Added QTriangulator.

Task-number: QT-2594

4 files changed, 3090 insertions, 2 deletions

diff --git a/src/gui/painting/qdatabuffer_p.h b/src/gui/painting/qdatabuffer_p.h
index efe238e..41203ed 100644
--- a/src/gui/painting/qdatabuffer_p.h
+++ b/src/gui/painting/qdatabuffer_p.h
@@ -81,7 +81,9 @@ public:
 
     inline Type &at(int i) { Q_ASSERT(i >= 0 && i < siz); return buffer[i]; }
     inline const Type &at(int i) const { Q_ASSERT(i >= 0 && i < siz); return buffer[i]; }
+    inline Type &last() { Q_ASSERT(!isEmpty()); return buffer[siz-1]; }
     inline const Type &last() const { Q_ASSERT(!isEmpty()); return buffer[siz-1]; }
+    inline Type &first() { Q_ASSERT(!isEmpty()); return buffer[0]; }
     inline const Type &first() const { Q_ASSERT(!isEmpty()); return buffer[0]; }
 
     inline void add(const Type &t) {
@@ -90,6 +92,11 @@ public:
         ++siz;
     }
 
+    inline void pop_back() {
+        Q_ASSERT(siz > 0);
+        --siz;
+    }
+
     inline void resize(int size) {
         reserve(size);
         siz = size;
diff --git a/src/opengl/gl2paintengineex/qtriangulator.cpp b/src/opengl/gl2paintengineex/qtriangulator.cpp
new file mode 100644
index 0000000..21d4b2e
--- /dev/null
+++ b/src/opengl/gl2paintengineex/qtriangulator.cpp
@@ -0,0 +1,2981 @@
+/****************************************************************************
+**
+** Copyright (C) 2009 Nokia Corporation and/or its subsidiary(-ies).
+** All rights reserved.
+** Contact: Nokia Corporation (qt-info@nokia.com)
+**
+** This file is part of the QtOpenGL module of the Qt Toolkit.
+**
+** $QT_BEGIN_LICENSE:LGPL$
+** No Commercial Usage
+** This file contains pre-release code and may not be distributed.
+** You may use this file in accordance with the terms and conditions
+** contained in the Technology Preview License Agreement accompanying
+** this package.
+**
+** GNU Lesser General Public License Usage
+** Alternatively, this file may be used under the terms of the GNU Lesser
+** General Public License version 2.1 as published by the Free Software
+** Foundation and appearing in the file LICENSE.LGPL included in the
+** packaging of this file.  Please review the following information to
+** ensure the GNU Lesser General Public License version 2.1 requirements
+** will be met: http://www.gnu.org/licenses/old-licenses/lgpl-2.1.html.
+**
+** In addition, as a special exception, Nokia gives you certain additional
+** rights.  These rights are described in the Nokia Qt LGPL Exception
+** version 1.1, included in the file LGPL_EXCEPTION.txt in this package.
+**
+** If you have questions regarding the use of this file, please contact
+** Nokia at qt-info@nokia.com.
+**
+**
+**
+**
+**
+**
+**
+**
+** $QT_END_LICENSE$
+**
+****************************************************************************/
+
+#include "qtriangulator_p.h"
+
+#include <QtGui/qdialog.h>
+#include <QtGui/qevent.h>
+#include <QtGui/qpainter.h>
+#include <QtGui/qpainterpath.h>
+#include <QtGui/private/qbezier_p.h>
+#include <QtGui/private/qdatabuffer_p.h>
+#include <QtCore/qbitarray.h>
+#include <QtCore/qvarlengtharray.h>
+#include <QtCore/qqueue.h>
+#include <QtCore/qglobal.h>
+#include <QtCore/qpoint.h>
+#include <QtCore/qalgorithms.h>
+#include <QtDebug>
+
+#include <math.h>
+
+QT_BEGIN_NAMESPACE
+
+//#define Q_TRIANGULATOR_DEBUG
+
+#define Q_FIXED_POINT_SCALE 32
+
+// Quick sort.
+template <class T, class LessThan>
+static void sort(T *array, int count, LessThan lessThan)
+{
+    // If the number of elements fall below some threshold, use insertion sort.
+    const int INSERTION_SORT_LIMIT = 7; // About 7 is fastest on my computer...
+    if (count <= INSERTION_SORT_LIMIT) {
+        for (int i = 1; i < count; ++i) {
+            T temp = array[i];
+            int j = i;
+            while (j > 0 && lessThan(temp, array[j - 1])) {
+                array[j] = array[j - 1];
+                --j;
+            }
+            array[j] = temp;
+        }
+        return;
+    }
+
+    int high = count - 1;
+    int low = 0;
+    int mid = high / 2;
+    if (lessThan(array[mid], array[low]))
+        qSwap(array[mid], array[low]);
+    if (lessThan(array[high], array[mid]))
+        qSwap(array[high], array[mid]);
+    if (lessThan(array[mid], array[low]))
+        qSwap(array[mid], array[low]);
+
+    --high;
+    ++low;
+    qSwap(array[mid], array[high]);
+    int pivot = high;
+    --high;
+
+    while (low <= high) {
+        while (!lessThan(array[pivot], array[low])) {
+            ++low;
+            if (low > high)
+                goto sort_loop_end;
+        }
+        while (!lessThan(array[high], array[pivot])) {
+            --high;
+            if (low > high)
+                goto sort_loop_end;
+        }
+        qSwap(array[low], array[high]);
+        ++low;
+        --high;
+    }
+sort_loop_end:
+    if (low != pivot)
+        qSwap(array[pivot], array[low]);
+    sort(array, low, lessThan);
+    sort(array + low + 1, count - low - 1, lessThan);
+}
+
+// Quick sort.
+template <class T>
+static void sort(T *array, int count)
+{
+    // If the number of elements fall below some threshold, use insertion sort.
+    const int INSERTION_SORT_LIMIT = 25; // About 25 is fastest on my computer...
+    if (count <= INSERTION_SORT_LIMIT) {
+        for (int i = 1; i < count; ++i) {
+            T temp = array[i];
+            int j = i;
+            while (j > 0 && (temp < array[j - 1])) {
+                array[j] = array[j - 1];
+                --j;
+            }
+            array[j] = temp;
+        }
+        return;
+    }
+
+    int high = count - 1;
+    int low = 0;
+    int mid = high / 2;
+    if ((array[mid] < array[low]))
+        qSwap(array[mid], array[low]);
+    if ((array[high] < array[mid]))
+        qSwap(array[high], array[mid]);
+    if ((array[mid] < array[low]))
+        qSwap(array[mid], array[low]);
+
+    --high;
+    ++low;
+    qSwap(array[mid], array[high]);
+    int pivot = high;
+    --high;
+
+    while (low <= high) {
+        while (!(array[pivot] < array[low])) {
+            ++low;
+            if (low > high)
+                goto sort_loop_end;
+        }
+        while (!(array[high] < array[pivot])) {
+            --high;
+            if (low > high)
+                goto sort_loop_end;
+        }
+        qSwap(array[low], array[high]);
+        ++low;
+        --high;
+    }
+sort_loop_end:
+    if (low != pivot)
+        qSwap(array[pivot], array[low]);
+    sort(array, low);
+    sort(array + low + 1, count - low - 1);
+}
+
+//============================================================================//
+//                                 QFraction                                  //
+//============================================================================//
+
+// Fraction must be in the range [0, 1)
+struct QFraction
+{
+    // Comparison operators must not be called on invalid fractions.
+    inline bool operator < (const QFraction &other) const;
+    inline bool operator == (const QFraction &other) const;
+    inline bool operator != (const QFraction &other) const {return !(*this == other);}
+    inline bool operator > (const QFraction &other) const {return other < *this;}
+    inline bool operator >= (const QFraction &other) const {return !(*this < other);}
+    inline bool operator <= (const QFraction &other) const {return !(*this > other);}
+
+    inline bool isValid() const {return denominator != 0;}
+
+    // numerator and denominator must not have common denominators.
+    quint64 numerator, denominator;
+};
+
+static inline quint64 gcd(quint64 x, quint64 y)
+{
+    while (y != 0) {
+        quint64 z = y;
+        y = x % y;
+        x = z;
+    }
+    return x;
+}
+
+static inline int compare(quint64 a, quint64 b)
+{
+    return (a > b) - (a < b);
+}
+
+// Compare a/b with c/d.
+// Return negative if less, 0 if equal, positive if greater.
+// a < b, c < d
+static int qCompareFractions(quint64 a, quint64 b, quint64 c, quint64 d)
+{
+    const quint64 LIMIT = Q_UINT64_C(0x100000000);
+    for (;;) {
+        // If the products 'ad' and 'bc' fit into 64 bits, they can be directly compared.
+        if (b < LIMIT && d < LIMIT)
+            return compare(a * d, b * c);
+
+        if (a == 0 || c == 0)
+            return compare(a, c);
+
+        // a/b < c/d  <=>  d/c < b/a
+        quint64 b_div_a = b / a;
+        quint64 d_div_c = d / c;
+        if (b_div_a != d_div_c)
+            return compare(d_div_c, b_div_a);
+
+        // floor(d/c) == floor(b/a)
+        // frac(d/c) < frac(b/a) ?
+        // frac(x/y) = (x%y)/y
+        d -= d_div_c * c; //d %= c;
+        b -= b_div_a * a; //b %= a;
+        qSwap(a, d);
+        qSwap(b, c);
+    }
+}
+
+// Fraction must be in the range [0, 1)
+// Assume input is valid.
+static QFraction qFraction(quint64 n, quint64 d) {
+    QFraction result;
+    if (n == 0) {
+        result.numerator = 0;
+        result.denominator = 1;
+    } else {
+        quint64 g = gcd(n, d);
+        result.numerator = n / g;
+        result.denominator = d / g;
+    }
+    return result;
+}
+
+inline bool QFraction::operator < (const QFraction &other) const
+{
+    return qCompareFractions(numerator, denominator, other.numerator, other.denominator) < 0;
+}
+
+inline bool QFraction::operator == (const QFraction &other) const
+{
+    return numerator == other.numerator && denominator == other.denominator;
+}
+
+//============================================================================//
+//                                 QPodPoint                                  //
+//============================================================================//
+
+struct QPodPoint
+{
+    inline bool operator < (const QPodPoint &other) const
+    {
+        if (y != other.y)
+            return y < other.y;
+        return x < other.x;
+    }
+
+    inline bool operator > (const QPodPoint &other) const {return other < *this;}
+    inline bool operator <= (const QPodPoint &other) const {return !(*this > other);}
+    inline bool operator >= (const QPodPoint &other) const {return !(*this < other);}
+    inline bool operator == (const QPodPoint &other) const {return x == other.x && y == other.y;}
+    inline bool operator != (const QPodPoint &other) const {return x != other.x || y != other.y;}
+
+    inline QPodPoint &operator += (const QPodPoint &other) {x += other.x; y += other.y; return *this;}
+    inline QPodPoint &operator -= (const QPodPoint &other) {x -= other.x; y -= other.y; return *this;}
+    inline QPodPoint operator + (const QPodPoint &other) const {QPodPoint result = {x + other.x, y + other.y}; return result;}
+    inline QPodPoint operator - (const QPodPoint &other) const {QPodPoint result = {x - other.x, y - other.y}; return result;}
+
+    int x;
+    int y;
+};
+
+static inline qint64 qCross(const QPodPoint &u, const QPodPoint &v)
+{
+    return qint64(u.x) * qint64(v.y) - qint64(u.y) * qint64(v.x);
+}
+
+static inline qint64 qDot(const QPodPoint &u, const QPodPoint &v)
+{
+    return qint64(u.x) * qint64(v.x) + qint64(u.y) * qint64(v.y);
+}
+
+// Return positive value if 'p' is to the right of the line 'v1'->'v2', negative if left of the
+// line and zero if exactly on the line.
+// The returned value is the z-component of the qCross product between 'v2-v1' and 'p-v1',
+// which is twice the signed area of the triangle 'p'->'v1'->'v2' (positive for CW order).
+static inline qint64 qPointDistanceFromLine(const QPodPoint &p, const QPodPoint &v1, const QPodPoint &v2)
+{
+    return qCross(v2 - v1, p - v1);
+}
+
+static inline bool qPointIsLeftOfLine(const QPodPoint &p, const QPodPoint &v1, const QPodPoint &v2)
+{
+    return qPointDistanceFromLine(p, v1, v2) < 0;
+}
+
+// Return:
+// -1 if u < v
+//  0 if u == v
+//  1 if u > v
+static int comparePoints(const QPodPoint &u, const QPodPoint &v)
+{
+    if (u.y < v.y)
+        return -1;
+    if (u.y > v.y)
+        return 1;
+    if (u.x < v.x)
+        return -1;
+    if (u.x > v.x)
+        return 1;
+    return 0;
+}
+
+//============================================================================//
+//                             QIntersectionPoint                             //
+//============================================================================//
+
+struct QIntersectionPoint
+{
+    inline bool isValid() const {return xOffset.isValid() && yOffset.isValid();}
+    QPodPoint round() const;
+    inline bool isAccurate() const {return xOffset.numerator == 0 && yOffset.numerator == 0;}
+    bool operator < (const QIntersectionPoint &other) const;
+    bool operator == (const QIntersectionPoint &other) const;
+    inline bool operator != (const QIntersectionPoint &other) const {return !(*this == other);}
+    inline bool operator > (const QIntersectionPoint &other) const {return other < *this;}
+    inline bool operator >= (const QIntersectionPoint &other) const {return !(*this < other);}
+    inline bool operator <= (const QIntersectionPoint &other) const {return !(*this > other);}
+    bool isOnLine(const QPodPoint &u, const QPodPoint &v) const;
+
+    QPodPoint upperLeft;
+    QFraction xOffset;
+    QFraction yOffset;
+};
+
+static inline QIntersectionPoint qIntersectionPoint(const QPodPoint &point)
+{
+    // m_upperLeft = point, m_xOffset = 0/1, m_yOffset = 0/1.
+    QIntersectionPoint p = {point, {0, 1}, {0, 1}};
+    return p;
+}
+
+static inline QIntersectionPoint qIntersectionPoint(int x, int y)
+{
+    // m_upperLeft = (x, y), m_xOffset = 0/1, m_yOffset = 0/1.
+    QIntersectionPoint p = {{x, y}, {0, 1}, {0, 1}};
+    return p;
+}
+
+static QIntersectionPoint qIntersectionPoint(const QPodPoint &u1, const QPodPoint &u2, const QPodPoint &v1, const QPodPoint &v2)
+{
+    QIntersectionPoint result = {{0, 0}, {0, 0}, {0, 0}};
+
+    QPodPoint u = u2 - u1;
+    QPodPoint v = v2 - v1;
+    qint64 d1 = qCross(u, v1 - u1);
+    qint64 d2 = qCross(u, v2 - u1);
+    qint64 det = d2 - d1;
+    qint64 d3 = qCross(v, u1 - v1);
+    qint64 d4 = d3 - det; //qCross(v, u2 - v1);
+
+    // Check that the math is correct.
