**F. Aurenhammer**

Let denote a set of points in -space . A Gale
transform of assigns to each point in a vector in space
such that the resulting -tuple of vectors reflects all affinely invariant
properties of . 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.