Papers on Caustics and Bidirectional Ray Tracing

Since 1986, a number of researchers have developed far more robust and flexible algorithms than the simple backward ray tracing approach described in the SIGGRAPH `86 course notes on ray tracing. A good heading for all such work is bidirectional ray tracing, since the main distinguishing feature of this class of algorithms is that rays are traced in both directions, from the light sources as well as from the eye. Here is a partial list of papers that are well work looking at if you are interested in this subject.

Paul S. Heckbert, "Adaptive Radiosity Textures for Bidirectional Ray Tracing", Computer Graphics, 24(4):145-154, July, 1990.
Mark Watt, "Light-water interaction using backward beam tracing", Computer Graphics, 24(4):377-385, July, 1990.
Steven Collins, "Adaptive Splatting for Specular to Diffuse Light Transport", Proceedings of the Fifth Eurographics Workshop on Rendering, Darmstadt, Germany, June 1992, pages 119-135.
Eric Veach and Leonidas Guibas, "Bidirectional Estimators for Light Transport", Proceedings of the Fifth Eurographics Workshop on Rendering, Darmstadt, Germany, June 1992, pages 147-162.
Don Mitchell and Pat Hanrahan, "Illumination from Curved Reflectors", Computer Graphics, 26(2):283-291, July 1992.
Steven Collins, "Reconstruction of Illumination from Area Luminaires", In Rendering Techniques `95, pages 274-283, edited by P. M. Hanrahan and W. Purgathofer, Springer-Verlag, New York, 1995.
Eric Veach and Leonidas J. Guibas, "Optimally Combining Sampling Techniques for Monte Carlo Rendering", in Computer Graphics Proceedings, Annual Conference Series, ACM SIGGRAPH `95, pages 419-428, 1995.

Density estimation is another interesting line of research that is much more viable than the approach explored in the backward ray tracing notes. See the following paper by Shirley et al. for a detailed description of the approach.

Peter Shirley, Bretton Wade, Philip M. Hubbard, David Zareski, Bruce Walter, and Donald P. Greenberg, "Global Illumination via Density-Estimation", In Rendering Techniques `95, pages 219-230, edited by P. M. Hanrahan and W. Purgathofer, Springer-Verlag, New York, 1995.

Historical Notes

The year 1986 could be called The Year of the Caustic in computer graphics. In that year Jim Kajiya published his paper on the rendering equation and produced images that captured all modes of light transport, including caustics formed by glass spheres. Kajiya generated the images using Monte Carlo path tracing, which sparked a flurry of research activity in Monte Carlo global illumination. Another example of caustics from 1986 was a paper by Masa Inakage, which also appeared in the SIGGRAPH course notes on ray tracing. Inakage rendered the caustics formed by convex lenses using the lens maker's formula. The full reference to Inakage's paper is

Masa Inakage, "Reflection and Refraction Model for Ray Tracing", Developments in Ray Tracing, SIGGRAPH `86 Course Notes, Volume 12, August 1986

Note that the word caustic has a different meaning in the computer graphics literature than it does in the optics literature. In computer graphics the word "caustic" is frequently used to describe any point or area that is brightly illuminated by light that is reflected by a mirror or transmitted through a transparent object (such as a lens). In geometrical optics, a caustic curve consists of singularities where the intensity (or irradiance) is infinite, which is only possible with respect to point light sources.

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