/*

-----------------------------------------------------------------------------

This source file is part of OGRE

    (Object-oriented Graphics Rendering Engine)

For the latest info, see http://www.ogre3d.org/

Copyright (c) 2000-2014 Torus Knot Software Ltd

Permission is hereby granted, free of charge, to any person obtaining a copy

of this software and associated documentation files (the "Software"), to deal

in the Software without restriction, including without limitation the rights

to use, copy, modify, merge, publish, distribute, sublicense, and/or sell

copies of the Software, and to permit persons to whom the Software is

furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in

all copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR

IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,

FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE

AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER

LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,

OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN

THE SOFTWARE.

-----------------------------------------------------------------------------

*/

#ifndef __Matrix4__

#define __Matrix4__

// Precompiler options

#include "OgrePrerequisites.h"

#include "OgreMatrix3.h"

#include "OgreVector.h"

namespace Ogre

{

    /** \addtogroup Core

    *  @{

    */

    /** \addtogroup Math

    *  @{

    */

    class Matrix4;

    class Affine3;

    Matrix4 operator*(const Matrix4 &m, const Matrix4 &m2);

    /** Class encapsulating a standard 4x4 homogeneous matrix.

        OGRE uses column vectors when applying matrix multiplications,

        This means a vector is represented as a single column, 4-row

        matrix. This has the effect that the transformations implemented

        by the matrices happens right-to-left e.g. if vector V is to be

        transformed by M1 then M2 then M3, the calculation would be

        M3 * M2 * M1 * V. The order that matrices are concatenated is

        vital since matrix multiplication is not commutative, i.e. you

        can get a different result if you concatenate in the wrong order.

        @par

            The use of column vectors and right-to-left ordering is the

            standard in most mathematical texts, and is the same as used in

            OpenGL. It is, however, the opposite of Direct3D, which has

            inexplicably chosen to differ from the accepted standard and uses

            row vectors and left-to-right matrix multiplication.

        @par

            OGRE deals with the differences between D3D and OpenGL etc.

            internally when operating through different render systems. OGRE

            users only need to conform to standard maths conventions, i.e.

            right-to-left matrix multiplication, (OGRE transposes matrices it

            passes to D3D to compensate).

        @par

            The generic form M * V which shows the layout of the matrix

            entries is shown below:

            <pre>

                [ m[0][0]  m[0][1]  m[0][2]  m[0][3] ]   {x}

                | m[1][0]  m[1][1]  m[1][2]  m[1][3] | * {y}

                | m[2][0]  m[2][1]  m[2][2]  m[2][3] |   {z}

                [ m[3][0]  m[3][1]  m[3][2]  m[3][3] ]   {1}

            </pre>

    */

    template<int rows, typename T> class TransformBase

    {

    protected:

        /// The matrix entries, indexed by [row][col].

        T m[rows][4];

        // do not reduce storage for affine for compatibility with SSE, shader mat4 types

    public:

        /// Do <b>NOT</b> initialize for efficiency.

        TransformBase() {}

        template<typename U>

        explicit TransformBase(const U* ptr) {

            for (int i = 0; i < rows; i++)

                for (int j = 0; j < 4; j++)

                    m[i][j] = T(ptr[i*4 + j]);

        }

        template<typename U>

        explicit TransformBase(const TransformBase<rows, U>& o) : TransformBase(o[0]) {}

        T* operator[](size_t iRow)

        {

            assert(iRow < rows);

            return m[iRow];

        }

        const T* operator[](size_t iRow) const

        {

            assert(iRow < rows);

            return m[iRow];

        }

        /// Sets the translation transformation part of the matrix.

        void setTrans( const Vector<3, T>& v )

        {

            assert(rows > 2);

            m[0][3] = v[0];

            m[1][3] = v[1];

            m[2][3] = v[2];

        }

        /// Extracts the translation transformation part of the matrix.

        Vector<3, T> getTrans() const

        {

            assert(rows > 2);

            return Vector<3, T>(m[0][3], m[1][3], m[2][3]);

        }

        /// Sets the scale part of the matrix.

        void setScale( const Vector<3, T>& v )

        {

            assert(rows > 2);

            m[0][0] = v[0];

            m[1][1] = v[1];

            m[2][2] = v[2];

        }

        /** Function for writing to a stream.

