)
{
    return fuzzyIsNull(a.x() - b.x())
           && fuzzyIsNull(a.y() - b.y());
}
 
//#define QDEBUG_CLIPPER
static qreal dot(const QPointF &a, const QPointF &b)
{
    return a.x() * b.x() + a.y() * b.y();
}
 
static void normalize(double &x, double &y)
{
    double reciprocal = 1 / qSqrt(x * x + y * y);
    x *= reciprocal;
    y *= reciprocal;
}
 
struct QIntersection
{
    qreal alphaA;
    qreal alphaB;
 
    QPointF pos;
};
Q_DECLARE_TYPEINFO(QIntersection, Q_PRIMITIVE_TYPE);
 
class QIntersectionFinder
{
public:
    void produceIntersections(QPathSegments &segments);
    bool hasIntersections(const QPathSegments &a, const QPathSegments &b) const;
 
private:
    bool linesIntersect(const QLineF &a, const QLineF &b) const;
};
 
bool QIntersectionFinder::linesIntersect(const QLineF &a, const QLineF &b) const
{
    const QPointF p1 = a.p1();
    const QPointF p2 = a.p2();
 
    const QPointF q1 = b.p1();
    const QPointF q2 = b.p2();
 
    if (comparePoints(p1, p2) || comparePoints(q1, q2))
        return false;
 
    const bool p1_equals_q1 = comparePoints(p1, q1);
    const bool p2_equals_q2 = comparePoints(p2, q2);
 
    if (p1_equals_q1 && p2_equals_q2)
        return true;
 
    const bool p1_equals_q2 = comparePoints(p1, q2);
    const bool p2_equals_q1 = comparePoints(p2, q1);
 
    if (p1_equals_q2 && p2_equals_q1)
        return true;
 
    const QPointF pDelta = p2 - p1;
    const QPointF qDelta = q2 - q1;
 
    const qreal par = pDelta.x() * qDelta.y() - pDelta.y() * qDelta.x();
 
    if (qFuzzyIsNull(par)) {
        const QPointF normal(-pDelta.y(), pDelta.x());
 
        // coinciding?
        if (qFuzzyIsNull(dot(normal, q1 - p1))) {
            const qreal dp = dot(pDelta, pDelta);
 
            const qreal tq1 = dot(pDelta, q1 - p1);
            const qreal tq2 = dot(pDelta, q2 - p1);
 
            if ((tq1 > 0 && tq1 < dp) || (tq2 > 0 && tq2 < dp))
                return true;
 
            const qreal dq = dot(qDelta, qDelta);
 
            const qreal tp1 = dot(qDelta, p1 - q1);
            const qreal tp2 = dot(qDelta, p2 - q1);
 
            if ((tp1 > 0 && tp1 < dq) || (tp2 > 0 && tp2 < dq))
                return true;
        }
 
        return false;
    }
 
    const qreal invPar = 1 / par;
 
    const qreal tp = (qDelta.y() * (q1.x() - p1.x()) -
                      qDelta.x() * (q1.y() - p1.y())) * invPar;
 
    if (tp < 0 || tp > 1)
        return false;
 
    const qreal tq = (pDelta.y() * (q1.x() - p1.x()) -
                      pDelta.x() * (q1.y() - p1.y())) * invPar;
 
    return tq >= 0 && tq <= 1;
}
 
bool QIntersectionFinder::hasIntersections(const QPathSegments &a, const QPathSegments &b) const
{
    if (a.segments() == 0 || b.segments() == 0)
        return false;
 
    const QRectF &rb0 = b.elementBounds(0);
 
    qreal minX = rb0.left();
    qreal minY = rb0.top();
    qreal maxX = rb0.right();
    qreal maxY = rb0.bottom();
 
    for (int i = 1; i < b.segments(); ++i) {
        const QRectF &r = b.elementBounds(i);
        minX = qMin(minX, r.left());
        minY = qMin(minY, r.top());
        maxX = qMax(maxX, r.right());
        maxY = qMax(maxY, r.bottom());
    }
 
    QRectF rb(minX, minY, maxX - minX, maxY - minY);
 
    for (int i = 0; i < a.segments(); ++i) {
        const QRectF &r1 = a.elementBounds(i);
 
        if (r1.left() > rb.right() || rb.left() > r1.right())
            continue;
        if (r1.top() > rb.bottom() || rb.top() > r1.bottom())
            continue;
 
        for (int j = 0; j < b.segments(); ++j) {
            const QRectF &r2 = b.elementBounds(j);
 
            if (r1.left() > r2.right() || r2.left() > r1.right())
                continue;
            if (r1.top() > r2.bottom() || r2.top() > r1.bottom())
                continue;
 
            if (linesIntersect(a.lineAt(i), b.lineAt(j)))
                return true;
        }
    }
 
    return false;
}
 
namespace {
struct TreeNode
{
    qreal splitLeft;
    qreal splitRight;
    bool leaf;
 
    int lowestLeftIndex;
    int lowestRightIndex;
 
    union {
        struct {
            int first;
            int last;
        } interval;
        struct {
            int left;
            int right;
        } children;
    } index;
};
 
struct RectF
{
    qreal x1;
    qreal y1;
    qreal x2;
    qreal y2;
};
 
class SegmentTree
{
public:
    SegmentTree(QPathSegments &segments);
 
    void produceIntersections(int segment);
 
private:
    TreeNode buildTree(int first, int last, int depth, const RectF &bounds);
 
    void produceIntersectionsLeaf(const TreeNode &node, int segment);
    void produceIntersections(const TreeNode &node, int segment, const RectF &segmentBounds, const RectF &nodeBounds, int axis);
    void intersectLines(const QLineF &a, const QLineF &b, QDataBuffer<QIntersection> &intersections);
 
    QPathSegments &m_segments;
    QList<int> m_index;
 
    RectF m_bounds;
 
    QList<TreeNode> m_tree;
    QDataBuffer<QIntersection> m_intersections;
};
 
SegmentTree::SegmentTree(QPathSegments &segments)
    : m_segments(segments),
      m_intersections(0)
{
    m_bounds.x1 = qt_inf();
    m_bounds.y1 = qt_inf();
    m_bounds.x2 = -qt_inf();
    m_bounds.y2 = -qt_inf();
 
    m_index.resize(m_segments.segments());
 
    for (int i = 0; i < m_index.size(); ++i) {
        m_index[i] = i;
 
        const QRectF &segmentBounds = m_segments.elementBounds(i);
 
        if (segmentBounds.left() < m_bounds.x1)
            m_bounds.x1 = segmentBounds.left();
        if (segmentBounds.top() < m_bounds.y1)
            m_bounds.y1 = segmentBounds.top();
        if (segmentBounds.right() > m_bounds.x2)
            m_bounds.x2 = segmentBounds.right();
        if (segmentBounds.bottom() > m_bounds.y2)
            m_bounds.y2 = segmentBounds.bottom();
    }
 
    m_tree.resize(1);
 
    TreeNode root = buildTree(0, m_index.size(), 0, m_bounds);
    m_tree[0] = root;
}
 
static inline qreal coordinate(const QPointF &pos, int axis)
{
    return axis == 0 ? pos.x() : pos.y();
}
 
TreeNode SegmentTree::buildTree(int first, int last, int depth, const RectF &bounds)
{
    if (depth >= 24 || (last - first) <= 10) {
        TreeNode node = {};
        node.leaf = true;
        node.index.interval.first = first;
        node.index.interval.last = last;
 
        return node;
    }
 
    int splitAxis = (depth & 1);
 
    TreeNode node;
    node.leaf = false;
 
    qreal split = 0.5f * ((&bounds.x1)[splitAxis] + (&bounds.x2)[splitAxis]);
 
    node.splitLeft = (&bounds.x1)[splitAxis];
    node.splitRight = (&bounds.x2)[splitAxis];
 
    node.lowestLeftIndex = INT_MAX;
    node.lowestRightIndex = INT_MAX;
 
    const int treeSize = m_tree.size();
 
    node.index.children.left = treeSize;
    node.index.children.right = treeSize + 1;
 
    m_tree.resize(treeSize + 2);
 
    int l = first;
    int r = last - 1;
 
