var HALF_PI = Math.PI/2;
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var FORTPI = Math.PI/4;
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var EPSLN = 1.0e-10;
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var qsfnz = require('../common/qsfnz');
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var adjust_lon = require('../common/adjust_lon');
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/*
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reference
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"New Equal-Area Map Projections for Noncircular Regions", John P. Snyder,
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The American Cartographer, Vol 15, No. 4, October 1988, pp. 341-355.
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*/
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exports.S_POLE = 1;
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exports.N_POLE = 2;
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exports.EQUIT = 3;
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exports.OBLIQ = 4;
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/* Initialize the Lambert Azimuthal Equal Area projection
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------------------------------------------------------*/
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exports.init = function() {
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var t = Math.abs(this.lat0);
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if (Math.abs(t - HALF_PI) < EPSLN) {
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this.mode = this.lat0 < 0 ? this.S_POLE : this.N_POLE;
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}
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else if (Math.abs(t) < EPSLN) {
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this.mode = this.EQUIT;
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}
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else {
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this.mode = this.OBLIQ;
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}
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if (this.es > 0) {
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var sinphi;
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this.qp = qsfnz(this.e, 1);
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this.mmf = 0.5 / (1 - this.es);
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this.apa = this.authset(this.es);
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switch (this.mode) {
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case this.N_POLE:
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this.dd = 1;
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break;
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case this.S_POLE:
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this.dd = 1;
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break;
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case this.EQUIT:
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this.rq = Math.sqrt(0.5 * this.qp);
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this.dd = 1 / this.rq;
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this.xmf = 1;
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this.ymf = 0.5 * this.qp;
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break;
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case this.OBLIQ:
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this.rq = Math.sqrt(0.5 * this.qp);
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sinphi = Math.sin(this.lat0);
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this.sinb1 = qsfnz(this.e, sinphi) / this.qp;
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this.cosb1 = Math.sqrt(1 - this.sinb1 * this.sinb1);
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this.dd = Math.cos(this.lat0) / (Math.sqrt(1 - this.es * sinphi * sinphi) * this.rq * this.cosb1);
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this.ymf = (this.xmf = this.rq) / this.dd;
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this.xmf *= this.dd;
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break;
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}
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}
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else {
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if (this.mode === this.OBLIQ) {
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this.sinph0 = Math.sin(this.lat0);
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this.cosph0 = Math.cos(this.lat0);
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}
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}
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};
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/* Lambert Azimuthal Equal Area forward equations--mapping lat,long to x,y
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-----------------------------------------------------------------------*/
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exports.forward = function(p) {
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/* Forward equations
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-----------------*/
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var x, y, coslam, sinlam, sinphi, q, sinb, cosb, b, cosphi;
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var lam = p.x;
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var phi = p.y;
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lam = adjust_lon(lam - this.long0);
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if (this.sphere) {
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sinphi = Math.sin(phi);
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cosphi = Math.cos(phi);
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coslam = Math.cos(lam);
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if (this.mode === this.OBLIQ || this.mode === this.EQUIT) {
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y = (this.mode === this.EQUIT) ? 1 + cosphi * coslam : 1 + this.sinph0 * sinphi + this.cosph0 * cosphi * coslam;
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if (y <= EPSLN) {
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return null;
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}
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y = Math.sqrt(2 / y);
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x = y * cosphi * Math.sin(lam);
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y *= (this.mode === this.EQUIT) ? sinphi : this.cosph0 * sinphi - this.sinph0 * cosphi * coslam;
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}
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else if (this.mode === this.N_POLE || this.mode === this.S_POLE) {
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if (this.mode === this.N_POLE) {
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coslam = -coslam;
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}
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if (Math.abs(phi + this.phi0) < EPSLN) {
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return null;
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}
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y = FORTPI - phi * 0.5;
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y = 2 * ((this.mode === this.S_POLE) ? Math.cos(y) : Math.sin(y));
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x = y * Math.sin(lam);
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y *= coslam;
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}
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}
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else {
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sinb = 0;
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cosb = 0;
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b = 0;
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coslam = Math.cos(lam);
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sinlam = Math.sin(lam);
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sinphi = Math.sin(phi);
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q = qsfnz(this.e, sinphi);
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if (this.mode === this.OBLIQ || this.mode === this.EQUIT) {
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sinb = q / this.qp;
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cosb = Math.sqrt(1 - sinb * sinb);
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}
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switch (this.mode) {
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case this.OBLIQ:
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b = 1 + this.sinb1 * sinb + this.cosb1 * cosb * coslam;
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break;
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case this.EQUIT:
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b = 1 + cosb * coslam;
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break;
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case this.N_POLE:
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b = HALF_PI + phi;
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q = this.qp - q;
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break;
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case this.S_POLE:
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b = phi - HALF_PI;
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q = this.qp + q;
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break;
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}
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if (Math.abs(b) < EPSLN) {
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return null;
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}
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switch (this.mode) {
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case this.OBLIQ:
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case this.EQUIT:
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b = Math.sqrt(2 / b);
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if (this.mode === this.OBLIQ) {
