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import {
LAT_BANDS,
bandNorth,
bandSouth,
centralMeridian,
fromUps,
fromUtm,
toUps,
toUtm,
} from '../utm/utm'
/**
* Military Grid Reference System (MGRS), including the UPS polar areas.
* Lettering follows NGA TM 8358.1 / GEOTRANS.
*/
import type { MgrsPrecision } from './precision'
const COL_SETS = ['ABCDEFGH', 'JKLMNPQR', 'STUVWXYZ']
const ROW_LETTERS = 'ABCDEFGHJKLMNPQRSTUV'
const UPS_ROWS = 'ABCDEFGHJKLMNPQRSTUVWXYZ'
const UPS_COLS_WEST = 'JKLPQRSTUXYZ'
const UPS_COLS_EAST = 'ABCFGHJKLPQR'
export interface MgrsParts {
zone: number | null // null for UPS
band: string
square: string
easting: string
northing: string
}
/** 100 km square letters for a UTM coordinate. */
export function utmSquareId(
zone: number,
easting: number,
northing: number,
): string {
const set = COL_SETS[(zone - 1) % 3]!
const col = set[Math.floor(easting / 100_000) - 1] ?? '?'
const rowOffset = zone % 2 === 0 ? 5 : 0
const rowIdx = (Math.floor((northing % 2_000_000) / 100_000) + rowOffset) % 20
return col + ROW_LETTERS[rowIdx]!
}
/**
* Truncate to whole metres, allowing for float error just below a whole metre. The square
* letters and the digits both come from this value, so 99,999.9999 m cannot give the digits of
* the next square inside the letters of this one.
*/
function toWholeMetres(value: number): number {
return Math.floor(value + 1e-6)
}
/** Truncate (never round) whole metres to the requested resolution, as MGRS requires. */
function truncDigits(metres: number, precision: MgrsPrecision): string {
if (precision === 0) return ''
const v = Math.floor((metres % 100_000) / Math.pow(10, 5 - precision))
return String(v).padStart(precision, '0')
}
export function toMgrsParts(
p: LatLon,
precision: MgrsPrecision = 5,
): MgrsParts {
if (p.lat > 84 || p.lat < -80) {
const ups = toUps(p)
const easting = toWholeMetres(ups.easting)
const northing = toWholeMetres(ups.northing)
// The polar zones split at easting 2,000,000 (the 0° and 180° meridians). Deciding by the
// longitude's sign puts the pole itself, at exactly 2,000,000, past the west letter table.
const west = easting < 2_000_000
const band = ups.hemisphere === 'N' ? (west ? 'Y' : 'Z') : west ? 'A' : 'B'
const fe = west ? 800_000 : 2_000_000
const fn = ups.hemisphere === 'N' ? 1_300_000 : 800_000
const cols = west ? UPS_COLS_WEST : UPS_COLS_EAST
const col = cols[Math.floor((easting - fe) / 100_000)] ?? '?'
const row = UPS_ROWS[Math.floor((northing - fn) / 100_000)] ?? '?'
return {
zone: null,
band,
square: col + row,
easting: truncDigits(easting, precision),
northing: truncDigits(northing, precision),
}
}
const u = toUtm(p)
const easting = toWholeMetres(u.easting)
const northing = toWholeMetres(u.northing)
return {
zone: u.zone,
band: u.band,
square: utmSquareId(u.zone, easting, northing),
easting: truncDigits(easting, precision),
northing: truncDigits(northing, precision),
}
}
export function toMgrs(
p: LatLon,
precision: MgrsPrecision = 5,
spaced = false,
): string {
const m = toMgrsParts(p, precision)
const gzd = (m.zone ?? '') + m.band
const parts = [gzd, m.square, m.easting, m.northing].filter(Boolean)
return spaced ? parts.join(' ') : parts.join('')
}
const MGRS_RE = /^(\d{1,2})?([A-HJ-NP-Z])([A-HJ-NP-Z]{2})(\d*)$/
export function isMgrs(s: string): boolean {
const m = MGRS_RE.exec(s.replace(/\s+/g, '').toUpperCase())
return !!m && m[4]!.length % 2 === 0 && m[4]!.length <= 10
}
export interface MgrsDecoded {
/** South-west corner of the referenced square. */
sw: LatLon
/** Centre of the referenced square. */
center: LatLon
/** Square size in metres. */
size: number
}
/** Decode an MGRS string. */
export function fromMgrs(input: string): MgrsDecoded {
const s = input.replace(/\s+/g, '').toUpperCase()
const m = MGRS_RE.exec(s)
if (!m) throw new Error(`Invalid MGRS "${input}"`)
// NOTE: the pattern makes the band, square and digit groups required; only the zone is optional.
