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# -*- coding: utf-8 -*- 

 

u'''(INTERNAL) Private base classes for elliposiodal, spherical and N-/vectorial 

C{Cartesian}s. 

 

After I{(C) Chris Veness 2011-2015} published under the same MIT Licence**, 

see U{https://www.Movable-Type.co.UK/scripts/latlong.html}, 

U{https://www.Movable-Type.co.UK/scripts/latlong-vectors.html} and 

U{https://www.Movable-Type.co.UK/scripts/geodesy/docs/latlon-ellipsoidal.js.html}.. 

''' 

 

# from pygeodesy.basics import _xinstanceof # from .datums 

from pygeodesy.constants import EPS0, isnear0, _1_0, _N_1_0, _2_0, _4_0, _6_0 

from pygeodesy.datums import Datum, _spherical_datum, _WGS84, _xinstanceof 

from pygeodesy.errors import _IsnotError, _ValueError, _xdatum, _xkwds 

from pygeodesy.fmath import cbrt, hypot_, hypot2, sqrt # hypot 

from pygeodesy.fsums import Fmt, fsum_ 

from pygeodesy.interns import NN, _COMMASPACE_, _height_, _not_ 

from pygeodesy.interns import _ellipsoidal_, _spherical_ # PYCHOK used! 

from pygeodesy.lazily import _ALL_DOCS, _ALL_LAZY, _ALL_MODS as _MODS 

from pygeodesy.namedTuples import Bearing2Tuple, Height, LatLon4Tuple, Vector4Tuple, \ 

Vector3Tuple # PYCHOK .ellipsoidal-, .sphericalBase 

from pygeodesy.props import deprecated_method, Property, Property_RO, \ 

property_doc_, _update_all 

# from pygeodesy.resections impoty cassini, collins5, pierlot, tienstra7 

# from pygeodesy.streprs import Fmt # from .fsums 

# from pygeodesy.units import Height # from .namedTuples 

from pygeodesy.vector3d import Vector3d, _xyzhdn3 

 

# from math import sqrt # from .fmath 

 

__all__ = _ALL_LAZY.cartesianBase 

__version__ = '22.09.14' 

 

 

class CartesianBase(Vector3d): 

'''(INTERNAL) Base class for ellipsoidal and spherical C{Cartesian}. 

''' 

_datum = None # L{Datum}, to be overriden 

_height = None # height (L{Height}), set or approximated 

 

def __init__(self, x_xyz, y=None, z=None, datum=None, ll=None, name=NN): 

'''New C{Cartesian...}. 

 

@arg x_xyz: Cartesian X coordinate (C{scalar}) or a C{Cartesian}, 

L{Ecef9Tuple}, L{Vector3Tuple} or L{Vector4Tuple}. 

@kwarg y: Cartesian Y coordinate (C{scalar}), ignored if B{C{x_xyz}} 

is not C{scalar}, otherwise same units as B{C{x_xyz}}. 

@kwarg z: Cartesian Z coordinate (C{scalar}), ignored if B{C{x_xyz}} 

is not C{scalar}, otherwise same units as B{C{x_xyz}}. 

@kwarg datum: Optional datum (L{Datum}, L{Ellipsoid}, L{Ellipsoid2} 

or L{a_f2Tuple}). 

@kwarg ll: Optional, original latlon (C{LatLon}). 

@kwarg name: Optional name (C{str}). 

 

@raise TypeError: Non-scalar B{C{x_xyz}}, B{C{y}} or B{C{z}} 

coordinate or B{C{x_xyz}} not an L{Ecef9Tuple}, 

L{Vector3Tuple} or L{Vector4Tuple}. 

''' 

h, d, n = _xyzhdn3(x_xyz, None, datum, ll) 

Vector3d.__init__(self, x_xyz, y=y, z=z, ll=ll, name=name or n) 

if h is not None: 

self._height = Height(h) 

if d is not None: 

self.datum = d 

 

# def __matmul__(self, other): # PYCHOK Python 3.5+ 

# '''Return C{NotImplemented} for C{c_ = c @ datum} and C{c_ = c @ transform}. 

# ''' 

# return NotImplemented if isinstance(other, (Datum, Transform)) else \ 

# _NotImplemented(self, other) 

 

def cassini(self, pointB, pointC, alpha, beta, useZ=False): 

'''3-Point resection between this and 2 other points using U{Cassini 

<https://NL.WikiPedia.org/wiki/Achterwaartse_insnijding>}'s method. 

