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Mathematical Visualization pp 281–291Cite as

Exploring Low Dimensional Objects in High Dimensional Spaces

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Abstract

We discuss general principles and a software implementation for visualizing low dimensional objects in high dimensional spaces. By high dimensional space we mean euclidian space of dimension greater than four. The low dimensional objects are modeled, mathematically, by simplicial complexes of dimension 4 or less. A particular software visualization project, named Hew, is discussed. An example of an embedded three dimensional projective space is featured in the figures.

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Listing of mathematical videos

  1. STAFF OF GEOMETRY CENTER, Not Knot,A.K. Peters, Wellesley MA.

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  2. Staff OF Geometry Center, Shape of Space,Geometry Center, Minneapolis, MN.

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  5. D. Roseman, Unraveling in 4 Dimensions, video (18 mins) produced at the Geometry Center, distributed by Great Media, Nicassio CA, ( July 1994 )

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Listing of software

  1. Staff OF Geometry Center, Geomview, software, Geometry Center, Minneapolis, Minn. Available via anonymous ftp from geom umn edu.

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  2. D. Roseman, J. Berdine, Hew, written University of Iowa (1996)

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  3. A.J. Hanson, ET AL, Mesh View 4D, a 4d surface viewer for meshes for SGI machines, available via ftp from the Geometry Center (1994).

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  4. G. Chapell, G. Francis, C. Hartman, slice, written at NCSA (1995)

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Iowa, Iowa City, Iowa, USA

    Dennis Roseman

Authors
  1. Dennis Roseman
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Editor information

Editors and Affiliations

  1. Wissenschaftliche Visualisierung, Konrad-Zuse-Zentrum für Informationstechnik Berlin, Takustraße 7, D-14195, Berlin, Germany

    Hans-Christian Hege

  2. Fachbereich 3, Mathematik, Technische Universität Berlin, Straße des 17. Juni 136, D-10623, Berlin, Germany

    Konrad Polthier

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© 1998 Springer-Verlag Berlin Heidelberg

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Roseman, D. (1998). Exploring Low Dimensional Objects in High Dimensional Spaces. In: Hege, HC., Polthier, K. (eds) Mathematical Visualization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-03567-2_21

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  • DOI: https://doi.org/10.1007/978-3-662-03567-2_21

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-08373-0

  • Online ISBN: 978-3-662-03567-2

  • eBook Packages: Springer Book Archive

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