proj4/lib/projections/tmerc.js

Proj4js is a JavaScript library to transform point coordinates from one coordinate system to another, including datum transformations.

var e0fn = require('../common/e0fn');
var e1fn = require('../common/e1fn');
var e2fn = require('../common/e2fn');
var e3fn = require('../common/e3fn');
var mlfn = require('../common/mlfn');
var adjust_lon = require('../common/adjust_lon');
var HALF_PI = Math.PI/2;
var EPSLN = 1.0e-10;
var sign = require('../common/sign');
var asinz = require('../common/asinz');

exports.init = function() {
  this.e0 = e0fn(this.es);
  this.e1 = e1fn(this.es);
  this.e2 = e2fn(this.es);
  this.e3 = e3fn(this.es);
  this.ml0 = this.a * mlfn(this.e0, this.e1, this.e2, this.e3, this.lat0);
};

/**
    Transverse Mercator Forward  - long/lat to x/y
    long/lat in radians
  */
exports.forward = function(p) {
  var lon = p.x;
  var lat = p.y;

  var delta_lon = adjust_lon(lon - this.long0);
  var con;
  var x, y;
  var sin_phi = Math.sin(lat);
  var cos_phi = Math.cos(lat);

  if (this.sphere) {
    var b = cos_phi * Math.sin(delta_lon);
    if ((Math.abs(Math.abs(b) - 1)) < 0.0000000001) {
      return (93);
    }
    else {
      x = 0.5 * this.a * this.k0 * Math.log((1 + b) / (1 - b));
      con = Math.acos(cos_phi * Math.cos(delta_lon) / Math.sqrt(1 - b * b));
      if (lat < 0) {
        con = -con;
      }
      y = this.a * this.k0 * (con - this.lat0);
    }
  }
  else {
    var al = cos_phi * delta_lon;
    var als = Math.pow(al, 2);
    var c = this.ep2 * Math.pow(cos_phi, 2);
    var tq = Math.tan(lat);
    var t = Math.pow(tq, 2);
    con = 1 - this.es * Math.pow(sin_phi, 2);
    var n = this.a / Math.sqrt(con);
    var ml = this.a * mlfn(this.e0, this.e1, this.e2, this.e3, lat);

    x = this.k0 * n * al * (1 + als / 6 * (1 - t + c + als / 20 * (5 - 18 * t + Math.pow(t, 2) + 72 * c - 58 * this.ep2))) + this.x0;
    y = this.k0 * (ml - this.ml0 + n * tq * (als * (0.5 + als / 24 * (5 - t + 9 * c + 4 * Math.pow(c, 2) + als / 30 * (61 - 58 * t + Math.pow(t, 2) + 600 * c - 330 * this.ep2))))) + this.y0;

  }
  p.x = x;
  p.y = y;
  return p;
};

/**
    Transverse Mercator Inverse  -  x/y to long/lat
  */
exports.inverse = function(p) {
  var con, phi;
  var delta_phi;
  var i;
  var max_iter = 6;
  var lat, lon;

  if (this.sphere) {
    var f = Math.exp(p.x / (this.a * this.k0));
    var g = 0.5 * (f - 1 / f);
    var temp = this.lat0 + p.y / (this.a * this.k0);
    var h = Math.cos(temp);
    con = Math.sqrt((1 - h * h) / (1 + g * g));
    lat = asinz(con);
    if (temp < 0) {
      lat = -lat;
    }
    if ((g === 0) && (h === 0)) {
      lon = this.long0;
    }
    else {
      lon = adjust_lon(Math.atan2(g, h) + this.long0);
    }
  }
  else { // ellipsoidal form
    var x = p.x - this.x0;
    var y = p.y - this.y0;

    con = (this.ml0 + y / this.k0) / this.a;
    phi = con;
    for (i = 0; true; i++) {
      delta_phi = ((con + this.e1 * Math.sin(2 * phi) - this.e2 * Math.sin(4 * phi) + this.e3 * Math.sin(6 * phi)) / this.e0) - phi;
      phi += delta_phi;
      if (Math.abs(delta_phi) <= EPSLN) {
        break;
      }
      if (i >= max_iter) {
        return (95);
      }
    } // for()
    if (Math.abs(phi) < HALF_PI) {
      var sin_phi = Math.sin(phi);
      var cos_phi = Math.cos(phi);
      var tan_phi = Math.tan(phi);
      var c = this.ep2 * Math.pow(cos_phi, 2);
      var cs = Math.pow(c, 2);
      var t = Math.pow(tan_phi, 2);
      var ts = Math.pow(t, 2);
      con = 1 - this.es * Math.pow(sin_phi, 2);
      var n = this.a / Math.sqrt(con);
      var r = n * (1 - this.es) / con;
      var d = x / (n * this.k0);
      var ds = Math.pow(d, 2);
      lat = phi - (n * tan_phi * ds / r) * (0.5 - ds / 24 * (5 + 3 * t + 10 * c - 4 * cs - 9 * this.ep2 - ds / 30 * (61 + 90 * t + 298 * c + 45 * ts - 252 * this.ep2 - 3 * cs)));
      lon = adjust_lon(this.long0 + (d * (1 - ds / 6 * (1 + 2 * t + c - ds / 20 * (5 - 2 * c + 28 * t - 3 * cs + 8 * this.ep2 + 24 * ts))) / cos_phi));
    }
    else {
      lat = HALF_PI * sign(y);
      lon = this.long0;
    }
  }
  p.x = lon;
  p.y = lat;
  return p;
};
exports.names = ["Transverse_Mercator", "Transverse Mercator", "tmerc"];