/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -  */
    /*  Latitude/longitude spherical geodesy formulae & scripts (c) Chris Veness 2002-2010            */
    /*   - www.movable-type.co.uk/scripts/latlong.html                                                */
    /*                                                                                                */
    /*  Sample usage:                                                                                 */
    /*    var p1 = new LatLon(51.5136, -0.0983);                                                      */
    /*    var p2 = new LatLon(51.4778, -0.0015);                                                      */
    /*    var dist = p1.distanceTo(p2);          // in km                                             */
    /*    var brng = p1.bearingTo(p2);           // in degrees clockwise from north                   */
    /*    ... etc                                                                                     */
    /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -  */

    /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -  */
    /*  Note that minimal error checking is performed in this example code!                           */
    /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -  */


    /**
    * Creates a point on the earth's surface at the supplied latitude / longitude
    *
    * @constructor
    * @param {Number} lat: latitude in numeric degrees
    * @param {Number} lon: longitude in numeric degrees
    * @param {Number} [rad=6371]: radius of earth if different value is required from standard 6,371km
    */
    function LatLon(lat, lon, rad) {
        if (typeof rad == 'undefined') rad = 6371;  // earth's mean radius in km
        this._lat = lat;
        this._lon = lon;
        this._radius = rad;
    }


    /**
    * Returns the distance from this point to the supplied point, in km 
    * (using Haversine formula)
    *
    * from: Haversine formula - R. W. Sinnott, "Virtues of the Haversine",
    *       Sky and Telescope, vol 68, no 2, 1984
    *
    * @param   {LatLon} point: Latitude/longitude of destination point
    * @param   {Number} [precision=4]: no of significant digits to use for returned value
    * @returns {Number} Distance in km between this point and destination point
    */
    LatLon.prototype.distanceTo = function (point, precision) {
        // default 4 sig figs reflects typical 0.3% accuracy of spherical model
        if (typeof precision == 'undefined') precision = 4;

        var R = this._radius;
        var lat1 = this._lat.toRad(), lon1 = this._lon.toRad();
        var lat2 = point._lat.toRad(), lon2 = point._lon.toRad();
        var dLat = lat2 - lat1;
        var dLon = lon2 - lon1;

        var a = Math.sin(dLat / 2) * Math.sin(dLat / 2) +
          Math.cos(lat1) * Math.cos(lat2) *
          Math.sin(dLon / 2) * Math.sin(dLon / 2);
        var c = 2 * Math.atan2(Math.sqrt(a), Math.sqrt(1 - a));
        var d = R * c;
        return d.toPrecisionFixed(precision);
    }


    /**
    * Returns the (initial) bearing from this point to the supplied point, in degrees
    *   see http://williams.best.vwh.net/avform.htm#Crs
    *
    * @param   {LatLon} point: Latitude/longitude of destination point
    * @returns {Number} Initial bearing in degrees from North
    */
    LatLon.prototype.bearingTo = function (point) {
        var lat1 = this._lat.toRad(), lat2 = point._lat.toRad();
        var dLon = (point._lon - this._lon).toRad();

        var y = Math.sin(dLon) * Math.cos(lat2);
        var x = Math.cos(lat1) * Math.sin(lat2) -
          Math.sin(lat1) * Math.cos(lat2) * Math.cos(dLon);
        var brng = Math.atan2(y, x);

        return brng.toDeg();//(brng.toDeg() + 360) % 360;
    }


    /**
    * Returns final bearing arriving at supplied destination point from this point; the final bearing 
    * will differ from the initial bearing by varying degrees according to distance and latitude
    *
    * @param   {LatLon} point: Latitude/longitude of destination point
    * @returns {Number} Final bearing in degrees from North
    */
    LatLon.prototype.finalBearingTo = function (point) {
        // get initial bearing from supplied point back to this point...
        var lat1 = point._lat.toRad(), lat2 = this._lat.toRad();
        var dLon = (this._lon - point._lon).toRad();

        var y = Math.sin(dLon) * Math.cos(lat2);
        var x = Math.cos(lat1) * Math.sin(lat2) -
          Math.sin(lat1) * Math.cos(lat2) * Math.cos(dLon);
        var brng = Math.atan2(y, x);

