David P. Dobkin
Abstract
Patterns used for supersampling in graphics have been analyzed from statistical and signal-processing viewpoints. We present an analysis based on a type of isotropic discrepancy—how good patterns are at estimating the area in a region of defined type. We present algorithms for computing discrepancy relative to regions that are defined by rectangles, halfplanes, and higher-dimensional figures. Experimental evidence shows that popular supersampling patterns have discrepancies with better asymptotic behavior than random sampling, which is not inconsistent with theoretical bounds on discrepancy.
- ALEXANDER, R. 1990. Geometric methods in the study of irregularities of distribution. Combinatorica 10, 115-136.Google Scholar
Cross Ref
- BECK, J. AND CHEN, W. W. L. 1987. Irregularities of Distribution. Cambridge University Press, Cambridge, MA.Google Scholar
- BECK, g. Personal communication, 1993.Google Scholar
- CHAZELLE, B. 1993. Geometric discrepancy revisited. Proceedings of 34th IEEE Symposium on the Foundations of Computer Science. IEEE, New York, pp. 392-399.Google ScholarDigital Library
- CHAZELLE, B., MATOU~SEK, J., AND SHARIR, M. 1995. An elementary approach to lower bounds in geometric discrepancy. Discrete Comput. Geom. 13, 3-4, 363-381.Google ScholarDigital Library
- COOK, R. L., PORTER, T., AND CARPENTER, L. 1984. Distributed ray tracing. Comput. Graph. 18, 3, 137-145. Google ScholarDigital Library
- COOK, R. L. 1986. Stochastic sampling in computer graphics. ACM Trans. Graph. 5, 1, 51-72. Google ScholarDigital Library
- DE BERG, M. 1996. Computing half-plane and strip discrepancy of planar point sets. Comput. Geom. Theor. Appl. 6, 2, 69-83. Google ScholarDigital Library
- DIPPE, M. A. Z. AND WOLD, E.H. 1985. Antialiasing through stochastic sampling. Comput. Graph. 19, 3, 69-78. Google ScholarDigital Library
- DOBKIN, D. P. AND EPPSTEIN, D. 1993. Computing the discrepancy. In Proceedings of the 9th ACM Symposium on Computational Geometry, 47-52. Google ScholarDigital Library
- DOBKIN, D. P., GUNOPULOS, D., AND MAASS, W. 1994. Computing the rectangle discrepancy. Manuscript.Google Scholar
- 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.Google Scholar
- EDELSBRUNNER, H. AND GUIBAS, L. 1989. Topologically sweeping an arrangement. J. Comput. Syst. Sci. 38, 165-194. Google ScholarDigital Library
- HALTON, g. H. 1970. A retrospective and prospective survey of the Monte Carlo method. SIAM Rev. 12, 1-63.Google ScholarDigital Library
- HERSHBERGER, J. AND SURI, S. 1991. Offline maintenance of planar configurations. In Proceedings of the 2nd ACM/SIAM Symposium on Discrete Algorithms, 32-41. Google ScholarDigital Library
- KAJIYA, J.T. 1986. The rendering equation. Comput. Graph. 20, 143-150. Google ScholarDigital Library
- LEE, M., REDNER, R. A., AND USELTON, S. P. 1985. Statistically optimized sampling for distributed ray tracing. Comput. Graph. 19, 3, 61-67. Google ScholarDigital Library
- MITCHELL, D.P. 1987. Generating antialiased images at low sampling densities. Comput. Graph. 21, 4, 65-72. Google ScholarDigital Library
- MITCHELL, D. P. 1991. Spectrally optimal sampling for distribution ray tracing. Comput. Graph. 25, 4, 157-164. Google ScholarDigital Library
- NEIDERREITER, H. 1978. Quasi-Monte Carlo methods and pseudo-random numbers. Bull. Am. Math. Soc. 84, 957-1041.Google ScholarCross Ref
- NEIDERREITER, H. 1992. Quasirandom sampling computer graphics. In Proceedings of the 3rd International Seminar on Digital Image Processing in Medicine (Riga, Latvia), 29-33.Google Scholar
- OVERMARS, M. AND VAN LEEUWEN, J. 1981. Maintenance of configurations in the plane. J. Comput. Syst. Sci. 23, 166-204.Google ScholarCross Ref
- OVERMARS, M. AND YAP, C.K. 1991. New upper bounds in Klee's measure problem. SIAM J. Comput. 20, 1034-1045. Google ScholarDigital Library
- PAINTER, J. AND SLOAN, K. 1989. Antialiased ray tracing by adaptive progressive refinement. Comput. Graph. 23, 3, 281-288. Google ScholarDigital Library
- PURGATHOFER, W. 1986. A statistical model for adaptive stochastic sampling. In Proceedings of Eurographics, 145-152.Google Scholar
- SHIRLEY, P. 1991. Discrepancy as a quality measure for sample distributions. In Proceedings of Eurographics, 183-193.Google Scholar
- WARNOCK, T.T. 1971. Computational investigations of low-discrepancy point sets. InApplications of Number Theory to Numerical Analysis, S. K. Zaremba, Ed., Academic Press, 319-344.Google Scholar
- WHITTED, T. 1980. An improved illumination model for shaded display. Commun. ACM 23, 343-349. Google ScholarDigital Library
Index Terms
- Computing the discrepancy with applications to supersampling patterns
Recommendations
Amortized supersampling
We present a real-time rendering scheme that reuses shading samples from earlier time frames to achieve practical antialiasing of procedural shaders. Using a reprojection strategy, we maintain several sets of shading estimates at subpixel precision, and ...
Display supersampling
Supersampling is widely used by graphics hardware to render anti-aliased images. In conventional supersampling, multiple scene samples are computationally combined to produce a single screen pixel. We consider a novel imaging paradigm that we call ...
High-quality shear-warp volume rendering using efficient supersampling and pre-integration technique
ICAT'06: Proceedings of the 16th international conference on Advances in Artificial Reality and Tele-ExistenceAs shear-warp volume rendering is the fastest rendering method, image quality is not good as that of other high-quality rendering methods. In this paper, we propose two methods to improve the image quality of shear-warp volume rendering. First, the ...
Comments