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inverse-transpose

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Hi, I am using the inverse transpose to transform normal vectors. But suppose D is the inverse transpose of a matrix M and that I am using homogeneous coordinates (w=0 for vectors). When I write D*v, where v = (x,y,z,0)^T (column vector), the w component of the product is not zero if M contained a translation. So it seems that vectors are no longer transforming to vectors. Am I doing something wrong or does the inverse-transpose derivation assume a linear transformation (not affine)?

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I think you have to just do the inverse-transpose thing with the upper 3x3 submatrix. I'm not sure how to unify this with homogeneous coordinates, but if you just use this submatrix, you'll get the right answer because translations shouldn't matter for normals anyway.

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This page explains the maths of transforming planes and normals:
clicky

Basically, for your question, you can just ignore the w of the result, and just renormalize x,y,z (in case M's 3x3 submatrix is not orthogonal).

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