
# -*- coding: utf-8 -*-

u'''(INTERNAL) Private base classes for elliposiodal, spherical and N-/vectorial
C{Cartesian}s.

After I{(C) Chris Veness 2011-2015} published under the same MIT Licence**,
see U{https://www.Movable-Type.co.UK/scripts/latlong.html},
U{https://www.Movable-Type.co.UK/scripts/latlong-vectors.html} and
U{https://www.Movable-Type.co.UK/scripts/geodesy/docs/latlon-ellipsoidal.js.html}..
'''

# from pygeodesy.basics import _xinstanceof  # from .datums
from pygeodesy.constants import EPS0, isnear0, _1_0, _N_1_0, _2_0, _4_0, _6_0
from pygeodesy.datums import Datum, _spherical_datum, _WGS84, _xinstanceof
from pygeodesy.errors import _IsnotError, _ValueError, _xdatum, _xkwds
from pygeodesy.fmath import cbrt, hypot_, hypot2, sqrt  # hypot
from pygeodesy.fsums import Fmt, fsum_
from pygeodesy.interns import NN, _COMMASPACE_, _height_, _not_
from pygeodesy.interns import _ellipsoidal_, _spherical_  # PYCHOK used!
from pygeodesy.lazily import _ALL_DOCS, _ALL_LAZY, _ALL_MODS as _MODS
from pygeodesy.namedTuples import Bearing2Tuple, Height, LatLon4Tuple, Vector4Tuple, \
                                  Vector3Tuple  # PYCHOK .ellipsoidal-, .sphericalBase
from pygeodesy.props import deprecated_method, Property, Property_RO, \
                            property_doc_, _update_all
# from pygeodesy.resections impoty cassini, collins5, pierlot, tienstra7
# from pygeodesy.streprs import Fmt  # from .fsums
# from pygeodesy.units import Height  # from .namedTuples
from pygeodesy.vector3d import Vector3d, _xyzhdn3

# from math import sqrt  # from .fmath

__all__ = _ALL_LAZY.cartesianBase
__version__ = '22.11.03'


class CartesianBase(Vector3d):
    '''(INTERNAL) Base class for ellipsoidal and spherical C{Cartesian}.
    '''
    _datum  = None  # L{Datum}, to be overriden
    _height = None  # height (L{Height}), set or approximated

    def __init__(self, x_xyz, y=None, z=None, datum=None, ll=None, name=NN):
        '''New C{Cartesian...}.

           @arg x_xyz: Cartesian X coordinate (C{scalar}) or a C{Cartesian},
                       L{Ecef9Tuple}, L{Vector3Tuple} or L{Vector4Tuple}.
           @kwarg y: Cartesian Y coordinate (C{scalar}), ignored if B{C{x_xyz}}
                     is not C{scalar}, otherwise same units as B{C{x_xyz}}.
           @kwarg z: Cartesian Z coordinate (C{scalar}), ignored if B{C{x_xyz}}
                     is not C{scalar}, otherwise same units as B{C{x_xyz}}.
           @kwarg datum: Optional datum (L{Datum}, L{Ellipsoid}, L{Ellipsoid2}
                         or L{a_f2Tuple}).
           @kwarg ll: Optional, original latlon (C{LatLon}).
           @kwarg name: Optional name (C{str}).

           @raise TypeError: Non-scalar B{C{x_xyz}}, B{C{y}} or B{C{z}}
                             coordinate or B{C{x_xyz}} not an L{Ecef9Tuple},
                             L{Vector3Tuple} or L{Vector4Tuple}.
        '''
        h, d, n = _xyzhdn3(x_xyz, None, datum, ll)
        Vector3d.__init__(self, x_xyz, y=y, z=z, ll=ll, name=name or n)
        if h is not None:
            self._height = Height(h)
        if d is not None:
            self.datum = d

#   def __matmul__(self, other):  # PYCHOK Python 3.5+
#       '''Return C{NotImplemented} for C{c_ = c @ datum} and C{c_ = c @ transform}.
#       '''
#       return NotImplemented if isinstance(other, (Datum, Transform)) else \
#             _NotImplemented(self, other)

    def cassini(self, pointB, pointC, alpha, beta, useZ=False):
        '''3-Point resection between this and 2 other points using U{Cassini
           <https://NL.WikiPedia.org/wiki/Achterwaartse_insnijding>}'s method.

