  We present the DIRTY radiative transfer model in this paper and a companion
paper. This model computes the polarized radiative transfer of photons from
arbitrary distributions of stars through arbitrary distributions of dust using
Monte Carlo techniques. The dust re-emission is done self-consistently with the
dust absorption and scattering and includes all three important emission paths:
equilibrium thermal emission, non-equilibrium thermal emission, and the
aromatic features emission. The algorithm used for the radiative transfer
allows for the efficient computation of the appearance of a model system as
seen from any viewing direction. We present a simple method for computing an
upper limit on the output quantity uncertainties for Monte Carlo radiative
transfer models which use the weighted photon approach.
