“The hemi-cube: a radiosity solution for complex environments” by Greenberg and Cohen

  • ©Donald P. Greenberg and Michael Cohen




    The hemi-cube: a radiosity solution for complex environments



    This paper presents a comprehensive method to calculate object to object diffuse reflections within complex environments containing hidden surfaces and shadows. In essence, each object in the environment is treated as a secondary light source. The method provides an accurate representation of the “diffuse” and “ambient” terms found in typical image synthesis algorithms. The phenomena of “color bleeding” from one surface to another, shading within shadow envelopes, and penumbras along shadow boundaries are accurately reproduced. Additional advantages result because computations are indepedent of viewer position. This allows the efficient rendering of multiple views of the same scene for dynamic sequences. Light sources can be modulated and object reflectivities can be changed, with minimal extra computation. The procedures extend the radiosity method beyond the bounds previously imposed.


    1. Amanatides, John. Ray Tracing with Cones. ACM Computer Graphics (Proceedings 1985), pp. 129-135.
    2. Cook, Robert. Distributed Ray Tracing. ACM Computer Graphics (Proceedings 1984), 137’145.
    3. Foley, J. D. and Van Dam, A. Fundamentals of Computer Graphics. Addison-Wesley Publishin9 CO., 1982.
    4. Goral, Cindy M., Torrance, Kenneth E., Greenberg, Donald P., Battaile, Bennett, Modeling the Interaction of Light Between Diffuse Surfaces, ACM Co~uter Graphics (Proceedings 1984), pp~213-222.
    5. Gouraud, Henri, Computer Display of Curved Surfaces, Ph.D. Dissertation, University of Utah, 1971.
    6. Hornbeck, Robert W., Numerical Methods. Quantum Publishers, 1975, pp 101-106.
    7. Meyer, Gary W., Rushmeier, Holly E., Cohen, Michael F., Greenberg, Donald P., Torrance, Kenneth E., Assessing the Realism of Computer Gr~hics Images~ submitted for publication, 1985.
    8. Newman, William M. and Sproull, Robert F., Principles of interactive Computer Graphics, McGraw Hill, 1979.
    9. Phong, Bui Tuong, Illuminat~on for Computer Generated Images, Ph.D. Dissertation, University of Utah, 1973.
    10. Siegel, Robert and Howell, John R., Thermal Radiation Heat Transfer, He~ Publishing Corp., 1978.
    11. Sparrow, E. M. and Cess R. D., Radiation Heat Transfer, Hemisphere Publishing Corp., i978.
    12. Weghorst, Hank, Hooper, Gary, and Greenberg, Donald P., Improved Computational Methods for Ray Tracing, ACM Transactions on Graphics, Jan, 1984, pp. 52–69.
    13. Whitted, Turner, An Improved Illumination Model for Shaded Display, Communications of the ACM, June, 1980.

ACM Digital Library Publication:

Overview Page: