Make QGeoProjectionWebMercator use a projection matrix

This patch changes the way QGeoProjectionWebMercator implements
its operations -to and -from screen coordinates.
By using a double matrix 4x4 instead of only scaling and shifting this
will make it possible to convert coordinates also in presence of
bearing and tilting != 0

Change-Id: I6a74a9675a7ad397ec6ad32f4274f897aa7694b1
Reviewed-by: Alex Blasche <alexander.blasche@qt.io>

1 files changed, 946 insertions, 0 deletions

diff --git a/src/positioning/qdoublematrix4x4_p.h b/src/positioning/qdoublematrix4x4_p.h
new file mode 100644
index 00000000..3ce7b312
--- /dev/null
+++ b/src/positioning/qdoublematrix4x4_p.h
@@ -0,0 +1,946 @@
+/****************************************************************************
+**
+** Copyright (C) 2016 The Qt Company Ltd.
+** Contact: https://www.qt.io/licensing/
+**
+** This file is part of the QtGui module of the Qt Toolkit.
+**
+** $QT_BEGIN_LICENSE:LGPL$
+** Commercial License Usage
+** Licensees holding valid commercial Qt licenses may use this file in
+** accordance with the commercial license agreement provided with the
+** Software or, alternatively, in accordance with the terms contained in
+** a written agreement between you and The Qt Company. For licensing terms
+** and conditions see https://www.qt.io/terms-conditions. For further
+** information use the contact form at https://www.qt.io/contact-us.
+**
+** GNU Lesser General Public License Usage
+** Alternatively, this file may be used under the terms of the GNU Lesser
+** General Public License version 3 as published by the Free Software
+** Foundation and appearing in the file LICENSE.LGPL3 included in the
+** packaging of this file. Please review the following information to
+** ensure the GNU Lesser General Public License version 3 requirements
+** will be met: https://www.gnu.org/licenses/lgpl-3.0.html.
+**
+** GNU General Public License Usage
+** Alternatively, this file may be used under the terms of the GNU
+** General Public License version 2.0 or (at your option) the GNU General
+** Public license version 3 or any later version approved by the KDE Free
+** Qt Foundation. The licenses are as published by the Free Software
+** Foundation and appearing in the file LICENSE.GPL2 and LICENSE.GPL3
+** included in the packaging of this file. Please review the following
+** information to ensure the GNU General Public License requirements will
+** be met: https://www.gnu.org/licenses/gpl-2.0.html and
+** https://www.gnu.org/licenses/gpl-3.0.html.
+**
+** $QT_END_LICENSE$
+**
+****************************************************************************/
+
+#ifndef QDOUBLEMATRIX4X4_H
+#define QDOUBLEMATRIX4X4_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 <QtPositioning/private/qpositioningglobal_p.h>
+#include <QtPositioning/private/qdoublevector3d_p.h>
+#include <QtCore/qmetatype.h>
+#include <QtCore/QRectF>
+#include <QtGui/qmatrix4x4.h>
+
+QT_BEGIN_NAMESPACE
+
+/*
+ * This class is a copy/paste/replace of QMatrix4x4
+ * No algorithm has been changed.
+ * Some methods have been removed.
+ */
+
+class Q_POSITIONING_PRIVATE_EXPORT QDoubleMatrix4x4
+{
+public:
+    inline QDoubleMatrix4x4() { setToIdentity(); }
+    explicit QDoubleMatrix4x4(Qt::Initialization) : flagBits(General) {}
+    explicit QDoubleMatrix4x4(const double *values);
+    inline QDoubleMatrix4x4(double m11, double m12, double m13, double m14,
+                      double m21, double m22, double m23, double m24,
+                      double m31, double m32, double m33, double m34,
+                      double m41, double m42, double m43, double m44);
+
+    QDoubleMatrix4x4(const double *values, int cols, int rows);
+
+    inline const double& operator()(int row, int column) const;
+    inline double& operator()(int row, int column);
+
+    inline bool isAffine() const;
+
+    inline bool isIdentity() const;
+    inline void setToIdentity();
+
+    inline void fill(double value);
+
+    double determinant() const;
+    QDoubleMatrix4x4 inverted(bool *invertible = Q_NULLPTR) const;
+    QDoubleMatrix4x4 transposed() const;
+
+    inline QDoubleMatrix4x4& operator+=(const QDoubleMatrix4x4& other);
+    inline QDoubleMatrix4x4& operator-=(const QDoubleMatrix4x4& other);
