Short note: Efficient and accurate rotation of finite spherical harmonics expansions

Authors:
C. Lessig;T. de Witt;E. Fiume
Affiliations:
Department of Computer Science, University of Toronto, Toronto M5S 2E4, ON, Canada;Department of Computer Science, University of Toronto, Toronto M5S 2E4, ON, Canada;Department of Computer Science, University of Toronto, Toronto M5S 2E4, ON, Canada
Venue:
Journal of Computational Physics
Year:
2012

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Abstract

Spherical harmonics are employed in a wide range of applications in computational science and physics, and many of them require the rotation of functions. We present an efficient and accurate algorithm for the rotation of finite spherical harmonics expansions. Exploiting the pointwise action of the rotation group on functions on the sphere, we obtain the spherical harmonics expansion of a rotated signal from function values at rotated sampling points. The number of sampling points and their location permits one to balance performance and accuracy, making our technique well-suited for a wide range of applications. Numerical experiments comparing different sampling schemes and various techniques from the literature are presented, making this the first thorough evaluation of spherical harmonics rotation algorithms.