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Tensor Invariants and Glyph Design

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Visualization and Processing of Tensors and Higher Order Descriptors for Multi-Valued Data

Part of the book series: Mathematics and Visualization ((MATHVISUAL))

Abstract

Tensors provide a mathematical language for the description of many physical phenomena. They appear everywhere where the dependence of multiple vector fields is approximated as linear. Due to this generality they occur in various application areas, either as result or intermediate product of simulations. As different as these applications, is the physical meaning and relevance of particular mathematical properties. In this context, domain specific tensor invariants that describe the entities of interest play a crucial role. Due to their importance, we propose to build any tensor visualization upon a set of carefully chosen tensor invariants. In this chapter we focus on glyph-based representations, which still belong to the most frequently used tensor visualization methods. For the effectiveness of such visualizations the right choice of glyphs is essential. This chapter summarizes some common glyphs, mostly with origin in mechanical engineering, and link their interpretation to specific tensor invariants.

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Author information

Authors and Affiliations

  1. Zuse Institute Berlin, Berlin, Germany

    Andrea Kratz & Cornelia Auer

  2. German Aerospace Center, Braunschweig, Germany

    Ingrid Hotz

Authors
  1. Andrea Kratz
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  2. Cornelia Auer
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  3. Ingrid Hotz
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Corresponding author

Correspondence to Andrea Kratz .

Editor information

Editors and Affiliations

  1. Dept. of Radiology, Harvard Medical School, Brigham, and Women's Hospital, Boston, Massachusetts, USA

    Carl-Fredrik Westin

  2. Technical University of Delft, Dept of Computer Graphics and Visualization, Delft, The Netherlands

    Anna Vilanova

  3. Universität des Saarlandes, Dept. of Mathematics, Saarbrücken, Germany

    Bernhard Burgeth

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Kratz, A., Auer, C., Hotz, I. (2014). Tensor Invariants and Glyph Design. In: Westin, CF., Vilanova, A., Burgeth, B. (eds) Visualization and Processing of Tensors and Higher Order Descriptors for Multi-Valued Data. Mathematics and Visualization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-54301-2_2

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