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Wargaming on a Globe (Note: Graphic-intensive topic) - 9/3/2008 5:49:02 PM   
BoredStiff

 

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As most people know, or should know, flat maps are not an accurate representation of the surface of the earth. Generally speaking, the larger the area shown, the more distorted and inaccurate the map becomes, usually and especially near the edges, although it depends on which map projection is used.

Here is a typical Mercator projection map of the type often used to show the earth.



A couple of obvious problems with this: The increasingly gross distortions of the landmasses near the poles. Alaska, Northern Canada, Greenland, Scandinavia and Siberia are all much larger than they should be. Even more extreme is the size of Antarctica near the south pole.
Also, scrolling across the poles would not be possible if this map were used in a wargame, or at least wouldn't make any sense.
Nor do the areas near the poles come together as they actually do on a globe. In the above map, Siberia is many thousands of miles away from northern Canada, for example, when in reality it is much closer on a globe.

Using various modified flat-map projections doesn't solve these problems.
OK, hopefully most people here already knew all this.

The only accurate way of mapping the earth, or parts thereof, is to use a sphere/globe. (Yes, I know the earth is slightly egg-shaped, being a little wider at the equator than from pole to pole, but that is irrelevant and a perfect sphere would be just fine for the purpose of this discussion.)



Unfortunately, from everything I've been able to learn, it is impossible to impose a contiguous polygonal grid across the entirety of a globe. In other words, a globe cannot be completely overlaid with a contiguous hexagonal grid, or any other kind of grid, without resorting to some other polygonal shape in some area(s). A good example of this is a soccer ball.



Note that while the white polygons are hexagons, the black ones are pentagons.

The closest I've been able to find on the 'net that shows what I would consider an ideal global grid, is this graphic (source):



Sorry about the size of this, but I need to keep it big in order to point out the problems, which are two-fold.
First, while all the polygons in this grid are hexagons, the polygon I marked with a red X at the center is a pentagon. This is the point at which all the other polygons come together and due to the curvature of the sphere this apparently cannot be a hexagon.
Secondly, it is obvious that the sides of the hexagons nearest the center pentagon are distorted to various degrees, again presumably due to the curvature of the sphere. I don't know how such an irregular grid could be hard-coded into a computer wargame - it probably can't.
A similar situation presumably exists on the other side of this globe, at the south pole. Note that these areas of anomalies don't necessarily have to be at the poles, they could be located anywhere on the sphere, but the poles would probably be the best places, since those areas would presumbably be least used in a wargame.
Im presuming a lot, ain't I? But I think I'm making sense.

So what's the solution?

The most obvious solution is to not have a polygonal grid at all, but to simply depict areas, such as with the typical area maps of games like Empires in Arms, for example.
I myself am one of those people who is partial to having some kind of a grid, because area maps usually tend to have some areas that end up being more important than others, for various reasons, although I'll be the first to acknowledge that I have almost no experience with games that utilize area maps.

Another thing to consider - and maybe herein lies a solution - is that, when depicting a sphere/globe, only part of the earth would be visible to the player at any given time. No more than half the planet would be visible, even at the most extreme zoom-out level.

Let's imagine the ideal zoom level for my hypothetical wargame is similar to this graphic:



This happens to show a square grid, but a hexagonal grid could just as easily be used.

This then, might be the zoom level at which most game actions would take place, such as moving units, initiating and resolving combats, etc.

As the player scrolls around the map, the grid would stay stationary while the sphere beneath it moves. In this way, the polygonal anomalies shown on the large global map above might be avoided.

However, I'm not sure this actually solves the problem, because various locations on the map would still always have to be in the same locations in relation to one another and be the same distance apart, regardless of how the player scrolls the map.

That sounds a little confusing, so let me try to clarify.
In a conventional hex-grid wargame, a given location will always be in the same hex on the map. In fact, hexes are often numbered (AA07 and so forth). Likewise, any two locations will always be the same number of hexes apart from each other. For example, if city X is at hex AA01 and city Y is at hex AA05, it means there are 3 hexes between the cities, AA02, AA03 and AA04.

So, while hex numbering in my above system would probably be pointless, if not impossible, the relationship of any two points on the map, say between cities X and Y above, still need to be kept constant in terms of the overlaying hexagonal grid, no matter how the player rotates the underlying globe. That is, they always have to be four hexes apart and in the same direction of movment.
In order to accomplish this, the computer might be programmed to convert real-life distances into hex distances, so that the distance between say, Dallas and El Paso, which might be 300 miles, would be translated into say, 10 hexagons.

Well, I'm not sure if those last parts make sense to readers.

In any case, I'd like to see a strategy/wargame utilizing a rotatable globe as a map, even if it's an area map.

EDIT: Another possible solution might lie with a gridless pixel-to-pixel system, such as I understand is used in games like Conquest of the Aegean, which I haven't played.

< Message edited by BoredStiff -- 9/17/2008 3:00:46 AM >


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RE: Wargaming on a Globe (Note: Graphic-intensive topic) - 9/3/2008 6:03:24 PM   
andym


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But the earth IS flat!!!!

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RE: Wargaming on a Globe (Note: Graphic-intensive topic) - 9/3/2008 7:32:13 PM   
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quote:

ORIGINAL: BoredStiff

In any case, I'd like to see a strategy/wargame utilizing a rotatable globe as a map, even if it's an area map.

UFO and X-COM series. Check out UFO: Alien Invasion. Doesn't cost any

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RE: Wargaming on a Globe (Note: Graphic-intensive topic) - 9/3/2008 8:32:16 PM   
Capt. Harlock


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quote:

ORIGINAL: BoredStiff

In any case, I'd like to see a strategy/wargame utilizing a rotatable globe as a map, even if it's an area map.

EDIT: Another possible solution might lie with a gridless pixel-to-pixel system, such as I understand is used in games like Conquest of the Aegean, which I haven't played.


A well-thought out post, especially as to placing the pentagons in a hexagon grid at the poles. Note, however, that by definition pixels occupy a non-zero area, so that effectively pixels are a grid.

A gridless system, which I would guess has everything defined in positional coordinates and then has the computer move the map the appropriate distance for viewing, would work very well for naval games. On land, however, you have things like roads, rivers, and railways, which compel movement along pre-determined paths. That seems more difficult to me.

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RE: Wargaming on a Globe (Note: Graphic-intensive topic) - 9/3/2008 9:01:04 PM   
sterckxe


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quote:

ORIGINAL: Capt. Harlock
A gridless system, which I would guess has everything defined in positional coordinates and then has the computer move the map the appropriate distance for viewing, would work very well for naval games. On land, however, you have things like roads, rivers, and railways, which compel movement along pre-determined paths. That seems more difficult to me.


Check out "Highway to the Reich" and "Conquest of the Aegean" as excellent examples of games which don't use grids, but continuous coordinates and which manage this very well.

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RE: Wargaming on a Globe (Note: Graphic-intensive topic) - 9/3/2008 9:44:43 PM   
TonyE


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One of our toys at Stratsims, http://www.stratsims.com/CIC_MP01.asp does the spherical globe thing (2D engine even, strange eh).



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RE: Wargaming on a Globe (Note: Graphic-intensive topic) - 9/4/2008 12:04:08 AM   
BoredStiff

 

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quote:

ORIGINAL: Capt. Harlock

A well-thought out post,

Good, I tried to be as clear as possible with a subject in which I don't know the technical language.

quote:

Note, however, that by definition pixels occupy a non-zero area, so that effectively pixels are a grid.

I'm not sure what you mean by non-zero, but I understand your point and was aware of the issue. To put it another way, pixels basically represent the center of polygons, presumably hexagons, and if pixels were able to be spaced equidistantly from one another across the entirety of a globe, then so would polygons, which unfortunately they are not.
Back to square one, no pun intended.

quote:

A gridless system, which I would guess has everything defined in positional coordinates and then has the computer move the map the appropriate distance for viewing, would work very well for naval games. On land, however, you have things like roads, rivers, and railways, which compel movement along pre-determined paths. That seems more difficult to me.

I think I understand what you're saying. This relates back to the point I was making about locations always having to be properly distanced in relation to one another, both with a polygonal system or a pixel system.

