Hexagon Tiles: Like them, love them, or RAGGGEEEE!!!

davane said:

Both have their issues, and neither solves all the problems any grid-based system will encounter on the very basis that it's a model so simplify the theoretical reality being represented. So why the switch?

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Because hexes gets rid of the unrealistic corner movement of squares.

None of the issues with square based grids is best solved by "let's use hexes instead", and many of the advantages of squares are sacrificed with this change.

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False. The main issue with squares is that the 8 directions aren't of the same type. 4 lets you cross a side to another square while 4 lets you cross a corner. The corners then let you move faster (by almost 50%), makes staging an attack from a corner important (as you get less enemy squares to cross), and lets enemies sneak through holes, which needs twice as many units, or a ZOC feature to fix.

The only issue with hexes is that you cannot move straight S/E. So what?

davane said:

May main arguement here is, and has always been, is about the the point of switching to hex grids from square grids.

Both have their issues, and neither solves all the problems any grid-based system will encounter on the very basis that it's a model so simplify the theoretical reality being represented. So why the switch? The ultimate answer is because it is different. Because it's new. However it is not neccesarily better. It seems like the decision to change was made first, and then the justification was made afterwards. None of the issues with square based grids is best solved by "let's use hexes instead", and many of the advantages of squares are sacrificed with this change.

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Until thus far you've been fairly unsuccesful in arguing that hexes introduce new problems. Your arguments thus far are centered around straight and staggered fronts. But the facts of these are:

*Hexes increase the number of possible straight fronts from 2 to 3.
*Hexes increase the number of staggered fronts from 2 to 3.
*The issues with staggered fronts are the same with both square and hex based grids.

So basically hexes increase the number of possible fronts on all respect without introducing new issues.

The only possible issue I see is that you can move a straight front in a perpendicular direction with 1 move. But this is somewhat of a non-issue.

1) It has been confirmed that most units will be able to move 2 squares. And it is always possible to move a straight front perpendicular to the front by 2 moves.
2) In general the geography of the terrain (the presence of hills and forests, and obstacles such as mountains and oceans) will prevent the formation of perfectly straight fronts and straight fronts staying straight. It is not likely that a straight frontline is more than 4 tiles long before having to bend. Having bends in a front is where hexes really are and advantage over squares.

Everstar1981 said:

There doesn't have to be a perfect map made of hexagons, they could just make them go up to the tip of each poles and then have an unaccessible area. It would be kinda like Civ 4 but with more usable space so you could skirt around the poles and still cross over the top or bottom of the world. Or perhaps you could just jump across this "space" to a symmetrical tile on the opposing side but couldn't stop within this "space".

There could even be a bonus to be the first to discover a pole like the Civ 4 bonus to ship movement for circumventing the world. Naturally you would need certain techs to survive the extreme cold of the poles.

Anyways, point is that there are methods that could work if they play around with it a little without needing to resort to those pesky pentagons.

EDIT: You know... that still may not work. At least I'm out there on the edge!

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If you make a tiling of hexagons, every latitude will always have the same number of hexes. No matter what you do of how you deform the hexes. From a game point of view this means that every latitude has the same length. This means that the best you can do with just hexes is a cylinder or a torus.

DPyro said:

You don't need a perfect hexagonal sphere, just use slightly unregular hexagons and you can come up with a pretty good approximation of a sphere.

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You cannot make a tiling on a sphere with only tiles that 6 sides, no matter how irregular you make them. This is a hard mathematical fact.

The change to hexes looks like a very good idea to me. I never understood why we had to play with squares and always move in diagonals. With hexes, every move is equivalent, no more zigzag exploits.

False. The main issue with squares is that the 8 directions aren't of the same type. 4 lets you cross a side to another square while 4 lets you cross a corner. The corners then let you move faster (by almost 50%), makes staging an attack from a corner important (as you get less enemy squares to cross), and lets enemies sneak through holes, which needs twice as many units, or a ZOC feature to fix.

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Wrong.

