Path differentials and applications

  • Frank Suykens
  • Yves D. Willems
Part of the Eurographics book series (EUROGRAPH)


Photo-realistic rendering algorithms such as Monte Carlo ray tracing sample individual paths to compute images. Noise and aliasing artefacts are usually reduced by supersampling. Knowledge about the neighborhood of the path, such as an estimated footprint, can be used to reduce these artefacts without having to trace additional paths. The recently introduced ray differentials estimate such a footprint for classical ray tracing, by computing ray derivatives with respect to the image plane. The footprint proves to be useful for filtering textures locally on surfaces. In this paper, we generalize the use of these derivatives to arbitrary path sampling, including general reflection and refraction functions. Sampling new directions introduces additional partial derivatives, which are all combined into a footprint estimate. Additionally the path gradient is introduced; it gives the rate of change of the path contribution. When this change is too steep the size of the footprint is reduced. The resulting footprint can be used in any global illumination algorithm that is based on path sampling. Two applications show its potential: texture filtering in distributed ray tracing and a novel hierarchical approach to particle tracing radiosity.


Global Illumination Light Transport Path Differential Differential Vector Path Gradient 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    John Amanatides. Ray tracing with cones. Computer Graphics, 18(3): 129–135, July 1984.CrossRefGoogle Scholar
  2. 2.
    Philippe Bekaert. Personal Communication. 2001.Google Scholar
  3. 3.
    M. Chen and J. Arvo. Perturbation methods for interactive specular reflections. In Hans Hagen, editor, IEEE Transactions on Visualization and Computer Graphics, volume 6(3), pages 253–264. IEEE Computer Society, 2000.Google Scholar
  4. 4.
    Steven Collins. Adaptive Splatting for Specular to Diffuse Light Transport. In Fifth Eurographics Workshop on Rendering, pages 119–135, Darmstadt, Germany, June 1994.Google Scholar
  5. 5.
    Paul S. Heckbert. Adaptive radiosity textures for bidirectional ray tracing. Computer Graphics, 24(4):145–154, August 1990.CrossRefGoogle Scholar
  6. 6.
    Paul S. Heckbert and Pat Hanrahan. Beam tracing polygonal objects. Computer Graphics, 18(3):119–127, July 1984.CrossRefGoogle Scholar
  7. 7.
    Homan Igehy. Tracing ray differentials. Computer Graphics, 33(Annual Conference Series):179–186, 1999.Google Scholar
  8. 8.
    Henrik Wann Jensen. Global illumination using photon maps. In Xavier Pueyo and Peter Schröder, editors, Eurographics Rendering Workshop 1996, pages 21–30, New York City, NY, June 1996. Eurographics, Springer Wien. ISBN 3-211-82883-4.Google Scholar
  9. 9.
    M. Kalos and P. Whitlock. Monte Carlo Methods, Volume I: Basics. J. Wiley, New York, 1986.MATHCrossRefGoogle Scholar
  10. 10.
    S. N. Pattanaik and S. P. Mudur. Computation of global illumination by monte carlo simulation of the particle model of light. Third Eurographics Workshop on Rendering, pages 71–83, May 1992.Google Scholar
  11. 11.
    Mikio Shinya, Tokiichiro Takahashi, and Seiichiro Naito. Principles and applications of pencil tracing. Computer Graphics, 21(4):45–54, July 1987.CrossRefGoogle Scholar
  12. 12.
    Peter Shirley, Bretton Wade, Philip M. Hubbard, David Zareski, Bruce Walter, and Donald P. Greenberg. Global Illumination via Density Estimation. In P. M. Hanrahan and W. Purgathofer, editors, Rendering Techniques’ 95 (Proceedings of the Sixth Eurographics Workshop on Rendering), pages 219–230, New York, NY, 1995. Springer-Verlag.Google Scholar
  13. 13.
    F. Suykens. Path differentials and applications. Technical Report CW307, Department of Computer Science, K.U. Leuven, Leuven, Belgium, May 2001.Google Scholar
  14. 14.
    Robert F. Tobler, Alexander Wilkie, Martin Feda, and Werner Purgathofer. A hierarchical subdivision algorithm for stochastic radiosity methods. In Julie Dorsey and Philipp Slusallek, editors, Eurographics Rendering Workshop 1997, pages 193–204, June 1997.Google Scholar

Copyright information

© Springer-Verlag Wien 2001

Authors and Affiliations

  • Frank Suykens
    • 1
  • Yves D. Willems
    • 1
  1. 1.Department of Computer ScienceK. U.LeuvenBelgium

Personalised recommendations