 

@arg pointB: Second point (C{Cartesian}, L{Vector3d}, C{Vector3Tuple}, 

C{Vector4Tuple} or C{Vector2Tuple} if C{B{useZ}=False}). 

@arg pointC: Center point (C{Cartesian}, L{Vector3d}, C{Vector3Tuple}, 

C{Vector4Tuple} or C{Vector2Tuple} if C{B{useZ}=False}). 

@arg alpha: Angle subtended by triangle side C{b} from B{C{pointA}} to 

B{C{pointC}} (C{degrees}, non-negative). 

@arg beta: Angle subtended by triangle side C{a} from B{C{pointB}} to 

B{C{pointC}} (C{degrees}, non-negative). 

@kwarg useZ: If C{True}, use and interpolate the Z component, otherwise 

force C{z=INT0} (C{bool}). 

 

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

 

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

 

@raise ResectionError: Near-coincident, -colinear or -concyclic points 

or negative or invalid B{C{alpha}} or B{C{beta}}. 

 

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

 

@see: U{Three Point Resection Problem<https://Dokumen.tips/documents/ 

three-point-resection-problem-introduction-kaestner-burkhardt-method.html>} 

and function L{pygeodesy.cassini}. 

''' 

return _MODS.resections.cassini(self, pointB, pointC, alpha, beta, 

useZ=useZ, datum=self.datum) 

 

@deprecated_method 

def collins(self, pointB, pointC, alpha, beta, useZ=False): 

'''DEPRECATED, use method L{collins5}.''' 

return self.collins5(pointB, pointC, alpha, beta, useZ=useZ) 

 

def collins5(self, pointB, pointC, alpha, beta, useZ=False): 

'''3-Point resection between this and 2 other points using U{Collins<https://Dokumen.tips/ 

documents/three-point-resection-problem-introduction-kaestner-burkhardt-method.html>}' method. 

 

@arg pointB: Second point (C{Cartesian}, L{Vector3d}, C{Vector3Tuple}, 

C{Vector4Tuple} or C{Vector2Tuple} if C{B{useZ}=False}). 

@arg pointC: Center point (C{Cartesian}, L{Vector3d}, C{Vector3Tuple}, 

C{Vector4Tuple} or C{Vector2Tuple} if C{B{useZ}=False}). 

@arg alpha: Angle subtended by triangle side C{b} from B{C{pointA}} to 

B{C{pointC}} (C{degrees}, non-negative). 

@arg beta: Angle subtended by triangle side C{a} from B{C{pointB}} to 

B{C{pointC}} (C{degrees}, non-negative). 

@kwarg useZ: If C{True}, use and interpolate the Z component, otherwise 

force C{z=INT0} (C{bool}). 

 

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

 

@return: L{Collins5Tuple}C{(pointP, pointH, a, b, c)} with survey C{pointP}, 

auxiliary C{pointH}, each an instance of this (sub-)class and 

triangle sides C{a}, C{b} and C{c}. 

 

@raise ResectionError: Near-coincident, -colinear or -concyclic points 

or negative or invalid B{C{alpha}} or B{C{beta}}. 

 

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

 

@see: U{Collins' methode<https://NL.WikiPedia.org/wiki/Achterwaartse_insnijding>} 

and function L{pygeodesy.collins5}. 

''' 

return _MODS.resections.collins5(self, pointB, pointC, alpha, beta, 

useZ=useZ, datum=self.datum) 

 

@property_doc_(''' this cartesian's datum (L{Datum}).''') 

def datum(self): 

'''Get this cartesian's datum (L{Datum}). 

''' 

return self._datum 

 

@datum.setter # PYCHOK setter! 

def datum(self, datum): 

'''Set this cartesian's C{datum} I{without conversion} 

(L{Datum}), ellipsoidal or spherical. 

 

@raise TypeError: The B{C{datum}} is not a L{Datum}. 

''' 

d = _spherical_datum(datum, name=self.name) 

if self._datum: # is not None 

if self._datum.isEllipsoidal and not d.isEllipsoidal: 

raise _IsnotError(_ellipsoidal_, datum=datum) 

elif self._datum.isSpherical and not d.isSpherical: 

raise _IsnotError(_spherical_, datum=datum) 

if self._datum != d: 

_update_all(self) 

self._datum = d 

 

def destinationXyz(self, delta, Cartesian=None, **Cartesian_kwds): 

'''Calculate the destination using a I{local} delta from this cartesian. 

 

@arg delta: Local delta to the destination (L{XyzLocal}, L{Enu}, 

L{Ned} or L{Local9Tuple}). 

@kwarg Cartesian: Optional (geocentric) class to return the 

destination or C{None}. 

@kwarg Cartesian_kwds: Optional, additional B{C{Cartesian}} keyword 

arguments, ignored if C{B{Cartesian} is None}. 

 

@return: Destination as a C{B{Cartesian}(x, y, z, **B{Cartesian_kwds})} 

instance or if C{B{Cartesian} is None}, an L{Ecef9Tuple}C{(x, y, 

z, lat, lon, height, C, M, datum)} with C{M=None} always. 

 

@raise TypeError: Invalid B{C{delta}}, B{C{Cartesian}} or 

B{C{Cartesian_kwds}}. 

''' 

if Cartesian is None: 

r = self._ltp._local2ecef(delta, nine=True) 

else: 

r = self._ltp._local2ecef(delta, nine=False) 

r = Cartesian(*r, **_xkwds(Cartesian_kwds, datum=self.datum)) 

return r._xnamed(r) if self.name else r 

 

@Property_RO 

def Ecef(self): 

'''Get the ECEF I{class} (L{EcefKarney}), I{lazily}. 

''' 

return _MODS.ecef.EcefKarney # default 

 

@Property_RO 

def _ecef9(self): 

'''(INTERNAL) Helper for L{toEcef}, L{toLocal} and L{toLtp} (L{Ecef9Tuple}). 

''' 

return self.Ecef(self.datum, name=self.name).reverse(self, M=True) 

 

def hartzell(self, los=None, earth=None): 

'''Compute the intersection of a Line-Of-Sight (los) from this certesian 

Point-Of-View (pov) with this cartesian's ellipsoid surface. 

 

@kwarg los: Line-Of-Sight, I{direction} to earth (L{Vector3d}) or 

C{None} to point to the ellipsoid's center. 

@kwarg earth: The earth model (L{Datum}, L{Ellipsoid}, L{Ellipsoid2}, 

L{a_f2Tuple} or C{scalar} radius in C{meter}) overriding 

this cartesian's C{datum} ellipsoid. 

 

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

 

@raise IntersectionError: Null C{pov} or B{C{los}} vector, this C{pov} 

is inside the ellipsoid or B{C{los}} points 

outside the ellipsoid or in an opposite direction. 

 

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

 

@see: Function C{hartzell} for further details. 

''' 

return _MODS.formy.hartzell(self, los=los, earth=earth or self.datum) 

 

@Property 

def height(self): 

'''Get the height (C{meter}). 

''' 

return self._height4.h if self._height is None else self._height 

 

@height.setter # PYCHOK setter! 

def height(self, height): 

'''Set the height (C{meter}). 

 

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

 

@raise ValueError: Invalid B{C{height}}. 

''' 

h = Height(height) 

if self._height != h: 

_update_all(self) 

self._height = h 

 

@Property_RO 

def _height4(self): 

'''(INTERNAL) Get this C{height4}-tuple. 

