Domain Decomposition for Multiresolution Analysis

Abstract

This paper describes a method for converting an arbitrary mesh with irregular connectivity to a semi-regular multiresolution representation. A shape image encoding geometric and differential properties of the input model is computed. Standard image processing operations lead to an initial decomposition of the model that conforms to its salient features. A triangulation step performed on the resulting partition in image space, followed by resampling and multiresolution analysis in object space, complete the procedure. The conversion technique is automatic, takes into account surface properties for deriving a base domain, and is computationally efficient as the bulk of the processing is carried out in image space. Besides domain decomposition, our image-based approach to handling geometry may be used in the context of related applications, including model simplification, remeshing, and wireframe generation.