Skip to main content
SpringerLink
Log in

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

  • Published:
Programming and Computer Software Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

REFERENCES

  1. Kajiya, J.T., The Rendering Equation, Proc. of the Int. Conf. on Computer Graphics and Interactive Techniques (SIGGRAPH'86), 1986, pp. 143–150.

  2. Szirmay-Karlos, L., Monte Carlo Methods in Global Illumination, Vienna: Institute of Computer Graphics, Vienna University of Technology, 1999.

    Google Scholar 

  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.htm

  4. Sobol', I.M., Mnogomernye kvadraturnye formuly i funktsii Khaara(Multidimensional Quadrature Rules and Haar Functions), Moscow: Nauka, 1969.

    Google Scholar 

  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.

  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.

    Article  Google Scholar 

  7. Lafortune, E.P. and Willems, Y.D., Bi-directional Path Tracing, Computer Graphics Proc., Alvor (Portugal), 1993, pp. 145–153.

  8. Veach, E. and Guibas, L.J., Optimally Combining Sampling Techniques for Monte Carlo Rendering, SIGGRAPH' 95 Proc., Addison-Wesley, 1995, pp. 77–102.

  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.

    Article  Google Scholar 

  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.

  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.

  12. Sobol', I.M., Chislennye metody Monte-Karlo(Numerical Monte Carlo Methods), Moscow: Nauka, 1973.

    Google Scholar 

  13. Dmitriev, K., From Monte Carlo to Quasi-Monte Carlo Methods, Graphicon'2002, pp. 53–58.

  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.

  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.

  16. Debevec, P., Fong, N., and Lemmon, D., Image-Based Lighting, SIGGRAPH Course, 2002, no. 5.

  17. http://www.integra.jp

Download references

Author information

Authors and Affiliations

  1. Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Miusskaya pl. 4, Moscow, 125047, Russia

    A. G. Voloboi, V. A. Galaktionov, K. A. Dmitriev & E. A. Kopylov

Authors
  1. A. G. Voloboi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. V. A. Galaktionov
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. K. A. Dmitriev
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. E. A. Kopylov
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Voloboi, A.G., Galaktionov, V.A., Dmitriev, K.A. et al. Bidirectional Ray Tracing for the Integration of Illumination by the Quasi-Monte Carlo Method. Programming and Computer Software 30, 258–265 (2004). https://doi.org/10.1023/B:PACS.0000043051.47471.aa

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/B:PACS.0000043051.47471.aa

Keywords

Search

Navigation