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