A computable function, defined over the sphere, is constructed, which is of classC1 at least and which approximates a given set of data. The construction is based upon tensor product spline basisfunctions, while at the poles of the spherical system of coordinates modified basisfunctions, suggested by the spherical harmonics expansion, are introduced to recover the continuity order at these points. Convergence experiments, refining the grid, are performed and results are compared with similar results available in literature. The approximation accuracy is compared with that of the expansion in terms of spherical harmonics. The use of piecewise approximation, with locally supported basisfunctions, versus approximation with spherical harmonics is discussed.
- tensor product splines
- Approximation over the sphere
- spherical harmonics