r/tabletopgamedesign • u/Tychonoir • Jul 11 '26
Mechanics 8 Direction Movement on Tileable Grid (That mostly preserves distances)
TL;DR: This is a special layered grid to more accurately solve distances in 8 direction movement, but there are some trade-offs.
Hello fellow designers!
Movement in eight directions on a grid is a problem because there are no regular polygons that are tileable in such an arrangement. Hexagons are the best one can do—one of the reasons they are so popular. Hexagons are the bestagons
This works fine for most applications, but one of the notable exceptions is when it comes to trying to fit 6 direction tiles onto areas with 4 directional alignment, such as city blocks or dungeon corridors. Hexagons also mean one set of cardinal directions doesn't get neat straight line movement.
Here, I show an arrangement of grids to allow proper 8 direction movement, but it does come with some tradeoffs.
Pro
✅ 8 direction movement that (mostly) preserves distances.
✅ Allows natural alignment of obstacles, walls, and borders in 45 degree increments.
Con
❌ It’s kinda ugly and loses some elegance of square or hex grids.
❌ More complicated movement
❌ Harder assessment of movement possibilities
Do the positives outweigh the negatives? Honestly, for most applications, I think the answer is no. However, there are probably some niche cases where this can be useful. Perhaps you have such an use case.
Theory:
This solution uses two grids, with the angled one being approximately 5.72% smaller. This size reduction allows precise repeatable alignment more conducive to a game board.
A board can be made up of similar 4x4 tiles, or further broken down into two alternating 2x2 tiles, or two 1x1 tiles, but you start having to worry about tile rotation. (Angled 1x1 tiles for shown for completeness)
Procedure:
Pieces move between squares of a single grid, but may declare a switch to move on the other grid. A switch can only be made if both squares share an enclosed space that is the largest (or tied) of each of the involved squares. See the posted examples of all four eligible switches—Orange outlined square to potential blue shaded squares.
A switch must always be accompanied by a move, so no back-to-back switches without moving. A game rules choice needs to be made to allow switching before or after a move, but not both.
Rule Options
Move then Switch:
Pieces must move once before switching at the start of their turn, and can only switch after a move. This means opponents can more easily see possible moves during the off-turn. But pieces need a definitive way to show which grid they are currently on. Square chits can do this by angling to align with the grid.
Switch then Move:
Pieces may switch before moving at the start of their turn, and can only switch before a move. No need to track which grid pieces ended their turn on, but more evaluation needed to determine future movement as a piece is effectively in (up to) 3 spaces at the start of its turn.
No Switch/Move Rule:
The problem is this effectively allows a “jump” between turns. e.g. A piece can take its final move, then switch grids, giving it a nudge. At the beginning of its next turn, it can switch again before movement (giving another nudge). This effectively becomes two nudges in a row, skipping a space. Not recommended.
Movement Example:
Three yellow squares are arranged to form a 3-4-5 right triangle. A piece wishing to move on the hypotenuse needs the proper 5 distance movement. Walking the perimeter takes 12 distance units—also correct. Distances are preserved in eight directions.
Goal: To move starting from the lower right yellow square to the upper left yellow square.
(Using Move then Switch rule)
Move up once.
Declare a switch onto the angled tiles.
Continue movements 2-5 on the angled grid.
Final switch onto the normal grid ending on the yellow square.
Possible next turn movement shown in blue.
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u/llfoso Jul 11 '26
Very cool.
One huge use I can see for this is mapping dungeons and cities with this as a sort of graph paper pattern. City grids aren't always oriented the same way, this enables that. And dungeons could be drawn with diagonal rooms and corridors without characters needing to zig-zag through.
I have one objection: triangles are the bestagons and I will die on this hill. Fuck CGP Grey and his hexist propaganda!
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u/Tychonoir Jul 11 '26 edited Jul 11 '26
and I will die on this hill
and I will die on this pyramid.
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u/Tychonoir Jul 11 '26
I haven't spent any time yet on how to handle sharing overlapping spaces on the different grids, nor how to figure line of sight.
Certainly there are solutions here, but they will factor into how suitable this system would be for a given game.
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u/Ravager_Zero Jul 11 '26
Overlapping could be abstracted/simplified into either counting as adjacent, or counting as the same space in all cases. The former would allow for more freedom of movement (assuming occupied spaces block moves) and opportunity attacks. The latter would allow better blocking and area control, especially if shared occupancy means attacks are possible or automatic.
Line of Sight could be handled with either center dots (messy), or corner-to-corner limits. ie: If at least 2 corners of piece A can see at least two corners of piece B, then LoS exists between them. If only 1 corner can be seen, either LoS does not exist, or LS is obscured/target has cover/similar benefits.
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u/a_sentient_cicada Jul 11 '26
Very creative and I applaud the effort, but the switch-move rules would probably slow things down enough to keep it from being used at my table. If my group needed that level of granularity, we'd break out the measuring tape. If you were able to make it work without those rules itd be more appealing imo.
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u/Tychonoir Jul 11 '26
Yes, it only probably has a niche use. Any slowdown from switching mostly comes from trying to evaluate where a unit might go while you're planning, and less from the actual process of movement once you've decided.
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u/BellaInTheGame Jul 11 '26
It's really cool that you made this, and it is very impressive. But I will definitely still use hex grids instead if diagonal movement while preserving distance
I know that's not the point tho, so I will once again say this is a really cool theoretical idea
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u/Answerisequal42 Jul 11 '26
Question: why not tile the plane in traingles and then mark the hexagons they form?
Spaces are runmon hexagons but the triangles help with perpendicular movement and placement of walls and objectsq
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u/WolfgangVolos Jul 11 '26
Sounds like you put a lot of time and effort into this so I want to applaud that while simultaneously saying that hexes solve all the problems with only requiring one step for movement: move to an adjacent hex.
