@vizlabdev/geodesy
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Libraries of geodesy functions
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JavaScript
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
/* Geodesy tools for conversions between (historical) datums (c) Chris Veness 2005-2019 */
/* MIT Licence */
/* www.movable-type.co.uk/scripts/latlong-convert-coords.html */
/* www.movable-type.co.uk/scripts/geodesy-library.html#latlon-ellipsoidal-datum */
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
const {LatLonEllipsoidal, Cartesian, Dms } = require('./latlon-ellipsoidal.js');
/**
* Historical geodetic datums: a latitude/longitude point defines a geographic location on or
* above/below the earth’s surface, measured in degrees from the equator & the International
* Reference Meridian and metres above the ellipsoid, and based on a given datum. The datum is
* based on a reference ellipsoid and tied to geodetic survey reference points.
*
* Modern geodesy is generally based on the WGS84 datum (as used for instance by GPS systems), but
* previously various reference ellipsoids and datum references were used.
*
* This module extends the core latlon-ellipsoidal module to include ellipsoid parameters and datum
* transformation parameters, and methods for converting between different (generally historical)
* datums.
*
* It can be used for UK Ordnance Survey mapping (OS National Grid References are still based on the
* otherwise historical OSGB36 datum), as well as for historical purposes.
*
* q.v. Ordnance Survey ‘A guide to coordinate systems in Great Britain’ Section 6,
* www.ordnancesurvey.co.uk/docs/support/guide-coordinate-systems-great-britain.pdf, and also
* www.ordnancesurvey.co.uk/blog/2014/12/2.
*
* @module latlon-ellipsoidal-datum
*/
/*
* Ellipsoid parameters; exposed through static getter below.
*/
const ellipsoids = {
WGS84: { a: 6378137, b: 6356752.314245, f: 1/298.257223563 },
Airy1830: { a: 6377563.396, b: 6356256.909, f: 1/299.3249646 },
AiryModified: { a: 6377340.189, b: 6356034.448, f: 1/299.3249646 },
Bessel1841: { a: 6377397.155, b: 6356078.962818, f: 1/299.1528128 },
Clarke1866: { a: 6378206.4, b: 6356583.8, f: 1/294.978698214 },
Clarke1880IGN: { a: 6378249.2, b: 6356515.0, f: 1/293.466021294 },
GRS80: { a: 6378137, b: 6356752.314140, f: 1/298.257222101 },
Intl1924: { a: 6378388, b: 6356911.946, f: 1/297 }, // aka Hayford
WGS72: { a: 6378135, b: 6356750.5, f: 1/298.26 },
};
/*
* Datums; exposed through static getter below.
*/
const datums = {
// transforms: t in metres, s in ppm, r in arcseconds tx ty tz s rx ry rz
ED50: { ellipsoid: ellipsoids.Intl1924, transform: [ 89.5, 93.8, 123.1, -1.2, 0.0, 0.0, 0.156 ] }, // epsg.io/1311
ETRS89: { ellipsoid: ellipsoids.GRS80, transform: [ 0, 0, 0, 0, 0, 0, 0 ] }, // epsg.io/1149; @ 1-metre level
Irl1975: { ellipsoid: ellipsoids.AiryModified, transform: [ -482.530, 130.596, -564.557, -8.150, 1.042, 0.214, 0.631 ] }, // epsg.io/1954
NAD27: { ellipsoid: ellipsoids.Clarke1866, transform: [ 8, -160, -176, 0, 0, 0, 0 ] },
NAD83: { ellipsoid: ellipsoids.GRS80, transform: [ 0.9956, -1.9103, -0.5215, -0.00062, 0.025915, 0.009426, 0.011599 ] },
NTF: { ellipsoid: ellipsoids.Clarke1880IGN, transform: [ 168, 60, -320, 0, 0, 0, 0 ] },
OSGB36: { ellipsoid: ellipsoids.Airy1830, transform: [ -446.448, 125.157, -542.060, 20.4894, -0.1502, -0.2470, -0.8421 ] }, // epsg.io/1314
Potsdam: { ellipsoid: ellipsoids.Bessel1841, transform: [ -582, -105, -414, -8.3, 1.04, 0.35, -3.08 ] },
TokyoJapan: { ellipsoid: ellipsoids.Bessel1841, transform: [ 148, -507, -685, 0, 0, 0, 0 ] },
WGS72: { ellipsoid: ellipsoids.WGS72, transform: [ 0, 0, -4.5, -0.22, 0, 0, 0.554 ] },