    // partition into left and right sets
    while (l <= r) {
        const int index = m_index.at(l);
        const QRectF &segmentBounds = m_segments.elementBounds(index);
 
        qreal lowCoordinate = coordinate(segmentBounds.topLeft(), splitAxis);
 
        if (coordinate(segmentBounds.center(), splitAxis) < split) {
            qreal highCoordinate = coordinate(segmentBounds.bottomRight(), splitAxis);
            if (highCoordinate > node.splitLeft)
                node.splitLeft = highCoordinate;
            if (index < node.lowestLeftIndex)
                node.lowestLeftIndex = index;
            ++l;
        } else {
            if (lowCoordinate < node.splitRight)
                node.splitRight = lowCoordinate;
            if (index < node.lowestRightIndex)
                node.lowestRightIndex = index;
            qSwap(m_index[l], m_index[r]);
            --r;
        }
    }
 
    RectF lbounds = bounds;
    (&lbounds.x2)[splitAxis] = node.splitLeft;
 
    RectF rbounds = bounds;
    (&rbounds.x1)[splitAxis] = node.splitRight;
 
    TreeNode left = buildTree(first, l, depth + 1, lbounds);
    m_tree[node.index.children.left] = left;
 
    TreeNode right = buildTree(l, last, depth + 1, rbounds);
    m_tree[node.index.children.right] = right;
 
    return node;
}
 
void SegmentTree::intersectLines(const QLineF &a, const QLineF &b, QDataBuffer<QIntersection> &intersections)
{
    const QPointF p1 = a.p1();
    const QPointF p2 = a.p2();
 
    const QPointF q1 = b.p1();
    const QPointF q2 = b.p2();
 
    if (comparePoints(p1, p2) || comparePoints(q1, q2))
        return;
 
    const bool p1_equals_q1 = comparePoints(p1, q1);
    const bool p2_equals_q2 = comparePoints(p2, q2);
 
    if (p1_equals_q1 && p2_equals_q2)
        return;
 
    const bool p1_equals_q2 = comparePoints(p1, q2);
    const bool p2_equals_q1 = comparePoints(p2, q1);
 
    if (p1_equals_q2 && p2_equals_q1)
        return;
 
    const QPointF pDelta = p2 - p1;
    const QPointF qDelta = q2 - q1;
 
    const qreal par = pDelta.x() * qDelta.y() - pDelta.y() * qDelta.x();
 
    if (qFuzzyIsNull(par)) {
        const QPointF normal(-pDelta.y(), pDelta.x());
 
        // coinciding?
        if (qFuzzyIsNull(dot(normal, q1 - p1))) {
            const qreal invDp = 1 / dot(pDelta, pDelta);
 
            const qreal tq1 = dot(pDelta, q1 - p1) * invDp;
            const qreal tq2 = dot(pDelta, q2 - p1) * invDp;
 
            if (tq1 > 0 && tq1 < 1) {
                QIntersection intersection;
                intersection.alphaA = tq1;
                intersection.alphaB = 0;
                intersection.pos = q1;
                intersections.add(intersection);
            }
 
            if (tq2 > 0 && tq2 < 1) {
                QIntersection intersection;
                intersection.alphaA = tq2;
                intersection.alphaB = 1;
                intersection.pos = q2;
                intersections.add(intersection);
            }
 
            const qreal invDq = 1 / dot(qDelta, qDelta);
 
            const qreal tp1 = dot(qDelta, p1 - q1) * invDq;
            const qreal tp2 = dot(qDelta, p2 - q1) * invDq;
 
            if (tp1 > 0 && tp1 < 1) {
                QIntersection intersection;
                intersection.alphaA = 0;
                intersection.alphaB = tp1;
                intersection.pos = p1;
                intersections.add(intersection);
            }
 
            if (tp2 > 0 && tp2 < 1) {
                QIntersection intersection;
                intersection.alphaA = 1;
                intersection.alphaB = tp2;
                intersection.pos = p2;
                intersections.add(intersection);
            }
        }
 
        return;
    }
 
    // if the lines are not parallel and share a common end point, then they
    // don't intersect
    if (p1_equals_q1 || p1_equals_q2 || p2_equals_q1 || p2_equals_q2)
        return;
 
 
    const qreal tp = (qDelta.y() * (q1.x() - p1.x()) -
                      qDelta.x() * (q1.y() - p1.y())) / par;
    const qreal tq = (pDelta.y() * (q1.x() - p1.x()) -
                      pDelta.x() * (q1.y() - p1.y())) / par;
 
    if (tp<0 || tp>1 || tq<0 || tq>1)
        return;
 
    const bool p_zero = qFuzzyIsNull(tp);
    const bool p_one = qFuzzyIsNull(tp - 1);
 
    const bool q_zero = qFuzzyIsNull(tq);
    const bool q_one = qFuzzyIsNull(tq - 1);
 
    if ((q_zero || q_one) && (p_zero || p_one))
        return;
 
    QPointF pt;
    if (p_zero) {
        pt = p1;
    } else if (p_one) {
        pt = p2;
    } else if (q_zero) {
        pt = q1;
    } else if (q_one) {
        pt = q2;
    } else {
        pt = q1 + (q2 - q1) * tq;
    }
 
    QIntersection intersection;
    intersection.alphaA = tp;
    intersection.alphaB = tq;
    intersection.pos = pt;
    intersections.add(intersection);
}
 
void SegmentTree::produceIntersections(int segment)
{
    const QRectF &segmentBounds = m_segments.elementBounds(segment);
 
    RectF sbounds;
    sbounds.x1 = segmentBounds.left();
    sbounds.y1 = segmentBounds.top();
    sbounds.x2 = segmentBounds.right();
    sbounds.y2 = segmentBounds.bottom();
 
    produceIntersections(m_tree.at(0), segment, sbounds, m_bounds, 0);
}
 
void SegmentTree::produceIntersectionsLeaf(const TreeNode &node, int segment)
{
    const QRectF &r1 = m_segments.elementBounds(segment);
    const QLineF lineA = m_segments.lineAt(segment);
 
    for (int i = node.index.interval.first; i < node.index.interval.last; ++i) {
        const int other = m_index.at(i);
        if (other >= segment)
            continue;
 
        const QRectF &r2 = m_segments.elementBounds(other);
 
        if (r1.left() > r2.right() || r2.left() > r1.right())
            continue;
        if (r1.top() > r2.bottom() || r2.top() > r1.bottom())
            continue;
 
        m_intersections.reset();
 
        const QLineF lineB = m_segments.lineAt(other);
 
        intersectLines(lineA, lineB, m_intersections);
 
        for (int k = 0; k < m_intersections.size(); ++k) {
            QPathSegments::Intersection i_isect, j_isect;
            i_isect.t = m_intersections.at(k).alphaA;
            j_isect.t = m_intersections.at(k).alphaB;
 
            i_isect.vertex = j_isect.vertex = m_segments.addPoint(m_intersections.at(k).pos);
 
            i_isect.next = 0;
            j_isect.next = 0;
 
            m_segments.addIntersection(segment, i_isect);
            m_segments.addIntersection(other, j_isect);
        }
    }
}
 
void SegmentTree::produceIntersections(const TreeNode &node, int segment, const RectF &segmentBounds, const RectF &nodeBounds, int axis)
{
    if (node.leaf) {
        produceIntersectionsLeaf(node, segment);
        return;
    }
 
    RectF lbounds = nodeBounds;
    (&lbounds.x2)[axis] = node.splitLeft;
 
