View Full Version : Toroidal World: Warlords Map Option


drkodos
Jul 25, 2006, 09:48 PM
I think these are new map options because I do not remember seeing them before:

Cylindrical vs Toroidal vs Flat world.


I am assuming the old global maps are considered Cylindrical or would that be Toroidal?

The Flat option is like a Plains map where the edges do not wrap around?


I've been a bit too busy playing a game as the Vikings to get a game started just to explore the options and I chose Fractal/Cylindrical thinking it was the closest to the old Globe maps but perhaps someone has some insight on the differences these choices make on gameplay and they would be willing to share their wisdom.



Thanks in advance!

bioelectricclam
Jul 25, 2006, 10:16 PM
A toroid is a donut-shaped world...so if you keep heading north you'll eventually be in the south...and if you keep heading west you'll be east.

Cylinder or whatever is the classic view, where you only wrap around the globe heading east/west.

And flat is a flat world. Every side has an edge.

Jaybe
Jul 26, 2006, 02:01 AM
I think these are new map options because I do not remember seeing them before:

Cylindrical vs Toroidal vs Flat world.
The only change is in the terminoligy, because Flat wasn't a user option before (though some map types were flat maps).

drkodos
Jul 26, 2006, 10:12 AM
A toroid is a donut-shaped world...so if you keep heading north you'll eventually be in the south...and if you keep heading west you'll be east.

Cylinder or whatever is the classic view, where you only wrap around the globe heading east/west.

And flat is a flat world. Every side has an edge.


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.



"Homer, you idea of a Donut Shaped universe is intriguig." Stephen Hawking

Neal Down
Jul 26, 2006, 12:00 PM
Toroid is donut shaped, drkodos, not like a globe. Think about it, if you cross the north pole on a globe, do you suddenly find yourself on the south pole heading north? No, you find yourself on the other side of the world, south of the north pole, heading south. On a toroid, when you cross the north side of the map, you suddenly find yourself on the south side, heading north. Does that explain it?

drkodos
Jul 26, 2006, 09:41 PM
Toroid is donut shaped, drkodos, not like a globe. Think about it, if you cross the north pole on a globe, do you suddenly find yourself on the south pole heading north? No, you find yourself on the other side of the world, south of the north pole, heading south. On a toroid, when you cross the north side of the map, you suddenly find yourself on the south side, heading north. Does that explain it?


Not really.

I undestarnd that a toroid is a donut shape. That part I get.

But:

If it is a donut, and the donut itself has some mass/thickness to it, as I approach the top of the donut, let's call that heading North. I am headed North. When I cross the northern most point on the donut I am on, I am now on the other side, but now I am headed south, but I am still on the Northern part of that side. I am not SOUTH until I pass the equator of the donut.

I do not see how it being a donut makes me reappear at the bottom of the donut.

All I understand is that there is no Pole. If I were to lay a donut flat on the table, where it touches the table would be a line, a circle in fact. Laying a globe on a flat surface would have merely a single point in contact with the flat surface.

So, there is a circle line around the top of the donut, and around the bottom. The Northern most and southern most parts of the donut are circles, not points or poles.

By crossing over that line, I am moving in a different direction relative to that line. At first I was moving toward it, then after crossing it I am moving away from it.

BUT, I do not all of a sudden transport to the other line, on the opposite side of donut. I just start the journey toward that other line, once I cross the Northern most part.

meatwad4289
Jul 26, 2006, 10:28 PM
all it means is that that map wraps N and south now, like the traditional east and west wrap..

drkodos
Jul 26, 2006, 10:39 PM
all it means is that that map wraps N and south now, like the traditional east and west wrap..


That is what I thought, but that is not really a toroidal shape. In fact, it is not a normal geometric shape whatsoever.

I'm not saying I have issue with it, but giving it a name that impies one thing when it is not that thing at all is a bit misleading/confusing.

In the 3 dimensional universe we live in, it is impossible to have a shape that wraps that way (northern region touching the southern region) while simultaneously wrapping east and west. It has to be one way or the other, or it must be like spheroid, as I described in my post above, where N & S can never touch each other.

ngraner42
Jul 26, 2006, 11:07 PM
Take a paper towel and tape the top to the bottom. This will give you a cylinder, then curl the two open ends around until they meet. Top and bottom will touch, left and right sides will touch, and you will be holding a doughnut.

bioelectricclam
Jul 26, 2006, 11:13 PM
What seems to be giving your trouble Doc Kodos is that you are trying to envision the object as a 3-d shape, which it technically is...but in the game it is actually represented by a 2-d grid. Take the donut shape, and try to flatten it out in your head (play-do might help).

