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Filename : proj.js
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/**
 * Contains methods for transforming point on sphere to
 * Cartesian coordinates using various projections.
 * @class
 */
jvm.Proj = {
  degRad: 180 / Math.PI,
  radDeg: Math.PI / 180,
  radius: 6381372,

  sgn: function(n){
    if (n > 0) {
      return 1;
    } else if (n < 0) {
      return -1;
    } else {
      return n;
    }
  },

  /**
   * Converts point on sphere to the Cartesian coordinates using Miller projection
   * @param {Number} lat Latitude in degrees
   * @param {Number} lng Longitude in degrees
   * @param {Number} c Central meridian in degrees
   */
  mill: function(lat, lng, c){
    return {
      x: this.radius * (lng - c) * this.radDeg,
      y: - this.radius * Math.log(Math.tan((45 + 0.4 * lat) * this.radDeg)) / 0.8
    };
  },

  /**
   * Inverse function of mill()
   * Converts Cartesian coordinates to point on sphere using Miller projection
   * @param {Number} x X of point in Cartesian system as integer
   * @param {Number} y Y of point in Cartesian system as integer
   * @param {Number} c Central meridian in degrees
   */
  mill_inv: function(x, y, c){
    return {
      lat: (2.5 * Math.atan(Math.exp(0.8 * y / this.radius)) - 5 * Math.PI / 8) * this.degRad,
      lng: (c * this.radDeg + x / this.radius) * this.degRad
    };
  },

  /**
   * Converts point on sphere to the Cartesian coordinates using Mercator projection
   * @param {Number} lat Latitude in degrees
   * @param {Number} lng Longitude in degrees
   * @param {Number} c Central meridian in degrees
   */
  merc: function(lat, lng, c){
    return {
      x: this.radius * (lng - c) * this.radDeg,
      y: - this.radius * Math.log(Math.tan(Math.PI / 4 + lat * Math.PI / 360))
    };
  },

  /**
   * Inverse function of merc()
   * Converts Cartesian coordinates to point on sphere using Mercator projection
   * @param {Number} x X of point in Cartesian system as integer
   * @param {Number} y Y of point in Cartesian system as integer
   * @param {Number} c Central meridian in degrees
   */
  merc_inv: function(x, y, c){
    return {
      lat: (2 * Math.atan(Math.exp(y / this.radius)) - Math.PI / 2) * this.degRad,
      lng: (c * this.radDeg + x / this.radius) * this.degRad
    };
  },

  /**
   * Converts point on sphere to the Cartesian coordinates using Albers Equal-Area Conic
   * projection
   * @see <a href="http://mathworld.wolfram.com/AlbersEqual-AreaConicProjection.html">Albers Equal-Area Conic projection</a>
   * @param {Number} lat Latitude in degrees
   * @param {Number} lng Longitude in degrees
   * @param {Number} c Central meridian in degrees
   */
  aea: function(lat, lng, c){
    var fi0 = 0,
        lambda0 = c * this.radDeg,
        fi1 = 29.5 * this.radDeg,
        fi2 = 45.5 * this.radDeg,
        fi = lat * this.radDeg,
        lambda = lng * this.radDeg,
        n = (Math.sin(fi1)+Math.sin(fi2)) / 2,
        C = Math.cos(fi1)*Math.cos(fi1)+2*n*Math.sin(fi1),
        theta = n*(lambda-lambda0),
        ro = Math.sqrt(C-2*n*Math.sin(fi))/n,
        ro0 = Math.sqrt(C-2*n*Math.sin(fi0))/n;

    return {
      x: ro * Math.sin(theta) * this.radius,
      y: - (ro0 - ro * Math.cos(theta)) * this.radius
    };
  },

