It is conjectured that for every convex disks K, the translative covering
density of K and the lattice covering density of K are identical. It is well
known that this conjecture is true for every centrally symmetric convex disks.
For the non-symmetric case, we only know that the conjecture is true for
triangles. In this paper, we prove the conjecture for a class of convex disks
(quarter-convex disks), which includes all triangles and convex quadrilaterals