  We continue the development of a manifestly 4-dimensional, completely
covariant, approach to transformation optics in linear dielectric materials
begun in a previous paper. This approach, which generalizes the Plebanski based
approach, is systematically applicable for all transformations and all general
linear materials. Importantly, it enables useful applications such as arbitrary
relative motion, transformations from arbitrary non-vacuum initial dielectric
media, and arbitrary space-times. This approach is demonstrated for a resulting
material that moves with uniform linear velocity. The inverse problem of this
covariant approach is shown to generalize Gordon's "optical metric".
