2022
Bujack, Roxana
Discussion and Visualization of Distinguished Hyperbolic Trajectories as a Generalization of Critical Points to 2D Time-dependent Flow Proceedings Article
In: 2022 Topological Data Analysis and Visualization (TopoInVis), pp. 59-69, 2022.
Abstract | Links | BibTeX | Tags: flow, Topology, Vector field, visualization
@inproceedings{9975815,
title = {Discussion and Visualization of Distinguished Hyperbolic Trajectories as a Generalization of Critical Points to 2D Time-dependent Flow},
author = {Roxana Bujack},
url = {http://www.informatik.uni-leipzig.de/~bujack/2022topoInVis.pdf},
doi = {10.1109/TopoInVis57755.2022.00013},
year = {2022},
date = {2022-01-01},
urldate = {2022-01-01},
booktitle = {2022 Topological Data Analysis and Visualization (TopoInVis)},
pages = {59-69},
abstract = {Classical vector field topology has proven to be a useful visualization technique for steady flow, but its straightforward application to time-dependent flows lacks physical meaning. Necessary requirements for physical meaningfulness include the results to be objective, i.e., independent of the frame of reference of the observer, and Lagrangian, i.e., that the generalized critical points are trajectories. We analyze whether the theoretical concept of distinguished hyperbolic trajectories provides a physically meaningful generalization to classical critical points and if the existing extraction algorithms correctly compute what has been defined mathematically. We show that both theory and algorithms constitute a significant improvement over previous methods.We further present a method to visualize a time-dependent flow field in the reference frames of distinguished trajectories. The result is easy to interpret because it makes these trajectories look like classical critical points for each instance in time, but it is meaningful because it is Lagrangian and objective.},
keywords = {flow, Topology, Vector field, visualization},
pubstate = {published},
tppubtype = {inproceedings}
}
Classical vector field topology has proven to be a useful visualization technique for steady flow, but its straightforward application to time-dependent flows lacks physical meaning. Necessary requirements for physical meaningfulness include the results to be objective, i.e., independent of the frame of reference of the observer, and Lagrangian, i.e., that the generalized critical points are trajectories. We analyze whether the theoretical concept of distinguished hyperbolic trajectories provides a physically meaningful generalization to classical critical points and if the existing extraction algorithms correctly compute what has been defined mathematically. We show that both theory and algorithms constitute a significant improvement over previous methods.We further present a method to visualize a time-dependent flow field in the reference frames of distinguished trajectories. The result is easy to interpret because it makes these trajectories look like classical critical points for each instance in time, but it is meaningful because it is Lagrangian and objective.
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1.
Bujack, Roxana
Discussion and Visualization of Distinguished Hyperbolic Trajectories as a Generalization of Critical Points to 2D Time-dependent Flow Proceedings Article
In: 2022 Topological Data Analysis and Visualization (TopoInVis), pp. 59-69, 2022.
@inproceedings{9975815,
title = {Discussion and Visualization of Distinguished Hyperbolic Trajectories as a Generalization of Critical Points to 2D Time-dependent Flow},
author = {Roxana Bujack},
url = {http://www.informatik.uni-leipzig.de/~bujack/2022topoInVis.pdf},
doi = {10.1109/TopoInVis57755.2022.00013},
year = {2022},
date = {2022-01-01},
urldate = {2022-01-01},
booktitle = {2022 Topological Data Analysis and Visualization (TopoInVis)},
pages = {59-69},
abstract = {Classical vector field topology has proven to be a useful visualization technique for steady flow, but its straightforward application to time-dependent flows lacks physical meaning. Necessary requirements for physical meaningfulness include the results to be objective, i.e., independent of the frame of reference of the observer, and Lagrangian, i.e., that the generalized critical points are trajectories. We analyze whether the theoretical concept of distinguished hyperbolic trajectories provides a physically meaningful generalization to classical critical points and if the existing extraction algorithms correctly compute what has been defined mathematically. We show that both theory and algorithms constitute a significant improvement over previous methods.We further present a method to visualize a time-dependent flow field in the reference frames of distinguished trajectories. The result is easy to interpret because it makes these trajectories look like classical critical points for each instance in time, but it is meaningful because it is Lagrangian and objective.},
keywords = {},
pubstate = {published},
tppubtype = {inproceedings}
}
Classical vector field topology has proven to be a useful visualization technique for steady flow, but its straightforward application to time-dependent flows lacks physical meaning. Necessary requirements for physical meaningfulness include the results to be objective, i.e., independent of the frame of reference of the observer, and Lagrangian, i.e., that the generalized critical points are trajectories. We analyze whether the theoretical concept of distinguished hyperbolic trajectories provides a physically meaningful generalization to classical critical points and if the existing extraction algorithms correctly compute what has been defined mathematically. We show that both theory and algorithms constitute a significant improvement over previous methods.We further present a method to visualize a time-dependent flow field in the reference frames of distinguished trajectories. The result is easy to interpret because it makes these trajectories look like classical critical points for each instance in time, but it is meaningful because it is Lagrangian and objective.