neon/mat_aos.h

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/*
   Copyright (C) 2009 Sony Computer Entertainment Inc.
   All rights reserved.

This software is provided 'as-is', without any express or implied warranty.
In no event will the authors be held liable for any damages arising from the use of this software.
Permission is granted to anyone to use this software for any purpose, 
including commercial applications, and to alter it and redistribute it freely, 
subject to the following restrictions:

1. The origin of this software must not be misrepresented; you must not claim that you wrote the original software. If you use this software in a product, an acknowledgment in the product documentation would be appreciated but is not required.
2. Altered source versions must be plainly marked as such, and must not be misrepresented as being the original software.
3. This notice may not be removed or altered from any source distribution.

*/

#ifndef _VECTORMATH_MAT_AOS_CPP_H
#define _VECTORMATH_MAT_AOS_CPP_H

namespace Vectormath {
namespace Aos {

//-----------------------------------------------------------------------------
// Constants

#define _VECTORMATH_PI_OVER_2 1.570796327f

//-----------------------------------------------------------------------------
// Definitions

inline Matrix3::Matrix3( const Matrix3 & mat )
{
    mCol0 = mat.mCol0;
    mCol1 = mat.mCol1;
    mCol2 = mat.mCol2;
}

inline Matrix3::Matrix3( float scalar )
{
    mCol0 = Vector3( scalar );
    mCol1 = Vector3( scalar );
    mCol2 = Vector3( scalar );
}

inline Matrix3::Matrix3( const Quat & unitQuat )
{
    float qx, qy, qz, qw, qx2, qy2, qz2, qxqx2, qyqy2, qzqz2, qxqy2, qyqz2, qzqw2, qxqz2, qyqw2, qxqw2;
    qx = unitQuat.getX();
    qy = unitQuat.getY();
    qz = unitQuat.getZ();
    qw = unitQuat.getW();
    qx2 = ( qx + qx );
    qy2 = ( qy + qy );
    qz2 = ( qz + qz );
    qxqx2 = ( qx * qx2 );
    qxqy2 = ( qx * qy2 );
    qxqz2 = ( qx * qz2 );
    qxqw2 = ( qw * qx2 );
    qyqy2 = ( qy * qy2 );
    qyqz2 = ( qy * qz2 );
    qyqw2 = ( qw * qy2 );
    qzqz2 = ( qz * qz2 );
    qzqw2 = ( qw * qz2 );
    mCol0 = Vector3( ( ( 1.0f - qyqy2 ) - qzqz2 ), ( qxqy2 + qzqw2 ), ( qxqz2 - qyqw2 ) );
    mCol1 = Vector3( ( qxqy2 - qzqw2 ), ( ( 1.0f - qxqx2 ) - qzqz2 ), ( qyqz2 + qxqw2 ) );
    mCol2 = Vector3( ( qxqz2 + qyqw2 ), ( qyqz2 - qxqw2 ), ( ( 1.0f - qxqx2 ) - qyqy2 ) );
}

inline Matrix3::Matrix3( const Vector3 & _col0, const Vector3 & _col1, const Vector3 & _col2 )
{
    mCol0 = _col0;
    mCol1 = _col1;
    mCol2 = _col2;
}

inline Matrix3 & Matrix3::setCol0( const Vector3 & _col0 )
{
    mCol0 = _col0;
    return *this;
}

inline Matrix3 & Matrix3::setCol1( const Vector3 & _col1 )
{
    mCol1 = _col1;
    return *this;
}

inline Matrix3 & Matrix3::setCol2( const Vector3 & _col2 )
{
    mCol2 = _col2;
    return *this;
}

inline Matrix3 & Matrix3::setCol( int col, const Vector3 & vec )
{
    *(&mCol0 + col) = vec;
    return *this;
}

inline Matrix3 & Matrix3::setRow( int row, const Vector3 & vec )
{
    mCol0.setElem( row, vec.getElem( 0 ) );
    mCol1.setElem( row, vec.getElem( 1 ) );
    mCol2.setElem( row, vec.getElem( 2 ) );
    return *this;
}

inline Matrix3 & Matrix3::setElem( int col, int row, float val )
{
    Vector3 tmpV3_0;
    tmpV3_0 = this->getCol( col );
    tmpV3_0.setElem( row, val );
    this->setCol( col, tmpV3_0 );
    return *this;
}

inline float Matrix3::getElem( int col, int row ) const
{
    return this->getCol( col ).getElem( row );
}

inline const Vector3 Matrix3::getCol0( ) const
{
    return mCol0;
}

inline const Vector3 Matrix3::getCol1( ) const
{
    return mCol1;
}

inline const Vector3 Matrix3::getCol2( ) const
{
    return mCol2;
}

inline const Vector3 Matrix3::getCol( int col ) const
{
    return *(&mCol0 + col);
}

inline const Vector3 Matrix3::getRow( int row ) const
{
    return Vector3( mCol0.getElem( row ), mCol1.getElem( row ), mCol2.getElem( row ) );
}

inline Vector3 & Matrix3::operator []( int col )
{
    return *(&mCol0 + col);
}

inline const Vector3 Matrix3::operator []( int col ) const
{
    return *(&mCol0 + col);
}

inline Matrix3 & Matrix3::operator =( const Matrix3 & mat )
{
    mCol0 = mat.mCol0;
    mCol1 = mat.mCol1;
    mCol2 = mat.mCol2;
    return *this;
}

inline const Matrix3 transpose( const Matrix3 & mat )
{
    return Matrix3(
        Vector3( mat.getCol0().getX(), mat.getCol1().getX(), mat.getCol2().getX() ),
        Vector3( mat.getCol0().getY(), mat.getCol1().getY(), mat.getCol2().getY() ),
        Vector3( mat.getCol0().getZ(), mat.getCol1().getZ(), mat.getCol2().getZ() )
    );
}

inline const Matrix3 inverse( const Matrix3 & mat )
{
    Vector3 tmp0, tmp1, tmp2;
    float detinv;
    tmp0 = cross( mat.getCol1(), mat.getCol2() );
    tmp1 = cross( mat.getCol2(), mat.getCol0() );
    tmp2 = cross( mat.getCol0(), mat.getCol1() );
    detinv = ( 1.0f / dot( mat.getCol2(), tmp2 ) );
    return Matrix3(
        Vector3( ( tmp0.getX() * detinv ), ( tmp1.getX() * detinv ), ( tmp2.getX() * detinv ) ),
        Vector3( ( tmp0.getY() * detinv ), ( tmp1.getY() * detinv ), ( tmp2.getY() * detinv ) ),
        Vector3( ( tmp0.getZ() * detinv ), ( tmp1.getZ() * detinv ), ( tmp2.getZ() * detinv ) )
    );
}

inline float determinant( const Matrix3 & mat )
{
    return dot( mat.getCol2(), cross( mat.getCol0(), mat.getCol1() ) );
}

inline const Matrix3 Matrix3::operator +( const Matrix3 & mat ) const
{
    return Matrix3(
        ( mCol0 + mat.mCol0 ),
        ( mCol1 + mat.mCol1 ),
        ( mCol2 + mat.mCol2 )
    );
}

inline const Matrix3 Matrix3::operator -( const Matrix3 & mat ) const
{
    return Matrix3(
        ( mCol0 - mat.mCol0 ),
        ( mCol1 - mat.mCol1 ),
        ( mCol2 - mat.mCol2 )
    );
}

inline Matrix3 & Matrix3::operator +=( const Matrix3 & mat )
{
    *this = *this + mat;
    return *this;
}

inline Matrix3 & Matrix3::operator -=( const Matrix3 & mat )
{
    *this = *this - mat;
    return *this;
}

inline const Matrix3 Matrix3::operator -( ) const
{
    return Matrix3(
        ( -mCol0 ),
        ( -mCol1 ),
        ( -mCol2 )
    );
}

