.from: http://www.movable-type.co.uk/scripts/latlong.html
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
/* Latitude/longitude spherical geodesy formulae & scripts (c) Chris Veness 2002-2011 */
/* - 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
// only accept numbers or valid numeric strings
this._lat = typeof(lat)=='number' ? lat : typeof(lat)=='string' && lat.trim()!='' ? +lat : NaN;
this._lon = typeof(lon)=='number' ? lon : typeof(lon)=='string' && lon.trim()!='' ? +lon : NaN;
this._radius = typeof(rad)=='number' ? rad : typeof(rad)=='string' && trim(lon)!='' ? +rad : NaN;
}
/**
* 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()+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);
lon3 = (lon3+3*Math.PI) % (2*Math.PI) - Math.PI; // normalise to -180..+180º
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 = typeof(dist)=='number' ? dist : typeof(dist)=='string' && dist.trim()!='' ? +dist : NaN;
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..+180º
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) {
brng1 = typeof brng1 == 'number' ? brng1 : typeof brng1 == 'string' && trim(brng1)!='' ? +brng1 : NaN;
brng2 = typeof brng2 == 'number' ? brng2 : typeof brng2 == 'string' && trim(brng2)!='' ? +brng2 : NaN;
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+3*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';
if (isNaN(this._lat) || isNaN(this._lon)) return '-,-';
return Geo.toLat(this._lat, format, dp) + ', ' + Geo.toLon(this._lon, format, dp);
}
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
// ---- extend Number object with methods for converting degrees/radians
/** Converts numeric degrees to radians */
if (typeof(Number.prototype.toRad) === "undefined") {
Number.prototype.toRad = function() {
return this * Math.PI / 180;
}
}
/** Converts radians to numeric (signed) degrees */
if (typeof(Number.prototype.toDeg) === "undefined") {
Number.prototype.toDeg = function() {
return this * 180 / Math.PI;
}
}
/**
* Formats 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) {
if (isNaN(this)) return 'NaN';
var numb = this < 0 ? -this : this; // can't take log of -ve number...
var sign = this < 0 ? '-' : '';
if (numb == 0) { // can't take log of zero, just format with precision zeros
var n = '0.';
while (precision--) n += '0';
return n
}
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;
}
}
/** Trims whitespace from string (q.v. blog.stevenlevithan.com/archives/faster-trim-javascript) */
if (typeof(String.prototype.trim) === "undefined") {
String.prototype.trim = function() {
return String(this).replace(/^\s\s*/, '').replace(/\s\s*$/, '');
}
}
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
/* Geodesy representation conversion functions (c) Chris Veness 2002-2011 */
/* - www.movable-type.co.uk/scripts/latlong.html */
/* */
/* Sample usage: */
/* var lat = Geo.parseDMS('51° 28′ 40.12″ N'); */
/* var lon = Geo.parseDMS('000° 00′ 05.31″ W'); */
/* var p1 = new LatLon(lat, lon); */
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
var Geo = {}; // Geo namespace, representing static class
/**
* Parses string representing degrees/minutes/seconds into numeric degrees
*
* This is very flexible on formats, allowing signed decimal degrees, or deg-min-sec optionally
* suffixed by compass direction (NSEW). A variety of separators are accepted (eg 3º 37' 09"W)
* or fixed-width format without separators (eg 0033709W). Seconds and minutes may be omitted.
* (Note minimal validation is done).
*
* @param {String|Number} dmsStr: Degrees or deg/min/sec in variety of formats
* @returns {Number} Degrees as decimal number
* @throws {TypeError} dmsStr is an object, perhaps DOM object without .value?
*/
Geo.parseDMS = function(dmsStr) {
if (typeof deg == 'object') throw new TypeError('Geo.parseDMS - dmsStr is [DOM?] object');
// check for signed decimal degrees without NSEW, if so return it directly
if (typeof dmsStr === 'number' && isFinite(dmsStr)) return Number(dmsStr);
// strip off any sign or compass dir'n & split out separate d/m/s
var dms = String(dmsStr).trim().replace(/^-/,'').replace(/[NSEW]$/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 'NaN'; // 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!
}
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
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