What's the big deal about Hexagonal map grids?

Well each one has its disaventages. In hexagonal distances are equal and correct, but you have only 6 straight directions, so either N-S or E-W is going to be a zig-zag.

Why doesnt anyone like the totalwar aproach, a gridless map, with zones of control?. Of course for the economic layer, the terrain is still divided in cells so the city screen would be the same (here i prefer the hexagons, as they give concentric circles around the city)

ParadigmShifter said:

Well both are metrics.

Orthogonal only movement is the L¹ norm, while diagonal same distance as orthogonal is the L-infinity norm.

http://en.wikipedia.org/wiki/Lp_space

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Wow, good stuff!

karadoc said:

Since you guys are all talking about geometry and distances and metrics etc, I'd like to just point out again that the real planet earth is spherical. So realistically, the circumference of the globe should get shorter when further from the equator. What this mean for civ is that apparently the cost of moving a particular physical distance not only depends on which direction you go, but also where you are on the planet... east-west movement is relatively more expensive close to the equator (in civ, not in real life)

I'm just trying to highlight the fact that the whole system is a pretty crude approximation anyway; even more so if you take into account the number of years it takes to move a couple of square according to the game clock. In my opinion, being geometrically realistic is a very low priority for Civ games. Being a factor of sqrt(2) out in the cost of diagonal movement is really a non-issue. In my opinion, the more important issues related to the hex vs square debate are how many units it takes to block someone, and easy it is to understand/play the game.

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Quite true, however, I think we should care about the metric for gameplay as well as realism. When we look at a game screen, we intuitively judge distances based on the Euclidean metric, and thus it goes against our intuition to be able to travel in the same amount of time from the bottom-left corner to the top right as to the top-left.

This shows up in other gameplay idiosyncrasies as well. For example, city cultural boundaries are clearly low-resolution approximations of a circle. Since the culture boundary determines the city's LOS, the city tends to have less warning of units approaching on a diagonal.

Perhaps I missed it, but has anyone pointed out that a hexgrid has a "grain?" If you turn the hexgrid by 90 degrees, E-W movement becomes straightline, and N-S then takes on the "zigzag." Depending on the purposes of the particular game, the grain of a hexgrid is a significant factor.

(Slightly OT, but) If realism is the goal, MO is that regional maps are best, ala risk etc. And of course the paradox series of games refine this idea to great extent. The empire-building games I've enjoyed most throughout the years have had this feature. Any grid, while making things simpler, will result in unrealistic results. The exception to this might be games that attempt to simulate operational or tactical level combat, where terrestrial curvature, etc. are not significant.

Kind of hard to do that with random maps, you could do a Voronoi diagram I suppose

http://en.wikipedia.org/wiki/Voronoi_diagram

Peregrine said:

Perhaps I missed it, but has anyone pointed out that a hexgrid has a "grain?" If you turn the hexgrid by 90 degrees, E-W movement becomes straightline, and N-S then takes on the "zigzag." Depending on the purposes of the particular game, the grain of a hexgrid is a significant factor.

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Yes, this is the difference between optimal movement direction and the least desirable direction. Since the hex-grid has 6-fold rotational symmetry, rotating by 30, 90, 120, etc. will inverte which directions are good for movement and which are bad.

The same thing happens on a square, except that the symmetry is 4-fold, so that rotations which produce this effect are 45, 135, 225, and 315.

Nicol.Bolas said:

I suggest dodecagon grid for even more grid realism

http://en.wikipedia.org/wiki/File:Tile_46b.svg

its perfect..... the yellow and purple tiles would be tiles as well, so in reality it´s a combination of dodecagon, hexagon and square tiles

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Flipping brilliant!!! I'm loving it!!! Now THIS could be the start of an awesome new generation of CIV!!!

Okay...maybe I just liked the look of the multicolor grid for the dodecagon pattern, but here's an even simpler idea: why not an OCTAGONAL grid?

In an octagonal grid, intuitively you'd think movement in all directions is equal, but it isn't...diagonal moves between octagons are separated by a square.

