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Prepare for misc.ianrenton.com going offline
This commit is contained in:
Ian Renton
+3
-3
@@ -16,7 +16,7 @@ L.WorkedAllBritainIreland = L.LayerGroup.extend({
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// Workaround to load the geodesy modules in non-modular code. Once we have loaded all three modules, trigger a
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// first draw.
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import("https://misc.ianrenton.com/Leaflet.WorkedAllBritainIreland/modules/geodesy/osgridref.js")
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import(new URL('./modules/geodesy/osgridref.js', import.meta.url).href)
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.then(module => {
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this._osGridLibrary = module;
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if (this._ieGridLibrary && this._utmLibrary) {
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@@ -27,7 +27,7 @@ L.WorkedAllBritainIreland = L.LayerGroup.extend({
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console.log("Error loading OS Grid Ref library, GB WAB squares may not be available.");
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console.log(error);
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});
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import("https://misc.ianrenton.com/Leaflet.WorkedAllBritainIreland/modules/geodesy/iegridref.js")
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import(new URL('./modules/geodesy/iegridref.js', import.meta.url).href)
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.then(module => {
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this._ieGridLibrary = module;
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if (this._osGridLibrary && this._utmLibrary) {
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@@ -38,7 +38,7 @@ L.WorkedAllBritainIreland = L.LayerGroup.extend({
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console.log("Error loading IE Grid Ref library, NI WAB squares may not be available.");
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console.log(error);
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});
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import("https://misc.ianrenton.com/Leaflet.WorkedAllBritainIreland/modules/geodesy/utm_ci.js")
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import(new URL('./modules/geodesy/utm_ci.js', import.meta.url).href)
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.then(module => {
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this._utmLibrary = module;
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if (this._osGridLibrary && this._ieGridLibrary) {
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+22
@@ -0,0 +1,22 @@
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The MIT License (MIT)
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Copyright (c) 2014 Chris Veness
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With some additional code & modifications by Ian Renton, 2025
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Permission is hereby granted, free of charge, to any person obtaining a copy
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of this software and associated documentation files (the "Software"), to deal
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in the Software without restriction, including without limitation the rights
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to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
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copies of the Software, and to permit persons to whom the Software is
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furnished to do so, subject to the following conditions:
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The above copyright notice and this permission notice shall be included in all
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copies or substantial portions of the Software.
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THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
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IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
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FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
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AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
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LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
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OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
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SOFTWARE.
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+326
@@ -0,0 +1,326 @@
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/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
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/* Ordnance Survey of Ireland Grid Reference funcs (c) Chris Veness 2005-2021 & Ian Renton 2025 */
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/* MIT Licence */
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/* www.movable-type.co.uk/scripts/latlong-gridref.html */
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/* www.movable-type.co.uk/scripts/geodesy-library.html#IeGridRef */
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/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
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import LatLonEllipsoidal, { Dms } from 'https://cdn.jsdelivr.net/npm/geodesy@2/latlon-ellipsoidal-datum.js';
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/**
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* Ordnance Survey of Ireland & Northern Ireland grid reference calculations, based on the
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* IeGridRef class in the geodesy library at https://github.com/chrisveness/geodesy
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*/
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/* IeGridRef - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
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const nationalGrid = {
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trueOrigin: { lat: 53.5, lon: -8 }, // true origin of Irish grid 53°30′N, 8°W
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falseOrigin: { easting: -200e3, northing: -250e3 }, // easting & northing of false origin, metres from true origin
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scaleFactor: 1.000035, // scale factor on central meridian
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ellipsoid: LatLonEllipsoidal.ellipsoids.Airy1830,
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};
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/**
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* Irish Grid References with methods to parse and convert them to latitude/longitude points.
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*/
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class IeGridRef {
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/**
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* Creates an IeGridRef object.
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*
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* @param {number} easting - Easting in metres from OS Grid false origin.
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* @param {number} northing - Northing in metres from OS Grid false origin.
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*
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* @example
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* import IeGridRef from '/js/geodesy/IeGridRef.js';
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* const gridref = new IeGridRef(651409, 313177);
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*/
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constructor(easting, northing) {
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this.easting = Number(easting);
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this.northing = Number(northing);
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if (isNaN(easting) || this.easting<0 || this.easting>7000e3) throw new RangeError(`invalid easting ‘${easting}’`);
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if (isNaN(northing) || this.northing<0 || this.northing>13000e3) throw new RangeError(`invalid northing ‘${northing}’`);
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}
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/**
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* Converts ‘this’ Irish Grid Reference easting/northing coordinate to latitude/longitude
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* (SW corner of grid square).
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*
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* While OS Grid References are based on OSGB-36, the Ordnance Survey have deprecated the use of
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* OSGB-36 for latitude/longitude coordinates (in favour of WGS-84), hence this function returns
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* WGS-84 by default, with OSGB-36 as an option. See www.ordnancesurvey.co.uk/blog/2014/12/2.
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*
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* Note formulation implemented here due to Thomas, Redfearn, etc is as published by OS, but is
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* inferior to Krüger as used by e.g. Karney 2011.
