import {LonLat} from "../LonLat";
import {Quat} from "../math/Quat";
import {Vec3} from "../math/Vec3";
import {DEGREES, EPS1, EPS12, EPS15, RADIANS, zeroTwoPI} from "../math";
export interface IInverseResult {
distance: number;
initialAzimuth: number;
finalAzimuth: number;
}
export interface IDirectResult {
destination: LonLat;
finalAzimuth: number;
}
/**
* Class represents a plant ellipsoid.
* @class
* @param {number} equatorialSize - Equatorial ellipsoid size.
* @param {number} polarSize - Polar ellipsoid size.
*/
class Ellipsoid {
/**
* Equatorial size
* @type {number}
* @protected
*/
protected _a: number;
/**
* Polar size
* @type {number}
* @protected
*/
protected _b: number;
protected _flattening: number;
protected _f: number;
protected _a2: number;
protected _b2: number;
protected _e: number;
protected _e2: number;
protected _e22: number;
protected _k: number;
protected _k2: number;
protected _radii: Vec3;
protected _radii2: Vec3;
protected _invRadii: Vec3;
public _invRadii2: Vec3;
constructor(equatorialSize: number = 1, polarSize: number = 1) {
this._a = equatorialSize;
this._b = polarSize;
this._flattening = (equatorialSize - polarSize) / equatorialSize;
this._f = 1 / this._flattening;
this._a2 = equatorialSize * equatorialSize;
this._b2 = polarSize * polarSize;
const qa2b2 = Math.sqrt(this._a2 - this._b2);
this._e = qa2b2 / equatorialSize;
this._e2 = this._e * this._e;
this._e22 = this._e2 * this._e2;
this._k = qa2b2 / polarSize;
this._k2 = this._k * this._k;
this._radii = new Vec3(equatorialSize, equatorialSize, polarSize);
this._radii2 = new Vec3(this._a2, this._a2, this._b2);
this._invRadii = new Vec3(1.0 / equatorialSize, 1.0 / equatorialSize, 1.0 / polarSize);
this._invRadii2 = new Vec3(1.0 / this._a2, 1.0 / this._a2, 1.0 / this._b2);
}
/**
* Returns the distance travelling from ‘this’ point to destination point along a rhumb line.
* @param {LonLat} startLonLat coordinates.
* @param {LonLat} endLonLat coordinates
* @returns {number} Distance in m between this point and destination point (same units as radius).
*/
public rhumbDistanceTo(startLonLat: LonLat, endLonLat: LonLat): number {
const f1 = startLonLat.lat * RADIANS;
const f2 = endLonLat.lat * RADIANS;
const df = f2 - f1;
let d = Math.abs(endLonLat.lon - startLonLat.lon) * RADIANS;
if (Math.abs(d) > Math.PI) d = d > 0 ? -(2 * Math.PI - d) : (2 * Math.PI + d);
const dd = Math.log(Math.tan(f2 / 2 + Math.PI / 4) / Math.tan(f1 / 2 + Math.PI / 4));
const q = Math.abs(dd) > 10e-12 ? df / dd : Math.cos(f1);
const t = Math.sqrt(df * df + q * q * d * d); // angular distance in radians
return t * this._a;
}
/**
* Returns the point at given fraction between two points on the great circle.
* @param {LonLat} lonLat1 - Longitude/Latitude of source point.
* @param {LonLat} lonLat2 - Longitude/Latitude of destination point.
* @param {number} fraction - Fraction between the two points (0 = source point, 1 = destination point).
* @returns {LonLat} Intermediate point between points.
*/
public getIntermediatePointOnGreatCircle(lonLat1: LonLat, lonLat2: LonLat, fraction: number): LonLat {
if (fraction == 0) return lonLat1.clone();
if (fraction == 1) return lonLat2.clone();
const inverse = this.inverse(lonLat1, lonLat2);
const dist = inverse.distance;
const azimuth = inverse.initialAzimuth;
return isNaN(azimuth) ? lonLat1 : this.getGreatCircleDestination(lonLat1, azimuth, dist * fraction);
}
/**
* REMOVE ASAP after
* @param lonLat1
* @param lonLat2
* @returns {number}
*/
static getBearing(lonLat1: LonLat, lonLat2: LonLat): number {
let f1 = lonLat1.lat * RADIANS,
l1 = lonLat1.lon * RADIANS;
let f2 = lonLat2.lat * RADIANS,
l2 = lonLat2.lon * RADIANS;
let y = Math.sin(l2 - l1) * Math.cos(f2);
let x = Math.cos(f1) * Math.sin(f2) - Math.sin(f1) * Math.cos(f2) * Math.cos(l2 - l1);
return Math.atan2(y, x) * DEGREES;
}
public getFlattening(): number {
return this._flattening;
}
/**
* Gets ellipsoid equatorial size.
