CONVEXITY PRESERVING INTERPOLATORY SUBDIVISION SCHEMES

We construct local subdivision schemes that interpolate functional uni variate data and that preserve convexity. The resulting limit function of these schemes is continuous and convex for arbitrary convex data. Moreover this class of schemes is restricted to a subdivision scheme t hat generates a limit function that is convex and continuously differe ntiable for strictly convex date. The approximation order of this sche me is four. Some generalizations, such as tension control and piecewis e convexity preservation, are briefly discussed.