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*
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* @param {LatLon.datum} [datum=WGS84] - Datum to convert grid reference into.
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* @returns {LatLon} Latitude/longitude of supplied grid reference.
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*
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* @example
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* const gridref = new IeGridRef(651409.903, 313177.270);
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* const pWgs84 = gridref.toLatLon(); // 52°39′28.723″N, 001°42′57.787″E
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* // to obtain (historical) OSGB36 lat/lon point:
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* const pOsgb = gridref.toLatLon(LatLon.datums.OSGB36); // 52°39′27.253″N, 001°43′04.518″E
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*/
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toLatLon(datum=LatLonEllipsoidal.datums.WGS84) {
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const { easting: E, northing: N } = this;
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const { a, b } = nationalGrid.ellipsoid; // a = 6377563.396, b = 6356256.909
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const φ0 = nationalGrid.trueOrigin.lat.toRadians(); // latitude of true origin
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const λ0 = nationalGrid.trueOrigin.lon.toRadians(); // longitude of true origin
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const E0 = -nationalGrid.falseOrigin.easting; // easting of true origin
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const N0 = -nationalGrid.falseOrigin.northing; // northing of true origin
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const F0 = nationalGrid.scaleFactor; // scale factor
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const e2 = 1 - (b*b)/(a*a); // eccentricity squared
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const n = (a-b)/(a+b), n2 = n*n, n3 = n*n*n; // n, n², n³
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let φ=φ0, M=0;
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do {
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φ = (N-N0-M)/(a*F0) + φ;
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const Ma = (1 + n + (5/4)*n2 + (5/4)*n3) * (φ-φ0);
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const Mb = (3*n + 3*n2 + (21/8)*n3) * Math.sin(φ-φ0) * Math.cos(φ+φ0);
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const Mc = ((15/8)*n2 + (15/8)*n3) * Math.sin(2*(φ-φ0)) * Math.cos(2*(φ+φ0));
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const Md = (35/24)*n3 * Math.sin(3*(φ-φ0)) * Math.cos(3*(φ+φ0));
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M = b * F0 * (Ma - Mb + Mc - Md); // meridional arc
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} while (Math.abs(N-N0-M) >= 0.00001); // ie until < 0.01mm
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const cosφ = Math.cos(φ), sinφ = Math.sin(φ);
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const ν = a*F0/Math.sqrt(1-e2*sinφ*sinφ); // nu = transverse radius of curvature
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const ρ = a*F0*(1-e2)/Math.pow(1-e2*sinφ*sinφ, 1.5); // rho = meridional radius of curvature
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const η2 = ν/ρ-1; // eta = ?
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const tanφ = Math.tan(φ);
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const tan2φ = tanφ*tanφ, tan4φ = tan2φ*tan2φ, tan6φ = tan4φ*tan2φ;
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const secφ = 1/cosφ;
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const ν3 = ν*ν*ν, ν5 = ν3*ν*ν, ν7 = ν5*ν*ν;
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const VII = tanφ/(2*ρ*ν);
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const VIII = tanφ/(24*ρ*ν3)*(5+3*tan2φ+η2-9*tan2φ*η2);
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const IX = tanφ/(720*ρ*ν5)*(61+90*tan2φ+45*tan4φ);
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const X = secφ/ν;
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const XI = secφ/(6*ν3)*(ν/ρ+2*tan2φ);
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const XII = secφ/(120*ν5)*(5+28*tan2φ+24*tan4φ);
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const XIIA = secφ/(5040*ν7)*(61+662*tan2φ+1320*tan4φ+720*tan6φ);
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const dE = (E-E0), dE2 = dE*dE, dE3 = dE2*dE, dE4 = dE2*dE2, dE5 = dE3*dE2, dE6 = dE4*dE2, dE7 = dE5*dE2;
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φ = φ - VII*dE2 + VIII*dE4 - IX*dE6;
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const λ = λ0 + X*dE - XI*dE3 + XII*dE5 - XIIA*dE7;
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let point = new LatLon_IeGridRef(φ.toDegrees(), λ.toDegrees(), 0, LatLonEllipsoidal.datums.OSGB36);
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if (datum != LatLonEllipsoidal.datums.OSGB36) {
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// if point is required in datum other than OSGB36, convert it
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point = point.convertDatum(datum);
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// convertDatum() gives us a LatLon: convert to LatLon_IeGridRef which includes toOsGrid()
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point = new LatLon_IeGridRef(point.lat, point.lon, point.height, point.datum);
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}
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return point;
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}
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/**
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* Parses grid reference to IeGridRef object.
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*
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* Accepts standard grid references (eg 'G 387 148'), with or without whitespace separators, from
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* two-digit references up to 10-digit references (1m × 1m square), or fully numeric comma-separated
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* references in metres (eg '438700,114800').
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*
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* @param {string} gridref - Standard format OS Grid Reference.
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* @returns {IeGridRef} Numeric version of grid reference in metres from false origin (SW corner of
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* supplied grid square).
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* @throws {Error} Invalid grid reference.