So what if we made the squares represent a kind of penalty for units passing through them? Would a percentage of unit damage be too harsh?

Think of it this way: You have to push your units extra hard to get them there, and the price is that they're worn out a little by the time they arrive at the tile.

The system so very much resembles a standard square grid, and Firaxis puts a lot of hidden polish under the hood of their games, that I wouldn't be surprised if such a modifier already exists, hidden from the gamer.

Belarin said:

Quite true, however, I think we should care about the metric for gameplay as well as realism. When we look at a game screen, we intuitively judge distances based on the Euclidean metric, and thus it goes against our intuition to be able to travel in the same amount of time from the bottom-left corner to the top right as to the top-left.

This shows up in other gameplay idiosyncrasies as well. For example, city cultural boundaries are clearly low-resolution approximations of a circle. Since the culture boundary determines the city's LOS, the city tends to have less warning of units approaching on a diagonal.

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I agree that it's a bit unintuitive that traveling diagonally lets you move 'further' for the same cost; but I on the small movement scales I think the approximation works fine. Other effects, such as different terrain costs, play a much larger role most of the time in Civ4.

In a different game that I've played, moving diagonally costs 1.5, and it rounds up. So, for example, if you have 2 movement points then you can move east then north-east, but you can't move north-east and then east. If you have 3 movement points then you can move north-east twice, or east twice and then north-east.. and so on. I think that system is pretty fair, and it worked well for that particular game, but I wouldn't like to have such a system in Civ4 because I think it would be a bit fiddly - it would require more micromanagement and such, and so it would just be a distraction from the core game-play. In that sense, I think the simplicity of the cheap diagonal moves in Civ4 is good.

You're right about the impact cultural borders thing. It take fewer moves in enemy territory to approach a city diagonally rather than horizontally or vertically; and that's a bit weird. I guess that comes about because the cultural borders don't follow the same distance rules (ie. diagonal isn't cheap for culture like it is for movement; otherwise we'd get square cultural borders instead of round cultural borders).

Hexes don't have any of these diagonal cost issues, so I suppose they are superior in that sense. But I still find it easier to read the map with squares; maybe just because that's what I'm use to. With the square grid, I find it easier to see how close things are, and what the quickest path through the terrain is. With hexes, when even a direct path on flat land is a wiggly line, I find it a bit harder to read the map. -- In my mind, all of these issues are of pretty low importance in a Civ4. I don't have a strong preference for hexes or squares.

yturk39 said:

In an octagonal grid, intuitively you'd think movement in all directions is equal, but it isn't...diagonal moves between octagons are separated by a square.

So what if we made the squares represent a kind of penalty for units passing through them? Would a percentage of unit damage be too harsh?

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An octagonal grid is effectively the same as the square grid with diagonal movement. If you want, you could have that 1% penalty for diagonal movement on a square grid; and you could chop the corners off the tiles so that they looked like octagons... I think I'd prefer to just leave them as squares.

Netich said:

Why doesnt anyone like the totalwar aproach, a gridless map, with zones of control?.

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Probably cos it stuffed the total war game system up entirely for years! hopefully its finally works in shogun.

karadoc said:

An octagonal grid is effectively the same as the square grid with diagonal movement...you could chop the corners off the tiles so that they looked like octagons...I think I'd prefer to just leave them as squares.

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Haha. True that. I guess looking at the Octagonal grid helped me visualize the problem a bit more clearly. Your right; square grid works just as well. I still think compensating for diagonal movement with a penalty of some kind could add some challenge.

Polygons with more than 6 sides are always going to be messy because you need several types to achieve tessellation.
I also think we should consider functionality over aesthetics. You can achieve hex-like behaviour with square tiles... just indent every other row by half a the tile width. If you need an example, look at your keyboard.

*

Regarding increased movement costs for diagonals: I see no problem with that. We already accept that can move onto a hill with a fraction of a movement point left, so this would remove more bias than it introduces if we use a sane number.
I'd prefer to stick close to the maths behind it and use square root of 2 rather than arbitrarily declare the multiplier to be 1.5 though.

