Toroidal World: Warlords Map Option

[Ben Music]

The diagram explains it. The North and South "Poles" touch, so to speak

 

[DaviddesJ]

Thanks for explanation, but the going North to end up south is a bit confusing for my addled brain. I thought maybe it was like a real Globe where you can cross over the poles to the other hemisphere like the way transarctic flights go.

If moving off the north edge takes you to an opposite point on the north edge (i.e., 180 degrees away), then you get a map which is topologically a Klein bottle. This is not a spherical shape (like the Earth), and not a toroidal shape, either.

I agree this would be a good option to provide, and it wouldn't seem hard to implement. Although the Klein bottle is topologically an odd shape, it would work fine in Civ4 in the sense of still having a clearly defined polar and equatorial regions (unlike the torus).

 

[ngraner42]

You really should have two ice zones, to represent poles, but we could assume an orientation relative to the sun where one pole is cold and the other warm (equator is the second pole).

 

[naterator]

i think ngraner42 just hit the nail on the head as to the confusion. the land placement is such as to make a minimap that looks normal. since all 4 corners are on the equator, there should be 2 polar strips across the middle of the whole thing, not something that most players would love. alternately, you could have a pangea, for example, that looked like 4 big continents coming off each corner, but in reality are connected. the corners being jungle and funky minimap would take some getting used to, but so does the doughnut shaped world.
maybe they should just call it x wrap or x-y wrap?

 

[occam]

DrKodos,

Your objection conflates two issues with the toroidal approach.

There is an obvious spatial problem that a cylinder turned into a toroid must buckle in the process -- so a flat 2-D map is inaccurate in terms of scale, just like a Mercator 2-D drawing, but worse! This is an actual problem that Civ faces and makes the "toroidal" label slightly inaccurate although I promise that a true topologist would willingly ignore the stretching issue and label it a toroid ... but it does not relate to wrapping.

A second possible problem is the wrapping issue, and this is a FALSE problem. You propose something like 'wrapping N/S must involve teleportation" and then stress that teleportation doesn't really happen. As the post by naterator above mine suggests, the point corresponds to the northernmost on the toroid is not necessarily at the top of your map. What a silly assumption! The Arctic is about 2/3 up and the Antartic is about 2/3 down a flat attempt to represent a toroid. You hit the North ice zone, go a little further [which is now South on the toroid but is still labelled (by Firaxis? or Kodos!) as North on your minimap]. Eventually you encounter the border discontinuity on the back side (the internal equator) and have to teleport on the 2-d version of the map. Let me repeat: the northernmost part of the flat map may be the internal equator of the doughnut. Just like the backside of the cylinder is still shown in 2-D maps, even though it is hidden by a 3-D body.

Incidentally, I feel that most of your outrage at the wrapping teleport will apply to just 1 wrap. I could steal most of your 'teleportation bad' rhetoric, for example: "if I sail my caravel East, I should reappear in that vicinity, not to the far West!" right? But you like the E/W way?

=========

But even more fundamentally:
To deal with toroids in general, you have to move beyond N/S, period. Just blank out that label. What is South from the Northern circle? Inner or outer? That's right, there are 2 Souths! Ok, so starting right there, you have to rewrite all the labels.

- Occam

 

[MoonBase]

That object as described, where both N & S wrap AND E & W wrap does not exist in the known universe. It cannot be 3 dimensionally represented, and it certainly cannot be 2 dimensionally represented. It can only be represented through non-Euclidian geometric mathematics. You cannot wrap both N&S and E&W on a two dimensional map and have it reflect any type of reality in the universe.

A globe is non-Euclidian geometry, as well.