* @public
* @returns {number} -
*/
public getEquatorialSize(): number {
return this._a;
}
public get equatorialSize(): number {
return this._a;
}
public get equatorialSizeSqr(): number {
return this._a2;
}
/**
* Gets ellipsoid polar size.
* @public
* @returns {number} -
*/
public getPolarSize(): number {
return this._b;
}
public get polarSize(): number {
return this._b;
}
public get polarSizeSqr(): number {
return this._b2;
}
/**
* Calculate cartesian coordinates by its ECEF geodetic coordinates.
* @public
* @param {LonLat} lonlat - Geodetic coordinates.
* @returns {Vec3} -
*/
public lonLatToCartesian(lonlat: LonLat): Vec3 {
return this.geodeticToCartesian(lonlat.lon, lonlat.lat, lonlat.height);
}
/**
* Calculate cartesian coordinates by its ECEF geodetic coordinates.
* @public
* @param {LonLat} lonlat - Geodetic coordinates.
* @param {Vec3} res - Output variable reference.
* @returns {Vec3} -
*/
public lonLatToCartesianRes(lonlat: LonLat, res: Vec3): Vec3 {
return this.geodeticToCartesian(lonlat.lon, lonlat.lat, lonlat.height, res);
}
/**
* Gets cartesian ECEF from Wgs84 geodetic coordinates.
* @public
* @param {Number} lon - Longitude.
* @param {Number} lat - Latitude.
* @param {Number} height - Height.
* @param {Vec3} res - Output result variable.
* @returns {Vec3} -
*/
public geodeticToCartesian(lon: number, lat: number, height: number = 0, res: Vec3 = new Vec3()): Vec3 {
let latrad = RADIANS * lat,
lonrad = RADIANS * lon;
let slt = Math.sin(latrad);
let N = this._a / Math.sqrt(1 - this._e2 * slt * slt);
let nc = (N + height) * Math.cos(latrad);
res.x = nc * Math.cos(lonrad);
res.y = nc * Math.sin(lonrad);
res.z = (N * (1 - this._e2) + height) * slt;
return res;
}
/**
* Gets Wgs84 geodetic coordinates from cartesian ECEF.
* @public
* @param {Vec3} p - Cartesian coordinates.
* @returns {LonLat} -
*/
public projToSurface(p: Vec3): Vec3 {
let pX = p.x || 0.0,
pY = p.y || 0.0,
pZ = p.z || 0.0;
let length = Math.sqrt(pX * pX + pY * pY + pZ * pZ);
if (length === 0) {
return this.lonLatToCartesian(new LonLat());
}
let invRadii2X = this._invRadii2.x,
invRadii2Y = this._invRadii2.y,
invRadii2Z = this._invRadii2.z;
let x2 = pX * pX * invRadii2X,
y2 = pY * pY * invRadii2Y,
z2 = pZ * pZ * invRadii2Z;
let norm = x2 + y2 + z2;
let ratio = Math.sqrt(1.0 / norm);
let first = p.scaleTo(ratio);
if (norm < EPS1) {
return !Number.isFinite(ratio) ? new Vec3() : first
}
let lambda = ((1.0 - ratio) * length) / first.mulA(this._invRadii2).length();
let m_X = 0.0, m_Y = 0.0, m_Z = 0.0;
do {
m_X = 1.0 / (1.0 + lambda * invRadii2X);
m_Y = 1.0 / (1.0 + lambda * invRadii2Y);
m_Z = 1.0 / (1.0 + lambda * invRadii2Z);
let m_X2 = m_X * m_X,
m_Y2 = m_Y * m_Y,
m_Z2 = m_Z * m_Z;
let func = x2 * m_X2 + y2 * m_Y2 + z2 * m_Z2 - 1.0;
if (Math.abs(func) < EPS12) {
break;
}
let m_X3 = m_X2 * m_X,
m_Y3 = m_Y2 * m_Y,
m_Z3 = m_Z2 * m_Z;
