spherical maps

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coregames
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spherical maps

Post by coregames »

The World in Flames forum had a discussion a while back (World in Flames >> Spherical global map) that generated a lot of interest and feedback. While I do think MWiF should use the projections that the board game uses (other than possibly unifying the scale), the idea of a spherical projection (icosohedral most likely) is very attractive. Might Matrix produce a hex-based game on a world-wide scale that uses such a projection? Does anyone know of a game that currently does this? I have been projecting hex grids onto various size Fuller Dymaxion maps of the earth, trying to get a feel for how such a mapping convention might work, and I think the subject merits discussion outside the WiF forum. Here's an optimized scratch image of a Fuller map of the world at 100 miles (~ 160 km) per hex:

Image

Of course, this projection would probably not be available for a wargame, given Fuller's legacy, but it is food for thought.
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RE: spherical maps

Post by Dave Ferguson »

no images that I can find!

The idea sounds good for global games where the distance between locations is important. graphically it should be easy to handle as each location is just a co-ordinate point. Over smaller areas, say a continent a traditional map projection is OK, as long as the correct projection is used. IMO there is nothing worse than seeing a map of my favourite campaign with gross distortions.
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RE: spherical maps

Post by coregames »

yep, must have hit the wrong button... the pic is in the post now though.
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RE: spherical maps

Post by rhondabrwn »

I like the idea, though it certainly does take a mental shift of gears to grasp the changed perspective.

Here's a different twist. What about an actual 3-D wargame where the playing map WAS a rotating globe. When zoomed in it would be fairly typical of a traditional wargame, but when you jumped back into strategic or operational mode you would have an actual globe with correct distance and directional orientation upon which to plot your grand strategy.

Hmmm.... imagine WiTP played on such a map!
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RE: spherical maps

Post by David Clark »

I did a whole bunch of research into this a couple of years ago. The projection you're looking for is the Icosahedral Snyder Equal Area (ISEA) projection - a relative of Fullers projection.

http://www.sou.edu/cs/sahr/dgg/isea/isea.html

The idea is simple - you map the earth onto a Icosahedron (a twenty-sided die for you rpgers). Each face is an equalilateral triangle, into which hexagons pack perfectly. The only trouble comes at the points of the triangles - these have to be pentagons, not hexagons. So you write your code to handle hexagon movement, and write pentagons as a special case. There's even code on that page to generate the verticies for you - you can build an opengl model for any given mesh density pretty much from the code provided. I did it in Python once; it took me an evening.

Now you have a giant 3-d sphere, covered in thousands of projected hexagons (and twenty pentagons). Take an ordinary map, read in latitude and longitude values, and map those to the hexagons. Now you have a giant Earth, covered in hexagons. Build your wargame around that.

I coded enough to know it's feasible, but be warned - you either want BIG hexes, or a LOT of hexes. At ten miles from one side to another, you're looking at several hundred THOUSAND hexes.

Hope this helps.
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RE: spherical maps

Post by coregames »

ORIGINAL: David Clark

...but be warned - you either want BIG hexes, or a LOT of hexes. At ten miles from one side to another, you're looking at several hundred THOUSAND hexes.

I think the vertices-at-poles projection from the site you mentioned is the one used in Invasion: Earth, by GDW, a wargame set in their Traveller future history.

Yes, certainly that would be a giant map... perhaps by doing blow-up scale for critical battles a game could make effective use of this. A game could have a grand scale 100 miles per hex, an even 50 hexes long per side on each triangular face of the icosohedron. The players could run the entire war on that scale, which is just barely manageable for a board game, and so easily doable on the computer. If they wanted to micromanage the war to some extent, they could fight certain battles realtime at a smaller scale (perhaps 10 miles per hex). In this case, most of the larger hexes, when zoomed in on, could be from a limited set of maps with a rotational component to increase variety without having to map every 10 mile area of land on Earth. Only special hexes and important urban regions would need to be unique.

