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# -*- coding: utf-8 -*- 

 

u'''(INTERNAL) Base classes L{LatLonNvectorBase} and L{NvectorBase} 

and function L{sumOf} for C{N-vectorial} ellipsoidal and spherical 

C{Cartesian}s and C{LatLon}s. 

 

Pure Python implementation of C{n-vector}-based geodesy tools for 

ellipsoidal earth models, transcribed from JavaScript originals by 

I{(C) Chris Veness 2005-2016} and published under the same MIT Licence**, 

see U{Vector-based geodesy 

<https://www.Movable-Type.co.UK/scripts/latlong-vectors.html>}. 

 

@newfield example: Example, Examples 

''' 

 

from pygeodesy.basics import len2, property_doc_, property_RO, \ 

_xattrs 

from pygeodesy.ecef import EcefVeness 

from pygeodesy.fmath import fsum, hypot_ 

from pygeodesy.formy import n_xyz2latlon, n_xyz2philam 

from pygeodesy.latlonBase import LatLonBase 

from pygeodesy.lazily import _ALL_DOCS 

from pygeodesy.named import Vector3Tuple, Vector4Tuple 

from pygeodesy.units import Height 

from pygeodesy.vector3d import Vector3d, VectorError, \ 

sumOf as _sumOf, _xyzhdn6 

 

# from math import atan2, cos, sin 

 

# all public constants, classes and functions 

__all__ = _ALL_DOCS('LatLonNvectorBase') + ( 

'NorthPole', 'SouthPole', # constants 

'NvectorBase', # classes 

'sumOf') # functions 

__version__ = '20.04.21' 

 

 

class NvectorBase(Vector3d): # XXX kept private 

'''Base class for ellipsoidal and spherical C{Nvector}s. 

''' 

_datum = None #: (INTERNAL) L{Datum}, overriden. 

_Ecef = EcefVeness #: (INTERNAL) Preferred C{Ecef...} class, backward compatible. 

_h = 0 #: (INTERNAL) Height (C{meter}). 

_H = '' #: Heigth prefix (C{str}), '↑' in JS version 

_latlon = None #: (INTERNAL) Cached latlon (L{LatlLon2Tuple}). 

_philam = None #: (INTERNAL) Cached philam (L{PhiLam2Tuple}). 

 

def __init__(self, x, y=None, z=None, h=0, ll=None, datum=None, name=''): 

'''New n-vector normal to the earth's surface. 

 

@arg x: An C{Nvector}, L{Vector3Tuple}, L{Vector4Tuple} or 

the C{X} coordinate (C{scalar}). 

@arg y: The C{Y} coordinate (C{scalar}) if B{C{x}} C{scalar}. 

@arg z: The C{Z} coordinate (C{scalar}) if B{C{x}} C{scalar}. 

@kwarg h: Optional height above surface (C{meter}). 

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

@kwarg datum: Optional, I{pass-thru} datum (C{Datum}). 

@kwarg name: Optional name (C{str}). 

 

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

coordinate or B{C{x}} not an C{Nvector}, 

L{Vector3Tuple} or L{Vector4Tuple}. 

 

@example: 

 

>>> from pygeodesy.sphericalNvector import Nvector 

>>> v = Nvector(0.5, 0.5, 0.7071, 1) 

>>> v.toLatLon() # 45.0°N, 045.0°E, +1.00m 

''' 

x, y, z, h, d, n = _xyzhdn6(x, y, z, h, datum, ll) 

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

if h: 

self.h = h 

if d: # just pass-thru 

self._datum = d 

 

def _update(self, updated, *attrs): 

'''(INTERNAL) Zap cached attributes if updated. 

''' 

if updated: 

Vector3d._update(self, updated, '_latlon', '_philam', *attrs) 

 

@property_RO 

def datum(self): 

'''Get the I{pass-thru} datum (C{Datum}) or C{None}. 

''' 

return self._datum 

 

@property_RO 

def Ecef(self): 

'''Get the ECEF I{class} (L{EcefKarney} or L{EcefVeness}). 

