Squares, Hexes, Octagons...

[frekk]

I like hexes better. They more accurately calculate distance, and of course, this is *actually important* in the game because of things like distance from the capitol, city radius, and so on.

6 or 8 directions, so what? Really, what difference does it make? A few people have said they feel strange without an E-W N-S combination; but that's just because they're not used to it. People said the same thing about isometric maps because everything was "tilted", guess what? They got used to it.

I can see just a single practical argument against hex maps, and it does concern me somewhat: keyboard interface.

Has anyone given any thought to completely alternate systems, like using provinces? That would greatly reduce micromanagement but I'm not so sure about it myself.

[Jon Shafer]

Provinces have been discussed ad nauseum many a time. Soren has already announced that the game will be tile-based.

And besides, with provinces you're talking about "a whole new game."

[paramir]

it hink we should do civ 4 on a 2d map!

[alms66]

Originally posted by Trip
And besides, with provinces you're talking about "a whole new game."

Which is better than the same old game again and again, as has been done in the past (civ series included). It's time for some major changes to the Civ series. There is no getting past that. If they continue to ignore it, they'll loose out to another developer. Period.

Originally posted by paramir
it hink we should do civ 4 on a 2d map!

I agree 100%, but it's already done. 3d graphics are here to stay, so I guess we who actually enjoy quality over fads are going to have to cope. I have yet to see a 3d game that comes close to looking as good as a 2d game (speaking about an individual piece of artwork - not the quantity that can be produced) can look. While the Civ3 artwork wasn't the best I've ever seen, it was far better than any 3d game I've ever seen.

[GodSpawn]

[In reply to: The OP]

I would much prefer the following scheme:

* Square Grid, and
* Floating point unit coordinates.

By "floating point unit coordinates" I mean that the actual position of a unit or entity is held to a much higher degree of accuracy than the grid.

When the program displays the unit, it would display in its most accurate position, ignoring the grid.

The square containing the unit would be known, however, and it would be used wherever it is needed, for example when seeing which units can attack each other, or when computing the effect of roads and railways.

I think we could get the best of both worlds that way:

* Simple visualisation and 8-direction movement, and
* Accurate movement and range calculations.

Obviously, there would be other ramifications of doing this, but hopefully nothing insurmountable.

(Note that this is really a proposal for a hybrid system where movement is tileless but combat is grid-based.)

[Urban Ranger]

I think a gridless coordinate system is the best.

When you move a unit, the game uses a path finding algorithm with modifiers (your preferences) to see how long it will take. When you accept a route, the unit moves there by itself automatically.

[joncnunn]

There are only three polygons that tile:

1. Equalaterial triangle.

2. Squares.

3. Hexagons.

Regular Octagons collide with each other.

Proof:

Place one regular octogon. Check
Place another regular octogon of same size east touching the original. Check.

Now try to place a regular octagon of same size NE of orginal one. overlaps with the one east.

[clinton]

For the spherically inclined.



It is many hexagons with 12 pentagons. Like an extreme football.

Wikipedia Link

Edit: Oops, just revived an ultra ancient thread. Thats what I get for using search.

[Rommel2D]

N/m, my memory must be going...

[Lul Thyme]

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

I've seen a couple people bringing this up (Vince as well)and it sound mighty cool to say but it's not that simple.
For example the surface of a sphere is non-Euclidean.
A theorem says a graph is embedable on a sphere if and only if it is planar.
So going to a sphere changes nothing with regards to the allowable underlying graph.
Unless you're talking about going on a torus or something.... (and even then , I'm pretty sure, locally the properties of a large graph would be similar to a planar graph)

[vulture]

Originally posted by Lul Thyme

I've seen a couple people bringing this up (Vince as well)and it sound mighty cool to say but I'm calling BS.
The underlying graph would still have to be locally planar and in a planar graph the average degree (of a finite graph) has to be under 6. So you cant have all regions touching 6 others....
Hexagonal is the limit case.
(I'm assuming your octagonal tiling gives access to more than 6 neighbours or else what is the point right? I could create a square tiling where each tile is an octagon...)
I may be forgetting something but I'll think some more about it...

Maybe you could make octagonal tiling work in a space of net negative curvature and allowing sharp edges (think of an icosahedron as a space of positive curvature with 'sharp edges'). The vertices where the tiles meet are not locally planar by any stretch of the imagination, and in a negatively curved space the sum of the interior angles a the vertex will be greater than 360 degrees.

Whether the tiling is actually possible in such a space, I don't know. And since it isn't locally planar, it would have to be distorted significantly to show the vertices on a 2 dimensional screen.

[Lul Thyme]

I'm not sure you understand.
I'm talking about the planarity of the graph, not the space.
For example any graph on a sphere is planar (yes globably planar) even if the sphere is non-planar.
I don't see what mankes you say that the "vertices where the tiles meet are not locally planar".
A vertex by itself is planar....

I'm not saying you're wrong, I'm not sure at all I understand what you're getting at.

My main point is this:
I assume by octagonal tiling they meant that each "tile" touches 8 other.
My point is that I do not think this is possible to have such a graph embedded on a surface even in most non-euclidean geometry. I don't actually think the curvature helps in any way. Holes might ( a sphere with enough holes would probably work)...

[vulture]

Originally posted by Lul Thyme
I'm not sure you understand.
I'm talking about the planarity of the graph, not the space.
For example any graph on a sphere is planar (yes globably planar) even if the sphere is non-planar.
I don't see what mankes you say that the "vertices where the tiles meet are not locally planar".
A vertex by itself is planar....

I'm not saying you're wrong, I'm not sure at all I understand what you're getting at.

My main point is this:
I assume by octagonal tiling they meant that each "tile" touches 8 other.
My point is that I do not think this is possible to have such a graph embedded on a surface even in most non-euclidean geometry. I don't actually think the curvature helps in any way. Holes might ( a sphere with enough holes would probably work)...

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.

That's all with spaces of positive global curvature (constant curvature for the sphere, for icosohedron it is zero on the faces and infinite at the edges and vertices). Now think about spaces of negative curvature. You can certainly cram in more than 360 degrees worth of tiling at a non-analytic vertex (if the space is analytic everywhere, a smooth function, then obviously it is still planar on small scales, and only planar tilings are possible there). At a sharp fold or apex in a negatively curved space you could get 7 (or more) triangles meeting (as compared with 6 in flat space, and 5, 4 or 3 in positively curved spaces - icosohedrons, octohedrons or tetrahedrons respectively). None of these spaces are actually 'curved', they are flat and discontinuous, but have the effect of being curved globally, rather than locally. In that kind of space, octagonal tiling may be possible.

[Addled Platypus]

nice bump clinton

[Vince278]

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

[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.

[VJ]

Another fan of hex-based movement here.

[Lul Thyme]

Originally posted by Enigma_Nova

Code:

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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