inline const Matrix3 absPerElem( const Matrix3 & mat )
{
    return Matrix3(
        absPerElem( mat.getCol0() ),
        absPerElem( mat.getCol1() ),
        absPerElem( mat.getCol2() )
    );
}

inline const Matrix3 Matrix3::operator *( float scalar ) const
{
    return Matrix3(
        ( mCol0 * scalar ),
        ( mCol1 * scalar ),
        ( mCol2 * scalar )
    );
}

inline Matrix3 & Matrix3::operator *=( float scalar )
{
    *this = *this * scalar;
    return *this;
}

inline const Matrix3 operator *( float scalar, const Matrix3 & mat )
{
    return mat * scalar;
}

inline const Vector3 Matrix3::operator *( const Vector3 & vec ) const
{
    return Vector3(
        ( ( ( mCol0.getX() * vec.getX() ) + ( mCol1.getX() * vec.getY() ) ) + ( mCol2.getX() * vec.getZ() ) ),
        ( ( ( mCol0.getY() * vec.getX() ) + ( mCol1.getY() * vec.getY() ) ) + ( mCol2.getY() * vec.getZ() ) ),
        ( ( ( mCol0.getZ() * vec.getX() ) + ( mCol1.getZ() * vec.getY() ) ) + ( mCol2.getZ() * vec.getZ() ) )
    );
}

inline const Matrix3 Matrix3::operator *( const Matrix3 & mat ) const
{
    return Matrix3(
        ( *this * mat.mCol0 ),
        ( *this * mat.mCol1 ),
        ( *this * mat.mCol2 )
    );
}

inline Matrix3 & Matrix3::operator *=( const Matrix3 & mat )
{
    *this = *this * mat;
    return *this;
}

inline const Matrix3 mulPerElem( const Matrix3 & mat0, const Matrix3 & mat1 )
{
    return Matrix3(
        mulPerElem( mat0.getCol0(), mat1.getCol0() ),
        mulPerElem( mat0.getCol1(), mat1.getCol1() ),
        mulPerElem( mat0.getCol2(), mat1.getCol2() )
    );
}

inline const Matrix3 Matrix3::identity( )
{
    return Matrix3(
        Vector3::xAxis( ),
        Vector3::yAxis( ),
        Vector3::zAxis( )
    );
}

inline const Matrix3 Matrix3::rotationX( float radians )
{
    float s, c;
    s = sinf( radians );
    c = cosf( radians );
    return Matrix3(
        Vector3::xAxis( ),
        Vector3( 0.0f, c, s ),
        Vector3( 0.0f, -s, c )
    );
}

inline const Matrix3 Matrix3::rotationY( float radians )
{
    float s, c;
    s = sinf( radians );
    c = cosf( radians );
    return Matrix3(
        Vector3( c, 0.0f, -s ),
        Vector3::yAxis( ),
        Vector3( s, 0.0f, c )
    );
}

inline const Matrix3 Matrix3::rotationZ( float radians )
{
    float s, c;
    s = sinf( radians );
    c = cosf( radians );
    return Matrix3(
        Vector3( c, s, 0.0f ),
        Vector3( -s, c, 0.0f ),
        Vector3::zAxis( )
    );
}

inline const Matrix3 Matrix3::rotationZYX( const Vector3 & radiansXYZ )
{
    float sX, cX, sY, cY, sZ, cZ, tmp0, tmp1;
    sX = sinf( radiansXYZ.getX() );
    cX = cosf( radiansXYZ.getX() );
    sY = sinf( radiansXYZ.getY() );
    cY = cosf( radiansXYZ.getY() );
    sZ = sinf( radiansXYZ.getZ() );
    cZ = cosf( radiansXYZ.getZ() );
    tmp0 = ( cZ * sY );
    tmp1 = ( sZ * sY );
    return Matrix3(
        Vector3( ( cZ * cY ), ( sZ * cY ), -sY ),
        Vector3( ( ( tmp0 * sX ) - ( sZ * cX ) ), ( ( tmp1 * sX ) + ( cZ * cX ) ), ( cY * sX ) ),
        Vector3( ( ( tmp0 * cX ) + ( sZ * sX ) ), ( ( tmp1 * cX ) - ( cZ * sX ) ), ( cY * cX ) )
    );
}

inline const Matrix3 Matrix3::rotation( float radians, const Vector3 & unitVec )
{
    float x, y, z, s, c, oneMinusC, xy, yz, zx;
    s = sinf( radians );
    c = cosf( radians );
    x = unitVec.getX();
    y = unitVec.getY();
    z = unitVec.getZ();
    xy = ( x * y );
    yz = ( y * z );
    zx = ( z * x );
    oneMinusC = ( 1.0f - c );
    return Matrix3(
        Vector3( ( ( ( x * x ) * oneMinusC ) + c ), ( ( xy * oneMinusC ) + ( z * s ) ), ( ( zx * oneMinusC ) - ( y * s ) ) ),
        Vector3( ( ( xy * oneMinusC ) - ( z * s ) ), ( ( ( y * y ) * oneMinusC ) + c ), ( ( yz * oneMinusC ) + ( x * s ) ) ),
        Vector3( ( ( zx * oneMinusC ) + ( y * s ) ), ( ( yz * oneMinusC ) - ( x * s ) ), ( ( ( z * z ) * oneMinusC ) + c ) )
    );
}

inline const Matrix3 Matrix3::rotation( const Quat & unitQuat )
{
    return Matrix3( unitQuat );
}

inline const Matrix3 Matrix3::scale( const Vector3 & scaleVec )
{
    return Matrix3(
        Vector3( scaleVec.getX(), 0.0f, 0.0f ),
        Vector3( 0.0f, scaleVec.getY(), 0.0f ),
        Vector3( 0.0f, 0.0f, scaleVec.getZ() )
    );
}

inline const Matrix3 appendScale( const Matrix3 & mat, const Vector3 & scaleVec )
{
    return Matrix3(
        ( mat.getCol0() * scaleVec.getX( ) ),
        ( mat.getCol1() * scaleVec.getY( ) ),
        ( mat.getCol2() * scaleVec.getZ( ) )
    );
}

inline const Matrix3 prependScale( const Vector3 & scaleVec, const Matrix3 & mat )
{
    return Matrix3(
        mulPerElem( mat.getCol0(), scaleVec ),
        mulPerElem( mat.getCol1(), scaleVec ),
        mulPerElem( mat.getCol2(), scaleVec )
    );
}

inline const Matrix3 select( const Matrix3 & mat0, const Matrix3 & mat1, bool select1 )
{
    return Matrix3(
        select( mat0.getCol0(), mat1.getCol0(), select1 ),
        select( mat0.getCol1(), mat1.getCol1(), select1 ),
        select( mat0.getCol2(), mat1.getCol2(), select1 )
    );
}

#ifdef _VECTORMATH_DEBUG

inline void print( const Matrix3 & mat )
{
    print( mat.getRow( 0 ) );
    print( mat.getRow( 1 ) );
    print( mat.getRow( 2 ) );
}

inline void print( const Matrix3 & mat, const char * name )
{
    printf("%s:\n", name);
    print( mat );
}

