Alternatives to the Square Grid

[Mr. Mask]

Most games use square grids. Everyone understands them, and they're even used in chess. The problem I see with them, is when you try to work with diagonals.

Situation and Analysis: Tactics games, like Tactics Ogre, discourage you from making use of the diagonal axis. You can't move diagonally, you can't attack diagonally with most hand-weapons, and you can't set your characters facing diagonally. There are exceptions, like XCOM, but those games work heavily on ranged combat relatively divorced from the grid. Notably with XCOM, I believe it costs more TUs (action points) to move diagonally.

Games like Advanced Wars and Fire Emblem do have ranged attacks that are closely tied to the grid, but diagonals are not a strong point of those. To illustrate, let's look at some Advanced Wars attack ranges: http://lparchive.org/Advance-Wars-2/Update%2002/35-01_day7_4.png
You can attack diagonally, but it is quite different from attacking horizontally or vertically.

When I tried to design some attack ranged based off diagonal facing, they ended up pretty warped. It seems very hard to design them so that they have the same range and coverage as a horizontal or vertical facing. Either they have notably more range and coverage, or notably less.
And that'd be fine if the game was designed around facing vertically being weaker or stronger than the other facings, but I don't want that.


For the reason described, I'm looking for alternatives to a square grid. More specifically, I'm looking for a grid that handles eight directions with the same fidelity. Hex grids almost cut it, but it feels a little funny without the extra two directions. I could just use an octagon grid, though it does seem a little messy and confusing. (https://www.google.com.au/search?q=octagon+grid&hl=en&source=lnms&tbm=isch&sa=X&ei=B7xNVK_vM9CA8gXhqoGgDQ&ved=0CAgQ_AUoAQ&biw=1680&bih=900)

It seems hopeless, like there aren't any alternatives I can use in grids. I might have to look into something more like Warhammer Disckwars.
With a computer game version you get a bit more flexibility, and can have it on a pure measurement basis, or with circular cells like in Silent Storm. Only problem I see with that method is that distances are a bit harder for players to read.


Anyone have any experience with this problem, or thoughts on what I might look into? Or maybe I'm just not designing my diagonal attack ranges correctly (my brain hates working that way)?

['Neath the Moon]

I had an idea recently for a triangle grid, which is used sort of like a hex-grid, although it might already be a thing, and I'm not totally sure how it would work. My idea, though, was that it's a grid of small equilateral triangles, sized so that six of them make a hexagon comparable to one from a hex-grid. Each figure occupies a hexagon of one size or another, and since it's made up of triangles it can be a true hexagon regardless of size. Movement would be measured in shifts of a single row of triangles in any given direction, allowing for closer to even movement. It would also have less dead space in the event of right angles.

I haven't got a clue if this is particularly close to what you're looking for, but I would have just forgotten about this idea if I didn't write it somewhere.

[Mr. Mask]

As you say, I'm not sure if it fits my game's bill, but that does sound like a really awesome grid. Had a friend with a similar idea, but I think his was a puzzle game.

No worries about posting your idea here, it's better to get it written down than be forgotten.

[JusticeZero]

Use a featureless space, with circular bases for everything with the right radius and measure everything with string.
Seriously, people choose between square or hexagonal grids because geometrically, those are your options. Period. There isn't some nifty grid option that people mysteriously don't use with a bigger polygon; hexagon is the polygon with the largest number of surfaces that will touch, and squares avoid the issue of zigzagging when navigating 90 degree corner laden areas. Triangles have the problems of both. And that's the three shapes that you have to choose from in Euclidean space for a grid. If you were a Lovecraftian horror, you might have a small number of other options, but they aren't actually going to be any better.

[rs2excelsior]

Yep, the only three shapes that will form a grid by themselves are triangles, squares, and hexagons. A lot of old wargames use hex grids, which is what I'm most familiar with. The movement feels natural, it's the same distance to the center of every adjacent hexagon, and it's great for figuring ranges and areas of effect. As long as your range isn't ridiculously huge, a "hex of hexes" (every hex that's within a given range from a center hex) approximates a circle well enough.

[Milodiah]

Yep, the only three shapes that will form a grid by themselves are triangles, squares, and hexagons. A lot of old wargames use hex grids, which is what I'm most familiar with. The movement feels natural, it's the same distance to the center of every adjacent hexagon, and it's great for figuring ranges and areas of effect. As long as your range isn't ridiculously huge, a "hex of hexes" (every hex that's within a given range from a center hex) approximates a circle well enough.

I once heard someone say that one of the side effects of trying to interpret circles in a system of squared grids is that apparently pi = 4. It's like the ending of the Hitch-hiker's Guide to the Galaxy series; if you've got a problem that basic in your universe, then of course everything will come out to be wonky.

