  We give asymptotic estimates for the number of non-overlapping homothetic
copies of some centrally symmetric oval $B$ which have a common point with a
2-dimensional domain $F$ having rectifiable boundary, extending previous work
of the L.Fejes-Toth, K.Borockzy Jr., D.G.Larman, S.Sezgin, C.Zong and the
authors. The asymptotics compute the length of the boundary $\partial F$ in the
Minkowski metric determined by $B$. The core of the proof consists of a method
for sliding convex beads along curves with positive reach in the Minkowski
plane. We also prove that level sets are rectifiable subsets, extending a
theorem of Erd\"os, Oleksiv and Pesin for the Euclidean space to the Minkowski
space.
