2001 (English)In: Geometric Computing using Clifford Algebra, Springer, 2001, 5Chapter in book (Refereed)
The aim of this chapter is to contribute to David Hestenes’ vision - formulated on his web-site 1 - of desiging a universal geometric calculus based on geometric algebra. To this purpose we introduce a framework for geometric computations which we call geo-MAP (geo-Metric-Affine-Projective) unification. It makes use of geometric algebra to embed the representation of euclidean, affine and projective geometry in a way that enables coherent shifts between these different perspectives. To illustrate the versatility and usefulness of this framework, it is applied to a classical problem of plane geometrical optics, namely how to compute the envelope of the rays emanating from a point source of light after they have been reflected in a smoothly curved mirror. Moreover, in the appendix, we present a simple proof of the fact that the ‘natural basis candidate’ of a geometric algebra - the set of finite subsets of its formal variables - does in fact form a vector space basis for the algebra. This theorem opens the possibility of a deductive presentation of geometric algebra to a wider audience.
Place, publisher, year, edition, pages
Springer, 2001, 5.
Computer and Information Science
IdentifiersURN: urn:nbn:se:kth:diva-82674OAI: oai:DiVA.org:kth-82674DiVA: diva2:498491
NR 201408052012-02-122012-02-12Bibliographically approved