Levine, Joshua A.
Nonato, Luis Gustavo
KAUST Grant NumberKUS-CI-016-04
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AbstractRobust analysis of vector fields has been established as an important tool for deriving insights from the complex systems these fields model. Many analysis techniques rely on computing streamlines, a task often hampered by numerical instabilities. Approaches that ignore the resulting errors can lead to inconsistencies that may produce unreliable visualizations and ultimately prevent in-depth analysis. We propose a new representation for vector fields on surfaces that replaces numerical integration through triangles with linear maps defined on its boundary. This representation, called edge maps, is equivalent to computing all possible streamlines at a user defined error threshold. In spite of this error, all the streamlines computed using edge maps will be pairwise disjoint. Furthermore, our representation stores the error explicitly, and thus can be used to produce more informative visualizations. Given a piecewise-linear interpolated vector field, a recent result  shows that there are only 23 possible map classes for a triangle, permitting a concise description of flow behaviors. This work describes the details of computing edge maps, provides techniques to quantify and refine edge map error, and gives qualitative and visual comparisons to more traditional techniques. © 2011 IEEE.
CitationBhatia H, Jadhav S, Bremer P-T, Chen G, Levine JA, et al. (2011) Edge maps: Representing flow with bounded error. 2011 IEEE Pacific Visualization Symposium. Available: http://dx.doi.org/10.1109/pacificvis.2011.5742375.
SponsorsThis work is supported in part by the National Science Foundation awards IIS-I045032, OCI-0904631, OCI-0906379 and CCF-0702817, and by King Abdullah University of Science and Technology (KAUST) Award No. KUS-CI-016-04. This work was also performed under the auspices of the U.S. Department of Energy by the University of Utah under contracts DE-SCOOOI922, DE-AC52-07NA27344, and DE-FC02-06ER25781, and Lawrence Livermore National Laboratory (LLNL) under contract DE-AC52-07NA27344. We are grateful to Jackie Chen for the dataset from Figure 11, Robert S. Laramee for the diesel engine dataset from Figure 13, and Paul Miller, William Cabot, and Andrew Cook for the bubbles dataset from Figure 14. Attila Gyulassy and Philippe P. Pebay provided many useful comments and discussions. LLNL-PROC-463631.