Using Gale transforms in computational geometry
- Cite this article as:
- Aurenhammer, F. Mathematical Programming (1991) 52: 179. doi:10.1007/BF01582886
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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.