Hexagon Grids

[occam]

You don't move any faster, it only looks that way because, graphically, the square is widest at the diagonals. I would've thought that this was obvious.

I am stunned by the authority with which you made this false claim.

How many moves does it take to move a king* from one corner to another on a chessboard? Did you notice the answer is the same for opposite and adjacent corners? (You do understand that opposite and adjacent corners are different distances away?)

Chess players have known the OPPOSITE to your claim for hundreds of years when studying king moves in the endgame. It is an established fact diagonal paths fail to preserve distance on square grid gameboards.

- O

* or a civ unit

 

[Wolfwood]

You don't move any faster, it only looks that way because, graphically, the square is widest at the diagonals. I would've thought that this was obvious.

I think you mixed up the word "mathematically" with "graphically" above...

And that's the whole point - you move faster diagonally, because you move a longer distance in a single move than you would if you moved to an adjacent square.

 

[Traitorfish]

I think you mixed up the word "mathematically" with "graphically" above...

And that's the whole point - you move faster diagonally, because you move a longer distance in a single move than you would if you moved to an adjacent square.

But in game terms, you don't actually move any faster. The tiles are effectively a set of co-ordinates, the fact that they appear as squares is simply a graphical representation of them. The co-ordinates have no "physical" distance between them.
Look, if two units both move east five tiles, but one also moves north five tiles at the same time (i.e. moving diagonally) they are both the same distance east. They are both 5 tiles from their starting point. Either one could then move five vertical tiles and land on the same tile as the other unit. They are both five tiles from each, and five tiles from their starting point, therefore they have formed an equilateral triangle with the starting tile. And, as all sides of an equilateral triangle are the same length, they have, in game terms, moved the same distance. Simple.
As I said, this distance is only greater graphically. Mathematically, it's identical.

 

[LordRahl]

As I said, this distance is only greater graphically. Mathematically, it's identical.

Actually the distance is greater both graphically, mathematically. And the only reason you are able to traverse it in the same time, is because you do move faster diagonally. Consider the following:

xxxxC
xxxxx
xxxxx
xxxxx
AxxxB

We have the following points and their coordinates:
A(0,0), B(5,0), c(5,5)

Distance between two points in cartesian coordinates is calculated in the following fassion (using pithagorean thorem):
d = sqrt[(x2-x1)^2 +(y2-y1)^2]

In our case we'll get the following:
AB = 5
BC = 5
AC = 5sqrt(2) =~ 7

So diagonally you are moving effectively a distance of 7 tiles in the same time it takes to move the distance of 5 tiles otherwise - hence you are moving faster.

 

[occam]

And, as all sides of an equilateral triangle are the same length, they have, in game terms, moved the same distance. Simple.
As I said, this distance is only greater graphically. Mathematically, it's identical.

Doesn't your equilateral triangle have at least one right angle? Doesn't that cause your "mathematical" alarm bells to ring?

Another flaw in your reasoning is you are measuring distance by squares, which embeds your own conclusion into your assumptions. A 'square' is not a unit of distance for evaluating whether or not squares preserve distance. Using squares to measure distance confuses the map for the territory.

Seriously, please research this subject before posting further. It is getting embarrassing. A quick, confirming reference to get you started:
http://en.wikipedia.org/wiki/Hex_map

Chess players have known for centuries and PnP gamers have known for decades that square grids are tricky.

- O

 

[Traitorfish]

Hmm. I may have to admit that I'm wrong.
Still, whatever the maths, the game works fine as it is, I wouldn't say that it needs a new system.

 

[dcbandicoot]

The current grid is really similar to octagonal.. I don't see the big fuss with hexagonal, I really prefer this system.

Edit: Perhaps not, scratch that comment. Still, I like the current system because that's what I'm used to, though either way, I don't care, Civ is Civ.

 

[mythmonster2]

This is a pretty good idea, but still probably not coming out anytime soon for CIV but hey, who knows, maybe it'll be in CiV (yeah, that's what I think the Civilization 5 symbol will be)

 

[Wolfwood]

Unfortunately, I must admit that I doubt that hexagons will be included in Civ5. There was quite a movement before Civ4 was released to get the hexagons in and it was pretty much ignored back then...

 

[playshogi]

Another advantage of hexagons is that you can cover a globe with them (and a few pentagons) and have a real planet to play on. There would be 12 pentagons, but these could always be impassable mountains. A disadvantage would be that cities can't be 21 squares anymore--they would be 19 hexes.

 

[da_Vinci]

But in game terms, you don't actually move any faster. The tiles are effectively a set of co-ordinates, the fact that they appear as squares is simply a graphical representation of them. The co-ordinates have no "physical" distance between them.

