Using gale transforms in computational geometry
Let P denote a set of n⩾d+1 points in d-space Rd. A Gale transform of P assigns to each point in P a vector in space Rn−d−1 such that the resulting n-tuple of vectors reflects all affinely invariant properties of P. 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 sketches applications to convex hull and visibility problems. An application to scene analysis is worked out in some more detail.
KeywordsComputational Geometry Scene Analysis Open Halfspaces Discrete Apply Math Sketch Application
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