Multiresolution constraints for designing subdivision surfaces via local smoothing

Subdivision surfaces provide an efficient means of representing surfaces of arbitrary topological type. In recent years, multiresolution modeling with variational smoothing has played an important role in controlling such surfaces. This paper presents a new model of multiresolution constraints that can be applied to subdivision surfaces. The advantage of this model is that different geometric constraints can be imposed on the surfaces at different resolution levels. The model employs the wavelet-based framework of Lounsbery, et al. (1997), to represent the subdivision surfaces in a hierarchical fashion. In the proposed framework, local smooth filtering is used to obtain the optimal surface shape at each resolution level. Controlling the number of iterations for the local smoothing operations allows us to modify the smoothness of the subdivision surfaces even when the same set of constraints is given. Several design examples are included to demonstrate the capability of this model