  In a 2D liquid crystal, each topological defect has a topological charge and
a characteristic orientation, and hence can be regarded as an oriented
particle. Theories predict that the trajectories of annihilating defects depend
on their relative orientation. Recently, these predictions have been tested in
experiments on smectic-C films. Those experiments find curved trajectories that
are similar to the predictions, but the detailed relationship between the
defect orientations and the far-field director is different. To understand this
difference, we extend the previous theories by adding the effects of elastic
anisotropy, and find that it significantly changes the curved trajectories.
