Skip to main content

Solves all kinds of geographical position calculations.

Project description


pkg_img tests_img docs_img Maintainability coverage_img versions_img PyPI - Downloads

The nvector library is a suite of tools written in Python to solve geographical position calculations. Currently the following operations are implemented:

  • Calculate the surface distance between two geographical positions.

  • Convert positions given in one reference frame into another reference frame.

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

  • Find the mean position (center/midpoint) of several geographical positions.

  • Find the intersection between two paths.

  • Find the cross track distance between a path and a position.

Using n-vector, the calculations become simple and non-singular. Full accuracy is achieved for any global position (and for any distance).


In this library, we represent position with an “n-vector”, which is the normal vector to the Earth model (the same reference ellipsoid that is used for latitude and longitude). When using n-vector, all Earth-positions are treated equally, and there is no need to worry about singularities or discontinuities. An additional benefit with using n-vector is that many position calculations can be solved with simple vector algebra (e.g. dot product and cross product).

Converting between n-vector and latitude/longitude is unambiguous and easy using the provided functions.

n_E is n-vector in the program code, while in documents we use nE. E denotes an Earth-fixed coordinate frame, and it indicates that the three components of n-vector are along the three axes of E. More details about the notation and reference frames can be found in the documentation.

Documentation and code

Official documentation:

Kenneth Gade (2010):

A Nonsingular Horizontal Position Representation, The Journal of Navigation, Volume 63, Issue 03, pp 395-417, July 2010.

Bleeding edge:

Official releases available at:

Install nvector

If you have pip installed and are online, then simply type:

$ pip install nvector

to get the lastest stable version. Using pip also has the advantage that all requirements are automatically installed.

You can download nvector and all dependencies to a folder “pkg”, by the following:

$ pip install –download=pkg nvector

To install the downloaded nvector, just type:

$ pip install –no-index –find-links=pkg nvector

Verifying installation

To verify that nvector can be seen by Python, type python from your shell. Then at the Python prompt, try to import nvector:

>>> import nvector as nv
>>> print(nv.__version__)

To test if the toolbox is working correctly paste the following in an interactive python session:

import nvector as nv


$ py.test –pyargs nvector –doctest-modules

at the command prompt.

Getting Started

Below the object-oriented solution to some common geodesic problems are given. In the first example the functional solution is also given. The functional solutions to the remaining problems can be found in the functional examples section of the tutorial.

Example 1: “A and B to delta”

Given two positions, A and B as latitudes, longitudes and depths relative to Earth, E.

Find the exact vector between the two positions, given in meters north, east, and down, and find the direction (azimuth) to B, relative to north. Assume WGS-84 ellipsoid. The given depths are from the ellipsoid surface. Use position A to define north, east, and down directions. (Due to the curvature of Earth and different directions to the North Pole, the north, east, and down directions will change (relative to Earth) for different places. Position A must be outside the poles for the north and east directions to be defined.)

>>> import numpy as np
>>> import nvector as nv
>>> wgs84 = nv.FrameE(name='WGS84')
>>> pointA = wgs84.GeoPoint(latitude=1, longitude=2, z=3, degrees=True)
>>> pointB = wgs84.GeoPoint(latitude=4, longitude=5, z=6, degrees=True)
Step1: Find p_AB_N (delta decomposed in N).
>>> p_AB_N = pointA.delta_to(pointB)
>>> x, y, z = p_AB_N.pvector.ravel()
>>> 'Ex1: delta north, east, down = {0:8.2f}, {1:8.2f}, {2:8.2f}'.format(x, y, z)
'Ex1: delta north, east, down = 331730.23, 332997.87, 17404.27'
Step2: Also find the direction (azimuth) to B, relative to north:
>>> 'azimuth = {0:4.2f} deg'.format(p_AB_N.azimuth_deg)
'azimuth = 45.11 deg'
>>> 'elevation = {0:4.2f} deg'.format(p_AB_N.elevation_deg)
'elevation = 2.12 deg'
>>> 'distance = {0:4.2f} m'.format(p_AB_N.length)
'distance = 470356.72 m'
Functional Solution:
>>> import numpy as np
>>> import nvector as nv
>>> from nvector import rad, deg
>>> lat_EA, lon_EA, z_EA = rad(1), rad(2), 3
>>> lat_EB, lon_EB, z_EB = rad(4), rad(5), 6
Step1: Convert to n-vectors:
>>> n_EA_E = nv.lat_lon2n_E(lat_EA, lon_EA)
>>> n_EB_E = nv.lat_lon2n_E(lat_EB, lon_EB)
Step2: Find p_AB_E (delta decomposed in E).WGS-84 ellipsoid is default:
>>> p_AB_E = nv.n_EA_E_and_n_EB_E2p_AB_E(n_EA_E, n_EB_E, z_EA, z_EB)
Step3: Find R_EN for position A:
>>> R_EN = nv.n_E2R_EN(n_EA_E)
Step4: Find p_AB_N (delta decomposed in N).
>>> p_AB_N =, p_AB_E).ravel()
>>> x, y, z = p_AB_N
>>> 'Ex1: delta north, east, down = {0:8.2f}, {1:8.2f}, {2:8.2f}'.format(x, y, z)
'Ex1: delta north, east, down = 331730.23, 332997.87, 17404.27'
Step5: Also find the direction (azimuth) to B, relative to north:
>>> azimuth = np.arctan2(y, x)
>>> 'azimuth = {0:4.2f} deg'.format(deg(azimuth))
'azimuth = 45.11 deg'
>>> distance = np.linalg.norm(p_AB_N)
>>> elevation = np.arcsin(z / distance)
>>> 'elevation = {0:4.2f} deg'.format(deg(elevation))
'elevation = 2.12 deg'
>>> 'distance = {0:4.2f} m'.format(distance)
'distance = 470356.72 m'
See also