+    Q_ASSERT(d4 == qCross(v, u2 - v1));
+
+    // The intersection point can be expressed as:
+    // v1 - v * d1/det
+    // v2 - v * d2/det
+    // u1 + u * d3/det
+    // u2 + u * d4/det
+
+    // I'm only interested in lines that are crossing, so ignore parallel lines even if they overlap.
+    if (det == 0)
+        return result;
+
+    if (det < 0) {
+        det = -det;
+        d1 = -d1;
+        d2 = -d2;
+        d3 = -d3;
+        d4 = -d4;
+    }
+
+    // I'm only interested in lines intersecting at their interior, not at their end points.
+    // The lines intersect at their interior if and only if 'd1 < 0', 'd2 > 0', 'd3 < 0' and 'd4 > 0'.
+    if (d1 >= 0 || d2 <= 0 || d3 <= 0 || d4 >= 0)
+        return result;
+
+    // Calculate the intersection point as follows:
+    // v1 - v * d1/det | v1 <= v2 (component-wise)
+    // v2 - v * d2/det | v2 < v1 (component-wise)
+
+    // Assuming 21 bits per vector component.
+    // TODO: Make code path for 31 bits per vector component.
+    if (v.x >= 0) {
+        result.upperLeft.x = v1.x + (-v.x * d1) / det;
+        result.xOffset = qFraction(quint64(-v.x * d1) % quint64(det), quint64(det));
+    } else {
+        result.upperLeft.x = v2.x + (-v.x * d2) / det;
+        result.xOffset = qFraction(quint64(-v.x * d2) % quint64(det), quint64(det));
+    }
+
+    if (v.y >= 0) {
+        result.upperLeft.y = v1.y + (-v.y * d1) / det;
+        result.yOffset = qFraction(quint64(-v.y * d1) % quint64(det), quint64(det));
+    } else {
+        result.upperLeft.y = v2.y + (-v.y * d2) / det;
+        result.yOffset = qFraction(quint64(-v.y * d2) % quint64(det), quint64(det));
+    }
+
+    Q_ASSERT(result.xOffset.isValid());
+    Q_ASSERT(result.yOffset.isValid());
+    return result;
+}
+
+QPodPoint QIntersectionPoint::round() const
+{
+    QPodPoint result = upperLeft;
+    if (2 * xOffset.numerator >= xOffset.denominator)
+        ++result.x;
+    if (2 * yOffset.numerator >= yOffset.denominator)
+        ++result.y;
+    return result;
+}
+
+bool QIntersectionPoint::operator < (const QIntersectionPoint &other) const
+{
+    if (upperLeft.y != other.upperLeft.y)
+        return upperLeft.y < other.upperLeft.y;
+    if (yOffset != other.yOffset)
+        return yOffset < other.yOffset;
+    if (upperLeft.x != other.upperLeft.x)
+        return upperLeft.x < other.upperLeft.x;
+    return xOffset < other.xOffset;
+}
+
+bool QIntersectionPoint::operator == (const QIntersectionPoint &other) const
+{
+    return upperLeft == other.upperLeft && xOffset == other.xOffset && yOffset == other.yOffset;
+}
+
+// Returns true if this point is on the infinite line passing through 'u' and 'v'.
+bool QIntersectionPoint::isOnLine(const QPodPoint &u, const QPodPoint &v) const
+{
+    // TODO: Make code path for coordinates with more than 21 bits.
+    const QPodPoint p = upperLeft - u;
+    const QPodPoint q = v - u;
+    bool isHorizontal = p.y == 0 && yOffset.numerator == 0;
+    bool isVertical = p.x == 0 && xOffset.numerator == 0;
+    if (isHorizontal && isVertical)
+        return true;
+    if (isHorizontal)
+        return q.y == 0;
+    if (q.y == 0)
+        return false;
+    if (isVertical)
+        return q.x == 0;
+    if (q.x == 0)
+        return false;
+
+    // At this point, 'p+offset' and 'q' cannot lie on the x or y axis.
+
+    if (((q.x < 0) == (q.y < 0)) != ((p.x < 0) == (p.y < 0)))
+        return false; // 'p + offset' and 'q' pass through different quadrants.
+    
+    // Move all coordinates into the first quadrant.
+    quint64 nx, ny;
+    if (p.x < 0)
+        nx = quint64(-p.x) * xOffset.denominator - xOffset.numerator;
+    else
+        nx = quint64(p.x) * xOffset.denominator + xOffset.numerator;
+    if (p.y < 0)
+        ny = quint64(-p.y) * yOffset.denominator - yOffset.numerator;
+    else
+        ny = quint64(p.y) * yOffset.denominator + yOffset.numerator;
+
+    return qFraction(quint64(qAbs(q.x)) * xOffset.denominator, quint64(qAbs(q.y)) * yOffset.denominator) == qFraction(nx, ny);
+}
+
+//============================================================================//
+//                                  QMaxHeap                                  //
+//============================================================================//
+
+template <class T>
+class QMaxHeap
+{
+public:
+    inline int size() const {return m_data.size();}
+    inline bool empty() const {return m_data.isEmpty();}
+    inline bool isEmpty() const {return m_data.isEmpty();}
+    void push(const T &x);
+    T pop();
+    inline const T &top() const {return m_data.first();}
+private:
+    static inline int parent(int i) {return (i - 1) / 2;}
+    static inline int left(int i) {return 2 * i + 1;}
+    static inline int right(int i) {return 2 * i + 2;}
+
+    QDataBuffer<T> m_data;
+};
+
+template <class T>
+void QMaxHeap<T>::push(const T &x)
+{
+    int current = m_data.size();
+    int parent = QMaxHeap::parent(current);
+    m_data.add(x);
+    while (current != 0 && m_data.at(parent) < x) {
+        m_data.at(current) = m_data.at(parent);
+        current = parent;
+        parent = QMaxHeap::parent(current);
+    }
+    m_data.at(current) = x;
+}
+
+template <class T>
+T QMaxHeap<T>::pop()
+{
+    T result = m_data.first();
+    T back = m_data.last();
+    m_data.pop_back();
+    if (!m_data.isEmpty()) {
+        int current = 0;
+        for (;;) {
+            int left = QMaxHeap::left(current);
+            int right = QMaxHeap::right(current);
+            if (left >= m_data.size())
+                break;
+            int greater = left;
+            if (right < m_data.size() && m_data.at(left) < m_data.at(right))
+                greater = right;
+            if (m_data.at(greater) < back)
+                break;
+            m_data.at(current) = m_data.at(greater);
+            current = greater;
+        }
+        m_data.at(current) = back;
+    }
+    return result;
+}
+
+//============================================================================//
+//                                  QRBTree                                   //
+//============================================================================//
+
+template <class T>
+struct QRBTree
+{
+    struct Node
+    {
+        inline Node() : parent(0), left(0), right(0), red(true) { }
+        inline ~Node() {if (left) delete left; if (right) delete right;}
+        T data;
+        Node *parent;
+        Node *left;
+        Node *right;
+        bool red;
+    };
+
+    inline QRBTree() : root(0), freeList(0) { }
+    inline ~QRBTree();
+
+    inline void clear();
+
+    void attachBefore(Node *parent, Node *child);
+    void attachAfter(Node *parent, Node *child);
+
+    inline Node *front(Node *node) const;
+    inline Node *back(Node *node) const;
+    Node *next(Node *node) const;
+    Node *previous(Node *node) const;
+
+    inline void deleteNode(Node *&node);
+    inline Node *newNode();
+
+    // Return 1 if 'left' comes after 'right', 0 if equal, and -1 otherwise.
+    // 'left' and 'right' cannot be null.
+    int order(Node *left, Node *right);
+    inline bool verify() const;
+
+private:
+    void rotateLeft(Node *node);
+    void rotateRight(Node *node);
+    void update(Node *node);
+
+    inline void attachLeft(Node *parent, Node *child);
+    inline void attachRight(Node *parent, Node *child);
+
+    int blackDepth(Node *top) const;
+    bool checkRedBlackProperty(Node *top) const;
+
+    void swapNodes(Node *n1, Node *n2);
+    void detach(Node *node);
+
+    // 'node' must be black. rebalance will reduce the depth of black nodes by one in the sibling tree.
+    void rebalance(Node *node);
+
+public:
+    Node *root;
+private:
+    Node *freeList;
+};
+
+template <class T>
+inline QRBTree<T>::~QRBTree()
+{
+    clear();
+    while (freeList) {
+        // Avoid recursively calling the destructor, as this list may become large.
+        Node *next = freeList->right;
+        freeList->right = 0;
+        delete freeList;
+        freeList = next;
+    }
+}
+
+template <class T>
+inline void QRBTree<T>::clear()
+{
+    if (root)
+        delete root;
+    root = 0;
+}
+
+template <class T>
+void QRBTree<T>::rotateLeft(Node *node)
+{
+    //   |            |
+    //   N            B
+    //  / \          / \
+    // A   B  --->  N   D
+    //    / \      / \
+    //   C   D    A   C
+
+    Node *&ref = (node->parent ? (node == node->parent->left ? node->parent->left : node->parent->right) : root);
+    ref = node->right;
+    node->right->parent = node->parent;
+
+    //   :
+    //   N
+    //  / :|
+    // A   B
+    //    / \
+    //   C   D
+
+    node->right = ref->left;
+    if (ref->left)
+        ref->left->parent = node;
+
+    //   :   |
+    //   N   B
+    //  / \ : \
+    // A   C   D
+
+    ref->left = node;
+    node->parent = ref;
+
+    //     |
+    //     B
+    //    / \
+    //   N   D
+    //  / \
+    // A   C
+}
+
+template <class T>
+void QRBTree<T>::rotateRight(Node *node)
+{
+    //     |            |
+    //     N            A
+    //    / \          / \
+    //   A   B  --->  C   N
+    //  / \              / \
+    // C   D            D   B
+
+    Node *&ref = (node->parent ? (node == node->parent->left ? node->parent->left : node->parent->right) : root);
+    ref = node->left;
+    node->left->parent = node->parent;
+
+    node->left = ref->right;
+    if (ref->right)
+        ref->right->parent = node;
+
+    ref->right = node;
+    node->parent = ref;
+}
+
+template <class T>
+void QRBTree<T>::update(Node *node) // call this after inserting a node
+{
+    for (;;) {
+        Node *parent = node->parent;
+
+        // if the node is the root, color it black
+        if (!parent) {
+            node->red = false;
+            return;
+        }
+
+        // if the parent is black, the node can be left red
+        if (!parent->red)
+            return;
+
+        // at this point, the parent is red and cannot be the root
+        Node *grandpa = parent->parent;
+        Q_ASSERT(grandpa);
+
+        Node *uncle = (parent == grandpa->left ? grandpa->right : grandpa->left);
+        if (uncle && uncle->red) {
+            // grandpa's black, parent and uncle are red.
+            // let parent and uncle be black, grandpa red and recursively update grandpa.
+            Q_ASSERT(!grandpa->red);
+            parent->red = false;
+            uncle->red = false;
+            grandpa->red = true;
+            node = grandpa;
+            continue;
+        }
+
+        // at this point, uncle is black
+        if (node == parent->right && parent == grandpa->left)
+            rotateLeft(node = parent);
+        else if (node == parent->left && parent == grandpa->right)
+            rotateRight(node = parent);
+        parent = node->parent;
+
+        if (parent == grandpa->left) {
+            rotateRight(grandpa);
+            parent->red = false;
+            grandpa->red = true;
+        } else {
+            rotateLeft(grandpa);
+            parent->red = false;
+            grandpa->red = true;
+        }
+        return;
+    }
+}
+
+template <class T>
+inline void QRBTree<T>::attachLeft(Node *parent, Node *child)
+{
+    Q_ASSERT(!parent->left);
+    parent->left = child;
+    child->parent = parent;
+    update(child);
+}
+
+template <class T>
+inline void QRBTree<T>::attachRight(Node *parent, Node *child)
+{
+    Q_ASSERT(!parent->right);
+    parent->right = child;
+    child->parent = parent;
+    update(child);
+}
+
+template <class T>
+void QRBTree<T>::attachBefore(Node *parent, Node *child)
+{
+    if (!root)
+        update(root = child);
+    else if (!parent)
+        attachRight(back(root), child);
+    else if (parent->left)
+        attachRight(back(parent->left), child);
+    else
+        attachLeft(parent, child);
+}
+
+template <class T>
+void QRBTree<T>::attachAfter(Node *parent, Node *child)
+{
+    if (!root)
+        update(root = child);
+    else if (!parent)
+        attachLeft(front(root), child);
+    else if (parent->right)
+        attachLeft(front(parent->right), child);
+    else
+        attachRight(parent, child);
+}
+
+template <class T>
+void QRBTree<T>::swapNodes(Node *n1, Node *n2)
+{
+    // Since iterators must not be invalidated, it is not sufficient to only swap the data.
+    if (n1->parent == n2) {
+        n1->parent = n2->parent;
+        n2->parent = n1;
+    } else if (n2->parent == n1) {
+        n2->parent = n1->parent;
+        n1->parent = n2;
+    } else {
+        qSwap(n1->parent, n2->parent);
+    }
+
+    qSwap(n1->left, n2->left);
+    qSwap(n1->right, n2->right);
+    qSwap(n1->red, n2->red);
+
+    if (n1->parent) {
+        if (n1->parent->left == n2)
+            n1->parent->left = n1;
+        else
+            n1->parent->right = n1;
+    } else {
+        root = n1;
+    }
+
+    if (n2->parent) {
+        if (n2->parent->left == n1)
+            n2->parent->left = n2;
+        else
+            n2->parent->right = n2;
+    } else {
+        root = n2;
+    }
+
+    if (n1->left)
+        n1->left->parent = n1;
+    if (n1->right)
+        n1->right->parent = n1;
+
+    if (n2->left)
+        n2->left->parent = n2;
+    if (n2->right)
+        n2->right->parent = n2;
+}
+
+template <class T>
+void QRBTree<T>::detach(Node *node) // call this before removing a node.
+{
+    if (node->right)
+        swapNodes(node, front(node->right));
+
+    Node *child = (node->left ? node->left : node->right);
+
+    if (!node->red) {
+        if (child && child->red)
+            child->red = false;
+        else
+            rebalance(node);
+    }
+
+    Node *&ref = (node->parent ? (node == node->parent->left ? node->parent->left : node->parent->right) : root);
+    ref = child;
+    if (child)
+        child->parent = node->parent;
+    node->left = node->right = node->parent = 0;
+}
+
+// 'node' must be black. rebalance will reduce the depth of black nodes by one in the sibling tree.
+template <class T>
+void QRBTree<T>::rebalance(Node *node)
+{
+    Q_ASSERT(!node->red);
+    for (;;) {
+        if (!node->parent)
+            return;
+
+        // at this point, node is not a parent, it is black, thus it must have a sibling.
