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.
Bujack, Roxana; Bresciani, Etienne; Waters, Jiajia; Schroeder, Will
Topological Segmentation of 2D Vector Fields Journal Article
In: 2022, (LEVIA'22. Leipzig, 06.04.2022 - 07.04.2022).
Abstract | Links | BibTeX | Tags: segmentation, Topology, Vector field
@article{bujack2022topological,
title = {Topological Segmentation of 2D Vector Fields},
author = {Roxana Bujack and Etienne Bresciani and Jiajia Waters and Will Schroeder},
url = {http://www.informatik.uni-leipzig.de/~bujack/2022Levia.pdf},
doi = {https://doi.org/10.36730/2022.1.levia.5},
year = {2022},
date = {2022-01-01},
urldate = {2022-01-01},
abstract = {ector field topology has a long tradition as a visualization tool. The separatrices segment the domain visually into canonical regions in which all streamlines behave qualitatively the same. But application scientists often need more than just a nice image for their data analysis, and, to best of our knowledge, so far no workflow has been proposed to extract the critical points, the associated separatrices, and then provide the induced segmentation on the data level. We present a workflow that computes the segmentation of the domain of a 2D vector field based on its separatrices. We show how it can be used for the extraction of quantitative information about each segment in two applications: groundwater flow and heat exchange.},
note = {LEVIA'22. Leipzig, 06.04.2022 - 07.04.2022},
keywords = {segmentation, Topology, Vector field},
pubstate = {published},
tppubtype = {article}
}
ector field topology has a long tradition as a visualization tool. The separatrices segment the domain visually into canonical regions in which all streamlines behave qualitatively the same. But application scientists often need more than just a nice image for their data analysis, and, to best of our knowledge, so far no workflow has been proposed to extract the critical points, the associated separatrices, and then provide the induced segmentation on the data level. We present a workflow that computes the segmentation of the domain of a 2D vector field based on its separatrices. We show how it can be used for the extraction of quantitative information about each segment in two applications: groundwater flow and heat exchange.
2021
Bujack, Roxana; Tsai, Karen; Morley, Steven; Bresciani, Etienne
Open source vector field topology Journal Article
In: SoftwareX, vol. 15, pp. 100787, 2021, ISSN: 2352-7110.
Abstract | Links | BibTeX | Tags: Critical point, Separatrix, Topology, Vector field
@article{BUJACK2021100787,
title = {Open source vector field topology},
author = {Roxana Bujack and Karen Tsai and Steven Morley and Etienne Bresciani},
url = {http://www.informatik.uni-leipzig.de/~bujack/2021SoftwareX.pdf},
doi = {https://doi.org/10.1016/j.softx.2021.100787},
issn = {2352-7110},
year = {2021},
date = {2021-01-01},
urldate = {2021-01-01},
journal = {SoftwareX},
volume = {15},
pages = {100787},
abstract = {A myriad of physical phenomena, such as fluid flows, magnetic fields, and population dynamics are described by vector fields. More often than not, vector fields are complex and their analysis is challenging. Vector field topology is a powerful analysis technique that consists in identifying the most essential structure of a vector field. Its topological features include critical points and separatrices, which segment the domain into regions of coherent flow behavior, provide a sparse and semantically meaningful representation of the underlying data. However, a broad adoption of this formidable technique has been hampered by the lack of open source software implementing it. The Visualization Toolkit (VTK) now contains the filter vtkVectorFieldTopology that extracts the topological skeleton of 2D and 3D vector fields. This paper describes our implementation and demonstrates its broad applicability with two real-world examples from hydrology and space physics.},
keywords = {Critical point, Separatrix, Topology, Vector field},
pubstate = {published},
tppubtype = {article}
}
A myriad of physical phenomena, such as fluid flows, magnetic fields, and population dynamics are described by vector fields. More often than not, vector fields are complex and their analysis is challenging. Vector field topology is a powerful analysis technique that consists in identifying the most essential structure of a vector field. Its topological features include critical points and separatrices, which segment the domain into regions of coherent flow behavior, provide a sparse and semantically meaningful representation of the underlying data. However, a broad adoption of this formidable technique has been hampered by the lack of open source software implementing it. The Visualization Toolkit (VTK) now contains the filter vtkVectorFieldTopology that extracts the topological skeleton of 2D and 3D vector fields. This paper describes our implementation and demonstrates its broad applicability with two real-world examples from hydrology and space physics.
