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[2][2] * m[3][3] - m[3][2] * m[2][3];
    float Coef02 = m[1][2] * m[3][3] - m[3][2] * m[1][3];
    float Coef03 = m[1][2] * m[2][3] - m[2][2] * m[1][3];
    
    float Coef04 = m[2][1] * m[3][3] - m[3][1] * m[2][3];
    float Coef06 = m[1][1] * m[3][3] - m[3][1] * m[1][3];
    float Coef07 = m[1][1] * m[2][3] - m[2][1] * m[1][3];
    
    float Coef08 = m[2][1] * m[3][2] - m[3][1] * m[2][2];
    float Coef10 = m[1][1] * m[3][2] - m[3][1] * m[1][2];
    float Coef11 = m[1][1] * m[2][2] - m[2][1] * m[1][2];
    
    float Coef12 = m[2][0] * m[3][3] - m[3][0] * m[2][3];
    float Coef14 = m[1][0] * m[3][3] - m[3][0] * m[1][3];
    float Coef15 = m[1][0] * m[2][3] - m[2][0] * m[1][3];
    
    float Coef16 = m[2][0] * m[3][2] - m[3][0] * m[2][2];
    float Coef18 = m[1][0] * m[3][2] - m[3][0] * m[1][2];
    float Coef19 = m[1][0] * m[2][2] - m[2][0] * m[1][2];
    
    float Coef20 = m[2][0] * m[3][1] - m[3][0] * m[2][1];
    float Coef22 = m[1][0] * m[3][1] - m[3][0] * m[1][1];
    float Coef23 = m[1][0] * m[2][1] - m[2][0] * m[1][1];
    
    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[1][0], m[0][0], m[0][0], m[0][0]);
    vec4 Vec1 = vec4(m[1][1], m[0][1], m[0][1], m[0][1]);
    vec4 Vec2 = vec4(m[1][2], m[0][2], m[0][2], m[0][2]);
    vec4 Vec3 = vec4(m[1][3], m[0][3], m[0][3], m[0][3]);
    
    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[0][0], Inverse[1][0], Inverse[2][0], Inverse[3][0]);
    
    float Determinant = dot(m[0], Row0);
    
    Inverse /= Determinant;
    
    return Inverse;
}

mat3 inverse_mat3(mat3 m)
{
    float Determinant = 
          m[0][0] * (m[1][1] * m[2][2] - m[2][1] * m[1][2])
        - m[1][0] * (m[0][1] * m[2][2] - m[2][1] * m[0][2])
        + m[2][0] * (m[0][1] * m[1][2] - m[1][1] * m[0][2]);
    
    mat3 Inverse;
    Inverse[0][0] = + (m[1][1] * m[2][2] - m[2][1] * m[1][2]);
    Inverse[1][0] = - (m[1][0] * m[2][2] - m[2][0] * m[1][2]);
    Inverse[2][0] = + (m[1][0] * m[2][1] - m[2][0] * m[1][1]);
    Inverse[0][1] = - (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[2][1] = - (m[0][0] * m[2][1] - m[2][0] * m[0][1]);
    Inverse[0][2] = + (m[0][1] * m[1][2] - m[1][1] * m[0][2]);
    Inverse[1][2] = - (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;
}