The technique of using boolean operations (intersection, unions, etc) to model 3D objects is called Constructive Solid Geometry. I'm not aware of any Processing library that does CSG, but I just found this Java modeling tool called UnBBoolean that is precisely for CSG. However, this tool includes a bunch of GUI you probably don't need, and appears to be no longer in development. However, within its code includes a small library called j3bool which does all the underlying boolean operations. Maybe you can adapt this code to your needs.