''' 

try: 

r = self.datum.ellipsoid.height4(self, normal=True) 

except (AttributeError, ValueError): # no datum, null cartesian, 

r = Vector4Tuple(self.x, self.y, self.z, 0, name=self.height4.__name__) 

return r 

 

def height4(self, earth=None, normal=True, Cartesian=None, **Cartesian_kwds): 

'''Compute the height of this cartesian above or below and the projection 

on this datum's ellipsoid surface. 

 

@kwarg earth: A datum, ellipsoid or earth radius I{overriding} this 

datum (L{Datum}, L{Ellipsoid}, L{Ellipsoid2}, L{a_f2Tuple} 

or C{meter}, conventionally). 

@kwarg normal: If C{True} the projection is the nearest point on the 

ellipsoid's surface, otherwise the intersection of the 

radial line to the center and the ellipsoid's surface. 

@kwarg Cartesian: Optional class to return the height and projection 

(C{Cartesian}) or C{None}. 

@kwarg Cartesian_kwds: Optional, additional B{C{Cartesian}} keyword 

arguments, ignored if C{B{Cartesian} is None}. 

 

@note: Use keyword argument C{height=0} to override C{B{Cartesian}.height} 

to {0} or any other C{scalar}, conventionally in C{meter}. 

 

@return: An instance of B{C{Cartesian}} or if C{B{Cartesian} is None}, a 

L{Vector4Tuple}C{(x, y, z, h)} with the I{projection} C{x}, C{y} 

and C{z} coordinates and height C{h} in C{meter}, conventionally. 

 

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

 

@see: L{Ellipsoid.height4} for more information. 

''' 

d = self.datum if earth is None else earth 

r = self._height4 if normal and d == self.datum else \ 

_spherical_datum(d).ellipsoid.height4(self, normal=normal) 

if Cartesian is not None: 

kwds = Cartesian_kwds.copy() 

h = kwds.pop(_height_, None) 

r = Cartesian(r, **kwds) 

if h is not None: 

r.height = Height(height=h) 

return r 

 

@Property_RO 

def isEllipsoidal(self): 

'''Check whether this cartesian is ellipsoidal (C{bool} or C{None} if unknown). 

''' 

return self.datum.isEllipsoidal if self._datum else None 

 

@Property_RO 

def isSpherical(self): 

'''Check whether this cartesian is spherical (C{bool} or C{None} if unknown). 

''' 

return self.datum.isSpherical if self._datum else None 

 

@Property_RO 

def latlon(self): 

'''Get this cartesian's (geodetic) lat- and longitude in C{degrees} (L{LatLon2Tuple}C{(lat, lon)}). 

''' 

return self.toEcef().latlon 

 

@Property_RO 

def latlonheight(self): 

'''Get this cartesian's (geodetic) lat-, longitude in C{degrees} with height (L{LatLon3Tuple}C{(lat, lon, height)}). 

''' 

return self.toEcef().latlonheight 

 

@Property_RO 

def latlonheightdatum(self): 

'''Get this cartesian's (geodetic) lat-, longitude in C{degrees} with height and datum (L{LatLon4Tuple}C{(lat, lon, height, datum)}). 

''' 

return self.toEcef().latlonheightdatum 

 

@Property_RO 

def _ltp(self): 

'''(INTERNAL) Cache for L{toLtp}. 

''' 

return _MODS.ltp.Ltp(self._ecef9, ecef=self.Ecef(self.datum), name=self.name) 

 

@Property_RO 

def _N_vector(self): 

'''(INTERNAL) Get the (C{nvectorBase._N_vector_}). 

''' 

x, y, z, h = self._n_xyzh4(self.datum) 

return _MODS.nvectorBase._N_vector_(x, y, z, h=h, name=self.name) 

 

def _n_xyzh4(self, datum): 

'''(INTERNAL) Get the n-vector components as L{Vector4Tuple}. 

