var adjust_lon = require('../common/adjust_lon');
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var HALF_PI = Math.PI/2;
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var EPSLN = 1.0e-10;
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var asinz = require('../common/asinz');
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/* Initialize the Van Der Grinten projection
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----------------------------------------*/
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exports.init = function() {
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//this.R = 6370997; //Radius of earth
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this.R = this.a;
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};
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exports.forward = function(p) {
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var lon = p.x;
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var lat = p.y;
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/* Forward equations
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-----------------*/
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var dlon = adjust_lon(lon - this.long0);
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var x, y;
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if (Math.abs(lat) <= EPSLN) {
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x = this.x0 + this.R * dlon;
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y = this.y0;
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}
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var theta = asinz(2 * Math.abs(lat / Math.PI));
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if ((Math.abs(dlon) <= EPSLN) || (Math.abs(Math.abs(lat) - HALF_PI) <= EPSLN)) {
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x = this.x0;
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if (lat >= 0) {
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y = this.y0 + Math.PI * this.R * Math.tan(0.5 * theta);
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}
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else {
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y = this.y0 + Math.PI * this.R * -Math.tan(0.5 * theta);
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}
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// return(OK);
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}
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var al = 0.5 * Math.abs((Math.PI / dlon) - (dlon / Math.PI));
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var asq = al * al;
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var sinth = Math.sin(theta);
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var costh = Math.cos(theta);
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var g = costh / (sinth + costh - 1);
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var gsq = g * g;
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var m = g * (2 / sinth - 1);
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var msq = m * m;
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var con = Math.PI * this.R * (al * (g - msq) + Math.sqrt(asq * (g - msq) * (g - msq) - (msq + asq) * (gsq - msq))) / (msq + asq);
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if (dlon < 0) {
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con = -con;
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}
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x = this.x0 + con;
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//con = Math.abs(con / (Math.PI * this.R));
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var q = asq + g;
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con = Math.PI * this.R * (m * q - al * Math.sqrt((msq + asq) * (asq + 1) - q * q)) / (msq + asq);
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if (lat >= 0) {
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//y = this.y0 + Math.PI * this.R * Math.sqrt(1 - con * con - 2 * al * con);
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y = this.y0 + con;
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}
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else {
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//y = this.y0 - Math.PI * this.R * Math.sqrt(1 - con * con - 2 * al * con);
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y = this.y0 - con;
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}
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p.x = x;
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p.y = y;
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return p;
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};
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/* Van Der Grinten inverse equations--mapping x,y to lat/long
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---------------------------------------------------------*/
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exports.inverse = function(p) {
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var lon, lat;
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var xx, yy, xys, c1, c2, c3;
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var a1;
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var m1;
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var con;
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var th1;
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var d;
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/* inverse equations
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-----------------*/
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p.x -= this.x0;
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p.y -= this.y0;
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con = Math.PI * this.R;
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xx = p.x / con;
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yy = p.y / con;
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xys = xx * xx + yy * yy;
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c1 = -Math.abs(yy) * (1 + xys);
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c2 = c1 - 2 * yy * yy + xx * xx;
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c3 = -2 * c1 + 1 + 2 * yy * yy + xys * xys;
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d = yy * yy / c3 + (2 * c2 * c2 * c2 / c3 / c3 / c3 - 9 * c1 * c2 / c3 / c3) / 27;
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a1 = (c1 - c2 * c2 / 3 / c3) / c3;
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m1 = 2 * Math.sqrt(-a1 / 3);
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con = ((3 * d) / a1) / m1;
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if (Math.abs(con) > 1) {
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if (con >= 0) {
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con = 1;
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}
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else {
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con = -1;
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}
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}
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th1 = Math.acos(con) / 3;
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if (p.y >= 0) {
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lat = (-m1 * Math.cos(th1 + Math.PI / 3) - c2 / 3 / c3) * Math.PI;
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}
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else {
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lat = -(-m1 * Math.cos(th1 + Math.PI / 3) - c2 / 3 / c3) * Math.PI;
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}
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if (Math.abs(xx) < EPSLN) {
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lon = this.long0;
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}
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else {
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lon = adjust_lon(this.long0 + Math.PI * (xys - 1 + Math.sqrt(1 + 2 * (xx * xx - yy * yy) + xys * xys)) / 2 / xx);
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}
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p.x = lon;
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p.y = lat;
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return p;
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};
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exports.names = ["Van_der_Grinten_I", "VanDerGrinten", "vandg"];
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