Abstract
We continue the development of a manifestly four-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, and in particular for a moving cloak. The inverse problem of this covariant approach is shown to generalize Gordon's 'optical metric'.