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

u'''I{Local Tangent Plane} (LTP) and I{local} cartesian coordinates.

I{Local cartesian} and I{local tangent plane} classes L{LocalCartesian}, approximations L{ChLVa}
and L{ChLVe} and L{Ltp}, L{ChLV}, L{LocalError}, L{Attitude} and L{Frustum}.

@see: U{Local tangent plane coordinates<https://WikiPedia.org/wiki/Local_tangent_plane_coordinates>}
      and class L{LocalCartesian}, transcoded from I{Charles Karney}'s C++ classU{LocalCartesian
      <https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1LocalCartesian.html>}.
'''
# make sure int/int division yields float quotient, see .basics
from __future__ import division as _; del _  # PYCHOK semicolon

from pygeodesy.basics import isscalar, issubclassof, map1, _xargs_names
from pygeodesy.constants import EPS, INT0, _umod_360, _0_0, _0_01, _0_5, _1_0, \
                               _2_0, _60_0, _90_0, _100_0, _180_0, _3600_0, \
                               _N_1_0  # PYCHOK used!
from pygeodesy.datums import _WGS84, _xinstanceof
from pygeodesy.ecef import _EcefBase, EcefKarney, _llhn4, _xyzn4
from pygeodesy.errors import _NotImplementedError, _TypesError, _ValueError, \
                             _xattr, _xkwds, _xkwds_get
from pygeodesy.fmath import fabs, fdot, Fhorner
from pygeodesy.fsums import _floor, Fsum, fsumf_, fsum1f_
from pygeodesy.interns import NN, _0_, _COMMASPACE_, _DOT_, _ecef_, _height_, \
                             _invalid_, _lat0_, _lon0_, _ltp_, _M_, _name_, _too_
# from pygeodesy.lazily import _ALL_LAZY  # from vector3d
from pygeodesy.ltpTuples import Attitude4Tuple, ChLVEN2Tuple, ChLV9Tuple, \
                                ChLVYX2Tuple, Footprint5Tuple, Local9Tuple, \
                                ChLVyx2Tuple, _XyzLocals4, _XyzLocals5, Xyz4Tuple
from pygeodesy.named import _NamedBase, notOverloaded
from pygeodesy.namedTuples import LatLon3Tuple, LatLon4Tuple, Vector3Tuple
from pygeodesy.props import Property, Property_RO, property_doc_, property_RO, \
                           _update_all
from pygeodesy.streprs import Fmt, strs, unstr
from pygeodesy.units import Bearing, Degrees, Meter
from pygeodesy.utily import cotd, _loneg, sincos2d, sincos2d_, tand, tand_, \
                            wrap180, wrap360
from pygeodesy.vector3d import _ALL_LAZY, Vector3d

# from math import fabs, floor as _floor  # from .fmath, .fsums

__all__ = _ALL_LAZY.ltp
__version__ = '23.09.22'

_height0_ = _height_ + _0_
_narrow_  = 'narrow'
_wide_    = 'wide'
_Xyz_     = 'Xyz'


def _fov_2(**fov):
    # Half a field-of-view angle in C{degrees}.
    f = Degrees(Error=LocalError, **fov) * _0_5
    if EPS < f < _90_0:
        return f
    t = _invalid_ if f < 0 else _too_(_wide_ if f > EPS else _narrow_)
    raise LocalError(txt=t, **fov)


class Attitude(_NamedBase):
    '''The orientation of a plane or camera in space.
    '''
    _alt  = Meter(  alt =_0_0)
    _roll = Degrees(roll=_0_0)
    _tilt = Degrees(tilt=_0_0)
    _yaw  = Bearing(yaw =_0_0)

    def __init__(self, alt_attitude=INT0, tilt=INT0, yaw=INT0, roll=INT0, name=NN):
        '''New L{Attitude}.

           @kwarg alt_attitude: An altitude (C{meter}) above earth or an attitude
                                (L{Attitude} or L{Attitude4Tuple}) with the
                                C{B{alt}itude}, B{C{tilt}}, B{C{yaw}} and B{C{roll}}.
           @kwarg tilt: Pitch, elevation from horizontal (C{degrees180}), negative down
                        (clockwise rotation along and around the x- or East axis).
           @kwarg yaw: Bearing, heading (compass C{degrees360}), clockwise from North
                       (counter-clockwise rotation along and around the z- or Up axis).
           @kwarg roll: Roll, bank (C{degrees180}), positive to the right and down
                        (clockwise rotation along and around the y- or North axis).
           @kwarg name: Optional name C{str}).

           @raise AttitudeError: Invalid B{C{alt_attitude}}, B{C{tilt}}, B{C{yaw}} or
                                 B{C{roll}}.

           @see: U{Principal axes<https://WikiPedia.org/wiki/Aircraft_principal_axes>} and
                 U{Yaw, pitch, and roll rotations<http://MSL.CS.UIUC.edu/planning/node102.html>}.
        '''
        if isscalar(alt_attitude):
            t = Attitude4Tuple(alt_attitude, tilt, yaw, roll)
        else:
            try:
                t = alt_attitude.atyr
            except AttributeError:
                raise AttitudeError(alt=alt_attitude, tilt=tilt, yaw=yaw, rol=roll)
        for n, v in t.items():
            if v:
                setattr(self, n, v)
        n = name or t.name
        if n:
            self.name = n

    @property_doc_(' altitude above earth in C{meter}.')
    def alt(self):
        return self._alt

    @alt.setter  # PYCHOK setter!
    def alt(self, alt):  # PYCHOK no cover
        a = Meter(alt=alt, Error=AttitudeError)
        if self._alt != a:
            _update_all(self)
            self._alt = a

    altitude = alt

    @Property_RO
    def atyr(self):
        '''Return this attitude's alt[itude], tilt, yaw and roll as an L{Attitude4Tuple}.
        '''
        return Attitude4Tuple(self.alt, self.tilt, self.yaw, self.roll, name=self.name)

    @Property_RO
    def matrix(self):
        '''Get the 3x3 rotation matrix C{R(yaw)·R(tilt)·R(roll)}, aka I{ZYX} (C{float}, row-order).

