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# -*- coding: utf-8 -*- 

 

u'''(INTERNAL) base classes for elliposiodal, spherical and vectorial C{LatLon}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/geodesy/docs/latlon-ellipsoidal.js.html>} 

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

 

@newfield example: Example, Examples 

''' 

 

from pygeodesy.dms import F_D, F_DMS, latDMS, lonDMS, parseDMS, parseDMS2 

from pygeodesy.ecef import EcefKarney 

from pygeodesy.fmath import EPS, favg, scalar 

from pygeodesy.formy import antipode, compassAngle, equirectangular, euclidean, \ 

haversine, isantipode, points2, vincentys 

from pygeodesy.lazily import _ALL_DOCS 

from pygeodesy.named import Bounds2Tuple, LatLon2Tuple, _NamedBase, \ 

PhiLam2Tuple, Vector3Tuple, _xattrs 

from pygeodesy.utily import R_M, property_RO, sincos2, _TypeError 

from pygeodesy.vector3d import Vector3d 

 

from math import asin, cos, degrees, radians 

 

# XXX the following classes are listed only to get 

# Epydoc to include class and method documentation 

__all__ = _ALL_DOCS('LatLonBase') 

__version__ = '19.10.19' 

 

 

class LatLonBase(_NamedBase): 

'''(INTERNAL) Base class for C{LatLon} points on spherical or 

ellipsoidal earth models. 

''' 

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

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

_Ecef = EcefKarney #: (INTERNAL) Preferred C{Ecef...} class. 

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

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

_lat = 0 #: (INTERNAL) Latitude (C{degrees}). 

_latlon = None #: (INTERNAL) Cached (L{LatLon2Tuple}). 

_lon = 0 #: (INTERNAL) Longitude (C{degrees}). 

_name = '' #: (INTERNAL) name (C{str}). 

_v3d = None #: (INTERNAL) Cached toVector3d (L{Vector3d}). 

_v4t = None #: (INTERNAL) Cached toNvector (L{Vector4Tuple}). 

 

def __init__(self, lat, lon, height=0, name=''): 

'''New C{LatLon}. 

 

@param lat: Latitude (C{degrees} or DMS C{str} with N or S suffix). 

@param lon: Longitude (C{degrees} or DMS C{str} with E or W suffix). 

@keyword height: Optional height (C{meter} above or below the earth surface). 

@keyword name: Optional name (C{str}). 

 

@return: New instance (C{LatLon}). 

 

@raise RangeError: Value of B{C{lat}} or B{C{lon}} outside the valid 

range and C{rangerrors} set to C{True}. 

 

@raise ValueError: Invalid B{C{lat}} or B{C{lon}}. 

 

@example: 

 

>>> p = LatLon(50.06632, -5.71475) 

>>> q = LatLon('50°03′59″N', """005°42'53"W""") 

''' 

self._lat, self._lon = parseDMS2(lat, lon) # PYCHOK LatLon2Tuple 

if height: # elevation 

self._height = scalar(height, None, name='height') 

if name: 

self.name = name 

 

def __eq__(self, other): 

return self.isequalTo(other) 

 

def __ne__(self, other): 

return not self.isequalTo(other) 

 

def __str__(self): 

return self.toStr(form=F_D, prec=6) 

 

def _havg(self, other, f=0.5): 

'''(INTERNAL) Weighted, average height. 

 

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

@keyword f: Optional fraction (C{float}). 

 

@return: Average, fractional height (C{float}). 

''' 

return favg(self.height, other.height, f=f) 

 

def _update(self, updated): 

'''(INTERNAL) Reset caches if updated. 

''' 

if updated: # reset caches 

self._ab = self._e9t = self._latlon = \ 

self._v3d = self._v4t = None 

 

def _xcopy(self, *attrs): 

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

''' 

return _xattrs(self.classof(self.lat, self.lon), 

self, '_height', *attrs) 

 

def antipode(self, height=None): 

'''Return the antipode, the point diametrically opposite 

to this point. 

