matrix4.h

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// Copyright (C) 2002-2011 Nikolaus Gebhardt
// This file is part of the "Irrlicht Engine".
// For conditions of distribution and use, see copyright notice in irrlicht.h

#ifndef __IRR_MATRIX_H_INCLUDED__
#define __IRR_MATRIX_H_INCLUDED__

#include "irrMath.h"
#include "vector3d.h"
#include "vector2d.h"
#include "plane3d.h"
#include "aabbox3d.h"
#include "rect.h"
#include "irrString.h"

// enable this to keep track of changes to the matrix
// and make simpler identity check for seldomly changing matrices
// otherwise identity check will always compare the elements
//#define USE_MATRIX_TEST

// this is only for debugging purposes
//#define USE_MATRIX_TEST_DEBUG

#if defined( USE_MATRIX_TEST_DEBUG )

struct MatrixTest
{
        MatrixTest () : ID(0), Calls(0) {}
        char buf[256];
        int Calls;
        int ID;
};
static MatrixTest MTest;

#endif

namespace irr
{
namespace core
{


        template <class T>
        class CMatrix4
        {
                public:

                        enum eConstructor
                        {
                                EM4CONST_NOTHING = 0,
                                EM4CONST_COPY,
                                EM4CONST_IDENTITY,
                                EM4CONST_TRANSPOSED,
                                EM4CONST_INVERSE,
                                EM4CONST_INVERSE_TRANSPOSED
                        };


                        CMatrix4( eConstructor constructor = EM4CONST_IDENTITY );

                        CMatrix4(const CMatrix4<T>& other, eConstructor constructor = EM4CONST_COPY);

                        T& operator()(const s32 row, const s32 col)
                        { 
#if defined ( USE_MATRIX_TEST )
                                definitelyIdentityMatrix=false;
#endif
                                return M[ row * 4 + col ];
                        }

                        const T& operator()(const s32 row, const s32 col) const { return M[row * 4 + col]; }

                        T& operator[](u32 index)
                        { 
#if defined ( USE_MATRIX_TEST )
                                definitelyIdentityMatrix=false; 
#endif
                                return M[index];
                        }

                        const T& operator[](u32 index) const { return M[index]; }

                        inline CMatrix4<T>& operator=(const CMatrix4<T> &other);

                        inline CMatrix4<T>& operator=(const T& scalar);

                        const T* pointer() const { return M; }
                        T* pointer() 
                        { 
#if defined ( USE_MATRIX_TEST )
                                definitelyIdentityMatrix=false;
#endif
                                return M;
                        }

                        bool operator==(const CMatrix4<T> &other) const;

                        bool operator!=(const CMatrix4<T> &other) const;

                        CMatrix4<T> operator+(const CMatrix4<T>& other) const;

                        CMatrix4<T>& operator+=(const CMatrix4<T>& other);

                        CMatrix4<T> operator-(const CMatrix4<T>& other) const;

                        CMatrix4<T>& operator-=(const CMatrix4<T>& other);


                        inline CMatrix4<T>& setbyproduct(const CMatrix4<T>& other_a,const CMatrix4<T>& other_b );


                        CMatrix4<T>& setbyproduct_nocheck(const CMatrix4<T>& other_a,const CMatrix4<T>& other_b );


                        CMatrix4<T> operator*(const CMatrix4<T>& other) const;


                        CMatrix4<T>& operator*=(const CMatrix4<T>& other);

                        CMatrix4<T> operator*(const T& scalar) const;

                        CMatrix4<T>& operator*=(const T& scalar);

                        inline CMatrix4<T>& makeIdentity();

                        inline bool isIdentity() const;

                        inline bool isOrthogonal() const;

                        bool isIdentity_integer_base () const;

                        CMatrix4<T>& setTranslation( const vector3d<T>& translation );

                        vector3d<T> getTranslation() const;

                        CMatrix4<T>& setInverseTranslation( const vector3d<T>& translation );

                        inline CMatrix4<T>& setRotationRadians( const vector3d<T>& rotation );

                        CMatrix4<T>& setRotationDegrees( const vector3d<T>& rotation );


                        core::vector3d<T> getRotationDegrees() const;


                        inline CMatrix4<T>& setInverseRotationRadians( const vector3d<T>& rotation );


                        CMatrix4<T>& setInverseRotationDegrees( const vector3d<T>& rotation );

                        CMatrix4<T>& setScale( const vector3d<T>& scale );

                        CMatrix4<T>& setScale( const T scale ) { return setScale(core::vector3d<T>(scale,scale,scale)); }

                        core::vector3d<T> getScale() const;

                        void inverseTranslateVect( vector3df& vect ) const;

                        void inverseRotateVect( vector3df& vect ) const;

                        void rotateVect( vector3df& vect ) const;

                        void rotateVect(core::vector3df& out, const core::vector3df& in) const;

                        void rotateVect(T *out,const core::vector3df &in) const;

                        void transformVect( vector3df& vect) const;

                        void transformVect( vector3df& out, const vector3df& in ) const;

                        void transformVect(T *out,const core::vector3df &in) const;
                        void transformVec3(T *out, const T * in) const;

                        void translateVect( vector3df& vect ) const;

                        void transformPlane( core::plane3d<f32> &plane) const;

                        void transformPlane( const core::plane3d<f32> &in, core::plane3d<f32> &out) const;


                        void transformBox(core::aabbox3d<f32>& box) const;


                        void transformBoxEx(core::aabbox3d<f32>& box) const;

                        void multiplyWith1x4Matrix(T* matrix) const;


                        bool makeInverse();



                        bool getInversePrimitive ( CMatrix4<T>& out ) const;


                        bool getInverse(CMatrix4<T>& out) const;

                        CMatrix4<T>& buildProjectionMatrixPerspectiveFovRH(f32 fieldOfViewRadians, f32 aspectRatio, f32 zNear, f32 zFar);

                        CMatrix4<T>& buildProjectionMatrixPerspectiveFovLH(f32 fieldOfViewRadians, f32 aspectRatio, f32 zNear, f32 zFar);

                        CMatrix4<T>& buildProjectionMatrixPerspectiveFovInfinityLH(f32 fieldOfViewRadians, f32 aspectRatio, f32 zNear, f32 epsilon=0);

                        CMatrix4<T>& buildProjectionMatrixPerspectiveRH(f32 widthOfViewVolume, f32 heightOfViewVolume, f32 zNear, f32 zFar);

                        CMatrix4<T>& buildProjectionMatrixPerspectiveLH(f32 widthOfViewVolume, f32 heightOfViewVolume, f32 zNear, f32 zFar);

                        CMatrix4<T>& buildProjectionMatrixOrthoLH(f32 widthOfViewVolume, f32 heightOfViewVolume, f32 zNear, f32 zFar);

                        CMatrix4<T>& buildProjectionMatrixOrthoRH(f32 widthOfViewVolume, f32 heightOfViewVolume, f32 zNear, f32 zFar);

                        CMatrix4<T>& buildCameraLookAtMatrixLH(
                                        const vector3df& position,
                                        const vector3df& target,
                                        const vector3df& upVector);

                        CMatrix4<T>& buildCameraLookAtMatrixRH(
                                        const vector3df& position,
                                        const vector3df& target,
                                        const vector3df& upVector);


                        CMatrix4<T>& buildShadowMatrix(const core::vector3df& light, core::plane3df plane, f32 point=1.0f);


                        CMatrix4<T>& buildNDCToDCMatrix( const core::rect<s32>& area, f32 zScale);


                        CMatrix4<T> interpolate(const core::CMatrix4<T>& b, f32 time) const;

                        CMatrix4<T> getTransposed() const;

                        inline void getTransposed( CMatrix4<T>& dest ) const;


                        CMatrix4<T>& buildRotateFromTo(const core::vector3df& from, const core::vector3df& to);


                        void setRotationCenter(const core::vector3df& center, const core::vector3df& translate);


                        void buildAxisAlignedBillboard(const core::vector3df& camPos,
                                                const core::vector3df& center,
                                                const core::vector3df& translation,
                                                const core::vector3df& axis,
                                                const core::vector3df& from);

                        /*
                                construct 2D Texture transformations
                                rotate about center, scale, and transform.
                        */
                        CMatrix4<T>& buildTextureTransform( f32 rotateRad,
                                        const core::vector2df &rotatecenter,
                                        const core::vector2df &translate,
                                        const core::vector2df &scale);


                        CMatrix4<T>& setTextureRotationCenter( f32 radAngle );


                        CMatrix4<T>& setTextureTranslate( f32 x, f32 y );


                        CMatrix4<T>& setTextureTranslateTransposed( f32 x, f32 y );


                        CMatrix4<T>& setTextureScale( f32 sx, f32 sy );


                        CMatrix4<T>& setTextureScaleCenter( f32 sx, f32 sy );

                        CMatrix4<T>& setM(const T* data);

                        void setDefinitelyIdentityMatrix( bool isDefinitelyIdentityMatrix);

                        bool getDefinitelyIdentityMatrix() const;

                        bool equals(const core::CMatrix4<T>& other, const T tolerance=(T)ROUNDING_ERROR_f64) const;

                private:
                        T M[16];
#if defined ( USE_MATRIX_TEST )

                        mutable u32 definitelyIdentityMatrix;
#endif
#if defined ( USE_MATRIX_TEST_DEBUG )
                        u32 id;
                        mutable u32 calls;
#endif

