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

u'''Named, I{Local Tangent Plane} (LTP) tuples.

Local coordinate classes L{XyzLocal}, L{Enu}, L{Ned} and L{Aer}
and local coordinate tuples L{Local9Tuple}, L{Xyz4Tuple}, L{Enu4Tuple},
L{Ned4Tuple}, L{Aer4Tuple}, L{ChLV9Tuple}, L{ChLVEN2Tuple},
L{ChLVYX2Tuple}, L{ChLVyx2Tuple} and L{Footprint5Tuple}.

@see: References in module L{ltp}.
'''

from pygeodesy.basics import isscalar, issubclassof
from pygeodesy.constants import _0_0, _1_0, _90_0, _N_90_0
from pygeodesy.dms import F_D, toDMS
from pygeodesy.errors import _TypeError, _TypesError, _xattr, _xkwds
from pygeodesy.fmath import hypot, hypot_
from pygeodesy.interns import NN, _4_, _azimuth_, _center_, _COMMASPACE_, \
                             _down_, _east_, _ecef_, _elevation_, _height_, \
                             _lat_, _lon_, _ltp_, _M_, _north_, _not_, _up_, \
                             _X_, _x_, _xyz_, _Y_, _y_, _z_
from pygeodesy.lazily import _ALL_DOCS, _ALL_LAZY, _ALL_MODS as _MODS
from pygeodesy.named import _NamedBase, _NamedTuple, notOverloaded, \
                            _Pass, _xnamed
from pygeodesy.namedTuples import LatLon2Tuple, PhiLam2Tuple, Vector3Tuple
from pygeodesy.props import deprecated_method, deprecated_Property_RO, \
                            Property_RO, property_RO
from pygeodesy.streprs import Fmt, fstr, strs, _xzipairs
from pygeodesy.units import Bearing, Degrees, Degrees_, Height, Lat, Lon, \
                            Meter, Meter_
from pygeodesy.utily import atan2d, atan2b, sincos2_, sincos2d_
from pygeodesy.vector3d import Vector3d

from math import cos, radians

__all__ = _ALL_LAZY.ltpTuples
__version__ = '23.10.12'

_aer_        = 'aer'
_alt_        = 'alt'
_enu_        = 'enu'
_h__         = 'h_'
_ned_        = 'ned'
_local_      = 'local'
_roll_       = 'roll'
_slantrange_ = 'slantrange'
_tilt_       = 'tilt'
_uvw_        = 'uvw'
_yaw_        = 'yaw'


def _er2gr(e, r):
    '''(INTERNAL) Elevation and slant range to ground range.
    '''
    c = cos(radians(e))
    return Meter_(groundrange=r * c)


def _toStr2(inst, prec=None, fmt=Fmt.SQUARE, sep=_COMMASPACE_):
    '''(INTERNAL) Get attribute name and value strings, joined and bracketed.
    '''
    a = inst._toStr  # 'aer', 'enu', 'ned', 'xyz'
    t = getattr(inst, a + _4_, ())[:len(a)] or getattr(inst, a)
    t = strs(t, prec=3 if prec is None else prec)
    if sep:
        t = sep.join(t)
        if fmt:
            t = fmt(t)
    return a, t


def _4Tuple2Cls(inst, Cls, Cls_kwds):
    '''(INTERNAL) Convert 4-Tuple to C{Cls} instance.
    '''
    if Cls is None:
        return inst
    elif issubclassof(Cls, Aer):
        return inst.xyzLocal.toAer(Aer=Cls, **Cls_kwds)
    elif issubclassof(Cls, Enu):  # PYCHOK no cover
        return inst.xyzLocal.toEnu(Enu=Cls, **Cls_kwds)
    elif issubclassof(Cls, Ned):
        return inst.xyzLocal.toNed(Ned=Cls, **Cls_kwds)
    elif issubclassof(Cls, XyzLocal):  # PYCHOK no cover
        return inst.xyzLocal.toXyz(Xyz=Cls, **Cls_kwds)
    elif Cls is Local9Tuple:  # PYCHOK no cover
        return inst.xyzLocal.toLocal9Tuple(**Cls_kwds)
    n = inst.__class__.__name__[:3]  # PYCHOK no cover
    raise _TypesError(n, Cls, Aer, Enu, Ned, XyzLocal)


def _xyz2aer4(inst):
    '''(INTERNAL) Convert C{(x, y, z}) to C{(A, E, R)}.
    '''
    x, y, z, _ = inst.xyz4
    A = Bearing(azimuth=atan2b(x, y))
    E = Degrees(elevation=atan2d(z, hypot(x, y)))
    R = Meter(slantrange=hypot_(x, y, z))
    return Aer4Tuple(A, E, R, inst.ltp, name=inst.name)


def _xyzLocal(*Types, **name_inst):
    '''(INTERNAL) Get C{inst} or C{inst.xyzLocal}.
    '''
    n, inst = name_inst.popitem()
    if isinstance(inst, Types):
        return None
    try:
        return inst.xyzLocal
    except (AttributeError, TypeError):
        raise _TypeError(n, inst, txt=_not_(_local_))


class _NamedAerNed(_NamedBase):
    '''(INTERNAL) Base class for classes C{Aer} and C{Ned}.
    '''
    _ltp =  None  # local tangent plane (C{Ltp}), origin

    @Property_RO
    def ltp(self):
        '''Get the I{local tangent plane} (L{Ltp}).
        '''
        return self._ltp

    def toAer(self, Aer=None, **Aer_kwds):
        '''Get the I{local} I{Azimuth, Elevation, slant Range} (AER) components.

           @kwarg Aer: Class to return AER (L{Aer}) or C{None}.
           @kwarg Aer_kwds: Optional, additional B{L{Aer}} keyword
                            arguments, ignored if B{C{Aer}} is C{None}.

           @return: AER as an L{Aer} instance or if C{B{Aer} is None},
                    an L{Aer4Tuple}C{(azimuth, elevation, slantrange, ltp)}.
        '''
        return self.xyz4._toXyz(Aer, Aer_kwds)

    def toEnu(self, Enu=None, **Enu_kwds):
        '''Get the I{local} I{East, North, Up} (ENU) components.

           @kwarg Enu: Class to return ENU (L{Enu}) or C{None}.
           @kwarg Enu_kwds: Optional, additional B{L{Enu}} keyword
                            arguments, ignored if C{B{Enu} is None}.

           @return: ENU as an L{Enu} instance or if C{B{Enu} is None},
                    an L{Enu4Tuple}C{(east, north, up, ltp)}.
        '''
        return self.xyz4._toXyz(Enu, Enu_kwds)

    def toNed(self, Ned=None, **Ned_kwds):
        '''Get the I{local} I{North, East, Down} (NED) components.

           @kwarg Ned: Class to return NED (L{Ned}) or C{None}.
           @kwarg Ned_kwds: Optional, additional B{L{Ned}} keyword
                            arguments, ignored if B{C{Ned}} is C{None}.

           @return: NED as an L{Ned} instance or if C{B{Ned} is None},
                    an L{Ned4Tuple}C{(north, east, down, ltp)}.
        '''
        return self.xyz4._toXyz(Ned, Ned_kwds)

    def toXyz(self, Xyz=None, **Xyz_kwds):
        '''Get the local I{X, Y, Z} (XYZ) components.

           @kwarg Xyz: Class to return XYZ (L{XyzLocal}, L{Enu},
                       L{Ned}, L{Aer}) or C{None}.
           @kwarg Xyz_kwds: Optional, additional B{C{Xyz}} keyword
                            arguments, ignored if C{B{Xyz} is None}.

           @return: XYZ as an B{C{Xyz}} instance or if C{B{Xyz} is None},
                    an L{Xyz4Tuple}C{(x, y, z, ltp)}.

