  We present numerical studies of first-order and continuous filling
transitions, in wedges of arbitrary opening angle $\psi$, using a microscopic
fundamental measure density functional model with short-ranged fluid-fluid
forces and long-ranged wall-fluid forces. In this system the wetting transition
characteristic of the planar wall-fluid interface is always first-order
regardless of the strength of the wall-fluid potential $\varepsilon_w$. In the
wedge geometry however the order of the filling transition depends not only on
$\varepsilon_w$ but also the opening angle $\psi$. In particular we show that
even if the wetting transition is strongly first-order the filling transition
is continuous for sufficient acute wedges. We show further that the change in
the order of the transition occurs via a tricritical point as opposed to a
critical-end point. These results extend previous effective Hamiltonian
predictions which were limited only to shallow wedges.
