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Diffstat (limited to 'src/gui/opengl/qtriangulator.cpp')
| -rw-r--r-- | src/gui/opengl/qtriangulator.cpp | 2621 |
1 files changed, 2621 insertions, 0 deletions
diff --git a/src/gui/opengl/qtriangulator.cpp b/src/gui/opengl/qtriangulator.cpp new file mode 100644 index 0000000000..67c2a6494e --- /dev/null +++ b/src/gui/opengl/qtriangulator.cpp @@ -0,0 +1,2621 @@ +/**************************************************************************** +** +** Copyright (C) 2011 Nokia Corporation and/or its subsidiary(-ies). +** All rights reserved. +** Contact: Nokia Corporation (qt-info@nokia.com) +** +** This file is part of the QtGui module of the Qt Toolkit. +** +** $QT_BEGIN_LICENSE:LGPL$ +** GNU Lesser General Public License Usage +** 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. +** +** GNU General Public License Usage +** Alternatively, this file may be used under the terms of the GNU General +** Public License version 3.0 as published by the Free Software Foundation +** and appearing in the file LICENSE.GPL included in the packaging of this +** file. Please review the following information to ensure the GNU General +** Public License version 3.0 requirements will be met: +** http://www.gnu.org/copyleft/gpl.html. +** +** Other Usage +** Alternatively, this file may be used in accordance with the terms and +** conditions contained in a signed written agreement between you and Nokia. +** +** +** +** +** +** $QT_END_LICENSE$ +** +****************************************************************************/ + +#include "qtriangulator_p.h" + +#include <QtWidgets/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 <private/qopenglcontext_p.h> +#include <private/qopenglextensions_p.h> +#include <private/qrbtree_p.h> + +#include <math.h> + +QT_BEGIN_NAMESPACE + +//#define Q_TRIANGULATOR_DEBUG + +#define Q_FIXED_POINT_SCALE 32 + +// Quick sort. +template <class T, class LessThan> +#ifdef Q_CC_RVCT // RVCT 2.2 doesn't see recursive _static_ template function +void sort(T *array, int count, LessThan lessThan) +#else +static void sort(T *array, int count, LessThan lessThan) +#endif +{ + // 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> +#ifdef Q_CC_RVCT +void sort(T *array, int count) // RVCT 2.2 doesn't see recursive _static_ template function +#else +static void sort(T *array, int count) +#endif +{ + // 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); +} + +template<typename T> +struct QVertexSet +{ + inline QVertexSet() { } + inline QVertexSet(const QVertexSet<T> &other) : vertices(other.vertices), indices(other.indices) { } + QVertexSet<T> &operator = (const QVertexSet<T> &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<T> indices; // [i[0], j[0], k[0], i[1], j[1], k[1], i[2], ...] +}; + +//============================================================================// +// 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 QT_PREPEND_NAMESPACE(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) +{ + // upperLeft = point, xOffset = 0/1, yOffset = 0/1. + QIntersectionPoint p = {{point.x, point.y}, {0, 1}, {0, 1}}; + return p; +} + +static inline QIntersectionPoint qIntersectionPoint(int x, int y) +{ + // upperLeft = (x, y), xOffset = 0/1, 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: + QMaxHeap() : m_data(0) {} + 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; +} + +//============================================================================// +// 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 // +//============================================================================// +template<typename T> +class QTriangulator +{ +public: + typedef QVarLengthArray<int, 6> ShortArray; + + //================================// + // QTriangulator::ComplexToSimple // + //================================// + friend class ComplexToSimple; + class ComplexToSimple + { + public: + inline ComplexToSimple(QTriangulator<T> *parent) : m_parent(parent), + m_edges(0), m_events(0), m_splits(0) { } + 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<T> *parent) : m_parent(parent), m_edges(0), m_upperVertex(0) { } + void decompose(); + private: + enum VertexType {MergeVertex, EndVertex, RegularVertex, StartVertex, SplitVertex}; + + struct Edge + { + QRBTree<int>::Node *node; + int helper, twin, next, previous; + T 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<T> *parent) : m_parent(parent) { } + void decompose(); + private: + inline T 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((qint32)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((qint32)indices(i)), + m_parent->m_vertices.at((qint32)indices(j)), m_parent->m_vertices.at((qint32)indices(k))); + } + + QTriangulator<T> *m_parent; + int m_first; + int m_length; + }; + + inline QTriangulator() : m_vertices(0) { } + + // 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. + QVertexSet<T> triangulate(); + QVertexSet<T> polyline(); +private: + QDataBuffer<QPodPoint> m_vertices; + QVector<T> m_indices; + uint