The break-down battles could be fought on sets of hexes lifted out of the larger map and assembled into a smaller battle map at 10 times the scale of the strategic map. Battles that lasted longer than the larger turn scale (one month?) could include reinforcements moved in from the adjacent strategic map spaces. With enough memory or network capacity, perhaps the entire war could be fought at the zoomed-in scale, with command structures in place so that lots of people got involved via internet play as regional commanders.

Because of the accurate world-wide scale, subs could go under the polar ice cap, planes and missiles could take polar routes, etc..., and all of these extreme latitude activities would have minimal distortion. Perhaps a cold-war, modern or near-future WWIII type game would benefit the most from the global projection.
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RE: spherical maps

Post by coregames »

ORIGINAL: rhondabrwn

Here's a different twist. What about an actual 3-D wargame where the playing map WAS a rotating globe. When zoomed in it would be fairly typical of a traditional wargame, but when you jumped back into strategic or operational mode you would have an actual globe with correct distance and directional orientation upon which to plot your grand strategy.

This is a great idea, in keeping with my last post. The game could use the icosohedral projection, with hexes for the coordinate system, but maybe the hexes don't have to be apparent. You could dispense with the grid lines and just use it for location mapping. It would still be a bit odd when a unit was on a vertex space. Has anyone seen a use of the rhombic triacontahedron in a projection? That is the equivilent of a 30-sided die, which has diamond shaped faces that are equal to two stacked equilateral triangles, which means hexes would map evenly onto them.

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RE: spherical maps

Post by rhondabrwn »

I think you guys are on to something here... sounds workable to me. I'd like to see such a game.
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RE: spherical maps

Post by David Clark »

I figured it would be good for a modern naval wargame with global scope - sort of a Victory's Fleet-style treatment, only covering the whole planet. I got kind of excited about the whole thing until I really started to crunch the numbers on how much time would be needed. Out of reach of a hobbyist, and no-one buys wargames anymore.

One could write such a game to use an ungridded sphere, of course, and it would be a little simpler - sort of a "Harpoon on a sphere". Still, there's a certain appeal to hexes - unit position becomes more discrete; less zoom-dependant.

The best way to do the math for this projection, I think, is just to calculate movement and pathfinding on a sphere, then map back to the hex-system. There are plenty of algorithms for hexmaps, but they all assume a flat map - there would be trouble over face edges and at the verticies. Other problems present themselves at the corners - since they're pentagons, a unit occupying one could only be attacked by five neighbours, not six - a defensive advantage. Heh.

Fun to imagine. Less fun to code.
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RE: spherical maps

Post by coregames »

ORIGINAL: David Clark
Other problems present themselves at the corners - since they're pentagons, a unit occupying one could only be attacked by five neighbours, not six - a defensive advantage.
There are two projections in which all of the vertices fall on water. I agree that graphically, in keeping with rhondabrwn's post in this thread, the zoomed out scale should map evenly onto a sphere, so you would definitely want to keep all of the land hexes complete. It then resembles a sort of "soccerball" with really small pentagons at the vertices.

As to mapping onto a spherical grid, do you mean a longitude/latitude coordinate system? An icos grid with hexes is far more accurate for the purposes of a game, in my opinion, especially if the vertices all fall over water.
...no-one buys wargames anymore.

If that is case, then why am I going to buy GGWaW when it goes gold? Unless you were referring to boardgames in particular. In that case, I admit I like having at least the theoretical possibility of playing a game over a large table top(s), even a monster game like World in Flames. I am thankful, however, that computers make such games much more managable.
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RE: spherical maps

Post by ravinhood »

ORIGINAL: rhondabrwn

I like the idea, though it certainly does take a mental shift of gears to grasp the changed perspective.

Here's a different twist. What about an actual 3-D wargame where the playing map WAS a rotating globe. When zoomed in it would be fairly typical of a traditional wargame, but when you jumped back into strategic or operational mode you would have an actual globe with correct distance and directional orientation upon which to plot your grand strategy.

