We define the antiumbra and the antipenumbra of a convex area light source shining through a sequence of convex areal holes in three dimensions. The antiumbra is the volume from which all points on the light source can be seen. The antipenumbra is the volume from which some, but not all, of the light source can be seen. We show that the antipenumbra is, in general, a disconnected set bounded by portions of quadric surfaces, and describe an implemented
Seth J. Teller