C2C2 rational quartic interpolation spline with local shape preserving property

We present an explicit representation of a general C2C2 rational quartic interpolation spline with three families of local shape parameters. Sufficient conditions for the proposed interpolant to preserve locally the shape of positive, monotonic, and/or convex set of data are given. The approximation order of the interpolant is O(h2)O(h2) or O(h3)O(h3).