/*******************************************************************************
|
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 - Proj4js.common.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 lon, lat;
|
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;
|
}
|
};
|
