How to calculate the lat/lng of a point a certain distance away from another using Nodejs or javascript

Question

I need to find a square area using a latitude and longitude(x,y) as the following figure

I need to get all the other 3 corner latitude and longitude by adding 10kms to each side. I am using Node.js/javascript to implement this.

and this should work anywhere on the globe? i.e. if (x,y) is (90, 0)? or is it simply a case of (10km due east, 10km south) and (10km south, 10km east) — Jaromanda X, Sep 27 '18 at 05:10
@JaromandaX first of all i need a simple case to east and to south. — Sonia Wilson, Sep 27 '18 at 05:21
@S.Serpooshan you're assuming x,y are geometric coordinates rather than degrees of latitude and longitude — Jaromanda X, Sep 27 '18 at 05:21
by the way, latitude (north/south) is more like `y` and longitude (east/west) is more like `x` — Jaromanda X, Sep 27 '18 at 05:25
Please read [Under what circumstances may I add “urgent” or other similar phrases to my question, in order to obtain faster answers?](//meta.stackoverflow.com/q/326569) - the summary is that this is not an ideal way to address volunteers, and is probably counterproductive to obtaining answers. Please refrain from adding this to your questions. — halfer, Sep 27 '18 at 09:21

score 2 · Accepted Answer · answered Sep 27 '18 at 08:02

Referring to the below geometry diagram, the only co-ordinate you need to calculate is - (x2, y2) and rest of the two co-ordinate you can calculate using current long, lat - (x1, y1) and computed - (x2, y2)

So basically you need a function which will take current lat, long i.e. - (x1, y1), a distance which is √2 * 10km in your example and bearing angle to point (x2, y2) which at 135 degrees.

let llFromDistance = function(latitude, longitude, distance, bearing) {
  // taken from: https://stackoverflow.com/a/46410871/13549 
  // distance in KM, bearing in degrees

  const R = 6378.1; // Radius of the Earth
  const brng = bearing * Math.PI / 180; // Convert bearing to radian
  let lat = latitude * Math.PI / 180; // Current coords to radians
  let lon = longitude * Math.PI / 180;

  // Do the math magic
  lat = Math.asin(Math.sin(lat) * Math.cos(distance / R) + Math.cos(lat) * Math.sin(distance / R) * Math.cos(brng));
  lon += Math.atan2(Math.sin(brng) * Math.sin(distance / R) * Math.cos(lat), Math.cos(distance / R) - Math.sin(lat) * Math.sin(lat));

  // Coords back to degrees and return
  return [(lat * 180 / Math.PI), (lon * 180 / Math.PI)];

}

console.log(llFromDistance(19.0659115, 72.8574557, Math.sqrt(2)*10, 135))

score 1 · Answer 2 · answered Sep 27 '18 at 05:30

Here's a function I've used - not sure of it's usefulness when close to the poles though

const fn = (latitude, longitude, distanceInKm, bearingInDegrees) => {
    const R = 6378.1;
    const dr = Math.PI / 180;
    const bearing = bearingInDegrees * dr;
    let lat = latitude * dr;
    let lon = longitude * dr;

    lat = Math.asin(Math.sin(lat) * Math.cos(distanceInKm / R) + Math.cos(lat) * Math.sin(distanceInKm / R) * Math.cos(bearing));
    lon += Math.atan2(
        Math.sin(bearing) * Math.sin(distanceInKm / R) * Math.cos(lat), 
        Math.cos(distanceInKm / R) - Math.sin(lat) * Math.sin(lat)
    );
    lat /= dr;
    lon /= dr;
    return {lat, lon};
}

so, the points would be

fn(y, x, 10, 90), // top right
fn(y, x, 10 * Math.sqrt(2), 135), // bottom right (Pythagoras rules!)
fn(y, x, 10, 180) // bottom left

How to calculate the lat/lng of a point a certain distance away from another using Nodejs or javascript

2 Answers2