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/*
===========================================================================
Doom 3 BFG Edition GPL Source Code
Copyright (C) 1993-2012 id Software LLC, a ZeniMax Media company.
This file is part of the Doom 3 BFG Edition GPL Source Code ("Doom 3 BFG Edition Source Code").
Doom 3 BFG Edition Source Code is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
Doom 3 BFG Edition Source Code is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with Doom 3 BFG Edition Source Code. If not, see <http://www.gnu.org/licenses/>.
In addition, the Doom 3 BFG Edition Source Code is also subject to certain additional terms. You should have received a copy of these additional terms immediately following the terms and conditions of the GNU General Public License which accompanied the Doom 3 BFG Edition Source Code. If not, please request a copy in writing from id Software at the address below.
If you have questions concerning this license or the applicable additional terms, you may contact in writing id Software LLC, c/o ZeniMax Media Inc., Suite 120, Rockville, Maryland 20850 USA.
===========================================================================
*/
#pragma hdrstop
#include "precompiled.h"
//===============================================================
//
// idMat2
//
//===============================================================
idMat2 mat2_zero( idVec2( 0, 0 ), idVec2( 0, 0 ) );
idMat2 mat2_identity( idVec2( 1, 0 ), idVec2( 0, 1 ) );
/*
============
idMat2::InverseSelf
============
*/
bool idMat2::InverseSelf()
{
// 2+4 = 6 multiplications
// 1 division
double det, invDet, a;
det = mat[0][0] * mat[1][1] - mat[0][1] * mat[1][0];
if( idMath::Fabs( det ) < MATRIX_INVERSE_EPSILON )
{
return false;
}
invDet = 1.0f / det;
a = mat[0][0];
mat[0][0] = mat[1][1] * invDet;
mat[0][1] = - mat[0][1] * invDet;
mat[1][0] = - mat[1][0] * invDet;
mat[1][1] = a * invDet;
return true;
}
/*
============
idMat2::InverseFastSelf
============
*/
bool idMat2::InverseFastSelf()
{
#if 1
// 2+4 = 6 multiplications
// 1 division
double det, invDet, a;
det = mat[0][0] * mat[1][1] - mat[0][1] * mat[1][0];
if( idMath::Fabs( det ) < MATRIX_INVERSE_EPSILON )
{
return false;
}
invDet = 1.0f / det;
a = mat[0][0];
mat[0][0] = mat[1][1] * invDet;
mat[0][1] = - mat[0][1] * invDet;
mat[1][0] = - mat[1][0] * invDet;
mat[1][1] = a * invDet;
return true;
#else
// 2*4 = 8 multiplications
// 2 division
float* mat = reinterpret_cast<float*>( this );
double d, di;
float s;
di = mat[0];
s = di;
mat[0 * 2 + 0] = d = 1.0f / di;
mat[0 * 2 + 1] *= d;
d = -d;
mat[1 * 2 + 0] *= d;
d = mat[1 * 2 + 0] * di;
mat[1 * 2 + 1] += mat[0 * 2 + 1] * d;
di = mat[1 * 2 + 1];
s *= di;
mat[1 * 2 + 1] = d = 1.0f / di;
mat[1 * 2 + 0] *= d;
d = -d;
mat[0 * 2 + 1] *= d;
d = mat[0 * 2 + 1] * di;
mat[0 * 2 + 0] += mat[1 * 2 + 0] * d;
return ( s != 0.0f && !IEEE_FLT_IS_NAN( s ) );
#endif
}
/*
=============
idMat2::ToString
=============
*/
const char* idMat2::ToString( int precision ) const
{
return idStr::FloatArrayToString( ToFloatPtr(), GetDimension(), precision );
}
//===============================================================
//
// idMat3
//
//===============================================================
idMat3 mat3_zero( idVec3( 0, 0, 0 ), idVec3( 0, 0, 0 ), idVec3( 0, 0, 0 ) );
idMat3 mat3_identity( idVec3( 1, 0, 0 ), idVec3( 0, 1, 0 ), idVec3( 0, 0, 1 ) );
/*
========================
idMat3::ToAngles
returns the pitch/yaw/roll each in the range [-180, 180] degrees
========================
*/
idAngles idMat3::ToAngles() const
{
idAngles angles;
float s = idMath::Sqrt( mat[0][0] * mat[0][0] + mat[0][1] * mat[0][1] );
if( s > idMath::FLT_EPSILON )
{
angles.pitch = RAD2DEG( - idMath::ATan( mat[0][2], s ) );
angles.yaw = RAD2DEG( idMath::ATan( mat[0][1], mat[0][0] ) );
angles.roll = RAD2DEG( idMath::ATan( mat[1][2], mat[2][2] ) );
}
else
{
angles.pitch = mat[0][2] < 0.0f ? 90.0f : -90.0f;
angles.yaw = RAD2DEG( - idMath::ATan( mat[1][0], mat[1][1] ) );
angles.roll = 0.0f;
}
return angles;
}
/*
============
idMat3::ToQuat
============
*/
idQuat idMat3::ToQuat() const
{
idQuat q;
float trace;
float s;
float t;
int i;
int j;
int k;
static int next[ 3 ] = { 1, 2, 0 };
trace = mat[ 0 ][ 0 ] + mat[ 1 ][ 1 ] + mat[ 2 ][ 2 ];
if( trace > 0.0f )
{
t = trace + 1.0f;
s = idMath::InvSqrt( t ) * 0.5f;
q[3] = s * t;
q[0] = ( mat[ 2 ][ 1 ] - mat[ 1 ][ 2 ] ) * s;
q[1] = ( mat[ 0 ][ 2 ] - mat[ 2 ][ 0 ] ) * s;
q[2] = ( mat[ 1 ][ 0 ] - mat[ 0 ][ 1 ] ) * s;
}
else
{
i = 0;
if( mat[ 1 ][ 1 ] > mat[ 0 ][ 0 ] )
{
i = 1;
}
if( mat[ 2 ][ 2 ] > mat[ i ][ i ] )
{
i = 2;
}
j = next[ i ];
k = next[ j ];
t = ( mat[ i ][ i ] - ( mat[ j ][ j ] + mat[ k ][ k ] ) ) + 1.0f;
s = idMath::InvSqrt( t ) * 0.5f;
q[i] = s * t;
q[3] = ( mat[ k ][ j ] - mat[ j ][ k ] ) * s;
q[j] = ( mat[ j ][ i ] + mat[ i ][ j ] ) * s;
q[k] = ( mat[ k ][ i ] + mat[ i ][ k ] ) * s;
}
return q;
}
/*
============
idMat3::ToCQuat
============
*/
idCQuat idMat3::ToCQuat() const
{
idQuat q = ToQuat();
if( q.w < 0.0f )
{
return idCQuat( -q.x, -q.y, -q.z );
}
return idCQuat( q.x, q.y, q.z );
}
/*
============
idMat3::ToRotation
============
*/
idRotation idMat3::ToRotation() const
{
idRotation r;
float trace;
float s;
float t;
int i;
int j;
int k;
static int next[ 3 ] = { 1, 2, 0 };
trace = mat[ 0 ][ 0 ] + mat[ 1 ][ 1 ] + mat[ 2 ][ 2 ];
if( trace > 0.0f )
{
t = trace + 1.0f;
s = idMath::InvSqrt( t ) * 0.5f;
r.angle = s * t;
r.vec[0] = ( mat[ 2 ][ 1 ] - mat[ 1 ][ 2 ] ) * s;
r.vec[1] = ( mat[ 0 ][ 2 ] - mat[ 2 ][ 0 ] ) * s;
r.vec[2] = ( mat[ 1 ][ 0 ] - mat[ 0 ][ 1 ] ) * s;
}
else
{
i = 0;
if( mat[ 1 ][ 1 ] > mat[ 0 ][ 0 ] )
{
i = 1;
}
if( mat[ 2 ][ 2 ] > mat[ i ][ i ] )
{
i = 2;
}
j = next[ i ];
k = next[ j ];
t = ( mat[ i ][ i ] - ( mat[ j ][ j ] + mat[ k ][ k ] ) ) + 1.0f;
s = idMath::InvSqrt( t ) * 0.5f;
r.vec[i] = s * t;
r.angle = ( mat[ k ][ j ] - mat[ j ][ k ] ) * s;
r.vec[j] = ( mat[ j ][ i ] + mat[ i ][ j ] ) * s;
r.vec[k] = ( mat[ k ][ i ] + mat[ i ][ k ] ) * s;
}
r.angle = idMath::ACos( r.angle );
float lengthSqr = r.vec.LengthSqr();
if( ( idMath::Fabs( r.angle ) < 1e-10f ) || ( lengthSqr < 1e-10f ) )
{
r.vec.Set( 0.0f, 0.0f, 1.0f );
r.angle = 0.0f;
}
else
{
r.vec *= idMath::InvSqrt( lengthSqr );
r.angle *= 2.0f * idMath::M_RAD2DEG;
}
r.origin.Zero();
r.axis = *this;
r.axisValid = true;
return r;
}
/*
=================
idMat3::ToAngularVelocity
=================
*/
idVec3 idMat3::ToAngularVelocity() const
{
idRotation rotation = ToRotation();
return rotation.GetVec() * DEG2RAD( rotation.GetAngle() );
}
/*
============
idMat3::Determinant
============
*/
float idMat3::Determinant() const
{
float det2_12_01 = mat[1][0] * mat[2][1] - mat[1][1] * mat[2][0];
float det2_12_02 = mat[1][0] * mat[2][2] - mat[1][2] * mat[2][0];
float det2_12_12 = mat[1][1] * mat[2][2] - mat[1][2] * mat[2][1];
return mat[0][0] * det2_12_12 - mat[0][1] * det2_12_02 + mat[0][2] * det2_12_01;
}
/*
============
idMat3::InverseSelf
============
*/
bool idMat3::InverseSelf()
{
// 18+3+9 = 30 multiplications
// 1 division
idMat3 inverse;
double det, invDet;
inverse[0][0] = mat[1][1] * mat[2][2] - mat[1][2] * mat[2][1];
inverse[1][0] = mat[1][2] * mat[2][0] - mat[1][0] * mat[2][2];
inverse[2][0] = mat[1][0] * mat[2][1] - mat[1][1] * mat[2][0];
det = mat[0][0] * inverse[0][0] + mat[0][1] * inverse[1][0] + mat[0][2] * inverse[2][0];
if( idMath::Fabs( det ) < MATRIX_INVERSE_EPSILON )
{
return false;
}
invDet = 1.0f / det;
inverse[0][1] = mat[0][2] * mat[2][1] - mat[0][1] * mat[2][2];
inverse[0][2] = mat[0][1] * mat[1][2] - mat[0][2] * mat[1][1];
inverse[1][1] = mat[0][0] * mat[2][2] - mat[0][2] * mat[2][0];
inverse[1][2] = mat[0][2] * mat[1][0] - mat[0][0] * mat[1][2];
inverse[2][1] = mat[0][1] * mat[2][0] - mat[0][0] * mat[2][1];
inverse[2][2] = mat[0][0] * mat[1][1] - mat[0][1] * mat[1][0];
mat[0][0] = inverse[0][0] * invDet;
mat[0][1] = inverse[0][1] * invDet;
mat[0][2] = inverse[0][2] * invDet;
mat[1][0] = inverse[1][0] * invDet;
mat[1][1] = inverse[1][1] * invDet;
mat[1][2] = inverse[1][2] * invDet;
mat[2][0] = inverse[2][0] * invDet;
mat[2][1] = inverse[2][1] * invDet;
mat[2][2] = inverse[2][2] * invDet;
return true;
}
/*
============
idMat3::InverseFastSelf
============
*/
bool idMat3::InverseFastSelf()
{
#if 1
// 18+3+9 = 30 multiplications
// 1 division
idMat3 inverse;
double det, invDet;
inverse[0][0] = mat[1][1] * mat[2][2] - mat[1][2] * mat[2][1];
inverse[1][0] = mat[1][2] * mat[2][0] - mat[1][0] * mat[2][2];
inverse[2][0] = mat[1][0] * mat[2][1] - mat[1][1] * mat[2][0];
det = mat[0][0] * inverse[0][0] + mat[0][1] * inverse[1][0] + mat[0][2] * inverse[2][0];
if( idMath::Fabs( det ) < MATRIX_INVERSE_EPSILON )
{
return false;
}
invDet = 1.0f / det;
inverse[0][1] = mat[0][2] * mat[2][1] - mat[0][1] * mat[2][2];
inverse[0][2] = mat[0][1] * mat[1][2] - mat[0][2] * mat[1][1];
inverse[1][1] = mat[0][0] * mat[2][2] - mat[0][2] * mat[2][0];
inverse[1][2] = mat[0][2] * mat[1][0] - mat[0][0] * mat[1][2];
inverse[2][1] = mat[0][1] * mat[2][0] - mat[0][0] * mat[2][1];
inverse[2][2] = mat[0][0] * mat[1][1] - mat[0][1] * mat[1][0];
mat[0][0] = inverse[0][0] * invDet;
mat[0][1] = inverse[0][1] * invDet;
mat[0][2] = inverse[0][2] * invDet;
mat[1][0] = inverse[1][0] * invDet;
mat[1][1] = inverse[1][1] * invDet;
mat[1][2] = inverse[1][2] * invDet;
mat[2][0] = inverse[2][0] * invDet;
mat[2][1] = inverse[2][1] * invDet;
mat[2][2] = inverse[2][2] * invDet;
return true;
#elif 0
// 3*10 = 30 multiplications
// 3 divisions
float* mat = reinterpret_cast<float*>( this );
float s;
double d, di;
di = mat[0];
s = di;
mat[0] = d = 1.0f / di;
mat[1] *= d;
mat[2] *= d;
d = -d;
mat[3] *= d;
mat[6] *= d;
d = mat[3] * di;
mat[4] += mat[1] * d;
mat[5] += mat[2] * d;
d = mat[6] * di;
mat[7] += mat[1] * d;
mat[8] += mat[2] * d;
di = mat[4];
s *= di;
mat[4] = d = 1.0f / di;
mat[3] *= d;
mat[5] *= d;
d = -d;
mat[1] *= d;
mat[7] *= d;
d = mat[1] * di;
mat[0] += mat[3] * d;
mat[2] += mat[5] * d;
d = mat[7] * di;
mat[6] += mat[3] * d;
mat[8] += mat[5] * d;
di = mat[8];
s *= di;
mat[8] = d = 1.0f / di;
mat[6] *= d;
mat[7] *= d;
d = -d;
mat[2] *= d;
mat[5] *= d;
d = mat[2] * di;
mat[0] += mat[6] * d;
mat[1] += mat[7] * d;
d = mat[5] * di;
mat[3] += mat[6] * d;
mat[4] += mat[7] * d;
return ( s != 0.0f && !IEEE_FLT_IS_NAN( s ) );
#else
// 4*2+4*4 = 24 multiplications
// 2*1 = 2 divisions
idMat2 r0;
float r1[2], r2[2], r3;
float det, invDet;
float* mat = reinterpret_cast<float*>( this );
// r0 = m0.Inverse(); // 2x2
det = mat[0 * 3 + 0] * mat[1 * 3 + 1] - mat[0 * 3 + 1] * mat[1 * 3 + 0];
if( idMath::Fabs( det ) < MATRIX_INVERSE_EPSILON )
{
return false;
}
invDet = 1.0f / det;
r0[0][0] = mat[1 * 3 + 1] * invDet;
r0[0][1] = - mat[0 * 3 + 1] * invDet;
r0[1][0] = - mat[1 * 3 + 0] * invDet;
r0[1][1] = mat[0 * 3 + 0] * invDet;
// r1 = r0 * m1; // 2x1 = 2x2 * 2x1
r1[0] = r0[0][0] * mat[0 * 3 + 2] + r0[0][1] * mat[1 * 3 + 2];
r1[1] = r0[1][0] * mat[0 * 3 + 2] + r0[1][1] * mat[1 * 3 + 2];
// r2 = m2 * r1; // 1x1 = 1x2 * 2x1
r2[0] = mat[2 * 3 + 0] * r1[0] + mat[2 * 3 + 1] * r1[1];
// r3 = r2 - m3; // 1x1 = 1x1 - 1x1
r3 = r2[0] - mat[2 * 3 + 2];
// r3.InverseSelf();
if( idMath::Fabs( r3 ) < MATRIX_INVERSE_EPSILON )
{
return false;
}
r3 = 1.0f / r3;
// r2 = m2 * r0; // 1x2 = 1x2 * 2x2
r2[0] = mat[2 * 3 + 0] * r0[0][0] + mat[2 * 3 + 1] * r0[1][0];
r2[1] = mat[2 * 3 + 0] * r0[0][1] + mat[2 * 3 + 1] * r0[1][1];
// m2 = r3 * r2; // 1x2 = 1x1 * 1x2
mat[2 * 3 + 0] = r3 * r2[0];
mat[2 * 3 + 1] = r3 * r2[1];
// m0 = r0 - r1 * m2; // 2x2 - 2x1 * 1x2
mat[0 * 3 + 0] = r0[0][0] - r1[0] * mat[2 * 3 + 0];
mat[0 * 3 + 1] = r0[0][1] - r1[0] * mat[2 * 3 + 1];
mat[1 * 3 + 0] = r0[1][0] - r1[1] * mat[2 * 3 + 0];
mat[1 * 3 + 1] = r0[1][1] - r1[1] * mat[2 * 3 + 1];
// m1 = r1 * r3; // 2x1 = 2x1 * 1x1
mat[0 * 3 + 2] = r1[0] * r3;
mat[1 * 3 + 2] = r1[1] * r3;
// m3 = -r3;
mat[2 * 3 + 2] = -r3;
return true;
#endif
}
/*
============
idMat3::InertiaTranslate
============
*/
idMat3 idMat3::InertiaTranslate( const float mass, const idVec3& centerOfMass, const idVec3& translation ) const
{
idMat3 m;
idVec3 newCenter;
newCenter = centerOfMass + translation;
m[0][0] = mass * ( ( centerOfMass[1] * centerOfMass[1] + centerOfMass[2] * centerOfMass[2] )
- ( newCenter[1] * newCenter[1] + newCenter[2] * newCenter[2] ) );
m[1][1] = mass * ( ( centerOfMass[0] * centerOfMass[0] + centerOfMass[2] * centerOfMass[2] )
- ( newCenter[0] * newCenter[0] + newCenter[2] * newCenter[2] ) );
m[2][2] = mass * ( ( centerOfMass[0] * centerOfMass[0] + centerOfMass[1] * centerOfMass[1] )
- ( newCenter[0] * newCenter[0] + newCenter[1] * newCenter[1] ) );
m[0][1] = m[1][0] = mass * ( newCenter[0] * newCenter[1] - centerOfMass[0] * centerOfMass[1] );
m[1][2] = m[2][1] = mass * ( newCenter[1] * newCenter[2] - centerOfMass[1] * centerOfMass[2] );
m[0][2] = m[2][0] = mass * ( newCenter[0] * newCenter[2] - centerOfMass[0] * centerOfMass[2] );
return ( *this ) + m;
}
/*
============
idMat3::InertiaTranslateSelf
============
*/
idMat3& idMat3::InertiaTranslateSelf( const float mass, const idVec3& centerOfMass, const idVec3& translation )
{
idMat3 m;
idVec3 newCenter;
newCenter = centerOfMass + translation;
m[0][0] = mass * ( ( centerOfMass[1] * centerOfMass[1] + centerOfMass[2] * centerOfMass[2] )
- ( newCenter[1] * newCenter[1] + newCenter[2] * newCenter[2] ) );
m[1][1] = mass * ( ( centerOfMass[0] * centerOfMass[0] + centerOfMass[2] * centerOfMass[2] )
- ( newCenter[0] * newCenter[0] + newCenter[2] * newCenter[2] ) );
m[2][2] = mass * ( ( centerOfMass[0] * centerOfMass[0] + centerOfMass[1] * centerOfMass[1] )
- ( newCenter[0] * newCenter[0] + newCenter[1] * newCenter[1] ) );
m[0][1] = m[1][0] = mass * ( newCenter[0] * newCenter[1] - centerOfMass[0] * centerOfMass[1] );
m[1][2] = m[2][1] = mass * ( newCenter[1] * newCenter[2] - centerOfMass[1] * centerOfMass[2] );
m[0][2] = m[2][0] = mass * ( newCenter[0] * newCenter[2] - centerOfMass[0] * centerOfMass[2] );
( *this ) += m;
return ( *this );
}
/*
============
idMat3::InertiaRotate
============
*/
idMat3 idMat3::InertiaRotate( const idMat3& rotation ) const
{
// NOTE: the rotation matrix is stored column-major
return rotation.Transpose() * ( *this ) * rotation;
}
/*
============
idMat3::InertiaRotateSelf
============
*/
idMat3& idMat3::InertiaRotateSelf( const idMat3& rotation )
{
// NOTE: the rotation matrix is stored column-major
*this = rotation.Transpose() * ( *this ) * rotation;
return *this;
}
/*
=============
idMat3::ToString
=============
*/
const char* idMat3::ToString( int precision ) const
{
return idStr::FloatArrayToString( ToFloatPtr(), GetDimension(), precision );
}
//===============================================================
//
// idMat4
//
//===============================================================
idMat4 mat4_zero( idVec4( 0, 0, 0, 0 ), idVec4( 0, 0, 0, 0 ), idVec4( 0, 0, 0, 0 ), idVec4( 0, 0, 0, 0 ) );
idMat4 mat4_identity( idVec4( 1, 0, 0, 0 ), idVec4( 0, 1, 0, 0 ), idVec4( 0, 0, 1, 0 ), idVec4( 0, 0, 0, 1 ) );
/*
============
idMat4::Transpose
============
*/
idMat4 idMat4::Transpose() const
{
idMat4 transpose;
int i, j;
for( i = 0; i < 4; i++ )
{
for( j = 0; j < 4; j++ )
{
transpose[ i ][ j ] = mat[ j ][ i ];
}
}
return transpose;
}
/*
============
idMat4::TransposeSelf
============
*/
idMat4& idMat4::TransposeSelf()
{
float temp;
int i, j;
for( i = 0; i < 4; i++ )
{
for( j = i + 1; j < 4; j++ )
{
temp = mat[ i ][ j ];
mat[ i ][ j ] = mat[ j ][ i ];
mat[ j ][ i ] = temp;
}
}
return *this;
}
/*
============
idMat4::Determinant
============
*/
float idMat4::Determinant() const
{
// 2x2 sub-determinants
float det2_01_01 = mat[0][0] * mat[1][1] - mat[0][1] * mat[1][0];
float det2_01_02 = mat[0][0] * mat[1][2] - mat[0][2] * mat[1][0];
float det2_01_03 = mat[0][0] * mat[1][3] - mat[0][3] * mat[1][0];
float det2_01_12 = mat[0][1] * mat[1][2] - mat[0][2] * mat[1][1];
float det2_01_13 = mat[0][1] * mat[1][3] - mat[0][3] * mat[1][1];
float det2_01_23 = mat[0][2] * mat[1][3] - mat[0][3] * mat[1][2];
// 3x3 sub-determinants
float det3_201_012 = mat[2][0] * det2_01_12 - mat[2][1] * det2_01_02 + mat[2][2] * det2_01_01;
float det3_201_013 = mat[2][0] * det2_01_13 - mat[2][1] * det2_01_03 + mat[2][3] * det2_01_01;
float det3_201_023 = mat[2][0] * det2_01_23 - mat[2][2] * det2_01_03 + mat[2][3] * det2_01_02;
float det3_201_123 = mat[2][1] * det2_01_23 - mat[2][2] * det2_01_13 + mat[2][3] * det2_01_12;
return ( - det3_201_123 * mat[3][0] + det3_201_023 * mat[3][1] - det3_201_013 * mat[3][2] + det3_201_012 * mat[3][3] );
}
/*
============
idMat4::InverseSelf
============
*/
bool idMat4::InverseSelf()
{
// 84+4+16 = 104 multiplications
// 1 division
double det, invDet;
// 2x2 sub-determinants required to calculate 4x4 determinant
float det2_01_01 = mat[0][0] * mat[1][1] - mat[0][1] * mat[1][0];
float det2_01_02 = mat[0][0] * mat[1][2] - mat[0][2] * mat[1][0];
float det2_01_03 = mat[0][0] * mat[1][3] - mat[0][3] * mat[1][0];
float det2_01_12 = mat[0][1] * mat[1][2] - mat[0][2] * mat[1][1];
float det2_01_13 = mat[0][1] * mat[1][3] - mat[0][3] * mat[1][1];
float det2_01_23 = mat[0][2] * mat[1][3] - mat[0][3] * mat[1][2];
// 3x3 sub-determinants required to calculate 4x4 determinant
float det3_201_012 = mat[2][0] * det2_01_12 - mat[2][1] * det2_01_02 + mat[2][2] * det2_01_01;
float det3_201_013 = mat[2][0] * det2_01_13 - mat[2][1] * det2_01_03 + mat[2][3] * det2_01_01;
float det3_201_023 = mat[2][0] * det2_01_23 - mat[2][2] * det2_01_03 + mat[2][3] * det2_01_02;
float det3_201_123 = mat[2][1] * det2_01_23 - mat[2][2] * det2_01_13 + mat[2][3] * det2_01_12;