#endif

inline Matrix4::Matrix4( const Matrix4 & mat )
{
    mCol0 = mat.mCol0;
    mCol1 = mat.mCol1;
    mCol2 = mat.mCol2;
    mCol3 = mat.mCol3;
}

inline Matrix4::Matrix4( float scalar )
{
    mCol0 = Vector4( scalar );
    mCol1 = Vector4( scalar );
    mCol2 = Vector4( scalar );
    mCol3 = Vector4( scalar );
}

inline Matrix4::Matrix4( const Transform3 & mat )
{
    mCol0 = Vector4( mat.getCol0(), 0.0f );
    mCol1 = Vector4( mat.getCol1(), 0.0f );
    mCol2 = Vector4( mat.getCol2(), 0.0f );
    mCol3 = Vector4( mat.getCol3(), 1.0f );
}

inline Matrix4::Matrix4( const Vector4 & _col0, const Vector4 & _col1, const Vector4 & _col2, const Vector4 & _col3 )
{
    mCol0 = _col0;
    mCol1 = _col1;
    mCol2 = _col2;
    mCol3 = _col3;
}

inline Matrix4::Matrix4( const Matrix3 & mat, const Vector3 & translateVec )
{
    mCol0 = Vector4( mat.getCol0(), 0.0f );
    mCol1 = Vector4( mat.getCol1(), 0.0f );
    mCol2 = Vector4( mat.getCol2(), 0.0f );
    mCol3 = Vector4( translateVec, 1.0f );
}

inline Matrix4::Matrix4( const Quat & unitQuat, const Vector3 & translateVec )
{
    Matrix3 mat;
    mat = Matrix3( unitQuat );
    mCol0 = Vector4( mat.getCol0(), 0.0f );
    mCol1 = Vector4( mat.getCol1(), 0.0f );
    mCol2 = Vector4( mat.getCol2(), 0.0f );
    mCol3 = Vector4( translateVec, 1.0f );
}

inline Matrix4 & Matrix4::setCol0( const Vector4 & _col0 )
{
    mCol0 = _col0;
    return *this;
}

inline Matrix4 & Matrix4::setCol1( const Vector4 & _col1 )
{
    mCol1 = _col1;
    return *this;
}

inline Matrix4 & Matrix4::setCol2( const Vector4 & _col2 )
{
    mCol2 = _col2;
    return *this;
}

inline Matrix4 & Matrix4::setCol3( const Vector4 & _col3 )
{
    mCol3 = _col3;
    return *this;
}

inline Matrix4 & Matrix4::setCol( int col, const Vector4 & vec )
{
    *(&mCol0 + col) = vec;
    return *this;
}

inline Matrix4 & Matrix4::setRow( int row, const Vector4 & vec )
{
    mCol0.setElem( row, vec.getElem( 0 ) );
    mCol1.setElem( row, vec.getElem( 1 ) );
    mCol2.setElem( row, vec.getElem( 2 ) );
    mCol3.setElem( row, vec.getElem( 3 ) );
    return *this;
}

inline Matrix4 & Matrix4::setElem( int col, int row, float val )
{
    Vector4 tmpV3_0;
    tmpV3_0 = this->getCol( col );
    tmpV3_0.setElem( row, val );
    this->setCol( col, tmpV3_0 );
    return *this;
}

inline float Matrix4::getElem( int col, int row ) const
{
    return this->getCol( col ).getElem( row );
}

inline const Vector4 Matrix4::getCol0( ) const
{
    return mCol0;
}

inline const Vector4 Matrix4::getCol1( ) const
{
    return mCol1;
}

inline const Vector4 Matrix4::getCol2( ) const
{
    return mCol2;
}

inline const Vector4 Matrix4::getCol3( ) const
{
    return mCol3;
}

inline const Vector4 Matrix4::getCol( int col ) const
{
    return *(&mCol0 + col);
}

inline const Vector4 Matrix4::getRow( int row ) const
{
    return Vector4( mCol0.getElem( row ), mCol1.getElem( row ), mCol2.getElem( row ), mCol3.getElem( row ) );
}

inline Vector4 & Matrix4::operator []( int col )
{
    return *(&mCol0 + col);
}

inline const Vector4 Matrix4::operator []( int col ) const
{
    return *(&mCol0 + col);
}

inline Matrix4 & Matrix4::operator =( const Matrix4 & mat )
{
    mCol0 = mat.mCol0;
    mCol1 = mat.mCol1;
    mCol2 = mat.mCol2;
    mCol3 = mat.mCol3;
    return *this;
}

inline const Matrix4 transpose( const Matrix4 & mat )
{
    return Matrix4(
        Vector4( mat.getCol0().getX(), mat.getCol1().getX(), mat.getCol2().getX(), mat.getCol3().getX() ),
        Vector4( mat.getCol0().getY(), mat.getCol1().getY(), mat.getCol2().getY(), mat.getCol3().getY() ),
        Vector4( mat.getCol0().getZ(), mat.getCol1().getZ(), mat.getCol2().getZ(), mat.getCol3().getZ() ),
        Vector4( mat.getCol0().getW(), mat.getCol1().getW(), mat.getCol2().getW(), mat.getCol3().getW() )
    );
}

inline const Matrix4 inverse( const Matrix4 & mat )
{
    Vector4 res0, res1, res2, res3;
    float mA, mB, mC, mD, mE, mF, mG, mH, mI, mJ, mK, mL, mM, mN, mO, mP, tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, detInv;
    mA = mat.getCol0().getX();
    mB = mat.getCol0().getY();
    mC = mat.getCol0().getZ();
    mD = mat.getCol0().getW();
    mE = mat.getCol1().getX();
    mF = mat.getCol1().getY();
    mG = mat.getCol1().getZ();
    mH = mat.getCol1().getW();
    mI = mat.getCol2().getX();
    mJ = mat.getCol2().getY();
    mK = mat.getCol2().getZ();
    mL = mat.getCol2().getW();
    mM = mat.getCol3().getX();
    mN = mat.getCol3().getY();
    mO = mat.getCol3().getZ();
    mP = mat.getCol3().getW();
    tmp0 = ( ( mK * mD ) - ( mC * mL ) );
    tmp1 = ( ( mO * mH ) - ( mG * mP ) );
    tmp2 = ( ( mB * mK ) - ( mJ * mC ) );
    tmp3 = ( ( mF * mO ) - ( mN * mG ) );
    tmp4 = ( ( mJ * mD ) - ( mB * mL ) );
    tmp5 = ( ( mN * mH ) - ( mF * mP ) );
    res0.setX( ( ( ( mJ * tmp1 ) - ( mL * tmp3 ) ) - ( mK * tmp5 ) ) );
    res0.setY( ( ( ( mN * tmp0 ) - ( mP * tmp2 ) ) - ( mO * tmp4 ) ) );
    res0.setZ( ( ( ( mD * tmp3 ) + ( mC * tmp5 ) ) - ( mB * tmp1 ) ) );
    res0.setW( ( ( ( mH * tmp2 ) + ( mG * tmp4 ) ) - ( mF * tmp0 ) ) );
    detInv = ( 1.0f / ( ( ( ( mA * res0.getX() ) + ( mE * res0.getY() ) ) + ( mI * res0.getZ() ) ) + ( mM * res0.getW() ) ) );
    res1.setX( ( mI * tmp1 ) );
    res1.setY( ( mM * tmp0 ) );
    res1.setZ( ( mA * tmp1 ) );
    res1.setW( ( mE * tmp0 ) );
    res3.setX( ( mI * tmp3 ) );
    res3.setY( ( mM * tmp2 ) );
    res3.setZ( ( mA * tmp3 ) );
    res3.setW( ( mE * tmp2 ) );
    res2.setX( ( mI * tmp5 ) );
    res2.setY( ( mM * tmp4 ) );
    res2.setZ( ( mA * tmp5 ) );
    res2.setW( ( mE * tmp4 ) );
    tmp0 = ( ( mI * mB ) - ( mA * mJ ) );
    tmp1 = ( ( mM * mF ) - ( mE * mN ) );
    tmp2 = ( ( mI * mD ) - ( mA * mL ) );
    tmp3 = ( ( mM * mH ) - ( mE * mP ) );
    tmp4 = ( ( mI * mC ) - ( mA * mK ) );
    tmp5 = ( ( mM * mG ) - ( mE * mO ) );
    res2.setX( ( ( ( mL * tmp1 ) - ( mJ * tmp3 ) ) + res2.getX() ) );
    res2.setY( ( ( ( mP * tmp0 ) - ( mN * tmp2 ) ) + res2.getY() ) );
    res2.setZ( ( ( ( mB * tmp3 ) - ( mD * tmp1 ) ) - res2.getZ() ) );
    res2.setW( ( ( ( mF * tmp2 ) - ( mH * tmp0 ) ) - res2.getW() ) );
    res3.setX( ( ( ( mJ * tmp5 ) - ( mK * tmp1 ) ) + res3.getX() ) );
    res3.setY( ( ( ( mN * tmp4 ) - ( mO * tmp0 ) ) + res3.getY() ) );
    res3.setZ( ( ( ( mC * tmp1 ) - ( mB * tmp5 ) ) - res3.getZ() ) );
    res3.setW( ( ( ( mG * tmp0 ) - ( mF * tmp4 ) ) - res3.getW() ) );
    res1.setX( ( ( ( mK * tmp3 ) - ( mL * tmp5 ) ) - res1.getX() ) );
    res1.setY( ( ( ( mO * tmp2 ) - ( mP * tmp4 ) ) - res1.getY() ) );
    res1.setZ( ( ( ( mD * tmp5 ) - ( mC * tmp3 ) ) + res1.getZ() ) );
    res1.setW( ( ( ( mH * tmp4 ) - ( mG * tmp2 ) ) + res1.getW() ) );
    return Matrix4(
        ( res0 * detInv ),
        ( res1 * detInv ),
        ( res2 * detInv ),
        ( res3 * detInv )
    );
}