         */

        inline friend std::ostream& operator<<(std::ostream& o, const TransformBase& mat)

        {

            o << "Matrix" << rows << "x4(";

            for (size_t i = 0; i < rows; ++i)

            {

                for (size_t j = 0; j < 4; ++j)

                {

                    o << mat[i][j];

                    if(j != 3)

                        o << ", ";

                }

                if(i != (rows - 1))

                    o << "; ";

            }

            o << ")";

            return o;

        }

    };

    struct _OgreExport TransformBaseReal : public TransformBase<4, Real>

    {

        /// Do <b>NOT</b> initialize for efficiency.

        TransformBaseReal() {}

        template<typename U>

        explicit TransformBaseReal(const U* ptr) : TransformBase(ptr) {}

        /** Builds a translation matrix

        */

        void makeTrans( const Vector3& v )

        {

            makeTrans(v.x, v.y, v.z);

        }

        void makeTrans( Real tx, Real ty, Real tz )

        {

            m[0][0] = 1.0; m[0][1] = 0.0; m[0][2] = 0.0; m[0][3] = tx;

            m[1][0] = 0.0; m[1][1] = 1.0; m[1][2] = 0.0; m[1][3] = ty;

            m[2][0] = 0.0; m[2][1] = 0.0; m[2][2] = 1.0; m[2][3] = tz;

            m[3][0] = 0.0; m[3][1] = 0.0; m[3][2] = 0.0; m[3][3] = 1.0;

        }

        /** Assignment from 3x3 matrix.

        */

        void set3x3Matrix(const Matrix3& mat3)

        {

            m[0][0] = mat3[0][0]; m[0][1] = mat3[0][1]; m[0][2] = mat3[0][2];

            m[1][0] = mat3[1][0]; m[1][1] = mat3[1][1]; m[1][2] = mat3[1][2];

            m[2][0] = mat3[2][0]; m[2][1] = mat3[2][1]; m[2][2] = mat3[2][2];

        }

        /** Extracts the rotation / scaling part of the Matrix as a 3x3 matrix.

        */

        Matrix3 linear() const

        {

            return Matrix3(m[0][0], m[0][1], m[0][2],

                           m[1][0], m[1][1], m[1][2],

                           m[2][0], m[2][1], m[2][2]);

        }

        OGRE_DEPRECATED void extract3x3Matrix(Matrix3& m3x3) const { m3x3 = linear(); }

        OGRE_DEPRECATED Quaternion extractQuaternion() const { return Quaternion(linear()); }

        Real determinant() const;

        Matrix4 transpose() const;

        /** Building a Affine3 from orientation / scale / position.

            Transform is performed in the order scale, rotate, translation, i.e. translation is independent

            of orientation axes, scale does not affect size of translation, rotation and scaling are always

            centered on the origin.

        */

        void makeTransform(const Vector3& position, const Vector3& scale, const Quaternion& orientation);

        /** Building an inverse Affine3 from orientation / scale / position.

            As makeTransform except it build the inverse given the same data as makeTransform, so

            performing -translation, -rotate, 1/scale in that order.

        */

        void makeInverseTransform(const Vector3& position, const Vector3& scale, const Quaternion& orientation);

    };

    /// Transform specialization for projective - encapsulating a 4x4 Matrix

    class _OgreExport Matrix4 : public TransformBaseReal

    {

    public:

        /// Do <b>NOT</b> initialize the matrix for efficiency.

        Matrix4() {}

        Matrix4(

            Real m00, Real m01, Real m02, Real m03,

            Real m10, Real m11, Real m12, Real m13,

            Real m20, Real m21, Real m22, Real m23,

            Real m30, Real m31, Real m32, Real m33 )

        {

            m[0][0] = m00; m[0][1] = m01; m[0][2] = m02; m[0][3] = m03;

            m[1][0] = m10; m[1][1] = m11; m[1][2] = m12; m[1][3] = m13;

            m[2][0] = m20; m[2][1] = m21; m[2][2] = m22; m[2][3] = m23;

            m[3][0] = m30; m[3][1] = m31; m[3][2] = m32; m[3][3] = m33;

        }

        template<typename U>

        explicit Matrix4(const U* ptr) : TransformBaseReal(ptr) {}

        explicit Matrix4 (const Real* arr)

        {

            memcpy(m,arr,16*sizeof(Real));

        }

        /** Creates a standard 4x4 transformation matrix with a zero translation part from a rotation/scaling 3x3 matrix.

         */

        explicit Matrix4(const Matrix3& m3x3)

        {

          operator=(IDENTITY);

          operator=(m3x3);

        }

        /** Creates a standard 4x4 transformation matrix with a zero translation part from a rotation/scaling Quaternion.

