Shape-Preserving Polynomial Interpolation Scheme

The cubic polynomial interpolation schemes are presented for the shape preservation of positive, monotone and convex 2D data. A GC1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \text{GC}^{1} $$\end{document} cubic interpolant with two free parameters in Ball form is constructed. The constraints are developed on these free parameters to preserve the shapes of data. The order of approximation of the developed shape-preserving schemes is Ohi2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ O\left( {h_{i}^{2} } \right) $$\end{document}.