Well, if grid systems are out, then lets at least have a game using a spherical/global area map. Shouldn't be anything too difficult about that.
In addition to the usual random map generation, such a game might have options that would let players create random area patterns, so that at least not every game ends up in battles for the same key areas. Likewise, there might be an option to determine the size of areas, with larger areas making for faster playing games and smaller areas a longer playing games.

Anyway, just some thoughts.

< Message edited by BoredStiff -- 9/4/2008 12:16:49 AM >


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RE: Wargaming on a Globe (Note: Graphic-intensive topic) - 9/4/2008 12:31:55 AM   
BoredStiff

 

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quote:

ORIGINAL: Matti Kuokkanen

UFO and X-COM series. Check out UFO: Alien Invasion. Doesn't cost any

Can you post a screenie of how the game utilizes a globe? All I see when I Google the game are the usual flat maps.

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RE: Wargaming on a Globe (Note: Graphic-intensive topic) - 9/4/2008 12:35:02 AM   
BoredStiff

 

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quote:

ORIGINAL: TonyE

One of our toys at Stratsims, http://www.stratsims.com/CIC_MP01.asp does the spherical globe thing (2D engine even, strange eh).

One of their screenies pretty much looks exactly like what I have in mind. Unfortunately, it appears to be strictly a naval game, true?

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RE: Wargaming on a Globe (Note: Graphic-intensive topic) - 9/4/2008 12:52:36 AM   
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I like the hex grid map of globe.The way I see is that,eeach hex doesn't have to be perfect,as long as each hex is big enough to fit the units for the game.I can see a World in Flames or WitP type game with that globe grid.

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RE: Wargaming on a Globe (Note: Graphic-intensive topic) - 9/4/2008 2:46:45 AM   
Neilster


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I proposed a hex-based but (roughly) spherical map for World in Flames in 2004. I consulted with my Maths lecturer who's a geometry expert about it but that went no further because he was too busy.

Cheers, Neilster


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RE: Wargaming on a Globe (Note: Graphic-intensive topic) - 9/4/2008 4:48:46 AM   
BoredStiff

 

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quote:

ORIGINAL: Neilster

I proposed a hex-based but (roughly) spherical map for World in Flames in 2004. I consulted with my Maths lecturer who's a geometry expert about it but that went no further because he was too busy.

Cheers, Neilster

I've been told it's not possible to cover a sphere/globe with a grid of evenly shaped and sized polygons.
I've raised the issue in other forums and have been told as much by various people. I also read as much in one of my Google searches.
Forum member Capt. Harlock, who chimed in uptopic, also seems to confirm this and in his profile he says he's an aeronautical engineer.

I raised the issue here because there seems to be a good number of game developers here who might see it and perhaps some of them might at least get some new ideas on how to present maps for strategy games.
I see no reason, for example, why an area map on a rotatable globe could not be done. That, in itself, would be a very appealing, not to mention unique, aside from the naval game someone linked to uptopic.

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RE: Wargaming on a Globe (Note: Graphic-intensive topic) - 9/4/2008 5:55:33 AM   
Fred98


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quote:

ORIGINAL: BoredStiff
I see no reason, for example, why an area map on a rotatable globe could not be done.




It would be impracticle for the players.

My first ever wargame was Risde and Decline of the Third Reich. At a glance you can see the whole of the map.

Years later a PC version was released. I had to page around to see the map. Ultimately it was about 3 screns high and 4 screens wide.

The inability to see the whole screen at one glance was a great disadvantage.

If the map were shaped like a globe I could not see the whole screen at a glance.

-













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RE: Wargaming on a Globe (Note: Graphic-intensive topic) - 9/4/2008 7:04:27 AM   
BoredStiff

 

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quote:

ORIGINAL: Joe 98


If the map were shaped like a globe I could not see the whole screen at a glance.

That's no different from any other wargame.

< Message edited by BoredStiff -- 9/4/2008 7:12:23 AM >


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RE: Wargaming on a Globe (Note: Graphic-intensive topic) - 9/4/2008 8:36:27 AM   
Marc von Martial


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quote:

ORIGINAL: BoredStiff

quote:

ORIGINAL: Joe 98
If the map were shaped like a globe I could not see the whole screen at a glance.

