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?

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?

• javascript

• This thread might be useful for you stackoverflow./questions/14560999/… – user3783243 Commented Jan 7, 2020 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 Commented Jan 7, 2020 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 Commented Jan 7, 2020 at 18:14
• 2 @MikeRobinson You mean "if it is less than the radius ..." – Teemu Commented Jan 7, 2020 at 18:16
• 41.5408446218337, -8.612296123028727 is one point and 41.536558, lng: -8.627487 is the other, no? – user3783243 Commented Jan 7, 2020 at 18:20

3 Answers 3

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;
}

An expression for this would be:

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

You can adjust the parison 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

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/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.