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*
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* @example
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* const grid = IeGridRef.parse('G 51409 13177'); // grid: { easting: 651409, northing: 313177 }
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*/
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static parse(gridref) {
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gridref = String(gridref).trim();
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// check for fully numeric comma-separated gridref format
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let match = gridref.match(/^(\d+),\s*(\d+)$/);
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if (match) return new IeGridRef(match[1], match[2]);
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// validate format
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match = gridref.match(/^[ABCDEFGHJKLMNOPQRSTUVWXYZ]\s*[0-9]+\s*[0-9]+$/i);
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if (!match) throw new Error(`invalid grid reference ‘${gridref}’`);
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// get numeric values of letter references, mapping A->0, B->1, C->2, etc:
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let l1 = gridref.toUpperCase().charCodeAt(0) - 'A'.charCodeAt(0); // 100km square
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// shuffle down letters after 'I' since 'I' is not used in grid:
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if (l1 > 7) l1--;
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// convert grid letters into 100km-square indexes from false origin (grid square SV):
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const e100km = l1 % 5;
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const n100km = 4 - Math.floor(l1 / 5);
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// skip grid letters to get numeric (easting/northing) part of ref
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let en = gridref.slice(1).trim().split(/\s+/);
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// if e/n not whitespace separated, split half way
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if (en.length == 1) en = [ en[0].slice(0, en[0].length / 2), en[0].slice(en[0].length / 2) ];
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// validation
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if (en[0].length != en[1].length) throw new Error(`invalid grid reference ‘${gridref}’`);
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// standardise to 10-digit refs (metres)
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en[0] = en[0].padEnd(5, '0');
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en[1] = en[1].padEnd(5, '0');
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const e = e100km + en[0];
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const n = n100km + en[1];
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return new IeGridRef(e, n);
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}
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/**
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* Converts ‘this’ numeric grid reference to standard OS of Ireland Grid Reference.
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*
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* @param {number} [digits=10] - Precision of returned grid reference (10 digits = metres);
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* digits=0 will return grid reference in numeric format.
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* @returns {string} This grid reference in standard format.
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*
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* @example
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* const gridref = new IeGridRef(651409, 313177).toString(8); // 'TG 5140 1317'
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* const gridref = new IeGridRef(651409, 313177).toString(0); // '651409,313177'
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*/
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toString(digits=10) {
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if (![ 0,2,4,6,8,10,12,14,16 ].includes(Number(digits))) throw new RangeError(`invalid precision ‘${digits}’`); // eslint-disable-line comma-spacing
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let { easting: e, northing: n } = this;
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// use digits = 0 to return numeric format (in metres) - note northing may be >= 1e7
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if (digits == 0) {
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const format = { useGrouping: false, minimumIntegerDigits: 6, maximumFractionDigits: 3 };
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const ePad = e.toLocaleString('en', format);
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const nPad = n.toLocaleString('en', format);
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return `${ePad},${nPad}`;
|
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}
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|
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// get the 100km-grid indices
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const e100km = Math.floor(e / 100000), n100km = Math.floor(n / 100000);
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|
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// translate those into the numeric equivalent of the grid letters
|
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let l1 = (n100km) * 5 % 25 + e100km % 5;
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return null; // haven't done this maths yet
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// compensate for skipped 'I' and calculate grid letter
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if (l1 > 7) l1++;
|
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const letter = String.fromCharCode(l1 + 'A'.charCodeAt(0));
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// strip 100km-grid indices from easting & northing, and reduce precision
|
||||
e = Math.floor((e % 100000) / Math.pow(10, 5 - digits / 2));
|
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n = Math.floor((n % 100000) / Math.pow(10, 5 - digits / 2));
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||||
|
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// pad eastings & northings with leading zeros
|
||||
e = e.toString().padStart(digits/2, '0');
|
||||
n = n.toString().padStart(digits/2, '0');
|
||||
|
||||
return `${letter} ${e} ${n}`;
|
||||
}
|
||||
|
||||
}
|
||||
|
||||
|
||||
/* LatLon_IeGridRef - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
|
||||
|
||||
|
||||
/**
|
||||
* Extends LatLon class with method to convert LatLon point to Irish Grid Reference.
|
||||
*
|
||||
* @extends LatLonEllipsoidal
|
||||
*/
|
||||
class LatLon_IeGridRef extends LatLonEllipsoidal {
|
||||
|
||||
/**
|
||||
* Converts latitude/longitude to Ordnance Survey of Ireland grid reference easting/northing coordinate.
|
||||
*
|
||||
* @returns {IeGridRef} Irish 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
|
||||
const λ0 = nationalGrid.trueOrigin.lon.toRadians(); // longitude of true origin
|
||||
const E0 = -nationalGrid.falseOrigin.easting; // easting of true origin
|
||||
const N0 = -nationalGrid.falseOrigin.northing; // northing of true origin
|
||||
const F0 = nationalGrid.scaleFactor; // scale factor
|
||||
|
||||
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*n2 + (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 IeGridRef(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_IeGridRef.
