Advected Tangent Curves: A General Scheme for Characteristic Curves of Flow Fields
Advected Tangent Curves: A General Scheme for Characteristic Curves of Flow Fields
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平流正切曲线：流场特征曲线的一般方案
DOI：
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发表时间：
2012
期刊：
影响因子：
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通讯作者：
H. Theisel
中科院分区：
文献类型：
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作者：
T. Weinkauf;H. Hege;H. Theisel
我们提出了第一个通用的计划来描述所有四种类型的流场的特征曲线-流，路径，条纹，和时间线-作为切线曲线的派生矢量场。因此，所有这些线可以通过一个简单的自治ODE系统的集成。我们的方法借鉴了最近推出的切线曲线描述的条纹线的主要思想。我们提供了第一个描述的时间线作为切线曲线的派生向量场，以前只能构造在一个几何的方式。此外，我们的计划产生了新类型的曲线。特别是，我们引入平流流线作为时间线隐喻的无参数变体。通过我们对特征曲线的新颖数学描述，大量的特征提取和分析工具变得可用于所有类型的特征曲线，而这些特征曲线以前仅适用于流线和路径线。我们将重点介绍其中一些可能的应用，包括时间线曲率场的计算和旋转平流流线核心的提取。
We present the first general scheme to describe all four types of characteristic curves of flow fields – stream, path, streak, and time lines – as tangent curves of a derived vector field. Thus, all these lines can be obtained by a simple integration of an autonomous ODE system. Our approach draws on the principal ideas of the recently introduced tangent curve description of streak lines. We provide the first description of time lines as tangent curves of a derived vector field, which could previously only be constructed in a geometric manner. Furthermore, our scheme gives rise to new types of curves. In particular, we introduce advected stream lines as a parameter‐free variant of the time line metaphor. With our novel mathematical description of characteristic curves, a large number of feature extraction and analysis tools becomes available for all types of characteristic curves, which were previously only available for stream and path lines. We will highlight some of these possible applications including the computation of time line curvature fields and the extraction of cores of swirling advected stream lines.