Eurovis: Eurographics Conference on Visualization

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https://diglib.eg.org/handle/10.2312/392

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Browsing Eurovis: Eurographics Conference on Visualization by Subject "and systems"

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    Stable Morse Decompositions for Piecewise Constant Vector Fields on Surfaces
    (The Eurographics Association and Blackwell Publishing Ltd., 2011) Szymczak, Andrzej; H. Hauser, H. Pfister, and J. J. van Wijk
    Numerical simulations and experimental observations are inherently imprecise. Therefore, most vector fields of interest in scientific visualization are known only up to an error. In such cases, some topological features, especially those not stable enough, may be artifacts of the imprecision of the input. This paper introduces a technique to compute topological features of user-prescribed stability with respect to perturbation of the input vector field. In order to make our approach simple and efficient, we develop our algorithms for the case of piecewise constant (PC) vector fields. Our approach is based on a super-transition graph, a common graph representation of all PC vector fields whose vector value in a mesh triangle is contained in a convex set of vectors associated with that triangle. The graph is used to compute a Morse decomposition that is coarse enough to be correct for all vector fields satisfying the constraint. Apart from computing stable Morse decompositions, our technique can also be used to estimate the stability of Morse sets with respect to perturbation of the vector field or to compute topological features of continuous vector fields using the PC framework.
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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.