|
||||
*/
|
||||
convertDatum(toDatum) {
|
||||
const osieED = super.convertDatum(toDatum); // returns LatLonEllipsoidal_Datum
|
||||
const osieOSGR = new LatLon_IeGridRef(osieED.lat, osieED.lon, osieED.height, osieED.datum);
|
||||
return osieOSGR;
|
||||
}
|
||||
|
||||
}
|
||||
|
||||
|
||||
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
|
||||
|
||||
export { IeGridRef as default, LatLon_IeGridRef as LatLon, Dms };
|
||||
+348
@@ -0,0 +1,348 @@
|
||||
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
|
||||
/* 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 'https://cdn.jsdelivr.net/npm/geodesy@2/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*n2 + (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+)$/);
|
||||
if (match) return new OsGridRef(match[1], match[2]);
|
||||
|
||||
// validate format
|
||||
match = gridref.match(/^[HNOST][ABCDEFGHJKLMNOPQRSTUVWXYZ]\s*[0-9]+\s*[0-9]+$/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*n2 + (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 };
|
||||
+413
@@ -0,0 +1,413 @@
|
||||
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
|
||||
/* UTM / WGS-84 Conversion Functions (c) Chris Veness 2014-2022 & Ian Renton 2025 */
|
||||
/* MIT Licence */
|
||||
/* www.movable-type.co.uk/scripts/latlong-utm-mgrs.html */
|
||||
/* www.movable-type.co.uk/scripts/geodesy-library.html#utm */
|
||||
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
|
||||
|
||||
/* eslint-disable indent */
|
||||
|
||||
import LatLonEllipsoidal, { Dms } from 'https://cdn.jsdelivr.net/npm/geodesy@2/latlon-ellipsoidal-datum.js';
|
||||
|
||||
|
||||
/**
|
||||
* The Universal Transverse Mercator (UTM) system is a 2-dimensional Cartesian coordinate system
|
||||
* providing locations on the surface of the Earth.
|
||||
*
|
||||
* UTM is a set of 60 transverse Mercator projections, normally based on the WGS-84 ellipsoid.
|
||||
* Within each zone, coordinates are represented as eastings and northings, measures in metres; e.g.
|
||||
* ‘31 N 448251 5411932’.
|
||||
*
|
||||
* This method based on Karney 2011 ‘Transverse Mercator with an accuracy of a few nanometers’,
|
||||
* building on Krüger 1912 ‘Konforme Abbildung des Erdellipsoids in der Ebene’.
|
||||
*
|
||||
* @module utm
|
||||
*/
|
||||
|
||||
|
||||
/* Utm - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
|
||||
|
||||
|
||||
/**
|
||||
* UTM coordinates, with functions to parse them and convert them to LatLon points.
|
||||
*/
|
||||
class Utm {
|
||||
|
||||
/**
|
||||
* Creates a Utm coordinate object comprising zone, hemisphere, easting, northing on a given
|
||||
* datum (normally WGS84).
|
||||
*
|
||||
* @param {number} zone - UTM 6° longitudinal zone (1..60 covering 180°W..180°E).
|
||||
* @param {string} hemisphere - N for northern hemisphere, S for southern hemisphere.
|
||||
* @param {number} easting - Easting in metres from false easting (-500km from central meridian).
|
||||
* @param {number} northing - Northing in metres from equator (N) or from false northing -10,000km (S).
|
||||
* @param {LatLon.datums} [datum=WGS84] - Datum UTM coordinate is based on.
|
||||
* @param {number} [convergence=null] - Meridian convergence (bearing of grid north
|
||||
* clockwise from true north), in degrees.
|
||||
* @param {number} [scale=null] - Grid scale factor.
|
||||
* @params {boolean=true} verifyEN - Check easting/northing is within 'normal' values (may be
|
||||
* suppressed for extended coherent coordinates or alternative datums
|
||||
* e.g. ED50 (epsg.io/23029).
|
||||
* @throws {TypeError} Invalid UTM coordinate.
|
||||
*
|
||||
* @example
|
||||
* import Utm from '/js/geodesy/utm.js';
|
||||
* const utmCoord = new Utm(31, 'N', 448251, 5411932);
|
||||
*/
|
||||
constructor(zone, hemisphere, easting, northing, datum=LatLonEllipsoidal.datums.WGS84, convergence=null, scale=null, verifyEN=true) {
|
||||
if (!(1<=zone && zone<=60)) throw new RangeError(`invalid UTM zone ‘${zone}’`);
|
||||
if (zone != parseInt(zone)) throw new RangeError(`invalid UTM zone ‘${zone}’`);
|
||||
if (typeof hemisphere != 'string' || !hemisphere.match(/[NS]/i)) throw new RangeError(`invalid UTM hemisphere ‘${hemisphere}’`);
|
||||
if (verifyEN) { // (rough) range-check of E/N values
|
||||
if (!(0<=easting && easting<=1000e3)) throw new RangeError(`invalid UTM easting ‘${easting}’`);
|
||||
if (hemisphere.toUpperCase()=='N' && !(0<=northing && northing<9329006)) throw new RangeError(`invalid UTM northing ‘${northing}’`);
|
||||
if (hemisphere.toUpperCase()=='S' && !(1116914<northing && northing<=10000e3)) throw new RangeError(`invalid UTM northing ‘${northing}’`);
|
||||
}
|
||||
if (!datum || datum.ellipsoid==undefined) throw new TypeError(`unrecognised datum ‘${datum}’`);
|
||||
|
||||
this.zone = Number(zone);
|
||||
this.hemisphere = hemisphere.toUpperCase();
|
||||
this.easting = Number(easting);
|
||||
this.northing = Number(northing);
|
||||
this.datum = datum;
|
||||
this.convergence = convergence===null ? null : Number(convergence);
|
||||
this.scale = scale===null ? null : Number(scale);
|
||||
}
|
||||
|
||||
|
||||
/**
|
||||
* Converts UTM zone/easting/northing coordinate to latitude/longitude.