+        Node *sibling = (node == node->parent->left ? node->parent->right : node->parent->left);
+        Q_ASSERT(sibling);
+
+        if (sibling->red) {
+            sibling->red = false;
+            node->parent->red = true;
+            if (node == node->parent->left)
+                rotateLeft(node->parent);
+            else
+                rotateRight(node->parent);
+            sibling = (node == node->parent->left ? node->parent->right : node->parent->left);
+            Q_ASSERT(sibling);
+        }
+
+        // at this point, the sibling is black.
+        Q_ASSERT(!sibling->red);
+
+        if ((!sibling->left || !sibling->left->red) && (!sibling->right || !sibling->right->red)) {
+            bool parentWasRed = node->parent->red;
+            sibling->red = true;
+            node->parent->red = false;
+            if (parentWasRed)
+                return;
+            node = node->parent;
+            continue;
+        }
+
+        // at this point, at least one of the sibling's children is red.
+
+        if (node == node->parent->left) {
+            if (!sibling->right || !sibling->right->red) {
+                Q_ASSERT(sibling->left);
+                sibling->red = true;
+                sibling->left->red = false;
+                rotateRight(sibling);
+
+                sibling = sibling->parent;
+                Q_ASSERT(sibling);
+            }
+            sibling->red = node->parent->red;
+            node->parent->red = false;
+
+            Q_ASSERT(sibling->right->red);
+            sibling->right->red = false;
+            rotateLeft(node->parent);
+        } else {
+            if (!sibling->left || !sibling->left->red) {
+                Q_ASSERT(sibling->right);
+                sibling->red = true;
+                sibling->right->red = false;
+                rotateLeft(sibling);
+
+                sibling = sibling->parent;
+                Q_ASSERT(sibling);
+            }
+            sibling->red = node->parent->red;
+            node->parent->red = false;
+
+            Q_ASSERT(sibling->left->red);
+            sibling->left->red = false;
+            rotateRight(node->parent);
+        }
+        return;
+    }
+}
+
+template <class T>
+inline typename QRBTree<T>::Node *QRBTree<T>::front(Node *node) const
+{
+    while (node->left)
+        node = node->left;
+    return node;
+}
+
+template <class T>
+inline typename QRBTree<T>::Node *QRBTree<T>::back(Node *node) const
+{
+    while (node->right)
+        node = node->right;
+    return node;
+}
+
+template <class T>
+typename QRBTree<T>::Node *QRBTree<T>::next(Node *node) const
+{
+    if (node->right)
+        return front(node->right);
+    while (node->parent && node == node->parent->right)
+        node = node->parent;
+    return node->parent;
+}
+
+template <class T>
+typename QRBTree<T>::Node *QRBTree<T>::previous(Node *node) const
+{
+    if (node->left)
+        return back(node->left);
+    while (node->parent && node == node->parent->left)
+        node = node->parent;
+    return node->parent;
+}
+
+template <class T>
+int QRBTree<T>::blackDepth(Node *top) const
+{
+    if (!top)
+        return 0;
+    int leftDepth = blackDepth(top->left);
+    int rightDepth = blackDepth(top->right);
+    if (leftDepth != rightDepth)
+        return -1;
+    if (!top->red)
+        ++leftDepth;
+    return leftDepth;
+}
+
+template <class T>
+bool QRBTree<T>::checkRedBlackProperty(Node *top) const
+{
+    if (!top)
+        return true;
+    if (top->left && !checkRedBlackProperty(top->left))
+        return false;
+    if (top->right && !checkRedBlackProperty(top->right))
+        return false;
+    return !(top->red && ((top->left && top->left->red) || (top->right && top->right->red)));
+}
+
+template <class T>
+inline bool QRBTree<T>::verify() const
+{
+    return checkRedBlackProperty(root) && blackDepth(root) != -1;
+}
+
+template <class T>
+inline void QRBTree<T>::deleteNode(Node *&node)
+{
+    Q_ASSERT(node);
+    detach(node);
+    node->right = freeList;
+    freeList = node;
+    node = 0;
+}
+
+template <class T>
+inline typename QRBTree<T>::Node *QRBTree<T>::newNode()
+{
+    if (freeList) {
+        Node *node = freeList;
+        freeList = freeList->right;
+        node->parent = node->left = node->right = 0;
+        node->red = true;
+        return node;
+    }
+    return new Node;
+}
+
+// Return 1 if 'left' comes after 'right', 0 if equal, and -1 otherwise.
+// 'left' and 'right' cannot be null.
+template <class T>
+int QRBTree<T>::order(Node *left, Node *right)
+{
+    Q_ASSERT(left && right);
+    if (left == right)
+        return 0;
+
+    QVector<Node *> leftAncestors;
+    QVector<Node *> rightAncestors;
+    while (left) {
+        leftAncestors.push_back(left);
+        left = left->parent;
+    }
+    while (right) {
+        rightAncestors.push_back(right);
+        right = right->parent;
+    }
+    Q_ASSERT(leftAncestors.back() == root && rightAncestors.back() == root);
+
+    while (!leftAncestors.empty() && !rightAncestors.empty() && leftAncestors.back() == rightAncestors.back()) {
+        leftAncestors.pop_back();
+        rightAncestors.pop_back();
+    }
+
+    if (!leftAncestors.empty())
+        return (leftAncestors.back() == leftAncestors.back()->parent->left ? -1 : 1);
+
+    if (!rightAncestors.empty())
+        return (rightAncestors.back() == rightAncestors.back()->parent->right ? -1 : 1);
+
+    // The code should never reach this point.
+    Q_ASSERT(!leftAncestors.empty() || !rightAncestors.empty());
+    return 0;
+}
+
+//============================================================================//
+//                                 QInt64Hash                                 //
+//============================================================================//
+
+// Copied from qhash.cpp
+static const uchar prime_deltas[] = {
+    0,  0,  1,  3,  1,  5,  3,  3,  1,  9,  7,  5,  3,  9, 25,  3,
+    1, 21,  3, 21,  7, 15,  9,  5,  3, 29, 15,  0,  0,  0,  0,  0
+};
+
+// Copied from qhash.cpp
+static inline int primeForNumBits(int numBits)
+{
+    return (1 << numBits) + prime_deltas[numBits];
+}
+
+static inline int primeForCount(int count)
+{
+    int low = 0;
+    int high = 32;
+    for (int i = 0; i < 5; ++i) {
+        int mid = (high + low) / 2;
+        if (count >= 1 << mid)
+            low = mid;
+        else
+            high = mid;
+    }
+    return primeForNumBits(high);
+}
+
+// Hash set of quint64s. Elements cannot be removed without clearing the
+// entire set. A value of -1 is used to mark unused entries.
+class QInt64Set
+{
+public:
+    inline QInt64Set(int capacity = 64);
+    inline ~QInt64Set() {if (m_array) delete[] m_array;}
+    inline bool isValid() const {return m_array;}
+    void insert(quint64 key);
+    bool contains(quint64 key) const;
+    inline void clear();
+private:
+    bool rehash(int capacity);
+
+    static const quint64 UNUSED;
+
+    quint64 *m_array;
+    int m_capacity;
+    int m_count;
+};
+
+const quint64 QInt64Set::UNUSED = quint64(-1);
+
+inline QInt64Set::QInt64Set(int capacity)
+{
+    m_capacity = primeForCount(capacity);
+    m_array = new quint64[m_capacity];
+    if (m_array)
+        clear();
+    else
+        m_capacity = 0;
+}
+
+bool QInt64Set::rehash(int capacity)
+{
+    quint64 *oldArray = m_array;
+    int oldCapacity = m_capacity;
+
+    m_capacity = capacity;
+    m_array = new quint64[m_capacity];
+    if (m_array) {
+        clear();
+        if (oldArray) {
+            for (int i = 0; i < oldCapacity; ++i) {
+                if (oldArray[i] != UNUSED)
+                    insert(oldArray[i]);
+            }
+            delete[] oldArray;
+        }
+        return true;
+    } else {
+        m_capacity = oldCapacity;
+        m_array = oldArray;
+        return false;
+    }
+}
+
+void QInt64Set::insert(quint64 key)
+{
+    if (m_count > 3 * m_capacity / 4)
+        rehash(primeForCount(2 * m_capacity));
+    Q_ASSERT_X(m_array, "QInt64Hash<T>::insert", "Hash set not allocated.");
+    int index = int(key % m_capacity);
+    for (int i = 0; i < m_capacity; ++i) {
+        index += i;
+        if (index >= m_capacity)
+            index -= m_capacity;
+        if (m_array[index] == key)
+            return;
+        if (m_array[index] == UNUSED) {
+            ++m_count;
+            m_array[index] = key;
+            return;
+        }
+    }
+    Q_ASSERT_X(0, "QInt64Hash<T>::insert", "Hash set full.");
+}
+
+bool QInt64Set::contains(quint64 key) const
+{
+    Q_ASSERT_X(m_array, "QInt64Hash<T>::contains", "Hash set not allocated.");
+    int index = int(key % m_capacity);
+    for (int i = 0; i < m_capacity; ++i) {
+        index += i;
+        if (index >= m_capacity)
+            index -= m_capacity;
+        if (m_array[index] == key)
+            return true;
+        if (m_array[index] == UNUSED)
+            return false;
+    }
+    return false;
+}
+
+inline void QInt64Set::clear()
+{
+    Q_ASSERT_X(m_array, "QInt64Hash<T>::clear", "Hash set not allocated.");
+    for (int i = 0; i < m_capacity; ++i)
+        m_array[i] = UNUSED;
+    m_count = 0;
+}
+
+//============================================================================//
+//                                QRingBuffer                                 //
+//============================================================================//
+
+// T must be POD.
+template <class T>
+class QRingBuffer
+{
+public:
+    inline QRingBuffer() : m_array(0), m_head(0), m_size(0), m_capacity(0) { }
+    inline ~QRingBuffer() {if (m_array) delete[] m_array;}
+    bool reallocate(int capacity);
+    inline const T &head() const {Q_ASSERT(m_size > 0); return m_array[m_head];}
+    inline const T &dequeue();
+    inline void enqueue(const T &x);
+    inline bool isEmpty() const {return m_size == 0;}
+private:
+    T *m_array;
+    int m_head;
+    int m_size;
+    int m_capacity;
+};
+
+template <class T>
+bool QRingBuffer<T>::reallocate(int capacity)
+{
+    T *oldArray = m_array;
+    m_array = new T[capacity];
+    if (m_array) {
+        if (oldArray) {
+            if (m_head + m_size > m_capacity) {
+                memcpy(m_array, oldArray + m_head, (m_capacity - m_head) * sizeof(T));
+                memcpy(m_array + (m_capacity - m_head), oldArray, (m_head + m_size - m_capacity) * sizeof(T));
+            } else {
+                memcpy(m_array, oldArray + m_head, m_size * sizeof(T));
+            }
+            delete[] oldArray;
+        }
+        m_capacity = capacity;
+        m_head = 0;
+        return true;
+    } else {
+        m_array = oldArray;
+        return false;
+    }
+}
+
+template <class T>
+inline const T &QRingBuffer<T>::dequeue()
+{
+    Q_ASSERT(m_size > 0);
+    Q_ASSERT(m_array);
+    Q_ASSERT(m_capacity >= m_size);
+    int index = m_head;
+    if (++m_head >= m_capacity)
+        m_head -= m_capacity;
+    --m_size;
+    return m_array[index];
+}
+
+template <class T>
+inline void QRingBuffer<T>::enqueue(const T &x)
+{
+    if (m_size == m_capacity)
+        reallocate(qMax(2 * m_capacity, 64));
+    int index = m_head + m_size;
+    if (index >= m_capacity)
+        index -= m_capacity;
+    m_array[index] = x;
+    ++m_size;
+}
+
+//============================================================================//
+//                               QTriangulator                                //
+//============================================================================//
+
+class QTriangulator
+{
+public:
+    typedef QVarLengthArray<int, 6> ShortArray;
+
+    //================================//
+    // QTriangulator::ComplexToSimple //
+    //================================//
+    friend class ComplexToSimple;
+    class ComplexToSimple
+    {
+    public:
+        inline ComplexToSimple(QTriangulator *parent) : m_parent(parent) { }
+        void decompose();
+    private:
+        struct Edge
+        {
+            inline int &upper() {return pointingUp ? to : from;}
+            inline int &lower() {return pointingUp ? from : to;}
+            inline int upper() const {return pointingUp ? to : from;}
+            inline int lower() const {return pointingUp ? from : to;}
+
+            QRBTree<int>::Node *node;
+            int from, to; // vertex
+            int next, previous; // edge
+            int winding;
+            bool mayIntersect;
+            bool pointingUp, originallyPointingUp;
+        };
+
+        friend class CompareEdges;
+        class CompareEdges
+        {
+        public:
+            inline CompareEdges(ComplexToSimple *parent) : m_parent(parent) { }
+            bool operator () (int i, int j) const;
+        private:
+            ComplexToSimple *m_parent;
+        };
+
+        struct Intersection
+        {
+            bool operator < (const Intersection &other) const {return other.intersectionPoint < intersectionPoint;}
+
+            QIntersectionPoint intersectionPoint;
+            int vertex;
+            int leftEdge;
+            int rightEdge;
+        };
+
+        struct Split
+        {
+            int vertex;
+            int edge;
+            bool accurate;
+        };
+
+        struct Event
+        {
+            enum Type {Upper, Lower};
+            inline bool operator < (const Event &other) const;
+
+            QPodPoint point;
+            Type type;
+            int edge;
+        };
+
+#ifdef Q_TRIANGULATOR_DEBUG
+        friend class DebugDialog;
+        friend class QTriangulator;
+        class DebugDialog : public QDialog
+        {
+        public:
+            DebugDialog(ComplexToSimple *parent, int currentVertex);
+        protected:
+            void paintEvent(QPaintEvent *);
+            void wheelEvent(QWheelEvent *);
+            void mouseMoveEvent(QMouseEvent *);
+            void mousePressEvent(QMouseEvent *);
+        private:
+            ComplexToSimple *m_parent;
+            QRectF m_window;
+            QPoint m_lastMousePos;
+            int m_vertex;
+        };
+#endif
+
+        void initEdges();
+        bool calculateIntersection(int left, int right);
+        bool edgeIsLeftOfEdge(int leftEdgeIndex, int rightEdgeIndex) const;
+        QRBTree<int>::Node *searchEdgeLeftOf(int edgeIndex) const;
+        QRBTree<int>::Node *searchEdgeLeftOf(int edgeIndex, QRBTree<int>::Node *after) const;
+        QPair<QRBTree<int>::Node *, QRBTree<int>::Node *> bounds(const QPodPoint &point) const;
+        QPair<QRBTree<int>::Node *, QRBTree<int>::Node *> outerBounds(const QPodPoint &point) const;
+        void splitEdgeListRange(QRBTree<int>::Node *leftmost, QRBTree<int>::Node *rightmost, int vertex, const QIntersectionPoint &intersectionPoint);
+        void reorderEdgeListRange(QRBTree<int>::Node *leftmost, QRBTree<int>::Node *rightmost);
+        void sortEdgeList(const QPodPoint eventPoint);
+        void fillPriorityQueue();
+        void calculateIntersections();
+        int splitEdge(int splitIndex);
+        bool splitEdgesAtIntersections();
+        void insertEdgeIntoVectorIfWanted(ShortArray &orderedEdges, int i);
+        void removeUnwantedEdgesAndConnect();
+        void removeUnusedPoints();
+
+        QTriangulator *m_parent;
+        QDataBuffer<Edge> m_edges;
+        QRBTree<int> m_edgeList;
+        QDataBuffer<Event> m_events;
+        QDataBuffer<Split> m_splits;
+        QMaxHeap<Intersection> m_topIntersection;
+        QInt64Set m_processedEdgePairs;
+        int m_initialPointCount;
+    };
+#ifdef Q_TRIANGULATOR_DEBUG
+    friend class ComplexToSimple::DebugDialog;
+#endif
+
+    //=================================//
+    // QTriangulator::SimpleToMonotone //
+    //=================================//
+    friend class SimpleToMonotone;
+    class SimpleToMonotone
+    {
+    public:
+        inline SimpleToMonotone(QTriangulator *parent) : m_parent(parent) { }
+        void decompose();
+    private:
+        enum VertexType {MergeVertex, EndVertex, RegularVertex, StartVertex, SplitVertex};
+
+        struct Edge
+        {
+            QRBTree<int>::Node *node;
+            int helper, twin, next, previous;
+            quint32 from, to;
+            VertexType type;
+            bool pointingUp;
+            int upper() const {return (pointingUp ? to : from);}
+            int lower() const {return (pointingUp ? from : to);}
+        };
+
+        friend class CompareVertices;
+        class CompareVertices
+        {
+        public:
+            CompareVertices(SimpleToMonotone *parent) : m_parent(parent) { }
+            bool operator () (int i, int j) const;
+        private:
+            SimpleToMonotone *m_parent;
+        };
+
+        void setupDataStructures();
+        void removeZeroLengthEdges();
+        void fillPriorityQueue();
+        bool edgeIsLeftOfEdge(int leftEdgeIndex, int rightEdgeIndex) const;
+        // Returns the rightmost edge not to the right of the given edge.
