Space Gaming - 2d vs 3d maps

A discussion group on Facebook that talks about Traveller related items has been talking about 3d mapping vs 2d mapping.  I am a big fan of Classic Traveller (1977) and its derivative games.  Those include MegaTraveller, T4, T20, T5 and Mongoose Traveller.  One of the things about them, however, is that going back to the original, they render star maps in a 2d fashion, typically on a hex grid.  Let me say, that I am a big fan of the 2d representation, because it is not true (form a Physics sense) but it does represent a presentation of game/setting information in an intuitive and extremely useful format. What could be better?

On a Traveller map, the first thing you will notice is hexagons, some with "world systems" marked in it.  Each hexagon represents a parsec (roughly 3.26 light years), and any parsec that has a solar system in it that is potentially of interest, has a marker on it showing such.  This is a nice reality on the space involved, for each hexagon might be home to several solar systems (if a denser region of the galaxy, this might be a higher number), or it might be void.  But regardless, only "interesting" systems are marked.  That means, systems that either might have a civilization/colony on them, or might represent the possibility for such.

Regina Subsector - from the Traveller Wiki

But the maps are in 2 dimensions.  Originally they were in simple black and white, and these days it is common to find them in color, with the various regions and system colors indicating some details.  But the maps are still on a 2d hex grid.  So on the example above, the planetary system Forboldn is 1 hexagon away from Knorbes, which means an approximate 1 parsec difference between them.  This is great for the game, because the interstellar capabilities of the ships are measured in the ability to 'jump' between points of normal space, that are limited in (because of the technology involved) distances of roughly 1 parsec.  So a jump-1 ship could travel from 1 hexagon to another (a vast distance) in the space of a week - but that makes this rendering of the starmap very useful for game navigation.

But what about a 3d version of space - you know since space is basically a 3 dimensional construct, and all that...  Well, there have been some game maps that have done a good job on this.  I would like to talk about three, briefly, but in the light of a tabletop gaming constraint.  That constraint is that the map should be able to be printed out and passed around at the table, as an artifact to be consulted during game play.  A very nice 3d map on a computer that can be rotated, zoomed in and out of, is fabulous, but of more limited use during tabletop gaming.  In computer gaming, however- but that is a different story.  On to the examples I have.

Space Opera
In the game Space Opera, the materials that were released by Fantasy Games Unlimited (the publisher of the game) were often placed on planets in their published Sectors.  These were regions of space, published as game setting modules, that featured a number of planetary systems in a cube of space.  The examples below are from The Mercantile League (which, if I recall, is Star Sector Atlas #2).

The maps were published in their 8.5x11 Star Sector Atlas books, and the scale (which required the use of a ruler on the page to determine distances) was typically 1mm to 1 light year.  So you get out your ruler, determine that two worlds are 36mm apart from each other on the page, and you say "They are 36 light years apart".   Without having to use X and Y coordinates, and without having to do the Pythagorean Theorem calculation -- square root of ((x1 - x2)^2 + (y1 - y2)^2).

But, the 3d portion comes in with the fact that each world had a positive or negative measure (in light years, or LY) above or below the plane of the map.  So, taking the difference of these two gives you a second measure, the difference in the Z coordinate between the two points.  So now, with the X/Y measure in hand (the distance on the page), and the Z measure (calculated from +/- height differences) you can get the absolute 3d difference by again applying pythagoras as above.

The game publications gave you, in each Star Sector Atlas, a basic travel distance table that listed the distances (and some game economic factors) for the pairings of the more interesting/important worlds within the sector, so the distances were already calculated.

Finally, the last thing that was provided, in terms of a mapping assistant, for the FGU Space Opera Star Sector Atlas products, was the map showing the common space lanes (i.e. - the ones described in the "Fares and Cargo Rates" table).  This was simply the sector map with star lanes drawn on it.

Pros/Cons of the FGU method - these are easy enough to understand, and having the Z coordinate on the map makes for an easy transition to 3d.  As always, with a 2d depiction of 3d space, the map can be illusionary in some instances, where there is a sharp Z difference between two points that are otherwise (X/Y) close on the map.  These maps are nice because there is no real grid (they would come, later, with an Index, matricing a number vs. a letter axis, to make finding planets a little easier), but the obverse of that coin is that you need a ruler graduated in millimeters (or would have to convert inches, each to 25.4 mm), in order to find distances that are not on the quick look up table.

Universe
The SPI effort to enter the roleplaying game market was with the game Universe.  Universe had three very nice things going for it.

1. The character generation sequence had a great way to compare physical stats for characters from different geophysical planetary backgrounds (i.e. - difference in physical parameters based on the planetary environment you were born/raised in). 
2. The starship construction/combat rules were very nice (describing a setting with generally common ship hulls, perhaps as in the Niven Ringworld universe, but with different modular components), as you might expect from an experience board game publisher that had devised printed several sets of starship combat rules by the time the RPG arrived.  In this case it is the DeltaVee game.
3. The 3d space map of the area roughly in a sphere of about +/- 25 light years around Earth.

This article is interested in discussing the space map.  It worked, in concept, very similar to the map from FGU but with some important differences.  It incorporated iconography and color (as do the more modern Traveller maps) to indicate something about the stellar systems mapped.  In the case of Universe the colors correspond to the stellar sequence.  Different from the FGU Space Opera maps, it used a graph/grid to show the location of the worlds, so you did not need to use a ruler to find the difference of planets. But it did mean you had to apply Pythagoras.  One of the nicest things about the Universe map is the fact that it included the X,Y and Z coordinates for each system.  Also, Earth/Sol is at (0,0,0) so measure to other worlds from Earth is pretty easy to do.

Finally, the third method of showing a 3d space on a 2d map is from the old Metagaming science fiction empire building game, Godsfire.  This game represented three dimensional space on a hex map.  The measurements for space were abstracted (slightly) and objects pressed on to a hex map, to make counting and measuring movement and disances between star systems to be quite easy (just count the hexes).  The Z component was brought in by making sure that each hexagon only represented the space at the plane of the map.

Within the hexagon, there was a series of 11 spaces, 5 representing levels below the map, 1 representing the planar level of the map, and five representing levels above the map.  As this was a map for a multiplayer wargame, moving objects on the map was necessary, and could be accommodated by moving the object (ship, fleet, etc) by moving it "up" or "down" within a single hex, or from hex to hex (arriving at the same level in the new hex, as the level that you departed the old hex from.

Pros/Cons - It is abstracted (as mentioned), and not as precise as the other methods, but it is certainly quick to navigate and move pieces around in.  Very simple and straightforward for campaigning and wargaming.

As you can see from the image, each "hexagon" is actually represented as a square, but using offset rows, means each is spatially related to the six around it (essentially a hexagon).  And the spiral showing the levels (from +5 down to -5) within the hex.  Very convenient.

This map was used by a group I played in years ago, as the campaign map for a Leviathan wargaming campaign.  It was an elegant way to do three dimensions, and it was very interesting to see players get surprised by a fleet that appeared similar, only to realize that it was at +4, and they were -3, adding (effectively) 7 more spaces of difference between the two fleets.

So, there.  Three different methods of doing 3d mapping, on a 2d space, with different pros and cons for each.

If interested in this topic, I can (not strongly enough) recommend Winchell Chung's page on 3-D Starmaps over at his Project Rho website.  Winch is a wargamer and artist and generally interested in the intersection between science and sci-fi and gaming, and his web pages are chock full of the most excellent information.