  We generalize the semi-analytical line transfer (SALT) model recently
introduced by Scarlata \& Panagia (2015) for modeling galactic outflows, to
account for bi-conical geometries of various opening angles and orientations
with respect to the line-of-sight to the observer, as well as generalized
velocity fields. We model the absorption and emission component of the line
profile resulting from resonant absorption in the bi-conical outflow. We show
how the outflow geometry impacts the resulting line profile. We use simulated
spectra with different geometries and velocity fields to study how well the
outflow parameters can be recovered. We find that geometrical parameters
(including the opening angle and the orientation) are always well recovered.
The density and velocity field parameters are reliably recovered when both an
absorption and an emission component are visible in the spectra. This condition
implies that the velocity and density fields for narrow cones oriented
perpendicular to the line of sight will remain unconstrained.