''' 

def _ErrorEPS0(x): 

return _ValueError(origin=self, txt=Fmt.PARENTSPACED(EPS0=x)) 

 

_xinstanceof(Datum, datum=datum) 

# <https://www.Movable-Type.co.UK/scripts/geodesy/docs/ 

# latlon-nvector-ellipsoidal.js.html#line309>, 

# <https://GitHub.com/pbrod/nvector>/src/nvector/core.py> 

# _equation23 and <https://www.NavLab.net/nvector> 

E = datum.ellipsoid 

x, y, z = self.xyz 

 

# Kenneth Gade eqn 23 

p = hypot2(x, y) * E.a2_ 

q = (z**2 * E.e21) * E.a2_ 

r = fsum_(p, q, -E.e4) / _6_0 

s = (p * q * E.e4) / (_4_0 * r**3) 

t = cbrt(fsum_(_1_0, s, sqrt(s * (_2_0 + s)))) 

if isnear0(t): 

raise _ErrorEPS0(t) 

 

u = r * fsum_(_1_0, t, _1_0 / t) 

v = sqrt(u**2 + E.e4 * q) 

t = v * _2_0 

if t < EPS0: # isnear0 

raise _ErrorEPS0(t) 

w = E.e2 * fsum_(u, v, -q) / t 

 

k = sqrt(fsum_(u, v, w**2)) - w 

if isnear0(k): 

raise _ErrorEPS0(k) 

t = k + E.e2 

if isnear0(t): 

raise _ErrorEPS0(t) 

e = k / t 

# d = e * hypot(x, y) 

 

# tmp = 1 / hypot(d, z) == 1 / hypot(e * hypot(x, y), z) 

t = hypot_(x * e, y * e, z) # == 1 / tmp 

if t < EPS0: # isnear0 

raise _ErrorEPS0(t) 

h = fsum_(k, E.e2, _N_1_0) / k * t 

s = e / t # == e * tmp 

return Vector4Tuple(x * s, y * s, z / t, h, name=self.name) 

 

@Property_RO 

def philam(self): 

'''Get this cartesian's (geodetic) lat- and longitude in C{radians} (L{PhiLam2Tuple}C{(phi, lam)}). 

''' 

return self.toEcef().philam 

 

@Property_RO 

def philamheight(self): 

'''Get this cartesian's (geodetic) lat-, longitude in C{radians} with height (L{PhiLam3Tuple}C{(phi, lam, height)}). 

''' 

return self.toEcef().philamheight 

 

@Property_RO 

def philamheightdatum(self): 

'''Get this cartesian's (geodetic) lat-, longitude in C{radians} with height and datum (L{PhiLam4Tuple}C{(phi, lam, height, datum)}). 

''' 

return self.toEcef().philamheightdatum 

 

def pierlot(self, point2, point3, alpha12, alpha23, useZ=False): 

'''3-Point resection between this and two other points using U{Pierlot 

<http://www.Telecom.ULg.ac.Be/triangulation>}'s method C{ToTal}. 

 

@arg point2: Second point (C{Cartesian}, L{Vector3d}, C{Vector3Tuple}, 

C{Vector4Tuple} or C{Vector2Tuple} if C{B{useZ}=False}). 

@arg point3: Third point (C{Cartesian}, L{Vector3d}, C{Vector3Tuple}, 

C{Vector4Tuple} or C{Vector2Tuple} if C{B{useZ}=False}). 

@arg alpha12: Angle subtended from this point to B{C{point2}} (C{degrees}). 

@arg alpha23: Angle subtended from B{C{point2}} to B{C{point3}} (C{degrees}). 

@kwarg useZ: If C{True}, interpolate the Z component, otherwise use C{z=INT0} 

(C{bool}). 

 

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

 

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

 

@raise ResectionError: Near-coincident, -colinear or -concyclic points 

or invalid B{C{alpha12}} or B{C{alpha23}}. 

 

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

 

@see: U{V. Pierlot, M. Van Droogenbroeck, "A New Three Object Triangulation 

Algorithm for Mobile Robot Positioning"<https://ORBi.ULiege.Be/ 

bitstream/2268/157469/1/Pierlot2014ANewThree.pdf>}, U{18 Triangulation 

Algorithms for 2D Positioning (also known as the Resection Problem) 

<http://www.Telecom.ULg.ac.Be/triangulation>} and functions 

L{pygeodesy.pierlot}. 

