
Re: "real world" uses of topology?
Posted:
Mar 4, 2001 12:05 PM


"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.

