Generate coordinates with Minimum/Maximum distance from given coordinates

Question

Background:

I am trying to create a coordinates generator for Unit Testing my code. I would like to try to test cases for methods like:

// Check if within 10km.
// Should pass because it is 0 - 10km from location
location.isWithin(generateLocation(location, 10), 10) === true

// Check if within 10km.
// Should fail because it is 20 - 25km from location
location.isWithin(generateLocation(location, 25, 20), 10) === false

I have tried lots of Stackoverflow answers I never found one answer to this problem.

What I have tried:

function generateNearbyLocation(latitude, longitude, max, min = 0) {
  // Convert max in kilometers to degrees
  const radiusInDegrees = (max * 1000) / 111300;

  const u = Math.random();
  const v = Math.random();

  // random radius
  const w = radiusInDegrees * Math.sqrt(u);

  // random angle
  const t = 2 * Math.PI * v;

  const x = w * Math.cos(t);
  const x1 = x / Math.cos(latitude);
  const y1 = w * Math.sin(t);

  // Not working attempt to add Minimum distance
  // const newLatitude = latitude + (min * 1000 / 111300) + y1;
  // const newLongitude = longitude + (min * 1000 / 111300) + x1;

  const newLatitude = latitude + y1;
  const newLongitude = longitude + x1;
  const distance = getDistanceFromLatLonInKm(latitude, longitude, newLatitude, newLongitude);

  return {
    newLatitude,
    newLongitude,
    distance
  };
}

This works but is not accurate. Even with max of 10, it sometimes generate 11km coordinates.

Here's a playground that I made: https://jsbin.com/hakemubogo/edit?js,console

---

EDIT

I found a much more accurate formula from another answer but still can't create minimum distance.

function generateLocation(latitude, longitude, max, min = 0) {
  const EARTH_RADIUS = 6371; // km
  const DEGREE = EARTH_RADIUS * 2 * Math.PI / 360 * 1000; // 1° latitude in meters

  const r = (max * 1000) * Math.random() ** 0.5;
  const theta = Math.random() * 2 * Math.PI; // random * (360deg in radians)

  const dy = r * Math.sin(theta);
  const dx = r * Math.cos(theta);

  const newLatitude = latitude + dy / DEGREE;
  const newLongitude = longitude + dx / (DEGREE * Math.cos(deg2rad(latitude)));
  const distance = getDistanceFromLatLonInKm(latitude, longitude, newLatitude, newLongitude);

  return {
    newLatitude,
    newLongitude,
    distance
  };
}

Answer 1

I was able to finally figure it out. According to this answer:

If you have a center (x,y) and you move on the x axis by 30 meters and on the y axis by another 30 meters your distance from the center won't be 30.

It turns out the variable r should be the one I'm adjusting and not the newLatitude and newLongitude.

(max * 1000) * Math.random() ** 0.5 is only generating random [0 - max] value (in a non-uniform way).

Therefore, what I need to add is just add the minimum distance on variable r so it generates [min-max]

const maxKm = max * 1000;
const minKm = min * 1000;
const r = ((maxKm - minKm + 1) * Math.random() ** 0.5) + minKm;

See this answer how to generate number within range: link.

The only thing I added is the ** 0.5 part.

Full code:

// Final Code Here
function generateLocation(latitude, longitude, max, min = 0) {
  if (min > max) {
    throw new Error(`min(${min}) cannot be greater than max(${max})`);
  }

  // earth radius in km
  const EARTH_RADIUS = 6371;

   // 1° latitude in meters
  const DEGREE = EARTH_RADIUS * 2 * Math.PI / 360 * 1000;

  // random distance within [min-max] in km in a non-uniform way
  const maxKm = max * 1000;
  const minKm = min * 1000;
  const r = ((maxKm - minKm + 1) * Math.random() ** 0.5) + minKm;

  // random angle
  const theta = Math.random() * 2 * Math.PI;

  const dy = r * Math.sin(theta);
  const dx = r * Math.cos(theta);

  let newLatitude = latitude + dy / DEGREE;
  let newLongitude = longitude + dx / (DEGREE * Math.cos(deg2rad(latitude)));

  const distance = getDistanceFromLatLonInKm(latitude, longitude, newLatitude, newLongitude);

  return {
    newLatitude,
    newLongitude,
    distance: Math.round(distance)
  };
}

// See https://stackoverflow.com/a/27943/10975709
function getDistanceFromLatLonInKm(lat1,lon1,lat2,lon2) {
  var R = 6371; // Radius of the earth in km
  var dLat = deg2rad(lat2-lat1);  // deg2rad below
  var dLon = deg2rad(lon2-lon1); 
  var a = 
    Math.sin(dLat/2) * Math.sin(dLat/2) +
    Math.cos(deg2rad(lat1)) * Math.cos(deg2rad(lat2)) * 
    Math.sin(dLon/2) * Math.sin(dLon/2)
    ; 
  var c = 2 * Math.atan2(Math.sqrt(a), Math.sqrt(1-a)); 
  var d = R * c; // Distance in km

  return d;
}

function deg2rad(deg) {
  return deg * (Math.PI/180)
}

console.log(generateLocation(15.143262, 120.583843, 25, 20))