This transformation is an invertible origin-, distance- and orientation-preserving isometry
This transformation is an distance- and orientation-preserving isometry,
but not the origin
This is an rotation followed by translation
it preserves angle sizes and maps parallel lines to parallel lines.
Orientation is lost if the scaling factor is negative.
A similarity is an uniform scaling, followed by a rotation, followed by translation.
Similarities share the same constructors as the isometry.
Though most of them take one additional parameter: the uniform scaling factor.