In Civ IV, the eight directions are treated as equal, and thus THEY ARE EQUAL.

Diagonal movement does not strictly let you move faster. One square diagonally is exactly as far as one square horizontally or vertically. A target that is five squares north requires five squares of movement. A target that is five squares east is five squares away. A target that is five squares north east is five squares away. All of these distances are the same in game terms.

You can move one square north-east, followed by one square north-west. This is the same as travelling two squares north. You are no further north than you would be is you moved two squares north. Likewise, if you move two squares north-east, you are no more north than if you moved two squares north. Nor are you any more east than if you moved two squares east. You have not moved any further/faster by using diagonals.

The only possible advantage gained from moving diagonally is that it is a straight line if your are trying to reach a target that is in a diagonal direction. Yes, going north east IS quicker than going north and then east. However, this is no different than going directly north to a nothern target is faster than going east and then north, or even north-east then north.

It must be remembered that grid-based systems, whether squares or hexes, are models with built in assumptions. One key assumtion with these is that it does not matter where in the tile an object is - it is always assumed and represented as being in the centre of the tile.

Another assumption is whether or not diagonal movement is identical to non-diagonal movement. This can differ depending on the specific grid, but in Civ IV, we actually see instances where it is treated as identical in some respects (unit movement) but not indentical in others (culture expansion and the BFC). In any model, you are supposed to choose one decision or the other. Many of the issues caused with diagonals come down to the fact that both are being used in the same model. This is NOT an issue of square-based systems, but rather an issue caused to bad game design.

*Hexes increase the number of possible straight fronts from 2 to 3.
*Hexes increase the number of staggered fronts from 2 to 3.
*The issues with staggered fronts are the same with both square and hex based grids.

So basically hexes increase the number of possible fronts on all respect without introducing new issues.

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The new issue is that the orientation of the hex matters, and this means that you get situations where a tile can be attacked from the north or south by only two units (excluding ranged bombardments), where as the same tile can be attacked from the east or west by three units (excluding ranged bombardments). Compare this to the square grid where a single tile can be attacked by three tiles in any direction, be it north, east, or north-east.

Ther four cardinal direction of north, south, east, and west are important because they directly correspond to the axes of the typical 2d space that humanity exists in (despite being 3d beings, because we lack the ability to inately travel in the 3d dimension of up and down without aid, these directions are mostly neglected). These directions are much more important to retain, yet instinctive straigh-line movement in at least one axis is lost with hexes.

So, all unit move at least two hexes. But do all units move in exactly even amounts of tiles at all times? What about terrain? Any odd movement value at all precludes the ability to move a front perpendicular in any direction. Thus this remains an issue.

Plus, more fronts is not neccessarily better. Why is having the possibilty of 3 straight fronts and 3 diagonal/staggered fronts better than the possibility of 2 straight fronts and 2 staggered fronts?

Also, you get the fact that even with the straight fronts are the fronts where the tile can only be attacked from two adjacent tiles, and neither of them is directly in front of the front, but instead displaced half a hex to either side.

These are all issues that arise to get rid of the issues sneaking through diagonals that stems from the fact that Civ IV does not follow perfect games design princples such as consistancy within the games rules and models.

Ultimately, either a case of change for change's sake, or throwing the baby out with the bathwater, both of which are not good for the series.

davane said:

...One square diagonally is exactly as far as one square horizontally or vertically...

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Pythagoras is spinning in his grave.

davane said:

In Civ IV, the eight directions are treated as equal, and thus THEY ARE EQUAL.

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Cerrtainly not. But if you shout even higher, it may help

Diagonal movement does not strictly let you move faster. One square diagonally is exactly as far as one square horizontally or vertically. A target that is five squares north requires five squares of movement. A target that is five squares east is five squares away. A target that is five squares north east is five squares away. All of these distances are the same in game terms.

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No, they're not. If you move diagonally back and forth, you will discover more land in the same time, and if you attack diagonally, you will need to cross less squares of enemy land to reach the enemy city. Both because you move faster diagonally. Have you heard of Pythagoras btw.?

