CODEWITHSUNDEEP
javascriptmath
Igor P.
Igor P.

Reputation: 1477

Calculating position from another GPS position + distance

Developing a Javascript application, I am looking for a way to calculate the GPS coordinates of a target point, coming from another position (latitude|longitude) + a certain distance (e. g. 20km further south). To express this as a spoken question one could say: what are the GPS coordinates of my current position plus 20 km to the north|south?

Pseudo formula:

TargetPosition = KnownPosition + Distance

where:

Any ideas for the fomula?

Upvotes: 1

Views: 1459

Answers (2)

Terry Lennox
Terry Lennox

Reputation: 30725

Once we know the meridional distance in km, and knowing this is 360° of latitude, we can calculate the offset due to moving north or south by x kilometres.

For every degree we move north or south we move (40007.86 / 360) = 111.13 km.

Also we'll include some error checking for locations near the poles..

And I'll add a more general formula for getting a new location given an offset north and east. (Negative for south and west as is the usual convention), this will only be accurate for small displacements.

function getNewLatitude(latitude, distanceKm) {
    const meridionalRadiuskm = 40007.86;
    latitude = (latitude + distanceKm / (meridionalRadiuskm / 360));
    if (latitude > 90) return 180 - latitude;
    if (latitude < -90) return -(180 + latitude);
    return latitude;
}

console.log(getNewLatitude(50, 100));
console.log(getNewLatitude(50, -100));

// This function may also be useful, you can use this to get a new location base on a north/south / east/west offset in km. Note that accuracy will start to reduce as the offset increases. 
function getNewLocation(lat, lon, offsetNorthKm, offsetEastKm) {
    // The approximate distance in kilometres of one degree at 0,0.
    const ONE_DEGREE_KM = 111.32;

    const deltaLatitude = offsetNorthKm / ONE_DEGREE_KM;
    const deltaLongitude = offsetEastKm / (ONE_DEGREE_KM * Math.cos(Math.PI * lat / 180));

    let result = { 
        lat:  lat + deltaLatitude,
        lon:  lon + deltaLongitude
    }
    return result;
}

Upvotes: 2

adelriosantiago
adelriosantiago

Reputation: 8134

You can use the Geolib library and it will give you more precise results especially near the poles.

Example: This will compute 15000 meters bearing 180 degress (south) from the provided lat/long.

geolib.computeDestinationPoint(
    { latitude: 52.518611, longitude: 13.408056 },
    15000,
    180
);

Note that the direction is given in degrees (0 = 360 = north, 180 = south, etc). Using this library will also allow you do other interesting computations like:

  • Get distances between 2 points
  • Get center of an array of points
  • Get compass direction
  • Find nearest point
  • and more

Upvotes: 1

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