L.LatLng.UTM.js

/*
 * 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);