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Playfield topology
edit12.214.116.18 (talk · contribs · WHOIS) 'Changed the word "torus" to "grid." There's no telling where the torus myth got started, but the game stores the playfield in an ordinary array with three dimensions; in no way a torus.'
Start a new game, remove some pieces, then scroll around the board. After moving 32 squares in any of the 8 cardinal directions, you end up where you started. This behavior has the same topology as a torus. Yes, the program stores the playfield in a grid, but the edges of the grid are handled as if the north and south edges and the west and east edges are glued together. --Damian Yerrick (talk | stalk) 20:40, 24 February 2008 (UTC)
- I understand that. They call it "wrapping." If X < 0 Then X = X + Width. While a grid applied to a torus will result in this kind of wrapping, the play field itself looks nothing like a torus. Consider Pac-Man. If you go through the tunnel on the right side of the screen, you end up on the left side of the screen. Does this mean that the play field in Pac-Man is a torus? --12.214.116.18 (talk) 17:58, 26 February 2008 (UTC)
- A playfield that wraps in one dimension (west-east or north-south), as in Pac-Man, is homeomorphic to a cylinder. A playfield that wraps in both, as in Tetrisphere, is homeomorphic to a torus. This torus is is the cartesian product of the north-south circle with the west-east circle; each of these circles is 32 units long. --Damian Yerrick (talk | stalk) 03:08, 29 February 2008 (UTC)
- "The underlying topology of the game's playfield more closely resembles a grid of 32x32 squares per layer, wrapped at the edges, than a sphere." - The underlying topology is that of a torus. The argument that it doesn't look or feel like a torus holds no weight when considering the topology. If Pac-Man had multiple tunnels at the top/bottom and sides it's topology would also be that of a torus, and indeed there are a number of games, such as the very early Space War, that can play that way. 1dragon (talk) 15:06, 12 July 2009 (UTC)
- For those interested in the sphere Vs torus debate, here's - https://www.reddit.com/r/Games/comments/3d805y/ff7_takes_place_on_a_doughnut/ - an interesting discussion that in part points out that many games have a similar layout (that joins right to left, and top to bottom) and are essentially the equivalent to toruses (donuts). It's counter-intuitive to think this way for the game Tetrisphere, as the gameplay is visually represented as a ball/sphere. Here is another ref: https://www.quora.com/How-can-a-sphere-be-tiled-with-squares-with-minimal-distortion-if-the-goal-was-to-create-a-2D-square-grid-game-like-a-classic-2D-Pokemon-game-on-a-spherical-world 1dragon (talk) 08:22, 6 February 2022 (UTC)
- "The underlying topology of the game's playfield more closely resembles a grid of 32x32 squares per layer, wrapped at the edges, than a sphere." - The underlying topology is that of a torus. The argument that it doesn't look or feel like a torus holds no weight when considering the topology. If Pac-Man had multiple tunnels at the top/bottom and sides it's topology would also be that of a torus, and indeed there are a number of games, such as the very early Space War, that can play that way. 1dragon (talk) 15:06, 12 July 2009 (UTC)
- A playfield that wraps in one dimension (west-east or north-south), as in Pac-Man, is homeomorphic to a cylinder. A playfield that wraps in both, as in Tetrisphere, is homeomorphic to a torus. This torus is is the cartesian product of the north-south circle with the west-east circle; each of these circles is 32 units long. --Damian Yerrick (talk | stalk) 03:08, 29 February 2008 (UTC)