matrix_inverse.inl

 
 
namespace glm
{
    template<typename T, qualifier Q>
    GLM_FUNC_QUALIFIER mat<3, 3, T, Q> affineInverse(mat<3, 3, T, Q> const& m)
    {
        mat<2, 2, T, Q> const Inv(inverse(mat<2, 2, T, Q>(m)));
 
        return mat<3, 3, T, Q>(
            vec<3, T, Q>(Inv[0], static_cast<T>(0)),
            vec<3, T, Q>(Inv[1], static_cast<T>(0)),
            vec<3, T, Q>(-Inv * vec<2, T, Q>(m[2]), static_cast<T>(1)));
    }
 
    template<typename T, qualifier Q>
    GLM_FUNC_QUALIFIER mat<4, 4, T, Q> affineInverse(mat<4, 4, T, Q> const& m)
    {
        mat<3, 3, T, Q> const Inv(inverse(mat<3, 3, T, Q>(m)));
 
        return mat<4, 4, T, Q>(
            vec<4, T, Q>(Inv[0], static_cast<T>(0)),
            vec<4, T, Q>(Inv[1], static_cast<T>(0)),
            vec<4, T, Q>(Inv[2], static_cast<T>(0)),
            vec<4, T, Q>(-Inv * vec<3, T, Q>(m[3]), static_cast<T>(1)));
    }
 
    template<typename T, qualifier Q>
    GLM_FUNC_QUALIFIER mat<2, 2, T, Q> inverseTranspose(mat<2, 2, T, Q> const& m)
    {
        T Determinant = m[0][0] * m[1][1] - m[1][0] * m[0][1];
 
        mat<2, 2, T, Q> Inverse(
            + m[1][1] / Determinant,
            - m[0][1] / Determinant,
            - m[1][0] / Determinant,
            + m[0][0] / Determinant);
 
        return Inverse;
    }
 
    template<typename T, qualifier Q>
    GLM_FUNC_QUALIFIER mat<3, 3, T, Q> inverseTranspose(mat<3, 3, T, Q> const& m)
    {
        T Determinant =
            + m[0][0] * (m[1][1] * m[2][2] - m[1][2] * m[2][1])
            - m[0][1] * (m[1][0] * m[2][2] - m[1][2] * m[2][0])
            + m[0][2] * (m[1][0] * m[2][1] - m[1][1] * m[2][0]);
 
        mat<3, 3, T, Q> Inverse;
        Inverse[0][0] = + (m[1][1] * m[2][2] - m[2][1] * m[1][2]);
        Inverse[0][1] = - (m[1][0] * m[2][2] - m[2][0] * m[1][2]);
        Inverse[0][2] = + (m[1][0] * m[2][1] - m[2][0] * m[1][1]);
        Inverse[1][0] = - (m[0][1] * m[2][2] - m[2][1] * m[0][2]);
        Inverse[1][1] = + (m[0][0] * m[2][2] - m[2][0] * m[0][2]);
        Inverse[1][2] = - (m[0][0] * m[2][1] - m[2][0] * m[0][1]);
        Inverse[2][0] = + (m[0][1] * m[1][2] - m[1][1] * m[0][2]);
        Inverse[2][1] = - (m[0][0] * m[1][2] - m[1][0] * m[0][2]);
        Inverse[2][2] = + (m[0][0] * m[1][1] - m[1][0] * m[0][1]);
        Inverse /= Determinant;
 