A Mercator-projection map of the earth takes the surface of a sphere(Earth) and lays it out flat, stretching the north and south to achieve a roughly rectangular shape (there's more stretching involved with mercator, but that's unimportant right now). The East and West edges of this rectangular 2-d map touch "in reality" (that is, on the sphere, they're the same line; the cut that was made, from the North Pole to the South Pole, in order to peel the map off of the sphere). The North and South edges do not touch each other (though they do sorta touch themselves, as on the sphere they're both basically points )


If you took a donut (toroid), made a slice all the way around the inner edge(the 'hole'), and made another slice around the tube, you'd be able to peel the surface off like...well, a peel. If you took this peel and laid it out flat (exactly as Mercator did with that sphere) you'd have a roughly rectangular 2-d map of the surface of the donut.
The East and West edges of this map were, while it was on the donut, the around-the-tube cut. The North and South edges of this map, while it was on the donut, were the around-the-hole cut.

That is the world being represented as a 2-d rectangle in the "toroid world" option. The East and West are one line encircling the tube of the donut, the North and West are one line encircling the "hole" of the donut. As an inhabitant of the Donut World was traveling along the surface, say from the outside of the tube towards the inside, they'd approach the around-the-hole line (they'd be traveling "North" from the map-maker's perspective). They would, eventually reach the around-the-hole line (the North edge of the Map). They would then cross that line (would jump from the North edge to the South edge), and now be heading away from it (heading away from the South edge = heading North).


THAT is how a toroidal world works.

 

[MoonBase]

BTW, Drkodos, The Ringworld is not a toroid, in terms of its surface. It's merely a rectangle, topologically speaking.

To use the Ringworld as an example of toroidal mapping, one must not stop the map of the surface at the Atmosphere Walls: you must continue that map all the way along the backside of the Scrith structure.

Where ever you decide to make the "meridian" of your map that includes the backside of the Ringworld, that line will be both the North and South poles of your rectangular 2-d map projection.

For example: If I, in my perfectly invulnerable and vacuum-ready, able-to-stick-to-Scrith jogging suit, decided to walk along the "North-South" axis of the Ringworld, I might choose to start at the "top" Atmosphere Wall. I might even choose to call that "The North Line", just because.

I walk away from this line, across the inner surface of the Ringworld. Since this is "Away from North", it's fair to call it "in a southerly direction".
Eventually, I come to the other Atmosphere Wall. But why stop there? The Ringworld has more surface for me to walk on, still going at a 90 degree angle from the North Line: the backside of the Ring!

So, I call this second Atmosphere Wall "The Equator" (just for giggles), and I continue walking at a right angle to it and to the North Line.

The backside is boring and drab, and tough to stick to, but it's as broad as the inside. Eventually, I'll come to another Atmosphere Wall, which because I'm tired of walking, I'll call "The South Line".

But low and behold, "The South Line" and "The North Line" are one and the same. I've walking in one single direction, and wound up exactly where I started. Crossing the North Line puts me right next to the South Line, and vice versa.

This map of the Ringworld would have a "south half" comprised entirely of barren Scrith, but it would be a toroidal map.

 

[MoonBase]

BTW, to anyone who doesn't know what the Ringworld is, I apologize for the geekiness of that last. Trust me, if you'd read the books, everything I said would've made sense.


And I didn't even mention Rishathra!

 

[Holycannoli]

If I sail my Caravel up to the North (top) edge of the screen I should reappear at another point that is also at the top of the screen, but either left or right (east or west) from where I left the screen, if I was on a globe represented in 2 dimensions.

This is correct. That's why I don't really play toroidal. There's something very weird about moving north off the map and appearing to the south.

It's not possible to simulate a spherical planet in Civ. All we have is a rectangular map and there's just no way to practically simulate a globe on a plain rectangle. And it would seem even weirder to move north off the northwest corner of the map and reappear on the top again just to the right of the center of the map (center of the map being longitude 0, and both edges of the map being longitude 180 since the map wraps around, making both edges the same exact point on the map) than it would to go from top to bottom!

As a game feature it just wouldn't feel right and would be impractical. You'd need a "globe" shaped map, probably 3D, where you could constantly rotate and center your point-of-view ,to make that work. Civ isn't that advanced yet Maybe one day it will be. Maybe one day it truly can simulate a globe using a 3D globe map.