This paper deals with the shape preserving interpolation problem for visualization of 3D positive data. A required display of 3D data looks smooth and pleasant. A rational bi-cubic function involving six shape parameters is presented for this objective which is an extension of piecewise rational function in the form of cubic/quadratic involving three shape parameters. Simple data dependent cons...

Interpolation is a common technique for predicting unknown data points within the range of discrete known data points. In image processing and analysis applications, image interpolation is employed for changing image resolution but also for tasks like image rotation and other transformations. Classical image interpolation algorithms such as nearest neighbour, bilinear and bicubic interpolation ...

We present a new stability analysis for the second barycentric formula, showing that this formula is backward stable when the relevant Lebesgue constant is small.

This work deals with the problem of constructing sectional-curvature preserving (scp) C 2-continuous surfaces, which interpolate point-sets lying on planes perpendicular to a three-dimensional spine curve. The proposed method of solution employs skinning surfaces, whose skeletal lines and blending functions belong to a special family of polynomial splines of non-uniform degree, already used for...

Many kinetic models of the Boltzmann equation have a diiusive scaling that leads to the Navier-Stokes type parabolic equations as the small scaling parameter approaches zero. In practical applications, it is desirable to develop a class of numerical schemes that can work uniformly with respect to this relaxation parameter, from the rareeed kinetic regimes to the hydrodynamic diiusive regimes. A...

Kernel functions are suitable tools for scattered data interpolation and approximation. We first review basic features of kernel-based multivariate interpolation, before we turn to the construction and the characterization of positive definite kernels and their associated reproducing kernel Hilbert spaces. The optimality of the resulting kernel-based interpolation scheme is shown. Moreover, we ...