Most visibility culling algorithms require convexity of occluders. And those algorithms that do not are much more efficient when convexity is met. Occluder synthesis algorithms lessen this limitation by extracting big convex objects from bulky concave sets. Occluder fusion algorithms generate convex occluders that are conservatively equivalent to sets of unconnected objects in terms of visibility. In this paper we prove that convexity requirements can be shifted from the occluders to their umbra with no loss of efficiency, and use this property to show how some special non-planar, non-convex polylines we call hoops can be used to compute occlusion efficiently. Hoops allow to compute occlusion of big, twisted objects that have no big interior convex sets and were thus rejected by previous approaches.