# Squared grids, diagonal movements

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X3M
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Joined: 10/28/2013

So, what is the question here?

Games that use a square grid, yet also allow for diagonal movement(or taking an action of some sort) in the best possible way.
Thus without measurement tapes or other fancy stuff.

While I just recently stumbled accross AN answer while sitting on my toilet and curiously observing my toiletwalls.

Quote:

Moving to a square that is adjacent, movement costs 2.
Moving to a diagonal placed square, movement costs 3.

(or 1 and 1.5)

Movement uses as much diagonal as possible.

Thus if mr.Farmer wants to move 5 fields. And has 10 points for doing so. mr.Farmer can move 5 to the north, south, west or east. But when going diagonal, only 3 squares.
For a place that is 4 to the north and 2 to the west, mr. Farmer also needs 10 points. Because there is only 2 movement to the north (4) and 2 to the north west (6) = 10.

***

While squared grids usuall show a diamond patern of distance. And hexagons a hexagon patern. This new(?) idea would create a octagon patern. Which is rounder than a hexagon patern.

I am just very curious if someone else has thought of this, idea?
Has it been used in games?
What games?
What do you guys think, would it be good for use?
Simple or hard to understand?

let-off studios
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Joined: 02/07/2011
Offset Grid

Have you thought of using an offset grid?

In this, every other row is "offset" by half the width of a grid square. The result is that each square has six possible adjacent squares into which a unit may move.

The only drawback of this I can imagine is that it only allows perfectly "straight" movement horizontally or diagonally, but not vertically. If you're okay with "zigzag" patterns for moving vertically, then this should be okay for your needs. I personally find this much more satisfying than a regular squared grid, and use it for any area-control game I conceive where hexagons are not usable for some reason. Creating an offset grid is also much more convenient for prototyping, as you don't need to make exact drawings or cuts for hexagons, but squares allow just as many movement options.

https://4.bp.blogspot.com/-2Kw2mwCRsUA/VSg9tvfJ0aI/AAAAAAAAFOI/DQ1E2U-ra...

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Joined: 09/02/2014
Yeah the 2 for orthogonal/3

Yeah the 2 for orthogonal/3 for diagonal is one fix for the fact that a diagonal move is actually root 2 units of distance.

Another I've played with (and is used in eg D&D) is each *second* diagonal move costs 2 moves. I think this is slightly more manageable if you're using *small* numbers of movement points (like if you have 3 moves, then it's fairly simple). But with larger amounts it becomes easy to lose track of the alternating diagonal move costs.

I quite like hex-based because it avoids this problem (but does only give you 6 directions rather than 8)

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Joined: 09/02/2014
The "staggered square"

The "staggered square" approach is functionally the same as hexes, it just looks different.

(yeah I can see that it would look better on some map designs, which I guess is what you mean by somewhere that hexes wont work)

Stormyknight1976
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Joined: 04/08/2012
Square grids

I have done the same for Dymino Monsters. I took two index cards and cut them in half. Then over lapping them creating a plus sign.

Then took one index card and laid it diagonal to for a hex style gride.

This allows the cards to face any direction.

See my prototype playmats in the artwork album on this site to see what I am talking about.

X3M
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Joined: 10/28/2013
There is more to it after all

let-off studios wrote:
Have you thought of using an offset grid?

This zig zag is a hexagon grid in my eyes. I am well aware of them. Used themselves A LOT in the past for prototyping. I am not looking for possible grids because I have them all. I am looking for possible rules regarding diagonal moves on square grids. Only to compare them with what I have thought of.

Personally, I thought you knew me to a certain extend to know that I have 40+ hexagon maps all over the place? Perhaps I should have declared that in my first post.

iamseph wrote:
Yeah the 2 for orthogonal/3 for diagonal is one fix for the fact that a diagonal move is actually root 2 units of distance.

Another I've played with (and is used in eg D&D) is each *second* diagonal move costs 2 moves. I think this is slightly more manageable if you're using *small* numbers of movement points (like if you have 3 moves, then it's fairly simple). But with larger amounts it becomes easy to lose track of the alternating diagonal move costs.

I quite like hex-based because it avoids this problem (but does only give you 6 directions rather than 8)

I love hexagons too, despite only being able to move to 6 directions.

Would moving with 2 points every other movement, not be more confusing? A fixed amount of 3 every diagonal move sounds better.
Trying to create a movement circle for this is confusing as well.

