Polya’s Urn Model and Computer Aided Geometric Design

In this paper Polya’s urn model is used to generate blending functions for computer aided geometric design. There are over a dozen geometric properties which are currently considered to be desirable for computer aided geometric design. Curves and surfaces which use blending functions generated from Polya’s urn model are shown to share many of these geometric properties. Derivations of these geometric properties are traced back to the probabilistic interpretation of the blending functions.