           @raise TypeError: Invalid B{C{Xyz}}.
        '''
        return self.xyz4._toXyz(Xyz, Xyz_kwds)

    @Property_RO
    def xyz(self):
        '''Get the I{local} C{(X, Y, Z)} coordinates (L{Vector3Tuple}C{(x, y, z)}).
        '''
        return Vector3Tuple(self.x, self.y, self.z, name=self.name)  # like Ecef9Tuple.xyz, Local6tuple.xyz

    @property_RO
    def xyz4(self):  # PYCHOK no cover
        '''I{Must be overloaded}.'''
        notOverloaded(self)

    @Property_RO
    def xyzLocal(self):
        '''Get this AER or NED as an L{XyzLocal}.
        '''
        return XyzLocal(self.xyz4, name=self.name)


class Aer(_NamedAerNed):
    '''Local C{Azimuth-Elevation-Range} (AER) in a I{local tangent plane}.
    '''
    _azimuth    = _0_0   # bearing from North (C{degrees360})
    _elevation  = _0_0   # tilt, pitch from horizon (C{degrees}).
#   _ltp        =  None  # local tangent plane (C{Ltp}), origin
    _slantrange = _0_0   # distance (C{Meter})
    _toStr      = _aer_

    def __init__(self, azimuth_aer, elevation=0, slantrange=0, ltp=None, name=NN):
        '''New L{Aer}.

           @arg azimuth_aer: Scalar azimuth, bearing from North (compass C{degrees})
                             or a previous I{local} instance (L{Aer}, L{Aer4Tuple},
                             L{Enu}, L{Enu4Tuple}, L{Local9Tuple}, L{Ned},
                             L{Ned4Tuple}, L{XyzLocal} or L{Xyz4Tuple}).
           @kwarg elevation: Scalar angle I{above} the horizon, I{above} B{C{ltp}}
                             (C{degrees}, horizon is 0, zenith +90 and nadir -90),
                             only used with scalar B{C{azimuth_aer}}.
           @kwarg slantrange: Scalar distance (C{meter}), only used with scalar
                              B{C{azimuth_aer}}.
           @kwarg ltp: The I{local tangent plane}, (geodetic) origin (L{Ltp},
                       L{LocalCartesian}).
           @kwarg name: Optional name (C{str}).

           @raise TypeError: Invalid B{C{azimuth_aer}} or B{C{ltp}}.

           @raise UnitError: Invalid B{C{azimuth_aer}}, B{C{elevation}} or
                             or B{C{slantrange}}.
        '''
        if isscalar(azimuth_aer):
            self._azimuth    = Bearing(azimuth=azimuth_aer)
            self._elevation  = Degrees_(elevation=elevation, low=_N_90_0, high=_90_0)
            self._slantrange = Meter_(slantrange=slantrange)
            p, n = ltp, name
        else:  # PYCHOK no cover
            p = _xyzLocal(Aer, Aer4Tuple, Ned, azimuth_aer=azimuth_aer)
            aer = p.toAer() if p else azimuth_aer
            self._azimuth, self._elevation, self._slantrange = \
              aer.azimuth,   aer.elevation,   aer.slantrange
            p = _xattr(aer, ltp=ltp)
            n =  name or _xattr(aer, name=name)

        if p:
            self._ltp = _MODS.ltp._xLtp(p)
        if name:
            self.name = n

    @Property_RO
    def aer4(self):
        '''Get the C{(azimuth, elevation, slantrange, ltp)} components (L{Aer4Tuple}).
        '''
        return Aer4Tuple(self.azimuth, self.elevation, self.slantrange, self.ltp, name=self.name)

    @Property_RO
    def azimuth(self):
        '''Get the Azimuth, bearing from North (C{degrees360}).
        '''
        return self._azimuth

    @Property_RO
    def down(self):
        '''Get the Down component (C{meter}).
        '''
        return self.xyzLocal.down

    @Property_RO
    def east(self):
        '''Get the East component (C{meter}).
        '''
        return self.xyzLocal.east

    @Property_RO
    def elevation(self):
        '''Get the Elevation, tilt above horizon (C{degrees90}).
        '''
        return self._elevation

    @Property_RO
    def groundrange(self):
        '''Get the I{ground range}, distance (C{meter}).
        '''
        return _er2gr(self._elevation, self._slantrange)

    @Property_RO
    def north(self):
        '''Get the North component (C{meter}).
        '''
        return self.xyzLocal.north

    @Property_RO
    def slantrange(self):
        '''Get the I{slant Range}, distance (C{meter}).
        '''
        return self._slantrange

    def toRepr(self, prec=None, fmt=Fmt.SQUARE, sep=_COMMASPACE_, **unused):  # PYCHOK expected
        '''Return a string representation of this AER as azimuth
           (bearing), elevation and slant range.

           @kwarg prec: Number of (decimal) digits, unstripped (C{int}).
           @kwarg fmt: Enclosing backets format (C{str}).
           @kwarg sep: Optional separator between AERs (C{str}).

           @return: This AER as "[A:degrees360, E:degrees90, R:meter]" (C{str}).
        '''
        t = (toDMS(self.azimuth,    form=F_D, prec=prec, ddd=0),
             toDMS(self.elevation,  form=F_D, prec=prec, ddd=0),
             fstr( self.slantrange, prec=3 if prec is None else prec))
        return _xzipairs(self._toStr.upper(), t, sep=sep, fmt=fmt)

    def toStr(self, **prec_fmt_sep):  # PYCHOK expected
        '''Return a string representation of this AER.

           @kwarg prec_fmt_sep: Keyword arguments C{B{prec}=3} for the
                                number of (decimal) digits, unstripped
                                (C{int}), C{B{fmt}='[]'} the enclosing
                                backets format (C{str}) and separator
                                C{B{sep}=', '} to join (C{str}).

           @return: This AER as "[degrees360, degrees90, meter]" (C{str}).
        '''
        _, t = _toStr2(self, **prec_fmt_sep)
        return t

    @Property_RO
    def up(self):
        '''Get the Up component (C{meter}).
        '''
        return self.xyzLocal.up

    @Property_RO
    def x(self):
        '''Get the X component (C{meter}).
        '''
        return self.xyz4.x

    @Property_RO
    def xyz4(self):
        '''Get the C{(x, y, z, ltp)} components (L{Xyz4Tuple}).
        '''
        sA, cA, sE, cE = sincos2d_(self._azimuth, self._elevation)
        R = self._slantrange
        r = cE * R  # ground range
        return Xyz4Tuple(sA * r, cA * r, sE * R, self.ltp, name=self.name)

    @Property_RO
    def y(self):
        '''Get the Y component (C{meter}).
        '''
        return self.xyz4.y

    @Property_RO
    def z(self):
        '''Get the Z component (C{meter}).
        '''
        return self.xyz4.z


class Aer4Tuple(_NamedTuple):
    '''4-Tuple C{(azimuth, elevation, slantrange, ltp)},
       all in C{meter} except C{ltp}.
    '''
    _Names_ = (_azimuth_, _elevation_, _slantrange_, _ltp_)
    _Units_ = ( Meter,     Meter,       Meter,       _Pass)

    def _toAer(self, Cls, Cls_kwds):
        '''(INTERNAL) Return C{Cls(..., **Cls_kwds)} instance.
        '''
        if issubclassof(Cls, Aer):
            return Cls(*self, **_xkwds(Cls_kwds, name=self.name))
        else:
            return _4Tuple2Cls(self, Cls, Cls_kwds)

    @Property_RO
    def groundrange(self):
        '''Get the I{ground range}, distance (C{meter}).
        '''
        return _er2gr(self.elevation, self.slantrange)  # PYCHOK _Tuple

    @Property_RO
    def xyzLocal(self):
        '''Get this L{Aer4Tuple} as an L{XyzLocal}.
        '''
        return Aer(self).xyzLocal


class Attitude4Tuple(_NamedTuple):
    '''4-Tuple C{(alt, tilt, yaw, roll)} with C{altitude} in (positive)
       C{meter} and C{tilt}, C{yaw} and C{roll} in C{degrees} representing
       the attitude of a plane or camera.
    '''
    _Names_ = (_alt_, _tilt_,  _yaw_,   _roll_)
    _Units_ = ( Meter, Bearing, Degrees, Degrees)

    @Property_RO
    def atyr(self):
        '''Return this attitude (L{Attitude4Tuple}).
        '''
        return self

    @Property_RO
    def tyr3d(self):
        '''Get this attitude's (3-D) directional vector (L{Vector3d}).
        '''
        return _MODS.ltp.Attitude(self).tyr3d


class Ned(_NamedAerNed):
    '''Local C{North-Eeast-Down} (NED) location in a I{local tangent plane}.

