How to subtract a circle from an arbitrary polygon

Question

If for an argon polygon with vertices stored both clockwise and counterclockwise (shown as a black rectangle in the diagram), I need to take into account an arbitrary number of circles (red in the diagram) from this polygon. Deleting a circle could split the polygon into two separate polygons (as shown on the second line in the diagram).

I'm not sure where to start.

Example http://www.freeimagehosting.net/uploads/89a0276d9d.jpg

Answer 1

: , , . ( , .) . , , , . , , , , , , , .

Answer 2

( Delphi ++), , : http://sourceforge.net/projects/polyclipping/