eligibilite/js/proj4js/lib/projections/omerc.js

var tsfnz = require('../common/tsfnz');
var adjust_lon = require('../common/adjust_lon');
var phi2z = require('../common/phi2z');
var HALF_PI = Math.PI/2;
var FORTPI = Math.PI/4;
var EPSLN = 1.0e-10;

/* Initialize the Oblique Mercator  projection
    ------------------------------------------*/
exports.init = function() {
  this.no_off = this.no_off || false;
  this.no_rot = this.no_rot || false;

  if (isNaN(this.k0)) {
    this.k0 = 1;
  }
  var sinlat = Math.sin(this.lat0);
  var coslat = Math.cos(this.lat0);
  var con = this.e * sinlat;

  this.bl = Math.sqrt(1 + this.es / (1 - this.es) * Math.pow(coslat, 4));
  this.al = this.a * this.bl * this.k0 * Math.sqrt(1 - this.es) / (1 - con * con);
  var t0 = tsfnz(this.e, this.lat0, sinlat);
  var dl = this.bl / coslat * Math.sqrt((1 - this.es) / (1 - con * con));
  if (dl * dl < 1) {
    dl = 1;
  }
  var fl;
  var gl;
  if (!isNaN(this.longc)) {
    //Central point and azimuth method

    if (this.lat0 >= 0) {
      fl = dl + Math.sqrt(dl * dl - 1);
    }
    else {
      fl = dl - Math.sqrt(dl * dl - 1);
    }
    this.el = fl * Math.pow(t0, this.bl);
    gl = 0.5 * (fl - 1 / fl);
    this.gamma0 = Math.asin(Math.sin(this.alpha) / dl);
    this.long0 = this.longc - Math.asin(gl * Math.tan(this.gamma0)) / this.bl;

  }
  else {
    //2 points method
    var t1 = tsfnz(this.e, this.lat1, Math.sin(this.lat1));
    var t2 = tsfnz(this.e, this.lat2, Math.sin(this.lat2));
    if (this.lat0 >= 0) {
      this.el = (dl + Math.sqrt(dl * dl - 1)) * Math.pow(t0, this.bl);
    }
    else {
      this.el = (dl - Math.sqrt(dl * dl - 1)) * Math.pow(t0, this.bl);
    }
    var hl = Math.pow(t1, this.bl);
    var ll = Math.pow(t2, this.bl);
    fl = this.el / hl;
    gl = 0.5 * (fl - 1 / fl);
    var jl = (this.el * this.el - ll * hl) / (this.el * this.el + ll * hl);
    var pl = (ll - hl) / (ll + hl);
    var dlon12 = adjust_lon(this.long1 - this.long2);
    this.long0 = 0.5 * (this.long1 + this.long2) - Math.atan(jl * Math.tan(0.5 * this.bl * (dlon12)) / pl) / this.bl;
    this.long0 = adjust_lon(this.long0);
    var dlon10 = adjust_lon(this.long1 - this.long0);
    this.gamma0 = Math.atan(Math.sin(this.bl * (dlon10)) / gl);
    this.alpha = Math.asin(dl * Math.sin(this.gamma0));
  }

  if (this.no_off) {
    this.uc = 0;
  }
  else {
    if (this.lat0 >= 0) {
      this.uc = this.al / this.bl * Math.atan2(Math.sqrt(dl * dl - 1), Math.cos(this.alpha));
    }
    else {
      this.uc = -1 * this.al / this.bl * Math.atan2(Math.sqrt(dl * dl - 1), Math.cos(this.alpha));
    }
  }

};


/* Oblique Mercator forward equations--mapping lat,long to x,y
    ----------------------------------------------------------*/
exports.forward = function(p) {
  var lon = p.x;
  var lat = p.y;
  var dlon = adjust_lon(lon - this.long0);
  var us, vs;
  var con;
  if (Math.abs(Math.abs(lat) - HALF_PI) <= EPSLN) {
    if (lat > 0) {
      con = -1;
    }
    else {
      con = 1;
    }
    vs = this.al / this.bl * Math.log(Math.tan(FORTPI + con * this.gamma0 * 0.5));
    us = -1 * con * HALF_PI * this.al / this.bl;
  }
  else {
    var t = tsfnz(this.e, lat, Math.sin(lat));
    var ql = this.el / Math.pow(t, this.bl);
    var sl = 0.5 * (ql - 1 / ql);
    var tl = 0.5 * (ql + 1 / ql);
    var vl = Math.sin(this.bl * (dlon));
    var ul = (sl * Math.sin(this.gamma0) - vl * Math.cos(this.gamma0)) / tl;
    if (Math.abs(Math.abs(ul) - 1) <= EPSLN) {
      vs = Number.POSITIVE_INFINITY;
    }
    else {
      vs = 0.5 * this.al * Math.log((1 - ul) / (1 + ul)) / this.bl;
    }
    if (Math.abs(Math.cos(this.bl * (dlon))) <= EPSLN) {
      us = this.al * this.bl * (dlon);
    }
    else {
      us = this.al * Math.atan2(sl * Math.cos(this.gamma0) + vl * Math.sin(this.gamma0), Math.cos(this.bl * dlon)) / this.bl;
    }
  }

  if (this.no_rot) {
    p.x = this.x0 + us;
    p.y = this.y0 + vs;
  }
  else {

    us -= this.uc;
    p.x = this.x0 + vs * Math.cos(this.alpha) + us * Math.sin(this.alpha);
    p.y = this.y0 + us * Math.cos(this.alpha) - vs * Math.sin(this.alpha);
  }
  return p;
};

exports.inverse = function(p) {
  var us, vs;
  if (this.no_rot) {
    vs = p.y - this.y0;
    us = p.x - this.x0;
  }
  else {
    vs = (p.x - this.x0) * Math.cos(this.alpha) - (p.y - this.y0) * Math.sin(this.alpha);
    us = (p.y - this.y0) * Math.cos(this.alpha) + (p.x - this.x0) * Math.sin(this.alpha);
    us += this.uc;
  }
  var qp = Math.exp(-1 * this.bl * vs / this.al);
  var sp = 0.5 * (qp - 1 / qp);
  var tp = 0.5 * (qp + 1 / qp);
  var vp = Math.sin(this.bl * us / this.al);
  var up = (vp * Math.cos(this.gamma0) + sp * Math.sin(this.gamma0)) / tp;
  var ts = Math.pow(this.el / Math.sqrt((1 + up) / (1 - up)), 1 / this.bl);
  if (Math.abs(up - 1) < EPSLN) {
    p.x = this.long0;
    p.y = HALF_PI;
  }
  else if (Math.abs(up + 1) < EPSLN) {
    p.x = this.long0;
    p.y = -1 * HALF_PI;
  }
  else {
    p.y = phi2z(this.e, ts);
    p.x = adjust_lon(this.long0 - Math.atan2(sp * Math.cos(this.gamma0) - vp * Math.sin(this.gamma0), Math.cos(this.bl * us / this.al)) / this.bl);
  }
  return p;
};

exports.names = ["Hotine_Oblique_Mercator", "Hotine Oblique Mercator", "Hotine_Oblique_Mercator_Azimuth_Natural_Origin", "Hotine_Oblique_Mercator_Azimuth_Center", "omerc"];