"""
Created on 29. des. 2015

@author: pab
"""
from __future__ import division, print_function
from functools import partial
import numpy as np
from numpy import deprecate
from numpy.linalg import norm
from geographiclib.geodesic import Geodesic as _Geodesic
from nvector._core import (mdot, select_ellipsoid, rad, deg, zyx2R,
                           lat_lon2n_E, n_E2lat_lon, n_E2R_EN, n_E_and_wa2R_EL,
                           n_EB_E2p_EB_E, p_EB_E2n_EB_E, unit,
                           closest_point_on_great_circle,
                           great_circle_distance, euclidean_distance,
                           cross_track_distance, intersect,
                           mean_horizontal_position,
                           E_rotation, on_great_circle_path)
from nvector import _examples
from nvector._common import test_docstrings, use_docstring_from
import warnings

__all__ = ['FrameE', 'FrameB', 'FrameL', 'FrameN', 'GeoPoint', 'GeoPath',
           'Nvector', 'ECEFvector', 'Pvector', 'diff_positions',
           'delta_E', 'delta_N', 'delta_L']


class _DeltaE(object):
    __doc__ = """
    Returns cartesian delta vector from positions a to b decomposed in E.

    Parameters
    ----------
    point_a, point_b: Nvector, GeoPoint or ECEFvector objects
        position a and b, decomposed in E.

    Returns
    -------
    p_ab_E:  ECEFvector
        Cartesian position vector(s) from a to b, decomposed in E.

    Notes
    -----
    The calculation is exact, taking the ellipsity of the Earth into account.
    It is also non-singular as both n-vector and p-vector are non-singular
    (except for the center of the Earth).

    Examples
    --------

    {0}

    See also
    --------
    n_EA_E_and_p_AB_E2n_EB_E,
    p_EB_E2n_EB_E,
    n_EB_E2p_EB_E.
    """.format(_examples.get_examples([1]))


@use_docstring_from(_DeltaE)
def delta_E(point_a, point_b):
    # Function 1. in Section 5.4 in Gade (2010):
    p_EA_E = point_a.to_ecef_vector()
    p_EB_E = point_b.to_ecef_vector()
    p_AB_E = -p_EA_E + p_EB_E
    return p_AB_E


@deprecate
def diff_positions(point_a, point_b):
    """Deprecated use delta_E instead.
    """
    return delta_E(point_a, point_b)


def delta_N(point_a, point_b):
    """Returns cartesian delta vector from positions a to b decomposed in N.

    Parameters
    ----------
    point_a, point_b: Nvector, GeoPoint or ECEFvector objects
        position a and b, decomposed in E.

    See also
    --------
    delta_E, delta_L
    """
    # p_ab_E = delta_E(point_a, point_b)
    # p_ab_N = p_ab_E.change_frame(....)
    return delta_E(point_a, point_b).change_frame(FrameN(point_a))


def _delta(self, other):
    """Returns cartesian delta vector from positions a to b decomposed in N."""
    return delta_N(self, other)


def delta_L(point_a, point_b, wander_azimuth=0):
    """Returns cartesian delta vector from positions a to b decomposed in L.

    Parameters
    ----------
    point_a, point_b: Nvector, GeoPoint or ECEFvector objects
        position a and b, decomposed in E.
    wander_azimuth: real scalar
        Angle [rad] between the x-axis of L and the north direction.

    See also
    --------
    delta_E, delta_N
    """
    local_frame = FrameL(point_a, wander_azimuth=wander_azimuth)
    # p_ab_E = delta_E(point_a, point_b)
    # p_ab_L = p_ab_E.change_frame(....)
    return delta_E(point_a, point_b).change_frame(local_frame)


class GeoPoint(object):
    """
    Geographical position given as latitude, longitude, depth in frame E.

    Parameters
    ----------
    latitude, longitude: real scalars or vectors of length n.
        Geodetic latitude and longitude given in [rad or deg]
    z: real scalar or vector of length n.
        Depth(s) [m]  relative to the ellipsoid (depth = -height)
    frame: FrameE object
        reference ellipsoid. The default ellipsoid model used is WGS84, but
        other ellipsoids/spheres might be specified.
    degrees: bool
        True if input are given in degrees otherwise radians are assumed.

    Examples
    --------
    Solve geodesic problems.

    The following illustrates its use

    >>> import nvector as nv
    >>> wgs84 = nv.FrameE(name='WGS84')

    The geodesic inverse problem

    >>> point_a = wgs84.GeoPoint(-41.32, 174.81, degrees=True)
    >>> point_b = wgs84.GeoPoint(40.96, -5.50, degrees=True)
    >>> s12, az1, az2 = point_a.distance_and_azimuth(point_b, degrees=True)
    >>> 's12 = {:5.2f}, az1 = {:5.2f}, az2 = {:5.2f}'.format(s12, az1, az2)
    's12 = 19959679.27, az1 = 161.07, az2 = 18.83'

    The geodesic direct problem

    >>> point_a = wgs84.GeoPoint(40.6, -73.8, degrees=True)
    >>> az1, distance = 45, 10000e3
    >>> point_b, az2 = point_a.displace(distance, az1, degrees=True)
    >>> lat2, lon2 = point_b.latitude_deg, point_b.longitude_deg
    >>> msg = 'lat2 = {:5.2f}, lon2 = {:5.2f}, az2 = {:5.2f}'
    >>> msg.format(lat2, lon2, az2)
    'lat2 = 32.64, lon2 = 49.01, az2 = 140.37'

