A Unified Framework for Digital Geometry Processing
Kun Zhou · Chinese Journal of Computers · 2002
With the increasing use of 3D geometry in industry, algorithms processing geometric signals become more and more important. Despite the promising recent progress of digital geometry processing, it still lacks a unified solution to address all issues of geometry like digital image processing. With solid theoretic foundation, the framework for digital signal processing over arbitrary meshes presented in this paper meets this requirement. The key idea of the framework is to construct global spherical (or planar) parameterizations for meshes, transform all attributes of meshes into spherical (or planar) signals and use spherical (or planar) orthonormal analysis tool to process these signals. With the framework, all image processing techniques can be extended to 3D meshes. This paper also describes how to perform signal filtering, multi resolution editing and geometry compression and gives some experimental results.