Example 1 at

Example 2: “B and delta to C”

A radar or sonar attached to a vehicle B (Body coordinate frame) measures the distance and direction to an object C. We assume that the distance and two angles (typically bearing and elevation relative to B) are already combined to the vector p_BC_B (i.e. the vector from B to C, decomposed in B). The position of B is given as n_EB_E and z_EB, and the orientation (attitude) of B is given as R_NB (this rotation matrix can be found from roll/pitch/yaw by using zyx2R).

Find the exact position of object C as n-vector and depth ( n_EC_E and z_EC ), assuming Earth ellipsoid with semi-major axis a and flattening f. For WGS-72, use a = 6 378 135 m and f = 1/298.26.

>>> import numpy as np
>>> import nvector as nv
>>> wgs72 = nv.FrameE(name='WGS72')
>>> wgs72 = nv.FrameE(a=6378135, f=1.0/298.26)
Step 1: Position and orientation of B is given 400m above E:
>>> n_EB_E = wgs72.Nvector(nv.unit([[1], [2], [3]]), z=-400)
>>> frame_B = nv.FrameB(n_EB_E, yaw=10, pitch=20, roll=30, degrees=True)
Step 2: Delta BC decomposed in B
>>> p_BC_B = frame_B.Pvector(np.r_[3000, 2000, 100].reshape((-1, 1)))
Step 3: Decompose delta BC in E
>>> p_BC_E = p_BC_B.to_ecef_vector()
Step 4: Find point C by adding delta BC to EB
>>> p_EB_E = n_EB_E.to_ecef_vector()
>>> p_EC_E = p_EB_E + p_BC_E
>>> pointC = p_EC_E.to_geo_point()
>>> lat, lon, z = pointC.latlon_deg
>>> msg = 'Ex2: PosC: lat, lon = {:4.4f}, {:4.4f} deg,  height = {:4.2f} m'
>>> msg.format(lat, lon, -z)
'Ex2: PosC: lat, lon = 53.3264, 63.4681 deg,  height = 406.01 m'
See also

Example 2 at

Example 3: “ECEF-vector to geodetic latitude”

Position B is given as an “ECEF-vector” p_EB_E (i.e. a vector from E, the center of the Earth, to B, decomposed in E). Find the geodetic latitude, longitude and height (latEB, lonEB and hEB), assuming WGS-84 ellipsoid.

>>> import numpy as np
>>> import nvector as nv
>>> wgs84 = nv.FrameE(name='WGS84')
>>> position_B = 6371e3 * np.vstack((0.9, -1, 1.1))  # m
>>> p_EB_E = wgs84.ECEFvector(position_B)
>>> pointB = p_EB_E.to_geo_point()
>>> lat, lon, z = pointB.latlon_deg
>>> 'Ex3: Pos B: lat, lon = {:4.4f}, {:4.4f} deg, height = {:9.3f} m'.format(lat, lon, -z)
'Ex3: Pos B: lat, lon = 39.3787, -48.0128 deg, height = 4702059.834 m'
See also

Example 3 at

Example 4: “Geodetic latitude to ECEF-vector”

Geodetic latitude, longitude and height are given for position B as latEB, lonEB and hEB, find the ECEF-vector for this position, p_EB_E.

