I think it's more popular nowadays to do a search on an adjacency graph of polygons and then smooth the path with something like the funnel algorithm. http://digestingduck.blogspot.ca/2010/03/simple-stupid-funne...
There's another approach you can take for continuous space pathfinding, however, which is to use visibility graphs.
See http://www.cs.kent.edu/~dragan/ST-Spring2016/visibility%20gr..., for example, for some explanation and diagrams.
This is the approach I used in PathEngine (www.pathengine.com).
A lot of people are put off by the possibility for graph explosion in situations where there are a lot of obstacles in an open environment, but PathEngine works around this quite effectively by detecting these kinds of obstacles and pulling them out of the visibility graph (and pathfinding search).
After the initial graph search, the path is modified to avoid these obstacles locally (by pushing the path around the obstacles, essentially), before it's returned from the pathfinding query.
So the way it's set up in PathEngine this optimisation is largely hidden from application code (code that calls into the pathfinding API).
Leaving this to be handled later on, by agent local obstacle avoidance, could also work..