C2 Positivity-Preserving Rational Cubic Ball Interpolation

A curve interpolation scheme is developed using rational cubic Ball basis functions, which involves three shape parameters. The scheme has parameters that can be used either to preserve shape of the curve or to increase its smoothness. In this paper, we discuss an interpolation problem for positive data. Sufficient conditions are derived to preserve shape of positive data, and extra features needed to modify shape of the curve when desired. The degree of smoothness attained is C-2 continuity. Comparison between our proposed scheme with existing scheme is given. Numerical results indicate that on proposed scheme works well for all tested data sets.