Error bounds for a convexity-preserving interpolation and its limit function

Convexity - Preserving Scattered Data Interpolation 33 2 . 3 Convexity Conditions

This study deals with constructing a convexity-preserving bivariate C interpolants to scattered data whenever the original data are convex. Sufficient conditions on lower bound of Bézier points are derived in order to ensure that surfaces comprising cubic Bézier triangular patches are always convex and satisfy C continuity conditions. Initial gradients at the data sites are estimated and then m...

On Convexity Preserving C1 Hermite Spline Interpolation

The aim of this paper is to present a general approach to the problem of shape preserving interpolation. The problem of convexity preserving interpolation using C Hermite splines with one free generating function is considered.

Convexity-preserving Interpolation of Scattered Data

We describe a detailed computational procedure which, given data values at arbitrarily distributed points in the plane, determines if the data are convex and, if so, constructs a smooth convex surface that interpolates the data. The method consists of constructing a triangulation of the nodes (data abscissae) for which the triangle-based piecewise linear interpolant is convex, computing a set o...

Error bounds for bivariate piecewise hermite interpolation

Error bounds for anisotropic RBF interpolation

We present error bounds for the interpolation with anisotropically transformed radial basis functions for both function and its partial derivatives. The bounds rely on a growth function and do not contain unknown constants. For polyharmonic basic functions in R we show that the anisotropic estimates predict a significant improvement of the approximation error if both the target function and the...