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# gargantuan

a guest Jun 29th, 2009 613 Never
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1. // -------------------------------------------------------------------------------------
2.
3. /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -  */
4. /*  Latitude/longitude spherical geodesy formulae & scripts (c) Chris Veness 2002-2009            */
5. /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -  */
6. /* Pasted from the original locationhttp://www.movable-type.co.uk/scripts/latlong.html */
7.
8. /*
9.  * Use Haversine formula to Calculate distance (in km) between two points specified by
10.  * latitude/longitude (in numeric degrees)
11.  *
12.  * from: Haversine formula - R. W. Sinnott, "Virtues of the Haversine",
13.  *       Sky and Telescope, vol 68, no 2, 1984
14.  *       http://www.census.gov/cgi-bin/geo/gisfaq?Q5.1
15.  *
16.  * example usage from form:
17.  *   result.value = LatLon.distHaversine(lat1.value.parseDeg(), long1.value.parseDeg(),
18.  *                                       lat2.value.parseDeg(), long2.value.parseDeg());
19.  * where lat1, long1, lat2, long2, and result are form fields
20.  */
21. LatLon.distHaversine = function(lat1, lon1, lat2, lon2) {
22.   var R = 6371; // earth's mean radius in km
26.
27.   var a = Math.sin(dLat/2) * Math.sin(dLat/2) +
28.           Math.cos(lat1) * Math.cos(lat2) *
29.           Math.sin(dLon/2) * Math.sin(dLon/2);
30.   var c = 2 * Math.atan2(Math.sqrt(a), Math.sqrt(1-a));
31.   var d = R * c;
32.   return d;
33. }
34.
35.
36. /*
37.  * Use Law of Cosines to calculate distance (in km) between two points specified by latitude/longitude
38.  * (in numeric degrees).
39.  */
40. LatLon.distCosineLaw = function(lat1, lon1, lat2, lon2) {
41.   var R = 6371; // earth's mean radius in km
44.   return d;
45. }
46.
47.
48. /*
49.  * calculate (initial) bearing between two points
50.  *   see http://williams.best.vwh.net/avform.htm#Crs
51.  */
52. LatLon.bearing = function(lat1, lon1, lat2, lon2) {
55.
56.   var y = Math.sin(dLon) * Math.cos(lat2);
57.   var x = Math.cos(lat1)*Math.sin(lat2) -
58.           Math.sin(lat1)*Math.cos(lat2)*Math.cos(dLon);
59.   return Math.atan2(y, x).toBrng();
60. }
61.
62.
63. /*
64.  * calculate midpoint of great circle line between p1 & p2.
65.  *   see http://mathforum.org/library/drmath/view/51822.html for derivation
66.  */
67. LatLon.midPoint = function(lat1, lon1, lat2, lon2) {
71.
72.   var Bx = Math.cos(lat2) * Math.cos(dLon);
73.   var By = Math.cos(lat2) * Math.sin(dLon);
74.
75.   lat3 = Math.atan2(Math.sin(lat1)+Math.sin(lat2),
76.                     Math.sqrt((Math.cos(lat1)+Bx)*(Math.cos(lat1)+Bx) + By*By ) );
77.   lon3 = lon1.toRad() + Math.atan2(By, Math.cos(lat1) + Bx);
78.
79.   if (isNaN(lat3) || isNaN(lon3)) return null;
80.   return new LatLon(lat3.toDeg(), lon3.toDeg());
81. }
82.
83.
84. /*
85.  * calculate destination point given start point, initial bearing (deg) and distance (km)
86.  *   see http://williams.best.vwh.net/avform.htm#LL
87.  */
88. LatLon.prototype.destPoint = function(brng, d) {
89.   var R = 6371; // earth's mean radius in km
92.
