jtBaseApp/node_modules/proj4/lib/projections/somerc.js

/*
  references:
    Formules et constantes pour le Calcul pour la
    projection cylindrique conforme à axe oblique et pour la transformation entre
    des systèmes de référence.
    http://www.swisstopo.admin.ch/internet/swisstopo/fr/home/topics/survey/sys/refsys/switzerland.parsysrelated1.31216.downloadList.77004.DownloadFile.tmp/swissprojectionfr.pdf
  */

export function init() {
  var phy0 = this.lat0;
  this.lambda0 = this.long0;
  var sinPhy0 = Math.sin(phy0);
  var semiMajorAxis = this.a;
  var invF = this.rf;
  var flattening = 1 / invF;
  var e2 = 2 * flattening - Math.pow(flattening, 2);
  var e = this.e = Math.sqrt(e2);
  this.R = this.k0 * semiMajorAxis * Math.sqrt(1 - e2) / (1 - e2 * Math.pow(sinPhy0, 2));
  this.alpha = Math.sqrt(1 + e2 / (1 - e2) * Math.pow(Math.cos(phy0), 4));
  this.b0 = Math.asin(sinPhy0 / this.alpha);
  var k1 = Math.log(Math.tan(Math.PI / 4 + this.b0 / 2));
  var k2 = Math.log(Math.tan(Math.PI / 4 + phy0 / 2));
  var k3 = Math.log((1 + e * sinPhy0) / (1 - e * sinPhy0));
  this.K = k1 - this.alpha * k2 + this.alpha * e / 2 * k3;
}

export function forward(p) {
  var Sa1 = Math.log(Math.tan(Math.PI / 4 - p.y / 2));
  var Sa2 = this.e / 2 * Math.log((1 + this.e * Math.sin(p.y)) / (1 - this.e * Math.sin(p.y)));
  var S = -this.alpha * (Sa1 + Sa2) + this.K;

  // spheric latitude
  var b = 2 * (Math.atan(Math.exp(S)) - Math.PI / 4);

  // spheric longitude
  var I = this.alpha * (p.x - this.lambda0);

  // psoeudo equatorial rotation
  var rotI = Math.atan(Math.sin(I) / (Math.sin(this.b0) * Math.tan(b) + Math.cos(this.b0) * Math.cos(I)));

  var rotB = Math.asin(Math.cos(this.b0) * Math.sin(b) - Math.sin(this.b0) * Math.cos(b) * Math.cos(I));

  p.y = this.R / 2 * Math.log((1 + Math.sin(rotB)) / (1 - Math.sin(rotB))) + this.y0;
  p.x = this.R * rotI + this.x0;
  return p;
}

export function inverse(p) {
  var Y = p.x - this.x0;
  var X = p.y - this.y0;

  var rotI = Y / this.R;
  var rotB = 2 * (Math.atan(Math.exp(X / this.R)) - Math.PI / 4);

  var b = Math.asin(Math.cos(this.b0) * Math.sin(rotB) + Math.sin(this.b0) * Math.cos(rotB) * Math.cos(rotI));
  var I = Math.atan(Math.sin(rotI) / (Math.cos(this.b0) * Math.cos(rotI) - Math.sin(this.b0) * Math.tan(rotB)));

  var lambda = this.lambda0 + I / this.alpha;

  var S = 0;
  var phy = b;
  var prevPhy = -1000;
  var iteration = 0;
  while (Math.abs(phy - prevPhy) > 0.0000001) {
    if (++iteration > 20) {
      //...reportError("omercFwdInfinity");
      return;
    }
    //S = Math.log(Math.tan(Math.PI / 4 + phy / 2));
    S = 1 / this.alpha * (Math.log(Math.tan(Math.PI / 4 + b / 2)) - this.K) + this.e * Math.log(Math.tan(Math.PI / 4 + Math.asin(this.e * Math.sin(phy)) / 2));
    prevPhy = phy;
    phy = 2 * Math.atan(Math.exp(S)) - Math.PI / 2;
  }

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

export var names = ["somerc"];
export default {
  init: init,
  forward: forward,
  inverse: inverse,
  names: names
};