       @see: L{Enu} and L{Ltp}.
    '''
    _down  = _0_0   # down, -XyzLocal.z (C{meter}).
    _east  = _0_0   # east, XyzLocal.y (C{meter}).
#   _ltp   =  None  # local tangent plane (C{Ltp}), origin
    _north = _0_0   # north, XyzLocal.x (C{meter})
    _toStr = _ned_

    def __init__(self, north_ned, east=0, down=0, ltp=None, name=NN):
        '''New L{Ned} vector.

           @arg north_ned: Scalar North component (C{meter}) or a previous
                           I{local} instance (L{Ned}, L{Ned4Tuple}, L{Aer},
                           L{Aer4Tuple}, L{Enu}, L{Enu4Tuple}, L{Local9Tuple},
                           L{XyzLocal} or L{Xyz4Tuple}).
           @kwarg east: Scalar East component (C{meter}), only used with
                        scalar B{C{north_ned}}.
           @kwarg down: Scalar Down component, normal to I{inside} surface
                        of the ellipsoid or sphere (C{meter}), only used with
                        scalar B{C{north_ned}}.
           @kwarg ltp: The I{local tangent plane}, (geodetic) origin (L{Ltp},
                       L{LocalCartesian}).
           @kwarg name: Optional name (C{str}).

           @raise TypeError: Invalid B{C{north_ned}} or B{C{ltp}}.

           @raise UnitError: Invalid B{C{north_ned}}, B{C{east}} or B{C{down}}.
        '''
        if isscalar(north_ned):
            self._north = Meter(north=north_ned or _0_0)
            self._east  = Meter(east=east or _0_0)
            self._down  = Meter(down=down or _0_0)
            p, n = ltp, name
        else:  # PYCHOK no cover
            p = _xyzLocal(Ned, Ned4Tuple, Aer, north_ned=north_ned)
            ned = p.toNed() if p else north_ned
            self._north, self._east, self._down = ned.north, ned.east, ned.down
            p = _xattr(ned, ltp=ltp)
            n =  name or _xattr(ned, name=name)

        if p:
            self._ltp = _MODS.ltp._xLtp(p)
        if n:
            self.name = n

    @Property_RO
    def aer4(self):
        '''Get the C{(azimuth, elevation, slantrange, ltp)} components (L{Aer4Tuple}).
        '''
        return _xyz2aer4(self)

    @Property_RO
    def azimuth(self):
        '''Get the Azimuth, bearing from North (C{degrees360}).
        '''
        return self.aer4.azimuth

    @deprecated_Property_RO
    def bearing(self):
        '''DEPRECATED, use C{azimuth}.'''
        return self.azimuth

    @Property_RO
    def down(self):
        '''Get the Down component (C{meter}).
        '''
        return self._down

    @Property_RO
    def east(self):
        '''Get the East component (C{meter}).
        '''
        return self._east

    @Property_RO
    def elevation(self):
        '''Get the Elevation, tilt above horizon (C{degrees90}).
        '''
        return self.aer4.elevation  # neg(degrees90(asin1(self.down / self.length))))

    @Property_RO
    def groundrange(self):
        '''Get the I{ground range}, distance (C{meter}).
        '''
        return Meter(groundrange=hypot(self.north, self.east))

    @deprecated_Property_RO
    def length(self):
        '''DEPRECATED, use C{slantrange}.'''
        return self.slantrange

    @deprecated_Property_RO
    def ned(self):
        '''DEPRECATED, use property C{ned4}.'''
        return _MODS.deprecated.Ned3Tuple(self.north, self.east, self.down, name=self.name)

    @Property_RO
    def ned4(self):
        '''Get the C{(north, east, down, ltp)} components (L{Ned4Tuple}).
        '''
        return Ned4Tuple(self.north, self.east, self.down, self.ltp, name=self.name)

    @Property_RO
    def north(self):
        '''Get the North component (C{meter}).
        '''
        return self._north

    @Property_RO
    def slantrange(self):
        '''Get the I{slant Range}, distance (C{meter}).
        '''
        return self.aer4.slantrange

    @deprecated_method
    def to3ned(self):  # PYCHOK no cover
        '''DEPRECATED, use property L{ned4}.'''
        return self.ned  # XXX deprecated too

    def toRepr(self, prec=None, fmt=Fmt.SQUARE, sep=_COMMASPACE_, **unused):  # PYCHOK expected
        '''Return a string representation of this NED.

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

           @return: This NED as "[N:meter, E:meter, D:meter]" (C{str}).
        '''
        a, t = _toStr2(self, prec=prec, fmt=NN, sep=NN)
        return _xzipairs(a.upper(), t, sep=sep, fmt=fmt)

    def toStr(self, **prec_fmt_sep):  # PYCHOK expected
        '''Return a string representation of this NED.

           @kwarg prec_fmt_sep: Keyword arguments C{B{prec}=3} for the
                                number of (decimal) digits, unstripped
                                (C{int}), C{B{fmt}='[]'} the enclosing
                                backets format (C{str}) and separator
                                C{B{sep}=', '} to join (C{str}).

           @return: This NED as "[meter, meter, meter]" (C{str}).
        '''
        _, t = _toStr2(self, **prec_fmt_sep)
        return t

    @deprecated_method
    def toVector3d(self):
        '''DEPRECATED, use property L{xyz}.'''
        return self.xyz

    @Property_RO
    def up(self):
        '''Get the Up component (C{meter}).
        '''
        return Meter(up=-self._down)  # negated

    @Property_RO
    def x(self):
        '''Get the X component (C{meter}).
        '''
        return Meter(x=self._east)  # 2nd arg, E

    @Property_RO
    def xyz4(self):
        '''Get the C{(x, y, z, ltp)} components (L{Xyz4Tuple}).
        '''
        return Xyz4Tuple(self.x, self.y, self.z, self.ltp, name=self.name)

    @Property_RO
    def y(self):
        '''Get the Y component (C{meter}).
        '''
        return Meter(y=self._north)  # 1st arg N

    @Property_RO
    def z(self):
        '''Get the Z component (C{meter}).
        '''
        return Meter(z=-self._down)  # negated


class Ned4Tuple(_NamedTuple):
    '''4-Tuple C{(north, east, down, ltp)}, all in C{meter} except C{ltp}.
    '''
    _Names_ = (_north_, _east_, _down_, _ltp_)
    _Units_ = ( Meter,   Meter,  Meter, _Pass)

    def _toNed(self, Cls, Cls_kwds):
        '''(INTERNAL) Return C{Cls(..., **Cls_kwds)} instance.
        '''
        if issubclassof(Cls, Ned):
            return Cls(*self, **_xkwds(Cls_kwds, name=self.name))
        else:
            return _4Tuple2Cls(self, Cls, Cls_kwds)

    @Property_RO
    def xyzLocal(self):
        '''Get this L{Ned4Tuple} as an L{XyzLocal}.
        '''
        return Ned(self).xyzLocal


class _Vector3d(Vector3d):

    _toStr = _xyz_

    def toRepr(self, prec=None, fmt=Fmt.SQUARE, sep=_COMMASPACE_, **unused):  # PYCHOK expected
        '''Return a string representation of this ENU/NED/XYZ.

