  The Opaque Cover Problem (OCP), also known as the Beam Detector Problem, is
the problem of finding, for a set S in Euclidean space, the minimum-length set
F which intersects every straight line passing through S. In spite of its
simplicity, the problem remains remarkably intractable. The aim of this paper
is to establish a framework and fundamental results for minimum opaque covers
where S is a polygonal region in two-dimensional space. We begin by giving some
general results about opaque covers, and describe the close connection that the
OCP has with the Point Goalie Problem. We then consider properties of graphical
solutions to the OCP when S is a convex polygonal region in the plane.