 

@keyword height: Optional height of the antipode, height 

of this point otherwise (C{meter}). 

 

@return: The antipodal point (C{LatLon}). 

''' 

a, b = antipode(self.lat, self.lon) # PYCHOK LatLon2Tuple 

h = self.height if height is None else height 

return self.classof(a, b, height=h) 

 

def bounds(self, wide, high, radius=R_M): 

'''DEPRECATED, use method C{boundsOf}. 

''' 

return self.boundsOf(wide, high, radius=radius) 

 

def boundsOf(self, wide, high, radius=R_M): 

'''Return the SE and NW lat-/longitude of a great circle 

bounding box centered at this location. 

 

@param wide: Longitudinal box width (C{meter}, same units as 

B{C{radius}} or C{degrees} if B{C{radius}} is C{None}). 

@param high: Latitudinal box height (C{meter}, same units as 

B{C{radius}} or C{degrees} if B{C{radius}} is C{None}). 

@keyword radius: Optional, mean earth radius (C{meter}). 

 

@return: A L{Bounds2Tuple}C{(latlonSW, latlonNE)}, the 

lower-left and upper-right corner (C{LatLon}). 

 

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

''' 

w = wide * 0.5 

h = high * 0.5 

if radius > EPS: 

a, _ = self.to2ab() 

ca = cos(a) 

if ca > EPS: 

w = degrees(asin(w / radius) / ca) 

else: 

w = 0 # XXX 

h = degrees(h / radius) 

w, h = abs(w), abs(h) 

 

r = Bounds2Tuple(self.classof(self.lat - h, self.lon - w, height=self.height), 

self.classof(self.lat + h, self.lon + w, height=self.height)) 

return self._xnamed(r) 

 

def compassAngle(self, other): 

'''DEPRECATED, use method C{compassAngleTo}. 

''' 

return self.compassAngleTo(other) 

 

def compassAngleTo(self, other, adjust=True, wrap=False): 

'''Return the angle from North for the direction vector between 

this and an other point. 

 

Suitable only for short, non-near-polar vectors up to a few 

hundred Km or Miles. Use method C{initialBearingTo} for 

larger distances. 

 

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

@keyword adjust: Adjust the longitudinal delta by the 

cosine of the mean latitude (C{bool}). 

@keyword wrap: Wrap and L{unroll180} longitudes and longitudinal 

delta (C{bool}). 

 

@return: Compass angle from North (C{degrees360}). 

 

@raise TypeError: The B{C{other}} point is not C{LatLon}. 

 

@note: Courtesy Martin Schultz. 

 

@see: U{Local, flat earth approximation 

<https://www.EdWilliams.org/avform.htm#flat>}. 

''' 

self.others(other) 

return compassAngle(self.lat, self.lon, other.lat, other.lon, 

adjust=adjust, wrap=wrap) 

 

def copy(self): 

'''Copy this point. 

 

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

''' 

return self._xcopy() 

 

@property_RO 

def datum(self): 

'''Get this point's datum. I{Must be overloaded}. 

''' 

self._notOverloaded('datum') 

 

def _distanceTo(self, func, other, radius, **options): 

'''(INTERNAL) Helper for methods C{<func>To}. 

''' 

self.others(other) 

if radius is None: 

radius = self._datum.ellipsoid.R1 if self._datum else R_M 

return func(self.lat, self.lon, other.lat, other.lon, 

radius=radius, **options) 

 

@property_RO 

def Ecef(self): 

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

''' 

return self._Ecef 

 

def equals(self, other, eps=None): 

'''DEPRECATED, use method C{isequalTo}. 

''' 

return self.isequalTo(other, eps=eps) 

 

def equals3(self, other, eps=None): 

'''DEPRECATED, use method C{isequalTo3}. 

