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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, Eugene Zhang, Bob Laramee Orcid Logo

IEEE Transactions on Visualization and Computer Graphics, Volume: 22, Issue: 3, Pages: 1248 - 1260

Swansea University Author: Bob Laramee Orcid Logo

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DOI (Published version): 10.1109/TVCG.2015.2484343

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 neutr...

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Published in: IEEE Transactions on Visualization and Computer Graphics
ISSN: 1077-2626
Published: 2016
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URI: https://cronfa.swan.ac.uk/Record/cronfa24560
first_indexed 2015-11-21T01:53:34Z
last_indexed 2021-01-29T03:39:47Z
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spelling 2021-01-28T13:08:01.1694959 v2 24560 2015-11-20 Feature Surfaces in Symmetric Tensor Fields Based on Eigenvalue Manifold 7737f06e2186278a925f6119c48db8b1 0000-0002-3874-6145 Bob Laramee Bob Laramee true false 2015-11-20 MACS 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. Journal Article IEEE Transactions on Visualization and Computer Graphics 22 3 1248 1260 1077-2626 31 12 2016 2016-12-31 10.1109/TVCG.2015.2484343 COLLEGE NANME Mathematics and Computer Science School COLLEGE CODE MACS Swansea University 2021-01-28T13:08:01.1694959 2015-11-20T12:25:39.5948203 Faculty of Science and Engineering School of Mathematics and Computer Science - Computer Science Jonathan Palacios 1 Harry Yeh 2 Wenping Wang 3 Yue Zhang 4 Robert S. Laramee 5 Ritesh Sharma 6 Thomas Schultz 7 Eugene Zhang 8 Bob Laramee 0000-0002-3874-6145 9
title Feature Surfaces in Symmetric Tensor Fields Based on Eigenvalue Manifold
spellingShingle Feature Surfaces in Symmetric Tensor Fields Based on Eigenvalue Manifold
Bob Laramee
title_short Feature Surfaces in Symmetric Tensor Fields Based on Eigenvalue Manifold
title_full Feature Surfaces in Symmetric Tensor Fields Based on Eigenvalue Manifold
title_fullStr Feature Surfaces in Symmetric Tensor Fields Based on Eigenvalue Manifold
title_full_unstemmed Feature Surfaces in Symmetric Tensor Fields Based on Eigenvalue Manifold
title_sort Feature Surfaces in Symmetric Tensor Fields Based on Eigenvalue Manifold
author_id_str_mv 7737f06e2186278a925f6119c48db8b1
author_id_fullname_str_mv 7737f06e2186278a925f6119c48db8b1_***_Bob Laramee
author Bob Laramee
author2 Jonathan Palacios
Harry Yeh
Wenping Wang
Yue Zhang
Robert S. Laramee
Ritesh Sharma
Thomas Schultz
Eugene Zhang
Bob Laramee
format Journal article
container_title IEEE Transactions on Visualization and Computer Graphics
container_volume 22
container_issue 3
container_start_page 1248
publishDate 2016
institution Swansea University
issn 1077-2626
doi_str_mv 10.1109/TVCG.2015.2484343
college_str Faculty of Science and Engineering
hierarchytype
hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Mathematics and Computer Science - Computer Science{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Mathematics and Computer Science - Computer Science
document_store_str 0
active_str 0
description 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.
published_date 2016-12-31T12:52:17Z
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score 11.048237

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