    """

    def __init__(self, latitude, longitude, z=0, frame=None, degrees=False):
        if degrees:
            latitude, longitude = rad(latitude, longitude)
        self.latitude = latitude
        self.longitude = longitude
        self.z = z
        self.frame = _default_frame(frame)

    @property
    def latlon_deg(self):
        """(latitude_deg, longitude_deg, z) tuple, angles are in degree."""
        return self.latitude_deg, self.longitude_deg, self.z

    @property
    def latlon(self):
        """(latitude, longitude, z) tuple, angles are in radian."""
        return self.latitude, self.longitude, self.z

    @property
    def latitude_deg(self):
        """latitude in degrees."""
        return deg(self.latitude)

    @property
    def longitude_deg(self):
        """longitude in degrees."""
        return deg(self.longitude)

    def to_ecef_vector(self):
        """
        Returns position as ECEFvector object.

        See also
        --------
        ECEFvector
        """
        return self.to_nvector().to_ecef_vector()

    def to_geo_point(self):
        """
        Returns position as GeoPoint object.

        See also
        --------
        GeoPoint
        """

        return self

    def to_nvector(self):
        """
        Returns position as Nvector object.

        See also
        --------
        Nvector
        """
        latitude, longitude = self.latitude, self.longitude
        n_vector = lat_lon2n_E(latitude, longitude, self.frame.R_Ee)
        return Nvector(n_vector, self.z, self.frame)

    delta_to = _delta

    def displace(self, distance, azimuth, long_unroll=False, degrees=False):
        """
        Returns position b computed from current position, distance and azimuth.

        Parameters
        ----------
        distance: real scalar
            ellipsoidal distance [m] between position A and B.
        azimuth_a:
            azimuth [rad or deg] of line at position A.
        degrees: bool
            azimuths are given in degrees if True otherwise in radians.

        Returns
        -------
        point_b:  GeoPoint object
            latitude and longitude of position B.
        azimuth_b
            azimuth [rad or deg] of line at position B.

        """
        frame = self.frame
        z = self.z
        if not degrees:
            azimuth = deg(azimuth)
        lat_a, lon_a = self.latitude_deg, self.longitude_deg
        lat_b, lon_b, azimuth_b = frame.direct(lat_a, lon_a, azimuth, distance,
                                               z=z, long_unroll=long_unroll,
                                               degrees=True)

        point_b = frame.GeoPoint(latitude=lat_b, longitude=lon_b, z=z, degrees=True)
        if not degrees:
            return point_b, rad(azimuth_b)
        return point_b, azimuth_b

    def distance_and_azimuth(self, point, long_unroll=False, degrees=False):
        """
        Returns ellipsoidal distance between positions as well as the direction.

        Parameters
        ----------
        point:  GeoPoint object
            Latitude and longitude of position b.
        degrees: bool
            azimuths are returned in degrees if True otherwise in radians.

        Returns
        -------
        s_ab: real scalar or vector of length n.
            ellipsoidal distance [m] between position a and b at their average height.
        azimuth_a, azimuth_b: real scalars or vectors of length n.
            direction [rad or deg] of line at position a and b relative to
            North, respectively.

        References
        ----------
        C. F. F. Karney, Algorithms for geodesics, J. Geodesy 87(1), 43-55

        `geographiclib <https://pypi.python.org/pypi/geographiclib>`_
        """
        _check_frames(self, point)
        gpoint = point.to_geo_point()
        lat_a, lon_a = self.latitude, self.longitude
        lat_b, lon_b = gpoint.latitude, gpoint.longitude
        z = 0.5 * (self.z + gpoint.z)  # Average depth

        if degrees:
            lat_a, lon_a, lat_b, lon_b = deg(lat_a, lon_a, lat_b, lon_b)

        return self.frame.inverse(lat_a, lon_a, lat_b, lon_b, z, long_unroll, degrees)


class _Common(object):
    def __eq__(self, other):
        try:
            return self is other or self._is_equal_to(other, rtol=1e-12, atol=1e-14)
        except AttributeError:
            return False

    def __ne__(self, other):
        return not self.__eq__(other)


class Nvector(_Common):
    """
    Geographical position given as n-vector and depth in frame E

    Parameters
    ----------
    normal: 3 x n array
        n-vector(s) [no unit] decomposed in E.
    z: real scalar or vector of length n.
        Depth(s) [m]  relative to the ellipsoid (depth = -height)
    frame: FrameE object
        reference ellipsoid. The default ellipsoid model used is WGS84, but
        other ellipsoids/spheres might be specified.

    Notes
    -----
    The position of B (typically body) relative to E (typically Earth) is
    given into this function as n-vector, n_EB_E and a depth, z relative to the
    ellipsiod.

    See also
    --------
    GeoPoint, ECEFvector, Pvector
    """

    def __init__(self, normal, z=0, frame=None):
        self.normal = normal
        self.z = z
        self.frame = _default_frame(frame)

    def to_ecef_vector(self):
        """
        Returns position as ECEFvector object.