    RectF rbounds = nodeBounds;
    (&rbounds.x1)[axis] = node.splitRight;
 
    if (segment > node.lowestLeftIndex && (&segmentBounds.x1)[axis] <= node.splitLeft)
        produceIntersections(m_tree.at(node.index.children.left), segment, segmentBounds, lbounds, !axis);
 
    if (segment > node.lowestRightIndex && (&segmentBounds.x2)[axis] >= node.splitRight)
        produceIntersections(m_tree.at(node.index.children.right), segment, segmentBounds, rbounds, !axis);
}
 
}
 
void QIntersectionFinder::produceIntersections(QPathSegments &segments)
{
    SegmentTree tree(segments);
 
    for (int i = 0; i < segments.segments(); ++i)
        tree.produceIntersections(i);
}
 
class QKdPointTree
{
public:
    enum Traversal {
        TraverseBoth,
        TraverseLeft,
        TraverseRight,
        TraverseNone
    };
 
    struct Node {
        int point;
        int id;
 
        Node *left;
        Node *right;
    };
 
    QKdPointTree(const QPathSegments &segments)
        : m_segments(&segments)
        , m_nodes(m_segments->points())
        , m_id(0)
    {
        m_nodes.resize(m_segments->points());
 
        for (int i = 0; i < m_nodes.size(); ++i) {
            m_nodes.at(i).point = i;
            m_nodes.at(i).id = -1;
        }
 
        m_rootNode = build(0, m_nodes.size());
    }
 
    int build(int begin, int end, int depth = 0);
 
    Node *rootNode()
    {
        return &m_nodes.at(m_rootNode);
    }
 
    inline int nextId()
    {
        return m_id++;
    }
 
private:
    const QPathSegments *m_segments;
    QDataBuffer<Node> m_nodes;
 
    int m_rootNode;
    int m_id;
};
 
template <typename T>
void qTraverseKdPointTree(QKdPointTree::Node &node, T &t, int depth = 0)
{
    QKdPointTree::Traversal status = t(node, depth);
 
    const bool traverseRight = (status == QKdPointTree::TraverseBoth || status == QKdPointTree::TraverseRight);
    const bool traverseLeft = (status == QKdPointTree::TraverseBoth || status == QKdPointTree::TraverseLeft);
 
    if (traverseLeft && node.left)
        QT_PREPEND_NAMESPACE(qTraverseKdPointTree<T>)(*node.left, t, depth + 1);
 
    if (traverseRight && node.right)
        QT_PREPEND_NAMESPACE(qTraverseKdPointTree<T>)(*node.right, t, depth + 1);
}
 
static inline qreal component(const QPointF &point, unsigned int i)
{
    Q_ASSERT(i < 2);
    const qreal components[] = { point.x(), point.y() };
    return components[i];
}
 
int QKdPointTree::build(int begin, int end, int depth)
{
    Q_ASSERT(end > begin);
 
    const qreal pivot = component(m_segments->pointAt(m_nodes.at(begin).point), depth & 1);
 
    int first = begin + 1;
    int last = end - 1;
 
    while (first <= last) {
        const qreal value = component(m_segments->pointAt(m_nodes.at(first).point), depth & 1);
 
        if (value < pivot)
            ++first;
        else {
            qSwap(m_nodes.at(first), m_nodes.at(last));
            --last;
        }
    }
 
    if (last != begin)
        qSwap(m_nodes.at(last), m_nodes.at(begin));
 
    if (last > begin)
        m_nodes.at(last).left = &m_nodes.at(build(begin, last, depth + 1));
    else
        m_nodes.at(last).left = nullptr;
 
    if (last + 1 < end)
        m_nodes.at(last).right = &m_nodes.at(build(last + 1, end, depth + 1));
    else
        m_nodes.at(last).right = nullptr;
 
    return last;
}
 
class QKdPointFinder
{
public:
    QKdPointFinder(int point, const QPathSegments &segments, QKdPointTree &tree)
        : m_result(-1)
        , m_segments(&segments)
        , m_tree(&tree)
    {
        pointComponents[0] = segments.pointAt(point).x();
        pointComponents[1] = segments.pointAt(point).y();
    }
 
    inline QKdPointTree::Traversal operator()(QKdPointTree::Node &node, int depth)
    {
        if (m_result != -1)
            return QKdPointTree::TraverseNone;
 
        const QPointF &nodePoint = m_segments->pointAt(node.point);
 
        const qreal pivotComponents[] = { nodePoint.x(), nodePoint.y() };
 
        const qreal pivot = pivotComponents[depth & 1];
        const qreal value = pointComponents[depth & 1];
 
        if (fuzzyIsNull(pivot - value)) {
            const qreal pivot2 = pivotComponents[(depth + 1) & 1];
            const qreal value2 = pointComponents[(depth + 1) & 1];
 
            if (fuzzyIsNull(pivot2 - value2)) {
                if (node.id < 0)
                    node.id = m_tree->nextId();
 
                m_result = node.id;
                return QKdPointTree::TraverseNone;
            } else
                return QKdPointTree::TraverseBoth;
        } else if (value < pivot) {
            return QKdPointTree::TraverseLeft;
        } else {
            return QKdPointTree::TraverseRight;
        }
    }
 
    int result() const
    {
        return m_result;
    }
 
private:
    qreal pointComponents[2];
    int m_result;
    const QPathSegments *m_segments;
    QKdPointTree *m_tree;
};
 
// merge all points that are within qFuzzyCompare range of each other
void QPathSegments::mergePoints()
{
    QKdPointTree tree(*this);
 
    if (tree.rootNode()) {
        QDataBuffer<QPointF> mergedPoints(points());
        QDataBuffer<int> pointIndices(points());
 
        for (int i = 0; i < points(); ++i) {
            QKdPointFinder finder(i, *this, tree);
            QT_PREPEND_NAMESPACE(qTraverseKdPointTree<QKdPointFinder>)(*tree.rootNode(), finder);
 
            Q_ASSERT(finder.result() != -1);
 
            if (finder.result() >= mergedPoints.size())
                mergedPoints << m_points.at(i);
 
            pointIndices << finder.result();
        }
 
        for (int i = 0; i < m_segments.size(); ++i) {
            m_segments.at(i).va = pointIndices.at(m_segments.at(i).va);
            m_segments.at(i).vb = pointIndices.at(m_segments.at(i).vb);
        }
 
        for (int i = 0; i < m_intersections.size(); ++i)
            m_intersections.at(i).vertex = pointIndices.at(m_intersections.at(i).vertex);
 
        m_points.swap(mergedPoints);
    }
}
 
void QWingedEdge::intersectAndAdd()
{
    QIntersectionFinder finder;
    finder.produceIntersections(m_segments);
 
    m_segments.mergePoints();
 
    for (int i = 0; i < m_segments.points(); ++i)
        addVertex(m_segments.pointAt(i));
 
    QDataBuffer<QPathSegments::Intersection> intersections(m_segments.segments());
    for (int i = 0; i < m_segments.segments(); ++i) {
        intersections.reset();
 
        int pathId = m_segments.pathId(i);
 
        const QPathSegments::Intersection *isect = m_segments.intersectionAt(i);
        while (isect) {
            intersections << *isect;
 
            if (isect->next) {
                isect += isect->next;
            } else {
                isect = nullptr;
            }
        }
 
        std::sort(intersections.data(), intersections.data() + intersections.size());
 
        int first = m_segments.segmentAt(i).va;
        int second = m_segments.segmentAt(i).vb;
 
        int last = first;
        for (int j = 0; j < intersections.size(); ++j) {
            const QPathSegments::Intersection &isect = intersections.at(j);
 
            QPathEdge *ep = edge(addEdge(last, isect.vertex));
 
            if (ep) {
                const int dir = m_segments.pointAt(last).y() < m_segments.pointAt(isect.vertex).y() ? 1 : -1;
                if (pathId == 0)
                    ep->windingA += dir;
                else
                    ep->windingB += dir;
            }
 
            last = isect.vertex;
        }
 
        QPathEdge *ep = edge(addEdge(last, second));
 
        if (ep) {
            const int dir = m_segments.pointAt(last).y() < m_segments.pointAt(second).y() ? 1 : -1;
            if (pathId == 0)
                ep->windingA += dir;
            else
                ep->windingB += dir;
        }
    }
}
 
