32-Issue 3

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https://diglib.eg.org/handle/10.2312/181

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Browsing 32-Issue 3 by Subject "and systems"

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    Towards Multifield Scalar Topology Based on Pareto Optimality
    (The Eurographics Association and Blackwell Publishing Ltd., 2013) Huettenberger, Lars; Heine, Christian; Carr, Hamish; Scheuermann, Gerik; Garth, Christoph; B. Preim, P. Rheingans, and H. Theisel
    How can the notion of topological structures for single scalar fields be extended to multifields? In this paper we propose a definition for such structures using the concepts of Pareto optimality and Pareto dominance. Given a set of piecewise-linear, scalar functions over a common simplical complex of any dimension, our method finds regions of ''consensus'' among single fields' critical points and their connectivity relations. We show that our concepts are useful to data analysis on real-world examples originating from fluid-flow simulations; in two cases where the consensus of multiple scalar vortex predictors is of interest and in another case where one predictor is studied under different simulation parameters. We also compare the properties of our approach with current alternatives.
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    Visualizing Robustness of Critical Points for 2D Time-Varying Vector Fields
    (The Eurographics Association and Blackwell Publishing Ltd., 2013) Wang, Bei; Rosen, Paul; Skraba, Primoz; Bhatia, Harsh; Pascucci, Valerio; B. Preim, P. Rheingans, and H. Theisel
    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.