Positivity-preserving C2 rational cubic spline interpolation

Abstract

This work addresses the shape preserving interpolation problem for visualization of positive data. A piecewise rational function in cubic/quadratic form involving three shape parameters is presented. Simple data dependent conditions for a single shape parameter are derived to preserve the inherited shape feature (positivity) of data. The remaining two shape parameters are left free for the designer to modify the shape of positive curves as per industrial needs. The interpolant is not only C 2 , local, computationally economical, but it is also a visually pleasant and smooth in comparison with existing schemes. Several numerical examples are supplied to illustrate the proposed interpolant.