const [, zoneStr, band = '', sq = '', digits = ''] = m
Iif (digits.length % 2 !== 0 || digits.length > 10)
throw new Error('MGRS needs an even number of digits (max 10)')
const precision = digits.length / 2
const size = Math.pow(10, 5 - precision)
const e100 = precision ? Number(digits.slice(0, precision)) * size : 0
const n100 = precision ? Number(digits.slice(precision)) * size : 0
const at = (de: number, dn: number): LatLon =>
decodeAt(zoneStr, band, sq, e100 + de, n100 + dn)
return { sw: at(0, 0), center: at(size / 2, size / 2), size }
}
/**
* How far outside its latitude band a decoded point may fall. A 100 km square can start about
* 0.9° beyond the band it is named for, so "31X CV" at 72°N has its corner in band W. The row
* letters repeat every 2,000 km (about 18°), so this margin cannot pick the wrong cycle.
*/
const BAND_TOLERANCE_DEGREES = 1.5
function decodeAt(
zoneStr: string | undefined,
band: string,
sq: string,
e100: number,
n100: number,
): LatLon {
const col = sq[0]!
const row = sq[1]!
if (!zoneStr) {
Iif (!'ABYZ'.includes(band))
throw new Error('A grid zone number is required outside the polar areas')
const west = band === 'A' || band === 'Y'
const north = band === 'Y' || band === 'Z'
const cols = west ? UPS_COLS_WEST : UPS_COLS_EAST
const ci = cols.indexOf(col)
const ri = UPS_ROWS.indexOf(row)
Iif (ci < 0 || ri < 0) throw new Error(`Invalid UPS 100 km square "${sq}"`)
const fe = west ? 800_000 : 2_000_000
const fn = north ? 1_300_000 : 800_000
return fromUps(
north ? 'N' : 'S',
fe + ci * 100_000 + e100,
fn + ri * 100_000 + n100,
)
}
const zone = Number(zoneStr)
Iif (zone < 1 || zone > 60) throw new Error(`Invalid grid zone ${zone}`)
Iif (!LAT_BANDS.includes(band))
throw new Error(`Invalid latitude band "${band}"`)
const set = COL_SETS[(zone - 1) % 3]!
const ci = set.indexOf(col)
Iif (ci < 0)
throw new Error(`Column letter "${col}" is not valid in zone ${zone}`)
const rowOffset = zone % 2 === 0 ? 5 : 0
const ri = ROW_LETTERS.indexOf(row)
Iif (ri < 0) throw new Error(`Invalid row letter "${row}"`)
const easting = (ci + 1) * 100_000 + e100
const rowNorthing = ((((ri - rowOffset) % 20) + 20) % 20) * 100_000 + n100
const hemisphere = band >= 'N' ? 'N' : 'S'
// Resolve the 2,000 km row cycle from the latitude band.
const south = bandSouth(band)
const bandMin = toUtm(
{ lat: south, lon: centralMeridian(zone) },
zone,
).northing
let northing = rowNorthing
while (northing < bandMin - 100_000) northing += 2_000_000
const p = fromUtm(zone, hemisphere, easting, northing)
Iif (
p.lat < south - BAND_TOLERANCE_DEGREES ||
p.lat > bandNorth(band) + BAND_TOLERANCE_DEGREES
) {
throw new Error(`Square ${sq} does not fall in band ${band}`)
}
return p
}
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