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Continuous Histograms for Anisotropy of 2D Symmetric Piece-wise Linear Tensor Fields
Linköping University, Department of Science and Technology, Media and Information Technology. Linköping University, Faculty of Science & Engineering.ORCID iD: 0000-0001-5352-1086
Linköping University, Department of Science and Technology, Media and Information Technology. Linköping University, Faculty of Science & Engineering.ORCID iD: 0000-0001-7285-0483
2021 (English)In: Anisotropy Across Fields and Scales / [ed] Evren Özarslan, Thomas Schultz, Eugene Zhang, and Andrea Fuster, Cham: Springer, 2021, p. 39-70Chapter in book (Refereed)
Abstract [en]

In this chapter we present an accurate derivation of the distribution of scalar invariants with quadratic behavior represented as continuous histograms. The anisotropy field, computed from a two-dimensional piece-wise linear tensor field, is used as an example and is discussed in all details. Histograms visualizing an approximation of the distribution of scalar values play an important role in visualization. They are used as an interface for the design of transfer-functions for volume rendering or feature selection in interactive interfaces. While there are standard algorithms to compute continuous histograms for piece-wise linear scalar fields, they are not directly applicable to tensor invariants with non-linear, often even non-convex behavior in cells when applying linear tensor interpolation. Our derivation is based on a sub-division of the mesh in triangles that exhibit a monotonic behavior. We compare the results to a naïve approach based on linear interpolation on the original mesh or the subdivision.

Place, publisher, year, edition, pages
Cham: Springer, 2021. p. 39-70
Series
Mathematics and Visualization, ISSN 1612-3786
Keywords [en]
Anisotropy, tensor field, merge tree, histogram, topology
National Category
Computer Sciences
Identifiers
URN: urn:nbn:se:liu:diva-178640DOI: 10.1007/978-3-030-56215-1_3Libris ID: dtjx1m4fb5dktbxdISBN: 9783030562144 (print)OAI: oai:DiVA.org:liu-178640DiVA, id: diva2:1587630
Funder
Swedish e‐Science Research CenterAvailable from: 2021-08-25 Created: 2021-08-25 Last updated: 2022-02-22Bibliographically approved

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Publisher's full texthttps://libris.kb.se/bib/dtjx1m4fb5dktbxd

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Masood, Talha BinHotz, Ingrid

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CiteExportLink to record
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Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
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More styles
Language
  • de-DE
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  • en-US
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  • sv-SE
  • Other locale
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Output format
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  • asciidoc
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