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>

4 files changed, 2068 insertions, 1 deletions

diff --git a/src/positioning/positioning.pro b/src/positioning/positioning.pro
index b5c6ee46..c4c9cc6c 100644
--- a/src/positioning/positioning.pro
+++ b/src/positioning/positioning.pro
@@ -52,6 +52,7 @@ PRIVATE_HEADERS += \
                     qwebmercator_p.h \
                     qpositioningglobal_p.h \
                     qlocationdata_simulator_p.h \
+                    qdoublematrix4x4_p.h \
                     qgeopath_p.h
 
 SOURCES += \
@@ -76,7 +77,8 @@ SOURCES += \
             qdoublevector3d.cpp \
             qgeopath.cpp \
             qlocationdata_simulator.cpp \
-            qwebmercator.cpp
+            qwebmercator.cpp \
+            qdoublematrix4x4.cpp
 
 HEADERS += $$PUBLIC_HEADERS $$PRIVATE_HEADERS
 
diff --git a/src/positioning/qdoublematrix4x4.cpp b/src/positioning/qdoublematrix4x4.cpp
new file mode 100644
index 00000000..bca38075
--- /dev/null
+++ b/src/positioning/qdoublematrix4x4.cpp
@@ -0,0 +1,1111 @@
+/****************************************************************************
+**
+** 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.
+**
+** $QT_END_LICENSE$
+**
+****************************************************************************/
+
+#include "qdoublematrix4x4_p.h"
+#include <QtCore/qmath.h>
+//#include <QtCore/qvariant.h>
+#include <cmath>
+
+QT_BEGIN_NAMESPACE
+
+static const double inv_dist_to_plane = 1.0 / 1024.0;
+
+QDoubleMatrix4x4::QDoubleMatrix4x4(const double *values)
+{
+    for (int row = 0; row < 4; ++row)
+        for (int col = 0; col < 4; ++col)
+            m[col][row] = values[row * 4 + col];
+    flagBits = General;
+}
+
+QDoubleMatrix4x4::QDoubleMatrix4x4(const double *values, int cols, int rows)
+{
+    for (int col = 0; col < 4; ++col) {
+        for (int row = 0; row < 4; ++row) {
+            if (col < cols && row < rows)
+                m[col][row] = values[col * rows + row];
+            else if (col == row)
+                m[col][row] = 1.0;
+            else
+                m[col][row] = 0.0;
+        }
+    }
+    flagBits = General;
+}
+
+static inline double matrixDet2(const double m[4][4], int col0, int col1, int row0, int row1)
+{
+    return m[col0][row0] * m[col1][row1] - m[col0][row1] * m[col1][row0];
+}
+
+static inline double matrixDet3
+    (const double m[4][4], int col0, int col1, int col2,
+     int row0, int row1, int row2)
+{
+    return m[col0][row0] * matrixDet2(m, col1, col2, row1, row2)
+            - m[col1][row0] * matrixDet2(m, col0, col2, row1, row2)
+            + m[col2][row0] * matrixDet2(m, col0, col1, row1, row2);
+}
+
+static inline double matrixDet4(const double m[4][4])
+{
+    double det;
+    det  = m[0][0] * matrixDet3(m, 1, 2, 3, 1, 2, 3);
+    det -= m[1][0] * matrixDet3(m, 0, 2, 3, 1, 2, 3);
+    det += m[2][0] * matrixDet3(m, 0, 1, 3, 1, 2, 3);
+    det -= m[3][0] * matrixDet3(m, 0, 1, 2, 1, 2, 3);
+    return det;
+}
+
+double QDoubleMatrix4x4::determinant() const
+{
+    if ((flagBits & ~(Translation | Rotation2D | Rotation)) == Identity)
+        return 1.0;
+
+    if (flagBits < Rotation2D)
+        return m[0][0] * m[1][1] * m[2][2]; // Translation | Scale
+    if (flagBits < Perspective)
+        return matrixDet3(m, 0, 1, 2, 0, 1, 2);
+    return matrixDet4(m);
+}
+
+QDoubleMatrix4x4 QDoubleMatrix4x4::inverted(bool *invertible) const
+{
+    // Handle some of the easy cases first.
+    if (flagBits == Identity) {
+        if (invertible)
+            *invertible = true;
+        return QDoubleMatrix4x4();
+    } else if (flagBits == Translation) {
+        QDoubleMatrix4x4 inv;
+        inv.m[3][0] = -m[3][0];
+        inv.m[3][1] = -m[3][1];
+        inv.m[3][2] = -m[3][2];
+        inv.flagBits = Translation;
+        if (invertible)
+            *invertible = true;
+        return inv;
+    } else if (flagBits < Rotation2D) {
+        // Translation | Scale
+        if (m[0][0] == 0 || m[1][1] == 0 || m[2][2] == 0) {
+            if (invertible)
+                *invertible = false;
+            return QDoubleMatrix4x4();
+        }
+        QDoubleMatrix4x4 inv;
+        inv.m[0][0] = 1.0 / m[0][0];
+        inv.m[1][1] = 1.0 / m[1][1];
+        inv.m[2][2] = 1.0 / m[2][2];
+        inv.m[3][0] = -m[3][0] * inv.m[0][0];
+        inv.m[3][1] = -m[3][1] * inv.m[1][1];
+        inv.m[3][2] = -m[3][2] * inv.m[2][2];
+        inv.flagBits = flagBits;
+
+        if (invertible)
+            *invertible = true;
+        return inv;
+    } else if ((flagBits & ~(Translation | Rotation2D | Rotation)) == Identity) {
+        if (invertible)
+            *invertible = true;
+        return orthonormalInverse();
+    } else if (flagBits < Perspective) {
+        QDoubleMatrix4x4 inv(1); // The "1" says to not load the identity.