         */

        explicit Matrix4(const Quaternion& rot)

        {

          Matrix3 m3x3;

          rot.ToRotationMatrix(m3x3);

          *this = IDENTITY;

          *this = m3x3;

        }

        Matrix4& operator=(const Matrix3& mat3) {

            set3x3Matrix(mat3);

            return *this;

        }

        OGRE_DEPRECATED Matrix4 concatenate(const Matrix4& m2) const { return *this * m2; }

        /** Tests 2 matrices for equality.

        */

        inline bool operator == ( const Matrix4& m2 ) const

        {

            if( 

                m[0][0] != m2.m[0][0] || m[0][1] != m2.m[0][1] || m[0][2] != m2.m[0][2] || m[0][3] != m2.m[0][3] ||

                m[1][0] != m2.m[1][0] || m[1][1] != m2.m[1][1] || m[1][2] != m2.m[1][2] || m[1][3] != m2.m[1][3] ||

                m[2][0] != m2.m[2][0] || m[2][1] != m2.m[2][1] || m[2][2] != m2.m[2][2] || m[2][3] != m2.m[2][3] ||

                m[3][0] != m2.m[3][0] || m[3][1] != m2.m[3][1] || m[3][2] != m2.m[3][2] || m[3][3] != m2.m[3][3] )

                return false;

            return true;

        }

        /** Tests 2 matrices for inequality.

        */

        inline bool operator != ( const Matrix4& m2 ) const

        {

            if( 

                m[0][0] != m2.m[0][0] || m[0][1] != m2.m[0][1] || m[0][2] != m2.m[0][2] || m[0][3] != m2.m[0][3] ||

                m[1][0] != m2.m[1][0] || m[1][1] != m2.m[1][1] || m[1][2] != m2.m[1][2] || m[1][3] != m2.m[1][3] ||

                m[2][0] != m2.m[2][0] || m[2][1] != m2.m[2][1] || m[2][2] != m2.m[2][2] || m[2][3] != m2.m[2][3] ||

                m[3][0] != m2.m[3][0] || m[3][1] != m2.m[3][1] || m[3][2] != m2.m[3][2] || m[3][3] != m2.m[3][3] )

                return true;

            return false;

        }

        static const Matrix4 ZERO;

        static const Matrix4 IDENTITY;

        /** Useful little matrix which takes 2D clipspace {-1, 1} to {0,1}

            and inverts the Y. */

        static const Matrix4 CLIPSPACE2DTOIMAGESPACE;

        inline Matrix4 operator*(Real scalar) const

        {

            return Matrix4(

                scalar*m[0][0], scalar*m[0][1], scalar*m[0][2], scalar*m[0][3],

                scalar*m[1][0], scalar*m[1][1], scalar*m[1][2], scalar*m[1][3],

                scalar*m[2][0], scalar*m[2][1], scalar*m[2][2], scalar*m[2][3],

                scalar*m[3][0], scalar*m[3][1], scalar*m[3][2], scalar*m[3][3]);

        }

        Matrix4 adjoint() const;

        Matrix4 inverse() const;

    };

    /// Transform specialization for 3D Affine - encapsulating a 3x4 Matrix

    class _OgreExport Affine3 : public TransformBaseReal

    {

    public:

        /// Do <b>NOT</b> initialize the matrix for efficiency.

        Affine3() {}

        /// @copydoc TransformBaseReal::makeTransform

        Affine3(const Vector3& position, const Quaternion& orientation, const Vector3& scale = Vector3::UNIT_SCALE)

        {

            makeTransform(position, scale, orientation);

        }

        template<typename U>

        explicit Affine3(const U* ptr)

        {

            for (int i = 0; i < 3; i++)

                for (int j = 0; j < 4; j++)

                    m[i][j] = Real(ptr[i*4 + j]);

            m[3][0] = 0, m[3][1] = 0, m[3][2] = 0, m[3][3] = 1;

        }

        explicit Affine3(const Real* arr)

        {

            memcpy(m, arr, 12 * sizeof(Real));

            m[3][0] = 0, m[3][1] = 0, m[3][2] = 0, m[3][3] = 1;

        }

        Affine3(

            Real m00, Real m01, Real m02, Real m03,

            Real m10, Real m11, Real m12, Real m13,

            Real m20, Real m21, Real m22, Real m23)