>>> import nvector as nv
>>> wgs84 = nv.FrameE(name='WGS84')
>>> pointB = wgs84.GeoPoint(latitude=1, longitude=2, z=-3, degrees=True)
>>> p_EB_E = pointB.to_ecef_vector()
>>> 'Ex4: p_EB_E = {} m'.format(p_EB_E.pvector.ravel().tolist())
'Ex4: p_EB_E = [6373290.277218279, 222560.20067473652, 110568.82718178593] m'
See also

Example 4 at

Example 5: “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. The Euclidean distance (chord length) dAB should also be found. Use Earth radius 6371e3 m. Compare the results with exact calculations for the WGS-84 ellipsoid.

Solution for a sphere:
>>> import numpy as np
>>> import nvector as nv
>>> frame_E = nv.FrameE(a=6371e3, f=0)
>>> positionA = frame_E.GeoPoint(latitude=88, longitude=0, degrees=True)
>>> positionB = frame_E.GeoPoint(latitude=89, longitude=-170, degrees=True)
>>> s_AB, azia, azib = positionA.distance_and_azimuth(positionB)
>>> p_AB_E = positionB.to_ecef_vector() - positionA.to_ecef_vector()
>>> d_AB = p_AB_E.length
>>> msg = 'Ex5: Great circle and Euclidean distance = {}'
>>> msg = msg.format('{:5.2f} km, {:5.2f} km')
>>> msg.format(s_AB / 1000, d_AB / 1000)
'Ex5: Great circle and Euclidean distance = 332.46 km, 332.42 km'
Alternative sphere solution:
>>> path = nv.GeoPath(positionA, positionB)
>>> s_AB2 = path.track_distance(method='greatcircle')
>>> d_AB2 = path.track_distance(method='euclidean')
>>> msg.format(s_AB2 / 1000, d_AB2 / 1000)
'Ex5: Great circle and Euclidean distance = 332.46 km, 332.42 km'
Exact solution for the WGS84 ellipsoid:
>>> wgs84 = nv.FrameE(name='WGS84')
>>> point1 = wgs84.GeoPoint(latitude=88, longitude=0, degrees=True)
>>> point2 = wgs84.GeoPoint(latitude=89, longitude=-170, degrees=True)
>>> s_12, azi1, azi2 = point1.distance_and_azimuth(point2)
>>> p_12_E = point2.to_ecef_vector() - point1.to_ecef_vector()
>>> d_12 = p_12_E.length
>>> msg = 'Ellipsoidal and Euclidean distance = {:5.2f} km, {:5.2f} km'
>>> msg.format(s_12 / 1000, d_12 / 1000)
'Ellipsoidal and Euclidean distance = 333.95 km, 333.91 km'
See also

Example 5 at

Example 6 “Interpolated position”

Given the position of B at time t0 and t1, n_EB_E(t0) and n_EB_E(t1).

Find an interpolated position at time ti, n_EB_E(ti). All positions are given as n-vectors.

>>> import nvector as nv
>>> wgs84 = nv.FrameE(name='WGS84')
>>> n_EB_E_t0 = wgs84.GeoPoint(89, 0, degrees=True).to_nvector()
>>> n_EB_E_t1 = wgs84.GeoPoint(89, 180, degrees=True).to_nvector()
>>> path = nv.GeoPath(n_EB_E_t0, n_EB_E_t1)
>>> t0 = 10.
>>> t1 = 20.
>>> ti = 16.  # time of interpolation
>>> ti_n = (ti - t0) / (t1 - t0) # normalized time of interpolation
>>> g_EB_E_ti = path.interpolate(ti_n).to_geo_point()
>>> lat_ti, lon_ti, z_ti = g_EB_E_ti.latlon_deg
>>> msg = 'Ex6, Interpolated position: lat, lon = {:2.1f} deg, {:2.1f} deg'
>>> msg.format(lat_ti, lon_ti)
'Ex6, Interpolated position: lat, lon = 89.8 deg, 180.0 deg'
Vectorized solution:
>>> t = np.array([10, 20])
>>> nvectors = wgs84.GeoPoint([89, 89], [0, 180], degrees=True).to_nvector()
>>> nvectors_i = nvectors.interpolate(ti, t, kind='linear')
>>> lati, loni, zi = nvectors_i.to_geo_point().latlon_deg
>>> msg.format(lat_ti, lon_ti)
'Ex6, Interpolated position: lat, lon = 89.8 deg, 180.0 deg'
See also

Example 6 at

Example 7: “Mean position”

Three positions A, B, and C are given as n-vectors n_EA_E, n_EB_E, and n_EC_E. Find the mean position, M, given as n_EM_E. Note that the calculation is independent of the depths of the positions.

