Sqrt(3)-Subdivision Schemes: Maximal Sum Rule Orders

Subdivision with finitely supported masks is an efficient method to create discrete multiscale representations of smooth surfaces for CAGD applications. Recently a new subdivision scheme for triangular meshes, called sqrt(3)-subdivision, has been studied. In comparison to dyadic subdivision which is based on the dilation matrix 2I, sqrt(3)-subdivision is basedon a dilation M with det M = 3. This has certain advantages, for example a slower growth for the number of control points.