eligibilite/js/proj4js/lib/projections/vandg.js

var adjust_lon = require('../common/adjust_lon');
var HALF_PI = Math.PI/2;
var EPSLN = 1.0e-10;
var asinz = require('../common/asinz');
/* Initialize the Van Der Grinten projection
  ----------------------------------------*/
exports.init = function() {
  //this.R = 6370997; //Radius of earth
  this.R = this.a;
};

exports.forward = function(p) {

  var lon = p.x;
  var lat = p.y;

  /* Forward equations
    -----------------*/
  var dlon = adjust_lon(lon - this.long0);
  var x, y;

  if (Math.abs(lat) <= EPSLN) {
    x = this.x0 + this.R * dlon;
    y = this.y0;
  }
  var theta = asinz(2 * Math.abs(lat / Math.PI));
  if ((Math.abs(dlon) <= EPSLN) || (Math.abs(Math.abs(lat) - HALF_PI) <= EPSLN)) {
    x = this.x0;
    if (lat >= 0) {
      y = this.y0 + Math.PI * this.R * Math.tan(0.5 * theta);
    }
    else {
      y = this.y0 + Math.PI * this.R * -Math.tan(0.5 * theta);
    }
    //  return(OK);
  }
  var al = 0.5 * Math.abs((Math.PI / dlon) - (dlon / Math.PI));
  var asq = al * al;
  var sinth = Math.sin(theta);
  var costh = Math.cos(theta);

  var g = costh / (sinth + costh - 1);
  var gsq = g * g;
  var m = g * (2 / sinth - 1);
  var msq = m * m;
  var con = Math.PI * this.R * (al * (g - msq) + Math.sqrt(asq * (g - msq) * (g - msq) - (msq + asq) * (gsq - msq))) / (msq + asq);
  if (dlon < 0) {
    con = -con;
  }
  x = this.x0 + con;
  //con = Math.abs(con / (Math.PI * this.R));
  var q = asq + g;
  con = Math.PI * this.R * (m * q - al * Math.sqrt((msq + asq) * (asq + 1) - q * q)) / (msq + asq);
  if (lat >= 0) {
    //y = this.y0 + Math.PI * this.R * Math.sqrt(1 - con * con - 2 * al * con);
    y = this.y0 + con;
  }
  else {
    //y = this.y0 - Math.PI * this.R * Math.sqrt(1 - con * con - 2 * al * con);
    y = this.y0 - con;
  }
  p.x = x;
  p.y = y;
  return p;
};

/* Van Der Grinten inverse equations--mapping x,y to lat/long
  ---------------------------------------------------------*/
exports.inverse = function(p) {
  var lon, lat;
  var xx, yy, xys, c1, c2, c3;
  var a1;
  var m1;
  var con;
  var th1;
  var d;

  /* inverse equations
    -----------------*/
  p.x -= this.x0;
  p.y -= this.y0;
  con = Math.PI * this.R;
  xx = p.x / con;
  yy = p.y / con;
  xys = xx * xx + yy * yy;
  c1 = -Math.abs(yy) * (1 + xys);
  c2 = c1 - 2 * yy * yy + xx * xx;
  c3 = -2 * c1 + 1 + 2 * yy * yy + xys * xys;
  d = yy * yy / c3 + (2 * c2 * c2 * c2 / c3 / c3 / c3 - 9 * c1 * c2 / c3 / c3) / 27;
  a1 = (c1 - c2 * c2 / 3 / c3) / c3;
  m1 = 2 * Math.sqrt(-a1 / 3);
  con = ((3 * d) / a1) / m1;
  if (Math.abs(con) > 1) {
    if (con >= 0) {
      con = 1;
    }
    else {
      con = -1;
    }
  }
  th1 = Math.acos(con) / 3;
  if (p.y >= 0) {
    lat = (-m1 * Math.cos(th1 + Math.PI / 3) - c2 / 3 / c3) * Math.PI;
  }
  else {
    lat = -(-m1 * Math.cos(th1 + Math.PI / 3) - c2 / 3 / c3) * Math.PI;
  }

  if (Math.abs(xx) < EPSLN) {
    lon = this.long0;
  }
  else {
    lon = adjust_lon(this.long0 + Math.PI * (xys - 1 + Math.sqrt(1 + 2 * (xx * xx - yy * yy) + xys * xys)) / 2 / xx);
  }

  p.x = lon;
  p.y = lat;
  return p;
};
exports.names = ["Van_der_Grinten_I", "VanDerGrinten", "vandg"];