Most visibility culling algorithms require convexity of occluders. Occluder
synthesis algorithms attempt to construct large convex occluders inside bu
lky non-convex sets. Occluder fusion algorithms generate convex occluders t
hat are contained in the umbra cast by a group of objects given an area lig
ht. 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 prope
rty to show how some special non-planar non-convex closed polylines that we
call "hoops" can be used to compute occlusion efficiently for objects that
have no large interior convex sets and were thus rejected by previous appr
oaches.