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Issue No.04 - July/August (2002 vol.22)
pp: 58-67
Stephen Mann , University of Waterloo
Leo Dorst , University of Amsterdam
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 coordinate-free specification of computational constructions. It contains primitives of any dimensionality (rather than just vectors). This second paper on the subject uses the basic products to represent rotations (naturally incorporating quaternions), intersections, and differentiation. It shows how using well-chosen geometric algebra models, we can eliminate special cases in incidence relationships, yet still have the efficiency of the Plucker coordinate intersection computations.</p>
INDEX TERMS
geometric algebra, Clifford algebra, rotation reprensentation, quaternions, dualization, meet, join, Plucker coordinates, homogeneous coordinates, geometric differentiation, computational geometry
CITATION
Stephen Mann, Leo Dorst, "Geometric Algebra: A Computational Framework for Geometrical Applications (Part 2)", IEEE Computer Graphics and Applications, vol.22, no. 4, pp. 58-67, July/August 2002, doi:10.1109/MCG.2002.1016699
REFERENCES
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2. C. Doran and A. Lasenby, Physical Applications of Geometric Algebra, 2001, http://www.mrao.cam.ac.uk/~cliffordptIIIcourse /.
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7. D. Hestenes, "Old Wine in New Bottles," Geometric Algebra: A Geometric Approach to Computer Vision, Quantum and Neural Computing, Robotics, and Engineering, E. Bayro-Corrochano and G. Sobczyk, eds., Birkhäuser, Boston, 2001, pp. 498-520.
8. D. Fontijne, GAIGEN: A Geometric Algebra Implementation Generator, http://carol.wins.uva.nl/~fontijnegaigen /.
9. R.N. Goldman, "The Ambient Spaces of Computer Graphics and Geometric Modeling," IEEE Computer Graphics and Applications, vol. 20, no. 2, Mar./Apr. 2000, pp. 76-84.
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