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Parallel Coordinates for Visualizing Multi-Dimensional Geometry

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By means of parallel coordinates a mapping R NR 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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© 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.

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  • Publisher Name: Springer, Tokyo

  • Print ISBN: 978-4-431-68059-8

  • Online ISBN: 978-4-431-68057-4

  • eBook Packages: Springer Book Archive