: . .
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.
2.
Bujack, Roxana; Bresciani, Etienne; Waters, Jiajia; Schroeder, Will
Topological Segmentation of 2D Vector Fields Journal Article
In: 2022, (LEVIA'22. Leipzig, 06.04.2022 - 07.04.2022).
@article{bujack2022topological,
title = {Topological Segmentation of 2D Vector Fields},
author = {Roxana Bujack and Etienne Bresciani and Jiajia Waters and Will Schroeder},
url = {http://www.informatik.uni-leipzig.de/~bujack/2022Levia.pdf},
doi = {https://doi.org/10.36730/2022.1.levia.5},
year = {2022},
date = {2022-01-01},
urldate = {2022-01-01},
abstract = {ector field topology has a long tradition as a visualization tool. The separatrices segment the domain visually into canonical regions in which all streamlines behave qualitatively the same. But application scientists often need more than just a nice image for their data analysis, and, to best of our knowledge, so far no workflow has been proposed to extract the critical points, the associated separatrices, and then provide the induced segmentation on the data level. We present a workflow that computes the segmentation of the domain of a 2D vector field based on its separatrices. We show how it can be used for the extraction of quantitative information about each segment in two applications: groundwater flow and heat exchange.},
note = {LEVIA'22. Leipzig, 06.04.2022 - 07.04.2022},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
ector field topology has a long tradition as a visualization tool. The separatrices segment the domain visually into canonical regions in which all streamlines behave qualitatively the same. But application scientists often need more than just a nice image for their data analysis, and, to best of our knowledge, so far no workflow has been proposed to extract the critical points, the associated separatrices, and then provide the induced segmentation on the data level. We present a workflow that computes the segmentation of the domain of a 2D vector field based on its separatrices. We show how it can be used for the extraction of quantitative information about each segment in two applications: groundwater flow and heat exchange.
3.
Bujack, Roxana; Tsai, Karen; Morley, Steven; Bresciani, Etienne
Open source vector field topology Journal Article
In: SoftwareX, vol. 15, pp. 100787, 2021, ISSN: 2352-7110.
@article{BUJACK2021100787,
title = {Open source vector field topology},
author = {Roxana Bujack and Karen Tsai and Steven Morley and Etienne Bresciani},
url = {http://www.informatik.uni-leipzig.de/~bujack/2021SoftwareX.pdf},
doi = {https://doi.org/10.1016/j.softx.2021.100787},
issn = {2352-7110},
year = {2021},
date = {2021-01-01},
urldate = {2021-01-01},
journal = {SoftwareX},
volume = {15},
pages = {100787},
abstract = {A myriad of physical phenomena, such as fluid flows, magnetic fields, and population dynamics are described by vector fields. More often than not, vector fields are complex and their analysis is challenging. Vector field topology is a powerful analysis technique that consists in identifying the most essential structure of a vector field. Its topological features include critical points and separatrices, which segment the domain into regions of coherent flow behavior, provide a sparse and semantically meaningful representation of the underlying data. However, a broad adoption of this formidable technique has been hampered by the lack of open source software implementing it. The Visualization Toolkit (VTK) now contains the filter vtkVectorFieldTopology that extracts the topological skeleton of 2D and 3D vector fields. This paper describes our implementation and demonstrates its broad applicability with two real-world examples from hydrology and space physics.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
A myriad of physical phenomena, such as fluid flows, magnetic fields, and population dynamics are described by vector fields. More often than not, vector fields are complex and their analysis is challenging. Vector field topology is a powerful analysis technique that consists in identifying the most essential structure of a vector field. Its topological features include critical points and separatrices, which segment the domain into regions of coherent flow behavior, provide a sparse and semantically meaningful representation of the underlying data. However, a broad adoption of this formidable technique has been hampered by the lack of open source software implementing it. The Visualization Toolkit (VTK) now contains the filter vtkVectorFieldTopology that extracts the topological skeleton of 2D and 3D vector fields. This paper describes our implementation and demonstrates its broad applicability with two real-world examples from hydrology and space physics.