“Statistically optimized sampling for distributed ray tracing” by Uselton, Redner and Lee

  • ©Samuel P. Uselton, Richard A. Redner, and Mark E. Lee




    Statistically optimized sampling for distributed ray tracing



    Cook, Porter, and Carpenter coined the phrase “distributed ray tracing” to describe a technique for using each ray of a super-sampled ray tracing procedure as a sample in several dimensions to achieve effects such as penumbras and motion blur in addition to spatial anti-aliasing. The shade to be displayed at a pixel is a weighted integral of the image function. The purpose of using many rays per pixel is to estimate the value of this integral. In this work, a relationship between the number of sample rays and the quality of the estimate of this integral is derived. Furthermore, the number of rays required does not depend on the dimensionality of the space being sampled, but only on the variance of the multi-dimensional image function. The algorithm has been optimized through the use of statistical testing and stratified sampling.


    1. Amanatides, J. Ray tracing with cones. Computer Graphics 18,3 (July 1984),pp. 129-135.
    2. Catmull, E. Computer display of curved surfaces. Proceedings IEEE Conference on Computer Graphics, Pattern Recognition and Data Structures (Hay 1975).
    3. Catmull, E. A hidden-surface algorithm with antl-aliasing. Computer Graphics 12,3 (Aug. 1978), pp. 1-5.
    4. Cook, R. L., Porter, T. and Carpenter, L. Distributed ray tracing. Computer Graphics 18,3 (July 1984), pp. 137-145.
    5. Crow, F.C.The aliasing problem in computer-generated shaded images. Comm. ACM 20,11 {Nov. i977)~ pp. 799-805.
    6. Crow, F. C. The use of grayscale for improved raster display of vectors and characters. Computer Graphics 12,3 (Aug. 1978), pp. i-5.
    7. Crow, F. C. A comparison of anti-aliasing techniques. IEEE Computer Graphics and Applications i,I (Jan. 1981), pp. 40-49.
    8. Feller, W.An Introduction to Probability Theory and Its Applications. John Wiley and Sons, 1971.
    9. Flume, E., Fournler, A. and Rudolph, L. A parallel scan conversion algorithm with antialiasing for a general-purpose ultracomputer. Computer Graphics 17,3 (July 1983), pp. 141-150.
    10. Fuchs, H. and Barros~ J. Generating smooth 2-d monocolor line drawings on video displays. Computer Graphics 13,2 (July 1979), pp. 260-269.
    11. Heckbert, P. S. and Hanrahan, P. Beam tracing polygonal objects. Computer Graphics 18,3 (July 1984), pp. 119-127.
    12. Kish, L. Survey Sampling. John Wiley and Sons, 1965.
    13. Lee, M. g. and Uselton, S. P. A shading model for rendering objects with body color. Technical Report F85-C-5, Amoco Production Company – Tulsa Research Center, Tulsa OK (1985).
    14. Turkowski, K. Anti-aliasing through the use of coordinate transformations. ACM Transactions on Graphics 1,3 (July 1982), pp. 215-234.
    15. Whitted, T.An improved illumination model for shaded display. Comm. ACM 23,6 (June 1980), pp. 343-349.
    16. Whitted, T. Anti-aliased line drawing using brush extrusion. Computer Graphics 17,3 (july 1983), pp. 151-156.

ACM Digital Library Publication: