Multiresolution analysis for surfaces of arbitrary topological type

TLDR

Multiresolution analysis and wavelets are efficient tools for representing functions at multiple levels of detail, used in image compression, physical simulation, and numerical analysis. The authors introduce subdivision‑surface wavelets that extend representable functions and envision applications such as continuous level‑of‑detail control for graphics rendering, model compression, and faster global illumination. They construct subdivision‑surface wavelets applicable to functions on compact surfaces of arbitrary topology, demonstrated on spherical domains via shape approximation of a polyhedral model and color approximation of global terrain data. The approach enables level‑of‑detail control on spherical domains, as shown by shape approximation of a polyhedral model and color approximation of global terrain data.

Abstract

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.