Honing Geometric Algebra for Its Use in the Computer Sciences

Abstract

A computer scientist first pointed to geometric algebra as a promising way to ‘do geometry’ is likely to find a rather confusing collection of material, of which very little is experienced as immediately relevant to the kind of geometrical problems occurring in practice. Literature ranges from highly theoretical mathematics to highly theoretical physics, with relatively little in between apart from some papers on the projective geometry of vision [143]. After perusing some of these, the computer scientist may well wonder what all the fuss is about, and decide to stick with the old way of doing things, i.e. in every application a bit of linear algebra, a bit of differential geometry, a bit of vector calculus, each sensibly used, but ad hoc in their connections. That this approach tends to split up actual issues in the application into modules that match this traditional way of doing geometry (rather than into natural divisions matching the nature of the problem) is seen as ‘the way things are’.