You can move one square north-east, followed by one square north-west. This is the same as travelling two squares north.

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Wrong again. Assuming you can see adjacent tiles only, you will have uncovered three more squares of land by moving diagonally. If you see two squares away, you will have uncovered 5 more. This is a natural result of the fact that you move longer.

The only possible advantage gained from moving diagonally is that it is a straight line if your are trying to reach a target that is in a diagonal direction. Yes, going north east IS quicker than going north and then east. However, this is no different than going directly north to a nothern target is faster than going east and then north, or even north-east then north

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Are you telling me that you haven't discovered that you uncover more land in the same number of turns by moving diagonally (see above), and that you can spend less time in enemy land by moving diagonally (typically one square less of movement)?

Another more abstract proof that going diagonally is going faster. We all know that a straight line is shortest, right? If you need to go 4 squares north with a move 2 unit, you can spend 2 turns going straight north, or 1 turn NE followed by 1 turn NW. The latter is not a straight line, thus longer. But since you reach 4 squares north in the same time, you're going faster.
Now assume you need to go 4 squares NE. The only way to reach there in 2 turns is to go straight NE along the diagonal. If you go even 1 square N, you will need another turn. How can you explain this if the 8 directions are equal?

Another assumption is whether or not diagonal movement is identical to non-diagonal movement. This can differ depending on the specific grid, but in Civ IV, we actually see instances where it is treated as identical in some respects (unit movement)

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As proven above, the 8 directions are not treated identical for movement, so your argument fails.

The new issue is that the orientation of the hex matters, and this means that you get situations where a tile can be attacked from the north or south by only two units (excluding ranged bombardments), where as the same tile can be attacked from the east or west by three units (excluding ranged bombardments). Compare this to the square grid where a single tile can be attacked by three tiles in any direction, be it north, east, or north-east.

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This is only a "problem" in your head, since you cannot let go of the 4 NSEW directions. Hexes, by their nature, have 6 equal directions, and the orientation doesn't matter among those 6. Change orientation by 60 degrees, and nothing changes. You only get a problem when you insist to apply the square orientation on the hexes.

The rest of your argument is based on you keeping applying the four cardinal direction onto the hex grid. You must accept that instead of 4 (or 8) directions, there are now 6 equal directions, and then the remaining "problems" disappear.

I could write a long, drawn out response, but my arguement will come down to two key points, which I will iterate as follows:

1) Forget Pythagoras.

This is not relevent, because it does not feature in the model being discussed. This is because we are talking about unit movement, which is a single value that determines distance not direction. This is because diagonal movement is treated the same as non-diagonal movement - one square is one square.

You move four squares in any direction, even a random direction, you have moved four squares. Thus, if you move four squares north, you have travelled the same distance as if you travelled four squares east or four squares south east.

You start talking about Pythagoras, you are no longer treating diagonal movement the same as non-diagonal movement, and thus are discussing a different model entirely. You start taking into account direction, then you are talking vectors, which is entirely different. Arguing the four squares north is different from four squares north-east is moot, because it's also different from four squares east.

2) This is change for change's sake, and the arguements prove that. Hexes are the newcomer here, yet the solution is to stop trying to impose existing concepts onto the new model, when my arguement is that I don't think much of the new model because it can't handle the existing concepts. This is simply justification after the fact.

Just as the problems come from imposing four cardinal directions on a hex based grid, they are also caused by imposing a hex-based grid on the four cardianl directions. Likewise, just as one solution is to accept the hex and 6 directions while abandoning the square and it's 8 directions, another solution is to retain the square and it's 8 directions and abandon the hex. Both are equally viable answers here.

Yet it's as if hexes are a done deal already. Why? Sure, hexes are different from squares, but this does not make them neccessarily better. Just because hexes are in Civ V doesn't make them better. In everything I have read about Civ V so far, I have not seen any justification to favour hexes over squares outside of graphics and allowing for more natural world maps. This is not a justification in my eyes, but change for changes sake (or, even worse, an example of style over substance that is plaguing video games development at the present time).

