DMCA
Discrete Multiscale Vector Field Decomposition (2003)
Cached
Download Links
- [www-grail.usc.edu]
- [www.geometry.caltech.edu]
- [geometry.caltech.edu]
- DBLP
Other Repositories/Bibliography
| Citations: | 92 - 10 self |
BibTeX
@MISC{Tong03discretemultiscale,
author = {Yiying Tong and Santiago Lombeyda and Anil N. Hirani and Mathieu Desbrun},
title = {Discrete Multiscale Vector Field Decomposition},
year = {2003}
}
Share
 |
 |
 |
 |
||
OpenURL
Abstract
While 2D and 3D vector fields are ubiquitous in computational sciences, their use in graphics is often limited to regular grids, where computations are easily handled through finite-difference methods. In this paper, we propose a set of simple and accurate tools for the analysis of 3D discrete vector fields on arbitrary tetrahedral grids. We introduce a variational, multiscale decomposition of vector fields into three intuitive components: a divergence-free part, a curl-free part, and a harmonic part. We show how our discrete approach matches its well-known smooth analog, called the HelmotzHodge decomposition, and that the resulting computational tools have very intuitive geometric interpretation. We demonstrate the versatility of these tools in a series of applications, ranging from data visualization to fluid and deformable object simulation.
Keyphrases
discrete multiscale vector field decomposition vector field harmonic part finite-difference method divergence-free part helmotzhodge decomposition data visualization computational tool intuitive geometric interpretation discrete approach discrete vector field regular grid accurate tool well-known smooth analog intuitive component curl-free part computational science arbitrary tetrahedral grid deformable object simulation multiscale decomposition