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

           @return: This XYZ/ENU as "[E:meter, N:meter, U:meter]",
                    "[N:meter, E:meter, D:meter]",
                    "[U:meter, V:meter, W:meter]" respectively
                    "[X:meter, Y:meter, Z:meter]" (C{str}).
        '''
        a, t = _toStr2(self, prec=prec, fmt=NN, sep=NN)
        return _xzipairs(a.upper(), t, sep=sep, fmt=fmt)

    def toStr(self, **prec_fmt_sep):  # PYCHOK expected
        '''Return a string representation of this XYZ.

           @kwarg prec_fmt_sep: Keyword arguments C{B{prec}=3} for the
                                number of (decimal) digits, unstripped
                                (C{int}), C{B{fmt}='[]'} the enclosing
                                backets format (C{str}) and separator
                                C{B{sep}=', '} to join (C{str}).

           @return: This XYZ as "[meter, meter, meter]" (C{str}).
        '''
        _, t = _toStr2(self, **prec_fmt_sep)
        return t


class XyzLocal(_Vector3d):
    '''Local C{(x, y, z)} in a I{local tangent plane} (LTP),
       also base class for local L{Enu}.
    '''
    _ltp = None  # local tangent plane (C{Ltp}), origin

    def __init__(self, x_xyz, y=0, z=0, ltp=None, name=NN):
        '''New L{XyzLocal}.

           @arg x_xyz: Scalar X component (C{meter}), C{positive east} or a
                       previous I{local} instance (L{XyzLocal}, L{Xyz4Tuple},
                       L{Aer}, L{Aer4Tuple}, L{Enu}, L{Enu4Tuple},
                       L{Local9Tuple}, L{Ned} or L{Ned4Tuple}).
           @kwarg y: Scalar Y component (C{meter}), only used with scalar
                     B{C{x_xyz}}, C{positive north}.
           @kwarg z: Scalar Z component, normal C{positive up} from the
                     surface of the ellipsoid or sphere (C{meter}), only
                     used with scalar B{C{x_xyz}}.
           @kwarg ltp: The I{local tangent plane}, (geodetic) origin (L{Ltp},
                       L{LocalCartesian}).

           @raise TypeError: Invalid B{C{x_xyz}} or B{C{ltp}}.

           @raise UnitError: Invalid scalar B{C{x_xyz}}, B{C{y}} or B{C{z}}.
        '''
        if isscalar(x_xyz):
            self._x = Meter(x=x_xyz or _0_0)
            self._y = Meter(y=y or _0_0)
            self._z = Meter(z=z or _0_0)
            p, n = ltp, name
        else:
            xyz = _xyzLocal(XyzLocal, Xyz4Tuple, Local9Tuple, x_xyz=x_xyz) or x_xyz
            self._x, self._y, self._z = xyz.x, xyz.y, xyz.z
            p = _xattr(xyz, ltp=ltp)
            n =  name or _xattr(xyz, name=NN)

        if p:
            self._ltp = _MODS.ltp._xLtp(p)
        if n:
            self.name = n

    def __str__(self):
        return self.toStr()

    @Property_RO
    def aer4(self):
        '''Get the C{(azimuth, elevation, slantrange, ltp)} components (L{Aer4Tuple}).
        '''
        return _xyz2aer4(self)

    @Property_RO
    def azimuth(self):
        '''Get the Azimuth, bearing from North (C{degrees360}).

           @see: U{Azimuth<https://GSSC.ESA.int/navipedia/index.php/
                 Transformations_between_ECEF_and_ENU_coordinates>}.
        '''
        return self.aer4.azimuth

    def classof(self, *args, **kwds):  # PYCHOK no cover
        '''Create another instance of this very class.

           @arg args: Optional, positional arguments.
           @kwarg kwds: Optional, keyword arguments.

           @return: New instance (C{self.__class__}).
        '''
        kwds = _xkwds(kwds, ltp=self.ltp, name=self.name)
        return self.__class__(*args, **kwds)

    @Property_RO
    def down(self):
        '''Get the Down component (C{meter}).
        '''
        return Meter(down=-self.z)

    @property_RO
    def ecef(self):
        '''Get this LTP's ECEF converter (C{Ecef...} I{instance}).
        '''
        return self.ltp.ecef

    @Property_RO
    def east(self):
        '''Get the East component (C{meter}).
        '''
        return Meter(east=self.x)

    @Property_RO
    def elevation(self):
        '''Get the Elevation, tilt above horizon (C{degrees90}).

           @see: U{Elevation<https://GSSC.ESA.int/navipedia/index.php/
                 Transformations_between_ECEF_and_ENU_coordinates>}.
        '''
        return self.aer4.elevation  # neg(degrees90(asin1(self.down / self.length))))

    @Property_RO
    def enu4(self):
        '''Get the C{(east, north, up, ltp)} components (L{Enu4Tuple}).
        '''
        return Enu4Tuple(self.east, self.north, self.up, self.ltp, name=self.name)

    @Property_RO
    def groundrange(self):
        '''Get the I{ground range}, distance (C{meter}).
        '''
        return Meter(groundrange=hypot(self.x, self.y))

    @Property_RO
    def ltp(self):
        '''Get the I{local tangent plane} (L{Ltp}).
        '''
        return self._ltp

    @Property_RO
    def ned4(self):
        '''Get the C{(north, east, down, ltp)} components (L{Ned4Tuple}).
        '''
        return Ned4Tuple(self.north, self.east, self.down, self.ltp, name=self.name)

    @Property_RO
    def north(self):
        '''Get the North component (C{meter}).
        '''
        return Meter(north=self.y)

    @Property_RO
    def slantrange(self):
        '''Get the I{slant Range}, distance (C{meter}).
        '''
        return self.aer4.slantrange

    def toAer(self, Aer=None, **Aer_kwds):
        '''Get the local I{Azimuth, Elevation, slantRange} components.

           @kwarg Aer: Class to return AER (L{Aer}) or C{None}.
           @kwarg Aer_kwds: Optional, additional B{C{Aer}} keyword
                            arguments, ignored if C{B{Aer} is None}.

           @return: AER as an L{Aer} instance or if C{B{Aer} is None}, an
                    L{Aer4Tuple}C{(azimuth, elevation, slantrange, ltp)}.

           @raise TypeError: Invalid B{C{Aer}}.
        '''
        return self.aer4._toAer(Aer, Aer_kwds)

    def toCartesian(self, Cartesian=None, ltp=None, **Cartesian_kwds):
        '''Get the geocentric C{(x, y, z)} (ECEF) coordinates of this local.

           @kwarg Cartesian: Optional class to return C{(x, y, z)} (C{Cartesian})
                             or C{None}.
           @kwarg ltp: Optional I{local tangent plane} (LTP) (L{Ltp}),
                       overriding this C{ltp}.
           @kwarg Cartesian_kwds: Optional, additional B{C{Cartesian}} keyword
                                  arguments, ignored if C{B{Cartesian} is None}.

           @return: A B{C{Cartesian}} instance of 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{ltp}}, B{C{Cartesian}} or
                             B{C{Cartesian_kwds}} argument.
        '''
        ltp = _MODS.ltp._xLtp(ltp, self.ltp)
        if Cartesian is None:
            r = ltp._local2ecef(self, nine=True)
        else:
            x, y, z = ltp._local2ecef(self)
            kwds = _xkwds(Cartesian_kwds, datum=ltp.datum)
            r = Cartesian(x, y, z, **kwds)
        return _xnamed(r, self.name or ltp.name)

    def toEnu(self, Enu=None, **Enu_kwds):
        '''Get the local I{East, North, Up} (ENU) components.

