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

["rwetmore@xxxxxxxxxxxx" <rwetmore@xxxxxxxxxxxx>]

<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.


Note, a normal set is represented by a half torus, and there are two
normal sets in a super-tile that contains the entire torus surface.

When one maps this to a 2-D torus-world, one usually does a standard
Mercator projection, i.e. stretch the latitudinal lines as one moves to
the poles, but shrink the longitudinal direction correspondingly to
preserve constant area of any square patch. A cut along any longitudinal
line allows one to peel and flatten the map out onto a 2-D plane.

Cheers,
RossW
=====

Marcelo Burda wrote:
> Le dim 22/02/2004 à 15:48, Ross Wetmore a écrit :
> 
>>Jason Short wrote:
>>
>>><URL: http://rt.freeciv.org/Ticket/Display.html?id=7287 >
>>>
>>>rwetmore@xxxxxxxxxxxx wrote:
[...]
> Yes torus is easy, but not sphere like!
> Can you make a map of real Earth in a torus? no.
> Can you make a map of Earth in quincuntial? Yes.
> Yes quicuntial is a litle harder to code. but i am coded it, pleas help
> me to make it easy to undestand.
[...]
> Marcelo.