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Interactive 3D Space Group Visualization with CLUCalc and Crystallographic Subperiodic Groups in Geometric Algebra

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Geometric Algebra Computing

Abstract

The Space Group Visualizer (SGV) for all 230 3D space groups is a standalone PC application based on the visualization software CLUCalc. We first explain the unique geometric algebra structure behind the SGV. In the second part we review the main features of the SGV: The GUI, group and symmetry selection, mouse pointer interactivity, and visualization options. We further introduce the joint use with Hahn (Space-group Symmetry, 5th edn., International Tables of Crystallography, vol. A, Springer, Dordrecht, 2005). In the third part we explain how to represent the 162 so-called subperiodic groups of crystallography in geometric algebra. We construct a new compact geometric algebra group representation symbol, which allows us to read off the complete set of geometric algebra generators. For clarity, we moreover state explicitly which generators are chosen. The group symbols are based on the representation of point groups in geometric algebra by versors.

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Authors and Affiliations

  1. Department of Applied Physics, University of Fukui, Bunkyo 3-9-1, 910-8507, Fukui, Japan

    Eckhard M. S. Hitzer & Daisuke Ichikawa

  2. Institute for Informatics, University of Kiel, 24118, Kiel, Germany

    Christian Perwass

Authors
  1. Eckhard M. S. Hitzer
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  2. Christian Perwass
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  3. Daisuke Ichikawa
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Correspondence to Eckhard M. S. Hitzer .

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Editors and Affiliations

  1. , CINVESTAV, Unidad Guadalajara, Av. Científica 1145, Colonia el Bajío, Zapopan, 45015, Mexico

    Eduardo Bayro-Corrochano

  2. Inst. Informatik, Universität Leipzig, Leipzig, Germany

    Gerik Scheuermann

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Hitzer, E.M.S., Perwass, C., Ichikawa, D. (2010). Interactive 3D Space Group Visualization with CLUCalc and Crystallographic Subperiodic Groups in Geometric Algebra. In: Bayro-Corrochano, E., Scheuermann, G. (eds) Geometric Algebra Computing. Springer, London. https://doi.org/10.1007/978-1-84996-108-0_18

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  • DOI: https://doi.org/10.1007/978-1-84996-108-0_18

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  • Online ISBN: 978-1-84996-108-0

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