|
||||
*
|
||||
* Implements Karney’s method, using Krüger series to order n⁶, giving results accurate to 5nm
|
||||
* for distances up to 3900km from the central meridian.
|
||||
*
|
||||
* @param {Utm} utmCoord - UTM coordinate to be converted to latitude/longitude.
|
||||
* @returns {LatLon} Latitude/longitude of supplied grid reference.
|
||||
*
|
||||
* @example
|
||||
* const grid = new Utm(31, 'N', 448251.795, 5411932.678);
|
||||
* const latlong = grid.toLatLon(); // 48°51′29.52″N, 002°17′40.20″E
|
||||
*/
|
||||
toLatLon() {
|
||||
const { zone: z, hemisphere: h } = this;
|
||||
|
||||
const falseEasting = 500e3, falseNorthing = 10000e3;
|
||||
|
||||
const { a, f } = this.datum.ellipsoid; // WGS-84: a = 6378137, f = 1/298.257223563;
|
||||
|
||||
const k0 = 0.9996; // UTM scale on the central meridian
|
||||
|
||||
const x = this.easting - falseEasting; // make x ± relative to central meridian
|
||||
const y = h=='S' ? this.northing - falseNorthing : this.northing; // make y ± relative to equator
|
||||
|
||||
// ---- from Karney 2011 Eq 15-22, 36:
|
||||
|
||||
const e = Math.sqrt(f*(2-f)); // eccentricity
|
||||
const n = f / (2 - f); // 3rd flattening
|
||||
const n2 = n*n, n3 = n*n2, n4 = n*n3, n5 = n*n4, n6 = n*n5;
|
||||
|
||||
const A = a/(1+n) * (1 + 1/4*n2 + 1/64*n4 + 1/256*n6); // 2πA is the circumference of a meridian
|
||||
|
||||
const η = x / (k0*A);
|
||||
const ξ = y / (k0*A);
|
||||
|
||||
const β = [ null, // note β is one-based array (6th order Krüger expressions)
|
||||
1/2*n - 2/3*n2 + 37/96*n3 - 1/360*n4 - 81/512*n5 + 96199/604800*n6,
|
||||
1/48*n2 + 1/15*n3 - 437/1440*n4 + 46/105*n5 - 1118711/3870720*n6,
|
||||
17/480*n3 - 37/840*n4 - 209/4480*n5 + 5569/90720*n6,
|
||||
4397/161280*n4 - 11/504*n5 - 830251/7257600*n6,
|
||||
4583/161280*n5 - 108847/3991680*n6,
|
||||
20648693/638668800*n6 ];
|
||||
|
||||
let ξʹ = ξ;
|
||||
for (let j=1; j<=6; j++) ξʹ -= β[j] * Math.sin(2*j*ξ) * Math.cosh(2*j*η);
|
||||
|
||||
let ηʹ = η;
|
||||
for (let j=1; j<=6; j++) ηʹ -= β[j] * Math.cos(2*j*ξ) * Math.sinh(2*j*η);
|
||||
|
||||
const sinhηʹ = Math.sinh(ηʹ);
|
||||
const sinξʹ = Math.sin(ξʹ), cosξʹ = Math.cos(ξʹ);
|
||||
|
||||
const τʹ = sinξʹ / Math.sqrt(sinhηʹ*sinhηʹ + cosξʹ*cosξʹ);
|
||||
|
||||
let δτi = null;
|
||||
let τi = τʹ;
|
||||
do {
|
||||
const σi = Math.sinh(e*Math.atanh(e*τi/Math.sqrt(1+τi*τi)));
|
||||
const τiʹ = τi * Math.sqrt(1+σi*σi) - σi * Math.sqrt(1+τi*τi);
|
||||
δτi = (τʹ - τiʹ)/Math.sqrt(1+τiʹ*τiʹ)
|
||||
* (1 + (1-e*e)*τi*τi) / ((1-e*e)*Math.sqrt(1+τi*τi));
|
||||
τi += δτi;
|
||||
} while (Math.abs(δτi) > 1e-12); // using IEEE 754 δτi -> 0 after 2-3 iterations
|
||||
// note relatively large convergence test as δτi toggles on ±1.12e-16 for eg 31 N 400000 5000000
|
||||
const τ = τi;
|
||||
|
||||
const φ = Math.atan(τ);
|
||||
|
||||
let λ = Math.atan2(sinhηʹ, cosξʹ);
|
||||
|
||||
// ---- convergence: Karney 2011 Eq 26, 27
|
||||
|
||||
let p = 1;
|
||||
for (let j=1; j<=6; j++) p -= 2*j*β[j] * Math.cos(2*j*ξ) * Math.cosh(2*j*η);
