This article presents a generalized B -spline surface subdivision scheme of arbitrary order with a tension parameter. We first propose a tensor-product subdivision scheme that produces k u × k v order generalized B -spline limit surfaces. Generalized B -spline surface is the unified and extended form of B -splines, trigonometric B -splines and hyperbolic B -splines (Fang et al. 2010). The tensor product subdivision scheme can be used to generate various surfaces of revolution, including those generated by classical analytic curves that can be exactly represented by generalized B -spline curves. By extending a bi-order (say k ) tensor-product scheme to meshes of arbitrary topology, we further propose a generalized surface subdivision scheme with a tension parameter. Several well-known subdivision schemes, including Doo–Sabin subdivision, Catmull–Clark subdivision, and two other subdivision schemes proposed by Morin et al. (2001) and Stam (2001), become special cases of the generalized subdivision scheme. The tension parameter can be used to adjust the shape of subdivision surfaces. The scheme produces higher order C k − 2 continuous limit surfaces except at extraordinary points where the continuity is C 1 . Convenient and hierarchical methods are also presented for embedding sharp features and semi-sharp features on the resulting limit surfaces. 
A generalized surface subdivision scheme of arbitrary order with a tension parameter