I am once again trying to use Boost Geometry for and mobile app and have run into a snag. I am trying to take a box (or polygon of some arbitrary shape), shoot a ray around, then divide up the box/polygon using the sequence of points. A quick example is shown in the following image.

I basically let the ray keep traveling and bouncing off edges until it intersects itself. I have this part working great.

I had first prototyped this in Matlab using the polybool function to then take the intersection and difference of the sequence of points with the original box/polygon. This worked great and divided the box/polygon up into the 6 regions shown in the image ({1,2,3,4,6} were generated from the difference computation and {5} was generated from the intersection computation). So then I switched over to trying to doing the same thing with the intersection and difference functionality of Boost Geometry, but keep getting exceptions about self-intersections.

So, my question is whether 

1) there is a better way to do this with an algorithm that already exists in Boost Geometry?

2) if not, is there a paper or website you know of that describes this kind of algorithm that I can implement myself using Boost Geometry as the geometry toolkit?