What do you think of the implementation of a truly round world through hex grids?

[Wodan]

Making the globe spherical is a minor point. Much more beneficial is the tactical advantages to gameplay.

Wodan

 

[r_rolo1]

I couldn't find a proof on the web, not even at mathworld.

I think what r_rolo1 said is correct though, has he got a link for that?

I have the proof, but on paper....

Will try to post it in a spoiler when I got time for that

 

[lutzj]

What about a cube-shaped world? A little fudging the corners, and we could have something without having to mess too much with game balance or the underlying engine.

EDIT: 5 th post!

 

[Wodan]

Lutzj, here you go.

Wodan

 

[Nodles]

There are only 9 regular polyhedrons possible, and only 6 of these resemble a globe shape. (The others are "star shaped".) 4 of these 6 are made up of triangles (the other two, the cube and the dodecahedron, are made up of squares and pentagons, respectively. Long story short, making a solid figure out of congruent hexagons is PHYSICALLY IMPOSSIBLE

I see...

One last vestige of hope for this idea, insipired by this picture: notice how rare are pentagons on those geodesic grids, rare to the point i couldnt locate one. One possibility that crossed my mind is that these grids of the Earth haves only two pentagons, one at each pole.

This possibility makes a lot of sense. If im not mistaken, those grids were built to allow the use of finite differences to solve differential equations. AFAIK, finite differences cant handle irregular grids (that being the domain of finite elements), the grid must be regular and neatly arranged.

An interpretations of this is that there are pentagon-shaped "holes" in that globe. This means those "globes" are not closed surfaces, and therefore not restricted to the laws of regular polyhedrons. Those "holes" are of course singularities which are not considered in the calculations. However, as long as there are only two of them, one of each sitting at each pole, they are acceptable "aberrations", since most of the interesting results involve areas farther away from the poles.

The same thing can be said of civilization world maps: It would be undesirable to build cities EXACTLY at the poles, since they should be surrounded by ice glaciers which are normally associated with unproductive land. Of course it would suck to travel with planes and rockets through the poles and spot that pentagon-shaped "hole" in the world, but its more of an aesthetic issue.

Of course, it remains to be proven that 1000+ hexagons plus 2 pentagons can build a sphere-like closed surface.

 

[zeise]

A minor point that no-one has mantioned that i thought i'd bring up, just to be picky, is that the world is not truly a sphere, i have no idea how this would impact the making of the Earth as it is but no doubt it would probably make it harder to achieve.

 

[Verge]

A minor point that no-one has mantioned that i thought i'd bring up, just to be picky, is that the world is not truly a sphere, i have no idea how this would impact the making of the Earth as it is but no doubt it would probably make it harder to achieve.

"Picky" and "minor" are appropriate terms for the point you are making. Earth's deviation from a perfect sphere is only about 0.3%.

The difference between the Earth's equatorial radius and polar radius is less than 50 km if I recall correctly, a negligible amount given the Earth's mean radius of 6,371 km. Overall, the flattening of Earth's spherical shape is a paltry ~0.00335, which means the Earth is actually closer to a perfect sphere than planets like Jupiter or Saturn.

 

[ParadigmShifter]

Hey, the moon is more perfectly round than earth

 

[Seven05]

Second, why give up two axes of movement? With a hex map, you have six direction you can go, from any given tile. The square tile maps used by Civ allow eight different directions.

Because on a square tile map you end up with the impossible, the case where four evenly spaced points on the map aranaged as a square are all the exact same distance apart. So if you have a square of four points; a, b, c and d the distance between any two of them, regardless of whether they are adjacent, is identical. In Civ this creates an interesting dilema, I can place four cities arranges in a square pattern and a land or sea unit could reach any of them from any of the others using the exact same number of movement points but an air unit would not be able to do the same because for some reason air units only get to travel their full range if heading in one of four directions, not eight

 

[Catan_Settler]

I think it's a great idea and if implemented well could add a new dimension to gameplay. Somebody else mentioned triangles. What if the map were built of triangles, and they were used to actually model the mountain ranges and valleys and whatnot... Like Google Earth when you tilt the camera angle. We could have a truly 3 dimensional world where the slope of a hill affected the combat odds, as opposed to it just being a flat "hill" tile. I think there's definitely something to this idea, although I'm not sure if Firaxis is interested in messing with their proven franchise... A great idea for exploration by other game developers though to be sure. I'm wondering if this Nodles fellow could be one of them.

 

[Nodles]

LOL, not at all Im just a grad student with some fascination for mathematics and whose hobby is procrastinating.

I guess i should look into the papers of the guys who developed the geodesic grid back in the '60s. One point i want to make clear however, is that im trying first to solve the spheric world grid problem, which is basically geometric. If i manage to figure that out, another aesthetic ideas such as 3d terrain (which are IMO basically eye-candy) can be considered.