I'm new to libGDX and from what I can tell the Intersector class has overlap methods for Rectangle/Rectangle, Circle/Circle, Circle/Rectangle, and Polygon/Polygon, but for some reason it doesn't seem to have any methods for checking Polygon/Rectangle or Polygon/Circle.
Is there a recommended way to check for collision between polygon and rect/circle?
Also, is there some reason why this has been left out of the Intersector class? (ie, should I avoid it? If so, what's the recommended alternative?)
The best way to handle those collisions would be to use a physics engine like Box2D which already comes packed with Libgdx. When a collision occurs in Box2D a event gets fired and you can easly handle that event. So you should probably take a look here.
Of course there are other ways of dealing of dealing with collision detection. With a little bit of maths you could probaly figure out just what you need on your own, also Box2D comes with alot of other features that will benefit you.