           @see: The matrix M of case 10 in U{Appendix A
                 <https://ntrs.NASA.gov/api/citations/19770019231/downloads/19770019231.pdf>}.
        '''
        def _5to3(x, y, _y, z, _z):
            return x, fsum1f_(y, _y), fsum1f_(z, _z)

        r0, r1, r2 = self._rows3
        return _5to3(*r0), _5to3(*r1), r2

    @property_doc_(' roll/bank in C{degrees180}, positive to the right and down.')
    def roll(self):
        return self._roll

    @roll.setter  # PYCHOK setter!
    def roll(self, roll):
        r = Degrees(roll=roll, wrap=wrap180, Error=AttitudeError)
        if self._roll != r:
            _update_all(self)
            self._roll = r

    bank = roll

    @Property_RO
    def _rows3(self):
        # to follow the definitions of rotation angles alpha, beta and gamma:
        # negate yaw since yaw is counter-clockwise around the z-axis, swap
        # tilt and roll since tilt is around the x- and roll around the y-axis
        sa, ca, sb, cb, sg, cg = sincos2d_(-self.yaw, self.roll, self.tilt)
        return ((ca * cb,  ca * sb * sg, -sa * cg,  ca * sb * cg,  sa * sg),
                (sa * cb,  sa * sb * sg,  ca * cg,  sa * sb * cg, -ca * sg),
                (    -sb,       cb * sg,                 cb * cg))

    def rotate(self, x_xyz, y=None, z=None, Vector=None, **Vector_kwds):
        '''Transform a (local) cartesian by this attitude's matrix.

           @arg x_xyz: X component of vector (C{scalar}) or (3-D) vector
                       (C{Cartesian}, L{Vector3d} or L{Vector3Tuple}).
           @kwarg y: Y component of vector (C{scalar}), same units as B{C{x}}.
           @kwarg z: Z component of vector (C{scalar}), same units as B{C{x}}.
           @kwarg Vector: Class to return transformed point (C{Cartesian},
                          L{Vector3d} or C{Vector3Tuple}) 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}} instance or a L{Vector3Tuple}C{(x, y, z)} if
                    C{B{Vector}=None}.

           @raise AttitudeError: Invalid B{C{x_xyz}}, B{C{y}} or B{C{z}}.

           @see: U{Yaw, pitch, and roll rotations<http://MSL.CS.UIUC.edu/planning/node102.html>}.
        '''
        try:
            try:
                x, y, z = map( float, x_xyz.xyz)
            except AttributeError:
                x, y, z = map1(float, x_xyz, y, z)
        except (TypeError, ValueError) as x:
            raise AttitudeError(x_xyz=x_xyz, y=y, z=z, cause=x)

        X, Y, Z = self._rows3
        X = fdot(X, x, y, y, z, z)
        Y = fdot(Y, x, y, y, z, z)
        Z = fdot(Z, x, y, z)
        return Vector3Tuple(X, Y, Z, name=self.name) if Vector is None else \
                     Vector(X, Y, Z, **_xkwds(Vector_kwds, name=self.name))

    @property_doc_(' tilt/pitch/elevation from horizontal in C{degrees180}, negative down.')
    def tilt(self):
        return self._tilt

    @tilt.setter  # PYCHOK setter!
    def tilt(self, tilt):
        t = Degrees(tilt=tilt, wrap=wrap180, Error=AttitudeError)
        if self._tilt != t:
            _update_all(self)
            self._tilt = t

    elevation = pitch = tilt

    def toStr(self, prec=6, sep=_COMMASPACE_, **unused):  # PYCHOK signature
        '''Format this attitude as string.

           @kwarg prec: The C{float} precision, number of decimal digits (0..9).
                        Trailing zero decimals are stripped for B{C{prec}} values
                        of 1 and above, but kept for negative B{C{prec}} values.
           @kwarg sep: Separator to join (C{str}).

           @return: This attitude (C{str}).
        '''
        return self.atyr.toStr(prec=prec, sep=sep)

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

           @see: U{Yaw, pitch, and roll rotations<http://MSL.CS.UIUC.edu/planning/node102.html>}.
        '''
        def _r2d(r):
            return fsumf_(_N_1_0, *r)

        return Vector3d(*map(_r2d, self._rows3), name=tyr3d.__name__)

    @property_doc_(' yaw/bearing/heading in compass C{degrees360}, clockwise from North.')
    def yaw(self):
        return self._yaw

    @yaw.setter  # PYCHOK setter!
    def yaw(self, yaw):
        y = Bearing(yaw=yaw, Error=AttitudeError)
        if self._yaw != y:
            _update_all(self)
            self._yaw = y

    bearing = heading = yaw


class AttitudeError(_ValueError):
    '''An L{Attitude} or L{Attitude4Tuple} issue.
    '''
    pass


class Frustum(_NamedBase):
    '''A rectangular pyramid, typically representing a camera's I{field-of-view}
       (fov) and the intersection with (or projection to) a I{local tangent plane}.

       @see: U{Viewing frustum<https://WikiPedia.org/wiki/Viewing_frustum>}.
    '''
    _h_2     = _0_0   # half hfov in degrees
    _ltp     =  None  # local tangent plane
    _tan_h_2 = _0_0   # tan(_h_2)
    _v_2     = _0_0   # half vfov in degrees

    def __init__(self, hfov, vfov, ltp=None):
        '''New L{Frustum}.

           @arg hfov: Horizontal field-of-view (C{degrees180}).
           @arg vfov: Vertical field-of-view (C{degrees180}).
           @kwarg ltp: Optional I{local tangent plane} (L{Ltp}).

           @raise LocalError: Invalid B{C{hfov}} or B{C{vfov}}.
        '''
        self._h_2 = h = _fov_2(hfov=hfov)
        self._v_2 =     _fov_2(vfov=vfov)

        self._tan_h_2 = tand(h, fov_2=h)

        if ltp:
            self._ltp = _xLtp(ltp)

    def footprint5(self, alt_attitude, tilt=0, yaw=0, roll=0, z=_0_0, ltp=None):  # MCCABE 15
        '''Compute the center and corners of the intersection with (or projection
           to) the I{local tangent plane} (LTP).

           @arg alt_attitude: An altitude (C{meter}) above I{local tangent plane} or
                              an attitude (L{Attitude} or L{Attitude4Tuple}) with the
                              C{B{alt}itude}, B{C{tilt}}, B{C{yaw}} and B{C{roll}}.
           @kwarg tilt: Pitch, elevation from horizontal (C{degrees}), negative down
                        (clockwise rotation along and around the x- or East axis).
           @kwarg yaw: Bearing, heading (compass C{degrees}), clockwise from North
                       (counter-clockwise rotation along and around the z- or Up axis).
           @kwarg roll: Roll, bank (C{degrees}), positive to the right and down
                        (clockwise rotation along and around the y- or North axis).
           @kwarg z: Optional height of the footprint (C{meter}) above I{local tangent plane}.
           @kwarg ltp: The I{local tangent plane} (L{Ltp}), overriding this
                       frustum's C{ltp}.

           @return: A L{Footprint5Tuple}C{(center, upperleft, upperight, loweright,
                    lowerleft)} with the C{center} and 4 corners, each an L{Xyz4Tuple}.

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

           @raise UnitError: Invalid B{C{altitude}}, B{C{tilt}}, B{C{roll}} or B{C{z}}.

           @raise ValueError: If B{C{altitude}} too low, B{C{z}} too high or B{C{tilt}}
                              or B{C{roll}} -including B{C{vfov}} respectively B{C{hfov}}-
                              over the horizon.