That's no different from any other wargame.



Well, there are plenty of wargames were you at least have the chance to see almost everything at a glance.
With a 3D globe you would still not be able to see everything at a glance even if you have a huge monitor / panel you play on.

I agree it is pretty impractible for the gamer.

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RE: Wargaming on a Globe (Note: Graphic-intensive topic) - 9/4/2008 11:01:28 AM   
Neilster


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quote:

ORIGINAL: Marc von Martial


quote:

ORIGINAL: BoredStiff

quote:

ORIGINAL: Joe 98
If the map were shaped like a globe I could not see the whole screen at a glance.

That's no different from any other wargame.



Well, there are plenty of wargames were you at least have the chance to see almost everything at a glance.
With a 3D globe you would still not be able to see everything at a glance even if you have a huge monitor / panel you play on.

I agree it is pretty impractible for the gamer.

But in the real world of monitors you often won't be able to see anything of value if looking at the entire world on a 2D map. It's all too small. With a 3D map you can actually see more hexes for a given 2D display area, it's just that many of them are away from the centre and distorted. You just need some snazzy and intuitive controls to spin the globe to check everything out quickly.

Cheers, Neilster





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RE: Wargaming on a Globe (Note: Graphic-intensive topic) - 9/4/2008 11:14:38 AM   
Neilster


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quote:

ORIGINAL: BoredStiff


quote:

ORIGINAL: Neilster

I proposed a hex-based but (roughly) spherical map for World in Flames in 2004. I consulted with my Maths lecturer who's a geometry expert about it but that went no further because he was too busy.

Cheers, Neilster

I've been told it's not possible to cover a sphere/globe with a grid of evenly shaped and sized polygons.
I've raised the issue in other forums and have been told as much by various people. I also read as much in one of my Google searches.
Forum member Capt. Harlock, who chimed in uptopic, also seems to confirm this and in his profile he says he's an aeronautical engineer.

I raised the issue here because there seems to be a good number of game developers here who might see it and perhaps some of them might at least get some new ideas on how to present maps for strategy games.
I see no reason, for example, why an area map on a rotatable globe could not be done. That, in itself, would be a very appealing, not to mention unique, aside from the naval game someone linked to uptopic.

I was hoping it is possible to construct a very many sided polyhedron out of hexes. According to Wikipedia though "There exists no polyhedron whose faces are all identical and are regular polygons with six or more sides because the vertex of three regular hexagons defines a plane". Well...that settles that then. The problem of course is that we have inherited hexagons from a 2D world and we are trying to make the leap into the third dimension (like that Simpsons episode where Homer gets sucked into the real world. "Hmmmm...erotic cakes!" Simpsons fans will know what I mean).

If we are to stick with hexes I think there's a solution. We construct a spheroidal object from hexagons that don't quite touch, (making the hexes slightly smaller to preserve overall dimension I suppose). It's not a polyhedron but who cares about such theoretical mathematical concepts when the tiny gaps will allow us to make an Earth-like shape out of hexagons, which is what we're after.

Imagine you have dozens of flat-topped hexagonal thumb-tacks and an orange. You could push all the hex tacks into the orange without them clashing (as would happen theoretically) if you left a small gap between each one.

We already usually have a black line around our hexes to delineate them anyway. You could even adjust the gaps minutely to accommodate the difference between polar and equatorial radii (which from memory is approximately 60km or about half a MWiF hex and hence probably not worth worrying about).

MWiF has over 72,000 hexes but many of them currently only exist (near the Poles) due to distortion. By making a spheroidal map you could reduce that number to say, 60,000 hexes. That would approximate a sphere pretty well.

A 3D map ain't going to happen for MWiF 1 anyway. It may make more sense for MWiF 2 with Cold War stuff like bombers over the poles. In short, for 3D maps it's easier to abandon hexes. I mean, they're an abstraction that made paper wargaming easier. They still do a good job in many computer games but in 3D they're mostly more trouble than they're worth.

Cheers, Neilster


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RE: Wargaming on a Globe (Note: Graphic-intensive topic) - 9/4/2008 2:00:38 PM   
105mm Howitzer


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Maybe we should ask the little people living in the center of the earth what they think of this.