        // ... & reverse it by adding 180°
        return (brng.toDeg() + 180) % 360;
    }


    /**
    * Returns the midpoint between this point and the supplied point.
    *   see http://mathforum.org/library/drmath/view/51822.html for derivation
    *
    * @param   {LatLon} point: Latitude/longitude of destination point
    * @returns {LatLon} Midpoint between this point and the supplied point
    */
    LatLon.prototype.midpointTo = function (point) {
        lat1 = this._lat.toRad(), lon1 = this._lon.toRad();
        lat2 = point._lat.toRad();
        var dLon = (point._lon - this._lon).toRad();

        var Bx = Math.cos(lat2) * Math.cos(dLon);
        var By = Math.cos(lat2) * Math.sin(dLon);

        lat3 = Math.atan2(Math.sin(lat1) + Math.sin(lat2),
                    Math.sqrt((Math.cos(lat1) + Bx) * (Math.cos(lat1) + Bx) + By * By));
        lon3 = lon1 + Math.atan2(By, Math.cos(lat1) + Bx);

        return new LatLon(lat3.toDeg(), lon3.toDeg());
    }


    /**
    * Returns the destination point from this point having travelled the given distance (in km) on the 
    * given initial bearing (bearing may vary before destination is reached)
    *
    *   see http://williams.best.vwh.net/avform.htm#LL
    *
    * @param   {Number} brng: Initial bearing in degrees
    * @param   {Number} dist: Distance in km
    * @returns {LatLon} Destination point
    */
    LatLon.prototype.destinationPoint = function (brng, dist) {
        dist = dist / this._radius;  // convert dist to angular distance in radians
        brng = brng.toRad();  // 
        var lat1 = this._lat.toRad(), lon1 = this._lon.toRad();

        var lat2 = Math.asin(Math.sin(lat1) * Math.cos(dist) +
                        Math.cos(lat1) * Math.sin(dist) * Math.cos(brng));
        var lon2 = lon1 + Math.atan2(Math.sin(brng) * Math.sin(dist) * Math.cos(lat1),
                               Math.cos(dist) - Math.sin(lat1) * Math.sin(lat2));
        lon2 = (lon2 + 3 * Math.PI) % (2 * Math.PI) - Math.PI;  // normalise to -180...+180

        if (isNaN(lat2) || isNaN(lon2)) return null;
        return new LatLon(lat2.toDeg(), lon2.toDeg());
    }


    /**
    * Returns the point of intersection of two paths defined by point and bearing
    *
    *   see http://williams.best.vwh.net/avform.htm#Intersection
    *
    * @param   {LatLon} p1: First point
    * @param   {Number} brng1: Initial bearing from first point
    * @param   {LatLon} p2: Second point
    * @param   {Number} brng2: Initial bearing from second point
    * @returns {LatLon} Destination point (null if no unique intersection defined)
    */
    LatLon.intersection = function (p1, brng1, p2, brng2) {
        lat1 = p1._lat.toRad(), lon1 = p1._lon.toRad();
        lat2 = p2._lat.toRad(), lon2 = p2._lon.toRad();
        brng13 = brng1.toRad(), brng23 = brng2.toRad();
        dLat = lat2 - lat1, dLon = lon2 - lon1;

        dist12 = 2 * Math.asin(Math.sqrt(Math.sin(dLat / 2) * Math.sin(dLat / 2) +
    Math.cos(lat1) * Math.cos(lat2) * Math.sin(dLon / 2) * Math.sin(dLon / 2)));
        if (dist12 == 0) return null;

