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

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

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



Billy Naylor wrote:
> <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.
[...]
> 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

This is already the case if you just think about it.

In the model outlined above, if one moves north at the top edge of the map
one enters a tile that is equivalent to one 180 degrees around/along the
top border. Because the inside half of the torus is just another wrapped
image of the outside, it is the same as moving off the west edge and
entering on the east in a standard cylinder.

Note there are *no* problems with ZoC or any adjacency relationships. If
one sets up a suitable scrolling mapview or canvas, one can move continuously
through and over the poles, and there is absolutely no difference than doing
so through any other point. One can make cities at the poles and carry out
any other operations as game mechanics fully supports this without change.


The problem Marcelo has is that there isn't just one tile representing the
pole. There is a line of tiles that goes all the way across the map. The map
plays fine because there is no rule that depends on poles being points, but
to a mathematician, the fact that one doesn't have a single tile pole is
aesthetically displeasing. Most people don't care about this because maps
have been drawn this way in a 2-D projection since the dawn of time so we
grow up with this distortion and don't hink much about it.


Cheers,
RossW
=====