        };

        // Default constructor
        template <class T>
        inline CMatrix4<T>::CMatrix4( eConstructor constructor )
#if defined ( USE_MATRIX_TEST )
                : definitelyIdentityMatrix(BIT_UNTESTED)
#endif
#if defined ( USE_MATRIX_TEST_DEBUG )
                ,id ( MTest.ID++), calls ( 0 )
#endif
        {
                switch ( constructor )
                {
                        case EM4CONST_NOTHING:
                        case EM4CONST_COPY:
                                break;
                        case EM4CONST_IDENTITY:
                        case EM4CONST_INVERSE:
                        default:
                                makeIdentity();
                                break;
                }
        }

        // Copy constructor
        template <class T>
        inline CMatrix4<T>::CMatrix4( const CMatrix4<T>& other, eConstructor constructor)
#if defined ( USE_MATRIX_TEST )
                : definitelyIdentityMatrix(BIT_UNTESTED)
#endif
#if defined ( USE_MATRIX_TEST_DEBUG )
                ,id ( MTest.ID++), calls ( 0 )
#endif
        {
                switch ( constructor )
                {
                        case EM4CONST_IDENTITY:
                                makeIdentity();
                                break;
                        case EM4CONST_NOTHING:
                                break;
                        case EM4CONST_COPY:
                                *this = other;
                                break;
                        case EM4CONST_TRANSPOSED:
                                other.getTransposed(*this);
                                break;
                        case EM4CONST_INVERSE:
                                if (!other.getInverse(*this))
                                        memset(M, 0, 16*sizeof(T));
                                break;
                        case EM4CONST_INVERSE_TRANSPOSED:
                                if (!other.getInverse(*this))
                                        memset(M, 0, 16*sizeof(T));
                                else
                                        *this=getTransposed();
                                break;
                }
        }

        template <class T>
        inline CMatrix4<T> CMatrix4<T>::operator+(const CMatrix4<T>& other) const
        {
                CMatrix4<T> temp ( EM4CONST_NOTHING );

                temp[0] = M[0]+other[0];
                temp[1] = M[1]+other[1];
                temp[2] = M[2]+other[2];
                temp[3] = M[3]+other[3];
                temp[4] = M[4]+other[4];
                temp[5] = M[5]+other[5];
                temp[6] = M[6]+other[6];
                temp[7] = M[7]+other[7];
                temp[8] = M[8]+other[8];
                temp[9] = M[9]+other[9];
                temp[10] = M[10]+other[10];
                temp[11] = M[11]+other[11];
                temp[12] = M[12]+other[12];
                temp[13] = M[13]+other[13];
                temp[14] = M[14]+other[14];
                temp[15] = M[15]+other[15];

                return temp;
        }

        template <class T>
        inline CMatrix4<T>& CMatrix4<T>::operator+=(const CMatrix4<T>& other)
        {
                M[0]+=other[0];
                M[1]+=other[1];
                M[2]+=other[2];
                M[3]+=other[3];
                M[4]+=other[4];
                M[5]+=other[5];
                M[6]+=other[6];
                M[7]+=other[7];
                M[8]+=other[8];
                M[9]+=other[9];
                M[10]+=other[10];
                M[11]+=other[11];
                M[12]+=other[12];
                M[13]+=other[13];
                M[14]+=other[14];
                M[15]+=other[15];

                return *this;
        }

        template <class T>
        inline CMatrix4<T> CMatrix4<T>::operator-(const CMatrix4<T>& other) const
        {
                CMatrix4<T> temp ( EM4CONST_NOTHING );

                temp[0] = M[0]-other[0];
                temp[1] = M[1]-other[1];
                temp[2] = M[2]-other[2];
                temp[3] = M[3]-other[3];
                temp[4] = M[4]-other[4];
                temp[5] = M[5]-other[5];
                temp[6] = M[6]-other[6];
                temp[7] = M[7]-other[7];
                temp[8] = M[8]-other[8];
                temp[9] = M[9]-other[9];
                temp[10] = M[10]-other[10];
                temp[11] = M[11]-other[11];
                temp[12] = M[12]-other[12];
                temp[13] = M[13]-other[13];
                temp[14] = M[14]-other[14];
                temp[15] = M[15]-other[15];

                return temp;
        }

        template <class T>
        inline CMatrix4<T>& CMatrix4<T>::operator-=(const CMatrix4<T>& other)
        {
                M[0]-=other[0];
                M[1]-=other[1];
                M[2]-=other[2];
                M[3]-=other[3];
                M[4]-=other[4];
                M[5]-=other[5];
                M[6]-=other[6];
                M[7]-=other[7];
                M[8]-=other[8];
                M[9]-=other[9];
                M[10]-=other[10];
                M[11]-=other[11];
                M[12]-=other[12];
                M[13]-=other[13];
                M[14]-=other[14];
                M[15]-=other[15];

                return *this;
        }

        template <class T>
        inline CMatrix4<T> CMatrix4<T>::operator*(const T& scalar) const
        {
                CMatrix4<T> temp ( EM4CONST_NOTHING );

                temp[0] = M[0]*scalar;
                temp[1] = M[1]*scalar;
                temp[2] = M[2]*scalar;
                temp[3] = M[3]*scalar;
                temp[4] = M[4]*scalar;
                temp[5] = M[5]*scalar;
                temp[6] = M[6]*scalar;
                temp[7] = M[7]*scalar;
                temp[8] = M[8]*scalar;
                temp[9] = M[9]*scalar;
                temp[10] = M[10]*scalar;
                temp[11] = M[11]*scalar;
                temp[12] = M[12]*scalar;
                temp[13] = M[13]*scalar;
                temp[14] = M[14]*scalar;
                temp[15] = M[15]*scalar;

                return temp;
        }

        template <class T>
        inline CMatrix4<T>& CMatrix4<T>::operator*=(const T& scalar)
        {
                M[0]*=scalar;
                M[1]*=scalar;
                M[2]*=scalar;
                M[3]*=scalar;
                M[4]*=scalar;
                M[5]*=scalar;
                M[6]*=scalar;
                M[7]*=scalar;
                M[8]*=scalar;
                M[9]*=scalar;
                M[10]*=scalar;
                M[11]*=scalar;
                M[12]*=scalar;
                M[13]*=scalar;
                M[14]*=scalar;
                M[15]*=scalar;

                return *this;
        }

        template <class T>
        inline CMatrix4<T>& CMatrix4<T>::operator*=(const CMatrix4<T>& other)
        {
#if defined ( USE_MATRIX_TEST )
                // do checks on your own in order to avoid copy creation
                if ( !other.isIdentity() )
                {
                        if ( this->isIdentity() )
                        {
                                return (*this = other);
                        }
                        else
                        {
                                CMatrix4<T> temp ( *this );
                                return setbyproduct_nocheck( temp, other );
                        }
                }
                return *this;
#else
                CMatrix4<T> temp ( *this );
                return setbyproduct_nocheck( temp, other );
#endif
        }

        // set this matrix to the product of two other matrices
        // goal is to reduce stack use and copy
        template <class T>
        inline CMatrix4<T>& CMatrix4<T>::setbyproduct_nocheck(const CMatrix4<T>& other_a,const CMatrix4<T>& other_b )
        {
                const T *m1 = other_a.M;
                const T *m2 = other_b.M;

                M[0] = m1[0]*m2[0] + m1[4]*m2[1] + m1[8]*m2[2] + m1[12]*m2[3];
                M[1] = m1[1]*m2[0] + m1[5]*m2[1] + m1[9]*m2[2] + m1[13]*m2[3];
                M[2] = m1[2]*m2[0] + m1[6]*m2[1] + m1[10]*m2[2] + m1[14]*m2[3];
                M[3] = m1[3]*m2[0] + m1[7]*m2[1] + m1[11]*m2[2] + m1[15]*m2[3];

                M[4] = m1[0]*m2[4] + m1[4]*m2[5] + m1[8]*m2[6] + m1[12]*m2[7];
                M[5] = m1[1]*m2[4] + m1[5]*m2[5] + m1[9]*m2[6] + m1[13]*m2[7];
                M[6] = m1[2]*m2[4] + m1[6]*m2[5] + m1[10]*m2[6] + m1[14]*m2[7];
                M[7] = m1[3]*m2[4] + m1[7]*m2[5] + m1[11]*m2[6] + m1[15]*m2[7];

                M[8] = m1[0]*m2[8] + m1[4]*m2[9] + m1[8]*m2[10] + m1[12]*m2[11];
                M[9] = m1[1]*m2[8] + m1[5]*m2[9] + m1[9]*m2[10] + m1[13]*m2[11];
                M[10] = m1[2]*m2[8] + m1[6]*m2[9] + m1[10]*m2[10] + m1[14]*m2[11];
                M[11] = m1[3]*m2[8] + m1[7]*m2[9] + m1[11]*m2[10] + m1[15]*m2[11];

                M[12] = m1[0]*m2[12] + m1[4]*m2[13] + m1[8]*m2[14] + m1[12]*m2[15];
                M[13] = m1[1]*m2[12] + m1[5]*m2[13] + m1[9]*m2[14] + m1[13]*m2[15];
                M[14] = m1[2]*m2[12] + m1[6]*m2[13] + m1[10]*m2[14] + m1[14]*m2[15];
                M[15] = m1[3]*m2[12] + m1[7]*m2[13] + m1[11]*m2[14] + m1[15]*m2[15];
#if defined ( USE_MATRIX_TEST )
                definitelyIdentityMatrix=false;
#endif
                return *this;
        }