Just caught the end of this argument, but davane, you are way off base. To say moving horizontally and vertically is the same as moving diagonally makes no sense. Even a beginner in Civ figures pretty quickly that when you're exploring at the beginning of the game, you move across the continent much faster if you move diagonal than if you move horizontal and vertical. That's because moving diagonal covers more area than moving horizontal and vertical. You stand no chance at winning this argument. It's time to concede.

I think it's clear that hexes have many advantages, both aesthetically and functionally. I agree with davane that diagonal movement does not necessarily have to cause problems, but when you feel the need to make the area around a city into a 'fat cross' so that it looks round, then you are creating problems with diagonal movement. Just the fact that hexes force you to move over an edge is a very welcome simplification of the rules that will prevent such unwanted consequences in the future.

davane said:

I could write a long, drawn out response, but my arguement will come down to two key points, which I will iterate as follows:

1) Forget Pythagoras.

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wut

davane said:

This is because diagonal movement is treated the same as non-diagonal movement - one square is one square.

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Who are you, Stalin? You can't just impose communism on polygons. .

davane said:

Yet it's as if hexes are a done deal already. Why? Sure, hexes are different from squares, but this does not make them neccessarily better. Just because hexes are in Civ V doesn't make them better. In everything I have read about Civ V so far, I have not seen any justification to favour hexes over squares outside of graphics and allowing for more natural world maps.

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What about basic math? Here's the distance system with squares, as it is currently.

Let NS be the north/south axis and EW be the east/west axis.
Let AB be the northwest/southeast axis and let CD be the northeast/southwest axis.
Let ns(x) be movement along the NS axis, same for ew(x), ab(x), cd(x).

|d| means distance.

Da Rules
1. |ns(1)| = |ew(1)| = 1 (the distance by moving 1 in the nsew directions is one map tile)
2. |ns(d)| = |ew(d)| (the distance you move NS is the same distance EW)
3. |ab(d)| = |cd(d)| (the same for diagonals)
4. ns(1) + ew(1) = cd(1) (a move north by 1 and east by 1 is equivalent to moving northeast by 1)

Let's say we're starting at the origin {0,0}. In {u,v} u is distance to the north from the origin (negative if south) and
the same for v for east. It's just like a good ole xy graph!

Choose an arbitrary point (n,m). If the NS,EW,AB,CD axis are all equivalent, it should always take n+m moves to get there. If it isn't...

5. ns(n) = n
6. ew(m) = m

7. {n,m} = ns(n) + ew(m) (To get to point {n,m}, you have to go north by n and east by m from the origin)

8:
|{n,m}|
|ns(n) + ew(m)| //by 7
|ns(n)| + |ew(m)|
|n| + |m| //by 5 & 6

So we proved that to get to (n,m) moving in the NSEW cardinal directions tasks |n + m| moves, but its common sense.

So what about the diagonals? Let's try getting there using cardinal and diagonal movement.

|{n,m}|
|ns(n) + ew(m)| //by 7
|ns(n) + ew(n + m - n)|
|ns(n) + ew(n) + ew(m - n)|
|cd(n) + ew(m - n)|
|cd(n) + m - n|
|cd(n)| + |m - n| //by 4
n + |m - n|

But using just cardinal directions is always |n| + |m|
if n = 0, n + |m - n| = |m| = |n| + |m|
otherwise, if m > n, n + |m - n| = n + m - n = m <= |n| + |m|
if m < n, n + |m - n| = n + n - m = 2n - m <= |n| + |m|


What does this mean?
Using diagonals will get you there at least as fast, but probably faster than using just cardinal directions.


tl;dr: moving diagonally ain't the same as moving cardinally.

davane said:

You move four squares in any direction, even a random direction, you have moved four squares. Thus, if you move four squares north, you have travelled the same distance as if you travelled four squares east or four squares south east.

