Google-maps – Calculate longitude/latitude

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Given the following input:

known longitudes/latitudes of 1..n locations
known distance between locations 1..n and another location "m"

How can I calculate the longitude/latitude of the location "m"?

Best Answer

This sounds like a basic latitude-longitude triangulation question. The common approaches are outlined in a Yahoo! Answers topic here. There are likely libraries to do this in many languages. A google search for "latitude longitude triangulation" plus your language of choice will likely reveal some existing code to use. "Geocoding" is another common task rolled into similar libraries, so that may be another useful keyword.

Edit: As others have mentioned, "trilateration" seems to be the best term. However, depending on your data and requirements, there are simpler approximation solutions that may satisfy your requirements.

The Yahoo! Answers post is quoted below for convenience:

"For larger distances, spherical geometry. For relatively small ones, treat the earth as flat, and the coordinates as xy coordinates. For the distances to work with the degrees of the coordinates, you will have to use the cosine function to convert from one to the other. (While degrees of latitude are about 69 miles all over the earth, degrees of longitude vary from the same at the equator to 0 at the poles.)

You have the center points of three circles and the radius of those circles. They are supposed to intersect at one point, so you can treat them in pairs to find the intersection points of each and throw out the ones that don't match http://mathworld.wolfram.com/Circle-CircleIntersection.html." (mike1942f)

Related Solutions

Calculate distance between two latitude-longitude points? (Haversine formula)

This link might be helpful to you, as it details the use of the Haversine formula to calculate the distance.

Excerpt:

This script [in Javascript] calculates great-circle distances between the two points – that is, the shortest distance over the earth’s surface – using the ‘Haversine’ formula.

function getDistanceFromLatLonInKm(lat1,lon1,lat2,lon2) {
  var R = 6371; // Radius of the earth in km
  var dLat = deg2rad(lat2-lat1);  // deg2rad below
  var dLon = deg2rad(lon2-lon1); 
  var a = 
    Math.sin(dLat/2) * Math.sin(dLat/2) +
    Math.cos(deg2rad(lat1)) * Math.cos(deg2rad(lat2)) * 
    Math.sin(dLon/2) * Math.sin(dLon/2)
    ; 
  var c = 2 * Math.atan2(Math.sqrt(a), Math.sqrt(1-a)); 
  var d = R * c; // Distance in km
  return d;
}

function deg2rad(deg) {
  return deg * (Math.PI/180)
}

Calculate distance between 2 GPS coordinates

Calculate the distance between two coordinates by latitude and longitude, including a Javascript implementation.

West and South locations are negative. Remember minutes and seconds are out of 60 so S31 30' is -31.50 degrees.

Don't forget to convert degrees to radians. Many languages have this function. Or its a simple calculation: radians = degrees * PI / 180.

function degreesToRadians(degrees) {
  return degrees * Math.PI / 180;
}

function distanceInKmBetweenEarthCoordinates(lat1, lon1, lat2, lon2) {
  var earthRadiusKm = 6371;

  var dLat = degreesToRadians(lat2-lat1);
  var dLon = degreesToRadians(lon2-lon1);

  lat1 = degreesToRadians(lat1);
  lat2 = degreesToRadians(lat2);

  var a = Math.sin(dLat/2) * Math.sin(dLat/2) +
          Math.sin(dLon/2) * Math.sin(dLon/2) * Math.cos(lat1) * Math.cos(lat2); 
  var c = 2 * Math.atan2(Math.sqrt(a), Math.sqrt(1-a)); 
  return earthRadiusKm * c;
}

Here are some examples of usage:

distanceInKmBetweenEarthCoordinates(0,0,0,0)  // Distance between same 
                                              // points should be 0
0

distanceInKmBetweenEarthCoordinates(51.5, 0, 38.8, -77.1) // From London
                                                          // to Arlington
5918.185064088764

Best Answer

Related Solutions

Calculate distance between two latitude-longitude points? (Haversine formula)

Calculate distance between 2 GPS coordinates

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