det = ( - det3_201_123 * mat[3][0] + det3_201_023 * mat[3][1] - det3_201_013 * mat[3][2] + det3_201_012 * mat[3][3] );
if( idMath::Fabs( det ) < MATRIX_INVERSE_EPSILON )
{
return false;
}
invDet = 1.0f / det;
// remaining 2x2 sub-determinants
float det2_03_01 = mat[0][0] * mat[3][1] - mat[0][1] * mat[3][0];
float det2_03_02 = mat[0][0] * mat[3][2] - mat[0][2] * mat[3][0];
float det2_03_03 = mat[0][0] * mat[3][3] - mat[0][3] * mat[3][0];
float det2_03_12 = mat[0][1] * mat[3][2] - mat[0][2] * mat[3][1];
float det2_03_13 = mat[0][1] * mat[3][3] - mat[0][3] * mat[3][1];
float det2_03_23 = mat[0][2] * mat[3][3] - mat[0][3] * mat[3][2];
float det2_13_01 = mat[1][0] * mat[3][1] - mat[1][1] * mat[3][0];
float det2_13_02 = mat[1][0] * mat[3][2] - mat[1][2] * mat[3][0];
float det2_13_03 = mat[1][0] * mat[3][3] - mat[1][3] * mat[3][0];
float det2_13_12 = mat[1][1] * mat[3][2] - mat[1][2] * mat[3][1];
float det2_13_13 = mat[1][1] * mat[3][3] - mat[1][3] * mat[3][1];
float det2_13_23 = mat[1][2] * mat[3][3] - mat[1][3] * mat[3][2];
// remaining 3x3 sub-determinants
float det3_203_012 = mat[2][0] * det2_03_12 - mat[2][1] * det2_03_02 + mat[2][2] * det2_03_01;
float det3_203_013 = mat[2][0] * det2_03_13 - mat[2][1] * det2_03_03 + mat[2][3] * det2_03_01;
float det3_203_023 = mat[2][0] * det2_03_23 - mat[2][2] * det2_03_03 + mat[2][3] * det2_03_02;
float det3_203_123 = mat[2][1] * det2_03_23 - mat[2][2] * det2_03_13 + mat[2][3] * det2_03_12;
float det3_213_012 = mat[2][0] * det2_13_12 - mat[2][1] * det2_13_02 + mat[2][2] * det2_13_01;
float det3_213_013 = mat[2][0] * det2_13_13 - mat[2][1] * det2_13_03 + mat[2][3] * det2_13_01;
float det3_213_023 = mat[2][0] * det2_13_23 - mat[2][2] * det2_13_03 + mat[2][3] * det2_13_02;
float det3_213_123 = mat[2][1] * det2_13_23 - mat[2][2] * det2_13_13 + mat[2][3] * det2_13_12;
float det3_301_012 = mat[3][0] * det2_01_12 - mat[3][1] * det2_01_02 + mat[3][2] * det2_01_01;
float det3_301_013 = mat[3][0] * det2_01_13 - mat[3][1] * det2_01_03 + mat[3][3] * det2_01_01;
float det3_301_023 = mat[3][0] * det2_01_23 - mat[3][2] * det2_01_03 + mat[3][3] * det2_01_02;
float det3_301_123 = mat[3][1] * det2_01_23 - mat[3][2] * det2_01_13 + mat[3][3] * det2_01_12;
mat[0][0] = - det3_213_123 * invDet;
mat[1][0] = + det3_213_023 * invDet;
mat[2][0] = - det3_213_013 * invDet;
mat[3][0] = + det3_213_012 * invDet;
mat[0][1] = + det3_203_123 * invDet;
mat[1][1] = - det3_203_023 * invDet;
mat[2][1] = + det3_203_013 * invDet;
mat[3][1] = - det3_203_012 * invDet;
mat[0][2] = + det3_301_123 * invDet;
mat[1][2] = - det3_301_023 * invDet;
mat[2][2] = + det3_301_013 * invDet;
mat[3][2] = - det3_301_012 * invDet;
mat[0][3] = - det3_201_123 * invDet;
mat[1][3] = + det3_201_023 * invDet;
mat[2][3] = - det3_201_013 * invDet;
mat[3][3] = + det3_201_012 * invDet;
return true;
}
/*
============
idMat4::InverseFastSelf
============
*/
bool idMat4::InverseFastSelf()
{
#if 0
// 84+4+16 = 104 multiplications
// 1 division
double det, invDet;
// 2x2 sub-determinants required to calculate 4x4 determinant
float det2_01_01 = mat[0][0] * mat[1][1] - mat[0][1] * mat[1][0];
float det2_01_02 = mat[0][0] * mat[1][2] - mat[0][2] * mat[1][0];
float det2_01_03 = mat[0][0] * mat[1][3] - mat[0][3] * mat[1][0];
float det2_01_12 = mat[0][1] * mat[1][2] - mat[0][2] * mat[1][1];
float det2_01_13 = mat[0][1] * mat[1][3] - mat[0][3] * mat[1][1];
float det2_01_23 = mat[0][2] * mat[1][3] - mat[0][3] * mat[1][2];
// 3x3 sub-determinants required to calculate 4x4 determinant
float det3_201_012 = mat[2][0] * det2_01_12 - mat[2][1] * det2_01_02 + mat[2][2] * det2_01_01;
float det3_201_013 = mat[2][0] * det2_01_13 - mat[2][1] * det2_01_03 + mat[2][3] * det2_01_01;
float det3_201_023 = mat[2][0] * det2_01_23 - mat[2][2] * det2_01_03 + mat[2][3] * det2_01_02;
float det3_201_123 = mat[2][1] * det2_01_23 - mat[2][2] * det2_01_13 + mat[2][3] * det2_01_12;
det = ( - det3_201_123 * mat[3][0] + det3_201_023 * mat[3][1] - det3_201_013 * mat[3][2] + det3_201_012 * mat[3][3] );
if( idMath::Fabs( det ) < MATRIX_INVERSE_EPSILON )
{
return false;
}
invDet = 1.0f / det;
// remaining 2x2 sub-determinants
float det2_03_01 = mat[0][0] * mat[3][1] - mat[0][1] * mat[3][0];
float det2_03_02 = mat[0][0] * mat[3][2] - mat[0][2] * mat[3][0];
float det2_03_03 = mat[0][0] * mat[3][3] - mat[0][3] * mat[3][0];
float det2_03_12 = mat[0][1] * mat[3][2] - mat[0][2] * mat[3][1];
float det2_03_13 = mat[0][1] * mat[3][3] - mat[0][3] * mat[3][1];
float det2_03_23 = mat[0][2] * mat[3][3] - mat[0][3] * mat[3][2];
float det2_13_01 = mat[1][0] * mat[3][1] - mat[1][1] * mat[3][0];
float det2_13_02 = mat[1][0] * mat[3][2] - mat[1][2] * mat[3][0];
float det2_13_03 = mat[1][0] * mat[3][3] - mat[1][3] * mat[3][0];
float det2_13_12 = mat[1][1] * mat[3][2] - mat[1][2] * mat[3][1];
float det2_13_13 = mat[1][1] * mat[3][3] - mat[1][3] * mat[3][1];
float det2_13_23 = mat[1][2] * mat[3][3] - mat[1][3] * mat[3][2];
// remaining 3x3 sub-determinants
float det3_203_012 = mat[2][0] * det2_03_12 - mat[2][1] * det2_03_02 + mat[2][2] * det2_03_01;
float det3_203_013 = mat[2][0] * det2_03_13 - mat[2][1] * det2_03_03 + mat[2][3] * det2_03_01;
float det3_203_023 = mat[2][0] * det2_03_23 - mat[2][2] * det2_03_03 + mat[2][3] * det2_03_02;
float det3_203_123 = mat[2][1] * det2_03_23 - mat[2][2] * det2_03_13 + mat[2][3] * det2_03_12;
float det3_213_012 = mat[2][0] * det2_13_12 - mat[2][1] * det2_13_02 + mat[2][2] * det2_13_01;
float det3_213_013 = mat[2][0] * det2_13_13 - mat[2][1] * det2_13_03 + mat[2][3] * det2_13_01;
float det3_213_023 = mat[2][0] * det2_13_23 - mat[2][2] * det2_13_03 + mat[2][3] * det2_13_02;
float det3_213_123 = mat[2][1] * det2_13_23 - mat[2][2] * det2_13_13 + mat[2][3] * det2_13_12;
float det3_301_012 = mat[3][0] * det2_01_12 - mat[3][1] * det2_01_02 + mat[3][2] * det2_01_01;
float det3_301_013 = mat[3][0] * det2_01_13 - mat[3][1] * det2_01_03 + mat[3][3] * det2_01_01;
float det3_301_023 = mat[3][0] * det2_01_23 - mat[3][2] * det2_01_03 + mat[3][3] * det2_01_02;
float det3_301_123 = mat[3][1] * det2_01_23 - mat[3][2] * det2_01_13 + mat[3][3] * det2_01_12;
mat[0][0] = - det3_213_123 * invDet;
mat[1][0] = + det3_213_023 * invDet;
mat[2][0] = - det3_213_013 * invDet;
mat[3][0] = + det3_213_012 * invDet;
mat[0][1] = + det3_203_123 * invDet;
mat[1][1] = - det3_203_023 * invDet;
mat[2][1] = + det3_203_013 * invDet;
mat[3][1] = - det3_203_012 * invDet;
mat[0][2] = + det3_301_123 * invDet;
mat[1][2] = - det3_301_023 * invDet;
mat[2][2] = + det3_301_013 * invDet;
mat[3][2] = - det3_301_012 * invDet;
mat[0][3] = - det3_201_123 * invDet;
mat[1][3] = + det3_201_023 * invDet;
mat[2][3] = - det3_201_013 * invDet;
mat[3][3] = + det3_201_012 * invDet;
return true;
#elif 0
// 4*18 = 72 multiplications
// 4 divisions
float* mat = reinterpret_cast<float*>( this );
float s;
double d, di;
di = mat[0];
s = di;
mat[0] = d = 1.0f / di;
mat[1] *= d;
mat[2] *= d;
mat[3] *= d;
d = -d;
mat[4] *= d;
mat[8] *= d;
mat[12] *= d;
d = mat[4] * di;
mat[5] += mat[1] * d;
mat[6] += mat[2] * d;
mat[7] += mat[3] * d;
d = mat[8] * di;
mat[9] += mat[1] * d;
mat[10] += mat[2] * d;
mat[11] += mat[3] * d;
d = mat[12] * di;
mat[13] += mat[1] * d;
mat[14] += mat[2] * d;
mat[15] += mat[3] * d;
di = mat[5];
s *= di;
mat[5] = d = 1.0f / di;
mat[4] *= d;
mat[6] *= d;
mat[7] *= d;
d = -d;
mat[1] *= d;
mat[9] *= d;
mat[13] *= d;
d = mat[1] * di;
mat[0] += mat[4] * d;
mat[2] += mat[6] * d;
mat[3] += mat[7] * d;
d = mat[9] * di;
mat[8] += mat[4] * d;
mat[10] += mat[6] * d;
mat[11] += mat[7] * d;
d = mat[13] * di;
mat[12] += mat[4] * d;
mat[14] += mat[6] * d;
mat[15] += mat[7] * d;
di = mat[10];
s *= di;
mat[10] = d = 1.0f / di;
mat[8] *= d;
mat[9] *= d;
mat[11] *= d;
d = -d;
mat[2] *= d;
mat[6] *= d;
mat[14] *= d;
d = mat[2] * di;
mat[0] += mat[8] * d;
mat[1] += mat[9] * d;
mat[3] += mat[11] * d;
d = mat[6] * di;
mat[4] += mat[8] * d;
mat[5] += mat[9] * d;
mat[7] += mat[11] * d;
d = mat[14] * di;
mat[12] += mat[8] * d;
mat[13] += mat[9] * d;
mat[15] += mat[11] * d;
di = mat[15];
s *= di;
mat[15] = d = 1.0f / di;
mat[12] *= d;
mat[13] *= d;
mat[14] *= d;
d = -d;
mat[3] *= d;
mat[7] *= d;
mat[11] *= d;
d = mat[3] * di;
mat[0] += mat[12] * d;
mat[1] += mat[13] * d;
mat[2] += mat[14] * d;
d = mat[7] * di;
mat[4] += mat[12] * d;
mat[5] += mat[13] * d;
mat[6] += mat[14] * d;
d = mat[11] * di;
mat[8] += mat[12] * d;
mat[9] += mat[13] * d;
mat[10] += mat[14] * d;
return ( s != 0.0f && !IEEE_FLT_IS_NAN( s ) );
#else
// 6*8+2*6 = 60 multiplications
// 2*1 = 2 divisions
idMat2 r0, r1, r2, r3;
float a, det, invDet;
float* mat = reinterpret_cast<float*>( this );
// r0 = m0.Inverse();
det = mat[0 * 4 + 0] * mat[1 * 4 + 1] - mat[0 * 4 + 1] * mat[1 * 4 + 0];
if( idMath::Fabs( det ) < MATRIX_INVERSE_EPSILON )
{
return false;
}
invDet = 1.0f / det;
r0[0][0] = mat[1 * 4 + 1] * invDet;
r0[0][1] = - mat[0 * 4 + 1] * invDet;
r0[1][0] = - mat[1 * 4 + 0] * invDet;
r0[1][1] = mat[0 * 4 + 0] * invDet;
// r1 = r0 * m1;
r1[0][0] = r0[0][0] * mat[0 * 4 + 2] + r0[0][1] * mat[1 * 4 + 2];
r1[0][1] = r0[0][0] * mat[0 * 4 + 3] + r0[0][1] * mat[1 * 4 + 3];
r1[1][0] = r0[1][0] * mat[0 * 4 + 2] + r0[1][1] * mat[1 * 4 + 2];
r1[1][1] = r0[1][0] * mat[0 * 4 + 3] + r0[1][1] * mat[1 * 4 + 3];
// r2 = m2 * r1;
r2[0][0] = mat[2 * 4 + 0] * r1[0][0] + mat[2 * 4 + 1] * r1[1][0];
r2[0][1] = mat[2 * 4 + 0] * r1[0][1] + mat[2 * 4 + 1] * r1[1][1];
r2[1][0] = mat[3 * 4 + 0] * r1[0][0] + mat[3 * 4 + 1] * r1[1][0];
r2[1][1] = mat[3 * 4 + 0] * r1[0][1] + mat[3 * 4 + 1] * r1[1][1];
// r3 = r2 - m3;
r3[0][0] = r2[0][0] - mat[2 * 4 + 2];
r3[0][1] = r2[0][1] - mat[2 * 4 + 3];
r3[1][0] = r2[1][0] - mat[3 * 4 + 2];
r3[1][1] = r2[1][1] - mat[3 * 4 + 3];
// r3.InverseSelf();
det = r3[0][0] * r3[1][1] - r3[0][1] * r3[1][0];
if( idMath::Fabs( det ) < MATRIX_INVERSE_EPSILON )
{
return false;
}
invDet = 1.0f / det;
a = r3[0][0];
r3[0][0] = r3[1][1] * invDet;
r3[0][1] = - r3[0][1] * invDet;
r3[1][0] = - r3[1][0] * invDet;
r3[1][1] = a * invDet;
// r2 = m2 * r0;
r2[0][0] = mat[2 * 4 + 0] * r0[0][0] + mat[2 * 4 + 1] * r0[1][0];
r2[0][1] = mat[2 * 4 + 0] * r0[0][1] + mat[2 * 4 + 1] * r0[1][1];
r2[1][0] = mat[3 * 4 + 0] * r0[0][0] + mat[3 * 4 + 1] * r0[1][0];
r2[1][1] = mat[3 * 4 + 0] * r0[0][1] + mat[3 * 4 + 1] * r0[1][1];
// m2 = r3 * r2;
mat[2 * 4 + 0] = r3[0][0] * r2[0][0] + r3[0][1] * r2[1][0];
mat[2 * 4 + 1] = r3[0][0] * r2[0][1] + r3[0][1] * r2[1][1];
mat[3 * 4 + 0] = r3[1][0] * r2[0][0] + r3[1][1] * r2[1][0];
mat[3 * 4 + 1] = r3[1][0] * r2[0][1] + r3[1][1] * r2[1][1];
// m0 = r0 - r1 * m2;
mat[0 * 4 + 0] = r0[0][0] - r1[0][0] * mat[2 * 4 + 0] - r1[0][1] * mat[3 * 4 + 0];
mat[0 * 4 + 1] = r0[0][1] - r1[0][0] * mat[2 * 4 + 1] - r1[0][1] * mat[3 * 4 + 1];
mat[1 * 4 + 0] = r0[1][0] - r1[1][0] * mat[2 * 4 + 0] - r1[1][1] * mat[3 * 4 + 0];
mat[1 * 4 + 1] = r0[1][1] - r1[1][0] * mat[2 * 4 + 1] - r1[1][1] * mat[3 * 4 + 1];
// m1 = r1 * r3;
mat[0 * 4 + 2] = r1[0][0] * r3[0][0] + r1[0][1] * r3[1][0];
mat[0 * 4 + 3] = r1[0][0] * r3[0][1] + r1[0][1] * r3[1][1];
mat[1 * 4 + 2] = r1[1][0] * r3[0][0] + r1[1][1] * r3[1][0];
mat[1 * 4 + 3] = r1[1][0] * r3[0][1] + r1[1][1] * r3[1][1];
// m3 = -r3;
mat[2 * 4 + 2] = -r3[0][0];
mat[2 * 4 + 3] = -r3[0][1];
mat[3 * 4 + 2] = -r3[1][0];
mat[3 * 4 + 3] = -r3[1][1];
return true;
#endif
}
/*
=============
idMat4::ToString
=============
*/
const char* idMat4::ToString( int precision ) const
{
return idStr::FloatArrayToString( ToFloatPtr(), GetDimension(), precision );
}
//===============================================================
//
// idMat5
//
//===============================================================
idMat5 mat5_zero( idVec5( 0, 0, 0, 0, 0 ), idVec5( 0, 0, 0, 0, 0 ), idVec5( 0, 0, 0, 0, 0 ), idVec5( 0, 0, 0, 0, 0 ), idVec5( 0, 0, 0, 0, 0 ) );
idMat5 mat5_identity( idVec5( 1, 0, 0, 0, 0 ), idVec5( 0, 1, 0, 0, 0 ), idVec5( 0, 0, 1, 0, 0 ), idVec5( 0, 0, 0, 1, 0 ), idVec5( 0, 0, 0, 0, 1 ) );
/*
============
idMat5::Transpose
============
*/
idMat5 idMat5::Transpose() const
{
idMat5 transpose;
int i, j;
for( i = 0; i < 5; i++ )
{
for( j = 0; j < 5; j++ )
{
transpose[ i ][ j ] = mat[ j ][ i ];
}
}
return transpose;
}
/*
============
idMat5::TransposeSelf
============
*/
idMat5& idMat5::TransposeSelf()
{
float temp;
int i, j;
for( i = 0; i < 5; i++ )
{
for( j = i + 1; j < 5; j++ )
{
temp = mat[ i ][ j ];
mat[ i ][ j ] = mat[ j ][ i ];
mat[ j ][ i ] = temp;
}
}
return *this;
}
/*
============
idMat5::Determinant
============
*/
float idMat5::Determinant() const
{
// 2x2 sub-determinants required to calculate 5x5 determinant
float det2_34_01 = mat[3][0] * mat[4][1] - mat[3][1] * mat[4][0];
float det2_34_02 = mat[3][0] * mat[4][2] - mat[3][2] * mat[4][0];
float det2_34_03 = mat[3][0] * mat[4][3] - mat[3][3] * mat[4][0];
float det2_34_04 = mat[3][0] * mat[4][4] - mat[3][4] * mat[4][0];
float det2_34_12 = mat[3][1] * mat[4][2] - mat[3][2] * mat[4][1];
float det2_34_13 = mat[3][1] * mat[4][3] - mat[3][3] * mat[4][1];
float det2_34_14 = mat[3][1] * mat[4][4] - mat[3][4] * mat[4][1];
float det2_34_23 = mat[3][2] * mat[4][3] - mat[3][3] * mat[4][2];
float det2_34_24 = mat[3][2] * mat[4][4] - mat[3][4] * mat[4][2];
float det2_34_34 = mat[3][3] * mat[4][4] - mat[3][4] * mat[4][3];
// 3x3 sub-determinants required to calculate 5x5 determinant
float det3_234_012 = mat[2][0] * det2_34_12 - mat[2][1] * det2_34_02 + mat[2][2] * det2_34_01;
float det3_234_013 = mat[2][0] * det2_34_13 - mat[2][1] * det2_34_03 + mat[2][3] * det2_34_01;
float det3_234_014 = mat[2][0] * det2_34_14 - mat[2][1] * det2_34_04 + mat[2][4] * det2_34_01;
float det3_234_023 = mat[2][0] * det2_34_23 - mat[2][2] * det2_34_03 + mat[2][3] * det2_34_02;
float det3_234_024 = mat[2][0] * det2_34_24 - mat[2][2] * det2_34_04 + mat[2][4] * det2_34_02;
float det3_234_034 = mat[2][0] * det2_34_34 - mat[2][3] * det2_34_04 + mat[2][4] * det2_34_03;
float det3_234_123 = mat[2][1] * det2_34_23 - mat[2][2] * det2_34_13 + mat[2][3] * det2_34_12;
float det3_234_124 = mat[2][1] * det2_34_24 - mat[2][2] * det2_34_14 + mat[2][4] * det2_34_12;
float det3_234_134 = mat[2][1] * det2_34_34 - mat[2][3] * det2_34_14 + mat[2][4] * det2_34_13;
float det3_234_234 = mat[2][2] * det2_34_34 - mat[2][3] * det2_34_24 + mat[2][4] * det2_34_23;
// 4x4 sub-determinants required to calculate 5x5 determinant
float det4_1234_0123 = mat[1][0] * det3_234_123 - mat[1][1] * det3_234_023 + mat[1][2] * det3_234_013 - mat[1][3] * det3_234_012;
float det4_1234_0124 = mat[1][0] * det3_234_124 - mat[1][1] * det3_234_024 + mat[1][2] * det3_234_014 - mat[1][4] * det3_234_012;
float det4_1234_0134 = mat[1][0] * det3_234_134 - mat[1][1] * det3_234_034 + mat[1][3] * det3_234_014 - mat[1][4] * det3_234_013;
float det4_1234_0234 = mat[1][0] * det3_234_234 - mat[1][2] * det3_234_034 + mat[1][3] * det3_234_024 - mat[1][4] * det3_234_023;
float det4_1234_1234 = mat[1][1] * det3_234_234 - mat[1][2] * det3_234_134 + mat[1][3] * det3_234_124 - mat[1][4] * det3_234_123;
// determinant of 5x5 matrix
return mat[0][0] * det4_1234_1234 - mat[0][1] * det4_1234_0234 + mat[0][2] * det4_1234_0134 - mat[0][3] * det4_1234_0124 + mat[0][4] * det4_1234_0123;
}
/*
============
idMat5::InverseSelf
============
*/
bool idMat5::InverseSelf()
{
// 280+5+25 = 310 multiplications
// 1 division
double det, invDet;
// 2x2 sub-determinants required to calculate 5x5 determinant
float det2_34_01 = mat[3][0] * mat[4][1] - mat[3][1] * mat[4][0];
float det2_34_02 = mat[3][0] * mat[4][2] - mat[3][2] * mat[4][0];
float det2_34_03 = mat[3][0] * mat[4][3] - mat[3][3] * mat[4][0];
float det2_34_04 = mat[3][0] * mat[4][4] - mat[3][4] * mat[4][0];
float det2_34_12 = mat[3][1] * mat[4][2] - mat[3][2] * mat[4][1];
float det2_34_13 = mat[3][1] * mat[4][3] - mat[3][3] * mat[4][1];
float det2_34_14 = mat[3][1] * mat[4][4] - mat[3][4] * mat[4][1];
float det2_34_23 = mat[3][2] * mat[4][3] - mat[3][3] * mat[4][2];
float det2_34_24 = mat[3][2] * mat[4][4] - mat[3][4] * mat[4][2];
float det2_34_34 = mat[3][3] * mat[4][4] - mat[3][4] * mat[4][3];
// 3x3 sub-determinants required to calculate 5x5 determinant
float det3_234_012 = mat[2][0] * det2_34_12 - mat[2][1] * det2_34_02 + mat[2][2] * det2_34_01;
float det3_234_013 = mat[2][0] * det2_34_13 - mat[2][1] * det2_34_03 + mat[2][3] * det2_34_01;
float det3_234_014 = mat[2][0] * det2_34_14 - mat[2][1] * det2_34_04 + mat[2][4] * det2_34_01;
float det3_234_023 = mat[2][0] * det2_34_23 - mat[2][2] * det2_34_03 + mat[2][3] * det2_34_02;
float det3_234_024 = mat[2][0] * det2_34_24 - mat[2][2] * det2_34_04 + mat[2][4] * det2_34_02;
float det3_234_034 = mat[2][0] * det2_34_34 - mat[2][3] * det2_34_04 + mat[2][4] * det2_34_03;
float det3_234_123 = mat[2][1] * det2_34_23 - mat[2][2] * det2_34_13 + mat[2][3] * det2_34_12;
float det3_234_124 = mat[2][1] * det2_34_24 - mat[2][2] * det2_34_14 + mat[2][4] * det2_34_12;
float det3_234_134 = mat[2][1] * det2_34_34 - mat[2][3] * det2_34_14 + mat[2][4] * det2_34_13;
float det3_234_234 = mat[2][2] * det2_34_34 - mat[2][3] * det2_34_24 + mat[2][4] * det2_34_23;
// 4x4 sub-determinants required to calculate 5x5 determinant
float det4_1234_0123 = mat[1][0] * det3_234_123 - mat[1][1] * det3_234_023 + mat[1][2] * det3_234_013 - mat[1][3] * det3_234_012;
float det4_1234_0124 = mat[1][0] * det3_234_124 - mat[1][1] * det3_234_024 + mat[1][2] * det3_234_014 - mat[1][4] * det3_234_012;
float det4_1234_0134 = mat[1][0] * det3_234_134 - mat[1][1] * det3_234_034 + mat[1][3] * det3_234_014 - mat[1][4] * det3_234_013;
float det4_1234_0234 = mat[1][0] * det3_234_234 - mat[1][2] * det3_234_034 + mat[1][3] * det3_234_024 - mat[1][4] * det3_234_023;
float det4_1234_1234 = mat[1][1] * det3_234_234 - mat[1][2] * det3_234_134 + mat[1][3] * det3_234_124 - mat[1][4] * det3_234_123;