WGS84: { ellipsoid: ellipsoids.WGS84, transform: [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ] },
};
/* sources:
* - ED50: www.gov.uk/guidance/oil-and-gas-petroleum-operations-notices#pon-4
* - Irl1975: www.osi.ie/wp-content/uploads/2015/05/transformations_booklet.pdf
* - NAD27: en.wikipedia.org/wiki/Helmert_transformation
* - NAD83: www.uvm.edu/giv/resources/WGS84_NAD83.pdf [strictly, WGS84(G1150) -> NAD83(CORS96) @ epoch 1997.0]
* (note NAD83(1986) ≡ WGS84(Original); confluence.qps.nl/pages/viewpage.action?pageId=29855173)
* - NTF: Nouvelle Triangulation Francaise geodesie.ign.fr/contenu/fichiers/Changement_systeme_geodesique.pdf
* - OSGB36: www.ordnancesurvey.co.uk/docs/support/guide-coordinate-systems-great-britain.pdf
* - Potsdam: kartoweb.itc.nl/geometrics/Coordinate%20transformations/coordtrans.html
* - TokyoJapan: www.geocachingtoolbox.com?page=datumEllipsoidDetails
* - WGS72: www.icao.int/safety/pbn/documentation/eurocontrol/eurocontrol wgs 84 implementation manual.pdf
*
* more transform parameters are available from earth-info.nga.mil/GandG/coordsys/datums/NATO_DT.pdf,
* www.fieldenmaps.info/cconv/web/cconv_params.js
*/
/* note:
* - ETRS89 reference frames are coincident with WGS-84 at epoch 1989.0 (ie null transform) at the one metre level.
*/
// freeze static properties
Object.keys(ellipsoids).forEach(e => Object.freeze(ellipsoids[e]));
Object.keys(datums).forEach(d => { Object.freeze(datums[d]); Object.freeze(datums[d].transform); });
/* LatLon - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
/**
* Latitude/longitude points on an ellipsoidal model earth, with ellipsoid parameters and methods
* for converting between datums and to geocentric (ECEF) cartesian coordinates.
*
* @extends LatLonEllipsoidal
*/
class LatLonEllipsoidal_Datum extends LatLonEllipsoidal {
/**
* Creates a geodetic latitude/longitude point on an ellipsoidal model earth using given datum.
*
* @param {number} lat - Latitude (in degrees).
* @param {number} lon - Longitude (in degrees).
* @param {number} [height=0] - Height above ellipsoid in metres.
* @param {LatLon.datums} datum - Datum this point is defined within.
*
* @example
* import LatLon from '/js/geodesy/latlon-ellipsoidal-datum.js';
* const p = new LatLon(53.3444, -6.2577, 17, LatLon.datums.Irl1975);
*/
constructor(lat, lon, height=0, datum=datums.WGS84) {
if (!datum || datum.ellipsoid==undefined) throw new TypeError(`unrecognised datum ‘${datum}’`);
super(lat, lon, height);
this._datum = datum;
}
/**
* Datum this point is defined within.
*/
get datum() {
return this._datum;
}
/**
* Ellipsoids with their parameters; semi-major axis (a), semi-minor axis (b), and flattening (f).
*
* Flattening f = (a−b)/a; at least one of these parameters is derived from defining constants.
*
* @example
* const a = LatLon.ellipsoids.Airy1830.a; // 6377563.396
*/
static get ellipsoids() {
return ellipsoids;
}
/**
* Datums; with associated ellipsoid, and Helmert transform parameters to convert from WGS-84
* into given datum.
*
* Note that precision of various datums will vary, and WGS-84 (original) is not defined to be
* accurate to better than ±1 metre. No transformation should be assumed to be accurate to
* better than a metre, for many datums somewhat less.
*
* This is a small sample of commoner datums from a large set of historical datums. I will add
* new datums on request.
*
* @example
* const a = LatLon.datums.OSGB36.ellipsoid.a; // 6377563.396
* const tx = LatLon.datums.OSGB36.transform; // [ tx, ty, tz, s, rx, ry, rz ]
* const availableDatums = Object.keys(LatLon.datums).join(', '); // ED50, Irl1975, NAD27, ...
*/
static get datums() {
return datums;
}
// note instance datum getter/setters are in LatLonEllipsoidal
/**
* Parses a latitude/longitude point from a variety of formats.
