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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Aurenhammer, F. Using Gale transforms in computational geometry. Mathematical Programming 52, 179–190 (1991). https://doi.org/10.1007/BF01582886
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DOI: https://doi.org/10.1007/BF01582886