Abstract
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. © 2012 IEEE.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 1383-1396 |
| Number of pages | 14 |
| Journal | IEEE Transactions on Visualization and Computer Graphics |
| Volume | 18 |
| Issue number | 9 |
| DOIs | |
| State | Published - Sep 2012 |
| Externally published | Yes |
Bibliographical note
KAUST Repository Item: Exported on 2020-10-01Acknowledged KAUST grant number(s): KUS-C1-016-04
Acknowledgements: This work is supported in part by the National Science Foundation awards IIS-1045032, OCI-0904631, OCI-0906379, and CCF-0702817, and by King Abdullah University of Science and Technology (KAUST) Award No. KUS-C1-016-04. This work was also performed under the auspices of the US Department of Energy (DOE) by the University of Utah under contracts DE-SC0001922, DE-AC52-07NA27344, and DE-FC02-06ER25781, and Lawrence Livermore National Laboratory (LLNL) under contract DE-AC52-07NA27344. The authors are grateful to Jackie Chen for the data set from Fig. 13, Robert S. Laramee for the combustion chamber data set from Fig. 17, and Paul Miller, William Cabot, and Andrew Cook for the bubbles data set from Fig. 16. We also thank Mathew Maltude from the Climate, Ocean and Sea Ice Modelling program at Los Alamos National Laboratory (LANL) and the BER Office of Science UV-CDAT team for providing us access to the ocean data from Figs. 22 and 23. Attila Gyulassy and Philippe P. Pebay provided many useful comments and discussions. LLNL-JRNL-485511.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.