How can you 'tile' a 3D globe if your existing artwork and maps are simple 2D grids?
Are there approaches that can re-use much of the artwork and such?
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I've built something like what you're looking for. I used this site mostly as a reference for the map build process. BUGS Geodesic Map
The basic steps:
In mine, the whole grid is one giant mesh, not repeated cell models (http://blog.chronoclast.com/search/label/OTD). For lower mesh resolutions this runs okay. If you're looking at tens of thousands of cells, you'll want to explore more dynamic mesh building - mine is all pre-built. Cells are textured off a page-map (2/9/16... textures per image) and can blend uv's (that was hard, took forever, still kind of meh).
Our game "Save Us!" used that. It is pretty fun to have rts on planet and control it. Save us gameplay (but the game is not fun at all :-))
Save Us! Uses regular 2D heightmap which is transformed to a sphere. It is easy to do, but has problem on sphere's poles. We just have there ocean. Not really nice solution, but works. Problem of non rectangular tiles is not big. It looks quite ok. For determining which tile is clicked we use color picking.
This is old project and the solution is not the best, but it is very very easy and quite good looking.
Much better solution should be usage of icosphere.