Thanks! Interestingly, most asteroid shooting games are on tori (toruses?); when you leave the screen from above you appear below and when you leave it from the side you appear from the other side. In the case of the real projective plane (or half sphere), when you leave at one point of the circle, you appear from the opposite point (there's no "other side of the sphere"); This is fun because no matter where you shoot, you'll hit yourself in the back if you don't move (this wouldn't be the case in the torus; only if you shoot upwards or sideways, or at a certain specific angles).