Grand Seiko polishes the cases of its watches with zaratsu kenma, Zaratsu polishing. The company explains that the surfaces are polished into a smooth mirror without distortion, and that the edges where flat and angled surfaces meet are made sharp. Its design principles say that each surface should, as a rule, be a mirror, with as little distortion as possible.
A craftsman profiled on Seiko’s site says that an error of a single micron ruins the surface.