        See also
        --------
        ECEFvector
        """
        frame = self.frame
        a, f, R_Ee = frame.a, frame.f, frame.R_Ee
        pvector = n_EB_E2p_EB_E(self.normal, depth=self.z, a=a, f=f, R_Ee=R_Ee)
        return ECEFvector(pvector, self.frame)

    def to_geo_point(self):
        """
        Returns position as GeoPoint object.

        See also
        --------
        GeoPoint
        """
        latitude, longitude = n_E2lat_lon(self.normal, R_Ee=self.frame.R_Ee)
        return GeoPoint(latitude, longitude, self.z, self.frame)

    def to_nvector(self):
        """
        Returns position as Nvector object.

        See also
        --------
        Nvector
        """
        return self

    delta_to = _delta

    def unit(self):
        """Normalizes self to unit vector(s)"""
        self.normal = unit(self.normal)

    @deprecate
    def mean_horizontal_position(self):
        """Deprecated. Use mean instead"""
        return self.mean()

    def mean(self):
        """
        Returns mean position of the n-vectors.
        """
        average_nvector = mean_horizontal_position(self.normal)
        return self.frame.Nvector(average_nvector, z=np.mean(self.z))

    def _is_equal_to(self, other, rtol=1e-12, atol=1e-14):
        options = dict(rtol=rtol, atol=atol)
        return (np.allclose(self.normal, other.normal, **options)
                and np.allclose(self.z, other.z, **options)
                and self.frame == other.frame)

    def __add__(self, other):
        _check_frames(self, other)
        return self.frame.Nvector(self.normal + other.normal, self.z + other.z)

    def __sub__(self, other):
        _check_frames(self, other)
        return self.frame.Nvector(self.normal - other.normal,
                                  self.z - other.z)

    def __neg__(self):
        return self.frame.Nvector(-self.normal, -self.z)

    def __mul__(self, scalar):
        """elementwise multiplication"""

        if not isinstance(scalar, Nvector):
            return self.frame.Nvector(self.normal * scalar, self.z * scalar)
        raise NotImplementedError('Only scalar multiplication is implemented')

    def __div__(self, scalar):
        """elementwise division"""
        if not isinstance(scalar, Nvector):
            return self.frame.Nvector(self.normal / scalar, self.z / scalar)
        raise NotImplementedError('Only scalar division is implemented')

    __truediv__ = __div__
    __radd__ = __add__
    __rmul__ = __mul__


class Pvector(_Common):
    """
    Cartesian position vector in relative to a frame.
    """
    def __init__(self, pvector, frame):
        self.pvector = pvector
        self.frame = frame

    def _is_equal_to(self, other, rtol=1e-12, atol=1e-14):
        options = dict(rtol=rtol, atol=atol)
        return (np.allclose(self.pvector, other.pvector, **options)
                and self.frame == other.frame)

    def to_ecef_vector(self):
        """
        Returns position as ECEFvector object.

        See also
        --------
        ECEFvector
        """

        n_frame = self.frame
        p_AB_N = self.pvector
        # p_AB_E = np.dot(n_frame.R_EN, p_AB_N)
        p_AB_E = mdot(n_frame.R_EN, p_AB_N[:, None, ...]).reshape(3, -1)
        return ECEFvector(p_AB_E, frame=n_frame.nvector.frame)

    def to_nvector(self):
        """
        Returns position as Nvector object.

        See also
        --------
        Nvector
        """

        return self.to_ecef_vector().to_nvector()

    def to_geo_point(self):
        """
        Returns position as GeoPoint object.

        See also
        --------
        GeoPoint
        """
        return self.to_ecef_vector().to_geo_point()

    delta_to = _delta

    @property
    def length(self):
        "Length of the pvector."
        return norm(self.pvector, axis=0)

    @property
    def azimuth_deg(self):
        """Azimuth in degree."""
        return deg(self.azimuth)

    @property
    def azimuth(self):
        """Azimuth in radian"""
        p_AB_N = self.pvector
        return np.arctan2(p_AB_N[1], p_AB_N[0])

    @property
    def elevation_deg(self):
        """Elevation in degree."""
        return deg(self.elevation)

    @property
    def elevation(self):
        """Elevation in radian."""
        z = self.pvector[2]
        return np.arcsin(z / self.length)


class ECEFvector(Pvector):
    __doc__ = """
    Geographical position given as Cartesian position vector in frame E

    Parameters
    ----------
    pvector: 3 x n array
        Cartesian position vector(s) [m] from E to B, decomposed in E.
    frame: FrameE object
        reference ellipsoid. The default ellipsoid model used is WGS84, but
        other ellipsoids/spheres might be specified.

    Notes
    -----
    The position of B (typically body) relative to E (typically Earth) is
    given into this function as p-vector, p_EB_E relative to the center of the
    frame.

    Examples
    --------

    {0}

    See also
    --------
    GeoPoint, ECEFvector, Pvector
    """.format(_examples.get_examples([3, 4]))

    def __init__(self, pvector, frame=None):
        super(ECEFvector, self).__init__(pvector, _default_frame(frame))

    def change_frame(self, frame):
        """
        Converts to Cartesian position vector in another frame

        Parameters
        ----------
        frame: FrameB, FrameN or frameL object
            local frame M used to convert p_AB_E (position vector from A to B,
            decomposed in E) to a cartesian vector p_AB_M decomposed in M.

