Axis separating algorithm for concave polygon splitted into convex ones

I'm trying to build a solid collision system but I'm blocked when I want to get the impacted edge.

So far I have: - Split my polygon if concave into triangles. - Merge back the triangles while forming a convex polygon.

So my object's body is defined by a vector of convex polygons.

I implemented the axis separating algorithm and it works well.

Now I would like to get the impacted edge but I can't manage to find a way to retrieve it.

I read that article: http://ift.tt/1LIl2fX

I understand(theoretically, I didn't test it) how to get the intersecting face between two polygons but how can I manage to retrieve the intersecting face of two bodies composed of multiple polygons ?

If anyone have ressources about that problem, I will be happy to read it. Thank you in advance.