Efficient and Accurate Rotation of Spherical Harmonics Expansions

Christian Lessig, Tyler de Witt, and Eugene Fiume


Our algorithm employs a sampling theorem for the sphere to rotate signals represented in Spherical Harmonics. In the above example, the locations of large cities have been used as sampling points, demonstrating the robustness and versatility of our technique.


Abstract: An efficient and accurate algorithm for rotating finite Spherical Harmonics expansions is presented. The technique employs a sampling theorem for the sphere which allows a rotated signal to be obtained by rotating sampling nodes. The performance of our algorithm is determined by the number and location of the sampling points, leading to a well-defined trade-off between speed and accuracy. Inde- pendent of the bandwidth, our algorithm is faster than any existing method and provides accuracy comparable to the best known tech- niques in the literature. Additionally, it is simple to implement and inherently data-parallel. Extensive numerical experiments comparing our approach to techniques in the literature are presented.


Publications

Christian Lessig, Tyler de Witt,  and Eugene Fiume, Efficient and Accurate Rotation of Finite Spherical Harmonics Expansions, Journal of Computational Physics, 2011. (preprint)

Code

Matlab reference implementation (demonstrates basic ideas).

C++ test framework (contains also implementations of various techniques from the literature; note that the libraries have been compiled for our machines and might have to be re-compiled).

Sample data (contains data for well-distributed and optimized sampling locations and the corresponding the sampling matrices for use with the above C++ framework).

lessig (at) dgp (dot) toronto (dot) edu May 2010