void mat3_invert(Real in[3][3], Real out[3][3])
{
Real det(mat3_determinant(in));
if (det == 0.0)
return;
det = 1.0 / det;
out[0][0] = (in[1][1] * in[2][2] -
in[1][2] * in[2][1]) * det;
out[1][0] = - (in[1][0] * in[2][2] -
in[1][2] * in[2][0]) * det;
out[2][0] = (in[1][0] * in[2][1] -
in[1][1] * in[2][0]) * det;
out[0][1] = - (in[0][1] * in[2][2] -
in[0][2] * in[2][1]) * det;
out[1][1] = (in[0][0] * in[2][2] -
in[0][2] * in[2][0]) * det;
out[2][1] = - (in[0][0] * in[2][1] -
in[0][1] * in[2][0]) * det;
out[0][2] = (in[0][1] * in[1][2] -
in[0][2] * in[1][1]) * det;
out[1][2] = - (in[0][0] * in[1][2] -
in[0][2] * in[1][0]) * det;
out[2][2] = (in[0][0] * in[1][1] -
in[0][1] * in[1][0]) * det;
}
/*
How do you find the adjoint of a 4x4 matrix?
Find the cofactor (determinant of the signed minor) of each entry, keeping in mind the sign array
(starting with + in the upper left corner):
[+ - + -]
[- + - +]
[+ - + -]
[- + - +]
//
// 11 12 13 14
// 21 22 23 24
// 31 32 33 34
// 41 42 43 44
//
// c = adjoint(a)
*/
void mat4_adjoint(mat4 &c, const mat4 &a)
{
mat3 m3;
mat4 m4;
// Create matrix of minors
// Apply +- pattern to create matrix of cofactors
// 11
m3.m11 = a.m22; m3.m12 = a.m23; m3.m13 = a.m24;
m3.m21 = a.m32; m3.m22 = a.m33; m3.m23 = a.m34;
m3.m31 = a.m42; m3.m32 = a.m43; m3.m33 = a.m44;
m4.m11 = mat3_determinant(m3);
// 12
m3.m11 = a.m21; m3.m12 = a.m23; m3.m13 = a.m24;
m3.m21 = a.m31; m3.m22 = a.m33; m3.m23 = a.m34;
m3.m31 = a.m41; m3.m32 = a.m43; m3.m33 = a.m44;
m4.m12 = -mat3_determinant(m3);
// 13
m3.m11 = a.m21; m3.m12 = a.m22; m3.m13 = a.m24;
m3.m21 = a.m31; m3.m22 = a.m32; m3.m23 = a.m34;
m3.m31 = a.m41; m3.m32 = a.m42; m3.m33 = a.m44;
m4.m13 = mat3_determinant(m3);
// 14
m3.m11 = a.m21; m3.m12 = a.m22; m3.m13 = a.m23;
m3.m21 = a.m31; m3.m22 = a.m32; m3.m23 = a.m33;
m3.m31 = a.m41; m3.m32 = a.m42; m3.m33 = a.m43;
m4.m14 = -mat3_determinant(m3);
// 21
m3.m11 = a.m12; m3.m12 = a.m13; m3.m13 = a.m14;
m3.m21 = a.m32; m3.m22 = a.m33; m3.m23 = a.m34;
m3.m31 = a.m42; m3.m32 = a.m43; m3.m33 = a.m44;
m4.m21 = -mat3_determinant(m3);
// 22
m3.m11 = a.m11; m3.m12 = a.m13; m3.m13 = a.m14;
m3.m21 = a.m31; m3.m22 = a.m33; m3.m23 = a.m34;
m3.m31 = a.m41; m3.m32 = a.m43; m3.m33 = a.m44;
m4.m22 = mat3_determinant(m3);
// 23
m3.m11 = a.m11; m3.m12 = a.m12; m3.m13 = a.m14;
m3.m21 = a.m31; m3.m22 = a.m32; m3.m23 = a.m34;
m3.m31 = a.m41; m3.m32 = a.m42; m3.m33 = a.m44;
m4.m23 = -mat3_determinant(m3);
// 24
m3.m11 = a.m11; m3.m12 = a.m12; m3.m13 = a.m13;
m3.m21 = a.m31; m3.m22 = a.m32; m3.m23 = a.m33;
m3.m31 = a.m41; m3.m32 = a.m42; m3.m33 = a.m43;
m4.m24 = mat3_determinant(m3);
// 31
m3.m11 = a.m12; m3.m12 = a.m13; m3.m13 = a.m14;
m3.m21 = a.m22; m3.m22 = a.m23; m3.m23 = a.m24;
m3.m31 = a.m42; m3.m32 = a.m43; m3.m33 = a.m44;
m4.m31 = mat3_determinant(m3);
// 32
m3.m11 = a.m11; m3.m12 = a.m13; m3.m13 = a.m14;
m3.m21 = a.m21; m3.m22 = a.m23; m3.m23 = a.m24;
m3.m31 = a.m41; m3.m32 = a.m43; m3.m33 = a.m44;
m4.m32 = -mat3_determinant(m3);
// 33
m3.m11 = a.m11; m3.m12 = a.m12; m3.m13 = a.m14;
m3.m21 = a.m21; m3.m22 = a.m22; m3.m23 = a.m24;
m3.m31 = a.m41; m3.m32 = a.m42; m3.m33 = a.m44;
m4.m33 = mat3_determinant(m3);
// 34
m3.m11 = a.m11; m3.m12 = a.m12; m3.m13 = a.m13;
m3.m21 = a.m21; m3.m22 = a.m22; m3.m23 = a.m23;
m3.m31 = a.m41; m3.m32 = a.m42; m3.m33 = a.m43;
m4.m34 = -mat3_determinant(m3);
// 41
m3.m11 = a.m12; m3.m12 = a.m13; m3.m13 = a.m14;
m3.m21 = a.m22; m3.m22 = a.m23; m3.m23 = a.m24;
m3.m31 = a.m32; m3.m32 = a.m33; m3.m33 = a.m34;
m4.m41 = -mat3_determinant(m3);
// 42
m3.m11 = a.m11; m3.m12 = a.m13; m3.m13 = a.m14;
m3.m21 = a.m21; m3.m22 = a.m23; m3.m23 = a.m24;
m3.m31 = a.m31; m3.m32 = a.m33; m3.m33 = a.m34;
m4.m42 = mat3_determinant(m3);
// 43
m3.m11 = a.m11; m3.m12 = a.m12; m3.m13 = a.m14;
m3.m21 = a.m21; m3.m22 = a.m22; m3.m23 = a.m24;
m3.m31 = a.m31; m3.m32 = a.m32; m3.m33 = a.m34;
m4.m43 = -mat3_determinant(m3);
// 44
m3.m11 = a.m11; m3.m12 = a.m12; m3.m13 = a.m13;
m3.m21 = a.m21; m3.m22 = a.m22; m3.m23 = a.m23;
m3.m31 = a.m31; m3.m32 = a.m32; m3.m33 = a.m33;
m4.m44 = mat3_determinant(m3);
// create adjoint by transposing
mat4_transpose(c, m4);
}