Abstract: A polygonal cover of a finite collection of pairwise disjoint convex compact sets in the plane is a finite collection of non-overlapping bounded convex polygons such that each polygon covers exactly one convex set. We show that computing a polygonal cover with worst case minimal number of sides reduces to computing a pseudo-triangulation of the collection of convex sets. We obtain a similar reduction for two related problems concerning convex compact sets in the plane~: computing a lighting set and computing a family of separating lines. Our main tool is the notion of screen graph (introduced in this paper) associated with a pseudo-triangulation.