I think that having the difference between 2 and 3 points, can make for some early on combat strategies too.
However, if it is less confusing when using 1 and 1.5. Than I ought to go with that.

Do you know something about soldiers turning on their spot? I was thinking of 1 point per 45 degrees, while movement costs 2 and 3. However, this dents in the octagon movement circle.

Stormyknight1976 wrote:
I have done the same for Dymino Monsters. I took two index cards and cut them in half. Then over lapping them creating a plus sign.

Then took one index card and laid it diagonal to for a hex style gride.

This allows the cards to face any direction.

See my prototype playmats in the artwork album on this site to see what I am talking about.

http://www.bgdf.com/image/four-player-open-battlefield-playmat-dymino-mo...

That one?

Looks interesting. And confusing. Confusing regarding the diagonal parts. It is hard to tell where exactly every card goes. Perhaps placing the cards diagonal will make this easy to see. Than judging from a picture. I don't think that only corners are sufficient. But that is my opinion.

Having one card taking up several fields, creates a sense of slowness and detailed movement. Something that I have not touched for a while. But perhaps I should go back to that to see what my experience can offer me nowadays.

If I where to do something similar on 5mm paper. Than having higher numbers would be less problematic. Although, pin point strategy in placement would be harder. (Unless I make big differences between every range class.)

***

A new world for exploration has opened for me. For example, I could simply print out all those old RTS games. And create some fitting rules.

***

Of course I was talking about moving circles. But figured that not all know what it means. And thus wanted to show examples from the internet. Then I got across what I was looking for.

Ow dmn, someone has beaten me to it. A guy called John Savard.
His explanation:
Al movement begins and ends on a white circle. Every white or red circle counts as 1.

Not only that, but this guy has a map placed under it as well to start with.

Original site regarding the boards:
Homepage:

gilamonster
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Joined: 08/21/2015
Funny - I've recently been

Funny - I've recently been thinking of doing something like this using hexagons. I'm very slowly trying to figure out rules for a grid-based WWII naval-themed wargame, and while I love hexagons, it irked me that the six directions of movement don't correspond well to four cardinal directions of a compass-rose. So then I thought: what if you could have a node halfway along each edge of a hexagon. Then you can move in 12 directions, not six, with half of those moves ending on an edge node. Now I can still have my NSEW compass directions and two movement directions between them - which is good, as ships have big turning circles. And the difference in distance is relatively small: moving between centers of two hexagons with sides 1 unit long equals a move of 1.73.. units, while moving to a node on the edge of an adjacant hexagon is 1.5 - so the error is about only 0.23 - about half of the error in assuming a diagonal move on a square grid is the same as a an orthogonal one.
Maybe you can adapt something like this to your existing hex maps?

By the way: email or pm me if you still need help with map editing issue; I haven't forgotten, just been quite busy.

Andrew

Edit: after drawing it out, I saw that in fact you still end up with a hexagonal distance pattern, which is as you say a poorer approximation than a octagon so no gain there (just with the number of movement directions).

let-off studios
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Joined: 02/07/2011
Needing Rules, Not Grids

X3M wrote:
let-off studios wrote:
Have you thought of using an offset grid?

This zig zag is a hexagon grid in my eyes. I am well aware of them. [...] Personally, I thought you knew me to a certain extend to know that I have 40+ hexagon maps all over the place? Perhaps I should have declared that in my first post.
My apologies. I don't visit frequently enough to catch everything.

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Joined: 09/02/2014
X3M wrote:iamseph wrote:Yeah

X3M wrote:
iamseph wrote:
Yeah the 2 for orthogonal/3 for diagonal is one fix for the fact that a diagonal move is actually root 2 units of distance.

Another I've played with (and is used in eg D&D) is each *second* diagonal move costs 2 moves. I think this is slightly more manageable if you're using *small* numbers of movement points (like if you have 3 moves, then it's fairly simple). But with larger amounts it becomes easy to lose track of the alternating diagonal move costs.

I quite like hex-based because it avoids this problem (but does only give you 6 directions rather than 8)

I love hexagons too, despite only being able to move to 6 directions.

Would moving with 2 points every other movement, not be more confusing? A fixed amount of 3 every diagonal move sounds better.
Trying to create a movement circle for this is confusing as well.

I think that having the difference between 2 and 3 points, can make for some early on combat strategies too.
However, if it is less confusing when using 1 and 1.5. Than I ought to go with that.

I think both systems are less than perfect.