        // initial/final bearings between points
        brngA = Math.acos((Math.sin(lat2) - Math.sin(lat1) * Math.cos(dist12)) /
    (Math.sin(dist12) * Math.cos(lat1)));
        if (isNaN(brngA)) brngA = 0;  // protect against rounding
        brngB = Math.acos((Math.sin(lat1) - Math.sin(lat2) * Math.cos(dist12)) /
    (Math.sin(dist12) * Math.cos(lat2)));

        if (Math.sin(lon2 - lon1) > 0) {
            brng12 = brngA;
            brng21 = 2 * Math.PI - brngB;
        } else {
            brng12 = 2 * Math.PI - brngA;
            brng21 = brngB;
        }

        alpha1 = (brng13 - brng12 + Math.PI) % (2 * Math.PI) - Math.PI;  // angle 2-1-3
        alpha2 = (brng21 - brng23 + Math.PI) % (2 * Math.PI) - Math.PI;  // angle 1-2-3

        if (Math.sin(alpha1) == 0 && Math.sin(alpha2) == 0) return null;  // infinite intersections
        if (Math.sin(alpha1) * Math.sin(alpha2) < 0) return null;       // ambiguous intersection

        //alpha1 = Math.abs(alpha1);
        //alpha2 = Math.abs(alpha2);
        // ... Ed Williams takes abs of alpha1/alpha2, but seems to break calculation?

        alpha3 = Math.acos(-Math.cos(alpha1) * Math.cos(alpha2) +
                       Math.sin(alpha1) * Math.sin(alpha2) * Math.cos(dist12));
        dist13 = Math.atan2(Math.sin(dist12) * Math.sin(alpha1) * Math.sin(alpha2),
                       Math.cos(alpha2) + Math.cos(alpha1) * Math.cos(alpha3))
        lat3 = Math.asin(Math.sin(lat1) * Math.cos(dist13) +
                    Math.cos(lat1) * Math.sin(dist13) * Math.cos(brng13));
        dLon13 = Math.atan2(Math.sin(brng13) * Math.sin(dist13) * Math.cos(lat1),
                       Math.cos(dist13) - Math.sin(lat1) * Math.sin(lat3));
        lon3 = lon1 + dLon13;
        lon3 = (lon3 + Math.PI) % (2 * Math.PI) - Math.PI;  // normalise to -180..180º

        return new LatLon(lat3.toDeg(), lon3.toDeg());
    }


    /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -  */

    /**
    * Returns the distance from this point to the supplied point, in km, travelling along a rhumb line
    *
    *   see http://williams.best.vwh.net/avform.htm#Rhumb
    *
    * @param   {LatLon} point: Latitude/longitude of destination point
    * @returns {Number} Distance in km between this point and destination point
    */
    LatLon.prototype.rhumbDistanceTo = function (point) {
        var R = this._radius;
        var lat1 = this._lat.toRad(), lat2 = point._lat.toRad();
        var dLat = (point._lat - this._lat).toRad();
        var dLon = Math.abs(point._lon - this._lon).toRad();

        var dPhi = Math.log(Math.tan(lat2 / 2 + Math.PI / 4) / Math.tan(lat1 / 2 + Math.PI / 4));
        var q = (!isNaN(dLat / dPhi)) ? dLat / dPhi : Math.cos(lat1);  // E-W line gives dPhi=0
        // if dLon over 180° take shorter rhumb across 180° meridian:
        if (dLon > Math.PI) dLon = 2 * Math.PI - dLon;
        var dist = Math.sqrt(dLat * dLat + q * q * dLon * dLon) * R;

        return dist.toPrecisionFixed(4);  // 4 sig figs reflects typical 0.3% accuracy of spherical model
    }

    /**
    * Returns the bearing from this point to the supplied point along a rhumb line, in degrees
    *
    * @param   {LatLon} point: Latitude/longitude of destination point
    * @returns {Number} Bearing in degrees from North
    */
    LatLon.prototype.rhumbBearingTo = function (point) {
        var lat1 = this._lat.toRad(), lat2 = point._lat.toRad();
        var dLon = (point._lon - this._lon).toRad();

        var dPhi = Math.log(Math.tan(lat2 / 2 + Math.PI / 4) / Math.tan(lat1 / 2 + Math.PI / 4));
        if (Math.abs(dLon) > Math.PI) dLon = dLon > 0 ? -(2 * Math.PI - dLon) : (2 * Math.PI + dLon);
        var brng = Math.atan2(dLon, dPhi);