           @see: U{Principal axes<https://WikiPedia.org/wiki/Aircraft_principal_axes>}.
        '''
        def _xy2(a, e, h_2, tan_h_2, r):
            # left and right corners, or swapped
            if r < EPS:  # no roll
                r =  a * tan_h_2
                l = -r  # PYCHOK l is ell
            else:  # roll
                r, l = tand_(r - h_2, r + h_2, roll_hfov=r)  # PYCHOK l is ell
                r *= -a  # negate right positive
                l *= -a  # PYCHOK l is ell
            y = a * cotd(e, tilt_vfov=e)
            return (l, y), (r, y)

        def _xyz5(b, xy5, z, ltp):
            # rotate (x, y)'s by bearing, clockwise
            s, c = sincos2d(b)
            for x, y in xy5:
                yield Xyz4Tuple(fsum1f_(x * c,  y * s),
                                fsum1f_(y * c, -x * s), z, ltp)

        try:
            a, t, y, r = alt_attitude.atyr
        except AttributeError:
            a, t, y, r = alt_attitude, tilt, yaw, roll

        a = Meter(altitude=a)
        if a < EPS:  # too low
            raise _ValueError(altitude=a)
        if z:  # PYCHOK no cover
            z  = Meter(z=z)
            a -= z
            if a < EPS:  # z above a
                raise _ValueError(altitude_z=a)
        else:
            z = _0_0

        b =  Degrees(yaw=y, wrap=wrap360)  # bearing
        e = -Degrees(tilt=t, wrap=wrap180)  # elevation, pitch
        if not EPS < e < _180_0:
            raise _ValueError(tilt=t)
        if e > _90_0:
            e = _loneg(e)
            b = _umod_360(b + _180_0)

        r = Degrees(roll=r, wrap=wrap180)  # roll center
        x = (-a * tand(r, roll=r)) if r else _0_0
        y =   a * cotd(e, tilt=t)  # ground range
        if fabs(y) < EPS:
            y = _0_0

        # center and corners, clockwise from upperleft, rolled
        xy5 = ((x, y),) + _xy2(a, e - self._v_2,  self._h_2,  self._tan_h_2, r) \
                        + _xy2(a, e + self._v_2, -self._h_2, -self._tan_h_2, r)  # swapped
        # turn center and corners by yaw, clockwise
        p = self.ltp if ltp is None else ltp  # None OK
        return Footprint5Tuple(_xyz5(b, xy5, z, p))  # *_xyz5

    @Property_RO
    def hfov(self):
        '''Get the horizontal C{fov} (C{degrees}).
        '''
        return Degrees(hfov=self._h_2 * _2_0)

    @Property_RO
    def ltp(self):
        '''Get the I{local tangent plane} (L{Ltp}) or C{None}.
        '''
        return self._ltp

    def toStr(self, prec=3, fmt=Fmt.F, sep=_COMMASPACE_):  # PYCHOK signature
        '''Convert this frustum to a "hfov, vfov, ltp" string.

           @kwarg prec: Number of (decimal) digits, unstripped (0..8 or C{None}).
           @kwarg fmt: Optional, C{float} format (C{str}).
           @kwarg sep: Separator to join (C{str}).

           @return: Frustum in the specified form (C{str}).
        '''
        t = self.hfov, self.vfov
        if self.ltp:
            t += self.ltp,
        t = strs(t, prec=prec, fmt=fmt)
        return sep.join(t) if sep else t

    @Property_RO
    def vfov(self):
        '''Get the vertical C{fov} (C{degrees}).
        '''
        return Degrees(vfov=self._v_2 * _2_0)


class LocalError(_ValueError):
    '''A L{LocalCartesian} or L{Ltp} related issue.
    '''
    pass


class LocalCartesian(_NamedBase):
    '''Conversion between geodetic C{(lat, lon, height)} and I{local
       cartesian} C{(x, y, z)} coordinates with I{geodetic} origin
       C{(lat0, lon0, height0)}, transcoded from I{Karney}'s C++ class
       U{LocalCartesian<https://GeographicLib.SourceForge.io/C++/doc/
       classGeographicLib_1_1LocalCartesian.html>}.

       The C{z} axis is normal to the ellipsoid, the C{y} axis points due
       North.  The plane C{z = -height0} is tangent to the ellipsoid.

       The conversions all take place via geocentric coordinates using a
       geocentric L{EcefKarney}, by default the WGS84 datum/ellipsoid.

       @see: Class L{Ltp}.
    '''
    _ecef      = EcefKarney(_WGS84)
    _EcefClass = EcefKarney
    _lon00     = INT0  # self.lon0
    _t0        = None  # origin (..., lat0, lon0, height0, ...) L{Ecef9Tuple}
    _9Tuple    = Local9Tuple

    def __init__(self, latlonh0=INT0, lon0=INT0, height0=INT0, ecef=None, name=NN, **lon00):
        '''New L{LocalCartesian} converter.

           @kwarg latlonh0: The (geodetic) origin (C{LatLon}, L{LatLon4Tuple}, L{Ltp}
                            L{LocalCartesian} or L{Ecef9Tuple}) or the C{scalar}
                            latitude of the (goedetic) origin (C{degrees}).
           @kwarg lon0: Longitude of the (goedetic) origin (C{degrees}) for C{scalar}
                        B{C{latlonh0}}, ignored otherwise.
           @kwarg height0: Optional height (C{meter}, conventionally) at the (goedetic)
                           origin perpendicular to and above (or below) the ellipsoid's
                           surface and for C{scalar} B{C{latlonh0}}, ignored otherwise.
           @kwarg ecef: An ECEF converter (L{EcefKarney} I{only}) for C{scalar}
                        B{C{latlonh0}}, ignored otherwise.
           @kwarg name: Optional name (C{str}).
           @kwarg lon00: An arbitrary, I{polar} longitude (C{degrees}), overriding
                         the default C{B{lon00}=B{lon0}}, see method C{reverse}.

           @raise LocalError: If B{C{latlonh0}} not C{LatLon}, L{LatLon4Tuple}, L{Ltp},
                              L{LocalCartesian} or L{Ecef9Tuple} or B{C{latlonh0}},
                              B{C{lon0}}, B{C{height0}} or B{C{lon00}} invalid.

           @raise TypeError: Invalid B{C{ecef}} or not L{EcefKarney}.

           @note: If BC{latlonh0} is an L{Ltp} or L{LocalCartesian}, only C{lat0}, C{lon0},
                  C{height0} and I{polar} C{lon00} are copied, I{not} the ECEF converter.
        '''
        self.reset(latlonh0, lon0=lon0, height0=height0, ecef=ecef, name=name, **lon00)

    def __eq__(self, other):
        '''Compare this and an other instance.

           @arg other: The other ellipsoid (L{LocalCartesian} or L{Ltp}).

