
Re: "real world" uses of topology?
Posted:
Mar 4, 2001 4:15 PM


Yes, Kevin, that's what they did. I couldn't understand how it worked, so I made a meticulous map locating every square. When I was done. I realized it was the map of a torus.
Martin Green http://www.onforeignsoil.com Teach yourself Yiddish while you read the exciting autobiography of Falk Zolf.
"Kevin Foltinek" <foltinek@math.utexas.edu> wrote in message news://wo6lmqlihxb.fsf@linux41.ma.utexas.edu... > "Martin Green" <btestware@home.com> writes: > > > > Someone once developed a video game that was supposed to be > > > like a 3d version of Tetris. It was played on a spherical planet > > > that was laid out in a checkerboard. You could rotate the sphere > > > left, right, up, and down, and you always saw this checkerboard > > > pattern in front of you.Topologically, this is impossible on a shpere! > > > (Lines of longitude have to meet SOMEWHERE.) > > > How did the game developers solve this problem??? > > I haven't seen the game, so I'm merely speculating. > > Perhaps the spherical planet is not spherical, but toroidal. (Rather > like the universe in Asteroids, PacMan, etc., is a torus.) I think > it would be easy to give the illusion of a spherical planet, by > assigning a metric to the torus which has positive Gauss curvature in > the "visible" portion, and isometrically embedding that portion into > Euclidean 3space and performing the obvious projection. (Presumably > there are ways to do this which make the final mapping (x,y)_{torus} > > (x,y)_{display} computationally inexpensive.) > > Kevin.