lambda += 0.5 * func / (x2 * m_X3 * invRadii2X + y2 * m_Y3 * invRadii2Y + z2 * m_Z3 * invRadii2Z);
} while (true); // eslint-disable-line
return new Vec3(pX * m_X, pY * m_Y, pZ * m_Z);
}
/**
* Converts 3d cartesian coordinates to geodetic
* @param {Vec3} cart - Cartesian coordinates
* @returns {LonLat} - Geodetic coordinates
*/
public cartesianToLonLat(cart: Vec3): LonLat {
return this.cartesianToLonLatRes(cart);
}
/**
* Converts 3d cartesian coordinates to geodetic
* @param {Vec3} cart - Cartesian coordinates
* @param {LonLat} res - Link geodetic coordinates variable
* @returns {LonLat} - Geodetic coordinates
*/
public cartesianToLonLatRes(cart: Vec3, res: LonLat = new LonLat()): LonLat {
let p = this.projToSurface(cart);
let n = this.getSurfaceNormal3v(p),
h = cart.sub(p);
res.lon = Math.atan2(n.y, n.x) * DEGREES;
res.lat = Math.asin(n.z) * DEGREES;
res.height = Math.sign(h.dot(cart)) * h.length();
return res;
}
/**
* Gets ellipsoid surface normal.
* @public
* @param {Vec3} coord - Spatial coordinates.
* @return {Vec3} -
*/
public getSurfaceNormal3v(coord: Vec3): Vec3 {
let r2 = this._invRadii2;
let nx = coord.x * r2.x,
ny = coord.y * r2.y,
nz = coord.z * r2.z;
let l = 1.0 / Math.sqrt(nx * nx + ny * ny + nz * nz);
return new Vec3(nx * l, ny * l, nz * l);
}
public getGreatCircleDistance(lonLat1: LonLat, lonLat2: LonLat): number {
return this.inverse(lonLat1, lonLat2).distance;
}
/**
* Calculates the destination point given start point lat / lon, azimuth(deg) and distance (m).
* Source: http://movable-type.co.uk/scripts/latlong-vincenty-direct.html and optimized / cleaned up by Mathias Bynens <http://mathiasbynens.be/>
* Based on the Vincenty direct formula by T. Vincenty, “Direct and Inverse Solutions of Geodesics on the Ellipsoid with application of nested equations”, Survey Review, vol XXII no 176, 1975 <http://www.ngs.noaa.gov/PUBS_LIB/inverse.pdf>
* @param {LonLat} lonLat - Origin coordinates
* @param {number} azimuth - View azimuth in degrees
* @param {number} dist - Distance to the destination point coordinates in meters
* @returns {LonLat} - Destination point coordinates
*/
public getGreatCircleDestination(lonLat: LonLat, azimuth: number, dist: number): LonLat {
return this.direct(lonLat, azimuth, dist).destination;
}
/**
* Returns inverse Geodesic solution for two points
* @param {LonLat} lonLat1 - start coordinates point
* @param {LonLat} lonLat2 - end coordinates point
* @returns {IInverseResult} - Contains distance, initialAzimuth, and finalAzimuth values
*/
public inverse(lonLat1: LonLat, lonLat2: LonLat): IInverseResult {
let a = this._a, b = this._b, f = this._flattening;
const fi1 = lonLat1.lat * RADIANS, lambda1 = lonLat1.lon * RADIANS;
const fi2 = lonLat2.lat * RADIANS, lambda2 = lonLat2.lon * RADIANS;
const L = lambda2 - lambda1; // L = difference in longitude, U = reduced latitude, defined by tan U = (1-f)·tanφ.
