[FreecivDev] Re: (PR#7287) Extended Topologies
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<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 2D torusworld surface is thus an
> easy second step.
>
> 1) Take a spherical Earth and stick a straw through the NS 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 halftorus, 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 supertile that contains the entire torus surface.
>
> When one maps this to a 2D torusworld, 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 2D 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.
>
Ok, i need refulmulate the question!
Can you make a good map?
You make a nice mapart but in you torus you create N europa! N america
etc. etc.
in a sphere there are One Europa, etc, etc.
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 0Torus of R³, the torus is a 1Torus of R³, there
are 2Torus,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).
To call 2 topologies equals you need at last find a single relation
point by point.(homéomorphisme)
This is wrong to thinck you can assimilate 4Quincutial map to One torus
and say that is equals. in 4Quincuntial map you See 4 time all units!!
Torus(or twisted torus) are A clossed 2D space, sphere are a Clossed 2D
space! that is ok
But there are not equals!!!!!!!
there are not 11 point projection.
Quincuntial is A clossed 2D space and there are a 11 point
projection(and conformal) exept for 4 points. this is the best way to
project the sphere in a FLATE 2D if you like a clossed 2D space.
Why quincuntial as 4 singularitie? The sphere surface are not Flat, and
the Quincuntials surface are flat. This is compensated in the 4
singularities.
Best regards

. / . ' , . (*) ' ` ' ` .
 ,  ` , . , ' Marcelo Julián Burda .
/ ' \ ` \@_ ' . ' ` '
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
 [FreecivDev] Re: (PR#7287) Extended Topologies, (continued)
 [FreecivDev] Re: (PR#7287) Extended Topologies, Jason Short, 2004/02/21
 [FreecivDev] Re: (PR#7287) Extended Topologies, Marcelo Burda, 2004/02/22
 [FreecivDev] (PR#7287) Extended Topologies, Marcelo Burda, 2004/02/22
 [FreecivDev] Re: (PR#7287) Extended Topologies, rwetmore@xxxxxxxxxxxx, 2004/02/22
 [FreecivDev] Re: (PR#7287) Extended Topologies, Jason Short, 2004/02/22
 [FreecivDev] Re: (PR#7287) Extended Topologies, Marcelo Burda, 2004/02/22
 [FreecivDev] Re: (PR#7287) Extended Topologies, rwetmore@xxxxxxxxxxxx, 2004/02/23
 [FreecivDev] Re: (PR#7287) Extended Topologies, rwetmore@xxxxxxxxxxxx, 2004/02/23
 [FreecivDev] Re: (PR#7287) Extended Topologies, rwetmore@xxxxxxxxxxxx, 2004/02/23
 [FreecivDev] Re: (PR#7287) Extended Topologies, Jason Short, 2004/02/23
 [FreecivDev] Re: (PR#7287) Extended Topologies,
Marcelo Burda <=
 [FreecivDev] Re: (PR#7287) Extended Topologies, Marcelo Burda, 2004/02/23
 [FreecivDev] Re: (PR#7287) Extended Topologies(PR#6721), Marcelo Burda, 2004/02/23
 [FreecivDev] Re: (PR#7287) Extended Topologies, Morgan Jones, 2004/02/23
 [FreecivDev] Re: (PR#7287) Extended Topologies, Jason Short, 2004/02/23
 [FreecivDev] Re: (PR#7287) Extended Topologies, rwetmore@xxxxxxxxxxxx, 2004/02/23
 [FreecivDev] (PR#7287) Extended Topologies, Marcelo Burda, 2004/02/25
 [FreecivDev] (PR#7287) Extended Topologies, Marcelo Burda, 2004/02/25
 [FreecivDev] Re: (PR#7287) Extended Topologies, Jason Short, 2004/02/23