+    inline QDoubleMatrix4x4& operator*=(const QDoubleMatrix4x4& other);
+    inline QDoubleMatrix4x4& operator*=(double factor);
+    QDoubleMatrix4x4& operator/=(double divisor);
+    inline bool operator==(const QDoubleMatrix4x4& other) const;
+    inline bool operator!=(const QDoubleMatrix4x4& other) const;
+
+    friend QDoubleMatrix4x4 operator+(const QDoubleMatrix4x4& m1, const QDoubleMatrix4x4& m2);
+    friend QDoubleMatrix4x4 operator-(const QDoubleMatrix4x4& m1, const QDoubleMatrix4x4& m2);
+    friend QDoubleMatrix4x4 operator*(const QDoubleMatrix4x4& m1, const QDoubleMatrix4x4& m2);
+
+    friend QDoubleVector3D operator*(const QDoubleMatrix4x4& matrix, const QDoubleVector3D& vector);
+    friend QDoubleVector3D operator*(const QDoubleVector3D& vector, const QDoubleMatrix4x4& matrix);
+
+    friend QPoint operator*(const QPoint& point, const QDoubleMatrix4x4& matrix);
+    friend QPointF operator*(const QPointF& point, const QDoubleMatrix4x4& matrix);
+    friend QDoubleMatrix4x4 operator-(const QDoubleMatrix4x4& matrix);
+    friend QPoint operator*(const QDoubleMatrix4x4& matrix, const QPoint& point);
+    friend QPointF operator*(const QDoubleMatrix4x4& matrix, const QPointF& point);
+    friend QDoubleMatrix4x4 operator*(double factor, const QDoubleMatrix4x4& matrix);
+    friend QDoubleMatrix4x4 operator*(const QDoubleMatrix4x4& matrix, double factor);
+    friend Q_POSITIONING_PRIVATE_EXPORT QDoubleMatrix4x4 operator/(const QDoubleMatrix4x4& matrix, double divisor);
+
+    friend inline bool qFuzzyCompare(const QDoubleMatrix4x4& m1, const QDoubleMatrix4x4& m2);
+
+
+    void scale(const QDoubleVector3D& vector);
+    void translate(const QDoubleVector3D& vector);
+    void rotate(double angle, const QDoubleVector3D& vector);
+
+    void scale(double x, double y);
+    void scale(double x, double y, double z);
+    void scale(double factor);
+    void translate(double x, double y);
+    void translate(double x, double y, double z);
+    void rotate(double angle, double x, double y, double z = 0.0f);
+
+    void ortho(const QRect& rect);
+    void ortho(const QRectF& rect);
+    void ortho(double left, double right, double bottom, double top, double nearPlane, double farPlane);
+    void frustum(double left, double right, double bottom, double top, double nearPlane, double farPlane);
+    void perspective(double verticalAngle, double aspectRatio, double nearPlane, double farPlane);
+
+    void lookAt(const QDoubleVector3D& eye, const QDoubleVector3D& center, const QDoubleVector3D& up);
+
+    void viewport(const QRectF &rect);
+    void viewport(double left, double bottom, double width, double height, double nearPlane = 0.0f, double farPlane = 1.0f);
+    void flipCoordinates();
+
+    void copyDataTo(double *values) const;
+
+    QPoint map(const QPoint& point) const;
+    QPointF map(const QPointF& point) const;
+
+    QDoubleVector3D map(const QDoubleVector3D& point) const;
+    QDoubleVector3D mapVector(const QDoubleVector3D& vector) const;
+
+    QRect mapRect(const QRect& rect) const;
+    QRectF mapRect(const QRectF& rect) const;
+
+    inline double *data();
+    inline const double *data() const { return *m; }
+    inline const double *constData() const { return *m; }
+
+    void optimize();
+
+#ifndef QT_NO_DEBUG_STREAM
+    friend Q_POSITIONING_PRIVATE_EXPORT QDebug operator<<(QDebug dbg, const QDoubleMatrix4x4 &m);
+#endif
+
+private:
+    double m[4][4];          // Column-major order to match OpenGL.
+    int flagBits;           // Flag bits from the enum below.
+
+    // When matrices are multiplied, the flag bits are or-ed together.
+    enum {
+        Identity        = 0x0000, // Identity matrix
+        Translation     = 0x0001, // Contains a translation
+        Scale           = 0x0002, // Contains a scale
+        Rotation2D      = 0x0004, // Contains a rotation about the Z axis
+        Rotation        = 0x0008, // Contains an arbitrary rotation
+        Perspective     = 0x0010, // Last row is different from (0, 0, 0, 1)
+        General         = 0x001f  // General matrix, unknown contents
+    };
+
+    // Construct without initializing identity matrix.
+    explicit QDoubleMatrix4x4(int) { }
+
