Square root 3 -Subdivision Schemes: Maximal Sum Rule Orders

摘要

Abstract. 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 based on a dilation M with det M=3 . This has certain advantages, for example, a slower growth for the number of control points.