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Max Sinister
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quote: Originally posted by Leland
Not quite regular. In a geodesic sphere for example the triangles are only approximately regular (i.e. every angle is not exactly 60 degrees). On the other hand, dodecahedron for example consists of "non-distorted" regular triangles. |
Nitpick (geometry):
1. Yes, triangles on a sphere have angles bigger than 60 degrees, but it also depends upon the size of them: A triangle covering one eighth of the surface would have 90 degree angles, but if we have a sphere covered with several thousand or even ten thousand triangles, the difference wouldn't be noticable.
2. Don't you mean icosahedron? I think a dodecahedron has twelve pentagons, an icosahedron has 20 triangles as its sides.
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Leland
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quote: Originally posted by Max Sinister
Nitpick (geometry):
1. Yes, triangles on a sphere have angles bigger than 60 degrees, but it also depends upon the size of them: A triangle covering one eighth of the surface would have 90 degree angles, but if we have a sphere covered with several thousand or even ten thousand triangles, the difference wouldn't be noticable. |
Ah, but you have the pentagons (or the points around which you have only five triangles instead of six) to mess things up. The tiles next to the pentagons will always be distorted noticeably and you can't get away with this. The tiles farthest away from the pentagons (i.e. the tiles that are in the center of the hexagonal sides of the "soccer ball") will be more or less regular.
The difference between adjacent tiles might not be big enough to be an annoyance to the player (in fact I would love to see a game attempt a map like this), but nevertheless it would make map geometry complex enough to warrant a 3d or a vector based graphics engine.
quote: 2. Don't you mean icosahedron? I think a dodecahedron has twelve pentagons, an icosahedron has 20 triangles as its sides. |
I stand corrected.
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