This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
Adaptive Polygonalization of Implicitly Defined Surfaces
November/December 1990 (vol. 10 no. 6)
pp. 33-42

A method for finding an adaptive polygonal approximation of an implicitly defined surface is presented. For algebraic surfaces, the method yields an approximation guaranteed accurate to within some user-specified tolerance of the actual surface. This polygonalization can then be rendered using standard shaded polygon drawing techniques. A method for eliminating or improving the aspect ratios of the 'skinny' polygons that often arise in traditional polygonalization methods is also presented. This method has proved particularly useful in the creation of polygonalization for finite-element analysis.

1. J.F. Blinn, "A Generalization of Algebraic Surface Drawing,"ACM Trans. Graphics, Vol. 1, No. 3, July 1982, pp. 235-256.
2. G. Wyvill, C. McPheeters, and B. Wyvill, "Data Structure for Soft Objects,"Visual Computer, Vol. 2, No. 4, Aug. 1986, pp. 227-234.
3. J. Bloomenthal, "Polygonization of Implicit Surfaces,"Computer-Aided Geometric Design, Vol. 5, 1988, pp. 341-355.
4. C. Hoffmann and J. Hopcroft, "Automatic Surface Generation in Computer-Aided Design,"Visual Computer, Vol. 1, No. 2, Oct. 1985, pp. 92-100.
5. G. Farin,Curves and Surfaces for Computer Aided Geometric Design, Academic Press, Boston, 1988.
6. R. Farouki and J. Hinds, "A Hierarchy of Geometric Forms,"CG&A, Volume 5, No. 5, May 1985, pp. 51-78.
7. C.L. Bajaj et al., "Tracing Surface Intersections,"Computer Aided Geometric Design, Vol. 5, No, 4, Nov. 1988, pp. 285-307.
8. R. Farouki,Concise Piecewise-Linear Approximation of Algebraic Curves, Tech. Report RC 13724, IBM, Yorktown Heights, N.Y., 1988.
9. W.E. Lorensen and H.E. Cline, "Marching Cubes: A High-Resolution 3D Surface Construction Algorithm,"Computer Graphics(Proc. Siggraph 87), ACM Press, New York, Vol. 21, No. 4, 1987, pp. 163-169.
10. T. Sederberg, "Piecewise Algebraic Surface Patches,"Computer-Aided Geometric Design, Vol. 2, No. 1, 1985, pp. 53-59.
11. C. Petersen, B. Piper, and A. Worsey, "Adaptive Contouring of a Trivariate Interpolant,"Geometric Modeling: Algorithms and New Trends, G. Farin, ed., SIAM, Philadelphia, 1987, pp. 385- 395.
12. H.S.M. Coxeter,Regular Polytopes, MacMillan, New York, 1963.
13. D. Kalra and A. Barr, "Guaranteed Ray Intersection with Implicit Surfaces,"Computer Graphics(Proc. SIGGRAPH), Vol. 22, No. 4, July 1989, pp. 297-306.
14. M.A. Yerry, and M.S. Shephard, "Automatic Three-Dimensional Mesh Generation by the Modified Octree Technique,"Int'l J. Numerical Methods in Eng., Vol. 20, No. 11, Nov. 1984, pp. 1965-1990.
15. O.C. Zienkiewicz,The Finite Element Method, McGraw-Hill, New York, 1978.
16. D. Crawford, et al., "Parallel Adaptive Tessellation of Implicitly Defined Surfaces," Tech. Report TR-90-102, Rice University, Houston, Tex, 1990.

Citation:
Mark Hall, Joe Warren, "Adaptive Polygonalization of Implicitly Defined Surfaces," IEEE Computer Graphics and Applications, vol. 10, no. 6, pp. 33-42, Nov.-Dec. 1990, doi:10.1109/38.62694
Usage of this product signifies your acceptance of the Terms of Use.