+    QDoubleMatrix4x4 orthonormalInverse() const;
+
+    void projectedRotate(double angle, double x, double y, double z);
+};
+
+Q_DECLARE_TYPEINFO(QDoubleMatrix4x4, Q_MOVABLE_TYPE);
+
+inline QDoubleMatrix4x4::QDoubleMatrix4x4
+        (double m11, double m12, double m13, double m14,
+         double m21, double m22, double m23, double m24,
+         double m31, double m32, double m33, double m34,
+         double m41, double m42, double m43, double m44)
+{
+    m[0][0] = m11; m[0][1] = m21; m[0][2] = m31; m[0][3] = m41;
+    m[1][0] = m12; m[1][1] = m22; m[1][2] = m32; m[1][3] = m42;
+    m[2][0] = m13; m[2][1] = m23; m[2][2] = m33; m[2][3] = m43;
+    m[3][0] = m14; m[3][1] = m24; m[3][2] = m34; m[3][3] = m44;
+    flagBits = General;
+}
+
+inline const double& QDoubleMatrix4x4::operator()(int aRow, int aColumn) const
+{
+    Q_ASSERT(aRow >= 0 && aRow < 4 && aColumn >= 0 && aColumn < 4);
+    return m[aColumn][aRow];
+}
+
+inline double& QDoubleMatrix4x4::operator()(int aRow, int aColumn)
+{
+    Q_ASSERT(aRow >= 0 && aRow < 4 && aColumn >= 0 && aColumn < 4);
+    flagBits = General;
+    return m[aColumn][aRow];
+}
+
+Q_POSITIONING_PRIVATE_EXPORT QDoubleMatrix4x4 operator/(const QDoubleMatrix4x4& matrix, double divisor);
+
+inline bool QDoubleMatrix4x4::isAffine() const
+{
+    return m[0][3] == 0.0f && m[1][3] == 0.0f && m[2][3] == 0.0f && m[3][3] == 1.0f;
+}
+
+inline bool QDoubleMatrix4x4::isIdentity() const
+{
+    if (flagBits == Identity)
+        return true;
+    if (m[0][0] != 1.0f || m[0][1] != 0.0f || m[0][2] != 0.0f)
+        return false;
+    if (m[0][3] != 0.0f || m[1][0] != 0.0f || m[1][1] != 1.0f)
+        return false;
+    if (m[1][2] != 0.0f || m[1][3] != 0.0f || m[2][0] != 0.0f)
+        return false;
+    if (m[2][1] != 0.0f || m[2][2] != 1.0f || m[2][3] != 0.0f)
+        return false;
+    if (m[3][0] != 0.0f || m[3][1] != 0.0f || m[3][2] != 0.0f)
+        return false;
+    return (m[3][3] == 1.0f);
+}
+
+inline void QDoubleMatrix4x4::setToIdentity()
+{
+    m[0][0] = 1.0f;
+    m[0][1] = 0.0f;
+    m[0][2] = 0.0f;
+    m[0][3] = 0.0f;
+    m[1][0] = 0.0f;
+    m[1][1] = 1.0f;
+    m[1][2] = 0.0f;
+    m[1][3] = 0.0f;
+    m[2][0] = 0.0f;
+    m[2][1] = 0.0f;
+    m[2][2] = 1.0f;
+    m[2][3] = 0.0f;
+    m[3][0] = 0.0f;
+    m[3][1] = 0.0f;
+    m[3][2] = 0.0f;
+    m[3][3] = 1.0f;
+    flagBits = Identity;
+}
+
+inline void QDoubleMatrix4x4::fill(double value)
+{
+    m[0][0] = value;
+    m[0][1] = value;
+    m[0][2] = value;
+    m[0][3] = value;
+    m[1][0] = value;
+    m[1][1] = value;
+    m[1][2] = value;
+    m[1][3] = value;
+    m[2][0] = value;
+    m[2][1] = value;
+    m[2][2] = value;
+    m[2][3] = value;
+    m[3][0] = value;
+    m[3][1] = value;
+    m[3][2] = value;
+    m[3][3] = value;
+    flagBits = General;
+}
+
+inline QDoubleMatrix4x4& QDoubleMatrix4x4::operator+=(const QDoubleMatrix4x4& other)
+{
+    m[0][0] += other.m[0][0];
+    m[0][1] += other.m[0][1];
+    m[0][2] += other.m[0][2];
+    m[0][3] += other.m[0][3];
+    m[1][0] += other.m[1][0];
+    m[1][1] += other.m[1][1];
+    m[1][2] += other.m[1][2];
+    m[1][3] += other.m[1][3];
+    m[2][0] += other.m[2][0];
+    m[2][1] += other.m[2][1];
+    m[2][2] += other.m[2][2];
+    m[2][3] += other.m[2][3];
+    m[3][0] += other.m[3][0];
+    m[3][1] += other.m[3][1];
+    m[3][2] += other.m[3][2];
+    m[3][3] += other.m[3][3];
+    flagBits = General;
+    return *this;
+}
+
+inline QDoubleMatrix4x4& QDoubleMatrix4x4::operator-=(const QDoubleMatrix4x4& other)
+{
+    m[0][0] -= other.m[0][0];
+    m[0][1] -= other.m[0][1];
+    m[0][2] -= other.m[0][2];
+    m[0][3] -= other.m[0][3];
+    m[1][0] -= other.m[1][0];
+    m[1][1] -= other.m[1][1];
+    m[1][2] -= other.m[1][2];
+    m[1][3] -= other.m[1][3];
+    m[2][0] -= other.m[2][0];
+    m[2][1] -= other.m[2][1];
+    m[2][2] -= other.m[2][2];
+    m[2][3] -= other.m[2][3];
+    m[3][0] -= other.m[3][0];
+    m[3][1] -= other.m[3][1];
+    m[3][2] -= other.m[3][2];
+    m[3][3] -= other.m[3][3];
+    flagBits = General;
+    return *this;
+}
+
+inline QDoubleMatrix4x4& QDoubleMatrix4x4::operator*=(const QDoubleMatrix4x4& other)
+{
+    flagBits |= other.flagBits;
+
+    if (flagBits < Rotation2D) {
+        m[3][0] += m[0][0] * other.m[3][0];
+        m[3][1] += m[1][1] * other.m[3][1];
+        m[3][2] += m[2][2] * other.m[3][2];
+
+        m[0][0] *= other.m[0][0];
+        m[1][1] *= other.m[1][1];
+        m[2][2] *= other.m[2][2];
+        return *this;
+    }
+
+    double m0, m1, m2;
+    m0 = m[0][0] * other.m[0][0]
+            + m[1][0] * other.m[0][1]
+            + m[2][0] * other.m[0][2]
+            + m[3][0] * other.m[0][3];
+    m1 = m[0][0] * other.m[1][0]
+            + m[1][0] * other.m[1][1]
+            + m[2][0] * other.m[1][2]
+            + m[3][0] * other.m[1][3];
+    m2 = m[0][0] * other.m[2][0]
+            + m[1][0] * other.m[2][1]
+            + m[2][0] * other.m[2][2]
+            + m[3][0] * other.m[2][3];
+    m[3][0] = m[0][0] * other.m[3][0]
+            + m[1][0] * other.m[3][1]
+            + m[2][0] * other.m[3][2]
+            + m[3][0] * other.m[3][3];
+    m[0][0] = m0;
+    m[1][0] = m1;
+    m[2][0] = m2;
+
+    m0 = m[0][1] * other.m[0][0]
+            + m[1][1] * other.m[0][1]
+            + m[2][1] * other.m[0][2]
+            + m[3][1] * other.m[0][3];
+    m1 = m[0][1] * other.m[1][0]
+            + m[1][1] * other.m[1][1]
+            + m[2][1] * other.m[1][2]
+            + m[3][1] * other.m[1][3];
+    m2 = m[0][1] * other.m[2][0]
+            + m[1][1] * other.m[2][1]
+            + m[2][1] * other.m[2][2]
+            + m[3][1] * other.m[2][3];
+    m[3][1] = m[0][1] * other.m[3][0]
+            + m[1][1] * other.m[3][1]
+            + m[2][1] * other.m[3][2]
+            + m[3][1] * other.m[3][3];
+    m[0][1] = m0;
+    m[1][1] = m1;
+    m[2][1] = m2;
+
+    m0 = m[0][2] * other.m[0][0]
+            + m[1][2] * other.m[0][1]
+            + m[2][2] * other.m[0][2]
+            + m[3][2] * other.m[0][3];
+    m1 = m[0][2] * other.m[1][0]
+            + m[1][2] * other.m[1][1]
+            + m[2][2] * other.m[1][2]
+            + m[3][2] * other.m[1][3];
+    m2 = m[0][2] * other.m[2][0]
+            + m[1][2] * other.m[2][1]
+            + m[2][2] * other.m[2][2]
+            + m[3][2] * other.m[2][3];
+    m[3][2] = m[0][2] * other.m[3][0]
+            + m[1][2] * other.m[3][1]
+            + m[2][2] * other.m[3][2]
+            + m[3][2] * other.m[3][3];
+    m[0][2] = m0;
+    m[1][2] = m1;
+    m[2][2] = m2;
+
+    m0 = m[0][3] * other.m[0][0]
+            + m[1][3] * other.m[0][1]
+            + m[2][3] * other.m[0][2]
+            + m[3][3] * other.m[0][3];
+    m1 = m[0][3] * other.m[1][0]
+            + m[1][3] * other.m[1][1]
+            + m[2][3] * other.m[1][2]
+            + m[3][3] * other.m[1][3];
+    m2 = m[0][3] * other.m[2][0]
+            + m[1][3] * other.m[2][1]
+            + m[2][3] * other.m[2][2]
+            + m[3][3] * other.m[2][3];
+    m[3][3] = m[0][3] * other.m[3][0]
+            + m[1][3] * other.m[3][1]
+            + m[2][3] * other.m[3][2]
+            + m[3][3] * other.m[3][3];
+    m[0][3] = m0;
+    m[1][3] = m1;
+    m[2][3] = m2;
+    return *this;
+}
+
+inline QDoubleMatrix4x4& QDoubleMatrix4x4::operator*=(double factor)
+{
+    m[0][0] *= factor;
+    m[0][1] *= factor;
+    m[0][2] *= factor;
+    m[0][3] *= factor;
+    m[1][0] *= factor;
+    m[1][1] *= factor;
+    m[1][2] *= factor;
+    m[1][3] *= factor;
+    m[2][0] *= factor;
+    m[2][1] *= factor;
+    m[2][2] *= factor;
+    m[2][3] *= factor;
+    m[3][0] *= factor;
+    m[3][1] *= factor;
+    m[3][2] *= factor;
+    m[3][3] *= factor;
+    flagBits = General;
+    return *this;
+}
+
+inline bool QDoubleMatrix4x4::operator==(const QDoubleMatrix4x4& other) const
+{
+    return m[0][0] == other.m[0][0] &&
+           m[0][1] == other.m[0][1] &&
+           m[0][2] == other.m[0][2] &&
+           m[0][3] == other.m[0][3] &&
+           m[1][0] == other.m[1][0] &&
+           m[1][1] == other.m[1][1] &&
+           m[1][2] == other.m[1][2] &&
+           m[1][3] == other.m[1][3] &&
+           m[2][0] == other.m[2][0] &&
+           m[2][1] == other.m[2][1] &&
+           m[2][2] == other.m[2][2] &&
+           m[2][3] == other.m[2][3] &&
+           m[3][0] == other.m[3][0] &&
+           m[3][1] == other.m[3][1] &&
+           m[3][2] == other.m[3][2] &&
+           m[3][3] == other.m[3][3];
+}
+
+inline bool QDoubleMatrix4x4::operator!=(const QDoubleMatrix4x4& other) const
