Flow visualization with quantified spatial and temporal errors using edge maps

Harsh Bhatia, Shreeraj Jadhav, Peer Timo Bremer, Guoning Chen, Joshua A. Levine, Luis Gustavo Nonato, Valerio Pascucci

Research output: Contribution to journalArticlepeer-review

33 Scopus citations


Robust analysis of vector fields has been established as an important tool for deriving insights from the complex systems these fields model. Traditional analysis and visualization techniques rely primarily on computing streamlines through numerical integration. The inherent numerical errors of such approaches are usually ignored, leading to inconsistencies that cause unreliable visualizations and can ultimately prevent in-depth analysis. We propose a new representation for vector fields on surfaces that replaces numerical integration through triangles with maps from the triangle boundaries to themselves. This representation, called edge maps, permits a concise description of flow behaviors and is equivalent to computing all possible streamlines at a user defined error threshold. Independent of this error streamlines computed using edge maps are guaranteed to be consistent up to floating point precision, enabling the stable extraction of features such as the topological skeleton. Furthermore, our representation explicitly stores spatial and temporal errors which we use to produce more informative visualizations. This work describes the construction of edge maps, the error quantification, and a refinement procedure to adhere to a user defined error bound. Finally, we introduce new visualizations using the additional information provided by edge maps to indicate the uncertainty involved in computing streamlines and topological structures.

Original languageEnglish (US)
Article number6051431
Pages (from-to)1383-1396
Number of pages14
JournalIEEE Transactions on Visualization and Computer Graphics
Issue number9
StatePublished - 2012
Externally publishedYes


  • Vector fields
  • edge maps
  • error quantification

ASJC Scopus subject areas

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


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