           @return: C{True} if equal, C{False} otherwise.
        '''
        return other is self or (isinstance(other, self.__class__) and
                                            other.ecef == self.ecef and
                                            other._t0  == self._t0)

    @Property_RO
    def datum(self):
        '''Get the ECEF converter's datum (L{Datum}).
        '''
        return self.ecef.datum

    @Property_RO
    def ecef(self):
        '''Get the ECEF converter (L{EcefKarney}).
        '''
        return self._ecef

    def _ecef2local(self, ecef, Xyz, Xyz_kwds):
        '''(INTERNAL) Convert geocentric/geodetic to local, like I{forward}.

           @arg ecef: Geocentric (and geodetic) (L{Ecef9Tuple}).
           @arg Xyz: An L{XyzLocal}, L{Enu} or L{Ned} I{class} or C{None}.
           @arg Xyz_kwds: B{C{Xyz}} keyword arguments, ignored if C{B{Xyz} is None}.

           @return: An C{B{Xyz}(x, y, z, ltp, **B{Xyz_kwds}} instance or if
                    C{B{Xyz} is None}, a L{Local9Tuple}C{(x, y, z, lat, lon,
                    height, ltp, ecef, M)} with this C{ltp}, B{C{ecef}}
                    (L{Ecef9Tuple}) converted to this C{datum} and C{M=None},
                    always.
        '''
        ltp = self
        if ecef.datum != ltp.datum:
            ecef = ecef.toDatum(ltp.datum)
        x, y, z = self.M.rotate(ecef.xyz, *ltp._t0_xyz)
        r = Local9Tuple(x, y, z, ecef.lat, ecef.lon, ecef.height,
                                 ltp, ecef, None, name=ecef.name)
        if Xyz:
            if not issubclassof(Xyz, *_XyzLocals4):  # Vector3d
                raise _TypesError(_Xyz_, Xyz, *_XyzLocals4)
            r = r.toXyz(Xyz=Xyz, **Xyz_kwds)
        return r

    @Property_RO
    def ellipsoid(self):
        '''Get the ECEF converter's ellipsoid (L{Ellipsoid}).
        '''
        return self.ecef.datum.ellipsoid

    def forward(self, latlonh, lon=None, height=0, M=False, name=NN):
        '''Convert I{geodetic} C{(lat, lon, height)} to I{local} cartesian
           C{(x, y, z)}.

           @arg latlonh: Either a C{LatLon}, L{Ltp}, L{Ecef9Tuple} or C{scalar}
                         (geodetic) latitude (C{degrees}).
           @kwarg lon: Optional C{scalar} (geodetic) longitude for C{scalar}
                       B{C{latlonh}} (C{degrees}).
           @kwarg height: Optional height (C{meter}, conventionally) perpendicular
                          to and above (or below) the ellipsoid's surface.
           @kwarg M: Optionally, return the I{concatenated} rotation L{EcefMatrix},
                     iff available (C{bool}).
           @kwarg name: Optional name (C{str}).

           @return: A L{Local9Tuple}C{(x, y, z, lat, lon, height, ltp, ecef, M)}
                    with I{local} C{x}, C{y}, C{z}, I{geodetic} C{(lat}, C{lon},
                    C{height}, this C{ltp}, C{ecef} (L{Ecef9Tuple}) with
                    I{geocentric} C{x}, C{y}, C{z} (and I{geodetic} C{lat},
                    C{lon}, C{height}) and the I{concatenated} rotation matrix
                    C{M} (L{EcefMatrix}) if requested.

           @raise LocalError: If B{C{latlonh}} not C{scalar}, C{LatLon}, L{Ltp},
                              L{Ecef9Tuple} or invalid or if B{C{lon}} not
                              C{scalar} for C{scalar} B{C{latlonh}} or invalid
                              or if B{C{height}} invalid.
        '''
        lat, lon, h, n = _llhn4(latlonh, lon, height, Error=LocalError, name=name)
        t = self.ecef._forward(lat, lon, h, n, M=M)
        x, y, z = self.M.rotate(t.xyz, *self._t0_xyz)
        m = self.M.multiply(t.M) if M else None
        return self._9Tuple(x, y, z, lat, lon, h, self, t, m, name=n or self.name)

    @Property_RO
    def height0(self):
        '''Get the origin's height (C{meter}).
        '''
        return self._t0.height

    @Property_RO
    def lat0(self):
        '''Get the origin's latitude (C{degrees}).
        '''
        return self._t0.lat

    @Property_RO
    def latlonheight0(self):
        '''Get the origin's lat-, longitude and height (L{LatLon3Tuple}C{(lat, lon, height)}).
        '''
        return LatLon3Tuple(self.lat0, self.lon0, self.height0, name=self.name)

    def _local2ecef(self, local, nine=False, M=False):
        '''(INTERNAL) Convert I{local} to geocentric/geodetic, like I{.reverse}.

           @arg local: Local (L{XyzLocal}, L{Enu}, L{Ned}, L{Aer} or L{Local9Tuple}).
           @kwarg nine: Return 3- or 9-tuple (C{bool}).
           @kwarg M: Include the rotation matrix (C{bool}).

           @return: A I{geocentric} 3-tuple C{(x, y, z)} or if C{B{nine}=True},
                    an L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M, datum)},
                    optionally including rotation matrix C{M} or C{None}.
        '''
        t = self.M.unrotate(local.xyz, *self._t0_xyz)
        if nine:
            t = self.ecef.reverse(*t, M=M)
        return t

    @Property_RO
    def lon0(self):
        '''Get the origin's longitude (C{degrees}).
        '''
        return self._t0.lon

    @Property
    def lon00(self):
        '''Get the arbitrary, I{polar} longitude (C{degrees}).
        '''
        return self._lon00

    @lon00.setter  # PYCHOK setter!
    def lon00(self, lon00):
        '''Set the arbitrary, I{polar} longitude (C{degrees}).
        '''
        # lon00 <https://GitHub.com/mrJean1/PyGeodesy/issues/77>
        self._lon00 = Degrees(lon00=lon00)

    @Property_RO
    def M(self):
        '''Get the rotation matrix (C{EcefMatrix}).
        '''
        return self._t0.M

    def reset(self, latlonh0=INT0, lon0=INT0, height0=INT0, ecef=None, name=NN, **lon00):
        '''Reset this converter, see L{LocalCartesian.__init__} and L{Ltp.__init__} for more details.
        '''
        if isinstance(latlonh0, LocalCartesian):
            if self._t0:
                _update_all(self)
            self._ecef  = latlonh0.ecef
            self._lon00 = latlonh0.lon00
            self._t0    = latlonh0._t0
            n           = name or latlonh0.name
        else:
            lat0, lon0, height0, n = _llhn4(latlonh0, lon0, height0, suffix=_0_,
                                            Error=LocalError, name=name or self.name)
            if ecef:  # PYCHOK no cover
                _xinstanceof(self._EcefClass, ecef=ecef)
                _update_all(self)
                self._ecef = ecef
            elif self._t0:
                _update_all(self)
            self._t0 = self.ecef._forward(lat0, lon0, height0, n, M=True)
            self.lon00 = _xattr(latlonh0, lon00=_xkwds_get(lon00, lon00=lon0))
        if n:
            self.rename(n)

    def reverse(self, xyz, y=None, z=None, M=False, name=NN, **lon00):
        '''Convert I{local} C{(x, y, z)} to I{geodetic} C{(lat, lon, height)}.

