How to cut concave polygon?

How to cut concave polygon?
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Hope to get help on one problem.

I am trying to cut concave polygon(having texture) with straight line…
For convex polygons, i found good tutorial from Fruit Ninja Game Tutorial at
But for non-convex(concave) polygons, i couldn’t get good.

I will be appreciated at any algorithm or precious advice.


I describe more details about my current situation.

I followed fruit ninja tutorial, and i could complete convex polygon cutting.
But I need cutting concave polygons, too.
Because box2d doesn’t support concave polygons and vertices’ count is limited as 8, so I divided concave polygon to several convex ones.
And then I get start and end position of line to be used in cutting.
At this point, which method or algorithm will be efficient for cutting total polygon and getting 2 sub polygons?
One polygon will be cut by a line and i must get 2 sub polygons as result.

Any thought or link will be appreciated…