|Re: [eigen] Transform products|
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- To: eigen@xxxxxxxxxxxxxxxxxxx
- Subject: Re: [eigen] Transform products
- From: Benoit Jacob <jacob.benoit.1@xxxxxxxxx>
- Date: Thu, 19 Feb 2009 15:20:11 +0100
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I think the following question needs to be adressed first: couldn't we
just assume that the last row is 0,...,0,1 ? Is there really any use
case for non-affine transformations? Thus the last row would be there
just for seamless interoperability with OpenGL.
Or do you have a real use case where the last row is not 0,...,0,1 ?
2009/2/19 Gael Guennebaud <gael.guennebaud@xxxxxxxxx>:
> Hi list,
> there still remains a few issues with the product: Transform * matrix_expression
> Let d be the dimension of the ambient space (so that the Transform
> object actually correspond to a d+1 x d+1 matrix). Currently we allow:
> 1 - Transform * [d x d] => Transform
> 2 - Transform * [d+1 x d+1] => trivial product expression
> 3 - Transform * [d+1 x 1] => trivial product expression
> 4 - Transform * [d x 1] => complex [d x 1] expression including the
> homogeneous normalization
> a) the 4-th case is not plenty satisfactory:
> a1 - should it returns an homogeneous vector ?
> a2 - or automatically does the normalization as it currently does ?
> a3 - or should we offer a way to skip the normalization assuming the
> transformation is affine (last row = [0 ... 0 1]) ?
> Well, these questions are more complementary and I guess the answer is
> yes for all, the problem is rather how to expose all these variants ?
> a proposal:
> for a3 let's add "t.affine() * v" where affine() would return a
> kind of [d x d+1] proxy with overloaded operator *.
> for a1 and a2, two options:
> p1) keep the default as it because it is safe
> and for a1... well I don't know, anyway the user can still
> build and homogeneous one for the rhs.
> p2) let's return a "homogeneous" object which would
> automatically be converted to a [d x 1] vector if needed
> (ideally would have to be done in MatrixBase)
> b) second issue: We want to be able to perform a batch transformation
> of a set of N vectors. Again two cases:
> b1 - Transform * [d+1 x N] => this is trivial, we just have to merge
> the above cases 1 and 2 into a more generic one. DONE
> b2 - Transform * [d x N] => same issues than the ones discussed
> above excepted that the involved expressions are much more complicated
> ! For instance the affine case would be:
> t.matrix().linear() * [d x N] + t.matrix().translation() *
> This last example also shows that maybe it would be useful to have a
> "replicate" expression mapping a vector to a matrix with constant rows
> or constant columns ? This would be simpler than using a matrix
> product for that.
> And of course all the above discussion also holds for the transpose
> cases, i.e., matrix_expression * Transform.
> opinion, idea ?