inline const Matrix4 affineInverse( const Matrix4 & mat )
{
    Transform3 affineMat;
    affineMat.setCol0( mat.getCol0().getXYZ( ) );
    affineMat.setCol1( mat.getCol1().getXYZ( ) );
    affineMat.setCol2( mat.getCol2().getXYZ( ) );
    affineMat.setCol3( mat.getCol3().getXYZ( ) );
    return Matrix4( inverse( affineMat ) );
}

inline const Matrix4 orthoInverse( const Matrix4 & mat )
{
    Transform3 affineMat;
    affineMat.setCol0( mat.getCol0().getXYZ( ) );
    affineMat.setCol1( mat.getCol1().getXYZ( ) );
    affineMat.setCol2( mat.getCol2().getXYZ( ) );
    affineMat.setCol3( mat.getCol3().getXYZ( ) );
    return Matrix4( orthoInverse( affineMat ) );
}

inline float determinant( const Matrix4 & mat )
{
    float dx, dy, dz, dw, mA, mB, mC, mD, mE, mF, mG, mH, mI, mJ, mK, mL, mM, mN, mO, mP, tmp0, tmp1, tmp2, tmp3, tmp4, tmp5;
    mA = mat.getCol0().getX();
    mB = mat.getCol0().getY();
    mC = mat.getCol0().getZ();
    mD = mat.getCol0().getW();
    mE = mat.getCol1().getX();
    mF = mat.getCol1().getY();
    mG = mat.getCol1().getZ();
    mH = mat.getCol1().getW();
    mI = mat.getCol2().getX();
    mJ = mat.getCol2().getY();
    mK = mat.getCol2().getZ();
    mL = mat.getCol2().getW();
    mM = mat.getCol3().getX();
    mN = mat.getCol3().getY();
    mO = mat.getCol3().getZ();
    mP = mat.getCol3().getW();
    tmp0 = ( ( mK * mD ) - ( mC * mL ) );
    tmp1 = ( ( mO * mH ) - ( mG * mP ) );
    tmp2 = ( ( mB * mK ) - ( mJ * mC ) );
    tmp3 = ( ( mF * mO ) - ( mN * mG ) );
    tmp4 = ( ( mJ * mD ) - ( mB * mL ) );
    tmp5 = ( ( mN * mH ) - ( mF * mP ) );
    dx = ( ( ( mJ * tmp1 ) - ( mL * tmp3 ) ) - ( mK * tmp5 ) );
    dy = ( ( ( mN * tmp0 ) - ( mP * tmp2 ) ) - ( mO * tmp4 ) );
    dz = ( ( ( mD * tmp3 ) + ( mC * tmp5 ) ) - ( mB * tmp1 ) );
    dw = ( ( ( mH * tmp2 ) + ( mG * tmp4 ) ) - ( mF * tmp0 ) );
    return ( ( ( ( mA * dx ) + ( mE * dy ) ) + ( mI * dz ) ) + ( mM * dw ) );
}

inline const Matrix4 Matrix4::operator +( const Matrix4 & mat ) const
{
    return Matrix4(
        ( mCol0 + mat.mCol0 ),
        ( mCol1 + mat.mCol1 ),
        ( mCol2 + mat.mCol2 ),
        ( mCol3 + mat.mCol3 )
    );
}

inline const Matrix4 Matrix4::operator -( const Matrix4 & mat ) const
{
    return Matrix4(
        ( mCol0 - mat.mCol0 ),
        ( mCol1 - mat.mCol1 ),
        ( mCol2 - mat.mCol2 ),
        ( mCol3 - mat.mCol3 )
    );
}

inline Matrix4 & Matrix4::operator +=( const Matrix4 & mat )
{
    *this = *this + mat;
    return *this;
}

inline Matrix4 & Matrix4::operator -=( const Matrix4 & mat )
{
    *this = *this - mat;
    return *this;
}

inline const Matrix4 Matrix4::operator -( ) const
{
    return Matrix4(
        ( -mCol0 ),
        ( -mCol1 ),
        ( -mCol2 ),
        ( -mCol3 )
    );
}

inline const Matrix4 absPerElem( const Matrix4 & mat )
{
    return Matrix4(
        absPerElem( mat.getCol0() ),
        absPerElem( mat.getCol1() ),
        absPerElem( mat.getCol2() ),
        absPerElem( mat.getCol3() )
    );
}

inline const Matrix4 Matrix4::operator *( float scalar ) const
{
    return Matrix4(
        ( mCol0 * scalar ),
        ( mCol1 * scalar ),
        ( mCol2 * scalar ),
        ( mCol3 * scalar )
    );
}

inline Matrix4 & Matrix4::operator *=( float scalar )
{
    *this = *this * scalar;
    return *this;
}

inline const Matrix4 operator *( float scalar, const Matrix4 & mat )
{
    return mat * scalar;
}

inline const Vector4 Matrix4::operator *( const Vector4 & vec ) const
{
    return Vector4(
        ( ( ( ( mCol0.getX() * vec.getX() ) + ( mCol1.getX() * vec.getY() ) ) + ( mCol2.getX() * vec.getZ() ) ) + ( mCol3.getX() * vec.getW() ) ),
        ( ( ( ( mCol0.getY() * vec.getX() ) + ( mCol1.getY() * vec.getY() ) ) + ( mCol2.getY() * vec.getZ() ) ) + ( mCol3.getY() * vec.getW() ) ),
        ( ( ( ( mCol0.getZ() * vec.getX() ) + ( mCol1.getZ() * vec.getY() ) ) + ( mCol2.getZ() * vec.getZ() ) ) + ( mCol3.getZ() * vec.getW() ) ),
        ( ( ( ( mCol0.getW() * vec.getX() ) + ( mCol1.getW() * vec.getY() ) ) + ( mCol2.getW() * vec.getZ() ) ) + ( mCol3.getW() * vec.getW() ) )
    );
}

inline const Vector4 Matrix4::operator *( const Vector3 & vec ) const
{
    return Vector4(
        ( ( ( mCol0.getX() * vec.getX() ) + ( mCol1.getX() * vec.getY() ) ) + ( mCol2.getX() * vec.getZ() ) ),
        ( ( ( mCol0.getY() * vec.getX() ) + ( mCol1.getY() * vec.getY() ) ) + ( mCol2.getY() * vec.getZ() ) ),
        ( ( ( mCol0.getZ() * vec.getX() ) + ( mCol1.getZ() * vec.getY() ) ) + ( mCol2.getZ() * vec.getZ() ) ),
        ( ( ( mCol0.getW() * vec.getX() ) + ( mCol1.getW() * vec.getY() ) ) + ( mCol2.getW() * vec.getZ() ) )
    );
}