        // set this matrix to the product of two other matrices
        // goal is to reduce stack use and copy
        template <class T>
        inline CMatrix4<T>& CMatrix4<T>::setbyproduct(const CMatrix4<T>& other_a, const CMatrix4<T>& other_b )
        {
#if defined ( USE_MATRIX_TEST )
                if ( other_a.isIdentity () )
                        return (*this = other_b);
                else
                if ( other_b.isIdentity () )
                        return (*this = other_a);
                else
                        return setbyproduct_nocheck(other_a,other_b);
#else
                return setbyproduct_nocheck(other_a,other_b);
#endif
        }

        template <class T>
        inline CMatrix4<T> CMatrix4<T>::operator*(const CMatrix4<T>& m2) const
        {
#if defined ( USE_MATRIX_TEST )
                // Testing purpose..
                if ( this->isIdentity() )
                        return m2;
                if ( m2.isIdentity() )
                        return *this;
#endif

                CMatrix4<T> m3 ( EM4CONST_NOTHING );

                const T *m1 = M;

                m3[0] = m1[0]*m2[0] + m1[4]*m2[1] + m1[8]*m2[2] + m1[12]*m2[3];
                m3[1] = m1[1]*m2[0] + m1[5]*m2[1] + m1[9]*m2[2] + m1[13]*m2[3];
                m3[2] = m1[2]*m2[0] + m1[6]*m2[1] + m1[10]*m2[2] + m1[14]*m2[3];
                m3[3] = m1[3]*m2[0] + m1[7]*m2[1] + m1[11]*m2[2] + m1[15]*m2[3];

                m3[4] = m1[0]*m2[4] + m1[4]*m2[5] + m1[8]*m2[6] + m1[12]*m2[7];
                m3[5] = m1[1]*m2[4] + m1[5]*m2[5] + m1[9]*m2[6] + m1[13]*m2[7];
                m3[6] = m1[2]*m2[4] + m1[6]*m2[5] + m1[10]*m2[6] + m1[14]*m2[7];
                m3[7] = m1[3]*m2[4] + m1[7]*m2[5] + m1[11]*m2[6] + m1[15]*m2[7];

                m3[8] = m1[0]*m2[8] + m1[4]*m2[9] + m1[8]*m2[10] + m1[12]*m2[11];
                m3[9] = m1[1]*m2[8] + m1[5]*m2[9] + m1[9]*m2[10] + m1[13]*m2[11];
                m3[10] = m1[2]*m2[8] + m1[6]*m2[9] + m1[10]*m2[10] + m1[14]*m2[11];
                m3[11] = m1[3]*m2[8] + m1[7]*m2[9] + m1[11]*m2[10] + m1[15]*m2[11];

                m3[12] = m1[0]*m2[12] + m1[4]*m2[13] + m1[8]*m2[14] + m1[12]*m2[15];
                m3[13] = m1[1]*m2[12] + m1[5]*m2[13] + m1[9]*m2[14] + m1[13]*m2[15];
                m3[14] = m1[2]*m2[12] + m1[6]*m2[13] + m1[10]*m2[14] + m1[14]*m2[15];
                m3[15] = m1[3]*m2[12] + m1[7]*m2[13] + m1[11]*m2[14] + m1[15]*m2[15];
                return m3;
        }



        template <class T>
        inline vector3d<T> CMatrix4<T>::getTranslation() const
        {
                return vector3d<T>(M[12], M[13], M[14]);
        }


        template <class T>
        inline CMatrix4<T>& CMatrix4<T>::setTranslation( const vector3d<T>& translation )
        {
                M[12] = translation.X;
                M[13] = translation.Y;
                M[14] = translation.Z;
#if defined ( USE_MATRIX_TEST )
                definitelyIdentityMatrix=false;
#endif
                return *this;
        }

        template <class T>
        inline CMatrix4<T>& CMatrix4<T>::setInverseTranslation( const vector3d<T>& translation )
        {
                M[12] = -translation.X;
                M[13] = -translation.Y;
                M[14] = -translation.Z;
#if defined ( USE_MATRIX_TEST )
                definitelyIdentityMatrix=false;
#endif
                return *this;
        }

        template <class T>
        inline CMatrix4<T>& CMatrix4<T>::setScale( const vector3d<T>& scale )
        {
                M[0] = scale.X;
                M[5] = scale.Y;
                M[10] = scale.Z;
#if defined ( USE_MATRIX_TEST )
                definitelyIdentityMatrix=false;
#endif
                return *this;
        }


        template <class T>
        inline vector3d<T> CMatrix4<T>::getScale() const
        {
                // See http://www.robertblum.com/articles/2005/02/14/decomposing-matrices

                // Deal with the 0 rotation case first
                // Prior to Irrlicht 1.6, we always returned this value.
                if(core::iszero(M[1]) && core::iszero(M[2]) &&
                        core::iszero(M[4]) && core::iszero(M[6]) &&
                        core::iszero(M[8]) && core::iszero(M[9]))
                        return vector3d<T>(M[0], M[5], M[10]);

                // We have to do the full calculation.
                return vector3d<T>(sqrtf(M[0] * M[0] + M[1] * M[1] + M[2] * M[2]),
                                                        sqrtf(M[4] * M[4] + M[5] * M[5] + M[6] * M[6]),
                                                        sqrtf(M[8] * M[8] + M[9] * M[9] + M[10] * M[10]));
        }

        template <class T>
        inline CMatrix4<T>& CMatrix4<T>::setRotationDegrees( const vector3d<T>& rotation )
        {
                return setRotationRadians( rotation * core::DEGTORAD );
        }

        template <class T>
        inline CMatrix4<T>& CMatrix4<T>::setInverseRotationDegrees( const vector3d<T>& rotation )
        {
                return setInverseRotationRadians( rotation * core::DEGTORAD );
        }

        template <class T>
        inline CMatrix4<T>& CMatrix4<T>::setRotationRadians( const vector3d<T>& rotation )
        {
                const f64 cr = cos( rotation.X );
                const f64 sr = sin( rotation.X );
                const f64 cp = cos( rotation.Y );
                const f64 sp = sin( rotation.Y );
                const f64 cy = cos( rotation.Z );
                const f64 sy = sin( rotation.Z );

                M[0] = (T)( cp*cy );
                M[1] = (T)( cp*sy );
                M[2] = (T)( -sp );

                const f64 srsp = sr*sp;
                const f64 crsp = cr*sp;

                M[4] = (T)( srsp*cy-cr*sy );
                M[5] = (T)( srsp*sy+cr*cy );
                M[6] = (T)( sr*cp );

                M[8] = (T)( crsp*cy+sr*sy );
                M[9] = (T)( crsp*sy-sr*cy );
                M[10] = (T)( cr*cp );
#if defined ( USE_MATRIX_TEST )
                definitelyIdentityMatrix=false;
#endif
                return *this;
        }



        template <class T>
        inline core::vector3d<T> CMatrix4<T>::getRotationDegrees() const
        {
                const CMatrix4<T> &mat = *this;
                core::vector3d<T> scale = getScale();
                // we need to check for negative scale on to axes, which would bring up wrong results
                if (scale.Y<0 && scale.Z<0)
                {
                        scale.Y =-scale.Y;
                        scale.Z =-scale.Z;
                }
                else if (scale.X<0 && scale.Z<0)
                {
                        scale.X =-scale.X;
                        scale.Z =-scale.Z;
                }
                else if (scale.X<0 && scale.Y<0)
                {
                        scale.X =-scale.X;
                        scale.Y =-scale.Y;
                }
                const core::vector3d<f64> invScale(core::reciprocal(scale.X),core::reciprocal(scale.Y),core::reciprocal(scale.Z));

                f64 Y = -asin(core::clamp(mat[2]*invScale.X, -1.0, 1.0));
                const f64 C = cos(Y);
                Y *= RADTODEG64;

                f64 rotx, roty, X, Z;

                if (!core::iszero(C))
                {
                        const f64 invC = core::reciprocal(C);
                        rotx = mat[10] * invC * invScale.Z;
                        roty = mat[6] * invC * invScale.Y;
                        X = atan2( roty, rotx ) * RADTODEG64;
                        rotx = mat[0] * invC * invScale.X;
                        roty = mat[1] * invC * invScale.X;
                        Z = atan2( roty, rotx ) * RADTODEG64;
                }
                else
                {
                        X = 0.0;
                        rotx = mat[5] * invScale.Y;
                        roty = -mat[4] * invScale.Y;
                        Z = atan2( roty, rotx ) * RADTODEG64;
                }

                // fix values that get below zero
                if (X < 0.0) X += 360.0;
                if (Y < 0.0) Y += 360.0;
                if (Z < 0.0) Z += 360.0;

                return vector3d<T>((T)X,(T)Y,(T)Z);
        }


        template <class T>
        inline CMatrix4<T>& CMatrix4<T>::setInverseRotationRadians( const vector3d<T>& rotation )
        {
                f64 cr = cos( rotation.X );
                f64 sr = sin( rotation.X );
                f64 cp = cos( rotation.Y );
                f64 sp = sin( rotation.Y );
                f64 cy = cos( rotation.Z );
                f64 sy = sin( rotation.Z );

