HIERARCHICAL COMPUTATION OF HERMITE SPHERICAL INTERPOLANT

In this paper, we propose to extend the hierarchical bivariateHermite Interpolant to the spherical case. Let T be an arbitraryspherical triangle of the unit sphere S and  let u be a functiondefined over the triangle T. For k\in \mathbb{N}, we consider aHermite spherical Interpolant problem H_k defined by some datascheme \mathcal{D}_k(u) and which admits a unique solution p_kin the space B_{n_k}(T) of homogeneous Bernstein-B\'ezierpolynomials of degree n_k=2k (resp. n_k=2k+1) defined on T. Wediscuss the case when the data scheme \mathcal{D}_{r}(u) arenested, i.e., \mathcal{D}_{r-1}(u)\subset \mathcal{D}_{r}(u) forall 1 \leq r \leq k. This, give a recursive formulae to computethe polynomial p_k. Moreover, this decomposition give a new basisfor the space B_{n_k}(T), which are the hierarchical structure.The method is illustrated by a simple numerical example.

HIERARCHICAL COMPUTATION OF HERMITE SPHERICAL INTERPOLANT Keywords:

Spherical splines , Hermite interpolation , Recursive computation