>>> import nvector as nv
>>> points = nv.GeoPoint(latitude=[90, 60, 50],
...                      longitude=[0, 10, -20], degrees=True)
>>> nvectors = points.to_nvector()
>>> n_EM_E = nvectors.mean()
>>> g_EM_E = n_EM_E.to_geo_point()
>>> lat, lon = g_EM_E.latitude_deg, g_EM_E.longitude_deg
>>> msg = 'Ex7: Pos M: lat, lon = {:4.4f}, {:4.4f} deg'
>>> msg.format(lat, lon)
'Ex7: Pos M: lat, lon = 67.2362, -6.9175 deg'
See also

Example 7 at

Example 8: “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, and we see that this is similar to Example 2, but now the delta is given as an azimuth and a great circle distance. (“The second/inverse geodetic problem” for a sphere is already solved in Examples 1 and 5.)

Exact solution:
>>> import numpy as np
>>> import nvector as nv
>>> frame = nv.FrameE(a=6371e3, f=0)
>>> pointA = frame.GeoPoint(latitude=80, longitude=-90, degrees=True)
>>> pointB, azimuthb = pointA.displace(distance=1000, azimuth=200, degrees=True)
>>> lat, lon = pointB.latitude_deg, pointB.longitude_deg
>>> msg = 'Ex8, Destination: lat, lon = {:4.4f} deg, {:4.4f} deg'
>>> msg.format(lat, lon)
'Ex8, Destination: lat, lon = 79.9915 deg, -90.0177 deg'
>>> np.allclose(azimuthb, -160.01742926820506)
Greatcircle solution:
>>> pointB2, azimuthb = pointA.displace(distance=1000,
...                                     azimuth=200,
...                                     degrees=True,
...                                     method='greatcircle')
>>> lat2, lon2 = pointB2.latitude_deg, pointB.longitude_deg
>>> msg.format(lat2, lon2)
'Ex8, Destination: lat, lon = 79.9915 deg, -90.0177 deg'
>>> np.allclose(azimuthb, -160.0174292682187)
See also

Example 8 at

Example 9: “Intersection of two paths”

Define a path from two given positions (at the surface of a spherical Earth), as the great circle that goes through the two points.

Path A is given by A1 and A2, while path B is given by B1 and B2.

Find the position C where the two great circles intersect.

>>> import nvector as nv
>>> pointA1 = nv.GeoPoint(10, 20, degrees=True)
>>> pointA2 = nv.GeoPoint(30, 40, degrees=True)
>>> pointB1 = nv.GeoPoint(50, 60, degrees=True)
>>> pointB2 = nv.GeoPoint(70, 80, degrees=True)
>>> pathA = nv.GeoPath(pointA1, pointA2)
>>> pathB = nv.GeoPath(pointB1, pointB2)
>>> pointC = pathA.intersect(pathB)
>>> pointC = pointC.to_geo_point()
>>> lat, lon = pointC.latitude_deg, pointC.longitude_deg
>>> msg = 'Ex9, Intersection: lat, lon = {:4.4f}, {:4.4f} deg'
>>> msg.format(lat, lon)
'Ex9, Intersection: lat, lon = 40.3186, 55.9019 deg'
Check that PointC is not between A1 and A2 or B1 and B2:
>>> pathA.on_path(pointC)
>>> pathB.on_path(pointC)
Check that PointC is on the great circle going through path A and path B:
>>> pathA.on_great_circle(pointC)
>>> pathB.on_great_circle(pointC)
See also

Example 9 at

Example 10: “Cross track distance”

Path A is given by the two positions A1 and A2 (similar to the previous example).

Find the cross track distance sxt between the path A (i.e. the great circle through A1 and A2) and the position B (i.e. the shortest distance at the surface, between the great circle and B).

Also find the Euclidean distance dxt between B and the plane defined by the great circle. Use Earth radius 6371e3.

Finally, find the intersection point on the great circle and determine if it is between position A1 and A2.

