aea.js
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/*******************************************************************************
NAME ALBERS CONICAL EQUAL AREA
PURPOSE: Transforms input longitude and latitude to Easting and Northing
for the Albers Conical Equal Area projection. The longitude
and latitude must be in radians. The Easting and Northing
values will be returned in meters.
PROGRAMMER DATE
---------- ----
T. Mittan, Feb, 1992
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.aea = {
init : function() {
if (Math.abs(this.lat1 + this.lat2) < Proj4js.common.EPSLN) {
Proj4js.reportError("aeaInitEqualLatitudes");
return;
}
this.temp = this.b / this.a;
this.es = 1.0 - Math.pow(this.temp,2);
this.e3 = Math.sqrt(this.es);
this.sin_po=Math.sin(this.lat1);
this.cos_po=Math.cos(this.lat1);
this.t1=this.sin_po;
this.con = this.sin_po;
this.ms1 = Proj4js.common.msfnz(this.e3,this.sin_po,this.cos_po);
this.qs1 = Proj4js.common.qsfnz(this.e3,this.sin_po,this.cos_po);
this.sin_po=Math.sin(this.lat2);
this.cos_po=Math.cos(this.lat2);
this.t2=this.sin_po;
this.ms2 = Proj4js.common.msfnz(this.e3,this.sin_po,this.cos_po);
this.qs2 = Proj4js.common.qsfnz(this.e3,this.sin_po,this.cos_po);
this.sin_po=Math.sin(this.lat0);
this.cos_po=Math.cos(this.lat0);
this.t3=this.sin_po;
this.qs0 = Proj4js.common.qsfnz(this.e3,this.sin_po,this.cos_po);
if (Math.abs(this.lat1 - this.lat2) > Proj4js.common.EPSLN) {
this.ns0 = (this.ms1 * this.ms1 - this.ms2 *this.ms2)/ (this.qs2 - this.qs1);
} else {
this.ns0 = this.con;
}
this.c = this.ms1 * this.ms1 + this.ns0 * this.qs1;
this.rh = this.a * Math.sqrt(this.c - this.ns0 * this.qs0)/this.ns0;
},
/* Albers Conical Equal Area forward equations--mapping lat,long to x,y
-------------------------------------------------------------------*/
forward: function(p){
var lon=p.x;
var lat=p.y;
this.sin_phi=Math.sin(lat);
this.cos_phi=Math.cos(lat);
var qs = Proj4js.common.qsfnz(this.e3,this.sin_phi,this.cos_phi);
var rh1 =this.a * Math.sqrt(this.c - this.ns0 * qs)/this.ns0;
var theta = this.ns0 * Proj4js.common.adjust_lon(lon - this.long0);
var x = rh1 * Math.sin(theta) + this.x0;
var y = this.rh - rh1 * Math.cos(theta) + this.y0;
p.x = x;
p.y = y;
return p;
},
inverse: function(p) {
var rh1,qs,con,theta,lon,lat;
p.x -= this.x0;
p.y = this.rh - p.y + this.y0;
if (this.ns0 >= 0) {
rh1 = Math.sqrt(p.x *p.x + p.y * p.y);
con = 1.0;
} else {
rh1 = -Math.sqrt(p.x * p.x + p.y *p.y);
con = -1.0;
}
theta = 0.0;
if (rh1 != 0.0) {
theta = Math.atan2(con * p.x, con * p.y);
}
con = rh1 * this.ns0 / this.a;
qs = (this.c - con * con) / this.ns0;
if (this.e3 >= 1e-10) {
con = 1 - .5 * (1.0 -this.es) * Math.log((1.0 - this.e3) / (1.0 + this.e3))/this.e3;
if (Math.abs(Math.abs(con) - Math.abs(qs)) > .0000000001 ) {
lat = this.phi1z(this.e3,qs);
} else {
if (qs >= 0) {
lat = .5 * PI;
} else {
lat = -.5 * PI;
}
}
} else {
lat = this.phi1z(e3,qs);
}
lon = Proj4js.common.adjust_lon(theta/this.ns0 + this.long0);
p.x = lon;
p.y = lat;
return p;
},
/* Function to compute phi1, the latitude for the inverse of the
Albers Conical Equal-Area projection.
-------------------------------------------*/
phi1z: function (eccent,qs) {
var con, com, dphi;
var phi = Proj4js.common.asinz(.5 * qs);
if (eccent < Proj4js.common.EPSLN) return phi;
var eccnts = eccent * eccent;
for (var i = 1; i <= 25; i++) {
sinphi = Math.sin(phi);
cosphi = Math.cos(phi);
con = eccent * sinphi;
com = 1.0 - con * con;
dphi = .5 * com * com / cosphi * (qs / (1.0 - eccnts) - sinphi / com + .5 / eccent * Math.log((1.0 - con) / (1.0 + con)));
phi = phi + dphi;
if (Math.abs(dphi) <= 1e-7) return phi;
}
Proj4js.reportError("aea:phi1z:Convergence error");
return null;
}
};