leaflet.utm
Version:
Converts LatLng to UTM WGS84 in Leaflet
648 lines (525 loc) • 21.6 kB
JavaScript
/*
* Extends L.LatLng to convert easily to UTM WGS84 coordinates
* and print with the desired format
*/
(function(L) {
if (typeof L === 'undefined') {
throw new Error('Leaflet must be included first');
}
// Constructor for 'class' L.Utm
L.Utm = function(x, y, zone, band, southHemi) {
this.x = +x;
this.y = +y;
this.zone = zone;
this.band = band;
this.southHemi = southHemi;
};
L.Utm.setDefaultOptions = function(o) {
// o can be an object or a function
L.Utm.prototype._defaultOptions = o;
};
L.Utm.prototype = {
// convert to string. Using the options you can
// specify another format.
toString: function(options) {
var def = {
decimals: 1,
sep: ',',
format: '{x}{sep} {y}{sep} {zone}{band}{sep} {datum}',
north: 'North',
south: 'South'
};
if (this._defaultOptions) {
// The user has the posibility to change the default options
var aux = this._defaultOptions;
if (typeof aux === 'function') aux = aux(options, def);
def = L.extend(def, aux);
}
options = L.extend(def, options);
var o = this.dic();
o.x = o.x.toFixed(options.decimals);
o.y = o.y.toFixed(options.decimals);
o.hemi = o.southHemi ? options.south : options.north;
o.sep = options.sep;
o.datum = 'WGS84';
return L.Util.template(options.format, o);
},
// returns a L.LatLng object
latLng: function(noExcep) {
try {
var ll = UC().UTM2LatLon(this);
return L.latLng(ll);
} catch (e) {
if (noExcep) return null;
throw e;
}
},
// convert to L.LatLng to check equality
equals: function(other) {
try {
return this.latLng().equals(other.latLng());
} catch (e) {
return false;
}
},
// returns a new object normalized to the proper zone, band...
normalize: function() {
var tmp = this.latLng(true);
return tmp ? tmp.utm() : null;
},
// returns a simple dictionary,
// with optional easting and northing values.
dic: function(eastingNorthing) {
var ret = {
x: this.x,
y: this.y,
zone: this.zone,
band: this.band,
southHemi: this.southHemi
};
if (eastingNorthing) {
ret.easting = this.x;
ret.northing = this.y;
}
return ret;
},
clone: function() {
return L.utm(this);
}
};
// factory to create Utm instances.
L.utm = function(x, y, zone, band, southHemi) {
if (x === undefined || x === null) {
return x;
}
if (x instanceof L.Utm) {
return x;
}
if (typeof x === 'object' && 'x' in x && 'y' in x && 'zone' in x) {
return new L.Utm(x.x, x.y, x.zone, x.band, x.southHemi);
}
return new L.Utm(x, y, zone, band, southHemi);
};
////////////////////////////
// Prototype in LatLng to get an Utm object.
// if zone is null, it is calculated.
L.LatLng.prototype.utm = function(zone, southHemi) {
var dic = UC().LatLon2UTM(
this.lat,
this.lng,
zone,
southHemi);
return L.utm(dic);
};
/////////////////////////////
// from http://home.hiwaay.net/~taylorc/toolbox/geography/geoutm.html
// Try to keep as unmodified as possible
/*eslint-disable */
function UC() {
var pi = 3.14159265358979;
/* Ellipsoid model constants (actual values here are for WGS84) */
var sm_a = 6378137.0;
var sm_b = 6356752.314;
var sm_EccSquared = 6.69437999013e-03;
var UTMScaleFactor = 0.9996;
/*
* DegToRad
*
* Converts degrees to radians.
*
*/
function DegToRad(deg) { return (deg / 180.0 * pi); }
/*
* RadToDeg
*
* Converts radians to degrees.
*
*/
function RadToDeg(rad) { return (rad / pi * 180.0); }
/*
* ArcLengthOfMeridian
*
* Computes the ellipsoidal distance from the equator to a point at a
* given latitude.
*
* Reference: Hoffmann-Wellenhof, B., Lichtenegger, H., and Collins, J.,
* GPS: Theory and Practice, 3rd ed. New York: Springer-Verlag Wien, 1994.
*
* Inputs:
* phi - Latitude of the point, in radians.