''' 

return self._Ecef 

 

@property_doc_(''' the height above surface (C{meter}).''') 

def h(self): 

'''Get the height above surface (C{meter}). 

''' 

return self._h 

 

@h.setter # PYCHOK setter! 

def h(self, h): 

'''Set the height above surface. 

 

@arg h: New height (C{meter}). 

 

@raise TypeError: If B{C{h}} invalid. 

 

@raise VectorError: If B{C{h}} invalid. 

''' 

h = Height(h, name='h', Error=VectorError) 

self._update(h != self._h, '_latlon', '_philam') 

self._h = h 

 

@property_doc_(''' the height prefix (C{str}).''') 

def H(self): 

'''Get the height prefix (C{str}). 

''' 

return self._H 

 

@H.setter # PYCHOK setter! 

def H(self, H): 

'''Set the height prefix. 

 

@arg H: New height prefix (C{str}). 

''' 

self._H = str(H) if H else '' 

 

@property_RO 

def isEllipsoidal(self): 

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

''' 

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

 

@property_RO 

def lam(self): 

'''Get the (geodetic) longitude in C{radians} (C{float}). 

''' 

return self.philamheight.lam 

 

@property_RO 

def lat(self): 

'''Get the (geodetic) latitude in C{degrees} (C{float}). 

''' 

return self.latlonheight.lat 

 

@property_RO 

def latlon(self): 

'''Get the (geodetic) lat-, longitude in C{degrees} (L{LatLon2Tuple}C{(lat, lon)}). 

''' 

if self._latlon is None: 

self._latlon = n_xyz2latlon(self.x, self.y, self.z) 

return self._xnamed(self._latlon) 

 

@property_RO 

def latlonheight(self): 

'''Get the (geodetic) lat-, longitude in C{degrees} and height (L{LatLon3Tuple}C{(lat, lon, height)}). 

''' 

return self._xnamed(self.latlon.to3Tuple(self.h)) 

 

@property_RO 

def lon(self): 

'''Get the (geodetic) longitude in C{degrees} (C{float}). 

''' 

return self.latlonheight.lon 

 

@property_RO 

def phi(self): 

'''Get the (geodetic) latitude in C{radians} (C{float}). 

''' 

return self.philamheight.phi 

 

@property_RO 

def philam(self): 

'''Get the (geodetic) lat-, longitude in C{radians} (L{PhiLam2Tuple}C{(phi, lam)}). 

''' 

if self._philam is None: 

self._philam = n_xyz2philam(self.x, self.y, self.z) 

return self._xnamed(self._philam) 

 

@property_RO 

def philamheight(self): 

'''Get the (geodetic) lat-, longitude in C{radians} and height (L{PhiLam3Tuple}C{(phi, lam, height)}). 

''' 

return self._xnamed(self.philam.to3Tuple(self.h)) 

 

def to2ab(self): # PYCHOK no cover 

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

 

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

''' 

return self.philam 

 

def to3abh(self, height=None): # PYCHOK no cover 

'''DEPRECATED, use method C{philamheight} or C{philam.to3Tuple}C{(}B{C{height}}C{)}. 

 

@kwarg height: Optional height, overriding this 

n-vector's height (C{meter}). 

 

@return: A L{PhiLam3Tuple}C{(phi, lam, height)}. 

 

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

''' 

return self.philamheight if height in (None, self.h) else \ 

self.philam.to3Tuple(height) 

 

def toCartesian(self, h=None, Cartesian=None, datum=None, **Cartesian_kwds): 

'''Convert this n-vector to C{Nvector}-based cartesian (ECEF) 

coordinates. 

 

@kwarg h: Optional height, overriding this n-vector's height (C{meter}). 

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

coordinates (L{Cartesian}). 

@kwarg datum: Optional, spherical datum (C{Datum}). 

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

keyword arguments, ignored if 

B{C{Cartesian=None}}. 

 

@return: The cartesian (ECEF) coordinates (B{C{Cartesian}}) or 

if B{C{Cartesian}} 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{Cartesian}}. 

 

@raise ValueError: Invalid B{C{h}}. 

