Are there any actual aversions of this trope in RP Gs, i.e. actual spherical overworlds?
Yet One More Idiot
I was just thinking about this particular trope, and I realised - geography is the study of the structures on the Earth (or another planet), but this trope is about the planet's shape itself. Shouldn't it technically be "Videogame Geometry" instead?
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Nah, geometry is even less associated with world shapes.
"For a successful technology, reality must take precedence over public relations, for Nature cannot be fooled." - Richard Feynman
Ahh, no, I got my words wrong; I was trying to remember the courses from my degree. :P Geometry is the measuring of the Earth. I think I should've said Topology? Ah, it doesn't matter anyway. :P
Can't game designers make it so the center and the edges of the map are actually the poles? I mean, wouldn't that solve turning the map into a Toroid?
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Actually, I think it might solve the problem. If you use standard stereographic projection of the globe (from the North Pole, projecting onto a plane through the equator), then the map that it produces has the South Pole at the origin (0,0), the equator goes to the unit circle, and the North Pole becomes the line at infinity. Which is exactly what you wanted, only infinitely large.
Cut the map down to a finite size (so you're ignoring a small portion near the North Pole), and you've got what you wanted. All points at the edge are the North Pole, and passing off the map at any point on that edge brings you to the same point on the other side. Except for the little polar region of the globe we cut off, which is the rest of the infinitely-sized projection.
Only such a map would not rectangular, like the ones commonly used by video game designers, it would be circular. But I'm sure that wouldn't pose a problem to the designers.
Final Fantasy II is a uniquely extreme example of the "torus-shaped planet" phenomenon: the map cannot even be projected onto a sphere without breaking up at least one of the continents.
Are there any other examples of this, and does this phenomenon have a name in geometry?