A Family of Spline Quasi-Interpolants on the Sphere

Abstract

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.

DOI: 10.1023/A:1025549029512

Cite this paper

@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} }