. So there isn't any distortion because the map obviously isn't a torus, its a flat map that is continuously joined on the computer. By the way the edges are joined, (top of screen rolls to bottom, left rolls to right.) the surface can be described a torus. A person moving on a theoretical subterfuge torus would see what we see when we scroll around.
. The reason it isn't a sphere is because there aren't poles to roll around. If I center on an outpost, and scroll up, there is another outpost that is directly opposite it. (You know, where the travel line switches from travel left to travel right, or vice versa.) You could then say that these two points form a 'pole' that the map orbits around. Of course, only spheres have poles. So it's a sphere then? No. Because if a sphere has a pole, no matter where you are on the equator, moving up will take you to the pole. Think of the arctic. If you stand on the equator and move forward, you end up in the arctic. If you move left along the equator, then move up, you still end up in the arctic.
. However, on the subterfuge world, if set two theoretical poles, go to the theoretical equator, and move up, I do not always end up at the pole. That's because the world is a torus, and the two poles I set aren't on opposite sided of a globe, they are on opposite sided of the cylinder. Think of a bagel if you can't visualize it. Hold a bagel, and stab a pencil through it. One outpost you selected is the entrance point, the other is the exit point. When you go from pole to pole, you're just going around and around these points. If you follow the equator right, or roll the bagel right, and then scroll up, you go around a new part of the cylinder.
. So, the map scroll functions as a torus, but there's no distortion because its not actually a physical torus.
Math is the worst.
-Isaac Newton