Extract Overlapping Polygon Data to Points

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I have a polygon data set of corn yield collected by a combine. However, as the combine drove through the field, there was slight overlap between passes, leading to overlapping polygons within the same shapefile. I also have a point dataset of sampling sites within the field. Occasionally, these points fall on locations where two polygons are overlapping. At each point, I would like to extract the value from whichever polygon has the higher yield.



I've thought of two ways to do this:


  1. If I can extract the values from both polygons to the attribute table, I can process the data in Matlab to get the maximum. However, most of the points are entirely contained within one polygon. I've tried doing a 'Join by spatial location' but because the polygons are in the same layer, it will only join one of the two records.

  2. Create new polygons for all the overlapping areas and then use join to extract the data.This example from Grass seems to do what I want, but I don't know how to do the behind-the-scenes programming. Is there a built-in function of Arc that can do the same thing?

I am using ArcMap 10 with spatial analyst. There are hundreds of polygons overlapping, so I'd like to use some sort of automated extraction. Thanks in advance!



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