Mathematical Programming

, Volume 52, Issue 1, pp 179–190

Using Gale transforms in computational geometry

  • Franz Aurenhammer

DOI: 10.1007/BF01582886

Cite this article as:
Aurenhammer, F. Mathematical Programming (1991) 52: 179. doi:10.1007/BF01582886


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.

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