C¹ convexity-preserving piecewise variable degree rational interpolation spline

Abstract

An explicit expression of a C¹ piecewise variable degree rational interpolation spline is developed, which produces a convex (concave) interpolant to given convex (concave) data directly. The interpolant contains two local shape parameters which serves as local tension factors. Convergence analysis shows that the interpolant has O(h²) or O(h³) approximation order.