+
+        double det = matrixDet3(m, 0, 1, 2, 0, 1, 2);
+        if (det == 0.0) {
+            if (invertible)
+                *invertible = false;
+            return QDoubleMatrix4x4();
+        }
+        det = 1.0 / det;
+
+        inv.m[0][0] =  matrixDet2(m, 1, 2, 1, 2) * det;
+        inv.m[0][1] = -matrixDet2(m, 0, 2, 1, 2) * det;
+        inv.m[0][2] =  matrixDet2(m, 0, 1, 1, 2) * det;
+        inv.m[0][3] = 0;
+        inv.m[1][0] = -matrixDet2(m, 1, 2, 0, 2) * det;
+        inv.m[1][1] =  matrixDet2(m, 0, 2, 0, 2) * det;
+        inv.m[1][2] = -matrixDet2(m, 0, 1, 0, 2) * det;
+        inv.m[1][3] = 0;
+        inv.m[2][0] =  matrixDet2(m, 1, 2, 0, 1) * det;
+        inv.m[2][1] = -matrixDet2(m, 0, 2, 0, 1) * det;
+        inv.m[2][2] =  matrixDet2(m, 0, 1, 0, 1) * det;
+        inv.m[2][3] = 0;
+        inv.m[3][0] = -inv.m[0][0] * m[3][0] - inv.m[1][0] * m[3][1] - inv.m[2][0] * m[3][2];
+        inv.m[3][1] = -inv.m[0][1] * m[3][0] - inv.m[1][1] * m[3][1] - inv.m[2][1] * m[3][2];
+        inv.m[3][2] = -inv.m[0][2] * m[3][0] - inv.m[1][2] * m[3][1] - inv.m[2][2] * m[3][2];
+        inv.m[3][3] = 1;
+        inv.flagBits = flagBits;
+
+        if (invertible)
+            *invertible = true;
+        return inv;
+    }
+
+    QDoubleMatrix4x4 inv(1); // The "1" says to not load the identity.
+
+    double det = matrixDet4(m);
+    if (det == 0.0) {
+        if (invertible)
+            *invertible = false;
+        return QDoubleMatrix4x4();
+    }
+    det = 1.0 / det;
+
+    inv.m[0][0] =  matrixDet3(m, 1, 2, 3, 1, 2, 3) * det;
+    inv.m[0][1] = -matrixDet3(m, 0, 2, 3, 1, 2, 3) * det;
+    inv.m[0][2] =  matrixDet3(m, 0, 1, 3, 1, 2, 3) * det;
+    inv.m[0][3] = -matrixDet3(m, 0, 1, 2, 1, 2, 3) * det;
+    inv.m[1][0] = -matrixDet3(m, 1, 2, 3, 0, 2, 3) * det;
+    inv.m[1][1] =  matrixDet3(m, 0, 2, 3, 0, 2, 3) * det;
+    inv.m[1][2] = -matrixDet3(m, 0, 1, 3, 0, 2, 3) * det;
+    inv.m[1][3] =  matrixDet3(m, 0, 1, 2, 0, 2, 3) * det;
+    inv.m[2][0] =  matrixDet3(m, 1, 2, 3, 0, 1, 3) * det;
+    inv.m[2][1] = -matrixDet3(m, 0, 2, 3, 0, 1, 3) * det;
+    inv.m[2][2] =  matrixDet3(m, 0, 1, 3, 0, 1, 3) * det;
+    inv.m[2][3] = -matrixDet3(m, 0, 1, 2, 0, 1, 3) * det;
+    inv.m[3][0] = -matrixDet3(m, 1, 2, 3, 0, 1, 2) * det;
+    inv.m[3][1] =  matrixDet3(m, 0, 2, 3, 0, 1, 2) * det;
+    inv.m[3][2] = -matrixDet3(m, 0, 1, 3, 0, 1, 2) * det;
+    inv.m[3][3] =  matrixDet3(m, 0, 1, 2, 0, 1, 2) * det;
+    inv.flagBits = flagBits;
+
+    if (invertible)
+        *invertible = true;
+    return inv;
+}
+
+QDoubleMatrix4x4 QDoubleMatrix4x4::transposed() const
+{
+    QDoubleMatrix4x4 result(1); // The "1" says to not load the identity.
+    for (int row = 0; row < 4; ++row) {
+        for (int col = 0; col < 4; ++col) {
+            result.m[col][row] = m[row][col];
+        }
+    }
+    // When a translation is transposed, it becomes a perspective transformation.
+    result.flagBits = (flagBits & Translation ? General : flagBits);
+    return result;
+}
+
+QDoubleMatrix4x4& QDoubleMatrix4x4::operator/=(double divisor)
+{
+    m[0][0] /= divisor;
+    m[0][1] /= divisor;
+    m[0][2] /= divisor;
+    m[0][3] /= divisor;
+    m[1][0] /= divisor;
+    m[1][1] /= divisor;
+    m[1][2] /= divisor;
+    m[1][3] /= divisor;
+    m[2][0] /= divisor;
+    m[2][1] /= divisor;
+    m[2][2] /= divisor;
+    m[2][3] /= divisor;
+    m[3][0] /= divisor;
+    m[3][1] /= divisor;
+    m[3][2] /= divisor;
+    m[3][3] /= divisor;
+    flagBits = General;
+    return *this;
+}
+
+QDoubleMatrix4x4 operator/(const QDoubleMatrix4x4& matrix, double divisor)
+{
+    QDoubleMatrix4x4 m(1); // The "1" says to not load the identity.