''' 

return _MODS.resections.pierlot(self, point2, point3, alpha12, alpha23, 

useZ=useZ, datum=self.datum) 

 

@deprecated_method 

def tienstra(self, pointB, pointC, alpha, beta=None, gamma=None, useZ=False): 

'''DEPRECATED, use method L{tienstra7}.''' 

return self.tienstra7(pointB, pointC, alpha, beta=beta, gamma=gamma, useZ=useZ) 

 

def tienstra7(self, pointB, pointC, alpha, beta=None, gamma=None, useZ=False): 

'''3-Point resection between this and two other points using U{Tienstra 

<https://WikiPedia.org/wiki/Tienstra_formula>}'s formula. 

 

@arg pointB: Second point (C{Cartesian}, L{Vector3d}, C{Vector3Tuple}, C{Vector4Tuple} or 

C{Vector2Tuple} if C{B{useZ}=False}). 

@arg pointC: Third point (C{Cartesian}, L{Vector3d}, C{Vector3Tuple}, C{Vector4Tuple} or 

C{Vector2Tuple} if C{B{useZ}=False}). 

@arg alpha: Angle subtended by triangle side C{a} from B{C{pointB}} to B{C{pointC}} (C{degrees}, 

non-negative). 

@kwarg beta: Angle subtended by triangle side C{b} from this to B{C{pointC}} (C{degrees}, 

non-negative) or C{None} if C{B{gamma} is not None}. 

@kwarg gamma: Angle subtended by triangle side C{c} from this to B{C{pointB}} (C{degrees}, 

non-negative) or C{None} if C{B{beta} is not None}. 

@kwarg useZ: If C{True}, use and interpolate the Z component, otherwise force C{z=INT0} 

(C{bool}). 

 

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

 

@return: L{Tienstra7Tuple}C{(pointP, A, B, C, a, b, c)} with survey C{pointP}, 

an instance of this (sub-)class and triangle angle C{A} at this point, 

C{B} at B{C{pointB}} and C{C} at B{C{pointC}} in C{degrees} and 

triangle sides C{a}, C{b} and C{c}. 

 

@raise ResectionError: Near-coincident, -colinear or -concyclic points or sum of 

B{C{alpha}}, B{C{beta}} and B{C{gamma}} not C{360} or 

negative B{C{alpha}}, B{C{beta}} or B{C{gamma}}. 

 

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

 

@see: U{3-Point Resection Solver<http://MesaMike.org/geocache/GC1B0Q9/tienstra/>}, 

U{V. Pierlot, M. Van Droogenbroeck, "A New Three Object Triangulation..." 

<http://www.Telecom.ULg.ac.Be/publi/publications/pierlot/Pierlot2014ANewThree/>}, 

U{18 Triangulation Algorithms...<http://www.Telecom.ULg.ac.Be/triangulation/>} 

and function L{pygeodesy.tienstra7}. 

''' 

return _MODS.resections.tienstra7(self, pointB, pointC, alpha, beta, gamma, 

useZ=useZ, datum=self.datum) 

 

@deprecated_method 

def to2ab(self): # PYCHOK no cover 

'''DEPRECATED, use property C{philam}. 

 

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

''' 

return self.philam 

 

@deprecated_method 

def to2ll(self): # PYCHOK no cover 

'''DEPRECATED, use property C{latlon}. 

 

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

''' 

return self.latlon 

 

@deprecated_method 

def to3llh(self, datum=None): # PYCHOK no cover 

'''DEPRECATED, use property L{latlonheightdatum} or L{latlonheight}. 

 

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

 

@note: This method returns a B{C{-4Tuple}} I{and not a} C{-3Tuple} 

as its name may suggest. 

''' 

t = self.toLatLon(datum=datum, LatLon=None) 

return LatLon4Tuple(t.lat, t.lon, t.height, t.datum, name=self.name) 

 

# def _to3LLh(self, datum, LL, **pairs): # OBSOLETE 

# '''(INTERNAL) Helper for C{subclass.toLatLon} and C{.to3llh}. 

# ''' 

# r = self.to3llh(datum) # LatLon3Tuple 

# if LL is not None: 

# r = LL(r.lat, r.lon, height=r.height, datum=datum, name=self.name) 

# for n, v in pairs.items(): 

# setattr(r, n, v) 

# return r 

 

def toDatum(self, datum2, datum=None): 

'''Convert this cartesian from one datum to an other. 