*
* Globals:
* sm_a - Ellipsoid model major axis.
* sm_b - Ellipsoid model minor axis.
*
* Returns:
* The ellipsoidal distance of the point from the equator, in meters.
*
*/
function ArcLengthOfMeridian(phi) {
var alpha, beta, gamma, delta, epsilon, n;
var result;
/* Precalculate n */
n = (sm_a - sm_b) / (sm_a + sm_b);
/* Precalculate alpha */
alpha =
((sm_a + sm_b) / 2.0) * (1.0 + (Math.pow(n, 2.0) / 4.0) + (Math.pow(n, 4.0) / 64.0));
/* Precalculate beta */
beta =
(-3.0 * n / 2.0) + (9.0 * Math.pow(n, 3.0) / 16.0) + (-3.0 * Math.pow(n, 5.0) / 32.0);
/* Precalculate gamma */
gamma = (15.0 * Math.pow(n, 2.0) / 16.0) + (-15.0 * Math.pow(n, 4.0) / 32.0);
/* Precalculate delta */
delta = (-35.0 * Math.pow(n, 3.0) / 48.0) + (105.0 * Math.pow(n, 5.0) / 256.0);
/* Precalculate epsilon */
epsilon = (315.0 * Math.pow(n, 4.0) / 512.0);
/* Now calculate the sum of the series and return */
result = alpha * (phi + (beta * Math.sin(2.0 * phi)) + (gamma * Math.sin(4.0 * phi)) +
(delta * Math.sin(6.0 * phi)) + (epsilon * Math.sin(8.0 * phi)));
return result;
}
/*
* UTMCentralMeridian
*
* Determines the central meridian for the given UTM zone.
*
* Inputs:
* zone - An integer value designating the UTM zone, range [1,60].
*
* Returns:
* The central meridian for the given UTM zone, in radians, or zero
* if the UTM zone parameter is outside the range [1,60].
* Range of the central meridian is the radian equivalent of [-177,+177].
*
*/
function UTMCentralMeridian(zone) {
var cmeridian;
cmeridian = DegToRad(-183.0 + (zone * 6.0));
return cmeridian;
}
/*
* FootpointLatitude
*
* Computes the footpoint latitude for use in converting transverse
* Mercator coordinates to ellipsoidal coordinates.
*
* Reference: Hoffmann-Wellenhof, B., Lichtenegger, H., and Collins, J.,
* GPS: Theory and Practice, 3rd ed. New York: Springer-Verlag Wien, 1994.
*
* Inputs:
* y - The UTM northing coordinate, in meters.
*
* Returns:
* The footpoint latitude, in radians.
*
*/
function FootpointLatitude(y) {
var y_, alpha_, beta_, gamma_, delta_, epsilon_, n;
var result;
/* Precalculate n (Eq. 10.18) */
n = (sm_a - sm_b) / (sm_a + sm_b);
/* Precalculate alpha_ (Eq. 10.22) */
/* (Same as alpha in Eq. 10.17) */
alpha_ = ((sm_a + sm_b) / 2.0) * (1 + (Math.pow(n, 2.0) / 4) + (Math.pow(n, 4.0) / 64));
/* Precalculate y_ (Eq. 10.23) */
y_ = y / alpha_;
/* Precalculate beta_ (Eq. 10.22) */
beta_ = (3.0 * n / 2.0) + (-27.0 * Math.pow(n, 3.0) / 32.0) +
(269.0 * Math.pow(n, 5.0) / 512.0);
/* Precalculate gamma_ (Eq. 10.22) */
gamma_ = (21.0 * Math.pow(n, 2.0) / 16.0) + (-55.0 * Math.pow(n, 4.0) / 32.0);
/* Precalculate delta_ (Eq. 10.22) */
delta_ = (151.0 * Math.pow(n, 3.0) / 96.0) + (-417.0 * Math.pow(n, 5.0) / 128.0);
/* Precalculate epsilon_ (Eq. 10.22) */
epsilon_ = (1097.0 * Math.pow(n, 4.0) / 512.0);
/* Now calculate the sum of the series (Eq. 10.21) */
result = y_ + (beta_ * Math.sin(2.0 * y_)) + (gamma_ * Math.sin(4.0 * y_)) +
(delta_ * Math.sin(6.0 * y_)) + (epsilon_ * Math.sin(8.0 * y_));
return result;
}
/*
* MapLatLonToXY
*
* Converts a latitude/longitude pair to x and y coordinates in the
* Transverse Mercator projection. Note that Transverse Mercator is not
* the same as UTM; a scale factor is required to convert between them.
