Topological Asteroids

See the mathematical background for this game here.

See the source code for this game here.

This is a game based on the classic 1979 Atari arcade game Asteroids, in which the player controls a ship and attempts to avoid and destroy asteroids floating around in space. The original arcade game takes place on a torus, with both the player's ship and the asteroids wrapping around from one side of the screen to the other, requiring the player to develop an intuitive understanding of how the game's space connects to itself in order to effectively play.
    
In this variant of the game, the player can choose from six different topological surfaces (the torus, Klein bottle, sphere, real projective plane, cylinder, and Möbius strip) to play on. All of these spaces wrap around in one or two directions, but some of them mirror or rotate objects as they move across edges, meaning that the player (and their controls) can become mirrored. It is possible to interpret each space as either consisting of a single screen whose edges connect to each other, or as an infinite array of tiles that fill the Euclidean plane. In order to better view these two interpretations, the camera can be adjusted to either remain fixed in space or follow the player.

THIS IS A FREE GAME. I encourage you to download it, play with it, and modify the source code as much as you like free of charge. If, however, you really, really want to pay for it and it is within your means to do so, I would not say no to your financial support.