Let P denote a set of points in d- space . A Gale transform of P assigns to each point in P a vector in space 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 addresses applications to convex hull and visibility problems. An application to scene analysis is worked out in detail.