You start talking about Pythagoras, you are no longer treating diagonal movement the same as non-diagonal movement, and thus are discussing a different model entirely. You start taking into account direction, then you are talking vectors, which is entirely different. Arguing the four squares north is different from four squares north-east is moot, because it's also different from four squares east.

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And yet you conveniently ignore my proof of the opposite, even though I explicitely ask you to explain it. So I'll ask again. If they are the same, how come a horse unit can move 4 squares directly north in 2 turns by moving 2 NE then 2 NW, but the same unit cannot move 4 squares directly NE by moving 2 N then 2 E?

But for the sake of your argument, this is nothing like 4N vs 4E, because those two directions are treated equally: If you first move 2 squares N, you still have 4 squares to go to reach 4E - and if you first move 2E you still have 4 squares to go to reach 4N. Thus those two directions are treated exactly the same.

So the bottom line is that you can move diagonally 1 turn and still reach directly N,S,E or W just as fast, while this is not true for any other direction combination, thus proving that the diagonals work different than the other.

The fact that you uncover more hidden land at the same time by moving diagonally is just another proof of this.

2) This is change for change's sake, and the arguements prove that.

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The fact that you don't like the change doesn't make it a "change for change's sake". I don't like the fact that they remove religions, but I am still able to see that they have a reason for it, and not just making a "change for change's sake".

Hexes are the newcomer here

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In Civ, yes, but in turned based games in general, you'll find that more than 90% use hexes, both computer and board games. So hexes are the norm, Civ has just been lagging behind, and I am glad they finally make the sensible step.

I have spent many, many hours on Panzer General so for me its a dream come true...
... And that the city grow on hex at the time revitalize the game for me

davane said:

Hexes are the newcomer here . . . In everything I have read about Civ V so far, I have not seen any justification to favour hexes over squares outside of graphics and allowing for more natural world maps. This is not a justification in my eyes, but change for changes sake (or, even worse, an example of style over substance that is plaguing video games development at the present time).

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Actually, you've kind of got it backwards. Hexes are quite old. They predate computer gaming altogether. Most of the old wargames and civ-type games that were popular in the 1970s, put out by companies like Avalon Hill or SPI, were hex-based (civ actually evolved as a simplified version of some of these games - squares were originally chosen because in 1991, when oodles of ram meant 4-8MB, saving every bit of code possible was crucial). There have been hex-based computer games for a very long time now. Off the top of my head: Empire of the Fading Suns, the Panzer General series (plus Fantasy General etc), Age of Wonders, Heroes of Might and Magic, etc etc. Not to mention numerous assorted wargames.

davane said:

Wrong.
The only possible advantage gained from moving diagonally is that it is a straight line if your are trying to reach a target that is in a diagonal direction. Yes, going north east IS quicker than going north and then east. However, this is no different than going directly north to a nothern target is faster than going east and then north, or even north-east then north.

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This is simply false. As others have pointed out. Moving diagonally reveals 5 new tiles (or equivalently after a diagonal move the unit is adjacent to 5 tiles that it wasnt adjacent to before) while a 'straight' move reveals only 3 new tiles.

This simpel fact has tactical implications in all sorts of situations.

The new issue is that the orientation of the hex matters, and this means that you get situations where a tile can be attacked from the north or south by only two units (excluding ranged bombardments), where as the same tile can be attacked from the east or west by three units (excluding ranged bombardments). Compare this to the square grid where a single tile can be attacked by three tiles in any direction, be it north, east, or north-east.

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Orientation of hexes matters about as much as the difference between the isometrical view in civ1/2/3 and "straight" view of civ4. What matters is that all tiles bordering on a city are tactically equivalent in the sense that they have exactly the same number of bordering tiles that also border on the city. This for example is not true in a square grid. A unit directly N,E,W,S of a city can move to four different tiles which also border on the city, while a unit on one of the diagonal tiles can move to only two other tiles that also border on the city.

