Re: [eigen] Do we need geometry refactoring?

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On Wed, Aug 18, 2010 at 3:34 PM, Benoit Jacob <jacob.benoit.1@xxxxxxxxx> wrote:
> Yep, it looks all good to me. Can you just clarify the apparent
> contradiction between what you said at the top (disallow 1)) and what you
> just said (allow the latter product).

It is not a contradiction equation 1) maps

  Transform x Matrix -> Transform

My new proposal is (and to do this uniquely for all Transforms and in
particular all valid RHS matrices).

  Transform x Matrix -> Matrix

Just to be sure, this will break some existing code because you cannot
directly assign the result to a Transform because the matrix
constructor is explicit.

Regarding affine transformations you are right. Mathematically
speaking, the upper left (Dim)x(Dim) part does not necessarily have to
be invertible. In the geometry or applied field where I come from,
affine transformations as well as projective transformations
(homographies) have to be invertible (or are defined to be
convertible). Since we are performing "primarily" point
transformations consisting for affine of a combination of shearing,
(anisotropic) scaling and rotation, I was expecting the Transform
class to represent geometric "invertible" transformations...

- Hauke

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