对称张量场模曲面的拓扑分析与无缝提取
Mode Surfaces of Symmetric Tensor Fields: Topological Analysis and Seamless Extraction
摘要：
模曲面是退化曲线和中性曲面的推广，它们构成了三维对称张量场拓扑。模式曲面的有效分析和可视化不仅可以提供对退化曲线和中性曲面的进一步了解，还可以提供对这些特征如何相互过渡的进一步了解。此外，模态曲面的几何和拓扑结构可以帮助域科学家更好地理解张量场的应用。现有的模式曲面提取方法可能会遗漏曲面中的特征。此外，从相邻单元提取的模式表面具有间隙，这使得它们的后续分析变得困难。在本文中，我们提供了新的分析模式表面的拓扑结构，包括一个共同的参数化的所有模式表面的张量场使用二维非对称张量。这不仅使我们能够更好地理解模式曲面中的结构及其与退化曲线和中性曲面的相互作用，而且还可以开发一种有效的算法来无缝地提取模式曲面，包括中性曲面。无缝模式表面使得能够有效地分析其几何结构，例如主曲率方向。我们将我们的分析和可视化应用于一些固体力学数据集。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