 

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

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

 

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

 

@raise TypeError: B{C{datum2}} or B{C{datum}} 

invalid. 

''' 

_xinstanceof(Datum, datum2=datum2) 

 

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

self.toDatum(datum) 

 

i, d = False, c.datum 

if d == datum2: 

return c.copy() if c is self else c 

 

elif d == _WGS84: 

d = datum2 # convert from WGS84 to datum2 

 

elif datum2 == _WGS84: 

i = True # convert to WGS84 by inverse transformation 

 

else: # neither datum2 nor c.datum is WGS84, invert to WGS84 first 

c = c.toTransform(d.transform, inverse=True, datum=_WGS84) 

d = datum2 

 

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

 

convertDatum = toDatum # for backward compatibility 

 

def toEcef(self): 

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

 

@return: An L{Ecef9Tuple}C{(x, y, z, lat, lon, height, 

C, M, datum)} with C{C} and C{M} if available. 

 

@raise EcefError: A C{.datum} or an ECEF issue. 

''' 

return self._ecef9 

 

def toLatLon(self, datum=None, height=None, LatLon=None, **LatLon_kwds): # see .ecef.Ecef9Tuple.toDatum 

'''Convert this cartesian to a geodetic (lat-/longitude) point. 

 

@kwarg datum: Optional datum (L{Datum}, L{Ellipsoid}, L{Ellipsoid2} 

or L{a_f2Tuple}). 

@kwarg height: Optional height, overriding the converted height 

(C{meter}), iff B{C{LatLon}} is not C{None}. 

@kwarg LatLon: Optional class to return the geodetic point 

(C{LatLon}) or C{None}. 

@kwarg LatLon_kwds: Optional, additional B{C{LatLon}} keyword 

arguments, ignored if C{B{LatLon} is None}. 

 

@return: The geodetic point (B{C{LatLon}}) or if B{C{LatLon}} 

is C{None}, an L{Ecef9Tuple}C{(x, y, z, lat, lon, 

height, C, M, datum)} with C{C} and C{M} if available. 

 

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

''' 

d = _spherical_datum(datum or self.datum, name=self.name) 

if d == self.datum: 

r = self.toEcef() 

else: 

c = self.toDatum(d) 

r = c.Ecef(d, name=self.name).reverse(c, M=LatLon is None) 

 

if LatLon: # class or .classof 

h = r.height if height is None else Height(height) 

r = LatLon(r.lat, r.lon, datum=r.datum, height=h, 

**_xkwds(LatLon_kwds, name=r.name)) 

_xdatum(r.datum, d) 

return r 

 

def toLocal(self, Xyz=None, ltp=None, **Xyz_kwds): 

'''Convert this I{geocentric} cartesian to I{local} C{X}, C{Y} and C{Z}. 

 

@kwarg Xyz: Optional class to return C{X}, C{Y} and C{Z} 

(L{XyzLocal}, L{Enu}, L{Ned}) or C{None}. 

@kwarg ltp: The I{local tangent plane} (LTP) to use, 

overriding this cartesian's LTP (L{Ltp}). 

@kwarg Xyz_kwds: Optional, additional B{C{Xyz}} keyword 

arguments, ignored if C{B{Xyz} is None}. 

 

@return: An B{C{Xyz}} instance or if C{B{Xyz} is None}, 

a L{Local9Tuple}C{(x, y, z, lat, lon, height, 

ltp, ecef, M)} with C{M=None} always. 

 

@raise TypeError: Invalid B{C{ltp}}. 

''' 

p = _MODS.ltp._xLtp(ltp, self._ltp) 

return p._ecef2local(self._ecef9, Xyz, Xyz_kwds) 

 

def toLtp(self, Ecef=None): 

'''Return the I{local tangent plane} (LTP) for this cartesian. 