           @kwarg Enu: Class to return ENU (L{Enu}) or C{None}.
           @kwarg Enu_kwds: Optional, additional B{C{Enu}} keyword
                            arguments, ignored if C{B{Enu} is None}.

           @return: ENU as an L{Enu} instance or if C{B{Enu} is None},
                    an L{Enu4Tuple}C{(east, north, up, ltp)}.
        '''
        return self.enu4._toEnu(Enu, Enu_kwds)

    def toLatLon(self, LatLon=None, ltp=None, **LatLon_kwds):
        '''Get the geodetic C{(lat, lon, height)} coordinates if this local.

           @kwarg LatLon: Optional class to return C{(x, y, z)} (C{LatLon})
                          or C{None}.
           @kwarg ltp: Optional I{local tangent plane} (LTP) (L{Ltp}),
                       overriding this ENU/NED/AER/XYZ's LTP.
           @kwarg LatLon_kwds: Optional, additional B{C{LatLon}} keyword
                               arguments, ignored if C{B{LatLon} is None}.

           @return: An B{C{LatLon}} instance of if C{B{LatLon} 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{ltp}}, B{C{LatLon}} or
                             B{C{LatLon_kwds}} argument.
        '''
        ltp = _MODS.ltp._xLtp(ltp, self.ltp)
        r = ltp._local2ecef(self, nine=True)
        if LatLon is None:
            r = _xnamed(r, self.name or ltp.name)
        else:
            kwds = _xkwds(LatLon_kwds, height=r.height, datum=r.datum,
                                       name=self.name or ltp.name)
            r = LatLon(r.lat, r.lon, **kwds)  # XXX ltp?
        return r

    def toLocal9Tuple(self, M=False, name=NN):
        '''Get this local as a C{Local9Tuple}.

           @kwarg M: Optionally include the rotation matrix (C{bool}).
           @kwarg name: Optional name (C{str}).

           @return: L{Local9Tuple}C{(x, y, z, lat, lon, height, ltp,
                    ecef, M)} with C{ltp} this C{Ltp}, C{ecef} an
                    L{Ecef9Tuple} and C{M} L{EcefMatrix} or C{None}.
        '''
        ltp = self.ltp  # see C{self.toLatLon}
        t = ltp._local2ecef(self, nine=True, M=M)
        return Local9Tuple(self.x, self.y, self.z, t.lat, t.lon, t.height,
                                           ltp, t, t.M, name=name or t.name)

    def toNed(self, Ned=None, **Ned_kwds):
        '''Get the local I{North, East, Down} (Ned) components.

           @kwarg Ned: Class to return NED (L{Ned}) or C{None}.
           @kwarg Ned_kwds: Optional, additional B{C{Ned}} keyword
                            arguments, ignored if C{B{Ned} is None}.

           @return: NED as an L{Ned} instance or if C{B{Ned} is None},
                    an L{Ned4Tuple}C{(north, east, down, ltp)}.
        '''
        return self.ned4._toNed(Ned, Ned_kwds)

    def toXyz(self, Xyz=None, **Xyz_kwds):
        '''Get the local I{X, Y, Z} (XYZ) components.

           @kwarg Xyz: Class to return XYZ (L{XyzLocal}, L{Enu},
                       L{Ned}, L{Aer}) or C{None}.
           @kwarg Xyz_kwds: Optional, additional B{C{Xyz}} keyword
                            arguments, ignored if C{B{Xyz} is None}.

           @return: XYZ as an B{C{Xyz}} instance or if C{B{Xyz} is None},
                    an L{Xyz4Tuple}C{(x, y, z, ltp)}.
        '''
        return self.xyz4._toXyz(Xyz, Xyz_kwds)

    @Property_RO
    def up(self):
        '''Get the Up component (C{meter}).
        '''
        return Meter(up=self.z)

#   @Property_RO
#   def x(self):  # see: Vector3d.x
#       '''Get the X component (C{meter}).
#       '''
#       return self._x

#   @Property_RO
#   def xyz(self):  # see: Vector3d.xyz
#       '''Get the I{local} C{(X, Y, Z)} coordinates (L{Vector3Tuple}C{(x, y, z)}).
#       '''
#       return Vector3Tuple(self.x, self.y, self.z, name=self.name)  # like Ecef9Tuple.xyz, Local6tuple.xyz

    @Property_RO
    def xyz4(self):
        '''Get the C{(x, y, z, ltp)} components (L{Xyz4Tuple}).
        '''
        return Xyz4Tuple(self.x, self.y, self.z, self.ltp, name=self.name)

    @Property_RO
    def xyzLocal(self):
        '''Get this L{XyzLocal}.
        '''
        return self

#   @Property_RO
#   def y(self):  # see: Vector3d.y
#       '''Get the Y component (C{meter}).
#       '''
#       return self._y

#   @Property_RO
#   def z(self):  # see: Vector3d.z
#       '''Get the Z component (C{meter}).
#       '''
#       return self._z


class Xyz4Tuple(_NamedTuple):
    '''4-Tuple C{(x, y, z, ltp)}, all in C{meter} except C{ltp}.
    '''
    _Names_ = (_x_,   _y_,   _z_,    _ltp_)
    _Units_ = ( Meter, Meter, Meter, _Pass)

    def _toXyz(self, Cls, Cls_kwds):
        '''(INTERNAL) Return C{Cls(..., **Cls_kwds)} instance.
        '''
        if issubclassof(Cls, XyzLocal):
            return Cls(*self, **_xkwds(Cls_kwds, name=self.name))
        else:
            return _4Tuple2Cls(self, Cls, Cls_kwds)

    @Property_RO
    def xyzLocal(self):
        '''Get this L{Xyz4Tuple} as an L{XyzLocal}.
        '''
        return XyzLocal(*self, name=self.name)


class Enu(XyzLocal):
    '''Local C{Eeast-North-Up} (ENU) location in a I{local tangent plane}.

       @see: U{East, North, Up (ENU)<https://GSSC.ESA.int/navipedia/index.php/
             Transformations_between_ECEF_and_ENU_coordinates>} coordinates.
    '''
    _toStr = _enu_

    def __init__(self, east_enu, north=0, up=0, ltp=None, name=NN):
        '''New L{Enu}.

           @arg east_enu: Scalar East component (C{meter}) or a previous
                          I{local} instance (L{Enu}, L{Enu4Tuple}, L{Aer},
                          L{Aer4Tuple}, L{Local9Tuple}, L{Ned}, L{Ned4Tuple},
                          L{XyzLocal} or L{Xyz4Tuple}).
           @kwarg north: Scalar North component (C{meter}) only used with
                         scalar B{C{east_enu}}.
           @kwarg up: Scalar Up component only used with scalar B{C{east_enu}},
                      normal from the surface of the ellipsoid or sphere (C{meter}).
           @kwarg ltp: The I{local tangent plane}, (geodetic) origin (L{Ltp},
                       L{LocalCartesian}).
           @kwarg name: Optional name (C{str}).

           @raise TypeError: Invalid B{C{east_enu}} or B{C{ltp}}.

           @raise UnitError: Invalid B{C{east_enu}}, B{C{north}} or B{C{up}}.
        '''
        XyzLocal.__init__(self, east_enu, north, up, ltp=ltp, name=name)

    def toUvw(self, location, Uvw=None, **Uvw_kwds):
        '''Get the I{u, v, w} (UVW) components at a location.

           @arg location: The geodetic (C{LatLon}) or geocentric (C{Cartesian},
                          L{Vector3d}) location from where to cast the L{Los}.
           @kwarg Uvw: Class to return UWV (L{Uvw}) or C{None}.
           @kwarg Uvw_kwds: Optional, additional B{L{Uvw}} keyword
                            arguments, ignored if C{B{Uvw} is None}.

