The Stochastic Ray Method for Radiosity

Laszlo Neumann, Werner Purgathofer, Robert F. Tobler, Attila Neumann, Pavol Elias, Martin Feda, Xavier Pueyo
The Stochastic Ray Method for Radiosity
TR-186-2-95-3, January 1995 [ paper]
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Abstract

This paper solves the system of radiosity equations with a numerical approach rather than with a physical interpretation as most current algorithms do. Due to the high complexity of the problem for highly complex scenes, a stochastic variation of Jacobi iteration is developed which converges stochastically to the correct solution. The new method, called Stochastic Ray Method, is a significant improvement of Stochastic Radiosity. A large number of independent rays is chosen stochastically by importance sampling of the patches according to their power after the previous iteration step. They all carry an equal amount of power into random directions, thereby representing together the total energy interreflection of the entire environment in a stochastic manner. Assuming a correctly distributed initial solution, which can be reached easily, the iteration process converges quickly and reduces the error in the result faster than other stochastic radiosity approaches. The new algorithm can easily be extended to treat various phenomena which are normally rather costly to incorporate in radiosity environments: specular reflection and specular transmittance, non-diffuse emission and point light sources.

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@techreport{Neumann-1995-SRM,
  title =      "The Stochastic Ray Method for Radiosity",
  author =     "Laszlo Neumann and Werner Purgathofer and Robert F. Tobler
               and Attila Neumann and Pavol Elias and Martin Feda and
               Xavier Pueyo",
  year =       "1995",
  abstract =   "This paper solves the system of radiosity equations with a
               numerical approach rather than with a physical
               interpretation as most current algorithms do. Due to the
               high complexity of the problem for highly complex scenes, a
               stochastic variation of Jacobi iteration is developed which
               converges stochastically to the correct solution. The new
               method, called Stochastic Ray Method, is a significant
               improvement of Stochastic Radiosity. A large number of
               independent rays is chosen stochastically by importance
               sampling of the patches according to their power after the
               previous iteration step. They all carry an equal amount of
               power into random directions, thereby representing together
               the total energy interreflection of the entire environment
               in a stochastic manner. Assuming a correctly distributed
               initial solution, which can be reached easily, the iteration
               process converges quickly and reduces the error in the
               result faster than other stochastic radiosity approaches.
               The new algorithm can easily be extended to treat various
               phenomena which are normally rather costly to incorporate in
               radiosity environments: specular reflection and specular
               transmittance, non-diffuse emission and                
               point light sources.",
  address =    "Favoritenstrasse 9-11/186, A-1040 Vienna, Austria",
  institution = "Institute of Computer Graphics and Algorithms, Vienna
               University of Technology",
  note =       "human contact: technical-report@cg.tuwien.ac.at",
  month =      jan,
  number =     "TR-186-2-95-3",
  keywords =   "rendering, radiosity, stochastic, raytracing",
  URL =        "http://www.cg.tuwien.ac.at/research/publications/1995/Neumann-1995-SRM/",
}