+{
+    return m[0][0] != other.m[0][0] ||
+           m[0][1] != other.m[0][1] ||
+           m[0][2] != other.m[0][2] ||
+           m[0][3] != other.m[0][3] ||
+           m[1][0] != other.m[1][0] ||
+           m[1][1] != other.m[1][1] ||
+           m[1][2] != other.m[1][2] ||
+           m[1][3] != other.m[1][3] ||
+           m[2][0] != other.m[2][0] ||
+           m[2][1] != other.m[2][1] ||
+           m[2][2] != other.m[2][2] ||
+           m[2][3] != other.m[2][3] ||
+           m[3][0] != other.m[3][0] ||
+           m[3][1] != other.m[3][1] ||
+           m[3][2] != other.m[3][2] ||
+           m[3][3] != other.m[3][3];
+}
+
+inline QDoubleMatrix4x4 operator+(const QDoubleMatrix4x4& m1, const QDoubleMatrix4x4& m2)
+{
+    QDoubleMatrix4x4 m(1);
+    m.m[0][0] = m1.m[0][0] + m2.m[0][0];
+    m.m[0][1] = m1.m[0][1] + m2.m[0][1];
+    m.m[0][2] = m1.m[0][2] + m2.m[0][2];
+    m.m[0][3] = m1.m[0][3] + m2.m[0][3];
+    m.m[1][0] = m1.m[1][0] + m2.m[1][0];
+    m.m[1][1] = m1.m[1][1] + m2.m[1][1];
+    m.m[1][2] = m1.m[1][2] + m2.m[1][2];
+    m.m[1][3] = m1.m[1][3] + m2.m[1][3];
+    m.m[2][0] = m1.m[2][0] + m2.m[2][0];
+    m.m[2][1] = m1.m[2][1] + m2.m[2][1];
+    m.m[2][2] = m1.m[2][2] + m2.m[2][2];
+    m.m[2][3] = m1.m[2][3] + m2.m[2][3];
+    m.m[3][0] = m1.m[3][0] + m2.m[3][0];
+    m.m[3][1] = m1.m[3][1] + m2.m[3][1];
+    m.m[3][2] = m1.m[3][2] + m2.m[3][2];
+    m.m[3][3] = m1.m[3][3] + m2.m[3][3];
+    m.flagBits = QDoubleMatrix4x4::General;
+    return m;
+}
+
+inline QDoubleMatrix4x4 operator-(const QDoubleMatrix4x4& m1, const QDoubleMatrix4x4& m2)
+{
+    QDoubleMatrix4x4 m(1);
+    m.m[0][0] = m1.m[0][0] - m2.m[0][0];
+    m.m[0][1] = m1.m[0][1] - m2.m[0][1];
+    m.m[0][2] = m1.m[0][2] - m2.m[0][2];
+    m.m[0][3] = m1.m[0][3] - m2.m[0][3];
+    m.m[1][0] = m1.m[1][0] - m2.m[1][0];
+    m.m[1][1] = m1.m[1][1] - m2.m[1][1];
+    m.m[1][2] = m1.m[1][2] - m2.m[1][2];
+    m.m[1][3] = m1.m[1][3] - m2.m[1][3];
+    m.m[2][0] = m1.m[2][0] - m2.m[2][0];
+    m.m[2][1] = m1.m[2][1] - m2.m[2][1];
+    m.m[2][2] = m1.m[2][2] - m2.m[2][2];
+    m.m[2][3] = m1.m[2][3] - m2.m[2][3];
+    m.m[3][0] = m1.m[3][0] - m2.m[3][0];
+    m.m[3][1] = m1.m[3][1] - m2.m[3][1];
+    m.m[3][2] = m1.m[3][2] - m2.m[3][2];
+    m.m[3][3] = m1.m[3][3] - m2.m[3][3];
+    m.flagBits = QDoubleMatrix4x4::General;
+    return m;
+}
+
+inline QDoubleMatrix4x4 operator*(const QDoubleMatrix4x4& m1, const QDoubleMatrix4x4& m2)
+{
+    int flagBits = m1.flagBits | m2.flagBits;
+    if (flagBits < QDoubleMatrix4x4::Rotation2D) {
+        QDoubleMatrix4x4 m = m1;
+        m.m[3][0] += m.m[0][0] * m2.m[3][0];
+        m.m[3][1] += m.m[1][1] * m2.m[3][1];
+        m.m[3][2] += m.m[2][2] * m2.m[3][2];
+
+        m.m[0][0] *= m2.m[0][0];
+        m.m[1][1] *= m2.m[1][1];
+        m.m[2][2] *= m2.m[2][2];
+        m.flagBits = flagBits;
+        return m;
+    }
+
+    QDoubleMatrix4x4 m(1);
+    m.m[0][0] = m1.m[0][0] * m2.m[0][0]
+              + m1.m[1][0] * m2.m[0][1]
+              + m1.m[2][0] * m2.m[0][2]
+              + m1.m[3][0] * m2.m[0][3];
+    m.m[0][1] = m1.m[0][1] * m2.m[0][0]
+              + m1.m[1][1] * m2.m[0][1]
+              + m1.m[2][1] * m2.m[0][2]
+              + m1.m[3][1] * m2.m[0][3];
+    m.m[0][2] = m1.m[0][2] * m2.m[0][0]
+              + m1.m[1][2] * m2.m[0][1]
+              + m1.m[2][2] * m2.m[0][2]
+              + m1.m[3][2] * m2.m[0][3];
+    m.m[0][3] = m1.m[0][3] * m2.m[0][0]
+              + m1.m[1][3] * m2.m[0][1]
+              + m1.m[2][3] * m2.m[0][2]
+              + m1.m[3][3] * m2.m[0][3];
+
+    m.m[1][0] = m1.m[0][0] * m2.m[1][0]
+              + m1.m[1][0] * m2.m[1][1]
+              + m1.m[2][0] * m2.m[1][2]
+              + m1.m[3][0] * m2.m[1][3];
+    m.m[1][1] = m1.m[0][1] * m2.m[1][0]
+              + m1.m[1][1] * m2.m[1][1]
+              + m1.m[2][1] * m2.m[1][2]
+              + m1.m[3][1] * m2.m[1][3];
+    m.m[1][2] = m1.m[0][2] * m2.m[1][0]
+              + m1.m[1][2] * m2.m[1][1]
+              + m1.m[2][2] * m2.m[1][2]
+              + m1.m[3][2] * m2.m[1][3];
+    m.m[1][3] = m1.m[0][3] * m2.m[1][0]
+              + m1.m[1][3] * m2.m[1][1]
+              + m1.m[2][3] * m2.m[1][2]
+              + m1.m[3][3] * m2.m[1][3];