 

@example: 

 

>>> v = Nvector(0.5, 0.5, 0.7071) 

>>> c = v.toCartesian() # [3194434, 3194434, 4487327] 

>>> p = c.toLatLon() # 45.0°N, 45.0°E 

''' 

x, y, z = self.x, self.y, self.z 

 

h = self.h if h is None else Height(h, name='h') 

d = datum or self.datum 

 

E = d.ellipsoid 

# Kenneth Gade eqn (22) 

n = E.b / hypot_(x * E.a_b, y * E.a_b, z) 

r = h + n * E.a_b**2 

 

c = self.Ecef(d).reverse(x * r, y * r, z * (n + h), M=True) 

if Cartesian is not None: # class or .classof 

c = Cartesian(c, **Cartesian_kwds) 

return self._xnamed(c) 

 

def to2ll(self): # PYCHOK no cover 

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

 

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

''' 

return self.latlon 

 

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

'''DEPRECATED, use property C{latlonheight} or C{latlon.to3Tuple}C{)}B{C{height}}C{)}. 

 

@kwarg height: Optional height, overriding this 

n-vector's height (C{meter}). 

 

@return: A L{LatLon3Tuple}C{(lat, lon, height)}. 

 

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

''' 

return self.latlonheight if height in (None, self.h) else \ 

self.latlon.to3Tuple(height) 

 

def toLatLon(self, height=None, LatLon=None, datum=None, **LatLon_kwds): 

'''Convert this n-vector to an C{Nvector}-based geodetic point. 

 

@kwarg height: Optional height, overriding this n-vector's 

height (C{meter}). 

@kwarg LatLon: Optional class to return the geodetic point 

(L{LatLon}) or C{None}. 

@kwarg datum: Optional, spherical datum (C{Datum}). 

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

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

 

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

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{LatLon}}. 

 

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

 

@example: 

 

>>> v = Nvector(0.5, 0.5, 0.7071) 

>>> p = v.toLatLon() # 45.0°N, 45.0°E 

''' 

# use self.Cartesian(Cartesian=None) if h == self.h and 

# d == self.datum, for better accuracy of the height 

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

r = self.Ecef(datum or self.datum).forward(self.latlon, height=h, M=True) 

if LatLon is not None: # class or .classof 

r = LatLon(r.lat, r.lon, r.height, datum=r.datum, **LatLon_kwds) 

return self._xnamed(r) 

 

def toStr(self, prec=5, fmt='(%s)', sep=', '): # PYCHOK expected 

'''Return a string representation of this n-vector. 

 

Height component is only included if non-zero. 

 

@kwarg prec: Optional number of decimals, unstripped (C{int}). 

@kwarg fmt: Optional enclosing backets format (C{str}). 

@kwarg sep: Optional separator between components (C{str}). 

 

@return: Comma-separated C{"(x, y, z [, h])"} enclosed in 

B{C{fmt}} brackets (C{str}). 

 

@example: 

 

>>> Nvector(0.5, 0.5, 0.7071).toStr() # (0.5, 0.5, 0.7071) 

>>> Nvector(0.5, 0.5, 0.7071, 1).toStr(-3) # (0.500, 0.500, 0.707, +1.00) 

''' 

t = Vector3d.toStr(self, prec=prec, fmt='%s', sep=sep) 

if self.h: 

t = '%s%s%s%+.2f' % (t, sep, self.H, self.h) 

return fmt % (t,) 

 

def toVector3d(self, norm=True): 

'''Convert this n-vector to a 3-D vector, I{ignoring 

the height}. 

 

@kwarg norm: Normalize the 3-D vector (C{bool}). 

 

@return: The (normalized) vector (L{Vector3d}). 

''' 

u = self.unit() 

v = Vector3d(u.x, u.y, u.z, name=self.name) 

return v.unit() if norm else v 

 

def to4xyzh(self, h=None): # PYCHOK no cover 

'''DEPRECATED, use property C{xyzh} or C{xyz.to4Tuple}C{(}B{C{h}}C{)}. 