           @arg xyz: A I{local} (L{XyzLocal}, L{Enu}, L{Ned}, L{Aer}, L{Local9Tuple}) or
                     local C{x} coordinate (C{scalar}).
           @kwarg y: Local C{y} coordinate for C{scalar} B{C{xyz}} and B{C{z}} (C{meter}).
           @kwarg z: Local C{z} coordinate for C{scalar} B{C{xyz}} and B{C{y}} (C{meter}).
           @kwarg M: Optionally, return the I{concatenated} rotation L{EcefMatrix}, iff
                     available (C{bool}).
           @kwarg name: Optional name (C{str}).
           @kwarg lon00: An arbitrary, I{polar} longitude (C{degrees}), returned for local
                         C{B{x}=0} and C{B{y}=0} at I{polar} latitudes C{abs(B{lat0}) == 90},
                         overriding property C{lon00} and default C{B{lon00}=B{lon0}}.

           @return: An L{Local9Tuple}C{(x, y, z, lat, lon, height, ltp, ecef, M)} with
                    I{local} C{x}, C{y}, C{z}, I{geodetic} C{lat}, C{lon}, C{height},
                    this C{ltp}, an C{ecef} (L{Ecef9Tuple}) with the I{geocentric} C{x},
                    C{y}, C{z} (and I{geodetic} C{lat}, C{lon}, C{height}) and the
                    I{concatenated} rotation matrix C{M} (L{EcefMatrix}) if requested.

           @raise LocalError: Invalid B{C{xyz}} or C{scalar} C{x} or B{C{y}} and/or B{C{z}}
                              not C{scalar} for C{scalar} B{C{xyz}}.
        '''
        x, y, z, n = _xyzn4(xyz, y, z, _XyzLocals5, Error=LocalError, name=name)
        c = self.M.unrotate((x, y, z), *self._t0_xyz)
        t = self.ecef.reverse(*c, M=M, lon00=_xkwds_get(lon00, lon00=self.lon00))
        m = self.M.multiply(t.M) if M else None
        return self._9Tuple(x, y, z, t.lat, t.lon, t.height, self, t, m, name=n or self.name)

    @Property_RO
    def _t0_xyz(self):
        '''(INTERNAL) Get C{(x0, y0, z0)} as L{Vector3Tuple}.
        '''
        return self._t0.xyz

    def toStr(self, prec=9, **unused):  # PYCHOK signature
        '''Return this L{LocalCartesian} as a string.

           @kwarg prec: Precision, number of (decimal) digits (0..9).

           @return: This L{LocalCartesian} representation (C{str}).
        '''
        return self.attrs(_lat0_, _lon0_, _height0_, _M_, _ecef_, _name_, prec=prec)


class Ltp(LocalCartesian):
    '''A I{local tangent plan} (LTP), a sub-class of C{LocalCartesian} with
       (re-)configurable ECEF converter.
    '''
    _EcefClass = _EcefBase

    def __init__(self, latlonh0=INT0, lon0=INT0, height0=INT0, ecef=None, name=NN, **lon00):
        '''New C{Ltp}, see L{LocalCartesian.__init__} for more details.

           @kwarg ecef: Optional ECEF converter (L{EcefKarney}, L{EcefFarrell21},
                        L{EcefFarrell22}, L{EcefSudano}, L{EcefVeness} or
                        L{EcefYou} I{instance}), overriding the default
                        L{EcefKarney}C{(datum=Datums.WGS84)} for C{scalar}.

           @raise TypeError: Invalid B{C{ecef}}.
        '''
        LocalCartesian.reset(self, latlonh0, lon0=lon0, height0=height0,
                                             ecef=ecef, name=name, **lon00)

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

    @ecef.setter  # PYCHOK setter!
    def ecef(self, ecef):
        '''Set this LTP's ECEF converter (C{Ecef...} I{instance}).

           @raise TypeError: Invalid B{C{ecef}}.
        '''
        _xinstanceof(_EcefBase, ecef=ecef)
        if ecef != self._ecef:  # PYCHOK no cover
            self.reset(self._t0)
            self._ecef = ecef


class _ChLV(object):
    '''(INTERNAL) Base class for C{ChLV*} classes.
    '''
    _03_falsing = ChLVyx2Tuple(0.6e6, 0.2e6)
#   _92_falsing = ChLVYX2Tuple(2.0e6, 1.0e6)  # _95_ - _03_
    _95_falsing = ChLVEN2Tuple(2.6e6, 1.2e6)

    def _ChLV9Tuple(self, fw, M, name, *Y_X_h_lat_lon_h):
        '''(INTERNAL) Helper for C{ChLVa/e.forward} and C{.reverse}.
        '''
        if bool(M):  # PYCHOK no cover
            m =  self.forward if fw else self.reverse  # PYCHOK attr
            n = _DOT_(self.__class__.__name__, m.__name__)
            raise _NotImplementedError(unstr(n, M=M), txt=None)
        t = Y_X_h_lat_lon_h + (self, self._t0, None)  # PYCHOK _t0
        return ChLV9Tuple(t, name=name)

    @property_RO
    def _enh_n_h(self):
        '''(INTERNAL) Get C{ChLV*.reverse} args[1:4] names, I{once}.
        '''
        t = _xargs_names(_ChLV.reverse)[1:4]
        _ChLV._enh_n_h = t  # overwrite this property_RO
        # assert _xargs_names( ChLV.reverse)[1:4] == t
        # assert _xargs_names(ChLVa.reverse)[1:4] == t
        # assert _xargs_names(ChLVe.reverse)[1:4] == t
        return t

    def forward(self, latlonh, lon=None, height=0, M=None, name=NN):  # PYCHOK no cover
        '''Convert WGS84 geodetic to I{Swiss} projection coordinates.  I{Must be overloaded}.

           @arg latlonh: Either a C{LatLon}, L{Ltp} or C{scalar} (geodetic) latitude (C{degrees}).
           @kwarg lon: Optional, C{scalar} (geodetic) longitude for C{scalar} B{C{latlonh}} (C{degrees}).
           @kwarg height: Optional, height, vertically above (or below) the surface of the ellipsoid
                          (C{meter}) for C{scalar} B{C{latlonh}} and B{C{lon}}.
           @kwarg M: If C{True}, return the I{concatenated} rotation L{EcefMatrix} iff available
                     for C{ChLV} only, C{None} otherwise (C{bool}).
           @kwarg name: Optional name (C{str}).