|
||||
let q = 0;
|
||||
for (let j=1; j<=6; j++) q += 2*j*β[j] * Math.sin(2*j*ξ) * Math.sinh(2*j*η);
|
||||
|
||||
const γʹ = Math.atan(Math.tan(ξʹ) * Math.tanh(ηʹ));
|
||||
const γʺ = Math.atan2(q, p);
|
||||
|
||||
const γ = γʹ + γʺ;
|
||||
|
||||
// ---- scale: Karney 2011 Eq 28
|
||||
|
||||
const sinφ = Math.sin(φ);
|
||||
const kʹ = Math.sqrt(1 - e*e*sinφ*sinφ) * Math.sqrt(1 + τ*τ) * Math.sqrt(sinhηʹ*sinhηʹ + cosξʹ*cosξʹ);
|
||||
const kʺ = A / a / Math.sqrt(p*p + q*q);
|
||||
|
||||
const k = k0 * kʹ * kʺ;
|
||||
|
||||
// ------------
|
||||
|
||||
const λ0 = ((z-1)*6 - 180 + 3).toRadians(); // longitude of central meridian
|
||||
λ += λ0; // move λ from zonal to global coordinates
|
||||
|
||||
// round to reasonable precision
|
||||
const lat = Number(φ.toDegrees().toFixed(14)); // nm precision (1nm = 10^-14°)
|
||||
const lon = Number(λ.toDegrees().toFixed(14)); // (strictly lat rounding should be φ⋅cosφ!)
|
||||
const convergence = Number(γ.toDegrees().toFixed(9));
|
||||
const scale = Number(k.toFixed(12));
|
||||
|
||||
const latLong = new LatLon_Utm(lat, lon, 0, this.datum);
|
||||
// ... and add the convergence and scale into the LatLon object ... wonderful JavaScript!
|
||||
latLong.convergence = convergence;
|
||||
latLong.scale = scale;
|
||||
|
||||
return latLong;
|
||||
}
|
||||
|
||||
/**
|
||||
* Parses a Channel Islands (WA/WV) grid reference.
|
||||
*/
|
||||
static parseChannelIslandGrid(gridref) {
|
||||
// validate format
|
||||
let match = gridref.match(/^W[AV]\s*[0-9]+\s*[0-9]+$/i);
|
||||
if (!match) throw new Error(`invalid grid reference ‘${gridref}’`);
|
||||
|
||||
// skip grid letters to get numeric (easting/northing) part of ref
|
||||
let en = gridref.slice(2).trim().split(/\s+/);
|
||||
// if e/n not whitespace separated, split half way
|
||||
if (en.length == 1) en = [ en[0].slice(0, en[0].length / 2), en[0].slice(en[0].length / 2) ];
|
||||
|
||||
// validation
|
||||
if (en[0].length != en[1].length) throw new Error(`invalid grid reference ‘${gridref}’`);
|
||||
|
||||
// standardise to 10-digit refs (metres)
|
||||
en[0] = en[0].padEnd(5, '0');
|
||||
en[1] = en[1].padEnd(5, '0');
|
||||
|
||||
let utmCoord = "30 N ";
|
||||
const e = 5 + en[0];
|
||||
utmCoord += e + " ";
|
||||
if (gridref.substring(0, 2) === "WA") {
|
||||
const n = 55 + en[1];
|
||||
utmCoord += n;
|
||||
} else if (gridref.substring(0, 2) === "WV") {
|
||||
const n = 54 + en[1];
|
||||
utmCoord += n;
|
||||
}
|
||||
|
||||
return Utm.parse(utmCoord);
|
||||
}
|
||||
|
||||
|
||||
/**
|
||||
* Parses string representation of UTM coordinate.
|
||||
*
|
||||
* A UTM coordinate comprises (space-separated)
|
||||
* - zone
|
||||
* - hemisphere
|
||||
* - easting
|
||||
* - northing.
|
||||
*
|
||||
* @param {string} utmCoord - UTM coordinate (WGS 84).
|
||||
* @param {Datum} [datum=WGS84] - Datum coordinate is defined in (default WGS 84).
|
||||
* @returns {Utm} Parsed UTM coordinate.
|
||||
* @throws {TypeError} Invalid UTM coordinate.