''' 

return self.isequalTo3(other, eps=eps) 

 

def equirectangularTo(self, other, radius=None, **options): 

'''Compute the distance between this and an other point 

using the U{Equirectangular Approximation / Projection 

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

 

Suitable only for short, non-near-polar distances up to a 

few hundred Km or Miles. Use method C{haversineTo} or 

C{distanceTo*} for more accurate and/or larger distances. 

 

See function L{equirectangular_} for more details, the 

available B{C{options}} and errors raised. 

 

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

@keyword radius: Optional, mean earth radius (C{meter}) or 

C{None} for the mean radius of this 

point's datum ellipsoid. 

@keyword options: Optional keyword arguments for function 

L{equirectangular}. 

 

@return: Distance (C{meter}, same units as B{C{radius}}). 

 

@raise TypeError: The B{C{other}} point is not C{LatLon}. 

 

@see: Function L{equirectangular}, methods C{euclideanTo}, 

C{distanceTo*}, C{haversineTo} and C{vincentysTo}. 

''' 

return self._distanceTo(equirectangular, other, radius, **options) 

 

def euclideanTo(self, other, radius=None, **options): 

'''Approximate the C{Euclidian} distance between this and 

an other point. 

 

See function L{euclidean} for the available B{C{options}}. 

 

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

@keyword radius: Optional, mean earth radius (C{meter}) or 

C{None} for the mean radius of this 

point's datum ellipsoid. 

@keyword options: Optional keyword arguments for function 

L{euclidean}. 

 

@return: Distance (C{meter}, same units as B{C{radius}}). 

 

@raise TypeError: The B{C{other}} point is not C{LatLon}. 

 

@see: Function L{euclidean}, methods C{equirectangularTo}, 

C{distanceTo*}, C{haversineTo} and C{vincentysTo}. 

''' 

return self._distanceTo(euclidean, other, radius, **options) 

 

def haversineTo(self, other, radius=None, wrap=False): 

'''Compute the distance between this and an other point using the 

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

formula. 

 

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

@keyword radius: Optional, mean earth radius (C{meter}) or 

C{None} for the mean radius of this 

point's datum ellipsoid. 

@keyword wrap: Wrap and L{unroll180} longitudes (C{bool}). 

 

@return: Distance (C{meter}, same units as B{C{radius}}). 

 

@raise TypeError: The B{C{other}} point is not C{LatLon}. 

 

@see: Function L{haversine}, methods C{equirectangularTo}, 

C{euclideanTo}, C{distanceTo*} and C{vincentysTo}. 

''' 

return self._distanceTo(haversine, other, radius, wrap=wrap) 

 

@property 

def height(self): 

'''Get the height (C{meter}). 

''' 

return self._height 

 

@height.setter # PYCHOK setter! 

def height(self, height): 

'''Set the height. 

 

@param height: New height (C{meter}). 

 

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

 

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

''' 

h = scalar(height, None, name='height') 

self._update(h != self._height) 

self._height = h 

 

def isantipodeTo(self, other, eps=EPS): 

'''Check whether this and an other point are antipodal, 

on diametrically opposite sides of the earth. 

 

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

@keyword eps: Tolerance for near-equality (C{degrees}). 

 

@return: C{True} if points are antipodal within the given 

tolerance, C{False} otherwise. 

''' 

return isantipode(self.lat, self.lon, 

other.lat, other.lon, eps=eps) 

 

def isantipode(self, other, eps=EPS): 

'''DEPRECATED, use method C{isantipodeTo}. 

''' 

return self.isantipodeTo(other, eps=eps) 

 

def isequalTo(self, other, eps=None): 

'''Compare this point with an other point. 

 

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

@keyword eps: Tolerance for equality (C{degrees}). 

 

@return: C{True} if both points are identical, 

I{ignoring} height, C{False} otherwise. 

 

@raise TypeError: The B{C{other}} point is not C{LatLon}. 

 

@see: Method L{isequalTo3}. 

