source: trunk/workshop-routing-foss4g/web/proj4js/lib/projCode/omerc.js @ 76

/*******************************************************************************
NAME                       OBLIQUE MERCATOR (HOTINE) 

PURPOSE:        Transforms input longitude and latitude to Easting and
                Northing for the Oblique Mercator projection.  The
                longitude and latitude must be in radians.  The Easting
                and Northing values will be returned in meters.

PROGRAMMER              DATE
----------              ----
T. Mittan               Mar, 1993

ALGORITHM REFERENCES

1.  Snyder, John P., "Map Projections--A Working Manual", U.S. Geological
    Survey Professional Paper 1395 (Supersedes USGS Bulletin 1532), United
    State Government Printing Office, Washington D.C., 1987.

2.  Snyder, John P. and Voxland, Philip M., "An Album of Map Projections",
    U.S. Geological Survey Professional Paper 1453 , United State Government
    Printing Office, Washington D.C., 1989.
*******************************************************************************/

Proj4js.Proj.omerc = {

  /* Initialize the Oblique Mercator  projection
    ------------------------------------------*/
  init: function() {
    if (!this.mode) this.mode=0;
    if (!this.lon1)   {this.lon1=0;this.mode=1;}
    if (!this.lon2)   this.lon2=0;
    if (!this.lat2)    this.lat2=0;

    /* Place parameters in static storage for common use
      -------------------------------------------------*/
    var temp = this.b/ this.a;
    var es = 1.0 - Math.pow(temp,2);
    var e = Math.sqrt(es);

    this.sin_p20=Math.sin(this.lat0);
    this.cos_p20=Math.cos(this.lat0);

    this.con = 1.0 - this.es * this.sin_p20 * this.sin_p20;
    this.com = Math.sqrt(1.0 - es);
    this.bl = Math.sqrt(1.0 + this.es * Math.pow(this.cos_p20,4.0)/(1.0 - es));
    this.al = this.a * this.bl * this.k0 * this.com / this.con;
    if (Math.abs(this.lat0) < Proj4js.common.EPSLN) {
       this.ts = 1.0;
       this.d = 1.0;
       this.el = 1.0;
    } else {
       this.ts = Proj4js.common.tsfnz(this.e,this.lat0,this.sin_p20);
       this.con = Math.sqrt(this.con);
       this.d = this.bl * this.com / (this.cos_p20 * this.con);
       if ((this.d * this.d - 1.0) > 0.0) {
          if (this.lat0 >= 0.0) {
             this.f = this.d + Math.sqrt(this.d * this.d - 1.0);
          } else {
             this.f = this.d - Math.sqrt(this.d * this.d - 1.0);
          }
       } else {
         this.f = this.d;
       }
       this.el = this.f * Math.pow(this.ts,this.bl);
    }

    //this.longc=52.60353916666667;

    if (this.mode != 0) {
       this.g = .5 * (this.f - 1.0/this.f);
       this.gama = Proj4js.common.asinz(Math.sin(this.alpha) / this.d);
       this.longc= this.longc - Proj4js.common.asinz(this.g * Math.tan(this.gama))/this.bl;

       /* Report parameters common to format B
       -------------------------------------*/
       //genrpt(azimuth * R2D,"Azimuth of Central Line:    ");
       //cenlon(lon_origin);
      // cenlat(lat_origin);

       this.con = Math.abs(this.lat0);
       if ((this.con > Proj4js.common.EPSLN) && (Math.abs(this.con - Proj4js.common.HALF_PI) > Proj4js.common.EPSLN)) {
            this.singam=Math.sin(this.gama);
            this.cosgam=Math.cos(this.gama);

            this.sinaz=Math.sin(this.alpha);
            this.cosaz=Math.cos(this.alpha);

            if (this.lat0>= 0) {
               this.u =  (this.al / this.bl) * Math.atan(Math.sqrt(this.d*this.d - 1.0)/this.cosaz);
            } else {
               this.u =  -(this.al / this.bl) *Math.atan(Math.sqrt(this.d*this.d - 1.0)/this.cosaz);
            }
          } else {
            Proj4js.reportError("omerc:Init:DataError");
          }
       } else {
       this.sinphi =Math. sin(this.at1);
       this.ts1 = Proj4js.common.tsfnz(this.e,this.lat1,this.sinphi);
       this.sinphi = Math.sin(this.lat2);
       this.ts2 = Proj4js.common.tsfnz(this.e,this.lat2,this.sinphi);
       this.h = Math.pow(this.ts1,this.bl);
       this.l = Math.pow(this.ts2,this.bl);
       this.f = this.el/this.h;
       this.g = .5 * (this.f - 1.0/this.f);
       this.j = (this.el * this.el - this.l * this.h)/(this.el * this.el + this.l * this.h);
       this.p = (this.l - this.h) / (this.l + this.h);
       this.dlon = this.lon1 - this.lon2;
       if (this.dlon < -Proj4js.common.PI) this.lon2 = this.lon2 - 2.0 * Proj4js.common.PI;
       if (this.dlon > Proj4js.common.PI) this.lon2 = this.lon2 + 2.0 * Proj4js.common.PI;
       this.dlon = this.lon1 - this.lon2;
       this.longc = .5 * (this.lon1 + this.lon2) -Math.atan(this.j * Math.tan(.5 * this.bl * this.dlon)/this.p)/this.bl;
       this.dlon  = Proj4js.common.adjust_lon(this.lon1 - this.longc);
       this.gama = Math.atan(Math.sin(this.bl * this.dlon)/this.g);
       this.alpha = Proj4js.common.asinz(this.d * Math.sin(this.gama));