        {

            m[0][0] = m00; m[0][1] = m01; m[0][2] = m02; m[0][3] = m03;

            m[1][0] = m10; m[1][1] = m11; m[1][2] = m12; m[1][3] = m13;

            m[2][0] = m20; m[2][1] = m21; m[2][2] = m22; m[2][3] = m23;

            m[3][0] = 0;   m[3][1] = 0;   m[3][2] = 0;   m[3][3] = 1;

        }

        /// extract the Affine part of a Matrix4

        explicit Affine3(const Matrix4& mat)

        {

            m[0][0] = mat[0][0]; m[0][1] = mat[0][1]; m[0][2] = mat[0][2]; m[0][3] = mat[0][3];

            m[1][0] = mat[1][0]; m[1][1] = mat[1][1]; m[1][2] = mat[1][2]; m[1][3] = mat[1][3];

            m[2][0] = mat[2][0]; m[2][1] = mat[2][1]; m[2][2] = mat[2][2]; m[2][3] = mat[2][3];

            m[3][0] = 0;         m[3][1] = 0;         m[3][2] = 0;         m[3][3] = 1;

        }

        Affine3& operator=(const Matrix3& mat3) {

            set3x3Matrix(mat3);

            return *this;

        }

        /** Tests 2 matrices for equality.

        */

        bool operator==(const Affine3& m2) const

        {

            if(

                m[0][0] != m2.m[0][0] || m[0][1] != m2.m[0][1] || m[0][2] != m2.m[0][2] || m[0][3] != m2.m[0][3] ||

                m[1][0] != m2.m[1][0] || m[1][1] != m2.m[1][1] || m[1][2] != m2.m[1][2] || m[1][3] != m2.m[1][3] ||

                m[2][0] != m2.m[2][0] || m[2][1] != m2.m[2][1] || m[2][2] != m2.m[2][2] || m[2][3] != m2.m[2][3] )

                return false;

            return true;

        }

        bool operator!=(const Affine3& m2) const { return !(*this == m2); }

        Affine3 inverse() const;

        /** Decompose to orientation / scale / position.

        */

        void decomposition(Vector3& position, Vector3& scale, Quaternion& orientation) const;

        /// every Affine3 transform is also a _const_ Matrix4

        operator const Matrix4&() const { return reinterpret_cast<const Matrix4&>(*this); }

        using TransformBaseReal::getTrans;

        /** Gets a translation matrix.

        */

        static Affine3 getTrans( const Vector3& v )

        {

            return getTrans(v.x, v.y, v.z);

        }

        /** Gets a translation matrix - variation for not using a vector.

        */

        static Affine3 getTrans( Real t_x, Real t_y, Real t_z )

        {

            return Affine3(1, 0, 0, t_x,

                           0, 1, 0, t_y,

                           0, 0, 1, t_z);

        }

        /** Gets a scale matrix.

        */

        static Affine3 getScale( const Vector3& v )

        {

            return getScale(v.x, v.y, v.z);

        }

        /** Gets a scale matrix - variation for not using a vector.

        */

        static Affine3 getScale( Real s_x, Real s_y, Real s_z )

        {

            return Affine3(s_x, 0, 0, 0,

                           0, s_y, 0, 0,

                           0, 0, s_z, 0);

        }

        static const Affine3 ZERO;

        static const Affine3 IDENTITY;

    };

    inline Matrix4 TransformBaseReal::transpose() const

    {

        return Matrix4(m[0][0], m[1][0], m[2][0], m[3][0],

                       m[0][1], m[1][1], m[2][1], m[3][1],

                       m[0][2], m[1][2], m[2][2], m[3][2],

                       m[0][3], m[1][3], m[2][3], m[3][3]);

    }

    /** Matrix addition.

    */

    inline Matrix4 operator+(const Matrix4& m, const Matrix4& m2)

    {

        Matrix4 r;

        r[0][0] = m[0][0] + m2[0][0];

        r[0][1] = m[0][1] + m2[0][1];

        r[0][2] = m[0][2] + m2[0][2];

        r[0][3] = m[0][3] + m2[0][3];

        r[1][0] = m[1][0] + m2[1][0];

        r[1][1] = m[1][1] + m2[1][1];

        r[1][2] = m[1][2] + m2[1][2];

        r[1][3] = m[1][3] + m2[1][3];

        r[2][0] = m[2][0] + m2[2][0];

        r[2][1] = m[2][1] + m2[2][1];

        r[2][2] = m[2][2] + m2[2][2];

        r[2][3] = m[2][3] + m2[2][3];

        r[3][0] = m[3][0] + m2[3][0];

        r[3][1] = m[3][1] + m2[3][1];

        r[3][2] = m[3][2] + m2[3][2];

        r[3][3] = m[3][3] + m2[3][3];

        return r;

    }

    /** Matrix subtraction.

