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Computer Graphics 1987 pp 25–44Cite as

Parallel Coordinates for Visualizing Multi-Dimensional Geometry

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Abstract

By means of parallel coordinates a mapping R N → R 2, which is not a projection is obtained. Relations among N variables, for any positive integer N, are “represented” by their planar images. These planar diagrams have geometrical properties corresponding to certain properties of the relation they represent. Starting from a point ← → line duality when N = 2, the representation of lines in R N is given and illustrated by an application to Air Traffic Control (i.e. for R 4). It is followed by the representation of hyperplanes, polytopes and more general convex and some nonconvex (i.e. “pretsels” in R N) hypersurfaces. An algorithm for constructing and exhibiting any interior point to such a hypersurface is shown. Such a display shows some local (i.e. near the point) properties of the hypersurface and information on the point’s proximity to the boundary. Graphics from the computer implementation of the representations and algorithms are included.

Keywords & Phrases

  • Computational Geometry
  • Parallel Coordinates
  • Multi-Dimensional Graphics Duality
  • Multi-dimensional Lines
  • Hyperplanes and Surfaces
  • Proximity
  • Conflict Avoidance
  • Air Traffic Control

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Bibliography

  1. D. Asimov (1985), The Grand Tour: A Tool For Viewing Multidimensional Data SIAM J. of Scient. & Stat. Comp. 6:128–143

    CrossRef  MathSciNet  MATH  Google Scholar 

  2. V. Barnett Edit. (1981), Interpreting Multivariate Data, Wiley, New York

    MATH  Google Scholar 

  3. V. G. Boltyanskii (1964), Envelopes, Translated from the Russian by R. B. Brown, Pergamon Press, New York

    Google Scholar 

  4. D. Brissom Edit. (1979), Hypergraphics: Visualizing Complex Relationships in Art, Science and Technology Amer. Assoc. Adv. Sc., Westview Press, Boulder Colorado

    Google Scholar 

  5. J.M. Chambers, W.S. Cleveland, B. Kleiner & P.A. Tukcy (1983) Graphical Methods for Data Analysis Duxbury Press, Boston

    MATH  Google Scholar 

  6. S. Cohan, D. C. Yang (1986) MobilityAnalysis Of Planar Four-Bar Mechanisms Through the Parallel Coordinate System, Mech. & Mach. Theor. 21:63–71

    CrossRef  Google Scholar 

  7. H. S. M. Coxeter (1974), Projective Geometry, Univ. of Toronto Press, Toronto

    CrossRef  MATH  Google Scholar 

  8. B. Dimsdale (1981), Conic Transformations, IBM Los Angeles Scientific Center Report # G320–2713

    Google Scholar 

  9. B. Dimsdale (1981), Operating Point Selection for Multivariate Systems, IBM Los Angeles Scientific Center Report # ZZ20–6249

    Google Scholar 

  10. B. Dimsdale (1982), The Hyperesp, IBM Los Angeles Scientific Center Report (Unpublished)

    Google Scholar 

  11. A. Inselberg (1981), N-Dimensional Graphics Part I: Lines & Hyperplanes, IBM Los Angeles Scientific Center Report # G320–2711

    Google Scholar 

  12. A. Inselberg (1985), The Plane with Parallel Coordinates,Special Issue on Computational Geometry The Visual Computer 1:69–91

    CrossRef  MATH  Google Scholar 

  13. A. Inselberg, B. Dimsdale (1986), Intelligent Process Control & Integrated Instrumentation,First Conference on Intelligent and Integrated Manufacturing Anaheim, CA, Dec. 1986, ASME vol.21 341–358

    Google Scholar 

  14. A. Inselberg, B. Dimsdale (1987) Representing Multi-dimensional Lines,to be submitted for publication

    Google Scholar 

  15. A. Inselberg, M. Reif, T. Chomut (1987) Convexity Algorithms in Parallel Coordinates,to appear in J. of ACM

    Google Scholar 

  16. E. Wegman (1986) Hyperdimensional Data Analysis Using Parallel Coordinates, Tech. Rep. #1, Center for Computational Statistics and Probability, George Mason Univ., Fairfax, VA

    Google Scholar 

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Authors
  1. Alfred Inselberg
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  2. Bernard Dimsdale
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Editor information

Editors and Affiliations

  1. Kunii Laboratory of Computer Science, Department of Information Science, Faculty of Science, The University of Tokyo, Japan

    Dr. Tosiyasu L. Kunii (Professor and Director) (Professor and Director)

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© 1987 Springer-Verlag Tokyo

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Inselberg, A., Dimsdale, B. (1987). Parallel Coordinates for Visualizing Multi-Dimensional Geometry. In: Kunii, T.L. (eds) Computer Graphics 1987. Springer, Tokyo. https://doi.org/10.1007/978-4-431-68057-4_3

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  • DOI: https://doi.org/10.1007/978-4-431-68057-4_3

  • Publisher Name: Springer, Tokyo

  • Print ISBN: 978-4-431-68059-8

  • Online ISBN: 978-4-431-68057-4

  • eBook Packages: Springer Book Archive

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