A new method for the formal solution of the 2D radiative transfer equation in
axial symmetry in the presence of arbitrary velocity fields is presented. The
combination of long and short characteristics methods is used to solve the
radiative transfer equation. We include the velocity field in detail using the
Local Lorentz Transformation. This allows us to obtain a significantly better
description of the photospheric region, where the gradient of the global
velocity is too small for the Sobolev approximation to be valid. Sample test
calculations for the case of a stellar wind and a rotating atmosphere are
presented.Comment: 11 pages, 19 figures. accepted by Astronomy and Astrophysic