[Illogictree]

Seriously, people choose between square or hexagonal grids because geometrically, those are your options. Period. There isn't some nifty grid option that people mysteriously don't use with a bigger polygon; hexagon is the polygon with the largest number of surfaces that will touch, and squares avoid the issue of zigzagging when navigating 90 degree corner laden areas. Triangles have the problems of both. And that's the three shapes that you have to choose from in Euclidean space for a grid.

Thought I'd chime in that technically the hexagon is the largest regular polygon that can tile a 2D surface (that's the mathematical term for covering a surface with identical shapes with no gaps). There are larger polygons, but they're irregular and thus pretty useless for gaming. Check out some of M.C. Escher's tessellations if you want to see.

So, yeah, you're pretty much stuck with what we've got. Either that or go gridless.

As to the pi=4 thing, Nedz in this forum has a link to that page (http://www.giantitp.com/forums/showsinglepost.php?p=14148691&postcount=1052) in his signature. The gist is that it starts out as pi=4 for the smallest area template and then gets less as the templates get bigger. Unfortunately DnD's area templates aren't quite correct because pi gets smaller than 3.14 after a certain point, when it should always get closer but not smaller. He does provide an example of a more 'correct' version of the offending template.

[Bulhakov]

Most battle games play without a grid, all you need is measurement tape and/or stick.

As for handling diagonals in a square grid, there are smarter options than just counting 1 diagonal distance = 2 linear distances. Some other options are:
http://cf.geekdo-images.com/images/pic1042798.jpg

[Mr. Mask]

Wow, there are a lot of intelligent, productive, and overall good replies to this thread. Thank you all for your good replies.

I did a lot of experiments, and I came close with a system that combined standing on the lines with standing on the spaces. But it seems that there really isn't any pattern or grid that has diagonals behave the same way as the X and Y axis. Not sure it's possible to design a pattern that does allow for that.

Thanks again for all your help. I guess I'll look into systems with measured movement (those Warhammer Diskwars tokens are an interesting idea).

[Necroticplague]

As to the pi=4 thing, Nedz in this forum has a link to that page (http://www.giantitp.com/forums/showsinglepost.php?p=14148691&postcount=1052) in his signature. The gist is that it starts out as pi=4 for the smallest area template and then gets less as the templates get bigger. Unfortunately DnD's area templates aren't quite correct because pi gets smaller than 3.14 after a certain point, when it should always get closer but not smaller. He does provide an example of a more 'correct' version of the offending template.

I always thought that the pi=4 came from the fact a circular space was represented by a square. So in dnd, 5-foot diameter circle=square 5 feet on one side. Since perimeter of a circle (a.k.a circumfrence)=pi*d, and we know the perimeter of the shape (20 feet) and well as the diameter (5 feet), we can solve and get pi=4.

This also works if you solve using the area of the square (25 feet^2)=pi*r^2 with a radius of 2.5 (half of the diameter of 5).

Of course, both of these only hold true within the bounds of a single square, and assuming that a square space is actually representative of a circle with diameter equal to the length of one side of the representative square. If the square is indeed representing a square, then the above math doesn't hold.

[RCgothic]

http://cf.geekdo-images.com/images/pic1042798.jpg

Technically the bottom left is cost 1.5 roundup. D&D uses 1.5 rounddown, which is subtely different again. You could also try rounding the total range rather than each square. There are different different costs and rounding. You could try.

Cost 1.4 roundnearest(total) is worth considering as pretty close to reality but it's a little tricky to work out without a calculator.

[JusticeZero]

I use diagonal cost =1. It doesn't actually cause any problems at all, and I have yet to hear anybody explain what abuses it opens up that anyone will care about.

[Milo v3]

I use diagonal cost =1. It doesn't actually cause any problems at all, and I have yet to hear anybody explain what abuses it opens up that anyone will care about.

With square grid it can make moving along diagonals at the last second faster than just moving straight to the place or... something....

I just use diagonal = 1, and even if it means my players zig-zag every now and then it's fine since the setting is pretty shonen-esque.

[Hytheter]

I could just use an octagon grid, though it does seem a little messy and confusing. (https://www.google.com.au/search?q=octagon+grid&hl=en&source=lnms&tbm=isch&sa=X&ei=B7xNVK_vM9CA8gXhqoGgDQ&ved=0CAgQ_AUoAQ&biw=1680&bih=900)

Unless you're using the squares in between, an octagon grid is actually identical to a square grid, only that the squares have the corners cut off.

[Jay R]

If you move 1 step to the right, and then one step forward, you are not one step from where you started; you are the square root of two steps from where you started. All attempts at an eight-way grid founder on this simple fact.

So your problem is the grid. Throw it out, and use a ruler. You can then move exactly (for instance) 40 feet in any direction at all, not merely 4, 6, or 8 directions.

