[Freeciv-Dev] Re: Corecleanup patch updates

[Jason Dorje Short <jshort@xxxxxxxxxxxxx>]

Mike Kaufman wrote:
> 
> On Sun, Aug 12, 2001 at 02:56:40AM +0200, Gaute B Strokkenes wrote:
> >
> > You're also assuming that you can normalize x and y coordinates
> > separately.  That's fine for rectangles, cylinders and tori but fails
> > for Möbius strips and Klein bottles.  The last two are perfectly
> > possibly, if a bit odd, choices of topology and it would be kind of
> > fun to support them.
> 
> The last two are not perfectly possible. Both those surfaces are
> non-orientable.

The rest of your discussion is quite interesting, but not important as
far as this question is concerned.

To repeat: not even all rectangles allow for independent normalization
of X and Y coordinates.  The orthogonal system proposed a few weeks ago
was a simple rectangle tilted at a 45 degree angle so that it would
appear flat with an orthogonal tileset.

  X X
X X X X
  X X X X
    X X X X
      X X X X
        X X X X
          X X

Tilt your head 45 degrees to the right to see the rectangle; it then
wraps off of the left and right sides.  Note that it is completely clean
topologically, but there is no possible way to normalize X and Y
coordinates independently because the axis of wrapping has components in
both directions.

Incidentally, I would call this a 12x2 rectangle.

jason