Anyways, trying to upload a picture I made to illustrate this, but right now it is in purgatory. I'll check back latter.

Willowmound
Jul 26, 2006, 11:16 PM
European doughnuts have holes in the middle. See, that would make for an interesting map! :)

drkodos
Jul 26, 2006, 11:17 PM
Take a paper towel and tape the top to the bottom. This will give you a cylinder, then curl the two open ends around until they meet. Top and bottom will touch, left and right sides will touch, and you will be holding a doughnut.


I can do that exercise mentally, but it is still not correct.

And if you actually do it physically, and read my post above and understand it, you will see that is indeed a toroidal shape, but that both East & West do not wrap simulaneously while Northern Polar area and Southern polar area touch.

Take the same Paper Towel Doughnut and lie it flat on the table in front of you.

Now run your finger up the side and over the top.

Your finger does not suddenly appear underneath the doughnut. It crosses over the top and starts to move downward.


Now, take the doughnut and stand it vertically, so that the hole is oriented up and down, facing you. Again, place your finger on a side near the top. Run your finger across the top, vertically up and over the top. Your finger again does not disappear and then reappear on the bottom of the doughnut. It needs to travel all the way down the other side.



Ever read Ringworld by Larry Niven? Not that is applies completely here, becaue it does not. But, it does creat a doughnut type ring world with life on the inside of the doughnut ring. Regardless of how you orient the world, you do not disappear from one edge and magically appear on the opposite edge by crossing over. If you travel the inside LOOP or the outside LOOP there is a wrap around.

But it cannot wrap around both ways simultaneous such that anything would cross over any single point and then reappear the maximum distance away from where it just was.

drkodos
Jul 26, 2006, 11:23 PM
What seems to be giving your trouble Doc Kodos is that you are trying to envision the object as a 3-d shape, which it technically is...but in the game it is actually represented by a 2-d grid. Take the donut shape, and try to flatten it out in your head (play-do might help).

Anyways, trying to upload a picture I made to illustrate this, but right now it is in purgatory. I'll check back latter.


I am not having trouble at all.

I understand it completely and what I am saying is that it is not a true toroidal shape. If it was, then going north would not make you end up at the Southern end just by crossing over the northern most point. It would merely make you cross over the north and then start HEADING south, without actually having changed direction of travel.

And the same would happen on a spehroidal globe. Doughnut or globe, same effects. The only difference is that a globe has a true polar axis that intersects the globe and a toroid exists around its axis and never touches it.

In order for both East and west to wrap AND north and south to wrap as suggested, they would all have to meet at the same single point is space, and that is impossible in both three or two dimensions.

bioelectricclam
Jul 26, 2006, 11:25 PM
http://img230.imageshack.us/my.php?image=toroidflatteningod0.jpg

The dotted lines represent the edges of the map. Does this help any?

See, going north doesnt mean that you are suddenly on the south edge...it means you have crossed the horizontal line in the illustration. Same with the sides.

drkodos
Jul 27, 2006, 12:01 AM
http://img230.imageshack.us/my.php?image=toroidflatteningod0.jpg

The dotted lines represent the edges of the map. Does this help any?

See, going north doesnt mean that you are suddenly on the south edge...it means you have crossed the horizontal line in the illustration. Same with the sides.


My argument was not with your assertion. Sorry for the confusion.

My argument was aimed at the notion that SOMEONE ELSE POSITED that travelling north on a toroid caused one to reappear on the south now traveling north.

Here is my point, in Civ terms:

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.

IF by sailing my caravel up to the top of the screen I reappear at the bottom of the screen AND if by sailing off the left edge I reappear at the right edge of the 2 dimensional screen, THAT SHAPE is not a toroid, but is a geometric shape that cannot exist in either a 3 or 2 dimensional world.

By sailing up and reappearing at the bottom, it suggest that those two edges meet and are not far apart. BUT, if that is the case, then one should not be able to sail to the left (west) and reappear on the right (east).

In a two dimensionsal representation of Globes, Cylinders, toroids, or even squares, in fact ANY 3D object at all, one need pick one way to wrap around and cannot choose to represent both by having object reappear on the opposite side of the screen from which it departed.

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. Pick one way to wrap.

bioelectrician: in the image you provided, by going off the screen to the north, one would reappear somewhere else on the northern edge, not the southern edge, and I agree that is what a true toroid is. BUT the argument was made that by going off the upper edge one would appear at the lower edge, and that is incorrect, if one is also able to wrap E & W. That is my point, and I understood it long before you posted the image, no offense.