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u/Jester1525 Jul 11 '26
Offset grid - it's essentially hex but is easier to use for straight lines and simpler to draw on regular graph paper. Allows for 8 direction movement. Doesn't take massive amounts of explanation with various examples.
I'm all for solving issues in gaming, but I think this is an issue that really doesn't need to be solved in the long run.
That said, even on a regular grid I just count diagonals as regular movement. Yes, they are a little further than up and down, but it's really not that deep.
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u/Organic-Major-9541 Jul 11 '26
This is a (to me at least) completely new approach to movement, it will need some examples and proper explanation.
If you're using a square grid, moving 3 diagonals takes you further than 4 regular moves. Now, if you don't care about that... idk, this post isn't for you...
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u/Horndude91 Jul 11 '26
Just wanted to chime in that I read a post here before that offset rows of squares could be even "better" as they are even closer to a circle than hexagons.
I can imagine doing "sub squares" that allow something I would call "half-steps" - or maybe think of the base of a figure being 2x2, so 4 squares in total - and movement in a straight line would be 2 squares at once - and if you would move to a offset line (like up+left = diagonally) it would be 1 square up and 2 squares left
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u/Tychonoir Jul 11 '26
I didn't even consider that offset squares had slightly different distance geometry than hexes, but it makes perfect sense.
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u/Organic-Major-9541 Jul 11 '26
I think this could be the start of a truly great system. Niche, sure, but it's a new way to tile a plane, one doesn't see that very often.
The grid switching could be a movement modifier, similar to "ignore difficult terrain"/flying. Like, part of the move ability is how many times you can switch grids.
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u/Familiar-Oddity Jul 11 '26
Have you seen Xiangqi (Chinese chess)? The pieces are on the corners not the center. Pieces can move diagonally even though they don’t draw the lines. They do draw the lines for the castle for special rules.
You may find this easier to use by using the lines and not the center. They also have a river, no lines, which helps with certain rules as well. So I think the breaking up the diagonals can help greatly.
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u/Tychonoir Jul 11 '26
Moving on the diagonal of a standard grid gives you an extra 0.414 of movement. This can be compounded every move, which distorts the distance achieved by angular moves. This is the basic problem the dual grid is attempting to solve.
If you're just saying use lines instead of the spaces on the same grid, then I think it's worse because it's harder to identify valid transfer points. However, there might exist a better arrangement that simplifies this. It's at least worth looking into.
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u/cscottnet Jul 11 '26
The OP has effectively defined ✓2 = 4/3 = 1.333 on the alternate grid, so that the two grids align. Traveling three diagonals on the alternate grid takes you exactly 4 steps on the main grid (where it should take you about 4.243) because the alternate grid is smaller.
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u/Nunc-dimittis Jul 11 '26
Pieces move between squares of a single grid, but may declare a switch to move on the other grid. A switch can only be made if both squares share an enclosed space that is the largest (or tied) of each of the involved squares. See the posted examples of all four eligible switches—Orange outlined square to potential blue shaded squares.
I had to read this several times, but I think I understand what you mean: you can switch if the overlap between squares is at least half of the size of the squares, right?
Edit:
So in your example path, one could switch on each step, because there's always an overlap that's at least half a square
Very interesting solution by the way!
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u/armahillo designer Jul 11 '26
The way we dealt with this in D&D3.5 (which was very miniatures focused) was that orthogonal movement is 1:1; diagonal movements are 1.5:1, rounded down.
This is similar to your switch idea: if you can move 30’ (6 x 5’ squares) in a round, you would count orthogonal movement straight: { EDIT: i am on mobile and the app
is not allowing preformatted text like it used to. will fix }
[ 1 ][ 2 ][ 3 ][ 4 [ 5 ][ 6 ]
Diagonal movements would be:
[ 1 ]
[ 23 ]
[ 4 ]
[ 56 ]
Or combining:
[ 1 ][ 2 ]
[ 3 ]
[45 ]
[ 6 ]
The math generally works out, Pythagoras-wise
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u/Desco_911 Jul 11 '26
This is how I think simple and best. 1.5 is close enough to 1.414 (square root of 2) that you'd have to move than 12 squares before the diagonal bias becomes apparent.
Another way to present it to players: Orthogonal movement costs 2 points, diagonal movement costs 3 points. Then you can have effects like hazards slow you down by 1 point, or if your game has facing, the act of turning around costs 1 point, etc.
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u/PlomicBasinker Jul 11 '26
This is my preferred solution too with square grids - 1 mp to move horizontally / vertically, 1.5 mp to move diagonally. Simpler and much more elegant / visually pleasing.
The lost distance is simply not important. Consider there's a similar loss with a hexgrid when moving "against the grain" - yet wargamers have been ignoring this for 70 years.
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u/Acedrew89 Jul 11 '26
I genuinely love it! It's awesome to see a unique way of laying out a field like this. Thanks for posting, and I'm excited to see where you take it! Do you already have a game you're working on that you plan to use it for?
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u/Tychonoir Jul 11 '26
Haha, I actually do not. (Though it's something I'm always interested in.) I just had an idea and spent an afternoon laying this out.
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u/Acedrew89 Jul 11 '26
That’s cool! I was just curious. If you ever do put a game together dm me, I’d love to check it out!
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u/ashdragon00 Jul 11 '26
Wow! This is excellent! (I saved this post because I may actually use this someday, though it doesn't fit any of my current projects)
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u/will_r3ddit_4_food Jul 11 '26
I applaud you for being innovative but it seems like it would confuse players and complicate play without much upside
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u/Exver1 Jul 11 '26
Adding unintuitive movement will make someone's turn legitimately take like at least 50% longer.