QWingedEdge::QWingedEdge() :
    m_edges(0),
    m_vertices(0),
    m_segments(0)
{
}
 
QWingedEdge::QWingedEdge(const QPainterPath &subject, const QPainterPath &clip) :
    m_edges(subject.elementCount()),
    m_vertices(subject.elementCount()),
    m_segments(subject.elementCount())
{
    m_segments.setPath(subject);
    m_segments.addPath(clip);
 
    intersectAndAdd();
}
 
QWingedEdge::TraversalStatus QWingedEdge::next(const QWingedEdge::TraversalStatus &status) const
{
    const QPathEdge *sp = edge(status.edge);
    Q_ASSERT(sp);
 
    TraversalStatus result;
    result.edge = sp->next(status.traversal, status.direction);
    result.traversal = status.traversal;
    result.direction = status.direction;
 
    const QPathEdge *rp = edge(result.edge);
    Q_ASSERT(rp);
 
    if (sp->vertex(status.direction) == rp->vertex(status.direction))
        result.flip();
 
    return result;
}
 
static bool isLine(const QBezier &bezier)
{
    const bool equal_1_2 = comparePoints(bezier.pt1(), bezier.pt2());
    const bool equal_2_3 = comparePoints(bezier.pt2(), bezier.pt3());
    const bool equal_3_4 = comparePoints(bezier.pt3(), bezier.pt4());
 
    // point?
    if (equal_1_2 && equal_2_3 && equal_3_4)
        return true;
 
    if (comparePoints(bezier.pt1(), bezier.pt4()))
        return equal_1_2 || equal_3_4;
 
    return (equal_1_2 && equal_3_4) || (equal_1_2 && equal_2_3) || (equal_2_3 && equal_3_4);
}
 
void QPathSegments::setPath(const QPainterPath &path)
{
    m_points.reset();
    m_intersections.reset();
    m_segments.reset();
 
    m_pathId = 0;
 
    addPath(path);
}
 
void QPathSegments::addPath(const QPainterPath &path)
{
    int firstSegment = m_segments.size();
 
    bool hasMoveTo = false;
    int lastMoveTo = 0;
    int last = 0;
    for (int i = 0; i < path.elementCount(); ++i) {
        int current = m_points.size();
 
        QPointF currentPoint;
        if (path.elementAt(i).type == QPainterPath::CurveToElement)
            currentPoint = path.elementAt(i+2);
        else
            currentPoint = path.elementAt(i);
 
        if (i > 0 && comparePoints(m_points.at(lastMoveTo), currentPoint))
            current = lastMoveTo;
        else
            m_points << currentPoint;
 
        switch (path.elementAt(i).type) {
        case QPainterPath::MoveToElement:
            if (hasMoveTo && last != lastMoveTo && !comparePoints(m_points.at(last), m_points.at(lastMoveTo)))
                m_segments << Segment(m_pathId, last, lastMoveTo);
            hasMoveTo = true;
            last = lastMoveTo = current;
            break;
        case QPainterPath::LineToElement:
            m_segments << Segment(m_pathId, last, current);
            last = current;
            break;
        case QPainterPath::CurveToElement:
            {
                QBezier bezier = QBezier::fromPoints(m_points.at(last), path.elementAt(i), path.elementAt(i+1), path.elementAt(i+2));
                if (isLine(bezier)) {
                    m_segments << Segment(m_pathId, last, current);
                } else {
                    QRectF bounds = bezier.bounds();
 
                    // threshold based on similar algorithm as in qtriangulatingstroker.cpp
                    int threshold = qMin<float>(64, qMax(bounds.width(), bounds.height()) * (2 * qreal(3.14) / 6));
 
                    if (threshold < 3) threshold = 3;
                    qreal one_over_threshold_minus_1 = qreal(1) / (threshold - 1);
 
                    for (int t = 1; t < threshold - 1; ++t) {
                        currentPoint = bezier.pointAt(t * one_over_threshold_minus_1);
 
                        int index = m_points.size();
                        m_segments << Segment(m_pathId, last, index);
                        last = index;
 
                        m_points << currentPoint;
                    }
 
                    m_segments << Segment(m_pathId, last, current);
                }
            }
            last = current;
            i += 2;
            break;
        default:
            Q_ASSERT(false);
            break;
        }
    }
 
    if (hasMoveTo && last != lastMoveTo && !comparePoints(m_points.at(last), m_points.at(lastMoveTo)))
        m_segments << Segment(m_pathId, last, lastMoveTo);
 
    for (int i = firstSegment; i < m_segments.size(); ++i) {
        const QLineF line = lineAt(i);
 
        qreal x1 = line.p1().x();
        qreal y1 = line.p1().y();
        qreal x2 = line.p2().x();
        qreal y2 = line.p2().y();
 
        if (x2 < x1)
            qSwap(x1, x2);
        if (y2 < y1)
            qSwap(y1, y2);
 
        m_segments.at(i).bounds = QRectF(x1, y1, x2 - x1, y2 - y1);
    }
 
    ++m_pathId;
}
 
qreal QWingedEdge::delta(int vertex, int a, int b) const
{
    const QPathEdge *ap = edge(a);
    const QPathEdge *bp = edge(b);
 
    double a_angle = ap->angle;
    double b_angle = bp->angle;
 
    if (vertex == ap->second)
        a_angle = ap->invAngle;
 
    if (vertex == bp->second)
        b_angle = bp->invAngle;
 
    double result = b_angle - a_angle;
 
    if (result >= 128.)
        return result - 128.;
    else if (result < 0)
        return result + 128.;
    else
        return result;
}
 
QWingedEdge::TraversalStatus QWingedEdge::findInsertStatus(int vi, int ei) const
{
    const QPathVertex *vp = vertex(vi);
 
    Q_ASSERT(vp);
    Q_ASSERT(ei >= 0);
    Q_ASSERT(vp->edge >= 0);
 
    int position = vp->edge;
    qreal d = 128.;
 
    TraversalStatus status;
    status.direction = edge(vp->edge)->directionTo(vi);
    status.traversal = QPathEdge::RightTraversal;
    status.edge = vp->edge;
 
#ifdef QDEBUG_CLIPPER
    const QPathEdge *ep = edge(ei);
    qDebug() << "Finding insert status for edge" << ei << "at vertex" << QPointF(*vp) << ", angles: " << ep->angle << ep->invAngle;
#endif
 
    do {
        status = next(status);
        status.flip();
 
        Q_ASSERT(edge(status.edge)->vertex(status.direction) == vi);
        qreal d2 = delta(vi, ei, status.edge);
 
#ifdef QDEBUG_CLIPPER
        const QPathEdge *op = edge(status.edge);
        qDebug() << "Delta to edge" << status.edge << d2 << ", angles: " << op->angle << op->invAngle;
#endif
 
        if (d2 < d) {
            position = status.edge;
            d = d2;
        }
    } while (status.edge != vp->edge);
 
    status.traversal = QPathEdge::LeftTraversal;
    status.direction = QPathEdge::Forward;
    status.edge = position;
 
    if (edge(status.edge)->vertex(status.direction) != vi)
        status.flip();
 
#ifdef QDEBUG_CLIPPER
    qDebug() << "Inserting edge" << ei << "to" << (status.traversal == QPathEdge::LeftTraversal ? "left" : "right") << "of edge" << status.edge;
#endif
 
    Q_ASSERT(edge(status.edge)->vertex(status.direction) == vi);
 
    return status;
}
 
void QWingedEdge::removeEdge(int ei)
{
    QPathEdge *ep = edge(ei);
 