Hmmm.... imagine WiTP played on such a map!

Heh Rhonda, X-Com has a rotating World, you can zoom in for a closeup of the area you are playing in and zoom out to view the world like you were in space. Of course it's not your hexed based game, but, it gives that world view atmosphere and movement is circular instead of flat side to side.
WE/I WANT 1:1 or something even 1:2 death animations in the KOIOS PANZER COMMAND SERIES don't forget Erik! ;) and Floating Paratroopers We grew up with Minor, Marginal and Decisive victories why rock the boat with Marginal, Decisive and Legendary?


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RE: spherical maps

Post by coregames »

original: ravinhood
...but, it gives that world view atmosphere and movement is circular instead of flat side to side

ravinhood, do you know what kind of coordinate system they used for X-Com? I want to get a better idea of how they do it.
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RE: spherical maps

Post by David Clark »

There are two projections in which all of the vertices fall on water. I agree that graphically, in keeping with rhondabrwn's post in this thread, the zoomed out scale should map evenly onto a sphere, so you would definitely want to keep all of the land hexes complete. It then resembles a sort of "soccerball" with really small pentagons at the vertices.

True. Unless you're thinking of a Naval game, in which case you want all the verticies to fall on land. Anyway, it's a minor problem - any naval game would have land units, and any land game would have naval units, so you have to deal with the pentagon issue somehow anyway. I'd just make them impassable terrain.
As to mapping onto a spherical grid, do you mean a longitude/latitude coordinate system? An icos grid with hexes is far more accurate for the purposes of a game, in my opinion, especially if the vertices all fall over water.

I was thinking of a way around the "just what does pathfinding become over triangle edges/around verticies" problem. Basically just project your current units position onto a sphere, calculate movement or whatever by great circle means, then project back onto the hex grid when you're done.
...no-one buys wargames anymore.

If that is case, then why am I going to buy GGWaW when it goes gold?

Sure; I'm being a bit facetious. I've bought FPG and UW from Matrix myself, after all. I'm just saying that if a SUCCESSFUL game published through Matrix or whoever sells, say, five hundred copies, and you net twenty dollars a copy... working on the game full time isn't an option. That's the problem with these globally-scoped games like we've been discussing - too huge for hobby development.
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RE: spherical maps

Post by coregames »

ORIGINAL: David Clark
Unless you're thinking of a Naval game

If you could keep the land hexes off of vertices you could use area movement for naval stuff.
I'd just make them impassable terrain.

This seems much less accurate than including one pentagonal space at each vertex, since each of the five hexes adjacent to the vertex then wind up having only five adjacencies.
Basically just project your current units position onto a sphere, calculate movement or whatever by great circle means, then project back onto the hex grid when you're done.

I can see using great circles for movement and range considerations, and then mapping back to an icos or other hex grid for discrete location. Hexes are amazingly versatile though. You might be able to dispense with the great circles if you allowed orientation along the hex corners, providing 12 options for direction instead of 6. This is the way Air Superiority does it, although a computer can handle the ratios better to allow even more accuracy (about 6:7 hex corner orientation vs. side orientation). This way there is no back-mapping needed. If the grid is going to be used anyway, it makes sense to get the most out of it.

As far as pathfinding... Perhaps the paths traced over vertices could change from side orientation to corner orientation, or vice-versa.

Just some thoughts... I enjoy this interchange
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RE: spherical maps

Post by ravinhood »

ravinhood, do you know what kind of coordinate system they used for X-Com? I want to get a better idea of how they do it.

Actually I have no idea how they did it. The world was huge zoomed in and you got X's and Squares that appeared on the screen at random times to show Alien activity or Alien bases (the squares). Any spot though on the map except interior land could become part of the alien activity though. Since in X-Com Terror from the Deep was more based on water warfare and coastal and ship combats.

