@vizlabdev/geodesy
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Libraries of geodesy functions
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JavaScript
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
/* Ordnance Survey Grid Reference functions (c) Chris Veness 2005-2021 */
/* MIT Licence */
/* www.movable-type.co.uk/scripts/latlong-gridref.html */
/* www.movable-type.co.uk/scripts/geodesy-library.html#osgridref */
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
import LatLonEllipsoidal, { Dms } from './latlon-ellipsoidal-datum.js';
/**
* Ordnance Survey OSGB grid references provide geocoordinate references for UK mapping purposes.
*
* Formulation implemented here due to Thomas, Redfearn, etc is as published by OS, but is inferior
* to Krüger as used by e.g. Karney 2011.
*
* www.ordnancesurvey.co.uk/documents/resources/guide-coordinate-systems-great-britain.pdf.
*
* Note OSGB grid references cover Great Britain only; Ireland and the Channel Islands have their
* own references.
*
* Note that these formulae are based on ellipsoidal calculations, and according to the OS are
* accurate to about 4–5 metres – for greater accuracy, a geoid-based transformation (OSTN15) must
* be used.
*/
/*
* Converted 2015 to work with WGS84 by default, OSGB36 as option;
* www.ordnancesurvey.co.uk/blog/2014/12/confirmation-on-changes-to-latitude-and-longitude
*/
/* OsGridRef - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
const nationalGrid = {
trueOrigin: { lat: 49, lon: -2 }, // true origin of grid 49°N,2°W on OSGB36 datum
falseOrigin: { easting: -400e3, northing: 100e3 }, // easting & northing of false origin, metres from true origin
scaleFactor: 0.9996012717, // scale factor on central meridian
ellipsoid: LatLonEllipsoidal.ellipsoids.Airy1830,
};
// note Irish National Grid uses t/o 53°30′N, 8°W, f/o 200kmW, 250kmS, scale factor 1.000035, on Airy 1830 Modified ellipsoid
/**
* OS Grid References with methods to parse and convert them to latitude/longitude points.
*/
class OsGridRef {
/**
* Creates an OsGridRef object.
*
* @param {number} easting - Easting in metres from OS Grid false origin.
* @param {number} northing - Northing in metres from OS Grid false origin.
*
* @example
* import OsGridRef from '/js/geodesy/osgridref.js';
* const gridref = new OsGridRef(651409, 313177);
*/
constructor(easting, northing) {
this.easting = Number(easting);
this.northing = Number(northing);
if (isNaN(easting) || this.easting<0 || this.easting>700e3) throw new RangeError(`invalid easting ‘${easting}’`);
if (isNaN(northing) || this.northing<0 || this.northing>1300e3) throw new RangeError(`invalid northing ‘${northing}’`);
}
/**
* Converts ‘this’ Ordnance Survey Grid Reference easting/northing coordinate to latitude/longitude
* (SW corner of grid square).
*
* While OS Grid References are based on OSGB-36, the Ordnance Survey have deprecated the use of
* OSGB-36 for latitude/longitude coordinates (in favour of WGS-84), hence this function returns
* WGS-84 by default, with OSGB-36 as an option. See www.ordnancesurvey.co.uk/blog/2014/12/2.
*
* Note formulation implemented here due to Thomas, Redfearn, etc is as published by OS, but is
* inferior to Krüger as used by e.g. Karney 2011.
*
* @param {LatLon.datum} [datum=WGS84] - Datum to convert grid reference into.
* @returns {LatLon} Latitude/longitude of supplied grid reference.