// determinant of 5x5 matrix
det = mat[0][0] * det4_1234_1234 - mat[0][1] * det4_1234_0234 + mat[0][2] * det4_1234_0134 - mat[0][3] * det4_1234_0124 + mat[0][4] * det4_1234_0123;
if( idMath::Fabs( det ) < MATRIX_INVERSE_EPSILON )
{
return false;
}
invDet = 1.0f / det;
// remaining 2x2 sub-determinants
float det2_23_01 = mat[2][0] * mat[3][1] - mat[2][1] * mat[3][0];
float det2_23_02 = mat[2][0] * mat[3][2] - mat[2][2] * mat[3][0];
float det2_23_03 = mat[2][0] * mat[3][3] - mat[2][3] * mat[3][0];
float det2_23_04 = mat[2][0] * mat[3][4] - mat[2][4] * mat[3][0];
float det2_23_12 = mat[2][1] * mat[3][2] - mat[2][2] * mat[3][1];
float det2_23_13 = mat[2][1] * mat[3][3] - mat[2][3] * mat[3][1];
float det2_23_14 = mat[2][1] * mat[3][4] - mat[2][4] * mat[3][1];
float det2_23_23 = mat[2][2] * mat[3][3] - mat[2][3] * mat[3][2];
float det2_23_24 = mat[2][2] * mat[3][4] - mat[2][4] * mat[3][2];
float det2_23_34 = mat[2][3] * mat[3][4] - mat[2][4] * mat[3][3];
float det2_24_01 = mat[2][0] * mat[4][1] - mat[2][1] * mat[4][0];
float det2_24_02 = mat[2][0] * mat[4][2] - mat[2][2] * mat[4][0];
float det2_24_03 = mat[2][0] * mat[4][3] - mat[2][3] * mat[4][0];
float det2_24_04 = mat[2][0] * mat[4][4] - mat[2][4] * mat[4][0];
float det2_24_12 = mat[2][1] * mat[4][2] - mat[2][2] * mat[4][1];
float det2_24_13 = mat[2][1] * mat[4][3] - mat[2][3] * mat[4][1];
float det2_24_14 = mat[2][1] * mat[4][4] - mat[2][4] * mat[4][1];
float det2_24_23 = mat[2][2] * mat[4][3] - mat[2][3] * mat[4][2];
float det2_24_24 = mat[2][2] * mat[4][4] - mat[2][4] * mat[4][2];
float det2_24_34 = mat[2][3] * mat[4][4] - mat[2][4] * mat[4][3];
// remaining 3x3 sub-determinants
float det3_123_012 = mat[1][0] * det2_23_12 - mat[1][1] * det2_23_02 + mat[1][2] * det2_23_01;
float det3_123_013 = mat[1][0] * det2_23_13 - mat[1][1] * det2_23_03 + mat[1][3] * det2_23_01;
float det3_123_014 = mat[1][0] * det2_23_14 - mat[1][1] * det2_23_04 + mat[1][4] * det2_23_01;
float det3_123_023 = mat[1][0] * det2_23_23 - mat[1][2] * det2_23_03 + mat[1][3] * det2_23_02;
float det3_123_024 = mat[1][0] * det2_23_24 - mat[1][2] * det2_23_04 + mat[1][4] * det2_23_02;
float det3_123_034 = mat[1][0] * det2_23_34 - mat[1][3] * det2_23_04 + mat[1][4] * det2_23_03;
float det3_123_123 = mat[1][1] * det2_23_23 - mat[1][2] * det2_23_13 + mat[1][3] * det2_23_12;
float det3_123_124 = mat[1][1] * det2_23_24 - mat[1][2] * det2_23_14 + mat[1][4] * det2_23_12;
float det3_123_134 = mat[1][1] * det2_23_34 - mat[1][3] * det2_23_14 + mat[1][4] * det2_23_13;
float det3_123_234 = mat[1][2] * det2_23_34 - mat[1][3] * det2_23_24 + mat[1][4] * det2_23_23;
float det3_124_012 = mat[1][0] * det2_24_12 - mat[1][1] * det2_24_02 + mat[1][2] * det2_24_01;
float det3_124_013 = mat[1][0] * det2_24_13 - mat[1][1] * det2_24_03 + mat[1][3] * det2_24_01;
float det3_124_014 = mat[1][0] * det2_24_14 - mat[1][1] * det2_24_04 + mat[1][4] * det2_24_01;
float det3_124_023 = mat[1][0] * det2_24_23 - mat[1][2] * det2_24_03 + mat[1][3] * det2_24_02;
float det3_124_024 = mat[1][0] * det2_24_24 - mat[1][2] * det2_24_04 + mat[1][4] * det2_24_02;
float det3_124_034 = mat[1][0] * det2_24_34 - mat[1][3] * det2_24_04 + mat[1][4] * det2_24_03;
float det3_124_123 = mat[1][1] * det2_24_23 - mat[1][2] * det2_24_13 + mat[1][3] * det2_24_12;
float det3_124_124 = mat[1][1] * det2_24_24 - mat[1][2] * det2_24_14 + mat[1][4] * det2_24_12;
float det3_124_134 = mat[1][1] * det2_24_34 - mat[1][3] * det2_24_14 + mat[1][4] * det2_24_13;
float det3_124_234 = mat[1][2] * det2_24_34 - mat[1][3] * det2_24_24 + mat[1][4] * det2_24_23;
float det3_134_012 = mat[1][0] * det2_34_12 - mat[1][1] * det2_34_02 + mat[1][2] * det2_34_01;
float det3_134_013 = mat[1][0] * det2_34_13 - mat[1][1] * det2_34_03 + mat[1][3] * det2_34_01;
float det3_134_014 = mat[1][0] * det2_34_14 - mat[1][1] * det2_34_04 + mat[1][4] * det2_34_01;
float det3_134_023 = mat[1][0] * det2_34_23 - mat[1][2] * det2_34_03 + mat[1][3] * det2_34_02;
float det3_134_024 = mat[1][0] * det2_34_24 - mat[1][2] * det2_34_04 + mat[1][4] * det2_34_02;
float det3_134_034 = mat[1][0] * det2_34_34 - mat[1][3] * det2_34_04 + mat[1][4] * det2_34_03;
float det3_134_123 = mat[1][1] * det2_34_23 - mat[1][2] * det2_34_13 + mat[1][3] * det2_34_12;
float det3_134_124 = mat[1][1] * det2_34_24 - mat[1][2] * det2_34_14 + mat[1][4] * det2_34_12;
float det3_134_134 = mat[1][1] * det2_34_34 - mat[1][3] * det2_34_14 + mat[1][4] * det2_34_13;
float det3_134_234 = mat[1][2] * det2_34_34 - mat[1][3] * det2_34_24 + mat[1][4] * det2_34_23;
// remaining 4x4 sub-determinants
float det4_0123_0123 = mat[0][0] * det3_123_123 - mat[0][1] * det3_123_023 + mat[0][2] * det3_123_013 - mat[0][3] * det3_123_012;
float det4_0123_0124 = mat[0][0] * det3_123_124 - mat[0][1] * det3_123_024 + mat[0][2] * det3_123_014 - mat[0][4] * det3_123_012;
float det4_0123_0134 = mat[0][0] * det3_123_134 - mat[0][1] * det3_123_034 + mat[0][3] * det3_123_014 - mat[0][4] * det3_123_013;
float det4_0123_0234 = mat[0][0] * det3_123_234 - mat[0][2] * det3_123_034 + mat[0][3] * det3_123_024 - mat[0][4] * det3_123_023;
float det4_0123_1234 = mat[0][1] * det3_123_234 - mat[0][2] * det3_123_134 + mat[0][3] * det3_123_124 - mat[0][4] * det3_123_123;
float det4_0124_0123 = mat[0][0] * det3_124_123 - mat[0][1] * det3_124_023 + mat[0][2] * det3_124_013 - mat[0][3] * det3_124_012;
float det4_0124_0124 = mat[0][0] * det3_124_124 - mat[0][1] * det3_124_024 + mat[0][2] * det3_124_014 - mat[0][4] * det3_124_012;
float det4_0124_0134 = mat[0][0] * det3_124_134 - mat[0][1] * det3_124_034 + mat[0][3] * det3_124_014 - mat[0][4] * det3_124_013;
float det4_0124_0234 = mat[0][0] * det3_124_234 - mat[0][2] * det3_124_034 + mat[0][3] * det3_124_024 - mat[0][4] * det3_124_023;
float det4_0124_1234 = mat[0][1] * det3_124_234 - mat[0][2] * det3_124_134 + mat[0][3] * det3_124_124 - mat[0][4] * det3_124_123;
float det4_0134_0123 = mat[0][0] * det3_134_123 - mat[0][1] * det3_134_023 + mat[0][2] * det3_134_013 - mat[0][3] * det3_134_012;
float det4_0134_0124 = mat[0][0] * det3_134_124 - mat[0][1] * det3_134_024 + mat[0][2] * det3_134_014 - mat[0][4] * det3_134_012;
float det4_0134_0134 = mat[0][0] * det3_134_134 - mat[0][1] * det3_134_034 + mat[0][3] * det3_134_014 - mat[0][4] * det3_134_013;
float det4_0134_0234 = mat[0][0] * det3_134_234 - mat[0][2] * det3_134_034 + mat[0][3] * det3_134_024 - mat[0][4] * det3_134_023;
float det4_0134_1234 = mat[0][1] * det3_134_234 - mat[0][2] * det3_134_134 + mat[0][3] * det3_134_124 - mat[0][4] * det3_134_123;
float det4_0234_0123 = mat[0][0] * det3_234_123 - mat[0][1] * det3_234_023 + mat[0][2] * det3_234_013 - mat[0][3] * det3_234_012;
float det4_0234_0124 = mat[0][0] * det3_234_124 - mat[0][1] * det3_234_024 + mat[0][2] * det3_234_014 - mat[0][4] * det3_234_012;
float det4_0234_0134 = mat[0][0] * det3_234_134 - mat[0][1] * det3_234_034 + mat[0][3] * det3_234_014 - mat[0][4] * det3_234_013;
float det4_0234_0234 = mat[0][0] * det3_234_234 - mat[0][2] * det3_234_034 + mat[0][3] * det3_234_024 - mat[0][4] * det3_234_023;
float det4_0234_1234 = mat[0][1] * det3_234_234 - mat[0][2] * det3_234_134 + mat[0][3] * det3_234_124 - mat[0][4] * det3_234_123;
mat[0][0] = det4_1234_1234 * invDet;
mat[0][1] = -det4_0234_1234 * invDet;
mat[0][2] = det4_0134_1234 * invDet;
mat[0][3] = -det4_0124_1234 * invDet;
mat[0][4] = det4_0123_1234 * invDet;
mat[1][0] = -det4_1234_0234 * invDet;
mat[1][1] = det4_0234_0234 * invDet;
mat[1][2] = -det4_0134_0234 * invDet;
mat[1][3] = det4_0124_0234 * invDet;
mat[1][4] = -det4_0123_0234 * invDet;
mat[2][0] = det4_1234_0134 * invDet;
mat[2][1] = -det4_0234_0134 * invDet;
mat[2][2] = det4_0134_0134 * invDet;
mat[2][3] = -det4_0124_0134 * invDet;
mat[2][4] = det4_0123_0134 * invDet;
mat[3][0] = -det4_1234_0124 * invDet;
mat[3][1] = det4_0234_0124 * invDet;
mat[3][2] = -det4_0134_0124 * invDet;
mat[3][3] = det4_0124_0124 * invDet;
mat[3][4] = -det4_0123_0124 * invDet;
mat[4][0] = det4_1234_0123 * invDet;
mat[4][1] = -det4_0234_0123 * invDet;
mat[4][2] = det4_0134_0123 * invDet;
mat[4][3] = -det4_0124_0123 * invDet;
mat[4][4] = det4_0123_0123 * invDet;
return true;
}
/*
============
idMat5::InverseFastSelf
============
*/
bool idMat5::InverseFastSelf()
{
#if 0
// 280+5+25 = 310 multiplications
// 1 division
double det, invDet;
// 2x2 sub-determinants required to calculate 5x5 determinant
float det2_34_01 = mat[3][0] * mat[4][1] - mat[3][1] * mat[4][0];
float det2_34_02 = mat[3][0] * mat[4][2] - mat[3][2] * mat[4][0];
float det2_34_03 = mat[3][0] * mat[4][3] - mat[3][3] * mat[4][0];
float det2_34_04 = mat[3][0] * mat[4][4] - mat[3][4] * mat[4][0];
float det2_34_12 = mat[3][1] * mat[4][2] - mat[3][2] * mat[4][1];
float det2_34_13 = mat[3][1] * mat[4][3] - mat[3][3] * mat[4][1];
float det2_34_14 = mat[3][1] * mat[4][4] - mat[3][4] * mat[4][1];
float det2_34_23 = mat[3][2] * mat[4][3] - mat[3][3] * mat[4][2];
float det2_34_24 = mat[3][2] * mat[4][4] - mat[3][4] * mat[4][2];
float det2_34_34 = mat[3][3] * mat[4][4] - mat[3][4] * mat[4][3];
// 3x3 sub-determinants required to calculate 5x5 determinant
float det3_234_012 = mat[2][0] * det2_34_12 - mat[2][1] * det2_34_02 + mat[2][2] * det2_34_01;
float det3_234_013 = mat[2][0] * det2_34_13 - mat[2][1] * det2_34_03 + mat[2][3] * det2_34_01;
float det3_234_014 = mat[2][0] * det2_34_14 - mat[2][1] * det2_34_04 + mat[2][4] * det2_34_01;
float det3_234_023 = mat[2][0] * det2_34_23 - mat[2][2] * det2_34_03 + mat[2][3] * det2_34_02;
float det3_234_024 = mat[2][0] * det2_34_24 - mat[2][2] * det2_34_04 + mat[2][4] * det2_34_02;
float det3_234_034 = mat[2][0] * det2_34_34 - mat[2][3] * det2_34_04 + mat[2][4] * det2_34_03;
float det3_234_123 = mat[2][1] * det2_34_23 - mat[2][2] * det2_34_13 + mat[2][3] * det2_34_12;
float det3_234_124 = mat[2][1] * det2_34_24 - mat[2][2] * det2_34_14 + mat[2][4] * det2_34_12;
float det3_234_134 = mat[2][1] * det2_34_34 - mat[2][3] * det2_34_14 + mat[2][4] * det2_34_13;
float det3_234_234 = mat[2][2] * det2_34_34 - mat[2][3] * det2_34_24 + mat[2][4] * det2_34_23;
// 4x4 sub-determinants required to calculate 5x5 determinant
float det4_1234_0123 = mat[1][0] * det3_234_123 - mat[1][1] * det3_234_023 + mat[1][2] * det3_234_013 - mat[1][3] * det3_234_012;
float det4_1234_0124 = mat[1][0] * det3_234_124 - mat[1][1] * det3_234_024 + mat[1][2] * det3_234_014 - mat[1][4] * det3_234_012;
float det4_1234_0134 = mat[1][0] * det3_234_134 - mat[1][1] * det3_234_034 + mat[1][3] * det3_234_014 - mat[1][4] * det3_234_013;
float det4_1234_0234 = mat[1][0] * det3_234_234 - mat[1][2] * det3_234_034 + mat[1][3] * det3_234_024 - mat[1][4] * det3_234_023;
float det4_1234_1234 = mat[1][1] * det3_234_234 - mat[1][2] * det3_234_134 + mat[1][3] * det3_234_124 - mat[1][4] * det3_234_123;
// determinant of 5x5 matrix
det = mat[0][0] * det4_1234_1234 - mat[0][1] * det4_1234_0234 + mat[0][2] * det4_1234_0134 - mat[0][3] * det4_1234_0124 + mat[0][4] * det4_1234_0123;
if( idMath::Fabs( det ) < MATRIX_INVERSE_EPSILON )
{
return false;
}
invDet = 1.0f / det;
// remaining 2x2 sub-determinants
float det2_23_01 = mat[2][0] * mat[3][1] - mat[2][1] * mat[3][0];
float det2_23_02 = mat[2][0] * mat[3][2] - mat[2][2] * mat[3][0];
float det2_23_03 = mat[2][0] * mat[3][3] - mat[2][3] * mat[3][0];
float det2_23_04 = mat[2][0] * mat[3][4] - mat[2][4] * mat[3][0];
float det2_23_12 = mat[2][1] * mat[3][2] - mat[2][2] * mat[3][1];
float det2_23_13 = mat[2][1] * mat[3][3] - mat[2][3] * mat[3][1];
float det2_23_14 = mat[2][1] * mat[3][4] - mat[2][4] * mat[3][1];
float det2_23_23 = mat[2][2] * mat[3][3] - mat[2][3] * mat[3][2];
float det2_23_24 = mat[2][2] * mat[3][4] - mat[2][4] * mat[3][2];
float det2_23_34 = mat[2][3] * mat[3][4] - mat[2][4] * mat[3][3];
float det2_24_01 = mat[2][0] * mat[4][1] - mat[2][1] * mat[4][0];
float det2_24_02 = mat[2][0] * mat[4][2] - mat[2][2] * mat[4][0];
float det2_24_03 = mat[2][0] * mat[4][3] - mat[2][3] * mat[4][0];
float det2_24_04 = mat[2][0] * mat[4][4] - mat[2][4] * mat[4][0];
float det2_24_12 = mat[2][1] * mat[4][2] - mat[2][2] * mat[4][1];
float det2_24_13 = mat[2][1] * mat[4][3] - mat[2][3] * mat[4][1];
float det2_24_14 = mat[2][1] * mat[4][4] - mat[2][4] * mat[4][1];
float det2_24_23 = mat[2][2] * mat[4][3] - mat[2][3] * mat[4][2];
float det2_24_24 = mat[2][2] * mat[4][4] - mat[2][4] * mat[4][2];
float det2_24_34 = mat[2][3] * mat[4][4] - mat[2][4] * mat[4][3];
// remaining 3x3 sub-determinants
float det3_123_012 = mat[1][0] * det2_23_12 - mat[1][1] * det2_23_02 + mat[1][2] * det2_23_01;
float det3_123_013 = mat[1][0] * det2_23_13 - mat[1][1] * det2_23_03 + mat[1][3] * det2_23_01;
float det3_123_014 = mat[1][0] * det2_23_14 - mat[1][1] * det2_23_04 + mat[1][4] * det2_23_01;
float det3_123_023 = mat[1][0] * det2_23_23 - mat[1][2] * det2_23_03 + mat[1][3] * det2_23_02;
float det3_123_024 = mat[1][0] * det2_23_24 - mat[1][2] * det2_23_04 + mat[1][4] * det2_23_02;
float det3_123_034 = mat[1][0] * det2_23_34 - mat[1][3] * det2_23_04 + mat[1][4] * det2_23_03;
float det3_123_123 = mat[1][1] * det2_23_23 - mat[1][2] * det2_23_13 + mat[1][3] * det2_23_12;
float det3_123_124 = mat[1][1] * det2_23_24 - mat[1][2] * det2_23_14 + mat[1][4] * det2_23_12;
float det3_123_134 = mat[1][1] * det2_23_34 - mat[1][3] * det2_23_14 + mat[1][4] * det2_23_13;
float det3_123_234 = mat[1][2] * det2_23_34 - mat[1][3] * det2_23_24 + mat[1][4] * det2_23_23;
float det3_124_012 = mat[1][0] * det2_24_12 - mat[1][1] * det2_24_02 + mat[1][2] * det2_24_01;
float det3_124_013 = mat[1][0] * det2_24_13 - mat[1][1] * det2_24_03 + mat[1][3] * det2_24_01;
float det3_124_014 = mat[1][0] * det2_24_14 - mat[1][1] * det2_24_04 + mat[1][4] * det2_24_01;
float det3_124_023 = mat[1][0] * det2_24_23 - mat[1][2] * det2_24_03 + mat[1][3] * det2_24_02;
float det3_124_024 = mat[1][0] * det2_24_24 - mat[1][2] * det2_24_04 + mat[1][4] * det2_24_02;
float det3_124_034 = mat[1][0] * det2_24_34 - mat[1][3] * det2_24_04 + mat[1][4] * det2_24_03;
float det3_124_123 = mat[1][1] * det2_24_23 - mat[1][2] * det2_24_13 + mat[1][3] * det2_24_12;
float det3_124_124 = mat[1][1] * det2_24_24 - mat[1][2] * det2_24_14 + mat[1][4] * det2_24_12;
float det3_124_134 = mat[1][1] * det2_24_34 - mat[1][3] * det2_24_14 + mat[1][4] * det2_24_13;
float det3_124_234 = mat[1][2] * det2_24_34 - mat[1][3] * det2_24_24 + mat[1][4] * det2_24_23;
float det3_134_012 = mat[1][0] * det2_34_12 - mat[1][1] * det2_34_02 + mat[1][2] * det2_34_01;
float det3_134_013 = mat[1][0] * det2_34_13 - mat[1][1] * det2_34_03 + mat[1][3] * det2_34_01;
float det3_134_014 = mat[1][0] * det2_34_14 - mat[1][1] * det2_34_04 + mat[1][4] * det2_34_01;
float det3_134_023 = mat[1][0] * det2_34_23 - mat[1][2] * det2_34_03 + mat[1][3] * det2_34_02;
float det3_134_024 = mat[1][0] * det2_34_24 - mat[1][2] * det2_34_04 + mat[1][4] * det2_34_02;
float det3_134_034 = mat[1][0] * det2_34_34 - mat[1][3] * det2_34_04 + mat[1][4] * det2_34_03;
float det3_134_123 = mat[1][1] * det2_34_23 - mat[1][2] * det2_34_13 + mat[1][3] * det2_34_12;
float det3_134_124 = mat[1][1] * det2_34_24 - mat[1][2] * det2_34_14 + mat[1][4] * det2_34_12;
float det3_134_134 = mat[1][1] * det2_34_34 - mat[1][3] * det2_34_14 + mat[1][4] * det2_34_13;
float det3_134_234 = mat[1][2] * det2_34_34 - mat[1][3] * det2_34_24 + mat[1][4] * det2_34_23;
// remaining 4x4 sub-determinants
float det4_0123_0123 = mat[0][0] * det3_123_123 - mat[0][1] * det3_123_023 + mat[0][2] * det3_123_013 - mat[0][3] * det3_123_012;
float det4_0123_0124 = mat[0][0] * det3_123_124 - mat[0][1] * det3_123_024 + mat[0][2] * det3_123_014 - mat[0][4] * det3_123_012;
float det4_0123_0134 = mat[0][0] * det3_123_134 - mat[0][1] * det3_123_034 + mat[0][3] * det3_123_014 - mat[0][4] * det3_123_013;
float det4_0123_0234 = mat[0][0] * det3_123_234 - mat[0][2] * det3_123_034 + mat[0][3] * det3_123_024 - mat[0][4] * det3_123_023;
float det4_0123_1234 = mat[0][1] * det3_123_234 - mat[0][2] * det3_123_134 + mat[0][3] * det3_123_124 - mat[0][4] * det3_123_123;
float det4_0124_0123 = mat[0][0] * det3_124_123 - mat[0][1] * det3_124_023 + mat[0][2] * det3_124_013 - mat[0][3] * det3_124_012;
float det4_0124_0124 = mat[0][0] * det3_124_124 - mat[0][1] * det3_124_024 + mat[0][2] * det3_124_014 - mat[0][4] * det3_124_012;
float det4_0124_0134 = mat[0][0] * det3_124_134 - mat[0][1] * det3_124_034 + mat[0][3] * det3_124_014 - mat[0][4] * det3_124_013;
float det4_0124_0234 = mat[0][0] * det3_124_234 - mat[0][2] * det3_124_034 + mat[0][3] * det3_124_024 - mat[0][4] * det3_124_023;
float det4_0124_1234 = mat[0][1] * det3_124_234 - mat[0][2] * det3_124_134 + mat[0][3] * det3_124_124 - mat[0][4] * det3_124_123;
float det4_0134_0123 = mat[0][0] * det3_134_123 - mat[0][1] * det3_134_023 + mat[0][2] * det3_134_013 - mat[0][3] * det3_134_012;
float det4_0134_0124 = mat[0][0] * det3_134_124 - mat[0][1] * det3_134_024 + mat[0][2] * det3_134_014 - mat[0][4] * det3_134_012;
float det4_0134_0134 = mat[0][0] * det3_134_134 - mat[0][1] * det3_134_034 + mat[0][3] * det3_134_014 - mat[0][4] * det3_134_013;
float det4_0134_0234 = mat[0][0] * det3_134_234 - mat[0][2] * det3_134_034 + mat[0][3] * det3_134_024 - mat[0][4] * det3_134_023;
float det4_0134_1234 = mat[0][1] * det3_134_234 - mat[0][2] * det3_134_134 + mat[0][3] * det3_134_124 - mat[0][4] * det3_134_123;
float det4_0234_0123 = mat[0][0] * det3_234_123 - mat[0][1] * det3_234_023 + mat[0][2] * det3_234_013 - mat[0][3] * det3_234_012;
float det4_0234_0124 = mat[0][0] * det3_234_124 - mat[0][1] * det3_234_024 + mat[0][2] * det3_234_014 - mat[0][4] * det3_234_012;
float det4_0234_0134 = mat[0][0] * det3_234_134 - mat[0][1] * det3_234_034 + mat[0][3] * det3_234_014 - mat[0][4] * det3_234_013;
