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[Graviton <>]

I have a set of non-overlapping polygons. These polygons can share nodes,
edges, but strictly no overlapping.

Now, I am going to mesh them using Constrainted Delaunay Triangulation (CDT)
technique. I can get the mesh without problem.

My problem is, after the mesh, I want to know which mesh element belongs to
which original polygon. MY current approach is to compute the centroid for
each mesh element, and check which of the original polygon this centroid
falls into. But I don't like this approach as it is very computationally
intensive.

Is there any efficient ways to do this ( in terms of Big O the runtime)? My
projects involve tens of thousands of polygons and I don't want the speed to
slow down.

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