Efficient Spherical Harmonic Evaluation
Authors: Peter-Pike Sloan

Editor: Cindy Grimm
Oregon State University
Editor-in-Chief: Morgan McGuire
NVIDIA & Williams College


The real spherical harmonics have been used extensively in computer graphics, but the conventional representation is in terms of spherical coordinates and involves expensive trigonometric functions. While the polynomial form is often listed for low orders, directly evaluating the basis functions independently is inefficient. This paper will describe in detail how recurrence relations can be used to generate pre-factored evaluation code that is smaller, more efficient, and presents a performance comparison of several alternative techniques to evaluate the spherical harmonics.

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Citation: Peter-Pike Sloan, Efficient Spherical Harmonic Evaluation, Journal of Computer Graphics Techniques (JCGT), vol. 2, no. 2, 84-90, 2013 Available online http://jcgt.org/published/0002/02/06/

Copyright: © 2013 Sloan

Received: 2013-07-01; Recommended: 2013-08-09; Published: 2013-09-08