    TraversalStatus status;
    status.direction = QPathEdge::Forward;
    status.traversal = QPathEdge::RightTraversal;
    status.edge = ei;
 
    TraversalStatus forwardRight = next(status);
    forwardRight.flipDirection();
 
    status.traversal = QPathEdge::LeftTraversal;
    TraversalStatus forwardLeft = next(status);
    forwardLeft.flipDirection();
 
    status.direction = QPathEdge::Backward;
    TraversalStatus backwardLeft = next(status);
    backwardLeft.flipDirection();
 
    status.traversal = QPathEdge::RightTraversal;
    TraversalStatus backwardRight = next(status);
    backwardRight.flipDirection();
 
    edge(forwardRight.edge)->setNext(forwardRight.traversal, forwardRight.direction, forwardLeft.edge);
    edge(forwardLeft.edge)->setNext(forwardLeft.traversal, forwardLeft.direction, forwardRight.edge);
 
    edge(backwardRight.edge)->setNext(backwardRight.traversal, backwardRight.direction, backwardLeft.edge);
    edge(backwardLeft.edge)->setNext(backwardLeft.traversal, backwardLeft.direction, backwardRight.edge);
 
    ep->setNext(QPathEdge::Forward, ei);
    ep->setNext(QPathEdge::Backward, ei);
 
    QPathVertex *a = vertex(ep->first);
    QPathVertex *b = vertex(ep->second);
 
    a->edge = backwardRight.edge;
    b->edge = forwardRight.edge;
}
 
static int commonEdge(const QWingedEdge &list, int a, int b)
{
    const QPathVertex *ap = list.vertex(a);
    Q_ASSERT(ap);
 
    const QPathVertex *bp = list.vertex(b);
    Q_ASSERT(bp);
 
    if (ap->edge < 0 || bp->edge < 0)
        return -1;
 
    QWingedEdge::TraversalStatus status;
    status.edge = ap->edge;
    status.direction = list.edge(status.edge)->directionTo(a);
    status.traversal = QPathEdge::RightTraversal;
 
    do {
        const QPathEdge *ep = list.edge(status.edge);
 
        if ((ep->first == a && ep->second == b)
            || (ep->first == b && ep->second == a))
            return status.edge;
 
        status = list.next(status);
        status.flip();
    } while (status.edge != ap->edge);
 
    return -1;
}
 
static double computeAngle(const QPointF &v)
{
#if 1
    if (v.x() == 0) {
        return v.y() <= 0 ? 0 : 64.;
    } else if (v.y() == 0) {
        return v.x() <= 0 ? 32. : 96.;
    }
 
    double vx = v.x();
    double vy = v.y();
    normalize(vx, vy);
    if (vy < 0) {
        if (vx < 0) { // 0 - 32
            return -32. * vx;
        } else { // 96 - 128
            return 128. - 32. * vx;
        }
    } else { // 32 - 96
        return 64. + 32. * vx;
    }
#else
    // doesn't seem to be robust enough
    return qAtan2(v.x(), v.y()) + Q_PI;
#endif
}
 
int QWingedEdge::addEdge(const QPointF &a, const QPointF &b)
{
    int fi = insert(a);
    int si = insert(b);
 
    return addEdge(fi, si);
}
 
int QWingedEdge::addEdge(int fi, int si)
{
    if (fi == si)
        return -1;
 
    int common = commonEdge(*this, fi, si);
    if (common >= 0)
        return common;
 
    m_edges << QPathEdge(fi, si);
 
    int ei = m_edges.size() - 1;
 
    QPathVertex *fp = vertex(fi);
    QPathVertex *sp = vertex(si);
 
    QPathEdge *ep = edge(ei);
 
    const QPointF tangent = QPointF(*sp) - QPointF(*fp);
    ep->angle = computeAngle(tangent);
    ep->invAngle = ep->angle + 64;
    if (ep->invAngle >= 128)
        ep->invAngle -= 128;
 
    QPathVertex *vertices[2] = { fp, sp };
    QPathEdge::Direction dirs[2] = { QPathEdge::Backward, QPathEdge::Forward };
 
#ifdef QDEBUG_CLIPPER
    printf("** Adding edge %d / vertices: %.07f %.07f, %.07f %.07f\n", ei, fp->x, fp->y, sp->x, sp->y);
#endif
 
    for (int i = 0; i < 2; ++i) {
        QPathVertex *vp = vertices[i];
        if (vp->edge < 0) {
            vp->edge = ei;
            ep->setNext(dirs[i], ei);
        } else {
            int vi = ep->vertex(dirs[i]);
            Q_ASSERT(vertex(vi) == vertices[i]);
 
            TraversalStatus os = findInsertStatus(vi, ei);
            QPathEdge *op = edge(os.edge);
 
            Q_ASSERT(vertex(op->vertex(os.direction)) == vertices[i]);
 
            TraversalStatus ns = next(os);
            ns.flipDirection();
            QPathEdge *np = edge(ns.edge);
 
            op->setNext(os.traversal, os.direction, ei);
            np->setNext(ns.traversal, ns.direction, ei);
 
            int oe = os.edge;
            int ne = ns.edge;
 
            os = next(os);
            ns = next(ns);
 
            os.flipDirection();
            ns.flipDirection();
 
            Q_ASSERT(os.edge == ei);
            Q_ASSERT(ns.edge == ei);
 
            ep->setNext(os.traversal, os.direction, oe);
            ep->setNext(ns.traversal, ns.direction, ne);
        }
    }
 
    Q_ASSERT(ep->next(QPathEdge::RightTraversal, QPathEdge::Forward) >= 0);
    Q_ASSERT(ep->next(QPathEdge::RightTraversal, QPathEdge::Backward) >= 0);
    Q_ASSERT(ep->next(QPathEdge::LeftTraversal, QPathEdge::Forward) >= 0);
    Q_ASSERT(ep->next(QPathEdge::LeftTraversal, QPathEdge::Backward) >= 0);
 
    return ei;
}
 
int QWingedEdge::insert(const QPathVertex &vertex)
{
    if (!m_vertices.isEmpty()) {
        const QPathVertex &last = m_vertices.last();
        if (vertex.x == last.x && vertex.y == last.y)
            return m_vertices.size() - 1;
 
        for (int i = 0; i < m_vertices.size(); ++i) {
            const QPathVertex &v = m_vertices.at(i);
            if (qFuzzyCompare(v.x, vertex.x) && qFuzzyCompare(v.y, vertex.y)) {
                return i;
            }
        }
    }
 
    m_vertices << vertex;
    return m_vertices.size() - 1;
}
 
static void addLineTo(QPainterPath &path, const QPointF &point)
{
    const int elementCount = path.elementCount();
    if (elementCount >= 2) {
        const QPainterPath::Element &middle = path.elementAt(elementCount - 1);
        if (middle.type == QPainterPath::LineToElement) {
            const QPointF first = path.elementAt(elementCount - 2);
            const QPointF d1 = point - first;
            const QPointF d2 = middle - first;
 
            const QPointF p(-d1.y(), d1.x());
 
            if (qFuzzyIsNull(dot(p, d2))) {
                path.setElementPositionAt(elementCount - 1, point.x(), point.y());
                return;
            }
        }
    }
 
    path.lineTo(point);
}
 
static void add(QPainterPath &path, const QWingedEdge &list, int edge, QPathEdge::Traversal traversal)
{
    QWingedEdge::TraversalStatus status;
    status.edge = edge;
    status.traversal = traversal;
    status.direction = QPathEdge::Forward;
 
    path.moveTo(*list.vertex(list.edge(edge)->first));
 
    do {
        const QPathEdge *ep = list.edge(status.edge);
 
        addLineTo(path, *list.vertex(ep->vertex(status.direction)));
 
        if (status.traversal == QPathEdge::LeftTraversal)
            ep->flag &= ~16;
        else
            ep->flag &= ~32;
 
        status = list.next(status);
    } while (status.edge != edge);
}
 
void QWingedEdge::simplify()
{
    for (int i = 0; i < edgeCount(); ++i) {
        const QPathEdge *ep = edge(i);
 