m_hint; +}; + +//============================================================================// +// QTriangulator // +//============================================================================// + +template <typename T> +QVertexSet<T> QTriangulator<T>::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(); + + QVertexSet<T> 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; +} + +template <typename T> +QVertexSet<T> QTriangulator<T>::polyline() +{ + 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(); + } + + QVertexSet<T> 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; +} + +template <typename T> +void QTriangulator<T>::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] = T(-1); //Q_TRIANGULATE_END_OF_POLYGON +} + +template <typename T> +void QTriangulator<T>::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(T(-1)); // Q_TRIANGULATE_END_OF_POLYGON + // Fall through. + case QPainterPath::LineToElement: + m_indices.push_back(T(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(T(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(T(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(T(-1)); // Q_TRIANGULATE_END_OF_POLYGON +} + +template <typename T> +void QTriangulator<T>::initialize(const QPainterPath &path, const QTransform &matrix, qreal lod) +{ + initialize(qtVectorPathForPath(path), matrix, lod); +} + +//============================================================================// +// QTriangulator::ComplexToSimple // +//============================================================================// +template <typename T> +void QTriangulator<T>::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(T(-1)); // Q_TRIANGULATE_END_OF_POLYGON + } +} + +template <typename T> +void QTriangulator<T>::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) == T(-1)) { // 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 +template <typename T> +bool QTriangulator<T>::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((qint32)e1.from); + const QPodPoint &u2 = m_parent->m_vertices.at((qint32)e1.to); + const QPodPoint &v1 = m_parent->m_vertices.at((qint32)e2.from); + const QPodPoint &v2 = m_parent->m_vertices.at((qint32)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 = QT_PREPEND_NAMESPACE(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; +} + +template <typename T> +bool QTriangulator<T>::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 = QT_PREPEND_NAMESPACE(qPointDistanceFromLine)(upper, l, u); + // d < 0: left, d > 0: right, d == 0: on top + if (d == 0) + d = QT_PREPEND_NAMESPACE(qPointDistanceFromLine)(m_parent->m_vertices.at(leftEdge.lower()), l, u); + return d < 0; +} + +template <typename T> +QRBTree<int>::Node *QTriangulator<T>::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; +} + +template <typename T> +QRBTree<int>::Node *QTriangulator<T>::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; +} + +template <typename T> +QPair<QRBTree<int>::Node *, QRBTree<int>::Node *> QTriangulator<T>::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()); + qint64 d = QT_PREPEND_NAMESPACE(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()); + qint64 d = QT_PREPEND_NAMESPACE(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()); + qint64 d = QT_PREPEND_NAMESPACE(qPointDistanceFromLine)(point, v1, v2); + Q_ASSERT(d <= 0); + if (d == 0) { + result.second = current; + current = current->right; + } else { + current = current->left; + } + } + + return result; +} + +template <typename T> +QPair<QRBTree<int>::Node *, QRBTree<int>::Node *> QTriangulator<T>::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()); + qint64 d = QT_PREPEND_NAMESPACE(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()); + qint64 d = QT_PREPEND_NAMESPACE(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()); + qint64 d = QT_PREPEND_NAMESPACE(qPointDistanceFromLine)(point, v1, v2); + Q_ASSERT(d <= 0); + if (d == 0) { + current = current->right; + } else { + result.second = current; + current = current->left; + } + } + + return result; +} + +template <typename T> +void QTriangulator<T>::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); + } +} + +template <typename T> +void QTriangulator<T>::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); +} + +template <typename T> +void QTriangulator<T>::ComplexToSimple::sortEdgeList(const QPodPoint eventPoint) +{ + QIntersectionPoint eventPoint2 = QT_PREPEND_NAMESPACE(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((qint32)edge.from); + const QPodPoint &v = m_parent->m_vertices.at((qint32)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((qint32)edge.from); + const QPodPoint &v = m_parent->m_vertices.at((qint32)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 + + } +} + +template <typename T> +void QTriangulator<T>::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)) { + QPodPoint upper = m_parent->m_vertices.at(m_edges.at(i).upper()); + QPodPoint lower = m_parent->m_vertices.at(m_edges.at(i).lower()); + Event