           @arg pointB: Second point (C{Cartesian}, L{Vector3d}, C{Vector3Tuple},
                        C{Vector4Tuple} or C{Vector2Tuple} if C{B{useZ}=False}).
           @arg pointC: Center point (C{Cartesian}, L{Vector3d}, C{Vector3Tuple},
                        C{Vector4Tuple} or C{Vector2Tuple} if C{B{useZ}=False}).
           @arg alpha: Angle subtended by triangle side C{b} from B{C{pointA}} to
                       B{C{pointC}} (C{degrees}, non-negative).
           @arg beta: Angle subtended by triangle side C{a} from B{C{pointB}} to
                      B{C{pointC}} (C{degrees}, non-negative).
           @kwarg useZ: If C{True}, use and interpolate the Z component, otherwise
                        force C{z=INT0} (C{bool}).

           @note: Typically, B{C{pointC}} is between this and B{C{pointB}}.

           @return: The survey point, an instance of this (sub-)class.

           @raise ResectionError: Near-coincident, -colinear or -concyclic points
                                  or negative or invalid B{C{alpha}} or B{C{beta}}.

           @raise TypeError: Invalid B{C{pointA}}, B{C{pointB}} or B{C{pointM}}.

           @see: U{Three Point Resection Problem<https://Dokumen.tips/documents/
                 three-point-resection-problem-introduction-kaestner-burkhardt-method.html>}
                 and function L{pygeodesy.cassini}.
        '''
        return _MODS.resections.cassini(self, pointB, pointC, alpha, beta,
                                              useZ=useZ, datum=self.datum)

    @deprecated_method
    def collins(self, pointB, pointC, alpha, beta, useZ=False):
        '''DEPRECATED, use method L{collins5}.'''
        return self.collins5(pointB, pointC, alpha, beta, useZ=useZ)

    def collins5(self, pointB, pointC, alpha, beta, useZ=False):
        '''3-Point resection between this and 2 other points using U{Collins<https://Dokumen.tips/
           documents/three-point-resection-problem-introduction-kaestner-burkhardt-method.html>}' method.

           @arg pointB: Second point (C{Cartesian}, L{Vector3d}, C{Vector3Tuple},
                        C{Vector4Tuple} or C{Vector2Tuple} if C{B{useZ}=False}).
           @arg pointC: Center point (C{Cartesian}, L{Vector3d}, C{Vector3Tuple},
                        C{Vector4Tuple} or C{Vector2Tuple} if C{B{useZ}=False}).
           @arg alpha: Angle subtended by triangle side C{b} from B{C{pointA}} to
                       B{C{pointC}} (C{degrees}, non-negative).
           @arg beta: Angle subtended by triangle side C{a} from B{C{pointB}} to
                      B{C{pointC}} (C{degrees}, non-negative).
           @kwarg useZ: If C{True}, use and interpolate the Z component, otherwise
                        force C{z=INT0} (C{bool}).

           @note: Typically, B{C{pointC}} is between this and B{C{pointB}}.

           @return: L{Collins5Tuple}C{(pointP, pointH, a, b, c)} with survey C{pointP},
                    auxiliary C{pointH}, each an instance of this (sub-)class and
                    triangle sides C{a}, C{b} and C{c}.

           @raise ResectionError: Near-coincident, -colinear or -concyclic points
                                  or negative or invalid B{C{alpha}} or B{C{beta}}.

           @raise TypeError: Invalid B{C{pointB}} or B{C{pointM}}.

           @see: U{Collins' methode<https://NL.WikiPedia.org/wiki/Achterwaartse_insnijding>}
                 and function L{pygeodesy.collins5}.
        '''
        return _MODS.resections.collins5(self, pointB, pointC, alpha, beta,
                                               useZ=useZ, datum=self.datum)

    @property_doc_(''' this cartesian's datum (L{Datum}).''')
    def datum(self):
        '''Get this cartesian's datum (L{Datum}).
        '''
        return self._datum

    @datum.setter  # PYCHOK setter!
    def datum(self, datum):
        '''Set this cartesian's C{datum} I{without conversion}
           (L{Datum}), ellipsoidal or spherical.

