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 ...

We investigate the use of non-homogeneous spherical poly-nomials for the approximation of functions deened on the sphere S 2. A spherical polynomial is the restriction to S 2 of a polynomial in the three coordinates x; y; z of R 3. Let P d be the space of spherical polynomials with degree d. We show that P d is the direct sum of H d and H d?1 , where H d denotes the space of homogeneous degree-...

The objective of the paper is to continue the study of an interesting class of rational splines in polar coordinates, introduced by SS anchez-Reyes 17] and independently by de Casteljau 6]. We refer to these curves as p-splines. They are a generalization of certain analogous of B ezier curves in polar coordinates which we call p-B ezier. We present an alternative way to have an exact representa...

We introduce a new class of distributions to model directional data, based on hyperspherical log-splines. The class is very flexible and can be used to model data that exhibit features that cannot be accommodated by typical parametric distributions, such as asymmetries and multimodality. The distributions are defined on hyperspheres of any dimension and thus, include the most common circular an...

Developable surfaces are modelled with pieces of right circular cones. These cone spline surfaces are well-suited for applications: They possess degree two parametric and implicit representations. Bending sequences and the development can be explicitly computed and the offsets are of the same type. The algorithms are based on elementary analytic and constructive geometry. There appear interesti...

Accurate registration of cortical structures plays a fundamental role in statistical analysis of brain images across population. This paper presents a novel framework for the non-rigid intersubject brain surface registration, using conformal structure and spherical thin-plate splines. By resorting to the conformal structure, complete characteristics regarding the intrinsic cortical geometry can...