26-01-2005 03:04									#1
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Before I begin, I realise the controversial nature of this post and understand that this will never be implemented. I do however want to post it, just so its out there.

One of my biggest annoyances with civ 2 was the cylindrical world, so I have alway been a fan of a spherical world. It was not till recently however that I realised that squares don't fit on a sphere. So I set out on a quest to find a polygon that would enable a map spherical map:

- every polygon is of the same type (this excludes the hexagon-pentagon mix of soccer balls)
- every polygon is adjacent to the same number of polygons (this excludes cubes the corner squares of which are adjacent to seven rather than eight squares)
-the polygons are regular

The only answer I can find is to use equilateral triangles. I didn't like the idea at first, but it doesn't look too bad...

Attachment: british isles as triangles.png
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	26-01-2005 07:32									#2
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Hi demipomme:

This has been discussed several times. Actually once we go to a continuous coordinate system (if we ever get there) then a sphere would be relatively easy. You should be able to find some of the earlier discussions by searching. I did one on "spher" but on got a Really old 1999 thread. There have been much more recent ones that I'm sure you can find if you're interested.

	27-01-2005 04:06									#3
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What are the likelihoods of a CCS being implimented then?

	29-01-2005 18:31									#4
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I still have a document on icosahedra somewhere on my files (there's something to do with pentagons when you're trying to pave a spgere correctly, but I don't remember all of it - it's somewhere on these forums).
The CCS is Gary's dream, so it very much depends on him having time to do it.

	29-01-2005 21:25									#5
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I always thought the problem with a CCs would be the question how you represent streets - it's easy for a unit to go from (x1, y1) to (x2, y2), but how do you get the fastest way from here to there? It's hard enough with tiles. Maybe it would help if you represented the roads not as one-dimensional lines, but as long-stretched areas, but I still don't know a working pathfinding algorithm. And that's what you'd need, right?

	30-01-2005 00:41									#6
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Before you give yourself a headache with the geometry, be aware that while there are several ways to tile a sphere with like polygons, none of them scale up to using a large number of tiles.

If you want a tile-based system with spherical geometry, you must accept that there will be a few corners, and then adapt your game mechanics so that they will not be terribly distorted at these corners.

	02-02-2005 02:14									#7
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quote: Originally posted by shimmin there are several ways to tile a sphere with like polygons, none of them scale up to using a large number of tiles.

As far as I can see, triangles do scale up. Four (or more) equilateral triangles fit in each equilateral triangle. See picture below.

There are really two separate issues in modelling a sphere:
1. dividing the surface into evenly sized units
2. presenting the sphere on a 2D screen (i.e. the use of projections)

Number 1 is solved by using triangles.

Number 2 can be ignored if the player only ever sees the world in 3D as a sphere. Zoomed in, it would look slightly flatter.

N.B. apologies for a mistake I made in the first post of this thread, even using triangles not every polygon is adjacent to the same number of polygons

	02-02-2005 02:17									#8
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Also, could someone explain CCS or point me in the direction of an explanation?

	02-02-2005 04:23									#9
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N.B. apologies for a mistake I made in the first post of this thread, even using triangles not every polygon is adjacent to the same number of polygons

That's part of what I was referring to: on the example you provide, most of the triangles have 12 neighbors, but some have only 11.

If this is acceptable, then you can also use squares: most of the squares have eight neighbors, but some will have 7.

	02-02-2005 08:40									#10
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In order to make a perfect sphere using anything but CCS some compromises will haveto be made.

FE: You could use hexigons, but you'd haveto accept that there would be exactly 5 pentagons, no matter what size.

Or triganles being the smallest unit, other than a pixel, to represent the map best would have exactly 5 areas where there would be 11 triangles vs. 12 as neigbors.

Compared to using squares, those disortions pale into signifgance.

There is no way around anything except with CCS.

Last edited by Lord God Jinnai on 02-02-2005 at 08:55

	02-02-2005 16:22									#11
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Or if you're willing to accept a spherical world and not a true sphere.

	03-02-2005 00:15									#12
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What would a CCS map look like?
If it is something like latitute and longitude, how do you counter for the increased resolution at high latitude?

I had a think about a sphere of squares and found this picture on the web. I can't visualise it, but couldn't you smooth it out into a sphere of squares?

Attachment: lego sphere.bmp
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	03-02-2005 03:45									#13
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quote: Originally posted by demipomme Also, could someone explain CCS or point me in the direction of an explanation?

CCS = Continuous Coordinate System

This is the type of movement system used in RTS games. Units don't rely on squares, they just move to a certain point in space (x & y coordinate). Presumably, cities and borders would work the same way for Clash.