Calculate bearing between two locations (lat, long)

Question

I\'m trying to develop my own augmented reality engine.

Searching on internet, I\'ve found this useful tutorial. Reading it I see that the important thing is bearing

Answer 1

/* Kirit vaghela answer has been modified.. Math.sin gives the radian value so to get degree value we need to pass Math.toRadians(value) inside Math.sin() or Math.cos() */

    double lat1 = 39.099912;
    double lat2 = 38.627089;
    double lng1 = -94.581213;
    double lng2 = -90.200203;

    double dLon = (lng2-lng1);
    double x = Math.sin(Math.toRadians(dLon)) * Math.cos(Math.toRadians(lat2));
    double y = Math.cos(Math.toRadians(lat1))*Math.sin(Math.toRadians(lat2)) - Math.sin(Math.toRadians(lat1))*Math.cos(Math.toRadians(lat2))*Math.cos(Math.toRadians(dLon));
    double bearing = Math.toDegrees((Math.atan2(x, y)));
    System.out.println("BearingAngle : "+bearing);

Answer 2

In the formula

float possibleAzimuth = (M_PI * .5f) - atan(latitudinalDifference / longitudinalDifference);

the term (M_PI * .5f) means π/2 which is 90°. That means that it is the same formula that you stated at first, because regarding to the figure above it holds

β = arctan (a/b) = 90° - arctan(b/a).

So both formulas are similar if a refers to the difference in longitude and b in the difference in latitude. The last formula calculates again the same using the first part of my equation.

Answer 3

I know this question is old, but here is an easier solution:

float bearing = loc1.bearingTo(loc2);

Answer 4

If you want you can take a look at the code used in mixare augmented reality engine, it's on github and there's an iPhone version as well: github.com/mixare

Answer 5

Try this for accurate result:

private static double degreeToRadians(double latLong) {
    return (Math.PI * latLong / 180.0);
}

private static double radiansToDegree(double latLong) {
    return (latLong * 180.0 / Math.PI);
}

public static double getBearing() {

//Source
JSONObject source = step.getJSONObject("start_location");
double lat1 = Double.parseDouble(source.getString("lat"));
double lng1 = Double.parseDouble(source.getString("lng"));

// destination
JSONObject destination = step.getJSONObject("end_location");
double lat2 = Double.parseDouble(destination.getString("lat"));
double lng2 = Double.parseDouble(destination.getString("lng"));

    double fLat = degreeToRadians(lat1);
    double fLong = degreeToRadians(lng1);
    double tLat = degreeToRadians(lat2);
    double tLong = degreeToRadians(lng2);

    double dLon = (tLong - fLong);

    double degree = radiansToDegree(Math.atan2(sin(dLon) * cos(tLat),
            cos(fLat) * sin(tLat) - sin(fLat) * cos(tLat) * cos(dLon)));

    if (degree >= 0) {
        return degree;
    } else {
        return 360 + degree;
    }
}

You can test bearing result on http://www.sunearthtools.com/tools/distance.php .

Answer 6

Calculate bearing

//Source
JSONObject source = step.getJSONObject("start_location");
double lat1 = Double.parseDouble(source.getString("lat"));
double lng1 = Double.parseDouble(source.getString("lng"));

// destination
JSONObject destination = step.getJSONObject("end_location");
double lat2 = Double.parseDouble(destination.getString("lat"));
double lng2 = Double.parseDouble(destination.getString("lng"));

double dLon = (lng2-lng1);
double y = Math.sin(dLon) * Math.cos(lat2);
double x = Math.cos(lat1)*Math.sin(lat2) - Math.sin(lat1)*Math.cos(lat2)*Math.cos(dLon);
double brng = Math.toDegrees((Math.atan2(y, x)));
brng = (360 - ((brng + 360) % 360));

Convert Degrees into Radians

Radians = Degrees * PI / 180

Convert Radians into Degrees

Degrees = Radians * 180 / PI