           @raise TypeError: The B{C{datum}} is not a L{Datum}.
        '''
        d = _spherical_datum(datum, name=self.name)
        if self._datum:  # is not None
            if self._datum.isEllipsoidal and not d.isEllipsoidal:
                raise _IsnotError(_ellipsoidal_, datum=datum)
            elif self._datum.isSpherical and not d.isSpherical:
                raise _IsnotError(_spherical_, datum=datum)
        if self._datum != d:
            _update_all(self)
            self._datum = d

    def destinationXyz(self, delta, Cartesian=None, **Cartesian_kwds):
        '''Calculate the destination using a I{local} delta from this cartesian.

           @arg delta: Local delta to the destination (L{XyzLocal}, L{Enu},
                       L{Ned} or L{Local9Tuple}).
           @kwarg Cartesian: Optional (geocentric) class to return the
                             destination or C{None}.
           @kwarg Cartesian_kwds: Optional, additional B{C{Cartesian}} keyword
                                  arguments, ignored if C{B{Cartesian} is None}.

           @return: Destination as a C{B{Cartesian}(x, y, z, **B{Cartesian_kwds})}
                    instance or if C{B{Cartesian} is None}, an L{Ecef9Tuple}C{(x, y,
                    z, lat, lon, height, C, M, datum)} with C{M=None} always.

           @raise TypeError: Invalid B{C{delta}}, B{C{Cartesian}} or
                             B{C{Cartesian_kwds}}.
        '''
        if Cartesian is None:
            r = self._ltp._local2ecef(delta, nine=True)
        else:
            r = self._ltp._local2ecef(delta, nine=False)
            r = Cartesian(*r, **_xkwds(Cartesian_kwds, datum=self.datum))
        return r._xnamed(r) if self.name else r

    @Property_RO
    def Ecef(self):
        '''Get the ECEF I{class} (L{EcefKarney}), I{lazily}.
        '''
        return _MODS.ecef.EcefKarney  # default

    @Property_RO
    def _ecef9(self):
        '''(INTERNAL) Helper for L{toEcef}, L{toLocal} and L{toLtp} (L{Ecef9Tuple}).
        '''
        return self.Ecef(self.datum, name=self.name).reverse(self, M=True)

    def hartzell(self, los=None, earth=None):
        '''Compute the intersection of a Line-Of-Sight (los) from this certesian
           Point-Of-View (pov) with this cartesian's ellipsoid surface.

           @kwarg los: Line-Of-Sight, I{direction} to earth (L{Vector3d}) or
                       C{None} to point to the ellipsoid's center.
           @kwarg earth: The earth model (L{Datum}, L{Ellipsoid}, L{Ellipsoid2},
                         L{a_f2Tuple} or C{scalar} radius in C{meter}) overriding
                         this cartesian's C{datum} ellipsoid.

           @return: The ellipsoid intersection (C{Cartesian}).

           @raise IntersectionError: Null C{pov} or B{C{los}} vector, this C{pov}
                                     is inside the ellipsoid or B{C{los}} points
                                     outside the ellipsoid or in an opposite direction.

           @raise TypeError: Invalid B{C{los}} or no B{C{datum}}.

           @see: Function C{hartzell} for further details.
        '''
        return _MODS.formy.hartzell(self, los=los, earth=earth or self.datum)

    @Property
    def height(self):
        '''Get the height (C{meter}).
        '''
        return self._height4.h if self._height is None else self._height

    @height.setter  # PYCHOK setter!
    def height(self, height):
        '''Set the height (C{meter}).

           @raise TypeError: Invalid B{C{height}} C{type}.

           @raise ValueError: Invalid B{C{height}}.
        '''
        h = Height(height)
        if self._height != h:
            _update_all(self)
            self._height = h

    @Property_RO
    def _height4(self):
        '''(INTERNAL) Get this C{height4}-tuple.
        '''
        try:
            r = self.datum.ellipsoid.height4(self, normal=True)
        except (AttributeError, ValueError):  # no datum, null cartesian,
            r = Vector4Tuple(self.x, self.y, self.z, 0, name=self.height4.__name__)
        return r

    def height4(self, earth=None, normal=True, Cartesian=None, **Cartesian_kwds):
        '''Compute the height of this cartesian above or below and the projection
           on this datum's ellipsoid surface.

