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Issue No. 06 - June (2016 vol. 22)
ISSN: 1077-2626
pp: 1683-1693
Primoz Skraba , Jozef Stefan Institute, Slovenia
Paul Rosen , , University of South Florida
Bei Wang , Scientific Computing and Imaging Institute, University of Utah
Guoning Chen , , University of Houston
Harsh Bhatia , Lawrence Livermore National Laboratory
Valerio Pascucci , Scientific Computing and Imaging Institute, University of Utah
ABSTRACT
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. We apply our method to synthetic and simulation datasets to demonstrate its effectiveness.
INDEX TERMS
Three-dimensional displays, Robustness, Topology, Visualization, Complexity theory, Electronic mail, Merging,Computational topology, Flow visualization, Vector field simplification, Robustness,computational topology, Flow visualization, vector field simplification, robustness
CITATION
Primoz Skraba, Paul Rosen, Bei Wang, Guoning Chen, Harsh Bhatia, Valerio Pascucci, "Critical Point Cancellation in 3D Vector Fields: Robustness and Discussion", IEEE Transactions on Visualization & Computer Graphics, vol. 22, no. , pp. 1683-1693, June 2016, doi:10.1109/TVCG.2016.2534538
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