A powerful and versatile method of shape-preserving interpolation is developed in terms of piecewise exponential functions with a tension factor associated with each interval. Knots coincide with data points, and the interpolant is formulated in terms of its values and first derivatives at these points. For a given set of derivatives, this enables the efficient computation of the minimum tensio...

A C curve interpolation scheme for monotonic data has been developed. This scheme uses piecewise rational cubic functions. The two families of parameters, in the description of the rational interpolant, have been constrained to preserve the shape of the data. The monotone rational cubic spline scheme has a unique representation.

In this paper, we consider multivariate interpolation with radial basis functions of finite smoothness. In particular, we show that interpolants by radial basis functions in R with finite smoothness of even order converge to a polyharmonic spline interpolant as the scale parameter of the radial basis functions goes to zero, i.e., the radial basis functions become increasingly flat.

A personal account of the author's encounters with multivariate splines during their early history. 1 Tensor product spline interpolation My first contact with multivariate splines occurred in August 1960. In my first year at the Harvard Graduate School, working as an RA for Garrett Birkhoff, I had not done too well but, nevertheless, had gotten married and so needed a better income than the RA...

We study a new simple quadrature rule based on integrating a C1 quadratic spline quasi-interpolant on a bounded interval. We give nodes and weights for uniform and non-uniform partitions. We also give error estimates for smooth functions and we compare this formula with Simpson’s rule.

Quasi-interpolation is a well-known technique to construct accurate approximants to a given set of data or a given function by means of a local approach. A quasi-interpolant is usually obtained as a linear combination of a given system of blending functions that form a convex partition of unity and possess a small local support. These properties ensure both numerical stability and local control...

In Computer Aided Geometric Design it is often needed to produce a positivity preserving curve according to the given positive data. The main focus of this work is to visualize the positive data in such a way that its display looks smooth and pleasant. A rational quadratic trigonometric spline function with three shape parameters has been developed. In the description of the rational quadratic ...

In this paper a method for interpolating planar data points by cubic G splines is presented. A spline is composed of polynomial segments that interpolate two data points, tangent directions and curvatures at these points. Necessary and sufficient, purely geometric conditions for the existence of such a polynomial interpolant are derived. The obtained results are extended to the case when the de...

In this paper we are interested in the approximation of continuous surface texture profiles defined only at discretely obtained points. A continuous representation is required in order to be able to apply filtration methods that assume uniform data spacing to practical data that in general is not uniformly spaced. By reconstructing surface profiles as natural cubic spline interpolants accuratel...