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Simplify complex polygon

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Does anyone know a good algorithm to simplify a complex polygon? That is -- turn a polygon with intersecting lines into a list of non-intersecting polygons?

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Polygon Tessellation? OpenGL has some functionality to split a concave polygon into a set of triangles.

http://www.flipcode.com/archives/Polygon_Tessellation_In_OpenGL.shtml

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I know about glu, and have been using it. I reached the extent of what it could do for me, so i've been trying out cgal. It has a bunch of great algorithms for polygons, but most of them only apply to simple polygons -- and they dont seem to have an algorithm to simplify a complex polygon. Any more suggestions?
I think I may be able to come up with something myself, but i'm not sure.

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