source: trunk/workshop-routing-foss4g/web/proj4js/lib/projCode/laea.js @ 81

/*******************************************************************************
NAME                  LAMBERT AZIMUTHAL EQUAL-AREA
 
PURPOSE:        Transforms input longitude and latitude to Easting and
                Northing for the Lambert Azimuthal Equal-Area projection.  The
                longitude and latitude must be in radians.  The Easting
                and Northing values will be returned in meters.

PROGRAMMER              DATE            
----------              ----           
D. Steinwand, EROS      March, 1991   

This function was adapted from the Lambert Azimuthal Equal Area projection
code (FORTRAN) in the General Cartographic Transformation Package software
which is available from the U.S. Geological Survey National Mapping Division.
 
ALGORITHM REFERENCES

1.  "New Equal-Area Map Projections for Noncircular Regions", John P. Snyder,
    The American Cartographer, Vol 15, No. 4, October 1988, pp. 341-355.

2.  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.

3.  "Software Documentation for GCTP General Cartographic Transformation
    Package", U.S. Geological Survey National Mapping Division, May 1982.
*******************************************************************************/

Proj4js.Proj.laea = {
  S_POLE: 1,
  N_POLE: 2,
  EQUIT: 3,
  OBLIQ: 4,


/* Initialize the Lambert Azimuthal Equal Area projection
  ------------------------------------------------------*/
  init: function() {
    var t = Math.abs(this.lat0);
    if (Math.abs(t - Proj4js.common.HALF_PI) < Proj4js.common.EPSLN) {
      this.mode = this.lat0 < 0. ? this.S_POLE : this.N_POLE;
    } else if (Math.abs(t) < Proj4js.common.EPSLN) {
      this.mode = this.EQUIT;
    } else {
      this.mode = this.OBLIQ;
    }
    if (this.es > 0) {
      var sinphi;
  
      this.qp = Proj4js.common.qsfnz(this.e, 1.0);
      this.mmf = .5 / (1. - this.es);
      this.apa = this.authset(this.es);
      switch (this.mode) {
        case this.N_POLE:
        case this.S_POLE:
          this.dd = 1.;
          break;
        case this.EQUIT:
          this.rq = Math.sqrt(.5 * this.qp);
          this.dd = 1. / this.rq;
          this.xmf = 1.;
          this.ymf = .5 * this.qp;
          break;
        case this.OBLIQ:
          this.rq = Math.sqrt(.5 * this.qp);
          sinphi = Math.sin(this.lat0);
          this.sinb1 = Proj4js.common.qsfnz(this.e, sinphi) / this.qp;
          this.cosb1 = Math.sqrt(1. - this.sinb1 * this.sinb1);
          this.dd = Math.cos(this.lat0) / (Math.sqrt(1. - this.es * sinphi * sinphi) * this.rq * this.cosb1);
          this.ymf = (this.xmf = this.rq) / this.dd;
          this.xmf *= this.dd;
          break;
      }
    } else {
      if (this.mode == this.OBLIQ) {
        this.sinph0 = Math.sin(this.lat0);
        this.cosph0 = Math.cos(this.lat0);
      }
    }
  },

/* Lambert Azimuthal Equal Area forward equations--mapping lat,long to x,y
  -----------------------------------------------------------------------*/
  forward: function(p) {

    /* Forward equations
      -----------------*/
    var x,y;
    var lam=p.x;
    var phi=p.y;
    lam = Proj4js.common.adjust_lon(lam - this.long0);
    
    if (this.sphere) {
        var coslam, cosphi, sinphi;
      
        sinphi = Math.sin(phi);
        cosphi = Math.cos(phi);
        coslam = Math.cos(lam);
        switch (this.mode) {
          case this.OBLIQ:
          case this.EQUIT:
            y = (this.mode == this.EQUIT) ? 1. + cosphi * coslam : 1. + this.sinph0 * sinphi + this.cosph0 * cosphi * coslam;
            if (y <= Proj4js.common.EPSLN) {
              Proj4js.reportError("laea:fwd:y less than eps");
              return null;
            }
            y = Math.sqrt(2. / y);
            x = y * cosphi * Math.sin(lam);
            y *= (this.mode == this.EQUIT) ? sinphi : this.cosph0 * sinphi - this.sinph0 * cosphi * coslam;
            break;
          case this.N_POLE:
            coslam = -coslam;
          case this.S_POLE:
            if (Math.abs(phi + this.phi0) < Proj4js.common.EPSLN) {
              Proj4js.reportError("laea:fwd:phi < eps");
              return null;
            }
            y = Proj4js.common.FORTPI - phi * .5;
            y = 2. * ((this.mode == this.S_POLE) ? Math.cos(y) : Math.sin(y));
            x = y * Math.sin(lam);
            y *= coslam;
            break;
        }
    } else {
        var coslam, sinlam, sinphi, q, sinb=0.0, cosb=0.0, b=0.0;
      