           @kwarg earth: A datum, ellipsoid, triaxial ellipsoid or earth radius
                         I{overriding} this datum (L{Datum}, L{Ellipsoid},
                         L{Ellipsoid2}, L{a_f2Tuple}, L{Triaxial}, L{Triaxial_},
                         L{JacobiConformal} or C{meter}, conventionally).
           @kwarg normal: If C{True} the projection is the nearest point on the
                          ellipsoid's surface, otherwise the intersection of the
                          radial line to the center and the ellipsoid's surface.
           @kwarg Cartesian: Optional class to return the height and projection
                             (C{Cartesian}) or C{None}.
           @kwarg Cartesian_kwds: Optional, additional B{C{Cartesian}} keyword
                                  arguments, ignored if C{B{Cartesian} is None}.

           @note: Use keyword argument C{height=0} to override C{B{Cartesian}.height}
                  to {0} or any other C{scalar}, conventionally in C{meter}.

           @return: An instance of B{C{Cartesian}} or if C{B{Cartesian} is None}, a
                    L{Vector4Tuple}C{(x, y, z, h)} with the I{projection} C{x}, C{y}
                    and C{z} coordinates and height C{h} in C{meter}, conventionally.

           @raise TriaxialError: No convergence in triaxial root finding.

           @raise TypeError: Invalid B{C{earth}}.

           @see: L{Ellipsoid.height4} and L{Triaxial_.height4} for more information.
        '''
        d = self.datum if earth is None else earth
        if normal and d == self.datum:
            r =  self._height4
        elif isinstance(d, _MODS.triaxials.Triaxial_):
            r =  d.height4(self, normal=normal)
        else:
            r = _spherical_datum(d).ellipsoid.height4(self, normal=normal)
        if Cartesian is not None:
            kwds = Cartesian_kwds.copy()
            h = kwds.pop(_height_, None)
            r = Cartesian(r, **kwds)
            if h is not None:
                r.height = Height(height=h)
        return r

    @Property_RO
    def isEllipsoidal(self):
        '''Check whether this cartesian is ellipsoidal (C{bool} or C{None} if unknown).
        '''
        return self.datum.isEllipsoidal if self._datum else None

    @Property_RO
    def isSpherical(self):
        '''Check whether this cartesian is spherical (C{bool} or C{None} if unknown).
        '''
        return self.datum.isSpherical if self._datum else None

    @Property_RO
    def latlon(self):
        '''Get this cartesian's (geodetic) lat- and longitude in C{degrees} (L{LatLon2Tuple}C{(lat, lon)}).
        '''
        return self.toEcef().latlon

    @Property_RO
    def latlonheight(self):
        '''Get this cartesian's (geodetic) lat-, longitude in C{degrees} with height (L{LatLon3Tuple}C{(lat, lon, height)}).
        '''
        return self.toEcef().latlonheight

    @Property_RO
    def latlonheightdatum(self):
        '''Get this cartesian's (geodetic) lat-, longitude in C{degrees} with height and datum (L{LatLon4Tuple}C{(lat, lon, height, datum)}).
        '''
        return self.toEcef().latlonheightdatum

    @Property_RO
    def _ltp(self):
        '''(INTERNAL) Cache for L{toLtp}.
        '''
        return _MODS.ltp.Ltp(self._ecef9, ecef=self.Ecef(self.datum), name=self.name)

    @Property_RO
    def _N_vector(self):
        '''(INTERNAL) Get the (C{nvectorBase._N_vector_}).
        '''
        x, y, z, h = self._n_xyzh4(self.datum)
        return _MODS.nvectorBase._N_vector_(x, y, z, h=h, name=self.name)

    def _n_xyzh4(self, datum):
        '''(INTERNAL) Get the n-vector components as L{Vector4Tuple}.
        '''
        def _ErrorEPS0(x):
            return _ValueError(origin=self, txt=Fmt.PARENTSPACED(EPS0=x))

        _xinstanceof(Datum, datum=datum)
        # <https://www.Movable-Type.co.UK/scripts/geodesy/docs/
        #        latlon-nvector-ellipsoidal.js.html#line309>,
        # <https://GitHub.com/pbrod/nvector>/src/nvector/core.py>
        # _equation23 and <https://www.NavLab.net/nvector>
        E = datum.ellipsoid
        x, y, z = self.xyz

