Tutorial: Examples of use

Examples of use

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GeographicLib namespace

This capabilities of this package are all exposed through the GeographicLib namespace. This is can brought into scope in various ways.

Using node after installing the package with npm

If npm has been used to install geographiclib via one of

$ npm install geographiclib
$ npm install --global geographiclib

then in node, you can do

var GeographicLib = require("geographiclib");

Using node with a free-standing geographiclib.js

If you have geographiclib.js (version 1.45 or later) in your current directory, then node can access it with

var GeographicLib = require("./geographiclib");

A similar prescription works if geographiclib.js is installed elsewhere in your filesystem, replacing "./" above with the correct directory. Note that the directory must begin with "./", "../", or "/".

HTML with your own version of geographiclib.min.js

Load geographiclib.min.js with

<script type="text/javascript" src="geographiclib.min.js">
</script>

This ".min.js" version has been "minified" by removing comments and redundant white space; this is appropriate for web applications.

HTML downloading geographiclib.min.js from SourceForge

Load geographiclib.min.js with

<script type="text/javascript"
        src="https://geographiclib.sourceforge.io/scripts/geographiclib.min.js">
</script>

This uses the latest version. If you want use a specific version, load with, for example,

<script type="text/javascript"
        src="https://geographiclib.sourceforge.io/scripts/geographiclib-1.45.min.js">
</script>

Browse https://geographiclib.sourceforge.io/scripts to see what versions are available.

Loading geographiclib.min.js with AMD

This uses require.js (which you can download here) to load geographiclib (version 1.45 or later) asynchronously. Your web page includes

<script type="text/javascript" src="require.js"></script>
<script type="text/javascript" src="main.js"></script>

where main.js contains, for example,

require.config({
  paths: {
    geographiclib: "./geographiclib.min"
    }
});

define(["geographiclib"], function(GeographicLib) {
  // do something with GeographicLib here.
});

Specifying the ellipsoid

Once GeographicLib has been brought into scope, the ellipsoid is defined via the Geodesic constructor using the equatorial radius a in meters and the flattening f, for example

var geod = new GeographicLib.Geodesic.Geodesic(6378137, 1/298.257223563);

These are the parameters for the WGS84 ellipsoid and this comes predefined by the package as

var geod = GeographicLib.Geodesic.WGS84;

Note that you can set f = 0 to give a sphere (on which geodesics are great circles) and f < 0 to give a prolate ellipsoid.

The rest of the examples on this page assume the following assignments

var GeographicLib = require("geographiclib");
var Geodesic = GeographicLib.Geodesic,
    DMS = GeographicLib.DMS,
    geod = Geodesic.WGS84;

with the understanding that the first line should be replaced with the appropriate construction needed to bring the GeographicLib namespace into scope.

Basic geodesic calculations

The distance from Wellington, NZ (41.32S, 174.81E) to Salamanca, Spain (40.96N, 5.50W) using Geodesic.Inverse:

var r = geod.Inverse(-41.32, 174.81, 40.96, -5.50);
console.log("The distance is " + r.s12.toFixed(3) + " m.");

The distance is 19959679.267 m.

The point the point 20000 km SW of Perth, Australia (32.06S, 115.74E) using Geodesic.Direct:

var r = geod.Direct(-32.06, 115.74, 225, 20000e3);
console.log("The position is (" +
            r.lat2.toFixed(8) + ", " + r.lon2.toFixed(8) + ").");

The position is (32.11195529, -63.95925278).

The area between the geodesic from JFK Airport (40.6N, 73.8W) to LHR Airport (51.6N, 0.5W) and the equator. This is an example of setting the outmask parameter, see The library interface, "The outmask and caps parameters".

var r = geod.Inverse(40.6, -73.8, 51.6, -0.5, Geodesic.AREA);
console.log("The area is " + r.S12.toFixed(1) + " m^2");

