We analyze the approximation order associated with a directed set of spaces, {Sh}h>0, each of which spanned by the hZZ-translates of one compactly supported function φh : IR s → C. Under a regularity condition on the sequence {φh}h, we show that the optimal approximation order (in the ∞-norm) is always realized by quasi-interpolants, hence in a linear way. These quasi-interpolants provide the b...

Interpolation by translates of \radial" basis functions is optimal in the sense that it minimizes the pointwise error functional among all comparable quasi{interpolants on a certain \native" space of functions F . Since these spaces are rather small for cases where is smooth, we study the behavior of interpolants on larger spaces of the form F 0 for less smooth functions 0. It turns out that in...

We use C 1 quintic superspline functions to interpolate any given scattered data. The space of C 1 quintic superspline functions is introduced in Lai and LeMehaute'99] and is an improvement of the Alfeld scheme of 3D scattered data interpolation. We have implemented the spline space in MATLAB and tested for the accuracy of reproduction of all quintic polynomials. We present some numerical evide...

abstract Evaluating and comparing the quality of surface interpolants is an important problem in computer graphics, computer aided geometric design and scientiic visualization. We introduce geometric uncertainty as a measure of interpolation error, level of conndence or quality of an interpolant. Geometric uncertainty can be estimated as a scalar or a vector-valued function that depends upon ge...

In this paper, we present an easy and e cient method for computing the range of a function by using spline quasi-interpolation. We exploit the close relationship between the spline function and its control polygon and use tight subdivision technique in order to obtain monotonic splines which make the range of the spline easy to compute. The proposed method is useful in case of given scattered d...

In this paper, we propose a new multilevel univariate approximation method with high order accuracy using radial basis function interpolation and cubic B-spline quasi-interpolation. The proposed approach includes two schemes, which are based on radial basis function interpolation with less center points, and cubic B-spline quasi-interpolation operator. Error analysis shows that our method produ...