// 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

#ifndef QMATRIX4X4_H

#define QMATRIX4X4_H

#include <QtGui/qtguiglobal.h>

#include <QtGui/qvector3d.h>

#include <QtGui/qvector4d.h>

#include <QtGui/qgenericmatrix.h>

#include <QtCore/qrect.h>

class tst_QMatrixNxN;

QT_BEGIN_NAMESPACE

#ifndef QT_NO_QUATERNION

class QQuaternion;

#endif

#ifndef QT_NO_MATRIX4X4

class QTransform;

class QVariant;

class Q_GUI_EXPORT QMatrix4x4

{

public:

    inline QMatrix4x4() { setToIdentity(); }

    explicit QMatrix4x4(Qt::Initialization) : flagBits(General) {}

    explicit QMatrix4x4(const float *values);

    inline QMatrix4x4(float m11, float m12, float m13, float m14,

                      float m21, float m22, float m23, float m24,

                      float m31, float m32, float m33, float m34,

                      float m41, float m42, float m43, float m44);

    template <int N, int M>

    explicit QMatrix4x4(const QGenericMatrix<N, M, float>& matrix);

    QMatrix4x4(const float *values, int cols, int rows);

    QMatrix4x4(const QTransform& transform);

    inline const float& operator()(int row, int column) const;

    inline float& operator()(int row, int column);

#ifndef QT_NO_VECTOR4D

    inline QVector4D column(int index) const;

    inline void setColumn(int index, const QVector4D& value);

    inline QVector4D row(int index) const;

    inline void setRow(int index, const QVector4D& value);

#endif

    inline bool isAffine() const;

    inline bool isIdentity() const;

    inline void setToIdentity();

    inline void fill(float value);

    double determinant() const;

    QMatrix4x4 inverted(bool *invertible = nullptr) const;

    QMatrix4x4 transposed() const;

    QMatrix3x3 normalMatrix() const;

    inline QMatrix4x4& operator+=(const QMatrix4x4& other);

    inline QMatrix4x4& operator-=(const QMatrix4x4& other);

    inline QMatrix4x4& operator*=(const QMatrix4x4& other);

    inline QMatrix4x4& operator*=(float factor);

    QMatrix4x4& operator/=(float divisor);

    inline bool operator==(const QMatrix4x4& other) const;

    inline bool operator!=(const QMatrix4x4& other) const;

    friend QMatrix4x4 operator+(const QMatrix4x4& m1, const QMatrix4x4& m2);

    friend QMatrix4x4 operator-(const QMatrix4x4& m1, const QMatrix4x4& m2);

    friend QMatrix4x4 operator*(const QMatrix4x4& m1, const QMatrix4x4& m2);

#ifndef QT_NO_VECTOR3D

#if QT_DEPRECATED_SINCE(6, 1)

    friend QVector3D operator*(const QMatrix4x4& matrix, const QVector3D& vector);

    friend QVector3D operator*(const QVector3D& vector, const QMatrix4x4& matrix);

#endif

#endif

#ifndef QT_NO_VECTOR4D

    friend QVector4D operator*(const QVector4D& vector, const QMatrix4x4& matrix);

    friend QVector4D operator*(const QMatrix4x4& matrix, const QVector4D& vector);

#endif

    friend QPoint operator*(const QPoint& point, const QMatrix4x4& matrix);

    friend QPointF operator*(const QPointF& point, const QMatrix4x4& matrix);

    friend QMatrix4x4 operator-(const QMatrix4x4& matrix);

#if QT_DEPRECATED_SINCE(6, 1)

    friend QPoint operator*(const QMatrix4x4& matrix, const QPoint& point);

    friend QPointF operator*(const QMatrix4x4& matrix, const QPointF& point);

#endif

    friend QMatrix4x4 operator*(float factor, const QMatrix4x4& matrix);

    friend QMatrix4x4 operator*(const QMatrix4x4& matrix, float factor);

    friend Q_GUI_EXPORT QMatrix4x4 operator/(const QMatrix4x4& matrix, float divisor);

    friend Q_GUI_EXPORT bool qFuzzyCompare(const QMatrix4x4& m1, const QMatrix4x4& m2) noexcept;

#ifndef QT_NO_VECTOR3D

    void scale(const QVector3D& vector);

    void translate(const QVector3D& vector);

    void rotate(float angle, const QVector3D& vector);

#endif

    void scale(float x, float y);

    void scale(float x, float y, float z);

    void scale(float factor);

    void translate(float x, float y);

    void translate(float x, float y, float z);

    void rotate(float angle, float x, float y, float z = 0.0f);

#ifndef QT_NO_QUATERNION

    void rotate(const QQuaternion& quaternion);