+        QRBTree<int>::Node *searchEdgeLeftOfEdge(int edgeIndex) const;
+        // Returns the rightmost edge left of the given point.
+        QRBTree<int>::Node *searchEdgeLeftOfPoint(int pointIndex) const;
+        void classifyVertex(int i);
+        void classifyVertices();
+        bool pointIsInSector(const QPodPoint &p, const QPodPoint &v1, const QPodPoint &v2, const QPodPoint &v3);
+        bool pointIsInSector(int vertex, int sector);
+        int findSector(int edge, int vertex);
+        void createDiagonal(int lower, int upper);
+        void monotoneDecomposition();
+
+        QTriangulator *m_parent;
+        QRBTree<int> m_edgeList;
+        QDataBuffer<Edge> m_edges;
+        QDataBuffer<int> m_upperVertex;
+        bool m_clockwiseOrder;
+    };
+
+    //====================================//
+    // QTriangulator::MonotoneToTriangles //
+    //====================================//
+    friend class MonotoneToTriangles;
+    class MonotoneToTriangles
+    {
+    public:
+        inline MonotoneToTriangles(QTriangulator *parent) : m_parent(parent) { }
+        void decompose();
+    private:
+        inline quint32 indices(int index) const {return m_parent->m_indices.at(index + m_first);}
+        inline int next(int index) const {return (index + 1) % m_length;}
+        inline int previous(int index) const {return (index + m_length - 1) % m_length;}
+        inline bool less(int i, int j) const {return m_parent->m_vertices.at(indices(i)) < m_parent->m_vertices.at(indices(j));}
+        inline bool leftOfEdge(int i, int j, int k) const
+        {
+            return qPointIsLeftOfLine(m_parent->m_vertices.at(indices(i)),
+                m_parent->m_vertices.at(indices(j)), m_parent->m_vertices.at(indices(k)));
+        }
+
+        QTriangulator *m_parent;
+        int m_first;
+        int m_length;
+    };
+
+    inline QTriangulator() { }
+
+    // Call this only once.
+    void initialize(const qreal *polygon, int count, uint hint, const QTransform &matrix);
+    // Call this only once.
+    void initialize(const QVectorPath &path, const QTransform &matrix, qreal lod);
+    // Call this only once.
+    void initialize(const QPainterPath &path, const QTransform &matrix, qreal lod);
+    // Call either triangulate() or polyline() only once.
+    QTriangleSet triangulate();
+    QPolylineSet polyline();
+private:
+    QDataBuffer<QPodPoint> m_vertices;
+    QVector<quint32> m_indices;
+    uint m_hint;
+};
+
+//============================================================================//
+//                               QTriangulator                                //
+//============================================================================//
+
+QTriangleSet QTriangulator::triangulate()
+{
+    for (int i = 0; i < m_vertices.size(); ++i) {
+        Q_ASSERT(qAbs(m_vertices.at(i).x) < (1 << 21));
+        Q_ASSERT(qAbs(m_vertices.at(i).y) < (1 << 21));
+    }
+
+    if (!(m_hint & (QVectorPath::OddEvenFill | QVectorPath::WindingFill)))
+        m_hint |= QVectorPath::OddEvenFill;
+
+    if (m_hint & QVectorPath::NonConvexShapeMask) {
+        ComplexToSimple c2s(this);
+        c2s.decompose();
+        SimpleToMonotone s2m(this);
+        s2m.decompose();
+    }
+    MonotoneToTriangles m2t(this);
+    m2t.decompose();
+
+    QTriangleSet result;
+    result.indices = m_indices;
+    result.vertices.resize(2 * m_vertices.size());
+    for (int i = 0; i < m_vertices.size(); ++i) {
+        result.vertices[2 * i + 0] = qreal(m_vertices.at(i).x) / Q_FIXED_POINT_SCALE;
+        result.vertices[2 * i + 1] = qreal(m_vertices.at(i).y) / Q_FIXED_POINT_SCALE;
+    }
+    return result;
+}
+
+QPolylineSet QTriangulator::polyline()
+{
+    QPolylineSet result;
+    result.indices = m_indices;
+    result.vertices.resize(2 * m_vertices.size());
+    for (int i = 0; i < m_vertices.size(); ++i) {
+        result.vertices[2 * i + 0] = qreal(m_vertices.at(i).x) / Q_FIXED_POINT_SCALE;
+        result.vertices[2 * i + 1] = qreal(m_vertices.at(i).y) / Q_FIXED_POINT_SCALE;
+    }
+    return result;
+}
+
+void QTriangulator::initialize(const qreal *polygon, int count, uint hint, const QTransform &matrix)
+{
+    m_hint = hint;
+    m_vertices.resize(count);
+    m_indices.resize(count + 1);
+    for (int i = 0; i < count; ++i) {
+        qreal x, y;
+        matrix.map(polygon[2 * i + 0], polygon[2 * i + 1], &x, &y);
+        m_vertices.at(i).x = qRound(x * Q_FIXED_POINT_SCALE);
+        m_vertices.at(i).y = qRound(y * Q_FIXED_POINT_SCALE);
+        m_indices[i] = i;
+    }
+    m_indices[count] = Q_TRIANGULATE_END_OF_POLYGON;
+}
+
+void QTriangulator::initialize(const QVectorPath &path, const QTransform &matrix, qreal lod)
+{
+    m_hint = path.hints();
+    // Curved paths will be converted to complex polygons.
+    m_hint &= ~QVectorPath::CurvedShapeMask;
+
+    const qreal *p = path.points();
+    const QPainterPath::ElementType *e = path.elements();
+    if (e) {
+        for (int i = 0; i < path.elementCount(); ++i, ++e, p += 2) {
+            switch (*e) {
+            case QPainterPath::MoveToElement:
+                if (!m_indices.isEmpty())
+                    m_indices.push_back(Q_TRIANGULATE_END_OF_POLYGON);
+                // Fall through.
+            case QPainterPath::LineToElement:
+                m_indices.push_back(quint32(m_vertices.size()));
+                m_vertices.resize(m_vertices.size() + 1);
+                qreal x, y;
+                matrix.map(p[0], p[1], &x, &y);
+                m_vertices.last().x = qRound(x * Q_FIXED_POINT_SCALE);
+                m_vertices.last().y = qRound(y * Q_FIXED_POINT_SCALE);
+                break;
+            case QPainterPath::CurveToElement:
+                {
+                    qreal pts[8];
+                    for (int i = 0; i < 4; ++i)
+                        matrix.map(p[2 * i - 2], p[2 * i - 1], &pts[2 * i + 0], &pts[2 * i + 1]);
+                    for (int i = 0; i < 8; ++i)
+                        pts[i] *= lod;
+                    QBezier bezier = QBezier::fromPoints(QPointF(pts[0], pts[1]), QPointF(pts[2], pts[3]), QPointF(pts[4], pts[5]), QPointF(pts[6], pts[7]));
+                    QPolygonF poly = bezier.toPolygon();
+                    // Skip first point, it already exists in 'm_vertices'.
+                    for (int j = 1; j < poly.size(); ++j) {
+                        m_indices.push_back(quint32(m_vertices.size()));
+                        m_vertices.resize(m_vertices.size() + 1);
+                        m_vertices.last().x = qRound(poly.at(j).x() * Q_FIXED_POINT_SCALE / lod);
+                        m_vertices.last().y = qRound(poly.at(j).y() * Q_FIXED_POINT_SCALE / lod);
+                    }
+                }
+                i += 2;
+                e += 2;
+                p += 4;
+                break;
+            default:
+                Q_ASSERT_X(0, "QTriangulator::triangulate", "Unexpected element type.");
+                break;
+            }
+        }
+    } else {
+        for (int i = 0; i < path.elementCount(); ++i, p += 2) {
+            m_indices.push_back(quint32(m_vertices.size()));
+            m_vertices.resize(m_vertices.size() + 1);
+            qreal x, y;
+            matrix.map(p[0], p[1], &x, &y);
+            m_vertices.last().x = qRound(x * Q_FIXED_POINT_SCALE);
+            m_vertices.last().y = qRound(y * Q_FIXED_POINT_SCALE);
+        }
+    }
+    m_indices.push_back(Q_TRIANGULATE_END_OF_POLYGON);
+}
+
+void QTriangulator::initialize(const QPainterPath &path, const QTransform &matrix, qreal lod)
+{
+    initialize(qtVectorPathForPath(path), matrix, lod);
+}
+
+//============================================================================//
+//                       QTriangulator::ComplexToSimple                       //
+//============================================================================//
+
+void QTriangulator::ComplexToSimple::decompose()
+{
+    m_initialPointCount = m_parent->m_vertices.size();
+    initEdges();
+    do {
+        calculateIntersections();
+    } while (splitEdgesAtIntersections());
+
+    removeUnwantedEdgesAndConnect();
+    removeUnusedPoints();
+
+    m_parent->m_indices.clear();
+    QBitArray processed(m_edges.size(), false);
+    for (int first = 0; first < m_edges.size(); ++first) {
+        // If already processed, or if unused path, skip.
+        if (processed.at(first) || m_edges.at(first).next == -1)
+            continue;
+
+        int i = first;
+        do {
+            Q_ASSERT(!processed.at(i));
+            Q_ASSERT(m_edges.at(m_edges.at(i).next).previous == i);
+            m_parent->m_indices.push_back(m_edges.at(i).from);
+            processed.setBit(i);
+            i = m_edges.at(i).next; // CCW order
+        } while (i != first);
+        m_parent->m_indices.push_back(Q_TRIANGULATE_END_OF_POLYGON);
+    }
+}
+
+void QTriangulator::ComplexToSimple::initEdges()
+{
+    // Initialize edge structure.
+    // 'next' and 'previous' are not being initialized at this point.
