libcruft-util/matrix4.cpp

/*
 * 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)
{
    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>
matrix<Rows,Cols,T>
cruft::inverse (const matrix<Rows,Cols,T> &m)
{
    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>;