Feature Surfaces in Symmetric Tensor Fields Based on Eigenvalue Manifold
Autor: | Thomas Schultz, Robert S. Laramee, Eugene Zhang, Harry Yeh, Yue Zhang, Ritesh Sharma, Jonathan Palacios, Wenping Wang |
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Rok vydání: | 2016 |
Předmět: |
Weyl tensor
Tensor contraction Pure mathematics Mathematical analysis 020207 software engineering 02 engineering and technology 01 natural sciences Computer Graphics and Computer-Aided Design 010305 fluids & plasmas Tensor field symbols.namesake Exact solutions in general relativity 0103 physical sciences Signal Processing 0202 electrical engineering electronic engineering information engineering symbols Ricci decomposition Symmetric tensor Computer Vision and Pattern Recognition Tensor Tensor density Software Mathematics |
Zdroj: | IEEE Transactions on Visualization and Computer Graphics. 22:1248-1260 |
ISSN: | 1077-2626 |
Popis: | 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 cause 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. |
Databáze: | OpenAIRE |
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