Mapping a 2D grid onto a sphere

[DarkDepths]

I have been asked to map a grid onto a sphere. The basic idea, as I understand it, is very similar to Civilization 4, if you have played it. If you haven't, the game basically works as a 2D RTS, but the 2D map is wrapped around a sphere that you can rotate and zoom in on and has 3D elements placed on the different grid tiles.

I have no idea how to accomplish this. I have worked quite extensively with 3D geometry and it seems to me that you can't fit a bunch of square onto a sphere. The squares must deform at some point.

In Civ 4, I think part of the way they get around this is by removing the poles from active play. They simply cover them with ice and say "You can't go there." I think that solves a portion of the problem, because most of the deformation usually occurs at the poles. However, the only truly perfect squares, methinks, would be in a ring around the equator. So again, I'm stuck.

Initially, I thought it would be best to essentially make it as a 2D game and map it onto a sphere. When I click a spot on the sphere, I would then (somehow) translate that into a grid cell. I'd make changes to the 2D grid, and then map it back onto the sphere.

The more I think about it though, the more horrible it sounds. I don't know how to map a 2D grid onto a sphere, I don't know how to pick a cell from a place on a sphere, I don't know how long it will take to map the grid to the sphere (so doing it 30 times a second might not be plausible), I just don't know!


So, any thoughts from you guys would be super duper cool!

Thanks!

Edit: I thought I should mention (since you will probably tell me to use google (:)) that I considered using the catmul-rom algorithm to make an approximate sphere with perfect square polygons. However, I was hoping to accomplish this without subdividing a sphere a gagillion times. By that I mean, ideally, I'd like to have as many grid cells as I want on a sphere with constant number of polygons.

[REDDemon]

u can make a ICO sphere split everi face in 4 pieces an repeat as you want (max 4 or 5 subdivision). then you can assume every 2 triangles are a quad. (not really. but if you zoom only local you can scale triangles to seem squares).

[DarkDepths]

Thanks for the reply, but your solution still requires me to subdivide the sphere many times.

I think I've changed my mind on exactly what I want to do. First, rather than using a square grid, I'll use a hexagonal grid. Secondly, it won't span the entire globe, it will be just a wide band around the equator with the poles blocked off.

I suppose my next question would be better suited in the beginners forum, but as it is currently a contemplation and not really an implementation, I think it might fit here...

So I guess the question would be, is it feasible/possible to get the coordinates of a texture based on where you click on a model. I don't know a lot about Texture coordinates, but it seems to my uneducated mind that I would need to make use of them for this task...