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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.ecef import EcefVeness 

from pygeodesy.fmath import fsum, hypot_, len2, scalar 

from pygeodesy.latlonBase import LatLonBase 

from pygeodesy.lazily import _ALL_DOCS, _2kwds 

from pygeodesy.named import LatLon3Tuple, Vector3Tuple, \ 

Vector4Tuple, _xattrs 

from pygeodesy.vector3d import Vector3d, VectorError, \ 

sumOf as _sumOf, _xyzhdn6 

from pygeodesy.utily import property_RO 

 

# from math import cos, sin 

 

# all public constants, classes and functions 

__all__ = _ALL_DOCS('LatLonNvectorBase') + ( 

'NorthPole', 'SouthPole', # constants 

'NvectorBase', # classes 

'sumOf') # functions 

__version__ = '19.10.21' 

 

 

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. 

_e9t = None #: (INTERNAL) Cached toCartesian (L{Ecef9Tuple}). 

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

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

 

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

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

 

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

the C{X} coordinate (C{scalar}). 

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

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

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

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

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

@keyword 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 _xcopy(self, *attrs): 

'''(INTERNAL) Make copy with add'l, subclass attributes. 

''' 

return Vector3d._xcopy(self, '_h', *attrs) 

 

def copy(self): 

'''Copy this vector. 

 

@return: The copy (C{Nvector} or subclass thereof). 

''' 

return self._xcopy() 

 

@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 

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. 

 

@param h: New height (C{meter}). 

 

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

 

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

''' 

h = scalar(h, None, name='h', Error=VectorError) 

self._update(h != self._h) 

self._h = h 

 

@property 

def H(self): 

'''Get the height prefix (C{str}). 

''' 

return self._H 

 

@H.setter # PYCHOK setter! 

def H(self, H): 

'''Set the height prefix. 

 

@param H: New height prefix (C{str}). 

''' 

self._H = str(H) if H else '' 

 

def to3abh(self, height=None): 

'''Convert this n-vector to (geodetic) lat-, longitude 

in C{radians} and height. 

 

@keyword height: Optional height, overriding this 

n-vector's height (C{meter}). 

 

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

''' 

h = self.h if height is None else height 

return Vector3d.to2ab(self)._3Tuple(h) 

 

def to3llh(self, height=None): 

'''Convert this n-vector to (geodetic) lat-, longitude 

in C{degrees} and height. 

 

@keyword height: Optional height, overriding this 

n-vector's height (C{meter}). 

 

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

''' 

r = self.toLatLon(height=height, LatLon=None) 

r = LatLon3Tuple(r.lat, r.lon, r.height) 

return self._xnamed(r) 

 

def to4xyzh(self, h=None): 

'''Return this n-vector's components as 4-tuple. 

 

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

height (C{meter}). 

 

@return: A L{Vector4Tuple}C{(x, y, z, h)}. 

''' 

r = Vector4Tuple(self.x, self.y, self.z, 

self.h if h is None else h) 

return self._xnamed(r) 

 

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

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

coordinates. 

 

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

height (C{meter}). 

@keyword Cartesian: Optional (sub-)class to return the 

(ECEF)coordinates (L{Cartesian}). 

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

@keyword kwds: Optional, additional C{name=value} pairs 

for B{C{Cartesian}} instance, provided 

B{C{Cartesian}} is not C{None}. 

 

@return: Cartesian (ECEF) coordinates (B{C{Cartesian}}). 

 

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

 

@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 

if h is None: 

h = self.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, **kwds) 

return self._xnamed(c) 

 

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

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

 

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

height (C{meter}). 

@keyword LatLon: Optional (sub-)class to return the 

point (L{LatLon}) or C{None}. 

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

@keyword kwds: Optional, additional C{name=value} pairs 

for B{C{LatLon}} instance, provided 

B{C{LatLon}} is not C{None}. 

 

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

C{B{LatLon}=None} or a L{LatLon3Tuple}C{(lat, 

lon, height)} if B{C{LatLon}} is C{None}. 

 

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

 

@example: 

 

>>> v = Nvector(0.5, 0.5, 0.7071) 

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

''' 

h = self.h if height is None else height 

d = datum or self.datum 

 

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

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

r = self.Ecef(d).forward(Vector3d.to2ll(self), height=h, M=True) 

if LatLon is not None: # class or .classof 

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

 

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

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

@keyword 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): 

'''Convert this n-vector to a normalized 3-d vector, 

I{ignoring the height}. 

 

@return: Normalized vector (L{Vector3d}). 

''' 

u = self.unit() 

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

 

def unit(self, ll=None): 

'''Normalize this vector to unit length. 

 

@keyword 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 

 

 

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

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

 

 

class LatLonNvectorBase(LatLonBase): 

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

and spherical C{LatLon} classes. 

''' 

 

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

'''Refine the class comparison. 

 

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

@keyword 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, **kwds): # PYCHOK signature 

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

height}. 

 

@keyword kwds: Optional, additional B{C{Nvector}} keyword 

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

Specify C{Nvector=...} to override this 

C{Nvector} class or set C{B{Nvector}=None}. 

 

@return: The B{C{Nvector}} components (C{Nvector}) or a 

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

 

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

''' 

kwds = _2kwds(kwds, Nvector=NvectorBase) 

return LatLonBase.toNvector(self, **kwds) 

 

 

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

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

 

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

@keyword Vector: Optional class for the vectorial sum 

(C{Nvector}) or C{None}. 

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

@keyword kwds: Optional, additional B{C{Vector}} keyword arguments, 

ignored if C{B{Vector}=None}. 

 

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

z, h)} if C{B{Vector}=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, **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.