*
* Reference: Hoffmann-Wellenhof, B., Lichtenegger, H., and Collins, J.,
* GPS: Theory and Practice, 3rd ed. New York: Springer-Verlag Wien, 1994.
*
* Inputs:
* phi - Latitude of the point, in radians.
* lambda - Longitude of the point, in radians.
* lambda0 - Longitude of the central meridian to be used, in radians.
*
* Outputs:
* xy - A 2-element array containing the x and y coordinates
* of the computed point.
*
* Returns:
* The function does not return a value.
*
*/
function MapLatLonToXY(phi, lambda, lambda0, xy) {
var N, nu2, ep2, t, t2, l;
var l3coef, l4coef, l5coef, l6coef, l7coef, l8coef;
var tmp;
/* Precalculate ep2 */
ep2 = (Math.pow(sm_a, 2.0) - Math.pow(sm_b, 2.0)) / Math.pow(sm_b, 2.0);
/* Precalculate nu2 */
nu2 = ep2 * Math.pow(Math.cos(phi), 2.0);
/* Precalculate N */
N = Math.pow(sm_a, 2.0) / (sm_b * Math.sqrt(1 + nu2));
/* Precalculate t */
t = Math.tan(phi);
t2 = t * t;
tmp = (t2 * t2 * t2) - Math.pow(t, 6.0);
/* Precalculate l */
l = lambda - lambda0;
/* Precalculate coefficients for l**n in the equations below
so a normal human being can read the expressions for easting
and northing
-- l**1 and l**2 have coefficients of 1.0 */
l3coef = 1.0 - t2 + nu2;
l4coef = 5.0 - t2 + 9 * nu2 + 4.0 * (nu2 * nu2);
l5coef = 5.0 - 18.0 * t2 + (t2 * t2) + 14.0 * nu2 - 58.0 * t2 * nu2;
l6coef = 61.0 - 58.0 * t2 + (t2 * t2) + 270.0 * nu2 - 330.0 * t2 * nu2;
l7coef = 61.0 - 479.0 * t2 + 179.0 * (t2 * t2) - (t2 * t2 * t2);
l8coef = 1385.0 - 3111.0 * t2 + 543.0 * (t2 * t2) - (t2 * t2 * t2);
/* Calculate easting (x) */
xy[0] = N * Math.cos(phi) * l +
(N / 6.0 * Math.pow(Math.cos(phi), 3.0) * l3coef * Math.pow(l, 3.0)) +
(N / 120.0 * Math.pow(Math.cos(phi), 5.0) * l5coef * Math.pow(l, 5.0)) +
(N / 5040.0 * Math.pow(Math.cos(phi), 7.0) * l7coef * Math.pow(l, 7.0));
/* Calculate northing (y) */
xy[1] = ArcLengthOfMeridian(phi) +
(t / 2.0 * N * Math.pow(Math.cos(phi), 2.0) * Math.pow(l, 2.0)) +
(t / 24.0 * N * Math.pow(Math.cos(phi), 4.0) * l4coef * Math.pow(l, 4.0)) +
(t / 720.0 * N * Math.pow(Math.cos(phi), 6.0) * l6coef * Math.pow(l, 6.0)) +
(t / 40320.0 * N * Math.pow(Math.cos(phi), 8.0) * l8coef * Math.pow(l, 8.0));
return;
}
/*
* MapXYToLatLon
*
* Converts x and y coordinates in the Transverse Mercator projection to
* a latitude/longitude pair. Note that Transverse Mercator is not
* the same as UTM; a scale factor is required to convert between them.
*
* Reference: Hoffmann-Wellenhof, B., Lichtenegger, H., and Collins, J.,
* GPS: Theory and Practice, 3rd ed. New York: Springer-Verlag Wien, 1994.
*
* Inputs:
* x - The easting of the point, in meters.
* y - The northing of the point, in meters.
* lambda0 - Longitude of the central meridian to be used, in radians.
*
* Outputs:
* philambda - A 2-element containing the latitude and longitude
* in radians.
*
* Returns:
* The function does not return a value.
