longitude points using haversine formula in javascript

Point 1: 50 03 59N , 005 42 53W

Point 2: 58 38 38N , 003 04 12W

This page presents a variety of calculations for latitude/longitude points, with the formulæ and code fragmentsfor implementing them.

All these formulæ are for calculations on the basis of a spherical earth (ignoring ellipsoidal effects) – which isaccurate enough for most purposes… [In fact, the earth is very slightly ellipsoidal; using a spherical model giveserrors typically up to 0.3% – see notes for further details].

Great-circle distance between two points

Enter the co-ordinates into the text boxes to try out the calculations. A variety of formats are accepted,principally:

deg-min-sec suffixed with N/S/E/W (e.g. 40°44′55″N, 73 59 11W), or

signed decimal degrees without compass direction, where negative indicates west/south (e.g.40.7486, -73.9864):

Distance: 968.9 km

Initial bearing: 009°07′11″

Final bearing: 011°16′31″

Midpoint: 54°21′44″N, 004°31′50″W

And you can see it on a map (aren’t those Google guys wonderful!)

Distance

This uses the ‘haversine’ formula to calculate the great-circle distance between two points – that is, the shortestdistance over the earth’s surface – giving an ‘as-the-crow-flies’ distance between the points (ignoring any hills, ofcourse!).

Haversine formula: a = sin²(Δlat/2) + cos(lat ).cos(lat ).sin²(Δlong/2)

c = 2.atan2(√a, √(1−a))

d = R.c

where R is earth’s radius (mean radius = 6,371km);note that angles need to be in radians to pass to trig functions!

JavaScript: var R = 6371; // km

var dLat = (lat2-lat1).toRad();

var dLon = (lon2-lon1).toRad();

var lat1 = lat1.toRad();

var lat2 = lat2.toRad();

var a = Math.sin(dLat/2) * Math.sin(dLat/2) +

*

1 2

Calculate distance and bearing between two Latitude/Longitude points usi... http://www.movable-type.co.uk/scripts/latlong.html

1 of 18 5/30/2012 6:54 PM

Math.sin(dLon/2) * Math.sin(dLon/2) * Math.cos(lat1) * Math.cos(lat2);

var c = 2 * Math.atan2(Math.sqrt(a), Math.sqrt(1-a));

var d = R * c;

The haversine formula ‘remains particularly well-conditioned for numerical computation even at smalldistances’ – unlike calculations based on the spherical law of cosines. The ‘versed sine’ is 1-cosθ, and the ‘half-versed-sine’ (1-cosθ)/2 = sin²(θ/2) as used above. It was published by R W Sinnott in Sky and Telescope, 1984,though known about for much longer by navigators. (For the curious, c is the angular distance in radians, and a isthe square of half the chord length between the points). A (surprisingly marginal) performance improvement canbe obtained, of course, by factoring out the terms which get squared.

Spherical Law of Cosines

In fact, when Sinnott published the haversine formula, computational precision was limited. Nowadays,JavaScript (and most modern computers & languages) use IEEE 754 64-bit floating-point numbers, which provide15 significant figures of precision. With this precision, the simple spherical law of cosines formula (cos c = cosa cos b + sin a sin b cos C) gives well-conditioned results down to distances as small as around 1 metre. (Note

that the geodetic form of the law of cosines is rearranged from the canonical one so that the latitude can be used directly,

rather than the colatitude).

This makes the simpler law of cosines a reasonable 1-line alternative to the haversine formula for manypurposes. The choice may be driven by coding context, available trig functions (in different languages), etc.

Spherical lawof cosines:

d = acos(sin(lat ).sin(lat )+cos(lat ).cos(lat ).cos(long −long )).R

JavaScript: var R = 6371; // km

var d = Math.acos(Math.sin(lat1)*Math.sin(lat2) +

Math.cos(lat1)*Math.cos(lat2) *

Math.cos(lon2-lon1)) * R;

Excel: =ACOS(SIN(lat1)*SIN(lat2)+COS(lat1)*COS(lat2)*COS(lon2-lon1))*6371

(Note that here and in all subsequent code fragments, for simplicity I do not show conversions from degrees to radians;see below for complete versions).

