Bearing from one coordinate to another

Question

I implemented the "bearing" formula from http://www.movable-type.co.uk/scripts/latlong.html. But it seems highly inaccurate - I suspect some mistakes in my implementation. Could you help me with finding it? My code is below:

protected static double bearing(double lat1, double lon1, double lat2, double lon2){

double longDiff= lon2-lon1;
double y = Math.sin(longDiff)*Math.cos(lat2);
double x = Math.cos(lat1)*Math.sin(lat2)-Math.sin(lat1)*Math.cos(lat2)*Math.cos(longDiff);

return Math.toDegrees((Math.atan2(y, x))+360)%360;
}

Answer 1

You just have your parentheses () in the wrong place.

You are adding degrees to a value in radians, which won't work. toDegrees() will do the conversion from radians to degrees for you, then you do the normalisation once you have a value in degrees.

You have:

 Math.toDegrees( (Math.atan2(y, x))+360 ) % 360;

But you need:

( Math.toDegrees(Math.atan2(y, x)) + 360 ) % 360;

Remember also that all inputs to Math.sin(), Math.cos() and all the other trigonometric functions must be in radians. If your inputs are degrees you'll need to convert them using Math.toRadians() first.

Answer 2

Here is the final code:

protected static double bearing(double lat1, double lon1, double lat2, double lon2){
  double longitude1 = lon1;
  double longitude2 = lon2;
  double latitude1 = Math.toRadians(lat1);
  double latitude2 = Math.toRadians(lat2);
  double longDiff= Math.toRadians(longitude2-longitude1);
  double y= Math.sin(longDiff)*Math.cos(latitude2);
  double x=Math.cos(latitude1)*Math.sin(latitude2)-Math.sin(latitude1)*Math.cos(latitude2)*Math.cos(longDiff);

  return (Math.toDegrees(Math.atan2(y, x))+360)%360;
}

Answer 3

Bearing from one coordinate to another And Find North,East,south,weast :)

     public class FindBearing {
            public static void main(String[] args) {
                System.out.println(" Your Result >>> "+FindBearing.bearing(19.2859590, 73.4966430, 19.2861020, 73.4988090));    
            }   
            protected static String bearing(double lat1, double lon1, double lat2, double lon2){
          double longitude1 = lon1;
          double longitude2 = lon2;
          double latitude1 = Math.toRadians(lat1);
          double latitude2 = Math.toRadians(lat2);
          double longDiff= Math.toRadians(longitude2-longitude1);
          double y= Math.sin(longDiff)*Math.cos(latitude2);
          double x=Math.cos(latitude1)*Math.sin(latitude2)-Math.sin(latitude1)*Math.cos(latitude2)*Math.cos(longDiff);
          double resultDegree= (Math.toDegrees(Math.atan2(y, x))+360)%360;
          String coordNames[] = {"N","NNE", "NE","ENE","E", "ESE","SE","SSE", "S","SSW", "SW","WSW", "W","WNW", "NW","NNW", "N"};
          double directionid = Math.round(resultDegree / 22.5); 
          // no of array contain 360/16=22.5
          if (directionid < 0) {
              directionid = directionid + 16;
               //no. of contains in array
          }
          String compasLoc=coordNames[(int) directionid];

          return resultDegree+" "+compasLoc;
        }
            }

Answer 4

A little bit cleaned up version of @IvanT answer:

public static double bearingInRadians(LatLng src, LatLng dst) {
    double srcLat = Math.toRadians(src.getLatitude());
    double dstLat = Math.toRadians(dst.getLatitude());
    double dLng = Math.toRadians(dst.getLongitude() - src.getLongitude());

    return Math.atan2(Math.sin(dLng) * Math.cos(dstLat),
            Math.cos(srcLat) * Math.sin(dstLat) - 
              Math.sin(srcLat) * Math.cos(dstLat) * Math.cos(dLng));
}

public static double bearingInDegrees(LatLng src, LatLng dst) {
    return Math.toDegrees((bearingInRadians(src, dst) + Math.PI) % Math.PI);
}

Where LatLng is:

public final class LatLng {
    private final double latitude;
    private final double longitude;

    public LatLng(double latitude, double longitude) {
        this.latitude = latitude;
        this.longitude = longitude;
    }

    public double getLatitude() {
        return latitude;
    }

    public double getLongitude() {
        return longitude;
    }
}