- Published 2003 in Numerical Algorithms

In this paper, we construct a local quasi-interpolant Q for fitting a function f defined on the sphere S. We first map the surface S onto a rectangular domain and next, by using the tensor product of polynomial splines and 2π-periodic trigonometric splines, we give the expression of Qf. The use of trigonometric splines is necessary to enforce some boundary conditions which are useful to ensure the C 2 continuity of the associated surface. Finally, we prove that Q realizes an accuracy of optimal order.

@article{Nouisser2003AFO,
title={A Family of Spline Quasi-Interpolants on the Sphere},
author={O. Nouisser and Driss Sbibih and Paul Sablonni{\`e}re},
journal={Numerical Algorithms},
year={2003},
volume={33},
pages={399-413}
}