Metadata-Version: 2.1
Name: nvector
Version: 0.7.5
Summary: Solves all kinds of geographical position calculations.
Home-page: https://github.com/pbrod/nvector/
Author: Per A. Brodtkorb
Author-email: per.andreas.brodtkorb@gmail.com
License: Simplified BSD
Description: 
        =======
        nvector
        =======
        
        |nvector_img| |tests_img| |docs_img| |health_img| |coverage_img| |versions_img| |downloads_img|
        
        The nvector library is a suite of tools written in Python to solve geographical position
        calculations like:
        
        * 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.
        
        
        Description
        ===========
        
        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 here:
        
        Documentation and code
        ======================
        
        Official documentation:
        
        http://www.navlab.net/nvector/
        
        http://nvector.readthedocs.io/en/latest/
        
        *Kenneth Gade (2010):*
            `A Nonsingular Horizontal Position Representation,
            The Journal of Navigation, Volume 63, Issue 03, pp 395-417, July 2010.
            <http://www.navlab.net/Publications/A_Nonsingular_Horizontal_Position_Representation.pdf>`_
        
        
        Bleeding edge: https://github.com/pbrod/nvector.
        
        Official releases available at: http://pypi.python.org/pypi/nvector.
        
        
        Installation
        ============
        
        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
        
        
        Unit tests
        ===========
        To test if the toolbox is working paste the following in an interactive
        python session::
        
           import nvector as nv
           nv.test('--doctest-modules')
        
        or
        
           $ py.test --pyargs nvector --doctest-modules
        
        at the command prompt.
        
        
        Acknowledgement
        ===============
        The `nvector package <http://pypi.python.org/pypi/nvector/>`_ for
        `Python <https://www.python.org/>`_ was written by Per A. Brodtkorb at
        `FFI (The Norwegian Defence Research Establishment) <http://www.ffi.no/en>`_
        based on the `nvector toolbox <http://www.navlab.net/nvector/#download>`_ for
        `Matlab <http://www.mathworks.com>`_ written by the navigation group at
        `FFI <http://www.ffi.no/en>`_.
        
        Most of the content is based on the following article:
        
        *Kenneth Gade (2010):*
            `A Nonsingular Horizontal Position Representation,
            The Journal of Navigation, Volume 63, Issue 03, pp 395-417, July 2010.
            <http://www.navlab.net/Publications/A_Nonsingular_Horizontal_Position_Representation.pdf>`_
        
        Thus this article should be cited in publications using this page or the
        downloaded program code.
        
        
        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
        `test_nvector.py
        <https://github.com/pbrod/nvector/blob/master/src/nvector/tests/test_nvector.py>`_.
        
        
        **Example 1: "A and B to delta"**
        ---------------------------------
        
        .. image:: http://www.navlab.net/images/ex1img.png
        
        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.  A must be outside the poles for the north and east
        directions to be defined.)
        
        Solution:
            >>> 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()
            >>> valtxt = '{0:8.2f}, {1:8.2f}, {2:8.2f}'.format(x, y, z)
            >>> 'Ex1: delta north, east, down = {}'.format(valtxt)
            'Ex1: delta north, east, down = 331730.23, 332997.87, 17404.27'
        
        Step2: Also find the direction (azimuth) to B, relative to north:
            >>> azimuth = p_AB_N.azimuth_deg
            >>> 'azimuth = {0:4.2f} deg'.format(azimuth)
            'azimuth = 45.11 deg'
        
        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 = np.dot(R_EN.T, p_AB_E).ravel()
            >>> valtxt = '{0:8.2f}, {1:8.2f}, {2:8.2f}'.format(*p_AB_N)
            >>> 'Ex1: delta north, east, down = {}'.format(valtxt)
            '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(p_AB_N[1], p_AB_N[0])
            >>> 'azimuth = {0:4.2f} deg'.format(deg(azimuth))
            'azimuth = 45.11 deg'
        
        See also
            `Example 1 at www.navlab.net <http://www.navlab.net/nvector/#example_1>`_
        
        
        **Example 2: "B and delta to C"**
        ---------------------------------
        
        .. image:: http://www.navlab.net/images/ex2img.png
        
        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.
        
        
        Solution:
            >>> 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 = {:4.2f}, {:4.2f} deg,  height = {:4.2f} m'
            >>> msg.format(lat, lon, -z)
            'Ex2: PosC: lat, lon = 53.33, 63.47 deg,  height = 406.01 m'
        
        See also
            `Example 2 at www.navlab.net <http://www.navlab.net/nvector/#example_2>`_
        
        
        **Example 3: "ECEF-vector to geodetic latitude"**
        -------------------------------------------------
        
        .. image:: http://www.navlab.net/images/ex3img.png
        
        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.
        
