  We show that the geometry-of-numbers method used by A. Bounemoura to obtain
filling times for linear flow on the torus satisfying Diophantine conditions
may be extended to the case of linear flow with truncated Diophantine
conditions, and we use these methods to recover the optimal estimate first
obtained by M. Berti, L. Biasco, and P. Bolle in 2003. We also briefly review
the dynamics of linear flow on the torus, previous results, optimality, and
applications of these estimates.
