Shape Preserving Data Interpolation Using Rational Cubic Ball Functions

Abstract

A smooth curve interpolation scheme for positive, monotone, and convex data is developed. This scheme uses rational cubic Ball representation with four shape parameters in its description. Conditions of two shape parameters are derived in such a way that they preserve the shape of the data, whereas the other two parameters remain free to enable the user to modify the shape of the curve. The degree of smoothness is $C^1$. The outputs from a number of numerical experiments are presented.