Equirectangular approximation

If performance is an issue and accuracy less important, for small distances Pythagoras’ theorem can be usedon an equirectangular projection:

x = Δlon.cos(lat)

y = Δlat

d = R.√x² + y²

JavaScript: var x = (lon2-lon1) * Math.cos((lat1+lat2)/2);

var y = (lat2-lat1);

var d = Math.sqrt(x*x + y*y) * R;

(lat/lon in radians!)

This uses just one trig and one sqrt function – as against half-a-dozen trig functions for cos law, and 7 trigs + 2sqrts for haversine. Accuracy is somewhat complex: along meridians there are no errors, otherwise they dependon distance, bearing, and latitude, but are small enough for many purposes (and often trivial compared with thespherical approximation itself).

Bearing

1

1 2 1 2 2 1

*

*


2 of 18 5/30/2012 6:54 PM

Baghdad to Osaka –not a constant bearing!

In general, your current heading will vary as you follow a great circle path(orthodrome); the final heading will differ from the initial heading by varyingdegrees according to distance and latitude (if you were to go from say 35°N,45°E(Baghdad) to 35°N,135°E (Osaka), you would start on a heading of 60° and end upon a heading of 120°!).

This formula is for the initial bearing (sometimes referred to as forward azimuth)which if followed in a straight line along a great-circle arc will take you from thestart point to the end point:

Formula: θ = atan2( sin(Δlong).cos(lat ),

cos(lat ).sin(lat ) − sin(lat ).cos(lat ).cos(Δlong) )

JavaScript: 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).toDeg();

Excel: =ATAN2(COS(lat1)*SIN(lat2)-SIN(lat1)*COS(lat2)*COS(lon2-lon1),

SIN(lon2-lon1)*COS(lat2))

* Note that Excel reverses the arguments to ATAN2 – see notes below

Since atan2 returns values in the range -π ... +π (that is, -180° ... +180°), to normalise the result to a compass bearing(in the range 0° ... 360°, with -ve values transformed into the range 180° ... 360°), convert to degrees and then use(θ+360) % 360, where % is modulo.

For final bearing, simply take the initial bearing from the end point to the start point and reverse it (using θ = (θ+180) %360).

Midpoint

This is the half-way point along a great circle path between the two points.

Formula: Bx = cos(lat ).cos(Δlong)

By = cos(lat ).sin(Δlong)

lat = atan2(sin(lat ) + sin(lat ), √((cos(lat )+Bx)² + By²))

lon = lon + atan2(By, cos(lat )+Bx)

JavaScript: var Bx = Math.cos(lat2) * Math.cos(dLon);

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

var lat3 = Math.atan2(Math.sin(lat1)+Math.sin(lat2),

Math.sqrt( (Math.cos(lat1)+Bx)*(Math.cos(lat1)+Bx) + By*By) );

var lon3 = lon1 + Math.atan2(By, Math.cos(lat1) + Bx);

Just as the initial bearing may vary from the final bearing, the midpoint may not be located half-way betweenlatitudes/longitudes; the midpoint between 35°N,45°E and 35°N,135°E is around 45°N,90°E.

Destination point given distance and bearing from start point

Given a start point, initial bearing, and distance, this will calculate the destination point and final bearingtravelling along a (shortest distance) great circle arc.

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2

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m 1 2 1

m 1 1


3 of 18 5/30/2012 6:54 PM

Start point: 53°19′14″N , 001°43′47″W

Bearing: 096°01′18″

Distance: 124.8 km

Point 1: 51.885 N , 0.235 E Brng 1: 108.63°

Point 2: 49.008 N , 2.549 E Brng 2: 32.72°

Destination point along great-circle given distance and bearing from start point

Destination point: 53°11′18″N, 000°08′00″E

Final bearing: 097°30′52″

view map

Formula: lat = asin(sin(lat )*cos(d/R) + cos(lat )*sin(d/R)*cos(θ))

lon = lon + atan2(sin(θ)*sin(d/R)*cos(lat ), cos(d/R)−sin(lat )*sin(lat ))

θ is the bearing (in radians, clockwise from north);

d/R is the angular distance (in radians), where d is the distance travelled and R is the earth’s radius

JavaScript: var lat2 = Math.asin( Math.sin(lat1)*Math.cos(d/R) +

Math.cos(lat1)*Math.sin(d/R)*Math.cos(brng) );

var lon2 = lon1 + Math.atan2(Math.sin(brng)*Math.sin(d/R)*Math.cos(lat1),

Math.cos(d/R)-Math.sin(lat1)*Math.sin(lat2));

Excel: lat2: =ASIN(SIN(lat1)*COS(d/R) + COS(lat1)*SIN(d/R)*COS(brng))

lon2: =lon1 + ATAN2(COS(d/R)-SIN(lat1)*SIN(lat2), SIN(brng)*SIN(d/R)*COS(lat1))

For final bearing, simply take the initial bearing from the end point to the start point and reverse it (using θ = (θ+180) %360).

