In this paper we generalize several results on uniform approximation orders with radial basis functions in (Buhmann, Dyn and Levin, 1993) and (Dyn and Ron, 1993) to L-approximation orders. These results apply, in particular, to approximants from spaces spanned by translates of radial basis functions by scattered centres. Examples to which our results apply include quasi-interpolation and least-...

Concepts of abstract harmonic analysis can be used to provide a unifying framework for basis function methods, like radial basis functions in Euclidean spaces or zonal basis functions on the sphere. To illustrate how these concepts can be applied reflection invariant functions are considered. A specialization of the BochnerGodement Theorem leads to a characterization of suitable basis functions. §

The generalized interpolation problem, known as the problem of reconstructing a multidimensional vector function f from a finite set of linear measures, is considered in Refs. (1) and (2). The solution of the generalized interpolation problem can be obtained as a linear combination of generating functions. Different basis functions can be used to solve the problem(3) – (7), in this paper Compac...

A method for achieving an arbitrary lift distribution with an arbitrary planform is presented. This is accomplished through optimizing aerodynamic twist for a given number of either known airfoils or airfoils to be designed. The spanwise locations of these airfoils are optimized to get as close to the desired lift distribution as possible. Airfoils are linearly interpolated between these points...

This paper gives an introduction to certain techniques for the construction of geometric objects from scattered data. Special emphasis is put on interpolation methods using compactly supported radial basis functions. x1. Introduction We assume a sample of multivariate scattered data to be given as a set X = solid to these data will be the range of a smooth function s : IR d ! IR D with s(x k) =...

If additional smoothness requirements and boundary conditions are met, the well–known approximation orders of scattered data interpolants by radial functions can roughly be doubled.

We present a novel Facial Motion Cloning method relying on the combination of the radial basis functions (RBF) based scattered data interpolation with the encoding capabilities of the MPEG-4 Facial and Body Animation (FBA) international standard. Beside from an initial manual selection of feature points, our method works fully automatically without user interaction. The produced talking head is...

A hierarchical scheme is presented for smoothly interpolating scattered data with radial basis functions of compact support. A nested sequence of subsets of the data is computed efficiently using successive Delaunay triangulations. The scale of the basis function at each level is determined from the current density of the points using information from the triangulation. The method is rotational...