It would be useful if that page had some diagrams.

Averaging the cartesian coordinates is what we used school - perhaps it was with smaller polygons.

Seeing what they've written about the "rectangle and trapezium", I think I see what they are getting at. You might have lots of points at one end of the shape. A simple average will then bring the calculated centre over to that side - when it shouldn't.
Yes integration is the way to go. It is a long time since I did this, but it looks/sounds like the momentum calculations we used to do at Univ...
(but in 2d and without the velocity component)


Richard

When I need to find the (approximate) centriod of a polygon I tend to do the following. Note it is very inaccurate and won't return the exact centroid, if you need it exact you would need to look at the stuff Winwead mentioned earlier with 3d Cartisian Coords.

Code:

        Dim i As Integer
        Dim x, y As Double
        Dim pt As Integer
        Dim intPoints As Integer
        Dim objShape As MapPoint.Shape

        For Each objShape In MyMap.Shapes


        intPoints = UBound(objShape.Vertices)

        x = 0
        y = 0

        For pt = 0 To intPoints
            If pt = intPoints Then
                Exit For
            Else
                CalcPos(MyMap, objShape.Vertices(pt).Location, dblLat, dblLon)
                x = x + dblLat
                y = y + dblLon
            End If
        Next pt

        Next
        x = x / intPoints
        y = y / intPoints

        objloc = MyMap.GetLocation(x, y, 100)

        MyMap.AddPushpin(objloc)

For CalcPos code see the appropriate article (I can't remember which one it was now)