const tanU1 = (1 - f) * Math.tan(fi1), cosU1 = 1 / Math.sqrt((1 + tanU1 * tanU1)), sinU1 = tanU1 * cosU1;
const tanU2 = (1 - f) * Math.tan(fi2), cosU2 = 1 / Math.sqrt((1 + tanU2 * tanU2)), sinU2 = tanU2 * cosU2;
const antipodal = Math.abs(L) > Math.PI / 2 || Math.abs(fi2 - fi1) > Math.PI / 2;
let lmb = L, sinLmb = null, cosLmb = null; // lmb - difference in longitude on an auxiliary sphere
let s = antipodal ? Math.PI : 0, sin_s = 0, cos_s = antipodal ? -1 : 1, sinSqs = null; // s - angular distance lonLat1 lonLat2 on the sphere
let cos2sm = 1; // sm - angular distance on the sphere from the equator to the midpoint of the line
let cosSqa = 1; // a - azimuth of the geodesic at the equator
let lmb_ = null, iterations = 0;
do {
sinLmb = Math.sin(lmb);
cosLmb = Math.cos(lmb);
sinSqs = (cosU2 * sinLmb) ** 2 + (cosU1 * sinU2 - sinU1 * cosU2 * cosLmb) ** 2;
if (Math.abs(sinSqs) < 1e-24) break; // co-incident/antipodal points (σ < ≈0.006mm)
sin_s = Math.sqrt(sinSqs);
cos_s = sinU1 * sinU2 + cosU1 * cosU2 * cosLmb;
s = Math.atan2(sin_s, cos_s);
const sin_a = cosU1 * cosU2 * sinLmb / sin_s;
cosSqa = 1 - sin_a * sin_a;
cos2sm = (cosSqa != 0) ? (cos_s - 2 * sinU1 * sinU2 / cosSqa) : 0; // on equatorial line cos²α = 0 (§6)
const C = f / 16 * cosSqa * (4 + f * (4 - 3 * cosSqa));
lmb_ = lmb;
lmb = L + (1 - C) * f * sin_a * (s + C * sin_s * (cos2sm + C * cos_s * (-1 + 2 * cos2sm * cos2sm)));
} while (Math.abs(lmb - lmb_) > EPS12 && ++iterations < 1000);
const uSq = cosSqa * (a * a - b * b) / (b * b);
const A = 1 + uSq / 16384 * (4096 + uSq * (-768 + uSq * (320 - 175 * uSq)));
const B = uSq / 1024 * (256 + uSq * (-128 + uSq * (74 - 47 * uSq)));
const ds = B * sin_s * (cos2sm + B / 4 * (cos_s * (-1 + 2 * cos2sm * cos2sm) - B / 6 * cos2sm * (-3 + 4 * sin_s * sin_s) * (-3 + 4 * cos2sm * cos2sm)));
const dist = b * A * (s - ds); // s = length of the geodesic
// note special handling of exactly antipodal points where sin²σ = 0 (due to discontinuity
// atan2(0, 0) = 0 but atan2(ε, 0) = π/2 / 90°) - in which case bearing is always meridional,
// due north (or due south!)
// α = azimuths of the geodesic; α2 the direction P₁ P₂ produced
const a1 = Math.abs(sinSqs) < Number.EPSILON ? 0 : Math.atan2(cosU2 * sinLmb, cosU1 * sinU2 - sinU1 * cosU2 * cosLmb);
const a2 = Math.abs(sinSqs) < Number.EPSILON ? Math.PI : Math.atan2(cosU1 * sinLmb, -sinU1 * cosU2 + cosU1 * sinU2 * cosLmb);
return {
distance: dist,
initialAzimuth: Math.abs(dist) < Number.EPSILON ? NaN : zeroTwoPI(a1) * DEGREES,
finalAzimuth: Math.abs(dist) < Number.EPSILON ? NaN : zeroTwoPI(a2) * DEGREES
};
}
/**
* Calculates the destination point given start point lat / lon, azimuth(deg) and distance (m).
