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Issue No.03 - May/June (2002 vol.22)
pp: 24-31
Leo Dorst , University of Amsterdam
Stephen Mann , University of Waterloo
ABSTRACT
<p>Geometric algebra is a consistent computational framework in which to define geometric primitives and their relationships. This algebraic approach contains all geometric operators and permits specification of constructions in a coordinate-free manner. Thus, the ideas of geometric algebra are important for developers of CAD systems. This article gives an introduction to the elements of geometric algebra, which contains primitives of any dimensionality (rather than just vectors) and an introduction to three of the products of geometric algebra-the geometric product, the inner product, and the outer product. These products are illustrated by using them to solve simple geometric problems.</p>
INDEX TERMS
geometric algebra, Clifford algebra, subspaces, blades, geometric product, inner product, outer product.
CITATION
Leo Dorst, Stephen Mann, "Geometric Algebra: A Computational Framework for Geometrical Applications (Part 1)", IEEE Computer Graphics and Applications, vol.22, no. 3, pp. 24-31, May/June 2002, doi:10.1109/MCG.2002.999785
REFERENCES
1. R. Goldman,"Illicit Expressions in Vector Algebra," ACM Trans. Graphics, vol. 4, no. 3, July 1985, pp. 223-243.
2. S. Mann, N. Litke,, and T. DeRose,A Coordinate Free Geometry ADT, research report CS-97-15, Computer Science Dept., Univ. of Waterloo, 1997, ftp://cs-archive.uwaterloo.ca/cs-archive CS-97-15/.
3. P. Lounesto,"Marcel Riesz's Work on Clifford Algebras," Clifford Numbers and Spinors, E.F. Bolinder and P. Lounesto, eds., Kluwer Academic Publishers, New York, 1993, pp. 119-241.
4. L. Dorst,"Honing Geometric Algebra for its Use in the Computer Sciences," Geometric Computing with Clifford Algebra, G. Sommer, ed., Springer, New York, 2001, pp. 127-152.
5. T.A. Bouma, L. Dorst,, and H. Pijls,"Geometric Algebra for Subspace Operations," to be published inApplicandae Mathematicae,2002,http://xxx.lanl.gov/abs/math.LA0104159.
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