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/**
* UTM (Universal Transverse Mercator) coordinate conversion utilities
* Converts WGS84 coordinates (latitude/longitude) to UTM coordinates
*/
export class UTMConverter {
// WGS84 ellipsoid parameters
static WGS84_A = 6378137.0; // semi-major axis in meters
static WGS84_F = 1 / 298.257223563; // flattening
static WGS84_E = 0.081819191; // eccentricity
static WGS84_ESQ = 0.00669438; // eccentricity squared
// UTM parameters
static UTM_SCALE_FACTOR = 0.9996;
static UTM_FALSE_EASTING = 500000; // in meters
static UTM_FALSE_NORTHING_N = 0; // for northern hemisphere
static UGM_FALSE_NORTHING_S = 10000000; // for southern hemisphere
/**
* Convert WGS84 coordinates to UTM
* @param {number} longitude - Longitude in decimal degrees
* @param {number} latitude - Latitude in decimal degrees
* @returns {Object} UTM coordinates with zone information
*/
static toUTM(longitude, latitude) {
// Validate input coordinates
if (longitude < -180 || longitude > 180) {
throw new Error(`Longitude ${longitude} is out of valid range [-180, 180]`);
}
if (latitude < -90 || latitude > 90) {
throw new Error(`Latitude ${latitude} is out of valid range [-90, 90]`);
}
const zone = UTMConverter.getUTMZone(longitude, latitude);
const hemisphere = latitude >= 0 ? "N" : "S";
// Convert to radians
const latRad = (latitude * Math.PI) / 180;
const lonRad = (longitude * Math.PI) / 180;
// Central meridian for the zone (in radians)
const lonOrigin = (((zone - 1) * 6 - 180 + 3) * Math.PI) / 180;
const dLon = lonRad - lonOrigin;
// Ellipsoid constants
const e = UTMConverter.WGS84_E;
const e2 = UTMConverter.WGS84_ESQ;
const e4 = e2 * e2;
const e6 = e4 * e2;
const N = UTMConverter.WGS84_A / Math.sqrt(1 - e2 * Math.sin(latRad) * Math.sin(latRad));
const T = Math.tan(latRad) * Math.tan(latRad);
const C = (e2 * Math.cos(latRad) * Math.cos(latRad)) / (1 - e2);
const A = Math.cos(latRad) * dLon;
const M =
UTMConverter.WGS84_A *
((1 - e2 / 4 - (3 * e4) / 64 - (5 * e6) / 256) * latRad -
((3 * e2) / 8 + (3 * e4) / 32 + (45 * e6) / 1024) * Math.sin(2 * latRad) +
((15 * e4) / 256 + (45 * e6) / 1024) * Math.sin(4 * latRad) -
((35 * e6) / 3072) * Math.sin(6 * latRad));
// Calculate easting
const easting =
UTMConverter.UTM_SCALE_FACTOR *
N *
(A +
((1 - T + C) * A * A * A) / 6 +
((5 - 18 * T + T * T + 72 * C - 58 * e2) * A * A * A * A * A) / 120) +
UTMConverter.UTM_FALSE_EASTING;
// Calculate northing
const northing =
UTMConverter.UTM_SCALE_FACTOR *
(M +
N *
Math.tan(latRad) *
((A * A) / 2 +
((5 - T + 9 * C + 4 * C * C) * A * A * A * A) / 24 +
((61 - 58 * T + T * T + 600 * C - 330 * e2) * A * A * A * A * A * A) / 720));
// Adjust northing for southern hemisphere
const adjustedNorthing =
hemisphere === "S" ? northing + UTMConverter.UGM_FALSE_NORTHING_S : northing;
return {
datum: "WGS84",
easting: Math.round(easting * 100) / 100, // Round to 2 decimal places
hemisphere: hemisphere,
northing: Math.round(adjustedNorthing * 100) / 100,
zone: zone,
};
}
/**
* Determine UTM zone from longitude and latitude
* @param {number} longitude - Longitude in decimal degrees
* @param {number} latitude - Latitude in decimal degrees
* @returns {number} UTM zone number
*/
static getUTMZone(longitude, latitude) {
// Special zones for Norway and Svalbard
if (latitude >= 56.0 && latitude < 64.0 && longitude >= 3.0 && longitude < 12.0) {
return 32;
}
// Special zones for Svalbard
if (latitude >= 72.0 && latitude < 84.0) {
if (longitude >= 0.0 && longitude < 9.0) return 31;
if (longitude >= 9.0 && longitude < 21.0) return 33;
if (longitude >= 21.0 && longitude < 33.0) return 35;
if (longitude >= 33.0 && longitude < 42.0) return 37;
}
// Standard zone calculation
let zone = Math.floor((longitude + 180) / 6) + 1;
