[kgkkxwjl] Mercator for games

From the point of view of the player, the map is an infinitely tall cylinder.  To the extreme north and south are vast unending stretches of boring frozen wasteland.  From the point of view of the player, everything is Euclidean, except for the wraparound of the cylinder.

Internally, the game occasionally computes a Mercator map projection (actually, its inverse) of the cylinder onto a sphere.  Maybe to calculate the locations of sun and stars in the sky, or to determine climate.  The North and South poles are not reachable by the player: they are infinitely far away.  This conveniently avoids issues like going so far north that one starts traveling south.

The game could model the real earth, though from the point of view of the player, it might be strange how Greenland actually is so large in the game, and Antarctica and the Arctic Ocean are infinite in area.

Can the game interestingly take advantage of the fact that Mercator is the only conformal cylindrical map projection?