Re: [eigen] Potential unsupported module: Lie Groups

[Christoph Hertzberg <chtz@xxxxxxxxxxxxxxxxxxxxxxxx>]

Hi,

I wrote a library MTK with similar goals some time ago. It is published 
here:
http://openslam.org/MTK

MTK is Eigen-based as well and supports manifold primitives such as R^n, 
SO(2), SO(3) but also S^2 which is not a Lie-Group (all primitives are 
templated for arbitrary scalar types).
If you are just interested in these, see here:
https://openslam.informatik.uni-freiburg.de/data/svn/MTK/trunk/cpp/mtk/types/

A strength of MTK is its ability to construct compound manifolds, e.g. 
SO(3) x R^3 x R^3 is again a manifold, etc.
From an algorithm's point of view, compound manifolds act like any 
other manifold, but from the user's point they are easily accessible by 
their sub-components.
The construction depends strongly on Boost-preprocessor macros, so I 
guess it would not be suited for integration into Eigen.

We backed up the theory behind our method in a paper:
"Integrating generic sensor fusion algorithms with sound state 
representations through encapsulation of manifolds"
The paper also emphasizes the advantage of using manifold-based 
representations over singular representations (such as Euler angles for 
SO(3)).



On 06.05.2012 17:24, Hauke Strasdat wrote:
> Also, a number of unit test are included (which verify that
> singularities in exp and log are sidestepped properly).

I'm afraid you missed a singularity for log of the negative unit 
quaternion (w=-1, v=0). Also, by using acos instead of atan, your 
results will degenerate if your quaternion gets denormalized over time.

> I am aware that this library has quite an overlap with the Geometry
> module. Still, I think it might be quite useful to
> some users since it offers additional functionality and a unified API.
> If there is some interest, I could add it as an unsupported Eigen
> module. In the long run,
> one could try to figure out, how to merge it or integrate it further
> with the Geometry module.

I think a first step could be to integrate quaternion exp and log into 
Eigen, maybe also add scaled-axis representation (i.e. the result of 
SO3::log) as another representation for rotations.


Christoph




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Dipl.-Inf. Christoph Hertzberg
Cartesium 0.049
Universität Bremen
Enrique-Schmidt-Straße 5
28359 Bremen

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