        return (brng.toDeg() + 360) % 360;
    }

    /**
    * Returns the destination point from this point having travelled the given distance (in km) on the 
    * given bearing along a rhumb line
    *
    * @param   {Number} brng: Bearing in degrees from North
    * @param   {Number} dist: Distance in km
    * @returns {LatLon} Destination point
    */
    LatLon.prototype.rhumbDestinationPoint = function (brng, dist) {
        var R = this._radius;
        var d = parseFloat(dist) / R;  // d = angular distance covered on earth's surface
        var lat1 = this._lat.toRad(), lon1 = this._lon.toRad();
        brng = brng.toRad();

        var lat2 = lat1 + d * Math.cos(brng);
        var dLat = lat2 - lat1;
        var dPhi = Math.log(Math.tan(lat2 / 2 + Math.PI / 4) / Math.tan(lat1 / 2 + Math.PI / 4));
        var q = (!isNaN(dLat / dPhi)) ? dLat / dPhi : Math.cos(lat1);  // E-W line gives dPhi=0
        var dLon = d * Math.sin(brng) / q;
        // check for some daft bugger going past the pole
        if (Math.abs(lat2) > Math.PI / 2) lat2 = lat2 > 0 ? Math.PI - lat2 : -(Math.PI - lat2);
        lon2 = (lon1 + dLon + 3 * Math.PI) % (2 * Math.PI) - Math.PI;

        return new LatLon(lat2.toDeg(), lon2.toDeg());
    }

    /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -  */


    /**
    * Returns the latitude of this point; signed numeric degrees if no format, otherwise format & dp 
    * as per Geo.toLat()
    *
    * @param   {String} [format]: Return value as 'd', 'dm', 'dms'
    * @param   {Number} [dp=0|2|4]: No of decimal places to display
    * @returns {Number|String} Numeric degrees if no format specified, otherwise deg/min/sec
    *
    * @requires Geo
    */
    LatLon.prototype.lat = function (format, dp) {
        if (typeof format == 'undefined') return this._lat;

        return Geo.toLat(this._lat, format, dp);
    }

    /**
    * Returns the longitude of this point; signed numeric degrees if no format, otherwise format & dp 
    * as per Geo.toLon()
    *
    * @param   {String} [format]: Return value as 'd', 'dm', 'dms'
    * @param   {Number} [dp=0|2|4]: No of decimal places to display
    * @returns {Number|String} Numeric degrees if no format specified, otherwise deg/min/sec
    *
    * @requires Geo
    */
    LatLon.prototype.lon = function (format, dp) {
        if (typeof format == 'undefined') return this._lon;

        return Geo.toLon(this._lon, format, dp);
    }

    /**
    * Returns a string representation of this point; format and dp as per lat()/lon()
    *
    * @param   {String} [format]: Return value as 'd', 'dm', 'dms'
    * @param   {Number} [dp=0|2|4]: No of decimal places to display
    * @returns {String} Comma-separated latitude/longitude
    *
    * @requires Geo
    */
    LatLon.prototype.toString = function (format, dp) {
        if (typeof format == 'undefined') format = 'dms';

        return Geo.toLat(this._lat, format, dp) + ', ' + Geo.toLon(this._lon, format, dp);
    }


    /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -  */

    // extend Number object with methods for converting degrees/radians

    /** Convert numeric degrees to radians */
    if (typeof (String.prototype.toRad) === "undefined") {
        Number.prototype.toRad = function () {
            return this * Math.PI / 180;
        }
    }

    /** Convert radians to numeric (signed) degrees */
    if (typeof (String.prototype.toDeg) === "undefined") {
        Number.prototype.toDeg = function () {
            return this * 180 / Math.PI;
        }
    }