+    m.m[0][0] = matrix.m[0][0] / divisor;
+    m.m[0][1] = matrix.m[0][1] / divisor;
+    m.m[0][2] = matrix.m[0][2] / divisor;
+    m.m[0][3] = matrix.m[0][3] / divisor;
+    m.m[1][0] = matrix.m[1][0] / divisor;
+    m.m[1][1] = matrix.m[1][1] / divisor;
+    m.m[1][2] = matrix.m[1][2] / divisor;
+    m.m[1][3] = matrix.m[1][3] / divisor;
+    m.m[2][0] = matrix.m[2][0] / divisor;
+    m.m[2][1] = matrix.m[2][1] / divisor;
+    m.m[2][2] = matrix.m[2][2] / divisor;
+    m.m[2][3] = matrix.m[2][3] / divisor;
+    m.m[3][0] = matrix.m[3][0] / divisor;
+    m.m[3][1] = matrix.m[3][1] / divisor;
+    m.m[3][2] = matrix.m[3][2] / divisor;
+    m.m[3][3] = matrix.m[3][3] / divisor;
+    m.flagBits = QDoubleMatrix4x4::General;
+    return m;
+}
+
+void QDoubleMatrix4x4::scale(const QDoubleVector3D& vector)
+{
+    double vx = vector.x();
+    double vy = vector.y();
+    double vz = vector.z();
+    if (flagBits < Scale) {
+        m[0][0] = vx;
+        m[1][1] = vy;
+        m[2][2] = vz;
+    } else if (flagBits < Rotation2D) {
+        m[0][0] *= vx;
+        m[1][1] *= vy;
+        m[2][2] *= vz;
+    } else if (flagBits < Rotation) {
+        m[0][0] *= vx;
+        m[0][1] *= vx;
+        m[1][0] *= vy;
+        m[1][1] *= vy;
+        m[2][2] *= vz;
+    } else {
+        m[0][0] *= vx;
+        m[0][1] *= vx;
+        m[0][2] *= vx;
+        m[0][3] *= vx;
+        m[1][0] *= vy;
+        m[1][1] *= vy;
+        m[1][2] *= vy;
+        m[1][3] *= vy;
+        m[2][0] *= vz;
+        m[2][1] *= vz;
+        m[2][2] *= vz;
+        m[2][3] *= vz;
+    }
+    flagBits |= Scale;
+}
+
+void QDoubleMatrix4x4::scale(double x, double y)
+{
+    if (flagBits < Scale) {
+        m[0][0] = x;
+        m[1][1] = y;
+    } else if (flagBits < Rotation2D) {
+        m[0][0] *= x;
+        m[1][1] *= y;
+    } else if (flagBits < Rotation) {
+        m[0][0] *= x;
+        m[0][1] *= x;
+        m[1][0] *= y;
+        m[1][1] *= y;
+    } else {
+        m[0][0] *= x;
+        m[0][1] *= x;
+        m[0][2] *= x;
+        m[0][3] *= x;
+        m[1][0] *= y;
+        m[1][1] *= y;
+        m[1][2] *= y;
+        m[1][3] *= y;
+    }
+    flagBits |= Scale;
+}
+
+void QDoubleMatrix4x4::scale(double x, double y, double z)
+{
+    if (flagBits < Scale) {
+        m[0][0] = x;
+        m[1][1] = y;
+        m[2][2] = z;
+    } else if (flagBits < Rotation2D) {
+        m[0][0] *= x;
+        m[1][1] *= y;
+        m[2][2] *= z;
+    } else if (flagBits < Rotation) {
+        m[0][0] *= x;
+        m[0][1] *= x;
+        m[1][0] *= y;
+        m[1][1] *= y;
+        m[2][2] *= z;
+    } else {
+        m[0][0] *= x;
+        m[0][1] *= x;
+        m[0][2] *= x;
+        m[0][3] *= x;
+        m[1][0] *= y;
+        m[1][1] *= y;
+        m[1][2] *= y;
+        m[1][3] *= y;
+        m[2][0] *= z;
+        m[2][1] *= z;
+        m[2][2] *= z;
+        m[2][3] *= z;
+    }
+    flagBits |= Scale;
+}
+
+void QDoubleMatrix4x4::scale(double factor)
+{
+    if (flagBits < Scale) {
+        m[0][0] = factor;
+        m[1][1] = factor;
+        m[2][2] = factor;
+    } else if (flagBits < Rotation2D) {
+        m[0][0] *= factor;
+        m[1][1] *= factor;
+        m[2][2] *= factor;
+    } else if (flagBits < Rotation) {
+        m[0][0] *= factor;
+        m[0][1] *= factor;
+        m[1][0] *= factor;
+        m[1][1] *= factor;
+        m[2][2] *= factor;
+    } else {
+        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;
+    }
+    flagBits |= Scale;
+}
+
+void QDoubleMatrix4x4::translate(const QDoubleVector3D& vector)
+{
+    double vx = vector.x();
+    double vy = vector.y();
+    double vz = vector.z();
+    if (flagBits == Identity) {
+        m[3][0] = vx;
+        m[3][1] = vy;
+        m[3][2] = vz;
+    } else if (flagBits == Translation) {
+        m[3][0] += vx;
+        m[3][1] += vy;
+        m[3][2] += vz;
+    } else if (flagBits == Scale) {
+        m[3][0] = m[0][0] * vx;
+        m[3][1] = m[1][1] * vy;
+        m[3][2] = m[2][2] * vz;
+    } else if (flagBits == (Translation | Scale)) {
+        m[3][0] += m[0][0] * vx;
+        m[3][1] += m[1][1] * vy;
+        m[3][2] += m[2][2] * vz;
+    } else if (flagBits < Rotation) {
+        m[3][0] += m[0][0] * vx + m[1][0] * vy;
+        m[3][1] += m[0][1] * vx + m[1][1] * vy;
+        m[3][2] += m[2][2] * vz;
+    } else {
+        m[3][0] += m[0][0] * vx + m[1][0] * vy + m[2][0] * vz;
+        m[3][1] += m[0][1] * vx + m[1][1] * vy + m[2][1] * vz;
+        m[3][2] += m[0][2] * vx + m[1][2] * vy + m[2][2] * vz;
+        m[3][3] += m[0][3] * vx + m[1][3] * vy + m[2][3] * vz;
+    }
+    flagBits |= Translation;
+}
+
+void QDoubleMatrix4x4::translate(double x, double y)
+{
+    if (flagBits == Identity) {
+        m[3][0] = x;
