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node_modules/proj4/lib/projections/somerc.js

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+/*
+  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
+};