#endif

    void ortho(const QRect& rect);

    void ortho(const QRectF& rect);

    void ortho(float left, float right, float bottom, float top, float nearPlane, float farPlane);

    void frustum(float left, float right, float bottom, float top, float nearPlane, float farPlane);

    void perspective(float verticalAngle, float aspectRatio, float nearPlane, float farPlane);

#ifndef QT_NO_VECTOR3D

    void lookAt(const QVector3D& eye, const QVector3D& center, const QVector3D& up);

#endif

    void viewport(const QRectF &rect);

    void viewport(float left, float bottom, float width, float height, float nearPlane = 0.0f, float farPlane = 1.0f);

    void flipCoordinates();

    void copyDataTo(float *values) const;

    QTransform toTransform() const;

    QTransform toTransform(float distanceToPlane) const;

    inline QPoint map(const QPoint& point) const;

    inline QPointF map(const QPointF& point) const;

#ifndef QT_NO_VECTOR3D

    inline QVector3D map(const QVector3D& point) const;

    inline QVector3D mapVector(const QVector3D& vector) const;

#endif

#ifndef QT_NO_VECTOR4D

    inline QVector4D map(const QVector4D& point) const;

#endif

    QRect mapRect(const QRect& rect) const;

    QRectF mapRect(const QRectF& rect) const;

    template <int N, int M>

    QGenericMatrix<N, M, float> toGenericMatrix() const;

    inline float *data();

    inline const float *data() const { return *m; }

    inline const float *constData() const { return *m; }

    void optimize();

    operator QVariant() const;

#ifndef QT_NO_DEBUG_STREAM

    friend Q_GUI_EXPORT QDebug operator<<(QDebug dbg, const QMatrix4x4 &m);

#endif

#if QT_VERSION < QT_VERSION_CHECK(7, 0, 0)

    void projectedRotate(float angle, float x, float y, float z, float distanceToPlane);

    // ### Qt7: Remove

    void projectedRotate(float angle, float x, float y, float z);

#else

    void projectedRotate(float angle, float x, float y, float z, float distanceToPlane = 1024.0);

#endif

    // When matrices are multiplied, the flag bits are or-ed together.

    // Note that the ordering of the bit values matters. (ident < t < s < r2d < r < p)

    enum Flag {

        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

    };

    Q_DECLARE_FLAGS(Flags, Flag)

    Flags flags() const { return flagBits; }

private:

    float m[4][4];          // Column-major order to match OpenGL.

    Flags flagBits;

    QMatrix4x4 orthonormalInverse() const;

    friend class ::tst_QMatrixNxN; // for access to flagBits

};

Q_DECLARE_OPERATORS_FOR_FLAGS(QMatrix4x4::Flags)

Unexecuted instantiation: operator|(QMatrix4x4::Flag, QMatrix4x4::Flag)

Unexecuted instantiation: operator|(QMatrix4x4::Flag, QFlags<QMatrix4x4::Flag>)

Unexecuted instantiation: operator&(QMatrix4x4::Flag, QMatrix4x4::Flag)

Unexecuted instantiation: operator&(QMatrix4x4::Flag, QFlags<QMatrix4x4::Flag>)

Unexecuted instantiation: operator^(QMatrix4x4::Flag, QMatrix4x4::Flag)

Unexecuted instantiation: operator^(QMatrix4x4::Flag, QFlags<QMatrix4x4::Flag>)

Unexecuted instantiation: operator|(QMatrix4x4::Flag, int)

QT_WARNING_PUSH

QT_WARNING_DISABLE_FLOAT_COMPARE

Q_DECLARE_TYPEINFO(QMatrix4x4, Q_PRIMITIVE_TYPE);

inline QMatrix4x4::QMatrix4x4

        (float m11, float m12, float m13, float m14,

         float m21, float m22, float m23, float m24,

         float m31, float m32, float m33, float m34,

         float m41, float m42, float m43, float 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;

}

template <int N, int M>

Q_INLINE_TEMPLATE QMatrix4x4::QMatrix4x4

    (const QGenericMatrix<N, M, float>& matrix)

{

    const float *values = matrix.constData();

    for (int matrixCol = 0; matrixCol < 4; ++matrixCol) {

        for (int matrixRow = 0; matrixRow < 4; ++matrixRow) {

            if (matrixCol < N && matrixRow < M)

                m[matrixCol][matrixRow] = values[matrixCol * M + matrixRow];

            else if (matrixCol == matrixRow)

                m[matrixCol][matrixRow] = 1.0f;

            else

                m[matrixCol][matrixRow] = 0.0f;

        }

    }

    flagBits = General;

