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Issue No.03 - May/June (1999 vol.19)
pp: 66-73
<p>The implementation and use of computer graphics and modeling systems rely upon mathematical operations on points and vectors. Many of these operations are a part of the internal graphics system; others are application-specific and required by users of such systems to derive geometric entities for the application. This tutorial reviews the basic ideas surrounding points and vectors in affine and projective spaces. I advocate using vector geometric analysis to simplify required derivations and implementations.</p> <p>A companion article in the July/August 1999 IEEE CG&A builds on this background and shows several specific applications of these techniques.</p>
James R. Miller, "Vector Geometry for Computer Graphics", IEEE Computer Graphics and Applications, vol.19, no. 3, pp. 66-73, May/June 1999, doi:10.1109/38.761552
1. J.R. Miller Applications of "Vector Geometry for Robustness and Speed," in preparation for IEEE CG&A, Vol. 19, No. 4, July/Aug. 1999.
2. J.R. Miller, "The Mathematics of Graphical Transformations: Vector Geometric and Coordinate-Based Approaches," DesignLab Tech. Report DL-1997-03, Univ. of Kansas, Lawrence, Ks., Jan. 1997.
3. 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.)
4. R.N. Goldman, "Illicit Expressions in Vector Algebra," ACM Trans. on Graphics, Vol. 4, No. 3, July 1985, pp. 223-243.
5. R.N. Goldman, "Vector Geometry: A Coordinate-Free Approach," Siggraph 85 Short Course No. 16, ACM Press, New York, July 1985.
6. E. Abbott, Flatland: A Romance of Many Dimensions, Princeton University Press, Cambridge, Mass., 1991. (Originally published circa 1880.)
7. D. Burger, Sphereland: A Fantasy about Curved Spaces and an Expanding Universe, HarperPerennial, Boulder, Colo., 1965.
8. A.K. Dewdney, The Planiverse: Computer Contact with a Two-Dimensional World, Poseidon Books/Simon&Schuster, New York, 1984.
9. G.E. Farin, Curves and Surfaces for Computer Aided Geometric Design: A Practical Guide, fourth ed. Academic Press, 1996.
10. J.D. Foley,A. van Dam,S.K. Feiner,, and J.F. Hughes,Computer Graphics: Principles and Practice,Menlo Park, Calif.: Addison-Wesley, 1990.
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