re closed under translations, rigid
motions, similarity, but not general affine transformations. Within a
class of compatible transformations, a frame may specify one uniquely
if it can be obtained by transforming the standard frame in only one
way. For instance, a point $(x,y)$ can be obtained from $(0,0)$
through a unique translation $T=(x,y)$. Likewise, a circle can be
obtained from the standard circle by a unique translation and
rescaling. However, neither a point or a circle is sufficient to fully
spec