Hierarchical Computation of Hermite Spherical Interpolant

In this paper, we propose to extend the hierarchical bivariate Hermite Interpolant to the spherical case. Let T be an arbitrary spherical triangle of the unit sphere S and let u be a function defined over the triangle T. For , we consider a Hermite spherical Interpolant problem H_k defined by some data scheme D_k(u) and which admits a unique solution p_k in the space B_nk (T) of homogeneous Bernstein-Bezier polynomials of degree n_k = 2k (resp.n_k = 2k + 1) defined on T. We discuss the case when the data scheme D_r(u) are nested, i.e., D_(r-1)(u) Dr(u) for all 1 < r < k. This, give a recursive formulae to compute the polynomial p_k. Moreover, this decomposition give a new basis for the space B_nk (T), which are the hierarchical structure. The method is illustrated by a simple numerical example.