+    int first = 0;
+    for (int i = 0; i < m_parent->m_indices.size(); ++i) {
+        if (m_parent->m_indices.at(i) == Q_TRIANGULATE_END_OF_POLYGON) {
+            if (m_edges.size() != first)
+                m_edges.last().to = m_edges.at(first).from;
+            first = m_edges.size();
+        } else {
+            Q_ASSERT(i + 1 < m_parent->m_indices.size());
+            // {node, from, to, next, previous, winding, mayIntersect, pointingUp, originallyPointingUp}
+            Edge edge = {0, m_parent->m_indices.at(i), m_parent->m_indices.at(i + 1), -1, -1, 0, true, false, false};
+            m_edges.add(edge);
+        }
+    }
+    if (first != m_edges.size())
+        m_edges.last().to = m_edges.at(first).from;
+    for (int i = 0; i < m_edges.size(); ++i) {
+        m_edges.at(i).originallyPointingUp = m_edges.at(i).pointingUp = 
+            m_parent->m_vertices.at(m_edges.at(i).to) < m_parent->m_vertices.at(m_edges.at(i).from);
+    }
+}
+
+// Return true if new intersection was found
+bool QTriangulator::ComplexToSimple::calculateIntersection(int left, int right)
+{
+    const Edge &e1 = m_edges.at(left);
+    const Edge &e2 = m_edges.at(right);
+
+    const QPodPoint &u1 = m_parent->m_vertices.at(e1.from);
+    const QPodPoint &u2 = m_parent->m_vertices.at(e1.to);
+    const QPodPoint &v1 = m_parent->m_vertices.at(e2.from);
+    const QPodPoint &v2 = m_parent->m_vertices.at(e2.to);
+    if (qMax(u1.x, u2.x) <= qMin(v1.x, v2.x))
+        return false;
+
+    quint64 key = (left > right ? (quint64(right) << 32) | quint64(left) : (quint64(left) << 32) | quint64(right));
+    if (m_processedEdgePairs.contains(key))
+        return false;
+    m_processedEdgePairs.insert(key);
+
+    Intersection intersection;
+    intersection.leftEdge = left;
+    intersection.rightEdge = right;
+    intersection.intersectionPoint = qIntersectionPoint(u1, u2, v1, v2);
+
+    if (!intersection.intersectionPoint.isValid())
+        return false;
+
+    Q_ASSERT(intersection.intersectionPoint.isOnLine(u1, u2));
+    Q_ASSERT(intersection.intersectionPoint.isOnLine(v1, v2));
+
+    intersection.vertex = m_parent->m_vertices.size();
+    m_topIntersection.push(intersection);
+    m_parent->m_vertices.add(intersection.intersectionPoint.round());
+    return true;
+}
+
+bool QTriangulator::ComplexToSimple::edgeIsLeftOfEdge(int leftEdgeIndex, int rightEdgeIndex) const
+{
+    const Edge &leftEdge = m_edges.at(leftEdgeIndex);
+    const Edge &rightEdge = m_edges.at(rightEdgeIndex);
+    const QPodPoint &u = m_parent->m_vertices.at(rightEdge.upper());
+    const QPodPoint &l = m_parent->m_vertices.at(rightEdge.lower());
+    const QPodPoint &upper = m_parent->m_vertices.at(leftEdge.upper());
+    if (upper.x < qMin(l.x, u.x))
+        return true;
+    if (upper.x > qMax(l.x, u.x))
+        return false;
+    qint64 d = qPointDistanceFromLine(upper, l, u);
+    // d < 0: left, d > 0: right, d == 0: on top
+    if (d == 0)
+        d = qPointDistanceFromLine(m_parent->m_vertices.at(leftEdge.lower()), l, u);
+    return d < 0;
+}
+
+QRBTree<int>::Node *QTriangulator::ComplexToSimple::searchEdgeLeftOf(int edgeIndex) const
+{
+    QRBTree<int>::Node *current = m_edgeList.root;
+    QRBTree<int>::Node *result = 0;
+    while (current) {
+        if (edgeIsLeftOfEdge(edgeIndex, current->data)) {
+            current = current->left;
+        } else {
+            result = current;
+            current = current->right;
+        }
+    }
+    return result;
+}
+
+QRBTree<int>::Node *QTriangulator::ComplexToSimple::searchEdgeLeftOf(int edgeIndex, QRBTree<int>::Node *after) const
+{
+    if (!m_edgeList.root)
+        return after;
+    QRBTree<int>::Node *result = after;
+    QRBTree<int>::Node *current = (after ? m_edgeList.next(after) : m_edgeList.front(m_edgeList.root));
+    while (current) {
+        if (edgeIsLeftOfEdge(edgeIndex, current->data))
+            return result;
+        result = current;
+        current = m_edgeList.next(current);
+    }
+    return result;
+}
+
+QPair<QRBTree<int>::Node *, QRBTree<int>::Node *> QTriangulator::ComplexToSimple::bounds(const QPodPoint &point) const
+{
+    QRBTree<int>::Node *current = m_edgeList.root;
+    QPair<QRBTree<int>::Node *, QRBTree<int>::Node *> result(0, 0);
+    while (current) {
+        const QPodPoint &v1 = m_parent->m_vertices.at(m_edges.at(current->data).lower());
+        const QPodPoint &v2 = m_parent->m_vertices.at(m_edges.at(current->data).upper());
+        int d = qPointDistanceFromLine(point, v1, v2);
+        if (d == 0) {
+            result.first = result.second = current;
+            break;
+        }
+        current = (d < 0 ? current->left : current->right);
+    }
+    if (current == 0)
+        return result;
+
+    current = result.first->left;
+    while (current) {
+        const QPodPoint &v1 = m_parent->m_vertices.at(m_edges.at(current->data).lower());
+        const QPodPoint &v2 = m_parent->m_vertices.at(m_edges.at(current->data).upper());
+        int d = qPointDistanceFromLine(point, v1, v2);
+        Q_ASSERT(d >= 0);
+        if (d == 0) {
+            result.first = current;
+            current = current->left;
+        } else {
+            current = current->right;
+        }
+    }
+
+    current = result.second->right;
+    while (current) {
+        const QPodPoint &v1 = m_parent->m_vertices.at(m_edges.at(current->data).lower());
+        const QPodPoint &v2 = m_parent->m_vertices.at(m_edges.at(current->data).upper());
+        int d = qPointDistanceFromLine(point, v1, v2);
+        Q_ASSERT(d <= 0);
+        if (d == 0) {
+            result.second = current;
+            current = current->right;
+        } else {
+            current = current->left;
+        }
+    }
+
+    return result;
+}
+
+QPair<QRBTree<int>::Node *, QRBTree<int>::Node *> QTriangulator::ComplexToSimple::outerBounds(const QPodPoint &point) const
+{
+    QRBTree<int>::Node *current = m_edgeList.root;
+    QPair<QRBTree<int>::Node *, QRBTree<int>::Node *> result(0, 0);
+
+    while (current) {
+        const QPodPoint &v1 = m_parent->m_vertices.at(m_edges.at(current->data).lower());
+        const QPodPoint &v2 = m_parent->m_vertices.at(m_edges.at(current->data).upper());
+        int d = qPointDistanceFromLine(point, v1, v2);
+        if (d == 0)
+            break;
+        if (d < 0) {
+            result.second = current;
+            current = current->left;
+        } else {
+            result.first = current;
+            current = current->right;
+        }
+    }
+
+    if (!current)
+        return result;
+
+    QRBTree<int>::Node *mid = current;
+
+    current = mid->left;
+    while (current) {
+        const QPodPoint &v1 = m_parent->m_vertices.at(m_edges.at(current->data).lower());
+        const QPodPoint &v2 = m_parent->m_vertices.at(m_edges.at(current->data).upper());
+        int d = qPointDistanceFromLine(point, v1, v2);
+        Q_ASSERT(d >= 0);
+        if (d == 0) {
+            current = current->left;
+        } else {
+            result.first = current;
+            current = current->right;
+        }
+    }
+
+    current = mid->right;
+    while (current) {
+        const QPodPoint &v1 = m_parent->m_vertices.at(m_edges.at(current->data).lower());
+        const QPodPoint &v2 = m_parent->m_vertices.at(m_edges.at(current->data).upper());
+        int d = qPointDistanceFromLine(point, v1, v2);
+        Q_ASSERT(d <= 0);
+        if (d == 0) {
+            current = current->right;
+        } else {
+            result.second = current;
+            current = current->left;
+        }
+    }
+
+    return result;
+}
+
+void QTriangulator::ComplexToSimple::splitEdgeListRange(QRBTree<int>::Node *leftmost, QRBTree<int>::Node *rightmost, int vertex, const QIntersectionPoint &intersectionPoint)
+{
+    Q_ASSERT(leftmost && rightmost);
+
+    // Split.
+    for (;;) {
+        const QPodPoint &u = m_parent->m_vertices.at(m_edges.at(leftmost->data).from);
+        const QPodPoint &v = m_parent->m_vertices.at(m_edges.at(leftmost->data).to);
+        Q_ASSERT(intersectionPoint.isOnLine(u, v));
+        const Split split = {vertex, leftmost->data, intersectionPoint.isAccurate()};
+        if (intersectionPoint.xOffset.numerator != 0 || intersectionPoint.yOffset.numerator != 0 || (intersectionPoint.upperLeft != u && intersectionPoint.upperLeft != v))
+            m_splits.add(split);
+        if (leftmost == rightmost)
+            break;
+        leftmost = m_edgeList.next(leftmost);
+    }
+}
+
+
+void QTriangulator::ComplexToSimple::reorderEdgeListRange(QRBTree<int>::Node *leftmost, QRBTree<int>::Node *rightmost)
+{
+    Q_ASSERT(leftmost && rightmost);
+
+    QRBTree<int>::Node *storeLeftmost = leftmost;
+    QRBTree<int>::Node *storeRightmost = rightmost;
+
+    // Reorder.
+    while (leftmost != rightmost) {
+        Edge &left = m_edges.at(leftmost->data);
+        Edge &right = m_edges.at(rightmost->data);
+        qSwap(left.node, right.node);
+        qSwap(leftmost->data, rightmost->data);
+        leftmost = m_edgeList.next(leftmost);
+        if (leftmost == rightmost)
+            break;
+        rightmost = m_edgeList.previous(rightmost);
+    }
+
+    rightmost = m_edgeList.next(storeRightmost);
+    leftmost = m_edgeList.previous(storeLeftmost);
+    if (leftmost)
+        calculateIntersection(leftmost->data, storeLeftmost->data);
+    if (rightmost)
+        calculateIntersection(storeRightmost->data, rightmost->data);
+}
+
+void QTriangulator::ComplexToSimple::sortEdgeList(const QPodPoint eventPoint)
+{
+    QIntersectionPoint eventPoint2 = qIntersectionPoint(eventPoint);
+    while (!m_topIntersection.isEmpty() && m_topIntersection.top().intersectionPoint < eventPoint2) {
+        Intersection intersection = m_topIntersection.pop();
+
+        QIntersectionPoint currentIntersectionPoint = intersection.intersectionPoint;
+        int currentVertex = intersection.vertex;
+
+        QRBTree<int>::Node *leftmost = m_edges.at(intersection.leftEdge).node;
+        QRBTree<int>::Node *rightmost = m_edges.at(intersection.rightEdge).node;
+
+        for (;;) {
+            QRBTree<int>::Node *previous = m_edgeList.previous(leftmost);
+            if (!previous)
+                break;
+            const Edge &edge = m_edges.at(previous->data);
+            const QPodPoint &u = m_parent->m_vertices.at(edge.from);
+            const QPodPoint &v = m_parent->m_vertices.at(edge.to);
+            if (!currentIntersectionPoint.isOnLine(u, v)) {
+                Q_ASSERT(!currentIntersectionPoint.isAccurate() || qCross(currentIntersectionPoint.upperLeft - u, v - u) != 0);
+                break;
+            }
+            leftmost = previous;
+        }
+
+        for (;;) {
+            QRBTree<int>::Node *next = m_edgeList.next(rightmost);
+            if (!next)
+                break;
+            const Edge &edge = m_edges.at(next->data);
+            const QPodPoint &u = m_parent->m_vertices.at(edge.from);
+            const QPodPoint &v = m_parent->m_vertices.at(edge.to);
+            if (!currentIntersectionPoint.isOnLine(u, v)) {
+                Q_ASSERT(!currentIntersectionPoint.isAccurate() || qCross(currentIntersectionPoint.upperLeft - u, v - u) != 0);
+                break;
+            }
+            rightmost = next;
+        }
+
+        Q_ASSERT(leftmost && rightmost);
+        splitEdgeListRange(leftmost, rightmost, currentVertex, currentIntersectionPoint);
+        reorderEdgeListRange(leftmost, rightmost);
+
+        while (!m_topIntersection.isEmpty() && m_topIntersection.top().intersectionPoint <= currentIntersectionPoint)
+            m_topIntersection.pop();
+
+#ifdef Q_TRIANGULATOR_DEBUG
+        DebugDialog dialog(this, intersection.vertex);
+        dialog.exec();
+#endif
+
+    }
+}
+
+void QTriangulator::ComplexToSimple::fillPriorityQueue()
+{
+    m_events.reset();
+    m_events.reserve(m_edges.size() * 2);
+    for (int i = 0; i < m_edges.size(); ++i) {
+        Q_ASSERT(m_edges.at(i).previous == -1 && m_edges.at(i).next == -1);
+        Q_ASSERT(m_edges.at(i).node == 0);
+        Q_ASSERT(m_edges.at(i).pointingUp == m_edges.at(i).originallyPointingUp);
+        Q_ASSERT(m_edges.at(i).pointingUp == (m_parent->m_vertices.at(m_edges.at(i).to) < m_parent->m_vertices.at(m_edges.at(i).from)));
+        // Ignore zero-length edges.
+        if (m_parent->m_vertices.at(m_edges.at(i).to) != m_parent->m_vertices.at(m_edges.at(i).from)) {
+            Event upperEvent = {m_parent->m_vertices.at(m_edges.at(i).upper()), Event::Upper, i};
+            Event lowerEvent = {m_parent->m_vertices.at(m_edges.at(i).lower()), Event::Lower, i};
+            m_events.add(upperEvent);
+            m_events.add(lowerEvent);
+        }
+    }
+    //qSort(m_events.data(), m_events.data() + m_events.size());
+    sort(m_events.data(), m_events.size());
+}
+
+void QTriangulator::ComplexToSimple::calculateIntersections()
+{
+    fillPriorityQueue();
+
+    Q_ASSERT(m_topIntersection.empty());
+    Q_ASSERT(m_edgeList.root == 0);
+
+    // Find all intersection points.
+    while (!m_events.isEmpty()) {
+        Event event = m_events.last();
+        sortEdgeList(event.point);
+
+        // Find all edges in the edge list that contain the current vertex and mark them to be split later.
+        QPair<QRBTree<int>::Node *, QRBTree<int>::Node *> range = bounds(event.point);
+        QRBTree<int>::Node *leftNode = range.first ? m_edgeList.previous(range.first) : 0;
+        int vertex = (event.type == Event::Upper ? m_edges.at(event.edge).upper() : m_edges.at(event.edge).lower());
+        QIntersectionPoint eventPoint = qIntersectionPoint(event.point);
+
+        if (range.first != 0) {
+            splitEdgeListRange(range.first, range.second, vertex, eventPoint);
+            reorderEdgeListRange(range.first, range.second);
+        }
+
+        // Handle the edges with start or end point in the current vertex.
+        while (!m_events.isEmpty() && m_events.last().point == event.point) {
+            event = m_events.last();
+            m_events.pop_back();
+            int i = event.edge;
+
+            if (m_edges.at(i).node) {
+                // Remove edge from edge list.
+                Q_ASSERT(event.type == Event::Lower);
+                QRBTree<int>::Node *left = m_edgeList.previous(m_edges.at(i).node);
+                QRBTree<int>::Node *right = m_edgeList.next(m_edges.at(i).node);
+                m_edgeList.deleteNode(m_edges.at(i).node);
+                if (!left || !right)
+                    continue;
+                calculateIntersection(left->data, right->data);
+            } else {
+                // Insert edge into edge list.
+                Q_ASSERT(event.type == Event::Upper);
+                QRBTree<int>::Node *left = searchEdgeLeftOf(i, leftNode);
+                m_edgeList.attachAfter(left, m_edges.at(i).node = m_edgeList.newNode());
+                m_edges.at(i).node->data = i;
+                QRBTree<int>::Node *right = m_edgeList.next(m_edges.at(i).node);
+                if (left)
+                    calculateIntersection(left->data, i);
+                if (right)
+                    calculateIntersection(i, right->data);
+            }
+        }
+        while (!m_topIntersection.isEmpty() && m_topIntersection.top().intersectionPoint <= eventPoint)
+            m_topIntersection.pop();
+#ifdef Q_TRIANGULATOR_DEBUG
+        DebugDialog dialog(this, vertex);
+        dialog.exec();
+#endif
+    }
+    m_processedEdgePairs.clear();
+}
+
+// Split an edge into two pieces at the given point.
+// The upper piece is pushed to the end of the 'm_edges' vector.
+// The lower piece replaces the old edge.
+// Return the edge whose 'from' is 'pointIndex'.
+int QTriangulator::ComplexToSimple::splitEdge(int splitIndex)
+{
+    const Split &split = m_splits.at(splitIndex);
+    Edge &lowerEdge = m_edges.at(split.edge);
+    Q_ASSERT(lowerEdge.node == 0);
+    Q_ASSERT(lowerEdge.previous == -1 && lowerEdge.next == -1);
+
+    if (lowerEdge.from == split.vertex)
+        return split.edge;
+    if (lowerEdge.to == split.vertex)
+        return lowerEdge.next;
+
+    // Check that angle >= 90 degrees.
+    //Q_ASSERT(qDot(m_points.at(m_edges.at(edgeIndex).from) - m_points.at(pointIndex),
+    //    m_points.at(m_edges.at(edgeIndex).to) - m_points.at(pointIndex)) <= 0);
+
+    Edge upperEdge = lowerEdge;
+    upperEdge.mayIntersect |= !split.accurate; // The edge may have been split before at an inaccurate split point.
