Vincenty vs Haversine Distance Calculations

JavaScript performance comparison

Revision 8 of this test case created

Info

This test compares JavaScript implementations of the two main different point-to-point distance calculation equations, Haversine and Vincenty.

Among geodetics enthusiasts, Haversine is perhaps slightly looked-down upon because its accuracy can be out by 0.3% or so, whereas Vincenty is apparently accurate to 0.5mm. Of course, both methods use a theoretical spheroid, and because no-one can actually travel on either theoretical spheroid, both are only an approximation :-)

More information on Haversine

More information on Vincenty

Preparation code

 
<script>
Benchmark.prototype.setup = function() {
    /** 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);
   
      s = s.toFixed(3); // round to 1mm precision
      return 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);
    }
};
</script>

Test runner

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Testing in unknown unknown
Test Ops/sec
Vincenty formula
distVincenty(-1.6668542888253446, -78.6364996433258, -1.6665540085087196,  -78.63842010498047);
pending…
Haversine formula
haversine(-1.6668542888253446, -78.6364996433258, -1.6665540085087196,  -78.63842010498047);
pending…

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