                M[0] = (T)( cp*cy );
                M[4] = (T)( cp*sy );
                M[8] = (T)( -sp );

                f64 srsp = sr*sp;
                f64 crsp = cr*sp;

                M[1] = (T)( srsp*cy-cr*sy );
                M[5] = (T)( srsp*sy+cr*cy );
                M[9] = (T)( sr*cp );

                M[2] = (T)( crsp*cy+sr*sy );
                M[6] = (T)( crsp*sy-sr*cy );
                M[10] = (T)( cr*cp );
#if defined ( USE_MATRIX_TEST )
                definitelyIdentityMatrix=false;
#endif
                return *this;
        }


        template <class T>
        inline CMatrix4<T>& CMatrix4<T>::makeIdentity()
        {
                memset(M, 0, 16*sizeof(T));
                M[0] = M[5] = M[10] = M[15] = (T)1;
#if defined ( USE_MATRIX_TEST )
                definitelyIdentityMatrix=true;
#endif
                return *this;
        }


        /*
                check identity with epsilon
                solve floating range problems..
        */
        template <class T>
        inline bool CMatrix4<T>::isIdentity() const
        {
#if defined ( USE_MATRIX_TEST )
                if (definitelyIdentityMatrix)
                        return true;
#endif
                if (!core::equals( M[12], (T)0 ) || !core::equals( M[13], (T)0 ) || !core::equals( M[14], (T)0 ) || !core::equals( M[15], (T)1 ))
                        return false;

                if (!core::equals( M[ 0], (T)1 ) || !core::equals( M[ 1], (T)0 ) || !core::equals( M[ 2], (T)0 ) || !core::equals( M[ 3], (T)0 ))
                        return false;

                if (!core::equals( M[ 4], (T)0 ) || !core::equals( M[ 5], (T)1 ) || !core::equals( M[ 6], (T)0 ) || !core::equals( M[ 7], (T)0 ))
                        return false;

                if (!core::equals( M[ 8], (T)0 ) || !core::equals( M[ 9], (T)0 ) || !core::equals( M[10], (T)1 ) || !core::equals( M[11], (T)0 ))
                        return false;
/*
                if (!core::equals( M[ 0], (T)1 ) ||
                        !core::equals( M[ 5], (T)1 ) ||
                        !core::equals( M[10], (T)1 ) ||
                        !core::equals( M[15], (T)1 ))
                        return false;

                for (s32 i=0; i<4; ++i)
                        for (s32 j=0; j<4; ++j)
                                if ((j != i) && (!iszero((*this)(i,j))))
                                        return false;
*/
#if defined ( USE_MATRIX_TEST )
                definitelyIdentityMatrix=true;
#endif
                return true;
        }


        /* Check orthogonality of matrix. */
        template <class T>
        inline bool CMatrix4<T>::isOrthogonal() const
        {
                T dp=M[0] * M[4 ] + M[1] * M[5 ] + M[2 ] * M[6 ] + M[3 ] * M[7 ];
                if (!iszero(dp))
                        return false;
                dp = M[0] * M[8 ] + M[1] * M[9 ] + M[2 ] * M[10] + M[3 ] * M[11];
                if (!iszero(dp))
                        return false;
                dp = M[0] * M[12] + M[1] * M[13] + M[2 ] * M[14] + M[3 ] * M[15];
                if (!iszero(dp))
                        return false;
                dp = M[4] * M[8 ] + M[5] * M[9 ] + M[6 ] * M[10] + M[7 ] * M[11];
                if (!iszero(dp))
                        return false;
                dp = M[4] * M[12] + M[5] * M[13] + M[6 ] * M[14] + M[7 ] * M[15];
                if (!iszero(dp))
                        return false;
                dp = M[8] * M[12] + M[9] * M[13] + M[10] * M[14] + M[11] * M[15];
                return (iszero(dp));
        }


        /*
                doesn't solve floating range problems..
                but takes care on +/- 0 on translation because we are changing it..
                reducing floating point branches
                but it needs the floats in memory..
        */
        template <class T>
        inline bool CMatrix4<T>::isIdentity_integer_base() const
        {
#if defined ( USE_MATRIX_TEST )
                if (definitelyIdentityMatrix)
                        return true;
#endif
                if(IR(M[0])!=F32_VALUE_1)       return false;
                if(IR(M[1])!=0)                 return false;
                if(IR(M[2])!=0)                 return false;
                if(IR(M[3])!=0)                 return false;

                if(IR(M[4])!=0)                 return false;
                if(IR(M[5])!=F32_VALUE_1)       return false;
                if(IR(M[6])!=0)                 return false;
                if(IR(M[7])!=0)                 return false;

                if(IR(M[8])!=0)                 return false;
                if(IR(M[9])!=0)                 return false;
                if(IR(M[10])!=F32_VALUE_1)      return false;
                if(IR(M[11])!=0)                return false;

                if(IR(M[12])!=0)                return false;
                if(IR(M[13])!=0)                return false;
                if(IR(M[13])!=0)                return false;
                if(IR(M[15])!=F32_VALUE_1)      return false;

#if defined ( USE_MATRIX_TEST )
                definitelyIdentityMatrix=true;
#endif
                return true;
        }


        template <class T>
        inline void CMatrix4<T>::rotateVect( vector3df& vect ) const
        {
                vector3df tmp = vect;
                vect.X = tmp.X*M[0] + tmp.Y*M[4] + tmp.Z*M[8];
                vect.Y = tmp.X*M[1] + tmp.Y*M[5] + tmp.Z*M[9];
                vect.Z = tmp.X*M[2] + tmp.Y*M[6] + tmp.Z*M[10];
        }

        template <class T>
        inline void CMatrix4<T>::rotateVect(core::vector3df& out, const core::vector3df& in) const
        {
                out.X = in.X*M[0] + in.Y*M[4] + in.Z*M[8];
                out.Y = in.X*M[1] + in.Y*M[5] + in.Z*M[9];
                out.Z = in.X*M[2] + in.Y*M[6] + in.Z*M[10];
        }

        template <class T>
        inline void CMatrix4<T>::rotateVect(T *out, const core::vector3df& in) const
        {
                out[0] = in.X*M[0] + in.Y*M[4] + in.Z*M[8];
                out[1] = in.X*M[1] + in.Y*M[5] + in.Z*M[9];
                out[2] = in.X*M[2] + in.Y*M[6] + in.Z*M[10];
        }

        template <class T>
        inline void CMatrix4<T>::inverseRotateVect( vector3df& vect ) const
        {
                vector3df tmp = vect;
                vect.X = tmp.X*M[0] + tmp.Y*M[1] + tmp.Z*M[2];
                vect.Y = tmp.X*M[4] + tmp.Y*M[5] + tmp.Z*M[6];
                vect.Z = tmp.X*M[8] + tmp.Y*M[9] + tmp.Z*M[10];
        }

        template <class T>
        inline void CMatrix4<T>::transformVect( vector3df& vect) const
        {
                f32 vector[3];

                vector[0] = vect.X*M[0] + vect.Y*M[4] + vect.Z*M[8] + M[12];
                vector[1] = vect.X*M[1] + vect.Y*M[5] + vect.Z*M[9] + M[13];
                vector[2] = vect.X*M[2] + vect.Y*M[6] + vect.Z*M[10] + M[14];

                vect.X = vector[0];
                vect.Y = vector[1];
                vect.Z = vector[2];
        }

        template <class T>
        inline void CMatrix4<T>::transformVect( vector3df& out, const vector3df& in) const
        {
                out.X = in.X*M[0] + in.Y*M[4] + in.Z*M[8] + M[12];
                out.Y = in.X*M[1] + in.Y*M[5] + in.Z*M[9] + M[13];
                out.Z = in.X*M[2] + in.Y*M[6] + in.Z*M[10] + M[14];
        }


        template <class T>
        inline void CMatrix4<T>::transformVect(T *out, const core::vector3df &in) const
        {
                out[0] = in.X*M[0] + in.Y*M[4] + in.Z*M[8] + M[12];
                out[1] = in.X*M[1] + in.Y*M[5] + in.Z*M[9] + M[13];
                out[2] = in.X*M[2] + in.Y*M[6] + in.Z*M[10] + M[14];
                out[3] = in.X*M[3] + in.Y*M[7] + in.Z*M[11] + M[15];
        }

        template <class T>
        inline void CMatrix4<T>::transformVec3(T *out, const T * in) const
        {
                out[0] = in[0]*M[0] + in[1]*M[4] + in[2]*M[8] + M[12];
                out[1] = in[0]*M[1] + in[1]*M[5] + in[2]*M[9] + M[13];
                out[2] = in[0]*M[2] + in[1]*M[6] + in[2]*M[10] + M[14];
        }


        template <class T>
        inline void CMatrix4<T>::transformPlane( core::plane3d<f32> &plane) const
        {
                vector3df member;
                // Transform the plane member point, i.e. rotate, translate and scale it.
                transformVect(member, plane.getMemberPoint());