+        m[3][1] = y;
+    } else if (flagBits == Translation) {
+        m[3][0] += x;
+        m[3][1] += y;
+    } else if (flagBits == Scale) {
+        m[3][0] = m[0][0] * x;
+        m[3][1] = m[1][1] * y;
+    } else if (flagBits == (Translation | Scale)) {
+        m[3][0] += m[0][0] * x;
+        m[3][1] += m[1][1] * y;
+    } else if (flagBits < Rotation) {
+        m[3][0] += m[0][0] * x + m[1][0] * y;
+        m[3][1] += m[0][1] * x + m[1][1] * y;
+    } else {
+        m[3][0] += m[0][0] * x + m[1][0] * y;
+        m[3][1] += m[0][1] * x + m[1][1] * y;
+        m[3][2] += m[0][2] * x + m[1][2] * y;
+        m[3][3] += m[0][3] * x + m[1][3] * y;
+    }
+    flagBits |= Translation;
+}
+
+void QDoubleMatrix4x4::translate(double x, double y, double z)
+{
+    if (flagBits == Identity) {
+        m[3][0] = x;
+        m[3][1] = y;
+        m[3][2] = z;
+    } else if (flagBits == Translation) {
+        m[3][0] += x;
+        m[3][1] += y;
+        m[3][2] += z;
+    } else if (flagBits == Scale) {
+        m[3][0] = m[0][0] * x;
+        m[3][1] = m[1][1] * y;
+        m[3][2] = m[2][2] * z;
+    } else if (flagBits == (Translation | Scale)) {
+        m[3][0] += m[0][0] * x;
+        m[3][1] += m[1][1] * y;
+        m[3][2] += m[2][2] * z;
+    } else if (flagBits < Rotation) {
+        m[3][0] += m[0][0] * x + m[1][0] * y;
+        m[3][1] += m[0][1] * x + m[1][1] * y;
+        m[3][2] += m[2][2] * z;
+    } else {
+        m[3][0] += m[0][0] * x + m[1][0] * y + m[2][0] * z;
+        m[3][1] += m[0][1] * x + m[1][1] * y + m[2][1] * z;
+        m[3][2] += m[0][2] * x + m[1][2] * y + m[2][2] * z;
+        m[3][3] += m[0][3] * x + m[1][3] * y + m[2][3] * z;
+    }
+    flagBits |= Translation;
+}
+
+void QDoubleMatrix4x4::rotate(double angle, const QDoubleVector3D& vector)
+{
+    rotate(angle, vector.x(), vector.y(), vector.z());
+}
+
+void QDoubleMatrix4x4::rotate(double angle, double x, double y, double z)
+{
+    if (angle == 0.0)
+        return;
+    double c, s;
+    if (angle == 90.0 || angle == -270.0) {
+        s = 1.0;
+        c = 0.0;
+    } else if (angle == -90.0 || angle == 270.0) {
+        s = -1.0;
+        c = 0.0;
+    } else if (angle == 180.0 || angle == -180.0) {
+        s = 0.0;
+        c = -1.0;
+    } else {
+        double a = angle * M_PI / 180.0;
+        c = std::cos(a);
+        s = std::sin(a);
+    }
+    if (x == 0.0) {
+        if (y == 0.0) {
+            if (z != 0.0) {
+                // Rotate around the Z axis.
+                if (z < 0)
+                    s = -s;
+                double tmp;
+                m[0][0] = (tmp = m[0][0]) * c + m[1][0] * s;
+                m[1][0] = m[1][0] * c - tmp * s;
+                m[0][1] = (tmp = m[0][1]) * c + m[1][1] * s;
+                m[1][1] = m[1][1] * c - tmp * s;
+                m[0][2] = (tmp = m[0][2]) * c + m[1][2] * s;
+                m[1][2] = m[1][2] * c - tmp * s;
+                m[0][3] = (tmp = m[0][3]) * c + m[1][3] * s;
+                m[1][3] = m[1][3] * c - tmp * s;
+
+                flagBits |= Rotation2D;
+                return;
+            }
+        } else if (z == 0.0) {
+            // Rotate around the Y axis.
+            if (y < 0)
+                s = -s;
+            double tmp;
+            m[2][0] = (tmp = m[2][0]) * c + m[0][0] * s;
+            m[0][0] = m[0][0] * c - tmp * s;
+            m[2][1] = (tmp = m[2][1]) * c + m[0][1] * s;
+            m[0][1] = m[0][1] * c - tmp * s;
+            m[2][2] = (tmp = m[2][2]) * c + m[0][2] * s;
+            m[0][2] = m[0][2] * c - tmp * s;
+            m[2][3] = (tmp = m[2][3]) * c + m[0][3] * s;
+            m[0][3] = m[0][3] * c - tmp * s;
+
+            flagBits |= Rotation;
+            return;
+        }
+    } else if (y == 0.0 && z == 0.0) {
+        // Rotate around the X axis.
+        if (x < 0)
+            s = -s;
+        double tmp;
+        m[1][0] = (tmp = m[1][0]) * c + m[2][0] * s;
+        m[2][0] = m[2][0] * c - tmp * s;
+        m[1][1] = (tmp = m[1][1]) * c + m[2][1] * s;
+        m[2][1] = m[2][1] * c - tmp * s;
+        m[1][2] = (tmp = m[1][2]) * c + m[2][2] * s;
+        m[2][2] = m[2][2] * c - tmp * s;
+        m[1][3] = (tmp = m[1][3]) * c + m[2][3] * s;
+        m[2][3] = m[2][3] * c - tmp * s;
+
+        flagBits |= Rotation;
+        return;
+    }
+
+    double len = double(x) * double(x) +
+                 double(y) * double(y) +
+                 double(z) * double(z);
+    if (!qFuzzyCompare(len, 1.0) && !qFuzzyIsNull(len)) {
+        len = std::sqrt(len);
+        x = double(double(x) / len);
+        y = double(double(y) / len);
+        z = double(double(z) / len);
+    }
+    double ic = 1.0 - c;
+    QDoubleMatrix4x4 rot(1); // The "1" says to not load the identity.
