  The unusual morphologies of the Andromeda spiral galaxy (M31) and its dwarf
companion M32 have been characterized observationally in great detail. The two
galaxies' apparent proximity suggests that Andromeda's prominent star-forming
ring as well as M32's compact elliptical structure may result from a recent
collision. Here we present the first self-consistent model of the M31-M32
interaction that simultaneously reproduces observed positions, velocities, and
morphologies for both galaxies. Andromeda's spiral structure is resolved in
unprecedented detail, showing that a rare head-on orbit is not necessary to
match Andromeda's ring-like morphology. The passage of M32 through Andromeda's
disk perturbs the disk velocity structure. We find tidal stripping of M32's
stars to be inefficient during the interaction, suggesting that some cEs are
intrinsically compact. Additionally, the orbital solution implies that M32 is
currently closer to the Milky Way than models have typically assumed, a
prediction that may be testable with upcoming observations.