*
* @example
* const gridref = new OsGridRef(651409.903, 313177.270);
* const pWgs84 = gridref.toLatLon(); // 52°39′28.723″N, 001°42′57.787″E
* // to obtain (historical) OSGB36 lat/lon point:
* const pOsgb = gridref.toLatLon(LatLon.datums.OSGB36); // 52°39′27.253″N, 001°43′04.518″E
*/
toLatLon(datum=LatLonEllipsoidal.datums.WGS84) {
const { easting: E, northing: N } = this;
const { a, b } = nationalGrid.ellipsoid; // a = 6377563.396, b = 6356256.909
const φ0 = nationalGrid.trueOrigin.lat.toRadians(); // latitude of true origin, 49°N
const λ0 = nationalGrid.trueOrigin.lon.toRadians(); // longitude of true origin, 2°W
const E0 = -nationalGrid.falseOrigin.easting; // easting of true origin, 400km
const N0 = -nationalGrid.falseOrigin.northing; // northing of true origin, -100km
const F0 = nationalGrid.scaleFactor; // 0.9996012717
const e2 = 1 - (b*b)/(a*a); // eccentricity squared
const n = (a-b)/(a+b), n2 = n*n, n3 = n*n*n; // n, n², n³
let φ=φ0, M=0;
do {
φ = (N-N0-M)/(a*F0) + φ;
const Ma = (1 + n + (5/4)*n2 + (5/4)*n3) * (φ-φ0);
const Mb = (3*n + 3*n*n + (21/8)*n3) * Math.sin(φ-φ0) * Math.cos(φ+φ0);
const Mc = ((15/8)*n2 + (15/8)*n3) * Math.sin(2*(φ-φ0)) * Math.cos(2*(φ+φ0));
const Md = (35/24)*n3 * Math.sin(3*(φ-φ0)) * Math.cos(3*(φ+φ0));
M = b * F0 * (Ma - Mb + Mc - Md); // meridional arc
} while (Math.abs(N-N0-M) >= 0.00001); // ie until < 0.01mm
const cosφ = Math.cos(φ), sinφ = Math.sin(φ);
const ν = a*F0/Math.sqrt(1-e2*sinφ*sinφ); // nu = transverse radius of curvature
const ρ = a*F0*(1-e2)/Math.pow(1-e2*sinφ*sinφ, 1.5); // rho = meridional radius of curvature
const η2 = ν/ρ-1; // eta = ?
const tanφ = Math.tan(φ);
const tan2φ = tanφ*tanφ, tan4φ = tan2φ*tan2φ, tan6φ = tan4φ*tan2φ;
const secφ = 1/cosφ;
const ν3 = ν*ν*ν, ν5 = ν3*ν*ν, ν7 = ν5*ν*ν;
const VII = tanφ/(2*ρ*ν);
const VIII = tanφ/(24*ρ*ν3)*(5+3*tan2φ+η2-9*tan2φ*η2);
const IX = tanφ/(720*ρ*ν5)*(61+90*tan2φ+45*tan4φ);
const X = secφ/ν;
const XI = secφ/(6*ν3)*(ν/ρ+2*tan2φ);
const XII = secφ/(120*ν5)*(5+28*tan2φ+24*tan4φ);
const XIIA = secφ/(5040*ν7)*(61+662*tan2φ+1320*tan4φ+720*tan6φ);
const dE = (E-E0), dE2 = dE*dE, dE3 = dE2*dE, dE4 = dE2*dE2, dE5 = dE3*dE2, dE6 = dE4*dE2, dE7 = dE5*dE2;
φ = φ - VII*dE2 + VIII*dE4 - IX*dE6;
const λ = λ0 + X*dE - XI*dE3 + XII*dE5 - XIIA*dE7;
let point = new LatLon_OsGridRef(φ.toDegrees(), λ.toDegrees(), 0, LatLonEllipsoidal.datums.OSGB36);
if (datum != LatLonEllipsoidal.datums.OSGB36) {
// if point is required in datum other than OSGB36, convert it
point = point.convertDatum(datum);
// convertDatum() gives us a LatLon: convert to LatLon_OsGridRef which includes toOsGrid()
point = new LatLon_OsGridRef(point.lat, point.lon, point.height, point.datum);
}
return point;
}
/**
* Parses grid reference to OsGridRef object.
*
* Accepts standard grid references (eg 'SU 387 148'), with or without whitespace separators, from
* two-digit references up to 10-digit references (1m × 1m square), or fully numeric comma-separated
* references in metres (eg '438700,114800').
*
* @param {string} gridref - Standard format OS Grid Reference.
* @returns {OsGridRef} Numeric version of grid reference in metres from false origin (SW corner of
* supplied grid square).
* @throws {Error} Invalid grid reference.