                // Transform the normal by the transposed inverse of the matrix
                CMatrix4<T> transposedInverse(*this, EM4CONST_INVERSE_TRANSPOSED);
                vector3df normal = plane.Normal;
                transposedInverse.transformVect(normal);

                plane.setPlane(member, normal);
        }

        template <class T>
        inline void CMatrix4<T>::transformPlane( const core::plane3d<f32> &in, core::plane3d<f32> &out) const
        {
                out = in;
                transformPlane( out );
        }

        template <class T>
        inline void CMatrix4<T>::transformBox(core::aabbox3d<f32>& box) const
        {
#if defined ( USE_MATRIX_TEST )
                if (isIdentity())
                        return;
#endif

                transformVect(box.MinEdge);
                transformVect(box.MaxEdge);
                box.repair();
        }

        template <class T>
        inline void CMatrix4<T>::transformBoxEx(core::aabbox3d<f32>& box) const
        {
#if defined ( USE_MATRIX_TEST )
                if (isIdentity())
                        return;
#endif

                const f32 Amin[3] = {box.MinEdge.X, box.MinEdge.Y, box.MinEdge.Z};
                const f32 Amax[3] = {box.MaxEdge.X, box.MaxEdge.Y, box.MaxEdge.Z};

                f32 Bmin[3];
                f32 Bmax[3];

                Bmin[0] = Bmax[0] = M[12];
                Bmin[1] = Bmax[1] = M[13];
                Bmin[2] = Bmax[2] = M[14];

                const CMatrix4<T> &m = *this;

                for (u32 i = 0; i < 3; ++i)
                {
                        for (u32 j = 0; j < 3; ++j)
                        {
                                const f32 a = m(j,i) * Amin[j];
                                const f32 b = m(j,i) * Amax[j];

                                if (a < b)
                                {
                                        Bmin[i] += a;
                                        Bmax[i] += b;
                                }
                                else
                                {
                                        Bmin[i] += b;
                                        Bmax[i] += a;
                                }
                        }
                }

                box.MinEdge.X = Bmin[0];
                box.MinEdge.Y = Bmin[1];
                box.MinEdge.Z = Bmin[2];

                box.MaxEdge.X = Bmax[0];
                box.MaxEdge.Y = Bmax[1];
                box.MaxEdge.Z = Bmax[2];
        }


        template <class T>
        inline void CMatrix4<T>::multiplyWith1x4Matrix(T* matrix) const
        {
                /*
                0  1  2  3
                4  5  6  7
                8  9  10 11
                12 13 14 15
                */

                T mat[4];
                mat[0] = matrix[0];
                mat[1] = matrix[1];
                mat[2] = matrix[2];
                mat[3] = matrix[3];

                matrix[0] = M[0]*mat[0] + M[4]*mat[1] + M[8]*mat[2] + M[12]*mat[3];
                matrix[1] = M[1]*mat[0] + M[5]*mat[1] + M[9]*mat[2] + M[13]*mat[3];
                matrix[2] = M[2]*mat[0] + M[6]*mat[1] + M[10]*mat[2] + M[14]*mat[3];
                matrix[3] = M[3]*mat[0] + M[7]*mat[1] + M[11]*mat[2] + M[15]*mat[3];
        }

        template <class T>
        inline void CMatrix4<T>::inverseTranslateVect( vector3df& vect ) const
        {
                vect.X = vect.X-M[12];
                vect.Y = vect.Y-M[13];
                vect.Z = vect.Z-M[14];
        }

        template <class T>
        inline void CMatrix4<T>::translateVect( vector3df& vect ) const
        {
                vect.X = vect.X+M[12];
                vect.Y = vect.Y+M[13];
                vect.Z = vect.Z+M[14];
        }


        template <class T>
        inline bool CMatrix4<T>::getInverse(CMatrix4<T>& out) const
        {

#if defined ( USE_MATRIX_TEST )
                if ( this->isIdentity() )
                {
                        out=*this;
                        return true;
                }
#endif
                const CMatrix4<T> &m = *this;

                f32 d = (m(0, 0) * m(1, 1) - m(0, 1) * m(1, 0)) * (m(2, 2) * m(3, 3) - m(2, 3) * m(3, 2)) -
                        (m(0, 0) * m(1, 2) - m(0, 2) * m(1, 0)) * (m(2, 1) * m(3, 3) - m(2, 3) * m(3, 1)) +
                        (m(0, 0) * m(1, 3) - m(0, 3) * m(1, 0)) * (m(2, 1) * m(3, 2) - m(2, 2) * m(3, 1)) +
                        (m(0, 1) * m(1, 2) - m(0, 2) * m(1, 1)) * (m(2, 0) * m(3, 3) - m(2, 3) * m(3, 0)) -
                        (m(0, 1) * m(1, 3) - m(0, 3) * m(1, 1)) * (m(2, 0) * m(3, 2) - m(2, 2) * m(3, 0)) +
                        (m(0, 2) * m(1, 3) - m(0, 3) * m(1, 2)) * (m(2, 0) * m(3, 1) - m(2, 1) * m(3, 0));

                if( core::iszero ( d ) )
                        return false;

                d = core::reciprocal ( d );

                out(0, 0) = d * (m(1, 1) * (m(2, 2) * m(3, 3) - m(2, 3) * m(3, 2)) +
                                m(1, 2) * (m(2, 3) * m(3, 1) - m(2, 1) * m(3, 3)) +
                                m(1, 3) * (m(2, 1) * m(3, 2) - m(2, 2) * m(3, 1)));
                out(0, 1) = d * (m(2, 1) * (m(0, 2) * m(3, 3) - m(0, 3) * m(3, 2)) +
                                m(2, 2) * (m(0, 3) * m(3, 1) - m(0, 1) * m(3, 3)) +
                                m(2, 3) * (m(0, 1) * m(3, 2) - m(0, 2) * m(3, 1)));
                out(0, 2) = d * (m(3, 1) * (m(0, 2) * m(1, 3) - m(0, 3) * m(1, 2)) +
                                m(3, 2) * (m(0, 3) * m(1, 1) - m(0, 1) * m(1, 3)) +
                                m(3, 3) * (m(0, 1) * m(1, 2) - m(0, 2) * m(1, 1)));
                out(0, 3) = d * (m(0, 1) * (m(1, 3) * m(2, 2) - m(1, 2) * m(2, 3)) +
                                m(0, 2) * (m(1, 1) * m(2, 3) - m(1, 3) * m(2, 1)) +
                                m(0, 3) * (m(1, 2) * m(2, 1) - m(1, 1) * m(2, 2)));
                out(1, 0) = d * (m(1, 2) * (m(2, 0) * m(3, 3) - m(2, 3) * m(3, 0)) +
                                m(1, 3) * (m(2, 2) * m(3, 0) - m(2, 0) * m(3, 2)) +
                                m(1, 0) * (m(2, 3) * m(3, 2) - m(2, 2) * m(3, 3)));
                out(1, 1) = d * (m(2, 2) * (m(0, 0) * m(3, 3) - m(0, 3) * m(3, 0)) +
                                m(2, 3) * (m(0, 2) * m(3, 0) - m(0, 0) * m(3, 2)) +
                                m(2, 0) * (m(0, 3) * m(3, 2) - m(0, 2) * m(3, 3)));
                out(1, 2) = d * (m(3, 2) * (m(0, 0) * m(1, 3) - m(0, 3) * m(1, 0)) +
                                m(3, 3) * (m(0, 2) * m(1, 0) - m(0, 0) * m(1, 2)) +
                                m(3, 0) * (m(0, 3) * m(1, 2) - m(0, 2) * m(1, 3)));
                out(1, 3) = d * (m(0, 2) * (m(1, 3) * m(2, 0) - m(1, 0) * m(2, 3)) +
                                m(0, 3) * (m(1, 0) * m(2, 2) - m(1, 2) * m(2, 0)) +
                                m(0, 0) * (m(1, 2) * m(2, 3) - m(1, 3) * m(2, 2)));
                out(2, 0) = d * (m(1, 3) * (m(2, 0) * m(3, 1) - m(2, 1) * m(3, 0)) +
                                m(1, 0) * (m(2, 1) * m(3, 3) - m(2, 3) * m(3, 1)) +
                                m(1, 1) * (m(2, 3) * m(3, 0) - m(2, 0) * m(3, 3)));
                out(2, 1) = d * (m(2, 3) * (m(0, 0) * m(3, 1) - m(0, 1) * m(3, 0)) +
                                m(2, 0) * (m(0, 1) * m(3, 3) - m(0, 3) * m(3, 1)) +
                                m(2, 1) * (m(0, 3) * m(3, 0) - m(0, 0) * m(3, 3)));
                out(2, 2) = d * (m(3, 3) * (m(0, 0) * m(1, 1) - m(0, 1) * m(1, 0)) +
                                m(3, 0) * (m(0, 1) * m(1, 3) - m(0, 3) * m(1, 1)) +
                                m(3, 1) * (m(0, 3) * m(1, 0) - m(0, 0) * m(1, 3)));
                out(2, 3) = d * (m(0, 3) * (m(1, 1) * m(2, 0) - m(1, 0) * m(2, 1)) +
                                m(0, 0) * (m(1, 3) * m(2, 1) - m(1, 1) * m(2, 3)) +
                                m(0, 1) * (m(1, 0) * m(2, 3) - m(1, 3) * m(2, 0)));
                out(3, 0) = d * (m(1, 0) * (m(2, 2) * m(3, 1) - m(2, 1) * m(3, 2)) +
                                m(1, 1) * (m(2, 0) * m(3, 2) - m(2, 2) * m(3, 0)) +
                                m(1, 2) * (m(2, 1) * m(3, 0) - m(2, 0) * m(3, 1)));
                out(3, 1) = d * (m(2, 0) * (m(0, 2) * m(3, 1) - m(0, 1) * m(3, 2)) +
                                m(2, 1) * (m(0, 0) * m(3, 2) - m(0, 2) * m(3, 0)) +
                                m(2, 2) * (m(0, 1) * m(3, 0) - m(0, 0) * m(3, 1)));
                out(3, 2) = d * (m(3, 0) * (m(0, 2) * m(1, 1) - m(0, 1) * m(1, 2)) +
                                m(3, 1) * (m(0, 0) * m(1, 2) - m(0, 2) * m(1, 0)) +
                                m(3, 2) * (m(0, 1) * m(1, 0) - m(0, 0) * m(1, 1)));
                out(3, 3) = d * (m(0, 0) * (m(1, 1) * m(2, 2) - m(1, 2) * m(2, 1)) +
                                m(0, 1) * (m(1, 2) * m(2, 0) - m(1, 0) * m(2, 2)) +
                                m(0, 2) * (m(1, 0) * m(2, 1) - m(1, 1) * m(2, 0)));