  /**
   * Converts Cartesian coordinates to the point on sphere using Albers Equal-Area Conic
   * projection
   * @see <a href="http://mathworld.wolfram.com/AlbersEqual-AreaConicProjection.html">Albers Equal-Area Conic projection</a>
   * @param {Number} x X of point in Cartesian system as integer
   * @param {Number} y Y of point in Cartesian system as integer
   * @param {Number} c Central meridian in degrees
   */
  aea_inv: function(xCoord, yCoord, c){
    var x = xCoord / this.radius,
        y = yCoord / this.radius,
        fi0 = 0,
        lambda0 = c * this.radDeg,
        fi1 = 29.5 * this.radDeg,
        fi2 = 45.5 * this.radDeg,
        n = (Math.sin(fi1)+Math.sin(fi2)) / 2,
        C = Math.cos(fi1)*Math.cos(fi1)+2*n*Math.sin(fi1),
        ro0 = Math.sqrt(C-2*n*Math.sin(fi0))/n,
        ro = Math.sqrt(x*x+(ro0-y)*(ro0-y)),
        theta = Math.atan( x / (ro0 - y) );

    return {
      lat: (Math.asin((C - ro * ro * n * n) / (2 * n))) * this.degRad,
      lng: (lambda0 + theta / n) * this.degRad
    };
  },

  /**
   * Converts point on sphere to the Cartesian coordinates using Lambert conformal
   * conic projection
   * @see <a href="http://mathworld.wolfram.com/LambertConformalConicProjection.html">Lambert Conformal Conic Projection</a>
   * @param {Number} lat Latitude in degrees
   * @param {Number} lng Longitude in degrees
   * @param {Number} c Central meridian in degrees
   */
  lcc: function(lat, lng, c){
    var fi0 = 0,
        lambda0 = c * this.radDeg,
        lambda = lng * this.radDeg,
        fi1 = 33 * this.radDeg,
        fi2 = 45 * this.radDeg,
        fi = lat * this.radDeg,
        n = Math.log( Math.cos(fi1) * (1 / Math.cos(fi2)) ) / Math.log( Math.tan( Math.PI / 4 + fi2 / 2) * (1 / Math.tan( Math.PI / 4 + fi1 / 2) ) ),
        F = ( Math.cos(fi1) * Math.pow( Math.tan( Math.PI / 4 + fi1 / 2 ), n ) ) / n,
        ro = F * Math.pow( 1 / Math.tan( Math.PI / 4 + fi / 2 ), n ),
        ro0 = F * Math.pow( 1 / Math.tan( Math.PI / 4 + fi0 / 2 ), n );

    return {
      x: ro * Math.sin( n * (lambda - lambda0) ) * this.radius,
      y: - (ro0 - ro * Math.cos( n * (lambda - lambda0) ) ) * this.radius
    };
  },

  /**
   * Converts Cartesian coordinates to the point on sphere using Lambert conformal conic
   * projection
   * @see <a href="http://mathworld.wolfram.com/LambertConformalConicProjection.html">Lambert Conformal Conic Projection</a>
   * @param {Number} x X of point in Cartesian system as integer
   * @param {Number} y Y of point in Cartesian system as integer
   * @param {Number} c Central meridian in degrees
   */
  lcc_inv: function(xCoord, yCoord, c){
    var x = xCoord / this.radius,
        y = yCoord / this.radius,
        fi0 = 0,
        lambda0 = c * this.radDeg,
        fi1 = 33 * this.radDeg,
        fi2 = 45 * this.radDeg,
        n = Math.log( Math.cos(fi1) * (1 / Math.cos(fi2)) ) / Math.log( Math.tan( Math.PI / 4 + fi2 / 2) * (1 / Math.tan( Math.PI / 4 + fi1 / 2) ) ),
        F = ( Math.cos(fi1) * Math.pow( Math.tan( Math.PI / 4 + fi1 / 2 ), n ) ) / n,
        ro0 = F * Math.pow( 1 / Math.tan( Math.PI / 4 + fi0 / 2 ), n ),
        ro = this.sgn(n) * Math.sqrt(x*x+(ro0-y)*(ro0-y)),
        theta = Math.atan( x / (ro0 - y) );

    return {
      lat: (2 * Math.atan(Math.pow(F/ro, 1/n)) - Math.PI / 2) * this.degRad,
      lng: (lambda0 + theta / n) * this.degRad
    };
  }
};