|
||||
*
|
||||
* @example
|
||||
* const utmCoord = Utm.parse('31 N 448251 5411932');
|
||||
* // utmCoord: {zone: 31, hemisphere: 'N', easting: 448251, northing: 5411932 }
|
||||
*/
|
||||
static parse(utmCoord, datum=LatLonEllipsoidal.datums.WGS84) {
|
||||
// match separate elements (separated by whitespace)
|
||||
utmCoord = utmCoord.trim().match(/\S+/g);
|
||||
|
||||
if (utmCoord==null || utmCoord.length!=4) throw new Error(`invalid UTM coordinate ‘${utmCoord}’`);
|
||||
|
||||
const zone = utmCoord[0], hemisphere = utmCoord[1], easting = utmCoord[2], northing = utmCoord[3];
|
||||
|
||||
return new this(zone, hemisphere, easting, northing, datum); // 'new this' as may return subclassed types
|
||||
}
|
||||
|
||||
|
||||
/**
|
||||
* Returns a string representation of a UTM coordinate.
|
||||
*
|
||||
* To distinguish from MGRS grid zone designators, a space is left between the zone and the
|
||||
* hemisphere.
|
||||
*
|
||||
* Note that UTM coordinates get rounded, not truncated (unlike MGRS grid references).
|
||||
*
|
||||
* @param {number} [digits=0] - Number of digits to appear after the decimal point (3 ≡ mm).
|
||||
* @returns {string} A string representation of the coordinate.
|
||||
*
|
||||
* @example
|
||||
* const utm = new Utm('31', 'N', 448251, 5411932).toString(4); // 31 N 448251.0000 5411932.0000
|
||||
*/
|
||||
toString(digits=0) {
|
||||
|
||||
const z = this.zone.toString().padStart(2, '0');
|
||||
const h = this.hemisphere;
|
||||
const e = this.easting.toFixed(digits);
|
||||
const n = this.northing.toFixed(digits);
|
||||
|
||||
return `${z} ${h} ${e} ${n}`;
|
||||
}
|
||||
|
||||
}
|
||||
|
||||
|
||||
/* LatLon_Utm - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
|
||||
|
||||
|
||||
/**
|
||||
* Extends LatLon with method to convert LatLon points to UTM coordinates.
|
||||
*
|
||||
* @extends LatLon
|
||||
*/
|
||||
class LatLon_Utm extends LatLonEllipsoidal {
|
||||
|
||||
/**
|
||||
* Converts latitude/longitude to UTM coordinate.
|
||||
*
|
||||
* Implements Karney’s method, using Krüger series to order n⁶, giving results accurate to 5nm
|
||||
* for distances up to 3900km from the central meridian.
|
||||
*
|
||||
* @param {number} [zoneOverride] - Use specified zone rather than zone within which point lies;
|
||||
* note overriding the UTM zone has the potential to result in negative eastings, and
|
||||
* perverse results within Norway/Svalbard exceptions.
|
||||
* @returns {Utm} UTM coordinate.
|
||||
* @throws {TypeError} Latitude outside UTM limits.
|
||||
*
|
||||
* @example
|
||||
* const latlong = new LatLon(48.8582, 2.2945);
|
||||
* const utmCoord = latlong.toUtm(); // 31 N 448252 5411933
|
||||
*/
|
||||
toUtm(zoneOverride=undefined) {
|
||||
if (!(-80<=this.lat && this.lat<=84)) throw new RangeError(`latitude ‘${this.lat}’ outside UTM limits`);
|
||||
|
||||
const falseEasting = 500e3, falseNorthing = 10000e3;
|
||||
|
||||
let zone = zoneOverride || Math.floor((this.lon+180)/6) + 1; // longitudinal zone
|
||||
let λ0 = ((zone-1)*6 - 180 + 3).toRadians(); // longitude of central meridian
|
||||
|
||||
// ---- handle Norway/Svalbard exceptions
|
||||
// grid zones are 8° tall; 0°N is offset 10 into latitude bands array
|
||||
const mgrsLatBands = 'CDEFGHJKLMNPQRSTUVWXX'; // X is repeated for 80-84°N
|
||||
const latBand = mgrsLatBands.charAt(Math.floor(this.lat/8+10));
|
||||
// adjust zone & central meridian for Norway
|
||||
if (zone==31 && latBand=='V' && this.lon>= 3) { zone++; λ0 += (6).toRadians(); }
|
||||
// adjust zone & central meridian for Svalbard
|
||||
if (zone==32 && latBand=='X' && this.lon< 9) { zone--; λ0 -= (6).toRadians(); }
|
||||
if (zone==32 && latBand=='X' && this.lon>= 9) { zone++; λ0 += (6).toRadians(); }
|
||||