93.   var lat2 = Math.asin( Math.sin(lat1)*Math.cos(d/R) +
94.                         Math.cos(lat1)*Math.sin(d/R)*Math.cos(brng) );
95.   var lon2 = lon1 + Math.atan2(Math.sin(brng)*Math.sin(d/R)*Math.cos(lat1),
96.                                Math.cos(d/R)-Math.sin(lat1)*Math.sin(lat2));
97.   lon2 = (lon2+Math.PI)%(2*Math.PI) - Math.PI;  // normalise to -180...+180
98.
99.   if (isNaN(lat2) || isNaN(lon2)) return null;
100.   return new LatLon(lat2.toDeg(), lon2.toDeg());
101. }
102.
103.
104. /*
105.  * calculate final bearing arriving at destination point given start point, initial bearing and distance
106.  */
107. LatLon.prototype.finalBrng = function(brng, d) {
108.   var p1 = this, p2 = p1.destPoint(brng, d);
109.   // get reverse bearing point 2 to point 1
110.   var rev = LatLon.bearing(p2.lat, p2.lon, p1.lat, p1.lon);
111.   // & reverse it by adding 180°
112.   var brng = (rev + 180) % 360;
113.   return brng;
114. }
115.
116.
117. /*
118.  * calculate distance, bearing, destination point on rhumb line
119.  *   see http://williams.best.vwh.net/avform.htm#Rhumb
120.  */
121. LatLon.distRhumb = function(lat1, lon1, lat2, lon2) {
122.   var R = 6371; // earth's mean radius in km
125.   var q = (Math.abs(dLat) > 1e-10) ? dLat/dPhi : Math.cos(lat1.toRad());
126.   // if dLon over 180° take shorter rhumb across 180° meridian:
127.   if (dLon > Math.PI) dLon = 2*Math.PI - dLon;
128.   var d = Math.sqrt(dLat*dLat + q*q*dLon*dLon);
129.   return d * R;
130. }
131.
132.
133. LatLon.brngRhumb = function(lat1, lon1, lat2, lon2) {
136.   if (Math.abs(dLon) > Math.PI) dLon = dLon>0 ? -(2*Math.PI-dLon) : (2*Math.PI+dLon);
137.   return Math.atan2(dLon, dPhi).toBrng();
138. }
139.
140.
141. LatLon.prototype.destPointRhumb = function(brng, dist) {
142.   var R = 6371; // earth's mean radius in km
143.   var d = parseFloat(dist)/R;
144.   // d = angular distance covered on earth's surface
147.
148.   var lat2 = lat1 + d*Math.cos(brng);
149.   var dLat = lat2-lat1;
150.   var dPhi = Math.log(Math.tan(lat2/2+Math.PI/4)/Math.tan(lat1/2+Math.PI/4));
151.   var q = (Math.abs(dLat) > 1e-10) ? dLat/dPhi : Math.cos(lat1);
152.   var dLon = d*Math.sin(brng)/q;
153.   // check for some daft bugger going past the pole
154.   if (Math.abs(lat2) > Math.PI/2) lat2 = lat2>0 ? Math.PI-lat2 : -(Math.PI-lat2);
155.   lon2 = (lon1+dLon+Math.PI)%(2*Math.PI) - Math.PI;
156.
157.   if (isNaN(lat2) || isNaN(lon2)) return null;
158.   return new LatLon(lat2.toDeg(), lon2.toDeg());
159. }
160.
161.
162. /*
163.  * construct a LatLon object: arguments in numeric degrees
164.  *
165.  * note all LatLong methods expect & return numeric degrees (for lat/long & for bearings)
166.  */
167. function LatLon(lat, lon) {
168.   this.lat = lat;
169.   this.lon = lon;
170. }
171.
172.
173. /*
174.  * represent point {lat, lon} in standard representation
175.  */
176. LatLon.prototype.toString = function() {
177.   return this.lat.toLat() + ', ' + this.lon.toLon();
178. }
179.
180. /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -  */
181.