#if defined ( USE_MATRIX_TEST )
                out.definitelyIdentityMatrix = definitelyIdentityMatrix;
#endif
                return true;
        }


        template <class T>
        inline bool CMatrix4<T>::getInversePrimitive ( CMatrix4<T>& out ) const
        {
                out.M[0 ] = M[0];
                out.M[1 ] = M[4];
                out.M[2 ] = M[8];
                out.M[3 ] = 0;

                out.M[4 ] = M[1];
                out.M[5 ] = M[5];
                out.M[6 ] = M[9];
                out.M[7 ] = 0;

                out.M[8 ] = M[2];
                out.M[9 ] = M[6];
                out.M[10] = M[10];
                out.M[11] = 0;

                out.M[12] = (T)-(M[12]*M[0] + M[13]*M[1] + M[14]*M[2]);
                out.M[13] = (T)-(M[12]*M[4] + M[13]*M[5] + M[14]*M[6]);
                out.M[14] = (T)-(M[12]*M[8] + M[13]*M[9] + M[14]*M[10]);
                out.M[15] = 1;

#if defined ( USE_MATRIX_TEST )
                out.definitelyIdentityMatrix = definitelyIdentityMatrix;
#endif
                return true;
        }

        template <class T>
        inline bool CMatrix4<T>::makeInverse()
        {
#if defined ( USE_MATRIX_TEST )
                if (definitelyIdentityMatrix)
                        return true;
#endif
                CMatrix4<T> temp ( EM4CONST_NOTHING );

                if (getInverse(temp))
                {
                        *this = temp;
                        return true;
                }

                return false;
        }


        template <class T>
        inline CMatrix4<T>& CMatrix4<T>::operator=(const CMatrix4<T> &other)
        {
                if (this==&other)
                        return *this;
                memcpy(M, other.M, 16*sizeof(T));
#if defined ( USE_MATRIX_TEST )
                definitelyIdentityMatrix=other.definitelyIdentityMatrix;
#endif
                return *this;
        }


        template <class T>
        inline CMatrix4<T>& CMatrix4<T>::operator=(const T& scalar)
        {
                for (s32 i = 0; i < 16; ++i)
                        M[i]=scalar;

#if defined ( USE_MATRIX_TEST )
                definitelyIdentityMatrix=false;
#endif
                return *this;
        }


        template <class T>
        inline bool CMatrix4<T>::operator==(const CMatrix4<T> &other) const
        {
#if defined ( USE_MATRIX_TEST )
                if (definitelyIdentityMatrix && other.definitelyIdentityMatrix)
                        return true;
#endif
                for (s32 i = 0; i < 16; ++i)
                        if (M[i] != other.M[i])
                                return false;

                return true;
        }


        template <class T>
        inline bool CMatrix4<T>::operator!=(const CMatrix4<T> &other) const
        {
                return !(*this == other);
        }


        // Builds a right-handed perspective projection matrix based on a field of view
        template <class T>
        inline CMatrix4<T>& CMatrix4<T>::buildProjectionMatrixPerspectiveFovRH(
                        f32 fieldOfViewRadians, f32 aspectRatio, f32 zNear, f32 zFar)
        {
                const f64 h = reciprocal(tan(fieldOfViewRadians*0.5));
                _IRR_DEBUG_BREAK_IF(aspectRatio==0.f); //divide by zero
                const T w = static_cast<T>(h / aspectRatio);

                _IRR_DEBUG_BREAK_IF(zNear==zFar); //divide by zero
                M[0] = w;
                M[1] = 0;
                M[2] = 0;
                M[3] = 0;

                M[4] = 0;
                M[5] = (T)h;
                M[6] = 0;
                M[7] = 0;

                M[8] = 0;
                M[9] = 0;
                M[10] = (T)(zFar/(zNear-zFar)); // DirectX version
//              M[10] = (T)(zFar+zNear/(zNear-zFar)); // OpenGL version
                M[11] = -1;

                M[12] = 0;
                M[13] = 0;
                M[14] = (T)(zNear*zFar/(zNear-zFar)); // DirectX version
//              M[14] = (T)(2.0f*zNear*zFar/(zNear-zFar)); // OpenGL version
                M[15] = 0;

#if defined ( USE_MATRIX_TEST )
                definitelyIdentityMatrix=false;
#endif
                return *this;
        }


        // Builds a left-handed perspective projection matrix based on a field of view
        template <class T>
        inline CMatrix4<T>& CMatrix4<T>::buildProjectionMatrixPerspectiveFovLH(
                        f32 fieldOfViewRadians, f32 aspectRatio, f32 zNear, f32 zFar)
        {
                const f64 h = reciprocal(tan(fieldOfViewRadians*0.5));
                _IRR_DEBUG_BREAK_IF(aspectRatio==0.f); //divide by zero
                const T w = static_cast<T>(h / aspectRatio);

                _IRR_DEBUG_BREAK_IF(zNear==zFar); //divide by zero
                M[0] = w;
                M[1] = 0;
                M[2] = 0;
                M[3] = 0;

                M[4] = 0;
                M[5] = (T)h;
                M[6] = 0;
                M[7] = 0;

                M[8] = 0;
                M[9] = 0;
                M[10] = (T)(zFar/(zFar-zNear));
                M[11] = 1;

                M[12] = 0;
                M[13] = 0;
                M[14] = (T)(-zNear*zFar/(zFar-zNear));
                M[15] = 0;

#if defined ( USE_MATRIX_TEST )
                definitelyIdentityMatrix=false;
#endif
                return *this;
        }


        // Builds a left-handed perspective projection matrix based on a field of view, with far plane culling at infinity
        template <class T>
        inline CMatrix4<T>& CMatrix4<T>::buildProjectionMatrixPerspectiveFovInfinityLH(
                        f32 fieldOfViewRadians, f32 aspectRatio, f32 zNear, f32 epsilon)
        {
                const f64 h = reciprocal(tan(fieldOfViewRadians*0.5));
                _IRR_DEBUG_BREAK_IF(aspectRatio==0.f); //divide by zero
                const T w = static_cast<T>(h / aspectRatio);

                M[0] = w;
                M[1] = 0;
                M[2] = 0;
                M[3] = 0;

                M[4] = 0;
                M[5] = (T)h;
                M[6] = 0;
                M[7] = 0;

                M[8] = 0;
                M[9] = 0;
                M[10] = (T)(1.f-epsilon);
                M[11] = 1;

                M[12] = 0;
                M[13] = 0;
                M[14] = (T)(zNear*(epsilon-1.f));
                M[15] = 0;

#if defined ( USE_MATRIX_TEST )
                definitelyIdentityMatrix=false;
#endif
                return *this;
        }


        // Builds a left-handed orthogonal projection matrix.
        template <class T>
        inline CMatrix4<T>& CMatrix4<T>::buildProjectionMatrixOrthoLH(
                        f32 widthOfViewVolume, f32 heightOfViewVolume, f32 zNear, f32 zFar)
        {
                _IRR_DEBUG_BREAK_IF(widthOfViewVolume==0.f); //divide by zero
                _IRR_DEBUG_BREAK_IF(heightOfViewVolume==0.f); //divide by zero
                _IRR_DEBUG_BREAK_IF(zNear==zFar); //divide by zero
                M[0] = (T)(2/widthOfViewVolume);
                M[1] = 0;
                M[2] = 0;
                M[3] = 0;

                M[4] = 0;
                M[5] = (T)(2/heightOfViewVolume);
                M[6] = 0;
                M[7] = 0;

                M[8] = 0;
                M[9] = 0;
                M[10] = (T)(1/(zFar-zNear));
                M[11] = 0;

                M[12] = 0;
                M[13] = 0;
                M[14] = (T)(zNear/(zNear-zFar));
                M[15] = 1;

#if defined ( USE_MATRIX_TEST )
                definitelyIdentityMatrix=false;
#endif
                return *this;
        }


        // Builds a right-handed orthogonal projection matrix.
        template <class T>
        inline CMatrix4<T>& CMatrix4<T>::buildProjectionMatrixOrthoRH(
                        f32 widthOfViewVolume, f32 heightOfViewVolume, f32 zNear, f32 zFar)
        {
                _IRR_DEBUG_BREAK_IF(widthOfViewVolume==0.f); //divide by zero
                _IRR_DEBUG_BREAK_IF(heightOfViewVolume==0.f); //divide by zero
                _IRR_DEBUG_BREAK_IF(zNear==zFar); //divide by zero
                M[0] = (T)(2/widthOfViewVolume);
                M[1] = 0;
                M[2] = 0;
                M[3] = 0;