        coslam = Math.cos(lam);
        sinlam = Math.sin(lam);
        sinphi = Math.sin(phi);
        q = Proj4js.common.qsfnz(this.e, sinphi);
        if (this.mode == this.OBLIQ || this.mode == this.EQUIT) {
          sinb = q / this.qp;
          cosb = Math.sqrt(1. - sinb * sinb);
        }
        switch (this.mode) {
          case this.OBLIQ:
            b = 1. + this.sinb1 * sinb + this.cosb1 * cosb * coslam;
            break;
          case this.EQUIT:
            b = 1. + cosb * coslam;
            break;
          case this.N_POLE:
            b = Proj4js.common.HALF_PI + phi;
            q = this.qp - q;
            break;
          case this.S_POLE:
            b = phi - Proj4js.common.HALF_PI;
            q = this.qp + q;
            break;
        }
        if (Math.abs(b) < Proj4js.common.EPSLN) {
            Proj4js.reportError("laea:fwd:b < eps");
            return null;
        }
        switch (this.mode) {
          case this.OBLIQ:
          case this.EQUIT:
            b = Math.sqrt(2. / b);
            if (this.mode == this.OBLIQ) {
              y = this.ymf * b * (this.cosb1 * sinb - this.sinb1 * cosb * coslam);
            } else {
              y = (b = Math.sqrt(2. / (1. + cosb * coslam))) * sinb * this.ymf;
            }
            x = this.xmf * b * cosb * sinlam;
            break;
          case this.N_POLE:
          case this.S_POLE:
            if (q >= 0.) {
              x = (b = Math.sqrt(q)) * sinlam;
              y = coslam * ((this.mode == this.S_POLE) ? b : -b);
            } else {
              x = y = 0.;
            }
            break;
        }
    }

    //v 1.0
    /*
    var sin_lat=Math.sin(lat);
    var cos_lat=Math.cos(lat);

    var sin_delta_lon=Math.sin(delta_lon);
    var cos_delta_lon=Math.cos(delta_lon);

    var g =this.sin_lat_o * sin_lat +this.cos_lat_o * cos_lat * cos_delta_lon;
    if (g == -1.0) {
      Proj4js.reportError("laea:fwd:Point projects to a circle of radius "+ 2.0 * R);
      return null;
    }
    var ksp = this.a * Math.sqrt(2.0 / (1.0 + g));
    var x = ksp * cos_lat * sin_delta_lon + this.x0;
    var y = ksp * (this.cos_lat_o * sin_lat - this.sin_lat_o * cos_lat * cos_delta_lon) + this.y0;
    */
    p.x = this.a*x + this.x0;
    p.y = this.a*y + this.y0;
    return p;
  },//lamazFwd()

/* Inverse equations
  -----------------*/
  inverse: function(p) {
    p.x -= this.x0;
    p.y -= this.y0;
    var x = p.x/this.a;
    var y = p.y/this.a;
    
    if (this.sphere) {
        var  cosz=0.0, rh, sinz=0.0;
      
        rh = Math.sqrt(x*x + y*y);
        var phi = rh * .5;
        if (phi > 1.) {
          Proj4js.reportError("laea:Inv:DataError");
          return null;
        }
        phi = 2. * Math.asin(phi);
        if (this.mode == this.OBLIQ || this.mode == this.EQUIT) {
          sinz = Math.sin(phi);
          cosz = Math.cos(phi);
        }
        switch (this.mode) {
        case this.EQUIT:
          phi = (Math.abs(rh) <= Proj4js.common.EPSLN) ? 0. : Math.asin(y * sinz / rh);
          x *= sinz;
          y = cosz * rh;
          break;
        case this.OBLIQ:
          phi = (Math.abs(rh) <= Proj4js.common.EPSLN) ? this.phi0 : Math.asin(cosz * sinph0 + y * sinz * cosph0 / rh);
          x *= sinz * cosph0;
          y = (cosz - Math.sin(phi) * sinph0) * rh;
          break;
        case this.N_POLE:
          y = -y;
          phi = Proj4js.common.HALF_PI - phi;
          break;
        case this.S_POLE:
          phi -= Proj4js.common.HALF_PI;
          break;
        }
        lam = (y == 0. && (this.mode == this.EQUIT || this.mode == this.OBLIQ)) ? 0. : Math.atan2(x, y);
    } else {
        var cCe, sCe, q, rho, ab=0.0;
      
