MULTIRESOLUTION ANALYSIS FOR SURFACES OF ARBITRARY TOPOLOGICAL TYPE

Multiresolution analysis and wavelets provide useful and efficient too ls for representing functions at multiple levels of detail. Wavelet re presentations have been used in a broad range of applications, includi ng 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 function s defined on R(2), the subdivision wavelets developed here may be appl ied 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 geomet ric models, and acceleration of global illumination algorithms. Level- of-detail control for spherical domains is illustrated using two examp les: shape approximation of a polyhedral model, and color approximatio n of global terrain data.