                M[4] = 0;
                M[5] = (T)(2/heightOfViewVolume);
                M[6] = 0;
                M[7] = 0;

                M[8] = 0;
                M[9] = 0;
                M[10] = (T)(1/(zNear-zFar));
                M[11] = 0;

                M[12] = 0;
                M[13] = 0;
                M[14] = (T)(zNear/(zNear-zFar));
                M[15] = 1;

#if defined ( USE_MATRIX_TEST )
                definitelyIdentityMatrix=false;
#endif
                return *this;
        }


        // Builds a right-handed perspective projection matrix.
        template <class T>
        inline CMatrix4<T>& CMatrix4<T>::buildProjectionMatrixPerspectiveRH(
                        f32 widthOfViewVolume, f32 heightOfViewVolume, f32 zNear, f32 zFar)
        {
                _IRR_DEBUG_BREAK_IF(widthOfViewVolume==0.f); //divide by zero
                _IRR_DEBUG_BREAK_IF(heightOfViewVolume==0.f); //divide by zero
                _IRR_DEBUG_BREAK_IF(zNear==zFar); //divide by zero
                M[0] = (T)(2*zNear/widthOfViewVolume);
                M[1] = 0;
                M[2] = 0;
                M[3] = 0;

                M[4] = 0;
                M[5] = (T)(2*zNear/heightOfViewVolume);
                M[6] = 0;
                M[7] = 0;

                M[8] = 0;
                M[9] = 0;
                M[10] = (T)(zFar/(zNear-zFar));
                M[11] = -1;

                M[12] = 0;
                M[13] = 0;
                M[14] = (T)(zNear*zFar/(zNear-zFar));
                M[15] = 0;

#if defined ( USE_MATRIX_TEST )
                definitelyIdentityMatrix=false;
#endif
                return *this;
        }


        // Builds a left-handed perspective projection matrix.
        template <class T>
        inline CMatrix4<T>& CMatrix4<T>::buildProjectionMatrixPerspectiveLH(
                        f32 widthOfViewVolume, f32 heightOfViewVolume, f32 zNear, f32 zFar)
        {
                _IRR_DEBUG_BREAK_IF(widthOfViewVolume==0.f); //divide by zero
                _IRR_DEBUG_BREAK_IF(heightOfViewVolume==0.f); //divide by zero
                _IRR_DEBUG_BREAK_IF(zNear==zFar); //divide by zero
                M[0] = (T)(2*zNear/widthOfViewVolume);
                M[1] = 0;
                M[2] = 0;
                M[3] = 0;

                M[4] = 0;
                M[5] = (T)(2*zNear/heightOfViewVolume);
                M[6] = 0;
                M[7] = 0;

                M[8] = 0;
                M[9] = 0;
                M[10] = (T)(zFar/(zFar-zNear));
                M[11] = 1;

                M[12] = 0;
                M[13] = 0;
                M[14] = (T)(zNear*zFar/(zNear-zFar));
                M[15] = 0;
#if defined ( USE_MATRIX_TEST )
                definitelyIdentityMatrix=false;
#endif
                return *this;
        }


        // Builds a matrix that flattens geometry into a plane.
        template <class T>
        inline CMatrix4<T>& CMatrix4<T>::buildShadowMatrix(const core::vector3df& light, core::plane3df plane, f32 point)
        {
                plane.Normal.normalize();
                const f32 d = plane.Normal.dotProduct(light);

                M[ 0] = (T)(-plane.Normal.X * light.X + d);
                M[ 1] = (T)(-plane.Normal.X * light.Y);
                M[ 2] = (T)(-plane.Normal.X * light.Z);
                M[ 3] = (T)(-plane.Normal.X * point);

                M[ 4] = (T)(-plane.Normal.Y * light.X);
                M[ 5] = (T)(-plane.Normal.Y * light.Y + d);
                M[ 6] = (T)(-plane.Normal.Y * light.Z);
                M[ 7] = (T)(-plane.Normal.Y * point);

                M[ 8] = (T)(-plane.Normal.Z * light.X);
                M[ 9] = (T)(-plane.Normal.Z * light.Y);
                M[10] = (T)(-plane.Normal.Z * light.Z + d);
                M[11] = (T)(-plane.Normal.Z * point);

                M[12] = (T)(-plane.D * light.X);
                M[13] = (T)(-plane.D * light.Y);
                M[14] = (T)(-plane.D * light.Z);
                M[15] = (T)(-plane.D * point + d);
#if defined ( USE_MATRIX_TEST )
                definitelyIdentityMatrix=false;
#endif
                return *this;
        }

        // Builds a left-handed look-at matrix.
        template <class T>
        inline CMatrix4<T>& CMatrix4<T>::buildCameraLookAtMatrixLH(
                                const vector3df& position,
                                const vector3df& target,
                                const vector3df& upVector)
        {
                vector3df zaxis = target - position;
                zaxis.normalize();

                vector3df xaxis = upVector.crossProduct(zaxis);
                xaxis.normalize();

                vector3df yaxis = zaxis.crossProduct(xaxis);

                M[0] = (T)xaxis.X;
                M[1] = (T)yaxis.X;
                M[2] = (T)zaxis.X;
                M[3] = 0;

                M[4] = (T)xaxis.Y;
                M[5] = (T)yaxis.Y;
                M[6] = (T)zaxis.Y;
                M[7] = 0;

                M[8] = (T)xaxis.Z;
                M[9] = (T)yaxis.Z;
                M[10] = (T)zaxis.Z;
                M[11] = 0;

                M[12] = (T)-xaxis.dotProduct(position);
                M[13] = (T)-yaxis.dotProduct(position);
                M[14] = (T)-zaxis.dotProduct(position);
                M[15] = 1;
#if defined ( USE_MATRIX_TEST )
                definitelyIdentityMatrix=false;
#endif
                return *this;
        }


        // Builds a right-handed look-at matrix.
        template <class T>
        inline CMatrix4<T>& CMatrix4<T>::buildCameraLookAtMatrixRH(
                                const vector3df& position,
                                const vector3df& target,
                                const vector3df& upVector)
        {
                vector3df zaxis = position - target;
                zaxis.normalize();

                vector3df xaxis = upVector.crossProduct(zaxis);
                xaxis.normalize();

                vector3df yaxis = zaxis.crossProduct(xaxis);

                M[0] = (T)xaxis.X;
                M[1] = (T)yaxis.X;
                M[2] = (T)zaxis.X;
                M[3] = 0;

                M[4] = (T)xaxis.Y;
                M[5] = (T)yaxis.Y;
                M[6] = (T)zaxis.Y;
                M[7] = 0;

                M[8] = (T)xaxis.Z;
                M[9] = (T)yaxis.Z;
                M[10] = (T)zaxis.Z;
                M[11] = 0;

                M[12] = (T)-xaxis.dotProduct(position);
                M[13] = (T)-yaxis.dotProduct(position);
                M[14] = (T)-zaxis.dotProduct(position);
                M[15] = 1;
#if defined ( USE_MATRIX_TEST )
                definitelyIdentityMatrix=false;
#endif
                return *this;
        }


        // creates a new matrix as interpolated matrix from this and the passed one.
        template <class T>
        inline CMatrix4<T> CMatrix4<T>::interpolate(const core::CMatrix4<T>& b, f32 time) const
        {
                CMatrix4<T> mat ( EM4CONST_NOTHING );

                for (u32 i=0; i < 16; i += 4)
                {
                        mat.M[i+0] = (T)(M[i+0] + ( b.M[i+0] - M[i+0] ) * time);
                        mat.M[i+1] = (T)(M[i+1] + ( b.M[i+1] - M[i+1] ) * time);
                        mat.M[i+2] = (T)(M[i+2] + ( b.M[i+2] - M[i+2] ) * time);
                        mat.M[i+3] = (T)(M[i+3] + ( b.M[i+3] - M[i+3] ) * time);
                }
                return mat;
        }


        // returns transposed matrix
        template <class T>
        inline CMatrix4<T> CMatrix4<T>::getTransposed() const
        {
                CMatrix4<T> t ( EM4CONST_NOTHING );
                getTransposed ( t );
                return t;
        }


        // returns transposed matrix
        template <class T>
        inline void CMatrix4<T>::getTransposed( CMatrix4<T>& o ) const
        {
                o[ 0] = M[ 0];
                o[ 1] = M[ 4];
                o[ 2] = M[ 8];
                o[ 3] = M[12];

                o[ 4] = M[ 1];
                o[ 5] = M[ 5];
                o[ 6] = M[ 9];
                o[ 7] = M[13];

                o[ 8] = M[ 2];
                o[ 9] = M[ 6];
                o[10] = M[10];
                o[11] = M[14];

                o[12] = M[ 3];
                o[13] = M[ 7];
                o[14] = M[11];
                o[15] = M[15];
#if defined ( USE_MATRIX_TEST )
                o.definitelyIdentityMatrix=definitelyIdentityMatrix;
#endif
        }