    */

    inline Matrix4 operator-(const Matrix4& m, const Matrix4& m2)

    {

        Matrix4 r;

        r[0][0] = m[0][0] - m2[0][0];

        r[0][1] = m[0][1] - m2[0][1];

        r[0][2] = m[0][2] - m2[0][2];

        r[0][3] = m[0][3] - m2[0][3];

        r[1][0] = m[1][0] - m2[1][0];

        r[1][1] = m[1][1] - m2[1][1];

        r[1][2] = m[1][2] - m2[1][2];

        r[1][3] = m[1][3] - m2[1][3];

        r[2][0] = m[2][0] - m2[2][0];

        r[2][1] = m[2][1] - m2[2][1];

        r[2][2] = m[2][2] - m2[2][2];

        r[2][3] = m[2][3] - m2[2][3];

        r[3][0] = m[3][0] - m2[3][0];

        r[3][1] = m[3][1] - m2[3][1];

        r[3][2] = m[3][2] - m2[3][2];

        r[3][3] = m[3][3] - m2[3][3];

        return r;

    }

    inline Matrix4 operator*(const Matrix4 &m, const Matrix4 &m2)

    {

        Matrix4 r;

        r[0][0] = m[0][0] * m2[0][0] + m[0][1] * m2[1][0] + m[0][2] * m2[2][0] + m[0][3] * m2[3][0];

        r[0][1] = m[0][0] * m2[0][1] + m[0][1] * m2[1][1] + m[0][2] * m2[2][1] + m[0][3] * m2[3][1];

        r[0][2] = m[0][0] * m2[0][2] + m[0][1] * m2[1][2] + m[0][2] * m2[2][2] + m[0][3] * m2[3][2];

        r[0][3] = m[0][0] * m2[0][3] + m[0][1] * m2[1][3] + m[0][2] * m2[2][3] + m[0][3] * m2[3][3];

        r[1][0] = m[1][0] * m2[0][0] + m[1][1] * m2[1][0] + m[1][2] * m2[2][0] + m[1][3] * m2[3][0];

        r[1][1] = m[1][0] * m2[0][1] + m[1][1] * m2[1][1] + m[1][2] * m2[2][1] + m[1][3] * m2[3][1];

        r[1][2] = m[1][0] * m2[0][2] + m[1][1] * m2[1][2] + m[1][2] * m2[2][2] + m[1][3] * m2[3][2];

        r[1][3] = m[1][0] * m2[0][3] + m[1][1] * m2[1][3] + m[1][2] * m2[2][3] + m[1][3] * m2[3][3];

        r[2][0] = m[2][0] * m2[0][0] + m[2][1] * m2[1][0] + m[2][2] * m2[2][0] + m[2][3] * m2[3][0];

        r[2][1] = m[2][0] * m2[0][1] + m[2][1] * m2[1][1] + m[2][2] * m2[2][1] + m[2][3] * m2[3][1];

        r[2][2] = m[2][0] * m2[0][2] + m[2][1] * m2[1][2] + m[2][2] * m2[2][2] + m[2][3] * m2[3][2];

        r[2][3] = m[2][0] * m2[0][3] + m[2][1] * m2[1][3] + m[2][2] * m2[2][3] + m[2][3] * m2[3][3];

        r[3][0] = m[3][0] * m2[0][0] + m[3][1] * m2[1][0] + m[3][2] * m2[2][0] + m[3][3] * m2[3][0];

        r[3][1] = m[3][0] * m2[0][1] + m[3][1] * m2[1][1] + m[3][2] * m2[2][1] + m[3][3] * m2[3][1];

        r[3][2] = m[3][0] * m2[0][2] + m[3][1] * m2[1][2] + m[3][2] * m2[2][2] + m[3][3] * m2[3][2];

        r[3][3] = m[3][0] * m2[0][3] + m[3][1] * m2[1][3] + m[3][2] * m2[2][3] + m[3][3] * m2[3][3];

        return r;

    }

    inline Affine3 operator*(const Affine3 &m, const Affine3 &m2)

