[R] placing labels in polygon center ?

[Barry Rowlingson]

> Trying to recall from my physics education, the mass centre is at the
> averages of the coordinates of the corners, isn't it?

  Perhaps for simple polygons it is... One thing it certainly isnt is 
the average of all the coordinates (a mistake I have seen geographers 
make!).

  Here's some code derived from the java source code here: 
http://astronomy.swin.edu.au/~pbourke/geometry/polyarea/

  You also get a PolygonArea function for free. Feed it a two-column 
matrix of X and Y coords. Out comes a vector of (x,y) for the centroid.

  PolygonArea <- function(polygon)
{
   N <- dim(polygon)[1]
	area = 0;

	for (i in 1:N) {
		j = 1+(i %% N)
		area = area + polygon[i,1] * polygon[j,2]
		area = area - polygon[i,2] * polygon[j,1]
	}

	area =area/2.0;
	return(abs(area))
}


PolygonCenterOfMass <- function(polygon)
{
   N <- dim(polygon)[1]
   cx=0 ; cy=0
   A=PolygonArea(polygon);

   factor=0;
   for (i in 1:N) {
     j = (i  %% N)+1
     factor=(polygon[i,1]*polygon[j,2]-polygon[j,1]*polygon[i,2])
     cx=cx+(polygon[i,1]+polygon[j,1])*factor
     cy=cy+(polygon[i,2]+polygon[j,2])*factor
   }
   A=A*6.0
   factor=1/A
   cx=cx*factor
   cy=cy*factor
   return(c(cx,cy))
}

  Something like this will end up in my Rmap library......

Baz