/*******************************************************************************
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NAME TRANSVERSE MERCATOR
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PURPOSE: Transforms input longitude and latitude to Easting and
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Northing for the Transverse Mercator projection. The
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longitude and latitude must be in radians. The Easting
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and Northing values will be returned in meters.
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ALGORITHM REFERENCES
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1. 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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2. Snyder, John P. and Voxland, Philip M., "An Album of Map Projections",
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U.S. Geological Survey Professional Paper 1453 , United State Government
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Printing Office, Washington D.C., 1989.
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*******************************************************************************/
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/**
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Initialize Transverse Mercator projection
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*/
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Proj4js.Proj.tmerc = {
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init : function() {
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this.e0 = Proj4js.common.e0fn(this.es);
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this.e1 = Proj4js.common.e1fn(this.es);
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this.e2 = Proj4js.common.e2fn(this.es);
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this.e3 = Proj4js.common.e3fn(this.es);
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this.ml0 = this.a * Proj4js.common.mlfn(this.e0, this.e1, this.e2, this.e3, this.lat0);
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},
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/**
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Transverse Mercator Forward - long/lat to x/y
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long/lat in radians
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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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var delta_lon = Proj4js.common.adjust_lon(lon - this.long0); // Delta longitude
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var con; // cone constant
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var x, y;
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var sin_phi=Math.sin(lat);
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var cos_phi=Math.cos(lat);
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if (this.sphere) { /* spherical form */
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var b = cos_phi * Math.sin(delta_lon);
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if ((Math.abs(Math.abs(b) - 1.0)) < .0000000001) {
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Proj4js.reportError("tmerc:forward: Point projects into infinity");
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return(93);
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} else {
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x = .5 * this.a * this.k0 * Math.log((1.0 + b)/(1.0 - b));
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con = Math.acos(cos_phi * Math.cos(delta_lon)/Math.sqrt(1.0 - b*b));
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if (lat < 0) con = - con;
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y = this.a * this.k0 * (con - this.lat0);
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}
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} else {
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var al = cos_phi * delta_lon;
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var als = Math.pow(al,2);
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var c = this.ep2 * Math.pow(cos_phi,2);
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var tq = Math.tan(lat);
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var t = Math.pow(tq,2);
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con = 1.0 - this.es * Math.pow(sin_phi,2);
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var n = this.a / Math.sqrt(con);
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var ml = this.a * Proj4js.common.mlfn(this.e0, this.e1, this.e2, this.e3, lat);
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x = this.k0 * n * al * (1.0 + als / 6.0 * (1.0 - t + c + als / 20.0 * (5.0 - 18.0 * t + Math.pow(t,2) + 72.0 * c - 58.0 * this.ep2))) + this.x0;
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y = this.k0 * (ml - this.ml0 + n * tq * (als * (0.5 + als / 24.0 * (5.0 - t + 9.0 * c + 4.0 * Math.pow(c,2) + als / 30.0 * (61.0 - 58.0 * t + Math.pow(t,2) + 600.0 * c - 330.0 * this.ep2))))) + this.y0;
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}
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p.x = x; p.y = y;
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return p;
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}, // tmercFwd()
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/**
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Transverse Mercator Inverse - x/y to long/lat
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*/
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inverse : function(p) {
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var con, phi; /* temporary angles */
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var delta_phi; /* difference between longitudes */
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var i;
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var max_iter = 6; /* maximun number of iterations */
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var lat, lon;
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if (this.sphere) { /* spherical form */
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var f = Math.exp(p.x/(this.a * this.k0));
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var g = .5 * (f - 1/f);
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var temp = this.lat0 + p.y/(this.a * this.k0);
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var h = Math.cos(temp);
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con = Math.sqrt((1.0 - h * h)/(1.0 + g * g));
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lat = Proj4js.common.asinz(con);
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if (temp < 0)
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lat = -lat;
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if ((g == 0) && (h == 0)) {
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lon = this.long0;
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} else {
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lon = Proj4js.common.adjust_lon(Math.atan2(g,h) + this.long0);
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}
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} else { // ellipsoidal form
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var x = p.x - this.x0;
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var y = p.y - this.y0;
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con = (this.ml0 + y / this.k0) / this.a;
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phi = con;
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for (i=0;true;i++) {
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delta_phi=((con + this.e1 * Math.sin(2.0*phi) - this.e2 * Math.sin(4.0*phi) + this.e3 * Math.sin(6.0*phi)) / this.e0) - phi;
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phi += delta_phi;
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if (Math.abs(delta_phi) <= Proj4js.common.EPSLN) break;
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if (i >= max_iter) {
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Proj4js.reportError("tmerc:inverse: Latitude failed to converge");
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return(95);
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}
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} // for()
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if (Math.abs(phi) < Proj4js.common.HALF_PI) {
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// sincos(phi, &sin_phi, &cos_phi);
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var sin_phi=Math.sin(phi);
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var cos_phi=Math.cos(phi);
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var tan_phi = Math.tan(phi);
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var c = this.ep2 * Math.pow(cos_phi,2);
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var cs = Math.pow(c,2);
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var t = Math.pow(tan_phi,2);
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var ts = Math.pow(t,2);
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con = 1.0 - this.es * Math.pow(sin_phi,2);
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var n = this.a / Math.sqrt(con);
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var r = n * (1.0 - this.es) / con;
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var d = x / (n * this.k0);
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var ds = Math.pow(d,2);
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lat = phi - (n * tan_phi * ds / r) * (0.5 - ds / 24.0 * (5.0 + 3.0 * t + 10.0 * c - 4.0 * cs - 9.0 * this.ep2 - ds / 30.0 * (61.0 + 90.0 * t + 298.0 * c + 45.0 * ts - 252.0 * this.ep2 - 3.0 * cs)));
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lon = Proj4js.common.adjust_lon(this.long0 + (d * (1.0 - ds / 6.0 * (1.0 + 2.0 * t + c - ds / 20.0 * (5.0 - 2.0 * c + 28.0 * t - 3.0 * cs + 8.0 * this.ep2 + 24.0 * ts))) / cos_phi));
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} else {
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lat = Proj4js.common.HALF_PI * Proj4js.common.sign(y);
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lon = this.long0;
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}
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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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} // tmercInv()
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};
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