Intersection of two paths given start points and bearings

This is a rather more complex calculation than most others on this page, but I've been asked for it a number oftimes. See below for the JavaScript.

Intersection of two great-circle paths

Intersectionpoint:

50°54′06″N,004°29′39″E

Formula: d = 2.asin( √(sin²(Δlat/2) + cos(lat ).cos(lat ).sin²(Δlon/2)) )

φ = acos( sin(lat ) − sin(lat ).cos(d ) / sin(d ).cos(lat ) )

φ = acos( sin(lat ) − sin(lat ).cos(d ) / sin(d ).cos(lat ) )

if sin(lon −lon ) > 0

θ = φ , θ = 2.π − φ

else

θ = 2.π − φ , θ = φ

α = (θ − θ + π) % 2.π − π

α = (θ − θ + π) % 2.π − π

2 1 1

2 1 1 1 2

12 1 2

1 2 1 12 12 1

2 1 2 12 12 2

2 1

12 1 21 2

12 1 21 2

1 1 12

2 21 2


4 of 18 5/30/2012 6:54 PM

α = acos( −cos(α ).cos(α ) + sin(α ).sin(α ).cos(d ) )

d = atan2( sin(d ).sin(α ).sin(α ), cos(α )+cos(α ).cos(α ) )

lat = asin( sin(lat ).cos(d ) + cos(lat ).sin(d ).cos(θ ) )

Δlon = atan2( sin(θ ).sin(d ).cos(lat ), cos(d )−sin(lat ).sin(lat ) )

lon = (lon +Δlon +π) % 2.π − π

where lat , lon , θ : 1st point & bearinglat , lon , θ : 2nd point & bearinglat , lon : intersection point

% = mod

note – if sin(α )=0 and sin(α )=0: infinite solutionsif sin(α ).sin(α ) < 0: ambiguous solutionthis formulation is not always well-conditioned for meridional or equatorial lines

Note this can also be solved using vectors rather than trigonometry:

For each point φ,λ (lat=φ, lon=λ), we can define a unit vector pointing to it from the centre of the

earth: u{x,y,z} = [ cosφ·cosλ, cosφ·sinλ, sinφ ] (taking x=0º, y=90º, z=north – note that these

formulæ depend on convention used for directions and handedness)And for any great circle defined by two points, we can define a unit vector N normal to the plane of

the circle: N(u , u ) = (u ×u ) / ||u ×u || where × is the vector cross product, and ||u|| the norm

(length of the vector)

The vector representing the intersection of the two great circles is then u = ±N( N(u , u ), N(u , u ) )

We can then get the latitude and longitude of P by φ = atan2(u , sqrt(u ² + u ²)), λ = atan2(u , u )

The antipodal intersection point is (-φ, λ+π)

Cross-track distance

Here’s a new one: I’ve sometimes been asked about distance of a point from a great-circle path (sometimescalled cross track error).

Formula: d = asin(sin(d /R)*sin(θ −θ )) * R

where d is distance from start point to third pointθ is (initial) bearing from start point to third pointθ is (initial) bearing from start point to end pointR is the earth’s radius

JavaScript: var dXt = Math.asin(Math.sin(d13/R)*Math.sin(brng13-brng12)) * R;

Here, the great-circle path is identified by a start point and an end point – depending on what initial data you’reworking from, you can use the formulæ above to obtain the relevant distance and bearings. The sign of d tellsyou which side of the path the third point is on.