inline const Vector4 Matrix4::operator *( const Point3 & pnt ) const
{
    return Vector4(
        ( ( ( ( mCol0.getX() * pnt.getX() ) + ( mCol1.getX() * pnt.getY() ) ) + ( mCol2.getX() * pnt.getZ() ) ) + mCol3.getX() ),
        ( ( ( ( mCol0.getY() * pnt.getX() ) + ( mCol1.getY() * pnt.getY() ) ) + ( mCol2.getY() * pnt.getZ() ) ) + mCol3.getY() ),
        ( ( ( ( mCol0.getZ() * pnt.getX() ) + ( mCol1.getZ() * pnt.getY() ) ) + ( mCol2.getZ() * pnt.getZ() ) ) + mCol3.getZ() ),
        ( ( ( ( mCol0.getW() * pnt.getX() ) + ( mCol1.getW() * pnt.getY() ) ) + ( mCol2.getW() * pnt.getZ() ) ) + mCol3.getW() )
    );
}

inline const Matrix4 Matrix4::operator *( const Matrix4 & mat ) const
{
    return Matrix4(
        ( *this * mat.mCol0 ),
        ( *this * mat.mCol1 ),
        ( *this * mat.mCol2 ),
        ( *this * mat.mCol3 )
    );
}

inline Matrix4 & Matrix4::operator *=( const Matrix4 & mat )
{
    *this = *this * mat;
    return *this;
}

inline const Matrix4 Matrix4::operator *( const Transform3 & tfrm ) const
{
    return Matrix4(
        ( *this * tfrm.getCol0() ),
        ( *this * tfrm.getCol1() ),
        ( *this * tfrm.getCol2() ),
        ( *this * Point3( tfrm.getCol3() ) )
    );
}

inline Matrix4 & Matrix4::operator *=( const Transform3 & tfrm )
{
    *this = *this * tfrm;
    return *this;
}

inline const Matrix4 mulPerElem( const Matrix4 & mat0, const Matrix4 & mat1 )
{
    return Matrix4(
        mulPerElem( mat0.getCol0(), mat1.getCol0() ),
        mulPerElem( mat0.getCol1(), mat1.getCol1() ),
        mulPerElem( mat0.getCol2(), mat1.getCol2() ),
        mulPerElem( mat0.getCol3(), mat1.getCol3() )
    );
}

inline const Matrix4 Matrix4::identity( )
{
    return Matrix4(
        Vector4::xAxis( ),
        Vector4::yAxis( ),
        Vector4::zAxis( ),
        Vector4::wAxis( )
    );
}

inline Matrix4 & Matrix4::setUpper3x3( const Matrix3 & mat3 )
{
    mCol0.setXYZ( mat3.getCol0() );
    mCol1.setXYZ( mat3.getCol1() );
    mCol2.setXYZ( mat3.getCol2() );
    return *this;
}

inline const Matrix3 Matrix4::getUpper3x3( ) const
{
    return Matrix3(
        mCol0.getXYZ( ),
        mCol1.getXYZ( ),
        mCol2.getXYZ( )
    );
}

inline Matrix4 & Matrix4::setTranslation( const Vector3 & translateVec )
{
    mCol3.setXYZ( translateVec );
    return *this;
}

inline const Vector3 Matrix4::getTranslation( ) const
{
    return mCol3.getXYZ( );
}

inline const Matrix4 Matrix4::rotationX( float radians )
{
    float s, c;
    s = sinf( radians );
    c = cosf( radians );
    return Matrix4(
        Vector4::xAxis( ),
        Vector4( 0.0f, c, s, 0.0f ),
        Vector4( 0.0f, -s, c, 0.0f ),
        Vector4::wAxis( )
    );
}

inline const Matrix4 Matrix4::rotationY( float radians )
{
    float s, c;
    s = sinf( radians );
    c = cosf( radians );
    return Matrix4(
        Vector4( c, 0.0f, -s, 0.0f ),
        Vector4::yAxis( ),
        Vector4( s, 0.0f, c, 0.0f ),
        Vector4::wAxis( )
    );
}

inline const Matrix4 Matrix4::rotationZ( float radians )
{
    float s, c;
    s = sinf( radians );
    c = cosf( radians );
    return Matrix4(
        Vector4( c, s, 0.0f, 0.0f ),
        Vector4( -s, c, 0.0f, 0.0f ),
        Vector4::zAxis( ),
        Vector4::wAxis( )
    );
}

inline const Matrix4 Matrix4::rotationZYX( const Vector3 & radiansXYZ )
{
    float sX, cX, sY, cY, sZ, cZ, tmp0, tmp1;
    sX = sinf( radiansXYZ.getX() );
    cX = cosf( radiansXYZ.getX() );
    sY = sinf( radiansXYZ.getY() );
    cY = cosf( radiansXYZ.getY() );
    sZ = sinf( radiansXYZ.getZ() );
    cZ = cosf( radiansXYZ.getZ() );
    tmp0 = ( cZ * sY );
    tmp1 = ( sZ * sY );
    return Matrix4(
        Vector4( ( cZ * cY ), ( sZ * cY ), -sY, 0.0f ),
        Vector4( ( ( tmp0 * sX ) - ( sZ * cX ) ), ( ( tmp1 * sX ) + ( cZ * cX ) ), ( cY * sX ), 0.0f ),
        Vector4( ( ( tmp0 * cX ) + ( sZ * sX ) ), ( ( tmp1 * cX ) - ( cZ * sX ) ), ( cY * cX ), 0.0f ),
        Vector4::wAxis( )
    );
}

inline const Matrix4 Matrix4::rotation( float radians, const Vector3 & unitVec )
{
    float x, y, z, s, c, oneMinusC, xy, yz, zx;
    s = sinf( radians );
    c = cosf( radians );
    x = unitVec.getX();
    y = unitVec.getY();
    z = unitVec.getZ();
    xy = ( x * y );
    yz = ( y * z );
    zx = ( z * x );
    oneMinusC = ( 1.0f - c );
    return Matrix4(
        Vector4( ( ( ( x * x ) * oneMinusC ) + c ), ( ( xy * oneMinusC ) + ( z * s ) ), ( ( zx * oneMinusC ) - ( y * s ) ), 0.0f ),
        Vector4( ( ( xy * oneMinusC ) - ( z * s ) ), ( ( ( y * y ) * oneMinusC ) + c ), ( ( yz * oneMinusC ) + ( x * s ) ), 0.0f ),
        Vector4( ( ( zx * oneMinusC ) + ( y * s ) ), ( ( yz * oneMinusC ) - ( x * s ) ), ( ( ( z * z ) * oneMinusC ) + c ), 0.0f ),
        Vector4::wAxis( )
    );
}

inline const Matrix4 Matrix4::rotation( const Quat & unitQuat )
{
    return Matrix4( Transform3::rotation( unitQuat ) );
}

inline const Matrix4 Matrix4::scale( const Vector3 & scaleVec )
{
    return Matrix4(
        Vector4( scaleVec.getX(), 0.0f, 0.0f, 0.0f ),
        Vector4( 0.0f, scaleVec.getY(), 0.0f, 0.0f ),
        Vector4( 0.0f, 0.0f, scaleVec.getZ(), 0.0f ),
        Vector4::wAxis( )
    );
}

inline const Matrix4 appendScale( const Matrix4 & mat, const Vector3 & scaleVec )
{
    return Matrix4(
        ( mat.getCol0() * scaleVec.getX( ) ),
        ( mat.getCol1() * scaleVec.getY( ) ),
        ( mat.getCol2() * scaleVec.getZ( ) ),
        mat.getCol3()
    );
}

