A generalized surface subdivision scheme of arbitrary order with a tension parameter

• Presents a generalized BB-spline surface subdivision with arbitrary order kk.
• The scheme is conveniently implemented using local operations.
• It produces Ck−2Ck−2 limit surfaces with C1C1 at extraordinary vertices.
• It can define exact analytic, sweeping and revolution surfaces.
• New rules for sharp and semi-sharp features are embedded in local operations.

This article presents a generalized BB-spline surface subdivision scheme of arbitrary order with a tension parameter. We first propose a tensor-product subdivision scheme that produces ku×kvku×kv order generalized BB-spline limit surfaces. Generalized BB-spline surface is the unified and extended form of BB-splines, trigonometric BB-splines and hyperbolic BB-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 BB-spline curves. By extending a bi-order (say kk) 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 Ck−2Ck−2 continuous limit surfaces except at extraordinary points where the continuity is C1C1. Convenient and hierarchical methods are also presented for embedding sharp features and semi-sharp features on the resulting limit surfaces.