c++ 2D computational geometry

I would like to know of ways to take the intersection, union, and difference of 2d objects whose online is described by Hermite Splines. Also I would like this to be efficient so that I could work on multiple collections many (1000+) Hermite Splines object in reasonable time ( ie a few minutes max in the worst case). If there any software libraries that you are using please also include a reference to them in your description as well.