        Returns
        -------
        p_AB_M:  Pvector object
            position vector from A to B, decomposed in frame M.

        See also
        --------
        n_EB_E2p_EB_E,
        n_EA_E_and_p_AB_E2n_EB_E,
        n_EA_E_and_n_EB_E2p_AB_E.
        """
        _check_frames(self, frame.nvector)
        p_AB_E = self.pvector
        p_AB_N = mdot(np.rollaxis(frame.R_EN, 1, 0), p_AB_E[:, None, ...])
        return Pvector(p_AB_N.reshape(3, -1), frame=frame)

    def to_ecef_vector(self):
        return self

    def to_geo_point(self):
        """
        Returns position as GeoPoint object.

        See also
        --------
        GeoPoint
        """
        return self.to_nvector().to_geo_point()

    def to_nvector(self):
        """
        Returns position as Nvector object.

        See also
        --------
        Nvector
        """
        frame = self.frame
        p_EB_E = self.pvector
        R_Ee = frame.R_Ee
        n_EB_E, depth = p_EB_E2n_EB_E(p_EB_E, a=frame.a, f=frame.f, R_Ee=R_Ee)
        return Nvector(n_EB_E, z=depth, frame=frame)

    delta_to = _delta

    def __add__(self, other):
        _check_frames(self, other)
        return ECEFvector(self.pvector + other.pvector, self.frame)

    def __sub__(self, other):
        _check_frames(self, other)
        return ECEFvector(self.pvector - other.pvector, self.frame)

    def __neg__(self):
        return ECEFvector(-self.pvector, self.frame)


class GeoPath(object):
    __doc__ = """
    Geographical path between two positions in Frame E

    Parameters
    ----------
     point_a, point_b: Nvector, GeoPoint or ECEFvector objects
        The path is defined by the line between point A and B, decomposed
        in E.

    Notes
    -----
    Please note that either point A or point B or both might be a vector of points.
    In this case the GeoPath instance represents all the paths between the points
    of A and the corresponding points of B.

    Examples
    --------

    {0}
    """.format(_examples.get_examples([5, 6, 9, 10]))

    def __init__(self, point_a, point_b):
        self.point_a = point_a
        self.point_b = point_b

    @property
    def positionA(self):
        """Deprecated use point_a instead"""
        warnings.warn('Deprecated use point_a instead', category=DeprecationWarning, stacklevel=2)
        return self.point_a


    @property
    def positionB(self):
        """Deprecated use point_a instead"""
        warnings.warn('Deprecated use point_b instead', category=DeprecationWarning, stacklevel=2)
        return self.point_b

    def nvectors(self):
        """ Returns point_a and point_b as n-vectors
        """
        return self.point_a.to_nvector(), self.point_b.to_nvector()

    def geo_points(self):
        """ Returns point_a and point_b as geo-points
        """
        return self.point_a.to_geo_point(), self.point_b.to_geo_point()

    def ecef_vectors(self):
        """ Returns point_a and point_b as  ECEF-vectors
        """
        return self.point_a.to_ecef_vector(), self.point_b.to_ecef_vector()

    def nvector_normals(self):
        """Returns nvector normals for position a and b"""
        nvector_a, nvector_b = self.nvectors()
        return nvector_a.normal, nvector_b.normal

    def _get_average_radius(self):
        # n1 = self.point_a.to_nvector()
        # n2 = self.point_b.to_nvector()
        # n_EM_E = mean_horizontal_position(np.hstack((n1.normal, n2.normal)))
        # p_EM_E = n1.frame.Nvector(n_EM_E).to_ecef_vector()
        # radius = norm(p_EM_E.pvector, axis=0)
        # radius = (norm(p_E1_E.pvector, axis=0) +
        #           norm(p_E2_E.pvector, axis=0)) / 2
        p_E1_E, p_E2_E = self.ecef_vectors()
        radius = (p_E1_E.length + p_E2_E.length) / 2
        return radius

    def cross_track_distance(self, point, method='greatcircle', radius=None):
        """
        Returns cross track distance from path to point.

        Parameters
        ----------
        point: GeoPoint, Nvector or ECEFvector object
            position to measure the cross track distance to.
        radius: real scalar
            radius of sphere in [m]. Default is the average height of points A and B.
        method: 'greatcircle' or 'euclidean'
            defining distance calculated.

        Returns
        -------
        distance: real scalar or vector
            distance in [m]
        """
        if radius is None:
            radius = self._get_average_radius()
        path = self.nvector_normals()
        n_c = point.to_nvector().normal
        return cross_track_distance(path, n_c, method=method, radius=radius)

    def track_distance(self, method='greatcircle', radius=None):
        """
        Returns the path distance computed at the average height.

