DocumentCode :
777376
Title :
Geometric algebra: a computational framework for geometrical applications. 2
Author :
Mann, Stephen ; Dorst, Leo
Author_Institution :
Sch. of Comput. Sci., Waterloo Univ., Ont., Canada
Volume :
22
Issue :
4
fYear :
2002
Firstpage :
58
Lastpage :
67
Abstract :
Every vector space with an inner product has a geometric algebra, whether or not you choose to use it. This article shows how to call on this structure to define common geometrical constructs, ensuring a consistent computational framework. The goal is to show you that this can be done and that it is compact, directly computational, and transcends the dimensionality of subspaces. We do not use geometric algebra to develop new algorithms for graphics, but hope to demonstrate that one can automatically take care of some of the lower level algorithmic aspects, without tricks, exceptions, or hidden degenerate cases by using geometric algebra as a language.
Keywords :
algebra; computational geometry; algorithmic aspects; differentiation; geometric algebra; intersections; rotations; Algebra; Equations; Goniometers; Radiofrequency interference; Switches;
fLanguage :
English
Journal_Title :
Computer Graphics and Applications, IEEE
Publisher :
ieee
ISSN :
0272-1716
Type :
jour
DOI :
10.1109/MCG.2002.1016699
Filename :
1016699
Link To Document :
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