Recursive computation of Hermite spherical spline interpolants

Abstract

Let u be a function defined on a spherical triangulation Δ of the unit sphere S. In this paper, we study a recursive method for the construction of a Hermite spline interpolant u k of class C k and degree 4 k + 1 on S, defined by some data scheme D k ( u ) . We show that when the data sets D r ( u ) are nested, i.e., D r - 1 ( u ) ⊂ D r ( u ) , 1 ⩽ r ⩽ k , the spline function u k can be decomposed as a sum of k + 1 simple elements. This decomposition leads to the construction of a new and interesting basis of a space of Hermite spherical splines. The theoretical results are illustrated by some numerical examples.