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Computer graphics. When transforming a coordinate system by a linear transformation represented by a matrix, normal vectors to surfaces transform differently th
by sixo 6y ago
Computer 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]