CONVEXITY-PRESERVING INTERPOLATORY PARAMETRIC SPLINES OF NONUNIFORM POLYNOMIAL DEGREE

In this paper we present a simple automatic algorithm for constructing C2 continuous planar parametric interpolants, which preserve the local-convexity information contained in the interpolation point set and the imposed boundary conditions. The algorithm exploits the shape-preserving capabilities of a special family of polynomial splines of non-uniform degree, introduced, for the case of functional data, in (Kaklis and Pandelis, 1990). The numerical performance of the algorithm is discussed for three data sets and various parameterizations.