Calculate latitude and longitude having meters distance from another latitude/longitude point

Question

I need to calculate latitude and longitude of a given point.

I know latitude and longitude of a reference point, and an value indicating meters on x and y axis from the reference point. Starting from this data I have to find latitude and longitude of the point.

I searched for similar questions but it looks like most questions are about finding distance between two lat/long points. I need to do the contrary.

How can I do? I use Java

Answer 1

Here is the best starting point for such questions: Aviation Formulary. They have all the formulas for doing such kinds of things.

From these formulary, I created my own Java util class. It uses a lot of internal stuff, so I cannot post the actual class here but to give you some examples on how to convert the knowledge from the formulary into Java code.

Here're some basic methods:

/**
 * the length of one degree of latitude (and one degree of longitude at equator) in meters.
 */
private static final int DEGREE_DISTANCE_AT_EQUATOR = 111329;
/**
 * the radius of the earth in meters.
 */
private static final double EARTH_RADIUS = 6378137; //meters
/**
 * the length of one minute of latitude in meters, i.e. one nautical mile in meters.
 */
private static final double MINUTES_TO_METERS = 1852d;
/**
 * the amount of minutes in one degree.
 */
private static final double DEGREE_TO_MINUTES = 60d;


/**
 * This method extrapolates the endpoint of a movement with a given length from a given starting point using a given
 * course.
 *
 * @param startPointLat the latitude of the starting point in degrees, must not be {@link Double#NaN}.
 * @param startPointLon the longitude of the starting point in degrees, must not be {@link Double#NaN}.
 * @param course        the course to be used for extrapolation in degrees, must not be {@link Double#NaN}.
 * @param distance      the distance to be extrapolated in meters, must not be {@link Double#NaN}.
 *
 * @return the extrapolated point.
 */
public static Point extrapolate(final double startPointLat, final double startPointLon, final double course,
                                final double distance) {
    //
    //lat =asin(sin(lat1)*cos(d)+cos(lat1)*sin(d)*cos(tc))
    //dlon=atan2(sin(tc)*sin(d)*cos(lat1),cos(d)-sin(lat1)*sin(lat))
    //lon=mod( lon1+dlon +pi,2*pi )-pi
    //
    // where:
    // lat1,lon1  -start pointi n radians
    // d          - distance in radians Deg2Rad(nm/60)
    // tc         - course in radians

    final double crs = Math.toRadians(course);
    final double d12 = Math.toRadians(distance / MINUTES_TO_METERS / DEGREE_TO_MINUTES);

    final double lat1 = Math.toRadians(startPointLat);
    final double lon1 = Math.toRadians(startPointLon);

    final double lat = Math.asin(Math.sin(lat1) * Math.cos(d12)
        + Math.cos(lat1) * Math.sin(d12) * Math.cos(crs));
    final double dlon = Math.atan2(Math.sin(crs) * Math.sin(d12) * Math.cos(lat1),
        Math.cos(d12) - Math.sin(lat1) * Math.sin(lat));
    final double lon = (lon1 + dlon + Math.PI) % (2 * Math.PI) - Math.PI;

    return new Point(Math.toDegrees(lat), Math.toDegrees(lon));
}

/**
 * calculates the length of one degree of longitude at the given latitude.
 *
 * @param latitude the latitude to calculate the longitude distance for, must not be {@link Double#NaN}.
 *
 * @return the length of one degree of longitude at the given latitude in meters.
 */
public static double longitudeDistanceAtLatitude(final double latitude) {

    final double longitudeDistanceScaleForCurrentLatitude = Math.cos(Math.toRadians(latitude));
    return DEGREE_DISTANCE_AT_EQUATOR * longitudeDistanceScaleForCurrentLatitude;
}