Toroidal World: Warlords Map Option

[drkodos]

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]

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]

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]

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]

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]

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]

all it means is that that map wraps N and south now, like the traditional east and west wrap..

 

[drkodos]

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]

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]

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]

European doughnuts have holes in the middle. See, that would make for an interesting map!

 

[drkodos]

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]

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]

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]

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]

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]

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]

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]

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]

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...