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Hoping for some advice on AI pathfinding terminology

Basically I have a town made of individual hex shaped tiles with buildings on them. Each tile will have footpaths too, and my little people will hopefully wander around the paths, travelling to other tiles via their path connections.

I'm fine with learning this stuff but just not sure exactly what terms to search for to get started!

Should I be looking up specific features for finding routes? Algorithms? Help!

@gamedev

@teahands Since graph theory et al haven been mentioned already, let me remind:
There's many ways to map a hex/any grid to a (nav) graph.
E.g.:
tiles=nodes&borders=edges seems "natural" to map but would mean your roads can only ever go from tile center to tile center.
t=e&b=n avoids directionless roads.
Corners=Nodes is how Settlers of Catan roads look like.
Any element of the grid (which itself could be a graph) could inform the nav graph, it doesn't have to be the same.

@Wortex17 Thanks, this took me a couple of read-throughs to actually understand because I'm that much of a noob, but it makes sense now and is definitely worth thinking about.

Will bear it in mind as I do all the homework reading I've been set :D

Wortex17

@teahands I was contemplating doing a graphic for better brevity instead, but didn't have enough time.
(Trimming text likely made it harder to read)
You might have convinced me to follow up with one.