*
* Latitude & longitude (in degrees) can be supplied as two separate parameters, as a single
* comma-separated lat/lon string, or as a single object with { lat, lon } or GeoJSON properties.
*
* The latitude/longitude values may be numeric or strings; they may be signed decimal or
* deg-min-sec (hexagesimal) suffixed by compass direction (NSEW); a variety of separators are
* accepted. Examples -3.62, '3 37 12W', '3°37′12″W'.
*
* Thousands/decimal separators must be comma/dot; use Dms.fromLocale to convert locale-specific
* thousands/decimal separators.
*
* @param {number|string|Object} lat|latlon - Geodetic Latitude (in degrees) or comma-separated lat/lon or lat/lon object.
* @param {number} [lon] - Longitude in degrees.
* @param {number} [height=0] - Height above ellipsoid in metres.
* @param {LatLon.datums} [datum=WGS84] - Datum this point is defined within.
* @returns {LatLon} Latitude/longitude point on ellipsoidal model earth using given datum.
* @throws {TypeError} Unrecognised datum.
*
* @example
* const p = LatLon.parse('51.47736, 0.0000', 0, LatLon.datums.OSGB36);
*/
static parse(...args) {
let datum = datums.WGS84;
// if the last argument is a datum, use that, otherwise use default WGS-84
if (args.length==4 || (args.length==3 && typeof args[2] == 'object')) datum = args.pop();
if (!datum || datum.ellipsoid==undefined) throw new TypeError(`unrecognised datum ‘${datum}’`);
const point = super.parse(...args);
point._datum = datum;
return point;
}
/**
* Converts ‘this’ lat/lon coordinate to new coordinate system.
*
* @param {LatLon.datums} toDatum - Datum this coordinate is to be converted to.
* @returns {LatLon} This point converted to new datum.
* @throws {TypeError} Unrecognised datum.
*
* @example
* const pWGS84 = new LatLon(51.47788, -0.00147, 0, LatLon.datums.WGS84);
* const pOSGB = pWGS84.convertDatum(LatLon.datums.OSGB36); // 51.4773°N, 000.0001°E
*/
convertDatum(toDatum) {
if (!toDatum || toDatum.ellipsoid==undefined) throw new TypeError(`unrecognised datum ‘${toDatum}’`);
const oldCartesian = this.toCartesian(); // convert geodetic to cartesian
const newCartesian = oldCartesian.convertDatum(toDatum); // convert datum
const newLatLon = newCartesian.toLatLon(); // convert cartesian back to geodetic
return newLatLon;
}
/**
* Converts ‘this’ point from (geodetic) latitude/longitude coordinates to (geocentric) cartesian
* (x/y/z) coordinates, based on the same datum.
*
* Shadow of LatLonEllipsoidal.toCartesian(), returning Cartesian augmented with
* LatLonEllipsoidal_Datum methods/properties.
*
* @returns {Cartesian} Cartesian point equivalent to lat/lon point, with x, y, z in metres from
* earth centre, augmented with reference frame conversion methods and properties.
*/
toCartesian() {
const cartesian = super.toCartesian();
const cartesianDatum = new Cartesian_Datum(cartesian.x, cartesian.y, cartesian.z, this.datum);
return cartesianDatum;
}
}
/* Cartesian - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
/**
* Augments Cartesian with datum the cooordinate is based on, and methods to convert between datums
* (using Helmert 7-parameter transforms) and to convert cartesian to geodetic latitude/longitude
* point.
*
* @extends Cartesian
*/
class Cartesian_Datum extends Cartesian {
/**
* Creates cartesian coordinate representing ECEF (earth-centric earth-fixed) point, on a given
* datum. The datum will identify the primary meridian (for the x-coordinate), and is also
* useful in transforming to/from geodetic (lat/lon) coordinates.
*
* @param {number} x - X coordinate in metres (=> 0°N,0°E).
* @param {number} y - Y coordinate in metres (=> 0°N,90°E).
* @param {number} z - Z coordinate in metres (=> 90°N).
* @param {LatLon.datums} [datum] - Datum this coordinate is defined within.
* @throws {TypeError} Unrecognised datum.
*
* @example
* import { Cartesian } from '/js/geodesy/latlon-ellipsoidal-datum.js';
* const coord = new Cartesian(3980581.210, -111.159, 4966824.522);
*/
constructor(x, y, z, datum=undefined) {
if (datum && datum.ellipsoid==undefined) throw new TypeError(`unrecognised datum ‘${datum}’`);
super(x, y, z);
if (datum) this._datum = datum;
}
/**
* Datum this point is defined within.
