Discrete multiscale vector field decomposition

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

Research output: Chapter in Book/Report/Conference proceedingConference contribution


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 Helmotz-Hodge 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)
Title of host publicationACM SIGGRAPH 2003 Papers, SIGGRAPH '03
Number of pages8
StatePublished - 2003
Externally publishedYes
EventACM SIGGRAPH 2003 Papers, SIGGRAPH '03 - San Diego, CA, United States
Duration: Jul 27 2003Jul 31 2003

Publication series

NameACM SIGGRAPH 2003 Papers, SIGGRAPH '03


OtherACM SIGGRAPH 2003 Papers, SIGGRAPH '03
Country/TerritoryUnited States
CitySan Diego, CA


  • Hodge decomposition
  • animation
  • scale-space description
  • variational approaches
  • vector fields
  • visualization

ASJC Scopus subject areas

  • Computer Graphics and Computer-Aided Design
  • Computer Vision and Pattern Recognition
  • Software


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