Adding distance to a GPS coordinate

Question

I'm trying to generate some points at random distances away from a fixed point using GPS.

How can I add distance in meters to a GPS coordinate? I've looked at UTM to GPS conversion but is there a simpler method to achieve this?

I'm working on Android platform just in case.

Cheers, fgs

Answer 1

• P0(lat0,lon0) : initial position (unit : degrees)
• dx,dy : random offsets from your initial position in meters

You can use an approximation to compute the position of the randomized position:

 lat = lat0 + (180/pi)*(dy/6378137)
 lon = lon0 + (180/pi)*(dx/6378137)/cos(lat0)

This is quite precise as long as the random distance offset is below 10-100 km

Edit: of course in Java Math.cos() expects radians so do use Math.cos(Math.PI/180.0*lat0) if lat0 is in degrees as assumed above.

Answer 2

To take a square I'm using this:

 private double[] getBoundingBox(final double pLatitude, final double pLongitude, final int pDistanceInMeters) {

    final double[] boundingBox = new double[4];

    final double latRadian = Math.toRadians(pLatitude);

    final double degLatKm = 110.574235;
    final double degLongKm = 110.572833 * Math.cos(latRadian);
    final double deltaLat = pDistanceInMeters / 1000.0 / degLatKm;
    final double deltaLong = pDistanceInMeters / 1000.0 / degLongKm;

    final double minLat = pLatitude - deltaLat;
    final double minLong = pLongitude - deltaLong;
    final double maxLat = pLatitude + deltaLat;
    final double maxLong = pLongitude + deltaLong;

    boundingBox[0] = minLat;
    boundingBox[1] = minLong;
    boundingBox[2] = maxLat;
    boundingBox[3] = maxLong;

    return boundingBox;
}

This returns an array with 4 coordinates, with them you can make a square with your original point in center.

Answer 3

A detailed outline is given at http://www.movable-type.co.uk/scripts/latlong.html.

If you, somewhere, need to interconvert longitude/latitude to UTM coordinates (the ones used in GPS) you may want to have a look at http://www.uwgb.edu/dutchs/UsefulData/UTMFormulas.htm

Answer 4

If you want to go east or north or west or south you can use this:

@SuppressLint("DefaultLocale")
public static double go_mock_loc(double xx_lat,double xx_long,double xx_dinstance,String Direction)
{
//  double xx_lat= 45.815005; 
//  double xx_long= 15.978501;

//  int xx_dinstance=500;

    int equator_circumference=6371000;
    int polar_circumference=6356800;

    double m_per_deg_long =  360 / polar_circumference;
    double rad_lat=(xx_lat* (Math.PI) / 180);
    double m_per_deg_lat = 360 / ( Math.cos(rad_lat) * equator_circumference);

    double deg_diff_long = xx_dinstance * m_per_deg_long;
    double deg_diff_lat  = xx_dinstance * m_per_deg_lat; 


    double xx_north_lat = xx_lat + deg_diff_long;
    //double xx_north_long= xx_long;
    double xx_south_lat = xx_lat - deg_diff_long;
    //double xx_south_long= xx_long;

    //double xx_east_lat = xx_lat;
    double xx_east_long= xx_long + deg_diff_lat;  
    //double xx_west_lat = xx_lat;
    double xx_west_long= xx_long - deg_diff_lat;

    if (Direction.toUpperCase().contains("NORTH")) {
        return xx_north_lat;
    } else if (Direction.toUpperCase().contains("SOUTH"))
    {
        return xx_south_lat;
    } else if (Direction.toUpperCase().contains("EAST"))
    {
        return xx_east_long;
    } else if (Direction.toUpperCase().contains("WEST"))
    {
        return xx_west_long;
    }
    else 
        return 0; 

}

Answer 5

rewrite @Ersin Gülbahar answer in Kotlin:

object LocationUtil {

enum class Direction {
    NORTH, SOUTH, EAST, WEST
}

fun addDistanceInMeters(
    latitude: Double,
    longitude: Double,
    distanceInMeters: Int,
    direction: Direction
): Pair<Double, Double> {
    val equatorCircumference = 6371000
    val polarCircumference = 6356800

    val mPerDegLong = (360 / polarCircumference.toDouble())
    val radLat = latitude * Math.PI / 180
    val mPerDegLat = 360 / (Math.cos(radLat) * equatorCircumference)

    val degDiffLong = distanceInMeters * mPerDegLong
    val degDiffLat = distanceInMeters * mPerDegLat

    val xxNorthLat = latitude + degDiffLong
    val xxSouthLat = latitude - degDiffLong
    val xxEastLong = longitude + degDiffLat
    val xxWestLong = longitude - degDiffLat

    return when (direction) {
        Direction.NORTH -> Pair(xxNorthLat, longitude)
        Direction.SOUTH -> Pair(xxSouthLat, longitude)
        Direction.EAST -> Pair(latitude, xxEastLong)
        Direction.WEST -> Pair(latitude, xxWestLong)
    }
}

}

Answer 6

I found that solution of @Bogdan Khrystov is very well. So here is C# version of his solution.

public enum GeoDirection
{
   NORTH = 1, SOUTH = 2, EAST = 3, WEST = 4
}            
    
public static Tuple<double, double> AddDistanceInMeters(double latitude, double longitude, int distanceInMeters, GeoDirection direction)
{
  var equatorCircumference = 6371000;
  var polarCircumference = 6356800;
    
  var mPerDegLong = 360 / (double)polarCircumference;
  var radLat = latitude * Math.PI / 180;
  var mPerDegLat = 360 / (Math.Cos(radLat) * equatorCircumference);
    
  var degDiffLong = distanceInMeters * mPerDegLong;
  var degDiffLat = distanceInMeters * mPerDegLat;
    
  var xxNorthLat = latitude + degDiffLong;
  var xxSouthLat = latitude - degDiffLong;
  var xxEastLong = longitude + degDiffLat;
  var xxWestLong = longitude - degDiffLat;
    
  switch (direction)
  {
    case GeoDirection.NORTH:
       return new Tuple<double, double>(xxNorthLat, longitude);
    case GeoDirection.SOUTH:
       return new Tuple<double, double>(xxSouthLat, longitude);
    case GeoDirection.EAST:
       return new Tuple<double, double>(latitude, xxEastLong);
    case GeoDirection.WEST:
       return new Tuple<double, double>(latitude, xxWestLong);
    default:
       return null;
    }
}