>>> import numpy as np
>>> import nvector as nv
>>> frame = nv.FrameE(a=6371e3, f=0)
>>> pointA1 = frame.GeoPoint(0, 0, degrees=True)
>>> pointA2 = frame.GeoPoint(10, 0, degrees=True)
>>> pointB = frame.GeoPoint(1, 0.1, degrees=True)
>>> pathA = nv.GeoPath(pointA1, pointA2)
>>> s_xt = pathA.cross_track_distance(pointB, method='greatcircle')
>>> d_xt = pathA.cross_track_distance(pointB, method='euclidean')
>>> val_txt = '{:4.2f} km, {:4.2f} km'.format(s_xt/1000, d_xt/1000)
>>> 'Ex10: Cross track distance: s_xt, d_xt = {}'.format(val_txt)
'Ex10: Cross track distance: s_xt, d_xt = 11.12 km, 11.12 km'
>>> pointC = pathA.closest_point_on_great_circle(pointB)
>>> np.allclose(pathA.on_path(pointC), True)
See also

Example 10 at


The nvector package for Python was written by Per A. Brodtkorb at FFI (The Norwegian Defence Research Establishment) based on the nvector toolbox for Matlab written by the navigation group at FFI. The nvector.core and nvector.rotation module is a vectorized reimplementation of the matlab nvector toolbox while the nvector.objects module is a new easy to use object oriented user interface to the nvector core functionality documented in [GB20].

Most of the content is based on the article by K. Gade [Gad10].

Thus this article should be cited in publications using this page or downloaded program code.

However, if you use any of the, FrameE.inverse, GeoPoint.distance_and_azimuth or GeoPoint.displace methods you should also cite the article by Karney [Kar13] because these methods call Karney’s geographiclib library to do the calculations.



Version 0.7.7, June 3, 2021

Per A Brodtkorb (27):
  • Added cartopy and matplotlib to requirements.txt

  • Updated appveyor.yml, setup.cfg and

  • Updated .gitignore to ignore .pytest_cache

  • Corrected failing doctests in

  • Updated version in

  • Updated failing docstrings for python 2.7 in

  • Added ‘# doctest: SKIP’ to all in order to avoid the doctests hangs on the testserver.

  • Fixed a bug in

  • Updated pycodestyle exlude section in setup.cfg Prettified, and

  • Updated pycodestyle ignore section in setup.cfg

  • Added doctest option to setup.cfg

  • Removed print statements in

  • Return “NotImplemented” instead of raising “NotImplementedError” in Nvector._mul__ and Nvector.__div__ in

  • Fixed .travis.yml so that he file paths in coverage.xml is discoverable

    under the sonar.sources folder. The problem is that SonarQube is analysing the checked-out source code (in src/nvector) but the actual unit tests and is run against the installed code (in build/lib/nvector). Thus the absolute files paths to the installed code in the generated coverage.xml were causing Sonar to show no coverage. The workaround was to use sed in the pipeline to replace every path to build/lib/nvector with src/nvector in coverage.xml.

  • Fixed a bug: Identical expressions should not be used on both sides of a binary operator in

  • Updated solutions to example 9

  • Added greatcircle method to GeoPoint.distance_and_azimuth in

  • Added _base_angle function that makes sure an angle is between -pi and pi.

  • Added test_direct_and_inverse in

  • Added interp_nvectors to docs/reference/nvector_summary.rst

  • Added vectorized interpolation routines: interp_nvectors function to and Nvector.interpolate to

  • Put try except around code in use_docstring to avoid attribute ‘__doc__’

    of ‘type’ objects is not writable errors for python2.

  • Added interp_nvectors

  • Reorganized _displace_great_circle

  • Added check that depths also are equal on in _on_ellipsoid_path and in _on_great_circle_path

  • Refactored code from use_docstring_from function into the use_docstring

    function in

  • Simplified the adding of examples to the docstrings of functions and classes in and

Version 0.7.6, December 18, 2020

Per A Brodtkorb (30):
  • Renamed to

  • Removed the module index from the appendix because it was incomplete.

  • Removed nvector.tests package from the reference chapter.

  • Added indent function to to avoid failure on python 2.7.

  • Moved isclose, allclose and array_to_list_dict from to

  • Moved the following function from to
    • test_n_E_and_wa2R_EL, test_R2zxy, test_R2zxy_x90, test_R2zxy_y90

    • test_R2zxy_z90, test_R2zxy_0, test_R2xyz test_R2xyz_with_vectors

  • Replaced assert_array_almost_equal with assert_allclose in

  • Renamed to

  • Added missing functions great_circle_normal and interpolate to the nvector_summary.rst

  • Moved the following functions related to rotation matrices from _core to rotation module:
    • E_rotation, n_E_and_wa2R_EL, n_E2R_EN, R_EL2n_E, R_EN2n_E, R2xyz, R2zyx, xyz2R, zyx2R

  • Renamed select_ellipsoid to get_ellipsoid

  • Moved the following utility functions from _core to util module:
    • deg, rad, mdot, nthroot, get_ellipsoid, unit, _check_length_deviation

  • Added _get_h1line and _make_summary to

  • Replaced numpy.rollaxis with numpy.swapaxes to make the code clearer.

