Squares, Hexes, Octagons...

[Lul Thyme]

Originally posted by vulture


Consider the good old icosohedron. The vertices, where the points of five (equilateral) triangles meet is decidedly non-planar. As shown by the fact that the sum of all the angles meeting there is 300 degrees. Certainly a sphere is approximately planar at any given point, but that's not true for an icosohedron - the space is non-analytic along edges and at vertices.

The Icosahedron is certainly planar as a graph.
What we care about is the underlying graph.
I can draw tiles on a plane such that each tile corresponds to a vertex of the icosahedron, and two tiles are adjacent if and only if they are adjacent vertices on the icosahedron...
The same is true for any platonic solid...
(Careful, of course my tiles will not be regular poygons, they won't even all be the same. They will have the right "adjacency" property though.)

Let's go back a bit.
What do we mean by a "tiling" in this case.
Why do we say we can tile with squares and hexagons but not with octogons.
Because we can draw tiles in the planes (for example squares and hexagons) such that each of them is adjacent to 4 and 6 other tiles respectively but not 8.
Now suppose I draw a square lattice on a plane and define "adjacency" to be all squares touching plus the diagonal one. Then each square is adjacent to 8 and you call this an octogonal tiling. This is what civ actually does.
But we can't actually draw it so that the "adjacent" tiles share part of an edge so we don't consider this a "true" solution.



For example going to a sphere (or even a space of negative curvature) doesn't help in this respect.

For example if you cut up the surface of a sphere in any different pieces, you can cut up the plane in pieces such that there is an isomorphism between the adjacency relation so that lowering the curvature (going from sphere to plane) did not help at all.

My point is that unless you take something like a torus with more and more holes as the graph grows this is the best you will be able to do.

Here is my claim :
if you have a surface with no holes, whatever curvature you like, you will NOT be able to draw a finite number of regions on it such that each region touches 6 or more other regions (touching in the usual sense, sharing part of an edge).

[Lul Thyme]

Originally posted by Vince278
Yes, one of my all time favorite threads. After all this time I'd still vote for hexes.

There are a lot of +\- but taking all in consideration, I would probably vote for hexes too.

[Enigma_Nova]

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[Shogun Gunner]

Originally posted by Vince278
Yes, one of my all time favorite threads. After all this time I'd still vote for hexes.

best trade-offs.

[RGBVideo]

Another fan of hex-based movement here.

[Lul Thyme]

Originally posted by Enigma_Nova

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There is one major side effect to all those "move many tiles to have a bigger number of options" ideas.
I'm not sure many have considered it.

Blockades are WAY WAY harder to do.

Take a square grid.
If you take units that have a movement 1 in a grid that works like civ and then suddenly increase all their movement to 10 say.

You might think nothing has changed because the relative movement is the same.

But strategic options become more limited because units can basically go anywhere so unless they are attacked, it becomes very hard to force them to attack to reach somewhere.

Some may consider this a plus others a minus, but it is to be considered.

Personally I think it is less strategic and it is one of the reason I'm not a big fan of similar schemes (like enigma_nova's)

[Mujadaddy]

TRIANGLES!!!!!!!

[Vercingettyrex]

Very interesting thread.

I'm neutral on the issue. Think that Firaxis would need a reason to change to Hexes and it would have to be a gameplay one.

[Drachasor]

Really, why have hexes or squares? We could have a much more free-form system* where you can move in any direction, not limited by trying to fit units into individual tiles on a grid.

True, there'd be some changes to the game. A minor ZOC effect would need to be instituted (you can't pass really close to another unit you are at war with without initiating combat). Also, cities would collected in a flat radius around them and be placed more freely--if one still wanted citizens working areas, that could still be done in a number of ways, such as dynamic tiling within a city's workable radius.