I remember once trying to explain to somebody that since my character could move five squares, he should be able to wind up four squares forward and three squares to the left, which is exactly five squares away. He never could grasp the Pythagorean Theorem, or the notion of moving straight in a direction not marked off in squares.

[JaminDM]

These are the official hex grid rules; and the facing rules that go well with them:
http://www.systemreferencedocuments.org/resources/systems/pennpaper/dnd35/soveliorsage/unearthedFacing.html

[nedz]

You could go old school and dispense with grids altogether, which is how AD&D etc. worked. It's the old war-gaming mechanic - you have a table and people use tape measures.

[Talakeal]

You could go old school and dispense with grids altogether, which is how AD&D etc. worked. It's the old war-gaming mechanic - you have a table and people use tape measures.

Tape measurers always incite arguments though. Whenever I see people playing Warhammer they are always arguing about precise distances, people moving an extra millimeter or going front to back or vice versa, claiming that your action fails because you are an imperceptibly small distance out of range, or getting bent out of shape when a model is accidentally moved. It is also a pain in the butt for short distances.

[PrincessCupcake]

Tape measurers always incite arguments though. Whenever I see people playing Warhammer they are always arguing about precise distances, people moving an extra millimeter or going front to back or vice versa, claiming that your action fails because you are an imperceptibly small distance out of range, or getting bent out of shape when a model is accidentally moved. It is also a pain in the butt for short distances.

Yeah, but that can be mitigated simply by calculating movement in 1 inch increments (or something similar) and having people round up to the nearest whole number for the purpose of ranged attacks, threatening, etc. (ala Savage Worlds)

[TheEmerged]

Tape measurers always incite arguments though. Whenever I see people playing Warhammer they are always arguing about precise distances, people moving an extra millimeter or going front to back or vice versa, claiming that your action fails because you are an imperceptibly small distance out of range, or getting bent out of shape when a model is accidentally moved. It is also a pain in the butt for short distances.

See, for me that falls under the same rule about lying for the card game Love Letter. The FAQ for that game responds to a question about players that lie about their cards by essentially saying, "You shouldn't be playing with people that would lie to win at something that is supposed to be fun."

That's how I feel about the "milimeter crowd" when wargaming with tape measures.

[Talakeal]

See, for me that falls under the same rule about lying for the card game Love Letter. The FAQ for that game responds to a question about players that lie about their cards by essentially saying, "You shouldn't be playing with people that would lie to win at something that is supposed to be fun."

That's how I feel about the "milimeter crowd" when wargaming with tape measures.

Me too. Unfortunatly none of my friends who play or the vast majority of pickup gamers at my local store do not feel the same way.

[JaminDM]

These are the official hex grid rules; and the facing rules that go well with them:
http://www.systemreferencedocuments.org/resources/systems/pennpaper/dnd35/soveliorsage/unearthedFacing.html

Yes, I'm quoting myself, but I noticed that nobody was commenting on it, so I've reposted it.

[Anonymouswizard]

I advocate for dispensing with the grid, either going with tape measures or theatre of the mind (which my current game is using, and what my next game will use). Out of the games I've played in during the last year where I enjoyed the visualisation system used for combat distances were measured in tube stations (this was Unknown Armies, a great game that I wish had my own copy of the rulebook for), or in one case train carriages. The idea was that we didn't need to know the details beyond 'can you get to them before combat ends', and could just break up the combat into groups (on your turn you decided which group you would move to, which determined who could hit you with melee attacks, it's what I'm currently doing in shadowrun. The major thing you have to do is specify if ranged groups are being screened by a melee group or not), which helps to speed up combat and frees table space (except when we had the tube map out, where if you wanted to move to another station it took ~20 rounds per stop).

I also like the idea of using algebra when using a square grid, as it allows you to keep the grid and get semi-realistic movement (I also plan to get a character with a 40ft [8 square] speed at some point, and pull out 10 feet to the left + 35 feet foward still gives me over half a square of movement left). But it might take too long for some groups.

[Broken Twin]

I prefer to run Theater of the Mind, but when it does become necessary to use a grid hex is my go to. Movement feels more organic to me on it.

[nedz]

Tape measurers always incite arguments though. Whenever I see people playing Warhammer they are always arguing about precise distances, people moving an extra millimeter or going front to back or vice versa, claiming that your action fails because you are an imperceptibly small distance out of range, or getting bent out of shape when a model is accidentally moved. It is also a pain in the butt for short distances.

Well you just need an umpire, ..., which is why we have DMs.

Also you can hand wave the precision a little, especially since a figure base size of around an inch, say, which corresponds to a number of feet — so just where exactly is your character in that area anyway ?

Also, Warhammer is a bad example since it's all about charging rather than tactics.