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| 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. | |||
| BibTex | x | ||
| @article{ 10.1109/MCG.2002.1016699, author = {Stephen Mann and Leo Dorst}, title = {Geometric Algebra: A Computational Framework for Geometrical Applications (Part 2)}, journal ={IEEE Computer Graphics and Applications}, volume = {22}, number = {4}, issn = {0272-1716}, year = {2002}, pages = {58-67}, doi = {http://doi.ieeecomputersociety.org/10.1109/MCG.2002.1016699}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, } | |||
| RefWorks Procite/RefMan/Endnote | x | ||
| TY - MGZN JO - IEEE Computer Graphics and Applications TI - Geometric Algebra: A Computational Framework for Geometrical Applications (Part 2) IS - 4 SN - 0272-1716 SP58 EP67 EPD - 58-67 A1 - Stephen Mann, A1 - Leo Dorst, PY - 2002 KW - geometric algebra KW - Clifford algebra KW - rotation reprensentation KW - quaternions KW - dualization KW - meet KW - join KW - Plucker coordinates KW - homogeneous coordinates KW - geometric differentiation KW - computational geometry 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 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.
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