Shape preserving C2 spline interpolation

In this paper we summarize the main results of [2] where an algorithm of shape preserving C-2 Spline interpolation for arbitrary 1-D discrete data is developed. We consider a classification of such data to separate the sections of linearity, the angles and the breaks. For the remaining data, we give a local algorithm of C-2 interpolation by generalized splines with automatic choice of parameters to retain the monotonicity and convexity properties of the data.