Computing D-convex hulls in the plane

A function f:R^d->R is called D-convex, where D is a set of vectors in R^d, if its restriction to each line parallel to a nonzero [email protected]?D is convex. The D-convex hull of a compact set [email protected]?R^d is the intersection of the zero sets of all nonnegative D-convex functions that are 0 on A. Matousek and Plechac provided an algorithm for computing the D-convex hull of a finite set in R^d for D consisting of d linearly independent vectors (in this case one speaks about separately convex hulls). Here we present a (polynomial-time) algorithm for the D-convex hull of a finite point set in the plane for arbitrary finite D.

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