Glyphs for General Second-Order 2D and 3D Tensors
Glyphs for General Second-Order 2D and 3D Tensors
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DOI：
10.1109/tvcg.2016.2598998
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发表时间：
2017
影响因子：
5.2
通讯作者：
Tim Gerrits;Christian Rössl;H. Theisel
中科院分区：
文献类型：
--
作者：
Tim Gerrits;Christian Rössl;H. Theisel
字形是可视化各种科学数据中二阶张量的强大工具，因为它们允许在几何属性中编码物理行为。大多数现有的技术都集中在对称张量上，并且排除了非对称张量，其中的特征向量可以是非正交的，也可以是复数的。提出了一种新的基于分段有理曲线曲面的二维和三维张量字形的构造方法，它具有如下性质：(A)等距不变性和(B)尺度不变性；(C)所有实特征值和特征向量的直接编码；(D)张量和字形之间的一一对应关系；(E)改变张量下的字形连续性。我们应用字形来可视化一些2D和3D矢量场的雅可比矩阵场。
Glyphs are a powerful tool for visualizing second-order tensors in a variety of scientic data as they allow to encode physical behavior in geometric properties. Most existing techniques focus on symmetric tensors and exclude non-symmetric tensors where the eigenvectors can be non-orthogonal or complex. We present a new construction of 2d and 3d tensor glyphs based on piecewise rational curves and surfaces with the following properties: invariance to (a) isometries and (b) scaling, (c) direct encoding of all real eigenvalues and eigenvectors, (d) one-to-one relation between the tensors and glyphs, (e) glyph continuity under changing the tensor. We apply the glyphs to visualize the Jacobian matrix fields of a number of 2d and 3d vector fields.