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latlon_and_geo.js 23KB

    /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ /* Latitude/longitude spherical geodesy formulae & scripts (c) Chris Veness 2002-2012 */ /* - 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! */ /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ /** * @requires Geo */ /** * 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 = (isFinite(dLat/dPhi)) ? dLat/dPhi : Math.cos(lat1); // E-W line gives dPhi=0 // if dLon over 180° take shorter rhumb across anti-meridian: if (Math.abs(dLon) > Math.PI) { dLon = dLon>0 ? -(2*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 dLat = d*Math.cos(brng); // nasty kludge to overcome ill-conditioned results around parallels of latitude: if (Math.abs(dLat) < 1e-10) dLat = 0; // dLat < 1 mm var lat2 = lat1 + dLat; var dPhi = Math.log(Math.tan(lat2/2+Math.PI/4)/Math.tan(lat1/2+Math.PI/4)); var q = (isFinite(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, normalise latitude if so 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 loxodromic midpoint (along a rhumb line) between this point and the supplied point. * see http://mathforum.org/kb/message.jspa?messageID=148837 * * @param {LatLon} point: Latitude/longitude of destination point * @returns {LatLon} Midpoint between this point and the supplied point */ LatLon.prototype.rhumbMidpointTo = function(point) { lat1 = this._lat.toRad(), lon1 = this._lon.toRad(); lat2 = point._lat.toRad(), lon2 = point._lon.toRad(); if (Math.abs(lon2-lon1) > Math.PI) lon1 += 2*Math.PI; // crossing anti-meridian var lat3 = (lat1+lat2)/2; var f1 = Math.tan(Math.PI/4 + lat1/2); var f2 = Math.tan(Math.PI/4 + lat2/2); var f3 = Math.tan(Math.PI/4 + lat3/2); var lon3 = ( (lon2-lon1)*Math.log(f3) + lon1*Math.log(f2) - lon2*Math.log(f1) ) / Math.log(f2/f1); if (!isFinite(lon3)) lon3 = (lon1+lon2)/2; // parallel of latitude lon3 = (lon3+3*Math.PI) % (2*Math.PI) - Math.PI; // normalise to -180..+180º return new LatLon(lat3.toDeg(), lon3.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 */ 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 */ 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 */ 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 /** 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) { // use standard toPrecision method var n = this.toPrecision(precision); // ... but replace +ve exponential format with trailing zeros n = n.replace(/(.+)e\+(.+)/, function(n, sig, exp) { sig = sig.replace(/\./, ''); // remove decimal from significand l = sig.length - 1; while (exp-- > l) sig = sig + '0'; // append zeros from exponent return sig; }); // ... and replace -ve exponential format with leading zeros n = n.replace(/(.+)e-(.+)/, function(n, sig, exp) { sig = sig.replace(/\./, ''); // remove decimal from significand while (exp-- > 1) sig = '0' + sig; // prepend zeros from exponent return '0.' + sig; }); return 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*$/, ''); } } /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ if (!window.console) window.console = { log: function() {} }; /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ /* Geodesy representation conversion functions (c) Chris Veness 2002-2012 */ /* - www.movable-type.co.uk/scripts/latlong.html */ /* */ /* Sample usage: */ /* var lat = Geo.parseDMS('51° 28′ 40.12″ N'); */ /* var lon = Geo.parseDMS('000° 00′ 05.31″ W'); */ /* var p1 = new LatLon(lat, lon); */ /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ var Geo = {}; // Geo namespace, representing static class /** * Parses string representing degrees/minutes/seconds into numeric degrees * * This is very flexible on formats, allowing signed decimal degrees, or deg-min-sec optionally * suffixed by compass direction (NSEW). A variety of separators are accepted (eg 3º 37' 09"W) * or fixed-width format without separators (eg 0033709W). Seconds and minutes may be omitted. * (Note minimal validation is done). * * @param {String|Number} dmsStr: Degrees or deg/min/sec in variety of formats * @returns {Number} Degrees as decimal number * @throws {TypeError} dmsStr is an object, perhaps DOM object without .value? */ Geo.parseDMS = function(dmsStr) { if (typeof deg == 'object') throw new TypeError('Geo.parseDMS - dmsStr is [DOM?] object'); // check for signed decimal degrees without NSEW, if so return it directly if (typeof dmsStr === 'number' && isFinite(dmsStr)) return Number(dmsStr); // strip off any sign or compass dir'n & split out separate d/m/s var dms = String(dmsStr).trim().replace(/^-/,'').replace(/[NSEW]$/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 null; // 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==null ? '–' : 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==null ? '–' : 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==null ? '–' : brng.replace('360', '0'); // just in case rounding took us up to 360º! } /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ if (!window.console) window.console = { log: function() {} };