        return Inverse;
    }
 
    template<typename T, qualifier Q>
    GLM_FUNC_QUALIFIER mat<4, 4, T, Q> inverseTranspose(mat<4, 4, T, Q> const& m)
    {
        T SubFactor00 = m[2][2] * m[3][3] - m[3][2] * m[2][3];
        T SubFactor01 = m[2][1] * m[3][3] - m[3][1] * m[2][3];
        T SubFactor02 = m[2][1] * m[3][2] - m[3][1] * m[2][2];
        T SubFactor03 = m[2][0] * m[3][3] - m[3][0] * m[2][3];
        T SubFactor04 = m[2][0] * m[3][2] - m[3][0] * m[2][2];
        T SubFactor05 = m[2][0] * m[3][1] - m[3][0] * m[2][1];
        T SubFactor06 = m[1][2] * m[3][3] - m[3][2] * m[1][3];
        T SubFactor07 = m[1][1] * m[3][3] - m[3][1] * m[1][3];
        T SubFactor08 = m[1][1] * m[3][2] - m[3][1] * m[1][2];
        T SubFactor09 = m[1][0] * m[3][3] - m[3][0] * m[1][3];
        T SubFactor10 = m[1][0] * m[3][2] - m[3][0] * m[1][2];
        T SubFactor11 = m[1][0] * m[3][1] - m[3][0] * m[1][1];
        T SubFactor12 = m[1][2] * m[2][3] - m[2][2] * m[1][3];
        T SubFactor13 = m[1][1] * m[2][3] - m[2][1] * m[1][3];
        T SubFactor14 = m[1][1] * m[2][2] - m[2][1] * m[1][2];
        T SubFactor15 = m[1][0] * m[2][3] - m[2][0] * m[1][3];
        T SubFactor16 = m[1][0] * m[2][2] - m[2][0] * m[1][2];
        T SubFactor17 = m[1][0] * m[2][1] - m[2][0] * m[1][1];
 
        mat<4, 4, T, Q> Inverse;
        Inverse[0][0] = + (m[1][1] * SubFactor00 - m[1][2] * SubFactor01 + m[1][3] * SubFactor02);
        Inverse[0][1] = - (m[1][0] * SubFactor00 - m[1][2] * SubFactor03 + m[1][3] * SubFactor04);
        Inverse[0][2] = + (m[1][0] * SubFactor01 - m[1][1] * SubFactor03 + m[1][3] * SubFactor05);
        Inverse[0][3] = - (m[1][0] * SubFactor02 - m[1][1] * SubFactor04 + m[1][2] * SubFactor05);
 
        Inverse[1][0] = - (m[0][1] * SubFactor00 - m[0][2] * SubFactor01 + m[0][3] * SubFactor02);
        Inverse[1][1] = + (m[0][0] * SubFactor00 - m[0][2] * SubFactor03 + m[0][3] * SubFactor04);
        Inverse[1][2] = - (m[0][0] * SubFactor01 - m[0][1] * SubFactor03 + m[0][3] * SubFactor05);
        Inverse[1][3] = + (m[0][0] * SubFactor02 - m[0][1] * SubFactor04 + m[0][2] * SubFactor05);
 
        Inverse[2][0] = + (m[0][1] * SubFactor06 - m[0][2] * SubFactor07 + m[0][3] * SubFactor08);
        Inverse[2][1] = - (m[0][0] * SubFactor06 - m[0][2] * SubFactor09 + m[0][3] * SubFactor10);
        Inverse[2][2] = + (m[0][0] * SubFactor07 - m[0][1] * SubFactor09 + m[0][3] * SubFactor11);
        Inverse[2][3] = - (m[0][0] * SubFactor08 - m[0][1] * SubFactor10 + m[0][2] * SubFactor11);
 
        Inverse[3][0] = - (m[0][1] * SubFactor12 - m[0][2] * SubFactor13 + m[0][3] * SubFactor14);
        Inverse[3][1] = + (m[0][0] * SubFactor12 - m[0][2] * SubFactor15 + m[0][3] * SubFactor16);
        Inverse[3][2] = - (m[0][0] * SubFactor13 - m[0][1] * SubFactor15 + m[0][3] * SubFactor17);
        Inverse[3][3] = + (m[0][0] * SubFactor14 - m[0][1] * SubFactor16 + m[0][2] * SubFactor17);
 
        T Determinant =
            + m[0][0] * Inverse[0][0]
            + m[0][1] * Inverse[0][1]
            + m[0][2] * Inverse[0][2]
            + m[0][3] * Inverse[0][3];
 
        Inverse /= Determinant;
 
        return Inverse;
    }
}//namespace glm