float det4_0234_0234 = mat[0][0] * det3_234_234 - mat[0][2] * det3_234_034 + mat[0][3] * det3_234_024 - mat[0][4] * det3_234_023;
float det4_0234_1234 = mat[0][1] * det3_234_234 - mat[0][2] * det3_234_134 + mat[0][3] * det3_234_124 - mat[0][4] * det3_234_123;
mat[0][0] = det4_1234_1234 * invDet;
mat[0][1] = -det4_0234_1234 * invDet;
mat[0][2] = det4_0134_1234 * invDet;
mat[0][3] = -det4_0124_1234 * invDet;
mat[0][4] = det4_0123_1234 * invDet;
mat[1][0] = -det4_1234_0234 * invDet;
mat[1][1] = det4_0234_0234 * invDet;
mat[1][2] = -det4_0134_0234 * invDet;
mat[1][3] = det4_0124_0234 * invDet;
mat[1][4] = -det4_0123_0234 * invDet;
mat[2][0] = det4_1234_0134 * invDet;
mat[2][1] = -det4_0234_0134 * invDet;
mat[2][2] = det4_0134_0134 * invDet;
mat[2][3] = -det4_0124_0134 * invDet;
mat[2][4] = det4_0123_0134 * invDet;
mat[3][0] = -det4_1234_0124 * invDet;
mat[3][1] = det4_0234_0124 * invDet;
mat[3][2] = -det4_0134_0124 * invDet;
mat[3][3] = det4_0124_0124 * invDet;
mat[3][4] = -det4_0123_0124 * invDet;
mat[4][0] = det4_1234_0123 * invDet;
mat[4][1] = -det4_0234_0123 * invDet;
mat[4][2] = det4_0134_0123 * invDet;
mat[4][3] = -det4_0124_0123 * invDet;
mat[4][4] = det4_0123_0123 * invDet;
return true;
#elif 0
// 5*28 = 140 multiplications
// 5 divisions
float* mat = reinterpret_cast<float*>( this );
float s;
double d, di;
di = mat[0];
s = di;
mat[0] = d = 1.0f / di;
mat[1] *= d;
mat[2] *= d;
mat[3] *= d;
mat[4] *= d;
d = -d;
mat[5] *= d;
mat[10] *= d;
mat[15] *= d;
mat[20] *= d;
d = mat[5] * di;
mat[6] += mat[1] * d;
mat[7] += mat[2] * d;
mat[8] += mat[3] * d;
mat[9] += mat[4] * d;
d = mat[10] * di;
mat[11] += mat[1] * d;
mat[12] += mat[2] * d;
mat[13] += mat[3] * d;
mat[14] += mat[4] * d;
d = mat[15] * di;
mat[16] += mat[1] * d;
mat[17] += mat[2] * d;
mat[18] += mat[3] * d;
mat[19] += mat[4] * d;
d = mat[20] * di;
mat[21] += mat[1] * d;
mat[22] += mat[2] * d;
mat[23] += mat[3] * d;
mat[24] += mat[4] * d;
di = mat[6];
s *= di;
mat[6] = d = 1.0f / di;
mat[5] *= d;
mat[7] *= d;
mat[8] *= d;
mat[9] *= d;
d = -d;
mat[1] *= d;
mat[11] *= d;
mat[16] *= d;
mat[21] *= d;
d = mat[1] * di;
mat[0] += mat[5] * d;
mat[2] += mat[7] * d;
mat[3] += mat[8] * d;
mat[4] += mat[9] * d;
d = mat[11] * di;
mat[10] += mat[5] * d;
mat[12] += mat[7] * d;
mat[13] += mat[8] * d;
mat[14] += mat[9] * d;
d = mat[16] * di;
mat[15] += mat[5] * d;
mat[17] += mat[7] * d;
mat[18] += mat[8] * d;
mat[19] += mat[9] * d;
d = mat[21] * di;
mat[20] += mat[5] * d;
mat[22] += mat[7] * d;
mat[23] += mat[8] * d;
mat[24] += mat[9] * d;
di = mat[12];
s *= di;
mat[12] = d = 1.0f / di;
mat[10] *= d;
mat[11] *= d;
mat[13] *= d;
mat[14] *= d;
d = -d;
mat[2] *= d;
mat[7] *= d;
mat[17] *= d;
mat[22] *= d;
d = mat[2] * di;
mat[0] += mat[10] * d;
mat[1] += mat[11] * d;
mat[3] += mat[13] * d;
mat[4] += mat[14] * d;
d = mat[7] * di;
mat[5] += mat[10] * d;
mat[6] += mat[11] * d;
mat[8] += mat[13] * d;
mat[9] += mat[14] * d;
d = mat[17] * di;
mat[15] += mat[10] * d;
mat[16] += mat[11] * d;
mat[18] += mat[13] * d;
mat[19] += mat[14] * d;
d = mat[22] * di;
mat[20] += mat[10] * d;
mat[21] += mat[11] * d;
mat[23] += mat[13] * d;
mat[24] += mat[14] * d;
di = mat[18];
s *= di;
mat[18] = d = 1.0f / di;
mat[15] *= d;
mat[16] *= d;
mat[17] *= d;
mat[19] *= d;
d = -d;
mat[3] *= d;
mat[8] *= d;
mat[13] *= d;
mat[23] *= d;
d = mat[3] * di;
mat[0] += mat[15] * d;
mat[1] += mat[16] * d;
mat[2] += mat[17] * d;
mat[4] += mat[19] * d;
d = mat[8] * di;
mat[5] += mat[15] * d;
mat[6] += mat[16] * d;
mat[7] += mat[17] * d;
mat[9] += mat[19] * d;
d = mat[13] * di;
mat[10] += mat[15] * d;
mat[11] += mat[16] * d;
mat[12] += mat[17] * d;
mat[14] += mat[19] * d;
d = mat[23] * di;
mat[20] += mat[15] * d;
mat[21] += mat[16] * d;
mat[22] += mat[17] * d;
mat[24] += mat[19] * d;
di = mat[24];
s *= di;
mat[24] = d = 1.0f / di;
mat[20] *= d;
mat[21] *= d;
mat[22] *= d;
mat[23] *= d;
d = -d;
mat[4] *= d;
mat[9] *= d;
mat[14] *= d;
mat[19] *= d;
d = mat[4] * di;
mat[0] += mat[20] * d;
mat[1] += mat[21] * d;
mat[2] += mat[22] * d;
mat[3] += mat[23] * d;
d = mat[9] * di;
mat[5] += mat[20] * d;
mat[6] += mat[21] * d;
mat[7] += mat[22] * d;
mat[8] += mat[23] * d;
d = mat[14] * di;
mat[10] += mat[20] * d;
mat[11] += mat[21] * d;
mat[12] += mat[22] * d;
mat[13] += mat[23] * d;
d = mat[19] * di;
mat[15] += mat[20] * d;
mat[16] += mat[21] * d;
mat[17] += mat[22] * d;
mat[18] += mat[23] * d;
return ( s != 0.0f && !IEEE_FLT_IS_NAN( s ) );
#else
// 86+30+6 = 122 multiplications
// 2*1 = 2 divisions
idMat3 r0, r1, r2, r3;
float c0, c1, c2, det, invDet;
float* mat = reinterpret_cast<float*>( this );
// r0 = m0.Inverse(); // 3x3
c0 = mat[1 * 5 + 1] * mat[2 * 5 + 2] - mat[1 * 5 + 2] * mat[2 * 5 + 1];
c1 = mat[1 * 5 + 2] * mat[2 * 5 + 0] - mat[1 * 5 + 0] * mat[2 * 5 + 2];
c2 = mat[1 * 5 + 0] * mat[2 * 5 + 1] - mat[1 * 5 + 1] * mat[2 * 5 + 0];
det = mat[0 * 5 + 0] * c0 + mat[0 * 5 + 1] * c1 + mat[0 * 5 + 2] * c2;
if( idMath::Fabs( det ) < MATRIX_INVERSE_EPSILON )
{
return false;
}
invDet = 1.0f / det;
r0[0][0] = c0 * invDet;
r0[0][1] = ( mat[0 * 5 + 2] * mat[2 * 5 + 1] - mat[0 * 5 + 1] * mat[2 * 5 + 2] ) * invDet;
r0[0][2] = ( mat[0 * 5 + 1] * mat[1 * 5 + 2] - mat[0 * 5 + 2] * mat[1 * 5 + 1] ) * invDet;
r0[1][0] = c1 * invDet;
r0[1][1] = ( mat[0 * 5 + 0] * mat[2 * 5 + 2] - mat[0 * 5 + 2] * mat[2 * 5 + 0] ) * invDet;
r0[1][2] = ( mat[0 * 5 + 2] * mat[1 * 5 + 0] - mat[0 * 5 + 0] * mat[1 * 5 + 2] ) * invDet;
r0[2][0] = c2 * invDet;
r0[2][1] = ( mat[0 * 5 + 1] * mat[2 * 5 + 0] - mat[0 * 5 + 0] * mat[2 * 5 + 1] ) * invDet;
r0[2][2] = ( mat[0 * 5 + 0] * mat[1 * 5 + 1] - mat[0 * 5 + 1] * mat[1 * 5 + 0] ) * invDet;
// r1 = r0 * m1; // 3x2 = 3x3 * 3x2
r1[0][0] = r0[0][0] * mat[0 * 5 + 3] + r0[0][1] * mat[1 * 5 + 3] + r0[0][2] * mat[2 * 5 + 3];
r1[0][1] = r0[0][0] * mat[0 * 5 + 4] + r0[0][1] * mat[1 * 5 + 4] + r0[0][2] * mat[2 * 5 + 4];
r1[1][0] = r0[1][0] * mat[0 * 5 + 3] + r0[1][1] * mat[1 * 5 + 3] + r0[1][2] * mat[2 * 5 + 3];
r1[1][1] = r0[1][0] * mat[0 * 5 + 4] + r0[1][1] * mat[1 * 5 + 4] + r0[1][2] * mat[2 * 5 + 4];
r1[2][0] = r0[2][0] * mat[0 * 5 + 3] + r0[2][1] * mat[1 * 5 + 3] + r0[2][2] * mat[2 * 5 + 3];
r1[2][1] = r0[2][0] * mat[0 * 5 + 4] + r0[2][1] * mat[1 * 5 + 4] + r0[2][2] * mat[2 * 5 + 4];
// r2 = m2 * r1; // 2x2 = 2x3 * 3x2
r2[0][0] = mat[3 * 5 + 0] * r1[0][0] + mat[3 * 5 + 1] * r1[1][0] + mat[3 * 5 + 2] * r1[2][0];
r2[0][1] = mat[3 * 5 + 0] * r1[0][1] + mat[3 * 5 + 1] * r1[1][1] + mat[3 * 5 + 2] * r1[2][1];
r2[1][0] = mat[4 * 5 + 0] * r1[0][0] + mat[4 * 5 + 1] * r1[1][0] + mat[4 * 5 + 2] * r1[2][0];
r2[1][1] = mat[4 * 5 + 0] * r1[0][1] + mat[4 * 5 + 1] * r1[1][1] + mat[4 * 5 + 2] * r1[2][1];
// r3 = r2 - m3; // 2x2 = 2x2 - 2x2
r3[0][0] = r2[0][0] - mat[3 * 5 + 3];
r3[0][1] = r2[0][1] - mat[3 * 5 + 4];
r3[1][0] = r2[1][0] - mat[4 * 5 + 3];
r3[1][1] = r2[1][1] - mat[4 * 5 + 4];
// r3.InverseSelf(); // 2x2
det = r3[0][0] * r3[1][1] - r3[0][1] * r3[1][0];
if( idMath::Fabs( det ) < MATRIX_INVERSE_EPSILON )
{
return false;
}
invDet = 1.0f / det;
c0 = r3[0][0];
r3[0][0] = r3[1][1] * invDet;
r3[0][1] = - r3[0][1] * invDet;
r3[1][0] = - r3[1][0] * invDet;
r3[1][1] = c0 * invDet;
// r2 = m2 * r0; // 2x3 = 2x3 * 3x3
r2[0][0] = mat[3 * 5 + 0] * r0[0][0] + mat[3 * 5 + 1] * r0[1][0] + mat[3 * 5 + 2] * r0[2][0];
r2[0][1] = mat[3 * 5 + 0] * r0[0][1] + mat[3 * 5 + 1] * r0[1][1] + mat[3 * 5 + 2] * r0[2][1];
r2[0][2] = mat[3 * 5 + 0] * r0[0][2] + mat[3 * 5 + 1] * r0[1][2] + mat[3 * 5 + 2] * r0[2][2];
r2[1][0] = mat[4 * 5 + 0] * r0[0][0] + mat[4 * 5 + 1] * r0[1][0] + mat[4 * 5 + 2] * r0[2][0];
r2[1][1] = mat[4 * 5 + 0] * r0[0][1] + mat[4 * 5 + 1] * r0[1][1] + mat[4 * 5 + 2] * r0[2][1];
r2[1][2] = mat[4 * 5 + 0] * r0[0][2] + mat[4 * 5 + 1] * r0[1][2] + mat[4 * 5 + 2] * r0[2][2];
// m2 = r3 * r2; // 2x3 = 2x2 * 2x3
mat[3 * 5 + 0] = r3[0][0] * r2[0][0] + r3[0][1] * r2[1][0];
mat[3 * 5 + 1] = r3[0][0] * r2[0][1] + r3[0][1] * r2[1][1];
mat[3 * 5 + 2] = r3[0][0] * r2[0][2] + r3[0][1] * r2[1][2];
mat[4 * 5 + 0] = r3[1][0] * r2[0][0] + r3[1][1] * r2[1][0];
mat[4 * 5 + 1] = r3[1][0] * r2[0][1] + r3[1][1] * r2[1][1];
mat[4 * 5 + 2] = r3[1][0] * r2[0][2] + r3[1][1] * r2[1][2];
// m0 = r0 - r1 * m2; // 3x3 = 3x3 - 3x2 * 2x3
mat[0 * 5 + 0] = r0[0][0] - r1[0][0] * mat[3 * 5 + 0] - r1[0][1] * mat[4 * 5 + 0];
mat[0 * 5 + 1] = r0[0][1] - r1[0][0] * mat[3 * 5 + 1] - r1[0][1] * mat[4 * 5 + 1];
mat[0 * 5 + 2] = r0[0][2] - r1[0][0] * mat[3 * 5 + 2] - r1[0][1] * mat[4 * 5 + 2];
mat[1 * 5 + 0] = r0[1][0] - r1[1][0] * mat[3 * 5 + 0] - r1[1][1] * mat[4 * 5 + 0];
mat[1 * 5 + 1] = r0[1][1] - r1[1][0] * mat[3 * 5 + 1] - r1[1][1] * mat[4 * 5 + 1];
mat[1 * 5 + 2] = r0[1][2] - r1[1][0] * mat[3 * 5 + 2] - r1[1][1] * mat[4 * 5 + 2];
mat[2 * 5 + 0] = r0[2][0] - r1[2][0] * mat[3 * 5 + 0] - r1[2][1] * mat[4 * 5 + 0];
mat[2 * 5 + 1] = r0[2][1] - r1[2][0] * mat[3 * 5 + 1] - r1[2][1] * mat[4 * 5 + 1];
mat[2 * 5 + 2] = r0[2][2] - r1[2][0] * mat[3 * 5 + 2] - r1[2][1] * mat[4 * 5 + 2];
// m1 = r1 * r3; // 3x2 = 3x2 * 2x2
mat[0 * 5 + 3] = r1[0][0] * r3[0][0] + r1[0][1] * r3[1][0];
mat[0 * 5 + 4] = r1[0][0] * r3[0][1] + r1[0][1] * r3[1][1];
mat[1 * 5 + 3] = r1[1][0] * r3[0][0] + r1[1][1] * r3[1][0];
mat[1 * 5 + 4] = r1[1][0] * r3[0][1] + r1[1][1] * r3[1][1];
mat[2 * 5 + 3] = r1[2][0] * r3[0][0] + r1[2][1] * r3[1][0];
mat[2 * 5 + 4] = r1[2][0] * r3[0][1] + r1[2][1] * r3[1][1];
// m3 = -r3; // 2x2 = - 2x2
mat[3 * 5 + 3] = -r3[0][0];
mat[3 * 5 + 4] = -r3[0][1];
mat[4 * 5 + 3] = -r3[1][0];
mat[4 * 5 + 4] = -r3[1][1];
return true;
#endif
}
/*
=============
idMat5::ToString
=============
*/
const char* idMat5::ToString( int precision ) const
{
return idStr::FloatArrayToString( ToFloatPtr(), GetDimension(), precision );
}
//===============================================================
//
// idMat6
//
//===============================================================
idMat6 mat6_zero( idVec6( 0, 0, 0, 0, 0, 0 ), idVec6( 0, 0, 0, 0, 0, 0 ), idVec6( 0, 0, 0, 0, 0, 0 ), idVec6( 0, 0, 0, 0, 0, 0 ), idVec6( 0, 0, 0, 0, 0, 0 ), idVec6( 0, 0, 0, 0, 0, 0 ) );
idMat6 mat6_identity( idVec6( 1, 0, 0, 0, 0, 0 ), idVec6( 0, 1, 0, 0, 0, 0 ), idVec6( 0, 0, 1, 0, 0, 0 ), idVec6( 0, 0, 0, 1, 0, 0 ), idVec6( 0, 0, 0, 0, 1, 0 ), idVec6( 0, 0, 0, 0, 0, 1 ) );
/*
============
idMat6::Transpose
============
*/
idMat6 idMat6::Transpose() const
{
idMat6 transpose;
int i, j;
for( i = 0; i < 6; i++ )
{
for( j = 0; j < 6; j++ )
{
transpose[ i ][ j ] = mat[ j ][ i ];
}
}
return transpose;
}
/*
============
idMat6::TransposeSelf
============
*/
idMat6& idMat6::TransposeSelf()
{
float temp;
int i, j;
for( i = 0; i < 6; i++ )
{
for( j = i + 1; j < 6; j++ )
{
temp = mat[ i ][ j ];
mat[ i ][ j ] = mat[ j ][ i ];
mat[ j ][ i ] = temp;
}
}
return *this;
}
/*
============
idMat6::Determinant
============
*/
float idMat6::Determinant() const
{
// 2x2 sub-determinants required to calculate 6x6 determinant
float det2_45_01 = mat[4][0] * mat[5][1] - mat[4][1] * mat[5][0];
float det2_45_02 = mat[4][0] * mat[5][2] - mat[4][2] * mat[5][0];
float det2_45_03 = mat[4][0] * mat[5][3] - mat[4][3] * mat[5][0];
float det2_45_04 = mat[4][0] * mat[5][4] - mat[4][4] * mat[5][0];
float det2_45_05 = mat[4][0] * mat[5][5] - mat[4][5] * mat[5][0];
float det2_45_12 = mat[4][1] * mat[5][2] - mat[4][2] * mat[5][1];
float det2_45_13 = mat[4][1] * mat[5][3] - mat[4][3] * mat[5][1];
float det2_45_14 = mat[4][1] * mat[5][4] - mat[4][4] * mat[5][1];
float det2_45_15 = mat[4][1] * mat[5][5] - mat[4][5] * mat[5][1];
float det2_45_23 = mat[4][2] * mat[5][3] - mat[4][3] * mat[5][2];
float det2_45_24 = mat[4][2] * mat[5][4] - mat[4][4] * mat[5][2];
float det2_45_25 = mat[4][2] * mat[5][5] - mat[4][5] * mat[5][2];
float det2_45_34 = mat[4][3] * mat[5][4] - mat[4][4] * mat[5][3];
float det2_45_35 = mat[4][3] * mat[5][5] - mat[4][5] * mat[5][3];
float det2_45_45 = mat[4][4] * mat[5][5] - mat[4][5] * mat[5][4];
// 3x3 sub-determinants required to calculate 6x6 determinant
float det3_345_012 = mat[3][0] * det2_45_12 - mat[3][1] * det2_45_02 + mat[3][2] * det2_45_01;
float det3_345_013 = mat[3][0] * det2_45_13 - mat[3][1] * det2_45_03 + mat[3][3] * det2_45_01;
float det3_345_014 = mat[3][0] * det2_45_14 - mat[3][1] * det2_45_04 + mat[3][4] * det2_45_01;
float det3_345_015 = mat[3][0] * det2_45_15 - mat[3][1] * det2_45_05 + mat[3][5] * det2_45_01;
float det3_345_023 = mat[3][0] * det2_45_23 - mat[3][2] * det2_45_03 + mat[3][3] * det2_45_02;
float det3_345_024 = mat[3][0] * det2_45_24 - mat[3][2] * det2_45_04 + mat[3][4] * det2_45_02;
float det3_345_025 = mat[3][0] * det2_45_25 - mat[3][2] * det2_45_05 + mat[3][5] * det2_45_02;
float det3_345_034 = mat[3][0] * det2_45_34 - mat[3][3] * det2_45_04 + mat[3][4] * det2_45_03;
float det3_345_035 = mat[3][0] * det2_45_35 - mat[3][3] * det2_45_05 + mat[3][5] * det2_45_03;
float det3_345_045 = mat[3][0] * det2_45_45 - mat[3][4] * det2_45_05 + mat[3][5] * det2_45_04;
float det3_345_123 = mat[3][1] * det2_45_23 - mat[3][2] * det2_45_13 + mat[3][3] * det2_45_12;
float det3_345_124 = mat[3][1] * det2_45_24 - mat[3][2] * det2_45_14 + mat[3][4] * det2_45_12;
float det3_345_125 = mat[3][1] * det2_45_25 - mat[3][2] * det2_45_15 + mat[3][5] * det2_45_12;
float det3_345_134 = mat[3][1] * det2_45_34 - mat[3][3] * det2_45_14 + mat[3][4] * det2_45_13;
float det3_345_135 = mat[3][1] * det2_45_35 - mat[3][3] * det2_45_15 + mat[3][5] * det2_45_13;
float det3_345_145 = mat[3][1] * det2_45_45 - mat[3][4] * det2_45_15 + mat[3][5] * det2_45_14;
float det3_345_234 = mat[3][2] * det2_45_34 - mat[3][3] * det2_45_24 + mat[3][4] * det2_45_23;
float det3_345_235 = mat[3][2] * det2_45_35 - mat[3][3] * det2_45_25 + mat[3][5] * det2_45_23;
float det3_345_245 = mat[3][2] * det2_45_45 - mat[3][4] * det2_45_25 + mat[3][5] * det2_45_24;
float det3_345_345 = mat[3][3] * det2_45_45 - mat[3][4] * det2_45_35 + mat[3][5] * det2_45_34;
// 4x4 sub-determinants required to calculate 6x6 determinant
float det4_2345_0123 = mat[2][0] * det3_345_123 - mat[2][1] * det3_345_023 + mat[2][2] * det3_345_013 - mat[2][3] * det3_345_012;
float det4_2345_0124 = mat[2][0] * det3_345_124 - mat[2][1] * det3_345_024 + mat[2][2] * det3_345_014 - mat[2][4] * det3_345_012;
float det4_2345_0125 = mat[2][0] * det3_345_125 - mat[2][1] * det3_345_025 + mat[2][2] * det3_345_015 - mat[2][5] * det3_345_012;
float det4_2345_0134 = mat[2][0] * det3_345_134 - mat[2][1] * det3_345_034 + mat[2][3] * det3_345_014 - mat[2][4] * det3_345_013;
float det4_2345_0135 = mat[2][0] * det3_345_135 - mat[2][1] * det3_345_035 + mat[2][3] * det3_345_015 - mat[2][5] * det3_345_013;
float det4_2345_0145 = mat[2][0] * det3_345_145 - mat[2][1] * det3_345_045 + mat[2][4] * det3_345_015 - mat[2][5] * det3_345_014;
float det4_2345_0234 = mat[2][0] * det3_345_234 - mat[2][2] * det3_345_034 + mat[2][3] * det3_345_024 - mat[2][4] * det3_345_023;
float det4_2345_0235 = mat[2][0] * det3_345_235 - mat[2][2] * det3_345_035 + mat[2][3] * det3_345_025 - mat[2][5] * det3_345_023;
float det4_2345_0245 = mat[2][0] * det3_345_245 - mat[2][2] * det3_345_045 + mat[2][4] * det3_345_025 - mat[2][5] * det3_345_024;
float det4_2345_0345 = mat[2][0] * det3_345_345 - mat[2][3] * det3_345_045 + mat[2][4] * det3_345_035 - mat[2][5] * det3_345_034;
float det4_2345_1234 = mat[2][1] * det3_345_234 - mat[2][2] * det3_345_134 + mat[2][3] * det3_345_124 - mat[2][4] * det3_345_123;
float det4_2345_1235 = mat[2][1] * det3_345_235 - mat[2][2] * det3_345_135 + mat[2][3] * det3_345_125 - mat[2][5] * det3_345_123;
float det4_2345_1245 = mat[2][1] * det3_345_245 - mat[2][2] * det3_345_145 + mat[2][4] * det3_345_125 - mat[2][5] * det3_345_124;
float det4_2345_1345 = mat[2][1] * det3_345_345 - mat[2][3] * det3_345_145 + mat[2][4] * det3_345_135 - mat[2][5] * det3_345_134;
float det4_2345_2345 = mat[2][2] * det3_345_345 - mat[2][3] * det3_345_245 + mat[2][4] * det3_345_235 - mat[2][5] * det3_345_234;
// 5x5 sub-determinants required to calculate 6x6 determinant
float det5_12345_01234 = mat[1][0] * det4_2345_1234 - mat[1][1] * det4_2345_0234 + mat[1][2] * det4_2345_0134 - mat[1][3] * det4_2345_0124 + mat[1][4] * det4_2345_0123;
float det5_12345_01235 = mat[1][0] * det4_2345_1235 - mat[1][1] * det4_2345_0235 + mat[1][2] * det4_2345_0135 - mat[1][3] * det4_2345_0125 + mat[1][5] * det4_2345_0123;
float det5_12345_01245 = mat[1][0] * det4_2345_1245 - mat[1][1] * det4_2345_0245 + mat[1][2] * det4_2345_0145 - mat[1][4] * det4_2345_0125 + mat[1][5] * det4_2345_0124;
float det5_12345_01345 = mat[1][0] * det4_2345_1345 - mat[1][1] * det4_2345_0345 + mat[1][3] * det4_2345_0145 - mat[1][4] * det4_2345_0135 + mat[1][5] * det4_2345_0134;
float det5_12345_02345 = mat[1][0] * det4_2345_2345 - mat[1][2] * det4_2345_0345 + mat[1][3] * det4_2345_0245 - mat[1][4] * det4_2345_0235 + mat[1][5] * det4_2345_0234;
float det5_12345_12345 = mat[1][1] * det4_2345_2345 - mat[1][2] * det4_2345_1345 + mat[1][3] * det4_2345_1245 - mat[1][4] * det4_2345_1235 + mat[1][5] * det4_2345_1234;
// determinant of 6x6 matrix
return mat[0][0] * det5_12345_12345 - mat[0][1] * det5_12345_02345 + mat[0][2] * det5_12345_01345 -
mat[0][3] * det5_12345_01245 + mat[0][4] * det5_12345_01235 - mat[0][5] * det5_12345_01234;
}
/*
============
idMat6::InverseSelf
============
*/
bool idMat6::InverseSelf()
{
// 810+6+36 = 852 multiplications
// 1 division
double det, invDet;
// 2x2 sub-determinants required to calculate 6x6 determinant
float det2_45_01 = mat[4][0] * mat[5][1] - mat[4][1] * mat[5][0];
float det2_45_02 = mat[4][0] * mat[5][2] - mat[4][2] * mat[5][0];
float det2_45_03 = mat[4][0] * mat[5][3] - mat[4][3] * mat[5][0];
float det2_45_04 = mat[4][0] * mat[5][4] - mat[4][4] * mat[5][0];
float det2_45_05 = mat[4][0] * mat[5][5] - mat[4][5] * mat[5][0];
