This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
Applications of Vector Geometry for Robustness and Speed
July/August 1999 (vol. 19 no. 4)
pp. 68-73
The implementation and use of computer graphics and modeling systems rely upon mathematical operations on points and vectors. An earlier companion article described the basic language and tools of vector geometric analysis (May/June 1999 CG&A). This article shows how to use those concepts to derive and implement common graphics and modeling operations that maximize speed and numerical reliability. The computer code is also easy to develop, in large part because the only special cases that arise are those intrinsic to the problem, not to the choice of coordinate system.

1. J.R. Miller, "Vector Geometry for Computer Graphics," IEEE CG&A, Vol. 19, No. 3, May/June 1999, pp. 66-73.
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.L.J. Howard et al., Practical Introduction in PHIGS and PHIGS Plus, Addision-Wesley, Reading, Mass., 1991.
4. M. Woo, J. Neider, and T. Davis, OpenGL Programming Guide: The Official Guide to Learning OpenGL, 2nd ed., Addison-Wesley Developers Press, 1997.
5. R.N. Goldman, "Matrices and Transformations," Graphics Gems, A. Glassner, ed., Academic Press, 1990, pp. 472-475.
6. J.D. Foley,A. van Dam,S.K. Feiner,, and J.F. Hughes,Computer Graphics: Principles and Practice,Menlo Park, Calif.: Addison-Wesley, 1990.
7. A.S. Glassner, "Useful 3D Geometry," in Graphics Gems, A.S. Glassner, ed., Academic Press, San Diego, 1990, pp. 297-300.
8. P. Georgiades, "Signed Distance from Point to Plane," in Graphics Gems III, D. Kirk, ed., Academic Press, San Diego, 1992, pp. 223-224.

Citation:
James R. Miller, "Applications of Vector Geometry for Robustness and Speed," IEEE Computer Graphics and Applications, vol. 19, no. 4, pp. 68-73, July-Aug. 1999, doi:10.1109/38.773966
Usage of this product signifies your acceptance of the Terms of Use.