if (zone==34 && latBand=='X' && this.lon< 21) { zone--; λ0 -= (6).toRadians(); }
|
||||
if (zone==34 && latBand=='X' && this.lon>=21) { zone++; λ0 += (6).toRadians(); }
|
||||
if (zone==36 && latBand=='X' && this.lon< 33) { zone--; λ0 -= (6).toRadians(); }
|
||||
if (zone==36 && latBand=='X' && this.lon>=33) { zone++; λ0 += (6).toRadians(); }
|
||||
|
||||
const φ = this.lat.toRadians(); // latitude ± from equator
|
||||
const λ = this.lon.toRadians() - λ0; // longitude ± from central meridian
|
||||
|
||||
// allow alternative ellipsoid to be specified
|
||||
const ellipsoid = this.datum ? this.datum.ellipsoid : LatLonEllipsoidal.ellipsoids.WGS84;
|
||||
const { a, f } = ellipsoid; // WGS-84: a = 6378137, f = 1/298.257223563;
|
||||
|
||||
const k0 = 0.9996; // UTM scale on the central meridian
|
||||
|
||||
// ---- easting, northing: Karney 2011 Eq 7-14, 29, 35:
|
||||
|
||||
const e = Math.sqrt(f*(2-f)); // eccentricity
|
||||
const n = f / (2 - f); // 3rd flattening
|
||||
const n2 = n*n, n3 = n*n2, n4 = n*n3, n5 = n*n4, n6 = n*n5;
|
||||
|
||||
const cosλ = Math.cos(λ), sinλ = Math.sin(λ), tanλ = Math.tan(λ);
|
||||
|
||||
const τ = Math.tan(φ); // τ ≡ tanφ, τʹ ≡ tanφʹ; prime (ʹ) indicates angles on the conformal sphere
|
||||
const σ = Math.sinh(e*Math.atanh(e*τ/Math.sqrt(1+τ*τ)));
|
||||
|
||||
const τʹ = τ*Math.sqrt(1+σ*σ) - σ*Math.sqrt(1+τ*τ);
|
||||
|
||||
const ξʹ = Math.atan2(τʹ, cosλ);
|
||||
const ηʹ = Math.asinh(sinλ / Math.sqrt(τʹ*τʹ + cosλ*cosλ));
|
||||
|
||||
const A = a/(1+n) * (1 + 1/4*n2 + 1/64*n4 + 1/256*n6); // 2πA is the circumference of a meridian
|
||||
|
||||
const α = [ null, // note α is one-based array (6th order Krüger expressions)
|
||||
1/2*n - 2/3*n2 + 5/16*n3 + 41/180*n4 - 127/288*n5 + 7891/37800*n6,
|
||||
13/48*n2 - 3/5*n3 + 557/1440*n4 + 281/630*n5 - 1983433/1935360*n6,
|
||||
61/240*n3 - 103/140*n4 + 15061/26880*n5 + 167603/181440*n6,
|
||||
49561/161280*n4 - 179/168*n5 + 6601661/7257600*n6,
|
||||
34729/80640*n5 - 3418889/1995840*n6,
|
||||
212378941/319334400*n6 ];
|
||||
|
||||
let ξ = ξʹ;
|
||||
for (let j=1; j<=6; j++) ξ += α[j] * Math.sin(2*j*ξʹ) * Math.cosh(2*j*ηʹ);
|
||||
|
||||
let η = ηʹ;
|
||||
for (let j=1; j<=6; j++) η += α[j] * Math.cos(2*j*ξʹ) * Math.sinh(2*j*ηʹ);
|
||||
|
||||
let x = k0 * A * η;
|
||||
let y = k0 * A * ξ;
|
||||
|
||||
// ---- convergence: Karney 2011 Eq 23, 24
|
||||
|
||||
let pʹ = 1;
|
||||
for (let j=1; j<=6; j++) pʹ += 2*j*α[j] * Math.cos(2*j*ξʹ) * Math.cosh(2*j*ηʹ);
|
||||
let qʹ = 0;
|
||||
for (let j=1; j<=6; j++) qʹ += 2*j*α[j] * Math.sin(2*j*ξʹ) * Math.sinh(2*j*ηʹ);
|
||||
|
||||
const γʹ = Math.atan(τʹ / Math.sqrt(1+τʹ*τʹ)*tanλ);
|
||||
const γʺ = Math.atan2(qʹ, pʹ);
|
||||
|
||||
const γ = γʹ + γʺ;
|
||||
|
||||
// ---- scale: Karney 2011 Eq 25
|
||||
|
||||
const sinφ = Math.sin(φ);
|
||||
const kʹ = Math.sqrt(1 - e*e*sinφ*sinφ) * Math.sqrt(1 + τ*τ) / Math.sqrt(τʹ*τʹ + cosλ*cosλ);
|
||||
const kʺ = A / a * Math.sqrt(pʹ*pʹ + qʹ*qʹ);
|
||||
|
||||
const k = k0 * kʹ * kʺ;
|
||||
|
||||
// ------------
|
||||
|
||||
// shift x/y to false origins
|
||||
x = x + falseEasting; // make x relative to false easting
|
||||
if (y < 0) y = y + falseNorthing; // make y in southern hemisphere relative to false northing
|
||||
|
||||
// round to reasonable precision
|
||||
x = Number(x.toFixed(9)); // nm precision
|
||||
y = Number(y.toFixed(9)); // nm precision
|
||||
const convergence = Number(γ.toDegrees().toFixed(9));
|
||||
const scale = Number(k.toFixed(12));
|
||||
|
||||
const h = this.lat>=0 ? 'N' : 'S'; // hemisphere
|
||||
|
||||
return new Utm(zone, h, x, y, this.datum, convergence, scale, !!zoneOverride);
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
|
||||
|
||||
export { Utm as default, LatLon_Utm as LatLon, Dms };
|
||||
Reference in New Issue
Block a user