        # Kenneth Gade eqn 23
        p = hypot2(x, y) * E.a2_
        q = (z**2 * E.e21) * E.a2_
        r = fsum_(p, q, -E.e4) / _6_0
        s = (p * q * E.e4) / (_4_0 * r**3)
        t = cbrt(fsum_(_1_0, s, sqrt(s * (_2_0 + s))))
        if isnear0(t):
            raise _ErrorEPS0(t)

        u = r * fsum_(_1_0, t, _1_0 / t)
        v = sqrt(u**2 + E.e4 * q)
        t = v * _2_0
        if t < EPS0:  # isnear0
            raise _ErrorEPS0(t)
        w = E.e2 * fsum_(u, v, -q) / t

        k = sqrt(fsum_(u, v, w**2)) - w
        if isnear0(k):
            raise _ErrorEPS0(k)
        t = k + E.e2
        if isnear0(t):
            raise _ErrorEPS0(t)
        e = k / t
#       d = e * hypot(x, y)

#       tmp = 1 / hypot(d, z) == 1 / hypot(e * hypot(x, y), z)
        t = hypot_(x * e, y * e, z)  # == 1 / tmp
        if t < EPS0:  # isnear0
            raise _ErrorEPS0(t)
        h = fsum_(k, E.e2, _N_1_0) / k * t
        s = e / t  # == e * tmp
        return Vector4Tuple(x * s, y * s, z / t, h, name=self.name)

    @Property_RO
    def philam(self):
        '''Get this cartesian's (geodetic) lat- and longitude in C{radians} (L{PhiLam2Tuple}C{(phi, lam)}).
        '''
        return self.toEcef().philam

    @Property_RO
    def philamheight(self):
        '''Get this cartesian's (geodetic) lat-, longitude in C{radians} with height (L{PhiLam3Tuple}C{(phi, lam, height)}).
        '''
        return self.toEcef().philamheight

    @Property_RO
    def philamheightdatum(self):
        '''Get this cartesian's (geodetic) lat-, longitude in C{radians} with height and datum (L{PhiLam4Tuple}C{(phi, lam, height, datum)}).
        '''
        return self.toEcef().philamheightdatum

    def pierlot(self, point2, point3, alpha12, alpha23, useZ=False):
        '''3-Point resection between this and two other points using U{Pierlot
           <http://www.Telecom.ULg.ac.Be/triangulation>}'s method C{ToTal}.

           @arg point2: Second point (C{Cartesian}, L{Vector3d}, C{Vector3Tuple},
                        C{Vector4Tuple} or C{Vector2Tuple} if C{B{useZ}=False}).
           @arg point3: Third point (C{Cartesian}, L{Vector3d}, C{Vector3Tuple},
                        C{Vector4Tuple} or C{Vector2Tuple} if C{B{useZ}=False}).
           @arg alpha12: Angle subtended from this point to B{C{point2}} (C{degrees}).
           @arg alpha23: Angle subtended from B{C{point2}} to B{C{point3}} (C{degrees}).
           @kwarg useZ: If C{True}, interpolate the Z component, otherwise use C{z=INT0}
                        (C{bool}).

           @note: This point, B{C{point2}} and B{C{point3}} are ordered counter-clockwise.

           @return: The survey (or robot) point, an instance of this (sub-)class.

           @raise ResectionError: Near-coincident, -colinear or -concyclic points
                                  or invalid B{C{alpha12}} or B{C{alpha23}}.

           @raise TypeError: Invalid B{C{point2}} or B{C{point3}}.

           @see: U{V. Pierlot, M. Van Droogenbroeck, "A New Three Object Triangulation
                 Algorithm for Mobile Robot Positioning"<https://ORBi.ULiege.Be/
                 bitstream/2268/157469/1/Pierlot2014ANewThree.pdf>}, U{18 Triangulation
                 Algorithms for 2D Positioning (also known as the Resection Problem)
                 <http://www.Telecom.ULg.ac.Be/triangulation>} and functions
                 L{pygeodesy.pierlot}.
        '''
        return _MODS.resections.pierlot(self, point2, point3, alpha12, alpha23,
                                              useZ=useZ, datum=self.datum)

    @deprecated_method
    def tienstra(self, pointB, pointC, alpha, beta=None, gamma=None, useZ=False):
        '''DEPRECATED, use method L{tienstra7}.'''
        return self.tienstra7(pointB, pointC, alpha, beta=beta, gamma=gamma, useZ=useZ)

    def tienstra7(self, pointB, pointC, alpha, beta=None, gamma=None, useZ=False):
        '''3-Point resection between this and two other points using U{Tienstra
           <https://WikiPedia.org/wiki/Tienstra_formula>}'s formula.

