IEEE VIS 2024 Content: Asymptotic Topology of 3D Linear Symmetric Tensor Fields

Asymptotic Topology of 3D Linear Symmetric Tensor Fields

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 Xinwei Lin - Oregon State University, Corvallis, United States

Yue Zhang - Oregon State University, Corvallis, United States

 Eugene Zhang - Oregon State University, Corvallis, United States

 Room: Bayshore III

2024-10-14T16:00:00ZGMT-0600Change your timezone on the schedule page
2024-10-14T16:00:00Z

Exemplar figure, described by caption below — The asymptotic behaviors of a 3D linear tensor field can be understood by the tensor mode function on the sphere of infinity.In this figure, we show the four topologically different cases: (a) two degenerate curves and the neutral surface with one boundary, (b) two degenerate curves and the neutral surface with three boundaries, (c) four degenerate curves and the neutral surface with one boundary, and (d) four degenerate curves and the neutral surface with three boundaries.In each of these cases, the degenerate curves intersect the sphere of infinity at the global maxima (yellow dots) and global minima (green dots) of the tensor mode function. Similarly, the neutral surface intersects the sphere of infinity at precisely the zeroth level set of the mode function.

Abstract

3D symmetric tensor fields have a wide range of applications in science and engineering. The topology of such fields can provide critical insight into not only the structures in tensor fields but also their respective applications. Existing research focuses on the extraction of topological features such as degenerate curves and neutral surfaces. In this paper, we investigate the asymptotic behaviors of these topological features in the sphere of infinity. Our research leads to both theoretical analysis and observations that can aid further classifications of tensor field topology.