       /* Report parameters common to format A
       -------------------------------------*/

       if (Math.abs(this.lat1 - this.lat2) <= Proj4js.common.EPSLN) {
          Proj4js.reportError("omercInitDataError");
          //return(202);
       } else {
          this.con = Math.abs(this.lat1);
       }
       if ((this.con <= Proj4js.common.EPSLN) || (Math.abs(this.con - HALF_PI) <= Proj4js.common.EPSLN)) {
           Proj4js.reportError("omercInitDataError");
                //return(202);
       } else {
         if (Math.abs(Math.abs(this.lat0) - Proj4js.common.HALF_PI) <= Proj4js.common.EPSLN) {
            Proj4js.reportError("omercInitDataError");
            //return(202);
         }
       }

       this.singam=Math.sin(this.gam);
       this.cosgam=Math.cos(this.gam);

       this.sinaz=Math.sin(this.alpha);
       this.cosaz=Math.cos(this.alpha);  


       if (this.lat0 >= 0) {
          this.u =  (this.al/this.bl) * Math.atan(Math.sqrt(this.d * this.d - 1.0)/this.cosaz);
       } else {
          this.u = -(this.al/this.bl) * Math.atan(Math.sqrt(this.d * this.d - 1.0)/this.cosaz);
       }
     }
  },


  /* Oblique Mercator forward equations--mapping lat,long to x,y
    ----------------------------------------------------------*/
  forward: function(p) {
    var theta;          /* angle                                        */
    var sin_phi, cos_phi;/* sin and cos value                           */
    var b;              /* temporary values                             */
    var c, t, tq;       /* temporary values                             */
    var con, n, ml;     /* cone constant, small m                       */
    var q,us,vl;
    var ul,vs;
    var s;
    var dlon;
    var ts1;

    var lon=p.x;
    var lat=p.y;
    /* Forward equations
      -----------------*/
    sin_phi = Math.sin(lat);
    dlon = Proj4js.common.adjust_lon(lon - this.longc);
    vl = Math.sin(this.bl * dlon);
    if (Math.abs(Math.abs(lat) - Proj4js.common.HALF_PI) > Proj4js.common.EPSLN) {
       ts1 = Proj4js.common.tsfnz(this.e,lat,sin_phi);
       q = this.el / (Math.pow(ts1,this.bl));
       s = .5 * (q - 1.0 / q);
       t = .5 * (q + 1.0/ q);
       ul = (s * this.singam - vl * this.cosgam) / t;
       con = Math.cos(this.bl * dlon);
       if (Math.abs(con) < .0000001) {
          us = this.al * this.bl * dlon;
       } else {
          us = this.al * Math.atan((s * this.cosgam + vl * this.singam) / con)/this.bl;
          if (con < 0) us = us + Proj4js.common.PI * this.al / this.bl;
       }
    } else {
       if (lat >= 0) {
          ul = this.singam;
       } else {
          ul = -this.singam;
       }
       us = this.al * lat / this.bl;
    }
    if (Math.abs(Math.abs(ul) - 1.0) <= Proj4js.common.EPSLN) {
       //alert("Point projects into infinity","omer-for");
       Proj4js.reportError("omercFwdInfinity");
       //return(205);
    }
    vs = .5 * this.al * Math.log((1.0 - ul)/(1.0 + ul)) / this.bl;
    us = us - this.u;
    var x = this.x0 + vs * this.cosaz + us * this.sinaz;
    var y = this.y0 + us * this.cosaz - vs * this.sinaz;

    p.x=x;
    p.y=y;
    return p;
  },

  inverse: function(p) {
    var delta_lon;      /* Delta longitude (Given longitude - center    */
    var theta;          /* angle                                        */
    var delta_theta;    /* adjusted longitude                           */
    var sin_phi, cos_phi;/* sin and cos value                           */
    var b;              /* temporary values                             */
    var c, t, tq;       /* temporary values                             */
    var con, n, ml;     /* cone constant, small m                       */
    var vs,us,q,s,ts1;
    var vl,ul,bs;
    var dlon;
    var  flag;

    /* Inverse equations
      -----------------*/
    p.x -= this.x0;
    p.y -= this.y0;
    flag = 0;
    vs = p.x * this.cosaz - p.y * this.sinaz;
    us = p.y * this.cosaz + p.x * this.sinaz;
    us = us + this.u;
    q = Math.exp(-this.bl * vs / this.al);
    s = .5 * (q - 1.0/q);
    t = .5 * (q + 1.0/q);
    vl = Math.sin(this.bl * us / this.al);
    ul = (vl * this.cosgam + s * this.singam)/t;
    if (Math.abs(Math.abs(ul) - 1.0) <= Proj4js.common.EPSLN)
       {
       lon = this.longc;
       if (ul >= 0.0) {
          lat = Proj4js.common.HALF_PI;
       } else {
         lat = -Proj4js.common.HALF_PI;
       }
    } else {
       con = 1.0 / this.bl;
       ts1 =Math.pow((this.el / Math.sqrt((1.0 + ul) / (1.0 - ul))),con);
       lat = Proj4js.common.phi2z(this.e,ts1);
       //if (flag != 0)
          //return(flag);
       //~ con = Math.cos(this.bl * us /al);
       theta = this.longc - Math.atan2((s * this.cosgam - vl * this.singam) , con)/this.bl;
       lon = Proj4js.common.adjust_lon(theta);
    }
    p.x=lon;
    p.y=lat;
    return p;
  }
};