           @arg pointB: Second point (C{Cartesian}, L{Vector3d}, C{Vector3Tuple}, C{Vector4Tuple} or
                        C{Vector2Tuple} if C{B{useZ}=False}).
           @arg pointC: Third point (C{Cartesian}, L{Vector3d}, C{Vector3Tuple}, C{Vector4Tuple} or
                        C{Vector2Tuple} if C{B{useZ}=False}).
           @arg alpha: Angle subtended by triangle side C{a} from B{C{pointB}} to B{C{pointC}} (C{degrees},
                       non-negative).
           @kwarg beta: Angle subtended by triangle side C{b} from this to B{C{pointC}} (C{degrees},
                        non-negative) or C{None} if C{B{gamma} is not None}.
           @kwarg gamma: Angle subtended by triangle side C{c} from this to B{C{pointB}} (C{degrees},
                         non-negative) or C{None} if C{B{beta} is not None}.
           @kwarg useZ: If C{True}, use and interpolate the Z component, otherwise force C{z=INT0}
                        (C{bool}).

           @note: This point, B{C{pointB}} and B{C{pointC}} are ordered clockwise.

           @return: L{Tienstra7Tuple}C{(pointP, A, B, C, a, b, c)} with survey C{pointP},
                    an instance of this (sub-)class and triangle angle C{A} at this point,
                    C{B} at B{C{pointB}} and C{C} at B{C{pointC}} in C{degrees} and
                    triangle sides C{a}, C{b} and C{c}.

           @raise ResectionError: Near-coincident, -colinear or -concyclic points or sum of
                                  B{C{alpha}}, B{C{beta}} and B{C{gamma}} not C{360} or
                                  negative B{C{alpha}}, B{C{beta}} or B{C{gamma}}.

           @raise TypeError: Invalid B{C{pointB}} or B{C{pointC}}.

           @see: U{3-Point Resection Solver<http://MesaMike.org/geocache/GC1B0Q9/tienstra/>},
                 U{V. Pierlot, M. Van Droogenbroeck, "A New Three Object Triangulation..."
                 <http://www.Telecom.ULg.ac.Be/publi/publications/pierlot/Pierlot2014ANewThree/>},
                 U{18 Triangulation Algorithms...<http://www.Telecom.ULg.ac.Be/triangulation/>}
                 and function L{pygeodesy.tienstra7}.
        '''
        return _MODS.resections.tienstra7(self, pointB, pointC, alpha, beta, gamma,
                                                useZ=useZ, datum=self.datum)

    @deprecated_method
    def to2ab(self):  # PYCHOK no cover
        '''DEPRECATED, use property C{philam}.

           @return: A L{PhiLam2Tuple}C{(phi, lam)}.
        '''
        return self.philam

    @deprecated_method
    def to2ll(self):  # PYCHOK no cover
        '''DEPRECATED, use property C{latlon}.

           @return: A L{LatLon2Tuple}C{(lat, lon)}.
        '''
        return self.latlon

    @deprecated_method
    def to3llh(self, datum=None):  # PYCHOK no cover
        '''DEPRECATED, use property L{latlonheightdatum} or L{latlonheight}.

           @return: A L{LatLon4Tuple}C{(lat, lon, height, datum)}.

           @note: This method returns a B{C{-4Tuple}} I{and not a} C{-3Tuple}
                  as its name may suggest.
        '''
        t = self.toLatLon(datum=datum, LatLon=None)
        return LatLon4Tuple(t.lat, t.lon, t.height, t.datum, name=self.name)

#   def _to3LLh(self, datum, LL, **pairs):  # OBSOLETE
#       '''(INTERNAL) Helper for C{subclass.toLatLon} and C{.to3llh}.
#       '''
#       r = self.to3llh(datum)  # LatLon3Tuple
#       if LL is not None:
#           r = LL(r.lat, r.lon, height=r.height, datum=datum, name=self.name)
#           for n, v in pairs.items():
#               setattr(r, n, v)
#       return r

    def toDatum(self, datum2, datum=None):
        '''Convert this cartesian from one datum to an other.

