Check if point is inside circle

Question

I have a GPS Coordinate of a spot called spotCoordinates and a center the a circle coordinates this.state.center and a radius in kilometers this.state.radius

I'm trying to make a method to check if the spotCoordinates is inside a circle but I don't know how I can add the radius to the coordinates and how to check if it's actually inside or not. It would be easier if it was a square.

 calculateParkingSpotsInTheArea = () => {
      this.state.parkingSpots.map(spot => {
          let spotCoordinates = spot.coordinates;
          console.log(spotCoordinates, this.state.center, this.state.radius);
          // Calculate if the parking spot is inside the circle
      });
  }

E.g Values printed in the console spotCoordinates = [41.5408446218337, -8.612296123028727] center = {lat: 41.536558, lng: -8.627487} radius = 25

Any help?

This thread might be useful for you https://stackoverflow.com/questions/14560999/using-the-haversine-formula-in-javascript — user3783243, Jan 07 '20 at 18:10
Use the Pythagorean Theorem to find the distance from the circle's midpoint. If it is less than the diameter of the circle, the point is inside. — Mike Robinson, Jan 07 '20 at 18:12
@user3783243 it's different. I don't have 2 coordinates. I need to calculate the circle "edges" from the center and radius — user12361681, Jan 07 '20 at 18:14
`41.5408446218337, -8.612296123028727` is one point and `41.536558, lng: -8.627487` is the other, no? — user3783243, Jan 07 '20 at 18:20
@user3783243 i tried the haversineDistance method and gives me strange values like `0.0021208675369022113`. How do I know if it's inside or not? — user12361681, Jan 07 '20 at 18:22
@user12361681 That is the distance between point 1 and point 2, in miles, so if you want it within the radius divide by 2, so if the return is < 12.5 it is within range — user3783243, Jan 07 '20 at 18:29

Addis · Accepted Answer · 2020-01-07T19:33:03.367

Credit to this SO link and Great-circle distance

let spotCoordinates1 = [41.5408446218337, -8.612296123028727];
let spotCoordinates2 = [38.817459, -9.282218]

let center = {lat: 41.536558, lng: -8.627487};
let radius = 25

checkIfInside(spotCoordinates1);
checkIfInside(spotCoordinates2);

function checkIfInside(spotCoordinates) {

    let newRadius = distanceInKmBetweenEarthCoordinates(spotCoordinates[0], spotCoordinates[1], center.lat, center.lng);
    console.log(newRadius)

    if( newRadius < radius ) {
        //point is inside the circle
        console.log('inside')
    }
    else if(newRadius > radius) {
        //point is outside the circle
        console.log('outside')
    }
    else {
        //point is on the circle
        console.log('on the circle')
    }

}

function distanceInKmBetweenEarthCoordinates(lat1, lon1, lat2, lon2) {
  var earthRadiusKm = 6371;

  var dLat = degreesToRadians(lat2-lat1);
  var dLon = degreesToRadians(lon2-lon1);

  lat1 = degreesToRadians(lat1);
  lat2 = degreesToRadians(lat2);

  var a = Math.sin(dLat/2) * Math.sin(dLat/2) +
          Math.sin(dLon/2) * Math.sin(dLon/2) * Math.cos(lat1) * Math.cos(lat2); 
  var c = 2 * Math.atan2(Math.sqrt(a), Math.sqrt(1-a)); 
  return earthRadiusKm * c;
}

function degreesToRadians(degrees) {
  return degrees * Math.PI / 180;
}

can you give me a coordinate that is outside? – Addis Jan 07 '20 at 18:46 — Addis, Jan 07 '20 at 18:46

