Abstract
A real function f on R^d is called D-convex, where D is a set of vectors in R^d, if its restriction to each line parallel to a nonzero v from D is convex. The D-convex hull of a compact set A in R^d is the intersection of the zero sets of all nonnegative D-convex functions that are 0 on A.
We present a (polynomial-time) algorithm for the D-convex hull of a finite point set in the plane for arbitrary finite D.