        Parameters
        ----------
        method:  'greatcircle',  'euclidean' or 'ellipsoidal'
            defining distance calculated.
        radius: real scalar
            radius of sphere. Default is the average height of points A and B
        """
        if method[:2] in {'ex', 'el'}:  # exact or ellipsoidal
            point_a, point_b = self.geo_points()
            s_ab, _angle1, _angle2 = point_a.distance_and_azimuth(point_b)
            return s_ab
        if radius is None:
            radius = self._get_average_radius()
        n_EA_E, n_EB_E = self.nvector_normals()

        if method[:2] == "eu":
            return euclidean_distance(n_EA_E, n_EB_E, radius)
        return great_circle_distance(n_EA_E, n_EB_E, radius)

    @deprecate
    def intersection(self, path):
        """
        Deprecated use intersect instead
        """
        return self.intersect(path)

    def intersect(self, path):
        """
        Returns the intersection(s) between the great circles of the two paths

        Parameters
        ----------
        path: GeoPath object
            path to intersect

        Returns
        -------
        point: GeoPoint
            point of intersection between paths
        """
        frame = self.point_a.frame
        path_a = self.nvector_normals()
        path_b = path.nvector_normals()
        n_EC_E = intersect(path_a, path_b)
        return frame.Nvector(n_EC_E)

    def _on_ellipsoid_path(self, point, rtol=1e-6, atol=1e-8):
        point_a, point_b = self.geo_points()
        distanceAB, azimuth_ab, _azi_ba = point_a.distance_and_azimuth(point_b)
        distanceAC, azimuth_ac, _azi_ca = point_a.distance_and_azimuth(point)
        return (np.isclose(distanceAC, 0, rtol=rtol, atol=atol)
                | ((distanceAB >= distanceAC)
                   & np.isclose(azimuth_ac, azimuth_ab, rtol=rtol, atol=atol)))

    def on_great_circle(self, point, rtol=1e-6, atol=1e-8):
        """Returns True if point is on the great circle."""
        distance = np.abs(self.cross_track_distance(point))
        return np.isclose(0, distance, rtol, atol)

    def _on_great_circle_path(self, point, radius=None, rtol=1e-6, atol=1e-8):
        if radius is None:
            radius = self._get_average_radius()
        path = self.nvector_normals()
        point_c = point.to_nvector().normal
        return on_great_circle_path(path, point_c, radius, rtol, atol)
# pointA, pointB = path
# p_ba = pointB - pointA
# p_ca = point_c - pointA
# is_parallell = np.all(np.isclose(np.cross(p_ba, p_ca, axis=0), 0,
#                                  rtol, atol), axis=0)
# same_direction = (np.all(np.sign(np.dot(p_ba.T, p_ca)) == 1, axis=0) &
#                   np.all(np.sign(p_ba) == np.sign(p_ca), axis=0))
# return (is_parallell & same_direction &
#          norm(p_ba, axis=0) >= norm(p_ca, axis=0))

    def on_path(self, point, method='greatcircle', rtol=1e-6, atol=1e-8):
        """
        Returns True if point is on the path between A and B

        Parameters
        ----------
        point : Nvector, GeoPoint or ECEFvector
            point to test
        method: 'greatcircle' or 'ellipsoid'
            defining the path.

        Examples
        --------
        >>> import nvector as nv
        >>> wgs84 = nv.FrameE(name='WGS84')
        >>> pointA = wgs84.GeoPoint(89, 0, degrees=True)
        >>> pointB = wgs84.GeoPoint(80, 0, degrees=True)
        >>> path = nv.GeoPath(pointA, pointB)
        >>> pointC = path.interpolate(0.6).to_geo_point()
        >>> np.allclose(path.on_path(pointC), True)
        True

        >>> pointD = path.interpolate(1.000000001).to_geo_point()
        >>> np.allclose(path.on_path(pointD), False)
        True
        >>> pointE = wgs84.GeoPoint(85, 0.0001, degrees=True)
        >>> np.allclose(path.on_path(pointE), False)
        True
        >>> pointC = path.interpolate(-2).to_geo_point()
        >>> np.allclose(path.on_path(pointC), False)
        True
        >>> path = nv.GeoPath(pointC, pointA)

        """
        if method[:2] in {'ex', 'el'}: # exact or ellipsoid
            return self._on_ellipsoid_path(point, rtol=rtol, atol=atol)
        return self._on_great_circle_path(point, rtol=rtol, atol=atol)

    def closest_point_on_great_circle(self, point):
        """
        Returns closest point on great circle path to the point.

        Parameters
        ----------
        point: GeoPoint
            point of intersection between paths

        Returns
        -------
        closest_point: GeoPoint
            closest point on path.

        Example
        -------
        >>> import nvector as nv
        >>> wgs84 = nv.FrameE(name='WGS84')
        >>> point_a = wgs84.GeoPoint(51., 1., degrees=True)
        >>> point_b = wgs84.GeoPoint(51., 2., degrees=True)
        >>> point_c = wgs84.GeoPoint(51., 2.9, degrees=True)
        >>> path = nv.GeoPath(point_a, point_b)
        >>> point = path.closest_point_on_great_circle(point_c)
        >>> path.on_path(point)[0]
        False
        >>> np.allclose((point.latitude_deg, point.longitude_deg),
        ...             ([50.99270338], [2.89977984]))
        True

        >>> np.allclose(GeoPath(point_c, point).track_distance(),  810.76312076)
        True

        """

        nvector = point.to_nvector()

        path = self.nvector_normals()
        n = closest_point_on_great_circle(path, nvector.normal)

        return nvector.frame.Nvector(n, nvector.z).to_geo_point()

    def closest_point_on_path(self, point):
        """
        Returns closest point on great circle path segment to the point.