inline const Matrix4 prependScale( const Vector3 & scaleVec, const Matrix4 & mat )
{
    Vector4 scale4;
    scale4 = Vector4( scaleVec, 1.0f );
    return Matrix4(
        mulPerElem( mat.getCol0(), scale4 ),
        mulPerElem( mat.getCol1(), scale4 ),
        mulPerElem( mat.getCol2(), scale4 ),
        mulPerElem( mat.getCol3(), scale4 )
    );
}

inline const Matrix4 Matrix4::translation( const Vector3 & translateVec )
{
    return Matrix4(
        Vector4::xAxis( ),
        Vector4::yAxis( ),
        Vector4::zAxis( ),
        Vector4( translateVec, 1.0f )
    );
}

inline const Matrix4 Matrix4::lookAt( const Point3 & eyePos, const Point3 & lookAtPos, const Vector3 & upVec )
{
    Matrix4 m4EyeFrame;
    Vector3 v3X, v3Y, v3Z;
    v3Y = normalize( upVec );
    v3Z = normalize( ( eyePos - lookAtPos ) );
    v3X = normalize( cross( v3Y, v3Z ) );
    v3Y = cross( v3Z, v3X );
    m4EyeFrame = Matrix4( Vector4( v3X ), Vector4( v3Y ), Vector4( v3Z ), Vector4( eyePos ) );
    return orthoInverse( m4EyeFrame );
}

inline const Matrix4 Matrix4::perspective( float fovyRadians, float aspect, float zNear, float zFar )
{
    float f, rangeInv;
    f = tanf( ( (float)( _VECTORMATH_PI_OVER_2 ) - ( 0.5f * fovyRadians ) ) );
    rangeInv = ( 1.0f / ( zNear - zFar ) );
    return Matrix4(
        Vector4( ( f / aspect ), 0.0f, 0.0f, 0.0f ),
        Vector4( 0.0f, f, 0.0f, 0.0f ),
        Vector4( 0.0f, 0.0f, ( ( zNear + zFar ) * rangeInv ), -1.0f ),
        Vector4( 0.0f, 0.0f, ( ( ( zNear * zFar ) * rangeInv ) * 2.0f ), 0.0f )
    );
}

inline const Matrix4 Matrix4::frustum( float left, float right, float bottom, float top, float zNear, float zFar )
{
    float sum_rl, sum_tb, sum_nf, inv_rl, inv_tb, inv_nf, n2;
    sum_rl = ( right + left );
    sum_tb = ( top + bottom );
    sum_nf = ( zNear + zFar );
    inv_rl = ( 1.0f / ( right - left ) );
    inv_tb = ( 1.0f / ( top - bottom ) );
    inv_nf = ( 1.0f / ( zNear - zFar ) );
    n2 = ( zNear + zNear );
    return Matrix4(
        Vector4( ( n2 * inv_rl ), 0.0f, 0.0f, 0.0f ),
        Vector4( 0.0f, ( n2 * inv_tb ), 0.0f, 0.0f ),
        Vector4( ( sum_rl * inv_rl ), ( sum_tb * inv_tb ), ( sum_nf * inv_nf ), -1.0f ),
        Vector4( 0.0f, 0.0f, ( ( n2 * inv_nf ) * zFar ), 0.0f )
    );
}

inline const Matrix4 Matrix4::orthographic( float left, float right, float bottom, float top, float zNear, float zFar )
{
    float sum_rl, sum_tb, sum_nf, inv_rl, inv_tb, inv_nf;
    sum_rl = ( right + left );
    sum_tb = ( top + bottom );
    sum_nf = ( zNear + zFar );
    inv_rl = ( 1.0f / ( right - left ) );
    inv_tb = ( 1.0f / ( top - bottom ) );
    inv_nf = ( 1.0f / ( zNear - zFar ) );
    return Matrix4(
        Vector4( ( inv_rl + inv_rl ), 0.0f, 0.0f, 0.0f ),
        Vector4( 0.0f, ( inv_tb + inv_tb ), 0.0f, 0.0f ),
        Vector4( 0.0f, 0.0f, ( inv_nf + inv_nf ), 0.0f ),
        Vector4( ( -sum_rl * inv_rl ), ( -sum_tb * inv_tb ), ( sum_nf * inv_nf ), 1.0f )
    );
}

inline const Matrix4 select( const Matrix4 & mat0, const Matrix4 & mat1, bool select1 )
{
    return Matrix4(
        select( mat0.getCol0(), mat1.getCol0(), select1 ),
        select( mat0.getCol1(), mat1.getCol1(), select1 ),
        select( mat0.getCol2(), mat1.getCol2(), select1 ),
        select( mat0.getCol3(), mat1.getCol3(), select1 )
    );
}

#ifdef _VECTORMATH_DEBUG

inline void print( const Matrix4 & mat )
{
    print( mat.getRow( 0 ) );
    print( mat.getRow( 1 ) );
    print( mat.getRow( 2 ) );
    print( mat.getRow( 3 ) );
}

inline void print( const Matrix4 & mat, const char * name )
{
    printf("%s:\n", name);
    print( mat );
}

#endif

inline Transform3::Transform3( const Transform3 & tfrm )
{
    mCol0 = tfrm.mCol0;
    mCol1 = tfrm.mCol1;
    mCol2 = tfrm.mCol2;
    mCol3 = tfrm.mCol3;
}

inline Transform3::Transform3( float scalar )
{
    mCol0 = Vector3( scalar );
    mCol1 = Vector3( scalar );
    mCol2 = Vector3( scalar );
    mCol3 = Vector3( scalar );
}

inline Transform3::Transform3( const Vector3 & _col0, const Vector3 & _col1, const Vector3 & _col2, const Vector3 & _col3 )
{
    mCol0 = _col0;
    mCol1 = _col1;
    mCol2 = _col2;
    mCol3 = _col3;
}

inline Transform3::Transform3( const Matrix3 & tfrm, const Vector3 & translateVec )
{
    this->setUpper3x3( tfrm );
    this->setTranslation( translateVec );
}

inline Transform3::Transform3( const Quat & unitQuat, const Vector3 & translateVec )
{
    this->setUpper3x3( Matrix3( unitQuat ) );
    this->setTranslation( translateVec );
}

inline Transform3 & Transform3::setCol0( const Vector3 & _col0 )
{
    mCol0 = _col0;
    return *this;
}

inline Transform3 & Transform3::setCol1( const Vector3 & _col1 )
{
    mCol1 = _col1;
    return *this;
}

inline Transform3 & Transform3::setCol2( const Vector3 & _col2 )
{
    mCol2 = _col2;
    return *this;
}

inline Transform3 & Transform3::setCol3( const Vector3 & _col3 )
{
    mCol3 = _col3;
    return *this;
}

inline Transform3 & Transform3::setCol( int col, const Vector3 & vec )
{
    *(&mCol0 + col) = vec;
    return *this;
}

inline Transform3 & Transform3::setRow( int row, const Vector4 & vec )
{
    mCol0.setElem( row, vec.getElem( 0 ) );
    mCol1.setElem( row, vec.getElem( 1 ) );
    mCol2.setElem( row, vec.getElem( 2 ) );
    mCol3.setElem( row, vec.getElem( 3 ) );
    return *this;
}

inline Transform3 & Transform3::setElem( int col, int row, float val )
{
    Vector3 tmpV3_0;
    tmpV3_0 = this->getCol( col );
    tmpV3_0.setElem( row, val );
    this->setCol( col, tmpV3_0 );
    return *this;
}

inline float Transform3::getElem( int col, int row ) const
{
    return this->getCol( col ).getElem( row );
}

