Fillet Operations with Recursive Subdivision Surfaces

Recursively subdividing polyhedral networks, often called polyhedral subdivision, has become one of the basic tools in Computer Aided Geometric Design(CAGD) for modeling complex surfaces. In this paper, we propose a set of rules for making fillet operations on polyhedral networks. The fillet operations are implemented by subdividing a polyhedral network one step with given fillet values of edges of the polyhedral network. After fillet operations, we tried two basic recursive subdivision methods Doo-Sabin and Catmull-Clark to generate surfaces. Generally, the number of edges that meet at one vertex is no restriction and the fillet values of every edge can be different. The fillet operations proposed here will strengthen the functions of Computer Graphics systems which use subdivision surfaces to model surfaces.