upperEvent = {{upper.x, upper.y}, Event::Upper, i}; + Event lowerEvent = {{lower.x, lower.y}, 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()); +} + +template <typename T> +void QTriangulator<T>::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 = QT_PREPEND_NAMESPACE(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'. +template <typename T> +int QTriangulator<T>::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; + } +} + +template <typename T> +bool QTriangulator<T>::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; +} + +template <typename T> +void QTriangulator<T>::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); +} + +template <typename T> +void QTriangulator<T>::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(QT_PREPEND_NAMESPACE(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 +} + +template <typename T> +void QTriangulator<T>::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); + } +} + +template <typename T> +bool QTriangulator<T>::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; +} + +template <typename T> +inline bool QTriangulator<T>::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 +template <typename T> +QTriangulator<T>::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)); +} + +template <typename T> +void QTriangulator<T>::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); + } +} + +template <typename T> +void QTriangulator<T>::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(); +} + +template <typename T> +void QTriangulator<T>::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(); + } +} + +template <typename T> +void QTriangulator<T>::ComplexToSimple::DebugDialog::mousePressEvent(QMouseEvent *event) +{ + if (event->button() == Qt::LeftButton) + m_lastMousePos = event->pos(); + event->accept(); +} + + +#endif + +//============================================================================// +// QTriangulator::SimpleToMonotone // +//============================================================================// +template <typename T> +void QTriangulator<T>::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() != T(-1)) // Q_TRIANGULATE_END_OF_POLYGON + m_parent->m_indices.push_back(T(-1)); // Q_TRIANGULATE_END_OF_POLYGON + } +} + +template <typename T> +void QTriangulator<T>::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) != T(-1)); // 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. + } +} + +template <typename T> +void QTriangulator<T>::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); + } +} + +template <typename T> +void QTriangulator<T>::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))); + //} +} + +template <typename T> +bool QTriangulator<T>::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 = QT_PREPEND_NAMESPACE(qPointDistanceFromLine)(m_parent->m_vertices.at(leftEdge.upper()), l, u); + // d < 0: left, d > 0: right, d == 0: on top + if (d == 0) + d = QT_PREPEND_NAMESPACE(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. +template <typename T> +QRBTree<int>::Node *QTriangulator<T>::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. +template <typename T> +QRBTree<int>::Node *QTriangulator<T>::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 = QT_PREPEND_NAMESPACE(qPointDistanceFromLine)(m_parent->m_vertices.at(pointIndex), p1, p2); + if (d <= 0) { + current = current->left; + } else { + result = current; + current = current->right; + } + } + return result; +} + +template <typename T> +void QTriangulator<T>::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 = QT_PREPEND_NAMESPACE(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); + } +} + +template <typename T> +void QTriangulator<T>::SimpleToMonotone::classifyVertices() +{ + for (int i = 0; i < m_edges.size(); ++i) + classifyVertex(i); +} + +template <typename T> +bool QTriangulator<T>::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; +} + +template <typename T> +bool QTriangulator<T>::SimpleToMonotone::pointIsInSector(int vertex, int sector) +{ + const QPodPoint ¢er = 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); +} + +template <typename T> +int QTriangulator<T>::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; +} + +template <typename T> +void QTriangulator<T>::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); +} + +template <typename T> +void QTriangulator<T>::SimpleToMonotone::monotoneDecomposition() +{ + if (m_edges.isEmpty()) + return; + + Q_ASSERT(!m_edgeList.root); + QDataBuffer<QPair<int, int> > diagonals(m_upperVertex.size()); + + 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((quint32)m_edges.at(i).from), + m_parent->m_vertices.at((quint32)m_edges.at(j).from), m_parent->m_vertices.at((quint32)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(QPair<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(QPair<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(QPair<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(QPair<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.validate()); + } 