proj4/lib/projections/cass.js

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

var mlfn = require('../common/mlfn');
var e0fn = require('../common/e0fn');
var e1fn = require('../common/e1fn');
var e2fn = require('../common/e2fn');
var e3fn = require('../common/e3fn');
var gN = require('../common/gN');
var adjust_lon = require('../common/adjust_lon');
var adjust_lat = require('../common/adjust_lat');
var imlfn = require('../common/imlfn');
var HALF_PI = Math.PI/2;
var EPSLN = 1.0e-10;
exports.init = function() {
  if (!this.sphere) {
    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);
  }
};



/* Cassini forward equations--mapping lat,long to x,y
  -----------------------------------------------------------------------*/
exports.forward = function(p) {

  /* Forward equations
      -----------------*/
  var x, y;
  var lam = p.x;
  var phi = p.y;
  lam = adjust_lon(lam - this.long0);

  if (this.sphere) {
    x = this.a * Math.asin(Math.cos(phi) * Math.sin(lam));
    y = this.a * (Math.atan2(Math.tan(phi), Math.cos(lam)) - this.lat0);
  }
  else {
    //ellipsoid
    var sinphi = Math.sin(phi);
    var cosphi = Math.cos(phi);
    var nl = gN(this.a, this.e, sinphi);
    var tl = Math.tan(phi) * Math.tan(phi);
    var al = lam * Math.cos(phi);
    var asq = al * al;
    var cl = this.es * cosphi * cosphi / (1 - this.es);
    var ml = this.a * mlfn(this.e0, this.e1, this.e2, this.e3, phi);

    x = nl * al * (1 - asq * tl * (1 / 6 - (8 - tl + 8 * cl) * asq / 120));
    y = ml - this.ml0 + nl * sinphi / cosphi * asq * (0.5 + (5 - tl + 6 * cl) * asq / 24);


  }

  p.x = x + this.x0;
  p.y = y + this.y0;
  return p;
};

/* Inverse equations
  -----------------*/
exports.inverse = function(p) {
  p.x -= this.x0;
  p.y -= this.y0;
  var x = p.x / this.a;
  var y = p.y / this.a;
  var phi, lam;

  if (this.sphere) {
    var dd = y + this.lat0;
    phi = Math.asin(Math.sin(dd) * Math.cos(x));
    lam = Math.atan2(Math.tan(x), Math.cos(dd));
  }
  else {
    /* ellipsoid */
    var ml1 = this.ml0 / this.a + y;
    var phi1 = imlfn(ml1, this.e0, this.e1, this.e2, this.e3);
    if (Math.abs(Math.abs(phi1) - HALF_PI) <= EPSLN) {
      p.x = this.long0;
      p.y = HALF_PI;
      if (y < 0) {
        p.y *= -1;
      }
      return p;
    }
    var nl1 = gN(this.a, this.e, Math.sin(phi1));

    var rl1 = nl1 * nl1 * nl1 / this.a / this.a * (1 - this.es);
    var tl1 = Math.pow(Math.tan(phi1), 2);
    var dl = x * this.a / nl1;
    var dsq = dl * dl;
    phi = phi1 - nl1 * Math.tan(phi1) / rl1 * dl * dl * (0.5 - (1 + 3 * tl1) * dl * dl / 24);
    lam = dl * (1 - dsq * (tl1 / 3 + (1 + 3 * tl1) * tl1 * dsq / 15)) / Math.cos(phi1);

  }

  p.x = adjust_lon(lam + this.long0);
  p.y = adjust_lat(phi);
  return p;

};
exports.names = ["Cassini", "Cassini_Soldner", "cass"];