libcruft-util/matrix4.cpp

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/*
2018-08-04 15:14:06 +10:00
* This Source Code Form is subject to the terms of the Mozilla Public
* License, v. 2.0. If a copy of the MPL was not distributed with this
* file, You can obtain one at http://mozilla.org/MPL/2.0/.
*
* Copyright 2015 Danny Robson <danny@nerdcruft.net>
*/
#include "matrix.hpp"
using cruft::matrix;
//-----------------------------------------------------------------------------
template <std::size_t Rows, std::size_t Cols, typename T>
T
cruft::determinant (const matrix<Rows,Cols,T> &m)
{
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static_assert (Rows == 4 && Cols == 4);
return m[0][3] * m[1][2] * m[2][1] * m[3][0] - m[0][2] * m[1][3] * m[2][1] * m[3][0] -
m[0][3] * m[1][1] * m[2][2] * m[3][0] + m[0][1] * m[1][3] * m[2][2] * m[3][0] +
m[0][2] * m[1][1] * m[2][3] * m[3][0] - m[0][1] * m[1][2] * m[2][3] * m[3][0] -
m[0][3] * m[1][2] * m[2][0] * m[3][1] + m[0][2] * m[1][3] * m[2][0] * m[3][1] +
m[0][3] * m[1][0] * m[2][2] * m[3][1] - m[0][0] * m[1][3] * m[2][2] * m[3][1] -
m[0][2] * m[1][0] * m[2][3] * m[3][1] + m[0][0] * m[1][2] * m[2][3] * m[3][1] +
m[0][3] * m[1][1] * m[2][0] * m[3][2] - m[0][1] * m[1][3] * m[2][0] * m[3][2] -
m[0][3] * m[1][0] * m[2][1] * m[3][2] + m[0][0] * m[1][3] * m[2][1] * m[3][2] +
m[0][1] * m[1][0] * m[2][3] * m[3][2] - m[0][0] * m[1][1] * m[2][3] * m[3][2] -
m[0][2] * m[1][1] * m[2][0] * m[3][3] + m[0][1] * m[1][2] * m[2][0] * m[3][3] +
m[0][2] * m[1][0] * m[2][1] * m[3][3] - m[0][0] * m[1][2] * m[2][1] * m[3][3] -
m[0][1] * m[1][0] * m[2][2] * m[3][3] + m[0][0] * m[1][1] * m[2][2] * m[3][3];
}
template float cruft::determinant (const matrix<4,4,float>&);
template double cruft::determinant (const matrix<4,4,double>&);
//-----------------------------------------------------------------------------
template <std::size_t Rows, std::size_t Cols, typename T>
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matrix<Rows,Cols,T>
cruft::inverse (const matrix<Rows,Cols,T> &m)
{
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static_assert (Rows == 4 && Cols == 4);
return matrix<4,4,T> {{
{ m[1][2]*m[2][3]*m[3][1]
-m[1][3]*m[2][2]*m[3][1]
+m[1][3]*m[2][1]*m[3][2]
-m[1][1]*m[2][3]*m[3][2]
-m[1][2]*m[2][1]*m[3][3]
+m[1][1]*m[2][2]*m[3][3],
m[0][3]*m[2][2]*m[3][1]
-m[0][2]*m[2][3]*m[3][1]
-m[0][3]*m[2][1]*m[3][2]
+m[0][1]*m[2][3]*m[3][2]
+m[0][2]*m[2][1]*m[3][3]
-m[0][1]*m[2][2]*m[3][3],
m[0][2]*m[1][3]*m[3][1]
-m[0][3]*m[1][2]*m[3][1]
+m[0][3]*m[1][1]*m[3][2]
-m[0][1]*m[1][3]*m[3][2]
-m[0][2]*m[1][1]*m[3][3]
+m[0][1]*m[1][2]*m[3][3],
m[0][3]*m[1][2]*m[2][1]
-m[0][2]*m[1][3]*m[2][1]
-m[0][3]*m[1][1]*m[2][2]
+m[0][1]*m[1][3]*m[2][2]
+m[0][2]*m[1][1]*m[2][3]
-m[0][1]*m[1][2]*m[2][3], },
{ m[1][3]*m[2][2]*m[3][0]
-m[1][2]*m[2][3]*m[3][0]
-m[1][3]*m[2][0]*m[3][2]
+m[1][0]*m[2][3]*m[3][2]
+m[1][2]*m[2][0]*m[3][3]
-m[1][0]*m[2][2]*m[3][3],
m[0][2]*m[2][3]*m[3][0]
-m[0][3]*m[2][2]*m[3][0]
+m[0][3]*m[2][0]*m[3][2]
-m[0][0]*m[2][3]*m[3][2]
-m[0][2]*m[2][0]*m[3][3]
+m[0][0]*m[2][2]*m[3][3],
m[0][3]*m[1][2]*m[3][0]
-m[0][2]*m[1][3]*m[3][0]
-m[0][3]*m[1][0]*m[3][2]
+m[0][0]*m[1][3]*m[3][2]
+m[0][2]*m[1][0]*m[3][3]
-m[0][0]*m[1][2]*m[3][3],
m[0][2]*m[1][3]*m[2][0]
-m[0][3]*m[1][2]*m[2][0]
+m[0][3]*m[1][0]*m[2][2]
-m[0][0]*m[1][3]*m[2][2]
-m[0][2]*m[1][0]*m[2][3]
+m[0][0]*m[1][2]*m[2][3], },
{ m[1][1]*m[2][3]*m[3][0]
-m[1][3]*m[2][1]*m[3][0]
+m[1][3]*m[2][0]*m[3][1]
-m[1][0]*m[2][3]*m[3][1]
-m[1][1]*m[2][0]*m[3][3]
+m[1][0]*m[2][1]*m[3][3],
m[0][3]*m[2][1]*m[3][0]
-m[0][1]*m[2][3]*m[3][0]
-m[0][3]*m[2][0]*m[3][1]
+m[0][0]*m[2][3]*m[3][1]
+m[0][1]*m[2][0]*m[3][3]
-m[0][0]*m[2][1]*m[3][3],
m[0][1]*m[1][3]*m[3][0]
-m[0][3]*m[1][1]*m[3][0]
+m[0][3]*m[1][0]*m[3][1]
-m[0][0]*m[1][3]*m[3][1]
-m[0][1]*m[1][0]*m[3][3]
+m[0][0]*m[1][1]*m[3][3],
m[0][3]*m[1][1]*m[2][0]
-m[0][1]*m[1][3]*m[2][0]
-m[0][3]*m[1][0]*m[2][1]
+m[0][0]*m[1][3]*m[2][1]
+m[0][1]*m[1][0]*m[2][3]
-m[0][0]*m[1][1]*m[2][3], },
{ m[1][2]*m[2][1]*m[3][0]
-m[1][1]*m[2][2]*m[3][0]
-m[1][2]*m[2][0]*m[3][1]
+m[1][0]*m[2][2]*m[3][1]
+m[1][1]*m[2][0]*m[3][2]
-m[1][0]*m[2][1]*m[3][2],
m[0][1]*m[2][2]*m[3][0]
-m[0][2]*m[2][1]*m[3][0]
+m[0][2]*m[2][0]*m[3][1]
-m[0][0]*m[2][2]*m[3][1]
-m[0][1]*m[2][0]*m[3][2]
+m[0][0]*m[2][1]*m[3][2],
m[0][2]*m[1][1]*m[3][0]
-m[0][1]*m[1][2]*m[3][0]
-m[0][2]*m[1][0]*m[3][1]
+m[0][0]*m[1][2]*m[3][1]
+m[0][1]*m[1][0]*m[3][2]
-m[0][0]*m[1][1]*m[3][2],
m[0][1]*m[1][2]*m[2][0]
-m[0][2]*m[1][1]*m[2][0]
+m[0][2]*m[1][0]*m[2][1]
-m[0][0]*m[1][2]*m[2][1]
-m[0][1]*m[1][0]*m[2][2]
+m[0][0]*m[1][1]*m[2][2], }
}} / determinant (m);
}
template cruft::matrix<4,4,float> cruft::inverse (const matrix<4,4,float>&);
template cruft::matrix<4,4,double> cruft::inverse (const matrix<4,4,double>&);
///////////////////////////////////////////////////////////////////////////////
template struct cruft::matrix<4,4,float>;
template struct cruft::matrix<4,4,double>;