  The present work introduces an efficient Monte Carlo algorithm for continuum
percolation composed of randomly-oriented rectangles. By conducting extensive
simulations, we report high precision percolation thresholds for a variety of
homogeneous systems with different rectangle aspect ratios. This work verifies
and extends the excluded area theory. It is confirmed that percolation
thresholds are dominated by the average excluded areas for both homogeneous and
heterogeneous rectangle systems (except for some special heterogeneous systems
where the rectangle lengths differ too much from one another). In terms of the
excluded areas, generalized formulae are proposed to effectively predict
precise percolation thresholds for all these rectangle systems. This work is
therefore helpful for both practical applications and theoretical studies
concerning relevant systems.
  The Erratum addresses errors in our earlier paper "Percolation thresholds of
two-dimensional continuum systems of rectangles" published in [Phys. Rev. E 88,
012101 (2013)].
