getPolygoneCentroid.js

function getPolygoneCentroid(polygone){
          var centroid = {x:0, y:0};
          var signedArea = 0;
          var x0 = 0; // Current vertex X
          var y0 = 0; // Current vertex Y
          var x1 = 0; // Next vertex X
          var y1 = 0; // Next vertex Y
          
          var a = 0;  // Partial signed area

          // For all vertices except last
          for (var i=0; i < polygone.geometry.getCoordinates()[0].length-1; ++i)
          {
              x0 = polygone.geometry.getCoordinates()[0][i][0];
              y0 = polygone.geometry.getCoordinates()[0][i][1];
              x1 = polygone.geometry.getCoordinates()[0][i+1][0];
              y1 = polygone.geometry.getCoordinates()[0][i+1][1];
              a = x0*y1 - x1*y0;
              signedArea += a;
              centroid.x += (x0 + x1)*a;
              centroid.y += (y0 + y1)*a;
          }

          // Do last vertex
          x0 = polygone.geometry.getCoordinates()[0][i][0];
          y0 = polygone.geometry.getCoordinates()[0][i][1];
          x1 = polygone.geometry.getCoordinates()[0][0][0];
          y1 = polygone.geometry.getCoordinates()[0][0][1];
          a = x0*y1 - x1*y0;
          signedArea += a;
          centroid.x += (x0 + x1)*a;
          centroid.y += (y0 + y1)*a;

          signedArea *= 0.5;
          centroid.x /= (6.0*signedArea);
          centroid.y /= (6.0*signedArea);
          return centroid;
}