At what point is it too much of a change to "not be Civ" any more. Maybe it would be worth trying irregularly shaped "tiles", Risk being the simple example. It would make for some really interesting tactical choices. One annoying thing though would be you'd have to have gridlines turned on all the time to see where the tiles were

If it's just hex vs square I couldn't care less to be honest. It's like worrying about what typeface a great novel is written in.

Iranon said:

*
Regarding increased movement costs for diagonals: I see no problem with that. We already accept that can move onto a hill with a fraction of a movement point left, so this would remove more bias than it introduces if we use a sane number.
I'd prefer to stick close to the maths behind it and use square root of 2 rather than arbitrarily declare the multiplier to be 1.5 though.

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now why do you think this isnt in civ game?
look at ufo: enemy unknown. it´s a tactical game on a square grid. basica movement costs 4, diagonal costs 6 IIRC
but units have 60 points of movement on average

now in civ the base movement is 1
unless you somehopw allow transfer movement over turns, it´s impossible to do.
the least amount of movement points to make this work would be 6, with base cost per 1 tile
2, and diagonal cost 3

this would speed up the movement of units tremendously, (relatively 3x basic movement which no unit currently has and 2x diagonal movement which was used for mounted and mechanized) so the game would have to have larger grid to keep the same feel

karadoc said:

you could have that 1% penalty for diagonal movement on a square grid...

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I was thinking closer to 10% damage to the unit, or whatever the amount of damage is that a non-promoted unit can heal in neutral territory over a single turn.

In a way, this would make the movement 3NE cost the same as 3N + 3E.

How?

3N + 3E = 6 turns; unit arrives at destination tile at full strength.

For a unit to arrive at 3NE (at full strength) using diagonal moves it requires the same number of moves; any combination will do:

1NE + heal + 1NE + heal +1NE + heal = 6 moves, unit is at same destination, same strength.

True, in this example the unit arrives at the tile one turn EARLIER than it would have following the 3N + 3E path, but that is now a tactical decision of the player: if you want to get there faster, push your troops harder to march further than normal, you'd pay a price for it (in this case, the troops are worn down a percentage of their strength, which can be recovered in one turn).

I guess the major disadvantage to this would be that it would seriously cramp the style of early game rush tactics, since the diagonal path to into a rival's cultural borders is often times the most stealthy, direct invasion route.

yturk39 said:

I was thinking closer to 10% damage to the unit, or whatever the amount of damage is that a non-promoted unit can heal in neutral territory over a single turn.

In a way, this would make the movement 3NE cost the same as 3N + 3E.

How?

3N + 3E = 6 turns; unit arrives at destination tile at full strength.

For a unit to arrive at 3NE (at full strength) using diagonal moves it requires the same number of moves; any combination will do:

1NE + heal + 1NE + heal +1NE + heal = 6 moves, unit is at same destination, same strength.

True, in this example the unit arrives at the tile one turn EARLIER than it would have following the 3N + 3E path, but that is now a tactical decision of the player: if you want to get there faster, push your troops harder to march further than normal, you'd pay a price for it (in this case, the troops are worn down a percentage of their strength, which can be recovered in one turn).

I guess the major disadvantage to this would be that it would seriously cramp the style of early game rush tactics, since the diagonal path to into a rival's cultural borders is often times the most stealthy, direct invasion route.

