Recursive computation of Hermite spherical spline interpolants

摘要

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 uk of class Ck and degree 4k+1 on S, defined by some data scheme Dk(u). We show that when the data sets Dr(u) are nested, i.e., Dr-1(u)⊂Dr(u), 1⩽r⩽k, the spline function uk 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.