 

@kwarg Ecef: Optional ECEF I{class} (L{EcefKarney}, ... 

L{EcefYou}), overriding this cartesian's C{Ecef}. 

''' 

return self._ltp if Ecef in (None, self.Ecef) else _MODS.ltp.Ltp( 

self._ecef9, ecef=Ecef(self.datum), name=self.name) 

 

def toNvector(self, Nvector=None, datum=None, **Nvector_kwds): 

'''Convert this cartesian to C{n-vector} components. 

 

@kwarg Nvector: Optional class to return the C{n-vector} 

components (C{Nvector}) or C{None}. 

@kwarg datum: Optional datum (L{Datum}, L{Ellipsoid}, L{Ellipsoid2} 

or L{a_f2Tuple}) overriding this cartesian's datum. 

@kwarg Nvector_kwds: Optional, additional B{C{Nvector}} keyword 

arguments, ignored if C{B{Nvector} is None}. 

 

@return: The C{unit, n-vector} components (B{C{Nvector}}) or a 

L{Vector4Tuple}C{(x, y, z, h)} if B{C{Nvector}} is C{None}. 

 

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

 

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

 

@example: 

 

>>> c = Cartesian(3980581, 97, 4966825) 

>>> n = c.toNvector() # (x=0.622818, y=0.00002, z=0.782367, h=0.242887) 

''' 

d = _spherical_datum(datum or self.datum, name=self.name) 

r = self._N_vector.xyzh if self.datum == d else self._n_xyzh4(d) 

 

if Nvector is not None: 

kwds = _xkwds(Nvector_kwds, h=r.h, datum=d) 

r = self._xnamed(Nvector(r.x, r.y, r.z, **kwds)) 

return r 

 

def toStr(self, prec=3, fmt=Fmt.SQUARE, sep=_COMMASPACE_): # PYCHOK expected 

'''Return the string representation of this cartesian. 

 

@kwarg prec: Number of (decimal) digits, unstripped (C{int}). 

@kwarg fmt: Enclosing backets format (string). 

@kwarg sep: Separator to join (string). 

 

@return: Cartesian represented as "[x, y, z]" (string). 

''' 

return Vector3d.toStr(self, prec=prec, fmt=fmt, sep=sep) 

 

def toTransform(self, transform, inverse=False, datum=None): 

'''Return a new cartesian by applying a Helmert transform 

to this cartesian. 

 

@arg transform: Transform to apply (L{Transform}). 

@kwarg inverse: Apply the inverse of the Helmert 

transform (C{bool}). 

@kwarg datum: Datum for the transformed cartesian (L{Datum}), 

overriding this cartesian's datum. 

 

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

 

@raise Valuerror: If C{B{inverse}=True} and B{C{datum}} 

is not L{Datums}C{.WGS84}. 

''' 

d = datum or self.datum 

if inverse and d != _WGS84: 

raise _ValueError(inverse=inverse, datum=d, 

txt=_not_(_WGS84.name)) 

 

xyz = transform.transform(*self.xyz, inverse=inverse) 

return self.classof(xyz, datum=d) 

 

def toVector(self, Vector=None, **Vector_kwds): 

'''Return this cartesian's components as vector. 

 

@kwarg Vector: Optional class to return the C{n-vector} 

components (L{Vector3d}) or C{None}. 

@kwarg Vector_kwds: Optional, additional B{C{Vector}} keyword 

arguments, ignored if C{B{Vector} is None}. 

 

@return: A B{C{Vector}} or an L{Vector3Tuple}C{(x, y, z)} 

if B{C{Vector}} is C{None}. 

 

@raise TypeError: Invalid B{C{Vector}} or B{C{Vector_kwds}}. 

''' 

return self.xyz if Vector is None else self._xnamed( 

Vector(self.x, self.y, self.z, **Vector_kwds)) 

 

 

__all__ += _ALL_DOCS(CartesianBase) 

 

# **) MIT License 

# 

# Copyright (C) 2016-2022 -- 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.