Computing the Discrepancy with Applications to Supersampling Patterns

ACM Transactions on Graphics

Volumn 15, Issue 4, 1996, Pages 354-376

  Dobkin, David P ^a   Eppstein, David ^b   Mitchell, Don P ^a  

^a PRINCETON UNIVERSITY   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Algorithms; Discrepancy; Experimentation; F.2.2 Analysis of Algorithms and Problem Complexity : Nonnumerical Algorithms and Problems geometrical problems and computations; I.3.3 Computer Graphics . Picture Image Generation antialiasing; Ray tracing

Indexed keywords

IMAGE GENERATION; ISOTROPIC DISCREPANCY; SUPERSAMPLING PATTERNS;

ALGORITHMS; ANTI-ALIASING; ASYMPTOTIC STABILITY; COMPUTATIONAL GEOMETRY; COMPUTATIONAL METHODS; ESTIMATION; IMAGE PROCESSING; NUMERICAL ANALYSIS; PATTERN RECOGNITION;

COMPUTER GRAPHICS;

EID: 0030264248     PISSN: 07300301     EISSN: None     Source Type: Journal    
DOI: 10.1145/234535.234536     Document Type: Article

References (28)

1. ALEXANDER, R. 1990. Geometric methods in the study of irregularities of distribution. Combinatorica 10, 115-136.
2. BECK, J. AND CHEN, W. W. L. 1987. Irregularities of Distribution. Cambridge University Press, Cambridge, MA.
3. BECK, J. Personal communication, 1993.
4. CHAZELLE, B. 1993. Geometric discrepancy revisited. Proceedings of 34th IEEE Symposium on the Foundations of Computer Science. IEEE, New York, pp. 392-399.
5. CHAZELLE, B., MATOUŜEK, J., AND SHARIR, M. 1995. An elementary approach to lower bounds in geometric discrepancy. Discrete Comput. Geom. 13, 3-4, 363-381.
6. COOK, R. L., PORTER, T., AND CARPENTER, L. 1984. Distributed ray tracing. Comput. Graph. 18, 3, 137-145.
7. COOK, R. L. 1986. Stochastic sampling in computer graphics. ACM Trans. Graph. 5, 1, 51-72.
8. DE BERG, M. 1996. Computing half-plane and strip discrepancy of planar point sets. Comput. Geom. Theor. Appl. 6, 2, 69-83.
9. DIPPE, M. A. Z. AND WOLD, E. H. 1985. Antialiasing through stochastic sampling. Comput. Graph. 19, 3, 69-78.
10. DOBKIN, D. P. AND EPPSTEIN, D. 1993. Computing the discrepancy. In Proceedings of the 9th ACM Symposium on Computational Geometry, 47-52.
11. DOBKIN, D. P., GUNOPULOS, D., AND MAASS, W. 1994. Computing the rectangle discrepancy. Manuscript.
12. DOBKIN, D. P. AND MITCHELL, D. P. 1993. Random-edge discrepancy of supersampling patterns. In Graphics Interface, York, Ont., Canadian Information Processing Society, 62-69.
13. EDELSBRUNNER, H. AND GUIBAS, L. 1989. Topologically sweeping an arrangement. J. Comput. Syst. Sci. 38, 165-194.
14. HALTON, J. H. 1970. A retrospective and prospective survey of the Monte Carlo method. SIAM Rev. 12, 1-63.
15. HERSHBERGER, J. AND SURI, S. 1991. Offline maintenance of planar configurations. In Proceedings of the 2nd ACM/SIAM Symposium on Discrete Algorithms, 32-41.
16. KAJIYA, J. T. 1986. The rendering equation. Comput. Graph. 20, 143-150.
17. LEE, M., REDNER, R. A., AND USELTON, S. P. 1985. Statistically optimized sampling for distributed ray tracing. Comput. Graph. 19, 3, 61-67.
18. MITCHELL, D. P. 1987. Generating antialiased images at low sampling densities. Comput. Graph. 21, 4, 65-72.
19. MITCHELL, D. P. 1991. Spectrally optimal sampling for distribution ray tracing. Comput. Graph. 25, 4, 157-164.
20. NEIDERREITER, H. 1978. Quasi-Monte Carlo methods and pseudo-random numbers. Bull. Am. Math. Soc. 84, 957-1041.
21. NEIDERREITER, H. 1992. Quasirandom sampling computer graphics. In Proceedings of the 3rd International Seminar on Digital Image Processing in Medicine (Riga, Latvia), 29-33.
22. OVERMARS, M. AND VAN LEEUWEN, J. 1981. Maintenance of configurations in the plane. J. Comput. Syst. Sci. 23, 166-204.
23. OVERMARS, M. AND YAP, C. K. 1991. New upper bounds in Klee's measure problem. SIAM J. Comput. 20, 1034-1045.
24. PAINTER, J. AND SLOAN, K. 1989. Antialiased ray tracing by adaptive progressive refinement. Comput. Graph. 23, 3, 281-288.
25. PURGATHOFER, W. 1986. A statistical model for adaptive stochastic sampling. In Proceedings of Eurographics, 145-152.
26. SHIRLEY, P. 1991. Discrepancy as a quality measure for sample distributions. In Proceedings of Eurographics, 183-193.
27. WARNOCK, T. T. 1971. Computational investigations of low-discrepancy point sets. In Applications of Number Theory to Numerical Analysis, S. K. Zaremba, Ed., Academic Press, 319-344.
28. WHITTED, T. 1980. An improved illumination model for shaded display. Commun. ACM 23, 343-349.