*
* Remarks:
* The local variables Nf, nuf2, tf, and tf2 serve the same purpose as
* N, nu2, t, and t2 in MapLatLonToXY, but they are computed with respect
* to the footpoint latitude phif.
*
* x1frac, x2frac, x2poly, x3poly, etc. are to enhance readability and
* to optimize computations.
*
*/
function MapXYToLatLon(x, y, lambda0, philambda) {
var phif, Nf, Nfpow, nuf2, ep2, tf, tf2, tf4, cf;
var x1frac, x2frac, x3frac, x4frac, x5frac, x6frac, x7frac, x8frac;
var x2poly, x3poly, x4poly, x5poly, x6poly, x7poly, x8poly;
/* Get the value of phif, the footpoint latitude. */
phif = FootpointLatitude(y);
/* Precalculate ep2 */
ep2 = (Math.pow(sm_a, 2.0) - Math.pow(sm_b, 2.0)) / Math.pow(sm_b, 2.0);
/* Precalculate cos (phif) */
cf = Math.cos(phif);
/* Precalculate nuf2 */
nuf2 = ep2 * Math.pow(cf, 2.0);
/* Precalculate Nf and initialize Nfpow */
Nf = Math.pow(sm_a, 2.0) / (sm_b * Math.sqrt(1 + nuf2));
Nfpow = Nf;
/* Precalculate tf */
tf = Math.tan(phif);
tf2 = tf * tf;
tf4 = tf2 * tf2;
/* Precalculate fractional coefficients for x**n in the equations
below to simplify the expressions for latitude and longitude. */
x1frac = 1.0 / (Nfpow * cf);
Nfpow *= Nf; /* now equals Nf**2) */
x2frac = tf / (2.0 * Nfpow);
Nfpow *= Nf; /* now equals Nf**3) */
x3frac = 1.0 / (6.0 * Nfpow * cf);
Nfpow *= Nf; /* now equals Nf**4) */
x4frac = tf / (24.0 * Nfpow);
Nfpow *= Nf; /* now equals Nf**5) */
x5frac = 1.0 / (120.0 * Nfpow * cf);
Nfpow *= Nf; /* now equals Nf**6) */
x6frac = tf / (720.0 * Nfpow);
Nfpow *= Nf; /* now equals Nf**7) */
x7frac = 1.0 / (5040.0 * Nfpow * cf);
Nfpow *= Nf; /* now equals Nf**8) */
x8frac = tf / (40320.0 * Nfpow);
/* Precalculate polynomial coefficients for x**n.
-- x**1 does not have a polynomial coefficient. */
x2poly = -1.0 - nuf2;
x3poly = -1.0 - 2 * tf2 - nuf2;
x4poly = 5.0 + 3.0 * tf2 + 6.0 * nuf2 - 6.0 * tf2 * nuf2 - 3.0 * (nuf2 * nuf2) -
9.0 * tf2 * (nuf2 * nuf2);
x5poly = 5.0 + 28.0 * tf2 + 24.0 * tf4 + 6.0 * nuf2 + 8.0 * tf2 * nuf2;
x6poly = -61.0 - 90.0 * tf2 - 45.0 * tf4 - 107.0 * nuf2 + 162.0 * tf2 * nuf2;
x7poly = -61.0 - 662.0 * tf2 - 1320.0 * tf4 - 720.0 * (tf4 * tf2);
x8poly = 1385.0 + 3633.0 * tf2 + 4095.0 * tf4 + 1575 * (tf4 * tf2);
/* Calculate latitude */
philambda[0] = phif + x2frac * x2poly * (x * x) + x4frac * x4poly * Math.pow(x, 4.0) +
x6frac * x6poly * Math.pow(x, 6.0) + x8frac * x8poly * Math.pow(x, 8.0);
/* Calculate longitude */
philambda[1] = lambda0 + x1frac * x + x3frac * x3poly * Math.pow(x, 3.0) +
x5frac * x5poly * Math.pow(x, 5.0) + x7frac * x7poly * Math.pow(x, 7.0);
return;
}
/*
* LatLonToUTMXY
*
* Converts a latitude/longitude pair to x and y coordinates in the
* Universal Transverse Mercator projection.
*
* Inputs:
* lat - Latitude of the point, in radians.
* lon - Longitude of the point, in radians.
* zone - UTM zone to be used for calculating values for x and y.