Yes it takes a bit more thought to think about the alternating cost of diagonal moves. But it has the advantage that your movement points = your straight line speed. I think this makes it easier to look at the map and quickly see how far you can move.

X3M wrote:
Do you know something about soldiers turning on their spot? I was thinking of 1 point per 45 degrees, while movement costs 2 and 3. However, this dents in the octagon movement circle.

I think this makes it too hard to turn around unless you're dealing with a LOT of movement points.

One example of something like this is space hulk. The terminators get 4 MP and it costs them one to turn 90 degrees on the spot. This means that it costs them half of their go just to turn around on the spot. Since their MP are also used for attacking, this makes facing critically important.
But that is the point, this is to represent that they **are** big, cumbersome suits of armour that take time to turn around (and really works in the close-quarters combat of the game).

But a normal soldier can turn on the spot much more quickly than that, so it doesn't make as much sense for their movement speed to halve just because they need to turn around. So if you had, say 30 movement points and it cost you 1 per facing change (so costs 4 to turn around with 8 facings) it's only a small speed loss. On the other hand... at that point, is it so small it's not worth even having it? I'd say so.

ElKobold
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Joined: 04/10/2015
my 2 cents

I think this only makes sense if you use the point-based movement system for something else as well. Like different terrain types costing different number of points etc.

I.e. if calculating optimal path is a part of the game.

Otherwise, you might want to ask yourself if this constant calculation (however simple) is necessary?

If you really need the diagonal movement, and the spread between the movement points isn't very large, you may use "you may move diagonally once per turn" instead. That would lead to similar pattern, but without calculation.

X3M
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Joined: 10/28/2013
gilamonster wrote: By the

gilamonster wrote:

By the way: email or pm me if you still need help with map editing issue; I haven't forgotten, just been quite busy.

Andrew

Sorry, I have yet to find time for this. Busy life as well. :D

gilamonster wrote:

Edit: after drawing it out, I saw that in fact you still end up with a hexagonal distance pattern, which is as you say a poorer approximation than a octagon so no gain there (just with the number of movement directions).

[The following is a ridiculous amount of math expressed in words. Which confirms most conclusions in this topic. aka. To Complex for gameplay]

Funny how I also tried with hexagons the wrong way first. It is much more difficult to picture how to do it right. But this method also requires one to have patience when figuring it out. Having a history of math helps a lot here. Which most players do not have.

(Could post about 2 more pages of math reasons here too of why things are as they are)

The thing is, while the hexagon sometimes shows the desired dodecagon. If you look closely to the corners, they are indeed still hexagons. There is only a short while of illusion at a distance of 4 and 5. But calculating backwards shows that these 2 are also hexagons mathematical speaking. In practise; the maximum movement is 5 for your desired dodecagon. If you use 6, you got your hexagon back. Period.

While 1.5 works for our square. The error is only 6%.
I don't think that 1.5 works for our hexagon. There the error is 15% (Which is 1% higher than comparing 1.5 to the root of the root of 3). Meaning that using 1.5 brings you closer to hexagons than to dodecagons.
This might sound strange. But have you tried 1.75 (1% error) instead of 1.5 for the hexagons?

BAAAM! Dodecagons!
Instead of 2 and 3. We can use 4 and 7 for movement now.

These 3 and 7 for "diagonal" movements also show at what minimum distance, you see the new desired shape.
3 for the square into an octagon.
7 for the hexagon into a dodecagon.
At 6 and 14, you have your reconfirmation.

While for the square grid, we can use a movement of 2 or more based on 2 and 3. 1 has no use here.

For the hexagon grid, based on 4 and 7, having numbers 1,2,3,5,6,9,10,13 and 17. Has no use.

Now, lets see at the required distance for the shape, and the corresponding numbers for movement.
The square has 3x2=6, next is 12
The hexagon has 7x4=28, next is 56

-->It becomes very impractical<--
No one wants to play a game that requires that much of math.
Who would like to try to get the most optimal movement out of 28? Let alone 29(4+4+4+7+7) Every time when you move your soldiers?

Back to the 2 and 3. Same reason, but ages go down. I figured that people like me have no problems with the squared grid. It is rather easy to follow.

But I would certainly not use it for a kids game. (If I ever would go as far as designing more games)

***

And the above shows what iamseph is saying. It is indeed better to avoid this complexity for the simpler games. While the octagon is rather easy in my eye's. And as the previously given link shows. It can be shown on maps as well for players to count in an easier way.
However. "uuugleee!" Not going to do that either.