Ther four cardinal direction of north, south, east, and west are important because they directly correspond to the axes of the typical 2d space that humanity exists in (despite being 3d beings, because we lack the ability to inately travel in the 3d dimension of up and down without aid, these directions are mostly neglected). These directions are much more important to retain, yet instinctive straigh-line movement in at least one axis is lost with hexes.

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Cartesian coordinates are not the only kind you know? It is not necessary to have axis that are perpendicular. You can for example have axis that are at a 60 degree angle, as in a hex grid. One of the nice thing about a hex grid is that you get intuitive straightline movement in three directions instead of two, and slightly less intuitive straightline movement in 3 others.

So, all unit move at least two hexes. But do all units move in exactly even amounts of tiles at all times? What about terrain? Any odd movement value at all precludes the ability to move a front perpendicular in any direction. Thus this remains an issue.

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The moment you have terrain you loose the ability to move a straight front in a perpendicular direction anyway since not all unit will be allowed the same moves.

Plus, more fronts is not neccessarily better. Why is having the possibilty of 3 straight fronts and 3 diagonal/staggered fronts better than the possibility of 2 straight fronts and 2 staggered fronts?

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True, but you were the one concerned about the loss of straight fronts.

Also, you get the fact that even with the straight fronts are the fronts where the tile can only be attacked from two adjacent tiles, and neither of them is directly in front of the front, but instead displaced half a hex to either side.

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Yes, so what? Why would that be a problem.

These are all issues that arise to get rid of the issues sneaking through diagonals that stems from the fact that Civ IV does not follow perfect games design princples such as consistancy within the games rules and models.

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No, some of the more serious issue with a square grid with diagonal moves is that the diagonal moves cross each other. This causes all sorts of ambiguities in the rules, such as the infamous land bridge/tidal straight issue, which has its equivalent in all sorts of tactical situations. If you ever played civ2 which featured much more spread out armies due to the rule that if a defender lost the whole stack was destroyed, you would be familiar with these.

This seems like just another thread where many members gang up against one. To most viewers, the reason is of course quite obvious, but I'd like to add a few comments to davane:

If you feel that the disadvantages of not being able to have straight NS and EW directions in hexes are bigger than the disadvantages of diagonals working differently than the non-diagonals (or even that the differences doesn't matter) - then you're of course not wrong in thinking so, as what you prefer is a purely subjective matter.

But when you argue that the diagonals are no different than the non-diagonals for movement (and other purposes), or that the change is just for change's sake, then you're objectively wrong - which is why I argue against you.


So if you change your argument to saying that you feel uncomfortable with the hexes and not being able to move straight E/W, then you have a case - though not one I share.

DPyro said:

You don't need a perfect hexagonal sphere, just use slightly unregular hexagons and you can come up with a pretty good approximation of a sphere.

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You don't. You can make a convex, downward slope on one side but that only results in an upward slope behind you, and never the twain shall meet.

Ribannah said:

You don't. You can make a convex, downward slope on one side but that only results in an upward slope behind you, and never the twain shall meet.

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I was just being optimistic
No, apparently you can't make a sphere out of hexagons of any kind. Poop. Civ 6 for a proper globe?

DPyro said:

I was just being optimistic
No, apparently you can't make a sphere out of hexagons of any kind. Poop. Civ 6 for a proper globe?

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Well you can make a .. really close approximation of Globe (technically a shape with 20 sides) out of Hexagons and 12 Pentagons.

I could see it being in an expansion pack.

There would be the issue that when you were near the pentagons, the map would not be representable on a flat surface. (so you would be forced into "Globe View")

Basically there would be 12 areas of the map where you would know the world was round.

DPyro said:

I was just being optimistic
No, apparently you can't make a sphere out of hexagons of any kind. Poop. Civ 6 for a proper globe?

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Frankly there's no need to represent the polar caps. They don't play a role in the game. The civ4 globe is really quite alright, and civ5 doesn't need anything more.

Globes can be mapped in hexagons, though. For example:

http://www.pyxisinnovation.com/pyxw...l_Snyder_Equal_Area_Aperture_3_Hexagonal_Grid