Mathematical Programming

, Volume 52, Issue 1–3, pp 179–190

Using Gale transforms in computational geometry

  • Franz Aurenhammer
Article
  • 116 Downloads

Abstract

LetP denote a set ofn ⩾ d+1 points ind-space ℝd. A Gale transform ofP assigns to each point inP a vector in space ℝn-d-1 such that the resultingn-tuple of vectors reflects all affinely invariant properties ofP. 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 addresses applications to convex hull and visibility problems. An application to scene analysis is worked out in detail.

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Copyright information

© The Mathematical Programming Society, Inc. 1991

Authors and Affiliations

  • Franz Aurenhammer
    • 1
  1. 1.Institutes for Information ProcessingGraz University of Technology and Austrian Computer SocietyGrazAustria

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