inline const Vector3 Transform3::getCol0( ) const
{
    return mCol0;
}

inline const Vector3 Transform3::getCol1( ) const
{
    return mCol1;
}

inline const Vector3 Transform3::getCol2( ) const
{
    return mCol2;
}

inline const Vector3 Transform3::getCol3( ) const
{
    return mCol3;
}

inline const Vector3 Transform3::getCol( int col ) const
{
    return *(&mCol0 + col);
}

inline const Vector4 Transform3::getRow( int row ) const
{
    return Vector4( mCol0.getElem( row ), mCol1.getElem( row ), mCol2.getElem( row ), mCol3.getElem( row ) );
}

inline Vector3 & Transform3::operator []( int col )
{
    return *(&mCol0 + col);
}

inline const Vector3 Transform3::operator []( int col ) const
{
    return *(&mCol0 + col);
}

inline Transform3 & Transform3::operator =( const Transform3 & tfrm )
{
    mCol0 = tfrm.mCol0;
    mCol1 = tfrm.mCol1;
    mCol2 = tfrm.mCol2;
    mCol3 = tfrm.mCol3;
    return *this;
}

inline const Transform3 inverse( const Transform3 & tfrm )
{
    Vector3 tmp0, tmp1, tmp2, inv0, inv1, inv2;
    float detinv;
    tmp0 = cross( tfrm.getCol1(), tfrm.getCol2() );
    tmp1 = cross( tfrm.getCol2(), tfrm.getCol0() );
    tmp2 = cross( tfrm.getCol0(), tfrm.getCol1() );
    detinv = ( 1.0f / dot( tfrm.getCol2(), tmp2 ) );
    inv0 = Vector3( ( tmp0.getX() * detinv ), ( tmp1.getX() * detinv ), ( tmp2.getX() * detinv ) );
    inv1 = Vector3( ( tmp0.getY() * detinv ), ( tmp1.getY() * detinv ), ( tmp2.getY() * detinv ) );
    inv2 = Vector3( ( tmp0.getZ() * detinv ), ( tmp1.getZ() * detinv ), ( tmp2.getZ() * detinv ) );
    return Transform3(
        inv0,
        inv1,
        inv2,
        Vector3( ( -( ( inv0 * tfrm.getCol3().getX() ) + ( ( inv1 * tfrm.getCol3().getY() ) + ( inv2 * tfrm.getCol3().getZ() ) ) ) ) )
    );
}

inline const Transform3 orthoInverse( const Transform3 & tfrm )
{
    Vector3 inv0, inv1, inv2;
    inv0 = Vector3( tfrm.getCol0().getX(), tfrm.getCol1().getX(), tfrm.getCol2().getX() );
    inv1 = Vector3( tfrm.getCol0().getY(), tfrm.getCol1().getY(), tfrm.getCol2().getY() );
    inv2 = Vector3( tfrm.getCol0().getZ(), tfrm.getCol1().getZ(), tfrm.getCol2().getZ() );
    return Transform3(
        inv0,
        inv1,
        inv2,
        Vector3( ( -( ( inv0 * tfrm.getCol3().getX() ) + ( ( inv1 * tfrm.getCol3().getY() ) + ( inv2 * tfrm.getCol3().getZ() ) ) ) ) )
    );
}

inline const Transform3 absPerElem( const Transform3 & tfrm )
{
    return Transform3(
        absPerElem( tfrm.getCol0() ),
        absPerElem( tfrm.getCol1() ),
        absPerElem( tfrm.getCol2() ),
        absPerElem( tfrm.getCol3() )
    );
}

inline const Vector3 Transform3::operator *( const Vector3 & vec ) const
{
    return Vector3(
        ( ( ( mCol0.getX() * vec.getX() ) + ( mCol1.getX() * vec.getY() ) ) + ( mCol2.getX() * vec.getZ() ) ),
        ( ( ( mCol0.getY() * vec.getX() ) + ( mCol1.getY() * vec.getY() ) ) + ( mCol2.getY() * vec.getZ() ) ),
        ( ( ( mCol0.getZ() * vec.getX() ) + ( mCol1.getZ() * vec.getY() ) ) + ( mCol2.getZ() * vec.getZ() ) )
    );
}

inline const Point3 Transform3::operator *( const Point3 & pnt ) const
{
    return Point3(
        ( ( ( ( mCol0.getX() * pnt.getX() ) + ( mCol1.getX() * pnt.getY() ) ) + ( mCol2.getX() * pnt.getZ() ) ) + mCol3.getX() ),
        ( ( ( ( mCol0.getY() * pnt.getX() ) + ( mCol1.getY() * pnt.getY() ) ) + ( mCol2.getY() * pnt.getZ() ) ) + mCol3.getY() ),
        ( ( ( ( mCol0.getZ() * pnt.getX() ) + ( mCol1.getZ() * pnt.getY() ) ) + ( mCol2.getZ() * pnt.getZ() ) ) + mCol3.getZ() )
    );
}

inline const Transform3 Transform3::operator *( const Transform3 & tfrm ) const
{
    return Transform3(
        ( *this * tfrm.mCol0 ),
        ( *this * tfrm.mCol1 ),
        ( *this * tfrm.mCol2 ),
        Vector3( ( *this * Point3( tfrm.mCol3 ) ) )
    );
}

inline Transform3 & Transform3::operator *=( const Transform3 & tfrm )
{
    *this = *this * tfrm;
    return *this;
}

inline const Transform3 mulPerElem( const Transform3 & tfrm0, const Transform3 & tfrm1 )
{
    return Transform3(
        mulPerElem( tfrm0.getCol0(), tfrm1.getCol0() ),
        mulPerElem( tfrm0.getCol1(), tfrm1.getCol1() ),
        mulPerElem( tfrm0.getCol2(), tfrm1.getCol2() ),
        mulPerElem( tfrm0.getCol3(), tfrm1.getCol3() )
    );
}

inline const Transform3 Transform3::identity( )
{
    return Transform3(
        Vector3::xAxis( ),
        Vector3::yAxis( ),
        Vector3::zAxis( ),
        Vector3( 0.0f )
    );
}

inline Transform3 & Transform3::setUpper3x3( const Matrix3 & tfrm )
{
    mCol0 = tfrm.getCol0();
    mCol1 = tfrm.getCol1();
    mCol2 = tfrm.getCol2();
    return *this;
}

inline const Matrix3 Transform3::getUpper3x3( ) const
{
    return Matrix3( mCol0, mCol1, mCol2 );
}

inline Transform3 & Transform3::setTranslation( const Vector3 & translateVec )
{
    mCol3 = translateVec;
    return *this;
}

inline const Vector3 Transform3::getTranslation( ) const
{
    return mCol3;
}

inline const Transform3 Transform3::rotationX( float radians )
{
    float s, c;
    s = sinf( radians );
    c = cosf( radians );
    return Transform3(
        Vector3::xAxis( ),
        Vector3( 0.0f, c, s ),
        Vector3( 0.0f, -s, c ),
        Vector3( 0.0f )
    );
}

inline const Transform3 Transform3::rotationY( float radians )
{
    float s, c;
    s = sinf( radians );
    c = cosf( radians );
    return Transform3(
        Vector3( c, 0.0f, -s ),
        Vector3::yAxis( ),
        Vector3( s, 0.0f, c ),
        Vector3( 0.0f )
    );
}

inline const Transform3 Transform3::rotationZ( float radians )
{
    float s, c;
    s = sinf( radians );
    c = cosf( radians );
    return Transform3(
        Vector3( c, s, 0.0f ),
        Vector3( -s, c, 0.0f ),
        Vector3::zAxis( ),
        Vector3( 0.0f )
    );
}

