Covering Earth with Hexagonal Map Tiles

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

Read "Geodesic Discrete Global Grid Systems" by Kevin Sahr, Denis White, and A. Jon Kimerling

You can find it here...

Answer 2

You can't cover a sphere with equal hexagons, but you could cover it with a geodesic, which is mostly hexagons, with 12 pentagons at the vertices of an icosohedron, and the hexagons slightly distorted to make it bulge into a sphere.

Answer 3

The first website that comes to mind is Amit's Game Programming Information and its collection of links on hexagonal grids.

Answer 4

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.

Answer 5

Hexagonal tiles are too complicated for regular geometry as applied to geospatial uses. Check out HTM for a similar thing with triangles or google for "Hierarchical Triangular Mesh" for other sources.

Answer 6

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.