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y = this.ymf * b * (this.cosb1 * sinb - this.sinb1 * cosb * coslam);
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}
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else {
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y = (b = Math.sqrt(2 / (1 + cosb * coslam))) * sinb * this.ymf;
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}
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x = this.xmf * b * cosb * sinlam;
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break;
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case this.N_POLE:
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case this.S_POLE:
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if (q >= 0) {
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x = (b = Math.sqrt(q)) * sinlam;
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y = coslam * ((this.mode === this.S_POLE) ? b : -b);
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}
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else {
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x = y = 0;
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}
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break;
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}
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}
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p.x = this.a * x + this.x0;
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p.y = this.a * y + this.y0;
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return p;
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};
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/* Inverse equations
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-----------------*/
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exports.inverse = function(p) {
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p.x -= this.x0;
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p.y -= this.y0;
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var x = p.x / this.a;
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var y = p.y / this.a;
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var lam, phi, cCe, sCe, q, rho, ab;
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if (this.sphere) {
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var cosz = 0,
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rh, sinz = 0;
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rh = Math.sqrt(x * x + y * y);
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phi = rh * 0.5;
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if (phi > 1) {
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return null;
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}
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phi = 2 * Math.asin(phi);
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if (this.mode === this.OBLIQ || this.mode === this.EQUIT) {
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sinz = Math.sin(phi);
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cosz = Math.cos(phi);
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}
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switch (this.mode) {
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case this.EQUIT:
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phi = (Math.abs(rh) <= EPSLN) ? 0 : Math.asin(y * sinz / rh);
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x *= sinz;
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y = cosz * rh;
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break;
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case this.OBLIQ:
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phi = (Math.abs(rh) <= EPSLN) ? this.phi0 : Math.asin(cosz * this.sinph0 + y * sinz * this.cosph0 / rh);
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x *= sinz * this.cosph0;
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y = (cosz - Math.sin(phi) * this.sinph0) * rh;
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break;
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case this.N_POLE:
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y = -y;
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phi = HALF_PI - phi;
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break;
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case this.S_POLE:
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phi -= HALF_PI;
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break;
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}
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lam = (y === 0 && (this.mode === this.EQUIT || this.mode === this.OBLIQ)) ? 0 : Math.atan2(x, y);
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}
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else {
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ab = 0;
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if (this.mode === this.OBLIQ || this.mode === this.EQUIT) {
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x /= this.dd;
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y *= this.dd;
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rho = Math.sqrt(x * x + y * y);
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if (rho < EPSLN) {
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p.x = 0;
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p.y = this.phi0;
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return p;
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}
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sCe = 2 * Math.asin(0.5 * rho / this.rq);
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cCe = Math.cos(sCe);
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x *= (sCe = Math.sin(sCe));
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if (this.mode === this.OBLIQ) {
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ab = cCe * this.sinb1 + y * sCe * this.cosb1 / rho;
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q = this.qp * ab;
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y = rho * this.cosb1 * cCe - y * this.sinb1 * sCe;
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}
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else {
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ab = y * sCe / rho;
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q = this.qp * ab;
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y = rho * cCe;
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}
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}
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else if (this.mode === this.N_POLE || this.mode === this.S_POLE) {
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if (this.mode === this.N_POLE) {
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y = -y;
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}
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q = (x * x + y * y);
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if (!q) {
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p.x = 0;
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p.y = this.phi0;
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return p;
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}
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ab = 1 - q / this.qp;
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if (this.mode === this.S_POLE) {
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ab = -ab;
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}
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}
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lam = Math.atan2(x, y);
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phi = this.authlat(Math.asin(ab), this.apa);
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}
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p.x = adjust_lon(this.long0 + lam);
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p.y = phi;
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return p;
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};
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/* determine latitude from authalic latitude */
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exports.P00 = 0.33333333333333333333;
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exports.P01 = 0.17222222222222222222;
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exports.P02 = 0.10257936507936507936;
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exports.P10 = 0.06388888888888888888;
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exports.P11 = 0.06640211640211640211;
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exports.P20 = 0.01641501294219154443;
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exports.authset = function(es) {
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var t;
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var APA = [];
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APA[0] = es * this.P00;
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t = es * es;
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APA[0] += t * this.P01;
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APA[1] = t * this.P10;
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t *= es;
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APA[0] += t * this.P02;
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APA[1] += t * this.P11;
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APA[2] = t * this.P20;
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return APA;
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};
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exports.authlat = function(beta, APA) {
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var t = beta + beta;
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return (beta + APA[0] * Math.sin(t) + APA[1] * Math.sin(t + t) + APA[2] * Math.sin(t + t + t));
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};
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exports.names = ["Lambert Azimuthal Equal Area", "Lambert_Azimuthal_Equal_Area", "laea"];
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