Core Lines in 3D Second‐Order Tensor Fields
Core Lines in 3D Second‐Order Tensor Fields
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DOI：
10.1111/cgf.13423
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发表时间：
2018-06
影响因子：
2.5
通讯作者：
Timo Oster;Christian Rössl;H. Theisel
中科院分区：
文献类型：
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作者：
Timo Oster;Christian Rössl;H. Theisel
涡旋是矢量场的重要特征，它表现出围绕一个共同核心的旋转行为。涡旋核心线的概念描述了这种旋涡行为的中心。在这项工作中，我们研究了这一概念在三维二阶张量场中的推广。在这里，特征向量的轨迹可以观察到类似于向量场中的涡流的行为。Sujudi和Haimes将向量场中的涡核线定义为流线平行于雅可比矩阵特征向量的位置。我们表明，一个类似的准则应用于张量场的特征向量轨迹产生结构稳定的线，我们称之为张量核心线。我们提供了这些结构的正式定义，并检查了它们的数学性质。我们还提出了一种分段线性张量场中提取张量核心线的数值算法。我们使用简单且鲁棒的根查找算法找到张量核心线与数据集的面的所有交点。将该算法应用于结构力学模拟得到的张量场表明，该算法能够有效地检测和可视化特征向量轨迹的旋转或双曲行为区域。
Vortices are important features in vector fields that show a swirling behavior around a common core. The concept of a vortex core line describes the center of this swirling behavior. In this work, we examine the extension of this concept to 3D second‐order tensor fields. Here, a behavior similar to vortices in vector fields can be observed for trajectories of the eigenvectors. Vortex core lines in vector fields were defined by Sujudi and Haimes to be the locations where stream lines are parallel to an eigenvector of the Jacobian. We show that a similar criterion applied to the eigenvector trajectories of a tensor field yields structurally stable lines that we call tensor core lines. We provide a formal definition of these structures and examine their mathematical properties. We also present a numerical algorithm for extracting tensor core lines in piecewise linear tensor fields. We find all intersections of tensor core lines with the faces of a dataset using a simple and robust root finding algorithm. Applying this algorithm to tensor fields obtained from structural mechanics simulations shows that it is able to effectively detect and visualize regions of rotational or hyperbolic behavior of eigenvector trajectories.