  • _atleast_3d now broadcast the input against each other.

  • Added examples to zyx2R

  • Added the following references to zyx2R, xyz2R, R2xyz, R2zyx:
  • Removed tabs from CHANGELOG.rst

  • Updated CHANGELOG.rst and prepared for release v0.7.6

  • Fixed the documentation so that it shows correctly in the reference manual.

  • Added logo.png and docs/reference/nvector.rst

  • Updated so it generates a valid README.rst file.

  • Updated THANKS.rst

  • Updated CHANGELOG.rst and prepare for release 0.7.6

  • Added Nvector documentation ref to refs1.bib and

  • Updated README.rst

  • Renamed requirements.readthedocs.txt to docs/requirements.txt

  • Added .readthedocs.yml

  • Added sphinxcontrib-bibtex to requirements.readthedocs.txt

  • Added missing docs/tutorials/images/ex3img.png

  • Deleted obsolete ex10img.png

  • Updated acknowledgement with reference to Karney’s article.

  • Updated README.rst by moving acknowledgement to the end with references.

  • Renamed position input argument to point in the FrameN, FrameB and FrameL classes.

  • Deleted

  • Renamed nvector.rst to nvector_summary.rst in docs/reference

  • Added example images to tutorials/images/ folder

  • Added Nvector logo, install.rst to docs

  • Added src/nvector/

  • Added docs/tutorials/whatsnext.rst

  • Reorganized the documentation in docs by splitting into:




    • and

  • Added docs/tutorials/index.rst, docs/intro/index.rst, docs/how-to/index.rst docs/appendix/index.rst and docs/make.bat

  • updated references.

Version 0.7.5, December 12, 2020

Per A Brodtkorb (32):
  • Updated CHANGELOG.rst and prepare for release 0.7.5

  • Changed so that GeoPath.on_great_circle and GeoPath.on_great_circle

    returns scalar result if the two points defining the path are scalars. See issue #10.

  • Fixed failing doctests.

  • Added doctest configuration to docs/

  • Added allclose to nvector/

  • Added array_to_list_dict and isclose functions in

    Replaced f-string in the __repr__ method of the _Common class in with format in order to work on python version 3.5 and below.

  • Made more robust.

  • Removed rtol parameter from the on_greatcircle function. See issue #12 for a discussion.

  • Added nvector solution to the GeoPoint.displace method.

  • Updated docs/

  • Updated README.rst and LICENSE.txt

  • Replaced import unittest with import pytest in

  • Fixed issue #10: Inconsistent return types in GeoPath.track_distance:
    • GeoPath, GeoPoint, Nvector and ECEFvector and Pvector now return scalars for the case where the input is not actually arrays of points but just single objects.

  • Added extra tests for issue #10 and updated old tests and the examples in the help headers.

  • Vectorized FrameE.inverse and methods.

  • Extended deg and rad functions in

  • Vectorized GeoPoint.distance_and_azimuth

  • Made import of cartopy in nvector.plot more robust.

  • Updated test_Ex10_cross_track_distance

  • Updated

  • Replaced deprecated sonar.XXXX.reportPath with sonar.XXXX.reportPaths

  • Simplified nvector/_core.__doc__

  • Updated .travis.yml

  • Changed the definition of sonar addon

  • Added CC_TEST_REPORTER_ID to .travis.yml

  • Added python 3.8 to the CI testing.

  • Changed so that is python 2.7 compatible again.

  • Updated

  • Renamed CHANGES.rst to CHANGELOG.rst

  • Updated setup.cfg and

  • Added

  • Updated

  • Removed conda-build from .travis.yml

  • Attempt to get travis to run the tests again….

  • API change: replaced “python doctests” with “python doctest”

  • Added doctest example to nvector._core._atleast_3d Made xyz2R and zyx2R code simpler.

  • Replaced deprecated Nvector.mean_horizontal_position with Nvector.mean in

  • Added mdot to __all__ in nvector/ and in documentation summary.

  • Sorted the the documentation summary by function name in nvector.rst

  • Removed –pyargs nvector –doctest-modules –pep8 from addopts section in setup.cfg

  • Updated documentation and added missing documentation.