           @arg datum2: Datum to convert I{to} (L{Datum}).
           @kwarg datum: Datum to convert I{from} (L{Datum}).

           @return: The converted point (C{Cartesian}).

           @raise TypeError: B{C{datum2}} or B{C{datum}}
                             invalid.
        '''
        _xinstanceof(Datum, datum2=datum2)

        c = self if datum in (None, self.datum) else \
            self.toDatum(datum)

        i, d = False, c.datum
        if d == datum2:
            return c.copy() if c is self else c

        elif d == _WGS84:
            d = datum2  # convert from WGS84 to datum2

        elif datum2 == _WGS84:
            i = True  # convert to WGS84 by inverse transformation

        else:  # neither datum2 nor c.datum is WGS84, invert to WGS84 first
            c = c.toTransform(d.transform, inverse=True, datum=_WGS84)
            d = datum2

        return c.toTransform(d.transform, inverse=i, datum=datum2)

    convertDatum = toDatum  # for backward compatibility

    def toEcef(self):
        '''Convert this cartesian to I{geodetic} (lat-/longitude) coordinates.

           @return: An L{Ecef9Tuple}C{(x, y, z, lat, lon, height,
                    C, M, datum)} with C{C} and C{M} if available.

           @raise EcefError: A C{.datum} or an ECEF issue.
        '''
        return self._ecef9

    def toLatLon(self, datum=None, height=None, LatLon=None, **LatLon_kwds):  # see .ecef.Ecef9Tuple.toDatum
        '''Convert this cartesian to a geodetic (lat-/longitude) point.

           @kwarg datum: Optional datum (L{Datum}, L{Ellipsoid}, L{Ellipsoid2}
                         or L{a_f2Tuple}).
           @kwarg height: Optional height, overriding the converted height
                          (C{meter}), iff B{C{LatLon}} is not C{None}.
           @kwarg LatLon: Optional class to return the geodetic point
                          (C{LatLon}) or C{None}.
           @kwarg LatLon_kwds: Optional, additional B{C{LatLon}} keyword
                               arguments, ignored if C{B{LatLon} is None}.

           @return: The geodetic point (B{C{LatLon}}) or if B{C{LatLon}}
                    is C{None}, an L{Ecef9Tuple}C{(x, y, z, lat, lon,
                    height, C, M, datum)} with C{C} and C{M} if available.

           @raise TypeError: Invalid B{C{datum}} or B{C{LatLon_kwds}}.
        '''
        d = _spherical_datum(datum or self.datum, name=self.name)
        if d == self.datum:
            r = self.toEcef()
        else:
            c = self.toDatum(d)
            r = c.Ecef(d, name=self.name).reverse(c, M=LatLon is None)

        if LatLon:  # class or .classof
            h = r.height if height is None else Height(height)
            r = LatLon(r.lat, r.lon, datum=r.datum, height=h,
                                  **_xkwds(LatLon_kwds, name=r.name))
        _xdatum(r.datum, d)
        return r

    def toLocal(self, Xyz=None, ltp=None, **Xyz_kwds):
        '''Convert this I{geocentric} cartesian to I{local} C{X}, C{Y} and C{Z}.

           @kwarg Xyz: Optional class to return C{X}, C{Y} and C{Z}
                       (L{XyzLocal}, L{Enu}, L{Ned}) or C{None}.
           @kwarg ltp: The I{local tangent plane} (LTP) to use,
                       overriding this cartesian's LTP (L{Ltp}).
           @kwarg Xyz_kwds: Optional, additional B{C{Xyz}} keyword
                            arguments, ignored if C{B{Xyz} is None}.

           @return: An B{C{Xyz}} instance or if C{B{Xyz} is None},
                    a L{Local9Tuple}C{(x, y, z, lat, lon, height,
                    ltp, ecef, M)} with C{M=None} always.

           @raise TypeError: Invalid B{C{ltp}}.
        '''
        p = _MODS.ltp._xLtp(ltp, self._ltp)
        return p._ecef2local(self._ecef9, Xyz, Xyz_kwds)

    def toLtp(self, Ecef=None):
        '''Return the I{local tangent plane} (LTP) for this cartesian.

