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 $kin mathbb{n}$, we consider ahermite spherical interpolant problem $h_k$ defined by some datascheme $mathcal{d}_k(u)$ and which admits a unique solution $p_k$in 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.