 

@example: 

 

>>> p = LatLon(52.205, 0.119) 

>>> q = LatLon(52.205, 0.119) 

>>> e = p.isequalTo(q) # True 

''' 

self.others(other) 

 

if eps and eps > 0: 

return abs(self.lat - other.lat) < eps and \ 

abs(self.lon - other.lon) < eps 

else: 

return self.lat == other.lat and \ 

self.lon == other.lon 

 

def isequalTo3(self, other, eps=None): 

'''Compare this point with an other point. 

 

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

@keyword eps: Tolerance for equality (C{degrees}). 

 

@return: C{True} if both points are identical 

I{including} height, C{False} otherwise. 

 

@raise TypeError: The B{C{other}} point is not C{LatLon}. 

 

@see: Method L{isequalTo}. 

 

@example: 

 

>>> p = LatLon(52.205, 0.119, 42) 

>>> q = LatLon(52.205, 0.119) 

>>> e = p.isequalTo3(q) # False 

''' 

return self.isequalTo(other, eps=eps) and self.height == other.height 

 

@property 

def lat(self): 

'''Get the latitude (C{degrees90}). 

''' 

return self._lat 

 

@lat.setter # PYCHOK setter! 

def lat(self, lat): 

'''Set the latitude. 

 

@param lat: New latitude (C{str[N|S]} or C{degrees}). 

 

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

''' 

lat = parseDMS(lat, suffix='NS', clip=90) 

self._update(lat != self._lat) 

self._lat = lat 

 

@property 

def latlon(self): 

'''Get the lat- and longitude (L{LatLon2Tuple}). 

''' 

if self._latlon is None: 

self._latlon = LatLon2Tuple(self._lat, self._lon) 

return self._xrenamed(self._latlon) 

 

@latlon.setter # PYCHOK setter! 

def latlon(self, latlonh): 

'''Set the lat- and longitude and optionally the height. 

 

@param latlonh: New lat-, longitude and height (2- or 

3-tuple of C{degrees} and C{meter}). 

 

@raise TypeError: Height of B{C{latlonh}} not C{scalar} or 

B{C{latlonh}} not C{list} or C{tuple}. 

 

@raise ValueError: Invalid B{C{latlonh}} or M{len(latlonh)}. 

 

@see: Function L{parse3llh} to parse a B{C{latlonh}} string 

into a 3-tuple (lat, lon, h). 

''' 

_TypeError(list, tuple, latlonh=latlonh) 

 

if len(latlonh) == 3: 

h = scalar(latlonh[2], None, name='latlonh') 

elif len(latlonh) != 2: 

raise ValueError('%s invalid: %r' % ('latlonh', latlonh)) 

else: 

h = self._height 

 

lat, lon = parseDMS2(latlonh[0], latlonh[1]) 

self._update(lat != self._lat or 

lon != self._lon or h != self._height) 

self._lat, self._lon, self._height = lat, lon, h 

 

@property_RO 

def latlonheight(self): 

'''Get the lat-, longitude and height (L{LatLon3Tuple}). 

''' 

return self.latlon._3Tuple(self.height) 

 

def latlon_(self, ndigits=0): 

'''DEPRECATED, use method C{latlon2}. 

''' 

return self.latlon2(ndigits) 

 

def latlon2(self, ndigits=0): 

'''Return this point's lat- and longitude in C{degrees}, rounded. 

 

@keyword ndigits: Number of decimal digits (C{int}). 

 

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

and rounded away from zero. 

 

@note: The C{round}ed values are always C{float}, also 

if B{C{ndigits}} is omitted. 

''' 

r = LatLon2Tuple(round(self.lat, ndigits), 

round(self.lon, ndigits)) 

return self._xnamed(r) 

 

def latlon2round(self, ndigits=0): 

'''DEPRECATED, use method C{latlon2}. 

''' 

return self.latlon2(ndigits) 

 

@property 

def lon(self): 

'''Get the longitude (C{degrees180}). 

''' 

return self._lon 

 

@lon.setter # PYCHOK setter! 

def lon(self, lon): 

'''Set the longitude. 

 

@param lon: New longitude (C{str[E|W]} or C{degrees}). 

