  In this paper, there are two sections. In Section 7, we simplify the
eigenvalue-based surplus shortline method for arbitrary finite polysquare
translation 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.
