please excuse the double reply here: > I have noticed your previous postings about Geometric Algebra and do find it > interesting, but struggle with figuring out how to apply it.
This is really an under explored area. The best applications are those that deal with inherently spatial tasks. The best way to think of GA is as a high-level spatial language where you can reason in terms of points, lines, spheres, etc. and deduce computational systems from them. It's literally a spatial logic just like Boolean algebra is a binary logic. some apps: the robotics group I mentioned earlier embeds the spatial structure/constraints/controls of the robot by linking together GA objects in a chain that effectively forms a spatial reasoning system. Other apps I've seen model the optics of various camera (catadioptric, stereo, ...) to recover spatial information about a scene. Other people use it to analyze complex valued vector fields. GA is also extremely useful for calculation rigid body motions. Every Euclidean motion (rotation, dilation, transversion, reflection) can be expressed in the form x' = VxV^-1 where V describes the transformation. It doesn't get any simpler than that. wes _______________________________________________ fonc mailing list fonc@vpri.org http://vpri.org/mailman/listinfo/fonc