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.validate()); + } + 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(QPair<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(QPair<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.validate()); + } else { + qWarning("Inconsistent polygon. (#5)"); + } + } else { + if (m_edges.at(m_edges.at(j).helper).type == MergeVertex) + diagonals.add(QPair<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.validate()); + } else { + qWarning("Inconsistent polygon. (#6)"); + } + } + break; + } + } + + for (int i = 0; i < diagonals.size(); ++i) + createDiagonal(diagonals.at(i).first, diagonals.at(i).second); +} + +template <typename T> +bool QTriangulator<T>::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 // +//============================================================================// +template <typename T> +void QTriangulator<T>::MonotoneToTriangles::decompose() +{ + QVector<T> result; + QDataBuffer<int> stack(m_parent->m_indices.size()); + 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) != T(-1)) { // 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 // +//============================================================================// + +static bool hasElementIndexUint() +{ + QOpenGLContext *context = QOpenGLContext::currentContext(); + if (!context) + return false; + return static_cast<QOpenGLExtensions *>(context->functions())->hasOpenGLExtension(QOpenGLExtensions::ElementIndexUint); +} + +Q_GUI_EXPORT QTriangleSet qTriangulate(const qreal *polygon, + int count, uint hint, const QTransform &matrix) +{ + QTriangleSet triangleSet; + if (hasElementIndexUint()) { + QTriangulator<quint32> triangulator; + triangulator.initialize(polygon, count, hint, matrix); + QVertexSet<quint32> vertexSet = triangulator.triangulate(); + triangleSet.vertices = vertexSet.vertices; + triangleSet.indices.setDataUint(vertexSet.indices); + + } else { + QTriangulator<quint16> triangulator; + triangulator.initialize(polygon, count, hint, matrix); + QVertexSet<quint16> vertexSet = triangulator.triangulate(); + triangleSet.vertices = vertexSet.vertices; + triangleSet.indices.setDataUshort(vertexSet.indices); + } + return triangleSet; +} + +Q_GUI_EXPORT QTriangleSet qTriangulate(const QVectorPath &path, + const QTransform &matrix, qreal lod) +{ + QTriangleSet triangleSet; + if (hasElementIndexUint()) { + QTriangulator<quint32> triangulator; + triangulator.initialize(path, matrix, lod); + QVertexSet<quint32> vertexSet = triangulator.triangulate(); + triangleSet.vertices = vertexSet.vertices; + triangleSet.indices.setDataUint(vertexSet.indices); + } else { + QTriangulator<quint16> triangulator; + triangulator.initialize(path, matrix, lod); + QVertexSet<quint16> vertexSet = triangulator.triangulate(); + triangleSet.vertices = vertexSet.vertices; + triangleSet.indices.setDataUshort(vertexSet.indices); + } + return triangleSet; +} + +QTriangleSet qTriangulate(const QPainterPath &path, + const QTransform &matrix, qreal lod) +{ + QTriangleSet triangleSet; + if (hasElementIndexUint()) { + QTriangulator<quint32> triangulator; + triangulator.initialize(path, matrix, lod); + QVertexSet<quint32> vertexSet = triangulator.triangulate(); + triangleSet.vertices = vertexSet.vertices; + triangleSet.indices.setDataUint(vertexSet.indices); + } else { + QTriangulator<quint16> triangulator; + triangulator.initialize(path, matrix, lod); + QVertexSet<quint16> vertexSet = triangulator.triangulate(); + triangleSet.vertices = vertexSet.vertices; + triangleSet.indices.setDataUshort(vertexSet.indices); + } + return triangleSet; +} + +QPolylineSet qPolyline(const QVectorPath &path, + const QTransform &matrix, qreal lod) +{ + QPolylineSet polyLineSet; + if (hasElementIndexUint()) { + QTriangulator<quint32> triangulator; + triangulator.initialize(path, matrix, lod); + QVertexSet<quint32> vertexSet = triangulator.polyline(); + polyLineSet.vertices = vertexSet.vertices; + polyLineSet.indices.setDataUint(vertexSet.indices); + } else { + QTriangulator<quint16> triangulator; + triangulator.initialize(path, matrix, lod); + QVertexSet<quint16> vertexSet = triangulator.polyline(); + polyLineSet.vertices = vertexSet.vertices; + polyLineSet.indices.setDataUshort(vertexSet.indices); + } + return polyLineSet; +} + +QPolylineSet qPolyline(const QPainterPath &path, + const QTransform &matrix, qreal lod) +{ + QPolylineSet polyLineSet; + if (hasElementIndexUint()) { + QTriangulator<quint32> triangulator; + triangulator.initialize(path, matrix, lod); + QVertexSet<quint32> vertexSet = triangulator.polyline(); + polyLineSet.vertices = vertexSet.vertices; + polyLineSet.indices.setDataUint(vertexSet.indices); + } else { + QTriangulator<quint16> triangulator; + triangulator.initialize(path, matrix, lod); + QVertexSet<quint16> vertexSet = triangulator.polyline(); + polyLineSet.vertices = vertexSet.vertices; + polyLineSet.indices.setDataUshort(vertexSet.indices); + } + return polyLineSet; +} + +QT_END_NAMESPACE |