Haversine formula with php

I want to use this formula with php. I have a database with some values of latitute and longitude saved.

I want to find, with a certain value of latitude and longitude in input, all the distances (in km) from this point with each point in the database. To do this, I used the formula on googlemaps api:

( 6371 * acos( cos( radians(37) ) * cos( radians( lat ) ) * cos( radians( lng ) - radians(-122) ) + sin( radians(37) ) * sin( radians( lat ) ) ) )

Of course using that in php I replaced radians with deg2rad.The values 37,-122 are my values of input and lat,lng are my values in the database.

Below there is my code. The problem is that there is something wrong but I don't understand what. The value of distance is of course wrong.

//values of latitude and longitute in input (Rome - eur, IT)
$center_lat = "41.8350";
$center_lng =  "12.470";

//connection to database. it works
(..)

//to take each value in the database:
    $query = "SELECT * FROM Dati";
    $result = mysql_query($query);
    while ($row = @mysql_fetch_assoc($result)){
        $lat=$row['Lat']);
        $lng=$row['Lng']);
    $distance =( 6371 * acos((cos(deg2rad($center_lat)) ) * (cos(deg2rad($lat))) * (cos(deg2rad($lng) - deg2rad($center_lng)) )+ ((sin(deg2rad($center_lat))) * (sin(deg2rad($lat))))) );
    }

For values for example: $lat= 41.9133741000 $lng= 12.5203944000

I have the output of distance="4826.9341106926"

Answers


The formula you used, seems to be the arccosine instead of the haversine formula. The haversine formula is indeed more appropriate to calculate the distance on a sphere, because it is not prone to rounding errors with antipodal points.

/**
 * Calculates the great-circle distance between two points, with
 * the Haversine formula.
 * @param float $latitudeFrom Latitude of start point in [deg decimal]
 * @param float $longitudeFrom Longitude of start point in [deg decimal]
 * @param float $latitudeTo Latitude of target point in [deg decimal]
 * @param float $longitudeTo Longitude of target point in [deg decimal]
 * @param float $earthRadius Mean earth radius in [m]
 * @return float Distance between points in [m] (same as earthRadius)
 */
function haversineGreatCircleDistance(
  $latitudeFrom, $longitudeFrom, $latitudeTo, $longitudeTo, $earthRadius = 6371000)
{
  // convert from degrees to radians
  $latFrom = deg2rad($latitudeFrom);
  $lonFrom = deg2rad($longitudeFrom);
  $latTo = deg2rad($latitudeTo);
  $lonTo = deg2rad($longitudeTo);

  $latDelta = $latTo - $latFrom;
  $lonDelta = $lonTo - $lonFrom;

  $angle = 2 * asin(sqrt(pow(sin($latDelta / 2), 2) +
    cos($latFrom) * cos($latTo) * pow(sin($lonDelta / 2), 2)));
  return $angle * $earthRadius;
}

P.S. I couldn't find an error in your code, so is it just a typo that you wrote $lat= 41.9133741000 $lat= 12.5203944000 ? Maybe you just calculated with $lat=12.5203944000 and $long=0 because you overwrote your $lat variable.

Edit:

Tested the code and it returned a correct result:

$center_lat = 41.8350;
$center_lng = 12.470;
$lat = 41.9133741000;
$lng = 12.5203944000;

// test with your arccosine formula
$distance =( 6371 * acos((cos(deg2rad($center_lat)) ) * (cos(deg2rad($lat))) * (cos(deg2rad($lng) - deg2rad($center_lng)) )+ ((sin(deg2rad($center_lat))) * (sin(deg2rad($lat))))) );
print($distance); // prints 9.662174538188

// test with my haversine formula
$distance = haversineGreatCircleDistance($center_lat, $center_lng, $lat, $lng, 6371);
print($distance); // prints 9.6621745381693

public function getDistanceBetweenTwoPoints($point1 , $point2){
    // array of lat-long i.e  $point1 = [lat,long]
    $earthRadius = 6371;  // earth radius in km
    $point1Lat = $point1[0];
    $point2Lat =$point2[0];
    $deltaLat = deg2rad($point2Lat - $point1Lat);
    $point1Long =$point1[1];
    $point2Long =$point2[1];
    $deltaLong = deg2rad($point2Long - $point1Long);
    $a = sin($deltaLat/2) * sin($deltaLat/2) + cos(deg2rad($point1Lat)) * cos(deg2rad($point2Lat)) * sin($deltaLong/2) * sin($deltaLong/2);
    $c = 2 * atan2(sqrt($a), sqrt(1-$a));

    $distance = $earthRadius * $c;
    return $distance;    // in km
}

from this link:

function getDistance($latitude1, $longitude1, $latitude2, $longitude2) {
    $earth_radius = 6371;

    $dLat = deg2rad($latitude2 - $latitude1);
    $dLon = deg2rad($longitude2 - $longitude1);

    $a = sin($dLat/2) * sin($dLat/2) + cos(deg2rad($latitude1)) * cos(deg2rad($latitude2)) * sin($dLon/2) * sin($dLon/2);
    $c = 2 * asin(sqrt($a));
    $d = $earth_radius * $c;

    return $d;
}

As you can see there are many differences between this as your code. I don't know if you have either a different approach to the formula or maybe some step when converting to PHP went wrong, but the above formula should work.


I calculate distances straight inside queries, using the following stored procedure:

CREATE FUNCTION GEODIST (lat1 DOUBLE, lon1 DOUBLE, lat2 DOUBLE, lon2 DOUBLE)
    RETURNS DOUBLE
    DETERMINISTIC
        BEGIN
            DECLARE dist DOUBLE;
            SET dist =  round(acos(cos(radians(lat1))*cos(radians(lon1))*cos(radians(lat2))*cos(radians(lon2)) + cos(radians(lat1))*sin(radians(lon1))*cos(radians(lat2))*sin(radians(lon2)) + sin(radians(lat1))*sin(radians(lat2))) * 6378.8, 1);
            RETURN dist;
        END|

You just execute the above as an SQl statement from within phpMyAdmin to create the procedure. Just notice the ending |, so in your SQL input window, choose for the | sign as limiter.

Then in a query, call it like this:

$sql = "
SELECT `locations`.`name`, GEODIST(`locations`.`lat`, `locations`.`lon`, " . $lat_to_calculate . ", " . $lon_to_calculate . ") AS `distance`
FROM `locations` ";

I found this to be a lot faster than calculating it in PHP after the query has been run.


I making the class of haversign which having the static fuction getDistance having the four paramters and it return the distance from the bot location points

class HaverSign {

     public static function getDistance($latitude1, $longitude1, $latitude2, $longitude2) {
        $earth_radius = 6371;

        $dLat = deg2rad($latitude2 - $latitude1);
        $dLon = deg2rad($longitude2 - $longitude1);

        $a = sin($dLat/2) * sin($dLat/2) + cos(deg2rad($latitude1)) * cos(deg2rad($latitude2)) * sin($dLon/2) * sin($dLon/2);
        $c = 2 * asin(sqrt($a));
        $d = $earth_radius * $c;

        return $d;
}
}

above class is stored at the root directory and root directory contains classes folder Call this by using the following way in any php page

include "../classes/HaverSign.php";
$haversign=new HaverSign();

$lat=18.5204;
$lon=73.8567;

$lat1=18.5404;
$lon1=73.8167;

$dist = $haversign->getDistance($lat,$lon,$lat1,$lon1);
echo $dist;

Output is as follow

4.7676529976827

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