Comp Newsgroup Archive :: comp.graphics.algorithms :: Re: transforming vector by affine transformation

On Feb 21, 5:03 pm, 'jraul' <,jrauli.…@yahoo.com>, wrote: >, >, The weights of the points only need to sum to one if the result >, needs to >, >, >, be a point. >, >, Thanks, that was the key part I did not know. The book I mentioned >, didn't give an explicit form for an affine transformation (matrix + >, vector), it just defines an affine transformation as a mapping from an >, affine space to an affine space that preserves affine combinations: >, >, A(a1P1 + ... + anPn) = a1*A(P1) + ... + an*A(Pn) >, >, where the weights sum to one. From this def, it was not clear that >, you could still apply this if your point combination did not sum to >, one. >, >, Off topic: Does anyone know where to get Derose's coordinate free >, approach paper online? I just find citations on a web search and not >, the actual paper. >, >, Note that points and vectors are different entities in >, >, >, affine spaces. >, >, >, Gino I don't know about Derose's paper but the paper 'Miller, J., R.: Vector Geometry for Computer Graphics, IEEE Computer Graphics and Applications, v.19 n.3, p.66-73, May 1999' covers the discussed stuff too (in quite a nice way :-)) Source.


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