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> One example is why you multiply normals by the world_inverse_tranpose I know linear algebra but I have no idea what the heck this means. Is this a gaming thi
by MiroF 6y ago
> One example is why you multiply normals by the world_inverse_tranpose
I know linear algebra but I have no idea what the heck this means. Is this a gaming thing?
- sixo 6y agoComputer graphics. When transforming a coordinate system by a linear transformation represented by a matrix, normal vectors to surfaces transform differently than regular vectors. GA/exterior algebra explains this: the useful thing we call normals is represented by the same data (a 3d vector) but actually has to have a a different "type" to make sense. In higher dimensions they are not interchangeable with vectors.
- MiroF 6y agoAh gotcha, why don't bivectors transform normally e: I'm restating the question in a form I understand, not asking it.
- ogogmad 6y agoIf T:V->V is a linear transformation and "^" is the exterior product then T(u^v)=T(u)^T(v). For example, let T be a reflection about the plane spanned by e1 and e2. Then T(e1^e2)=e1^e2, but T(e1 x e2) = -e1 x e2, where "x" denotes the cross product.
- MiroF 6y agoI should have been clear, I was restating their question, not asking it again.
- deleted 6y ago[deleted]
- aap_ 6y agoIn LA you calculate the normal of a plane by taking the cross product of two vectors lying in that plane. If you transform all three with the same matrix the normal will in the general case no longer be the cross product of the transformed vectors, you have to transform it with the inverse transpose matrix instead.
- MiroF 6y agoThanks, I think I was more confused by what `world_inverse_tranpose` is.