        If the point is within the extent of the segment, the point returned is
        on the segment path otherwise, it is the closest endpoint defining the
        path segment.

        Parameters
        ----------
        point: GeoPoint
            point of intersection between paths

        Returns
        -------
        closest_point: GeoPoint
            closest point on path segment.

        Example
        -------
        >>> import nvector as nv
        >>> wgs84 = nv.FrameE(name='WGS84')
        >>> pointA = wgs84.GeoPoint(51., 1., degrees=True)
        >>> pointB = wgs84.GeoPoint(51., 2., degrees=True)
        >>> pointC = wgs84.GeoPoint(51., 1.9, degrees=True)
        >>> path = nv.GeoPath(pointA, pointB)
        >>> point = path.closest_point_on_path(pointC)
        >>> np.allclose((point.latitude_deg, point.longitude_deg),
        ...             ([51.00038411380564], [1.900003311624411]))
        True
        >>> np.allclose(GeoPath(pointC, point).track_distance(),  42.67368351)
        True
        >>> pointD = wgs84.GeoPoint(51.0, 2.1, degrees=True)
        >>> pointE = path.closest_point_on_path(pointD) # 51.0000, 002.0000
        >>> pointE.latitude_deg, pointE.longitude_deg
        (51.0, 2.0)
        """
        point_c = self.closest_point_on_great_circle(point)
        if self.on_path(point_c):
            return point_c
        n0 = point.to_nvector().normal
        n1, n2 = self.nvector_normals()
        radius = self._get_average_radius()
        d1 = great_circle_distance(n1, n0, radius)
        d2 = great_circle_distance(n2, n0, radius)
        if d1 < d2:
            return self.point_a.to_geo_point()
        return self.point_b.to_geo_point()

    def interpolate(self, ti):
        """
        Returns the interpolated point along the path

        Parameters
        ----------
        ti: real scalar
            interpolation time assuming position A and B is at t0=0 and t1=1,
            respectively.

        Returns
        -------
        point: Nvector
            point of interpolation along path
        """
        point_a, point_b = self.nvectors()
        point_c = point_a + (point_b - point_a) * ti
        point_c.normal = unit(point_c.normal, norm_zero_vector=np.nan)
        return point_c


class FrameE(_Common):

    """
    Earth-fixed frame

    Parameters
    ----------
    a: real scalar, default WGS-84 ellipsoid.
        Semi-major axis of the Earth ellipsoid given in [m].
    f: real scalar, default WGS-84 ellipsoid.
        Flattening [no unit] of the Earth ellipsoid. If f==0 then spherical
        Earth with radius a is used in stead of WGS-84.
    name: string
        defining the default ellipsoid.
    axes: 'e' or 'E'
        defines axes orientation of E frame. Default is axes='e' which means
        that the orientation of the axis is such that:
        z-axis -> North Pole, x-axis -> Latitude=Longitude=0.

    Notes
    -----
    The frame is Earth-fixed (rotates and moves with the Earth) where the
    origin coincides with Earth's centre (geometrical centre of ellipsoid
    model).

    See also
    --------
    FrameN, FrameL, FrameB
    """

    def __init__(self, a=None, f=None, name='WGS84', axes='e'):
        if a is None or f is None:
            a, f, _full_name = select_ellipsoid(name)
        self.a = a
        self.f = f
        self.name = name
        self.R_Ee = E_rotation(axes)

    def _is_equal_to(self, other, rtol=1e-12, atol=1e-14):
        return (np.allclose(self.a, other.a, rtol=rtol, atol=atol)
                and np.allclose(self.f, other.f, rtol=rtol, atol=atol)
                and np.allclose(self.R_Ee, other.R_Ee, rtol=rtol, atol=atol))


    def inverse(self, lat_a, lon_a, lat_b, lon_b, z=0, long_unroll=False, degrees=False):
        """
        Returns ellipsoidal distance between positions as well as the direction.

        Parameters
        ----------
        lat_a, lon_a:  real scalars or vectors.
            Latitude and longitude of position a.
        lat_b, lon_b:  real scalars or vectors.
            Latitude and longitude of position b.
        z : real scalar or vector
            depth relative to Earth ellipsoid.
        degrees: bool
            angles are given in degrees if True otherwise in radians.

        Returns
        -------
        s_ab: real scalar or vector
            ellipsoidal distance [m] between position A and B.
        azimuth_a, azimuth_b:  real scalars or vectors.
            direction [rad or deg] of line at position A and B relative to
            North, respectively.

