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Last active Apr 4, 2018

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Google Apps Script for converting UTM coordinates to [latitude, longitude].
Copyright 2018 Google LLC.
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
https://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
// Heavily based on https://gis.stackexchange.com/a/278112/4412.
function UTM2LL(easting, northing, utm_zone, is_north) {
// First some validation:
if (easting < 160000 || easting > 840000) {
throw 'Outside permissible range of easting values.';
}
if (northing < 0) {
throw 'Negative values are not allowed for northing.';
}
if (northing > 10000000) {
throw 'Northing may not exceed 10,000,000.';
}
// Symbols as used in USGS PP 1395: Map Projections - A Working Manual
const DatumEqRad = [
6378137.0, 6378137.0, 6378137.0, 6378135.0, 6378160.0, 6378245.0, 6378206.4,
6378388.0, 6378388.0, 6378249.1, 6378206.4, 6377563.4, 6377397.2, 6377276.3
];
const DatumFlat = [
298.2572236, 298.2572236, 298.2572215, 298.2597208, 298.2497323,
298.2997381, 294.9786982, 296.9993621, 296.9993621, 293.4660167,
294.9786982, 299.3247788, 299.1527052, 300.8021499
];
const Item = 0; // default
const a = DatumEqRad[Item]; // equatorial radius (meters)
const f = 1 / DatumFlat[Item]; // polar flattening
const drad = Math.PI / 180; // convert degrees to radians
const k0 = 0.9996; // scale on central meridian
const b = a * (1 - f); // polar axis
const e = Math.sqrt(1 - (b / a) * (b / a)); // eccentricity
const esq = (1 - (b / a) * (b / a)); // e² for use in expansions
const e0sq = e * e / (1 - e * e); // e0² — always even powers
// Now the actual calculation:
const zcm = 3 + 6 * (utm_zone - 1) - 180; // central meridian of zone
const e1 = (1 - Math.sqrt(1 - e * e)) / (1 + Math.sqrt(1 - e * e));
const M0 = 0; // in case origin other than zero lat
const M = is_north ? // arc length along standard meridian
M0 + northing / k0 :
M0 + (northing - 10000000) / k;
const mu = M / (a * (1 - esq * (1 / 4 + esq * (3 / 64 + 5 * esq / 256))));
var phi1 = mu + e1 * (3 / 2 - 27 * e1 * e1 / 32) * Math.sin(2 * mu) + e1 * e1 * (21 / 16 - 55 * e1 * e1 / 32) * Math.sin(4 * mu);
phi1 = phi1 + e1 * e1 * e1 * (Math.sin(6 * mu) * 151 / 96 + e1 * Math.sin(8 * mu) * 1097 / 512);
const C1 = e0sq * Math.pow(Math.cos(phi1), 2);
const T1 = Math.pow(Math.tan(phi1), 2);
const N1 = a / Math.sqrt(1 - Math.pow(e * Math.sin(phi1), 2));
const R1 = N1 * (1 - e * e) / (1 - Math.pow(e * Math.sin(phi1), 2));
const D = (easting - 500000) / (N1 * k0);
var phi = (D * D) * (1 / 2 - D * D * (5 + 3 * T1 + 10 * C1 - 4 * C1 * C1 - 9 * e0sq) / 24);
phi = phi + Math.pow(D, 6) * (61 + 90 * T1 + 298 * C1 + 45 * T1 * T1 - 252 * e0sq - 3 * C1 * C1) / 720;
phi = phi1 - (N1 * Math.tan(phi1) / R1) * phi;
const lon = D * (1 + D * D * ((-1 - 2 * T1 - C1) / 6 + D * D * (5 - 2 * C1 + 28 * T1 - 3 * C1 * C1 + 8 * e0sq + 24 * T1 * T1) / 120)) / Math.cos(phi1);
return [
phi / drad,
zcm + lon / drad,
];
}
function UTM34N2LL(easting, northing) {
return UTM2LL(easting, northing, 34, true);
}
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