TY - GEN

T1 - Edge maps

T2 - 4th IEEE Pacific Visualization Symposium 2011, PacificVis 2011

AU - Bhatia, Harsh

AU - Jadhav, Shreeraj

AU - Bremer, Peer Timo

AU - Chen, Guoning

AU - Levine, Joshua A.

AU - Nonato, Luis Gustavo

AU - Pascucci, Valerio

PY - 2011

Y1 - 2011

N2 - Robust 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 [15] 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.

AB - Robust 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 [15] 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.

KW - Edge Maps

KW - Error Quantification

KW - Vector Fields

UR - http://www.scopus.com/inward/record.url?scp=79955685776&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79955685776&partnerID=8YFLogxK

U2 - 10.1109/PACIFICVIS.2011.5742375

DO - 10.1109/PACIFICVIS.2011.5742375

M3 - Conference contribution

AN - SCOPUS:79955685776

SN - 9781612849324

T3 - IEEE Pacific Visualization Symposium 2011, PacificVis 2011 - Proceedings

SP - 75

EP - 82

BT - IEEE Pacific Visualization Symposium 2011, PacificVis 2011 - Proceedings

Y2 - 1 March 2011 through 4 March 2011

ER -