Offset Approximation Algorithm for Subdivision Surfaces

Based on Catmull-Clark Subdivision scheme, a valid algorithm of offset approximation for Subdivision Surface is proposed. It can overcome the defect that previous approaches treat offset surface only as parametric surface, functional surface and algebraic surface. In this paper, by making the limit positions corresponding to new control vertices of offset surface are at their exact offset positions, we convert offset approximation problem into solving linear equation system. We also present a method for error control of offset approximation, meanwhile, how to compute maximum offset distance without self-intersection is discussed. The examples in the paper demonstrate explicitness and efficiency of our method.