Version 0.7.4, June 4, 2019

Per A Brodtkorb (2):
  • Fixed PyPi badge and added downloads badge in nvector/ and README.rst

  • Removed obsolete and wrong badges from docs/index.rst

Version 0.7.3, June 4, 2019

Per A Brodtkorb (6):
  • Renamed LICENSE.txt and THANKS.txt to LICENSE.rst and THANKS.rst

  • Updated README.rst and nvector/

  • Fixed issue 7# incorrect test for test_n_E_and_wa2R_EL.

  • Removed coveralls test coverage report.

  • Replaced coverage badge from coveralls to codecov.

  • Updated code-climate reporter.

  • Simplified duplicated code in nvector._core.

  • Added tests/

  • Added “–pyargs nvector” to pytest options in setup.cfg

  • Exclude from distribution in

  • Replaced health_img from landscape to codeclimate.

  • Updated travis to explicitly install pytest-cov and pytest-pep8

  • Removed dependence on pyscaffold

  • Added

  • Renamed to

Version 0.7.0, June 2, 2019

Gary van der Merwe (1):
  • Add interpolate to __all__ so that it can be imported

Per A Brodtkorb (26):
  • Updated long_description in setup.cfg

  • Replaced deprecated sphinx.ext.pngmath with sphinx.ext.imgmath

  • Added imgmath to requirements for building the docs.

  • Fixing shallow clone warning.

  • Replaced property ‘sonar.python.coverage.itReportPath’ with

    ‘sonar.python.coverage.reportPaths’ instead, because it is has been removed.

  • Drop python 3.4 support

  • Added python 3.7 support

  • Fixed a bug: Mixed scalars and np.array([1]) values don’t work with np.rad2deg function.

  • Added ETRS ELLIPSOID in Added ED50 as alias for International

    (Hayford)/European Datum in Added sad69 as alias for South American 1969 in

  • Simplified docstring for nv.test

  • Generalized the

  • Replaced aliases with the correct names in setup.cfg.

Version 0.6.0, December 9, 2018

Per A Brodtkorb (79):
  • Updated requirements in

  • Removed tox.ini

  • Updated documentation on how to set package version

  • Made a separate script to set package version in nvector/

  • Updated docstring for select_ellipsoid

  • Replace GeoPoint.geo_point with GeoPoint.displace and removed deprecated GeoPoint.geo_point

  • Update .travis.yml

  • Fix so that codeclimate is able to parse .travis.yml

  • Only run sonar and codeclimate reporter for python v3.6

  • Added

  • Pinned coverage to v4.3.4 due to fact that codeclimate reporter is only

    compatible with versions >=4.0,<4.4.

  • Updated with sonar scanner.

  • Added .pylintrc

  • Set up codeclimate reporter

  • Updated docstring for unit function.

  • Avoid division by zero in unit function.

  • Reenabled the doctest of plot_mean_position

  • Reset “pyscaffold==2.5.11”

  • Replaced deprecated basemap with cartopy.

  • Replaced doctest of plot_mean_position with test_plot_mean_position in

  • Fixed failing doctests for python v3.4 and v3.5 and made them more


  • Fixed failing doctests and made them more robust.

  • Increased pycoverage version to use.

  • moved nvector to src/nvector/

  • Reset the to require ‘pyscaffold==2.5.11’ which works on

    python version 3.4, 3.5 and 3.6. as well as 2.7

  • Updated unittests.

  • Updated tests.

  • Removed obsolete code

  • Added test for delta_L

  • Added corner testcase for


  • Added test for path.track_distance(method=’exact’)

  • Added delta_L a function thet teturn cartesian delta vector from

    positions A to B decomposed in L.

  • Simplified OO-solution in example 1 by using delta_N function

  • Refactored duplicated code

  • Vectorized code so that the frames can take more than one position at

    the time.

  • Keeping only the html docs in the distribution.

  • replaced link from latest to stable docs on readthedocs and updated

    crosstrack distance test.

  • updated documentation in

Version 0.5.2, March 7, 2017

Per A Brodtkorb (10):
  • Fixed tests in tests/

  • Updated to setup.cfg and tox.ini + pep8

  • updated .travis.yml

  • Updated Readme.rst with new example 10 picture and link to nvector docs at readthedocs.

  • updated official documentation links

  • Updated crosstrack distance tests.

Version 0.5.1, March 5, 2017

Cody (4):
  • Explicitely numbered replacement fields

  • Migrated % string formating

Per A Brodtkorb (29):
  • pep8

  • Updated failing examples

  • Updated README.rst

  • Removed obsolete pass statement

  • Documented functions

  • added .checkignore for quantifycode

  • moved test_docstrings and use_docstring_from into

  • Added .codeclimate.yml

  • Updated installation information in

  • Added GeoPath.on_path method. Clearified intersection example

  • Added great_circle_normal, cross_track_distance

  • Renamed intersection to intersect (Intersection is deprecated.)

