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# Pathfinding with units of different sizes

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### #1Roland_Y  Members   -  Reputation: 127

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Posted 08 April 2013 - 01:25 PM

Hi all,

I am actually working on a general purpose pathfinding library (written in Lua, find it here), mostly oriented for grid-based maps. I was looking for ways to integrate support for pathfinding with units of different sizes.

Actually, I am working with the assumption that all units are square (i.e. their widths and heights in tile units are the same).

I came across a very comprehensive article (about Annotated A-star and true clearance values for pathfinding). I succeeded in implementing it, and got it working with a wide range of search algorithms (A-star, Theta*, Dijkstra, DFS, Breadth-first search and Jump Point Search).

Yet, there are some small details of implementation I think I am still missing.

First of all, when an agent is 2x2 sized (i.e it occupies 4 tiles on the grid map), what tile can be assumed to be the agent position ? On the same page, clearance based pathfinding will fail in some cases. Let's consider the following map, where 0's are passable tiles, 1's are obstacles and 'x' matches walkable goal to be reached. Let's assume we are pathing with a 2x2 sized unit:

• Situation 1

00000000
00111100
001x0100
00100100
00000000

• Situation 2

00000000
00111100
0010x100
00100100
00000000

For situation 1, tile 4,3 has a clearance value of 2. No problem here. But, for situation 2, tile 5,3 has a clearance value is 1.

So depending on how the agent position is considered, pathfinding will fail while obviously, for each of the two situation, the agent could reasonably fit into the dead-end space.

Another scenario, with the same 2x2 sized agent:

0000000x
0000000x
0000000x
0000000x
xxxxxxxx

Well, assume all tiles are walkable here, so no obstacles. We want the object to reach any of the tile marked 'x', on the rightmost or bottom-most border. Each of these tiles have a clearance of 1, so annotated pathfinding wil obviously fail here again...Well, depending on how the agent's position is taken.

How should I work around this issue?

Best regards,

Roland.

### #2Lifepower  Members   -  Reputation: 125

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Posted 08 April 2013 - 05:23 PM

If you consider your units as having origin at top/left corner, you can precalculate for each cell on the map a 2D value, which indicates the biggest unit that can be placed at this location (at top/left corner), e.g.: (1,1), (2,2), etc., which considers any nearby walls. This needs to be calculated only once per map. After that, you execute normal A* or any similar path-finding algorithm, where you check your current unit size versus the size in each cell to determine if it's an obstacle or not (so 2x2 unit can't go on cell that has 1x1 value in it). Then, the final path will be an array of top-left corner positions that lead your unit from your current location to the desired one. If you have dynamic world where units also occupy locations, you can extend the approach to have references in each cell to unit occupying it, so you can apply this check in your path-finding algorithm. Does this make any sense?

### #3IADaveMark  Moderators   -  Reputation: 3495

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Posted 08 April 2013 - 10:11 PM

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