Convert polygons to optimized lat long radius

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I have a research project where I need to search Instagram and Twitter for geo coded data.

The APIs allow lat, long, and radius, but I have shape files with polygon shapes and some long lines (think long stretches of roads).

How do I take these shapes and convert them into one or many points to use?

I would need many if the radius is greater than the API max, or if the shape is such that one big circles has more space outside the shape than inside (L shapes where 2 or 3 smaller circles would more optimally cover the shape).

I am working in .NET.



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