[Freeciv-Dev] Re: (PR#7287) Extended Topologies

["Billy Naylor" <banjo@xxxxxxxxxx>]

<URL: http://rt.freeciv.org/Ticket/Display.html?id=7287 >

On Tue, 2004-02-24 at 13:27, Marcelo Burda wrote:
> <URL: http://rt.freeciv.org/Ticket/Display.html?id=7287 >
> 
> Le lun 23/02/2004 à 17:37, rwetmore@xxxxxxxxxxxx a écrit :
> > <URL: http://rt.freeciv.org/Ticket/Display.html?id=7287 >
> > 
> > 
> > Just for amusement's sake, here is a recipe to make a map of real Earth
> > in a torus. The projection to the 2-D torus-world surface is thus an
> > easy second step.
> > 
> > 1)  Take a spherical Earth and stick a straw through the N-S polar axis.
> > 
> > 2)  Widen the diameter of the straw stretching all the latitudinal lines
> >      correspondingly to maintain the hemispherical property of longitudinal
> >      cuts. Once the straw diameter is greater than the original diameter
> >      of the sphere you have a half-torus, namely the outer half.
> > 
> > 3)  Reflect the half torus through the cylinder walls of the straw and
> >      rotate the inner half torus by 180 degrees.
> > 
> > Voila, one has a torus with a map of the real Earth.
> > 

> Sorry, but torus can not canverted in sphere. there are not
> equals(homéomorphes) topologies(math). Torus has a hole, sphere not!!!
> (in math we separate the orineted clossed surfaces by the numbers of
> holes: a sphere is a 0-Torus of R³, the torus is a 1-Torus of R³, there
> are 2-Torus,etc. there are not equals!) 
> 
> If you make not single projection from sphere to torus. you can map over
> any object. But this is not the some Topology(math).

what if units could move through the top and come out on some other top
edge tile ?  Maybe the player could choose, or maybe it's halfway along.

Wouldn't this create the polar effect we're after?
It'd play hell with ZoC at the poles. 
 
--banjo