Multiresolution analysis and wavelets provide useful and efficient tools for representing functions at multiple levels of detail. Wavelet representations have been used in a broad range of applications, including image compression, physical simulation, and numerical analysis. In this article, we present a new class of wavelets, based on subdivision surfaces, that radically extends the class of representable functions. Whereas previous two-dimensional methods were restricted to functions difined on R 2 , the subdivision wavelets developed here may be applied to functions defined on compact surfaces of arbitrary topological type. We envision many applications of this work, including continuous level-of-detail control for graphics rendering, compression of geometric models, and acceleration of global illumination algorithms. Level-of-detail control for spherical domains is illustrated using two examples: shape approximation of a polyhedral model, and color approximation of global terrain data.

In computer graphics and geometric modeling, shapes are often represented by triangular meshes.With the advent of laser scanning systems, meshes of extreme complexity are rapidly becoming commonplace.Such meshes are notoriously expensive to store, transmit, render, and are awkward to edit.Multiresolution analysis offers a simple, unified, and theoretically sound approach to dealing with these problems.Lounsbery et al. have recently developed a technique for creating multiresolution representations for a restricted class of meshes with subdivision connectivity.Unfortunately, meshes encountered in practice typically do not meet this requirement.In this paper we present a method for overcoming the subdivision connectivity restriction, meaning that completely arbitrary meshes can now be converted to multiresolution form.The method is based on the approximation of an arbitrary initial mesh M by a mesh M J that has subdivision connectivity and is guaranteed to be within a specified tolerance.The key ingredient of our algorithm is the construction of a parametrization of M over a simple domain.We expect this parametrization to be of use in other contexts, such as texture mapping or the approximation of complex meshes by NURBS patches.