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RE: Wargaming on a Globe (Note: Graphic-intensive topic) - 9/4/2008 2:31:26 PM   
cdbeck


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Matrix's own UFO: ET uses the globe system mixed with a regional system (although do note that really this is a pixel system on a globe as you can target any point on that globe to fly your ships to).



Techinically, if you pull the zoom all the way back on Civilizations IV, you get a "globe" but it tends to look a bit more like a global cylinder than an actual globe.



There is an independent game designer, named Sascha Willems, working on a global strategy game called Projekt "W." You can DL this beta version is you wish. Find it here.
Here is his globe:




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RE: Wargaming on a Globe (Note: Graphic-intensive topic) - 9/4/2008 5:00:46 PM   
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http://www.airlinesimulation.com/

Airline 6 is also using a globe for some animations, and a flat projection for others. If you are interested in map making and projections, you can always check out Campaign Cartographer that have many products for making maps: http://www.profantasy.com/

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RE: Wargaming on a Globe (Note: Graphic-intensive topic) - 9/4/2008 8:23:49 PM   
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You'd have to establish different movement rates for different zones of poly's to account for the surface vector distance. I think there's been a few paper games that have incorporated rules like this.

Just because one hex is a pentagon, doesn't mean it's less movement to cross it. The degree of distortion of the hexes leads to error in distance across the hex, (under the assumption that 1 hex movement is the same for all hexes). I guess it boild down to what you are trying to accomplish with the grid system and how abstracted you want to be with it.

With computer games, I don't see any reason why movement can't be based on the surface vector, which brings up the question of why have a grid at all ?


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RE: Wargaming on a Globe (Note: Graphic-intensive topic) - 9/4/2008 9:26:48 PM   
TonyE


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quote:

ORIGINAL: BoredStiff


quote:

ORIGINAL: TonyE

One of our toys at Stratsims, http://www.stratsims.com/CIC_MP01.asp does the spherical globe thing (2D engine even, strange eh).

One of their screenies pretty much looks exactly like what I have in mind. Unfortunately, it appears to be strictly a naval game, true?


Strictly a basic play aid for paper wargamers yes. Very narrow in scope and function. That screenshot suggests properly that we have three map projections available, two flat and the spherical (which admittedly come from the globe component vendor, www.tglobe.com). I haven't done the hex thing successfully as yet but it is possible without a ton of distortion. There are a few people who overlay hex grids on Google Earth but I haven't seen a whole globe one yet (search Google for HexThingy).







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RE: Wargaming on a Globe (Note: Graphic-intensive topic) - 9/5/2008 12:59:40 AM   
Neilster


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quote:

ORIGINAL: Jeffrey H.

With computer games, I don't see any reason why movement can't be based on the surface vector, which brings up the question of why have a grid at all ?



In my case it came up in the conversion of World in Flames to the PC. The whole game is based around hexes so they have to stay. The point is the paper game abstracts lots of the world into off-map boxes and it has heaps of fudges and special rules to get around modelling a spherical planet with incomplete, distorted 2D maps.

MWiF (Matrix World in Flames) models the entire world. My thought was that if we are going to do that, and we have bulk computer power, perhaps a 3D map built out of hexes is a more elegant solution. Plus, a spinnable 60,000 sided hex-Earth, with, say, carrier task forces hammering away at the Japanese empire on one side and the long grey and tan snakes of the Eastern Front and combined operations war in the Mediterranean on the other would look extremely cool. Check out the image in BoredStiff's original post and imagine counters all over the place. Yummy.

"Hmm...how are my Atlantic convoys looking?" spin "And the South Pacific ones?" spin spin etc

Cheers, Neilster




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RE: Wargaming on a Globe (Note: Graphic-intensive topic) - 9/5/2008 2:50:20 AM   
Arjuna


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quote:

ORIGINAL: Jeffrey H.

You'd have to establish different movement rates for different zones of poly's to account for the surface vector distance. I think there's been a few paper games that have incorporated rules like this.

