Feature Surfaces in Symmetric Tensor Fields Based on Eigenvalue Manifold

Jonathan Palacios, Harry Yeh, Wenping Wang, Yue Zhang, Robert S. Laramee, Ritesh Sharma, Thomas Schultz und Eugene Zhang
In: IEEE Trans. on Visualization and Computer Graphics (2016), 22:3(1248-1260)
 

Abstract

Three-dimensional symmetric tensor fields have a wide range of applications in solid and fluid mechanics. Recent advances in the (topological) analysis of 3D symmetric tensor fields focus on degenerate tensors which form curves. In this paper, we introduce a number of feature surfaces, such as neutral surfaces and traceless surfaces, into tensor field analysis, based on the notion of eigenvalue manifold. Neutral surfaces are the boundary between linear tensors and planar tensors, and the traceless surfaces are the boundary between tensors of positive traces and those of negative traces. Degenerate curves, neutral surfaces, and traceless surfaces together form a partition of the eigenvalue manifold, which provides a more complete tensor field analysis than degenerate curves alone. We also extract and visualize the isosurfaces of tensor modes, tensor isotropy, and tensor magnitude, which we have found useful for domain applications in fluid and solid mechanics. Extracting neutral and traceless surfaces using the Marching Tetrahedra method can lead to the loss of geometric and topological details, which can lead to false physical interpretation. To robustly extract neutral surfaces and traceless surfaces, we develop a polynomial description of them which enables us to borrow techniques from algebraic surface extraction, a topic well-researched by the computer-aided design (CAD) community as well as the algebraic geometry community. In addition, we adapt the surface extraction technique, called A-patches, to improve the speed of finding degenerate curves. Finally, we apply our analysis to data from solid and fluid mechanics as well as scalar field analysis.

Stichwörter: A-patches, feature-based visualization, scalar fields, tensor field topology, Tensor field visualization, traceless tensors

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Bibtex

@ARTICLE{Zhang2016,
    author = {Palacios, Jonathan and Yeh, Harry and Wang, Wenping and Zhang, Yue and Laramee, Robert S. and
              Sharma, Ritesh and Schultz, Thomas and Zhang, Eugene},
     pages = {1248--1260},
     title = {Feature Surfaces in Symmetric Tensor Fields Based on Eigenvalue Manifold},
   journal = {IEEE Trans. on Visualization and Computer Graphics},
    volume = {22},
    number = {3},
      year = {2016},
  keywords = {A-patches, feature-based visualization, scalar fields, tensor field topology, Tensor field
              visualization, traceless tensors},
  abstract = {Three-dimensional symmetric tensor fields have a wide range of applications in solid and fluid
              mechanics. Recent advances in the (topological) analysis of 3D symmetric tensor fields focus on
              degenerate tensors which form curves. In this paper, we introduce a number of feature surfaces, such
              as neutral surfaces and traceless surfaces, into tensor field analysis, based on the notion of
              eigenvalue manifold. Neutral surfaces are the boundary between linear tensors and planar tensors,
              and the traceless surfaces are the boundary between tensors of positive traces and those of negative
              traces. Degenerate curves, neutral surfaces, and traceless surfaces together form a partition of the
              eigenvalue manifold, which provides a more complete tensor field analysis than degenerate curves
              alone. We also extract and visualize the isosurfaces of tensor modes, tensor isotropy, and tensor
              magnitude, which we have found useful for domain applications in fluid and solid mechanics.
              Extracting neutral and traceless surfaces using the Marching Tetrahedra method can lead to the loss
              of geometric and topological details, which can lead to false physical interpretation. To robustly
              extract neutral surfaces and traceless surfaces, we develop a polynomial description of them which
              enables us to borrow techniques from algebraic surface extraction, a topic well-researched by the
              computer-aided design (CAD) community as well as the algebraic
              geometry community. In addition, we adapt the surface extraction technique, called A-patches, to
              improve the speed of finding degenerate curves.
              Finally, we apply our analysis to data from solid and fluid mechanics as well as scalar field
              analysis.}
}