Efficient and accurate rotation of finite spherical harmonics expansions. (English) Zbl 1243.65037
Summary: 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.
MSC:
| 65D20 | Computation of special functions and constants, construction of tables |
| 33C55 | Spherical harmonics |
| 33F05 | Numerical approximation and evaluation of special functions |
Keywords:
spherical harmonics; reproducing kernel Hilbert spaces; rotation; algorithm; numerical experimentsReferences:
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