  Using the methods of general relativity Lindquist derived the radiative
transfer equation that is correct to all orders in v/c. Mihalas developed a
method of solution for the important case of monotonic velocity fields with
spherically symmetry. We have developed the generalized atmosphere code
PHOENIX, which in 1-D has used the framework of Mihalas to solve the radiative
transfer equation (RTE) in 1-D moving flows. We describe our recent work
including 3-D radiation transfer in PHOENIX and particularly including moving
flows exactly using a novel affine method. We briefly discuss quantitative
spectroscopy in supernovae.