''' 

return self.xyzh if h in (None, self.h) else \ 

self._xnamed(Vector4Tuple(self.x, self.y, self.z, h)) 

 

def unit(self, ll=None): 

'''Normalize this n-vector to unit length. 

 

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

 

@return: Normalized vector (C{Nvector}). 

''' 

if self._united is None: 

u = Vector3d.unit(self, ll=ll) # .copy() 

self._united = u._united = _xattrs(u, self, '_h') 

return self._united 

 

@property_RO 

def xyzh(self): 

'''Get this n-vector's components (L{Vector4Tuple}C{(x, y, z, h)}) 

''' 

return self._xnamed(self.xyz.to4Tuple(self.h)) 

 

 

NorthPole = NvectorBase(0, 0, +1, name='NorthPole') #: North pole (C{Nvector}). 

SouthPole = NvectorBase(0, 0, -1, name='SouthPole') #: South pole (C{Nvector}). 

 

 

class _N_vector_(NvectorBase): 

'''(INTERNAL) Minimal, low-overhead C{n-vector}. 

''' 

def __init__(self, x, y, z, h=0): 

self._x, self._y, self._z = x, y, z 

if h: 

self._h = h 

 

 

class LatLonNvectorBase(LatLonBase): 

'''(INTERNAL) Base class for n-vector-based ellipsoidal 

and spherical C{LatLon} classes. 

''' 

 

def _update(self, updated, *attrs, **kwds): # PYCHOK _Nv=None 

'''(INTERNAL) Zap cached attributes if updated. 

 

@see: C{ellipsoidalNvector.LatLon} and C{sphericalNvector.LatLon} 

for the special case of B{C{_Nv}}. 

''' 

if updated: 

_Nv = kwds.pop('_Nv', None) 

if _Nv is not None: 

if _Nv._fromll is not None: 

_Nv._fromll = None 

self._Nv = None 

LatLonBase._update(self, updated, *attrs) 

 

def others(self, other, name='other'): 

'''Refine the class comparison. 

 

@arg other: The other point (C{LatLon}). 

@kwarg name: Optional, other's name (C{str}). 

 

@raise TypeError: Incompatible B{C{other}} C{type}. 

''' 

try: 

LatLonBase.others(self, other, name=name) 

except TypeError: 

if not isinstance(other, NvectorBase): 

raise 

 

def toNvector(self, Nvector=NvectorBase, **Nvector_kwds): # PYCHOK signature 

'''Convert this point to C{Nvector} components, I{including 

height}. 

 

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

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

 

@return: An B{C{Nvector}} or a L{Vector4Tuple}C{(x, y, z, h)} if 

B{C{Nvector}} is C{None}. 

 

@raise TypeError: Invalid B{C{Nvector}} or B{C{Nvector_kwds}}. 

''' 

return LatLonBase.toNvector(self, Nvector=Nvector, **Nvector_kwds) 

 

 

def sumOf(nvectors, Vector=None, h=None, **Vector_kwds): 

'''Return the vectorial sum of two or more n-vectors. 

 

@arg nvectors: Vectors to be added (C{Nvector}[]). 

@kwarg Vector: Optional class for the vectorial sum (C{Nvector}) 

or C{None}. 

@kwarg h: Optional height, overriding the mean height (C{meter}). 

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

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

 

@return: Vectorial sum (B{C{Vector}}) or a L{Vector4Tuple}C{(x, y, 

z, h)} if B{C{Vector}} is C{None}. 

 

@raise VectorError: No B{C{nvectors}}. 

''' 

n, nvectors = len2(nvectors) 

if n < 1: 

raise VectorError('no nvectors: %r' & (n,)) 

 

if h is None: 

h = fsum(v.h for v in nvectors) / float(n) 

 

if Vector is None: 

r = _sumOf(nvectors, Vector=Vector3Tuple).to4Tuple(h) 

else: 

r = _sumOf(nvectors, Vector=Vector, h=h, **Vector_kwds) 

return r 

 

# **) MIT License 

# 

# Copyright (C) 2016-2020 -- 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.