Modeling with subdivision surfaces

Subdivision surfaces are an established modeling tool in computer graphics and computer-aided design. While the theoretical foundations of subdivision surfaces are well studied, the correlation between a control mesh and its subdivided limit surface still has some open-ended questions: Which topology should a control mesh have? Where should control vertices be placed? A modeler - human or software - is confronted with these questions and has to answer them. In this paper we analyze four characteristic situations. Each one consists of an analytical reference surface S and several variants of control meshes Ci. In order to concentrate on the topology of the control meshes, the geometrical positions of their control vertices have been determined and optimized automatically. As a result we identified the best topology of all Ci to represent the given surface S. Based on these results we derived heuristics to model with subdivision surfaces. These heuristics are beneficial for all modelers.