Mathematical Programming

, Volume 52, Issue 1, pp 179-190

First online:

Using Gale transforms in computational geometry

  • Franz AurenhammerAffiliated withInstitutes for Information Processing, Graz University of Technology and Austrian Computer Society

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LetP denote a set ofn ⩾ d+1 points ind-space ℝ d . A Gale transform ofP assigns to each point inP a vector in space ℝ n-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.