Shape Preserving C2 Rational Cubic Spline Interpolation

Abstract

In this study a piecewise rational function  with cubic numerator and linear denominator involving two shape parameters has been developed to address the problem of constructing positivity preserving curve through positive data, monotonicity preserving curve through monotone data and convexity preserving curve through convex data within one mathematical model. A simple data dependent condition for a single shape parameter has been derived to preserve the positivity, monotonicity and convexity of respectively positive, monotone and convex data. The remaining shape parameter is left free for the user to modify the shape of positive, monotone and convex curves when needs arise. We extended the result of [1] to a piecewise rational cubic function.