Re: [ublas] 3D translation, rotation in boost?

From: Paul C. Leopardi (paul.leopardi_at_[hidden])
Date: 2007-12-13 17:15:02

On Thu, 13 Dec 2007, Wilfried Holzke wrote:
> Hi,
>
> >> I want to use uBlas for matrix operations. Now I searching for
> >> procedures/methods to initialize matrices for translation or rotation in
> >> 3d space.
> >>
> >> Are there extension in boost for that purpose?
> >
> > not yet, but MTL4 should have this next year. I'm waiting for it.
> > Currently I use some small and unsupported library for
> > 3D operations - wildmagic.
> >
> > http://www.osl.iu.edu/research/mtl/mtl4/download.php3
>
> Is mtl4 an extension to ublas (which makes matrices and operations
> available) or something completely different?

It's something completely different. 

What do you want to do with matrices for rotation and translation? Do you want 
to use 4x4 matrices, quaternions? Did you know that quaternions are already 
included in Boost? 
http://www.boost.org/doc/html/boost_math/quaternions.html

There has been some discussion before about getting Boost Quaternion to work 
with Boost Ublas:
http://lists.boost.org/Archives/boost/2007/03/117493.php

If you want nD translation, rotation, conformal geometry, etc, you could take 
a look at rotors in particular and geometric algebra in general. 
http://www.geometricalgebra.net/quaternions.html
See Geometric Algebra For Computer Science
http://www.geometricalgebra.net/

Gaigen ( http://www.science.uva.nl/ga/gaigen/ ) yields a fast implementation 
of conformal geometric algebra for Daniel Fontijne's Raytracer example.
http://www.geometricalgebra.net/raytracer.html
There is possibly a faster one using O'Caml: 
http://wscg.zcu.cz/wscg2005/Papers_2005/Poster/D59-full.pdf

Lastly, there is my own humble contribution, GluCat: http://glucat.sf.net
I've written a GluCat implementation of an earlier version of Fontijne's 
Raytracer, ( http://staff.science.uva.nl/~fontijne/raytracer/ ) but have not 
published it. I therefore know that GluCat is up to the task, but not as fast 
as Gaigen. 

See also http://doi.ieeecomputersociety.org/10.1109/MCG.2003.1185582
Daniel Fontijne, Leo Dorst, "Modeling 3D Euclidean Geometry," IEEE Computer 
Graphics and Applications, vol. 23,  no. 2,  pp. 68-78,  Mar/Apr,  2003.

Best, Paul