Critical Point Cancellation in 3D Vector Fields: Robustness and Discussion
Vector field topology has been successfully applied to represent the structure of steady vector fields. Critical points, one of the essential components of vector field topology, play an important role in describing the complexity of the extracted structure. Simplifying vector fields via critical point cancellation has practical merit for interpreting the behaviors of complex vector fields such as turbulence. However, there is no effective technique that allows direct cancellation of critical points in 3D. This work fills this gap and introduces the first framework to directly cancel pairs or groups of 3D critical points in a hierarchical manner with a guaranteed minimum amount of perturbation based on their robustness, a quantitative measure of their stability. In addition, our framework does not require the extraction of the entire 3D topology, which contains nontrivial separation structures, and thus is computationally effective. Furthermore, our algorithm can remove critical points in any subregion of the domain whose degree is zero and handle complex boundary configurations, making it capable of addressing challenging scenarios that may not be resolved otherwise. Here, we apply our method to synthetic and simulation datasets to demonstrate its effectiveness.
 Authors:

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 Jozef Stefan Inst. (IJS), Ljubljana (Slovenia)
 Univ. of South Florida, Tampa, FL (United States)
 Univ. of Utah, Salt Lake City, UT (United States)
 Univ. of Houston, TX (United States)
 Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
 Publication Date:
 Report Number(s):
 LLNLJRNL733787
Journal ID: ISSN 10772626
 Grant/Contract Number:
 AC5207NA27344; AC0705ID14517
 Type:
 Accepted Manuscript
 Journal Name:
 IEEE Transactions on Visualization and Computer Graphics
 Additional Journal Information:
 Journal Volume: 22; Journal Issue: 6; Journal ID: ISSN 10772626
 Publisher:
 IEEE
 Research Org:
 Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
 Sponsoring Org:
 USDOE; National Science Foundation (NSF)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 97 MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; threedimensional displays; robustness; topology; visualization; complexity theory; electronic mail; merging; computational topology; flow visualization; vector field simplification
 OSTI Identifier:
 1416501
Skraba, Primoz, Rosen, Paul, Wang, Bei, Chen, Guoning, Bhatia, Harsh, and Pascucci, Valerio. Critical Point Cancellation in 3D Vector Fields: Robustness and Discussion. United States: N. p.,
Web. doi:10.1109/TVCG.2016.2534538.
Skraba, Primoz, Rosen, Paul, Wang, Bei, Chen, Guoning, Bhatia, Harsh, & Pascucci, Valerio. Critical Point Cancellation in 3D Vector Fields: Robustness and Discussion. United States. doi:10.1109/TVCG.2016.2534538.
Skraba, Primoz, Rosen, Paul, Wang, Bei, Chen, Guoning, Bhatia, Harsh, and Pascucci, Valerio. 2016.
"Critical Point Cancellation in 3D Vector Fields: Robustness and Discussion". United States.
doi:10.1109/TVCG.2016.2534538. https://www.osti.gov/servlets/purl/1416501.
@article{osti_1416501,
title = {Critical Point Cancellation in 3D Vector Fields: Robustness and Discussion},
author = {Skraba, Primoz and Rosen, Paul and Wang, Bei and Chen, Guoning and Bhatia, Harsh and Pascucci, Valerio},
abstractNote = {Vector field topology has been successfully applied to represent the structure of steady vector fields. Critical points, one of the essential components of vector field topology, play an important role in describing the complexity of the extracted structure. Simplifying vector fields via critical point cancellation has practical merit for interpreting the behaviors of complex vector fields such as turbulence. However, there is no effective technique that allows direct cancellation of critical points in 3D. This work fills this gap and introduces the first framework to directly cancel pairs or groups of 3D critical points in a hierarchical manner with a guaranteed minimum amount of perturbation based on their robustness, a quantitative measure of their stability. In addition, our framework does not require the extraction of the entire 3D topology, which contains nontrivial separation structures, and thus is computationally effective. Furthermore, our algorithm can remove critical points in any subregion of the domain whose degree is zero and handle complex boundary configurations, making it capable of addressing challenging scenarios that may not be resolved otherwise. Here, we apply our method to synthetic and simulation datasets to demonstrate its effectiveness.},
doi = {10.1109/TVCG.2016.2534538},
journal = {IEEE Transactions on Visualization and Computer Graphics},
number = 6,
volume = 22,
place = {United States},
year = {2016},
month = {2}
}