As for city placement, it would be possible to overlay a colored map or similar device to indicate which locations were best (judged by the overall quantity of resources gathered)--even 3 such maps, which could be overlayed on each other, one for each resource, could be used. Add an option to let the game snap your movement choice to a very close ideal location and that part of the game would be much like it is now.

-Drachasor

*In reality, of course, such a system would likely be composed of a bunch of very small squares, with individual units taking up a roughly circular area with a radius of 30+ squares or some such.

[Vercingettyrex]

The whole question of hexes and squares arises from the concept of units. You could theoretically abandon it altogether. Not an idea that I would wish to tout but one I'll use by way of example, you could have an army which has a base, something like a city. This base would be outside your capital or other city, but could rebase to other locations. Like a city the Army can be built up and has a special screen. Specialist items (for instance siege engineers) can be built in cities and sent to it. Developments in military theory allow more armys and more complexity. A navy would work in similar fashion.

In ancient times the army can only be given some simple initial orders. Scout, Defend and attack. In times of war. Blue arrows start to emanate from the Army base towards frontline locations. Enemy movements would be shown by Red arrows and Red blocks. The whole wargame thing would be given a highly conceptual strategic framework. Reports of battles would be given by your military advisor as well as progress and recommendations. To a great extent the tactical stuff would be out of your hands. Success would depend on luck and how well you've trained and equipped your army. For instance an element in determining outcomes might be the speed of the army and how good it's logistics are. And of course it's General.

Later on the Army can be given more complex commands. Such as fortify an area, provide civic assistance of some sort or another, loot, and pillage, defend in depth, blitzkrieg etc.

I think in recent years there are some wargames that use this method of displaying military movement, though I haven't played them, they are probably for die hard grognards and I would be the first to admit this would not be CIV, as we know it, and could be a real turn off. But I raise it to illustrate that any discussion of squares, parallelograms, hexagons etc must consider how units or armys should be played and what their scope is. There are imo subtle differences between hexes and squares or parallelograms that can really change game play mechanics. Hexes encourage zones of control and are better at creating the illusion of 360 degree movement. Squares have an abstract simplicity and are commonly understood, by anybody who has played draughts or chess. They both come from a boardgame background. If you really wanted to revolutionise CIV (circa version 7) , you might want to re-look at that heritage and consider whether it can be done away with.

But I think Firaxis would have to think long and hard before giving such a great Game that kind of an overhaul. You can have revolutions that lead onwards and upwards and you can have ones that lead to year zero. At present I think CIV IV marks a really great consolidation of all that has gone before and still leaves some room for improvement.

[Enigma_Nova]

Before you make that much of a change, see if the Hexes thing works out. We're not even sure if Civ will play the same way with hexes, let alone any other form of movement or zoning.
For one, a Hex city would only work 18 tiles (19 if you include the city itself).

[Vince278]

Space Empires 5 (due out in a few months or so...) marks a departure for the series. They are going from squares to hexes. The screenshots look nice, we'll see how well the hexes work there.

[Vince278]

Originally posted by Drachasor
Really, why have hexes or squares? We could have a much more free-form system* where you can move in any direction, not limited by trying to fit units into individual tiles on a grid.

I believe a vector based system was discussed earlier in the thread. It would be the best system to use (Civ would be alot like a table top wargame) but the most difficult to implement IMHO.

In a vector based system it would be best to use radial geometry for movement but the effect would be similar to the really small squares (or even hexes) you mentioned.

[Enigma_Nova]

A vector system works when your game is modelled on points. Civ 4, however, is modelled on areas - your cities occupy an area, work an area, and your units control an area.
In theory, a radial game would allow you to work 1/3rd of a plains hill, 1/3rd of a freshwater lake, 1/12th of a desert and 1/12th of flat grassland. While using floating points for the resources would be easy, do you have any idea how much micro and/or computation that would require?

[wardhali]

Originally posted by Leland
You could have an octagonal tiling in non-euclidean space!

no, you couldn't, there cant be an perfect octagon in non-euclidean space