The current implementation only deals with spherical water droplets, but the algorithm could be modified to produce effects that result from particles of other shapes, such as halos resulting from crystalline shapes, as described in Rainbows, Haloes, and Glories [ 1]. The directional lookup table described in part 2 would need to be recomputed to account for the different geometry, and the directional lookup would possibly need to be expanded to a higher dimension if the desired effect did not occur in a 1-dimensional angular space, as is the case with rainbows.

Another possibility would be to create a volumetric photon map-ping-based version of the multiple-scattering path tracing integrator. Photon mapping is a technique developed by Henrik Jensen in which virtual “photons” are sent from the light into the scene and stored in a tree structure when they reach a certain termination criteria [ 5]. The renderer literally shines light on the scene and stores where it hits. Then, in the rendering phase, the camera “collects” photons near the rays that it sends into the scene, producing results that, while not physically correct, have low noise. Another technique to try would be a bidirectional path tracer as proposed by Lafortune and Willems [ 6]. With bidirectional path tracing, sub-paths are traced both from the camera and from the light. Paths from the light or camera side that make small contributions to the resulting image can be ignored; essentially, importance sampling is performed on the sub-paths. Then, the sub-paths can be combined, and the result is an image with considerably less variance.

Acknowledgments

Thanks to Qiqi Wang for providing the volumetric dataset and algorithm for tracing through unstructured meshes. Also, thanks to Pat Hanrahan for providing support and advice on this project.

1. Greenler, R. 1990. Rainbows, Halos, and Glories. Cambridge University Press, Cambridge, UK.

2. Hanrahan, P. Law of reflection. https://graphics.stanford.edu/
wikis/cs348b-07/Reflection1Lecture/012.

3. Huibers, P. 1997. Models for the wavelength dependence of the index of refraction of water. Appl. Optics 36, 16.

4. Humphreys, G. and Pharr, M. 2004. Physically Based Rendering. Elsevier, San Francisco, CA.

5. Jensen, H. 2001. Realistic Image Synthesis Using Photon Mapping. AK Peters, Wellesley, MA.

6. Lafortune, E. and Willems, Y. D. 1993. Bi-directional path-tracing. In Proceedings of ACM Compugraphics. Alvor, Portugal. 145-153.

7. Nave, R. Fresnel’s Equations. http://hyperphysics.phy-astr.gsu.edu/
Hbase/phyopt/ freseq.html.
8. Weisstein, E. Snell’s law. http://scienceworld.wolfram.com/
physics/ SnellsLaw.html.

Biography James Hegarty ( jhegarty@stanford.edu) is a sophomore at Stanford University. He enjoys photography, playing guitar, and conducting computer graphics research.

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