Multiresolution analysis for surfaces of arbitrary topological type

Author:

Lounsbery Michael1,DeRose Tony D.1,Warren Joe1

Affiliation:

1. Univ. of Washington, Seattle

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.

Publisher

Association for Computing Machinery (ACM)

Subject

Computer Graphics and Computer-Aided Design

Reference42 articles.

1. BARTLE R.a. 1964. The Elements of Real Analysis. Wiley New York. BARTLE R.a. 1964. The Elements of Real Analysis. Wiley New York.

2. Fast wavelet transforms and numerical algorithms;BEYLKIN G.;Commun. Pure Appl. Math.,1991

3. Recursively generated B-spline surfaces on arbitrary topological meshes;CATMULL E.;Comput. Aided Des.,1978

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