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Geometric Algebra: A Computational Framework for Geometrical Applications (Part 1)
May/June 2002 (vol. 22 no. 3)
pp. 24-31
Leo Dorst, University of Amsterdam
Stephen Mann, University of Waterloo

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.

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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
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