* If zone is less than 1 or greater than 60, the routine
* will determine the appropriate zone from the value of lon.
*
* Outputs:
* xy - A 2-element array where the UTM x and y values will be stored.
*
* Returns:
* The UTM zone used for calculating the values of x and y.
*
*/
function LatLonToUTMXY(lat, lon, zone, xy) {
MapLatLonToXY(lat, lon, UTMCentralMeridian(zone), xy);
/* Adjust easting and northing for UTM system. */
xy[0] = xy[0] * UTMScaleFactor + 500000.0;
xy[1] = xy[1] * UTMScaleFactor;
if (xy[1] < 0.0) xy[1] = xy[1] + 10000000.0;
return zone;
}
/*
* UTMXYToLatLon
*
* Converts x and y coordinates in the Universal Transverse Mercator
* projection to a latitude/longitude pair.
*
* Inputs:
* x - The easting of the point, in meters.
* y - The northing of the point, in meters.
* zone - The UTM zone in which the point lies.
* southhemi - True if the point is in the southern hemisphere;
* false otherwise.
*
* Outputs:
* latlon - A 2-element array containing the latitude and
* longitude of the point, in radians.
*
* Returns:
* The function does not return a value.
*
*/
function UTMXYToLatLon(x, y, zone, southhemi, latlon) {
var cmeridian;
x -= 500000.0;
x /= UTMScaleFactor;
/* If in southern hemisphere, adjust y accordingly. */
if (southhemi) y -= 10000000.0;
y /= UTMScaleFactor;
cmeridian = UTMCentralMeridian(zone);
MapXYToLatLon(x, y, cmeridian, latlon);
return;
}
/*eslint-enable */
// Original code until here
////////////////////////////
var bands = 'CDEFGHJKLMNPQRSTUVWX';
var nBandIdx = bands.indexOf('N');
function calcBand(lat) {
if (lat < -80.0 || lat > 84.0) return ''
var bandIdx = Math.floor((lat + 80.0) / 8);
return bands.charAt(bandIdx) || 'X'; // cover extra X band
}
function calcZone(band, lon) {
var zone = Math.floor((lon + 180.0) / 6) + 1;
if (lon == 180.0) zone = 60;
if (band === 'V' && lon > 3.0 && lon < 7.0) {
// Norway exception:
zone = 32;
} else if (band === 'X') {
// Special zones for Svalbard
if (lon >= 0.0 && lon < 9.0) {
zone = 31;
}
else if (lon >= 9.0 && lon < 21.0) {
zone = 33;
}
else if (lon >= 21.0 && lon < 33.0) {
zone = 35;
}
else if (lon >= 33.0 && lon < 42.0) {
zone = 37;
}
}
return zone;
}
function UTM2LatLon(utm) {
if (utm.southHemi === undefined && utm.band === undefined) {
throw 'Undefined hemisphere in ' + utm.toString();
}
var southHemi = utm.southHemi;
var band = utm.band;
if (band && band.length == 1
&& bands.indexOf(band.toUpperCase()) >= 0) {
southHemi = bands.indexOf(band.toUpperCase()) < nBandIdx;
}
var latlon = new Array(2);
UTMXYToLatLon(utm.x, utm.y, utm.zone, southHemi, latlon);
if (Math.abs(latlon[0]) > pi/2) return null;
return {lat: RadToDeg(latlon[0]), lng: RadToDeg(latlon[1])};
}
function LatLon2UTM(lat, lon, zone, southHemi) {
function wrapLon(x) {
// don't use L.Util.wrapNum to be 0.7 compatible
var max = 180,
min = -180,
d = max - min;
return x === max ? x : ((x - min) % d + d) % d + min;
}
lon = wrapLon(lon);
var band = calcBand(lat);
zone = zone || calcZone(band, lon);
southHemi = (southHemi === undefined || southHemi === null) ?
lat < 0 : southHemi;
var xy = new Array(2);
zone = LatLonToUTMXY(DegToRad(lat), DegToRad(lon), zone, xy);
// This is the object returned
var ret = {
x: xy[0],
y: xy[1],
zone: zone,
band: band,
southHemi: southHemi
};
return ret;
}
return {
LatLon2UTM: LatLon2UTM,
UTM2LatLon: UTM2LatLon,
};
}
})(L);