           @return: UVW as a L{Uvw} instance or if C{B{Uvw} is None}, a
                    L{Uvw3Tuple}C{(u, v, w)}.

           @raise TypeError: InvalidB{C{location}}.

           @see: Function U{lookAtSpheroid<https://PyPI.org/project/pymap3d>}.
        '''
        try:
            sa, ca, sb, cb = sincos2_(*location.philam)
        except Exception as x:
            raise _TypeError(location=location, cause=x)
        e, n, u, _ = self.enu4

        t = ca * u - sa * n
        U = cb * t - sb * e
        V = cb * e + sb * t
        W = ca * n + sa * u
        return Uvw3Tuple(U, V, W, name=self.name) if Uvw is None else \
               Uvw(      U, V, W, **_xkwds(Uvw_kwds, name=self.name))

    @Property_RO
    def xyzLocal(self):
        '''Get this ENU as an L{XyzLocal}.
        '''
        return XyzLocal(*self.xyz4, name=self.name)


class Enu4Tuple(_NamedTuple):
    '''4-Tuple C{(east, north, up, ltp)}, in C{meter} except C{ltp}.
    '''
    _Names_ = (_east_, _north_, _up_,   _ltp_)
    _Units_ = ( Meter,  Meter,   Meter, _Pass)

    def _toEnu(self, Cls, Cls_kwds):
        '''(INTERNAL) Return C{Cls(..., **Cls_kwds)} instance.
        '''
        if issubclassof(Cls, XyzLocal):
            return Cls(*self, **_xkwds(Cls_kwds, name=self.name))
        else:
            return _4Tuple2Cls(self, Cls, Cls_kwds)

    @Property_RO
    def xyzLocal(self):
        '''Get this L{Enu4Tuple} as an L{XyzLocal}.
        '''
        return XyzLocal(*self, name=self.name)


class Local9Tuple(_NamedTuple):
    '''9-Tuple C{(x, y, z, lat, lon, height, ltp, ecef, M)} with I{local} C{x},
       C{y}, C{z} all in C{meter}, I{geodetic} C{lat}, C{lon}, C{height}, I{local
       tangent plane} C{ltp} (L{Ltp}), C{ecef} (L{Ecef9Tuple}) with I{geocentric}
       C{x}, C{y}, C{z}, I{geodetic} C{lat}, C{lon}, C{height} and I{concatenated}
       rotation matrix C{M} (L{EcefMatrix}) or C{None}.
    '''
    _Names_ = (_x_,   _y_,   _z_,   _lat_, _lon_, _height_, _ltp_, _ecef_, _M_)
    _Units_ = ( Meter, Meter, Meter, Lat,   Lon,   Height,  _Pass, _Pass,  _Pass)

    @Property_RO
    def azimuth(self):
        '''Get the I{local} Azimuth, bearing from North (C{degrees360}).
        '''
        return self.xyzLocal.aer4.azimuth

    @Property_RO
    def down(self):
        '''Get the I{local} Down, C{-z} component (C{meter}).
        '''
        return -self.z

    @Property_RO
    def east(self):
        '''Get the I{local} East, C{x} component (C{meter}).
        '''
        return self.x

    @Property_RO
    def elevation(self):
        '''Get the I{local} Elevation, tilt I{above} horizon (C{degrees90}).
        '''
        return self.xyzLocal.aer4.elevation

    @Property_RO
    def groundrange(self):
        '''Get the I{local} ground range, distance (C{meter}).
        '''
        return self.xyzLocal.aer4.groundrange

    @Property_RO
    def lam(self):
        '''Get the I{geodetic} longitude in C{radians} (C{float}).
        '''
        return self.philam.lam

    @Property_RO
    def latlon(self):
        '''Get the I{geodetic} lat-, longitude in C{degrees} (L{LatLon2Tuple}C{(lat, lon)}).
        '''
        return LatLon2Tuple(self.lat, self.lon, name=self.name)

    @Property_RO
    def latlonheight(self):
        '''Get the I{geodetic} lat-, longitude in C{degrees} and height (L{LatLon3Tuple}C{(lat, lon, height)}).
        '''
        return self.latlon.to3Tuple(self.height)

    @Property_RO
    def north(self):
        '''Get the I{local} North, C{y} component (C{meter}).
        '''
        return self.y

    @Property_RO
    def phi(self):
        '''Get the I{geodetic} latitude in C{radians} (C{float}).
        '''
        return self.philam.phi

    @Property_RO
    def philam(self):
        '''Get the I{geodetic} lat-, longitude in C{radians} (L{PhiLam2Tuple}C{(phi, lam)}).
        '''
        return PhiLam2Tuple(radians(self.lat), radians(self.lon), name=self.name)

    @Property_RO
    def philamheight(self):
        '''Get the I{geodetic} lat-, longitude in C{radians} and height (L{PhiLam3Tuple}C{(phi, lam, height)}).
        '''
        return self.philam.to3Tuple(self.height)

    @Property_RO
    def slantrange(self):
        '''Get the I{local} slant Range, distance (C{meter}).
        '''
        return self.xyzLocal.aer4.slantrange

    def toAer(self, Aer=None, **Aer_kwds):
        '''Get the I{local} I{Azimuth, Elevation, slant Range} (AER) components.

           @kwarg Aer: Class to return AER (L{Aer}) or C{None}.
           @kwarg Aer_kwds: Optional, additional B{L{Aer}} keyword
                            arguments, ignored if B{C{Aer}} is C{None}.

           @return: AER as an L{Aer} instance or if C{B{Aer} is None},
                    an L{Aer4Tuple}C{(azimuth, elevation, slantrange, ltp)}.
        '''
        return self.xyzLocal.toAer(Aer=Aer, **Aer_kwds)

    def toCartesian(self, Cartesian=None, **Cartesian_kwds):
        '''Convert this I{local} to I{geocentric} C{(x, y, z)} (ECEF).

           @kwarg Cartesian: Optional class to return C{(x, y, z)} (C{Cartesian})
                             or C{None}.
           @kwarg Cartesian_kwds: Optional, additional B{C{Cartesian}} keyword
                                  arguments, ignored if C{B{Cartesian} is None}.

           @return: A C{B{Cartesian}(x, y, z, **B{Cartesian_kwds})} instance
                    or a L{Vector4Tuple}C{(x, y, z, h)} if C{B{Cartesian} is None}.

           @raise TypeError: Invalid B{C{Cartesian}} or B{C{Cartesian_kwds}}
                             argument.
        '''
        return self.ecef.toCartesian(Cartesian=Cartesian, **Cartesian_kwds)  # PYCHOK _Tuple

    def toEnu(self, Enu=None, **Enu_kwds):
        '''Get the I{local} I{East, North, Up} (ENU) components.

           @kwarg Enu: Class to return ENU (L{Enu}) or C{None}.
           @kwarg Enu_kwds: Optional, additional B{L{Enu}} keyword
                            arguments, ignored if C{B{Enu} is None}.

           @return: ENU as an L{Enu} instance or if C{B{Enu} is None},
                    an L{Enu4Tuple}C{(east, north, up, ltp)}.
        '''
        return self.xyzLocal.toEnu(Enu=Enu, **Enu_kwds)

    def toLatLon(self, LatLon=None, **LatLon_kwds):
        '''Convert this I{local} to I{geodetic} C{(lat, lon, height)}.

           @kwarg LatLon: Optional class to return C{(lat, lon, height)}
                          (C{LatLon}) or C{None}.
           @kwarg LatLon_kwds: Optional, additional B{C{LatLon}} keyword
                               arguments, ignored if C{B{LatLon} is None}.

