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ArcGIS 10 — Polygon Centroid Options and Appropriateness (FeatureToPoint, Labels, etc)

I've found a couple of other Stack Exchange questions related to this, but just like the ArcGIS online help, they were not satisfying. For instance, How does ArcGIS calculate the "inside" ...
9
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How does ArcGIS calculate the “inside” point for “Feature to Point”

Let me back up and say that from what I understand there are two common ways to calculate the centroid of a polygon in ArcGIS: Using Calculate Geometry on fields within the attribute table of the ...