*
* @example
* const grid = OsGridRef.parse('TG 51409 13177'); // grid: { easting: 651409, northing: 313177 }
*/
static parse(gridref) {
gridref = String(gridref).trim();
// check for fully numeric comma-separated gridref format
let match = gridref.match(/^(\d+),\s*(\d+)$/);
if (match) return new OsGridRef(match[1], match[2]);
// validate format
match = gridref.match(/^[HNST][ABCDEFGHJKLMNOPQRSTUVWXYZ]\s*[0-9]+\s*[0-9]+$/i);
if (!match) throw new Error(`invalid grid reference ‘${gridref}’`);
// get numeric values of letter references, mapping A->0, B->1, C->2, etc:
let l1 = gridref.toUpperCase().charCodeAt(0) - 'A'.charCodeAt(0); // 500km square
let l2 = gridref.toUpperCase().charCodeAt(1) - 'A'.charCodeAt(0); // 100km square
// shuffle down letters after 'I' since 'I' is not used in grid:
if (l1 > 7) l1--;
if (l2 > 7) l2--;
// convert grid letters into 100km-square indexes from false origin (grid square SV):
const e100km = ((l1 - 2) % 5) * 5 + (l2 % 5);
const n100km = (19 - Math.floor(l1 / 5) * 5) - Math.floor(l2 / 5);
// skip grid letters to get numeric (easting/northing) part of ref
let en = gridref.slice(2).trim().split(/\s+/);
// if e/n not whitespace separated, split half way
if (en.length == 1) en = [ en[0].slice(0, en[0].length / 2), en[0].slice(en[0].length / 2) ];
// validation
if (en[0].length != en[1].length) throw new Error(`invalid grid reference ‘${gridref}’`);
// standardise to 10-digit refs (metres)
en[0] = en[0].padEnd(5, '0');
en[1] = en[1].padEnd(5, '0');
const e = e100km + en[0];
const n = n100km + en[1];
return new OsGridRef(e, n);
}
/**
* Converts ‘this’ numeric grid reference to standard OS Grid Reference.
*
* @param {number} [digits=10] - Precision of returned grid reference (10 digits = metres);
* digits=0 will return grid reference in numeric format.
* @returns {string} This grid reference in standard format.
*
* @example
* const gridref = new OsGridRef(651409, 313177).toString(8); // 'TG 5140 1317'
* const gridref = new OsGridRef(651409, 313177).toString(0); // '651409,313177'
*/
toString(digits=10) {
if (![ 0,2,4,6,8,10,12,14,16 ].includes(Number(digits))) throw new RangeError(`invalid precision ‘${digits}’`); // eslint-disable-line comma-spacing
let { easting: e, northing: n } = this;
// use digits = 0 to return numeric format (in metres) - note northing may be >= 1e7
if (digits == 0) {
const format = { useGrouping: false, minimumIntegerDigits: 6, maximumFractionDigits: 3 };
const ePad = e.toLocaleString('en', format);
const nPad = n.toLocaleString('en', format);
return `${ePad},${nPad}`;
}
// get the 100km-grid indices
const e100km = Math.floor(e / 100000), n100km = Math.floor(n / 100000);
// translate those into numeric equivalents of the grid letters
let l1 = (19 - n100km) - (19 - n100km) % 5 + Math.floor((e100km + 10) / 5);
let l2 = (19 - n100km) * 5 % 25 + e100km % 5;
// compensate for skipped 'I' and build grid letter-pairs
if (l1 > 7) l1++;
if (l2 > 7) l2++;
const letterPair = String.fromCharCode(l1 + 'A'.charCodeAt(0), l2 + 'A'.charCodeAt(0));
// strip 100km-grid indices from easting & northing, and reduce precision
e = Math.floor((e % 100000) / Math.pow(10, 5 - digits / 2));
n = Math.floor((n % 100000) / Math.pow(10, 5 - digits / 2));
// pad eastings & northings with leading zeros
e = e.toString().padStart(digits/2, '0');
n = n.toString().padStart(digits/2, '0');
return `${letterPair} ${e} ${n}`;
}
}
/* LatLon_OsGridRef - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
/**
* Extends LatLon class with method to convert LatLon point to OS Grid Reference.
*
* @extends LatLonEllipsoidal
*/
class LatLon_OsGridRef extends LatLonEllipsoidal {
/**
* Converts latitude/longitude to Ordnance Survey grid reference easting/northing coordinate.
*
* @returns {OsGridRef} OS Grid Reference easting/northing.
