  Monte Carlo radiative transfer, which has been demonstrated as a successful
algorithm for modeling radiation transport through the astrophysical medium,
relies on sampling of scattering phase functions. We review several classic
sampling algorithms such as the tabulated method and the accept-reject method
for sampling the scattering phase function. The tabulated method uses a
piecewise constant approximation for the true scattering phase function; we
improve its sampling performance on a small scattering angle by using piecewise
linear and piecewise log-linear approximations. It has previously been believed
that certain complicated analytic phase functions such as the Fournier-Forand
phase function cannot be simulated without approximations. We show that the
tabulated method combined with the accept-reject method can be applied to
sample such complicated scattering phase functions accurately. Furthermore, we
introduce the Gibbs sampling method for sampling complicated approximate
analytic phase functions. In addition, we propose a new modified
Henyey-Greenstein phase function with exponential decay terms for modeling
realistic dust scattering. Based on Monte Carlo simulations of radiative
transfer through a plane-parallel medium, we also demonstrate that the result
simulated with the new phase function can provide a good fit to the result
simulated with the realistic dust phase function.