           @return: A L{ChLV9Tuple}C{(Y, X, h_, lat, lon, height, ltp, ecef, M)} with the unfalsed
                    I{Swiss Y, X} coordinates, I{Swiss h_} height, the given I{geodetic} C{lat},
                    C{lon} and C{height}, this C{ChLV*} instance and C{ecef} (L{Ecef9Tuple}) at
                    I{Bern, Ch} and rotation matrix C{M}.  The returned C{ltp} is this C{ChLV},
                    C{ChLVa} or C{ChLVe} instance.

           @raise LocalError: Invalid or non-C{scalar} B{C{latlonh}}, B{C{lon}} or B{C{height}}.
        '''
        notOverloaded(self, latlonh, lon=lon, height=height, M=M, name=name)

    def reverse(self, enh_, n=None, h_=0, M=None, **name):  # PYCHOK no cover
        '''Convert I{Swiss} projection to WGS84 geodetic coordinates.  I{Must be overloaded}.

           @arg enh_: A Swiss projection (L{ChLV9Tuple}) or the C{scalar}, falsed I{Swiss E_LV95}
                     or I{y_LV03} easting (C{meter}).
           @kwarg n: Falsed I{Swiss N_LV85} or I{x_LV03} northing for C{scalar} B{C{enh_}} and
                     B{C{h_}} (C{meter}).
           @kwarg h_: I{Swiss h'} height for C{scalar} B{C{enh_}} and B{C{n}} (C{meter}).
           @kwarg M: If C{True}, return the I{concatenated} rotation L{EcefMatrix} iff available
                     for C{ChLV} only, C{None} otherwise (C{bool}).
           @kwarg name: Optional name (C{str}).

           @return: A L{ChLV9Tuple}C{(Y, X, h_, lat, lon, height, ltp, ecef, M)} with the unfalsed
                    I{Swiss Y, X} coordinates, I{Swiss h_} height, the given I{geodetic} C{lat},
                    C{lon} and C{height}, this C{ChLV*} instance and C{ecef} (L{Ecef9Tuple}) at
                    I{Bern, Ch} and rotation matrix C{M}.  The returned C{ltp} is this C{ChLV},
                    C{ChLVa} or C{ChLVe} instance.

           @raise LocalError: Invalid or non-C{scalar} B{C{enh_}}, B{C{n}} or B{C{h_}}.
        '''
        notOverloaded(self, enh_, n=n, h_=h_, M=M, **name)

    @staticmethod
    def _falsing2(LV95):
        '''(INTERNAL) Get the C{LV95} or C{LV03} falsing.
        '''
        return _ChLV._95_falsing if LV95 in (True, 95) else (
               _ChLV._03_falsing if LV95 in (False, 3) else ChLVYX2Tuple(0, 0))

    @staticmethod
    def _llh2abh_3(lat, lon, h):
        '''(INTERNAL) Helper for C{ChLVa/e.forward}.
        '''
        def _deg2ab(deg, sLL):
            # convert degrees to arc-seconds
            def _dms(ds, p, q, swap):
                d = _floor(ds)
                t = (ds - d) * p
                m = _floor(t)
                s = (t  - m) * p
                if swap:
                    d, s = s, d
                return d + (m + s * q) * q

            s = _dms(deg,  _60_0, _0_01, False)  # deg2sexag
            s = _dms(  s, _100_0, _60_0, True)   # sexag2asec
            return (s - sLL) / ChLV._s_ab

        a  = _deg2ab(lat, ChLV._sLat)  # phi', lat_aux
        b  = _deg2ab(lon, ChLV._sLon)  # lam', lng_aux
        h_ =  fsumf_(h,  -ChLV.Bern.height, 2.73 * b, 6.94 * a)
        return a, b, h_

    @staticmethod
    def _YXh_2abh3(Y, X, h_):
        '''(INTERNAL) Helper for C{ChLVa/e.reverse}.
        '''
        def _YX2ab(YX):
            return YX * ChLV._ab_m

        a, b = map1(_YX2ab, Y, X)
        h    = fsumf_(h_, ChLV.Bern.height, -12.6 * a, -22.64 * b)
        return a, b, h

    def _YXh_n4(self, enh_, n, h_, **name):
        '''(INTERNAL) Helper for C{ChLV*.reverse}.
        '''
        Y, X, h_, name = _xyzn4(enh_, n, h_, ChLV9Tuple,
                         _xyz_y_z_names=self._enh_n_h, **name)
        if isinstance(enh_, ChLV9Tuple):
            Y, X = enh_.Y, enh_.X
        else:  # isscalar(enh_)
            Y, X = ChLV.unfalse2(Y, X)  # PYCHOK ChLVYX2Tuple
        return Y, X, h_, name


class ChLV(_ChLV, Ltp):
    '''Conversion between I{WGS84 geodetic} and I{Swiss} projection coordinates using
       L{pygeodesy.EcefKarney}'s Earth-Centered, Earth-Fixed (ECEF) methods.

       @see: U{Swiss projection formulas<https://www.SwissTopo.admin.CH/en/maps-data-online/
             calculation-services.html>}, page 7ff, U{NAVREF<https://www.SwissTopo.admin.CH/en/
             maps-data-online/calculation-services/navref.html>}, U{REFRAME<https://www.SwissTopo.admin.CH/
             en/maps-data-online/calculation-services/reframe.html>} and U{SwissTopo Scripts GPS WGS84
             <-> LV03<https://GitHub.com/ValentinMinder/Swisstopo-WGS84-LV03>}.
    '''
    _9Tuple = ChLV9Tuple

    _ab_d =  0.36    # a, b units per degree, ...
    _ab_m =  1.0e-6  # ... per meter and ...
    _ab_M = _1_0     # ... per 1,000 kilometer
    _s_d  = _3600_0  # arc-seconds per degree ...
    _s_ab = _s_d / _ab_d  # ... and per a, b unit
    _sLat =  169028.66  # Bern, Ch in ...
    _sLon =   26782.5   # ... arc-seconds ...
    # lat, lon, height == 46°57'08.66", 7°26'22.50", 49.55m ("new" 46°57'07.89", 7°26'22.335")
    Bern  = LatLon4Tuple(_sLat / _s_d, _sLon / _s_d, 49.55, _WGS84, name='Bern')

    def __init__(self, latlonh0=Bern, **other_Ltp_kwds):
        '''New ECEF-based I{WGS84-Swiss} L{ChLV} converter, centered at I{Bern, Ch}.

           @kwarg latlonh0: The I{geodetic} origin and height, overriding C{Bern, Ch}.
           @kwarg other_Ltp_kwds: Optional, other L{Ltp.__init__} keyword arguments.