        
        Solution:
            >>> 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
            >>> msg = 'Ex3: Pos B: lat, lon = {:4.2f}, {:4.2f} deg, height = {:9.2f} m'
            >>> msg.format(lat, lon, -z)
            'Ex3: Pos B: lat, lon = 39.38, -48.01 deg, height = 4702059.83 m'
        
        See also
            `Example 3 at www.navlab.net <http://www.navlab.net/nvector/#example_3>`_
        
        
        **Example 4: "Geodetic latitude to ECEF-vector"**
        -------------------------------------------------
        
        .. image:: http://www.navlab.net/images/ex4img.png
        
        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.
        
        
        Solution:
            >>> 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 www.navlab.net <http://www.navlab.net/nvector/#example_4>`_
        
        
        **Example 5: "Surface distance"**
        ---------------------------------
        
        .. image:: http://www.navlab.net/images/ex5img.png
        
        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 www.navlab.net <http://www.navlab.net/nvector/#example_5>`_
        
        
        **Example 6 "Interpolated position"**
        -------------------------------------
        
        .. image:: http://www.navlab.net/images/ex6img.png
        
        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.
        
        
        Solution:
            >>> 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'
        
        See also
            `Example 6 at www.navlab.net <http://www.navlab.net/nvector/#example_6>`_
        
        
        **Example 7: "Mean position"**
        ------------------------------
        
        .. image:: http://www.navlab.net/images/ex7img.png
        
        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.
        
        
        Solution:
            >>> 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 = {:4.2f}, {:4.2f} deg'
            >>> msg.format(lat, lon)
            'Ex7: Pos M: lat, lon = 67.24, -6.92 deg'
        
        See also
            `Example 7 at www.navlab.net <http://www.navlab.net/nvector/#example_7>`_
        
        
        **Example 8: "A and azimuth/distance to B"**
        --------------------------------------------
        
        .. image:: http://www.navlab.net/images/ex8img.png
        
        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 <http://www.navlab.net/nvector/#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 <http://www.navlab.net/nvector/#example_1>`_ and
        `5 <http://www.navlab.net/nvector/#example_5>`_.)
        
        
        Solution:
            >>> 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 = {:4.2f} deg, {:4.2f} deg'
            >>> msg.format(lat, lon)
            'Ex8, Destination: lat, lon = 79.99 deg, -90.02 deg'
        
        See also
            `Example 8 at www.navlab.net <http://www.navlab.net/nvector/#example_8>`_
        
        
        **Example 9: "Intersection of two paths"**
        ------------------------------------------
        
        .. image:: http://www.navlab.net/images/ex9img.png
        
        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.
        
        
        Solution:
            >>> import numpy as np
            >>> 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)
            >>> np.allclose(pathA.on_path(pointC), pathB.on_path(pointC))
            True
            >>> np.allclose(pathA.on_great_circle(pointC),
            ...             pathB.on_great_circle(pointC))
            True
            >>> pointC = pointC.to_geo_point()
            >>> lat, lon = pointC.latitude_deg, pointC.longitude_deg
            >>> msg = 'Ex9, Intersection: lat, lon = {:4.2f}, {:4.2f} deg'
            >>> msg.format(lat, lon)
            'Ex9, Intersection: lat, lon = 40.32, 55.90 deg'
        
        See also
            `Example 9 at www.navlab.net <http://www.navlab.net/nvector/#example_9>`_
        
        
        **Example 10: "Cross track distance"**
        --------------------------------------
        
        .. image:: https://raw.githubusercontent.com/pbrod/Nvector/master/ex10img.png
        
        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.
        
        
        Solution:
            >>> 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)
            True
        
        See also
            `Example 10 at www.navlab.net <http://www.navlab.net/nvector/#example_10>`_
        
        
        
        See also
        ========
        `geographiclib <https://pypi.python.org/pypi/geographiclib>`_
        
        .. |nvector_img| image:: https://badge.fury.io/py/nvector.png
           :target: https://pypi.python.org/pypi/nvector/
        .. |tests_img| image:: https://travis-ci.org/pbrod/Nvector.svg?branch=master
           :target: https://travis-ci.org/pbrod/Nvector
        .. |docs_img| image:: https://readthedocs.org/projects/pip/badge/?version=stable
           :target: http://Nvector.readthedocs.org/en/stable/
        .. |health_img| image:: https://api.codeclimate.com/v1/badges/c04214bef610b25906fe/maintainability
           :target: https://codeclimate.com/github/pbrod/Nvector/maintainability
           :alt: Maintainability
        .. |coverage_img| image:: https://codecov.io/gh/pbrod/nvector/branch/master/graph/badge.svg
           :target: https://codecov.io/gh/pbrod/nvector
        .. |versions_img| image:: https://img.shields.io/pypi/pyversions/Nvector.svg
           :target: https://github.com/pbrod/nvector
        .. |downloads_img| image:: https://img.shields.io/pypi/dm/nvector.svg
           :alt: PyPI - Downloads
        
