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Title: 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 non-trivial 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.
 [1] ;  [2] ;  [3] ;  [4] ;  [5] ;  [3]
  1. Jozef Stefan Inst. (IJS), Ljubljana (Slovenia)
  2. Univ. of South Florida, Tampa, FL (United States)
  3. Univ. of Utah, Salt Lake City, UT (United States)
  4. Univ. of Houston, TX (United States)
  5. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Publication Date:
Report Number(s):
Journal ID: ISSN 1077-2626
Grant/Contract Number:
AC52-07NA27344; AC0705ID14517
Accepted Manuscript
Journal Name:
IEEE Transactions on Visualization and Computer Graphics
Additional Journal Information:
Journal Volume: 22; Journal Issue: 6; Journal ID: ISSN 1077-2626
Research Org:
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Sponsoring Org:
USDOE; National Science Foundation (NSF)
Country of Publication:
United States
97 MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; three-dimensional displays; robustness; topology; visualization; complexity theory; electronic mail; merging; computational topology; flow visualization; vector field simplification
OSTI Identifier: