A non-stationary Catmull–Clark subdivision scheme with shape control

Abstract

In this paper, a non-stationary Catmull–Clark subdivision scheme is presented which enables the user to change the shape of the surface obtained from a given initial mesh. Such a non-stationary subdivision scheme is constructed by taking tensor product of a properly modified cubic exponential B-spline scheme in the regular mesh and giving suitable rules in the neighborhoods of extraordinary points. For this new scheme, we show that it can generate tangent plane continuous surfaces. Besides, we propose a generalization, which could locally control the limit surface for the purpose of generating more flexible surfaces and providing some features control. Some examples are given to show the performance of the new schemes.