# Examples¶

## Initializing¶

The following examples all assume that the following commands have been carried out:

```>>> from geographiclib.geodesic import Geodesic
>>> import math
>>> geod = Geodesic.WGS84  # define the WGS84 ellipsoid
```

You can determine the ellipsoid parameters with the a and f member variables, for example,

```>>> geod.a, 1/geod.f
(6378137.0, 298.257223563)
```

If you need to use a different ellipsoid, construct one by, for example

```>>> geod = Geodesic(6378388, 1/297.0) # the international ellipsoid
```

## Basic geodesic calculations¶

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

```>>> g = geod.Inverse(-41.32, 174.81, 40.96, -5.50)
>>> print "The distance is {:.3f} m.".format(g['s12'])
The distance is 19959679.267 m.
```

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

```>>> g = geod.Direct(-32.06, 115.74, 225, 20000e3)
>>> print "The position is ({:.8f}, {:.8f}).".format(g['lat2'],g['lon2'])
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 the output mask parameter.

```>>> g = geod.Inverse(40.6, -73.8, 51.6, -0.5, Geodesic.AREA)
>>> print "The area is {:.1f}  m^2".format(g['S12'])
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.Line` and `GeodesicLine.Position`:

```>>> l = geod.InverseLine(40.1, 116.6, 37.6, -122.4)
>>> ds = 1000e3; n = int(math.ceil(l.s13 / ds))
>>> for i in range(n + 1):
...   if i == 0:
...     print "distance latitude longitude azimuth"
...   s = min(ds * i, l.s13)
...   g = l.Position(s, Geodesic.STANDARD | Geodesic.LONG_UNROLL)
...   print "{:.0f} {:.5f} {:.5f} {:.5f}".format(
...     g['s12'], g['lat2'], g['lon2'], g['azi2'])
...
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`. Here the spacing is about 1° of arc which means that the distance between the waypoints will be about 60 NM.

```>>> l = geod.InverseLine(40.1, 116.6, 37.6, -122.4,
...               Geodesic.LATITUDE | Geodesic.LONGITUDE)
>>> da = 1; n = int(math.ceil(l.a13 / da)); da = l.a13 / n
>>> for i in range(n + 1):
...   if i == 0:
...     print "latitude longitude"
...   a = da * i
...   g = l.ArcPosition(a, Geodesic.LATITUDE |
...                     Geodesic.LONGITUDE | Geodesic.LONG_UNROLL)
...   print "{:.5f} {:.5f}".format(g['lat2'], g['lon2'])
...
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:

```>>> p = geod.Polygon()
>>> 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 pnt in antarctica: