TY - GEN

T1 - Consistent approximation of local flow behavior for 2D vector fields using edge maps

AU - Jadhav, Shreeraj

AU - Bhatia, Harsh

AU - Bremer, Peer Timo

AU - Levine, Joshua A.

AU - Nonato, Luis Gustavo

AU - Pascucci, Valerio

N1 - Funding Information:
Acknowledgements This work is supported in part by the National Science Foundation awards IIS-1045032, OCI-0904631, OCI-0906379 and CCF-0702817. This work was also performed under the auspices of the U.S. Department of Energy 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. Attila Gyulassy and Philippe P. Pebay provided many useful comments and discussions. LLNL-CONF-468780.
Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 2012.

PY - 2012

Y1 - 2012

N2 - Vector fields, represented as vector values sampled on the vertices of a triangulation, are commonly used to model physical phenomena. To analyze and understand vector fields, practitioners use derived properties such as the paths of massless particles advected by the flow, called streamlines. However, currently available numerical methods for computing streamlines do not guarantee preservation of fundamental invariants such as the fact that streamlines cannot cross. The resulting inconsistencies can cause errors in the analysis, e.g., invalid topological skeletons, and thus lead to misinterpretations of the data. We propose an alternate representation for triangulated vector fields that exchanges vector values with an encoding of the transversal flow behavior of each triangle. We call this representation edge maps. This work focuses on the mathematical properties of edge maps; a companion paper discusses some of their applications[1]. Edge maps allow for a multi-resolution approximation of flow by merging adjacent streamlines into an interval based mapping. Consistency is enforced at any resolution if the merged sets maintain an order-preserving property. At the coarsest resolution, we define a notion of equivalency between edge maps, and show that there exist 23 equivalence classes describing all possible behaviors of piecewise linear flow within a triangle.

AB - Vector fields, represented as vector values sampled on the vertices of a triangulation, are commonly used to model physical phenomena. To analyze and understand vector fields, practitioners use derived properties such as the paths of massless particles advected by the flow, called streamlines. However, currently available numerical methods for computing streamlines do not guarantee preservation of fundamental invariants such as the fact that streamlines cannot cross. The resulting inconsistencies can cause errors in the analysis, e.g., invalid topological skeletons, and thus lead to misinterpretations of the data. We propose an alternate representation for triangulated vector fields that exchanges vector values with an encoding of the transversal flow behavior of each triangle. We call this representation edge maps. This work focuses on the mathematical properties of edge maps; a companion paper discusses some of their applications[1]. Edge maps allow for a multi-resolution approximation of flow by merging adjacent streamlines into an interval based mapping. Consistency is enforced at any resolution if the merged sets maintain an order-preserving property. At the coarsest resolution, we define a notion of equivalency between edge maps, and show that there exist 23 equivalence classes describing all possible behaviors of piecewise linear flow within a triangle.

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U2 - 10.1007/978-3-642-23175-9_10

DO - 10.1007/978-3-642-23175-9_10

M3 - Conference contribution

AN - SCOPUS:84864289494

SN - 9783319912738

SN - 9783540250326

SN - 9783540250760

SN - 9783540332749

SN - 9783540886051

SN - 9783642150135

SN - 9783642216077

SN - 9783642231742

SN - 9783642231742

SN - 9783642273421

SN - 9783642341403

SN - 9783642543005

T3 - Mathematics and Visualization

SP - 141

EP - 159

BT - Mathematics and Visualization

A2 - Peikert, Ronald

A2 - Fuchs, Raphael

A2 - Hauser, Helwig

A2 - Carr, Hamish

PB - Springer Heidelberg

T2 - 4th Workshop on Topology Based Methods in Data Analysis and Visualization, TopoInVis 2011

Y2 - 4 April 2011 through 6 April 2011

ER -