I have a question regarding the Feature to Point tool in ArcGIS Pro. Firstly, mathematically the following statement is true: The centroid of any triangle is located at the intersection of the median lines drawn from each corner vertex to the exact midpoint of the opposite side. Well I think that is true at least. Secondly in the Feature to Point tool, one has the option of ticking an "Inside" box - which if ticked forces the centre point to remain within the boundary of the polygon. If the box is not ticked then, as the Help box says for polygons "The output point will be located at the center of gravity (centroid) of the polygon.".
But, for a very obtuse scalene (spike shaped) triangle, if I run the Feature to Point tool (twice), once with the box ticked and once not, I get two points - both in exactly the same place. However, if I then create a series of median lines, the intersection of the median lines IS NOT at the same place as either Feature to Point tool points. They are separated by about 116 metres.
Surely the Feature to Point tool should return one point (from the two choices for ticking the inside box) that at least matches the point created by the intersection of the median lines.
For interest, my triangle has sides AB: 3848.74m; BC: 66610.22m; CA: 65965.34m. Very spiky. I am working in an Albers Equal Area projection, WGS84.
Am I missing something in the terminology? I understand the centroid is generally considered the centre of mass. I cannot find the exact method that ArcGISPro uses to calculate the centroid inside or not - likely this is proprietory???
Can anyone shed light on the method that ArcPro uses to calculate centroids? and or why my intersection of the median lines be different to either ArcPro centre point method?
Regards
Ben