+    rot.m[0][0] = x * x * ic + c;
+    rot.m[1][0] = x * y * ic - z * s;
+    rot.m[2][0] = x * z * ic + y * s;
+    rot.m[3][0] = 0.0;
+    rot.m[0][1] = y * x * ic + z * s;
+    rot.m[1][1] = y * y * ic + c;
+    rot.m[2][1] = y * z * ic - x * s;
+    rot.m[3][1] = 0.0;
+    rot.m[0][2] = x * z * ic - y * s;
+    rot.m[1][2] = y * z * ic + x * s;
+    rot.m[2][2] = z * z * ic + c;
+    rot.m[3][2] = 0.0;
+    rot.m[0][3] = 0.0;
+    rot.m[1][3] = 0.0;
+    rot.m[2][3] = 0.0;
+    rot.m[3][3] = 1.0;
+    rot.flagBits = Rotation;
+    *this *= rot;
+}
+
+void QDoubleMatrix4x4::projectedRotate(double angle, double x, double y, double z)
+{
+    // Used by QGraphicsRotation::applyTo() to perform a rotation
+    // and projection back to 2D in a single step.
+    if (angle == 0.0)
+        return;
+    double c, s;
+    if (angle == 90.0 || angle == -270.0) {
+        s = 1.0;
+        c = 0.0;
+    } else if (angle == -90.0 || angle == 270.0) {
+        s = -1.0;
+        c = 0.0;
+    } else if (angle == 180.0 || angle == -180.0) {
+        s = 0.0;
+        c = -1.0;
+    } else {
+        double a = angle * M_PI / 180.0;
+        c = std::cos(a);
+        s = std::sin(a);
+    }
+    if (x == 0.0) {
+        if (y == 0.0) {
+            if (z != 0.0) {
+                // Rotate around the Z axis.
+                if (z < 0)
+                    s = -s;
+                double tmp;
+                m[0][0] = (tmp = m[0][0]) * c + m[1][0] * s;
+                m[1][0] = m[1][0] * c - tmp * s;
+                m[0][1] = (tmp = m[0][1]) * c + m[1][1] * s;
+                m[1][1] = m[1][1] * c - tmp * s;
+                m[0][2] = (tmp = m[0][2]) * c + m[1][2] * s;
+                m[1][2] = m[1][2] * c - tmp * s;
+                m[0][3] = (tmp = m[0][3]) * c + m[1][3] * s;
+                m[1][3] = m[1][3] * c - tmp * s;
+
+                flagBits |= Rotation2D;
+                return;
+            }
+        } else if (z == 0.0) {
+            // Rotate around the Y axis.
+            if (y < 0)
+                s = -s;
+            m[0][0] = m[0][0] * c + m[3][0] * s * inv_dist_to_plane;
+            m[0][1] = m[0][1] * c + m[3][1] * s * inv_dist_to_plane;
+            m[0][2] = m[0][2] * c + m[3][2] * s * inv_dist_to_plane;
+            m[0][3] = m[0][3] * c + m[3][3] * s * inv_dist_to_plane;
+            flagBits = General;
+            return;
+        }
+    } else if (y == 0.0 && z == 0.0) {
+        // Rotate around the X axis.
+        if (x < 0)
+            s = -s;
+        m[1][0] = m[1][0] * c - m[3][0] * s * inv_dist_to_plane;
+        m[1][1] = m[1][1] * c - m[3][1] * s * inv_dist_to_plane;
+        m[1][2] = m[1][2] * c - m[3][2] * s * inv_dist_to_plane;
+        m[1][3] = m[1][3] * c - m[3][3] * s * inv_dist_to_plane;
+        flagBits = General;
+        return;
+    }
+    double len = double(x) * double(x) +
+                 double(y) * double(y) +
+                 double(z) * double(z);
+    if (!qFuzzyCompare(len, 1.0) && !qFuzzyIsNull(len)) {
+        len = std::sqrt(len);
+        x = double(double(x) / len);
+        y = double(double(y) / len);
+        z = double(double(z) / len);
+    }
+    double ic = 1.0 - c;
+    QDoubleMatrix4x4 rot(1); // The "1" says to not load the identity.
+    rot.m[0][0] = x * x * ic + c;
+    rot.m[1][0] = x * y * ic - z * s;
+    rot.m[2][0] = 0.0;
+    rot.m[3][0] = 0.0;
+    rot.m[0][1] = y * x * ic + z * s;
+    rot.m[1][1] = y * y * ic + c;
+    rot.m[2][1] = 0.0;
+    rot.m[3][1] = 0.0;
+    rot.m[0][2] = 0.0;
+    rot.m[1][2] = 0.0;
+    rot.m[2][2] = 1.0;
+    rot.m[3][2] = 0.0;
+    rot.m[0][3] = (x * z * ic - y * s) * -inv_dist_to_plane;
+    rot.m[1][3] = (y * z * ic + x * s) * -inv_dist_to_plane;
+    rot.m[2][3] = 0.0;
+    rot.m[3][3] = 1.0;
+    rot.flagBits = General;
+    *this *= rot;
+}
+
+void QDoubleMatrix4x4::ortho(const QRect& rect)
+{
+    // Note: rect.right() and rect.bottom() subtract 1 in QRect,
+    // which gives the location of a pixel within the rectangle,
+    // instead of the extent of the rectangle.  We want the extent.
+    // QRectF expresses the extent properly.
+    ortho(rect.x(), rect.x() + rect.width(), rect.y() + rect.height(), rect.y(), -1.0, 1.0);
+}
+
+void QDoubleMatrix4x4::ortho(const QRectF& rect)
+{
+    ortho(rect.left(), rect.right(), rect.bottom(), rect.top(), -1.0, 1.0);
+}
+
+void QDoubleMatrix4x4::ortho(double left, double right, double bottom, double top, double nearPlane, double farPlane)
+{
+    // Bail out if the projection volume is zero-sized.
+    if (left == right || bottom == top || nearPlane == farPlane)
+        return;
+
+    // Construct the projection.