+    lowerEdge.mayIntersect = !split.accurate;
+    if (lowerEdge.pointingUp) {
+        lowerEdge.to = upperEdge.from = split.vertex;
+        m_edges.add(upperEdge);
+        return m_edges.size() - 1;
+    } else {
+        lowerEdge.from = upperEdge.to = split.vertex;
+        m_edges.add(upperEdge);
+        return split.edge;
+    }
+}
+
+bool QTriangulator::ComplexToSimple::splitEdgesAtIntersections()
+{
+    for (int i = 0; i < m_edges.size(); ++i)
+        m_edges.at(i).mayIntersect = false;
+    bool checkForNewIntersections = false;
+    for (int i = 0; i < m_splits.size(); ++i) {
+        splitEdge(i);
+        checkForNewIntersections |= !m_splits.at(i).accurate;
+    }
+    for (int i = 0; i < m_edges.size(); ++i) {
+        m_edges.at(i).originallyPointingUp = m_edges.at(i).pointingUp =
+            m_parent->m_vertices.at(m_edges.at(i).to) < m_parent->m_vertices.at(m_edges.at(i).from);
+    }
+    m_splits.reset();
+    return checkForNewIntersections;
+}
+
+void QTriangulator::ComplexToSimple::insertEdgeIntoVectorIfWanted(ShortArray &orderedEdges, int i)
+{
+    // Edges with zero length should not reach this part.
+    Q_ASSERT(m_parent->m_vertices.at(m_edges.at(i).from) != m_parent->m_vertices.at(m_edges.at(i).to));
+
+    // Skip edges with unwanted winding number.
+    int windingNumber = m_edges.at(i).winding;
+    if (m_edges.at(i).originallyPointingUp)
+        ++windingNumber;
+
+    // Make sure exactly one fill rule is specified.
+    Q_ASSERT(((m_parent->m_hint & QVectorPath::WindingFill) != 0) != ((m_parent->m_hint & QVectorPath::OddEvenFill) != 0));
+
+    if ((m_parent->m_hint & QVectorPath::WindingFill) && windingNumber != 0 && windingNumber != 1)
+        return;
+
+    // Skip cancelling edges.
+    if (!orderedEdges.isEmpty()) {
+        int j = orderedEdges[orderedEdges.size() - 1];
+        // If the last edge is already connected in one end, it should not be cancelled.
+        if (m_edges.at(j).next == -1 && m_edges.at(j).previous == -1
+            && (m_parent->m_vertices.at(m_edges.at(i).from) == m_parent->m_vertices.at(m_edges.at(j).to))
+            && (m_parent->m_vertices.at(m_edges.at(i).to) == m_parent->m_vertices.at(m_edges.at(j).from))) {
+            orderedEdges.removeLast();
+            return;
+        }
+    }
+    orderedEdges.append(i);
+}
+
+void QTriangulator::ComplexToSimple::removeUnwantedEdgesAndConnect()
+{
+    Q_ASSERT(m_edgeList.root == 0);
+    // Initialize priority queue.
+    fillPriorityQueue();
+
+    ShortArray orderedEdges;
+
+    while (!m_events.isEmpty()) {
+        Event event = m_events.last();
+        int edgeIndex = event.edge;
+
+        // Check that all the edges in the list crosses the current scanline
+        //if (m_edgeList.root) {
+        //    for (QRBTree<int>::Node *node = m_edgeList.front(m_edgeList.root); node; node = m_edgeList.next(node)) {
+        //        Q_ASSERT(event.point <= m_points.at(m_edges.at(node->data).lower()));
+        //    }
+        //}
+
+        orderedEdges.clear();
+        QPair<QRBTree<int>::Node *, QRBTree<int>::Node *> b = outerBounds(event.point);
+        if (m_edgeList.root) {
+            QRBTree<int>::Node *current = (b.first ? m_edgeList.next(b.first) : m_edgeList.front(m_edgeList.root));
+            // Process edges that are going to be removed from the edge list at the current event point.
+            while (current != b.second) {
+                Q_ASSERT(current);
+                Q_ASSERT(m_edges.at(current->data).node == current);
+                Q_ASSERT(qIntersectionPoint(event.point).isOnLine(m_parent->m_vertices.at(m_edges.at(current->data).from), m_parent->m_vertices.at(m_edges.at(current->data).to)));
+                Q_ASSERT(m_parent->m_vertices.at(m_edges.at(current->data).from) == event.point || m_parent->m_vertices.at(m_edges.at(current->data).to) == event.point);
+                insertEdgeIntoVectorIfWanted(orderedEdges, current->data);
+                current = m_edgeList.next(current);
+            }
+        }
+
+        // Remove edges above the event point, insert edges below the event point.
+        do {
+            event = m_events.last();
+            m_events.pop_back();
+            edgeIndex = event.edge;
+
+            // Edges with zero length should not reach this part.
+            Q_ASSERT(m_parent->m_vertices.at(m_edges.at(edgeIndex).from) != m_parent->m_vertices.at(m_edges.at(edgeIndex).to));
+
+            if (m_edges.at(edgeIndex).node) {
+                Q_ASSERT(event.type == Event::Lower);
+                Q_ASSERT(event.point == m_parent->m_vertices.at(m_edges.at(event.edge).lower()));
+                m_edgeList.deleteNode(m_edges.at(edgeIndex).node);
+            } else {
+                Q_ASSERT(event.type == Event::Upper);
+                Q_ASSERT(event.point == m_parent->m_vertices.at(m_edges.at(event.edge).upper()));
+                QRBTree<int>::Node *left = searchEdgeLeftOf(edgeIndex, b.first);
+                m_edgeList.attachAfter(left, m_edges.at(edgeIndex).node = m_edgeList.newNode());
+                m_edges.at(edgeIndex).node->data = edgeIndex;
+            }
+        } while (!m_events.isEmpty() && m_events.last().point == event.point);
+
+        if (m_edgeList.root) {
+            QRBTree<int>::Node *current = (b.first ? m_edgeList.next(b.first) : m_edgeList.front(m_edgeList.root));
+
+            // Calculate winding number and turn counter-clockwise.
+            int currentWindingNumber = (b.first ? m_edges.at(b.first->data).winding : 0);
+            while (current != b.second) {
+                Q_ASSERT(current);
+                //Q_ASSERT(b.second == 0 || m_edgeList.order(current, b.second) < 0);
+                int i = current->data;
+                Q_ASSERT(m_edges.at(i).node == current);
+
+                // Winding number.
+                int ccwWindingNumber = m_edges.at(i).winding = currentWindingNumber;
+                if (m_edges.at(i).originallyPointingUp) {
+                    --m_edges.at(i).winding;
+                } else {
+                    ++m_edges.at(i).winding;
+                    ++ccwWindingNumber;
+                }
+                currentWindingNumber = m_edges.at(i).winding;
+
+                // Turn counter-clockwise.
+                if ((ccwWindingNumber & 1) == 0) {
+                    Q_ASSERT(m_edges.at(i).previous == -1 && m_edges.at(i).next == -1);
+                    qSwap(m_edges.at(i).from, m_edges.at(i).to);
+                    m_edges.at(i).pointingUp = !m_edges.at(i).pointingUp;
+                }
+
+                current = m_edgeList.next(current);
+            }
+
+            // Process edges that were inserted into the edge list at the current event point.
+            current = (b.second ? m_edgeList.previous(b.second) : m_edgeList.back(m_edgeList.root));
+            while (current != b.first) {
+                Q_ASSERT(current);
+                Q_ASSERT(m_edges.at(current->data).node == current);
+                insertEdgeIntoVectorIfWanted(orderedEdges, current->data);
+                current = m_edgeList.previous(current);
+            }
+        }
+        if (orderedEdges.isEmpty())
+            continue;
+
+        Q_ASSERT((orderedEdges.size() & 1) == 0);
+
+        // Connect edges.
+        // First make sure the first edge point towards the current point.
+        int i;
+        if (m_parent->m_vertices.at(m_edges.at(orderedEdges[0]).from) == event.point) {
+            i = 1;
+            int copy = orderedEdges[0]; // Make copy in case the append() will cause a reallocation.
+            orderedEdges.append(copy);
+        } else {
+            Q_ASSERT(m_parent->m_vertices.at(m_edges.at(orderedEdges[0]).to) == event.point);
+            i = 0;
+        }
+
+        // Remove references to duplicate points. First find the point with lowest index.
+        int pointIndex = INT_MAX;
+        for (int j = i; j < orderedEdges.size(); j += 2) {
+            Q_ASSERT(j + 1 < orderedEdges.size());
+            Q_ASSERT(m_parent->m_vertices.at(m_edges.at(orderedEdges[j]).to) == event.point);
+            Q_ASSERT(m_parent->m_vertices.at(m_edges.at(orderedEdges[j + 1]).from) == event.point);
+            if (m_edges.at(orderedEdges[j]).to < pointIndex)
+                pointIndex = m_edges.at(orderedEdges[j]).to;
+            if (m_edges.at(orderedEdges[j + 1]).from < pointIndex)
+                pointIndex = m_edges.at(orderedEdges[j + 1]).from;
+        }
+
+        for (; i < orderedEdges.size(); i += 2) {
+            // Remove references to duplicate points by making all edges reference one common point.
+            m_edges.at(orderedEdges[i]).to = m_edges.at(orderedEdges[i + 1]).from = pointIndex;
+
+            Q_ASSERT(m_edges.at(orderedEdges[i]).pointingUp || m_edges.at(orderedEdges[i]).previous != -1);
+            Q_ASSERT(!m_edges.at(orderedEdges[i + 1]).pointingUp || m_edges.at(orderedEdges[i + 1]).next != -1);
+
+            m_edges.at(orderedEdges[i]).next = orderedEdges[i + 1];
+            m_edges.at(orderedEdges[i + 1]).previous = orderedEdges[i];
+        }
+    } // end while
+}
+
+void QTriangulator::ComplexToSimple::removeUnusedPoints() {
+    QBitArray used(m_parent->m_vertices.size(), false);
+    for (int i = 0; i < m_edges.size(); ++i) {
+        Q_ASSERT((m_edges.at(i).previous == -1) == (m_edges.at(i).next == -1));
+        if (m_edges.at(i).next != -1)
+            used.setBit(m_edges.at(i).from);
+    }
+    QDataBuffer<quint32> newMapping(m_parent->m_vertices.size());
+    newMapping.resize(m_parent->m_vertices.size());
+    int count = 0;
+    for (int i = 0; i < m_parent->m_vertices.size(); ++i) {
+        if (used.at(i)) {
+            m_parent->m_vertices.at(count) = m_parent->m_vertices.at(i);
+            newMapping.at(i) = count;
+            ++count;
+        }
+    }
+    m_parent->m_vertices.resize(count);
+    for (int i = 0; i < m_edges.size(); ++i) {
+        m_edges.at(i).from = newMapping.at(m_edges.at(i).from);
+        m_edges.at(i).to = newMapping.at(m_edges.at(i).to);
+    }
+}
+
+bool QTriangulator::ComplexToSimple::CompareEdges::operator () (int i, int j) const
+{
+    int cmp = comparePoints(m_parent->m_parent->m_vertices.at(m_parent->m_edges.at(i).from),
+        m_parent->m_parent->m_vertices.at(m_parent->m_edges.at(j).from));
+    if (cmp == 0) {
+        cmp = comparePoints(m_parent->m_parent->m_vertices.at(m_parent->m_edges.at(i).to),
+            m_parent->m_parent->m_vertices.at(m_parent->m_edges.at(j).to));
+    }
+    return cmp > 0;
+}
+
+inline bool QTriangulator::ComplexToSimple::Event::operator < (const Event &other) const
+{
+    if (point == other.point)
+        return type < other.type; // 'Lower' has higher priority than 'Upper'.