    /** 
    * Format the significant digits of a number, using only fixed-point notation (no exponential)
    * 
    * @param   {Number} precision: Number of significant digits to appear in the returned string
    * @returns {String} A string representation of number which contains precision significant digits
    */
    if (typeof (Number.prototype.toPrecisionFixed) === "undefined") {
        Number.prototype.toPrecisionFixed = function (precision) {
            var numb = this < 0 ? -this : this;  // can't take log of -ve number...
            var sign = this < 0 ? '-' : '';

            if (numb == 0) { n = '0.'; while (precision--) n += '0'; return n };  // can't take log of zero

            var scale = Math.ceil(Math.log(numb) * Math.LOG10E);  // no of digits before decimal
            var n = String(Math.round(numb * Math.pow(10, precision - scale)));
            if (scale > 0) {  // add trailing zeros & insert decimal as required
                l = scale - n.length;
                while (l-- > 0) n = n + '0';
                if (scale < n.length) n = n.slice(0, scale) + '.' + n.slice(scale);
            } else {          // prefix decimal and leading zeros if required
                while (scale++ < 0) n = '0' + n;
                n = '0.' + n;
            }
            return sign + n;
        }
    }


    /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -  */
    /*  Geodesy representation conversion functions (c) Chris Veness 2002-2010                        */
    /*   - www.movable-type.co.uk/scripts/latlong.html                                                */
    /*                                                                                                */
    /*  Sample usage:                                                                                 */
    /*    var lat = Geo.parseDMS(' 51° 28' 40.12? N');                                                */
    /*    var lon = Geo.parseDMS('000° 00' 05.31? W');                                                */
    /*    var p1 = new LatLon(lat, lon);                                                              */
    /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -  */

    var Geo = {};  // Geo namespace, representing static class

    /**
    * Parses string representing degrees/minutes/seconds into numeric degrees
    *
    * This is very flexible on formats, allowing signed decimal degrees, or deg-min-sec optionally
    * suffixed by compass direction (NSEW). A variety of separators are accepted (eg 3º 37' 09"W) 
    * or fixed-width format without separators (eg 0033709W). Seconds and minutes may be omitted. 
    * (Note minimal validation is done).
    *
    * @param   {String|Number} dmsStr: Degrees or deg/min/sec in variety of formats
    * @returns {Number} Degrees as decimal number
    * @throws  {TypeError} dmsStr is an object, perhaps DOM object without .value?
    */
    Geo.parseDMS = function (dmsStr) {
        if (typeof deg == 'object') throw new TypeError('Geo.parseDMS - dmsStr is [DOM?] object');

        if (!isNaN(dmsStr)) return Number(dmsStr);  // ... signed decimal degrees without NSEW

        // strip off any sign or compass dir'n & split out separate d/m/s
        var dms = String(dmsStr).trim().replace(/^-/, '').replace(/[NSEW]$/i, '').split(/[^0-9.,]+/);
        if (dms[dms.length - 1] == '') dms.splice(dms.length - 1);  // from trailing symbol

        if (dms == '') return NaN;

        // and convert to decimal degrees...
        switch (dms.length) {
            case 3:  // interpret 3-part result as d/m/s
                var deg = dms[0] / 1 + dms[1] / 60 + dms[2] / 3600;
                break;
            case 2:  // interpret 2-part result as d/m
                var deg = dms[0] / 1 + dms[1] / 60;
                break;
            case 1:  // just d (possibly decimal) or non-separated dddmmss
                var deg = dms[0];
                // check for fixed-width unseparated format eg 0033709W
                if (/[NS]/i.test(dmsStr)) deg = '0' + deg;  // - normalise N/S to 3-digit degrees
                if (/[0-9]{7}/.test(deg)) deg = deg.slice(0, 3) / 1 + deg.slice(3, 5) / 60 + deg.slice(5) / 3600;
                break;
            default:
                return NaN;
        }
        if (/^-|[WS]$/i.test(dmsStr.trim())) deg = -deg; // take '-', west and south as -ve
        return Number(deg);
    }

    /**
    * Convert decimal degrees to deg/min/sec format
    *  - degree, prime, double-prime symbols are added, but sign is discarded, though no compass
    *    direction is added
    *
    * @private
    * @param   {Number} deg: Degrees
    * @param   {String} [format=dms]: Return value as 'd', 'dm', 'dms'
    * @param   {Number} [dp=0|2|4]: No of decimal places to use - default 0 for dms, 2 for dm, 4 for d
    * @returns {String} deg formatted as deg/min/secs according to specified format
    * @throws  {TypeError} deg is an object, perhaps DOM object without .value?
    */
    Geo.toDMS = function (deg, format, dp) {
        if (typeof deg == 'object') throw new TypeError('Geo.toDMS - deg is [DOM?] object');
        if (isNaN(deg)) return '';  // give up here if we can't make a number from deg

