distance.js

distance.js

/*!
 * JavaScript function to calculate the geodetic distance between two points specified by latitude/longitude using the Vincenty inverse formula for ellipsoids.
 *
 * Original scripts by Chris Veness
 * Taken from http://movable-type.co.uk/scripts/latlong-vincenty.html and optimized / cleaned up by Mathias Bynens <http://mathiasbynens.be/>
 * Based on the Vincenty direct formula by T. Vincenty, “Direct and Inverse Solutions of Geodesics on the Ellipsoid with application of nested equations”, Survey Review, vol XXII no 176, 1975 <http://www.ngs.noaa.gov/PUBS_LIB/inverse.pdf>
 *
 * @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 toRad(n) {
	return n * Math.PI / 180;
};

function distVincenty(lat1, lon1, lat2, lon2) {
	var a = 6378137,
		b = 6356752.3142,
		f = 1 / 298.257223563, // WGS-84 ellipsoid params
		L = toRad(lon2 - lon1),
		U1 = Math.atan((1 - f) * Math.tan(toRad(lat1))),
		U2 = Math.atan((1 - f) * Math.tan(toRad(lat2))),
		sinU1 = Math.sin(U1),
		cosU1 = Math.cos(U1),
		sinU2 = Math.sin(U2),
		cosU2 = Math.cos(U2),
		lambda = L,
		lambdaP,
		iterLimit = 100;
	do {
		var sinLambda = Math.sin(lambda),
			cosLambda = Math.cos(lambda),
			sinSigma = Math.sqrt((cosU2 * sinLambda) * (cosU2 * sinLambda) + (cosU1 * sinU2 - sinU1 * cosU2 * cosLambda) * (cosU1 * sinU2 - sinU1 * cosU2 * cosLambda));
		if (0 === sinSigma) {
			return 0; // co-incident points
		};
		var cosSigma = sinU1 * sinU2 + cosU1 * cosU2 * cosLambda,
			sigma = Math.atan2(sinSigma, cosSigma),
			sinAlpha = cosU1 * cosU2 * sinLambda / sinSigma,
			cosSqAlpha = 1 - sinAlpha * sinAlpha,
			cos2SigmaM = cosSigma - 2 * sinU1 * sinU2 / cosSqAlpha,
			C = f / 16 * cosSqAlpha * (4 + f * (4 - 3 * cosSqAlpha));
		if (isNaN(cos2SigmaM)) {
			cos2SigmaM = 0; // equatorial line: cosSqAlpha = 0 (§6)
		};
		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) {
		return NaN; // formula failed to converge
	};

	var uSq = cosSqAlpha * (a * a - b * b) / (b * b),
		A = 1 + uSq / 16384 * (4096 + uSq * (-768 + uSq * (320 - 175 * uSq))),
		B = uSq / 1024 * (256 + uSq * (-128 + uSq * (74 - 47 * uSq))),
		deltaSigma = B * sinSigma * (cos2SigmaM + B / 4 * (cosSigma * (-1 + 2 * cos2SigmaM * cos2SigmaM) - B / 6 * cos2SigmaM * (-3 + 4 * sinSigma * sinSigma) * (-3 + 4 * cos2SigmaM * cos2SigmaM))),
		s = b * A * (sigma - deltaSigma);
	return s.toFixed(3); // round to 1mm precision
};