The first keyword that comes to mind thinking about pathfinding, is the A* algorithm. The A* is a fast node based approach to compute the shortest way from start to finish over a bunch of nodes, because it's a geometrical simplified approach it's fast as well.
Also it's scalable:
More nodes, better results, weak performance...
Less nodes, bad results, fast performance...
In this case bad results mean for example unnecessary edges in the path. Also in general the computed way looks quite unnatural, so to use smooth algorithms is quite common or algorithm to generate curves instead of sharp edges.
To get a better insight I found following useful references:
