/*******************************************************************************
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NAME VAN DER GRINTEN
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PURPOSE: Transforms input Easting and Northing to longitude and
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latitude for the Van der Grinten projection. The
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Easting and Northing must be in meters. The longitude
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and latitude values will be returned in radians.
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PROGRAMMER DATE
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---------- ----
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T. Mittan March, 1993
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This function was adapted from the Van Der Grinten projection code
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(FORTRAN) in the General Cartographic Transformation Package software
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which is available from the U.S. Geological Survey National Mapping Division.
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ALGORITHM REFERENCES
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1. "New Equal-Area Map Projections for Noncircular Regions", John P. Snyder,
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The American Cartographer, Vol 15, No. 4, October 1988, pp. 341-355.
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2. Snyder, John P., "Map Projections--A Working Manual", U.S. Geological
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Survey Professional Paper 1395 (Supersedes USGS Bulletin 1532), United
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State Government Printing Office, Washington D.C., 1987.
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3. "Software Documentation for GCTP General Cartographic Transformation
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Package", U.S. Geological Survey National Mapping Division, May 1982.
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*******************************************************************************/
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Proj4js.Proj.vandg = {
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/* Initialize the Van Der Grinten projection
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----------------------------------------*/
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init: function() {
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this.R = 6370997.0; //Radius of earth
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},
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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 = Proj4js.common.adjust_lon(lon - this.long0);
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var x,y;
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if (Math.abs(lat) <= Proj4js.common.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 = Proj4js.common.asinz(2.0 * Math.abs(lat / Proj4js.common.PI));
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if ((Math.abs(dlon) <= Proj4js.common.EPSLN) || (Math.abs(Math.abs(lat) - Proj4js.common.HALF_PI) <= Proj4js.common.EPSLN)) {
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x = this.x0;
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if (lat >= 0) {
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y = this.y0 + Proj4js.common.PI * this.R * Math.tan(.5 * theta);
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} else {
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y = this.y0 + Proj4js.common.PI * this.R * - Math.tan(.5 * theta);
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}
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// return(OK);
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}
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var al = .5 * Math.abs((Proj4js.common.PI / dlon) - (dlon / Proj4js.common.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 - 1.0);
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var gsq = g * g;
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var m = g * (2.0 / sinth - 1.0);
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var msq = m * m;
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var con = Proj4js.common.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 / (Proj4js.common.PI * this.R));
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if (lat >= 0) {
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y = this.y0 + Proj4js.common.PI * this.R * Math.sqrt(1.0 - con * con - 2.0 * al * con);
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} else {
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y = this.y0 - Proj4js.common.PI * this.R * Math.sqrt(1.0 - con * con - 2.0 * al * 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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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 al,asq;
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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 = Proj4js.common.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) * (1.0 + xys);
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c2 = c1 - 2.0 * yy * yy + xx * xx;
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c3 = -2.0 * c1 + 1.0 + 2.0 * yy * yy + xys * xys;
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d = yy * yy / c3 + (2.0 * c2 * c2 * c2 / c3 / c3 / c3 - 9.0 * c1 * c2 / c3 /c3) / 27.0;
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a1 = (c1 - c2 * c2 / 3.0 / c3) / c3;
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m1 = 2.0 * Math.sqrt( -a1 / 3.0);
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con = ((3.0 * d) / a1) / m1;
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if (Math.abs(con) > 1.0) {
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if (con >= 0.0) {
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con = 1.0;
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} else {
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con = -1.0;
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}
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}
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th1 = Math.acos(con) / 3.0;
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if (p.y >= 0) {
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lat = (-m1 *Math.cos(th1 + Proj4js.common.PI / 3.0) - c2 / 3.0 / c3) * Proj4js.common.PI;
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} else {
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lat = -(-m1 * Math.cos(th1 + Proj4js.common.PI / 3.0) - c2 / 3.0 / c3) * Proj4js.common.PI;
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}
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if (Math.abs(xx) < Proj4js.common.EPSLN) {
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lon = this.long0;
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}
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lon = Proj4js.common.adjust_lon(this.long0 + Proj4js.common.PI * (xys - 1.0 + Math.sqrt(1.0 + 2.0 * (xx * xx - yy * yy) + xys * xys)) / 2.0 / xx);
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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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};
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