So, if a toridal map merely means a NS wrap instead of EW that does not make it a true toroid. It really just makes the map type another type of cylinder.

achilleszero
Jul 27, 2006, 01:06 AM
My argument was not with your assertion. Sorry for the confusion.

My argument was aimed at the notion that SOMEONE ELSE POSITED that travelling north on a toroid caused one to reappear on the south now traveling north.

Here is my point, in Civ terms:

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.

IF by sailing my caravel up to the top of the screen I reappear at the bottom of the screen AND if by sailing off the left edge I reappear at the right edge of the 2 dimensional screen, THAT SHAPE is not a toroid, but is a geometric shape that cannot exist in either a 3 or 2 dimensional world.

By sailing up and reappearing at the bottom, it suggest that those two edges meet and are not far apart. BUT, if that is the case, then one should not be able to sail to the left (west) and reappear on the right (east).

In a two dimensionsal representation of Globes, Cylinders, toroids, or even squares, in fact ANY 3D object at all, one need pick one way to wrap around and cannot choose to represent both by having object reappear on the opposite side of the screen from which it departed.

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. Pick one way to wrap.

bioelectrician: in the image you provided, by going off the screen to the north, one would reappear somewhere else on the northern edge, not the southern edge, and I agree that is what a true toroid is. BUT the argument was made that by going off the upper edge one would appear at the lower edge, and that is incorrect, if one is also able to wrap E & W. That is my point, and I understood it long before you posted the image, no offense.

So, if a toridal map merely means a NS wrap instead of EW that does not make it a true toroid. It really just makes the map type another type of cylinder.

Drkodos, everything that you claim can't possibly be true about the toroidal map is remarkably true. Bioelectricclam has explained it pretty well and even included pictures. I can't think of any simpler terms to put it in.

What should be hard to conceptualize is the standard civ map or any traditional 2d marcatur map that we use to represent the surface of the earth, which is in 3 dimensions. In these types of maps theyve taken the poles which are single points and stretched them into lines equivelant to the equator. That is why everthing close to the poles is so exagerrated.

Now in the toroidal world the poles are lines in fact they are the same line. So if you went over the north edge you would come out on the south edge. You dont loop there or teleport you just continuing on the surface of the toroid.

For creation of the toroidal world from the flat map there has to be alot of uneven compression and expansion of the outside edges just like with normal maps of our world.

Simply put torodial map is a real thing and can exist in our dimension and universe. You should be able to refrences to it in any advanced geometry, topography, or physics book.

Keith_C
Jul 27, 2006, 01:56 AM
Taking bioelectricclam's work and expanding it (badly, in paint), here's the same, but numbered, so you can see what's happening.

Rowain deWolf
Jul 27, 2006, 07:39 AM
Keith' picture does show it quite good.

The thing is on the toroid you don't have 2 poles you have only one icy plane which happens to be drawn on the northern/southern edge cause the cut was laid across the ice-field (easier for us humans)

Demartus
Jul 27, 2006, 01:19 PM
I think some of drkodos' confusion is that, in a toroid, is that when you reached the 'north' pole, you should start heading 'south', i.e. down the backside. And in the 2d representation of the toroid, you never move 'south', i.e. down the map.

That has more to do with the 2d representation of the surface of a 3d object. The map provided in Civ4 is accurate - a toroid world would 'wrap' as it does (Top-Bottom and Left-Right wrapping), as was well explained by the pictures. A person traveling with a compass would think they were moving first north, then south, though. But that would be impossible, or at least really difficult, and irrelevant, to model or represent in the 2d mapping.

meatwad4289
Jul 27, 2006, 01:57 PM
European doughnuts have holes in the middle. See, that would make for an interesting map! :)
European Doughnuts have holes i nthe middle? OMG that is so sweet, see here in the Good Ol'e U S of A we just have big empty spaces i nthe middle...

Ben Music
Jul 27, 2006, 02:03 PM
The diagram explains it. The North and South "Poles" touch, so to speak

DaviddesJ
Jul 27, 2006, 02:03 PM
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
Jul 27, 2006, 02:23 PM
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
Jul 27, 2006, 04:23 PM
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
Sep 01, 2006, 06:52 AM
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
Sep 01, 2006, 07:15 PM
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 :crazyeye: )


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
Sep 01, 2006, 07:30 PM
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
Sep 01, 2006, 07:35 PM
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! :blush:

Holycannoli
Sep 02, 2006, 01:31 AM
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.