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Specifically, the polygons are Voronoi/Thiessen polygons created from the points, and I want to find the average distance from within the polygon to the point within. A more general solution is welcomed.

If this is confusing, you may think about it as points evenly and infinitely distributed within a polygon, each having their own Euclidean distance to the point. I could perform an analysis on each polygon in this manner, but would much prefer a simple calculation that could be performed systematically (within Excel, for example).

David Giacomin
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  • Your problem is too general to have a simple answer, other than to just calculate the expected value. There are special cases where more is known, e,g, regular polygon, circle, etc. but these are unlikely to arise as Voronoi polygons. – Calvin Lin Jul 05 '13 at 20:11
  • It sounds like that is the answer then, as I thought there may be an all-encompassing equation one could follow for any area and point. – David Giacomin Jul 05 '13 at 21:56

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