Originally posted by Enigma_Nova
Save for the 8 corners where you can go north, east and south and end up at your starting location. :/
Drachsor: It may look like a sphere, but try combining the hemisphere in your link with itself to produce a sphere.
You'll notice that it doesn't quite fit.
That sphere has a line of squares going around the equator.
Each square has a neighbour on both the north and south.
That in effect creates a series of bands, which can only end up as having the same # of squares around the equator in a small circle around the pole.
It is, in effect, a distorted cylinder.
Save for the 8 corners where you can go north, east and south and end up at your starting location. :/
Drachsor: It may look like a sphere, but try combining the hemisphere in your link with itself to produce a sphere.
You'll notice that it doesn't quite fit.
That sphere has a line of squares going around the equator.
Each square has a neighbour on both the north and south.
That in effect creates a series of bands, which can only end up as having the same # of squares around the equator in a small circle around the pole.
It is, in effect, a distorted cylinder.
As for the example I gave, now that I look at it again, it has the same problem as the square. As you move up from the equator, you have less squares in each band (notice the vertical lines). So there will be squares that have north/south/east/west neighbors, but are lacking in diagonal neighbors. Basically, then, we can handle a sphere quite easily if we are willing to give up some diagonal neighbors.
Hmm, I am not sure if there is a way to map a square or hexagonal grid to sphere without having more or less neighbors in some areas.
-Drachasor
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