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

["Jason Short" <jdorje@xxxxxxxxxxxxxxxxxxxxx>]

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

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

>>You make a nice map-art but in you torus you create N europa! N america
>>etc. etc.
>>in a sphere there are One Europa, etc, etc.

I think what Ross is talking about is a reverse-wrap with a half-map 
offset.  So you have

   pqr-mno pqr-mno pqr-mno
   jkl-ghi jkl-ghi jkl-ghi
   def-abc def-abc def-abc
   abc def-ABC DEF-abc def
   ghi jkl-GHI JKL-ghi jkl
   mno pqr-MNO PQR-mno pqr
   pqr-mno pqr-mno pqr-mno
   jkl-ghi jkl-ghi jkl-ghi
   def-abc def-abc def-abc

We've considered this wrapping before but decided it was invalid.  I 
don't remember why.  Note that in 3 dimensions this can't be done as a 
sphere (it can be done as a torus with extra congruencies), but in 2D it 
looks okay...

jason