midpoint between two latitude and longitude

Question

I am trying to convert the code snippet given in this http://www.movable-type.co.uk/scripts/latlong.html into java. But I am not getting same result as that of site. Here is my code to find the midpoint between two points where their latitudes and longitudes are given

midPoint(12.870672,77.658964,12.974831,77.60935);
    public static void midPoint(double lat1,double lon1,double lat2,double lon2)
    {
   double dLon = Math.toRadians(lon2-lon1);
        double Bx = Math.cos(lat2) * Math.cos(dLon);
        double By = Math.cos(lat2) * Math.sin(dLon);
        double lat3 = Math.atan2(Math.sin(lat1)+Math.sin(lat2),Math.sqrt( (Math.cos(lat1)+Bx)*(Math.cos(lat1)+Bx) + By*By) );
        double lon3 = lon1 + Math.atan2(By, Math.cos(lat1) + Bx);
        System.out.print(lat3 +" " + lon3 );
    }

I am not sure whethe dLon is correct or not. So please help me guys to figure it out. P.S.I need to find the latitude and longitude of the midpoint

score 79 · Accepted Answer · answered Jan 11 '11 at 11:08

You need to convert to radians. Change it to the following:

public static void midPoint(double lat1,double lon1,double lat2,double lon2){

    double dLon = Math.toRadians(lon2 - lon1);

    //convert to radians
    lat1 = Math.toRadians(lat1);
    lat2 = Math.toRadians(lat2);
    lon1 = Math.toRadians(lon1);

    double Bx = Math.cos(lat2) * Math.cos(dLon);
    double By = Math.cos(lat2) * Math.sin(dLon);
    double lat3 = Math.atan2(Math.sin(lat1) + Math.sin(lat2), Math.sqrt((Math.cos(lat1) + Bx) * (Math.cos(lat1) + Bx) + By * By));
    double lon3 = lon1 + Math.atan2(By, Math.cos(lat1) + Bx);

    //print out in degrees
    System.out.println(Math.toDegrees(lat3) + " " + Math.toDegrees(lon3));
}

hi @dogbane i need one help. http://stackoverflow.com/questions/11758582/find-if-the-current-location-is-along-a-straight-line-drawn-between-two-points — RVG, Aug 03 '12 at 05:01

score 25 · Answer 2 · edited Dec 04 '18 at 10:29

25

Even easier with Android Google Maps Utilities:

LatLngBounds bounds = new LatLngBounds(start, dest);
bounds.getCenter();

Update: Better use the builder (for why see Bad Losers Answer):

LatLngBounds.builder().include(start).include(dest).build().getCenter();

edited Dec 04 '18 at 10:29

GhostCat

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answered Aug 24 '17 at 18:37

leonardkraemer

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Works well, and saved me some coding. Thanks. – dazed Jan 29 '18 at 11:18
@leonardkraemer OK but not perfect [antimeridian transgression not handled] - see my answer below. Thanks for putting me on the right track. – Bad Loser Sep 06 '18 at 21:55
As far as I remember the constructor even complains, when you put NE before SW so definitely use the builder. I probably kept my answer too simple just to point people in the right direction. Thanks for the hint. – leonardkraemer Sep 06 '18 at 23:00
Thank you very much for the 'update' section. Solved my problem. – DmitryKanunnikoff Nov 17 '18 at 19:25

Bad Loser · Answer 3 · 2018-09-06T21:48:57.327

Please use LatLngBounds with the builder rather than the constructor if you want to correctly handle transgression of the antimeridian (longitude +/-180).

Here is the test illustrating the problem:

LatLng mp = midPoint(new LatLng(-43.95139,-176.56111),new LatLng(-36.397816,174.663496));
public static LatLng midPoint (LatLng SW, LatLng NE) {
    LatLngBounds bounds = new LatLngBounds(SW, NE);
    Log.d("BAD!", bounds.toString() + " CENTRE: " + bounds.getCenter().toString());
    bounds = LatLngBounds.builder().include(SW).include(NE).build();
    Log.d("GOOD", bounds.toString() + " CENTRE: " + bounds.getCenter().toString());
    return bounds.getCenter();
}

Actual results:

BAD!: LatLngBounds{southwest=lat/lng: (-43.95139,-176.56111), northeast=lat/lng: (-36.397816,174.663496)} CENTRE: lat/lng: (-40.174603,-0.948807)
GOOD: LatLngBounds{southwest=lat/lng: (-43.95139,174.663496), northeast=lat/lng: (-36.397816,-176.56111)} CENTRE: lat/lng: (-40.174603,179.051193)