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I dont like this at all. it doesn´t sound like a good game design and something the AI could handle, it would never understand when to move diagionaly and when to avoid damage, as opposed to some abusive player.

also you can try this, it was used in civ2 for helicopter units.
instead of refuaeling they took 10% damage every turn.
I dont think it worked, before you did anything the helicopter was at 50/100. it inteded you to use them and rest them at cities, but modern warfare is just too fast for that.
if I went to modern war in any civ, I would take around 10 cities at the commencing of the war, and than many more every next turn.

so the only one using them was ai, who had them flying everywhere at 1/100 HP, waiting to get shot down by some forgotten archer

I don't either. Taking damage to move farther would be an AI disaster like the one unit per tile disaster in civ5. If the game mechanics were to be changed, I vote for supply and supply lines. It's strange that supply hasn't been included yet as civ is a strategic, not a tactical game. If a unit had to be supplied, the farther it moved the more supply it would consume- so if you moved your warrior 3 spaces it would eat an enormous amount of the entire army's food supply, or tanks would consume oil, etc. Real military units don't have a problem moving far, they have a hard time supporting themselves during and after great changes in location. This would change a lot of things- particularly the (?much despised?) stack of doom. I don't understand why the designers chose to make civ5 tactical when civ is a strategic game; the game should be about managing armies, not brigades or divisions.

Off topic here, feel free to ignore...

I'd love to see a grid-less version of Civ too, if it could be done nicely.

While we're wishing for the improbable... I'd like to see the number of tiles around a city which can be worked by its citizens be dependent on movement speed. So at the start, only the "tiles" or the terrain right next to the city. Then you build a road and citizens of the city can access one extra distance unit from the city along the road (they can get home in time for dinner or something). Later, with horse carts and then railroads (and then highways and oil, maybe) you can work tiles further away, and your city can grow. Also, with ships, (once you get sailing or whatever) you can access a few squares along the coastline immediately (or once you build a wharf/docks). Better ships, workable region expands.

In this way, in the old times you'd have more smaller cities. You could grow the more important towns, and eventually the smaller surrounding villages would become suburbs of the city, as really happens.

To access some remote resource in ancient times you might have to build a little workers camp ("city") near the resource, but in the modern era a fast rail network may allow access to the resource from a city a "long" way away.

I guess it has always bothered me about Civ that the space usable by a city is so rigidly fixed.

Basically, a population unit (currently represented by a city's worker) can work any tile (or region) which it can get to within some time measure. You could use the "cultural border" of a city to show the workable region, which grows with infrastructure developments and technology.

And to extend the concept further, I'd love to see something like the Colonization-style production system incorporated in some way. Citizens working the land produce food (and maybe grant access to resources such as ore or wood which is needed to build things. But to really produce stuff, you put citizens to work in a town/city. Not on a forest or mine. It always bothered me that a mine or watermill takes up as much space as a farm. This way, I could put the citizens from little suburb towns (which are within reach) to work in the main city in which I've a factory or whatever.

I think that'd be much more realistic and interesting. Any way of implementing parts of this with a mod, you think? I wonder if it would get too complicated...

I also liked the land ownership/boundaries used in Alpha Centauri. I'm really disappointed that that method hasn't been used in any other games I've come across.

Sorry for the ramble... Love to hear some other ideas.
A.

Saarud said:

In real life there is only one optimal route from place A to B. If we have two places of interest A and B. And B is directly 90 degrees (east) of A the optimal route is to go in 90 degress. If you by chance want to take the 45 degree (northeast) and then sway back to 135 degrees (southeast) after you travel half the distance (south east) you will travel 50% longer distance. Take a map and an overlay of both hexes and squares and you see that using hexes you get a fair distants in number of hexes compared to reallife while you won't get that using squares (unless you go directly in 0 degress, 90 degress, 180 degrees or 270 degress)

That's why I don't like squares the way Cvilization 4 presents them. If Civilization 4 would be upgraded and squares would stay I would suggest to double the movement distance for all units. Going straight should cost 2 while going diagional should cost 3. Atleast then you would get fair movements.

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Actually that is not true! Consider the north pole and the the south pole, which have infinitely many length-minimizing paths between them. Plenty of people think the universe has points like that as well (conjugate points for you math nerds)

Also the statement about hex grids is not true either. Moving "2E" has two length minimizing routes (bump north or bump south). Maybe this seems less unsatisfying though, because bother routes "look" like they should be the same distance.

The bottom line is that hexes are better... unless your map has some sort of coordinate system like Civ games do, in which case squares are over nine thousand times better.