Thanks.
Problem.
With a circle or rectangle centered about zero, the centroid is at zero/zero, also.
A 'rounded bar' (two circles with joining tangents, broken at intersections, and re-joined), moves the centroid slightly right of center if the bar was created horizontally, centered about x and y.
A 'dumbell' made the same way, but with a joining thin bar, moves the centroid WAY right.
I re-ordered the points list on the dumbell, so that the "starting point" was different, and it did not change the centroid. I then rotated the shape 180 degrees. That did move the centroid to the other side.
I think it has to do not with the starting point, but perhaps where the algorithm starts determining the surface area.
LLoyd