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Leo Dorst, Stephen Mann, "Geometric Algebra: A Computational Framework for Geometrical Applications (Part 1)," IEEE Computer Graphics and Applications, vol. 22, no. 3, pp. 2431, May/June, 2002.  
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@article{ 10.1109/MCG.2002.999785, author = {Leo Dorst and Stephen Mann}, title = {Geometric Algebra: A Computational Framework for Geometrical Applications (Part 1)}, journal ={IEEE Computer Graphics and Applications}, volume = {22}, number = {3}, issn = {02721716}, year = {2002}, pages = {2431}, doi = {http://doi.ieeecomputersociety.org/10.1109/MCG.2002.999785}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
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TY  MGZN JO  IEEE Computer Graphics and Applications TI  Geometric Algebra: A Computational Framework for Geometrical Applications (Part 1) IS  3 SN  02721716 SP24 EP31 EPD  2431 A1  Leo Dorst, A1  Stephen Mann, PY  2002 KW  geometric algebra KW  Clifford algebra KW  subspaces KW  blades KW  geometric product KW  inner product KW  outer product. VL  22 JA  IEEE Computer Graphics and Applications ER   
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 coordinatefree 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 algebrathe geometric product, the inner product, and the outer product. These products are illustrated by using them to solve simple geometric problems.
1. R. Goldman,"Illicit Expressions in Vector Algebra," ACM Trans. Graphics, vol. 4, no. 3, July 1985, pp. 223243.
2. S. Mann, N. Litke,, and T. DeRose,A Coordinate Free Geometry ADT, research report CS9715, Computer Science Dept., Univ. of Waterloo, 1997, ftp://csarchive.uwaterloo.ca/csarchive CS9715/.
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. 119241.
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. 127152.
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.