}

template <int N, int M>

QGenericMatrix<N, M, float> QMatrix4x4::toGenericMatrix() const

{

    QGenericMatrix<N, M, float> result;

    float *values = result.data();

    for (int matrixCol = 0; matrixCol < N; ++matrixCol) {

        for (int matrixRow = 0; matrixRow < M; ++matrixRow) {

            if (matrixCol < 4 && matrixRow < 4)

                values[matrixCol * M + matrixRow] = m[matrixCol][matrixRow];

            else if (matrixCol == matrixRow)

                values[matrixCol * M + matrixRow] = 1.0f;

            else

                values[matrixCol * M + matrixRow] = 0.0f;

        }

    }

    return result;

}

inline const float& QMatrix4x4::operator()(int aRow, int aColumn) const

{

    Q_ASSERT(aRow >= 0 && aRow < 4 && aColumn >= 0 && aColumn < 4);

    return m[aColumn][aRow];

}

inline float& QMatrix4x4::operator()(int aRow, int aColumn)

{

    Q_ASSERT(aRow >= 0 && aRow < 4 && aColumn >= 0 && aColumn < 4);

    flagBits = General;

    return m[aColumn][aRow];

}

#ifndef QT_NO_VECTOR4D

inline QVector4D QMatrix4x4::column(int index) const

{

    Q_ASSERT(index >= 0 && index < 4);

    return QVector4D(m[index][0], m[index][1], m[index][2], m[index][3]);

}

inline void QMatrix4x4::setColumn(int index, const QVector4D& value)

{

    Q_ASSERT(index >= 0 && index < 4);

    m[index][0] = value.x();

    m[index][1] = value.y();

    m[index][2] = value.z();

    m[index][3] = value.w();

    flagBits = General;

}

inline QVector4D QMatrix4x4::row(int index) const

{

    Q_ASSERT(index >= 0 && index < 4);

    return QVector4D(m[0][index], m[1][index], m[2][index], m[3][index]);

}

inline void QMatrix4x4::setRow(int index, const QVector4D& value)

{

    Q_ASSERT(index >= 0 && index < 4);

    m[0][index] = value.x();

    m[1][index] = value.y();

    m[2][index] = value.z();

    m[3][index] = value.w();

    flagBits = General;

}

#endif

Q_GUI_EXPORT QMatrix4x4 operator/(const QMatrix4x4& matrix, float divisor);

inline bool QMatrix4x4::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 QMatrix4x4::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 QMatrix4x4::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 QMatrix4x4::fill(float 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 QMatrix4x4& QMatrix4x4::operator+=(const QMatrix4x4& 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 QMatrix4x4& QMatrix4x4::operator-=(const QMatrix4x4& 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 QMatrix4x4& QMatrix4x4::operator*=(const QMatrix4x4& o)

{

    const QMatrix4x4 other = o; // prevent aliasing when &o == this ### Qt 6: take o by value

    flagBits |= other.flagBits;

    if (flagBits.toInt() < 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;

    }

    float 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 QMatrix4x4& QMatrix4x4::operator*=(float 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 QMatrix4x4::operator==(const QMatrix4x4& 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 QMatrix4x4::operator!=(const QMatrix4x4& 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 QMatrix4x4 operator+(const QMatrix4x4& m1, const QMatrix4x4& m2)

{

    Q_DECL_UNINITIALIZED

    QMatrix4x4 m(Qt::Uninitialized);

    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];

    return m;

}

inline QMatrix4x4 operator-(const QMatrix4x4& m1, const QMatrix4x4& m2)

{

    Q_DECL_UNINITIALIZED

    QMatrix4x4 m(Qt::Uninitialized);

    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];

    return m;

}

inline QMatrix4x4 operator*(const QMatrix4x4& m1, const QMatrix4x4& m2)

{

    Q_DECL_UNINITIALIZED

    QMatrix4x4 m(Qt::Uninitialized);

    QMatrix4x4::Flags flagBits = m1.flagBits | m2.flagBits;

    if (flagBits.toInt() < QMatrix4x4::Rotation2D) {

        // Scale | Translation

        m.m[0][0] = m1.m[0][0] * m2.m[0][0];

        m.m[0][1] = 0.0f;

        m.m[0][2] = 0.0f;

        m.m[0][3] = 0.0f;

        m.m[1][0] = 0.0f;

        m.m[1][1] = m1.m[1][1] * m2.m[1][1];

        m.m[1][2] = 0.0f;

        m.m[1][3] = 0.0f;

        m.m[2][0] = 0.0f;

        m.m[2][1] = 0.0f;

        m.m[2][2] = m1.m[2][2] * m2.m[2][2];

        m.m[2][3] = 0.0f;

        m.m[3][0] = m1.m[3][0] + m1.m[0][0] * m2.m[3][0];

        m.m[3][1] = m1.m[3][1] + m1.m[1][1] * m2.m[3][1];

        m.m[3][2] = m1.m[3][2] + m1.m[2][2] * m2.m[3][2];

        m.m[3][3] = 1.0f;

        m.flagBits = flagBits;

        return m;

    }

    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;

