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

I've just built an R package called dggridR which divides the surface of the Earth into equally sized hexagons for the purposes of binned spatial analysis.

Carsten makes this sound impossible in his answer, but, practically speaking, it's not. By introducing 12 pentagons all the rest of the hexagons fit together without an issue. Since you may have millions upon millions of cells for a highly-resolved grid, you can forget about those pentagons most of the time.

The maths of the transformation are complicated. You can find them in:

• Crider, John E. “Exact Equations for Fuller’s Map Projection and Inverse.” Cartographica: The International Journal for Geographic Information and Geovisualization 43.1 (2008): 67–72. Web.

• Snyder, John P. “An Equal-Area Map Projection For Polyhedral Globes.” Cartographica: The International Journal for Geographic Information and Geovisualization 29.1 (1992): 10–21. Web.

In the background dggridR relies on Kevin Sahr's DGGRID software.

You may also find the following references to be of use:

• Gregory, Matthew J. et al. “A Comparison of Intercell Metrics on Discrete Global Grid Systems.” Computers, Environment and Urban Systems 32.3 (2008): 188–203. CrossRef. Web.
• Kimerling, Jon A. et al. “Comparing Geometrical Properties of Global Grids.” Cartography and Geographic Information Science 26.4 (1999): 271–288. Print.
• Sahr, K. “Hexagonal Discrete Global GRID Systems for Geospatial Computing.” Archiwum Fotogrametrii, Kartografii i Teledetekcji Vol. 22 (2011): 363–376. Print.
• Sahr, Kevin. “Location Coding on Icosahedral Aperture 3 Hexagon Discrete Global Grids.” Computers, Environment and Urban Systems 32.3 (2008): 174–187. CrossRef. Web.
• Sahr, Kevin, Denis White, and A. Jon Kimerling. “Geodesic Discrete Global Grid Systems.” Cartography and Geographic Information Science 30.2 (2003): 121–134. Print.