  In this paper, there are two sections. In Section 7, we simplify the
eigenvalue-based surplus shortline method for arbitrary finite polysquare
surfaces. This makes it substantially simpler to determine the irregularity
exponents of some infinite orbits, and quicker to find the escape rate to
infinity of some orbits in some infinite models. In Section 8, our primary goal
is to extend the surplus shortline method, both this eigenvalue-based version
as well as the eigenvalue-free version, for application to a large class of
2-dimensional flat dynamical systems beyond polysquares, including all Veech
surfaces, and establish time-quantitative equidistribution and
time-quantitative superdensity of some infinite orbits in these new systems.