* Source: http://movable-type.co.uk/scripts/latlong-vincenty-direct.html and optimized / cleaned up by Mathias Bynens <http://mathiasbynens.be/>
* Based on the Vincenty direct formula by T. Vincenty, “Direct and Inverse Solutions of Geodesics on the Ellipsoid with application of nested equations”, Survey Review, vol XXII no 176, 1975 <http://www.ngs.noaa.gov/PUBS_LIB/inverse.pdf>
* @param {LonLat} lonLat - Origin coordinates
* @param {number} azimuth - View azimuth in degrees
* @param {number} dist - Distance to the destination point coordinates in meters
* @returns {{ destination: LonLat; finalAzimuth: number }} - Destination point coordinates
*/
public direct(lonLat: LonLat, azimuth: number, dist: number): IDirectResult {
let lon1 = lonLat.lon,
lat1 = lonLat.lat;
let a = this._a,
b = this._b,
f = this._flattening,
s = dist,
alpha1 = azimuth * RADIANS,
sinAlpha1 = Math.sin(alpha1),
cosAlpha1 = Math.cos(alpha1),
tanU1 = (1 - f) * Math.tan(lat1 * RADIANS),
cosU1 = 1 / Math.sqrt(1 + tanU1 * tanU1),
sinU1 = tanU1 * cosU1,
sigma1 = Math.atan2(tanU1, cosAlpha1),
sinAlpha = cosU1 * sinAlpha1,
cosSqAlpha = 1 - sinAlpha * sinAlpha,
uSq = (cosSqAlpha * (a * a - b * b)) / (b * b),
A = 1 + (uSq / 16384) * (4096 + uSq * (-768 + uSq * (320 - 175 * uSq))),
B = (uSq / 1024) * (256 + uSq * (-128 + uSq * (74 - 47 * uSq))),
sigma = s / (b * A),
sigmaP = 2 * Math.PI;
let cos2SigmaM = 0,
sinSigma = 0,
cosSigma = 0,
deltaSigma = 0;
while (Math.abs(sigma - sigmaP) > 1e-12) {
cos2SigmaM = Math.cos(2 * sigma1 + sigma);
sinSigma = Math.sin(sigma);
cosSigma = Math.cos(sigma);
deltaSigma = B * sinSigma *
(cos2SigmaM + (B / 4) *
(
cosSigma * (-1 + 2 * cos2SigmaM * cos2SigmaM) -
(B / 6) * cos2SigmaM * (-3 + 4 * sinSigma * sinSigma) * (-3 + 4 * cos2SigmaM * cos2SigmaM)
));
sigmaP = sigma;
sigma = s / (b * A) + deltaSigma;
}
let tmp = sinU1 * sinSigma - cosU1 * cosSigma * cosAlpha1,
lat2 = Math.atan2(
sinU1 * cosSigma + cosU1 * sinSigma * cosAlpha1,
(1 - f) * Math.sqrt(sinAlpha * sinAlpha + tmp * tmp)
),
lambda = Math.atan2(
sinSigma * sinAlpha1,
cosU1 * cosSigma - sinU1 * sinSigma * cosAlpha1
),
C = (f / 16.0) * cosSqAlpha * (4.0 + f * (4.0 - 3.0 * cosSqAlpha)),
L = lambda - (1.0 - C) * f * sinAlpha * (sigma + C * sinSigma * (cos2SigmaM + C * cosSigma * (-1.0 + 2.0 * cos2SigmaM * cos2SigmaM))),
revAz = Math.atan2(sinAlpha, -tmp);
return {
destination: new LonLat(lon1 + L * DEGREES, lat2 * DEGREES),
finalAzimuth: revAz * DEGREES
};
}
/**
* Returns cartesian coordinates of the intersection of a ray and an ellipsoid.
* If the ray doesn't hit ellipsoid returns null.
* @public
* @param {Vec3} origin - Ray origin point.
* @param {Vec3} direction - Ray direction.
* @returns {Vec3} -
*/
public hitRay(origin: Vec3, direction: Vec3): Vec3 | undefined {
let q = this._invRadii.mul(origin);
let w = this._invRadii.mul(direction);
let q2 = q.dot(q);
let qw = q.dot(w);
let difference, w2, product, discriminant, temp;
if (q2 > 1.0) {
// Outside ellipsoid.
if (qw >= 0.0) {
// Looking outward or tangent (0 intersections).
return undefined;
}
// qw < 0.0.
var qw2 = qw * qw;
difference = q2 - 1.0; // Positively valued.
w2 = w.dot(w);
product = w2 * difference;
let eps = Math.abs(qw2 - product);
if (eps > EPS15 && qw2 < product) {
// Imaginary roots (0 intersections).
return undefined;
} else if (qw2 > product) {
// Distinct roots (2 intersections).
discriminant = qw * qw - product;
temp = -qw + Math.sqrt(discriminant); // Avoid cancellation.
var root0 = temp / w2;
var root1 = difference / temp;
if (root0 < root1) {
return origin.add(direction.scaleTo(root0));
}
return origin.add(direction.scaleTo(root1));
} else {
// qw2 == product. Repeated roots (2 intersections).
var root = Math.sqrt(difference / w2);
return origin.add(direction.scaleTo(root));
}
} else if (q2 < 1.0) {
// Inside ellipsoid (2 intersections).
difference = q2 - 1.0; // Negatively valued.
w2 = w.dot(w);
product = w2 * difference; // Negatively valued.
discriminant = qw * qw - product;
temp = -qw + Math.sqrt(discriminant); // Positively valued.
return origin.add(direction.scaleTo(temp / w2));
} else {
// q2 == 1.0. On ellipsoid.
if (qw < 0.0) {
// Looking inward.
w2 = w.dot(w);
return origin.add(direction.scaleTo(-qw / w2));
}
// qw >= 0.0. Looking outward or tangent.