float det2_45_12 = mat[4][1] * mat[5][2] - mat[4][2] * mat[5][1];
float det2_45_13 = mat[4][1] * mat[5][3] - mat[4][3] * mat[5][1];
float det2_45_14 = mat[4][1] * mat[5][4] - mat[4][4] * mat[5][1];
float det2_45_15 = mat[4][1] * mat[5][5] - mat[4][5] * mat[5][1];
float det2_45_23 = mat[4][2] * mat[5][3] - mat[4][3] * mat[5][2];
float det2_45_24 = mat[4][2] * mat[5][4] - mat[4][4] * mat[5][2];
float det2_45_25 = mat[4][2] * mat[5][5] - mat[4][5] * mat[5][2];
float det2_45_34 = mat[4][3] * mat[5][4] - mat[4][4] * mat[5][3];
float det2_45_35 = mat[4][3] * mat[5][5] - mat[4][5] * mat[5][3];
float det2_45_45 = mat[4][4] * mat[5][5] - mat[4][5] * mat[5][4];
// 3x3 sub-determinants required to calculate 6x6 determinant
float det3_345_012 = mat[3][0] * det2_45_12 - mat[3][1] * det2_45_02 + mat[3][2] * det2_45_01;
float det3_345_013 = mat[3][0] * det2_45_13 - mat[3][1] * det2_45_03 + mat[3][3] * det2_45_01;
float det3_345_014 = mat[3][0] * det2_45_14 - mat[3][1] * det2_45_04 + mat[3][4] * det2_45_01;
float det3_345_015 = mat[3][0] * det2_45_15 - mat[3][1] * det2_45_05 + mat[3][5] * det2_45_01;
float det3_345_023 = mat[3][0] * det2_45_23 - mat[3][2] * det2_45_03 + mat[3][3] * det2_45_02;
float det3_345_024 = mat[3][0] * det2_45_24 - mat[3][2] * det2_45_04 + mat[3][4] * det2_45_02;
float det3_345_025 = mat[3][0] * det2_45_25 - mat[3][2] * det2_45_05 + mat[3][5] * det2_45_02;
float det3_345_034 = mat[3][0] * det2_45_34 - mat[3][3] * det2_45_04 + mat[3][4] * det2_45_03;
float det3_345_035 = mat[3][0] * det2_45_35 - mat[3][3] * det2_45_05 + mat[3][5] * det2_45_03;
float det3_345_045 = mat[3][0] * det2_45_45 - mat[3][4] * det2_45_05 + mat[3][5] * det2_45_04;
float det3_345_123 = mat[3][1] * det2_45_23 - mat[3][2] * det2_45_13 + mat[3][3] * det2_45_12;
float det3_345_124 = mat[3][1] * det2_45_24 - mat[3][2] * det2_45_14 + mat[3][4] * det2_45_12;
float det3_345_125 = mat[3][1] * det2_45_25 - mat[3][2] * det2_45_15 + mat[3][5] * det2_45_12;
float det3_345_134 = mat[3][1] * det2_45_34 - mat[3][3] * det2_45_14 + mat[3][4] * det2_45_13;
float det3_345_135 = mat[3][1] * det2_45_35 - mat[3][3] * det2_45_15 + mat[3][5] * det2_45_13;
float det3_345_145 = mat[3][1] * det2_45_45 - mat[3][4] * det2_45_15 + mat[3][5] * det2_45_14;
float det3_345_234 = mat[3][2] * det2_45_34 - mat[3][3] * det2_45_24 + mat[3][4] * det2_45_23;
float det3_345_235 = mat[3][2] * det2_45_35 - mat[3][3] * det2_45_25 + mat[3][5] * det2_45_23;
float det3_345_245 = mat[3][2] * det2_45_45 - mat[3][4] * det2_45_25 + mat[3][5] * det2_45_24;
float det3_345_345 = mat[3][3] * det2_45_45 - mat[3][4] * det2_45_35 + mat[3][5] * det2_45_34;
// 4x4 sub-determinants required to calculate 6x6 determinant
float det4_2345_0123 = mat[2][0] * det3_345_123 - mat[2][1] * det3_345_023 + mat[2][2] * det3_345_013 - mat[2][3] * det3_345_012;
float det4_2345_0124 = mat[2][0] * det3_345_124 - mat[2][1] * det3_345_024 + mat[2][2] * det3_345_014 - mat[2][4] * det3_345_012;
float det4_2345_0125 = mat[2][0] * det3_345_125 - mat[2][1] * det3_345_025 + mat[2][2] * det3_345_015 - mat[2][5] * det3_345_012;
float det4_2345_0134 = mat[2][0] * det3_345_134 - mat[2][1] * det3_345_034 + mat[2][3] * det3_345_014 - mat[2][4] * det3_345_013;
float det4_2345_0135 = mat[2][0] * det3_345_135 - mat[2][1] * det3_345_035 + mat[2][3] * det3_345_015 - mat[2][5] * det3_345_013;
float det4_2345_0145 = mat[2][0] * det3_345_145 - mat[2][1] * det3_345_045 + mat[2][4] * det3_345_015 - mat[2][5] * det3_345_014;
float det4_2345_0234 = mat[2][0] * det3_345_234 - mat[2][2] * det3_345_034 + mat[2][3] * det3_345_024 - mat[2][4] * det3_345_023;
float det4_2345_0235 = mat[2][0] * det3_345_235 - mat[2][2] * det3_345_035 + mat[2][3] * det3_345_025 - mat[2][5] * det3_345_023;
float det4_2345_0245 = mat[2][0] * det3_345_245 - mat[2][2] * det3_345_045 + mat[2][4] * det3_345_025 - mat[2][5] * det3_345_024;
float det4_2345_0345 = mat[2][0] * det3_345_345 - mat[2][3] * det3_345_045 + mat[2][4] * det3_345_035 - mat[2][5] * det3_345_034;
float det4_2345_1234 = mat[2][1] * det3_345_234 - mat[2][2] * det3_345_134 + mat[2][3] * det3_345_124 - mat[2][4] * det3_345_123;
float det4_2345_1235 = mat[2][1] * det3_345_235 - mat[2][2] * det3_345_135 + mat[2][3] * det3_345_125 - mat[2][5] * det3_345_123;
float det4_2345_1245 = mat[2][1] * det3_345_245 - mat[2][2] * det3_345_145 + mat[2][4] * det3_345_125 - mat[2][5] * det3_345_124;
float det4_2345_1345 = mat[2][1] * det3_345_345 - mat[2][3] * det3_345_145 + mat[2][4] * det3_345_135 - mat[2][5] * det3_345_134;
float det4_2345_2345 = mat[2][2] * det3_345_345 - mat[2][3] * det3_345_245 + mat[2][4] * det3_345_235 - mat[2][5] * det3_345_234;
// 5x5 sub-determinants required to calculate 6x6 determinant
float det5_12345_01234 = mat[1][0] * det4_2345_1234 - mat[1][1] * det4_2345_0234 + mat[1][2] * det4_2345_0134 - mat[1][3] * det4_2345_0124 + mat[1][4] * det4_2345_0123;
float det5_12345_01235 = mat[1][0] * det4_2345_1235 - mat[1][1] * det4_2345_0235 + mat[1][2] * det4_2345_0135 - mat[1][3] * det4_2345_0125 + mat[1][5] * det4_2345_0123;
float det5_12345_01245 = mat[1][0] * det4_2345_1245 - mat[1][1] * det4_2345_0245 + mat[1][2] * det4_2345_0145 - mat[1][4] * det4_2345_0125 + mat[1][5] * det4_2345_0124;
float det5_12345_01345 = mat[1][0] * det4_2345_1345 - mat[1][1] * det4_2345_0345 + mat[1][3] * det4_2345_0145 - mat[1][4] * det4_2345_0135 + mat[1][5] * det4_2345_0134;
float det5_12345_02345 = mat[1][0] * det4_2345_2345 - mat[1][2] * det4_2345_0345 + mat[1][3] * det4_2345_0245 - mat[1][4] * det4_2345_0235 + mat[1][5] * det4_2345_0234;
float det5_12345_12345 = mat[1][1] * det4_2345_2345 - mat[1][2] * det4_2345_1345 + mat[1][3] * det4_2345_1245 - mat[1][4] * det4_2345_1235 + mat[1][5] * det4_2345_1234;
// determinant of 6x6 matrix
det = mat[0][0] * det5_12345_12345 - mat[0][1] * det5_12345_02345 + mat[0][2] * det5_12345_01345 -
mat[0][3] * det5_12345_01245 + mat[0][4] * det5_12345_01235 - mat[0][5] * det5_12345_01234;
if( idMath::Fabs( det ) < MATRIX_INVERSE_EPSILON )
{
return false;
}
invDet = 1.0f / det;
// remaining 2x2 sub-determinants
float det2_34_01 = mat[3][0] * mat[4][1] - mat[3][1] * mat[4][0];
float det2_34_02 = mat[3][0] * mat[4][2] - mat[3][2] * mat[4][0];
float det2_34_03 = mat[3][0] * mat[4][3] - mat[3][3] * mat[4][0];
float det2_34_04 = mat[3][0] * mat[4][4] - mat[3][4] * mat[4][0];
float det2_34_05 = mat[3][0] * mat[4][5] - mat[3][5] * mat[4][0];
float det2_34_12 = mat[3][1] * mat[4][2] - mat[3][2] * mat[4][1];
float det2_34_13 = mat[3][1] * mat[4][3] - mat[3][3] * mat[4][1];
float det2_34_14 = mat[3][1] * mat[4][4] - mat[3][4] * mat[4][1];
float det2_34_15 = mat[3][1] * mat[4][5] - mat[3][5] * mat[4][1];
float det2_34_23 = mat[3][2] * mat[4][3] - mat[3][3] * mat[4][2];
float det2_34_24 = mat[3][2] * mat[4][4] - mat[3][4] * mat[4][2];
float det2_34_25 = mat[3][2] * mat[4][5] - mat[3][5] * mat[4][2];
float det2_34_34 = mat[3][3] * mat[4][4] - mat[3][4] * mat[4][3];
float det2_34_35 = mat[3][3] * mat[4][5] - mat[3][5] * mat[4][3];
float det2_34_45 = mat[3][4] * mat[4][5] - mat[3][5] * mat[4][4];
float det2_35_01 = mat[3][0] * mat[5][1] - mat[3][1] * mat[5][0];
float det2_35_02 = mat[3][0] * mat[5][2] - mat[3][2] * mat[5][0];
float det2_35_03 = mat[3][0] * mat[5][3] - mat[3][3] * mat[5][0];
float det2_35_04 = mat[3][0] * mat[5][4] - mat[3][4] * mat[5][0];
float det2_35_05 = mat[3][0] * mat[5][5] - mat[3][5] * mat[5][0];
float det2_35_12 = mat[3][1] * mat[5][2] - mat[3][2] * mat[5][1];
float det2_35_13 = mat[3][1] * mat[5][3] - mat[3][3] * mat[5][1];
float det2_35_14 = mat[3][1] * mat[5][4] - mat[3][4] * mat[5][1];
float det2_35_15 = mat[3][1] * mat[5][5] - mat[3][5] * mat[5][1];
float det2_35_23 = mat[3][2] * mat[5][3] - mat[3][3] * mat[5][2];
float det2_35_24 = mat[3][2] * mat[5][4] - mat[3][4] * mat[5][2];
float det2_35_25 = mat[3][2] * mat[5][5] - mat[3][5] * mat[5][2];
float det2_35_34 = mat[3][3] * mat[5][4] - mat[3][4] * mat[5][3];
float det2_35_35 = mat[3][3] * mat[5][5] - mat[3][5] * mat[5][3];
float det2_35_45 = mat[3][4] * mat[5][5] - mat[3][5] * mat[5][4];
// remaining 3x3 sub-determinants
float det3_234_012 = mat[2][0] * det2_34_12 - mat[2][1] * det2_34_02 + mat[2][2] * det2_34_01;
float det3_234_013 = mat[2][0] * det2_34_13 - mat[2][1] * det2_34_03 + mat[2][3] * det2_34_01;
float det3_234_014 = mat[2][0] * det2_34_14 - mat[2][1] * det2_34_04 + mat[2][4] * det2_34_01;
float det3_234_015 = mat[2][0] * det2_34_15 - mat[2][1] * det2_34_05 + mat[2][5] * det2_34_01;
float det3_234_023 = mat[2][0] * det2_34_23 - mat[2][2] * det2_34_03 + mat[2][3] * det2_34_02;
float det3_234_024 = mat[2][0] * det2_34_24 - mat[2][2] * det2_34_04 + mat[2][4] * det2_34_02;
float det3_234_025 = mat[2][0] * det2_34_25 - mat[2][2] * det2_34_05 + mat[2][5] * det2_34_02;
float det3_234_034 = mat[2][0] * det2_34_34 - mat[2][3] * det2_34_04 + mat[2][4] * det2_34_03;
float det3_234_035 = mat[2][0] * det2_34_35 - mat[2][3] * det2_34_05 + mat[2][5] * det2_34_03;
float det3_234_045 = mat[2][0] * det2_34_45 - mat[2][4] * det2_34_05 + mat[2][5] * det2_34_04;
float det3_234_123 = mat[2][1] * det2_34_23 - mat[2][2] * det2_34_13 + mat[2][3] * det2_34_12;
float det3_234_124 = mat[2][1] * det2_34_24 - mat[2][2] * det2_34_14 + mat[2][4] * det2_34_12;
float det3_234_125 = mat[2][1] * det2_34_25 - mat[2][2] * det2_34_15 + mat[2][5] * det2_34_12;
float det3_234_134 = mat[2][1] * det2_34_34 - mat[2][3] * det2_34_14 + mat[2][4] * det2_34_13;
float det3_234_135 = mat[2][1] * det2_34_35 - mat[2][3] * det2_34_15 + mat[2][5] * det2_34_13;
float det3_234_145 = mat[2][1] * det2_34_45 - mat[2][4] * det2_34_15 + mat[2][5] * det2_34_14;
float det3_234_234 = mat[2][2] * det2_34_34 - mat[2][3] * det2_34_24 + mat[2][4] * det2_34_23;
float det3_234_235 = mat[2][2] * det2_34_35 - mat[2][3] * det2_34_25 + mat[2][5] * det2_34_23;
float det3_234_245 = mat[2][2] * det2_34_45 - mat[2][4] * det2_34_25 + mat[2][5] * det2_34_24;
float det3_234_345 = mat[2][3] * det2_34_45 - mat[2][4] * det2_34_35 + mat[2][5] * det2_34_34;
float det3_235_012 = mat[2][0] * det2_35_12 - mat[2][1] * det2_35_02 + mat[2][2] * det2_35_01;
float det3_235_013 = mat[2][0] * det2_35_13 - mat[2][1] * det2_35_03 + mat[2][3] * det2_35_01;
float det3_235_014 = mat[2][0] * det2_35_14 - mat[2][1] * det2_35_04 + mat[2][4] * det2_35_01;
float det3_235_015 = mat[2][0] * det2_35_15 - mat[2][1] * det2_35_05 + mat[2][5] * det2_35_01;
float det3_235_023 = mat[2][0] * det2_35_23 - mat[2][2] * det2_35_03 + mat[2][3] * det2_35_02;
float det3_235_024 = mat[2][0] * det2_35_24 - mat[2][2] * det2_35_04 + mat[2][4] * det2_35_02;
float det3_235_025 = mat[2][0] * det2_35_25 - mat[2][2] * det2_35_05 + mat[2][5] * det2_35_02;
float det3_235_034 = mat[2][0] * det2_35_34 - mat[2][3] * det2_35_04 + mat[2][4] * det2_35_03;
float det3_235_035 = mat[2][0] * det2_35_35 - mat[2][3] * det2_35_05 + mat[2][5] * det2_35_03;
float det3_235_045 = mat[2][0] * det2_35_45 - mat[2][4] * det2_35_05 + mat[2][5] * det2_35_04;
float det3_235_123 = mat[2][1] * det2_35_23 - mat[2][2] * det2_35_13 + mat[2][3] * det2_35_12;
float det3_235_124 = mat[2][1] * det2_35_24 - mat[2][2] * det2_35_14 + mat[2][4] * det2_35_12;
float det3_235_125 = mat[2][1] * det2_35_25 - mat[2][2] * det2_35_15 + mat[2][5] * det2_35_12;
float det3_235_134 = mat[2][1] * det2_35_34 - mat[2][3] * det2_35_14 + mat[2][4] * det2_35_13;
float det3_235_135 = mat[2][1] * det2_35_35 - mat[2][3] * det2_35_15 + mat[2][5] * det2_35_13;
float det3_235_145 = mat[2][1] * det2_35_45 - mat[2][4] * det2_35_15 + mat[2][5] * det2_35_14;
float det3_235_234 = mat[2][2] * det2_35_34 - mat[2][3] * det2_35_24 + mat[2][4] * det2_35_23;
float det3_235_235 = mat[2][2] * det2_35_35 - mat[2][3] * det2_35_25 + mat[2][5] * det2_35_23;
float det3_235_245 = mat[2][2] * det2_35_45 - mat[2][4] * det2_35_25 + mat[2][5] * det2_35_24;
float det3_235_345 = mat[2][3] * det2_35_45 - mat[2][4] * det2_35_35 + mat[2][5] * det2_35_34;
float det3_245_012 = mat[2][0] * det2_45_12 - mat[2][1] * det2_45_02 + mat[2][2] * det2_45_01;
float det3_245_013 = mat[2][0] * det2_45_13 - mat[2][1] * det2_45_03 + mat[2][3] * det2_45_01;
float det3_245_014 = mat[2][0] * det2_45_14 - mat[2][1] * det2_45_04 + mat[2][4] * det2_45_01;
float det3_245_015 = mat[2][0] * det2_45_15 - mat[2][1] * det2_45_05 + mat[2][5] * det2_45_01;
float det3_245_023 = mat[2][0] * det2_45_23 - mat[2][2] * det2_45_03 + mat[2][3] * det2_45_02;
float det3_245_024 = mat[2][0] * det2_45_24 - mat[2][2] * det2_45_04 + mat[2][4] * det2_45_02;
float det3_245_025 = mat[2][0] * det2_45_25 - mat[2][2] * det2_45_05 + mat[2][5] * det2_45_02;
float det3_245_034 = mat[2][0] * det2_45_34 - mat[2][3] * det2_45_04 + mat[2][4] * det2_45_03;
float det3_245_035 = mat[2][0] * det2_45_35 - mat[2][3] * det2_45_05 + mat[2][5] * det2_45_03;
float det3_245_045 = mat[2][0] * det2_45_45 - mat[2][4] * det2_45_05 + mat[2][5] * det2_45_04;
float det3_245_123 = mat[2][1] * det2_45_23 - mat[2][2] * det2_45_13 + mat[2][3] * det2_45_12;
float det3_245_124 = mat[2][1] * det2_45_24 - mat[2][2] * det2_45_14 + mat[2][4] * det2_45_12;
float det3_245_125 = mat[2][1] * det2_45_25 - mat[2][2] * det2_45_15 + mat[2][5] * det2_45_12;
float det3_245_134 = mat[2][1] * det2_45_34 - mat[2][3] * det2_45_14 + mat[2][4] * det2_45_13;
float det3_245_135 = mat[2][1] * det2_45_35 - mat[2][3] * det2_45_15 + mat[2][5] * det2_45_13;
float det3_245_145 = mat[2][1] * det2_45_45 - mat[2][4] * det2_45_15 + mat[2][5] * det2_45_14;
float det3_245_234 = mat[2][2] * det2_45_34 - mat[2][3] * det2_45_24 + mat[2][4] * det2_45_23;
float det3_245_235 = mat[2][2] * det2_45_35 - mat[2][3] * det2_45_25 + mat[2][5] * det2_45_23;
float det3_245_245 = mat[2][2] * det2_45_45 - mat[2][4] * det2_45_25 + mat[2][5] * det2_45_24;
float det3_245_345 = mat[2][3] * det2_45_45 - mat[2][4] * det2_45_35 + mat[2][5] * det2_45_34;
// remaining 4x4 sub-determinants
float det4_1234_0123 = mat[1][0] * det3_234_123 - mat[1][1] * det3_234_023 + mat[1][2] * det3_234_013 - mat[1][3] * det3_234_012;
float det4_1234_0124 = mat[1][0] * det3_234_124 - mat[1][1] * det3_234_024 + mat[1][2] * det3_234_014 - mat[1][4] * det3_234_012;
float det4_1234_0125 = mat[1][0] * det3_234_125 - mat[1][1] * det3_234_025 + mat[1][2] * det3_234_015 - mat[1][5] * det3_234_012;
float det4_1234_0134 = mat[1][0] * det3_234_134 - mat[1][1] * det3_234_034 + mat[1][3] * det3_234_014 - mat[1][4] * det3_234_013;
float det4_1234_0135 = mat[1][0] * det3_234_135 - mat[1][1] * det3_234_035 + mat[1][3] * det3_234_015 - mat[1][5] * det3_234_013;
float det4_1234_0145 = mat[1][0] * det3_234_145 - mat[1][1] * det3_234_045 + mat[1][4] * det3_234_015 - mat[1][5] * det3_234_014;
float det4_1234_0234 = mat[1][0] * det3_234_234 - mat[1][2] * det3_234_034 + mat[1][3] * det3_234_024 - mat[1][4] * det3_234_023;
float det4_1234_0235 = mat[1][0] * det3_234_235 - mat[1][2] * det3_234_035 + mat[1][3] * det3_234_025 - mat[1][5] * det3_234_023;
float det4_1234_0245 = mat[1][0] * det3_234_245 - mat[1][2] * det3_234_045 + mat[1][4] * det3_234_025 - mat[1][5] * det3_234_024;
float det4_1234_0345 = mat[1][0] * det3_234_345 - mat[1][3] * det3_234_045 + mat[1][4] * det3_234_035 - mat[1][5] * det3_234_034;
float det4_1234_1234 = mat[1][1] * det3_234_234 - mat[1][2] * det3_234_134 + mat[1][3] * det3_234_124 - mat[1][4] * det3_234_123;
float det4_1234_1235 = mat[1][1] * det3_234_235 - mat[1][2] * det3_234_135 + mat[1][3] * det3_234_125 - mat[1][5] * det3_234_123;
float det4_1234_1245 = mat[1][1] * det3_234_245 - mat[1][2] * det3_234_145 + mat[1][4] * det3_234_125 - mat[1][5] * det3_234_124;
float det4_1234_1345 = mat[1][1] * det3_234_345 - mat[1][3] * det3_234_145 + mat[1][4] * det3_234_135 - mat[1][5] * det3_234_134;
float det4_1234_2345 = mat[1][2] * det3_234_345 - mat[1][3] * det3_234_245 + mat[1][4] * det3_234_235 - mat[1][5] * det3_234_234;
float det4_1235_0123 = mat[1][0] * det3_235_123 - mat[1][1] * det3_235_023 + mat[1][2] * det3_235_013 - mat[1][3] * det3_235_012;
float det4_1235_0124 = mat[1][0] * det3_235_124 - mat[1][1] * det3_235_024 + mat[1][2] * det3_235_014 - mat[1][4] * det3_235_012;
float det4_1235_0125 = mat[1][0] * det3_235_125 - mat[1][1] * det3_235_025 + mat[1][2] * det3_235_015 - mat[1][5] * det3_235_012;
float det4_1235_0134 = mat[1][0] * det3_235_134 - mat[1][1] * det3_235_034 + mat[1][3] * det3_235_014 - mat[1][4] * det3_235_013;
float det4_1235_0135 = mat[1][0] * det3_235_135 - mat[1][1] * det3_235_035 + mat[1][3] * det3_235_015 - mat[1][5] * det3_235_013;
float det4_1235_0145 = mat[1][0] * det3_235_145 - mat[1][1] * det3_235_045 + mat[1][4] * det3_235_015 - mat[1][5] * det3_235_014;
float det4_1235_0234 = mat[1][0] * det3_235_234 - mat[1][2] * det3_235_034 + mat[1][3] * det3_235_024 - mat[1][4] * det3_235_023;
float det4_1235_0235 = mat[1][0] * det3_235_235 - mat[1][2] * det3_235_035 + mat[1][3] * det3_235_025 - mat[1][5] * det3_235_023;
float det4_1235_0245 = mat[1][0] * det3_235_245 - mat[1][2] * det3_235_045 + mat[1][4] * det3_235_025 - mat[1][5] * det3_235_024;
float det4_1235_0345 = mat[1][0] * det3_235_345 - mat[1][3] * det3_235_045 + mat[1][4] * det3_235_035 - mat[1][5] * det3_235_034;
float det4_1235_1234 = mat[1][1] * det3_235_234 - mat[1][2] * det3_235_134 + mat[1][3] * det3_235_124 - mat[1][4] * det3_235_123;
float det4_1235_1235 = mat[1][1] * det3_235_235 - mat[1][2] * det3_235_135 + mat[1][3] * det3_235_125 - mat[1][5] * det3_235_123;
float det4_1235_1245 = mat[1][1] * det3_235_245 - mat[1][2] * det3_235_145 + mat[1][4] * det3_235_125 - mat[1][5] * det3_235_124;
float det4_1235_1345 = mat[1][1] * det3_235_345 - mat[1][3] * det3_235_145 + mat[1][4] * det3_235_135 - mat[1][5] * det3_235_134;