The along-track distance, from the start point to the closest point on the path to the third point, is

Formula: d = acos(cos(d /R)/cos(d /R)) * R

3 1 2 1 2 12

13 12 1 2 2 1 3

3 1 13 1 13 1

13 1 13 1 13 1 3

3 1 13

1 1 1

2 2 2

3 3

1 2

1 2

1 2 1 2 1 2

i 1 2 3 4

i z x y y x

xt 13 13 12

13

13

12

xt

at 13 xt


5 of 18 5/30/2012 6:54 PM

Point 1: 50 21 50N , 004 09 25W

Point 2: 42 21 04N , 071 02 27W

Start point: 51 07 32N , 001 20 17E

Bearing: 116°38′10

Distance: 40.23 km

where d is distance from start point to third pointd is cross-track distanceR is the earth’s radius

JavaScript: var dAt = Math.acos(Math.cos(d13/R)/Math.cos(dXt/R)) * R;

Closest point to the poles

And: ‘Clairaut’s formula’ will give you the maximum latitude of a great circle path, given a bearing and latitudeon the great circle:

Formula: lat = acos(abs(sin(θ)*cos(lat)))

JavaScript: var latMax = Math.acos(Math.abs(Math.sin(brng)*Math.cos(lat)));

Rhumb lines

A ‘rhumb line’ (or loxodrome) is a path of constant bearing, which crosses all meridians at the same angle.

Sailors used to (and sometimes still) navigate along rhumb lines since it is easier to follow a constant compassbearing than to be continually adjusting the bearing, as is needed to follow a great circle. Rhumb lines arestraight lines on a Mercator Projection map (also helpful for navigation).

Rhumb lines are generally longer than great-circle (orthodrome) routes. For instance, London to New York is 4%longer along a rhumb line than along a great circle – important for aviation fuel, but not particularly to sailingvessels. New York to Beijing – close to the most extreme example possible (though not sailable!) – is 30% longeralong a rhumb line.

Rhumb-line distance between two points

Distance: 5196 km

Bearing: 260°07′38″

view map

Destination point along rhumb line given distance and bearing from start point

Destination point: 50°57′48″N, 001°51′09″E

view map

Distance/bearing

These formulæ give the distance and (constant) bearing between two points.

13

xt

max


6 of 18 5/30/2012 6:54 PM

Formula: Δφ = ln(tan(lat /2+π/4)/tan(lat /2+π/4)) [= the ‘stretched’ latitude difference]

if E:W line, q = cos(lat1)

otherwise, q = Δlat/Δφ

d = √(Δlat² + q².Δlon²).R [pythagoras]

θ = atan2(Δlon, Δφ)

where ln is natural log, ∆lon is taking shortest route (<180º), and R is the earth’s radius

JavaScript: 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 (Math.abs(dLon) > Math.PI) {

dLon = dLon>0 ? -(2*Math.PI-dLon) : (2*Math.PI+dLon);

}

var d = Math.sqrt(dLat*dLat + q*q*dLon*dLon) * R;

var brng = Math.atan2(dLon, dPhi);

Destination

Given a start point and a distance d along constant bearing θ, this will calculate the destination point. If youmaintain a constant bearing along a rhumb line, you will gradually spiral in towards one of the poles.

Formula: α = d/R (angular distance)

lat = lat + α.cos(θ)

Δφ = ln(tan(lat /2+π/4)/tan(lat /2+π/4)) [= the ‘stretched’ latitude difference]

if E:W line q = cos(lat )

otherwise q = Δlat/Δφ

Δlon = α.sin(θ)/q

lon = (lon +Δlon+π) % 2.π − π

where ln is natural log and % is modulo, ∆lon is taking shortest route (<180°), and R is the earth’sradius

JavaScript: var dLat = d*Math.cos(brng);

var lat2 = lat1 + dLat;

var dPhi = Math.log(Math.tan(lat2/2+Math.PI/4)/Math.tan(lat1/2+Math.PI/4));


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+Math.PI)%(2*Math.PI) - Math.PI;

Mid-point

This formula for calculating the ‘loxodromic midpoint’, the point half-way along a rhumb line between two points,is due to Robert Hill and Clive Tooth (thx Axel!).

Formula: lat = (lat +lat )/2

f = tan(π/4+lat /2)

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7 of 18 5/30/2012 6:54 PM



lon = [ (lon −lon ).ln(f ) + lon .ln(f ) − lon .ln(f ) ] / ln(f /f )

where ln is natural log

JavaScript: var lat3 = (lat1+lat2)/2;

var f1 = Math.tan(Math.PI/4 + lat1/2);



var lon3 = ( (lon2-lon1)*Math.log(f3) + lon1*Math.log(f2) - lon2*Math.log(f1) ) /

Math.log(f2/f1);

Using the scripts in web pages

Using these scripts in web pages would be something like the following:

<script src="latlon.js">/* Latitude/Longitude formulae */</script>

<script src="geo.js">/* Geodesy representation conversions */</script>

...

