Filtered Local Shading in the Wavelet Domain

  • Paul Lalonde
  • Alain Fournier
Part of the Eurographics book series (EUROGRAPH)


Many global illumination algorithms generate directionally-and positionally-varying radiance data that then need to be somehow re-sampled and used for final shading. This operation should filter all light over the incident hemisphere through the BRDF to generate an accurate image. This can be done analytically for simple BRDFs, such as Lambertian or Phong-like BRDFs, but becomes more difficult in the presence of a general BRDF.

This paper presents an efficient method to calculate the reflected light in a given direction by filtering over all incident light directions. The method exploits wavelet representations of incident light and of the BRDF to compute the total relfected light in a given direction. For efficiency the incident light is restricted to a Haar transformed representation, while the BRDF can be represented and compressed with any appropriate basis. The method can be used with any system that can generate projections of incident light fields onto Haar wavelet bases.


Wavelet Coefficient Wavelet Base Haar Wavelet Bidirectional Reflectance Distribution Function Global Illumination 
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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  1. 1.
    G. Beylkin, Ronald R. Coifman, and V. Rokhlin. Fast wavelet transforms and numerical algorithms i. Communications on Pure and Applied Mathematics, 44:141–183, 1991.MathSciNetMATHCrossRefGoogle Scholar
  2. 2.
    Brian Cabral, Nelson Max, and Rebecca Springmeyer. Bidirectional reflection functions from surface bump maps. In Maureen C. Stone, editor, Computer Graphics (SIGGRAPH ‘87 Proceedings), volume 21, pages 273–281, July 1987.Google Scholar
  3. 3.
    Per H. Christensen, Eric J. Stolinitz, David H. Salesin, and Tony D. DeRose. Global illumination of glossy environments using wavelets and importance. ACM Transactions on Graphics, 15(1):37--71, January 1996. ISSN 0730–0301.CrossRefGoogle Scholar
  4. 4.
    Ingrid Daubechies. Ten Lectures on Wavelets, volume 61 of CBMS-NSF Regional Conference Series in Applied Mathematics. SIAM, Philadelphia, PA, 1992.MATHGoogle Scholar
  5. 5.
    Joel DeYoung and Alain Fournier. Properties of tabulated bidirectional reflectance distribution functions. In To appear, Proceedings of Graphics Interface ‘87, May 1997.Google Scholar
  6. 6.
    Jay S. Gondek, Gary W. Meyer, and Jonathan G. Newman. Wavelength dependent reflectance functions. In Andrew Glassner, editor, Proceedings of SIGGRAPH ‘84 (Orlando, Florida, July 24–29, 1994),Computer Graphics Proceedings, Annual Conference Series, pages 213–220. ACM SIGGRAPH, ACM Press, July 1994. ISBN 0–89791–667–0.Google Scholar
  7. 7.
    Steven J. Gortler, Radek Grzeszczuk, Richard Szeliski, and Michael F. Cohen. The lumigraph. In Holly Rushmeier, editor, SIGGRAPH 96 Conference Proceedings, Annual Conference Series, pages 43–54. ACM SIG-GRAPH, Addison. Wesley, August 1996. held in New Orleans, Louisiana, 04–09 August 1996.Google Scholar
  8. 8.
    David S. Immel, Michael F. Cohen, and Donald P. Greenberg. A radiosity method for non-diffuse environments. In David C. Evans and Russell J. Athay, editors, Computer Graphics (SIGGRAPH ‘86 Proceedings), volume 20, pages 133–142, August 1986.Google Scholar
  9. 9.
    American National Standards Institute. ANSI standard nomenclature and definitions for illuminating engineering,. ANSI/IES RP-16–1986, Illuminating Engineering Society, 345 East 47th Street, New York, NY 10017, June 1986.Google Scholar
  10. 10.
    Henrik Wann Jensen. Importance driven path tracing using the photon map. In Eurographics Rendering Workshop 1995. Eurographics, June 1995.Google Scholar
  11. 11.
    Paul Lalonde and Alain Fournier. Generating reflected directions from brdf data. Computer Graphics Forum, to appear, 1997. Eurographics ‘87 Conference issue.Google Scholar
  12. 12.
    Paul Lalonde and Alain Fournier. Representations and uses of light distribution functions. Technical report, Department of Computer Science, University of Brisith Columbia, April 1997. Available at Scholar
  13. 13.
    Marc Levoy and Pat Hanrahan. Light field rendering. In Holly Rushmeier, editor, SIGGRAPH 96 Conference Proceedings, Annual Conference Series, pages 31–42. ACM SIGGRAPH, Addison Wesley, August 1996. held in New Orleans, Louisiana, 04–09 August 1996.Google Scholar
  14. 14.
    Robert R. Lewis and Alain Fournier. Light-driven global illumination with a wavelet representation of light transport. In Seventh Eurographics Workshop on Rendering, Porto, Portugal, June 1996.Google Scholar
  15. 15.
    Eric J. Stollnitz, Tony D. DeRose, and David H. Salesin. Wavelets for computer graphics: A primer. IEEE Computer Graphics and Applications, 15(3), 1995.Google Scholar
  16. 16.
    Gregory J. Ward. Measuring and modeling anisotropic reflection. In Edwin E. Catmull, editor, Computer Graphics (SIGGRAPH ‘82 Proceedings), volume 26, pages 265–272, July 1992.Google Scholar
  17. 17.
    Stephen H. Westin, James R. Arvo, and Kenneth E. Torrance. Predicting reflectance functions from complex surfaces. In Edwin E. Catmull, editor, Computer Graphics (SIGGRAPH ‘82 Proceedings), volume 26, pages 255264, July 1992.Google Scholar

Copyright information

© Springer-Verlag/Wien 1997

Authors and Affiliations

  • Paul Lalonde
    • 1
  • Alain Fournier
    • 1
  1. 1.Department of Computer ScienceUniversity of British ColumbiaVancouverCanada

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