|Re: [eigen] get scaling out of transform?|
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- To: eigen@xxxxxxxxxxxxxxxxxxx
- Subject: Re: [eigen] get scaling out of transform?
- From: Benoit Jacob <jacob.benoit.1@xxxxxxxxx>
- Date: Wed, 21 Jan 2009 21:22:44 -0500
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There's another way that you can go, suffering again performance-wise
from the current lack of fixed-size specializations: use the
Matrix3d m = t.linear();
Matrix3d scaling = s.operatorSqrt();
Or if you just want the scaling amplitude, not its geometric
orientation, you just need:
Vector3d scalingAmplitude = s.eigenvalues().cwise().sqrt();
that requires both the QR and the Array modules.
2009/1/21 Benoit Jacob <jacob.benoit.1@xxxxxxxxx>:
> This is currently unimplemented in Transform, and the computation
> involved is really nontrivial.
> It is definitely on my TODO for 2.1.
> Here's an explanation. When you decompose a matrix as a product
> rotation*scaling, that's called the "polar decomposition". Computing
> the polar decomposition amounts to computing the SVD decomposition. In
> Eigen 2.1 we'll have a very good SVD with fixed-size specializations
> and I'll use that to implement scaling() and reimplement rotation()
> correctly in Transform.
> Meanwhile, if you don't care about performance, you can already use
> the SVD in Eigen 2.0 but it's slow if only for lack of fixed-size
> If the SVD of M is M = U D V^ (where ^ denotes adjoint, or
> transpose for real matrices)
> then you have M = U D U^ U V^
> So your scaling is U D U^
> and your rotation is U V^
> 2009/1/21 Ben Axelrod <baxelrod@xxxxxxxxxxxx>:
>> How can I get the scaling info out of the Transform class?