  We develop the theory of veering triangulations on oriented surfaces adapted
to moduli spaces of half-translation surfaces. We use veering triangulations to
give a coding of the Teichm\"uller flow on connected components of strata of
quadratic differentials. We prove that this coding, given by a countable shift,
has an approximate product structure and a roof function with exponential
tails. This makes it conducive to the study of the dynamics of Teichm\"uller
flow.
