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Mike
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distVincenty = function(p1, p2) {
    var ct = {
        a: 6378137,
        b: 6356752.3142,
        f: 1/298.257223563
    };
    var a = ct.a, b = ct.b, f = ct.f;

    var L = (p2.lon - p1.lon) * Math.PI/180;
    var U1 = Math.atan((1-f) * Math.tan(p1.lat*Math.PI/180));
    var U2 = Math.atan((1-f) * Math.tan(p2.lat*Math.PI/180));
    var sinU1 = Math.sin(U1), cosU1 = Math.cos(U1);
    var sinU2 = Math.sin(U2), cosU2 = Math.cos(U2);
    var lambda = L, lambdaP = 2*Math.PI;
    var iterLimit = 20;
    while (Math.abs(lambda-lambdaP) > 1e-12 && --iterLimit>0) {
        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 alpha = Math.asin(cosU1 * cosU2 * sinLambda / sinSigma);
        var cosSqAlpha = Math.cos(alpha) * Math.cos(alpha);
        var cos2SigmaM = cosSigma - 2*sinU1*sinU2/cosSqAlpha;
        var C = f/16*cosSqAlpha*(4+f*(4-3*cosSqAlpha));
        lambdaP = lambda;
        lambda = L + (1-C) * f * Math.sin(alpha) *
        (sigma + C*sinSigma*(cos2SigmaM+C*cosSigma*(-1+2*cos2SigmaM*cos2SigmaM)));
    }
    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);
    var d = s.toFixed(3)/1000; // round to 1mm precision
    return d;
};
distVincenty = function(p1, p2) {
    var ct = {
        a: 6378137,
        b: 6356752.3142,
        f: 1/298.257223563
    };
    var a = ct.a, b = ct.b, f = ct.f;

    var L = (p2.lon - p1.lon) * Math.PI/180;
    var U1 = Math.atan((1-f) * Math.tan(p1.lat*Math.PI/180));
    var U2 = Math.atan((1-f) * Math.tan(p2.lat*Math.PI/180));
    var sinU1 = Math.sin(U1), cosU1 = Math.cos(U1);
    var sinU2 = Math.sin(U2), cosU2 = Math.cos(U2);
    var lambda = L, lambdaP = 2*Math.PI;
    var iterLimit = 20;
    while (Math.abs(lambda-lambdaP) > 1e-12 && --iterLimit>0) {
        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 alpha = Math.asin(cosU1 * cosU2 * sinLambda / sinSigma);
        var cosSqAlpha = Math.cos(alpha) * Math.cos(alpha);
        var cos2SigmaM = cosSigma - 2*sinU1*sinU2/cosSqAlpha;
        var C = f/16*cosSqAlpha*(4+f*(4-3*cosSqAlpha));
        lambdaP = lambda;
        lambda = L + (1-C) * f * Math.sin(alpha) *
        (sigma + C*sinSigma*(cos2SigmaM+C*cosSigma*(-1+2*cos2SigmaM*cos2SigmaM)));
    }
    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);
    var d = s.toFixed(3)/1000; // round to 1mm precision
    return d;
};
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Mike
  • 12.9k
  • 1
  • 12
  • 18

Sphere gives the shortest distance on a spherical planet. What appears to be a straight line on a flat map isn't the shortest distance that an aircraft would fly, especially over long distances such as London to Tokyo

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