  The influence of the relativistic motion of the reference frame on the light
reflection law is investigated. The method is based on applying the
relativistic aberration affect for three light signals: incident, normal and
reflected rays. The form of the reflection law in the moving reference frame is
substantially modified and includes an additional parameter which is the
velocity vector of the reference frame.
  It is shown that the reflected ray, as measured by a moving observer, would
not in general be in the same plane as the incident and normal rays. A general
method to transform the form of any rigid surface in 3-dimensional space with
respect to the arbitrary directed relative motion of the reference frame is
detailed. This method is based on the light signals processes and the
invariance of the light velocity under Lorentz transformations. It is shown
that a moving observer will measure a plane surface as a hyperboloid. That
observer will also measure a spherical surface as an ellipsoid. A right line in
the plane is seen by a moving observer as a hyperbola. The whole analysis is
extended to the case of a uniform media.