Just because one hex is a pentagon, doesn't mean it's less movement to cross it. The degree of distortion of the hexes leads to error in distance across the hex, (under the assumption that 1 hex movement is the same for all hexes). I guess it boild down to what you are trying to accomplish with the grid system and how abstracted you want to be with it.

With computer games, I don't see any reason why movement can't be based on the surface vector, which brings up the question of why have a grid at all ?


Exactly, I couldn't agree more.

Hexes were introduced mid last century to provide a means by which board gamers could simply determine position and more importantly the distance between two locations. The basic premis is that they are equidistant, no matter the direction of travel. This is an abstraction, necessitated to make calculations simple for manual systems. It's not too bad for small map areas but once you want to cover any substantial part of the world, the abstraction becomes gross and unrealistic results occur.

Who remembers the old War in the Pacific board game, which attempted to adress the curvature of the earth issue by dividing the map into latitude zones, such that in the far north near Alaska hexes were only 4 movement points while those in the temperate zone were 5MPs and in the tropics 6MPs. This led to some very gamey behaviour skirting along the join to gain maximum movement - very silly indeed.

Moreover, hexes artifically constrain the direction of movement and artificially constrain the area occupied by units. They lead to ridiculous situations where a lone SNLF Marine Bn is just as good as controlling a hex as an entire army or can hold up the advance of the enemy for the same amount of time as an Army. Again, all very unrealistic.

With the computational power of today's computers we don't need to be constrained like this anymore. Provide a path tool which instantly calculates the best route and estimates the duration for you with just a couple of mouse clicks ( as we do in our upcoming Battles from the Bulge (BFTB) ). This method for determining route, distance and duration is both simpler and more realistic, as the PC can crunch the geometry and math to produce an accurate result in the blink of an eye.

So what you need a grid for is as a position reference for the placement of units. As such the grid does not need to be equidistant - it can cater for the earth's curvature. In real life the military use the good old Lat/Long grids. I see no reason why modern wargames shouldn't do likewise.

It's time we broke the shackles of our boardgame past and exploited the power of the PCs we are playing on.

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Post #: 24
RE: Wargaming on a Globe (Note: Graphic-intensive topic) - 9/5/2008 8:25:03 PM   
Kuokkanen

 

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quote:

ORIGINAL: BoredStiff


quote:

ORIGINAL: Matti Kuokkanen

UFO and X-COM series. Check out UFO: Alien Invasion. Doesn't cost any

Can you post a screenie of how the game utilizes a globe? All I see when I Google the game are the usual flat maps.

Flat map is optional. But I found the globe version. I guess it's the pixel map, which can be zoomed in and out.

Attachment (1)

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RE: Wargaming on a Globe (Note: Graphic-intensive topic) - 9/6/2008 12:48:56 PM   
Grell

 

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Interesting, I did not know that.

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RE: Wargaming on a Globe (Note: Graphic-intensive topic) - 9/17/2008 4:42:44 AM   
BoredStiff

 

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Global Hexagonal Grids are possible

I've looked at some more websites and emailed some people (only one of whom answered) and it seems that it is indeed possible to create hexagonal grids on a rotatable globe.

Uptopic, I discarded the possibility of hex grids because I mistakenly thought the resulting pentagons within the grid would render the grid useless in regard to wargaming.

Although the formation of pentagons apparently cannot be avoided, I've since discovered that the number of pentagons within a global hexagonal grid will always be limited to 12, regardless of how many hexagons make up the grid.
That's an important point, because it means that we can construct grids containing hundreds of thousands, even millions of hexagons, yet there will always be only 12 pentagons within the grid.
This is perfectly illustrated with the large globe graphic below:


(source)

I don't know how many hexagons comprise this grid, but it appears to be several thousand. Yet, in that sea of hexagons, there are only twelve pentagons, four of which can be seen as the red-colored polygons (not the circles, the dots), while the rest are similarly located in parts of the globe not visible.
Also shown in the above graphic, are certain other areas of (lesser) distortion.

From the point of view of a gamer, I think the 12 pentagons, as well as the other, lesser distortions, are something we could learn to live with, especially considering that these shortcomings seem minor, compared to the many benefits of being able to game on a rotatable hexagonal global grid.