        References
        ----------
        C. F. F. Karney, Algorithms for geodesics, J. Geodesy 87(1), 43-55

        `geographiclib <https://pypi.python.org/pypi/geographiclib>`_

        """
        if not degrees:
            lat_a, lon_a, lat_b, lon_b = deg(lat_a, lon_a, lat_b, lon_b)

        lat_a, lon_a, lat_b, lon_b, z = np.broadcast_arrays(lat_a, lon_a, lat_b, lon_b, z)
        fun = partial(self._inverse,  outmask=self._outmask(long_unroll))
        items = zip(*np.atleast_1d(lat_a, lon_a, lat_b, lon_b, z))
        sab, azia, azib = np.transpose([fun(lat_ai, lon_ai, lat_bi, lon_bi, z=zi)
                                        for lat_ai, lon_ai, lat_bi, lon_bi, zi in items])

        if not degrees:
            s_ab, azimuth_a, azimuth_b = sab.ravel(), rad(azia.ravel()), rad(azib.ravel())
        else:
            s_ab, azimuth_a, azimuth_b = sab.ravel(), azia.ravel(), azib.ravel()

        if np.ndim(lat_a) == 0:
            return s_ab[0], azimuth_a[0], azimuth_b[0]
        return s_ab, azimuth_a, azimuth_b

    def _inverse(self, lat_a, lon_a, lat_b, lon_b, z=0, outmask=None):
        geo = _Geodesic(self.a - z, self.f)
        result = geo.Inverse(lat_a, lon_a, lat_b, lon_b, outmask=outmask)
        return result['s12'], result['azi1'], result['azi2']


    def _outmask(self, long_unroll):
        if long_unroll:
            return _Geodesic.STANDARD | _Geodesic.LONG_UNROLL
        return _Geodesic.STANDARD

    def direct(self, lat_a, lon_a, azimuth, distance, z=0, long_unroll=False, degrees=False):
        """
        Returns position B computed from position A, distance and azimuth.

        Parameters
        ----------
        lat_a, lon_a:  real scalars or vectors of length n.
            Latitude and longitude [rad or deg] of position a.
        azimuth_a:  real scalar or vector of length n.
            azimuth [rad or deg] of line at position A.
        distance: real scalar or vector of length n.
            ellipsoidal distance [m] between position A and B.
        z: real scalar or vector of length n.
            depth relative to Earth ellipsoid.
        degrees: bool
            angles are given in degrees if True otherwise in radians.

        Returns
        -------
        lat_b, lon_b:  real scalars or vectors of length n
            Latitude and longitude of position b.
        azimuth_b: real scalar or vector of length n.
            azimuth [rad or deg] of line at position B.

        References
        ----------
        C. F. F. Karney, Algorithms for geodesics, J. Geodesy 87(1), 43-55

        `geographiclib <https://pypi.python.org/pypi/geographiclib>`_
        """
        if not degrees:
            lat_a, lon_a, azimuth = deg(lat_a, lon_a, azimuth)

        lat_a, lon_a, azimuth, distance, z = np.broadcast_arrays(lat_a, lon_a, azimuth, distance, z)
        fun = partial(self._direct,  outmask=self._outmask(long_unroll))

        items = zip(*np.atleast_1d(lat_a, lon_a, azimuth, distance, z))
        lab, lob, azib = np.transpose([fun(lat_ai, lon_ai, azimuthi, distancei, z=zi)
                                              for lat_ai, lon_ai, azimuthi, distancei, zi in items])
        if not degrees:
            latb, lonb, azimuth_b = rad(lab.ravel(), lob.ravel(), azib.ravel())
        else:
            latb, lonb, azimuth_b = lab.ravel(), lob.ravel(), azib.ravel()
        if np.ndim(lat_a) == 0:
            return latb[0], lonb[0], azimuth_b[0]
        return latb, lonb, azimuth_b

    def _direct(self, lat_a, lon_a, azimuth, distance, z=0, outmask=None):
        geo = _Geodesic(self.a - z, self.f)
        result = geo.Direct(lat_a, lon_a, azimuth, distance, outmask=outmask)
        latb, lonb, azimuth_b = result['lat2'], result['lon2'], result['azi2']
        return latb, lonb, azimuth_b

    @use_docstring_from(GeoPoint)
    def GeoPoint(self, *args, **kwds):
        kwds.pop('frame', None)
        return GeoPoint(*args, frame=self, **kwds)

    @use_docstring_from(Nvector)
    def Nvector(self, *args, **kwds):
        kwds.pop('frame', None)
        return Nvector(*args, frame=self, **kwds)

    @use_docstring_from(ECEFvector)
    def ECEFvector(self, *args, **kwds):
        kwds.pop('frame', None)
        return ECEFvector(*args, frame=self, **kwds)


class _LocalFrame(_Common):

    def Pvector(self, pvector):
        """Returns Pvector relative to the local frame."""
        return Pvector(pvector, frame=self)


class FrameN(_LocalFrame):
    __doc__ = """
    North-East-Down frame

    Parameters
    ----------
    position: ECEFvector, GeoPoint or Nvector object
        position of the vehicle (B) which also defines the origin of the local
        frame N. The origin is directly beneath or above the vehicle (B), at
        Earth's surface (surface of ellipsoid model).

    Notes
    -----
    The Cartesian frame is local and oriented North-East-Down, i.e.,
    the x-axis points towards north, the y-axis points towards east (both are
    horizontal), and the z-axis is pointing down.

    When moving relative to the Earth, the frame rotates about its z-axis
    to allow the x-axis to always point towards north. When getting close
    to the poles this rotation rate will increase, being infinite at the
    poles. The poles are thus singularities and the direction of the
    x- and y-axes are not defined here. Hence, this coordinate frame is
    NOT SUITABLE for general calculations.

