C2 Rational Cubic Ball Spline Functions

This study deals with the problems of shape preserving curves through positive curves through positive, constrained and convex data. The alternative curve interpolations are developed using a piecewise C2 rational cubic Ball spline function with three shape parameters in each subinterval. Simple data dependent conditions are derived for a single shape parameters to preserve the shape of data while the remaining two shape parameters are free used to modify the positive, constrained and convex curves as desired. Graphical results through different numerical examples are presented to show the effectiveness of the proposed schemes.