Dale Weiler #BLM

In 2D the sign of the determinant encodes the winding of the parallelogram formed by the 2 vectors.

If you'd like even more detail about this, please see FGED1, Section 3.2.2. It also highlights a distinction between normals calculated with a gradient and normals calculated with a cross product. @wolfgangengel @aras_p https://www.amazon.com/dp/0985811749/?tag=terathon-20 …

Really BEAUTIFUL! I've been there but never did the full derivation. BTW, I think you could expand "more efficient to compute and accurate" and specifically note how the 1/determinant in inverse() cancells out with the determinant., just in case some readers don't see it.

So if I understand this correctly, we can use mat3(cross(m[1].xyz, m[2].xyz), cross(m[2].xyz, m[0].xyz), cross(m[0].xyz, m[1].xyz)); as a replacement for transpose(inverse(m)) in all cases? Does it work on a shearing matrix?

I've never looked at this math before so I'm missing out on some basic stuff. (1) What is V in the N.V derivation? (2) I don't get how you go from 'cof M = (det M) (M^-1)ᵀ' to 'sign(det(M))*transpose(inverse(M))', i.e. you seem to just drop the magnitude of det(M).

I think the answer is that people only care about the orientation of normal vectors and not their magnitude. This series by @Reedbeta talks about the distinction in a bit more detail, and when you'd end up with one or the other: http://www.reedbeta.com/blog/normals-inverse-transpose-part-1/ …

A GLSL demo for it, and a compact implementation of cofactor(): https://www.shadertoy.com/view/3s33zj