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
STAFF OF GEOMETRY CENTER, Not Knot,A.K. Peters, Wellesley MA.
Staff OF Geometry Center, Shape of Space,Geometry Center, Minneapolis, MN.
D. Roseman, (with D. Mayer), Viewing Knotted Spheres in 4-space, video (8 mins) Produced at the Geometry Center, (June 1992).
D. Roseman, (With D. Mayer And O. Holt), Twisting and Turning in 4 Dimensions, video (19 mins) produced at the Geometry Center, distributed by Great Media, Nicassio CA, ( August 1993 ).
D. Roseman, Unraveling in 4 Dimensions, video (18 mins) produced at the Geometry Center, distributed by Great Media, Nicassio CA, ( July 1994 )
Listing of software
Staff OF Geometry Center, Geomview, software, Geometry Center, Minneapolis, Minn. Available via anonymous ftp from geom umn edu.
D. Roseman, J. Berdine, Hew, written University of Iowa (1996)
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).
G. Chapell, G. Francis, C. Hartman, slice, written at NCSA (1995)
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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
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