Calculate the center of latitude and longitude coordinates

Question

I'm looking for a elegant solution that calculates the center between several latitude-longitude coordinates (for example, to simply center a map to the center of a google-maps polygon).

Table: locations:

id |    city    |   latitude   |  longitude
-----------------------------------------------
1  |   Berlin   |   52.524268  |   13.406290
-----------------------------------------------
2  |   London   |   51.508129  |  -0.1280050    
-----------------------------------------------
3  |   Hamburg  |   53.551084  |   9.9936817
-----------------------------------------------
4  |  Amsterdam |   52.370215  |   4.8951678
-----------------------------------------------

The current calculation:

function calculateCenter($array_locations) {

    $minlat = false;
    $minlng = false;
    $maxlat = false;
    $maxlng = false;

    foreach ($array_locations as $geolocation) {

         if ($minlat === false) { $minlat = $geolocation['lat']; } else { $minlat = ($geolocation['lat'] < $minlat) ? $geolocation['lat'] : $minlat; }
         if ($maxlat === false) { $maxlat = $geolocation['lat']; } else { $maxlat = ($geolocation['lat'] > $maxlat) ? $geolocation['lat'] : $maxlat; }
         if ($minlng === false) { $minlng = $geolocation['lon']; } else { $minlng = ($geolocation['lon'] < $minlng) ? $geolocation['lon'] : $minlng; }
         if ($maxlng === false) { $maxlng = $geolocation['lon']; } else { $maxlng = ($geolocation['lon'] > $maxlng) ? $geolocation['lon'] : $maxlng; }
    }

    // Calculate the center
    $lat = $maxlat - (($maxlat - $minlat) / 2);
    $lon = $maxlng - (($maxlng - $minlng) / 2);

    return array($lat, $lon);
}

Answer 1

As you are using Google Maps you can use getBounds() method and getCenter() method.

I have rearranged your coordinates to form a Convex Polygon (All the vertices point 'outwards', away from the center).The polygon is closed by having the first coordinate as the first and last value in polygonCoords array.

See jsfiddle

var map; 
var polygon;
var bounds = new google.maps.LatLngBounds();
var i; 
var myLatLng = new google.maps.LatLng(52.5,6.6);
var myOptions = {
  zoom: 5,
  center: myLatLng,
  mapTypeId: google.maps.MapTypeId.TERRAIN
};
map = new google.maps.Map(document.getElementById("map_canvas"),
    myOptions);

var polygonCoords = [
    new google.maps.LatLng(52.524268,13.406290),
    new google.maps.LatLng(53.551084,9.9936817),
    new google.maps.LatLng(51.508129,-0.1280050),
    new google.maps.LatLng(52.370215,4.8951678),
    new google.maps.LatLng(52.524268,13.406290)//Start & end point 
    ];

polygon = new google.maps.Polygon({
   paths: polygonCoords,
   strokeColor: "#FF0000",
   strokeOpacity: 0.8,
   strokeWeight: 3,
   fillColor: "#FF0000",
   fillOpacity: 0.05
 });
 polygon.setMap(map);

for (i = 0; i < polygonCoords.length; i++) {
   bounds.extend(polygonCoords[i]);
}

// The Center of the polygon
var latlng = bounds.getCenter();

var marker = new google.maps.Marker({
  position: latlng, 
  map: map, 
  title:latlng.toString()
});

Answer 2

Averaging your latitudes and longitudes works in many cases, but have problems in a number of cases. Example, you have 2 cites, Tokyo (long = 140) and Seattle (long -122), your average longitude is 18, somewhere in Europe. You would expect something closer to the international date line, 180 degrees away.

The most direct, no problem method, is to average the vectors as if each originated from the earth's center.

Pseudo code, (assumes radians)

for each lat,long
  // assume 1 radii from the earth's center.
  // covert lat, long, and radii into x,y,z (spherical to cartesian coordinates)
  r=1, theta=pi/2 - lat, phi=long
  x = r*sin(theta)*cos(phi)
  y = r*sin(theta)*sin(phi)
  z = r*cos(theta)
  N++;
  // accumulate x,y,z
  sum_x += x, etc.
// average x,y,z
avg_x = sum_x/N, etc.
// convert x,y,z back to spherical co-ordinates to get the lat/long center. 
rho = sqrt(avg_x*avg_x + avg_y*avg_y + avg_z*avg_z)
lat = pi/2 - acos(avg_z/rho)  // acos() results are 0 to pi
long = atan2(avg_y, avg_x)  // 4 quadrant arctangent

[Edit Corrected spherical co-ordinates to cartesian]