Important to remember that the coordinates are intended to represent a physical reality: a landscape. The map doesn't represent the coordinates, the coordinates represent the map.

Regardless of the coordinate system you use (cartesian, polar, or some other), you can describe a square, and a circle in the square such that the sides of the square are tangential to the circle. The corners of the square are farther away from the center of the circle than any point on the circle, and farther way from the center than the tangential point at any side. This is an abstract geometric concept independent of coordinates and graphical representations.

The other illustration that may help clarify this is vectors. A wind blowing toward the northeast of force F has an east component of F divided by square root of 2, and a north component of F divided by square root of 2. These orthogonal components do not have force F each. So to get 1 square NE on a square grid, in one turn, you need a larger velocity vector than to get 1 square due east or due North.

Which means that in Civ, sea movement in the age of sail is fine in the squares system if one assumes that the prevailing winds blow simultaneously in both directions along both diagonals!

dV

 

[Diamondeye]

* Looks at his azerty keyboard *

Don't get it

Apart from this, I think this is an interesting idea, but it's hard to do such a big change. Perhaps BTS will allow modders to do this?

... Means that the 'S' key touches the keys a,w,e,d,x and z. If your keyboard was Civ, S would only touch a,w,d and x (and diagonally be connected to q,e,c, and z) - and be kinda strangelookin. Got it?

Anyway, I think the idea is good, definately.

 

[sagji]

Doesn't your equilateral triangle have at least one right angle? Doesn't that cause your "mathematical" alarm bells to ring?

- O

No - it is possible to have a right angled equilateral triange - however this requires that all three angles are right angles, and isn't possible on a flat surface.

 

[Diamondeye]

No - it is possible to have a right angled equilateral triange - however this requires that all three angles are right angles, and isn't possible on a flat surface.

and that has exactly what to do with this? I mean, we're fighting on nearly flat surface here...

 

[da_Vinci]

No - it is possible to have a right angled equilateral triange - however this requires that all three angles are right angles, and isn't possible on a flat surface.

Well, in geometry within a plane, a triangle by definition has angles that sum to 180 degrees. So regardless of three or more dimesional space, three right angles defy the definition of a triangle.

And, one needs to have three sides, and each side must meet the other two sides to form the three angles. With three right angles you can't even do that in three dimensional cartesian space ... you would need a forth dimension or some curved version of three dimensional space (getting beyond my level of knowledge here).

All of which means that equilateral right triangles, if they exist, are pretty irrelevant to Civ, as Diamondeye said.

dV

 

[RERomine]

As I recall, two points are required to define a line or line segment, three to define a plane, i.e. two dimensional or flat surface, so a fourth point, at least, would be required to define something in the third dimension. I can't picture an triangle that exists in anything other than a flat surface.

That said, in the Civ world, a move of 1 up, down, left, right or diagonally is the same distance. Whether it makes sense mathematically or visually doesn't matter; that is how it was defined and it does work. As long as the players understand that's how it works, everything is cool.

 

[hgthechinese]

Um.....as much as I would love to discuss the math, can we get back on the "square sucks and hex rules" theme of the post? (yup, that was my originial intention) this forum has been getting dramatic attention from the developers that I hope, if we make ourselves loud enough, CivV (that looks ********) will have a hex, or the square-hex as i posted earlier.

 

[da_Vinci]

That said, in the Civ world, a move of 1 up, down, left, right or diagonally is the same distance. Whether it makes sense mathematically or visually doesn't matter; that is how it was defined and it does work. As long as the players understand that's how it works, everything is cool.

What is the same is that is it consumes the same movement points (if no terrain differences), not that is the same distance. Geometrically, the diagonal distance is greater. Temporally, is it the same, since units moving diagnoally have added velocity to complete the diagonal move in the same time as the horizontal or vertical move.

But that is rather semantic hair-splitting, and practically it acts as if the distance were the same.

Um.....as much as I would love to discuss the math, can we get back on the "square sucks and hex rules" theme of the post? (yup, that was my originial intention) this forum has been getting dramatic attention from the developers that I hope, if we make ourselves loud enough, CivV (that looks ********) will have a hex, or the square-hex as i posted earlier.

Ok, back on topic ... I'd vote for the true hex, or the pseudo-hex (the offset square tiles).

dV

 

[Gyprsn]

I vote for hexes. I'd say Civ isn't perfect until it has the offset squares or hexes.

 

[LordRahl]

That said, in the Civ world, a move of 1 up, down, left, right or diagonally is the same distance. Whether it makes sense mathematically or visually doesn't matter; that is how it was defined and it does work. As long as the players understand that's how it works, everything is cool.

It's not the same distance, it just takes the same amount of time to travel.