        // if both sides are part of the inside then we can collapse the edge
        int flag = 0x3 << 4;
        if ((ep->flag & flag) == flag) {
            removeEdge(i);
 
            ep->flag &= ~flag;
        }
    }
}
 
QPainterPath QWingedEdge::toPath() const
{
    QPainterPath path;
 
    for (int i = 0; i < edgeCount(); ++i) {
        const QPathEdge *ep = edge(i);
 
        if (ep->flag & 16) {
            add(path, *this, i, QPathEdge::LeftTraversal);
        }
 
        if (ep->flag & 32)
            add(path, *this, i, QPathEdge::RightTraversal);
    }
 
    return path;
}
 
bool QPathClipper::intersect()
{
    if (subjectPath == clipPath)
        return true;
 
    QRectF r1 = subjectPath.controlPointRect();
    QRectF r2 = clipPath.controlPointRect();
    if (qMax(r1.x(), r2.x()) > qMin(r1.x() + r1.width(), r2.x() + r2.width()) ||
        qMax(r1.y(), r2.y()) > qMin(r1.y() + r1.height(), r2.y() + r2.height())) {
        // no way we could intersect
        return false;
    }
 
    bool subjectIsRect = pathToRect(subjectPath);
    bool clipIsRect = pathToRect(clipPath);
 
    if (subjectIsRect && clipIsRect)
        return true;
    else if (subjectIsRect)
        return clipPath.intersects(r1);
    else if (clipIsRect)
        return subjectPath.intersects(r2);
 
    QPathSegments a(subjectPath.elementCount());
    a.setPath(subjectPath);
    QPathSegments b(clipPath.elementCount());
    b.setPath(clipPath);
 
    QIntersectionFinder finder;
    if (finder.hasIntersections(a, b))
        return true;
 
    for (int i = 0; i < clipPath.elementCount(); ++i) {
        if (clipPath.elementAt(i).type == QPainterPath::MoveToElement) {
            const QPointF point = clipPath.elementAt(i);
            if (r1.contains(point) && subjectPath.contains(point))
                return true;
        }
    }
 
    for (int i = 0; i < subjectPath.elementCount(); ++i) {
        if (subjectPath.elementAt(i).type == QPainterPath::MoveToElement) {
            const QPointF point = subjectPath.elementAt(i);
            if (r2.contains(point) && clipPath.contains(point))
                return true;
        }
    }
 
    return false;
}
 
bool QPathClipper::contains()
{
    if (subjectPath == clipPath)
        return false;
 
    QRectF r1 = subjectPath.controlPointRect();
    QRectF r2 = clipPath.controlPointRect();
    if (qMax(r1.x(), r2.x()) > qMin(r1.x() + r1.width(), r2.x() + r2.width()) ||
        qMax(r1.y(), r2.y()) > qMin(r1.y() + r1.height(), r2.y() + r2.height())) {
        // no intersection -> not contained
        return false;
    }
 
    bool clipIsRect = pathToRect(clipPath);
    if (clipIsRect)
        return subjectPath.contains(r2);
 
    QPathSegments a(subjectPath.elementCount());
    a.setPath(subjectPath);
    QPathSegments b(clipPath.elementCount());
    b.setPath(clipPath);
 
    QIntersectionFinder finder;
    if (finder.hasIntersections(a, b))
        return false;
 
    for (int i = 0; i < clipPath.elementCount(); ++i) {
        if (clipPath.elementAt(i).type == QPainterPath::MoveToElement) {
            const QPointF point = clipPath.elementAt(i);
            if (!r1.contains(point) || !subjectPath.contains(point))
                return false;
        }
    }
 
    return true;
}
 
QPathClipper::QPathClipper(const QPainterPath &subject,
                           const QPainterPath &clip)
    : subjectPath(subject)
    , clipPath(clip)
{
    aMask = subjectPath.fillRule() == Qt::WindingFill ? ~0x0 : 0x1;
    bMask = clipPath.fillRule() == Qt::WindingFill ? ~0x0 : 0x1;
}
 
static void clear(QWingedEdge& list, int edge, QPathEdge::Traversal traversal)
{
    QWingedEdge::TraversalStatus status;
    status.edge = edge;
    status.traversal = traversal;
    status.direction = QPathEdge::Forward;
 
    do {
        if (status.traversal == QPathEdge::LeftTraversal)
            list.edge(status.edge)->flag |= 1;
        else
            list.edge(status.edge)->flag |= 2;
 
        status = list.next(status);
    } while (status.edge != edge);
}
 
template <typename InputIterator>
InputIterator qFuzzyFind(InputIterator first, InputIterator last, qreal val)
{
    while (first != last && !QT_PREPEND_NAMESPACE(qFuzzyCompare)(qreal(*first), qreal(val)))
        ++first;
    return first;
}
 
static bool fuzzyCompare(qreal a, qreal b)
{
    return qFuzzyCompare(a, b);
}
 
bool QPathClipper::pathToRect(const QPainterPath &path, QRectF *rect)
{
    if (path.elementCount() != 5)
        return false;
 
    const bool mightBeRect = path.elementAt(0).isMoveTo()
        && path.elementAt(1).isLineTo()
        && path.elementAt(2).isLineTo()
        && path.elementAt(3).isLineTo()
        && path.elementAt(4).isLineTo();
 
    if (!mightBeRect)
        return false;
 
    const qreal x1 = path.elementAt(0).x;
    const qreal y1 = path.elementAt(0).y;
 
    const qreal x2 = path.elementAt(1).x;
    const qreal y2 = path.elementAt(2).y;
 
    if (path.elementAt(1).y != y1)
        return false;
 
    if (path.elementAt(2).x != x2)
        return false;
 
    if (path.elementAt(3).x != x1 || path.elementAt(3).y != y2)
        return false;
 
    if (path.elementAt(4).x != x1 || path.elementAt(4).y != y1)
        return false;
 
    if (rect)
        rect->setCoords(x1, y1, x2, y2);
 
    return true;
}
 
 
QPainterPath QPathClipper::clip(Operation operation)
{
    op = operation;
 
    if (op != Simplify) {
        if (subjectPath == clipPath)
            return op == BoolSub ? QPainterPath() : subjectPath;
 
        bool subjectIsRect = pathToRect(subjectPath, nullptr);
        bool clipIsRect = pathToRect(clipPath, nullptr);
 
        const QRectF clipBounds = clipPath.boundingRect();
        const QRectF subjectBounds = subjectPath.boundingRect();
 
        if (!clipBounds.intersects(subjectBounds)) {
            switch (op) {
            case BoolSub:
                return subjectPath;
            case BoolAnd:
                return QPainterPath();
            case BoolOr: {
                QPainterPath result = subjectPath;
                if (result.fillRule() == clipPath.fillRule()) {
                    result.addPath(clipPath);
                } else if (result.fillRule() == Qt::WindingFill) {
                    result = result.simplified();
                    result.addPath(clipPath);
                } else {
                    result.addPath(clipPath.simplified());
                }
                return result;
             }
            default:
                break;
            }
        }
 
        if (clipBounds.contains(subjectBounds)) {
            if (clipIsRect) {
                switch (op) {
                case BoolSub:
                    return QPainterPath();
                case BoolAnd:
                    return subjectPath;
                case BoolOr:
                    return clipPath;
                default:
                    break;
                }
            }
        } else if (subjectBounds.contains(clipBounds)) {
            if (subjectIsRect) {
                switch (op) {
                case BoolSub:
                    if (clipPath.fillRule() == Qt::OddEvenFill) {
                        QPainterPath result = clipPath;
                        result.addRect(subjectBounds);
                        return result;
                    } else {
                        QPainterPath result = clipPath.simplified();
                        result.addRect(subjectBounds);
                        return result;
                    }
                case BoolAnd:
                    return clipPath;
                case BoolOr:
                    return subjectPath;
                default:
                    break;
                }
            }
        }
 
        if (op == BoolAnd) {
            if (subjectIsRect)
                return intersect(clipPath, subjectBounds);
            else if (clipIsRect)
                return intersect(subjectPath, clipBounds);
        }
    }
 
