  We establish sufficient conditions for finite convergence of the alternating
projections method for two non-intersecting and potentially nonconvex sets. Our
results are based on a generalization of the concept of intrinsic
transversality, which until now has been restricted to sets with nonempty
intersection. In the special case of a polyhedron and closed half space, our
sufficient conditions define the minimum distance between the two sets that is
required for alternating projections to converge in a single iteration.
