karney 1.0.9

Solves the direct and inverse geodesic problem.

Introduction to Karney

The karney library provides native Python implementations of a subset of the C++ library, GeographicLib. Currently the following operations are implemented:

• Calculate the surface distance between two geographical positions.

• Find the destination point given start point, azimuth/bearing and distance.

All the functions are vectorized and offer speeds comparable to compiled C++ code when operating on arrays.

Some common features of these functions:

Angles (latitude, longitude, azimuth) are measured in degrees or radians. Distances are measured in meters. The ellipsoid is specified as [a, f], where a = equatorial radius and f = flattening. Keep |f| <= 1/50 for full double precision accuracy.

Installation

$ pip install karney

Usage

Below the solution to two geodesic problems are given.

Surface distance

Find the surface distance sAB (i.e. great circle distance) between two positions A and B. The heights of A and B are ignored, i.e. if they don't have zero height, we seek the distance between the points that are at the surface of the Earth, directly above/below A and B. Use Earth radius 6371e3 m. Compare the results with exact calculations for the WGS-84 ellipsoid.

In geodesy this is known as "The second geodetic problem" or "The inverse geodetic problem" for a sphere/ellipsoid.

Solution for a sphere:

>>> import numpy as np
>>> from karney.geodesic import rad, sphere_distance_rad, distance

>>> latlon_a = (88, 0)
>>> latlon_b = (89, -170)
>>> latlons = latlon_a + latlon_b
>>> r_Earth = 6371e3  # m, mean Earth radius
>>> s_AB = sphere_distance_rad(*rad(latlons))[0]*r_Earth
>>> s_AB = distance(*latlons, a=r_Earth, f=0, degrees=True)[0] # or alternatively

>>> 'Ex5: Great circle = {:5.2f} km'.format(s_AB / 1000)
'Ex5: Great circle = 332.46 km'

Exact solution for the WGS84 ellipsoid:

>>> s_12, azi1, azi2 = distance(*latlons, degrees=True)
>>> 'Ellipsoidal distance = {:5.2f} km'.format(s_12 / 1000)
'Ellipsoidal distance = 333.95 km'

See also Example 5 at www.navlab.net

A and azimuth/distance to B

We have an initial position A, direction of travel given as an azimuth (bearing) relative to north (clockwise), and finally the distance to travel along a great circle given as sAB. Use Earth radius 6371e3 m to find the destination point B.

In geodesy this is known as "The first geodetic problem" or "The direct geodetic problem" for a sphere.

>>> import numpy as np
>>> from karney.geodesic import reckon
>>> lat, lon = 80, -90
>>> msg = 'Ex8, Destination: lat, lon = {:4.4f} deg, {:4.4f} deg'

Greatcircle solution:

>>> lat2, lon2, azi_b = reckon(lat, lon, distance=1000, azimuth=200, a=6371e3, f=0, degrees=True)

>>> msg.format(lat2, lon2)
'Ex8, Destination: lat, lon = 79.9915 deg, -90.0177 deg'

>>> np.allclose(azi_b, -160.0174292682187)
True

Exact solution:

>>> lat_b, lon_b, azi_b = reckon(lat, lon, distance=1000, azimuth=200, degrees=True)
>>> msg.format(lat_b, lon_b)
'Ex8, Destination: lat, lon = 79.9916 deg, -90.0176 deg'

>>> np.allclose(azi_b, -160.01742926820506)
True

See also Example 8 at www.navlab.net

Contributing

Interested in contributing? Check out the contributing guidelines. Please note that this project is released with a Code of Conduct. By contributing to this project, you agree to abide by its terms.

License

karney was created by Per A. Brodtkorb and is licensed under the terms of the MIT/X11 license.

Acknowledgements

The karney package for Python was written by Per A. Brodtkorb at FFI (The Norwegian Defence Research Establishment) based on the Geographic toolbox written by Charles Karney for Matlab and GNU Octave. The karney.geodesic module is a vectorized reimplementation of the Matlab/Octave GeographicLib toolbox.

The content is based on the article by Karney, 2013. Thus this article should be cited in publications using the software.

The karney package structure was created with cookiecutter and the py-pkgs-cookiecutter template.