论文标题
对称张量场的模式表面：拓扑分析和无缝提取
Mode Surfaces of Symmetric Tensor Fields: Topological Analysis and Seamless Extraction
论文作者
论文摘要
模式表面是变性曲线和中性表面的概括，构成了3D对称张量的场拓扑。对模式表面的有效分析和可视化可以提供对退化曲线和中性表面的额外洞察力，而且还可以提供这些特征如何相互转变。此外，模式表面的几何形状和拓扑可以帮助域科学家更好地了解其应用中的张量场。现有的模式表面提取方法可能会错过表面中的特征。此外，从相邻细胞中提取的模式表面有间隙，这使得其后续分析变得困难。在本文中，我们对模式表面的拓扑结构进行了新的分析，包括使用2D不对称张量的张量场所有模式表面的常见参数化。这使我们不仅可以更好地了解模式表面中的结构及其与退化曲线和中性表面的相互作用，而且还可以开发出有效的算法，以无缝提取模式表面，包括中性表面。无缝模式表面可以有效地分析其几何结构，例如主曲率方向。我们将分析和可视化应用于许多固体力学数据集。
Mode surfaces are the generalization of degenerate curves and neutral surfaces, which constitute 3D symmetric tensor field topology. Efficient analysis and visualization of mode surfaces can provide additional insight into not only degenerate curves and neutral surfaces, but also how these features transition into each other. Moreover, the geometry and topology of mode surfaces can help domain scientists better understand the tensor fields in their applications. Existing mode surface extraction methods can miss features in the surfaces. Moreover, the mode surfaces extracted from neighboring cells have gaps, which make their subsequent analysis difficult. In this paper, we provide novel analysis on the topological structures of mode surfaces, including a common parameterization of all mode surfaces of a tensor field using 2D asymmetric tensors. This allows us to not only better understand the structures in mode surfaces and their interactions with degenerate curves and neutral surfaces, but also develop an efficient algorithm to seamlessly extract mode surfaces, including neutral surfaces. The seamless mode surfaces enable efficient analysis of their geometric structures, such as the principal curvature directions. We apply our analysis and visualization to a number of solid mechanics data sets.
