Wavelet Multiresolution Representation of Curves and Surfaces

We develop wavelet methods for the multiresolution representation of parametric curves and surfaces. To support the representation, we construct a new family of compactly supported symmetric biorthogonal wavelets with interpolating scaling functions. The wavelets in these biorthogonal pairs have properties better suited for curves and surfaces than many commonly used lters. We also give examples of the applications of the wavelet approach: these include the derivation of compact hierarchical curve and surface representations using modiied wavelet compression , identifying smooth sections of surfaces and a subdivision-like intersection algorithm for discrete plane curves.