Using gale transforms in computational geometry

  • Franz Aurenhammer
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 333)

Abstract

Let P denote a set of n⩾d+1 points in d-space Rd. A Gale transform of P assigns to each point in P a vector in space Rn−d−1 such that the resulting n-tuple of vectors reflects all affinely invariant properties of P. First utilized by Gale in the 1950s, Gale transforms have been recognized as a powerful tool in combinatorial geometry.

This paper introduces Gale transforms to computational geometry. It offers a direct algorithm for their construction and sketches applications to convex hull and visibility problems. An application to scene analysis is worked out in some more detail.

Keywords

Computational Geometry Scene Analysis Open Halfspaces Discrete Apply Math Sketch Application 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1988

Authors and Affiliations

  • Franz Aurenhammer
    • 1
  1. 1.Institutes for Information ProcessingTechnical University of Graz and Austrian Computer SocietyGrazAustria

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