Titus · Answer 2 · 2020-01-07T19:37:32.677

1

You can calculate the point's distance from the center and see if that is smaller then the radius, here is an example:

const spotCoordinates = {
  lat: 41.5408446218337,
  lng: -8.612296123028727
};
const center = {
  lat: 41.536558,
  lng: -8.627487
};
const radius = 25;


function degreesToRadians(degrees) {
  return degrees * Math.PI / 180;
}

function distanceInKmBetweenEarthCoordinates(lat1, lon1, lat2, lon2) {
  var earthRadiusKm = 6371;

  var dLat = degreesToRadians(lat2-lat1);
  var dLon = degreesToRadians(lon2-lon1);

  lat1 = degreesToRadians(lat1);
  lat2 = degreesToRadians(lat2);

  var a = Math.sin(dLat/2) * Math.sin(dLat/2) +
          Math.sin(dLon/2) * Math.sin(dLon/2) * Math.cos(lat1) * Math.cos(lat2); 
  var c = 2 * Math.atan2(Math.sqrt(a), Math.sqrt(1-a)); 
  return earthRadiusKm * c;
}


function isInCircle(latLng) {
  const distance = distanceInKmBetweenEarthCoordinates(latLng.lat, latLng.lng, center.lat, center.lng);

  const calculationResult = distance <= radius;
  console.log("Is inside", calculationResult);
}

isInCircle(spotCoordinates);

And here is an example of this formula in action using Google Maps: https://jsfiddle.net/dpr9shz3/ to use the demo, just click anywhere on the map and the alert will specify the result of the calculation and whether the circle shape was clicked or not.

edited Jan 07 '20 at 19:37

answered Jan 07 '20 at 18:46

Titus

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I think this assumes that earth is flat. Nearby spots will not work. – user12361681 Jan 07 '20 at 18:48
@user12361681 It will be accurate enough if both the radius and distances are calculated for a flat surface, doing this for a shape like the earth has, it can be quite complex because earth is not a perfect sphere and the calculation will have to take into account how close to the poles the coordinates are. – Titus Jan 07 '20 at 18:56
@user12361681 I don't see any reason why this will not work for nearby spots. – Titus Jan 07 '20 at 18:57
It will work for a 3 mile radius then the error starts growing exponentially. – Luis Cadena Jan 07 '20 at 19:08
@user12361681 I've edited my answer and added a fiddle with a demo. The code here assume that the radius is in KM, the one in the demo uses meters. – Titus Jan 07 '20 at 19:39
@Titus don't you think it's almost the same as my answer? – Addis Jan 07 '20 at 19:44
@Addis I guess we both got the formula for calculating the distance between two points from the same place. – Titus Jan 07 '20 at 19:48

score 0 · Answer 3 · answered Jun 22 '21 at 07:03

An expression for this would be:

(center.x - pt.x)^2 + (center.y - pt.y)^2 < radius^2

You can adjust the comparison operator to check if the pt is on the circle (==) or if it is outside the circle boundary (>).

Here is a JavaScript function that will return -1 if the pt is inside the circle, 0 if it is on the circle and 1 if it is outside the circle.

/**
 * @description Check if a pt is in, on or outside of a circle.
 * @param {[float]} pt The point to test. An array of two floats - x and y coordinates.
 * @param {[float]} center The circle center. An array of two floats - x and y coordinates.
 * @param {float} r The circle radius.
 * @returns {-1 | 0 | 1} -1 if the point is inside, 0 if it is on and 1 if it is outside the circle.
 */
function ptInCircle(pt, center, r) {

    const lhs = Math.pow(center[0] - pt[0], 2) + Math.pow(center[1] - pt[1], 2);
    const rhs = Math.pow(r, 2);

    return lhs < rhs ? -1 : (lhs === rhs ? 0 : 1);
}

If you don't like the shorthand nested ternary operator, you can swap the return line for this:

if (lhs < rhs) {
    return -1
} else if (lhs === rhs) {
    return 0
} else {
    return 1
}

Usage:

ptInCircle([0, 1], [1, 0], 1)
// Returns 1

Check if point is inside circle

3 Answers3