Comparing vectors in different coordinate systems requires converting one of them to the other's basis, a process called change of basis.
Really liked the story on about cartesian coordinates and the fly! Read up a bit more the history of coordinate systems and though it was interesting that after Descartes, Newton came up with 10 different kinds of co-ordinate systems including the polar co-ordinate system!
@Tee-Dawg. Nice. Yeah, bugs have been part of computer graphics for a long time. ;-)