    QWingedEdge list(subjectPath, clipPath);
 
    doClip(list, ClipMode);
 
    QPainterPath path = list.toPath();
    return path;
}
 
bool QPathClipper::doClip(QWingedEdge &list, ClipperMode mode)
{
    QList<qreal> y_coords;
    y_coords.reserve(list.vertexCount());
    for (int i = 0; i < list.vertexCount(); ++i)
        y_coords << list.vertex(i)->y;
 
    std::sort(y_coords.begin(), y_coords.end());
    y_coords.erase(std::unique(y_coords.begin(), y_coords.end(), fuzzyCompare), y_coords.end());
 
#ifdef QDEBUG_CLIPPER
    printf("sorted y coords:\n");
    for (int i = 0; i < y_coords.size(); ++i) {
        printf("%.9f\n", y_coords.at(i));
    }
#endif
 
    bool found;
    do {
        found = false;
        int index = 0;
        qreal maxHeight = 0;
        for (int i = 0; i < list.edgeCount(); ++i) {
            QPathEdge *edge = list.edge(i);
 
            // have both sides of this edge already been handled?
            if ((edge->flag & 0x3) == 0x3)
                continue;
 
            QPathVertex *a = list.vertex(edge->first);
            QPathVertex *b = list.vertex(edge->second);
 
            if (qFuzzyCompare(a->y, b->y))
                continue;
 
            found = true;
 
            qreal height = qAbs(a->y - b->y);
            if (height > maxHeight) {
                index = i;
                maxHeight = height;
            }
        }
 
        if (found) {
            QPathEdge *edge = list.edge(index);
 
            QPathVertex *a = list.vertex(edge->first);
            QPathVertex *b = list.vertex(edge->second);
 
            // FIXME: this can be optimized by using binary search
            const int first = qFuzzyFind(y_coords.cbegin(), y_coords.cend(), qMin(a->y, b->y)) - y_coords.cbegin();
            const int last = qFuzzyFind(y_coords.cbegin() + first, y_coords.cend(), qMax(a->y, b->y)) - y_coords.cbegin();
 
            Q_ASSERT(first < y_coords.size() - 1);
            Q_ASSERT(last < y_coords.size());
 
            qreal biggestGap = y_coords.at(first + 1) - y_coords.at(first);
            int bestIdx = first;
            for (int i = first + 1; i < last; ++i) {
                qreal gap = y_coords.at(i + 1) - y_coords.at(i);
 
                if (gap > biggestGap) {
                    bestIdx = i;
                    biggestGap = gap;
                }
            }
            const qreal bestY = 0.5 * (y_coords.at(bestIdx) + y_coords.at(bestIdx + 1));
 
#ifdef QDEBUG_CLIPPER
            printf("y: %.9f, gap: %.9f\n", bestY, biggestGap);
#endif
 
            if (handleCrossingEdges(list, bestY, mode) && mode == CheckMode)
                return true;
 
            edge->flag |= 0x3;
        }
    } while (found);
 
    if (mode == ClipMode)
        list.simplify();
 
    return false;
}
 
static void traverse(QWingedEdge &list, int edge, QPathEdge::Traversal traversal)
{
    QWingedEdge::TraversalStatus status;
    status.edge = edge;
    status.traversal = traversal;
    status.direction = QPathEdge::Forward;
 
    do {
        int flag = status.traversal == QPathEdge::LeftTraversal ? 1 : 2;
 
        QPathEdge *ep = list.edge(status.edge);
 
        ep->flag |= (flag | (flag << 4));
 
#ifdef QDEBUG_CLIPPER
        qDebug() << "traverse: adding edge " << status.edge << ", mask:" << (flag << 4) <<ep->flag;
#endif
 
        status = list.next(status);
    } while (status.edge != edge);
}
 
struct QCrossingEdge
{
    int edge;
    qreal x;
 
    bool operator<(const QCrossingEdge &edge) const
    {
        return x < edge.x;
    }
};
Q_DECLARE_TYPEINFO(QCrossingEdge, Q_PRIMITIVE_TYPE);
 
static bool bool_op(bool a, bool b, QPathClipper::Operation op)
{
    switch (op) {
    case QPathClipper::BoolAnd:
        return a && b;
    case QPathClipper::BoolOr:
    case QPathClipper::Simplify:
        return a || b;
    case QPathClipper::BoolSub:
        return a && !b;
    default:
        Q_ASSERT(false);
        return false;
    }
}
 
bool QWingedEdge::isInside(qreal x, qreal y) const
{
    int winding = 0;
    for (int i = 0; i < edgeCount(); ++i) {
        const QPathEdge *ep = edge(i);
 
        // left xor right
        int w = ((ep->flag >> 4) ^ (ep->flag >> 5)) & 1;
 
        if (!w)
            continue;
 
        QPointF a = *vertex(ep->first);
        QPointF b = *vertex(ep->second);
 
        if ((a.y() < y && b.y() > y) || (a.y() > y && b.y() < y)) {
            qreal intersectionX = a.x() + (b.x() - a.x()) * (y - a.y()) / (b.y() - a.y());
 
            if (intersectionX > x)
                winding += w;
        }
    }
 
    return winding & 1;
}
 
static QList<QCrossingEdge> findCrossings(const QWingedEdge &list, qreal y)
{
    QList<QCrossingEdge> crossings;
    for (int i = 0; i < list.edgeCount(); ++i) {
        const QPathEdge *edge = list.edge(i);
        QPointF a = *list.vertex(edge->first);
        QPointF b = *list.vertex(edge->second);
 
        if ((a.y() < y && b.y() > y) || (a.y() > y && b.y() < y)) {
            const qreal intersection = a.x() + (b.x() - a.x()) * (y - a.y()) / (b.y() - a.y());
            const QCrossingEdge edge = { i, intersection };
            crossings << edge;
        }
    }
    return crossings;
}
 
bool QPathClipper::handleCrossingEdges(QWingedEdge &list, qreal y, ClipperMode mode)
{
    QList<QCrossingEdge> crossings = findCrossings(list, y);
 
    Q_ASSERT(!crossings.isEmpty());
    std::sort(crossings.begin(), crossings.end());
 
    int windingA = 0;
    int windingB = 0;
 
    int windingD = 0;
 
#ifdef QDEBUG_CLIPPER
    qDebug() << "crossings:" << crossings.size();
#endif
    for (int i = 0; i < crossings.size() - 1; ++i) {
        int ei = crossings.at(i).edge;
        const QPathEdge *edge = list.edge(ei);
 
        windingA += edge->windingA;
        windingB += edge->windingB;
 
        const bool hasLeft = (edge->flag >> 4) & 1;
        const bool hasRight = (edge->flag >> 4) & 2;
 
        windingD += hasLeft ^ hasRight;
 
        const bool inA = (windingA & aMask) != 0;
        const bool inB = (windingB & bMask) != 0;
        const bool inD = (windingD & 0x1) != 0;
 
        const bool inside = bool_op(inA, inB, op);
        const bool add = inD ^ inside;
 
#ifdef QDEBUG_CLIPPER
        printf("y %f, x %f, inA: %d, inB: %d, inD: %d, inside: %d, flag: %x, bezier: %p, edge: %d\n", y, crossings.at(i).x, inA, inB, inD, inside, edge->flag, edge->bezier, ei);
#endif
 
        if (add) {
            if (mode == CheckMode)
                return true;
 
            qreal y0 = list.vertex(edge->first)->y;
            qreal y1 = list.vertex(edge->second)->y;
 
            if (y0 < y1) {
                if (!(edge->flag & 1))
                    traverse(list, ei, QPathEdge::LeftTraversal);
 
                if (!(edge->flag & 2))
                    clear(list, ei, QPathEdge::RightTraversal);
            } else {
                if (!(edge->flag & 1))
                    clear(list, ei, QPathEdge::LeftTraversal);
 
                if (!(edge->flag & 2))
                    traverse(list, ei, QPathEdge::RightTraversal);
            }
 
