2D coordinate transformations
translation:     x’ = x + t     x = (x,y)
rotation:     x’ = R x + t
similarity:     x’ = s R x + t
affine:     x’ = A x + t
perspective:   x H x     x = (x,y,1)
   (x is a homogeneous coordinate)
These all form a nested group (closed w/ inv.)