Application of Quasi-Monte Carlo Sampling to the Multi Path Method for Radiosity

  • Francesc Castro
  • Mateu Sbert
Conference paper


The multi path method is a Monte Carlo technique that solves the radiosity problem, i.e. the illumination in a scene with diffuse (also called lambertian) surfaces. This technique uses random global lines for the transport of energy, contrary to the classic Monte Carlo techniques, in which the lines used are local to the surface where they exited from. The multi path technique borrows results from Integral Geometry to predict the correct transfer of energy, and can be shown to be a random walk method, in which a geometric path corresponds to several logical paths.

We will study in this paper the application of quasi-Monte Carlo sequences to the random sampling of the global lines. Important improvements in the efficiency of the multi path method for certain sequences will be demonstrated. Alternative ways of generating global lines will also be studied in the context of quasi-Monte Carlo.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [CW93]
    M. Cohen and J. Wallace. Radiosity and Realistic Image Synthesis. Academic Press Professional, 1993.Google Scholar
  2. [Kel96a]
    A. Keller. The Fast Calculation of Form Factors Using Low Discrepancy Sequences. Proc. of SCCG96 Budmerice, 1996.Google Scholar
  3. [Kel96b]
    A. Keller. Quasi-Monte Carlo Radiosity. Proceedings of Eurographics Workshop on Rendering, pages 102–111, 1996.Google Scholar
  4. [Kel97]
    A. Keller. Instant Radiosity. Computer Graphics Proceedings, Sig- graph’97, pages 49 – 56, 1997.Google Scholar
  5. [Neu95]
    L. Neumann. Monte Carlo Radiosity. Computing, 55, pages 23–42, 1995.CrossRefzbMATHMathSciNetGoogle Scholar
  6. [Neu92]
    H. Niederreiter. Random Number Generation and Quasi-Monte Carlo Methods, nsf-cbms. 1992.CrossRefGoogle Scholar
  7. [NNB97]
    L. Neumann, A. Neumann, and P. Bekaert. Radiosity with Well Distributed Ray Sets. Proceedings of Eurographics 97, pages 261–269, 1997.Google Scholar
  8. [Pre94]
    W.H. Press. Numerical Recipes in C. Cambridge University Press, 1994.Google Scholar
  9. [Rub81]
    Reuven Y. Rubinstein. Simulation and the Monte Carlo Method. 1981.Google Scholar
  10. [San76]
    L. Santaló. Integral Geometry and Geometric Probability. 1976.zbMATHGoogle Scholar
  11. [Sbe93]
    M. Sbert. An Integral Geometry Based Method for Fast Form-Factor Computation. Computer Graphics Forum (proc. Eurographics’93), 12, N. 3: 409–420, 1993.CrossRefGoogle Scholar
  12. [Sbe97a]
    M. Sbert. Error and Complexity of Random Walk Monte Carlo Radiosity. IEEE Transactions on Visualization and Computer Graphics, 3(1), 1997.Google Scholar
  13. [Sbe97b]
    M. Sbert. The Use of Global Random Directions to Compute Radiosity. Global Monte Carlo Methods. Ph.D. thesis. Universitat Politécnica de Catalunya, Barcelona, 1997.Google Scholar
  14. [SKFNC97]
    L. Szirmay-Kalos, T. Foris, L. Neumann, and B. Csebfalvi. An Analysis of Quasi-Monte Carlo Integration Applied to the Transillumination Radiosity Method. Proceedings of Eurographics 97, 1997.Google Scholar
  15. [Sol78]
    H. Solomon. Geometric Probability, siaam-cbms 28. 1978.CrossRefGoogle Scholar
  16. [SPNP96]
    M. Sbert, X. Pueyo, L. Neumann, and W Purgathofer. Global Multi- Path Monte Carlo Algorithms for Radiosity. The Visual Computer, pages 47–61, 1996.Google Scholar
  17. [SPP95]
    M. Sbert, F. Pérez, and X. Pueyo. Global Monte Carlo. A Progressive Solution. Rendering Techniques’95. Springer Wien New York, pages 231–239, 1995.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Francesc Castro
    • 1
  • Mateu Sbert
    • 1
  1. 1.Institut d’Informàtica i AplicacionsUniversitat de GironaGironaSpain

Personalised recommendations