+    double width = right - left;
+    double invheight = top - bottom;
+    double clip = farPlane - nearPlane;
+    QDoubleMatrix4x4 m(1);
+    m.m[0][0] = 2.0 / width;
+    m.m[1][0] = 0.0;
+    m.m[2][0] = 0.0;
+    m.m[3][0] = -(left + right) / width;
+    m.m[0][1] = 0.0;
+    m.m[1][1] = 2.0 / invheight;
+    m.m[2][1] = 0.0;
+    m.m[3][1] = -(top + bottom) / invheight;
+    m.m[0][2] = 0.0;
+    m.m[1][2] = 0.0;
+    m.m[2][2] = -2.0 / clip;
+    m.m[3][2] = -(nearPlane + farPlane) / clip;
+    m.m[0][3] = 0.0;
+    m.m[1][3] = 0.0;
+    m.m[2][3] = 0.0;
+    m.m[3][3] = 1.0;
+    m.flagBits = Translation | Scale;
+
+    // Apply the projection.
+    *this *= m;
+}
+
+void QDoubleMatrix4x4::frustum(double left, double right, double bottom, double top, double nearPlane, double farPlane)
+{
+    // Bail out if the projection volume is zero-sized.
+    if (left == right || bottom == top || nearPlane == farPlane)
+        return;
+
+    // Construct the projection.
+    QDoubleMatrix4x4 m(1);
+    double width = right - left;
+    double invheight = top - bottom;
+    double clip = farPlane - nearPlane;
+    m.m[0][0] = 2.0 * nearPlane / width;
+    m.m[1][0] = 0.0;
+    m.m[2][0] = (left + right) / width;
+    m.m[3][0] = 0.0;
+    m.m[0][1] = 0.0;
+    m.m[1][1] = 2.0 * nearPlane / invheight;
+    m.m[2][1] = (top + bottom) / invheight;
+    m.m[3][1] = 0.0;
+    m.m[0][2] = 0.0;
+    m.m[1][2] = 0.0;
+    m.m[2][2] = -(nearPlane + farPlane) / clip;
+    m.m[3][2] = -2.0 * nearPlane * farPlane / clip;
+    m.m[0][3] = 0.0;
+    m.m[1][3] = 0.0;
+    m.m[2][3] = -1.0;
+    m.m[3][3] = 0.0;
+    m.flagBits = General;
+
+    // Apply the projection.
+    *this *= m;
+}
+
+void QDoubleMatrix4x4::perspective(double verticalAngle, double aspectRatio, double nearPlane, double farPlane)
+{
+    // Bail out if the projection volume is zero-sized.
+    if (nearPlane == farPlane || aspectRatio == 0.0)
+        return;
+
+    // Construct the projection.
+    QDoubleMatrix4x4 m(1);
+    double radians = (verticalAngle / 2.0) * M_PI / 180.0;
+    double sine = std::sin(radians);
+    if (sine == 0.0)
+        return;
+    double cotan = std::cos(radians) / sine;
+    double clip = farPlane - nearPlane;
+    m.m[0][0] = cotan / aspectRatio;
+    m.m[1][0] = 0.0;
+    m.m[2][0] = 0.0;
+    m.m[3][0] = 0.0;
+    m.m[0][1] = 0.0;
+    m.m[1][1] = cotan;
+    m.m[2][1] = 0.0;
+    m.m[3][1] = 0.0;
+    m.m[0][2] = 0.0;
+    m.m[1][2] = 0.0;
+    m.m[2][2] = -(nearPlane + farPlane) / clip;
+    m.m[3][2] = -(2.0 * nearPlane * farPlane) / clip;
+    m.m[0][3] = 0.0;
+    m.m[1][3] = 0.0;
+    m.m[2][3] = -1.0;
+    m.m[3][3] = 0.0;
+    m.flagBits = General;
+
+    // Apply the projection.
+    *this *= m;
+}
+
+void QDoubleMatrix4x4::lookAt(const QDoubleVector3D& eye, const QDoubleVector3D& center, const QDoubleVector3D& up)
+{
+    QDoubleVector3D forward = center - eye;
+    if (qFuzzyIsNull(forward.x()) && qFuzzyIsNull(forward.y()) && qFuzzyIsNull(forward.z()))
+        return;
+
+    forward.normalize();
+    QDoubleVector3D side = QDoubleVector3D::crossProduct(forward, up).normalized();
+    QDoubleVector3D upVector = QDoubleVector3D::crossProduct(side, forward);
+
+    QDoubleMatrix4x4 m(1);
+    m.m[0][0] = side.x();
+    m.m[1][0] = side.y();
+    m.m[2][0] = side.z();
+    m.m[3][0] = 0.0;
+    m.m[0][1] = upVector.x();
+    m.m[1][1] = upVector.y();
+    m.m[2][1] = upVector.z();
+    m.m[3][1] = 0.0;
+    m.m[0][2] = -forward.x();
+    m.m[1][2] = -forward.y();
+    m.m[2][2] = -forward.z();
+    m.m[3][2] = 0.0;
+    m.m[0][3] = 0.0;
+    m.m[1][3] = 0.0;
+    m.m[2][3] = 0.0;
+    m.m[3][3] = 1.0;
+    m.flagBits = Rotation;
+
+    *this *= m;
+    translate(-eye);
+}
+
+void QDoubleMatrix4x4::viewport(double left, double bottom, double width, double height, double nearPlane, double farPlane)
+{
+    const double w2 = width / 2.0;
+    const double h2 = height / 2.0;
+
+    QDoubleMatrix4x4 m(1);
+    m.m[0][0] = w2;
+    m.m[1][0] = 0.0;
+    m.m[2][0] = 0.0;
+    m.m[3][0] = left + w2;
+    m.m[0][1] = 0.0;
+    m.m[1][1] = h2;
+    m.m[2][1] = 0.0;
+    m.m[3][1] = bottom + h2;
+    m.m[0][2] = 0.0;
+    m.m[1][2] = 0.0;
+    m.m[2][2] = (farPlane - nearPlane) / 2.0;
+    m.m[3][2] = (nearPlane + farPlane) / 2.0;
+    m.m[0][3] = 0.0;
+    m.m[1][3] = 0.0;
+    m.m[2][3] = 0.0;
+    m.m[3][3] = 1.0;
+    m.flagBits = General;
+
+    *this *= m;
+}
+
+void QDoubleMatrix4x4::flipCoordinates()
+{
+    // Multiplying the y and z coordinates with -1 does NOT flip between right-handed and
+    // left-handed coordinate systems, it just rotates 180 degrees around the x axis, so
+    // I'm deprecating this function.