The constructor technique produces a central longitude out by 180 degrees!

score 1 · Answer 4 · answered Jan 11 '11 at 11:07

You need to convert you lat and lon values used in the other formulas to Radians also. You can see this in the code ~3/5ths of the way down the page. The clue was given at the end of the spherical law of cosines distance formula:

(Note that here and in all subsequent code fragments, for simplicity I do not show conversions from degrees to radians; see below for complete versions).

score 1 · Answer 5 · answered Dec 09 '20 at 07:52

Here's @dogbane's Java code converted to TypeScript.

type LatLng = {
  lat: number;
  lng: number;
};

function calculateMidPoint(latLngA: LatLng, latLngB: LatLng) {
  function toRadians(degress: number): number {
    return degress * (Math.PI / 180);
  }

  function toDegrees(radians: number): string {
    return (radians * (180 / Math.PI)).toFixed(4);
  }

  const lngDiff = toRadians(latLngB.lng - latLngA.lng);
  const latA = toRadians(latLngA.lat);
  const latB = toRadians(latLngB.lat);
  const lngA = toRadians(latLngA.lng);

  const bx = Math.cos(latB) * Math.cos(lngDiff);
  const by = Math.cos(latB) * Math.sin(lngDiff);

  const latMidway = toDegrees(
    Math.atan2(
      Math.sin(latA) + Math.sin(latB),
      Math.sqrt((Math.cos(latA) + bx) * (Math.cos(latA) + bx) + by * by)
    )
  );
  const lngMidway = toDegrees(lngA + Math.atan2(by, Math.cos(latA) + bx));

  console.log(
    `Midway point between ${latLngA} and ${latLngB} is: Lat: ${latMidway}, lng: ${lngMidway}`
  );
}

score 0 · Answer 6 · answered Nov 25 '20 at 15:11

Following is @dogbane 's java code converted to Kotlin:

private fun midPoint(lat1: Double, lon1: Double, lat2: Double, lon2: Double) : String {
    var lat1 = lat1
    var lon1 = lon1
    var lat2 = lat2
    val dLon: Double = Math.toRadians(lon2 - lon1)
    //convert to radians
    lat1 = Math.toRadians(lat1)
    lat2 = Math.toRadians(lat2)
    lon1 = Math.toRadians(lon1)
    val Bx: Double = Math.cos(lat2) * Math.cos(dLon)
    val By: Double = Math.cos(lat2) * Math.sin(dLon)
    val lat3: Double = Math.atan2(Math.sin(lat1) + Math.sin(lat2), Math.sqrt((Math.cos(lat1) + Bx) * (Math.cos(lat1) + Bx) + By * By))
    val lon3: Double = lon1 + Math.atan2(By, Math.cos(lat1) + Bx)
    var result: String = ""
    result = Math.toDegrees(lat3).toString() + "," + Math.toDegrees(lon3).toString()
    return result;
}

score -2 · Answer 7 · answered Jan 11 '11 at 11:08

My last job I made a tracking module and I was using this formula to calculate the distance between 2 coordinates.

//Location lat and lon
double locLat = -23.548333;
double locLon = -46.636111;

//Destination lat and lon
double dstLat = -22.902778;
double dstLon = -43.206667;

double arcoAB = 90 - (dstLat);
double arcoAC = 90 - (locLat);

double difLon = locLon - (dstLon);

double cosA = Math.cos(Math.toRadians(arcoAC)) * Math.cos(Math.toRadians(arcoAB)) + Math.sin(Math.toRadians(arcoAC)) * Math.sin(Math.toRadians(arcoAB)) * Math.cos(Math.toRadians(difLon));
double acosCosA = Math.toDegrees(Math.acos(cosA));

double raio = 2 * Math.PI * 6371;
double distance = (raio * acosCosA) / 360;

return distance; //Distance in KM, convert to anything else (miles, meters..) if you need..

You can get the mid point dividing the distance by 2.

Ah, this another formula works too:

double dLat = Math.toRadians(dstLat - locLat);
double dLon = Math.toRadians(dstLon - locLon);

double a = Math.sin(dLat / 2) * Math.sin(dLat / 2)
           + Math.cos(Math.toRadians(locLat)) * Math.cos(Math.toRadians(dstLat))
           * Math.sin(dLon / 2) * Math.sin(dLon / 2);
double c = 2 * Math.atan2(Math.sqrt(a), Math.sqrt(1 - a));
double d = 6371 * c;

return d; //Distance in KM

But I need to find the latitude and longitude of the midpoint. How to do that? — CrazyCoder, Jan 11 '11 at 11:19

midpoint between two latitude and longitude

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