+    return other.point < point;
+}
+
+//============================================================================//
+//                QTriangulator::ComplexToSimple::DebugDialog                 //
+//============================================================================//
+
+#ifdef Q_TRIANGULATOR_DEBUG
+
+QTriangulator::ComplexToSimple::DebugDialog::DebugDialog(ComplexToSimple *parent, int currentVertex)
+    : m_parent(parent), m_vertex(currentVertex)
+{
+    QDataBuffer<QPodPoint> &vertices = m_parent->m_parent->m_vertices;
+    if (vertices.isEmpty())
+        return;
+    
+    int minX, maxX, minY, maxY;
+    minX = maxX = vertices.at(0).x;
+    minY = maxY = vertices.at(0).y;
+    for (int i = 1; i < vertices.size(); ++i) {
+        minX = qMin(minX, vertices.at(i).x);
+        maxX = qMax(maxX, vertices.at(i).x);
+        minY = qMin(minY, vertices.at(i).y);
+        maxY = qMax(maxY, vertices.at(i).y);
+    }
+    int w = maxX - minX;
+    int h = maxY - minY;
+    qreal border = qMin(w, h) / 10.0;
+    m_window = QRectF(minX - border, minY - border, (maxX - minX + 2 * border), (maxY - minY + 2 * border));
+}
+
+void QTriangulator::ComplexToSimple::DebugDialog::paintEvent(QPaintEvent *)
+{
+    QPainter p(this);
+    p.setRenderHint(QPainter::Antialiasing, true);
+    p.fillRect(rect(), Qt::black);
+    QDataBuffer<QPodPoint> &vertices = m_parent->m_parent->m_vertices;
+    if (vertices.isEmpty())
+        return;
+    
+    qreal halfPointSize = qMin(m_window.width(), m_window.height()) / 300.0;
+    p.setWindow(m_window.toRect());
+
+    p.setPen(Qt::white);
+
+    QDataBuffer<Edge> &edges = m_parent->m_edges;
+    for (int i = 0; i < edges.size(); ++i) {
+        QPodPoint u = vertices.at(edges.at(i).from);
+        QPodPoint v = vertices.at(edges.at(i).to);
+        p.drawLine(u.x, u.y, v.x, v.y);
+    }
+
+    for (int i = 0; i < vertices.size(); ++i) {
+        QPodPoint q = vertices.at(i);
+        p.fillRect(QRectF(q.x - halfPointSize, q.y - halfPointSize, 2 * halfPointSize, 2 * halfPointSize), Qt::red);
+    }
+
+    Qt::GlobalColor colors[6] = {Qt::red, Qt::green, Qt::blue, Qt::cyan, Qt::magenta, Qt::yellow};
+    p.setOpacity(0.5);
+    int count = 0;
+    if (m_parent->m_edgeList.root) {
+        QRBTree<int>::Node *current = m_parent->m_edgeList.front(m_parent->m_edgeList.root);
+        while (current) {
+            p.setPen(colors[count++ % 6]);
+            QPodPoint u = vertices.at(edges.at(current->data).from);
+            QPodPoint v = vertices.at(edges.at(current->data).to);
+            p.drawLine(u.x, u.y, v.x, v.y);
+            current = m_parent->m_edgeList.next(current);
+        }
+    }
+
+    p.setOpacity(1.0);
+    QPodPoint q = vertices.at(m_vertex);
+    p.fillRect(QRectF(q.x - halfPointSize, q.y - halfPointSize, 2 * halfPointSize, 2 * halfPointSize), Qt::green);
+
+    p.setPen(Qt::gray);
+    QDataBuffer<Split> &splits = m_parent->m_splits;
+    for (int i = 0; i < splits.size(); ++i) {
+        QPodPoint q = vertices.at(splits.at(i).vertex);
+        QPodPoint u = vertices.at(edges.at(splits.at(i).edge).from) - q;
+        QPodPoint v = vertices.at(edges.at(splits.at(i).edge).to) - q;
+        qreal uLen = sqrt(qreal(qDot(u, u)));
+        qreal vLen = sqrt(qreal(qDot(v, v)));
+        if (uLen) {
+            u.x *= 2 * halfPointSize / uLen;
+            u.y *= 2 * halfPointSize / uLen;
+        }
+        if (vLen) {
+            v.x *= 2 * halfPointSize / vLen;
+            v.y *= 2 * halfPointSize / vLen;
+        }
+        u += q;
+        v += q;
+        p.drawLine(u.x, u.y, v.x, v.y);        
+    }
+}
+
+void QTriangulator::ComplexToSimple::DebugDialog::wheelEvent(QWheelEvent *event)
+{
+    qreal scale = exp(-0.001 * event->delta());
+    QPointF center = m_window.center();
+    QPointF delta = scale * (m_window.bottomRight() - center);
+    m_window = QRectF(center - delta, center + delta);
+    event->accept();
+    update();
+}
+
+void QTriangulator::ComplexToSimple::DebugDialog::mouseMoveEvent(QMouseEvent *event)
+{
+    if (event->buttons() & Qt::LeftButton) {
+        QPointF delta = event->pos() - m_lastMousePos;
+        delta.setX(delta.x() * m_window.width() / width());
+        delta.setY(delta.y() * m_window.height() / height());
+        m_window.translate(-delta.x(), -delta.y());
+        m_lastMousePos = event->pos();
+        event->accept();
+        update();
+    }
+}
+
+void QTriangulator::ComplexToSimple::DebugDialog::mousePressEvent(QMouseEvent *event)
+{
+    if (event->button() == Qt::LeftButton)
+        m_lastMousePos = event->pos();
+    event->accept();
+}
+
+
+#endif
+
+//============================================================================//
+//                      QTriangulator::SimpleToMonotone                       //
+//============================================================================//
+
+void QTriangulator::SimpleToMonotone::decompose()
+{
+    setupDataStructures();
+    removeZeroLengthEdges();
+    monotoneDecomposition();
+
+    m_parent->m_indices.clear();
+    QBitArray processed(m_edges.size(), false);
+    for (int first = 0; first < m_edges.size(); ++first) {
+        if (processed.at(first))
+            continue;
+        int i = first;
+        do {
+            Q_ASSERT(!processed.at(i));
+            Q_ASSERT(m_edges.at(m_edges.at(i).next).previous == i);
+            m_parent->m_indices.push_back(m_edges.at(i).from);
+            processed.setBit(i);
+            i = m_edges.at(i).next;
+        } while (i != first);
+        if (m_parent->m_indices.size() > 0 && m_parent->m_indices.back() != Q_TRIANGULATE_END_OF_POLYGON)
+            m_parent->m_indices.push_back(Q_TRIANGULATE_END_OF_POLYGON);
+    }
+}
+
+void QTriangulator::SimpleToMonotone::setupDataStructures()
+{
+    int i = 0;
+    Edge e;
+    e.node = 0;
+    e.twin = -1;
+
+    while (i + 3 <= m_parent->m_indices.size()) {
+        int start = m_edges.size();
+
+        do {
+            e.from = m_parent->m_indices.at(i);
+            e.type = RegularVertex;
+            e.next = m_edges.size() + 1;
+            e.previous = m_edges.size() - 1;
+            m_edges.add(e);
+            ++i;
+            Q_ASSERT(i < m_parent->m_indices.size());
+        } while (m_parent->m_indices.at(i) != Q_TRIANGULATE_END_OF_POLYGON);
+
+        m_edges.last().next = start;
+        m_edges.at(start).previous = m_edges.size() - 1;
+        ++i; // Skip Q_TRIANGULATE_END_OF_POLYGON.
+    }
+
+    for (i = 0; i < m_edges.size(); ++i) {
+        m_edges.at(i).to = m_edges.at(m_edges.at(i).next).from;
+        m_edges.at(i).pointingUp = m_parent->m_vertices.at(m_edges.at(i).to) < m_parent->m_vertices.at(m_edges.at(i).from);
+        m_edges.at(i).helper = -1; // Not initialized here.
+    }
+}
+
+void QTriangulator::SimpleToMonotone::removeZeroLengthEdges()
+{
+    for (int i = 0; i < m_edges.size(); ++i) {
+        if (m_parent->m_vertices.at(m_edges.at(i).from) == m_parent->m_vertices.at(m_edges.at(i).to)) {
+            m_edges.at(m_edges.at(i).previous).next = m_edges.at(i).next;
+            m_edges.at(m_edges.at(i).next).previous = m_edges.at(i).previous;
+            m_edges.at(m_edges.at(i).next).from = m_edges.at(i).from;
+            m_edges.at(i).next = -1; // Mark as removed.
+        }
+    }
+
+    QDataBuffer<int> newMapping(m_edges.size());
+    newMapping.resize(m_edges.size());
+    int count = 0;
+    for (int i = 0; i < m_edges.size(); ++i) {
+        if (m_edges.at(i).next != -1) {
+            m_edges.at(count) = m_edges.at(i);
+            newMapping.at(i) = count;
+            ++count;
+        }
+    }
+    m_edges.resize(count);
+    for (int i = 0; i < m_edges.size(); ++i) {
+        m_edges.at(i).next = newMapping.at(m_edges.at(i).next);
+        m_edges.at(i).previous = newMapping.at(m_edges.at(i).previous);
+    }
+}
+
+void QTriangulator::SimpleToMonotone::fillPriorityQueue()
+{
+    m_upperVertex.reset();
+    m_upperVertex.reserve(m_edges.size());
+    for (int i = 0; i < m_edges.size(); ++i)
+        m_upperVertex.add(i);
+    CompareVertices cmp(this);
+    //qSort(m_upperVertex.data(), m_upperVertex.data() + m_upperVertex.size(), cmp);
+    sort(m_upperVertex.data(), m_upperVertex.size(), cmp);
+    //for (int i = 1; i < m_upperVertex.size(); ++i) {
+    //    Q_ASSERT(!cmp(m_upperVertex.at(i), m_upperVertex.at(i - 1)));
+    //}
+}
+
+bool QTriangulator::SimpleToMonotone::edgeIsLeftOfEdge(int leftEdgeIndex, int rightEdgeIndex) const
+{
+    const Edge &leftEdge = m_edges.at(leftEdgeIndex);
+    const Edge &rightEdge = m_edges.at(rightEdgeIndex);
+    const QPodPoint &u = m_parent->m_vertices.at(rightEdge.upper());
+    const QPodPoint &l = m_parent->m_vertices.at(rightEdge.lower());
+    qint64 d = qPointDistanceFromLine(m_parent->m_vertices.at(leftEdge.upper()), l, u);
+    // d < 0: left, d > 0: right, d == 0: on top
+    if (d == 0)
+        d = qPointDistanceFromLine(m_parent->m_vertices.at(leftEdge.lower()), l, u);
+    return d < 0;
+}
+
+// Returns the rightmost edge not to the right of the given edge.
+QRBTree<int>::Node *QTriangulator::SimpleToMonotone::searchEdgeLeftOfEdge(int edgeIndex) const
+{
+    QRBTree<int>::Node *current = m_edgeList.root;
+    QRBTree<int>::Node *result = 0;
+    while (current) {
+        if (edgeIsLeftOfEdge(edgeIndex, current->data)) {
+            current = current->left;
+        } else {
+            result = current;
+            current = current->right;
+        }
+    }
+    return result;
+}
+
+// Returns the rightmost edge left of the given point.
+QRBTree<int>::Node *QTriangulator::SimpleToMonotone::searchEdgeLeftOfPoint(int pointIndex) const
+{
+    QRBTree<int>::Node *current = m_edgeList.root;
+    QRBTree<int>::Node *result = 0;
+    while (current) {
+        const QPodPoint &p1 = m_parent->m_vertices.at(m_edges.at(current->data).lower());
+        const QPodPoint &p2 = m_parent->m_vertices.at(m_edges.at(current->data).upper());
+        qint64 d = qPointDistanceFromLine(m_parent->m_vertices.at(pointIndex), p1, p2);
+        if (d <= 0) {
+            current = current->left;
+        } else {
+            result = current;
+            current = current->right;
+        }
+    }
+    return result;
+}
+
+void QTriangulator::SimpleToMonotone::classifyVertex(int i)
+{
+    Edge &e2 = m_edges.at(i);
+    const Edge &e1 = m_edges.at(e2.previous);
+
+    bool startOrSplit = (e1.pointingUp && !e2.pointingUp);
+    bool endOrMerge = (!e1.pointingUp && e2.pointingUp);
+
+    const QPodPoint &p1 = m_parent->m_vertices.at(e1.from);
+    const QPodPoint &p2 = m_parent->m_vertices.at(e2.from);
+    const QPodPoint &p3 = m_parent->m_vertices.at(e2.to);
+    qint64 d = qPointDistanceFromLine(p1, p2, p3);
+    Q_ASSERT(d != 0 || (!startOrSplit && !endOrMerge));
+
+    e2.type = RegularVertex;
+
+    if (m_clockwiseOrder) {
+        if (startOrSplit)
+            e2.type = (d < 0 ? SplitVertex : StartVertex);
+        else if (endOrMerge)
+            e2.type = (d < 0 ? MergeVertex : EndVertex);
+    } else {
+        if (startOrSplit)
+            e2.type = (d > 0 ? SplitVertex : StartVertex);
+        else if (endOrMerge)
+            e2.type = (d > 0 ? MergeVertex : EndVertex);
+    }
+}
+
+void QTriangulator::SimpleToMonotone::classifyVertices()
+{
+    for (int i = 0; i < m_edges.size(); ++i)
+        classifyVertex(i);
+}
+
+bool QTriangulator::SimpleToMonotone::pointIsInSector(const QPodPoint &p, const QPodPoint &v1, const QPodPoint &v2, const QPodPoint &v3)
+{
+    bool leftOfPreviousEdge = !qPointIsLeftOfLine(p, v2, v1);
+    bool leftOfNextEdge = !qPointIsLeftOfLine(p, v3, v2);
+
+    if (qPointIsLeftOfLine(v1, v2, v3))
+        return leftOfPreviousEdge && leftOfNextEdge;
+    else
+        return leftOfPreviousEdge || leftOfNextEdge;
+}
+
+bool QTriangulator::SimpleToMonotone::pointIsInSector(int vertex, int sector)
+{
+    const QPodPoint &center = m_parent->m_vertices.at(m_edges.at(sector).from);
+    // Handle degenerate edges.
+    while (m_parent->m_vertices.at(m_edges.at(vertex).from) == center)
+        vertex = m_edges.at(vertex).next;
+    int next = m_edges.at(sector).next;
+    while (m_parent->m_vertices.at(m_edges.at(next).from) == center)
+        next = m_edges.at(next).next;
+    int previous = m_edges.at(sector).previous;
+    while (m_parent->m_vertices.at(m_edges.at(previous).from) == center)
+        previous = m_edges.at(previous).previous;
+
+    const QPodPoint &p = m_parent->m_vertices.at(m_edges.at(vertex).from);
+    const QPodPoint &v1 = m_parent->m_vertices.at(m_edges.at(previous).from);
+    const QPodPoint &v3 = m_parent->m_vertices.at(m_edges.at(next).from);
+    if (m_clockwiseOrder)
+        return pointIsInSector(p, v3, center, v1);
+    else
+        return pointIsInSector(p, v1, center, v3);
+}
+
+int QTriangulator::SimpleToMonotone::findSector(int edge, int vertex)
+{
+    while (!pointIsInSector(vertex, edge)) {
+        edge = m_edges.at(m_edges.at(edge).previous).twin;
+        Q_ASSERT(edge != -1);
+    }
+    return edge;
+}
+
+void QTriangulator::SimpleToMonotone::createDiagonal(int lower, int upper)
+{
+    lower = findSector(lower, upper);
+    upper = findSector(upper, lower);
+
+    int prevLower = m_edges.at(lower).previous;
+    int prevUpper = m_edges.at(upper).previous;
+
+    Edge e;
+
+    e.twin = m_edges.size() + 1;
+    e.next = upper;
+    e.previous = prevLower;
+    e.from = m_edges.at(lower).from;
+    e.to = m_edges.at(upper).from;
+    m_edges.at(upper).previous = m_edges.at(prevLower).next = int(m_edges.size());
+    m_edges.add(e);
+
+    e.twin = m_edges.size() - 1;
+    e.next = lower;
+    e.previous = prevUpper;
+    e.from = m_edges.at(upper).from;
+    e.to = m_edges.at(lower).from;
+    m_edges.at(lower).previous = m_edges.at(prevUpper).next = int(m_edges.size());
+    m_edges.add(e);
+}
+
+void QTriangulator::SimpleToMonotone::monotoneDecomposition()
+{
+    if (m_edges.isEmpty())
+        return;
+
+    Q_ASSERT(!m_edgeList.root);
+    QDataBuffer<std::pair<int, int> > diagonals;
+
+    int i = 0;
+    for (int index = 1; index < m_edges.size(); ++index) {
+        if (m_parent->m_vertices.at(m_edges.at(index).from) < m_parent->m_vertices.at(m_edges.at(i).from))
+            i = index;
+    }
+    Q_ASSERT(i < m_edges.size());
+    int j = m_edges.at(i).previous;
+    Q_ASSERT(j < m_edges.size());
+    m_clockwiseOrder = qPointIsLeftOfLine(m_parent->m_vertices.at(m_edges.at(i).from),
+        m_parent->m_vertices.at(m_edges.at(j).from), m_parent->m_vertices.at(m_edges.at(i).to));
+
+    classifyVertices();
+    fillPriorityQueue();
+
+    // debug: set helpers explicitly (shouldn't be necessary)
+    //for (int i = 0; i < m_edges.size(); ++i)
+    //    m_edges.at(i).helper = m_edges.at(i).upper();
+
+    while (!m_upperVertex.isEmpty()) {
+        i = m_upperVertex.last();
+        Q_ASSERT(i < m_edges.size());
+        m_upperVertex.pop_back();
+        j = m_edges.at(i).previous;
+        Q_ASSERT(j < m_edges.size());
+
+        QRBTree<int>::Node *leftEdgeNode = 0;
+
+        switch (m_edges.at(i).type) {
+        case RegularVertex:
+            // If polygon interior is to the right of the vertex...