<form>

Lat1: <input type="text" name="lat1" id="lat1"> Lon1: <input type="text" name="lon1" id="lon1">


<button onClick="var p1 = new LatLon(Geo.parseDMS(f.lat1.value), Geo.parseDMS(f.lon1.value));

var p2 = new LatLon(Geo.parseDMS(f.lat2.value), Geo.parseDMS(f.lon2.value));

alert(p1.distanceTo(p2));">Calculate distance</button>

</form>

If you use jQuery, the code can be separated from the HTML:

<script src="http://ajax.googleapis.com/ajax/libs/jquery/1.6.0/jquery.min.js"></script>

<script src="latlon.js">/* Latitude/Longitude formulae */</script>

<script src="geo.js">/* Geodesy representation conversions */</script>

<script>

$(document).ready(function() {

$('#calc-dist').click(function() {

var p1 = new LatLon(Geo.parseDMS($('#lat1').val()), Geo.parseDMS($('#lon1').val()));

var p2 = new LatLon(Geo.parseDMS($('#lat2').val()), Geo.parseDMS($('#lon2').val()));

$('#result-distance').html(p1.distanceTo(p2)+' km');

});

});

</script>

...

<form>



<button id="calc-dist">Calculate distance</button>

<output id="result-distance"></output>

</form>

Convert between degrees-minutes-seconds & decimal degrees

Latitude Longitude 1° ≈ 111 km (110.57 eq’l — 111.70 polar)

52°12′17.0″N 000°08′26.0″E 1′ ≈ 1.85 km (= 1 nm) 0.01° ≈ 1.11 km

52.20472 0.14056 1″ ≈ 30.9 m 0.0001° ≈ 11.1 m

No, I’ve not included decimal minutes: a decimal system is easy, a sexagesimal system has merits, but mixing the two is acomplete sow’s ear. Switch off the option on your GPS!

2 2

m m

m 2 1 m 1 2 2 1 2 1


8 of 18 5/30/2012 6:54 PM

Display calculation results as: deg/min/sec decimal degrees

Notes:

Accuracy: since the earth is not quite a sphere, there are small errors in using spherical geometry; the earthis actually roughly ellipsoidal (or more precisely, oblate spheroidal) with a radius varying between about6,378km (equatorial) and 6,357km (polar), and local radius of curvature varying from 6,336km (equatorialmeridian) to 6,399km (polar). 6,371 km is the generally accepted value for the Earth’s mean radius. Thismeans that errors from assuming spherical geometry might be up to 0.55% crossing the equator, thoughgenerally below 0.3%, depending on latitude and direction of travel. An accuracy of better than 3m in 1km ismostly good enough for me, but if you want greater accuracy, you could use the Vincenty formula forcalculating geodesic distances on ellipsoids, which gives results accurate to within 1mm. (Out of sheerperversity – I’ve never needed such accuracy – I looked up this formula and discovered the JavaScriptimplementation was simpler than I expected).Trig functions take arguments in radians, so latitude, longitude, and bearings in degrees (either decimal ordegrees/minutes/seconds) need to be converted to radians, rad = π.deg/180. When converting radians backto degrees (deg = 180.rad/π), West is negative if using signed decimal degrees. For bearings, values in therange -π to +π [-180° to +180°] need to be converted to 0 to +2π [0°–360°]; this can be done by(brng+2.π)%2.π [or brng+360)%360] where % is the modulo operator.The atan2() function widely used here takes two arguments, atan2(y, x), and computes the arc tangent ofthe ratio y/x. It is more flexible than atan(y/x), since it handles x=0, and it also returns values in all 4quadrants -π to +π (the atan function returns values in the range -π/2 to +π/2).All bearings are with respect to true north, 0°=N, 90°=E, etc; if you are working from a compass, magneticnorth varies from true north in a complex way around the earth, and the difference has to be compensated forby variances indicated on local maps.If you implement any formula involving atan2 in Microsoft Excel, you will need to reverse the arguments, asExcel has them the opposite way around from JavaScript – conventional order is atan2(y, x), but Excel usesatan2(x, y). To use atan2 in a (VBA) macro, you can use WorksheetFunction.Atan2().If you are using Google Maps, several of these functions are now provided in the Google Maps API V3‘spherical’ library (computeDistanceBetween(), computeHeading(), computeOffset(), interpolate(), etc; notethey use a default Earth radius of 6,378,137 meters).If you use Ordnance Survey Grid References, I have implemented a script for converting between Lat/Long& OS Grid References.I learned a lot from the US Census Bureau GIS FAQ which is no longer available, so I’ve made a copy.Thanks to Ed Williams’ Aviation Formulary for many of the formulæ.For miles, divide km by 1.609344For nautical miles, divide km by 1.852