           @return: An instance of C{B{LatLon}(lat, lon, **B{LatLon_kwds})}
                    or if C{B{LatLon} is None}, a L{LatLon3Tuple}C{(lat, lon,
                    height)} respectively L{LatLon4Tuple}C{(lat, lon, height,
                    datum)} depending on whether C{datum} is un-/specified.

           @raise TypeError: Invalid B{C{LatLon}} or B{C{LatLon_kwds}}
                             argument.
        '''
        return self.ecef.toLatLon(LatLon=LatLon, **LatLon_kwds)  # PYCHOK _Tuple

    def toNed(self, Ned=None, **Ned_kwds):
        '''Get the I{local} I{North, East, Down} (NED) components.

           @kwarg Ned: Class to return NED (L{Ned}) or C{None}.
           @kwarg Ned_kwds: Optional, additional B{L{Ned}} keyword
                            arguments, ignored if B{C{Ned}} is C{None}.

           @return: NED as an L{Ned} instance or if C{B{Ned} is None},
                    an L{Ned4Tuple}C{(north, east, down, ltp)}.
        '''
        return self.xyzLocal.toNed(Ned=Ned, **Ned_kwds)

    def toXyz(self, Xyz=None, **Xyz_kwds):
        '''Get the I{local} I{X, Y, Z} (XYZ) components.

           @kwarg Xyz: Class to return XYZ (L{XyzLocal}) or C{None}.
           @kwarg Xyz_kwds: Optional, additional B{C{Xyz}} keyword
                            arguments, ignored if C{B{Xyz} is None}.

           @return: XYZ as an B{C{Xyz}} instance or if C{B{Xyz} is None},
                    an L{Xyz4Tuple}C{(x, y, z, ltp)}.
        '''
        return self.xyzLocal.toXyz(Xyz=Xyz, **Xyz_kwds)

    @Property_RO
    def up(self):
        '''Get the I{local} Up, C{z} component (C{meter}).
        '''
        return self.z

    @Property_RO
    def xyz(self):
        '''Get the I{local} C{(X, Y, Z)} components (L{Vector3Tuple}C{(x, y, z)}).
        '''
        return Vector3Tuple(self.x, self.y, self.z, name=self.name)  # like Ecef9Tuple.xyz

    @Property_RO
    def xyzLocal(self):
        '''Get this L{Local9Tuple} as an L{XyzLocal}.
        '''
        return XyzLocal(*self.xyz, ltp=self.ltp, name=self.name)  # PYCHOK .ltp


_XyzLocals4 =  XyzLocal, Enu, Ned, Aer  # PYCHOK in .ltp
_XyzLocals5 = _XyzLocals4 + (Local9Tuple,)  # PYCHOK in .ltp


class Uvw(_Vector3d):
    '''3-D C{u-v-w} (UVW) components.
    '''
    _toStr = _uvw_

    def __init__(self, u_uvw, v=0, w=0, name=NN):
        '''New L{Uvw}.

           @arg u_uvw: Scalar U component (C{meter}) or a previous instance
                       (L{Uvw}, L{Uvw3Tuple}, L{Vector3d}).
           @kwarg v: V component (C{meter}) only used with scalar B{C{u_uvw}}.
           @kwarg w: W component (C{meter}) only used with scalar B{C{u_uvw}}.
           @kwarg name: Optional name (C{str}).

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

           @raise UnitError: Invalid B{C{east_enu}}, B{C{v}} or B{C{w}}.
        '''
        Vector3d.__init__(self, u_uvw, v, w, name=name)

    def toEnu(self, location, Enu=Enu, **Enu_kwds):
        '''Get the I{East, North, Up} (ENU) components at a location.

           @arg location: The geodetic (C{LatLon}) or geocentric (C{Cartesian},
                          L{Vector3d}) location from where to cast the L{Los}.
           @kwarg Enu: Class to return ENU (L{Enu}) or C{None}.
           @kwarg Enu_kwds: Optional, additional B{L{Enu}} keyword
                            arguments, ignored if C{B{Enu} is None}.

           @return: ENU as an L{Enu} instance or if C{B{Enu} is None}, an
                    L{Enu4Tuple}C{(east, north, up, ltp)} with C{ltp=None}.

           @raise TypeError: InvalidB{C{location}}.

           @see: Function U{lookAtSpheroid<https://PyPI.org/project/pymap3d>}.
        '''
        try:
            sa, ca, sb, cb = sincos2_(*location.philam)
        except Exception as x:
            raise _TypeError(location=location, cause=x)
        u, v, w = self.uvw

        t = cb * u + sb * v
        E = cb * v - sb * u
        N = ca * w - sa * t
        U = ca * t + sa * w
        return Enu4Tuple(E, N, U, name=self.name) if Enu is None else \
               Enu(      E, N, U, **_xkwds(Enu_kwds, name=self.name))

    u = Vector3d.x

    @Property_RO
    def uvw(self):
        '''Get the C{(U, V, W)} components (L{Uvw3Tuple}C{(u, v, w)}).
        '''
        return Uvw3Tuple(self.u, self.v, self.w, name=self.name)

    v = Vector3d.y
    w = Vector3d.z


class Uvw3Tuple(_NamedTuple):
    '''3-Tuple C{(u, v, w)}, in C{meter}.
    '''
    _Names_ = ('u',   'v',   'w')
    _Units_ = ( Meter, Meter, Meter)


class Los(Aer):
    '''A Line-Of-Sight (LOS) from a C{LatLon} or C{Cartesian} location.
    '''

    def __init__(self, azimuth_aer, elevation=0, name=NN):
        '''New L{Los}.

           @arg azimuth_aer: Scalar azimuth, bearing from North (compass C{degrees})
                             or a previous instance (L{Aer}, L{Aer4Tuple}, L{Enu},
                             L{Enu4Tuple} or L{Los}).
           @kwarg elevation: Scalar angle I{above} the horizon (C{degrees}, horizon
                             is 0, zenith +90, nadir -90), only used with scalar
                             B{C{azimuth_aer}}.
           @kwarg name: Optional name (C{str}).

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

           @raise UnitError: Invalid B{C{azimuth_aer}} or B{C{elevation}}.
        '''
        t = Aer(azimuth_aer, elevation)
        Aer.__init__(self, t.azimuth, t.elevation, slantrange=_1_0, name=name)

    def toUvw(self, location, Uvw=Uvw, **Uvw_kwds):
        '''Get this LOS' I{target} (UVW) components from a location.

           @arg location: The geodetic (C{LatLon}) or geocentric (C{Cartesian},
                          L{Vector3d}) location from where to cast the L{Los}.

           @see: Method L{Enu.toUvw} for further details.
        '''
        return self.toEnu().toUvw(location, Uvw=Uvw, **Uvw_kwds)

    def toEnu(self, Enu=Enu, **Enu_kwds):
        '''Get this LOS as I{East, North, Up} (ENU) components.

