Are there any simple (or well documented) algorithms for basic CSG operations on 2D polygons?

I'm looking for a way to 'add' a number of overlapping 2D collision shapes. These may be convex or concave, but will be closed shapes, defined as a set of line segments, with no self-intersections.

The use of this would be to construct a clean set of collision edges, for use with a 2D physics engine, from a scene consisting of many arbitrarily placed (and frequently overlapping) objects, each with their own collision shape.

To begin with, I only need to 'add' shapes, but the ability to 'subtract', to create holes, may also be useful.