Coordinate Systems (CS)
An abstract CS is a means of identifying a set positions in m-dimensional position-space (1 ? m ? 3) that is comprised of:
a. a CS domain,
b. a generating function, and
c. a CS range,
where:
d. the CS domain is a connected domain in the Euclidean space of n-tuples (1 ? n ? m), called the coordinate-space,
e. the generating function shall be a one-to-one, smooth, orientation preserving function from the CS domain onto the CS range, and
f. the CS range is a sub-set of position-space.