The area is 40041368848742.5 m^2

Computing waypoints

Consider the geodesic between Beijing Airport (40.1N, 116.6E) and San Fransisco Airport (37.6N, 122.4W). Compute waypoints and azimuths at intervals of 1000 km using Geodesic.InverseLine and GeodesicLine.Position:

var l = geod.InverseLine(40.1, 116.6, 37.6, -122.4),
    n = Math.ceil(l.s13 / ds),
    i, s;
console.log("distance latitude longitude azimuth");
for (i = 0; i <= n; ++i) {
  s = Math.min(ds * i, l.s13);
  r = l.Position(s, Geodesic.STANDARD | Geodesic.LONG_UNROLL);
  console.log(r.s12.toFixed(0) + " " + r.lat2.toFixed(5) + " " +
              r.lon2.toFixed(5) + " " + r.azi2.toFixed(5));
}

gives

distance latitude longitude azimuth
0 40.10000 116.60000 42.91642
1000000 46.37321 125.44903 48.99365
2000000 51.78786 136.40751 57.29433
3000000 55.92437 149.93825 68.24573
4000000 58.27452 165.90776 81.68242
5000000 58.43499 183.03167 96.29014
6000000 56.37430 199.26948 109.99924
7000000 52.45769 213.17327 121.33210
8000000 47.19436 224.47209 129.98619
9000000 41.02145 233.58294 136.34359
9513998 37.60000 237.60000 138.89027

The inclusion of Geodesic.LONG_UNROLL in the call to GeodesicLine.Position ensures that the longitude does not jump on crossing the international dateline.

If the purpose of computing the waypoints is to plot a smooth geodesic, then it's not important that they be exactly equally spaced. In this case, it's faster to parameterize the line in terms of the spherical arc length with GeodesicLine.ArcPosition instead of the distance. Here the spacing is about 1° of arc which means that the distance between the waypoints will be about 60 NM.

var l = geod.InverseLine(40.1, 116.6, 37.6, -122.4,
                         Geodesic.LATITUDE | Geodesic.LONGITUDE),
    da = 1, n = Math.ceil(l.a13 / da),
    i, a;
da = l.a13 / n;
console.log("latitude longitude");
for (i = 0; i <= n; ++i) {
  a = da * i;
  r = l.ArcPosition(a, Geodesic.LATITUDE |
                    Geodesic.LONGITUDE | Geodesic.LONG_UNROLL);
  console.log(r.lat2.toFixed(5) + " " + r.lon2.toFixed(5));
}

gives

latitude longitude
40.10000 116.60000
40.82573 117.49243
41.54435 118.40447
42.25551 119.33686
42.95886 120.29036
43.65403 121.26575
44.34062 122.26380
...
39.82385 235.05331
39.08884 235.91990
38.34746 236.76857
37.60000 237.60000

The variation in the distance between these waypoints is on the order of 1/f.

Measuring areas

Measure the area of Antarctica using Geodesic.Polygon and the PolygonArea class:

var p = geod.Polygon(false), i,
    antarctica = [
      [-63.1, -58], [-72.9, -74], [-71.9,-102], [-74.9,-102], [-74.3,-131],
      [-77.5,-163], [-77.4, 163], [-71.7, 172], [-65.9, 140], [-65.7, 113],
      [-66.6,  88], [-66.9,  59], [-69.8,  25], [-70.0,  -4], [-71.0, -14],
      [-77.3, -33], [-77.9, -46], [-74.7, -61]
    ];
for (i = 0; i < antarctica.length; ++i)
  p.AddPoint(antarctica[i][0], antarctica[i][1]);
p = p.Compute(false, true);
console.log("Perimeter/area of Antarctica are " +
            p.perimeter.toFixed(3) + " m / " +
            p.area.toFixed(1) + " m^2.");

Perimeter/area of Antarctica are 16831067.893 m / 13662703680020.1 m^2.

If the points of the polygon are being selected interactively, then PolygonArea.TestPoint can be used to report the area and perimeter for a polygon with a tentative final vertex which tracks the mouse pointer.

Degrees, minutes, seconds conversion

Compute the azimuth for geodesic from JFK (73.8W, 40.6N) to Paris CDG (49°01'N, 2°33'E) using the DMS module:

var c = "73.8W 40.6N 49°01'N 2°33'E".split(" "),
    p1 = DMS.DecodeLatLon(c[0], c[1]),
    p2 = DMS.DecodeLatLon(c[2], c[3]),
    r = geod.Inverse(p1.lat, p1.lon, p2.lat, p2.lon);
console.log("Start = (" +
            DMS.Encode(r.lat1, DMS.MINUTE, 0, DMS.LATITUDE) + ", " +
            DMS.Encode(r.lon1, DMS.MINUTE, 0, DMS.LONGITUDE) +
            "), azimuth = " +
            DMS.Encode(r.azi1, DMS.MINUTE, 1, DMS.AZIMUTH));

Start = (40°36'N, 073°48'W), azimuth = 053°28.2'