  • Simplified R2zyx with a call to R2xyz Improved accuracy for great circle cross track distance for small distances.

  • Added on_great_circle, _on_great_circle_path, _on_ellipsoid_path, closest_point_on_great_circle and closest_point_on_path to GeoPath

  • made __eq__ more robust for frames

  • Removed duplicated code

  • Updated tests

  • Removed fishy test

  • replaced zero n-vector with nan

  • Commented out failing test.

  • Added example 10 image

  • Added ‘closest_point_on_great_circle’, ‘on_great_circle’,’on_great_circle_path’.

  • Updated examples + documentation

  • Updated index depth

  • Updated README.rst and classifier in setup.cfg

Version 0.4.1, January 19, 2016

pbrod (46):

  • Cosmetic updates

  • Updated README.rst

  • updated docs and removed unused code

  • updated README.rst and .coveragerc

  • Refactored out _check_frames

  • Refactored out _default_frame

  • Updated .coveragerc

  • Added link to geographiclib

  • Updated external link

  • Updated documentation

  • Added figures to examples

  • Added GeoPath.interpolate + interpolation example 6

  • Added links to FFI homepage.

  • Updated documentation:
    • Added link to nvector toolbox for matlab

    • For each example added links to the more detailed explanation on the homepage

  • Updated link to nvector toolbox for matlab

  • Added link to nvector on pypi

  • Updated documentation fro FrameB, FrameE, FrameL and FrameN.

  • updated __all__ variable

  • Added missing R_Ee to function n_EA_E_and_n_EB_E2azimuth + updated documentation

  • Updated CHANGES.rst

  • Updated

  • Renamed to

  • All examples are now generated from

Version 0.1.3, January 1, 2016

pbrod (31):

  • Refactored

  • Updated tests

  • Updated docs

  • Moved tests to nvector/tests

  • Updated .coverage Added travis.yml, .landscape.yml

  • Deleted obsolete LICENSE

  • Updated README.rst

  • Removed ngs version

  • Fixed bug in .travis.yml

  • Updated .travis.yml

  • Removed dependence on

  • Updated README.rst

  • Updated examples

  • Deleted and added tox.ini

  • Renamed distance_rad_bearing_rad2point to n_EA_E_distance_and_azimuth2n_EB_E

  • Renamed azimuth to n_EA_E_and_n_EB_E2azimuth

  • Added tests for R2xyz as well as R2zyx

  • Removed backward compatibility

  • Added test_n_E_and_wa2R_EL

  • Refactored tests

  • Commented out failing tests on python 3+

  • updated CHANGES.rst

  • Removed bug in

Version 0.1.1, January 1, 2016

pbrod (31):
  • Initial commit: Translated code from Matlab to Python.

  • Added object oriented interface to nvector library

  • Added tests for object oriented interface

  • Added geodesic tests.

The content of this library is based on the following publication:

Gade, K. (2010). A Nonsingular Horizontal Position Representation, The Journal of Navigation, Volume 63, Issue 03, pp 395-417, July 2010. (

This paper should be cited in publications using this library.

Copyright (c) 2015-2021, Norwegian Defence Research Establishment (FFI) All rights reserved.

Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met:

1. Redistributions of source code must retain the above publication information, copyright notice, this list of conditions and the following disclaimer.

2. Redistributions in binary form must reproduce the above publication information, copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution.



  • Kenneth Gade, FFI: Main author of Matlab toolbox nvector.

  • Kristian Svartveit, FFI: Contributions to matlab code: R_Ee.m and unit.m.

  • Brita Hafskjold Gade, FFI: Contributions to matlab code: n_EB_E2p_EB_E.m, p_EB_E2n_EB_E.m

  • Per A Brodtkorb, FFI: Translation of nvector from matlab to Python and maintainer of the python version.

Download files

Download the file for your platform. If you're not sure which to choose, learn more about installing packages.

Source Distribution

nvector-0.7.7.tar.gz (5.4 MB view hashes)

Uploaded source

Built Distribution

nvector-0.7.7-py2.py3-none-any.whl (73.7 kB view hashes)

Uploaded py2 py3

Supported by

AWS AWS Cloud computing and Security Sponsor Datadog Datadog Monitoring Fastly Fastly CDN Google Google Download Analytics Microsoft Microsoft PSF Sponsor Pingdom Pingdom Monitoring Sentry Sentry Error logging StatusPage StatusPage Status page