Vincenty vs Haversine vs Spherical Law of Cosines Distance Calculations [test] (v3)

Revision 3 of this benchmark created by Marc van 't Hooft on February 8, 2013

Description

Setup

/** Converts numeric degrees to radians */
    if (typeof(Number.prototype.toRad) === "undefined") {
      Number.prototype.toRad = function() {
        return this * Math.PI / 180;
      }
    }
    
    /**
     * Calculates geodetic distance between two points specified by latitude/longitude using 
     * Vincenty inverse formula for ellipsoids
     *
     * @param   {Number} lat1, lon1: first point in decimal degrees
     * @param   {Number} lat2, lon2: second point in decimal degrees
     * @returns (Number} distance in metres between points
     */
    
    function distVincenty(lat1, lon1, lat2, lon2) {
      var a = 6378137,
          b = 6356752.314245,
          f = 1 / 298.257223563; // WGS-84 ellipsoid params
      var L = (lon2 - lon1).toRad();
      var U1 = Math.atan((1 - f) * Math.tan(lat1.toRad()));
      var U2 = Math.atan((1 - f) * Math.tan(lat2.toRad()));
      var sinU1 = Math.sin(U1),
          cosU1 = Math.cos(U1);
      var sinU2 = Math.sin(U2),
          cosU2 = Math.cos(U2);
    
      var lambda = L,
          lambdaP, iterLimit = 100;
      do {
        var sinLambda = Math.sin(lambda),
            cosLambda = Math.cos(lambda);
        var sinSigma = Math.sqrt((cosU2 * sinLambda) * (cosU2 * sinLambda) + (cosU1 * sinU2 - sinU1 * cosU2 * cosLambda) * (cosU1 * sinU2 - sinU1 * cosU2 * cosLambda));
        if (sinSigma == 0) return 0; // co-incident points
        var cosSigma = sinU1 * sinU2 + cosU1 * cosU2 * cosLambda;
        var sigma = Math.atan2(sinSigma, cosSigma);
        var sinAlpha = cosU1 * cosU2 * sinLambda / sinSigma;
        var cosSqAlpha = 1 - sinAlpha * sinAlpha;
        var cos2SigmaM = cosSigma - 2 * sinU1 * sinU2 / cosSqAlpha;
        if (isNaN(cos2SigmaM)) cos2SigmaM = 0; // equatorial line: cosSqAlpha=0 (§6)
        var C = f / 16 * cosSqAlpha * (4 + f * (4 - 3 * cosSqAlpha));
        lambdaP = lambda;
        lambda = L + (1 - C) * f * sinAlpha * (sigma + C * sinSigma * (cos2SigmaM + C * cosSigma * (-1 + 2 * cos2SigmaM * cos2SigmaM)));
      } while (Math.abs(lambda - lambdaP) > 1e-12 && --iterLimit > 0);
    
      if (iterLimit == 0) return NaN // formula failed to converge
      var uSq = cosSqAlpha * (a * a - b * b) / (b * b);
      var A = 1 + uSq / 16384 * (4096 + uSq * (-768 + uSq * (320 - 175 * uSq)));
      var B = uSq / 1024 * (256 + uSq * (-128 + uSq * (74 - 47 * uSq)));
      var deltaSigma = B * sinSigma * (cos2SigmaM + B / 4 * (cosSigma * (-1 + 2 * cos2SigmaM * cos2SigmaM) - B / 6 * cos2SigmaM * (-3 + 4 * sinSigma * sinSigma) * (-3 + 4 * cos2SigmaM * cos2SigmaM)));
      var s = b * A * (sigma - deltaSigma);
    
      return Math.round(s);
    }
    
    // Distance in kilometers between two points using the Haversine algo.
    
    
    function haversine(lat1, lon1, lat2, lon2) {
      var R = 6371;
      var dLat = (lat2 - lat1).toRad();
      var dLong = (lon2 - lon1).toRad();
    
      var a = Math.sin(dLat / 2) * Math.sin(dLat / 2) + Math.cos(lat1.toRad()) * Math.cos(lat2.toRad()) * Math.sin(dLong / 2) * Math.sin(dLong / 2);
      var c = 2 * Math.atan2(Math.sqrt(a), Math.sqrt(1 - a));
      var d = R * c;
    
      return Math.round(d);
    }
    
    
    //The Spherical Law of Cosines
    //Original source: "http://www.movable-type.co.uk/scripts/latlong.html"
    function SphericalCosinus(lat1, lon1, lat2, lon2) {
        var R = 6371; // km
        var dLon = (lon2-lon1).toRad(); 
        var lat1 = lat1.toRad();
        var lat2 = lat2.toRad();
        var d = Math.acos(Math.sin(lat1)*Math.sin(lat2) + 
                                                Math.cos(lat1)*Math.cos(lat2) *
                                                Math.cos(dLon)) * R;
    
        return Math.round(d);
    }

Test runner

distVincenty(-31.965379, 115.822077, -33.85789, 151.214806);

haversine(-31.965379, 115.822077, -33.85789, 151.214806);

SphericalCosinus(-31.965379, 115.822077, -33.85789, 151.214806);

Revisions

You can edit these tests or add more tests to this page by appending /edit to the URL.

• Revision 1: published on June 26, 2012
• Revision 2: published on July 10, 2012
• Revision 3: published by Marc van 't Hooft on February 8, 2013
• Revision 4: published on June 11, 2014
• Revision 5: published on March 14, 2015