Coordinate system characteristics
A CS is linear if it has an affine generating function
(a function is affine if it is a translation operator plus a linear operator)
A non-linear CS is curvilinear.
A linear CS is orthonormal if
3D CS case: the coordinates (1,0,0), (0,1,0),
and (0,0,1) are length one and mutually
perpendicular in position-space.
Surface and 2D CS case: the coordinates (1,0),and (0,0,1)
are length one and mutually perpendicular