           @see: L{Ltp.__init__} for more information.
        '''
        Ltp.__init__(self, latlonh0, **_xkwds(other_Ltp_kwds, ecef=None, name=ChLV.Bern.name))

    def forward(self, latlonh, lon=None, height=0, M=None, name=NN):  # PYCHOK unused M
        # overloaded for the _ChLV.forward.__doc__
        return Ltp.forward(self, latlonh, lon=lon, height=height, M=M, name=name)

    def reverse(self, enh_, n=None, h_=0, M=None, **name):  # PYCHOK signature
        # overloaded for the _ChLV.reverse.__doc__
        Y, X, h_, name = self._YXh_n4(enh_, n, h_, **name)
        return Ltp.reverse(self, Y, X, h_, M=M, name=name)

    @staticmethod
    def false2(Y, X, LV95=True, name=NN):
        '''Add the I{Swiss LV95} or I{LV03} falsing.

           @arg Y: Unfalsed I{Swiss Y} easting (C{meter}).
           @arg X: Unfalsed I{Swiss X} northing (C{meter}).
           @kwarg LV95: If C{True} add C{LV95} falsing, if C{False} add
                        C{LV03} falsing, otherwise leave unfalsed.
           @kwarg name: Optional name (C{str}).

           @return: A L{ChLVEN2Tuple}C{(E_LV95, N_LV95)} or a
                    L{ChLVyx2Tuple}C{(y_LV03, x_LV03)} with falsed B{C{Y}}
                    and B{C{X}}, otherwise a L{ChLVYX2Tuple}C{(Y, X)}
                    with B{C{Y}} and B{C{X}} as-is.
        '''
        e, n = t = _ChLV._falsing2(LV95)
        return t.classof(e + Y, n + X, name=name)

    @staticmethod
    def isLV03(e, n):
        '''Is C{(B{e}, B{n})} a valid I{Swiss LV03} projection?

           @arg e: Falsed (or unfalsed) I{Swiss} easting (C{meter}).
           @arg n: Falsed (or unfalsed) I{Swiss} northing (C{meter}).

           @return: C{True} if C{(B{e}, B{n})} is a valid, falsed I{Swiss
                    LV03}, projection C{False} otherwise.
        '''
        # @see: U{Map<https://www.SwissTopo.admin.CH/en/knowledge-facts/
        #       surveying-geodesy/reference-frames/local/lv95.html>}
        return 400.0e3 < e < 900.0e3 and 40.0e3 < n < 400.0e3

    @staticmethod
    def isLV95(e, n, raiser=True):
        '''Is C{(B{e}, B{n})} a valid I{Swiss LV95} or I{LV03} projection?

           @arg e: Falsed (or unfalsed) I{Swiss} easting (C{meter}).
           @arg n: Falsed (or unfalsed) I{Swiss} northing (C{meter}).
           @kwarg raiser: If C{True}, throw a L{LocalError} if B{C{e}} and
                          B{C{n}} are invalid I{Swiss LV95} nor I{LV03}.

           @return: C{True} or C{False} if C{(B{e}, B{n})} is a valid I{Swiss
                    LV95} respectively I{LV03} projection, C{None} otherwise.
        '''
        if ChLV.isLV03(e, n):
            return False
        elif ChLV.isLV03(e - 2.0e6, n - 1.0e6):  # _92_falsing = _95_ - _03_
            return True
        elif raiser:  # PYCHOK no cover
            raise LocalError(unstr(ChLV.isLV95, e=e, n=n))
        return None

    @staticmethod
    def unfalse2(e, n, LV95=None, name=NN):
        '''Remove the I{Swiss LV95} or I{LV03} falsing.

           @arg e: Falsed I{Swiss E_LV95} or I{y_LV03} easting (C{meter}).
           @arg n: Falsed I{Swiss N_LV95} or I{x_LV03} northing (C{meter}).
           @kwarg LV95: If C{True} remove I{LV95} falsing, if C{False} remove
                        I{LV03} falsing, otherwise use method C{isLV95(B{e},
                        B{n})}.
           @kwarg name: Optional name (C{str}).

           @return: A L{ChLVYX2Tuple}C{(Y, X)} with the unfalsed B{C{e}}
                    respectively B{C{n}}.
        '''
        Y, X = _ChLV._falsing2(ChLV.isLV95(e, n) if LV95 is None else LV95)
        return ChLVYX2Tuple(e - Y, n - X, name=name)


class ChLVa(_ChLV, LocalCartesian):
    '''Conversion between I{WGS84 geodetic} and I{Swiss} projection coordinates
       using the U{Approximate<https://www.SwissTopo.admin.CH/en/maps-data-online/
       calculation-services.html>} formulas, page 13.

       @see: Older U{references<https://GitHub.com/alphasldiallo/Swisstopo-WGS84-LV03>}.
    '''
    def __init__(self, name=ChLV.Bern.name):
        '''New I{Approximate WGS84-Swiss} L{ChLVa} converter, centered at I{Bern, Ch}.

           @kwarg name: Optional name (C{str}), overriding C{Bern.name}.
        '''
        LocalCartesian.__init__(self, latlonh0=ChLV.Bern, name=name)

    def forward(self, latlonh, lon=None, height=0, M=None, name=NN):
        # overloaded for the _ChLV.forward.__doc__
        lat, lon, h, name = _llhn4(latlonh, lon, height, name=name)
        a,  b, h_ = _ChLV._llh2abh_3(lat, lon, h)
        a2, b2    =  a**2, b**2

        Y = fsumf_( 72.37, 211455.93 * b,
                           -10938.51 * b * a,
                               -0.36 * b * a2,
                              -44.54 * b * b2)  # + 600_000
        X = fsumf_(147.07, 308807.95 * a,
                             3745.25 * b2,
                               76.63 * a2,
                             -194.56 * b2 * a,
                              119.79 * a2 * a)  # + 200_000
        return self._ChLV9Tuple(True, M, name, Y, X, h_, lat, lon, h)

    def reverse(self, enh_, n=None, h_=0, M=None, **name):  # PYCHOK signature
        # overloaded for the _ChLV.reverse.__doc__
        Y, X, h_, name = self._YXh_n4(enh_, n, h_, **name)
        a, b, h      =  _ChLV._YXh_2abh3(Y, X, h_)
        ab_d, a2, b2 =   ChLV._ab_d, a**2, b**2

        lat = Fsum(16.9023892, 3.238272 * b,
                              -0.270978 * a2,
                              -0.002528 * b2,
                              -0.0447   * a2 * b,
                              -0.014    * b2 * b).fover(ab_d)
        lon = Fsum( 2.6779094, 4.728982 * a,
                               0.791484 * a * b,
                               0.1306   * a * b2,
                              -0.0436   * a * a2).fover(ab_d)
        return self._ChLV9Tuple(False, M, name, Y, X, h_, lat, lon, h)


class ChLVe(_ChLV, LocalCartesian):
    '''Conversion between I{WGS84 geodetic} and I{Swiss} projection coordinates
       using the U{Ellipsoidal approximate<https://www.SwissTopo.admin.CH/en/
       maps-data-online/calculation-services.html>} formulas, pp 10-11 and U{Bolliger,
       J.<https://eMuseum.GGGS.CH/literatur-lv/liste-Dateien/1967_Bolliger_a.pdf>}
       pp 148-151 (also U{GGGS<https://eMuseum.GGGS.CH/literatur-lv/liste.htm>}).