float det4_1235_2345 = mat[1][2] * det3_235_345 - mat[1][3] * det3_235_245 + mat[1][4] * det3_235_235 - mat[1][5] * det3_235_234;
float det4_1245_0123 = mat[1][0] * det3_245_123 - mat[1][1] * det3_245_023 + mat[1][2] * det3_245_013 - mat[1][3] * det3_245_012;
float det4_1245_0124 = mat[1][0] * det3_245_124 - mat[1][1] * det3_245_024 + mat[1][2] * det3_245_014 - mat[1][4] * det3_245_012;
float det4_1245_0125 = mat[1][0] * det3_245_125 - mat[1][1] * det3_245_025 + mat[1][2] * det3_245_015 - mat[1][5] * det3_245_012;
float det4_1245_0134 = mat[1][0] * det3_245_134 - mat[1][1] * det3_245_034 + mat[1][3] * det3_245_014 - mat[1][4] * det3_245_013;
float det4_1245_0135 = mat[1][0] * det3_245_135 - mat[1][1] * det3_245_035 + mat[1][3] * det3_245_015 - mat[1][5] * det3_245_013;
float det4_1245_0145 = mat[1][0] * det3_245_145 - mat[1][1] * det3_245_045 + mat[1][4] * det3_245_015 - mat[1][5] * det3_245_014;
float det4_1245_0234 = mat[1][0] * det3_245_234 - mat[1][2] * det3_245_034 + mat[1][3] * det3_245_024 - mat[1][4] * det3_245_023;
float det4_1245_0235 = mat[1][0] * det3_245_235 - mat[1][2] * det3_245_035 + mat[1][3] * det3_245_025 - mat[1][5] * det3_245_023;
float det4_1245_0245 = mat[1][0] * det3_245_245 - mat[1][2] * det3_245_045 + mat[1][4] * det3_245_025 - mat[1][5] * det3_245_024;
float det4_1245_0345 = mat[1][0] * det3_245_345 - mat[1][3] * det3_245_045 + mat[1][4] * det3_245_035 - mat[1][5] * det3_245_034;
float det4_1245_1234 = mat[1][1] * det3_245_234 - mat[1][2] * det3_245_134 + mat[1][3] * det3_245_124 - mat[1][4] * det3_245_123;
float det4_1245_1235 = mat[1][1] * det3_245_235 - mat[1][2] * det3_245_135 + mat[1][3] * det3_245_125 - mat[1][5] * det3_245_123;
float det4_1245_1245 = mat[1][1] * det3_245_245 - mat[1][2] * det3_245_145 + mat[1][4] * det3_245_125 - mat[1][5] * det3_245_124;
float det4_1245_1345 = mat[1][1] * det3_245_345 - mat[1][3] * det3_245_145 + mat[1][4] * det3_245_135 - mat[1][5] * det3_245_134;
float det4_1245_2345 = mat[1][2] * det3_245_345 - mat[1][3] * det3_245_245 + mat[1][4] * det3_245_235 - mat[1][5] * det3_245_234;
float det4_1345_0123 = mat[1][0] * det3_345_123 - mat[1][1] * det3_345_023 + mat[1][2] * det3_345_013 - mat[1][3] * det3_345_012;
float det4_1345_0124 = mat[1][0] * det3_345_124 - mat[1][1] * det3_345_024 + mat[1][2] * det3_345_014 - mat[1][4] * det3_345_012;
float det4_1345_0125 = mat[1][0] * det3_345_125 - mat[1][1] * det3_345_025 + mat[1][2] * det3_345_015 - mat[1][5] * det3_345_012;
float det4_1345_0134 = mat[1][0] * det3_345_134 - mat[1][1] * det3_345_034 + mat[1][3] * det3_345_014 - mat[1][4] * det3_345_013;
float det4_1345_0135 = mat[1][0] * det3_345_135 - mat[1][1] * det3_345_035 + mat[1][3] * det3_345_015 - mat[1][5] * det3_345_013;
float det4_1345_0145 = mat[1][0] * det3_345_145 - mat[1][1] * det3_345_045 + mat[1][4] * det3_345_015 - mat[1][5] * det3_345_014;
float det4_1345_0234 = mat[1][0] * det3_345_234 - mat[1][2] * det3_345_034 + mat[1][3] * det3_345_024 - mat[1][4] * det3_345_023;
float det4_1345_0235 = mat[1][0] * det3_345_235 - mat[1][2] * det3_345_035 + mat[1][3] * det3_345_025 - mat[1][5] * det3_345_023;
float det4_1345_0245 = mat[1][0] * det3_345_245 - mat[1][2] * det3_345_045 + mat[1][4] * det3_345_025 - mat[1][5] * det3_345_024;
float det4_1345_0345 = mat[1][0] * det3_345_345 - mat[1][3] * det3_345_045 + mat[1][4] * det3_345_035 - mat[1][5] * det3_345_034;
float det4_1345_1234 = mat[1][1] * det3_345_234 - mat[1][2] * det3_345_134 + mat[1][3] * det3_345_124 - mat[1][4] * det3_345_123;
float det4_1345_1235 = mat[1][1] * det3_345_235 - mat[1][2] * det3_345_135 + mat[1][3] * det3_345_125 - mat[1][5] * det3_345_123;
float det4_1345_1245 = mat[1][1] * det3_345_245 - mat[1][2] * det3_345_145 + mat[1][4] * det3_345_125 - mat[1][5] * det3_345_124;
float det4_1345_1345 = mat[1][1] * det3_345_345 - mat[1][3] * det3_345_145 + mat[1][4] * det3_345_135 - mat[1][5] * det3_345_134;
float det4_1345_2345 = mat[1][2] * det3_345_345 - mat[1][3] * det3_345_245 + mat[1][4] * det3_345_235 - mat[1][5] * det3_345_234;
// remaining 5x5 sub-determinants
float det5_01234_01234 = mat[0][0] * det4_1234_1234 - mat[0][1] * det4_1234_0234 + mat[0][2] * det4_1234_0134 - mat[0][3] * det4_1234_0124 + mat[0][4] * det4_1234_0123;
float det5_01234_01235 = mat[0][0] * det4_1234_1235 - mat[0][1] * det4_1234_0235 + mat[0][2] * det4_1234_0135 - mat[0][3] * det4_1234_0125 + mat[0][5] * det4_1234_0123;
float det5_01234_01245 = mat[0][0] * det4_1234_1245 - mat[0][1] * det4_1234_0245 + mat[0][2] * det4_1234_0145 - mat[0][4] * det4_1234_0125 + mat[0][5] * det4_1234_0124;
float det5_01234_01345 = mat[0][0] * det4_1234_1345 - mat[0][1] * det4_1234_0345 + mat[0][3] * det4_1234_0145 - mat[0][4] * det4_1234_0135 + mat[0][5] * det4_1234_0134;
float det5_01234_02345 = mat[0][0] * det4_1234_2345 - mat[0][2] * det4_1234_0345 + mat[0][3] * det4_1234_0245 - mat[0][4] * det4_1234_0235 + mat[0][5] * det4_1234_0234;
float det5_01234_12345 = mat[0][1] * det4_1234_2345 - mat[0][2] * det4_1234_1345 + mat[0][3] * det4_1234_1245 - mat[0][4] * det4_1234_1235 + mat[0][5] * det4_1234_1234;
float det5_01235_01234 = mat[0][0] * det4_1235_1234 - mat[0][1] * det4_1235_0234 + mat[0][2] * det4_1235_0134 - mat[0][3] * det4_1235_0124 + mat[0][4] * det4_1235_0123;
float det5_01235_01235 = mat[0][0] * det4_1235_1235 - mat[0][1] * det4_1235_0235 + mat[0][2] * det4_1235_0135 - mat[0][3] * det4_1235_0125 + mat[0][5] * det4_1235_0123;
float det5_01235_01245 = mat[0][0] * det4_1235_1245 - mat[0][1] * det4_1235_0245 + mat[0][2] * det4_1235_0145 - mat[0][4] * det4_1235_0125 + mat[0][5] * det4_1235_0124;
float det5_01235_01345 = mat[0][0] * det4_1235_1345 - mat[0][1] * det4_1235_0345 + mat[0][3] * det4_1235_0145 - mat[0][4] * det4_1235_0135 + mat[0][5] * det4_1235_0134;
float det5_01235_02345 = mat[0][0] * det4_1235_2345 - mat[0][2] * det4_1235_0345 + mat[0][3] * det4_1235_0245 - mat[0][4] * det4_1235_0235 + mat[0][5] * det4_1235_0234;
float det5_01235_12345 = mat[0][1] * det4_1235_2345 - mat[0][2] * det4_1235_1345 + mat[0][3] * det4_1235_1245 - mat[0][4] * det4_1235_1235 + mat[0][5] * det4_1235_1234;
float det5_01245_01234 = mat[0][0] * det4_1245_1234 - mat[0][1] * det4_1245_0234 + mat[0][2] * det4_1245_0134 - mat[0][3] * det4_1245_0124 + mat[0][4] * det4_1245_0123;
float det5_01245_01235 = mat[0][0] * det4_1245_1235 - mat[0][1] * det4_1245_0235 + mat[0][2] * det4_1245_0135 - mat[0][3] * det4_1245_0125 + mat[0][5] * det4_1245_0123;
float det5_01245_01245 = mat[0][0] * det4_1245_1245 - mat[0][1] * det4_1245_0245 + mat[0][2] * det4_1245_0145 - mat[0][4] * det4_1245_0125 + mat[0][5] * det4_1245_0124;
float det5_01245_01345 = mat[0][0] * det4_1245_1345 - mat[0][1] * det4_1245_0345 + mat[0][3] * det4_1245_0145 - mat[0][4] * det4_1245_0135 + mat[0][5] * det4_1245_0134;
float det5_01245_02345 = mat[0][0] * det4_1245_2345 - mat[0][2] * det4_1245_0345 + mat[0][3] * det4_1245_0245 - mat[0][4] * det4_1245_0235 + mat[0][5] * det4_1245_0234;
float det5_01245_12345 = mat[0][1] * det4_1245_2345 - mat[0][2] * det4_1245_1345 + mat[0][3] * det4_1245_1245 - mat[0][4] * det4_1245_1235 + mat[0][5] * det4_1245_1234;
float det5_01345_01234 = mat[0][0] * det4_1345_1234 - mat[0][1] * det4_1345_0234 + mat[0][2] * det4_1345_0134 - mat[0][3] * det4_1345_0124 + mat[0][4] * det4_1345_0123;
float det5_01345_01235 = mat[0][0] * det4_1345_1235 - mat[0][1] * det4_1345_0235 + mat[0][2] * det4_1345_0135 - mat[0][3] * det4_1345_0125 + mat[0][5] * det4_1345_0123;
float det5_01345_01245 = mat[0][0] * det4_1345_1245 - mat[0][1] * det4_1345_0245 + mat[0][2] * det4_1345_0145 - mat[0][4] * det4_1345_0125 + mat[0][5] * det4_1345_0124;
float det5_01345_01345 = mat[0][0] * det4_1345_1345 - mat[0][1] * det4_1345_0345 + mat[0][3] * det4_1345_0145 - mat[0][4] * det4_1345_0135 + mat[0][5] * det4_1345_0134;
float det5_01345_02345 = mat[0][0] * det4_1345_2345 - mat[0][2] * det4_1345_0345 + mat[0][3] * det4_1345_0245 - mat[0][4] * det4_1345_0235 + mat[0][5] * det4_1345_0234;
float det5_01345_12345 = mat[0][1] * det4_1345_2345 - mat[0][2] * det4_1345_1345 + mat[0][3] * det4_1345_1245 - mat[0][4] * det4_1345_1235 + mat[0][5] * det4_1345_1234;
float det5_02345_01234 = mat[0][0] * det4_2345_1234 - mat[0][1] * det4_2345_0234 + mat[0][2] * det4_2345_0134 - mat[0][3] * det4_2345_0124 + mat[0][4] * det4_2345_0123;
float det5_02345_01235 = mat[0][0] * det4_2345_1235 - mat[0][1] * det4_2345_0235 + mat[0][2] * det4_2345_0135 - mat[0][3] * det4_2345_0125 + mat[0][5] * det4_2345_0123;
float det5_02345_01245 = mat[0][0] * det4_2345_1245 - mat[0][1] * det4_2345_0245 + mat[0][2] * det4_2345_0145 - mat[0][4] * det4_2345_0125 + mat[0][5] * det4_2345_0124;
float det5_02345_01345 = mat[0][0] * det4_2345_1345 - mat[0][1] * det4_2345_0345 + mat[0][3] * det4_2345_0145 - mat[0][4] * det4_2345_0135 + mat[0][5] * det4_2345_0134;
float det5_02345_02345 = mat[0][0] * det4_2345_2345 - mat[0][2] * det4_2345_0345 + mat[0][3] * det4_2345_0245 - mat[0][4] * det4_2345_0235 + mat[0][5] * det4_2345_0234;
float det5_02345_12345 = mat[0][1] * det4_2345_2345 - mat[0][2] * det4_2345_1345 + mat[0][3] * det4_2345_1245 - mat[0][4] * det4_2345_1235 + mat[0][5] * det4_2345_1234;
mat[0][0] = det5_12345_12345 * invDet;
mat[0][1] = -det5_02345_12345 * invDet;
mat[0][2] = det5_01345_12345 * invDet;
mat[0][3] = -det5_01245_12345 * invDet;
mat[0][4] = det5_01235_12345 * invDet;
mat[0][5] = -det5_01234_12345 * invDet;
mat[1][0] = -det5_12345_02345 * invDet;
mat[1][1] = det5_02345_02345 * invDet;
mat[1][2] = -det5_01345_02345 * invDet;
mat[1][3] = det5_01245_02345 * invDet;
mat[1][4] = -det5_01235_02345 * invDet;
mat[1][5] = det5_01234_02345 * invDet;
mat[2][0] = det5_12345_01345 * invDet;
mat[2][1] = -det5_02345_01345 * invDet;
mat[2][2] = det5_01345_01345 * invDet;
mat[2][3] = -det5_01245_01345 * invDet;
mat[2][4] = det5_01235_01345 * invDet;
mat[2][5] = -det5_01234_01345 * invDet;
mat[3][0] = -det5_12345_01245 * invDet;
mat[3][1] = det5_02345_01245 * invDet;
mat[3][2] = -det5_01345_01245 * invDet;
mat[3][3] = det5_01245_01245 * invDet;
mat[3][4] = -det5_01235_01245 * invDet;
mat[3][5] = det5_01234_01245 * invDet;
mat[4][0] = det5_12345_01235 * invDet;
mat[4][1] = -det5_02345_01235 * invDet;
mat[4][2] = det5_01345_01235 * invDet;
mat[4][3] = -det5_01245_01235 * invDet;
mat[4][4] = det5_01235_01235 * invDet;
mat[4][5] = -det5_01234_01235 * invDet;
mat[5][0] = -det5_12345_01234 * invDet;
mat[5][1] = det5_02345_01234 * invDet;
mat[5][2] = -det5_01345_01234 * invDet;
mat[5][3] = det5_01245_01234 * invDet;
mat[5][4] = -det5_01235_01234 * invDet;
mat[5][5] = det5_01234_01234 * invDet;
return true;
}
/*
============
idMat6::InverseFastSelf
============
*/
bool idMat6::InverseFastSelf()
{
#if 0
// 810+6+36 = 852 multiplications
// 1 division
double det, invDet;
// 2x2 sub-determinants required to calculate 6x6 determinant
float det2_45_01 = mat[4][0] * mat[5][1] - mat[4][1] * mat[5][0];
float det2_45_02 = mat[4][0] * mat[5][2] - mat[4][2] * mat[5][0];
float det2_45_03 = mat[4][0] * mat[5][3] - mat[4][3] * mat[5][0];
float det2_45_04 = mat[4][0] * mat[5][4] - mat[4][4] * mat[5][0];
float det2_45_05 = mat[4][0] * mat[5][5] - mat[4][5] * mat[5][0];
float det2_45_12 = mat[4][1] * mat[5][2] - mat[4][2] * mat[5][1];
float det2_45_13 = mat[4][1] * mat[5][3] - mat[4][3] * mat[5][1];
float det2_45_14 = mat[4][1] * mat[5][4] - mat[4][4] * mat[5][1];
float det2_45_15 = mat[4][1] * mat[5][5] - mat[4][5] * mat[5][1];
float det2_45_23 = mat[4][2] * mat[5][3] - mat[4][3] * mat[5][2];
float det2_45_24 = mat[4][2] * mat[5][4] - mat[4][4] * mat[5][2];
float det2_45_25 = mat[4][2] * mat[5][5] - mat[4][5] * mat[5][2];
float det2_45_34 = mat[4][3] * mat[5][4] - mat[4][4] * mat[5][3];
float det2_45_35 = mat[4][3] * mat[5][5] - mat[4][5] * mat[5][3];
float det2_45_45 = mat[4][4] * mat[5][5] - mat[4][5] * mat[5][4];
// 3x3 sub-determinants required to calculate 6x6 determinant
float det3_345_012 = mat[3][0] * det2_45_12 - mat[3][1] * det2_45_02 + mat[3][2] * det2_45_01;
float det3_345_013 = mat[3][0] * det2_45_13 - mat[3][1] * det2_45_03 + mat[3][3] * det2_45_01;
float det3_345_014 = mat[3][0] * det2_45_14 - mat[3][1] * det2_45_04 + mat[3][4] * det2_45_01;
float det3_345_015 = mat[3][0] * det2_45_15 - mat[3][1] * det2_45_05 + mat[3][5] * det2_45_01;
float det3_345_023 = mat[3][0] * det2_45_23 - mat[3][2] * det2_45_03 + mat[3][3] * det2_45_02;
float det3_345_024 = mat[3][0] * det2_45_24 - mat[3][2] * det2_45_04 + mat[3][4] * det2_45_02;
float det3_345_025 = mat[3][0] * det2_45_25 - mat[3][2] * det2_45_05 + mat[3][5] * det2_45_02;
float det3_345_034 = mat[3][0] * det2_45_34 - mat[3][3] * det2_45_04 + mat[3][4] * det2_45_03;
float det3_345_035 = mat[3][0] * det2_45_35 - mat[3][3] * det2_45_05 + mat[3][5] * det2_45_03;
float det3_345_045 = mat[3][0] * det2_45_45 - mat[3][4] * det2_45_05 + mat[3][5] * det2_45_04;
float det3_345_123 = mat[3][1] * det2_45_23 - mat[3][2] * det2_45_13 + mat[3][3] * det2_45_12;
float det3_345_124 = mat[3][1] * det2_45_24 - mat[3][2] * det2_45_14 + mat[3][4] * det2_45_12;
float det3_345_125 = mat[3][1] * det2_45_25 - mat[3][2] * det2_45_15 + mat[3][5] * det2_45_12;
float det3_345_134 = mat[3][1] * det2_45_34 - mat[3][3] * det2_45_14 + mat[3][4] * det2_45_13;
float det3_345_135 = mat[3][1] * det2_45_35 - mat[3][3] * det2_45_15 + mat[3][5] * det2_45_13;
float det3_345_145 = mat[3][1] * det2_45_45 - mat[3][4] * det2_45_15 + mat[3][5] * det2_45_14;
float det3_345_234 = mat[3][2] * det2_45_34 - mat[3][3] * det2_45_24 + mat[3][4] * det2_45_23;
float det3_345_235 = mat[3][2] * det2_45_35 - mat[3][3] * det2_45_25 + mat[3][5] * det2_45_23;
float det3_345_245 = mat[3][2] * det2_45_45 - mat[3][4] * det2_45_25 + mat[3][5] * det2_45_24;
float det3_345_345 = mat[3][3] * det2_45_45 - mat[3][4] * det2_45_35 + mat[3][5] * det2_45_34;
// 4x4 sub-determinants required to calculate 6x6 determinant
float det4_2345_0123 = mat[2][0] * det3_345_123 - mat[2][1] * det3_345_023 + mat[2][2] * det3_345_013 - mat[2][3] * det3_345_012;
float det4_2345_0124 = mat[2][0] * det3_345_124 - mat[2][1] * det3_345_024 + mat[2][2] * det3_345_014 - mat[2][4] * det3_345_012;
float det4_2345_0125 = mat[2][0] * det3_345_125 - mat[2][1] * det3_345_025 + mat[2][2] * det3_345_015 - mat[2][5] * det3_345_012;
float det4_2345_0134 = mat[2][0] * det3_345_134 - mat[2][1] * det3_345_034 + mat[2][3] * det3_345_014 - mat[2][4] * det3_345_013;
float det4_2345_0135 = mat[2][0] * det3_345_135 - mat[2][1] * det3_345_035 + mat[2][3] * det3_345_015 - mat[2][5] * det3_345_013;
float det4_2345_0145 = mat[2][0] * det3_345_145 - mat[2][1] * det3_345_045 + mat[2][4] * det3_345_015 - mat[2][5] * det3_345_014;
float det4_2345_0234 = mat[2][0] * det3_345_234 - mat[2][2] * det3_345_034 + mat[2][3] * det3_345_024 - mat[2][4] * det3_345_023;
float det4_2345_0235 = mat[2][0] * det3_345_235 - mat[2][2] * det3_345_035 + mat[2][3] * det3_345_025 - mat[2][5] * det3_345_023;
float det4_2345_0245 = mat[2][0] * det3_345_245 - mat[2][2] * det3_345_045 + mat[2][4] * det3_345_025 - mat[2][5] * det3_345_024;
float det4_2345_0345 = mat[2][0] * det3_345_345 - mat[2][3] * det3_345_045 + mat[2][4] * det3_345_035 - mat[2][5] * det3_345_034;
float det4_2345_1234 = mat[2][1] * det3_345_234 - mat[2][2] * det3_345_134 + mat[2][3] * det3_345_124 - mat[2][4] * det3_345_123;
float det4_2345_1235 = mat[2][1] * det3_345_235 - mat[2][2] * det3_345_135 + mat[2][3] * det3_345_125 - mat[2][5] * det3_345_123;
float det4_2345_1245 = mat[2][1] * det3_345_245 - mat[2][2] * det3_345_145 + mat[2][4] * det3_345_125 - mat[2][5] * det3_345_124;
float det4_2345_1345 = mat[2][1] * det3_345_345 - mat[2][3] * det3_345_145 + mat[2][4] * det3_345_135 - mat[2][5] * det3_345_134;
float det4_2345_2345 = mat[2][2] * det3_345_345 - mat[2][3] * det3_345_245 + mat[2][4] * det3_345_235 - mat[2][5] * det3_345_234;
// 5x5 sub-determinants required to calculate 6x6 determinant
float det5_12345_01234 = mat[1][0] * det4_2345_1234 - mat[1][1] * det4_2345_0234 + mat[1][2] * det4_2345_0134 - mat[1][3] * det4_2345_0124 + mat[1][4] * det4_2345_0123;
float det5_12345_01235 = mat[1][0] * det4_2345_1235 - mat[1][1] * det4_2345_0235 + mat[1][2] * det4_2345_0135 - mat[1][3] * det4_2345_0125 + mat[1][5] * det4_2345_0123;
float det5_12345_01245 = mat[1][0] * det4_2345_1245 - mat[1][1] * det4_2345_0245 + mat[1][2] * det4_2345_0145 - mat[1][4] * det4_2345_0125 + mat[1][5] * det4_2345_0124;
float det5_12345_01345 = mat[1][0] * det4_2345_1345 - mat[1][1] * det4_2345_0345 + mat[1][3] * det4_2345_0145 - mat[1][4] * det4_2345_0135 + mat[1][5] * det4_2345_0134;
float det5_12345_02345 = mat[1][0] * det4_2345_2345 - mat[1][2] * det4_2345_0345 + mat[1][3] * det4_2345_0245 - mat[1][4] * det4_2345_0235 + mat[1][5] * det4_2345_0234;
float det5_12345_12345 = mat[1][1] * det4_2345_2345 - mat[1][2] * det4_2345_1345 + mat[1][3] * det4_2345_1245 - mat[1][4] * det4_2345_1235 + mat[1][5] * det4_2345_1234;
// determinant of 6x6 matrix
det = mat[0][0] * det5_12345_12345 - mat[0][1] * det5_12345_02345 + mat[0][2] * det5_12345_01345 -
mat[0][3] * det5_12345_01245 + mat[0][4] * det5_12345_01235 - mat[0][5] * det5_12345_01234;
if( idMath::Fabs( det ) < MATRIX_INVERSE_EPSILON )
{
return false;
}
invDet = 1.0f / det;
// remaining 2x2 sub-determinants
float det2_34_01 = mat[3][0] * mat[4][1] - mat[3][1] * mat[4][0];
float det2_34_02 = mat[3][0] * mat[4][2] - mat[3][2] * mat[4][0];
float det2_34_03 = mat[3][0] * mat[4][3] - mat[3][3] * mat[4][0];
float det2_34_04 = mat[3][0] * mat[4][4] - mat[3][4] * mat[4][0];
float det2_34_05 = mat[3][0] * mat[4][5] - mat[3][5] * mat[4][0];
float det2_34_12 = mat[3][1] * mat[4][2] - mat[3][2] * mat[4][1];
