State of the Art in Time‐Dependent Flow Topology: Interpreting Physical Meaningfulness Through Mathematical Properties
State of the Art in Time‐Dependent Flow Topology: Interpreting Physical Meaningfulness Through Mathematical Properties
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DOI：
10.1111/cgf.14037
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发表时间：
2020-06
影响因子：
2.5
通讯作者：
R. Bujack;Lin Yan;I. Hotz;C. Garth;Bei Wang
中科院分区：
文献类型：
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作者：
R. Bujack;Lin Yan;I. Hotz;C. Garth;Bei Wang
我们提出了一份关于时间相关流拓扑的最新报告。我们调查了可视化领域的代表性论文，并提供了一种现有方法的分类，这些方法将流拓扑从时间无关的设置推广到时间相关的设置。方法分为四类：稳定拓扑跟踪、参考帧自适应、路径分类或聚类、临界点泛化。我们的独特贡献包括引入一组理想的数学性质来解释时间依赖流可视化的物理意义，推断与选择性研究论文相关的数学性质，并利用这些性质进行分类。在现有文献中确定的五个最重要的性质包括与稳定情况的符合，区域内划分的归纳，拉格朗日不变性，客观性和伽利略不变性。
We present a state‐of‐the‐art report on time‐dependent flow topology. We survey representative papers in visualization and provide a taxonomy of existing approaches that generalize flow topology from time‐independent to time‐dependent settings. The approaches are classified based upon four categories: tracking of steady topology, reference frame adaption, pathline classification or clustering, and generalization of critical points. Our unique contributions include introducing a set of desirable mathematical properties to interpret physical meaningfulness for time‐dependent flow visualization, inferring mathematical properties associated with selective research papers, and utilizing such properties for classification. The five most important properties identified in the existing literature include coincidence with the steady case, induction of a partition within the domain, Lagrangian invariance, objectivity, and Galilean invariance.