Regarding turning around, I think that if I use it. I will use a separate number for this.

I have seen many games where fast units can only turn slowly on the spot. And, as how you have put it, a slow soldier can actually turn fast on the spot.

If I can find a strategic value in these differences. I would like to apply it. If there is no strategic value in it; I consider it a waste of time for players.

***

ElKobold wrote:
I think this only makes sense if you use the point-based movement system for something else as well. Like different terrain types costing different number of points etc.

I.e. if calculating optimal path is a part of the game.

Otherwise, you might want to ask yourself if this constant calculation (however simple) is necessary?

If you really need the diagonal movement, and the spread between the movement points isn't very large, you may use "you may move diagonally once per turn" instead. That would lead to similar pattern, but without calculation.

In my "completer" wargame, terrain does have influence. But in a sence of space that is. It is a very easy concept. You look for your path. And see if each hexagon shows sufficient space. If not, you need to move your forces in 2 or more turns. Which also simulates slower movement.
This space can be different for different units. (normal, boats, hoovers)

The down side to that was that a part of your army could still cross over at the maximum speed. Meaning they would come into range and "cross over" in a sense.

Thus you mentioning different terrain costs for movement. Was spot on! I indeed had that idea as well. Just to keep forces as big as they are.

Another approach here from me is that if you move a double move at once, the costs would be 3 instead. But still, the maximum speed is not reduced in that matter.

gilamonster
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Joined: 08/21/2015

Your dodecagon method is great! But as you said,probably a bit complicated for some tastes...

I think there is a relatively mathless way (for players, at least) out of this problem. If we assume no rotation or terrain penalty, the unit can move anywhere in a circle per turn. If it moves less than the maximum, no problem. So all we do is make a template approximating a circle within which the unit can move. For a square grid, we can use something like this:
https://en.wikipedia.org/wiki/Midpoint_circle_algorithm
to determine how the boundary circle is approximated.

Of course in your case terrain is important, so we use concentric templates,
and divide up the move into multiple phases. So if a unit can move four concentric template-radii on level grassland, but enters a forest with a 50% speed penalty after having moved through only two template radii, then it can only advance one template distance into the forest. If it doesn't have enough, it stops. Though if there are a lot of terrain types close together this could become a book-keeping exercise.

In my case, where the ships' rate-of-turn is important, I can make the template an offset ellipse with the long axis in the starting direction. Except you'll need a lot of templates if you want to allow a large number of possible directions.

The other limitation is that this works best if units can a large number of squares per move, otherwise the rounding errors are glaringly apparent, and your template looks like that of a chess king.

X3M
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Joined: 10/28/2013
While templates are fun to

While templates are fun to draw. Their limit is the diversity of war games.

It looks like it is only useful if one uses the same template for several units. Maybe 2 or 3 extra.

And choose those templates that are easy to remember. Like how the diagonal movement shows a end group of 1, then adjacent away from the center 2, then 3 blocks. etc.

Which is also a possibility for any range. Some might be unfair. But if it works, these too come close to a circle.

It starts at range 1, with a block of 1.
Range 2 would be impossible to give this design.
Range 3 on the other hand would show 1 and then a group of 2. This group of 2 melts with another group of 2 into 1 big group of 3. But we assume only one corner to look at.

Ranges of 1, 3, 6 etc. are the only ones that support this principle. Thus all triangular numbers.

***

Bottom line is, that when we start using that method. With books etc. We might as well, simply use a ruler and join the warhammer group :)

Clearly this octagon is a bridge that could connect both worlds regarding range and movement. But this bridge is hard to build.

Or we need a computer to simulate the maximum range for us. Like how it is done in XCOM.

The more and more that I think about it. The clearer it becomes that we should stay away from the dodecagon.
The octagon on the other hand is easy enough for the heavy wargames. As long as a relative short distance is used.

I personally use 9 as a maximum. 12 is exceptional. With the 2 and 3 rule, this would be 18 and 24.

***

Now, to go back to limited moves through terrain. Instead of having penalties on the maximum number. I think it would be better to use a minimum number. And simply add bonusses for a clearer terrain type.
If an unit cannot move through a terrain, the multiplier is 0.
If an unit has a bonus through clear terrain, than a +1 would be sufficient as example. For some terrains, this bonus would count double.

While easy for players to play with. It would be harder to balance in design.