Shape-preserving piecewise rational interpolation with higher order continuity

A united form of the classical Hermite interpolation and shape-preserving interpolation is presented in this paper. The presented interpolation method provides higher order continuous shape-preserving interpolation splines. The given interpolants are explicit piecewise rational expressions without solving a linear or nonlinear system of consistency equations. By setting parameter values, the interpolation curve can be generated by choosing the classical piecewise Hermite interpolation polynomials or the presented piecewise rational expressions. For monotonicity-preserving and convexity-preserving interpolation, the appropriate values of a parameter are given on each subinterval. Numerical examples indicate that the given method produces visually pleasing curves.