        // used to scale <-1,-1><1,1> to viewport
        template <class T>
        inline CMatrix4<T>& CMatrix4<T>::buildNDCToDCMatrix( const core::rect<s32>& viewport, f32 zScale)
        {
                const f32 scaleX = (viewport.getWidth() - 0.75f ) * 0.5f;
                const f32 scaleY = -(viewport.getHeight() - 0.75f ) * 0.5f;

                const f32 dx = -0.5f + ( (viewport.UpperLeftCorner.X + viewport.LowerRightCorner.X ) * 0.5f );
                const f32 dy = -0.5f + ( (viewport.UpperLeftCorner.Y + viewport.LowerRightCorner.Y ) * 0.5f );

                makeIdentity();
                M[12] = (T)dx;
                M[13] = (T)dy;
                return setScale(core::vector3d<T>((T)scaleX, (T)scaleY, (T)zScale));
        }


        template <class T>
        inline CMatrix4<T>& CMatrix4<T>::buildRotateFromTo(const core::vector3df& from, const core::vector3df& to)
        {
                // unit vectors
                core::vector3df f(from);
                core::vector3df t(to);
                f.normalize();
                t.normalize();

                // axis multiplication by sin
                core::vector3df vs(t.crossProduct(f));

                // axis of rotation
                core::vector3df v(vs);
                v.normalize();

                // cosinus angle
                T ca = f.dotProduct(t); 

                core::vector3df vt(v * (1 - ca));

                M[0] = vt.X * v.X + ca;
                M[5] = vt.Y * v.Y + ca;
                M[10] = vt.Z * v.Z + ca;

                vt.X *= v.Y;
                vt.Z *= v.X;
                vt.Y *= v.Z;

                M[1] = vt.X - vs.Z;
                M[2] = vt.Z + vs.Y;
                M[3] = 0;

                M[4] = vt.X + vs.Z;
                M[6] = vt.Y - vs.X;
                M[7] = 0;

                M[8] = vt.Z - vs.Y;
                M[9] = vt.Y + vs.X;
                M[11] = 0;

                M[12] = 0;
                M[13] = 0;
                M[14] = 0;
                M[15] = 1;

                return *this;
        }


        template <class T>
        inline void CMatrix4<T>::buildAxisAlignedBillboard(
                                const core::vector3df& camPos,
                                const core::vector3df& center,
                                const core::vector3df& translation,
                                const core::vector3df& axis,
                                const core::vector3df& from)
        {
                // axis of rotation
                core::vector3df up = axis;
                up.normalize();
                const core::vector3df forward = (camPos - center).normalize();
                const core::vector3df right = up.crossProduct(forward).normalize();

                // correct look vector
                const core::vector3df look = right.crossProduct(up);

                // rotate from to
                // axis multiplication by sin
                const core::vector3df vs = look.crossProduct(from);

                // cosinus angle
                const f32 ca = from.dotProduct(look);   

                core::vector3df vt(up * (1.f - ca));

                M[0] = static_cast<T>(vt.X * up.X + ca);
                M[5] = static_cast<T>(vt.Y * up.Y + ca);
                M[10] = static_cast<T>(vt.Z * up.Z + ca);

                vt.X *= up.Y;
                vt.Z *= up.X;
                vt.Y *= up.Z;

                M[1] = static_cast<T>(vt.X - vs.Z);
                M[2] = static_cast<T>(vt.Z + vs.Y);
                M[3] = 0;

                M[4] = static_cast<T>(vt.X + vs.Z);
                M[6] = static_cast<T>(vt.Y - vs.X);
                M[7] = 0;

                M[8] = static_cast<T>(vt.Z - vs.Y);
                M[9] = static_cast<T>(vt.Y + vs.X);
                M[11] = 0;

                setRotationCenter(center, translation);
        }


        template <class T>
        inline void CMatrix4<T>::setRotationCenter(const core::vector3df& center, const core::vector3df& translation)
        {
                M[12] = -M[0]*center.X - M[4]*center.Y - M[8]*center.Z + (center.X - translation.X );
                M[13] = -M[1]*center.X - M[5]*center.Y - M[9]*center.Z + (center.Y - translation.Y );
                M[14] = -M[2]*center.X - M[6]*center.Y - M[10]*center.Z + (center.Z - translation.Z );
                M[15] = (T) 1.0;
#if defined ( USE_MATRIX_TEST )
                definitelyIdentityMatrix=false;
#endif
        }

        template <class T>
        inline CMatrix4<T>& CMatrix4<T>::buildTextureTransform( f32 rotateRad,
                        const core::vector2df &rotatecenter,
                        const core::vector2df &translate,
                        const core::vector2df &scale)
        {
                const f32 c = cosf(rotateRad);
                const f32 s = sinf(rotateRad);

                M[0] = (T)(c * scale.X);
                M[1] = (T)(s * scale.Y);
                M[2] = 0;
                M[3] = 0;

                M[4] = (T)(-s * scale.X);
                M[5] = (T)(c * scale.Y);
                M[6] = 0;
                M[7] = 0;

                M[8] = (T)(c * scale.X * rotatecenter.X + -s * rotatecenter.Y + translate.X);
                M[9] = (T)(s * scale.Y * rotatecenter.X +  c * rotatecenter.Y + translate.Y);
                M[10] = 1;
                M[11] = 0;

                M[12] = 0;
                M[13] = 0;
                M[14] = 0;
                M[15] = 1;
#if defined ( USE_MATRIX_TEST )
                definitelyIdentityMatrix=false;
#endif
                return *this;
        }


        // rotate about z axis, center ( 0.5, 0.5 )
        template <class T>
        inline CMatrix4<T>& CMatrix4<T>::setTextureRotationCenter( f32 rotateRad )
        {
                const f32 c = cosf(rotateRad);
                const f32 s = sinf(rotateRad);
                M[0] = (T)c;
                M[1] = (T)s;

                M[4] = (T)-s;
                M[5] = (T)c;

                M[8] = (T)(0.5f * ( s - c) + 0.5f);
                M[9] = (T)(-0.5f * ( s + c) + 0.5f);

#if defined ( USE_MATRIX_TEST )
                definitelyIdentityMatrix = definitelyIdentityMatrix && (rotateRad==0.0f);
#endif
                return *this;
        }


        template <class T>
        inline CMatrix4<T>& CMatrix4<T>::setTextureTranslate ( f32 x, f32 y )
        {
                M[8] = (T)x;
                M[9] = (T)y;

#if defined ( USE_MATRIX_TEST )
                definitelyIdentityMatrix = definitelyIdentityMatrix && (x==0.0f) && (y==0.0f);
#endif
                return *this;
        }


        template <class T>
        inline CMatrix4<T>& CMatrix4<T>::setTextureTranslateTransposed ( f32 x, f32 y )
        {
                M[2] = (T)x;
                M[6] = (T)y;

#if defined ( USE_MATRIX_TEST )
                definitelyIdentityMatrix = definitelyIdentityMatrix && (x==0.0f) && (y==0.0f) ;
#endif
                return *this;
        }

        template <class T>
        inline CMatrix4<T>& CMatrix4<T>::setTextureScale ( f32 sx, f32 sy )
        {
                M[0] = (T)sx;
                M[5] = (T)sy;
#if defined ( USE_MATRIX_TEST )
                definitelyIdentityMatrix = definitelyIdentityMatrix && (sx==1.0f) && (sy==1.0f);
#endif
                return *this;
        }


        template <class T>
        inline CMatrix4<T>& CMatrix4<T>::setTextureScaleCenter( f32 sx, f32 sy )
        {
                M[0] = (T)sx;
                M[5] = (T)sy;
                M[8] = (T)(0.5f - 0.5f * sx);
                M[9] = (T)(0.5f - 0.5f * sy);

#if defined ( USE_MATRIX_TEST )
                definitelyIdentityMatrix = definitelyIdentityMatrix && (sx==1.0f) && (sy==1.0f);
#endif
                return *this;
        }


        // sets all matrix data members at once
        template <class T>
        inline CMatrix4<T>& CMatrix4<T>::setM(const T* data)
        {
                memcpy(M,data, 16*sizeof(T));

#if defined ( USE_MATRIX_TEST )
                definitelyIdentityMatrix=false;
#endif
                return *this;
        }


        // sets if the matrix is definitely identity matrix
        template <class T>
        inline void CMatrix4<T>::setDefinitelyIdentityMatrix( bool isDefinitelyIdentityMatrix)
        {
#if defined ( USE_MATRIX_TEST )
                definitelyIdentityMatrix = isDefinitelyIdentityMatrix;
#endif
        }


        // gets if the matrix is definitely identity matrix
        template <class T>
        inline bool CMatrix4<T>::getDefinitelyIdentityMatrix() const
        {
#if defined ( USE_MATRIX_TEST )
                return definitelyIdentityMatrix;
#else
                return false;
#endif
        }


        template <class T>
        inline bool CMatrix4<T>::equals(const core::CMatrix4<T>& other, const T tolerance) const
        {
#if defined ( USE_MATRIX_TEST )
                if (definitelyIdentityMatrix && other.definitelyIdentityMatrix)
                        return true;
#endif
                for (s32 i = 0; i < 16; ++i)
                        if (!core::equals(M[i],other.M[i], tolerance))
                                return false;

                return true;
        }


        // Multiply by scalar.
        template <class T>
        inline CMatrix4<T> operator*(const T scalar, const CMatrix4<T>& mat)
        {
                return mat*scalar;
        }


        typedef CMatrix4<f32> matrix4;

        IRRLICHT_API extern const matrix4 IdentityMatrix;

} // end namespace core
} // end namespace irr

#endif