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

["Marcelo Burda" <NOSPAM_mburda@xxxxxxxxx>]

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

Le mer 25/02/2004 à 12:31, Billy Naylor a écrit :
> <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
> 
that broken all topological consept. this ideas is not a crazy one but a
North tile has 3+map.xsize nears tiles. this is really complex. Why
define ZoC in this case. this is not a good way.

notes about last proposal of Ross
---------------------------------
the mirror-offset is Best than classic topology but is far of a sphere
too. and this learn nothing to players. more bad player can thinck that
is a sphere topo. that is bad.(as teacher i prefer classic topo that
this bad one)
The good point of it is there are 0 singularities! easy for fist game
play.
But this is complex to implements:
this need a mirror-offset wraps at N, and S, and a simplest wraps E-W
the mirror part of mirror-offset wraps need a vertical flip. and a
vertical-flip canvas in clients.
This is the somme type of complex implement than the reverse-wraps and
reverse canvas in Quincuntial. i can moderate-easy extend the
quincuntial patch to make this but befor i need all extention in This
patch ( ExtendedTopologies.V2.XX) and all of extention in Quincuntial
(ExtendedTopologies.V3.XX)

FAQ:what is a mirror-offset wraps?

the canonical(real) maps is

ABCD
EFGH

Ywrap type is
simple,mirror, offset, mirror-offset, reversed

abcd   efgh    cdab    ghzf           hgfe
efgh   abcd    ghef    cdab           dcba
ABCD   ABCD    ABCD    ABCD           ABCD
EFGH   EFGH    EFGH    EFGH           EFGH

the mirror has the somme gameplay than no wraps wrap (Go from A to a is
a no move move !)

Notes about 0-Torus(sphere) and infinite plane
--------------------------------------
the infinite plane is a 0-Torus (a was wrong last time) to porobe it i
need a projection to map the sphere in the plane and the plane in the
space this exist, this is the stereographic projection.
This is a conformal projection as quincutial (canformal = equal angles)
We use  stereographic projection to make half planet maps. a full planet
map need a infinite map! but a full infinite maps has only one Europa,
one NZ etc etc. this is a 1-1

there is not posible to make the some with the 1-Torus(torus) or
2-Torus( torus of Klein) exept if you make Worms holes in the plane!
-- 
 . /  .     '    ,    .      (*)   '        `     '      `    .    
  |    ,  |   `     ,     .      ,   '  Marcelo Julián Burda      .
 /  '     \     `     \@_     '      .        '      `        '    
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