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Topic: "real world" uses of topology?
Replies: 15   Last Post: Mar 4, 2001 5:51 PM

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Kevin Foltinek

Posts: 680
Registered: 12/8/04
Re: "real world" uses of topology?
Posted: Mar 4, 2001 12:05 PM
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"Martin Green" <> writes:

> > Someone once developed a video game that was supposed to be
> > like a 3-d 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, Pac-Man, 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 3-space 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.)


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