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Issue No.02 - March/April (2000 vol.20)

pp: 76-84

DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/38.824547

ABSTRACT

Four types of ambient mathematical spaces underlie the algebra and geometry of computer graphics and geometric modeling: vector spaces, affine spaces, projective spaces, and Grassmann spaces. This article clarifies the relationships between these different ambient spaces and explains as well how they support the construction of the standard polynomial and rational freeform curves and surfaces of geometric design.

CITATION

Ron Goldman, "The Ambient Spaces of Computer Graphics and Geometric Modeling",

*IEEE Computer Graphics and Applications*, vol.20, no. 2, pp. 76-84, March/April 2000, doi:10.1109/38.824547REFERENCES

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The Application of Mechanics to Geometry, The University of Chicago Press, Chicago, 1974.- 3. A. Swimmer, "Ceva, Menelaus and the Associative Law," submitted for publication. Contact the author by e-mail at aswimmer@math.la.asu.edu or visithttp://math.la.asu.edu~aswimmer.
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Gesammelte Mathematische und Physikalische Werke [Collected Mathematical and Physical Work], B.G. Teubner, Leipzig, 1894-1911 (in German). - 9. D. Hestenes,
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Clifford Algebra to Geometric Calculus: A Unified Language for Mathematics and Physics, 3rd ed., Kluwer Academic, Dordrecht/Boston, 1992. |