See below for the source code of the JavaScript implementation. These functions should be simple to translateinto other languages if required.

Update January 2010: I have revised the scripts to be structured as methods of a LatLon object. Of course,JavaScript is a prototype-based rather than class-based language, so this is only nominally a class, butisolating code into a separate namespace is good JavaScript practice, and this approach may also make it clearerto implement these functions in other languages. If you’re not familiar with JavaScript syntax,LatLon.prototype.distanceTo = function(point) { ... }, for instance, defines a ‘distanceTo’ method of theLatLon object (/class) which takes a LatLon object as a parameter (and returns a number). The Geo namespaceacts as a static class for geodesy formatting / parsing / conversion functions. I have extended (polluted, if youlike) the base JavaScript object prototypes with trim(), toRad() toDeg(), and toPrecisionFixed() methods. I’veadopted JSDoc format for the descriptions.

I have also created a page illustrating the use of the spherical law of cosines for selecting points from adatabase within a specified bounding circle – the example is based on MySQL+PDO, but should be extensible toother DBMS platforms.


9 of 18 5/30/2012 6:54 PM

Several people have asked about example Excel spreadsheets, so I have implemented the distance & bearingand the destination point formulæ as spreadsheets, in a form which breaks down the all stages involved toillustrate the operation.

I offer these formulæ & scripts for free use and adaptation as my contribution to the open-sourceinfo-sphere from which I have received so much. You are welcome to re-use these scripts [undera simple attribution license, without any warranty express or implied] provided solely that youretain my copyright notice and a reference to this page.

If you would like to show your appreciation and support continued development of these scripts, Iwould most gratefully accept donations.

If you need any advice or development work done, I am available for consultancy.

If you have any queries or find any problems, contact me at [email protected].

© 2002-2012 Chris Veness

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

/* 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;


10 of 18 5/30/2012 6:54 PM

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;



}

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

/**

* 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

*


* @returns {Number} Distance in km between this point and destination point

*/

LatLon.prototype.rhumbDistanceTo = function(point) {



var dLat = (point._lat-this._lat).toRad();

var dLon = Math.abs(point._lon-this._lon).toRad();



// 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

*


* @returns {Number} Bearing in degrees from North

*/

LatLon.prototype.rhumbBearingTo = function(point) {




if (Math.abs(dLon) > Math.PI) dLon = dLon>0 ? -(2*Math.PI-dLon) : (2*Math.PI+dLon);

var brng = Math.atan2(dLon, dPhi);


}


13 of 18 5/30/2012 6:54 PM

/**

* 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 d = parseFloat(dist)/R; // d = angular distance covered on earth's surface


brng = brng.toRad();

var lat2 = lat1 + d*Math.cos(brng);

var dLat = lat2-lat1;



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;


}

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

/**

* 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()

*



* @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()

*



* @returns {String} Comma-separated latitude/longitude

*

* @requires Geo

*/

LatLon.prototype.toString = function(format, dp) {


14 of 18 5/30/2012 6:54 PM

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 */


15 of 18 5/30/2012 6:54 PM

/* */

/* 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


16 of 18 5/30/2012 6:54 PM

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<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<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)

*




* @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)

*





*/

Geo.toLon = function(deg, format, dp) {

var lon = Geo.toDMS(deg, format, dp);

return lon=='' ? '' : lon + (deg<0 ? 'W' : 'E');

}

/**


17 of 18 5/30/2012 6:54 PM

* Convert numeric degrees to deg/min/sec as a bearing (0º..360º)

*





*/

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!

}

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


18 of 18 5/30/2012 6:54 PM

longitude points using haversine formula in javascript

Documents

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