    {

        return Affine3(

            m[0][0] * m2[0][0] + m[0][1] * m2[1][0] + m[0][2] * m2[2][0],

            m[0][0] * m2[0][1] + m[0][1] * m2[1][1] + m[0][2] * m2[2][1],

            m[0][0] * m2[0][2] + m[0][1] * m2[1][2] + m[0][2] * m2[2][2],

            m[0][0] * m2[0][3] + m[0][1] * m2[1][3] + m[0][2] * m2[2][3] + m[0][3],

            m[1][0] * m2[0][0] + m[1][1] * m2[1][0] + m[1][2] * m2[2][0],

            m[1][0] * m2[0][1] + m[1][1] * m2[1][1] + m[1][2] * m2[2][1],

            m[1][0] * m2[0][2] + m[1][1] * m2[1][2] + m[1][2] * m2[2][2],

            m[1][0] * m2[0][3] + m[1][1] * m2[1][3] + m[1][2] * m2[2][3] + m[1][3],

            m[2][0] * m2[0][0] + m[2][1] * m2[1][0] + m[2][2] * m2[2][0],

            m[2][0] * m2[0][1] + m[2][1] * m2[1][1] + m[2][2] * m2[2][1],

            m[2][0] * m2[0][2] + m[2][1] * m2[1][2] + m[2][2] * m2[2][2],

            m[2][0] * m2[0][3] + m[2][1] * m2[1][3] + m[2][2] * m2[2][3] + m[2][3]);

    }

    /** Vector transformation using '*'.

        Transforms the given 3-D vector by the matrix, projecting the

        result back into <i>w</i> = 1.

        @note

            This means that the initial <i>w</i> is considered to be 1.0,

            and then all the tree elements of the resulting 3-D vector are

            divided by the resulting <i>w</i>.

    */

    inline Vector3 operator*(const Matrix4& m, const Vector3& v)

    {

        Vector3 r;

        Real fInvW = 1.0f / ( m[3][0] * v.x + m[3][1] * v.y + m[3][2] * v.z + m[3][3] );

        r.x = ( m[0][0] * v.x + m[0][1] * v.y + m[0][2] * v.z + m[0][3] ) * fInvW;

        r.y = ( m[1][0] * v.x + m[1][1] * v.y + m[1][2] * v.z + m[1][3] ) * fInvW;

        r.z = ( m[2][0] * v.x + m[2][1] * v.y + m[2][2] * v.z + m[2][3] ) * fInvW;

        return r;

    }

    /// @overload

    inline Vector3 operator*(const Affine3& m,const Vector3& v)

    {

        return Vector3(

                m[0][0] * v.x + m[0][1] * v.y + m[0][2] * v.z + m[0][3],

                m[1][0] * v.x + m[1][1] * v.y + m[1][2] * v.z + m[1][3],

                m[2][0] * v.x + m[2][1] * v.y + m[2][2] * v.z + m[2][3]);

    }

    inline Vector4 operator*(const Matrix4& m, const Vector4& v)

    {

        return Vector4(

            m[0][0] * v.x + m[0][1] * v.y + m[0][2] * v.z + m[0][3] * v.w,

            m[1][0] * v.x + m[1][1] * v.y + m[1][2] * v.z + m[1][3] * v.w,

            m[2][0] * v.x + m[2][1] * v.y + m[2][2] * v.z + m[2][3] * v.w,

            m[3][0] * v.x + m[3][1] * v.y + m[3][2] * v.z + m[3][3] * v.w);

    }

    inline Vector4 operator*(const Affine3& m, const Vector4& v)

    {

        return Vector4(

            m[0][0] * v.x + m[0][1] * v.y + m[0][2] * v.z + m[0][3] * v.w,

            m[1][0] * v.x + m[1][1] * v.y + m[1][2] * v.z + m[1][3] * v.w,

            m[2][0] * v.x + m[2][1] * v.y + m[2][2] * v.z + m[2][3] * v.w,

            v.w);

    }

    inline Vector4 operator * (const Vector4& v, const Matrix4& mat)

    {

        return Vector4(

            v.x*mat[0][0] + v.y*mat[1][0] + v.z*mat[2][0] + v.w*mat[3][0],

            v.x*mat[0][1] + v.y*mat[1][1] + v.z*mat[2][1] + v.w*mat[3][1],

            v.x*mat[0][2] + v.y*mat[1][2] + v.z*mat[2][2] + v.w*mat[3][2],

            v.x*mat[0][3] + v.y*mat[1][3] + v.z*mat[2][3] + v.w*mat[3][3]

            );

    }

    /** @} */

    /** @} */

}

#endif