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tobyprivett/vincenty_inverse.js

Created May 4, 2016 17:58
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vincenty_inverse.js
// from: http://www.movable-type.co.uk/scripts/latlong-vincenty.html
var sinα1 = Math.sin(α1);
var cosα1 = Math.cos(α1);
var tanU1 = (1-f) * Math.tan(φ1), cosU1 = 1 / Math.sqrt((1 + tanU1*tanU1)), sinU1 = tanU1 * cosU1;
var σ1 = Math.atan2(tanU1, cosα1);
var sinα = cosU1 * sinα1;
var cosSqα = 1 - sinα*sinα;
var uSq = cosSqα * (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 σ = s / (b*A), σʹ;
do {
var cos2σM = Math.cos(2*σ1 + σ);
var sinσ = Math.sin(σ);
var cosσ = Math.cos(σ);
var Δσ = B*sinσ*(cos2σM+B/4*(cosσ*(-1+2*cos2σM*cos2σM)-
B/6*cos2σM*(-3+4*sinσ*sinσ)*(-3+4*cos2σM*cos2σM)));
σʹ = σ;
σ = s / (b*A) + Δσ;
} while (Math.abs(σ-σʹ) > 1e-12);
var tmp = sinU1*sinσ - cosU1*cosσ*cosα1;
var φ2 = Math.atan2(sinU1*cosσ + cosU1*sinσ*cosα1, (1-f)*Math.sqrt(sinα*sinα + tmp*tmp));
var λ = Math.atan2(sinσ*sinα1, cosU1*cosσ - sinU1*sinσ*cosα1);
var C = f/16*cosSqα*(4+f*(4-3*cosSqα));
var L = λ - (1-C) * f * sinα *
(σ + C*sinσ*(cos2σM+C*cosσ*(-1+2*cos2σM*cos2σM)));
var λ2 = (λ1+L+3*Math.PI)%(2*Math.PI) - Math.PI; // normalise to -180...+180
var revAz = Math.atan2(sinα, -tmp);
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