Quadratic spherical spline quasi-interpolants on Powell--Sabin partitions

Spline quasi-interpolation methods are local tools approximating functions or discrete data. In this paper we deal with the problem of constructing quasi-interpolants in the space of quadratic spherical Powell-Sabin splines on uniform spherical triangulations of a sphere-like surface S. Discrete and differential quasi-interpolants of optimal approximation order are developed and numerical tests for illustrating theoretical results are presented.

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