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++ // Copyright (C) 2016 The Qt Company Ltd.
++ // SPDX-License-Identifier: LicenseRef-Qt-Commercial OR LGPL-3.0-only OR GPL-2.0-only OR GPL-3.0-only
++ // Qt-Security score:significant reason:default
++
++ #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/QDebug>
++ #include <QtCore/qmetatype.h>
++ #include <QtCore/QRectF>
++
++ 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_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 = 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_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_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,
++ double distanceToPlane = 1024.0);
++ };
++
++ Q_DECLARE_TYPEINFO(QDoubleMatrix4x4, Q_RELOCATABLE_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_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 QtPrivate::fuzzyCompare(m1.m[0][0], m2.m[0][0])
++ && QtPrivate::fuzzyCompare(m1.m[0][1], m2.m[0][1])
++ && QtPrivate::fuzzyCompare(m1.m[0][2], m2.m[0][2])
++ && QtPrivate::fuzzyCompare(m1.m[0][3], m2.m[0][3])
++ && QtPrivate::fuzzyCompare(m1.m[1][0], m2.m[1][0])
++ && QtPrivate::fuzzyCompare(m1.m[1][1], m2.m[1][1])
++ && QtPrivate::fuzzyCompare(m1.m[1][2], m2.m[1][2])
++ && QtPrivate::fuzzyCompare(m1.m[1][3], m2.m[1][3])
++ && QtPrivate::fuzzyCompare(m1.m[2][0], m2.m[2][0])
++ && QtPrivate::fuzzyCompare(m1.m[2][1], m2.m[2][1])
++ && QtPrivate::fuzzyCompare(m1.m[2][2], m2.m[2][2])
++ && QtPrivate::fuzzyCompare(m1.m[2][3], m2.m[2][3])
++ && QtPrivate::fuzzyCompare(m1.m[3][0], m2.m[3][0])
++ && QtPrivate::fuzzyCompare(m1.m[3][1], m2.m[3][1])
++ && QtPrivate::fuzzyCompare(m1.m[3][2], m2.m[3][2])
++ && QtPrivate::fuzzyCompare(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_EXPORT QDebug operator<<(QDebug dbg, const QDoubleMatrix4x4 &m);
++ #endif
++
++ #ifndef QT_NO_DATASTREAM
++ Q_POSITIONING_EXPORT QDataStream &operator<<(QDataStream &, const QDoubleMatrix4x4 &);
++ Q_POSITIONING_EXPORT QDataStream &operator>>(QDataStream &, QDoubleMatrix4x4 &);
++ #endif
++
++
++ QT_END_NAMESPACE
++
++
++ #endif // QDOUBLEMATRIX4X4_H