Geometric properties invariant to commonly occurring plane
transformations. Transformations lower in the table inherit the
invariants of those above, but the converse is not true.
The matrix 
is an invertible 
matrix,
is a 2D rotation matrix, and
a 2D translation. The distortion column shows
typical effects of the transformations on a square. Transformations
higher in the table can produce all the actions of the ones below.
These range from Euclidean, where only translations and rotations
occur, to projective where the square can be transformed to
any arbitrary quadrilateral (provided no three points are collinear).