How to make all faces convex? Assuming I have a model with several n-gonal faces, out of which some might not be convex polygons, what can I do to make blender split those that are concave to make sure all polygons are convex? 

I know about the "Triangulate" tool, but is there something that only splits the faces if they're convex?

Edit:

Added screenshot clarifying what I need:

So again: I need a tool that lets me select it all, and then subdivides the concave polugons into only convex ones.
Blender 2.75 now has a feature a tool to perform exactly this operation.

Mesh > Cleanup > Split Concave Faces