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Leland
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I have an idea for a pentagonal map... that is, a map whose tiles are regular pentagons that fill an arbitrarily large area.
First, start off with a dodecahedron (consisting of 12 regular pentagons) and think of it as a sphere with a circumference of 1. Now, imagine another sphere inside it, which is only slightly smaller, and that there's a circular "edge" which connects these two spheres so that if you walk over the edge you always either drop from the outer sphere to the inner one, or climb from the inner one to the outer one in a continuous manner. On a computer where we think of the surface of the sphere (i.e. the actual map we see) as flat, the spheres can be exactly the same size, so what we've got is a map consisting of two spheres.
More spheres can be added in similar manner... the "edge" now works as a teleporter that always drops you down one level, except in the final level it puts you all the way to the top (or, if you are walking in the other direction, does exactly the opposite). It might be a little bit difficult to visualize, but I think that this way it may be possible to have a uniform map of regular pentagons.
Does this work?
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geeslaka
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of the purple hand
Jun 2003
time: 22:27
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This is how a rectangular map could have the topological properties of a Klein botle.
code:
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| a|| c|| e|| g|
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|h ||b ||d ||f |
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The columns of lines represent smooth frictionless hemispheres that units slide over.without stopping.
If a unit goes left from point a it moves to point b.
c<->d e<->f g<->h
It might be a good idea after all.
Last edited by geeslaka on 08-07-2003 at 18:10
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Leland
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Actually, I realized that the scheme doesn't work out quite so easily. Back to the drawing board...
The "edge" was supposed to be just an arbitrary circumference of the sphere, like equator. It would have been totally invisible to the players. As for visualizing a map like that, well, I can think of multiple ways actually. One would be to allow gaps between tiles, and when scrolling the map the gaps would close so that they're least obtrusive at the exact center of the map. Another way would be to distort the map on the edges. Tiles would still be visible, but their shapes would be messed up. Next time, I think I'll try to come up with a visualization first and write the explanation around that. Maybe even make a little demo program or something.
To see weird topologies like this in actual games would probably require that the games themselves only have a very abstract representation of a map (e.g. as an arbitrary graph) and provides an API for plugging in new topologies and visualizations. I can't imagine that happening in commercial projects because it's beyond simple modding, but maybe an open-source project somewhere will take heed...
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Inverse Icarus
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flying too low to the ground
May 2001
time: 00:27
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i'm thinking about what gees said, and adapted it to simple shpereical maps. i think it would be fairly easy to "fake" the sphere by creating "warps" that took you from the top of one area to the top of another, equidistant from the center of the map. to (ab)use his example:
code:
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a->b, f->e. it's simple. you'd essentially be splitting the globe in half, creating a central line.
say you have n tiles horizontally (width). the (n/2) tile would then "warp" to the nth tile. from there it's just a matter of indexing to find out exactly where each tile warps to, and an algorithm could be easily made to record it into a customized, easily made data structure (namely a matrix made of up, down, left, right pointers, and tile data). the up and down pointers of the top and bottom tiles would point to their "warp" mates, and after the game is loaded all movements would be instant, with miniscule cpu usage.
the only issue with this is, well, it's fake. it's simply not a spherical map, it's a flat map that teleports units. sure, you can send a ship north from canada and pop out above russia, but you can never center the map in such a way that you could see both.
also, this might have a major impact on how land masses at the poles look on the map. it probably isn't a major problem, but you would see civ2esque ice caps for antartica, a long stretch across most of the bottom, rather than a real-looking landmass. cities on the top and bottom would also have to load the info/images from the other side of the map, but thats gravy. it would look a little odd having a city at the tippy top of the map though, since you couldn't see the tiles directly north of it.
another thing: what should happen when you scroll up off the map? should it go to the bottom, maintaining your x position, or should it warp to where the center tile goes to?
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Vince278
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The football has so few they had to add some pentagons to make it work. I'm not entirely sure on a huge scale.
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Leland
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The keyword is "geodesic sphere", in case anyone wants to google it up.
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06-07-2003 14:03
).
squares just do not lend themselves to strategy. A spherical map built of hexigons could make an excellent civ game, i think. 
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