+            if (m_edges.at(i).pointingUp == m_clockwiseOrder) {
+                if (m_edges.at(i).node) {
+                    Q_ASSERT(!m_edges.at(j).node);
+                    if (m_edges.at(m_edges.at(i).helper).type == MergeVertex)
+                        diagonals.add(std::pair<int, int>(i, m_edges.at(i).helper));
+                    m_edges.at(j).node = m_edges.at(i).node;
+                    m_edges.at(i).node = 0;
+                    m_edges.at(j).node->data = j;
+                    m_edges.at(j).helper = i;
+                } else if (m_edges.at(j).node) {
+                    Q_ASSERT(!m_edges.at(i).node);
+                    if (m_edges.at(m_edges.at(j).helper).type == MergeVertex)
+                        diagonals.add(std::pair<int, int>(i, m_edges.at(j).helper));
+                    m_edges.at(i).node = m_edges.at(j).node;
+                    m_edges.at(j).node = 0;
+                    m_edges.at(i).node->data = i;
+                    m_edges.at(i).helper = i;
+                } else {
+                    qWarning("Inconsistent polygon. (#1)");
+                }
+            } else {
+                leftEdgeNode = searchEdgeLeftOfPoint(m_edges.at(i).from);
+                if (leftEdgeNode) {
+                    if (m_edges.at(m_edges.at(leftEdgeNode->data).helper).type == MergeVertex)
+                        diagonals.add(std::pair<int, int>(i, m_edges.at(leftEdgeNode->data).helper));
+                    m_edges.at(leftEdgeNode->data).helper = i;
+                } else {
+                    qWarning("Inconsistent polygon. (#2)");
+                }
+            }
+            break;
+        case SplitVertex:
+            leftEdgeNode = searchEdgeLeftOfPoint(m_edges.at(i).from);
+            if (leftEdgeNode) {
+                diagonals.add(std::pair<int, int>(i, m_edges.at(leftEdgeNode->data).helper));
+                m_edges.at(leftEdgeNode->data).helper = i;
+            } else {
+                qWarning("Inconsistent polygon. (#3)");
+            }
+            // Fall through.
+        case StartVertex:
+            if (m_clockwiseOrder) {
+                leftEdgeNode = searchEdgeLeftOfEdge(j);
+                QRBTree<int>::Node *node = m_edgeList.newNode();
+                node->data = j;
+                m_edges.at(j).node = node;
+                m_edges.at(j).helper = i;
+                m_edgeList.attachAfter(leftEdgeNode, node);
+                Q_ASSERT(m_edgeList.verify());
+            } else  {
+                leftEdgeNode = searchEdgeLeftOfEdge(i);
+                QRBTree<int>::Node *node = m_edgeList.newNode();
+                node->data = i;
+                m_edges.at(i).node = node;
+                m_edges.at(i).helper = i;
+                m_edgeList.attachAfter(leftEdgeNode, node);
+                Q_ASSERT(m_edgeList.verify());
+            }
+            break;
+        case MergeVertex:
+            leftEdgeNode = searchEdgeLeftOfPoint(m_edges.at(i).from);
+            if (leftEdgeNode) {
+                if (m_edges.at(m_edges.at(leftEdgeNode->data).helper).type == MergeVertex)
+                    diagonals.add(std::pair<int, int>(i, m_edges.at(leftEdgeNode->data).helper));
+                m_edges.at(leftEdgeNode->data).helper = i;
+            } else {
+                qWarning("Inconsistent polygon. (#4)");
+            }
+            // Fall through.
+        case EndVertex:
+            if (m_clockwiseOrder) {
+                if (m_edges.at(m_edges.at(i).helper).type == MergeVertex)
+                    diagonals.add(std::pair<int, int>(i, m_edges.at(i).helper));
+                if (m_edges.at(i).node) {
+                    m_edgeList.deleteNode(m_edges.at(i).node);
+                    Q_ASSERT(m_edgeList.verify());
+                } else {
+                    qWarning("Inconsistent polygon. (#5)");
+                }
+            } else {
+                if (m_edges.at(m_edges.at(j).helper).type == MergeVertex)
+                    diagonals.add(std::pair<int, int>(i, m_edges.at(j).helper));
+                if (m_edges.at(j).node) {
+                    m_edgeList.deleteNode(m_edges.at(j).node);
+                    Q_ASSERT(m_edgeList.verify());
+                } else {
+                    qWarning("Inconsistent polygon. (#6)");
+                }
+            }
+            break;
+        }
+    }
+
+    for (int i = 0; i < diagonals.size(); ++i)
+        createDiagonal(diagonals.at(i).first, diagonals.at(i).second);
+}
+
+bool QTriangulator::SimpleToMonotone::CompareVertices::operator () (int i, int j) const
+{
+    if (m_parent->m_edges.at(i).from == m_parent->m_edges.at(j).from)
+        return m_parent->m_edges.at(i).type > m_parent->m_edges.at(j).type;
+    return m_parent->m_parent->m_vertices.at(m_parent->m_edges.at(i).from) >
+        m_parent->m_parent->m_vertices.at(m_parent->m_edges.at(j).from);
+}
+
+//============================================================================//
+//                     QTriangulator::MonotoneToTriangles                     //
+//============================================================================//
+
+void QTriangulator::MonotoneToTriangles::decompose()
+{
+    QVector<quint32> result;
+    QDataBuffer<int> stack;
+    m_first = 0;
+    // Require at least three more indices.
+    while (m_first + 3 <= m_parent->m_indices.size()) {
+        m_length = 0;
+        while (m_parent->m_indices.at(m_first + m_length) != Q_TRIANGULATE_END_OF_POLYGON) {
+            ++m_length;
+            Q_ASSERT(m_first + m_length < m_parent->m_indices.size());
+        }
+        if (m_length < 3) {
+            m_first += m_length + 1;
+            continue;
+        }
+
+        int minimum = 0;
+        while (less(next(minimum), minimum))
+            minimum = next(minimum);
+        while (less(previous(minimum), minimum))
+            minimum = previous(minimum);
+
+        stack.reset();
+        stack.add(minimum);
+        int left = previous(minimum);
+        int right = next(minimum);
+        bool stackIsOnLeftSide;
+        bool clockwiseOrder = leftOfEdge(minimum, left, right);
+
+        if (less(left, right)) {
+            stack.add(left);
+            left = previous(left);
+            stackIsOnLeftSide = true;
+        } else {
+            stack.add(right);
+            right = next(right);
+            stackIsOnLeftSide = false;
+        }
+
+        for (int count = 0; count + 2 < m_length; ++count)
+        {
+            Q_ASSERT(stack.size() >= 2);
+            if (less(left, right)) {
+                if (stackIsOnLeftSide == false) {
+                    for (int i = 0; i + 1 < stack.size(); ++i) {
+                        result.push_back(indices(stack.at(i + 1)));
+                        result.push_back(indices(left));
+                        result.push_back(indices(stack.at(i)));
+                    }
+                    stack.first() = stack.last();
+                    stack.resize(1);
+                } else {
+                    while (stack.size() >= 2 && (clockwiseOrder ^ !leftOfEdge(left, stack.at(stack.size() - 2), stack.last()))) {
+                        result.push_back(indices(stack.at(stack.size() - 2)));
+                        result.push_back(indices(left));
+                        result.push_back(indices(stack.last()));
+                        stack.pop_back();
+                    }
+                }
+                stack.add(left);
+                left = previous(left);
+                stackIsOnLeftSide = true;
+            } else {
+                if (stackIsOnLeftSide == true) {
+                    for (int i = 0; i + 1 < stack.size(); ++i) {
+                        result.push_back(indices(stack.at(i)));
+                        result.push_back(indices(right));
+                        result.push_back(indices(stack.at(i + 1)));
+                    }
+                    stack.first() = stack.last();
+                    stack.resize(1);
+                } else {
+                    while (stack.size() >= 2 && (clockwiseOrder ^ !leftOfEdge(right, stack.last(), stack.at(stack.size() - 2)))) {
+                        result.push_back(indices(stack.last()));
+                        result.push_back(indices(right));
+                        result.push_back(indices(stack.at(stack.size() - 2)));
+                        stack.pop_back();
+                    }
+                }
+                stack.add(right);
+                right = next(right);
+                stackIsOnLeftSide = false;
+            }
+        }
+
+        m_first += m_length + 1;
+    }
+    m_parent->m_indices = result;
+}
+
+//============================================================================//
+//                                qTriangulate                                //
+//============================================================================//
+
+QTriangleSet qTriangulate(const qreal *polygon, int count, uint hint, const QTransform &matrix)
+{
+    QTriangulator triangulator;
+    triangulator.initialize(polygon, count, hint, matrix);
+    return triangulator.triangulate();
+}
+
+QTriangleSet qTriangulate(const QVectorPath &path, const QTransform &matrix, qreal lod)
+{
+    QTriangulator triangulator;
+    triangulator.initialize(path, matrix, lod);
+    return triangulator.triangulate();
+}
+
+QTriangleSet qTriangulate(const QPainterPath &path, const QTransform &matrix, qreal lod)
+{
+    QTriangulator triangulator;
+    triangulator.initialize(path, matrix, lod);
+    return triangulator.triangulate();
+}
+
+QPolylineSet qPolyline(const QVectorPath &path, const QTransform &matrix, qreal lod)
+{
+    QTriangulator triangulator;
+    triangulator.initialize(path, matrix, lod);
+    return triangulator.polyline();
+}
+
+QPolylineSet qPolyline(const QPainterPath &path, const QTransform &matrix, qreal lod)
+{
+    QTriangulator triangulator;
+    triangulator.initialize(path, matrix, lod);
+    return triangulator.polyline();
+}
+
+QT_END_NAMESPACE
diff --git a/src/opengl/gl2paintengineex/qtriangulator_p.h b/src/opengl/gl2paintengineex/qtriangulator_p.h
new file mode 100644
index 0000000..da47666
--- /dev/null
+++ b/src/opengl/gl2paintengineex/qtriangulator_p.h
@@ -0,0 +1,98 @@
+/****************************************************************************
+**
+** Copyright (C) 2009 Nokia Corporation and/or its subsidiary(-ies).
+** All rights reserved.
+** Contact: Nokia Corporation (qt-info@nokia.com)
+**
+** This file is part of the QtOpenGL module of the Qt Toolkit.
+**
+** $QT_BEGIN_LICENSE:LGPL$
+** No Commercial Usage
+** This file contains pre-release code and may not be distributed.
+** You may use this file in accordance with the terms and conditions
+** contained in the Technology Preview License Agreement accompanying
+** this package.
+**
+** GNU Lesser General Public License Usage
+** Alternatively, this file may be used under the terms of the GNU Lesser
+** General Public License version 2.1 as published by the Free Software
+** Foundation and appearing in the file LICENSE.LGPL included in the
+** packaging of this file.  Please review the following information to
+** ensure the GNU Lesser General Public License version 2.1 requirements
+** will be met: http://www.gnu.org/licenses/old-licenses/lgpl-2.1.html.
+**
+** In addition, as a special exception, Nokia gives you certain additional
+** rights.  These rights are described in the Nokia Qt LGPL Exception
+** version 1.1, included in the file LGPL_EXCEPTION.txt in this package.
+**
+** If you have questions regarding the use of this file, please contact
+** Nokia at qt-info@nokia.com.
+**
+**
+**
+**
+**
+**
+**
+**
+** $QT_END_LICENSE$
+**
+****************************************************************************/
+
+#ifndef QTRIANGULATOR_P_H
+#define QTRIANGULATOR_P_H
+
+//
+//  W A R N I N G
+//  -------------
+//
+// This file is not part of the Qt API.  It exists purely as an
+// implementation detail.  This header file may change from version to
+// version without notice, or even be removed.
+//
+// We mean it.
+//
+
+#include <QtCore/qvector.h>
+#include <QtGui/private/qvectorpath_p.h>
+
+QT_BEGIN_NAMESPACE
+
+#define Q_TRIANGULATE_END_OF_POLYGON quint32(-1)
+
+struct QTriangleSet
+{
+    inline QTriangleSet() { }
+    inline QTriangleSet(const QTriangleSet &other) : vertices(other.vertices), indices(other.indices) { }
+    QTriangleSet &operator = (const QTriangleSet &other) {vertices = other.vertices; indices = other.indices; return *this;}
+
+    // The vertices of a triangle are given by: (x[i[n]], y[i[n]]), (x[j[n]], y[j[n]]), (x[k[n]], y[k[n]]), n = 0, 1, ...
+    QVector<qreal> vertices; // [x[0], y[0], x[1], y[1], x[2], ...]
+    QVector<quint32> indices; // [i[0], j[0], k[0], i[1], j[1], k[1], i[2], ...]
+};
+
+struct QPolylineSet
+{
+    inline QPolylineSet() { }
+    inline QPolylineSet(const QPolylineSet &other) : vertices(other.vertices), indices(other.indices) { }
+    QPolylineSet &operator = (const QPolylineSet &other) {vertices = other.vertices; indices = other.indices; return *this;}
+
+    QVector<qreal> vertices; // [x[0], y[0], x[1], y[1], x[2], ...]
+    QVector<quint32> indices;
+
+};
+
+// The vertex coordinates of the returned triangle set will be rounded to a grid with a mesh size
+// of 1/32. The polygon is first transformed, then scaled by 32, the coordinates are rounded to
+// integers, the polygon is triangulated, and then scaled back by 1/32.
+// 'hint' should be a combination of QVectorPath::Hints.
+// 'lod' is the level of detail. Default is 1. Curves are split into more lines when 'lod' is higher.
+QTriangleSet qTriangulate(const qreal *polygon, int count, uint hint = QVectorPath::PolygonHint | QVectorPath::OddEvenFill, const QTransform &matrix = QTransform());
+QTriangleSet qTriangulate(const QVectorPath &path, const QTransform &matrix = QTransform(), qreal lod = 1);
+QTriangleSet qTriangulate(const QPainterPath &path, const QTransform &matrix = QTransform(), qreal lod = 1);
+QPolylineSet qPolyline(const QVectorPath &path, const QTransform &matrix = QTransform(), qreal lod = 1);
+QPolylineSet qPolyline(const QPainterPath &path, const QTransform &matrix = QTransform(), qreal lod = 1);
+
+QT_END_NAMESPACE
+
+#endif
diff --git a/src/opengl/opengl.pro b/src/opengl/opengl.pro
index b2474ed..ec01db0 100644
--- a/src/opengl/opengl.pro
+++ b/src/opengl/opengl.pro
@@ -54,7 +54,8 @@ SOURCES	+= qgl.cpp \
                 gl2paintengineex/qpaintengineex_opengl2_p.h \
                 gl2paintengineex/qglengineshadersource_p.h \
                 gl2paintengineex/qglcustomshaderstage_p.h \
-                gl2paintengineex/qtriangulatingstroker_p.h
+                gl2paintengineex/qtriangulatingstroker_p.h \
+                gl2paintengineex/qtriangulator_p.h
 
     SOURCES +=  qglshaderprogram.cpp \
                 qglpixmapfilter.cpp \
@@ -67,7 +68,8 @@ SOURCES	+= qgl.cpp \
                 gl2paintengineex/qgl2pexvertexarray.cpp \
                 gl2paintengineex/qpaintengineex_opengl2.cpp \
                 gl2paintengineex/qglcustomshaderstage.cpp \
-                gl2paintengineex/qtriangulatingstroker.cpp
+                gl2paintengineex/qtriangulatingstroker.cpp \
+                gl2paintengineex/qtriangulator.cpp
 
 }