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James R. Miller, "Vector Geometry for Computer Graphics," IEEE Computer Graphics and Applications, vol. 19, no. 3, pp. 6673, May/June, 1999.  
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@article{ 10.1109/38.761552, author = {James R. Miller}, title = {Vector Geometry for Computer Graphics}, journal ={IEEE Computer Graphics and Applications}, volume = {19}, number = {3}, issn = {02721716}, year = {1999}, pages = {6673}, doi = {http://doi.ieeecomputersociety.org/10.1109/38.761552}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
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TY  MGZN JO  IEEE Computer Graphics and Applications TI  Vector Geometry for Computer Graphics IS  3 SN  02721716 SP66 EP73 EPD  6673 A1  James R. Miller, PY  1999 VL  19 JA  IEEE Computer Graphics and Applications ER   
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 applicationspecific 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.
A companion article in the July/August 1999 IEEE CG&A builds on this background and shows several specific applications of these techniques.
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 CoordinateBased Approaches," DesignLab Tech. Report DL199703, Univ. of Kansas, Lawrence, Ks., Jan. 1997.
3. T. DeRose, "A CoordinateFree Approach to Geometric Programming," Contemporary Approaches to Geometry for Computer Graphics and ComputerAided 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. 291306.)
4. R.N. Goldman, "Illicit Expressions in Vector Algebra," ACM Trans. on Graphics, Vol. 4, No. 3, July 1985, pp. 223243.
5. R.N. Goldman, "Vector Geometry: A CoordinateFree Approach," Siggraph 85 Short Course No. 16, ACM Press, New York, July 1985.
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1. R.N. Goldman, "Illicit Expressions in Vector Algebra," ACM Trans. on Graphics, Vol. 4, No. 3, July 1985, pp. 223243.
2. R.N. Goldman, "Vector Geometry: A CoordinateFree Approach," Siggraph 85 Short Course No. 16, ACM Press, New York, July 1985.
3. T. DeRose, "A CoordinateFree Approach to Geometric Programming," Contemporary Approaches to Geometry for Computer Graphics and ComputerAided 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. 291306.)
4. J.D. Foley,A. van Dam,S.K. Feiner,, and J.F. Hughes,Computer Graphics: Principles and Practice,Menlo Park, Calif.: AddisonWesley, 1990.
5. E. Angel, Interactive Computer Graphics: A TopDown Approach With OpenGL, AddisonWesley, Reading, Mass., 1997.
6. D. Hearn and M.P. Baker, Computer Graphics, Prentice Hall, Englewood, N.J., 2d ed., 1994.
7. F.S. Hill Jr, Computer Graphics, Macmillan Publishing, New York, 1990.
8. G. Farin, NURB Curves and Surfaces: From Projective Geometry to Practical Use, A.K. Peters, Natick, Mass., 1995.
9. G.E. Farin, Curves and Surfaces for Computer Aided Geometric Design: A Practical Guide, fourth ed. Academic Press, 1996.