+    if (flagBits < Rotation2D) {
+        // Translation | Scale
+        m[1][1] = -m[1][1];
+        m[2][2] = -m[2][2];
+    } else {
+        m[1][0] = -m[1][0];
+        m[1][1] = -m[1][1];
+        m[1][2] = -m[1][2];
+        m[1][3] = -m[1][3];
+        m[2][0] = -m[2][0];
+        m[2][1] = -m[2][1];
+        m[2][2] = -m[2][2];
+        m[2][3] = -m[2][3];
+    }
+    flagBits |= Scale;
+}
+
+void QDoubleMatrix4x4::copyDataTo(double *values) const
+{
+    for (int row = 0; row < 4; ++row)
+        for (int col = 0; col < 4; ++col)
+            values[row * 4 + col] = double(m[col][row]);
+}
+
+QRect QDoubleMatrix4x4::mapRect(const QRect& rect) const
+{
+    if (flagBits < Scale) {
+        // Translation
+        return QRect(qRound(rect.x() + m[3][0]),
+                     qRound(rect.y() + m[3][1]),
+                     rect.width(), rect.height());
+    } else if (flagBits < Rotation2D) {
+        // Translation | Scale
+        double x = rect.x() * m[0][0] + m[3][0];
+        double y = rect.y() * m[1][1] + m[3][1];
+        double w = rect.width() * m[0][0];
+        double h = rect.height() * m[1][1];
+        if (w < 0) {
+            w = -w;
+            x -= w;
+        }
+        if (h < 0) {
+            h = -h;
+            y -= h;
+        }
+        return QRect(qRound(x), qRound(y), qRound(w), qRound(h));
+    }
+
+    QPoint tl = map(rect.topLeft());
+    QPoint tr = map(QPoint(rect.x() + rect.width(), rect.y()));
+    QPoint bl = map(QPoint(rect.x(), rect.y() + rect.height()));
+    QPoint br = map(QPoint(rect.x() + rect.width(),
+                           rect.y() + rect.height()));
+
+    int xmin = qMin(qMin(tl.x(), tr.x()), qMin(bl.x(), br.x()));
+    int xmax = qMax(qMax(tl.x(), tr.x()), qMax(bl.x(), br.x()));
+    int ymin = qMin(qMin(tl.y(), tr.y()), qMin(bl.y(), br.y()));
+    int ymax = qMax(qMax(tl.y(), tr.y()), qMax(bl.y(), br.y()));
+
+    return QRect(xmin, ymin, xmax - xmin, ymax - ymin);
+}
+
+QRectF QDoubleMatrix4x4::mapRect(const QRectF& rect) const
+{
+    if (flagBits < Scale) {
+        // Translation
+        return rect.translated(m[3][0], m[3][1]);
+    } else if (flagBits < Rotation2D) {
+        // Translation | Scale
+        double x = rect.x() * m[0][0] + m[3][0];
+        double y = rect.y() * m[1][1] + m[3][1];
+        double w = rect.width() * m[0][0];
+        double h = rect.height() * m[1][1];
+        if (w < 0) {
+            w = -w;
+            x -= w;
+        }
+        if (h < 0) {
+            h = -h;
+            y -= h;
+        }
+        return QRectF(x, y, w, h);
+    }
+
+    QPointF tl = map(rect.topLeft()); QPointF tr = map(rect.topRight());
+    QPointF bl = map(rect.bottomLeft()); QPointF br = map(rect.bottomRight());
+
+    double xmin = qMin(qMin(tl.x(), tr.x()), qMin(bl.x(), br.x()));
+    double xmax = qMax(qMax(tl.x(), tr.x()), qMax(bl.x(), br.x()));
+    double ymin = qMin(qMin(tl.y(), tr.y()), qMin(bl.y(), br.y()));
+    double ymax = qMax(qMax(tl.y(), tr.y()), qMax(bl.y(), br.y()));
+
+    return QRectF(QPointF(xmin, ymin), QPointF(xmax, ymax));
+}
+
+QDoubleMatrix4x4 QDoubleMatrix4x4::orthonormalInverse() const
+{
+    QDoubleMatrix4x4 result(1);  // The '1' says not to load identity
+
+    result.m[0][0] = m[0][0];
+    result.m[1][0] = m[0][1];
+    result.m[2][0] = m[0][2];
+
+    result.m[0][1] = m[1][0];
+    result.m[1][1] = m[1][1];
+    result.m[2][1] = m[1][2];
+
+    result.m[0][2] = m[2][0];
+    result.m[1][2] = m[2][1];
+    result.m[2][2] = m[2][2];
+
+    result.m[0][3] = 0.0;
+    result.m[1][3] = 0.0;
+    result.m[2][3] = 0.0;
+
+    result.m[3][0] = -(result.m[0][0] * m[3][0] + result.m[1][0] * m[3][1] + result.m[2][0] * m[3][2]);
+    result.m[3][1] = -(result.m[0][1] * m[3][0] + result.m[1][1] * m[3][1] + result.m[2][1] * m[3][2]);
+    result.m[3][2] = -(result.m[0][2] * m[3][0] + result.m[1][2] * m[3][1] + result.m[2][2] * m[3][2]);
+    result.m[3][3] = 1.0;
+
+    result.flagBits = flagBits;
+
+    return result;
+}
+
+void QDoubleMatrix4x4::optimize()
+{
+    // If the last row is not (0, 0, 0, 1), the matrix is not a special type.
+    flagBits = General;
+    if (m[0][3] != 0 || m[1][3] != 0 || m[2][3] != 0 || m[3][3] != 1)
+        return;
+
+    flagBits &= ~Perspective;
+
+    // If the last column is (0, 0, 0, 1), then there is no translation.
+    if (m[3][0] == 0 && m[3][1] == 0 && m[3][2] == 0)
+        flagBits &= ~Translation;
+
+    // If the two first elements of row 3 and column 3 are 0, then any rotation must be about Z.