182. // extend String object with method for parsing degrees or lat/long values to numeric degrees
183. //
184. // this is very flexible on formats, allowing signed decimal degrees, or deg-min-sec suffixed by
185. // compass direction (NSEW). A variety of separators are accepted (eg 3º 37' 09"W) or fixed-width
186. // format without separators (eg 0033709W). Seconds and minutes may be omitted. (Minimal validation
187. // is done).
188.
189. String.prototype.parseDeg = function() {
190.   if (!isNaN(this)) return Number(this);                 // signed decimal degrees without NSEW
191.
192.   var degLL = this.replace(/^-/,'').replace(/[NSEW]/i,'');  // strip off any sign or compass dir'n
193.   var dms = degLL.split(/[^0-9.,]+/);                     // split out separate d/m/s
194.   for (var i in dms) if (dms[i]=='') dms.splice(i,1);    // remove empty elements (see note below)
195.   switch (dms.length) {                                  // convert to decimal degrees...
196.     case 3:                                              // interpret 3-part result as d/m/s
197.       var deg = dms[0]/1 + dms[1]/60 + dms[2]/3600; break;
198.     case 2:                                              // interpret 2-part result as d/m
199.       var deg = dms[0]/1 + dms[1]/60; break;
200.     case 1:                                              // decimal or non-separated dddmmss
201.       if (/[NS]/i.test(this)) degLL = '0' + degLL;       // - normalise N/S to 3-digit degrees
202.       var deg = dms[0].slice(0,3)/1 + dms[0].slice(3,5)/60 + dms[0].slice(5)/3600; break;
203.     default: return NaN;
204.   }
205.   if (/^-/.test(this) || /[WS]/i.test(this)) deg = -deg; // take '-', west and south as -ve
206.   return deg;
207. }
208. // note: whitespace at start/end will split() into empty elements (except in IE)
209.
210.
211. /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -  */
212.
213. // extend Number object with methods for converting degrees/radians
214.
216.   return this * Math.PI / 180;
217. }
218.
219. Number.prototype.toDeg = function() {  // convert radians to degrees (signed)
220.   return this * 180 / Math.PI;
221. }
222.
223. Number.prototype.toBrng = function() {  // convert radians to degrees (as bearing: 0...360)
224.   return (this.toDeg()+360) % 360;
225. }
226.
227.
228. /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -  */
229.
230. // extend Number object with methods for presenting bearings & lat/longs
231.
232. Number.prototype.toDMS = function() {  // convert numeric degrees to deg/min/sec
233.   var d = Math.abs(this);  // (unsigned result ready for appending compass dir'n)
234.   d += 1/7200;  // add ½ second for rounding
235.   var deg = Math.floor(d);
236.   var min = Math.floor((d-deg)*60);
237.   var sec = Math.floor((d-deg-min/60)*3600);
239.   if (deg<100) deg = '0' + deg; if (deg<10) deg = '0' + deg;
240.   if (min<10) min = '0' + min;
241.   if (sec<10) sec = '0' + sec;
242.   return deg + '\u00B0' + min + '\u2032' + sec + '\u2033';
243. }
244.
245. Number.prototype.toLat = function() {  // convert numeric degrees to deg/min/sec latitude
246.   return this.toDMS().slice(1) + (this<0 ? 'S' : 'N');  // knock off initial '0' for lat!
247. }
248.
249. Number.prototype.toLon = function() {  // convert numeric degrees to deg/min/sec longitude
250.   return this.toDMS() + (this>0 ? 'E' : 'W');
251. }
252.
253. Number.prototype.toPrecision = function(fig) {  // override toPrecision method with one which displays
254.   if (this == 0) return 0;                      // trailing zeros in place of exponential notation
255.   var scale = Math.ceil(Math.log(this)*Math.LOG10E);
256.   var mult = Math.pow(10, fig-scale);
257.   return Math.round(this*mult)/mult;
258. }
259.
260. /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -  */
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