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

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

<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.
>>
>>
>>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
>>=====
[...]
> Ok, i need refulmulate the question!
> Can you make a good map?

Good for what purpose ... the above torus mapping is good for a tilable
gaming surface, unlike the quincunx which has non-intuitive singularities
and severe problems because of them.

> 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.

Please, Marcelo do not make silly statements like this.

If one tiles a map to make it an infinite surface, there are an infinite
number of normal sets in the resulting 2-D plane. How many one chooses to
take as a base tile for understanding the mechanics really doen't matter.
Certainly to explain tiling, more than one is needed. What is needed now
is understanding of the mechanics of your map topology and specifically
the game playing mechanics since one is coding a game.

If you want to call the above a half-torus map so it contains only one normal
set that is fine. The wrapping at the half torus edges is one of the more
complex ones and there are at least two different half donut normal sets that
one can start from. It takes two of these to form a super tile with simple
wrapping or tiling properties. But this does not alter the 2-D projection or
its appearance as one scrolls a GUI window over it.

[...]
> This is wrong to thinck you can assimilate 4-Quincutial map to One torus
> and say that is equals. in 4-Quincuntial map you See 4 time all units!! 

No, again. Stop thinking about some mathematical point that no one cares
about and start thinking about what the 11-year old sees as the 2-D
surface, I know this can be hard :-).

What the GUI window displays depends on how big you make it. If you expand
it to cover a 3x3 sized map area you will see 9 maps. The big question is
whether Freeciv allows you to actually see all 9, or masks out all but a
given normal set. The latter is the current rule, so a big GUI window would
be mostly black tiles. But all this is client implementation stuff, and has
nothing to do with the basic model and logic one is trying to make
understandable.

The point of unrolling the wrapping to use 4 quincunxes so the super-tile
has simple wrapping at its edges, is just a trivial transformation to help
people see what the tiled 2-D surface really looks like, rather than trying to
do complex wrapping in their heads, or put it all together by looking through
a limited GUI window. It is the same as unrolling two earths into a torus
mapping.


Perhaps you need to stop thinking torus-world and just think simple tiling
when you consider the infinite 2-D map display, so your knee jerk problems
with torus and sphere associations don't keep getting in the way when
considering the projected 2-D surface properties.

[...]
> Quincuntial is A clossed 2D space and there are a 1-1 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.

It makes a reasonable single map, but not tilable one. The singularities
completly muck up the adjacencies across normal set boundaries. Like ratios
you need to put yourself in a normal person's shoes and not those of some
advanced mathetician and consider what they are seeing.

The fact that you admit you cannot make cities near the singularities is
just one indication of the underlying technical snafus and adjacency problems
that make it unplayable, and a likely minefield of future maintenance errors.

> Why quincuntial as 4 singularitie? The sphere surface are not Flat, and
> the Quincuntials surface are flat. This is compensated in the 4
> singularities.

Right. And a torus stretches the point at the poles into a line. When
flattening it, you do simple stretching of the latitudinal lines. No
singularities, just different stretches as compensation.

The distortions are different in each case. But for a tilable 2-D surface
the torus mapping is clearly far superior to your current quincunx model.
And since most wall maps are displayed using the same flattening model,
this means that map mechanics are intuitively understood by game players.


Until some of the problems with tiling quincunxes are worked out, I'm
afraid it doesn't quite measure up. I'd still like to see you spend some
effort trying to resolve the problems rather than trying to argue they do
not exist. But then, maybe the quincunx model is inherently broken and
unsuitable for game play. I haven't come to the conclusion there is no
solution yet though.

Part of coming to that solution is to understand how many sewing operations
cause the same headaches as qunicunxes, and if there are really only one or
two that are worth building into Extended Topologies. Are these problems
inherent to anything with a singularity? Are there no fixes or workarounds?

> Best regards


Cheers,
RossW
=====