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;
}

Remotion

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.

Tropho

Right! But still input params are ProcJobLocation.bearing(53.944592, 27.595215, 55.745752, 37.630768); and output is 359.11592632310266. Still there is some mistake. – Remotion

Your inputs seem to be in degrees. You need to convert them to radians using Math.toRadians(), otherwise Math.sin(), Math.cos() etc will give wrong results. – Tropho

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;
}

Remotion

where lat1, lon1, lat2 and lon2 are in radians???! Probably not. so why do you rename longitude1 and longitude2 ?? – Nonresident

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;
        }
            }

Azzieb

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;
    }
}

Grabowski