QGIS Core Centroid

/* /src/core/qgscentralpointpositionmanager.cpp */
int QgsCentralPointPositionManager::calculatePolygonCentroid( double x[], double y[], int numberOfPoints, double& centroidX, double& centroidY ) const
{
  register int i, j;
  double ai, atmp = 0, xtmp = 0, ytmp = 0;
  if ( numberOfPoints < 3 )
  {
    return 1;
  }

  for ( i = numberOfPoints - 1, j = 0; j < numberOfPoints; i = j, j++ )
  {
    ai = x[i] * y[j] - x[j] * y[i];
    atmp += ai;
    xtmp += ( x[j] + x[i] ) * ai;
    ytmp += ( y[j] + y[i] ) * ai;
  }
  if ( atmp == 0 )
  {
    return 2;
  }
  centroidX = xtmp / ( 3 * atmp );
  centroidY = ytmp / ( 3 * atmp );
  return 0;
}



/* /src/core/pal/pointset.cpp */
  void PointSet::getCentroid( double &px, double &py )
  {
    // for explanation see this page:
    // http://local.wasp.uwa.edu.au/~pbourke/geometry/polyarea/

    int i, j;
    double cx = 0, cy = 0, A = 0, tmp;
    for ( i = 0; i < nbPoints; i++ )
    {
      j = i + 1; if ( j == nbPoints ) j = 0;
      tmp = ( x[i] * y[j] - x[j] * y[i] );
      cx += ( x[i] + x[j] ) * tmp;
      cy += ( y[i] + y[j] ) * tmp;
      A += tmp;
    }

    px = cx / ( 3 * A );
    py = cy / ( 3 * A );
  }