' Polygon.ReturnCentroid

' Despite what ArcView's online help says, Polygon.ReturnCenter does NOT
' return the true centroid.  This routine is adapted from O'Rourke,
' Computational Geometry in C.

' Arguments:  thePolygon

' Returns:    theCentroid (Point)

thePolygon = SELF.Get(0)
if (thePolygon.AsList.Count > 1) then
   MsgBox.Error("This routine only works with simple polygons.","Centroid")
   return nil
end
plist = thePolygon.AsPolyLine.Flip.AsMultiPoint.AsList
n = plist.Count
CGx = 0
CGy = 0
Areasum2 = 0
for each i in 1..(n-2)
   x0 = plist.Get(0).GetX
   y0 = plist.Get(0).GetY
   x1 = plist.Get(i).GetX
   y1 = plist.Get(i).GetY
   x2 = plist.Get(i+1).GetX
   y2 = plist.Get(i+1).GetY
   Cent3x = x0 + x1 + x2
   Cent3y = y0 + y1 + y2
   A2 = ((x1 - x0) * (y2 - y0)) - ((x2 - x0) * (y1 - y0))
   CGx = CGx + (A2 * Cent3x)
   CGy = CGy + (A2 * Cent3y)
   Areasum2 = Areasum2 + A2
end
CGx = CGx / (3 * Areasum2)
CGy = CGy / (3 * Areasum2)
return CGx@CGy