       @note: Methods L{ChLVe.forward} and L{ChLVe.reverse} have an additional keyword
              argument C{B{gamma}=False} to approximate the I{meridian convergence}.
              If C{B{gamma}=True} a 2-tuple C{(t, gamma)} is returned with C{t} the
              usual result (C{ChLV9Tuple}) and C{gamma}, the I{meridian convergence}
              (decimal C{degrees}).  To convert C{gamma} to C{grades} or C{gons},
              use function L{pygeodesy.degrees2grades}.

       @see: Older U{references<https://GitHub.com/alphasldiallo/Swisstopo-WGS84-LV03>}.
    '''
    def __init__(self, name=ChLV.Bern.name):
        '''New I{Approximate WGS84-Swiss} L{ChLVe} converter, centered at I{Bern, Ch}.

           @kwarg name: Optional name (C{str}), overriding C{Bern.name}.
        '''
        LocalCartesian.__init__(self, latlonh0=ChLV.Bern, name=name)

    def forward(self, latlonh, lon=None, height=0, M=None, name=NN, gamma=False):  # PYCHOK gamma
        # overloaded for the _ChLV.forward.__doc__
        lat, lon, h, name = _llhn4(latlonh, lon, height, name=name)
        a, b, h_    = _ChLV._llh2abh_3(lat, lon, h)
        ab_M, z, _F =  ChLV._ab_M, 0, Fhorner

        B1 = _F(a, 211428.533991, -10939.608605, -2.658213, -8.539078, -0.00345, -0.007992)
        B3 = _F(a,    -44.232717,      4.291740, -0.309883,  0.013924)
        B5 = _F(a,      0.019784,     -0.004277)
        Y  = _F(b, z, B1, z, B3, z, B5).fover(ab_M)  # 1,000 Km!

        B0 = _F(a,    z,      308770.746371, 75.028131, 120.435227, 0.009488, 0.070332, -0.00001)
        B2 = _F(a, 3745.408911, -193.792705,  4.340858,  -0.376174, 0.004053)
        B4 = _F(a,   -0.734684,    0.144466, -0.011842)
        B6 =          0.000488
        X  = _F(b, B0, z, B2, z, B4, z, B6).fover(ab_M)  # 1,000 Km!

        t = self._ChLV9Tuple(True, M, name, Y, X, h_, lat, lon, h)
        if gamma:
            U1 = _F(a, 2255515.207166, 2642.456961,  1.284180, 2.577486, 0.001165)
            U3 = _F(a,    -412.991934,   64.106344, -2.679566, 0.123833)
            U5 = _F(a,       0.204129,   -0.037725)
            g  = _F(b, z, U1, z, U3, z, U5).fover(ChLV._ab_m)  # * ChLV._ab_d degrees?
            t  =  t, g
        return t

    def reverse(self, enh_, n=None, h_=0, M=None, name=NN, gamma=False):  # PYCHOK gamma
        # overloaded for the _ChLV.reverse.__doc__
        Y, X, h_, name = self._YXh_n4(enh_, n, h_, name=name)
        a, b, h    = _ChLV._YXh_2abh3(Y, X, h_)
        s_d, _F, z =  ChLV._s_d, Fhorner, 0

        A0  = _F(b,  ChLV._sLat, 32386.4877666, -25.486822, -132.457771, 0.48747, 0.81305, -0.0069)
        A2  = _F(b, -2713.537919, -450.442705,  -75.53194,   -14.63049, -2.7604)
        A4  = _F(b,    24.42786,    13.20703,     4.7476)
        A6  =          -0.4249
        lat = _F(a, A0, z, A2, z, A4, z, A6).fover(s_d)

        A1  = _F(b, 47297.3056722, 7925.714783, 1328.129667, 255.02202, 48.17474, 9.0243)
        A3  = _F(b,  -442.709889,  -255.02202,   -96.34947,  -30.0808)
        A5  = _F(b,     9.63495,      9.0243)
        lon = _F(a,  ChLV._sLon, A1, z, A3, z, A5).fover(s_d)
        #  == (ChLV._sLon + a * (A1 + a**2 * (A3 + a**2 * A5))) / s_d

        t = self._ChLV9Tuple(False, M, name, Y, X, h_, lat, lon, h)
        if gamma:
            U1 = _F(b, 106679.792202, 17876.57022, 4306.5241, 794.87772, 148.1545, 27.8725)
            U3 = _F(b,  -1435.508,     -794.8777,  -296.309,  -92.908)
            U5 = _F(b,     29.631,       27.873)
            g  = _F(a, z, U1, z, U3, z, U5).fover(ChLV._s_ab)  # degrees
            t  =  t, g
        return t


def tyr3d(tilt=INT0, yaw=INT0, roll=INT0, Vector=Vector3d, **Vector_kwds):
    '''Convert an attitude oriention into a (3-D) direction vector.

       @kwarg tilt: Pitch, elevation from horizontal (C{degrees}), negative down
                    (clockwise rotation along and around the x-axis).
       @kwarg yaw: Bearing, heading (compass C{degrees360}), clockwise from North
                   (counter-clockwise rotation along and around the z-axis).
       @kwarg roll: Roll, bank (C{degrees}), positive to the right and down
                    (clockwise rotation along and around the y-axis).

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

       @see: U{Yaw, pitch, and roll rotations<http://MSL.CS.UIUC.edu/planning/node102.html>}
             and function L{pygeodesy.hartzell} argument C{los}.
    '''
    d = Attitude4Tuple(_0_0, tilt, yaw, roll).tyr3d
    return d if Vector is type(d) else (
           Vector3Tuple(d.x, d.y, d.z, name=d.name) if Vector is None else
                 Vector(d.x, d.y, d.z, **_xkwds(Vector_kwds, name=d.name)))  # PYCHOK indent


def _xLtp(ltp, *dflt):
    '''(INTERNAL) Validate B{C{ltp}}.
    '''
    if dflt and ltp is None:
        ltp = dflt[0]
    if isinstance(ltp, (LocalCartesian, Ltp)):
        return ltp
    raise _TypesError(_ltp_, ltp, Ltp, LocalCartesian)

# **) MIT License
#
# Copyright (C) 2016-2023 -- mrJean1 at Gmail -- All Rights Reserved.
#
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# 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
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# OTHER DEALINGS IN THE SOFTWARE.
