GLSL反转矩阵inverse

低版本 vertex shader 可以使用，通常用来反转TBN矩阵，但是计算量很大。

代码来自 OpenGL Mathematics (GLM)

mat4 inverse_mat4(mat4 m)
{
    float Coef00 = m[][] * m[][] - m[][] * m[][];
    float Coef02 = m[][] * m[][] - m[][] * m[][];
    float Coef03 = m[][] * m[][] - m[][] * m[][];

    float Coef04 = m[][] * m[][] - m[][] * m[][];
    float Coef06 = m[][] * m[][] - m[][] * m[][];
    float Coef07 = m[][] * m[][] - m[][] * m[][];

    float Coef08 = m[][] * m[][] - m[][] * m[][];
    float Coef10 = m[][] * m[][] - m[][] * m[][];
    float Coef11 = m[][] * m[][] - m[][] * m[][];

    float Coef12 = m[][] * m[][] - m[][] * m[][];
    float Coef14 = m[][] * m[][] - m[][] * m[][];
    float Coef15 = m[][] * m[][] - m[][] * m[][];

    float Coef16 = m[][] * m[][] - m[][] * m[][];
    float Coef18 = m[][] * m[][] - m[][] * m[][];
    float Coef19 = m[][] * m[][] - m[][] * m[][];

    float Coef20 = m[][] * m[][] - m[][] * m[][];
    float Coef22 = m[][] * m[][] - m[][] * m[][];
    float Coef23 = m[][] * m[][] - m[][] * m[][];

    const vec4 SignA = vec4( 1.0, -1.0,  1.0, -1.0);
    const vec4 SignB = vec4(-1.0,  1.0, -1.0,  1.0);

    vec4 Fac0 = vec4(Coef00, Coef00, Coef02, Coef03);
    vec4 Fac1 = vec4(Coef04, Coef04, Coef06, Coef07);
    vec4 Fac2 = vec4(Coef08, Coef08, Coef10, Coef11);
    vec4 Fac3 = vec4(Coef12, Coef12, Coef14, Coef15);
    vec4 Fac4 = vec4(Coef16, Coef16, Coef18, Coef19);
    vec4 Fac5 = vec4(Coef20, Coef20, Coef22, Coef23);

    vec4 Vec0 = vec4(m[][], m[][], m[][], m[][]);
    vec4 Vec1 = vec4(m[][], m[][], m[][], m[][]);
    vec4 Vec2 = vec4(m[][], m[][], m[][], m[][]);
    vec4 Vec3 = vec4(m[][], m[][], m[][], m[][]);

    vec4 Inv0 = SignA * (Vec1 * Fac0 - Vec2 * Fac1 + Vec3 * Fac2);
    vec4 Inv1 = SignB * (Vec0 * Fac0 - Vec2 * Fac3 + Vec3 * Fac4);
    vec4 Inv2 = SignA * (Vec0 * Fac1 - Vec1 * Fac3 + Vec3 * Fac5);
    vec4 Inv3 = SignB * (Vec0 * Fac2 - Vec1 * Fac4 + Vec2 * Fac5);

    mat4 Inverse = mat4(Inv0, Inv1, Inv2, Inv3);

    vec4 Row0 = vec4(Inverse[][], Inverse[][], Inverse[][], Inverse[][]);

    float Determinant = dot(m[], Row0);

    Inverse /= Determinant;

    return Inverse;
}

mat3 inverse_mat3(mat3 m)
{
    float Determinant =
          m[][] * (m[][] * m[][] - m[][] * m[][])
        - m[][] * (m[][] * m[][] - m[][] * m[][])
        + m[][] * (m[][] * m[][] - m[][] * m[][]);

    mat3 Inverse;
    Inverse[][] = + (m[][] * m[][] - m[][] * m[][]);
    Inverse[][] = - (m[][] * m[][] - m[][] * m[][]);
    Inverse[][] = + (m[][] * m[][] - m[][] * m[][]);
    Inverse[][] = - (m[][] * m[][] - m[][] * m[][]);
    Inverse[][] = + (m[][] * m[][] - m[][] * m[][]);
    Inverse[][] = - (m[][] * m[][] - m[][] * m[][]);
    Inverse[][] = + (m[][] * m[][] - m[][] * m[][]);
    Inverse[][] = - (m[][] * m[][] - m[][] * m[][]);
    Inverse[][] = + (m[][] * m[][] - m[][] * m[][]);
    Inverse /= Determinant;

    return Inverse;
}