+    if (!m[0][2] && !m[1][2] && !m[2][0] && !m[2][1]) {
+        flagBits &= ~Rotation;
+        // If the six non-diagonal elements in the top left 3x3 matrix are 0, there is no rotation.
+        if (!m[0][1] && !m[1][0]) {
+            flagBits &= ~Rotation2D;
+            // Check for identity.
+            if (m[0][0] == 1 && m[1][1] == 1 && m[2][2] == 1)
+                flagBits &= ~Scale;
+        } else {
+            // If the columns are orthonormal and form a right-handed system, then there is no scale.
+            double det = matrixDet2(m, 0, 1, 0, 1);
+            double lenX = m[0][0] * m[0][0] + m[0][1] * m[0][1];
+            double lenY = m[1][0] * m[1][0] + m[1][1] * m[1][1];
+            double lenZ = m[2][2];
+            if (qFuzzyCompare(det, 1.0) && qFuzzyCompare(lenX, 1.0)
+                    && qFuzzyCompare(lenY, 1.0) && qFuzzyCompare(lenZ, 1.0))
+            {
+                flagBits &= ~Scale;
+            }
+        }
+    } else {
+        // If the columns are orthonormal and form a right-handed system, then there is no scale.
+        double det = matrixDet3(m, 0, 1, 2, 0, 1, 2);
+        double lenX = m[0][0] * m[0][0] + m[0][1] * m[0][1] + m[0][2] * m[0][2];
+        double lenY = m[1][0] * m[1][0] + m[1][1] * m[1][1] + m[1][2] * m[1][2];
+        double lenZ = m[2][0] * m[2][0] + m[2][1] * m[2][1] + m[2][2] * m[2][2];
+        if (qFuzzyCompare(det, 1.0) && qFuzzyCompare(lenX, 1.0)
+                && qFuzzyCompare(lenY, 1.0) && qFuzzyCompare(lenZ, 1.0))
+        {
+            flagBits &= ~Scale;
+        }
+    }
+}
+
+#ifndef QT_NO_DEBUG_STREAM
+
+QDebug operator<<(QDebug dbg, const QDoubleMatrix4x4 &m)
+{
+    QDebugStateSaver saver(dbg);
+    // Create a string that represents the matrix type.
+    QByteArray bits;
+    if (m.flagBits == QDoubleMatrix4x4::Identity) {
+        bits = "Identity";
+    } else if (m.flagBits == QDoubleMatrix4x4::General) {
+        bits = "General";
+    } else {
+        if ((m.flagBits & QDoubleMatrix4x4::Translation) != 0)
+            bits += "Translation,";
+        if ((m.flagBits & QDoubleMatrix4x4::Scale) != 0)
+            bits += "Scale,";
+        if ((m.flagBits & QDoubleMatrix4x4::Rotation2D) != 0)
+            bits += "Rotation2D,";
+        if ((m.flagBits & QDoubleMatrix4x4::Rotation) != 0)
+            bits += "Rotation,";
+        if ((m.flagBits & QDoubleMatrix4x4::Perspective) != 0)
+            bits += "Perspective,";
+        if (bits.size() > 0)
+            bits = bits.left(bits.size() - 1);
+    }
+
+    // Output in row-major order because it is more human-readable.
+    dbg.nospace() << "QDoubleMatrix4x4(type:" << bits.constData() << endl
+        << qSetFieldWidth(10)
+        << m(0, 0) << m(0, 1) << m(0, 2) << m(0, 3) << endl
+        << m(1, 0) << m(1, 1) << m(1, 2) << m(1, 3) << endl
+        << m(2, 0) << m(2, 1) << m(2, 2) << m(2, 3) << endl
+        << m(3, 0) << m(3, 1) << m(3, 2) << m(3, 3) << endl
+        << qSetFieldWidth(0) << ')';
+    return dbg;
+}
+
+#endif
+
+#ifndef QT_NO_DATASTREAM
+
+QDataStream &operator<<(QDataStream &stream, const QDoubleMatrix4x4 &matrix)
+{
+    for (int row = 0; row < 4; ++row)
+        for (int col = 0; col < 4; ++col)
+            stream << matrix(row, col);
+    return stream;
+}
+
+QDataStream &operator>>(QDataStream &stream, QDoubleMatrix4x4 &matrix)
+{
+    double x;
+    for (int row = 0; row < 4; ++row) {
+        for (int col = 0; col < 4; ++col) {
+            stream >> x;
+            matrix(row, col) = x;
+        }
+    }
+    matrix.optimize();
+    return stream;
+}
+
+#endif // QT_NO_DATASTREAM
+
+QT_END_NAMESPACE
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
diff --git a/src/positioning/qdoublevector2d_p.h b/src/positioning/qdoublevector2d_p.h
index c35899e4..69348ee1 100644
--- a/src/positioning/qdoublevector2d_p.h
+++ b/src/positioning/qdoublevector2d_p.h
@@ -91,6 +91,7 @@ public:
     inline QDoubleVector2D &operator*=(double factor);
     inline QDoubleVector2D &operator*=(const QDoubleVector2D &vector);
     inline QDoubleVector2D &operator/=(double divisor);
+    inline QDoubleVector2D &operator/=(const QDoubleVector2D &vector);
 
     Q_DECL_CONSTEXPR static inline double dotProduct(const QDoubleVector2D &v1, const QDoubleVector2D &v2)
     { return v1.xp * v2.xp + v1.yp * v2.yp; }
@@ -179,6 +180,13 @@ inline QDoubleVector2D &QDoubleVector2D::operator/=(double divisor)
     return *this;
 }
 
+inline QDoubleVector2D &QDoubleVector2D::operator/=(const QDoubleVector2D &vector)
+{
+    xp /= vector.xp;
+    yp /= vector.yp;
+    return *this;
+}
+
 Q_DECL_CONSTEXPR inline bool operator==(const QDoubleVector2D &v1, const QDoubleVector2D &v2)
 {
     return v1.xp == v2.xp && v1.yp == v2.yp;