            ++windingD;
        } else {
            if (!(edge->flag & 1))
                clear(list, ei, QPathEdge::LeftTraversal);
 
            if (!(edge->flag & 2))
                clear(list, ei, QPathEdge::RightTraversal);
        }
    }
 
    return false;
}
 
namespace {
 
QList<QPainterPath> toSubpaths(const QPainterPath &path)
{
 
    QList<QPainterPath> subpaths;
    if (path.isEmpty())
        return subpaths;
 
    QPainterPath current;
    for (int i = 0; i < path.elementCount(); ++i) {
        const QPainterPath::Element &e = path.elementAt(i);
        switch (e.type) {
        case QPainterPath::MoveToElement:
            if (current.elementCount() > 1)
                subpaths += current;
            current = QPainterPath();
            current.moveTo(e);
            break;
        case QPainterPath::LineToElement:
            current.lineTo(e);
            break;
        case QPainterPath::CurveToElement: {
            current.cubicTo(e, path.elementAt(i + 1), path.elementAt(i + 2));
            i+=2;
            break;
        }
        case QPainterPath::CurveToDataElement:
            Q_ASSERT(!"toSubpaths(), bad element type");
            break;
        }
    }
 
    if (current.elementCount() > 1)
        subpaths << current;
 
    return subpaths;
}
 
enum Edge
{
    Left, Top, Right, Bottom
};
 
static bool isVertical(Edge edge)
{
    return edge == Left || edge == Right;
}
 
template <Edge edge>
bool compare(const QPointF &p, qreal t)
{
    switch (edge)
    {
    case Left:
        return p.x() < t;
    case Right:
        return p.x() > t;
    case Top:
        return p.y() < t;
    default:
        return p.y() > t;
    }
}
 
template <Edge edge>
QPointF intersectLine(const QPointF &a, const QPointF &b, qreal t)
{
    QLineF line(a, b);
    switch (edge) {
    case Left:
    case Right:
        return line.pointAt((t - a.x()) / (b.x() - a.x()));
    default:
        return line.pointAt((t - a.y()) / (b.y() - a.y()));
    }
}
 
void addLine(QPainterPath &path, const QLineF &line)
{
    if (path.elementCount() > 0)
        path.lineTo(line.p1());
    else
        path.moveTo(line.p1());
 
    path.lineTo(line.p2());
}
 
template <Edge edge>
void clipLine(const QPointF &a, const QPointF &b, qreal t, QPainterPath &result)
{
    bool outA = compare<edge>(a, t);
    bool outB = compare<edge>(b, t);
    if (outA && outB)
        return;
 
    if (outA)
        addLine(result, QLineF(intersectLine<edge>(a, b, t), b));
    else if (outB)
        addLine(result, QLineF(a, intersectLine<edge>(a, b, t)));
    else
        addLine(result, QLineF(a, b));
}
 
void addBezier(QPainterPath &path, const QBezier &bezier)
{
    if (path.elementCount() > 0)
        path.lineTo(bezier.pt1());
    else
        path.moveTo(bezier.pt1());
 
    path.cubicTo(bezier.pt2(), bezier.pt3(), bezier.pt4());
}
 
template <Edge edge>
void clipBezier(const QPointF &a, const QPointF &b, const QPointF &c, const QPointF &d, qreal t, QPainterPath &result)
{
    QBezier bezier = QBezier::fromPoints(a, b, c, d);
 
    bool outA = compare<edge>(a, t);
    bool outB = compare<edge>(b, t);
    bool outC = compare<edge>(c, t);
    bool outD = compare<edge>(d, t);
 
    int outCount = int(outA) + int(outB) + int(outC) + int(outD);
 
    if (outCount == 4)
        return;
 
    if (outCount == 0) {
        addBezier(result, bezier);
        return;
    }
 
    QTransform flip = isVertical(edge) ? QTransform(0, 1, 1, 0, 0, 0) : QTransform();
    QBezier unflipped = bezier;
    QBezier flipped = bezier.mapBy(flip);
 
    qreal t0 = 0, t1 = 1;
    int stationary = flipped.stationaryYPoints(t0, t1);
 
    qreal segments[4];
    QPointF points[4];
    points[0] = unflipped.pt1();
    segments[0] = 0;
 
    int segmentCount = 0;
    if (stationary > 0) {
        ++segmentCount;
        segments[segmentCount] = t0;
        points[segmentCount] = unflipped.pointAt(t0);
    }
    if (stationary > 1) {
        ++segmentCount;
        segments[segmentCount] = t1;
        points[segmentCount] = unflipped.pointAt(t1);
    }
    ++segmentCount;
    segments[segmentCount] = 1;
    points[segmentCount] = unflipped.pt4();
 
    qreal lastIntersection = 0;
    for (int i = 0; i < segmentCount; ++i) {
        outA = compare<edge>(points[i], t);
        outB = compare<edge>(points[i+1], t);
 
        if (outA != outB) {
            qreal intersection = flipped.tForY(segments[i], segments[i+1], t);
 
            if (outB)
                addBezier(result, unflipped.getSubRange(lastIntersection, intersection));
 
            lastIntersection = intersection;
        }
    }
 
    if (!outB)
        addBezier(result, unflipped.getSubRange(lastIntersection, 1));
}
 
// clips a single subpath against a single edge
template <Edge edge>
QPainterPath clip(const QPainterPath &path, qreal t)
{
    QPainterPath result;
    for (int i = 1; i < path.elementCount(); ++i) {
        const QPainterPath::Element &element = path.elementAt(i);
        Q_ASSERT(!element.isMoveTo());
        if (element.isLineTo()) {
            clipLine<edge>(path.elementAt(i-1), path.elementAt(i), t, result);
        } else {
            clipBezier<edge>(path.elementAt(i-1), path.elementAt(i), path.elementAt(i+1), path.elementAt(i+2), t, result);
            i += 2;
        }
    }
 
    int last = path.elementCount() - 1;
    if (QPointF(path.elementAt(last)) != QPointF(path.elementAt(0)))
        clipLine<edge>(path.elementAt(last), path.elementAt(0), t, result);
 
    return result;
}
 
QPainterPath intersectPath(const QPainterPath &path, const QRectF &rect)
{
    QList<QPainterPath> subpaths = toSubpaths(path);
 
    QPainterPath result;
    result.setFillRule(path.fillRule());
    for (int i = 0; i < subpaths.size(); ++i) {
        QPainterPath subPath = subpaths.at(i);
        QRectF bounds = subPath.boundingRect();
        if (bounds.intersects(rect)) {
            if (bounds.left() < rect.left())
                subPath = clip<Left>(subPath, rect.left());
            if (bounds.right() > rect.right())
                subPath = clip<Right>(subPath, rect.right());
 
            bounds = subPath.boundingRect();
 
            if (bounds.top() < rect.top())
                subPath = clip<Top>(subPath, rect.top());
            if (bounds.bottom() > rect.bottom())
                subPath = clip<Bottom>(subPath, rect.bottom());
 
            if (subPath.elementCount() > 1)
                result.addPath(subPath);
        }
    }
    // The algorithm above might return one side of \a rect if there was no intersection,
    // so only return intersections that are not empty rectangles.
    if (result.boundingRect().isEmpty())
        return QPainterPath();
    else
        return result;
}
 
}
 
QPainterPath QPathClipper::intersect(const QPainterPath &path, const QRectF &rect)
{
    return intersectPath(path, rect);
}
 
QT_END_NAMESPACE