A unified subdivision scheme for polygonal modeling

Subdivision rules have traditionally been designed to generate smooth surfa ces from polygonal meshes. In this paper we propose to employ subdivision r ules as a polygonal modeling tool, specifically to add additional level of detail to meshes. However, existing subdivision schemes have several undesi rable properties making them ill suited for polygonal modeling. In this pap er we propose a general set of subdivision rules which provides users with more control over the subdivision process. Most existing subdivision scheme s are special cases. In particular we provide subdivision rules which blend approximating spline based schemes with interpolatory ones. Also, we gener alize subdivision to allow any number of refinements to be performed in a s ingle step.