// Handle zones 31-37 for northern Europe special cases
if (latitude >= 72.0 && latitude < 84.0 && longitude >= 0.0 && longitude < 42.0) {
if (longitude < 9.0) zone = 31;
else if (longitude < 21.0) zone = 33;
else if (longitude < 33.0) zone = 35;
else zone = 37;
}
return Math.min(Math.max(zone, 1), 60);
}
/**
* Convert UTM coordinates back to WGS84
* @param {number} easting - UTM easting in meters
* @param {number} northing - UTM northing in meters
* @param {number} zone - UTM zone number
* @param {string} hemisphere - 'N' for northern, 'S' for southern
* @returns {Object} WGS84 coordinates {longitude, latitude}
*/
static fromUTM(easting, northing, zone, hemisphere = "N") {
if (zone < 1 || zone > 60) {
throw new Error(`UTM zone ${zone} is out of valid range [1, 60]`);
}
// Adjust northing for southern hemisphere
const adjustedNorthing =
hemisphere === "S" ? northing - UTMConverter.UGM_FALSE_NORTHING_S : northing;
const e = UTMConverter.WGS84_E;
const e2 = UTMConverter.WGS84_ESQ;
const e4 = e2 * e2;
const e6 = e4 * e2;
// Remove false easting and scale factor
const x = (easting - UTMConverter.UTM_FALSE_EASTING) / UTMConverter.UTM_SCALE_FACTOR;
const y = adjustedNorthing / UTMConverter.UTM_SCALE_FACTOR;
// Footprint latitude
const M = y;
const mu = M / (UTMConverter.WGS84_A * (1 - e2 / 4 - (3 * e4) / 64 - (5 * e6) / 256));
const e1 = (1 - Math.sqrt(1 - e2)) / (1 + Math.sqrt(1 - e2));
const fp =
mu +
((3 * e1) / 2 - (27 * e1 * e1 * e1) / 32) * Math.sin(2 * mu) +
((21 * e1 * e1) / 16 - (55 * e1 * e1 * e1 * e1) / 32) * Math.sin(4 * mu) +
((151 * e1 * e1 * e1) / 96) * Math.sin(6 * mu);
// Calculate latitude and longitude
const C1 = (e2 * Math.cos(fp) * Math.cos(fp)) / (1 - e2);
const T1 = Math.tan(fp) * Math.tan(fp);
const N1 = UTMConverter.WGS84_A / Math.sqrt(1 - e2 * Math.sin(fp) * Math.sin(fp));
const R1 = (UTMConverter.WGS84_A * (1 - e2)) / (1 - e2 * Math.sin(fp) * Math.sin(fp)) ** 1.5;
const D = x / N1;
const lat =
fp -
((N1 * Math.tan(fp)) / R1) *
((D * D) / 2 -
((5 + 3 * T1 + 10 * C1 - 4 * C1 * C1 - 9 * e2) * D * D * D * D) / 24 +
((61 + 90 * T1 + 298 * C1 + 45 * T1 * T1 - 252 * e2 - 3 * C1 * C1) *
D *
D *
D *
D *
D *
D) /
720);
const lonOrigin = (((zone - 1) * 6 - 180 + 3) * Math.PI) / 180;
const lon =
lonOrigin +
(D -
((1 + 2 * T1 + C1) * D * D * D) / 6 +
((5 - 2 * C1 + 28 * T1 - 3 * C1 * C1 + 8 * e2 + 24 * T1 * T1) * D * D * D * D * D) / 120) /
Math.cos(fp);
return {
latitude: (lat * 180) / Math.PI,
longitude: (lon * 180) / Math.PI,
};
}
/**
* Convert Point geometry to UTM coordinates
* @param {Point} point - Point geometry
* @returns {Object} UTM coordinates
*/
static pointToUTM(point) {
return UTMConverter.toUTM(point.lng, point.lat);
}
/**
* Convert multiple coordinates to UTM
* @param {Coordinate[]} coordinates - Array of [longitude, latitude] pairs
* @returns {Object[]} Array of UTM coordinates
*/
static coordinatesToUTM(coordinates) {
return coordinates.map((coord) => UTMConverter.toUTM(coord[0], coord[1]));
}
}
// Convenience function for direct coordinate conversion
/**
* Convert WGS84 to UTM coordinates
* @param {number} lng - Longitude
* @param {number} lat - Latitude
* @returns {Object} UTM coordinates {easting, northing, zone, hemisphere}
*/
export function wgs84ToUTM(lng, lat) {
return UTMConverter.toUTM(lng, lat);
}
/**
* Convert UTM to WGS84 coordinates
* @param {number} easting - UTM easting
* @param {number} northing - UTM northing
* @param {number} zone - UTM zone
* @param {string} hemisphere - 'N' or 'S'
* @returns {Object} WGS84 coordinates {longitude, latitude}
*/
export function utmToWGS84(easting, northing, zone, hemisphere = "N") {
return UTMConverter.fromUTM(easting, northing, zone, hemisphere);
}
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