           @kwarg Ecef: Optional ECEF I{class} (L{EcefKarney}, ...
                        L{EcefYou}), overriding this cartesian's C{Ecef}.
        '''
        return self._ltp if Ecef in (None, self.Ecef) else _MODS.ltp.Ltp(
               self._ecef9, ecef=Ecef(self.datum), name=self.name)

    def toNvector(self, Nvector=None, datum=None, **Nvector_kwds):
        '''Convert this cartesian to C{n-vector} components.

           @kwarg Nvector: Optional class to return the C{n-vector}
                           components (C{Nvector}) or C{None}.
           @kwarg datum: Optional datum (L{Datum}, L{Ellipsoid}, L{Ellipsoid2}
                         or L{a_f2Tuple}) overriding this cartesian's datum.
           @kwarg Nvector_kwds: Optional, additional B{C{Nvector}} keyword
                                arguments, ignored if C{B{Nvector} is None}.

           @return: The C{unit, n-vector} components (B{C{Nvector}}) or a
                    L{Vector4Tuple}C{(x, y, z, h)} if B{C{Nvector}} is C{None}.

           @raise TypeError: Invalid B{C{datum}}.

           @raise ValueError: The B{C{Cartesian}} at origin.

           @example:

            >>> c = Cartesian(3980581, 97, 4966825)
            >>> n = c.toNvector()  # (x=0.622818, y=0.00002, z=0.782367, h=0.242887)
        '''
        d = _spherical_datum(datum or self.datum, name=self.name)
        r =  self._N_vector.xyzh if self.datum == d else self._n_xyzh4(d)

        if Nvector is not None:
            kwds = _xkwds(Nvector_kwds, h=r.h, datum=d)
            r = self._xnamed(Nvector(r.x, r.y, r.z, **kwds))
        return r

    def toStr(self, prec=3, fmt=Fmt.SQUARE, sep=_COMMASPACE_):  # PYCHOK expected
        '''Return the string representation of this cartesian.

           @kwarg prec: Number of (decimal) digits, unstripped (C{int}).
           @kwarg fmt: Enclosing backets format (string).
           @kwarg sep: Separator to join (string).

           @return: Cartesian represented as "[x, y, z]" (string).
        '''
        return Vector3d.toStr(self, prec=prec, fmt=fmt, sep=sep)

    def toTransform(self, transform, inverse=False, datum=None):
        '''Return a new cartesian by applying a Helmert transform
           to this cartesian.

           @arg transform: Transform to apply (L{Transform}).
           @kwarg inverse: Apply the inverse of the Helmert
                           transform (C{bool}).
           @kwarg datum: Datum for the transformed cartesian (L{Datum}),
                         overriding this cartesian's datum.

           @return: The transformed cartesian (C{Cartesian}).

           @raise Valuerror: If C{B{inverse}=True} and B{C{datum}}
                             is not L{Datums}C{.WGS84}.
        '''
        d = datum or self.datum
        if inverse and d != _WGS84:
            raise _ValueError(inverse=inverse, datum=d,
                              txt=_not_(_WGS84.name))

        xyz = transform.transform(*self.xyz, inverse=inverse)
        return self.classof(xyz, datum=d)

    def toVector(self, Vector=None, **Vector_kwds):
        '''Return this cartesian's components as vector.

           @kwarg Vector: Optional class to return the C{n-vector}
                          components (L{Vector3d}) or C{None}.
           @kwarg Vector_kwds: Optional, additional B{C{Vector}} keyword
                               arguments, ignored if C{B{Vector} is None}.

           @return: A B{C{Vector}} or a L{Vector3Tuple}C{(x, y, z)} if
                    B{C{Vector}} is C{None}.

           @raise TypeError: Invalid B{C{Vector}} or B{C{Vector_kwds}}.
        '''
        return self.xyz if Vector is None else self._xnamed(
               Vector(self.x, self.y, self.z, **Vector_kwds))


__all__ += _ALL_DOCS(CartesianBase)

# **) MIT License
#
# Copyright (C) 2016-2023 -- mrJean1 at Gmail -- All Rights Reserved.
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# Permission is hereby granted, free of charge, to any person obtaining a
# copy of this software and associated documentation files (the "Software"),
# to deal in the Software without restriction, including without limitation
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# and/or sell copies of the Software, and to permit persons to whom the
# Software is furnished to do so, subject to the following conditions:
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# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
# OTHER DEALINGS IN THE SOFTWARE.