        =========
        Changelog
        =========
        
        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/conf.py
              * Added allclose to nvector/objects.py
              * Added array_to_list_dict an isclose functions in nvector.objects.py
                 Replaced f-string in the __repr__ method of the _Common class in
                 nvector.objects.py with format in order to work on python version 3.5
                 and below. 
              * Made nvector.plot.py 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/conf.py
              * Updated README.rst and LICENSE.txt
              * Replaced import unittest with import pytest in test_frames.py
              * 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 FrameE.direct methods.
              * Extended deg and rad functions in _core.py.
              * Vectorized GeoPoint.distance_and_azimuth
              * Made import of cartopy in nvector.plot more robust.
              * Updated test_Ex10_cross_track_distance
              * Updated sonar-project.properties
              * 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 setup.py is python 2.7 compatible again.
              * Updated build_package.py
              * Renamed CHANGES.rst to CHANGELOG.rst
              * Updated setup.cfg and setup.py
              * Added license.py
              * Updated build_package.py
              * Removed conda-build from .travis.yml
              * Attempt to get travis to run the tests again....
              * API change: replaced "python setup.py doctests" with "python setup.py 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 test_frames.py
              * Added mdot to __all__ in nvector/_core.py 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/_info.py 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/_info.py
              * 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/__init__.py
              * Added "--pyargs nvector" to pytest options in setup.cfg
              * Exclude build_package.py from distribution in MANIFEST.in
              * Replaced healt_img from landscape to codeclimate.
              * Updated travis to explicitly install pytest-cov and pytest-pep8
              * Removed dependence on pyscaffold
              * Added MANIFEST.in
              * Renamed set_package_version.py to build_package.py
        
        
        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 _core.py Added ED50 as alias for International
                 (Hayford)/European Datum in _core.py Added sad69 as alias for South American 1969 in _core.py
              * Simplified docstring for nv.test
              * Generalized the setup.py.
              * Replaced aliases with the correct names in setup.cfg.
        
        
        Version 0.6.0, December 9, 2018
        ===============================
        
        Per A Brodtkorb (79):
              * Updated requirements in setup.py
              * Removed tox.ini
              * Updated documentation on how to set package version
              * Made a separate script to set package version in nvector/__init__.py
              * 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 sonar-project.properties
              * Pinned coverage to v4.3.4 due to fact that codeclimate reporter is only
                 compatible with Coverage.py 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
                 test_plot.py
              * Fixed failing doctests for python v3.4 and v3.5 and made them more
                 robust.
              * Fixed failing doctests and made them more robust.
              * Increased pycoverage version to use.
              * moved nvector to src/nvector/
              * Reset the setup.py 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
                 pointA.displace(distance=1000,azimuth=np.deg2rad(200))
              * 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 setup.py
        
        
        Version 0.5.2, March 7, 2017
        ============================
        
        
        Per A Brodtkorb (10):
              * Fixed tests in tests/test_frames.py
              * 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 _common.py
             * Added .codeclimate.yml
             * Updated installation information in _info.py
             * 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 conf.py
              * Renamed info.py to _info.py
              * All examples are now generated from _examples.py.
        
        
        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 navigator.py
              * Updated README.rst
              * Updated examples
              * Deleted skeleton.py and added tox.ini
              * Small refactoring     Renamed distance_rad_bearing_rad2point to n_EA_E_distance_and_azimuth2n_EB_E     updated tests
              * 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 setup.py
        
        
        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.
        (www.navlab.net/Publications/A_Nonsingular_Horizontal_Position_Representation.pdf)
        
        This paper should be cited in publications using this library.
        
        Copyright (c) 2015-2020, 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.
        
        THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
        "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED
        TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
        PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS
        BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
        CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
        SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
        INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
        CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
        ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF
        THE POSSIBILITY OF SUCH DAMAGE.
        ============
        Contributers
        ============
        
        * 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.
        
        
Platform: any
Classifier: Development Status :: 4 - Beta
Classifier: Programming Language :: Python
Classifier: Programming Language :: Python :: 2.7
Classifier: Programming Language :: Python :: 3.5
Classifier: Programming Language :: Python :: 3.6
Classifier: Programming Language :: Python :: 3.7
Classifier: Programming Language :: Python :: 3.8
Classifier: Environment :: Console
Classifier: Intended Audience :: Education
Classifier: Intended Audience :: Science/Research
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Classifier: Topic :: Scientific/Engineering :: Mathematics
Classifier: Topic :: Scientific/Engineering :: GIS
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Provides-Extra: build_sphinx