// return undefined
}
}
public getNorthFrameRotation(cartesian: Vec3): Quat {
let n = this.getSurfaceNormal3v(cartesian);
let t = Vec3.proj_b_to_plane(Vec3.NORTH, n);
return Quat.getLookRotation(t, n);
}
/**
* @todo this is not precise function, needs to be replaced or removed
* @param lonLat1
* @param bearing
* @param distance
* @returns {LonLat}
*/
public getBearingDestination(lonLat1: LonLat, bearing: number = 0.0, distance: number = 0): LonLat {
bearing = bearing * RADIANS;
var nlon = ((lonLat1.lon + 540) % 360) - 180;
var f1 = lonLat1.lat * RADIANS,
l1 = nlon * RADIANS;
var dR = distance / this._a;
var f2 = Math.asin(
Math.sin(f1) * Math.cos(dR) + Math.cos(f1) * Math.sin(dR) * Math.cos(bearing)
);
return new LonLat(
(l1 +
Math.atan2(
Math.sin(bearing) * Math.sin(dR) * Math.cos(f1),
Math.cos(dR) - Math.sin(f1) * Math.sin(f2)
)) *
DEGREES,
f2 * DEGREES
);
}
/**
* Returns the point at given fraction between two points on the great circle.
* @param {LonLat} lonLat1 - Longitude/Latitude of source point.
* @param {LonLat} lonLat2 - Longitude/Latitude of destination point.
* @param {number} fraction - Fraction between the two points (0 = source point, 1 = destination point).
* @returns {LonLat} Intermediate point between points.
*/
static getIntermediatePointOnGreatCircle(lonLat1: LonLat, lonLat2: LonLat, fraction: number): LonLat {
var f1 = lonLat1.lat * RADIANS,
l1 = lonLat1.lon * RADIANS;
var f2 = lonLat2.lat * RADIANS,
l2 = lonLat2.lon * RADIANS;
var sinf1 = Math.sin(f1),
cosf1 = Math.cos(f1),
sinl1 = Math.sin(l1),
cosl1 = Math.cos(l1);
var sinf2 = Math.sin(f2),
cosf2 = Math.cos(f2),
sinl2 = Math.sin(l2),
cosl2 = Math.cos(l2);
var df = f2 - f1,
dl = l2 - l1;
var a =
Math.sin(df / 2) * Math.sin(df / 2) +
Math.cos(f1) * Math.cos(f2) * Math.sin(dl / 2) * Math.sin(dl / 2);
var d = 2 * Math.atan2(Math.sqrt(a), Math.sqrt(1 - a));
var A = Math.sin((1 - fraction) * d) / Math.sin(d);
var B = Math.sin(fraction * d) / Math.sin(d);
var x = A * cosf1 * cosl1 + B * cosf2 * cosl2;
var y = A * cosf1 * sinl1 + B * cosf2 * sinl2;
var z = A * sinf1 + B * sinf2;
var f3 = Math.atan2(z, Math.sqrt(x * x + y * y));
var l3 = Math.atan2(y, x);
return new LonLat(((l3 * DEGREES + 540) % 360) - 180, f3 * DEGREES);
}
static getRhumbBearing(lonLat1: LonLat, lonLat2: LonLat): number {
var dLon = (lonLat2.lon - lonLat1.lon) * RADIANS;
var dPhi = Math.log(
Math.tan((lonLat2.lat * RADIANS) / 2 + Math.PI / 4) /
Math.tan((lonLat1.lat * RADIANS) / 2 + Math.PI / 4)
);
if (Math.abs(dLon) > Math.PI) {
if (dLon > 0) {
dLon = (2 * Math.PI - dLon) * -1;
} else {
dLon = 2 * Math.PI + dLon;
}
}
return (Math.atan2(dLon, dPhi) * DEGREES + 360) % 360;
}
}
export {Ellipsoid};