           @see: Method L{Aer.toEnu} for further details.
        '''
        return Aer.toEnu(self, Enu=Enu, **Enu_kwds)


class ChLV9Tuple(Local9Tuple):
    '''9-Tuple C{(Y, X, h_, lat, lon, height, ltp, ecef, M)} with I{B{unfalsed} Swiss
       (Y, X, h_)} coordinates and height, all in C{meter}, C{ltp} either a L{ChLV},
       L{ChLVa} or L{ChLVe} instance and C{ecef} (L{EcefKarney} I{at Bern, Ch}),
       otherwise like L{Local9Tuple}.
    '''
    _Names_ = (_Y_, _X_, _h__) + Local9Tuple._Names_[3:]

    @Property_RO
    def E_LV95(self):
        '''Get the B{falsed} I{Swiss E_LV95} easting (C{meter}).
        '''
        return self.EN2_LV95.E_LV95

    @Property_RO
    def EN2_LV95(self):
        '''Get the I{falsed Swiss (E_LV95, N_LV95)} easting and northing (L{ChLVEN2Tuple}).
        '''
        return ChLVEN2Tuple(*_MODS.ltp.ChLV.false2(self.Y, self.X, True), name=self.name)

    @Property_RO
    def h_LV03(self):
        '''Get the I{Swiss h_} height (C{meter}).
        '''
        return self.h_

    @Property_RO
    def h_LV95(self):
        '''Get the I{Swiss h_} height (C{meter}).
        '''
        return self.h_

    @property_RO
    def isChLV(self):
        '''Is this a L{ChLV}-generated L{ChLV9Tuple}?.
        '''
        return self.ltp.__class__ is _MODS.ltp.ChLV

    @property_RO
    def isChLVa(self):
        '''Is this a L{ChLVa}-generated L{ChLV9Tuple}?.
        '''
        return self.ltp.__class__ is _MODS.ltp.ChLVa

    @property_RO
    def isChLVe(self):
        '''Is this a L{ChLVe}-generated L{ChLV9Tuple}?.
        '''
        return self.ltp.__class__ is _MODS.ltp.ChLVe

    @Property_RO
    def N_LV95(self):
        '''Get the B{falsed} I{Swiss N_LV95} northing (C{meter}).
        '''
        return self.EN2_LV95.N_LV95

    @Property_RO
    def x(self):
        '''Get the I{local x, Swiss Y} easting (C{meter}).
        '''
        return self.Y

    @Property_RO
    def x_LV03(self):
        '''Get the B{falsed} I{Swiss x_LV03} northing (C{meter}).
        '''
        return self.yx2_LV03.x_LV03

    @Property_RO
    def y(self):
        '''Get the I{local y, Swiss X} northing (C{meter}).
        '''
        return self.X

    @Property_RO
    def y_LV03(self):
        '''Get the B{falsed} I{Swisss y_LV03} easting (C{meter}).
        '''
        return self.yx2_LV03.y_LV03

    @Property_RO
    def YX(self):
        '''Get the B{unfalsed} easting and northing (L{ChLVYX2Tuple}).
        '''
        return ChLVYX2Tuple(self.Y, self.X, name=self.name)

    @Property_RO
    def yx2_LV03(self):
        '''Get the B{falsed} I{Swiss (y_LV03, x_LV03)} easting and northing (L{ChLVyx2Tuple}).
        '''
        return ChLVyx2Tuple(*_MODS.ltp.ChLV.false2(self.Y, self.X, False), name=self.name)

    @Property_RO
    def z(self):
        '''Get the I{local z, Swiss h_} height (C{meter}).
        '''
        return self.h_


class ChLVYX2Tuple(_NamedTuple):
    '''2-Tuple C{(Y, X)} with B{unfalsed} I{Swiss LV95} easting and norting
       in C{meter}.
    '''
    _Names_ = (_Y_,   _X_)
    _Units_ = ( Meter, Meter)

    def false2(self, LV95=True):
        '''Return the falsed C{Swiss LV95} or C{LV03} version of the projection.

           @see: Function L{ChLV.false2} for more information.
        '''
        return _MODS.ltp.ChLV.false2(*self, LV95=LV95, name=self.name)


class ChLVEN2Tuple(_NamedTuple):
    '''2-Tuple C{(E_LV95, N_LV95)} with B{falsed} I{Swiss LV95} easting and
       norting in C{meter (2_600_000, 1_200_000)} and origin at C{Bern, Ch}.
    '''
    _Names_ = ('E_LV95', 'N_LV95')
    _Units_ = ChLVYX2Tuple._Units_

    def unfalse2(self):
        '''Return this projection as an B{unfalsed} L{ChLVYX2Tuple}.

           @see: Function L{ChLV.unfalse2} for more information.
        '''
        return _MODS.ltp.ChLV.unfalse2(*self, LV95=True, name=self.name)


class ChLVyx2Tuple(_NamedTuple):
    '''2-Tuple C{(y_LV03, x_LV03)} with B{falsed} I{Swiss LV03} easting and
       norting in C{meter (600_000, 200_000)} and origin at C{Bern, Ch}.
    '''
    _Names_ = ('y_LV03', 'x_LV03')
    _Units_ = ChLVYX2Tuple._Units_

    def unfalse2(self):
        '''Return this projection as an B{unfalsed} L{ChLVYX2Tuple}.

           @see: Function L{ChLV.unfalse2} for more information.
        '''
        return _MODS.ltp.ChLV.unfalse2(*self, LV95=False, name=self.name)


class Footprint5Tuple(_NamedTuple):
    '''5-Tuple C{(center, upperleft, upperight, loweright, lowerleft)}
       with the C{center} and 4 corners of the I{local} projection of
       a C{Frustum}, each an L{Xyz4Tuple}, L{XyzLocal}, C{LatLon}, etc.

       @note: Misspelling of C{upperight} and C{loweright} is I{intentional}.
    '''
    _Names_ = (_center_, 'upperleft', 'upperight', 'loweright', 'lowerleft')
    _Units_ = (_Pass,    _Pass,       _Pass,       _Pass,       _Pass)

    def toLatLon5(self, ltp=None, LatLon=None, **LatLon_kwds):
        '''Convert this footprint's C{center} and 4 corners to I{geodetic}
           C{LatLon(lat, lon, height)}s or C{LatLon3-} or C{-4Tuple}s.

           @kwarg ltp: The I{local tangent plane} (L{Ltp}), overriding this
                       footprint's C{center} or C{frustrum} C{ltp}.
           @kwarg LatLon: Optional I{geodetic} class (C{LatLon}) or C{None}.
           @kwarg LatLon_kwds: Optional, additional B{C{LatLon}} keyword
                               arguments, ignored if C{B{LatLon} is None}.

           @return: A L{Footprint5Tuple} of 5 C{B{LatLon}(lat, lon,
                    **B{LatLon_kwds})} instances or if C{B{LatLon} is None},
                    5 L{LatLon3Tuple}C{(lat, lon, height)}s respectively
                    5 L{LatLon4Tuple}C{(lat, lon, height, datum)}s depending
                    on keyword argument C{datum} is un-/specified.

           @raise TypeError: Invalid B{C{ltp}}, B{C{LatLon}} or B{C{LatLon_kwds}}.

           @see: Methods L{XyzLocal.toLatLon} and L{Footprint5Tuple.xyzLocal5}.
        '''
        kwds = _xkwds(LatLon_kwds, ltp=_MODS.ltp._xLtp(ltp, self.center.ltp),  # PYCHOK .center
                                   LatLon=LatLon, name=self.name,)
        return Footprint5Tuple(t.toLatLon(**kwds) for t in self.xyzLocal5())

    def xyzLocal5(self, ltp=None):
        '''Return this footprint's C{center} and 4 corners as 5 L{XyzLocal}s.

           @kwarg ltp: The I{local tangent plane} (L{Ltp}), overriding
                       the {center} and corner C{ltp}s.

           @return: A L{Footprint5Tuple} of 5 L{XyzLocal} instances.

           @raise TypeError: Invalid B{C{ltp}}.
        '''
        if ltp is None:
            p =  self
        else:
            p = _MODS.ltp._xLtp(ltp)
            p =  tuple(Xyz4Tuple(t.x, t.y, t.z, p) for t in self)
        return Footprint5Tuple(t.xyzLocal for t in p)


__all__ += _ALL_DOCS(_NamedAerNed)

# **) MIT License
#
# Copyright (C) 2016-2023 -- mrJean1 at Gmail -- All Rights Reserved.
#
# 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
# the rights to use, copy, modify, merge, publish, distribute, sublicense,
# 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:
#
# The above copyright notice and this permission notice shall be included
# in all copies or substantial portions of the Software.
#
# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.  IN NO EVENT SHALL
# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR
# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
# OTHER DEALINGS IN THE SOFTWARE.
