spherical maps

[coregames]

Highway to the Reich doesn't use a global spherical map does it? On a two-dimensional map, discrete location is much easier to keep track of without the use of "spaces". I understand about great circles and pathfinding, but it's not as simple as vector addition, since the geometry is non-euclidean (a vector cannot be extended indefinitely, and curvature comes into play). Of course, area movement compensates for this by an unusually huge Greenland on the Risk map... but hexes or a triangular grid projected onto an icosahedron are more accurate if polar distortion is to be avoided. I'm certain even HttR uses a grid of some kind, even if the increment is smaller than the units themselves, otherwise how could you ever calculate range? With a sphere, there is simply no way to map a square grid onto it without gross distortion, as in latitude and longitude. Some kind of discrete location must be available, no matter how small, and the best grid fit to reduce overall distortion is the icosahedral hex-based map.

[coregames]

This scale is pretty generalized... It Makes the Adriatic less than a hex wide for instance. A global scope game may be able to utilize this with the right rules, but I still think the above-mentioned 10-mile-per-hex breakdown scale would be useful for assembling fronts to allow tactical finesse.

[coregames]

ORIGINAL: coregames

I still think the above-mentioned 10-mile-per-hex breakdown scale would be useful for assembling fronts to allow tactical finesse.

As an example, imagine playing the game during a WWII scenario... most of the world is being handled at 250 mph scale when, in May of 1944, the Allies call for tactical maps of the north coast of France. In response, the German player calls for tactical maps of southern England, so air units have to count full range from their air bases. The corresponding 250 mile hexes from the strategic map would be assembled into a front, allowing smaller scale of units and time, as well as more hands-on management of operations in that theatre. The map of that theatre might resemble this if the scale were 12.5 miles per hex:






and then, at 10 mph for comparison:

[coregames]

ORIGINAL: Raverdave

Why the hell do you guys from the north insist on always showing Australia on the bottom of the map?[:-]

Raverdave, Rowland (and Pinder, God rest his soul) are from Australia, and they placed your country down under as well! Not that I wouldn't love to live there...

[pasternakski]

ORIGINAL: Raverdave

Why the hell do you guys from the north insist on always showing Australia on the bottom of the map?[:-]

Better?

[coregames]

I never noticed before how much the Earth looks like a surrealistic smiley face! And Indonesia is the Charlie Chaplin mustache...

[coregames]

I mentioned GDW's 1981 award-winning sci-fi game Invasion: Earth, set in their Traveller future history, earlier in this thread. The map is at 1140 km per hex, definitely grand strategic, but the idea was very much in keeping with the content discussed here. Obviously, computers could handle a much finer scale for such a map.

[rhondabrwn]

Hmm... I had lots of Traveler stuff,never picked that one up. Very interesting concept for the time and, as you state, very much in keeping with this thread's topic.

GDW always did have some interesting concepts for sci-fi game. Do you remember "Double Star" where the planetary systems orbited the two suns so that you had to anticipate that movement when trying to attack an enemy planet? The game was kinda of "ho hum" but the concept was cool.

[coregames]

ORIGINAL: rhondabrwn
Do you remember "Double Star" where the planetary systems orbited the two suns so that you had to anticipate that movement when trying to attack an enemy planet?

I never played Double Star, but I enjoy creative mechanics for games. Planning ahead to catch a planet at the right place in its orbit must be a fun challenge.

One of the interesting things about Invasion: Earth was the way they handled the situation in space around the planet. One box denoted close orbit, another, far orbit (with a space to denote the moon in it), etc... all the way to an outsystem box. It seems to me the game would have benefited from an orbital mechanic to handle where the moon was at a given moment in time, rather than simply using an abstract unmoving box.

In a computer game such as we are discussing in this thread, the surface of the moon can include its own icosahedral hex/triangle map, to differential between various moonbases and installations. Of course, orbital mechanics are fairly easy to simulate with a computer.

[Vanakalion]

Say goodbye to the icosahedron. The ideal projection of a world map consists of an inflated six-sided cylinder with a lid at the north and south poles (hexball projection). The cylinder is rolled up and the poles at the 54th and -54th latitude are unfolded upwards and downwards. The map is segmented into isosceles and equiangular triangles, which is not entirely dissimilar to the Dymaxion projection (Buckminster Fuller).
Contrary to what mathematicians claim, this map is completely filled with hexagons, which is revolutionary, especially in game design. In addition, the map is scalable and can be covered with hexagons at any scale.
If required, the poles can also be rolled along the 54th degree of latitude in 60° increments.
It is therefore possible to limit the current representation to one of the six gores with the poles. If necessary, you can also limit yourself to the northern and southern hemispheres, which makes things more manageable. At a scale of 20 km, world maps become gigantic and can no longer be displayed on monitors. In the vast majority of cases, you will not be able to avoid a scrollable interface.
Unfortunately, I am not aware of any software that can calculate this projection method in different scales.
The same applies to the Dymaxion projection, which is virtually distortion-free and hex-capable, but very idiosyncratic.

[ernieschwitz]

Contrary to what mathematicians claim, this map is completely filled with hexagons, which is revolutionary...

I am not sure what you mean by that? Where have you seen this claim?

[Curtis Lemay]

I would have more hope for a sinusoidal projection:

[Lobster]

Why use hexes at all? Why not just use a google earth 3d type of map and real distances? Zoom in and out to your hearts content.

[Vanakalion]

I am not sure what you mean by that? Where have you seen this claim?

All attempts to generate worlds without pentagons have failed miserably (see Civilization & co.)
This wisdom comes from several developer forums.

[Vanakalion]

I would have more hope for a sinusoidal projection:

Sinusoidal Inerrupted would be the very best solution. The more gores, the lower the distortion. Compare this with Tissot's indicatrix.
However, this projection method is not suitable for hexagons.

Alternatively, the HEALpix projection can be used. However, this must be compressed somewhat in width so that the angles at the poles are suitable for hexagons.


Strictly speaking, my hexball projection is a variant of the HEALpix projection.

[Vanakalion]

I mentioned GDW's 1981 award-winning sci-fi game Invasion: Earth, set in their Traveller future history.

Marc Miller, Frank Chadwick & team didn't know any better back then. HEALpix had not yet been born. Today, the world map and Traveller templates would be based on HEALpix. Maybe Marc will change this in Traveller 6.

[Curtis Lemay]

I would have more hope for a sinusoidal projection:

Sinusoidal Inerrupted would be the very best solution. The more gores, the lower the distortion. Compare this with Tissot's indicatrix.

Three parts instead of six sounds better to me. Six leaves North America, Russia, and the Pacific split.

However, this projection method is not suitable for hexagons.

Huh? I've got plenty of sinusoidal maps in TOAW - hexagons only. Sinusoidal maps are equal-area - critical that the hexes all be the same size.

[Curtis Lemay]

Huh? I've got plenty of sinusoidal maps in TOAW:

https://crossrl1.wixsite.com/my-toaw-si ... union-1941

[Vanakalion]

Why use hexes at all? Why not just use a google earth 3d type of map and real distances?

Does not work with board games and board game simulations such as Civilization & Co.

[RangerJoe]

Talk about bring back to life a very old thread.

I thought that spherical maps were called globes . . .