Shape Preserving Rational Bi-cubic Function for Positive Data

In this paper, an attempt has been made to construct a shape preserving rational bi-cubic interpolant (cubic/quadratic) with twelve free parameters to depict a more pleasant and smooth display of positive surface through positive data. Simple data dependent constraints are derived for four free parameters to preserve the positivity of data while the remaining eight are left free for designer’s choice to refine the positive surface as desired. The developed scheme is C, simple, local, computationally economical and time saving as compared to exis ting schemes. Numerical examples are provided to demonstrate that the proposed scheme is interactive and smooth. 2000 MR subject classification: 65D05 • 65D07 • 65D017 • 65D018 • 65U05 • 65U07