        switch (this.mode) {
          case this.EQUIT:
          case this.OBLIQ:
            x /= this.dd;
            y *=  this.dd;
            rho = Math.sqrt(x*x + y*y);
            if (rho < Proj4js.common.EPSLN) {
              p.x = 0.;
              p.y = this.phi0;
              return p;
            }
            sCe = 2. * Math.asin(.5 * rho / this.rq);
            cCe = Math.cos(sCe);
            x *= (sCe = Math.sin(sCe));
            if (this.mode == this.OBLIQ) {
              ab = cCe * this.sinb1 + y * sCe * this.cosb1 / rho
              q = this.qp * ab;
              y = rho * this.cosb1 * cCe - y * this.sinb1 * sCe;
            } else {
              ab = y * sCe / rho;
              q = this.qp * ab;
              y = rho * cCe;
            }
            break;
          case this.N_POLE:
            y = -y;
          case this.S_POLE:
            q = (x * x + y * y);
            if (!q ) {
              p.x = 0.;
              p.y = this.phi0;
              return p;
            }
            /*
            q = this.qp - q;
            */
            ab = 1. - q / this.qp;
            if (this.mode == this.S_POLE) {
              ab = - ab;
            }
            break;
        }
        lam = Math.atan2(x, y);
        phi = this.authlat(Math.asin(ab), this.apa);
    }

    /*
    var Rh = Math.Math.sqrt(p.x *p.x +p.y * p.y);
    var temp = Rh / (2.0 * this.a);

    if (temp > 1) {
      Proj4js.reportError("laea:Inv:DataError");
      return null;
    }

    var z = 2.0 * Proj4js.common.asinz(temp);
    var sin_z=Math.sin(z);
    var cos_z=Math.cos(z);

    var lon =this.long0;
    if (Math.abs(Rh) > Proj4js.common.EPSLN) {
       var lat = Proj4js.common.asinz(this.sin_lat_o * cos_z +this. cos_lat_o * sin_z *p.y / Rh);
       var temp =Math.abs(this.lat0) - Proj4js.common.HALF_PI;
       if (Math.abs(temp) > Proj4js.common.EPSLN) {
          temp = cos_z -this.sin_lat_o * Math.sin(lat);
          if(temp!=0.0) lon=Proj4js.common.adjust_lon(this.long0+Math.atan2(p.x*sin_z*this.cos_lat_o,temp*Rh));
       } else if (this.lat0 < 0.0) {
          lon = Proj4js.common.adjust_lon(this.long0 - Math.atan2(-p.x,p.y));
       } else {
          lon = Proj4js.common.adjust_lon(this.long0 + Math.atan2(p.x, -p.y));
       }
    } else {
      lat = this.lat0;
    }
    */
    //return(OK);
    p.x = Proj4js.common.adjust_lon(this.long0+lam);
    p.y = phi;
    return p;
  },//lamazInv()
  
/* determine latitude from authalic latitude */
  P00: .33333333333333333333,
  P01: .17222222222222222222,
  P02: .10257936507936507936,
  P10: .06388888888888888888,
  P11: .06640211640211640211,
  P20: .01641501294219154443,
  
  authset: function(es) {
    var t;
    var APA = new Array();
    APA[0] = es * this.P00;
    t = es * es;
    APA[0] += t * this.P01;
    APA[1] = t * this.P10;
    t *= es;
    APA[0] += t * this.P02;
    APA[1] += t * this.P11;
    APA[2] = t * this.P20;
    return APA;
  },
  
  authlat: function(beta, APA) {
    var t = beta+beta;
    return(beta + APA[0] * Math.sin(t) + APA[1] * Math.sin(t+t) + APA[2] * Math.sin(t+t+t));
  }
  
};