Does anyone know a good algorithm to simplify a complex polygon? That is -- turn a polygon with intersecting lines into a list of non-intersecting polygons?

I know about glu, and have been using it. I reached the extent of what it could do for me, so i've been trying out cgal. It has a bunch of great algorithms for polygons, but most of them only apply to simple polygons -- and they dont seem to have an algorithm to simplify a complex polygon. Any more suggestions?
I think I may be able to come up with something myself, but i'm not sure.