 

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

''' 

lon = parseDMS(lon, suffix='EW', clip=180) 

self._update(lon != self._lon) 

self._lon = lon 

 

@property_RO 

def philam(self): 

'''Get the lat- and longitude (L{PhiLam2Tuple}). 

''' 

return self._ab or self.to2ab() 

 

@property_RO 

def philamheight(self): 

'''Get the lat-, longitude and height (L{PhiLam3Tuple}). 

''' 

return self.philam._3Tuple(self.height) 

 

def philam2(self, ndigits=0): 

'''Return this point's lat- and longitude in C{radians}, rounded. 

 

@keyword ndigits: Number of decimal digits (C{int}). 

 

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

and rounded away from zero. 

 

@note: The C{round}ed values are always C{float}, also 

if B{C{ndigits}} is omitted. 

''' 

r = self._ab or self.to2ab() 

r = PhiLam2Tuple(round(r.phi, ndigits), 

round(r.lam, ndigits)) 

return self._xnamed(r) 

 

def points(self, points, closed=True): 

'''DEPRECATED, use method C{points2}. 

''' 

return self.points2(points, closed=closed) 

 

def points2(self, points, closed=True): 

'''Check a path or polygon represented by points. 

 

@param points: The path or polygon points (C{LatLon}[]) 

@keyword closed: Optionally, consider the polygon closed, 

ignoring any duplicate or closing final 

B{C{points}} (C{bool}). 

 

@return: A L{Points2Tuple}C{(number, points)}, C{int} 

and C{list} or C{tuple}. 

 

@raise TypeError: Some B{C{points}} are not C{LatLon}. 

 

@raise ValueError: Insufficient number of B{C{points}}. 

''' 

return points2(points, closed=closed, base=self) 

 

def to2ab(self): 

'''Return this point's lat- and longitude in C{radians}. 

 

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

''' 

if self._ab is None: 

self._ab = PhiLam2Tuple(radians(self.lat), radians(self.lon)) 

return self._xnamed(self._ab) 

 

def to3llh(self, height=None): 

'''Return this point's lat-, longitude and height. 

 

@keyword height: Optional height, overriding this 

point's height (C{meter}). 

 

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

''' 

h = self.height if height is None else height 

return self.latlon._3Tuple(h) 

 

def to3xyz(self): 

'''DEPRECATED, use method C{toVector}, C{toNvector} or C{toEcef}. 

 

@return: See method C{toVector} for C{B{Vector}=None}. 

''' 

return self.toVector() 

 

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

'''Convert this point to geocentric (ECEF cartesian) coordinates. 

 

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

geocentric coordinates (C{Cartesian}) 

or C{None}. 

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

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

 

@return: A B{C{Cartesian}} or if C{B{Cartesian}=None}, an 

L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M, 

datum)} with C{C} 0 and C{M} if available. 

 

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

''' 

r = self.toEcef() 

if Cartesian is not None: # class or .classof 

r = Cartesian(r, **kwds) 

r = self._xnamed(r) 

return r 

 

def toEcef(self): 

'''Convert this point to a geocentric coordinates, alse 

known as I{Earth-Centered, Earth-Fixed} (U{ECEF 

<https://WikiPedia.org/wiki/ECEF>}). 

 

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

C, M, datum)} with C{C} 0 and C{M} if available. 

 

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

''' 

if self._e9t is None: 

e = self.Ecef(self.datum).forward(self, M=True) 

self._e9t = self._xnamed(e) 

return self._e9t 

 

def toNvector(self, h=None, Nvector=None, **kwds): 

'''Convert this point to C{n-vector} (normal to the earth's 

surface) components, I{including height}. 

 

@keyword h: Optional height, overriding this point's 

height (C{meter}). 

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

C{n-vector} components (C{Nvector}) 

or C{None}. 

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

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

 

@return: A B{C{Nvector}} or an L{Vector4Tuple}C{(x, y, z, h)} 

if C{B{Nvector}=None}. 