*/
get datum() {
return this._datum;
}
set datum(datum) {
if (!datum || datum.ellipsoid==undefined) throw new TypeError(`unrecognised datum ‘${datum}’`);
this._datum = datum;
}
/**
* Converts ‘this’ (geocentric) cartesian (x/y/z) coordinate to (geodetic) latitude/longitude
* point (based on the same datum, or WGS84 if unset).
*
* Shadow of Cartesian.toLatLon(), returning LatLon augmented with LatLonEllipsoidal_Datum
* methods convertDatum, toCartesian, etc.
*
* @returns {LatLon} Latitude/longitude point defined by cartesian coordinates.
* @throws {TypeError} Unrecognised datum
*
* @example
* const c = new Cartesian(4027893.924, 307041.993, 4919474.294);
* const p = c.toLatLon(); // 50.7978°N, 004.3592°E
*/
toLatLon(deprecatedDatum=undefined) {
if (deprecatedDatum) {
console.info('datum parameter to Cartesian_Datum.toLatLon is deprecated: set datum before calling toLatLon()');
this.datum = deprecatedDatum;
}
const datum = this.datum || datums.WGS84;
if (!datum || datum.ellipsoid==undefined) throw new TypeError(`unrecognised datum ‘${datum}’`);
const latLon = super.toLatLon(datum.ellipsoid); // TODO: what if datum is not geocentric?
const point = new LatLonEllipsoidal_Datum(latLon.lat, latLon.lon, latLon.height, this.datum);
return point;
}
/**
* Converts ‘this’ cartesian coordinate to new datum using Helmert 7-parameter transformation.
*
* @param {LatLon.datums} toDatum - Datum this coordinate is to be converted to.
* @returns {Cartesian} This point converted to new datum.
* @throws {Error} Undefined datum.
*
* @example
* const c = new Cartesian(3980574.247, -102.127, 4966830.065, LatLon.datums.OSGB36);
* c.convertDatum(LatLon.datums.Irl1975); // [??,??,??]
*/
convertDatum(toDatum) {
// TODO: what if datum is not geocentric?
if (!toDatum || toDatum.ellipsoid == undefined) throw new TypeError(`unrecognised datum ‘${toDatum}’`);
if (!this.datum) throw new TypeError('cartesian coordinate has no datum');
let oldCartesian = null;
let transform = null;
if (this.datum == undefined || this.datum == datums.WGS84) {
// converting from WGS 84
oldCartesian = this;
transform = toDatum.transform;
}
if (toDatum == datums.WGS84) {
// converting to WGS 84; use inverse transform
oldCartesian = this;
transform = this.datum.transform.map(p => -p);
}
if (transform == null) {
// neither this.datum nor toDatum are WGS84: convert this to WGS84 first
oldCartesian = this.convertDatum(datums.WGS84);
transform = toDatum.transform;
}
const newCartesian = oldCartesian.applyTransform(transform);
newCartesian.datum = toDatum;
return newCartesian;
}
/**
* Applies Helmert 7-parameter transformation to ‘this’ coordinate using transform parameters t.
*
* This is used in converting datums (geodetic->cartesian, apply transform, cartesian->geodetic).
*
* @private
* @param {number[]} t - Transformation to apply to this coordinate.
* @returns {Cartesian} Transformed point.
*/
applyTransform(t) {
// this point
const { x: x1, y: y1, z: z1 } = this;
// transform parameters
const tx = t[0]; // x-shift in metres
const ty = t[1]; // y-shift in metres
const tz = t[2]; // z-shift in metres
const s = t[3]/1e6 + 1; // scale: normalise parts-per-million to (s+1)
const rx = (t[4]/3600).toRadians(); // x-rotation: normalise arcseconds to radians
const ry = (t[5]/3600).toRadians(); // y-rotation: normalise arcseconds to radians
const rz = (t[6]/3600).toRadians(); // z-rotation: normalise arcseconds to radians
// apply transform
const x2 = tx + x1*s - y1*rz + z1*ry;
const y2 = ty + x1*rz + y1*s - z1*rx;
const z2 = tz - x1*ry + y1*rx + z1*s;
return new Cartesian_Datum(x2, y2, z2);
}
}
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
module.exports.LatLonEllipsoidal = LatLonEllipsoidal_Datum;
module.exports.Cartesian = Cartesian_Datum;
module.exports.datums = datums;
module.exports.Dms = Dms;