Convexity-preserving interpolatory subdivision (Q1315804)

The authors present a subdivision algorithm for shape preserving function interpolation in \(\mathbb{R}\) and \(\mathbb{R}^ 2\). This algorithm is a useful and flexible tool for curve and surface generation in computer aided geometric design (CAGD). Complete demonstrations of each case are made. The method is based on iterative knot insertion and guarantees preservation of convexity. The paper is richly illustrated. A simplified algorithm useful on the construction of surfaces is also presented. To illustrate the behaviour of the method to fit data with shape preservation the authors present two numerical examples with corresponding figures.