  We consider discretization of the 'geometric cover problem' in the plane:
Given a set $P$ of $n$ points in the plane and a compact planar object $T_0$,
find a minimum cardinality collection of planar translates of $T_0$ such that
the union of the translates in the collection contains all the points in $P$.
We show that the geometric cover problem can be converted to a form of the
geometric set cover, which has a given finite-size collection of translates
rather than the infinite continuous solution space of the former. We propose a
reduced finite solution space that consists of distinct canonical translates
and present polynomial algorithms to find the reduce solution space for disks,
convex/non-convex polygons (including holes), and planar objects consisting of
finite Jordan curves.