*
* @example
* const grid = new LatLon(52.65798, 1.71605).toOsGrid(); // TG 51409 13177
* // for conversion of (historical) OSGB36 latitude/longitude point:
* const grid = new LatLon(52.65798, 1.71605).toOsGrid(LatLon.datums.OSGB36);
*/
toOsGrid() {
// if necessary convert to OSGB36 first
const point = this.datum == LatLonEllipsoidal.datums.OSGB36
? this
: this.convertDatum(LatLonEllipsoidal.datums.OSGB36);
const φ = point.lat.toRadians();
const λ = point.lon.toRadians();
const { a, b } = nationalGrid.ellipsoid; // a = 6377563.396, b = 6356256.909
const φ0 = nationalGrid.trueOrigin.lat.toRadians(); // latitude of true origin, 49°N
const λ0 = nationalGrid.trueOrigin.lon.toRadians(); // longitude of true origin, 2°W
const E0 = -nationalGrid.falseOrigin.easting; // easting of true origin, 400km
const N0 = -nationalGrid.falseOrigin.northing; // northing of true origin, -100km
const F0 = nationalGrid.scaleFactor; // 0.9996012717
const e2 = 1 - (b*b)/(a*a); // eccentricity squared
const n = (a-b)/(a+b), n2 = n*n, n3 = n*n*n; // n, n², n³
const cosφ = Math.cos(φ), sinφ = Math.sin(φ);
const ν = a*F0/Math.sqrt(1-e2*sinφ*sinφ); // nu = transverse radius of curvature
const ρ = a*F0*(1-e2)/Math.pow(1-e2*sinφ*sinφ, 1.5); // rho = meridional radius of curvature
const η2 = ν/ρ-1; // eta = ?
const Ma = (1 + n + (5/4)*n2 + (5/4)*n3) * (φ-φ0);
const Mb = (3*n + 3*n*n + (21/8)*n3) * Math.sin(φ-φ0) * Math.cos(φ+φ0);
const Mc = ((15/8)*n2 + (15/8)*n3) * Math.sin(2*(φ-φ0)) * Math.cos(2*(φ+φ0));
const Md = (35/24)*n3 * Math.sin(3*(φ-φ0)) * Math.cos(3*(φ+φ0));
const M = b * F0 * (Ma - Mb + Mc - Md); // meridional arc
const cos3φ = cosφ*cosφ*cosφ;
const cos5φ = cos3φ*cosφ*cosφ;
const tan2φ = Math.tan(φ)*Math.tan(φ);
const tan4φ = tan2φ*tan2φ;
const I = M + N0;
const II = (ν/2)*sinφ*cosφ;
const III = (ν/24)*sinφ*cos3φ*(5-tan2φ+9*η2);
const IIIA = (ν/720)*sinφ*cos5φ*(61-58*tan2φ+tan4φ);
const IV = ν*cosφ;
const V = (ν/6)*cos3φ*(ν/ρ-tan2φ);
const VI = (ν/120) * cos5φ * (5 - 18*tan2φ + tan4φ + 14*η2 - 58*tan2φ*η2);
const Δλ = λ-λ0;
const Δλ2 = Δλ*Δλ, Δλ3 = Δλ2*Δλ, Δλ4 = Δλ3*Δλ, Δλ5 = Δλ4*Δλ, Δλ6 = Δλ5*Δλ;
let N = I + II*Δλ2 + III*Δλ4 + IIIA*Δλ6;
let E = E0 + IV*Δλ + V*Δλ3 + VI*Δλ5;
N = Number(N.toFixed(3)); // round to mm precision
E = Number(E.toFixed(3));
try {
return new OsGridRef(E, N); // note: gets truncated to SW corner of 1m grid square
} catch (e) {
throw new Error(`${e.message} from (${point.lat.toFixed(6)},${point.lon.toFixed(6)}).toOsGrid()`);
}
}
/**
* Override LatLonEllipsoidal.convertDatum() with version which returns LatLon_OsGridRef.
*/
convertDatum(toDatum) {
const osgbED = super.convertDatum(toDatum); // returns LatLonEllipsoidal_Datum
const osgbOSGR = new LatLon_OsGridRef(osgbED.lat, osgbED.lon, osgbED.height, osgbED.datum);
return osgbOSGR;
}
}
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
export { OsGridRef as default, LatLon_OsGridRef as LatLon, Dms };