float det2_34_13 = mat[3][1] * mat[4][3] - mat[3][3] * mat[4][1];
float det2_34_14 = mat[3][1] * mat[4][4] - mat[3][4] * mat[4][1];
float det2_34_15 = mat[3][1] * mat[4][5] - mat[3][5] * mat[4][1];
float det2_34_23 = mat[3][2] * mat[4][3] - mat[3][3] * mat[4][2];
float det2_34_24 = mat[3][2] * mat[4][4] - mat[3][4] * mat[4][2];
float det2_34_25 = mat[3][2] * mat[4][5] - mat[3][5] * mat[4][2];
float det2_34_34 = mat[3][3] * mat[4][4] - mat[3][4] * mat[4][3];
float det2_34_35 = mat[3][3] * mat[4][5] - mat[3][5] * mat[4][3];
float det2_34_45 = mat[3][4] * mat[4][5] - mat[3][5] * mat[4][4];
float det2_35_01 = mat[3][0] * mat[5][1] - mat[3][1] * mat[5][0];
float det2_35_02 = mat[3][0] * mat[5][2] - mat[3][2] * mat[5][0];
float det2_35_03 = mat[3][0] * mat[5][3] - mat[3][3] * mat[5][0];
float det2_35_04 = mat[3][0] * mat[5][4] - mat[3][4] * mat[5][0];
float det2_35_05 = mat[3][0] * mat[5][5] - mat[3][5] * mat[5][0];
float det2_35_12 = mat[3][1] * mat[5][2] - mat[3][2] * mat[5][1];
float det2_35_13 = mat[3][1] * mat[5][3] - mat[3][3] * mat[5][1];
float det2_35_14 = mat[3][1] * mat[5][4] - mat[3][4] * mat[5][1];
float det2_35_15 = mat[3][1] * mat[5][5] - mat[3][5] * mat[5][1];
float det2_35_23 = mat[3][2] * mat[5][3] - mat[3][3] * mat[5][2];
float det2_35_24 = mat[3][2] * mat[5][4] - mat[3][4] * mat[5][2];
float det2_35_25 = mat[3][2] * mat[5][5] - mat[3][5] * mat[5][2];
float det2_35_34 = mat[3][3] * mat[5][4] - mat[3][4] * mat[5][3];
float det2_35_35 = mat[3][3] * mat[5][5] - mat[3][5] * mat[5][3];
float det2_35_45 = mat[3][4] * mat[5][5] - mat[3][5] * mat[5][4];
// remaining 3x3 sub-determinants
float det3_234_012 = mat[2][0] * det2_34_12 - mat[2][1] * det2_34_02 + mat[2][2] * det2_34_01;
float det3_234_013 = mat[2][0] * det2_34_13 - mat[2][1] * det2_34_03 + mat[2][3] * det2_34_01;
float det3_234_014 = mat[2][0] * det2_34_14 - mat[2][1] * det2_34_04 + mat[2][4] * det2_34_01;
float det3_234_015 = mat[2][0] * det2_34_15 - mat[2][1] * det2_34_05 + mat[2][5] * det2_34_01;
float det3_234_023 = mat[2][0] * det2_34_23 - mat[2][2] * det2_34_03 + mat[2][3] * det2_34_02;
float det3_234_024 = mat[2][0] * det2_34_24 - mat[2][2] * det2_34_04 + mat[2][4] * det2_34_02;
float det3_234_025 = mat[2][0] * det2_34_25 - mat[2][2] * det2_34_05 + mat[2][5] * det2_34_02;
float det3_234_034 = mat[2][0] * det2_34_34 - mat[2][3] * det2_34_04 + mat[2][4] * det2_34_03;
float det3_234_035 = mat[2][0] * det2_34_35 - mat[2][3] * det2_34_05 + mat[2][5] * det2_34_03;
float det3_234_045 = mat[2][0] * det2_34_45 - mat[2][4] * det2_34_05 + mat[2][5] * det2_34_04;
float det3_234_123 = mat[2][1] * det2_34_23 - mat[2][2] * det2_34_13 + mat[2][3] * det2_34_12;
float det3_234_124 = mat[2][1] * det2_34_24 - mat[2][2] * det2_34_14 + mat[2][4] * det2_34_12;
float det3_234_125 = mat[2][1] * det2_34_25 - mat[2][2] * det2_34_15 + mat[2][5] * det2_34_12;
float det3_234_134 = mat[2][1] * det2_34_34 - mat[2][3] * det2_34_14 + mat[2][4] * det2_34_13;
float det3_234_135 = mat[2][1] * det2_34_35 - mat[2][3] * det2_34_15 + mat[2][5] * det2_34_13;
float det3_234_145 = mat[2][1] * det2_34_45 - mat[2][4] * det2_34_15 + mat[2][5] * det2_34_14;
float det3_234_234 = mat[2][2] * det2_34_34 - mat[2][3] * det2_34_24 + mat[2][4] * det2_34_23;
float det3_234_235 = mat[2][2] * det2_34_35 - mat[2][3] * det2_34_25 + mat[2][5] * det2_34_23;
float det3_234_245 = mat[2][2] * det2_34_45 - mat[2][4] * det2_34_25 + mat[2][5] * det2_34_24;
float det3_234_345 = mat[2][3] * det2_34_45 - mat[2][4] * det2_34_35 + mat[2][5] * det2_34_34;
float det3_235_012 = mat[2][0] * det2_35_12 - mat[2][1] * det2_35_02 + mat[2][2] * det2_35_01;
float det3_235_013 = mat[2][0] * det2_35_13 - mat[2][1] * det2_35_03 + mat[2][3] * det2_35_01;
float det3_235_014 = mat[2][0] * det2_35_14 - mat[2][1] * det2_35_04 + mat[2][4] * det2_35_01;
float det3_235_015 = mat[2][0] * det2_35_15 - mat[2][1] * det2_35_05 + mat[2][5] * det2_35_01;
float det3_235_023 = mat[2][0] * det2_35_23 - mat[2][2] * det2_35_03 + mat[2][3] * det2_35_02;
float det3_235_024 = mat[2][0] * det2_35_24 - mat[2][2] * det2_35_04 + mat[2][4] * det2_35_02;
float det3_235_025 = mat[2][0] * det2_35_25 - mat[2][2] * det2_35_05 + mat[2][5] * det2_35_02;
float det3_235_034 = mat[2][0] * det2_35_34 - mat[2][3] * det2_35_04 + mat[2][4] * det2_35_03;
float det3_235_035 = mat[2][0] * det2_35_35 - mat[2][3] * det2_35_05 + mat[2][5] * det2_35_03;
float det3_235_045 = mat[2][0] * det2_35_45 - mat[2][4] * det2_35_05 + mat[2][5] * det2_35_04;
float det3_235_123 = mat[2][1] * det2_35_23 - mat[2][2] * det2_35_13 + mat[2][3] * det2_35_12;
float det3_235_124 = mat[2][1] * det2_35_24 - mat[2][2] * det2_35_14 + mat[2][4] * det2_35_12;
float det3_235_125 = mat[2][1] * det2_35_25 - mat[2][2] * det2_35_15 + mat[2][5] * det2_35_12;
float det3_235_134 = mat[2][1] * det2_35_34 - mat[2][3] * det2_35_14 + mat[2][4] * det2_35_13;
float det3_235_135 = mat[2][1] * det2_35_35 - mat[2][3] * det2_35_15 + mat[2][5] * det2_35_13;
float det3_235_145 = mat[2][1] * det2_35_45 - mat[2][4] * det2_35_15 + mat[2][5] * det2_35_14;
float det3_235_234 = mat[2][2] * det2_35_34 - mat[2][3] * det2_35_24 + mat[2][4] * det2_35_23;
float det3_235_235 = mat[2][2] * det2_35_35 - mat[2][3] * det2_35_25 + mat[2][5] * det2_35_23;
float det3_235_245 = mat[2][2] * det2_35_45 - mat[2][4] * det2_35_25 + mat[2][5] * det2_35_24;
float det3_235_345 = mat[2][3] * det2_35_45 - mat[2][4] * det2_35_35 + mat[2][5] * det2_35_34;
float det3_245_012 = mat[2][0] * det2_45_12 - mat[2][1] * det2_45_02 + mat[2][2] * det2_45_01;
float det3_245_013 = mat[2][0] * det2_45_13 - mat[2][1] * det2_45_03 + mat[2][3] * det2_45_01;
float det3_245_014 = mat[2][0] * det2_45_14 - mat[2][1] * det2_45_04 + mat[2][4] * det2_45_01;
float det3_245_015 = mat[2][0] * det2_45_15 - mat[2][1] * det2_45_05 + mat[2][5] * det2_45_01;
float det3_245_023 = mat[2][0] * det2_45_23 - mat[2][2] * det2_45_03 + mat[2][3] * det2_45_02;
float det3_245_024 = mat[2][0] * det2_45_24 - mat[2][2] * det2_45_04 + mat[2][4] * det2_45_02;
float det3_245_025 = mat[2][0] * det2_45_25 - mat[2][2] * det2_45_05 + mat[2][5] * det2_45_02;
float det3_245_034 = mat[2][0] * det2_45_34 - mat[2][3] * det2_45_04 + mat[2][4] * det2_45_03;
float det3_245_035 = mat[2][0] * det2_45_35 - mat[2][3] * det2_45_05 + mat[2][5] * det2_45_03;
float det3_245_045 = mat[2][0] * det2_45_45 - mat[2][4] * det2_45_05 + mat[2][5] * det2_45_04;
float det3_245_123 = mat[2][1] * det2_45_23 - mat[2][2] * det2_45_13 + mat[2][3] * det2_45_12;
float det3_245_124 = mat[2][1] * det2_45_24 - mat[2][2] * det2_45_14 + mat[2][4] * det2_45_12;
float det3_245_125 = mat[2][1] * det2_45_25 - mat[2][2] * det2_45_15 + mat[2][5] * det2_45_12;
float det3_245_134 = mat[2][1] * det2_45_34 - mat[2][3] * det2_45_14 + mat[2][4] * det2_45_13;
float det3_245_135 = mat[2][1] * det2_45_35 - mat[2][3] * det2_45_15 + mat[2][5] * det2_45_13;
float det3_245_145 = mat[2][1] * det2_45_45 - mat[2][4] * det2_45_15 + mat[2][5] * det2_45_14;
float det3_245_234 = mat[2][2] * det2_45_34 - mat[2][3] * det2_45_24 + mat[2][4] * det2_45_23;
float det3_245_235 = mat[2][2] * det2_45_35 - mat[2][3] * det2_45_25 + mat[2][5] * det2_45_23;
float det3_245_245 = mat[2][2] * det2_45_45 - mat[2][4] * det2_45_25 + mat[2][5] * det2_45_24;
float det3_245_345 = mat[2][3] * det2_45_45 - mat[2][4] * det2_45_35 + mat[2][5] * det2_45_34;
// remaining 4x4 sub-determinants
float det4_1234_0123 = mat[1][0] * det3_234_123 - mat[1][1] * det3_234_023 + mat[1][2] * det3_234_013 - mat[1][3] * det3_234_012;
float det4_1234_0124 = mat[1][0] * det3_234_124 - mat[1][1] * det3_234_024 + mat[1][2] * det3_234_014 - mat[1][4] * det3_234_012;
float det4_1234_0125 = mat[1][0] * det3_234_125 - mat[1][1] * det3_234_025 + mat[1][2] * det3_234_015 - mat[1][5] * det3_234_012;
float det4_1234_0134 = mat[1][0] * det3_234_134 - mat[1][1] * det3_234_034 + mat[1][3] * det3_234_014 - mat[1][4] * det3_234_013;
float det4_1234_0135 = mat[1][0] * det3_234_135 - mat[1][1] * det3_234_035 + mat[1][3] * det3_234_015 - mat[1][5] * det3_234_013;
float det4_1234_0145 = mat[1][0] * det3_234_145 - mat[1][1] * det3_234_045 + mat[1][4] * det3_234_015 - mat[1][5] * det3_234_014;
float det4_1234_0234 = mat[1][0] * det3_234_234 - mat[1][2] * det3_234_034 + mat[1][3] * det3_234_024 - mat[1][4] * det3_234_023;
float det4_1234_0235 = mat[1][0] * det3_234_235 - mat[1][2] * det3_234_035 + mat[1][3] * det3_234_025 - mat[1][5] * det3_234_023;
float det4_1234_0245 = mat[1][0] * det3_234_245 - mat[1][2] * det3_234_045 + mat[1][4] * det3_234_025 - mat[1][5] * det3_234_024;
float det4_1234_0345 = mat[1][0] * det3_234_345 - mat[1][3] * det3_234_045 + mat[1][4] * det3_234_035 - mat[1][5] * det3_234_034;
float det4_1234_1234 = mat[1][1] * det3_234_234 - mat[1][2] * det3_234_134 + mat[1][3] * det3_234_124 - mat[1][4] * det3_234_123;
float det4_1234_1235 = mat[1][1] * det3_234_235 - mat[1][2] * det3_234_135 + mat[1][3] * det3_234_125 - mat[1][5] * det3_234_123;
float det4_1234_1245 = mat[1][1] * det3_234_245 - mat[1][2] * det3_234_145 + mat[1][4] * det3_234_125 - mat[1][5] * det3_234_124;
float det4_1234_1345 = mat[1][1] * det3_234_345 - mat[1][3] * det3_234_145 + mat[1][4] * det3_234_135 - mat[1][5] * det3_234_134;
float det4_1234_2345 = mat[1][2] * det3_234_345 - mat[1][3] * det3_234_245 + mat[1][4] * det3_234_235 - mat[1][5] * det3_234_234;
float det4_1235_0123 = mat[1][0] * det3_235_123 - mat[1][1] * det3_235_023 + mat[1][2] * det3_235_013 - mat[1][3] * det3_235_012;
float det4_1235_0124 = mat[1][0] * det3_235_124 - mat[1][1] * det3_235_024 + mat[1][2] * det3_235_014 - mat[1][4] * det3_235_012;
float det4_1235_0125 = mat[1][0] * det3_235_125 - mat[1][1] * det3_235_025 + mat[1][2] * det3_235_015 - mat[1][5] * det3_235_012;
float det4_1235_0134 = mat[1][0] * det3_235_134 - mat[1][1] * det3_235_034 + mat[1][3] * det3_235_014 - mat[1][4] * det3_235_013;
float det4_1235_0135 = mat[1][0] * det3_235_135 - mat[1][1] * det3_235_035 + mat[1][3] * det3_235_015 - mat[1][5] * det3_235_013;
float det4_1235_0145 = mat[1][0] * det3_235_145 - mat[1][1] * det3_235_045 + mat[1][4] * det3_235_015 - mat[1][5] * det3_235_014;
float det4_1235_0234 = mat[1][0] * det3_235_234 - mat[1][2] * det3_235_034 + mat[1][3] * det3_235_024 - mat[1][4] * det3_235_023;
float det4_1235_0235 = mat[1][0] * det3_235_235 - mat[1][2] * det3_235_035 + mat[1][3] * det3_235_025 - mat[1][5] * det3_235_023;
float det4_1235_0245 = mat[1][0] * det3_235_245 - mat[1][2] * det3_235_045 + mat[1][4] * det3_235_025 - mat[1][5] * det3_235_024;
float det4_1235_0345 = mat[1][0] * det3_235_345 - mat[1][3] * det3_235_045 + mat[1][4] * det3_235_035 - mat[1][5] * det3_235_034;
float det4_1235_1234 = mat[1][1] * det3_235_234 - mat[1][2] * det3_235_134 + mat[1][3] * det3_235_124 - mat[1][4] * det3_235_123;
float det4_1235_1235 = mat[1][1] * det3_235_235 - mat[1][2] * det3_235_135 + mat[1][3] * det3_235_125 - mat[1][5] * det3_235_123;
float det4_1235_1245 = mat[1][1] * det3_235_245 - mat[1][2] * det3_235_145 + mat[1][4] * det3_235_125 - mat[1][5] * det3_235_124;
float det4_1235_1345 = mat[1][1] * det3_235_345 - mat[1][3] * det3_235_145 + mat[1][4] * det3_235_135 - mat[1][5] * det3_235_134;
float det4_1235_2345 = mat[1][2] * det3_235_345 - mat[1][3] * det3_235_245 + mat[1][4] * det3_235_235 - mat[1][5] * det3_235_234;
float det4_1245_0123 = mat[1][0] * det3_245_123 - mat[1][1] * det3_245_023 + mat[1][2] * det3_245_013 - mat[1][3] * det3_245_012;
float det4_1245_0124 = mat[1][0] * det3_245_124 - mat[1][1] * det3_245_024 + mat[1][2] * det3_245_014 - mat[1][4] * det3_245_012;
float det4_1245_0125 = mat[1][0] * det3_245_125 - mat[1][1] * det3_245_025 + mat[1][2] * det3_245_015 - mat[1][5] * det3_245_012;
float det4_1245_0134 = mat[1][0] * det3_245_134 - mat[1][1] * det3_245_034 + mat[1][3] * det3_245_014 - mat[1][4] * det3_245_013;
float det4_1245_0135 = mat[1][0] * det3_245_135 - mat[1][1] * det3_245_035 + mat[1][3] * det3_245_015 - mat[1][5] * det3_245_013;
float det4_1245_0145 = mat[1][0] * det3_245_145 - mat[1][1] * det3_245_045 + mat[1][4] * det3_245_015 - mat[1][5] * det3_245_014;
float det4_1245_0234 = mat[1][0] * det3_245_234 - mat[1][2] * det3_245_034 + mat[1][3] * det3_245_024 - mat[1][4] * det3_245_023;
float det4_1245_0235 = mat[1][0] * det3_245_235 - mat[1][2] * det3_245_035 + mat[1][3] * det3_245_025 - mat[1][5] * det3_245_023;
float det4_1245_0245 = mat[1][0] * det3_245_245 - mat[1][2] * det3_245_045 + mat[1][4] * det3_245_025 - mat[1][5] * det3_245_024;
float det4_1245_0345 = mat[1][0] * det3_245_345 - mat[1][3] * det3_245_045 + mat[1][4] * det3_245_035 - mat[1][5] * det3_245_034;
float det4_1245_1234 = mat[1][1] * det3_245_234 - mat[1][2] * det3_245_134 + mat[1][3] * det3_245_124 - mat[1][4] * det3_245_123;
float det4_1245_1235 = mat[1][1] * det3_245_235 - mat[1][2] * det3_245_135 + mat[1][3] * det3_245_125 - mat[1][5] * det3_245_123;
float det4_1245_1245 = mat[1][1] * det3_245_245 - mat[1][2] * det3_245_145 + mat[1][4] * det3_245_125 - mat[1][5] * det3_245_124;
float det4_1245_1345 = mat[1][1] * det3_245_345 - mat[1][3] * det3_245_145 + mat[1][4] * det3_245_135 - mat[1][5] * det3_245_134;
float det4_1245_2345 = mat[1][2] * det3_245_345 - mat[1][3] * det3_245_245 + mat[1][4] * det3_245_235 - mat[1][5] * det3_245_234;
float det4_1345_0123 = mat[1][0] * det3_345_123 - mat[1][1] * det3_345_023 + mat[1][2] * det3_345_013 - mat[1][3] * det3_345_012;
float det4_1345_0124 = mat[1][0] * det3_345_124 - mat[1][1] * det3_345_024 + mat[1][2] * det3_345_014 - mat[1][4] * det3_345_012;
float det4_1345_0125 = mat[1][0] * det3_345_125 - mat[1][1] * det3_345_025 + mat[1][2] * det3_345_015 - mat[1][5] * det3_345_012;
float det4_1345_0134 = mat[1][0] * det3_345_134 - mat[1][1] * det3_345_034 + mat[1][3] * det3_345_014 - mat[1][4] * det3_345_013;
float det4_1345_0135 = mat[1][0] * det3_345_135 - mat[1][1] * det3_345_035 + mat[1][3] * det3_345_015 - mat[1][5] * det3_345_013;
float det4_1345_0145 = mat[1][0] * det3_345_145 - mat[1][1] * det3_345_045 + mat[1][4] * det3_345_015 - mat[1][5] * det3_345_014;
float det4_1345_0234 = mat[1][0] * det3_345_234 - mat[1][2] * det3_345_034 + mat[1][3] * det3_345_024 - mat[1][4] * det3_345_023;
float det4_1345_0235 = mat[1][0] * det3_345_235 - mat[1][2] * det3_345_035 + mat[1][3] * det3_345_025 - mat[1][5] * det3_345_023;
float det4_1345_0245 = mat[1][0] * det3_345_245 - mat[1][2] * det3_345_045 + mat[1][4] * det3_345_025 - mat[1][5] * det3_345_024;
float det4_1345_0345 = mat[1][0] * det3_345_345 - mat[1][3] * det3_345_045 + mat[1][4] * det3_345_035 - mat[1][5] * det3_345_034;
float det4_1345_1234 = mat[1][1] * det3_345_234 - mat[1][2] * det3_345_134 + mat[1][3] * det3_345_124 - mat[1][4] * det3_345_123;
float det4_1345_1235 = mat[1][1] * det3_345_235 - mat[1][2] * det3_345_135 + mat[1][3] * det3_345_125 - mat[1][5] * det3_345_123;
float det4_1345_1245 = mat[1][1] * det3_345_245 - mat[1][2] * det3_345_145 + mat[1][4] * det3_345_125 - mat[1][5] * det3_345_124;
float det4_1345_1345 = mat[1][1] * det3_345_345 - mat[1][3] * det3_345_145 + mat[1][4] * det3_345_135 - mat[1][5] * det3_345_134;
float det4_1345_2345 = mat[1][2] * det3_345_345 - mat[1][3] * det3_345_245 + mat[1][4] * det3_345_235 - mat[1][5] * det3_345_234;
// remaining 5x5 sub-determinants
float det5_01234_01234 = mat[0][0] * det4_1234_1234 - mat[0][1] * det4_1234_0234 + mat[0][2] * det4_1234_0134 - mat[0][3] * det4_1234_0124 + mat[0][4] * det4_1234_0123;
float det5_01234_01235 = mat[0][0] * det4_1234_1235 - mat[0][1] * det4_1234_0235 + mat[0][2] * det4_1234_0135 - mat[0][3] * det4_1234_0125 + mat[0][5] * det4_1234_0123;
float det5_01234_01245 = mat[0][0] * det4_1234_1245 - mat[0][1] * det4_1234_0245 + mat[0][2] * det4_1234_0145 - mat[0][4] * det4_1234_0125 + mat[0][5] * det4_1234_0124;
float det5_01234_01345 = mat[0][0] * det4_1234_1345 - mat[0][1] * det4_1234_0345 + mat[0][3] * det4_1234_0145 - mat[0][4] * det4_1234_0135 + mat[0][5] * det4_1234_0134;
float det5_01234_02345 = mat[0][0] * det4_1234_2345 - mat[0][2] * det4_1234_0345 + mat[0][3] * det4_1234_0245 - mat[0][4] * det4_1234_0235 + mat[0][5] * det4_1234_0234;
float det5_01234_12345 = mat[0][1] * det4_1234_2345 - mat[0][2] * det4_1234_1345 + mat[0][3] * det4_1234_1245 - mat[0][4] * det4_1234_1235 + mat[0][5] * det4_1234_1234;
float det5_01235_01234 = mat[0][0] * det4_1235_1234 - mat[0][1] * det4_1235_0234 + mat[0][2] * det4_1235_0134 - mat[0][3] * det4_1235_0124 + mat[0][4] * det4_1235_0123;
float det5_01235_01235 = mat[0][0] * det4_1235_1235 - mat[0][1] * det4_1235_0235 + mat[0][2] * det4_1235_0135 - mat[0][3] * det4_1235_0125 + mat[0][5] * det4_1235_0123;
float det5_01235_01245 = mat[0][0] * det4_1235_1245 - mat[0][1] * det4_1235_0245 + mat[0][2] * det4_1235_0145 - mat[0][4] * det4_1235_0125 + mat[0][5] * det4_1235_0124;
float det5_01235_01345 = mat[0][0] * det4_1235_1345 - mat[0][1] * det4_1235_0345 + mat[0][3] * det4_1235_0145 - mat[0][4] * det4_1235_0135 + mat[0][5] * det4_1235_0134;
float det5_01235_02345 = mat[0][0] * det4_1235_2345 - mat[0][2] * det4_1235_0345 + mat[0][3] * det4_1235_0245 - mat[0][4] * det4_1235_0235 + mat[0][5] * det4_1235_0234;
float det5_01235_12345 = mat[0][1] * det4_1235_2345 - mat[0][2] * det4_1235_1345 + mat[0][3] * det4_1235_1245 - mat[0][4] * det4_1235_1235 + mat[0][5] * det4_1235_1234;
float det5_01245_01234 = mat[0][0] * det4_1245_1234 - mat[0][1] * det4_1245_0234 + mat[0][2] * det4_1245_0134 - mat[0][3] * det4_1245_0124 + mat[0][4] * det4_1245_0123;
float det5_01245_01235 = mat[0][0] * det4_1245_1235 - mat[0][1] * det4_1245_0235 + mat[0][2] * det4_1245_0135 - mat[0][3] * det4_1245_0125 + mat[0][5] * det4_1245_0123;
float det5_01245_01245 = mat[0][0] * det4_1245_1245 - mat[0][1] * det4_1245_0245 + mat[0][2] * det4_1245_0145 - mat[0][4] * det4_1245_0125 + mat[0][5] * det4_1245_0124;
float det5_01245_01345 = mat[0][0] * det4_1245_1345 - mat[0][1] * det4_1245_0345 + mat[0][3] * det4_1245_0145 - mat[0][4] * det4_1245_0135 + mat[0][5] * det4_1245_0134;
float det5_01245_02345 = mat[0][0] * det4_1245_2345 - mat[0][2] * det4_1245_0345 + mat[0][3] * det4_1245_0245 - mat[0][4] * det4_1245_0235 + mat[0][5] * det4_1245_0234;
float det5_01245_12345 = mat[0][1] * det4_1245_2345 - mat[0][2] * det4_1245_1345 + mat[0][3] * det4_1245_1245 - mat[0][4] * det4_1245_1235 + mat[0][5] * det4_1245_1234;
float det5_01345_01234 = mat[0][0] * det4_1345_1234 - mat[0][1] * det4_1345_0234 + mat[0][2] * det4_1345_0134 - mat[0][3] * det4_1345_0124 + mat[0][4] * det4_1345_0123;
float det5_01345_01235 = mat[0][0] * det4_1345_1235 - mat[0][1] * det4_1345_0235 + mat[0][2] * det4_1345_0135 - mat[0][3] * det4_1345_0125 + mat[0][5] * det4_1345_0123;
float det5_01345_01245 = mat[0][0] * det4_1345_1245 - mat[0][1] * det4_1345_0245 + mat[0][2] * det4_1345_0145 - mat[0][4] * det4_1345_0125 + mat[0][5] * det4_1345_0124;
float det5_01345_01345 = mat[0][0] * det4_1345_1345 - mat[0][1] * det4_1345_0345 + mat[0][3] * det4_1345_0145 - mat[0][4] * det4_1345_0135 + mat[0][5] * det4_1345_0134;
float det5_01345_02345 = mat[0][0] * det4_1345_2345 - mat[0][2] * det4_1345_0345 + mat[0][3] * det4_1345_0245 - mat[0][4] * det4_1345_0235 + mat[0][5] * det4_1345_0234;
float det5_01345_12345 = mat[0][1] * det4_1345_2345 - mat[0][2] * det4_1345_1345 + mat[0][3] * det4_1345_1245 - mat[0][4] * det4_1345_1235 + mat[0][5] * det4_1345_1234;
float det5_02345_01234 = mat[0][0] * det4_2345_1234 - mat[0][1] * det4_2345_0234 + mat[0][2] * det4_2345_0134 - mat[0][3] * det4_2345_0124 + mat[0][4] * det4_2345_0123;
float det5_02345_01235 = mat[0][0] * det4_2345_1235 - mat[0][1] * det4_2345_0235 + mat[0][2] * det4_2345_0135 - mat[0][3] * det4_2345_0125 + mat[0][5] * det4_2345_0123;
float det5_02345_01245 = mat[0][0] * det4_2345_1245 - mat[0][1] * det4_2345_0245 + mat[0][2] * det4_2345_0145 - mat[0][4] * det4_2345_0125 + mat[0][5] * det4_2345_0124;
float det5_02345_01345 = mat[0][0] * det4_2345_1345 - mat[0][1] * det4_2345_0345 + mat[0][3] * det4_2345_0145 - mat[0][4] * det4_2345_0135 + mat[0][5] * det4_2345_0134;
float det5_02345_02345 = mat[0][0] * det4_2345_2345 - mat[0][2] * det4_2345_0345 + mat[0][3] * det4_2345_0245 - mat[0][4] * det4_2345_0235 + mat[0][5] * det4_2345_0234;
float det5_02345_12345 = mat[0][1] * det4_2345_2345 - mat[0][2] * det4_2345_1345 + mat[0][3] * det4_2345_1245 - mat[0][4] * det4_2345_1235 + mat[0][5] * det4_2345_1234;
mat[0][0] = det5_12345_12345 * invDet;
mat[0][1] = -det5_02345_12345 * invDet;
mat[0][2] = det5_01345_12345 * invDet;
mat[0][3] = -det5_01245_12345 * invDet;
mat[0][4] = det5_01235_12345 * invDet;
mat[0][5] = -det5_01234_12345 * invDet;
mat[1][0] = -det5_12345_02345 * invDet;
mat[1][1] = det5_02345_02345 * invDet;
mat[1][2] = -det5_01345_02345 * invDet;
mat[1][3] = det5_01245_02345 * invDet;
mat[1][4] = -det5_01235_02345 * invDet;
mat[1][5] = det5_01234_02345 * invDet;
mat[2][0] = det5_12345_01345 * invDet;
mat[2][1] = -det5_02345_01345 * invDet;
mat[2][2] = det5_01345_01345 * invDet;
mat[2][3] = -det5_01245_01345 * invDet;
mat[2][4] = det5_01235_01345 * invDet;
mat[2][5] = -det5_01234_01345 * invDet;
mat[3][0] = -det5_12345_01245 * invDet;
mat[3][1] = det5_02345_01245 * invDet;
mat[3][2] = -det5_01345_01245 * invDet;
mat[3][3] = det5_01245_01245 * invDet;
mat[3][4] = -det5_01235_01245 * invDet;
mat[3][5] = det5_01234_01245 * invDet;
mat[4][0] = det5_12345_01235 * invDet;
mat[4][1] = -det5_02345_01235 * invDet;
mat[4][2] = det5_01345_01235 * invDet;
mat[4][3] = -det5_01245_01235 * invDet;
mat[4][4] = det5_01235_01235 * invDet;
mat[4][5] = -det5_01234_01235 * invDet;
mat[5][0] = -det5_12345_01234 * invDet;
mat[5][1] = det5_02345_01234 * invDet;
mat[5][2] = -det5_01345_01234 * invDet;
mat[5][3] = det5_01245_01234 * invDet;
mat[5][4] = -det5_01235_01234 * invDet;
mat[5][5] = det5_01234_01234 * invDet;
return true;
#elif 0
// 6*40 = 240 multiplications
// 6 divisions
float* mat = reinterpret_cast<float*>( this );
float s;
double d, di;
di = mat[0];
s = di;
mat[0] = d = 1.0f / di;
mat[1] *= d;
mat[2] *= d;
mat[3] *= d;
mat[4] *= d;
mat[5] *= d;
d = -d;
mat[6] *= d;
mat[12] *= d;
mat[18] *= d;
mat[24] *= d;
mat[30] *= d;
d = mat[6] * di;
mat[7] += mat[1] * d;
mat[8] += mat[2] * d;
mat[9] += mat[3] * d;
mat[10] += mat[4] * d;
mat[11] += mat[5] * d;
d = mat[12] * di;
mat[13] += mat[1] * d;
mat[14] += mat[2] * d;
mat[15] += mat[3] * d;
mat[16] += mat[4] * d;
mat[17] += mat[5] * d;
d = mat[18] * di;
mat[19] += mat[1] * d;
mat[20] += mat[2] * d;
mat[21] += mat[3] * d;
mat[22] += mat[4] * d;
mat[23] += mat[5] * d;
d = mat[24] * di;
mat[25] += mat[1] * d;
mat[26] += mat[2] * d;
mat[27] += mat[3] * d;
mat[28] += mat[4] * d;
mat[29] += mat[5] * d;
d = mat[30] * di;
mat[31] += mat[1] * d;
mat[32] += mat[2] * d;
mat[33] += mat[3] * d;
mat[34] += mat[4] * d;
mat[35] += mat[5] * d;
di = mat[7];
s *= di;
mat[7] = d = 1.0f / di;
mat[6] *= d;
mat[8] *= d;
mat[9] *= d;
mat[10] *= d;
mat[11] *= d;
d = -d;
mat[1] *= d;
mat[13] *= d;
mat[19] *= d;
mat[25] *= d;
mat[31] *= d;
d = mat[1] * di;
mat[0] += mat[6] * d;
mat[2] += mat[8] * d;
mat[3] += mat[9] * d;
mat[4] += mat[10] * d;
mat[5] += mat[11] * d;
d = mat[13] * di;
mat[12] += mat[6] * d;
mat[14] += mat[8] * d;
mat[15] += mat[9] * d;
mat[16] += mat[10] * d;
mat[17] += mat[11] * d;
d = mat[19] * di;
mat[18] += mat[6] * d;
mat[20] += mat[8] * d;
mat[21] += mat[9] * d;
mat[22] += mat[10] * d;
mat[23] += mat[11] * d;
d = mat[25] * di;
mat[24] += mat[6] * d;
mat[26] += mat[8] * d;
mat[27] += mat[9] * d;
mat[28] += mat[10] * d;
mat[29] += mat[11] * d;
d = mat[31] * di;
mat[30] += mat[6] * d;
mat[32] += mat[8] * d;
mat[33] += mat[9] * d;
mat[34] += mat[10] * d;
mat[35] += mat[11] * d;
di = mat[14];
s *= di;
mat[14] = d = 1.0f / di;
mat[12] *= d;
mat[13] *= d;
mat[15] *= d;
mat[16] *= d;
mat[17] *= d;
d = -d;
mat[2] *= d;
mat[8] *= d;
mat[20] *= d;
mat[26] *= d;
mat[32] *= d;
d = mat[2] * di;
mat[0] += mat[12] * d;
mat[1] += mat[13] * d;
mat[3] += mat[15] * d;
mat[4] += mat[16] * d;
mat[5] += mat[17] * d;
d = mat[8] * di;
mat[6] += mat[12] * d;
mat[7] += mat[13] * d;
mat[9] += mat[15] * d;
mat[10] += mat[16] * d;
mat[11] += mat[17] * d;
d = mat[20] * di;
mat[18] += mat[12] * d;
mat[19] += mat[13] * d;
mat[21] += mat[15] * d;
mat[22] += mat[16] * d;
mat[23] += mat[17] * d;
d = mat[26] * di;
mat[24] += mat[12] * d;
mat[25] += mat[13] * d;
mat[27] += mat[15] * d;
mat[28] += mat[16] * d;
mat[29] += mat[17] * d;
d = mat[32] * di;
mat[30] += mat[12] * d;
mat[31] += mat[13] * d;
mat[33] += mat[15] * d;
mat[34] += mat[16] * d;
mat[35] += mat[17] * d;
di = mat[21];
s *= di;
mat[21] = d = 1.0f / di;
mat[18] *= d;
mat[19] *= d;
mat[20] *= d;
mat[22] *= d;
mat[23] *= d;
d = -d;
mat[3] *= d;
mat[9] *= d;
mat[15] *= d;
mat[27] *= d;
mat[33] *= d;
d = mat[3] * di;
mat[0] += mat[18] * d;
mat[1] += mat[19] * d;
mat[2] += mat[20] * d;
mat[4] += mat[22] * d;
mat[5] += mat[23] * d;
d = mat[9] * di;
mat[6] += mat[18] * d;
mat[7] += mat[19] * d;
mat[8] += mat[20] * d;
mat[10] += mat[22] * d;
mat[11] += mat[23] * d;
d = mat[15] * di;
mat[12] += mat[18] * d;
mat[13] += mat[19] * d;
mat[14] += mat[20] * d;
mat[16] += mat[22] * d;
mat[17] += mat[23] * d;
d = mat[27] * di;
mat[24] += mat[18] * d;
mat[25] += mat[19] * d;
mat[26] += mat[20] * d;
mat[28] += mat[22] * d;
mat[29] += mat[23] * d;
d = mat[33] * di;
mat[30] += mat[18] * d;
mat[31] += mat[19] * d;
mat[32] += mat[20] * d;
mat[34] += mat[22] * d;
mat[35] += mat[23] * d;
di = mat[28];
s *= di;
mat[28] = d = 1.0f / di;
mat[24] *= d;
mat[25] *= d;
mat[26] *= d;
mat[27] *= d;
mat[29] *= d;
d = -d;
mat[4] *= d;
mat[10] *= d;
mat[16] *= d;
mat[22] *= d;
mat[34] *= d;
d = mat[4] * di;
mat[0] += mat[24] * d;
mat[1] += mat[25] * d;
mat[2] += mat[26] * d;
mat[3] += mat[27] * d;
mat[5] += mat[29] * d;
d = mat[10] * di;
mat[6] += mat[24] * d;
mat[7] += mat[25] * d;
mat[8] += mat[26] * d;
mat[9] += mat[27] * d;
mat[11] += mat[29] * d;
d = mat[16] * di;
mat[12] += mat[24] * d;
mat[13] += mat[25] * d;
mat[14] += mat[26] * d;
mat[15] += mat[27] * d;
mat[17] += mat[29] * d;
d = mat[22] * di;
mat[18] += mat[24] * d;
mat[19] += mat[25] * d;
mat[20] += mat[26] * d;
mat[21] += mat[27] * d;
mat[23] += mat[29] * d;
d = mat[34] * di;
mat[30] += mat[24] * d;
mat[31] += mat[25] * d;
mat[32] += mat[26] * d;
mat[33] += mat[27] * d;
mat[35] += mat[29] * d;
di = mat[35];
s *= di;
mat[35] = d = 1.0f / di;
mat[30] *= d;
mat[31] *= d;
mat[32] *= d;
mat[33] *= d;
mat[34] *= d;
d = -d;
mat[5] *= d;
mat[11] *= d;
mat[17] *= d;
mat[23] *= d;
mat[29] *= d;
d = mat[5] * di;
mat[0] += mat[30] * d;
mat[1] += mat[31] * d;
mat[2] += mat[32] * d;
mat[3] += mat[33] * d;
mat[4] += mat[34] * d;
d = mat[11] * di;
mat[6] += mat[30] * d;
mat[7] += mat[31] * d;
mat[8] += mat[32] * d;
mat[9] += mat[33] * d;
mat[10] += mat[34] * d;
d = mat[17] * di;
mat[12] += mat[30] * d;
mat[13] += mat[31] * d;
mat[14] += mat[32] * d;
mat[15] += mat[33] * d;
mat[16] += mat[34] * d;
d = mat[23] * di;
mat[18] += mat[30] * d;
mat[19] += mat[31] * d;
mat[20] += mat[32] * d;
mat[21] += mat[33] * d;
mat[22] += mat[34] * d;
d = mat[29] * di;
mat[24] += mat[30] * d;
mat[25] += mat[31] * d;
mat[26] += mat[32] * d;
mat[27] += mat[33] * d;
mat[28] += mat[34] * d;
return ( s != 0.0f && !IEEE_FLT_IS_NAN( s ) );
#else
// 6*27+2*30 = 222 multiplications
// 2*1 = 2 divisions
idMat3 r0, r1, r2, r3;
float c0, c1, c2, det, invDet;
float* mat = reinterpret_cast<float*>( this );
// r0 = m0.Inverse();
c0 = mat[1 * 6 + 1] * mat[2 * 6 + 2] - mat[1 * 6 + 2] * mat[2 * 6 + 1];
c1 = mat[1 * 6 + 2] * mat[2 * 6 + 0] - mat[1 * 6 + 0] * mat[2 * 6 + 2];
c2 = mat[1 * 6 + 0] * mat[2 * 6 + 1] - mat[1 * 6 + 1] * mat[2 * 6 + 0];
det = mat[0 * 6 + 0] * c0 + mat[0 * 6 + 1] * c1 + mat[0 * 6 + 2] * c2;
if( idMath::Fabs( det ) < MATRIX_INVERSE_EPSILON )
{
return false;
}
invDet = 1.0f / det;
r0[0][0] = c0 * invDet;
r0[0][1] = ( mat[0 * 6 + 2] * mat[2 * 6 + 1] - mat[0 * 6 + 1] * mat[2 * 6 + 2] ) * invDet;
r0[0][2] = ( mat[0 * 6 + 1] * mat[1 * 6 + 2] - mat[0 * 6 + 2] * mat[1 * 6 + 1] ) * invDet;
r0[1][0] = c1 * invDet;
r0[1][1] = ( mat[0 * 6 + 0] * mat[2 * 6 + 2] - mat[0 * 6 + 2] * mat[2 * 6 + 0] ) * invDet;
r0[1][2] = ( mat[0 * 6 + 2] * mat[1 * 6 + 0] - mat[0 * 6 + 0] * mat[1 * 6 + 2] ) * invDet;
r0[2][0] = c2 * invDet;
r0[2][1] = ( mat[0 * 6 + 1] * mat[2 * 6 + 0] - mat[0 * 6 + 0] * mat[2 * 6 + 1] ) * invDet;
r0[2][2] = ( mat[0 * 6 + 0] * mat[1 * 6 + 1] - mat[0 * 6 + 1] * mat[1 * 6 + 0] ) * invDet;
// r1 = r0 * m1;
r1[0][0] = r0[0][0] * mat[0 * 6 + 3] + r0[0][1] * mat[1 * 6 + 3] + r0[0][2] * mat[2 * 6 + 3];
r1[0][1] = r0[0][0] * mat[0 * 6 + 4] + r0[0][1] * mat[1 * 6 + 4] + r0[0][2] * mat[2 * 6 + 4];
r1[0][2] = r0[0][0] * mat[0 * 6 + 5] + r0[0][1] * mat[1 * 6 + 5] + r0[0][2] * mat[2 * 6 + 5];
r1[1][0] = r0[1][0] * mat[0 * 6 + 3] + r0[1][1] * mat[1 * 6 + 3] + r0[1][2] * mat[2 * 6 + 3];
r1[1][1] = r0[1][0] * mat[0 * 6 + 4] + r0[1][1] * mat[1 * 6 + 4] + r0[1][2] * mat[2 * 6 + 4];
r1[1][2] = r0[1][0] * mat[0 * 6 + 5] + r0[1][1] * mat[1 * 6 + 5] + r0[1][2] * mat[2 * 6 + 5];
r1[2][0] = r0[2][0] * mat[0 * 6 + 3] + r0[2][1] * mat[1 * 6 + 3] + r0[2][2] * mat[2 * 6 + 3];
r1[2][1] = r0[2][0] * mat[0 * 6 + 4] + r0[2][1] * mat[1 * 6 + 4] + r0[2][2] * mat[2 * 6 + 4];
r1[2][2] = r0[2][0] * mat[0 * 6 + 5] + r0[2][1] * mat[1 * 6 + 5] + r0[2][2] * mat[2 * 6 + 5];
// r2 = m2 * r1;
r2[0][0] = mat[3 * 6 + 0] * r1[0][0] + mat[3 * 6 + 1] * r1[1][0] + mat[3 * 6 + 2] * r1[2][0];
r2[0][1] = mat[3 * 6 + 0] * r1[0][1] + mat[3 * 6 + 1] * r1[1][1] + mat[3 * 6 + 2] * r1[2][1];
r2[0][2] = mat[3 * 6 + 0] * r1[0][2] + mat[3 * 6 + 1] * r1[1][2] + mat[3 * 6 + 2] * r1[2][2];
r2[1][0] = mat[4 * 6 + 0] * r1[0][0] + mat[4 * 6 + 1] * r1[1][0] + mat[4 * 6 + 2] * r1[2][0];
r2[1][1] = mat[4 * 6 + 0] * r1[0][1] + mat[4 * 6 + 1] * r1[1][1] + mat[4 * 6 + 2] * r1[2][1];
r2[1][2] = mat[4 * 6 + 0] * r1[0][2] + mat[4 * 6 + 1] * r1[1][2] + mat[4 * 6 + 2] * r1[2][2];
r2[2][0] = mat[5 * 6 + 0] * r1[0][0] + mat[5 * 6 + 1] * r1[1][0] + mat[5 * 6 + 2] * r1[2][0];
r2[2][1] = mat[5 * 6 + 0] * r1[0][1] + mat[5 * 6 + 1] * r1[1][1] + mat[5 * 6 + 2] * r1[2][1];
r2[2][2] = mat[5 * 6 + 0] * r1[0][2] + mat[5 * 6 + 1] * r1[1][2] + mat[5 * 6 + 2] * r1[2][2];
// r3 = r2 - m3;
r3[0][0] = r2[0][0] - mat[3 * 6 + 3];
r3[0][1] = r2[0][1] - mat[3 * 6 + 4];
r3[0][2] = r2[0][2] - mat[3 * 6 + 5];
r3[1][0] = r2[1][0] - mat[4 * 6 + 3];
r3[1][1] = r2[1][1] - mat[4 * 6 + 4];
r3[1][2] = r2[1][2] - mat[4 * 6 + 5];
r3[2][0] = r2[2][0] - mat[5 * 6 + 3];
r3[2][1] = r2[2][1] - mat[5 * 6 + 4];
r3[2][2] = r2[2][2] - mat[5 * 6 + 5];
// r3.InverseSelf();
r2[0][0] = r3[1][1] * r3[2][2] - r3[1][2] * r3[2][1];
r2[1][0] = r3[1][2] * r3[2][0] - r3[1][0] * r3[2][2];
r2[2][0] = r3[1][0] * r3[2][1] - r3[1][1] * r3[2][0];
det = r3[0][0] * r2[0][0] + r3[0][1] * r2[1][0] + r3[0][2] * r2[2][0];
if( idMath::Fabs( det ) < MATRIX_INVERSE_EPSILON )
{
return false;
}
invDet = 1.0f / det;
r2[0][1] = r3[0][2] * r3[2][1] - r3[0][1] * r3[2][2];
r2[0][2] = r3[0][1] * r3[1][2] - r3[0][2] * r3[1][1];
r2[1][1] = r3[0][0] * r3[2][2] - r3[0][2] * r3[2][0];
r2[1][2] = r3[0][2] * r3[1][0] - r3[0][0] * r3[1][2];
r2[2][1] = r3[0][1] * r3[2][0] - r3[0][0] * r3[2][1];
r2[2][2] = r3[0][0] * r3[1][1] - r3[0][1] * r3[1][0];
r3[0][0] = r2[0][0] * invDet;
r3[0][1] = r2[0][1] * invDet;
r3[0][2] = r2[0][2] * invDet;
r3[1][0] = r2[1][0] * invDet;
r3[1][1] = r2[1][1] * invDet;
r3[1][2] = r2[1][2] * invDet;
r3[2][0] = r2[2][0] * invDet;
r3[2][1] = r2[2][1] * invDet;
r3[2][2] = r2[2][2] * invDet;
// r2 = m2 * r0;
r2[0][0] = mat[3 * 6 + 0] * r0[0][0] + mat[3 * 6 + 1] * r0[1][0] + mat[3 * 6 + 2] * r0[2][0];
r2[0][1] = mat[3 * 6 + 0] * r0[0][1] + mat[3 * 6 + 1] * r0[1][1] + mat[3 * 6 + 2] * r0[2][1];
r2[0][2] = mat[3 * 6 + 0] * r0[0][2] + mat[3 * 6 + 1] * r0[1][2] + mat[3 * 6 + 2] * r0[2][2];
r2[1][0] = mat[4 * 6 + 0] * r0[0][0] + mat[4 * 6 + 1] * r0[1][0] + mat[4 * 6 + 2] * r0[2][0];
r2[1][1] = mat[4 * 6 + 0] * r0[0][1] + mat[4 * 6 + 1] * r0[1][1] + mat[4 * 6 + 2] * r0[2][1];
r2[1][2] = mat[4 * 6 + 0] * r0[0][2] + mat[4 * 6 + 1] * r0[1][2] + mat[4 * 6 + 2] * r0[2][2];
r2[2][0] = mat[5 * 6 + 0] * r0[0][0] + mat[5 * 6 + 1] * r0[1][0] + mat[5 * 6 + 2] * r0[2][0];
r2[2][1] = mat[5 * 6 + 0] * r0[0][1] + mat[5 * 6 + 1] * r0[1][1] + mat[5 * 6 + 2] * r0[2][1];
r2[2][2] = mat[5 * 6 + 0] * r0[0][2] + mat[5 * 6 + 1] * r0[1][2] + mat[5 * 6 + 2] * r0[2][2];
// m2 = r3 * r2;
mat[3 * 6 + 0] = r3[0][0] * r2[0][0] + r3[0][1] * r2[1][0] + r3[0][2] * r2[2][0];
mat[3 * 6 + 1] = r3[0][0] * r2[0][1] + r3[0][1] * r2[1][1] + r3[0][2] * r2[2][1];
mat[3 * 6 + 2] = r3[0][0] * r2[0][2] + r3[0][1] * r2[1][2] + r3[0][2] * r2[2][2];
mat[4 * 6 + 0] = r3[1][0] * r2[0][0] + r3[1][1] * r2[1][0] + r3[1][2] * r2[2][0];
mat[4 * 6 + 1] = r3[1][0] * r2[0][1] + r3[1][1] * r2[1][1] + r3[1][2] * r2[2][1];
mat[4 * 6 + 2] = r3[1][0] * r2[0][2] + r3[1][1] * r2[1][2] + r3[1][2] * r2[2][2];
mat[5 * 6 + 0] = r3[2][0] * r2[0][0] + r3[2][1] * r2[1][0] + r3[2][2] * r2[2][0];
mat[5 * 6 + 1] = r3[2][0] * r2[0][1] + r3[2][1] * r2[1][1] + r3[2][2] * r2[2][1];
mat[5 * 6 + 2] = r3[2][0] * r2[0][2] + r3[2][1] * r2[1][2] + r3[2][2] * r2[2][2];
// m0 = r0 - r1 * m2;
mat[0 * 6 + 0] = r0[0][0] - r1[0][0] * mat[3 * 6 + 0] - r1[0][1] * mat[4 * 6 + 0] - r1[0][2] * mat[5 * 6 + 0];
mat[0 * 6 + 1] = r0[0][1] - r1[0][0] * mat[3 * 6 + 1] - r1[0][1] * mat[4 * 6 + 1] - r1[0][2] * mat[5 * 6 + 1];
mat[0 * 6 + 2] = r0[0][2] - r1[0][0] * mat[3 * 6 + 2] - r1[0][1] * mat[4 * 6 + 2] - r1[0][2] * mat[5 * 6 + 2];
mat[1 * 6 + 0] = r0[1][0] - r1[1][0] * mat[3 * 6 + 0] - r1[1][1] * mat[4 * 6 + 0] - r1[1][2] * mat[5 * 6 + 0];
mat[1 * 6 + 1] = r0[1][1] - r1[1][0] * mat[3 * 6 + 1] - r1[1][1] * mat[4 * 6 + 1] - r1[1][2] * mat[5 * 6 + 1];
mat[1 * 6 + 2] = r0[1][2] - r1[1][0] * mat[3 * 6 + 2] - r1[1][1] * mat[4 * 6 + 2] - r1[1][2] * mat[5 * 6 + 2];
mat[2 * 6 + 0] = r0[2][0] - r1[2][0] * mat[3 * 6 + 0] - r1[2][1] * mat[4 * 6 + 0] - r1[2][2] * mat[5 * 6 + 0];
mat[2 * 6 + 1] = r0[2][1] - r1[2][0] * mat[3 * 6 + 1] - r1[2][1] * mat[4 * 6 + 1] - r1[2][2] * mat[5 * 6 + 1];
mat[2 * 6 + 2] = r0[2][2] - r1[2][0] * mat[3 * 6 + 2] - r1[2][1] * mat[4 * 6 + 2] - r1[2][2] * mat[5 * 6 + 2];
// m1 = r1 * r3;
mat[0 * 6 + 3] = r1[0][0] * r3[0][0] + r1[0][1] * r3[1][0] + r1[0][2] * r3[2][0];
mat[0 * 6 + 4] = r1[0][0] * r3[0][1] + r1[0][1] * r3[1][1] + r1[0][2] * r3[2][1];
mat[0 * 6 + 5] = r1[0][0] * r3[0][2] + r1[0][1] * r3[1][2] + r1[0][2] * r3[2][2];
mat[1 * 6 + 3] = r1[1][0] * r3[0][0] + r1[1][1] * r3[1][0] + r1[1][2] * r3[2][0];
mat[1 * 6 + 4] = r1[1][0] * r3[0][1] + r1[1][1] * r3[1][1] + r1[1][2] * r3[2][1];
mat[1 * 6 + 5] = r1[1][0] * r3[0][2] + r1[1][1] * r3[1][2] + r1[1][2] * r3[2][2];
mat[2 * 6 + 3] = r1[2][0] * r3[0][0] + r1[2][1] * r3[1][0] + r1[2][2] * r3[2][0];
mat[2 * 6 + 4] = r1[2][0] * r3[0][1] + r1[2][1] * r3[1][1] + r1[2][2] * r3[2][1];
mat[2 * 6 + 5] = r1[2][0] * r3[0][2] + r1[2][1] * r3[1][2] + r1[2][2] * r3[2][2];
// m3 = -r3;
mat[3 * 6 + 3] = -r3[0][0];
mat[3 * 6 + 4] = -r3[0][1];
mat[3 * 6 + 5] = -r3[0][2];
mat[4 * 6 + 3] = -r3[1][0];
mat[4 * 6 + 4] = -r3[1][1];
mat[4 * 6 + 5] = -r3[1][2];
mat[5 * 6 + 3] = -r3[2][0];
mat[5 * 6 + 4] = -r3[2][1];
mat[5 * 6 + 5] = -r3[2][2];
return true;
#endif
}
/*
=============
idMat6::ToString
=============
*/
const char* idMat6::ToString( int precision ) const
{
return idStr::FloatArrayToString( ToFloatPtr(), GetDimension(), precision );
}
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