 

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

''' 

if kwds or h not in (None, self.height): 

r = Vector3Tuple(*self.toVector3d().to3xyz()) 

r = r._4Tuple(self.height if h is None else h) 

if Nvector is not None: 

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

else: # self.height, no kwds 

r = self._v4t 

if r is None: 

r = Vector3Tuple(*self.toVector3d().to3xyz()) 

self._v4t = r = r._4Tuple(self.height) 

if Nvector is not None: 

r = Nvector(r.x, r.y, r.z, h=r.h, ll=self) 

return self._xnamed(r) 

 

def toStr(self, form=F_DMS, prec=None, m='m', sep=', '): # PYCHOK expected 

'''Convert this point to a "lat, lon [+/-height]" string, 

formatted in the given form. 

 

@keyword form: Optional format, F_D, F_DM, F_DMS for 

deg°, deg°min′, deg°min′sec″ (C{str}). 

@keyword prec: Optional number of decimal digits (0..8 or C{None}). 

@keyword m: Optional unit of the height (C{str}). 

@keyword sep: Optional separator to join (C{str}). 

 

@return: Point in the specified form (C{str}). 

 

@example: 

 

>>> LatLon(51.4778, -0.0016).toStr() # 51°28′40″N, 000°00′06″W 

>>> LatLon(51.4778, -0.0016).toStr(F_D) # 51.4778°N, 000.0016°W 

>>> LatLon(51.4778, -0.0016, 42).toStr() # 51°28′40″N, 000°00′06″W, +42.00m 

 

''' 

t = [latDMS(self.lat, form=form, prec=prec), 

lonDMS(self.lon, form=form, prec=prec)] 

if self.height: 

t += ['%+.2f%s' % (self.height, m)] 

return sep.join(t) 

 

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

'''Convert this point to C{n-vector} (normal to the earth's 

surface) components, I{ignoring height}. 

 

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

C{n-vector} components (L{Vector3d}) 

or C{None}. 

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

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

 

@return: A B{C{Vector}} or if C{B{Vector}=None}, an 

L{Vector3Tuple}C{(x, y, z)}. 

 

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

''' 

# Kenneth Gade eqn 3, but using right-handed 

# vector x -> 0°E,0°N, y -> 90°E,0°N, z -> 90°N 

a, b = self.to2ab() 

sa, ca, sb, cb = sincos2(a, b) 

r = Vector3Tuple(ca * cb, ca * sb, sa) 

if Vector is not None: 

r = Vector(r.x, r.y, r.z, **kwds) # PYCHOK Vector3Tuple 

return self._xnamed(r) 

 

def toVector3d(self): 

'''Convert this point to C{n-vector} (normal to the earth's 

surface) components, I{ignoring height}. 

 

@return: Unit vector (L{Vector3d}). 

''' 

if self._v3d is None: 

self._v3d = self.toVector(Vector=Vector3d) # XXX .unit() 

return self._v3d 

 

def vincentysTo(self, other, radius=None, wrap=False): 

'''Compute the distance between this and an other point using 

U{Vincenty's<https://WikiPedia.org/wiki/Great-circle_distance>} 

spherical formula. 

 

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

@keyword radius: Optional, mean earth radius (C{meter}) or 

C{None} for the mean radius of this 

point's datum ellipsoid. 

@keyword wrap: Wrap and L{unroll180} longitudes (C{bool}). 

 

@return: Distance (C{meter}, same units as B{C{radius}}). 

 

@raise TypeError: The B{C{other}} point is not C{LatLon}. 

 

@see: Function L{vincentys}, methods C{equirectangularTo}, 

C{euclideanTo}, C{distanceTo*} and C{haversineTo}. 

''' 

return self._distanceTo(vincentys, other, radius, wrap=wrap) 

 

# **) MIT License 

# 

# Copyright (C) 2016-2020 -- mrJean1 at Gmail -- All Rights Reserved. 

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# Software is furnished to do so, subject to the following conditions: 

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