Advertisement

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
Article

Abstract

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.

Keywords

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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

REFERENCES

  1. 1.
    Kajiya, J.T., The Rendering Equation, Proc. of the Int. Conf. on Computer Graphics and Interactive Techniques (SIGGRAPH'86), 1986, pp. 143–150.Google Scholar
  2. 2.
    Szirmay-Karlos, L., Monte Carlo Methods in Global Illumination, Vienna: Institute of Computer Graphics, Vienna University of Technology, 1999.Google Scholar
  3. 3.
    Khodulev, A., Comparison of Two Methods of Global Illumination Analysis, Technical Report of Keldysh Inst. Appl. Math., 1996; http://www.keldysh.ru/pages/cgraph/articles/ index.htmGoogle Scholar
  4. 4.
    Sobol', I.M., Mnogomernye kvadraturnye formuly i funktsii Khaara(Multidimensional Quadrature Rules and Haar Functions), Moscow: Nauka, 1969.Google Scholar
  5. 5.
    Keller, A., A Quasi-Monte Carlo Algorithm for the Global Illumination in the Radiosity Setting, in Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing, Niederreiter, H. and Shiue, P., Eds., Springer, 1995, pp. 239–251.Google Scholar
  6. 6.
    Szirmay-Karlos, L., Foris, T., Neumann, L., and Csebfalvi, B., An Analysis to Quasi-Monte Carlo IntegrationApplied to the Transllumination Radiosity Method, Computer Graphics Forum, 1997, vol. 16, no. 3, pp. 271–281.CrossRefGoogle Scholar
  7. 7.
    Lafortune, E.P. and Willems, Y.D., Bi-directional Path Tracing, Computer Graphics Proc., Alvor (Portugal), 1993, pp. 145–153.Google Scholar
  8. 8.
    Veach, E. and Guibas, L.J., Optimally Combining Sampling Techniques for Monte Carlo Rendering, SIGGRAPH' 95 Proc., Addison-Wesley, 1995, pp. 77–102.Google Scholar
  9. 9.
    Pattanaik, S.N. and Mudur, S.P., Adjoint Equations and Random Walks for Illumination Computation, ACM Trans. Graph., 1995, vol. 14, pp. 77–102.CrossRefGoogle Scholar
  10. 10.
    Castro, F., Martinez, R., and Sbert, M., Quasi-Monte Carlo and Extended First-Shot Improvements to the Multi-Path Method, Spring Conf. on Computer Graphics, 1998, pp. 91–102.Google Scholar
  11. 11.
    Kopylov. E.A., An Efficient Method for the Illumination Evaluation Based on the Use of the Probability Distribution Function for Ray Generation, Graphicon'2002, pp. 225–229.Google Scholar
  12. 12.
    Sobol', I.M., Chislennye metody Monte-Karlo(Numerical Monte Carlo Methods), Moscow: Nauka, 1973.Google Scholar
  13. 13.
    Dmitriev, K., From Monte Carlo to Quasi-Monte Carlo Methods, Graphicon'2002, pp. 53–58.Google Scholar
  14. 14.
    Kopylov. E.A., Khodulev, A.B., and Volevich, V.L., The Comparison of Illumination Maps Technique in Computer Graphics Software, Graphicon'98, pp. 146–152.Google Scholar
  15. 15.
    Maamari, F., TC.3.33 List of Proposed Test Cases, Ecole National des Travaux Publics de l'Etat, Laboratory of Building Sciences, Department of Civil Engineering and Building, URA CNRS 1652, 2002.Google Scholar
  16. 16.
    Debevec, P., Fong, N., and Lemmon, D., Image-Based Lighting, SIGGRAPH Course, 2002, no. 5.Google Scholar
  17. 17.
    http://www.integra.jpGoogle Scholar

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

Personalised recommendations