+
+    m.m[2][0] = m1.m[0][0] * m2.m[2][0]
+              + m1.m[1][0] * m2.m[2][1]
+              + m1.m[2][0] * m2.m[2][2]
+              + m1.m[3][0] * m2.m[2][3];
+    m.m[2][1] = m1.m[0][1] * m2.m[2][0]
+              + m1.m[1][1] * m2.m[2][1]
+              + m1.m[2][1] * m2.m[2][2]
+              + m1.m[3][1] * m2.m[2][3];
+    m.m[2][2] = m1.m[0][2] * m2.m[2][0]
+              + m1.m[1][2] * m2.m[2][1]
+              + m1.m[2][2] * m2.m[2][2]
+              + m1.m[3][2] * m2.m[2][3];
+    m.m[2][3] = m1.m[0][3] * m2.m[2][0]
+              + m1.m[1][3] * m2.m[2][1]
+              + m1.m[2][3] * m2.m[2][2]
+              + m1.m[3][3] * m2.m[2][3];
+
+    m.m[3][0] = m1.m[0][0] * m2.m[3][0]
+              + m1.m[1][0] * m2.m[3][1]
+              + m1.m[2][0] * m2.m[3][2]
+              + m1.m[3][0] * m2.m[3][3];
+    m.m[3][1] = m1.m[0][1] * m2.m[3][0]
+              + m1.m[1][1] * m2.m[3][1]
+              + m1.m[2][1] * m2.m[3][2]
+              + m1.m[3][1] * m2.m[3][3];
+    m.m[3][2] = m1.m[0][2] * m2.m[3][0]
+              + m1.m[1][2] * m2.m[3][1]
+              + m1.m[2][2] * m2.m[3][2]
+              + m1.m[3][2] * m2.m[3][3];
+    m.m[3][3] = m1.m[0][3] * m2.m[3][0]
+              + m1.m[1][3] * m2.m[3][1]
+              + m1.m[2][3] * m2.m[3][2]
+              + m1.m[3][3] * m2.m[3][3];
+    m.flagBits = flagBits;
+    return m;
+}
+
+inline QDoubleVector3D operator*(const QDoubleVector3D& vector, const QDoubleMatrix4x4& matrix)
+{
+    double x, y, z, w;
+    x = vector.x() * matrix.m[0][0] +
+        vector.y() * matrix.m[0][1] +
+        vector.z() * matrix.m[0][2] +
+        matrix.m[0][3];
+    y = vector.x() * matrix.m[1][0] +
+        vector.y() * matrix.m[1][1] +
+        vector.z() * matrix.m[1][2] +
+        matrix.m[1][3];
+    z = vector.x() * matrix.m[2][0] +
+        vector.y() * matrix.m[2][1] +
+        vector.z() * matrix.m[2][2] +
+        matrix.m[2][3];
+    w = vector.x() * matrix.m[3][0] +
+        vector.y() * matrix.m[3][1] +
+        vector.z() * matrix.m[3][2] +
+        matrix.m[3][3];
+    if (w == 1.0f)
+        return QDoubleVector3D(x, y, z);
+    else
+        return QDoubleVector3D(x / w, y / w, z / w);
+}
+
+inline QDoubleVector3D operator*(const QDoubleMatrix4x4& matrix, const QDoubleVector3D& vector)
+{
+    double x, y, z, w;
+    if (matrix.flagBits == QDoubleMatrix4x4::Identity) {
+        return vector;
+    } else if (matrix.flagBits < QDoubleMatrix4x4::Rotation2D) {
+        // Translation | Scale
+        return QDoubleVector3D(vector.x() * matrix.m[0][0] + matrix.m[3][0],
+                         vector.y() * matrix.m[1][1] + matrix.m[3][1],
+                         vector.z() * matrix.m[2][2] + matrix.m[3][2]);
+    } else if (matrix.flagBits < QDoubleMatrix4x4::Rotation) {
+        // Translation | Scale | Rotation2D
+        return QDoubleVector3D(vector.x() * matrix.m[0][0] + vector.y() * matrix.m[1][0] + matrix.m[3][0],
+                         vector.x() * matrix.m[0][1] + vector.y() * matrix.m[1][1] + matrix.m[3][1],
+                         vector.z() * matrix.m[2][2] + matrix.m[3][2]);
+    } else {
+        x = vector.x() * matrix.m[0][0] +
+            vector.y() * matrix.m[1][0] +
+            vector.z() * matrix.m[2][0] +
+            matrix.m[3][0];
+        y = vector.x() * matrix.m[0][1] +
+            vector.y() * matrix.m[1][1] +
+            vector.z() * matrix.m[2][1] +
+            matrix.m[3][1];
+        z = vector.x() * matrix.m[0][2] +
+            vector.y() * matrix.m[1][2] +
+            vector.z() * matrix.m[2][2] +
+            matrix.m[3][2];
+        w = vector.x() * matrix.m[0][3] +
+            vector.y() * matrix.m[1][3] +
+            vector.z() * matrix.m[2][3] +
+            matrix.m[3][3];
+        if (w == 1.0f)
+            return QDoubleVector3D(x, y, z);
+        else
+            return QDoubleVector3D(x / w, y / w, z / w);
+    }
+}
+
+inline QPoint operator*(const QPoint& point, const QDoubleMatrix4x4& matrix)
+{
+    double xin, yin;
+    double x, y, w;
+    xin = point.x();
+    yin = point.y();
+    x = xin * matrix.m[0][0] +
+        yin * matrix.m[0][1] +
+        matrix.m[0][3];
+    y = xin * matrix.m[1][0] +
+        yin * matrix.m[1][1] +
+        matrix.m[1][3];
+    w = xin * matrix.m[3][0] +
+        yin * matrix.m[3][1] +
+        matrix.m[3][3];
+    if (w == 1.0f)
+        return QPoint(qRound(x), qRound(y));
+    else
+        return QPoint(qRound(x / w), qRound(y / w));
+}
+
+inline QPointF operator*(const QPointF& point, const QDoubleMatrix4x4& matrix)
+{
+    double xin, yin;
+    double x, y, w;
+    xin = point.x();
+    yin = point.y();
+    x = xin * matrix.m[0][0] +
+        yin * matrix.m[0][1] +
+        matrix.m[0][3];
+    y = xin * matrix.m[1][0] +
+        yin * matrix.m[1][1] +
+        matrix.m[1][3];
+    w = xin * matrix.m[3][0] +
+        yin * matrix.m[3][1] +
+        matrix.m[3][3];
+    if (w == 1.0f) {
+        return QPointF(double(x), double(y));
+    } else {
+        return QPointF(double(x / w), double(y / w));
+    }
+}
+
+inline QPoint operator*(const QDoubleMatrix4x4& matrix, const QPoint& point)
+{
+    double xin, yin;
+    double x, y, w;
+    xin = point.x();
+    yin = point.y();
+    if (matrix.flagBits == QDoubleMatrix4x4::Identity) {
+        return point;
+    } else if (matrix.flagBits < QDoubleMatrix4x4::Rotation2D) {
+        // Translation | Scale
+        return QPoint(qRound(xin * matrix.m[0][0] + matrix.m[3][0]),
+                      qRound(yin * matrix.m[1][1] + matrix.m[3][1]));
+    } else if (matrix.flagBits < QDoubleMatrix4x4::Perspective) {
+        return QPoint(qRound(xin * matrix.m[0][0] + yin * matrix.m[1][0] + matrix.m[3][0]),
+                      qRound(xin * matrix.m[0][1] + yin * matrix.m[1][1] + matrix.m[3][1]));
+    } else {
+        x = xin * matrix.m[0][0] +
+            yin * matrix.m[1][0] +
+            matrix.m[3][0];
+        y = xin * matrix.m[0][1] +
+            yin * matrix.m[1][1] +
+            matrix.m[3][1];
+        w = xin * matrix.m[0][3] +
+            yin * matrix.m[1][3] +
+            matrix.m[3][3];
+        if (w == 1.0f)
+            return QPoint(qRound(x), qRound(y));
+        else
+            return QPoint(qRound(x / w), qRound(y / w));
+    }
+}
+
+inline QPointF operator*(const QDoubleMatrix4x4& matrix, const QPointF& point)
+{
+    double xin, yin;
+    double x, y, w;
+    xin = point.x();
+    yin = point.y();
+    if (matrix.flagBits == QDoubleMatrix4x4::Identity) {
+        return point;
+    } else if (matrix.flagBits < QDoubleMatrix4x4::Rotation2D) {
+        // Translation | Scale
+        return QPointF(xin * matrix.m[0][0] + matrix.m[3][0],
+                       yin * matrix.m[1][1] + matrix.m[3][1]);
+    } else if (matrix.flagBits < QDoubleMatrix4x4::Perspective) {
+        return QPointF(xin * matrix.m[0][0] + yin * matrix.m[1][0] + matrix.m[3][0],
+                       xin * matrix.m[0][1] + yin * matrix.m[1][1] + matrix.m[3][1]);
+    } else {
+        x = xin * matrix.m[0][0] +
+            yin * matrix.m[1][0] +
+            matrix.m[3][0];
+        y = xin * matrix.m[0][1] +
+            yin * matrix.m[1][1] +
+            matrix.m[3][1];
+        w = xin * matrix.m[0][3] +
+            yin * matrix.m[1][3] +
+            matrix.m[3][3];
+        if (w == 1.0f) {
+            return QPointF(double(x), double(y));
+        } else {
+            return QPointF(double(x / w), double(y / w));
+        }
+    }
+}
+
+inline QDoubleMatrix4x4 operator-(const QDoubleMatrix4x4& matrix)
+{
+    QDoubleMatrix4x4 m(1);
+    m.m[0][0] = -matrix.m[0][0];
+    m.m[0][1] = -matrix.m[0][1];
+    m.m[0][2] = -matrix.m[0][2];
+    m.m[0][3] = -matrix.m[0][3];
+    m.m[1][0] = -matrix.m[1][0];
+    m.m[1][1] = -matrix.m[1][1];
+    m.m[1][2] = -matrix.m[1][2];
+    m.m[1][3] = -matrix.m[1][3];
+    m.m[2][0] = -matrix.m[2][0];
+    m.m[2][1] = -matrix.m[2][1];
+    m.m[2][2] = -matrix.m[2][2];
+    m.m[2][3] = -matrix.m[2][3];
+    m.m[3][0] = -matrix.m[3][0];
+    m.m[3][1] = -matrix.m[3][1];
+    m.m[3][2] = -matrix.m[3][2];
+    m.m[3][3] = -matrix.m[3][3];
+    m.flagBits = QDoubleMatrix4x4::General;
+    return m;
+}
+
+inline QDoubleMatrix4x4 operator*(double factor, const QDoubleMatrix4x4& matrix)
+{
+    QDoubleMatrix4x4 m(1);
+    m.m[0][0] = matrix.m[0][0] * factor;
+    m.m[0][1] = matrix.m[0][1] * factor;
+    m.m[0][2] = matrix.m[0][2] * factor;
+    m.m[0][3] = matrix.m[0][3] * factor;