inline const Transform3 Transform3::rotationZYX( const Vector3 & radiansXYZ )
{
    float sX, cX, sY, cY, sZ, cZ, tmp0, tmp1;
    sX = sinf( radiansXYZ.getX() );
    cX = cosf( radiansXYZ.getX() );
    sY = sinf( radiansXYZ.getY() );
    cY = cosf( radiansXYZ.getY() );
    sZ = sinf( radiansXYZ.getZ() );
    cZ = cosf( radiansXYZ.getZ() );
    tmp0 = ( cZ * sY );
    tmp1 = ( sZ * sY );
    return Transform3(
        Vector3( ( cZ * cY ), ( sZ * cY ), -sY ),
        Vector3( ( ( tmp0 * sX ) - ( sZ * cX ) ), ( ( tmp1 * sX ) + ( cZ * cX ) ), ( cY * sX ) ),
        Vector3( ( ( tmp0 * cX ) + ( sZ * sX ) ), ( ( tmp1 * cX ) - ( cZ * sX ) ), ( cY * cX ) ),
        Vector3( 0.0f )
    );
}

inline const Transform3 Transform3::rotation( float radians, const Vector3 & unitVec )
{
    return Transform3( Matrix3::rotation( radians, unitVec ), Vector3( 0.0f ) );
}

inline const Transform3 Transform3::rotation( const Quat & unitQuat )
{
    return Transform3( Matrix3( unitQuat ), Vector3( 0.0f ) );
}

inline const Transform3 Transform3::scale( const Vector3 & scaleVec )
{
    return Transform3(
        Vector3( scaleVec.getX(), 0.0f, 0.0f ),
        Vector3( 0.0f, scaleVec.getY(), 0.0f ),
        Vector3( 0.0f, 0.0f, scaleVec.getZ() ),
        Vector3( 0.0f )
    );
}

inline const Transform3 appendScale( const Transform3 & tfrm, const Vector3 & scaleVec )
{
    return Transform3(
        ( tfrm.getCol0() * scaleVec.getX( ) ),
        ( tfrm.getCol1() * scaleVec.getY( ) ),
        ( tfrm.getCol2() * scaleVec.getZ( ) ),
        tfrm.getCol3()
    );
}

inline const Transform3 prependScale( const Vector3 & scaleVec, const Transform3 & tfrm )
{
    return Transform3(
        mulPerElem( tfrm.getCol0(), scaleVec ),
        mulPerElem( tfrm.getCol1(), scaleVec ),
        mulPerElem( tfrm.getCol2(), scaleVec ),
        mulPerElem( tfrm.getCol3(), scaleVec )
    );
}

inline const Transform3 Transform3::translation( const Vector3 & translateVec )
{
    return Transform3(
        Vector3::xAxis( ),
        Vector3::yAxis( ),
        Vector3::zAxis( ),
        translateVec
    );
}

inline const Transform3 select( const Transform3 & tfrm0, const Transform3 & tfrm1, bool select1 )
{
    return Transform3(
        select( tfrm0.getCol0(), tfrm1.getCol0(), select1 ),
        select( tfrm0.getCol1(), tfrm1.getCol1(), select1 ),
        select( tfrm0.getCol2(), tfrm1.getCol2(), select1 ),
        select( tfrm0.getCol3(), tfrm1.getCol3(), select1 )
    );
}

#ifdef _VECTORMATH_DEBUG

inline void print( const Transform3 & tfrm )
{
    print( tfrm.getRow( 0 ) );
    print( tfrm.getRow( 1 ) );
    print( tfrm.getRow( 2 ) );
}

inline void print( const Transform3 & tfrm, const char * name )
{
    printf("%s:\n", name);
    print( tfrm );
}

#endif

inline Quat::Quat( const Matrix3 & tfrm )
{
    float trace, radicand, scale, xx, yx, zx, xy, yy, zy, xz, yz, zz, tmpx, tmpy, tmpz, tmpw, qx, qy, qz, qw;
    int negTrace, ZgtX, ZgtY, YgtX;
    int largestXorY, largestYorZ, largestZorX;

    xx = tfrm.getCol0().getX();
    yx = tfrm.getCol0().getY();
    zx = tfrm.getCol0().getZ();
    xy = tfrm.getCol1().getX();
    yy = tfrm.getCol1().getY();
    zy = tfrm.getCol1().getZ();
    xz = tfrm.getCol2().getX();
    yz = tfrm.getCol2().getY();
    zz = tfrm.getCol2().getZ();

    trace = ( ( xx + yy ) + zz );

    negTrace = ( trace < 0.0f );
    ZgtX = zz > xx;
    ZgtY = zz > yy;
    YgtX = yy > xx;
    largestXorY = ( !ZgtX || !ZgtY ) && negTrace;
    largestYorZ = ( YgtX || ZgtX ) && negTrace;
    largestZorX = ( ZgtY || !YgtX ) && negTrace;
    
    if ( largestXorY )
    {
        zz = -zz;
        xy = -xy;
    }
    if ( largestYorZ )
    {
        xx = -xx;
        yz = -yz;
    }
    if ( largestZorX )
    {
        yy = -yy;
        zx = -zx;
    }

    radicand = ( ( ( xx + yy ) + zz ) + 1.0f );
    scale = ( 0.5f * ( 1.0f / sqrtf( radicand ) ) );

    tmpx = ( ( zy - yz ) * scale );
    tmpy = ( ( xz - zx ) * scale );
    tmpz = ( ( yx - xy ) * scale );
    tmpw = ( radicand * scale );
    qx = tmpx;
    qy = tmpy;
    qz = tmpz;
    qw = tmpw;

    if ( largestXorY )
    {
        qx = tmpw;
        qy = tmpz;
        qz = tmpy;
        qw = tmpx;
    }
    if ( largestYorZ )
    {
        tmpx = qx;
        tmpz = qz;
        qx = qy;
        qy = tmpx;
        qz = qw;
        qw = tmpz;
    }

    mXYZW[0] = qx;
    mXYZW[1] = qy;
    mXYZW[2] = qz;
    mXYZW[3] = qw;
}

inline const Matrix3 outer( const Vector3 & tfrm0, const Vector3 & tfrm1 )
{
    return Matrix3(
        ( tfrm0 * tfrm1.getX( ) ),
        ( tfrm0 * tfrm1.getY( ) ),
        ( tfrm0 * tfrm1.getZ( ) )
    );
}

inline const Matrix4 outer( const Vector4 & tfrm0, const Vector4 & tfrm1 )
{
    return Matrix4(
        ( tfrm0 * tfrm1.getX( ) ),
        ( tfrm0 * tfrm1.getY( ) ),
        ( tfrm0 * tfrm1.getZ( ) ),
        ( tfrm0 * tfrm1.getW( ) )
    );
}

inline const Vector3 rowMul( const Vector3 & vec, const Matrix3 & mat )
{
    return Vector3(
        ( ( ( vec.getX() * mat.getCol0().getX() ) + ( vec.getY() * mat.getCol0().getY() ) ) + ( vec.getZ() * mat.getCol0().getZ() ) ),
        ( ( ( vec.getX() * mat.getCol1().getX() ) + ( vec.getY() * mat.getCol1().getY() ) ) + ( vec.getZ() * mat.getCol1().getZ() ) ),
        ( ( ( vec.getX() * mat.getCol2().getX() ) + ( vec.getY() * mat.getCol2().getY() ) ) + ( vec.getZ() * mat.getCol2().getZ() ) )
    );
}

inline const Matrix3 crossMatrix( const Vector3 & vec )
{
    return Matrix3(
        Vector3( 0.0f, vec.getZ(), -vec.getY() ),
        Vector3( -vec.getZ(), 0.0f, vec.getX() ),
        Vector3( vec.getY(), -vec.getX(), 0.0f )
    );
}

inline const Matrix3 crossMatrixMul( const Vector3 & vec, const Matrix3 & mat )
{
    return Matrix3( cross( vec, mat.getCol0() ), cross( vec, mat.getCol1() ), cross( vec, mat.getCol2() ) );
}

} // namespace Aos
} // namespace Vectormath

#endif