proj4
Version:
Proj4js is a JavaScript library to transform point coordinates from one coordinate system to another, including datum transformations.
289 lines (271 loc) • 7.54 kB
JavaScript
var HALF_PI = Math.PI/2;
var FORTPI = Math.PI/4;
var EPSLN = 1.0e-10;
var qsfnz = require('../common/qsfnz');
var adjust_lon = require('../common/adjust_lon');
/*
reference
"New Equal-Area Map Projections for Noncircular Regions", John P. Snyder,
The American Cartographer, Vol 15, No. 4, October 1988, pp. 341-355.
*/
exports.S_POLE = 1;
exports.N_POLE = 2;
exports.EQUIT = 3;
exports.OBLIQ = 4;
/* Initialize the Lambert Azimuthal Equal Area projection
------------------------------------------------------*/
exports.init = function() {
var t = Math.abs(this.lat0);
if (Math.abs(t - HALF_PI) < EPSLN) {
this.mode = this.lat0 < 0 ? this.S_POLE : this.N_POLE;
}
else if (Math.abs(t) < EPSLN) {
this.mode = this.EQUIT;
}
else {
this.mode = this.OBLIQ;
}
if (this.es > 0) {
var sinphi;
this.qp = qsfnz(this.e, 1);
this.mmf = 0.5 / (1 - this.es);
this.apa = this.authset(this.es);
switch (this.mode) {
case this.N_POLE:
this.dd = 1;
break;
case this.S_POLE:
this.dd = 1;
break;
case this.EQUIT:
this.rq = Math.sqrt(0.5 * this.qp);
this.dd = 1 / this.rq;
this.xmf = 1;
this.ymf = 0.5 * this.qp;
break;
case this.OBLIQ:
this.rq = Math.sqrt(0.5 * this.qp);
sinphi = Math.sin(this.lat0);
this.sinb1 = 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
-----------------------------------------------------------------------*/
exports.forward = function(p) {
/* Forward equations
-----------------*/
var x, y, coslam, sinlam, sinphi, q, sinb, cosb, b, cosphi;
var lam = p.x;
var phi = p.y;
lam = adjust_lon(lam - this.long0);
if (this.sphere) {
sinphi = Math.sin(phi);
cosphi = Math.cos(phi);
coslam = Math.cos(lam);
if (this.mode === this.OBLIQ || this.mode === this.EQUIT) {
y = (this.mode === this.EQUIT) ? 1 + cosphi * coslam : 1 + this.sinph0 * sinphi + this.cosph0 * cosphi * coslam;
if (y <= EPSLN) {
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;
}
else if (this.mode === this.N_POLE || this.mode === this.S_POLE) {
if (this.mode === this.N_POLE) {
coslam = -coslam;
}
if (Math.abs(phi + this.phi0) < EPSLN) {
return null;
}
y = FORTPI - phi * 0.5;
y = 2 * ((this.mode === this.S_POLE) ? Math.cos(y) : Math.sin(y));
x = y * Math.sin(lam);
y *= coslam;
}
}
else {
sinb = 0;
cosb = 0;
b = 0;
coslam = Math.cos(lam);
sinlam = Math.sin(lam);
sinphi = Math.sin(phi);
q = 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 = HALF_PI + phi;
q = this.qp - q;
break;
case this.S_POLE:
b = phi - HALF_PI;
q = this.qp + q;
break;
}
if (Math.abs(b) < EPSLN) {
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;
}
}
p.x = this.a * x + this.x0;
p.y = this.a * y + this.y0;
return p;
};
/* Inverse equations
-----------------*/
exports.inverse = function(p) {
p.x -= this.x0;
p.y -= this.y0;
var x = p.x / this.a;
var y = p.y / this.a;
var lam, phi, cCe, sCe, q, rho, ab;
if (this.sphere) {
var cosz = 0,
rh, sinz = 0;
rh = Math.sqrt(x * x + y * y);
phi = rh * 0.5;
if (phi > 1) {
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) <= EPSLN) ? 0 : Math.asin(y * sinz / rh);
x *= sinz;
y = cosz * rh;
break;
case this.OBLIQ:
phi = (Math.abs(rh) <= EPSLN) ? this.phi0 : Math.asin(cosz * this.sinph0 + y * sinz * this.cosph0 / rh);
x *= sinz * this.cosph0;
y = (cosz - Math.sin(phi) * this.sinph0) * rh;
break;
case this.N_POLE:
y = -y;
phi = HALF_PI - phi;
break;
case this.S_POLE:
phi -= HALF_PI;
break;
}
lam = (y === 0 && (this.mode === this.EQUIT || this.mode === this.OBLIQ)) ? 0 : Math.atan2(x, y);
}
else {
ab = 0;
if (this.mode === this.OBLIQ || this.mode === this.EQUIT) {
x /= this.dd;
y *= this.dd;
rho = Math.sqrt(x * x + y * y);
if (rho < EPSLN) {
p.x = 0;
p.y = this.phi0;
return p;
}
sCe = 2 * Math.asin(0.5 * 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;
}
}
else if (this.mode === this.N_POLE || this.mode === this.S_POLE) {
if (this.mode === this.N_POLE) {
y = -y;
}
q = (x * x + y * y);
if (!q) {
p.x = 0;
p.y = this.phi0;
return p;
}
ab = 1 - q / this.qp;
if (this.mode === this.S_POLE) {
ab = -ab;
}
}
lam = Math.atan2(x, y);
phi = this.authlat(Math.asin(ab), this.apa);
}
p.x = adjust_lon(this.long0 + lam);
p.y = phi;
return p;
};
/* determine latitude from authalic latitude */
exports.P00 = 0.33333333333333333333;
exports.P01 = 0.17222222222222222222;
exports.P02 = 0.10257936507936507936;
exports.P10 = 0.06388888888888888888;
exports.P11 = 0.06640211640211640211;
exports.P20 = 0.01641501294219154443;
exports.authset = function(es) {
var t;
var APA = [];
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;
};
exports.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));
};
exports.names = ["Lambert Azimuthal Equal Area", "Lambert_Azimuthal_Equal_Area", "laea"];