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Games wind up using cylinders because of the hairy ball theorem

http://en.wikipedia.org/wiki/Hairy_ball_theorem

There are always going to be points on a sphere that map poorly to 2D - if you've played Spore, think of the in-planet spaceship map, you wind up zooming through parts of the map and crawling through others while still going the same speed in-game.

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I don't think this is relevant in this case; I don't see how vector fields matter in a turn-based strategy game where all movement is quantized.

A unit's movement options are vectors. As it's designed, you've got vectors in the due directions and the medians between those, each scaled to be the size necessary to make the grid work as mapped from a sphere for the particular location. So the east vector at 45 N is root(2)/2 the size it is at the equator.

So if you've got an east vector for every square that is a function of the location, that means there's an east vector field. Same goes for the other seven options. Might as well make a zero at the poles, since one zero is weird, zeroes that don't line up are weird, and no one wants to settle at the poles anyway.

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