It is also very important to remember that these hex grids can be infinitely subdivided into ever smaller hexagons, until a desired resolution (scale) is reached (see charts below).
Regarding the above globe, for example, it is my opinion that a further division or two would be necessary before a scale useable for wargaming is obtained. Regardless, the number of pentagons would remain at 12.


Which polyhedron to use?

Until now, I've limited the discussion to hex grids originally made from a polyhedron called an icosahedron, in particular, a regular icosahdron, which has 20 triangular faces of equal area, as well as 12 vertices, which are the points at which the areas meet.
(As an aside, it is at these 12 points that the resulting pentagons will always be located. I highly recommend interested readers take a look at a short set of pictures that illustrate how a global hex grid is easily made from an icosahedron, starting here and ending with slide 9, the picture of the 10,242-hex globe.)


Regular Icosahedron
(20 sides, 12 vertices)

I have since learned that global hex grids can apparently also be derived from dodecahedrons, which are kind of the opposite of icosahedrons, but have 12 equal-area pentagonal faces and 20 vertices. Presumably, such grids will also have a constant number of pentagons, but I haven't come across any detailed information on that.


Regular Dodecahedron
(12 sides, 20 vertices)

Additionally, I had an email correspondence with someone who told me that grids can also be derived from other base solids, such as tetrahedrons, cubes and octahedrons, although I don't know whether those would indeed be hexagon grids or something else.

Regardless, most of the information dealing with hexagonal global grids available on the internet appears to indicate that these grids are mostly derived from icosahedrons, which I described above.


Useful charts

Here is a chart showing some of the characteristics of a global hex grid. I know this chart deals with a grid derived from an icosahedron, because it appears among the series of pictures I mentioned above, that show how a grid is made from an icosahedron.


(source)

The first column, "R", refers to the number of times the original icosahedron has been divided. The first division always appears to be labeled "0".
The second column gives the total number of hexagons ("cells") of the grid.
The sixth column gives the distance between hexes, center to center, which obviously also indicates the size of the hex. Thus, at resolution 5 there are a total of 40,962 hexes with each hex being about 120.5 kilometers (75 miles) across.

Here's another chart:


(source)

Note that this chart is of a hex grid that appears to be based on a dodecahedron, because the number of grid cells given at resolution 0 is 12, which corresponds to the original 12 faces of a dodecahedron.
Note also the different numbers of total cells (hexagons) given for each resolution as compared to the first chart above. This seems to indicate that various numbers of total hexagons can be derived, depending on what kind of polyhedron the grid is originally based on (icosahedrdon, dodecahedron, etc.).

Regardless of all of that, this is a most useful chart, because it gives a very good indication of the total numbers of hexagons (cells) that might be necessary on a global grid to attain a desired hex scale.

The chart is self-explanatory, considering the footnotes, and it's worthwhile to take a closer look.

The first column, "R", once agains indicates the resolution, or, how many times the original dodecahedron (in this case) has been divided.
The second column shows the area of each hexagon at a given resolution, in square kilometers.
The third column gives the total number of hexagons (given as "cells", presumably because it includes those pesky 12 pentagons).
The fourth column, according to footnote #2, gives the "diameter of a spherical cap of the same area as a hexagon of the specified resolution". In other words, it closely approximates the cross-dimension of a hex at a given resolution, which is what we need to know to determine scale.

So, looking at the chart, it seems there is a "sweet spot" between resolutions 8-12, inclusive, that might be useful for the purpose of wargaming.

At resolution 8, the fourth column shows a value of 99 kilometers (62 miles), which roughly corresponds to the cross-dimensional size of the hexagon. I think this resolution might be the smallest one on this chart that would be useful for making a global wargame, perhaps at the corps/army level.

Level 9 might be even better, with hex sizes at about 57 kilometers (35 miles), probably still good for corps/army-level games, which is what a global game should probably be. The number of hexes at this resolution is given at over 196,000. This is a large number, to be sure, but not much larger than the 150,000+ hexes in the Panzer Campaign Moscow '41 game - so certainly still doable, especially considering that Moscow '41 was designed for a 10-year-old game engine.

At level 10, the hex scale is about 33 kilometers (20 miles), with over 590,000 hexes.

