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Re: possibility of emulation


Jim Kingdon wrote:
Xconq on a Klein Bottle map, anyone?

Oh, that's different from hex vs non-hex (and probably easier).

Yes, I know. That's why I mentioned it in a different paragraph. However, the best type of tiling might change with the topology that one is dealing with.


xconq has the start of a cylindrical map (edges on top and bottom, but
if you go off the left edge you appear on the right with the same y
coordinate).

Right. All that you need to do is set the width of the playing area larger than the circumference.


There are plenty of computer games with a doughnut-shaped map (like
cylindrical, but wrap around top/bottom as well). (Mathematicians call
this one a torus).

Tori simply require two aligned folds of opposite edges. By aligned, I mean that each pair of corners that are to be joined share a common edge prior to being joined.


But twist one of the joins as we did for the Moebius
strip.

An anti-aligned fold.


Actually, it is probably easier to implement in xconq than it
is to visualize.

I would agree.


What all this does for gameplay, I don't know.  Might have a big
effect, given how easy it is to sneak past the AI at the edge of the
map.  But maybe the AI would just have another weak spot - I'm not
sure whether this weakness of the AI is a matter of geometry or just
of the AI not protecting its flanks/rear in general.

If the AI was properly done, it could have an advantage in the Klein Bottle case, just because the poor humans might get disoriented.


local plane approximations of multi-dimensional saddle curves or
spheroidal pieces. (There probably couldn't be any decent,
comprehensible representation beyond a certain zoom factor, so there
would be no world map.)

That would be interesting too (in mathematical terms, it is a question of changing the geometry, not just the topology).

I would consider it to be pretty much of a necessity in presenting the playing surface to the player.


Eric


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