+    m.m[1][0] = matrix.m[1][0] * factor;
+    m.m[1][1] = matrix.m[1][1] * factor;
+    m.m[1][2] = matrix.m[1][2] * factor;
+    m.m[1][3] = matrix.m[1][3] * factor;
+    m.m[2][0] = matrix.m[2][0] * factor;
+    m.m[2][1] = matrix.m[2][1] * factor;
+    m.m[2][2] = matrix.m[2][2] * factor;
+    m.m[2][3] = matrix.m[2][3] * factor;
+    m.m[3][0] = matrix.m[3][0] * factor;
+    m.m[3][1] = matrix.m[3][1] * factor;
+    m.m[3][2] = matrix.m[3][2] * factor;
+    m.m[3][3] = matrix.m[3][3] * factor;
+    m.flagBits = QDoubleMatrix4x4::General;
+    return m;
+}
+
+inline QDoubleMatrix4x4 operator*(const QDoubleMatrix4x4& matrix, double factor)
+{
+    QDoubleMatrix4x4 m(1);
+    m.m[0][0] = matrix.m[0][0] * factor;
+    m.m[0][1] = matrix.m[0][1] * factor;
+    m.m[0][2] = matrix.m[0][2] * factor;
+    m.m[0][3] = matrix.m[0][3] * factor;
+    m.m[1][0] = matrix.m[1][0] * factor;
+    m.m[1][1] = matrix.m[1][1] * factor;
+    m.m[1][2] = matrix.m[1][2] * factor;
+    m.m[1][3] = matrix.m[1][3] * factor;
+    m.m[2][0] = matrix.m[2][0] * factor;
+    m.m[2][1] = matrix.m[2][1] * factor;
+    m.m[2][2] = matrix.m[2][2] * factor;
+    m.m[2][3] = matrix.m[2][3] * factor;
+    m.m[3][0] = matrix.m[3][0] * factor;
+    m.m[3][1] = matrix.m[3][1] * factor;
+    m.m[3][2] = matrix.m[3][2] * factor;
+    m.m[3][3] = matrix.m[3][3] * factor;
+    m.flagBits = QDoubleMatrix4x4::General;
+    return m;
+}
+
+inline bool qFuzzyCompare(const QDoubleMatrix4x4& m1, const QDoubleMatrix4x4& m2)
+{
+    return qFuzzyCompare(m1.m[0][0], m2.m[0][0]) &&
+           qFuzzyCompare(m1.m[0][1], m2.m[0][1]) &&
+           qFuzzyCompare(m1.m[0][2], m2.m[0][2]) &&
+           qFuzzyCompare(m1.m[0][3], m2.m[0][3]) &&
+           qFuzzyCompare(m1.m[1][0], m2.m[1][0]) &&
+           qFuzzyCompare(m1.m[1][1], m2.m[1][1]) &&
+           qFuzzyCompare(m1.m[1][2], m2.m[1][2]) &&
+           qFuzzyCompare(m1.m[1][3], m2.m[1][3]) &&
+           qFuzzyCompare(m1.m[2][0], m2.m[2][0]) &&
+           qFuzzyCompare(m1.m[2][1], m2.m[2][1]) &&
+           qFuzzyCompare(m1.m[2][2], m2.m[2][2]) &&
+           qFuzzyCompare(m1.m[2][3], m2.m[2][3]) &&
+           qFuzzyCompare(m1.m[3][0], m2.m[3][0]) &&
+           qFuzzyCompare(m1.m[3][1], m2.m[3][1]) &&
+           qFuzzyCompare(m1.m[3][2], m2.m[3][2]) &&
+           qFuzzyCompare(m1.m[3][3], m2.m[3][3]);
+}
+
+inline QPoint QDoubleMatrix4x4::map(const QPoint& point) const
+{
+    return *this * point;
+}
+
+inline QPointF QDoubleMatrix4x4::map(const QPointF& point) const
+{
+    return *this * point;
+}
+
+inline QDoubleVector3D QDoubleMatrix4x4::map(const QDoubleVector3D& point) const
+{
+    return *this * point;
+}
+
+inline QDoubleVector3D QDoubleMatrix4x4::mapVector(const QDoubleVector3D& vector) const
+{
+    if (flagBits < Scale) {
+        // Translation
+        return vector;
+    } else if (flagBits < Rotation2D) {
+        // Translation | Scale
+        return QDoubleVector3D(vector.x() * m[0][0],
+                         vector.y() * m[1][1],
+                         vector.z() * m[2][2]);
+    } else {
+        return QDoubleVector3D(vector.x() * m[0][0] +
+                         vector.y() * m[1][0] +
+                         vector.z() * m[2][0],
+                         vector.x() * m[0][1] +
+                         vector.y() * m[1][1] +
+                         vector.z() * m[2][1],
+                         vector.x() * m[0][2] +
+                         vector.y() * m[1][2] +
+                         vector.z() * m[2][2]);
+    }
+}
+
+inline double *QDoubleMatrix4x4::data()
+{
+    // We have to assume that the caller will modify the matrix elements,
+    // so we flip it over to "General" mode.
+    flagBits = General;
+    return *m;
+}
+
+inline void QDoubleMatrix4x4::viewport(const QRectF &rect)
+{
+    viewport(rect.x(), rect.y(), rect.width(), rect.height());
+}
+
+#ifndef QT_NO_DEBUG_STREAM
+Q_POSITIONING_PRIVATE_EXPORT QDebug operator<<(QDebug dbg, const QDoubleMatrix4x4 &m);
+#endif
+
+#ifndef QT_NO_DATASTREAM
+Q_POSITIONING_PRIVATE_EXPORT QDataStream &operator<<(QDataStream &, const QDoubleMatrix4x4 &);
+Q_GUI_EXPORT QDataStream &operator>>(QDataStream &, QDoubleMatrix4x4 &);
+#endif
+
+
+QT_END_NAMESPACE
+
+
+#endif // QDOUBLEMATRIX4X4_H