In the report bug , there is only mention of the symmetry , but not of the rotations
I can think of the following symmetry operations (point group C6v, if you know group theory ):
- mirroring at one plane (for me, it is easier to think of the map as a 3D object with heights): creates maps for 2 players
- mirroring at three planes (in the main directions west-east, NW-SE,NE-SW): for 6 players
- (it is also possible to use the orthogonal planes (north-south and so on), but probably more difficult to implement
- mirroring at two orthogonal planes (e.g. W-E and N-S) (I am not sure whether that is possible): for 4 players
- rotation by 180°: for 2 players
- rotation by 120°: for 3 players
- rotation by 60°: for 6 players
Of course you can use multiples of the indicated player numbers, but the map is then not completely fair.
But at least , the symmetry axle which follows the same direction of the road from a building to its flag could create a symmetry that keeps things fair.
I have never thought of that, but you are right! However, I assume that the most natural mirror plane would be east-west, so that way would be a bit strange.
I think neither the symmetry nor the rotations (or translations) are hard to "algebrize"
Since the map internally works with Cartesian coordinates, rotation by 60°/120° are not that easy. Furthermore, you have to think about what you do at the borders (to use the symmetry operations, you have to cut the map somewhere, and then it is rectangular, which does not fit to rotation by 60°/120°.
"Only few people know how much one has to know in order to know how little one knows." - Werner Heisenberg