Spline subdivision schemes for compact sets with metric averages

Abstract

To define spline subdivision schemes for general compact sets, we use the representation of spline subdivision schemes in terms of repeated averages, and replace the usual average (convex combination) by a binary averaging operation between two compact sets, introduced in [1] and termed here the "metric average." These schemes are shown to converge in the Hausdorff metric, and to provide O(h) approximation.