Covering Earth with Hexagonal Map Tiles [closed]

Question

Many strategy games use hexagonal tiles. One of the main advantages is that the distance between the center of any tile and all its neighboring tiles is the same.

I was wondering if anyone has any thoughts on marrying a hexagonal tile system with the traditional geographic system (longitude/latitude). I think it would be interesting to cover a globe with hexagonal tiles and be able to map a geographic coordinate to a tile.

Has anyone seen anything remotely close to this before?

UPDATE

I'm looking for a way to subdivide the surface of a sphere so that each division has the same surface area. Ideally, the centers of adjacent sub-divisions would be equidistant.

Answer 1

Take a look at vraid/earthgen; it uses hexagons (plus a few pentagons) and includes source code (see planet/grid/create_grid.cpp).

As of 2018 a new version is available based on racket.

Answer 2

Well, lots of people have made the point that you can't tile the sphere with hexagonal tiles - maybe you are wondering why.

Euler stated (and there are lots of interesting and different proofs, and even a whole book) that given a tile of the sphere in x Polygons with y Edges total and z vertices total (for example, a cube has 6 polygons with 12 edges and 8 vertices) the formula

x - y + z = 2

always holds (mind the minus sign).

(BTW: it's a topological statement so a cube and a sphere - or, to be precise, only their border - is really the same here)

If you want to use only hexagons to tile a sphere, you end up with x hexagons, having 6*x edges. However, one edge is shared by each pair of hexagons. So, we only want to count 3*x of them, and 6*x vertices but, again, each of them is shared by 3 hexagons so you end up with 2*x edges.

Now, using the formula:

x - 3*x + 2*x = 2

you end up with the false statement 0 = 2 - so you really can't use only hexagons.

That's why the classical soccer ball looks like it does - of course modern ones are more fancy but the basic fact remains.