Calculate the center point of multiple latitude/longitude coordinate pairs

Question

Given a set of latitude and longitude points, how can I calculate the latitude and longitude of the center point of that set (aka a point that would center a view on all poi

Answer 1

I used a formula that I got from www.geomidpoint.com and wrote the following C++ implementation. The array and geocoords are my own classes whose functionality should be self-explanatory.

/*
 * midpoints calculated using formula from www.geomidpoint.com
 */
   geocoords geocoords::calcmidpoint( array& points )
   {
      if( points.empty() ) return geocoords();

      float cart_x = 0,
            cart_y = 0,
            cart_z = 0;

      for( auto& point : points )
      {
         cart_x += cos( point.lat.rad() ) * cos( point.lon.rad() );
         cart_y += cos( point.lat.rad() ) * sin( point.lon.rad() );
         cart_z += sin( point.lat.rad() );
      }

      cart_x /= points.numelems();
      cart_y /= points.numelems();
      cart_z /= points.numelems();

      geocoords mean;

      mean.lat.rad( atan2( cart_z, sqrt( pow( cart_x, 2 ) + pow( cart_y, 2 ))));
      mean.lon.rad( atan2( cart_y, cart_x ));

      return mean;
   }