The Community for Technology Leaders
RSS Icon
Subscribe
Issue No.02 - March/April (2000 vol.20)
pp: 76-84
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:10.1109/38.824547
REFERENCES
1. R.N. Goldman, "Illicit Expressions in Vector Algebra," ACM Trans. on Graphics, Vol. 4, No. 3, July 1985, pp. 223-243.
2. B.Y. Kogan, 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.
4. H.G. Grassmann, Gesammelte Mathematische und Physikalische Werke [Collected Mathematical and Physical Work], B.G. Teubner, Leipzig, 1894-1911 (in German).
5. J.D. Foley,A. van Dam,S.K. Feiner,, and J.F. Hughes,Computer Graphics: Principles and Practice,Menlo Park, Calif.: Addison-Wesley, 1990.
6. G.E. Farin, Curves and Surfaces for Computer Aided Geometric Design: A Practical Guide.New York: Academic Press, 1988.
7. G. Farin, NURB Curves and Surfaces: From Projective Geometry to Practical Use, A.K. Peters, Natick, Mass., 1995.
8. T. DeRose, "A Coordinate-Free Approach to Geometric Programming," Contemporary Approaches to Geometry for Computer Graphics and Computer-Aided Design, Siggraph 89 Short Course No. 14, ACM Press, New York, Aug. 1989. (A condensed version also appeared in Theory and Practice of Geometric Modeling, W. Strasser and H. Seidel, eds., Springer Verlag, Berlin, 1989, pp. 291-306.)
9. D. Hestenes, New Foundations for Classical Mechanics, 4th ed., Kluwer Academic, Dordrecht/Boston, 1992.
10. D. Hestenes and G. Sobczyk, Clifford Algebra to Geometric Calculus: A Unified Language for Mathematics and Physics, 3rd ed., Kluwer Academic, Dordrecht/Boston, 1992.
32 ms
(Ver 2.0)

Marketing Automation Platform Marketing Automation Tool