Level 11 has 19 km (12 mile) hexes, numbering over 1.7 million hexes.

Level 12 has 11 km (6.8 mile) hexes, numbering over 5.3 million hexes.

I think anything larger than that would be unplayable at a global scale.

Those then, are the possibilities. It should be kept in mind, once again, that the second chart appears to reflect a grid derived from a dodecahedron, as opposed to a grid made from an icosahedron, which would have different numbers of hexagons and hex sizes for a given resolution, as shown in the first chart.


More graphical examples


An example of a global climate model geodesic grid with a color-coded plot of the observed sea-surface temperature distribution. The continents are depicted in white. This grid has 10,242 cells, each of which is roughly 240 km across. Twelve of the cells are pentagons; the rest are hexagons. (source)


Four resolutions with approximate hexagon areas of:
(a) 210,000 km2
(b) 70,000 km2
(c) 23,000 km2
(d) 7,800 km2
(source)
(Note that, regarding globe (d) in the above picture, the 7,800 square-kilometer hexes would be about 88 kilometers (55 miles) across and thus at a scale that could be used for a corps/army level game. So this is what it approximately could look like, although there would obviously be a zoom function.)


What's possible and summary

Other than a standard globe, I can imagine a game that starts by letting the player select a number of parameters, much like in many existing flat-map games.

Firstly, perhaps several scales might be possible, in order to create shorter games (smaller scales) or games of longer duration (larger scales). Edit: On second thought, that might be too much too ask for.

Percentage of land/water, types of terrain, various weather effects which would create cold polar regions and hotter equatorial regions and everything inbetween and all with their applicable terrain (frozen oceans at the poles, etc.).

In short, everthing that has been done for various games with flat maps in the past, but applied to a rotatable global hex grid.

Basically, players would have the ability to create planets. The effect of seasons might also be fairly accurately modeled. Daylight/nightime might be too large a timescale to be playable at the global level, imo.

I can imagine games in which nuclear submarines and bombers would traverse arctic oceans, underneath pack ice in the case of subs, to launch their attacks.

It certainly seems possbile, from everything I've been able to learn, that hexagonal global grids can be made for use in wargaming, with a minimal amount of distortions.

Hexagonal global grids are only starting to be used in scientific applications, according to what I've read online, although the concept has been around since the 1970's.

No one, to the best of my knowledge, has done this in regard to computer gaming, wargames or otherwise. There are games that use global area maps, and according to another poster uptopic, a naval game that seems to use a hex grid in a limited way, but nothing close to what I described above.

So, any designers care to chime in here? What are your thoughts on this?


Main Sources:

Spherical Geodesic Grids:A New Approach to Modeling the Climate
(especially the pages on how hex grids are made, here)

Discrete Global Grid Research at Terra Cognita

PYXIS Innovation

English/Metric Conversion Calculator

< Message edited by BoredStiff -- 10/5/2008 2:38:15 AM >


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RE: Wargaming on a Globe (Note: Graphic-intensive topic) - 9/17/2008 5:31:30 PM   
Widell


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Also look at http://www.profantasy.com/products/ft.asp if your looking for map making tools. The commercial product sold by ProFantasy is, I believe, based on the free http://www.ridgenet.net/~jslayton/software.html

EDIT: I must throw in http://www.planetside.co.uk/terragen/ even if it's not for making planetary maps. It's free on the other hand....

< Message edited by Widell -- 9/17/2008 5:41:38 PM >


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RE: Wargaming on a Globe (Note: Graphic-intensive topic) - 9/17/2008 5:55:08 PM   
BoredStiff

 

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quote:

ORIGINAL: Widell

Also look at http://www.profantasy.com/products/ft.asp if your looking for map making tools. The commercial product sold by ProFantasy is, I believe, based on the free http://www.ridgenet.net/~jslayton/software.html

EDIT: I must throw in http://www.planetside.co.uk/terragen/ even if it's not for making planetary maps. It's free on the other hand....

The first program only makes flat maps - nothing new there.
I don't know what the second program is, just looks like pretty pictures, but it has nothing to do with global hex grids.

The whole point of this topic is rotatable, global hexagonal grids and how they might be applied to strategy/wargames.


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