    Examples
    --------

    {0}

    See also
    --------
    FrameE, FrameL, FrameB
    """.format(_examples.get_examples([1]))

    def __init__(self, position):
        nvector = position.to_nvector()
        self.nvector = Nvector(nvector.normal, z=0, frame=nvector.frame)

    @property
    def R_EN(self):
        """Rotation matrix to go between E and N frame"""
        nvector = self.nvector
        return n_E2R_EN(nvector.normal, nvector.frame.R_Ee)

    def _is_equal_to(self, other, rtol=1e-12, atol=1e-14):
        return (np.allclose(self.R_EN, other.R_EN, rtol=rtol, atol=atol)
                and self.nvector == other.nvector)


class FrameL(FrameN):

    """
    Local level, Wander azimuth frame

    Parameters
    ----------
    position: ECEFvector, GeoPoint or Nvector object
        position of the vehicle (B) which also defines the origin of the local
        frame L. The origin is directly beneath or above the vehicle (B), at
        Earth's surface (surface of ellipsoid model).
    wander_azimuth: real scalar
        Angle [rad] between the x-axis of L and the north direction.

    Notes
    -----
    The Cartesian frame is local and oriented Wander-azimuth-Down. This means
    that the z-axis is pointing down. Initially, the x-axis points towards
    north, and the y-axis points towards east, but as the vehicle moves they
    are not rotating about the z-axis (their angular velocity relative to the
    Earth has zero component along the z-axis).

    (Note: Any initial horizontal direction of the x- and y-axes is valid
    for L, but if the initial position is outside the poles, north and east
    are usually chosen for convenience.)

    The L-frame is equal to the N-frame except for the rotation about the
    z-axis, which is always zero for this frame (relative to E). Hence, at
    a given time, the only difference between the frames is an angle
    between the x-axis of L and the north direction; this angle is called
    the wander azimuth angle. The L-frame is well suited for general
    calculations, as it is non-singular.

    See also
    --------
    FrameE, FrameN, FrameB
    """

    def __init__(self, position, wander_azimuth=0):
        super(FrameL, self).__init__(position)
        self.wander_azimuth = wander_azimuth

    @property
    def R_EN(self):
        """Rotation matrix to go between E and L frame"""
        n_EA_E = self.nvector.normal
        R_Ee = self.nvector.frame.R_Ee
        return n_E_and_wa2R_EL(n_EA_E, self.wander_azimuth, R_Ee=R_Ee)


class FrameB(_LocalFrame):
    __doc__ = """
    Body frame

    Parameters
    ----------
    position: ECEFvector, GeoPoint or Nvector object
        position of the vehicle's reference point which also coincides with
        the origin of the frame B.
    yaw, pitch, roll: real scalars
        defining the orientation of frame B in [deg] or [rad].
    degrees : bool
        if True yaw, pitch, roll are given in degrees otherwise in radians

    Notes
    -----
    The frame is fixed to the vehicle where the x-axis points forward, the
    y-axis to the right (starboard) and the z-axis in the vehicle's down
    direction.

    Examples
    --------

    {0}

    See also
    --------
    FrameE, FrameL, FrameN
    """.format(_examples.get_examples([2]))

    def __init__(self, position, yaw=0, pitch=0, roll=0, degrees=False):
        self.nvector = position.to_nvector()
        if degrees:
            yaw, pitch, roll = rad(yaw), rad(pitch), rad(roll)
        self.yaw = yaw
        self.pitch = pitch
        self.roll = roll

    @property
    def R_EN(self):
        """Rotation matrix to go between E and B frame"""
        R_NB = zyx2R(self.yaw, self.pitch, self.roll)
        n_EB_E = self.nvector.normal
        R_EN = n_E2R_EN(n_EB_E, self.nvector.frame.R_Ee)
        return mdot(R_EN, R_NB)  # rotation matrix

    def _is_equal_to(self, other, rtol=1e-12, atol=1e-14):
        return (np.allclose(self.yaw, other.yaw, rtol=rtol, atol=atol)
                and np.allclose(self.pitch, other.pitch, rtol=rtol, atol=atol)
                and np.allclose(self.roll, other.roll, rtol=rtol, atol=atol)
                and np.allclose(self.R_EN, other.R_EN, rtol=rtol, atol=atol)
                and self.nvector == other.nvector)


def _check_frames(self, other):
    if not self.frame == other.frame:
        raise ValueError('Frames are unequal')


def _default_frame(frame):
    if frame is None:
        return FrameE()
    return frame


def example():
    import nvector as nv
    wgs84 = nv.FrameE(name='WGS84')
    pointA = wgs84.GeoPoint(latitude=81, longitude=0, degrees=True)
    pointB = wgs84.GeoPoint(latitude=80, longitude=0, degrees=True)
    path = nv.GeoPath(pointA, pointB)
    for point in [pointA, pointB]:
        print(np.allclose(path.on_path(point, method='exact'), True))

    wgs84 = nv.FrameE(name='WGS84')
    pointA = wgs84.GeoPoint(latitude=79, longitude=0, degrees=True)
    pointB = wgs84.GeoPoint(latitude=80, longitude=0, degrees=True)
    path = nv.GeoPath(pointA, pointB)
    for point in [pointA, pointB]:
        print(np.allclose(path.on_path(point, method='exact'), True))


if __name__ == "__main__":
    example()
    # test_docstrings(__file__)
