Discrete multiscale vector field decomposition

Yiying Tong, Santiago Lombeyda, Anil N. Hirani, Mathieu Desbrun

Research output: Contribution to journalConference articlepeer-review


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 languageEnglish (US)
Pages (from-to)445-452
Number of pages8
JournalACM Transactions on Graphics
Issue number3
StatePublished - Jul 2003
Externally publishedYes
EventACM SIGGRAPH 2003 - San Diego, CA, United States
Duration: Jul 27 2003Jul 31 2003


  • Animation
  • Hodge decomposition
  • Scale-space description
  • Variational approaches
  • Vector fields
  • Visualization

ASJC Scopus subject areas

  • Computer Graphics and Computer-Aided Design

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