}

#ifndef QT_NO_VECTOR3D

#if QT_DEPRECATED_SINCE(6, 1)

QT_DEPRECATED_VERSION_X_6_1("Extend the QVector3D to a QVector4D with 1.0 as the w coordinate before multiplying")

inline QVector3D operator*(const QVector3D& vector, const QMatrix4x4& matrix)

{

    float 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 QVector3D(x, y, z);

    else

        return QVector3D(x / w, y / w, z / w);

}

QT_DEPRECATED_VERSION_X_6_1("Use matrix.map(vector) instead")

inline QVector3D operator*(const QMatrix4x4& matrix, const QVector3D& vector)

{

    return matrix.map(vector);

}

#endif

#endif

#ifndef QT_NO_VECTOR4D

inline QVector4D operator*(const QVector4D& vector, const QMatrix4x4& matrix)

{

    float x, y, z, w;

    x = vector.x() * matrix.m[0][0] +

        vector.y() * matrix.m[0][1] +

        vector.z() * matrix.m[0][2] +

        vector.w() * matrix.m[0][3];

    y = vector.x() * matrix.m[1][0] +

        vector.y() * matrix.m[1][1] +

        vector.z() * matrix.m[1][2] +

        vector.w() * matrix.m[1][3];

    z = vector.x() * matrix.m[2][0] +

        vector.y() * matrix.m[2][1] +

        vector.z() * matrix.m[2][2] +

        vector.w() * matrix.m[2][3];

    w = vector.x() * matrix.m[3][0] +

        vector.y() * matrix.m[3][1] +

        vector.z() * matrix.m[3][2] +

        vector.w() * matrix.m[3][3];

    return QVector4D(x, y, z, w);

}

inline QVector4D operator*(const QMatrix4x4& matrix, const QVector4D& vector)

{

    float x, y, z, w;

    x = vector.x() * matrix.m[0][0] +

        vector.y() * matrix.m[1][0] +

        vector.z() * matrix.m[2][0] +

        vector.w() * matrix.m[3][0];

    y = vector.x() * matrix.m[0][1] +

        vector.y() * matrix.m[1][1] +

        vector.z() * matrix.m[2][1] +

        vector.w() * matrix.m[3][1];

    z = vector.x() * matrix.m[0][2] +

        vector.y() * matrix.m[1][2] +

        vector.z() * matrix.m[2][2] +

        vector.w() * matrix.m[3][2];

    w = vector.x() * matrix.m[0][3] +

        vector.y() * matrix.m[1][3] +

        vector.z() * matrix.m[2][3] +

        vector.w() * matrix.m[3][3];

    return QVector4D(x, y, z, w);

}

#endif

inline QPoint operator*(const QPoint& point, const QMatrix4x4& matrix)

{

    float xin, yin;

    float 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 QMatrix4x4& matrix)

{

    float xin, yin;

    float x, y, w;

    xin = float(point.x());

    yin = float(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(qreal(x), qreal(y));

    } else {

        return QPointF(qreal(x / w), qreal(y / w));

    }

}

#if QT_DEPRECATED_SINCE(6, 1)

QT_DEPRECATED_VERSION_X_6_1("Use matrix.map(point) instead")

inline QPoint operator*(const QMatrix4x4& matrix, const QPoint& point)

{

    return matrix.map(point);

}

QT_DEPRECATED_VERSION_X_6_1("Use matrix.map(point) instead")

inline QPointF operator*(const QMatrix4x4& matrix, const QPointF& point)

{

    return matrix.map(point);

}

#endif

inline QMatrix4x4 operator-(const QMatrix4x4& matrix)

{

    Q_DECL_UNINITIALIZED

    QMatrix4x4 m(Qt::Uninitialized);

    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];

    return m;

}

inline QMatrix4x4 operator*(float factor, const QMatrix4x4& matrix)

{

    Q_DECL_UNINITIALIZED

    QMatrix4x4 m(Qt::Uninitialized);

    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;

    return m;

}

inline QMatrix4x4 operator*(const QMatrix4x4& matrix, float factor)

{

    Q_DECL_UNINITIALIZED

    QMatrix4x4 m(Qt::Uninitialized);

    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;

    return m;

}

inline QPoint QMatrix4x4::map(const QPoint& point) const

{

    float xin, yin;

    float x, y, w;

    xin = point.x();

    yin = point.y();

    if (flagBits == QMatrix4x4::Identity) {

        return point;

    } else if (flagBits.toInt() < QMatrix4x4::Rotation2D) {

        // Translation | Scale

        return QPoint(qRound(xin * m[0][0] + m[3][0]),

                      qRound(yin * m[1][1] + m[3][1]));

    } else if (flagBits.toInt() < QMatrix4x4::Perspective) {

        return QPoint(qRound(xin * m[0][0] + yin * m[1][0] + m[3][0]),