        // default values
        if (typeof format == 'undefined') format = 'dms';
        if (typeof dp == 'undefined') {
            switch (format) {
                case 'd': dp = 4; break;
                case 'dm': dp = 2; break;
                case 'dms': dp = 0; break;
                default: format = 'dms'; dp = 0;  // be forgiving on invalid format
            }
        }

        deg = Math.abs(deg);  // (unsigned result ready for appending compass dir'n)

        switch (format) {
            case 'd':
                d = deg.toFixed(dp);     // round degrees
                if (d < 100) d = '0' + d;  // pad with leading zeros
                if (d < 10) d = '0' + d;
                dms = d + '\u00B0';      // add º symbol
                break;
            case 'dm':
                var min = (deg * 60).toFixed(dp);  // convert degrees to minutes & round
                var d = Math.floor(min / 60);    // get component deg/min
                var m = (min % 60).toFixed(dp);  // pad with trailing zeros
                if (d < 100) d = '0' + d;          // pad with leading zeros
                if (d < 10) d = '0' + d;
                if (m < 10) m = '0' + m;
                dms = d + '\u00B0' + m + '\u2032';  // add º, ' symbols
                break;
            case 'dms':
                var sec = (deg * 3600).toFixed(dp);  // convert degrees to seconds & round
                var d = Math.floor(sec / 3600);    // get component deg/min/sec
                var m = Math.floor(sec / 60) % 60;
                var s = (sec % 60).toFixed(dp);    // pad with trailing zeros
                if (d < 100) d = '0' + d;            // pad with leading zeros
                if (d < 10) d = '0' + d;
                if (m < 10) m = '0' + m;
                if (s < 10) s = '0' + s;
                dms = d + '\u00B0' + m + '\u2032' + s + '\u2033';  // add º, ', " symbols
                break;
        }

        return dms;
    }

    /**
    * Convert numeric degrees to deg/min/sec latitude (suffixed with N/S)
    *
    * @param   {Number} deg: Degrees
    * @param   {String} [format=dms]: Return value as 'd', 'dm', 'dms'
    * @param   {Number} [dp=0|2|4]: No of decimal places to use - default 0 for dms, 2 for dm, 4 for d
    * @returns {String} Deg/min/seconds
    */
    Geo.toLat = function (deg, format, dp) {
        var lat = Geo.toDMS(deg, format, dp);
        return lat == '' ? '' : lat.slice(1) + (deg < 0 ? 'S' : 'N');  // knock off initial '0' for lat!
    }

    /**
    * Convert numeric degrees to deg/min/sec longitude (suffixed with E/W)
    *
    * @param   {Number} deg: Degrees
    * @param   {String} [format=dms]: Return value as 'd', 'dm', 'dms'
    * @param   {Number} [dp=0|2|4]: No of decimal places to use - default 0 for dms, 2 for dm, 4 for d
    * @returns {String} Deg/min/seconds
    */
    Geo.toLon = function (deg, format, dp) {
        var lon = Geo.toDMS(deg, format, dp);
        return lon == '' ? '' : lon + (deg < 0 ? 'W' : 'E');
    }

    /**
    * Convert numeric degrees to deg/min/sec as a bearing (0º..360º)
    *
    * @param   {Number} deg: Degrees
    * @param   {String} [format=dms]: Return value as 'd', 'dm', 'dms'
    * @param   {Number} [dp=0|2|4]: No of decimal places to use - default 0 for dms, 2 for dm, 4 for d
    * @returns {String} Deg/min/seconds
    */
    Geo.toBrng = function (deg, format, dp) {
        deg = (Number(deg) + 360) % 360;  // normalise -ve values to 180º..360º
        var brng = Geo.toDMS(deg, format, dp);
        return brng.replace('360', '0');  // just in case rounding took us up to 360º!
    }

    /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -  */