You can download the full game at underdogs.com and look at it for yourself, it's only like a 13mb download and then you can see how the world works and how the camara works. Basically you could just right click on a spot on the world view and the screen would move to that spot also, very easy user interface for moving around the world map.
WE/I WANT 1:1 or something even 1:2 death animations in the KOIOS PANZER COMMAND SERIES don't forget Erik! ;) and Floating Paratroopers We grew up with Minor, Marginal and Decisive victories why rock the boat with Marginal, Decisive and Legendary?


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RE: spherical maps

Post by coregames »

I suppose now that GGWaW has gone gold, the question in this thread can be asked: why not dispense with hexes altogether, use an icos projection with area movement throughout? That way the spaces are all approximately equal area with no expansion or compression like we see in so many area movement games on a worldwide scale (can anyone say Risk?). The vertices problem disappears with the use of arbitrary adjacencies.
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RE: spherical maps

Post by David Clark »

Area movement is a great idea, and works very well for strategic games. I think it's much less appropriate for operational and tactical games, where weapon ranges may extend beyond adjacent areas - without homogenous distance units, forces could fire further in some directions than in others depending on the geometry.

Plus, hexes just look cool.
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RE: spherical maps

Post by coregames »

I tend to agree about strategic-scope games being the best use for area movement. Actually, I do prefer hexes in general, even for strategic games, but with GGWaW finally seeing daylight it seemed like an appropriate hypothetical for the moment.
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RE: spherical maps

Post by coregames »

I have read over the posts and I feel the basis is here for a good game idea; with feedback we could brainstorm the large issues here and if Matrix likes the idea maybe they will run with it! What say you, rhondabrwn, David Clark, ravinhood, and any others who like this kind of thing? More detailed discussion could happen in parallel through individual messages.
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RE: spherical maps

Post by coregames »

For now let's call it Project Global Scope.

I picture the interface being as rhonda suggested. The primary view can be the global scale (a 3-D rendering of the globe from space). Weather would be a nice touch, visible as clouds (two shades possible?) and hurricanes. A variety of other information should be available at this view, such as control of territory, satellite movements, possibly fleet markers.

The next zoom-in could be the one where the individual hex spaces would be visible on the map. The view could toggle between grid and no grid, and there would be a small icon of the color matching the major power occupying the space. The implicit hex grid would mapped onto the sphere so the view is as from a sub-orbital vantage point in space, with some curvature of the Earth visible, and with the weather patterns more developed and diversified. Spaces that were currently in conflict could have a separate tiny icon.

The next zoom-in could be close-up enough to keep track of the contents of a hex, based on unit type, Axis & Allies style. At this view, the map would be flat, and the larger hex grid (100 miles side-to-side) would be visible. The entire game could be played at this scale, with bimonthly turns. When passing over a vertex space, the map could automatically refold itself based on where the view was centered, or perhaps based on the path of a unit.

The final break-down would be for larger hexes (or regions of larger hexes) that are being contested. This would be at 5 miles to the smaller hex, so that each larger hex involved would become a battle hex, where the action is at one day per turn. In this manner, whole fronts of activity could be pieced together without needing to depict the whole war at the smaller scale. Short scenarios could be played at the smaller scale entirely. Computer resources allowing (such as online via network), an entire war could be fought at the smaller scale, using teams for each power, each with a command structure allowing them to split up the elements of their forces.

I envision the game as being very adaptable. The global scope seems to make the game mostly suitable to c. 1500 AD or later. Obviously, global wars would be its best use, so perhaps the earliest scenarios could start at the outbreak of WWI, and run (Civ Style) to some 21st century event, or (Risk Style) till there's only one power standing, based on the scenario being played.

The best scenarios would be WWII, Coldwar, and WWIII, but the scale variability would allow any military conflict of this or the last century to be recreated, with a time scale of as little as one day per turn. The profit model would be very scenario-oriented, sort of like publishing adventures for a roleplaying game. Speaking of which, on a side note, it could be used to handle longer time-scale events in role-playing games, especially if one expansion is a map editor that allows the game to be played in worlds other than modern Earth.

Any ideas?
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