Programming and Computer Software

, Volume 30, Issue 5, pp 258–265 | Cite as

Bidirectional Ray Tracing for the Integration of Illumination by the Quasi-Monte Carlo Method

  • A. G. Voloboi
  • V. A. Galaktionov
  • K. A. Dmitriev
  • E. A. Kopylov


Algorithms used to generate physically accurate images are usually based on the Monte Carlo methods for the forward and backward ray tracing. These methods are used to numerically solve the light energy transport equation (the rendering equation). Stochastic methods are used because the integration is performed in a high-dimensional space, and the convergence rate of the Monte Carlo methods is independent of the dimension. Nevertheless, modern studies are focused on quasi-random samples that depend on the dimension of the integration space and make it possible to achieve, under certain conditions, a high rate of convergence, which is necessary for interactive applications. In this paper, an approach to the development of an algorithm for the bidirectional ray tracing is suggested that reduces the overheads of the quasi-Monte Carlo integration caused by the high effective dimension and discontinuity of the integrand in the rendering equation. The pseudorandom and quasi-random integration methods are compared using the rendering equations that have analytical solutions.


Operating System Artificial Intelligence Monte Carlo Method Convergence Rate Transport Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© MAIK “Nauka/Interperiodica” 2004

Authors and Affiliations

  • A. G. Voloboi
    • 1
  • V. A. Galaktionov
    • 1
  • K. A. Dmitriev
    • 1
  • E. A. Kopylov
    • 1
  1. 1.Keldysh Institute of Applied MathematicsRussian Academy of SciencesRussia

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