Matrix Inverse

void Matrix4::Inverse( void )
{
  double det;
  Matrix4 ret;
  int i;
  ret.m_elements[0] =   m_elements[5]*m_elements[10]*m_elements[15] - m_elements[5]*m_elements[11]*m_elements[14] - m_elements[9]*m_elements[6]*m_elements[15]
  + m_elements[9]*m_elements[7]*m_elements[14] + m_elements[13]*m_elements[6]*m_elements[11] - m_elements[13]*m_elements[7]*m_elements[10];

  ret.m_elements[4] =  -m_elements[4]*m_elements[10]*m_elements[15] + m_elements[4]*m_elements[11]*m_elements[14] + m_elements[8]*m_elements[6]*m_elements[15]
  - m_elements[8]*m_elements[7]*m_elements[14] - m_elements[12]*m_elements[6]*m_elements[11] + m_elements[12]*m_elements[7]*m_elements[10];

  ret.m_elements[8] =   m_elements[4]*m_elements[9]*m_elements[15] - m_elements[4]*m_elements[11]*m_elements[13] - m_elements[8]*m_elements[5]*m_elements[15]
  + m_elements[8]*m_elements[7]*m_elements[13] + m_elements[12]*m_elements[5]*m_elements[11] - m_elements[12]*m_elements[7]*m_elements[9];

  ret.m_elements[12] = -m_elements[4]*m_elements[9]*m_elements[14] + m_elements[4]*m_elements[10]*m_elements[13] + m_elements[8]*m_elements[5]*m_elements[14]
  - m_elements[8]*m_elements[6]*m_elements[13] - m_elements[12]*m_elements[5]*m_elements[10] + m_elements[12]*m_elements[6]*m_elements[9];

  ret.m_elements[1] =  -m_elements[1]*m_elements[10]*m_elements[15] + m_elements[1]*m_elements[11]*m_elements[14] + m_elements[9]*m_elements[2]*m_elements[15]
  - m_elements[9]*m_elements[3]*m_elements[14] - m_elements[13]*m_elements[2]*m_elements[11] + m_elements[13]*m_elements[3]*m_elements[10];

  ret.m_elements[5] =   m_elements[0]*m_elements[10]*m_elements[15] - m_elements[0]*m_elements[11]*m_elements[14] - m_elements[8]*m_elements[2]*m_elements[15]
  + m_elements[8]*m_elements[3]*m_elements[14] + m_elements[12]*m_elements[2]*m_elements[11] - m_elements[12]*m_elements[3]*m_elements[10];

  ret.m_elements[9] =  -m_elements[0]*m_elements[9]*m_elements[15] + m_elements[0]*m_elements[11]*m_elements[13] + m_elements[8]*m_elements[1]*m_elements[15]
  - m_elements[8]*m_elements[3]*m_elements[13] - m_elements[12]*m_elements[1]*m_elements[11] + m_elements[12]*m_elements[3]*m_elements[9];

  ret.m_elements[13] =  m_elements[0]*m_elements[9]*m_elements[14] - m_elements[0]*m_elements[10]*m_elements[13] - m_elements[8]*m_elements[1]*m_elements[14]
  + m_elements[8]*m_elements[2]*m_elements[13] + m_elements[12]*m_elements[1]*m_elements[10] - m_elements[12]*m_elements[2]*m_elements[9];

  ret.m_elements[2] =   m_elements[1]*m_elements[6]*m_elements[15] - m_elements[1]*m_elements[7]*m_elements[14] - m_elements[5]*m_elements[2]*m_elements[15]
  + m_elements[5]*m_elements[3]*m_elements[14] + m_elements[13]*m_elements[2]*m_elements[7] - m_elements[13]*m_elements[3]*m_elements[6];

  ret.m_elements[6] =  -m_elements[0]*m_elements[6]*m_elements[15] + m_elements[0]*m_elements[7]*m_elements[14] + m_elements[4]*m_elements[2]*m_elements[15]
  - m_elements[4]*m_elements[3]*m_elements[14] - m_elements[12]*m_elements[2]*m_elements[7] + m_elements[12]*m_elements[3]*m_elements[6];

  ret.m_elements[10] =  m_elements[0]*m_elements[5]*m_elements[15] - m_elements[0]*m_elements[7]*m_elements[13] - m_elements[4]*m_elements[1]*m_elements[15]
  + m_elements[4]*m_elements[3]*m_elements[13] + m_elements[12]*m_elements[1]*m_elements[7] - m_elements[12]*m_elements[3]*m_elements[5];

  ret.m_elements[14] = -m_elements[0]*m_elements[5]*m_elements[14] + m_elements[0]*m_elements[6]*m_elements[13] + m_elements[4]*m_elements[1]*m_elements[14]
  - m_elements[4]*m_elements[2]*m_elements[13] - m_elements[12]*m_elements[1]*m_elements[6] + m_elements[12]*m_elements[2]*m_elements[5];

  ret.m_elements[3] =  -m_elements[1]*m_elements[6]*m_elements[11] + m_elements[1]*m_elements[7]*m_elements[10] + m_elements[5]*m_elements[2]*m_elements[11]
  - m_elements[5]*m_elements[3]*m_elements[10] - m_elements[9]*m_elements[2]*m_elements[7] + m_elements[9]*m_elements[3]*m_elements[6];

  ret.m_elements[7] =   m_elements[0]*m_elements[6]*m_elements[11] - m_elements[0]*m_elements[7]*m_elements[10] - m_elements[4]*m_elements[2]*m_elements[11]
  + m_elements[4]*m_elements[3]*m_elements[10] + m_elements[8]*m_elements[2]*m_elements[7] - m_elements[8]*m_elements[3]*m_elements[6];

  ret.m_elements[11] = -m_elements[0]*m_elements[5]*m_elements[11] + m_elements[0]*m_elements[7]*m_elements[9] + m_elements[4]*m_elements[1]*m_elements[11]
  - m_elements[4]*m_elements[3]*m_elements[9] - m_elements[8]*m_elements[1]*m_elements[7] + m_elements[8]*m_elements[3]*m_elements[5];

  ret.m_elements[15] =  m_elements[0]*m_elements[5]*m_elements[10] - m_elements[0]*m_elements[6]*m_elements[9] - m_elements[4]*m_elements[1]*m_elements[10]
  + m_elements[4]*m_elements[2]*m_elements[9] + m_elements[8]*m_elements[1]*m_elements[6] - m_elements[8]*m_elements[2]*m_elements[5];

  det = m_elements[0]*ret.m_elements[0] + m_elements[1]*ret.m_elements[4] + m_elements[2]*ret.m_elements[8] + m_elements[3]*ret.m_elements[12];
  if (det == 0)
    return;

  det = 1.0 / det;

  for (i = 0; i < 16; i++)
    m_elements[i] = float(ret.m_elements[i] * det);
}