Visualizing Robustness of Critical Points for 2D Time-Varying Vector Fields

• Published in: Computer Graphics Forum
• Main Authors: Wang, B., Rosen, P., Skraba, P., Bhatia, H., Pascucci, V.
• Other Authors: University of Utah, Salt Lake City, United States, Jozef Stefan Institute, Ljubljana, Slovenia
• Format: Article in Journal/Newspaper
• Language: unknown
• Published: Wiley 2013
• Subjects: Sea ice
• Online Access: http://hdl.handle.net/10754/600176; https://doi.org/10.1111/cgf.12109

Analyzing critical points and their temporal evolutions plays a crucial role in understanding the behavior of vector fields. A key challenge is to quantify the stability of critical points: more stable points may represent more important phenomena or vice versa. The topological notion of robustness is a tool which allows us to quantify rigorously the stability of each critical point. Intuitively, the robustness of a critical point is the minimum amount of perturbation necessary to cancel it within a local neighborhood, measured under an appropriate metric. In this paper, we introduce a new analysis and visualization framework which enables interactive exploration of robustness of critical points for both stationary and time-varying 2D vector fields. This framework allows the end-users, for the first time, to investigate how the stability of a critical point evolves over time. We show that this depends heavily on the global properties of the vector field and that structural changes can correspond to interesting behavior. We demonstrate the practicality of our theories and techniques on several datasets involving combustion and oceanic eddy simulations and obtain some key insights regarding their stable and unstable features. © 2013 The Author(s) Computer Graphics Forum © 2013 The Eurographics Association and Blackwell Publishing Ltd. We thank Jackie Chen for the combustion dataset. We also thank Mathew Maltude from the Climate, Ocean and Sea Ice Modelling program at Los Alamos National Laboratory (LANL) and the BER Office of Science UV-CDAT team for providing us the ocean datasets. We thank Amit Patel and Guoning Chen for insightful discussions. PR was supported in part by grants from DOE NETL and KAUST award KUS-C1-016-04. PS was supported by EU project TOPOSYS (FP7-ICT-318493-STREP). This work is supported in part by NSF OCI-0906379, NSF OCI-0904631, DOE/NEUP 120341, DOE/MAPD DESC000192, DOE/LLNL B597476, DOE/Codesign P01180734, and DOE/SciDAC DESC0007446.