“A hierarchical illumination algorithm for surfaces with glossy reflection” by Aupperle and Hanrahan

  • ©Larry Aupperle and Patrick (Pat) Hanrahan




    A hierarchical illumination algorithm for surfaces with glossy reflection



    We develop a radiance formulation for discrete three point transport,
    and a new measure and description of reflectance:area reflectance.
    This formulation and associated reflectance allow an estimate of error in the computation of radiance across triples of surface elements,
    and lead directly to a hierarchical refinement algorithm for global
    We have implemented and analyzed this algorithm over surfaces
    exhibiting glossy specular and diffuse reflection. Theoretical growth
    in light transport computation is shown to beO(n+k
    ) for sufficient
    refinement, where n is the number of elements at the finest level
    of subdivision over an environment consisting ofk input polygonal
    patches — this growth is exhibited in experimental trials. Naive
    application of three point transport would require computation over
    ) element-triple interactions


    1. Amanatides, J. (1992) Algorithms for the detection and elimination of specular aliasing. Proc. Graphics Intelface ’92, 86-93.
    2. Aupperle, L. (1993) Hierarchical algorithms for illumination. Doctoral Dissertation, Princeton University.
    3. Blinn, J.F. (1977) Models of light refection for computer synthesized pictures. Computer Graphics 11 (2), 192-198.
    4. Chen, S.E., Rushmeier, H.E., Miller, G., Turner, D. (1991) A progressive multi-pass method for global illumination. Computer Graphics 25 (4), 165-174.
    5. Cook, R.L. (1986) Stochastic sampling in computer graphics. ACM Transactions on Graphics 5 (1), 51-72.
    6. Hall, R. (1989) Illumination and color in computer generated imagery. Springer-Verlag, New York.
    7. Hanrahan, E, Salzman, D., Aupperle, L. (1991) A rapid hierarchical radiosity algorithm. Computer Graphics 25 (4), 197-206.
    8. Immel, D.S., Cohen, M.F., Greenberg, D.E (1986) A radiosity method for non-diffuse environments. Computer Graphics 20 (4), 133-142.
    9. Kajiya, J.T. (1986) The rendering equation. Computer Graphics 20 (4), 143-150.
    10. Mitchell, D. (1992) Manuscript.
    11. Nicodemus, EE., Richmond, J.C., Hsia, J.J., Ginsberg, I.W., Limperis, T. (1977) Geometrical considerations and nomenclature for reflectance. National Bureau of Standards monograph, no. 160.
    12. Shirley, E (1990) A ray tracing method for illumination calculation in diffuse-specular scenes. Proc. Graphics Interace ’90, 205-212.
    13. Sillion, EX., Arvo, J.R., Westin, S.H., Greenberg, D.E (1991) A global illumination solution for general reflectance distributions. Computer Graphics 25 (4), 187-196.
    14. Smits, B.E., Arvo, J.R., Salesin, D.H. (1992) An importancedriven radiosity algorithm. Computer Graphics 26 (2), 273-282.
    15. Torrance, K.E., Sparrow, E.M. (1967) Theory for off-specular reflection from roughened surfaces. J. of the Optical Society of America 57 (9), 1105-1114.
    16. Ward, G.J., Rubinstein, F.M., Clear, R.D. (1988) A ray tracing solution for diffuse environments. Computer Graphics 22 (3), 85- 92.

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