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.
Original language | English (US) |
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Pages (from-to) | 445-452 |
Number of pages | 8 |
Journal | ACM Transactions on Graphics |
Volume | 22 |
Issue number | 3 |
DOIs | |
State | Published - Jul 2003 |
Externally published | Yes |
Event | ACM SIGGRAPH 2003 - San Diego, CA, United States Duration: Jul 27 2003 → Jul 31 2003 |
Keywords
- Animation
- Hodge decomposition
- Scale-space description
- Variational approaches
- Vector fields
- Visualization
ASJC Scopus subject areas
- Computer Graphics and Computer-Aided Design