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# -*- coding: utf-8 -*- 

 

u'''(INTERNAL) Base class L{LatLonBase} for elliposiodal, spherical and 

N-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}. 

''' 

 

from pygeodesy.basics import isstr, _xinstanceof 

# from pygeodesy.datums import _spherical_datum # from .formy 

from pygeodesy.dms import F_D, F_DMS, latDMS, lonDMS, parse3llh 

from pygeodesy.errors import _incompatible, IntersectionError, _ValueError, \ 

_xdatum, _xError, _xkwds, _xkwds_not 

# from pygeodesy.fmath import favg # _MODS.fmath.favg 

from pygeodesy.formy import antipode, compassAngle, cosineAndoyerLambert_, \ 

cosineForsytheAndoyerLambert_, cosineLaw, \ 

equirectangular, euclidean, flatLocal_, \ 

flatPolar, hartzell, haversine, isantipode, \ 

latlon2n_xyz, _spherical_datum, thomas_, vincentys 

from pygeodesy.interns import EPS, EPS0, EPS1, EPS4, NN, R_M, _COMMASPACE_, \ 

_concentric_, _height_, _intersection_, _m_, \ 

_no_, _overlap_, _point_, _0_0, _0_5, _1_0 

from pygeodesy.iters import PointsIter, points2 

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

from pygeodesy.named import _NamedBase, notOverloaded 

from pygeodesy.namedTuples import Bounds2Tuple, LatLon2Tuple, PhiLam2Tuple, \ 

Trilaterate5Tuple, Vector3Tuple 

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

property_doc_, property_RO 

from pygeodesy.streprs import Fmt, hstr 

from pygeodesy.units import Distance_, Lat, Lon, Height, Radius, Radius_, Scalar_ 

from pygeodesy.utily import _unrollon, unrollPI 

from pygeodesy.vector2d import _circin6, Circin6Tuple, _circum3, Circum3Tuple, \ 

circum4_, Circum4Tuple, _radii11ABC 

from pygeodesy.vector3d import nearestOn6, Vector3d 

 

from math import asin, cos, degrees, radians 

 

__all__ = _ALL_LAZY.latlonBase 

__version__ = '22.04.22' 

 

 

class LatLonBase(_NamedBase): 

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

ellipsoidal earth models. 

''' 

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

_height = 0 # height (C{meter}), default 

_lat = 0 # latitude (C{degrees}) 

_lon = 0 # longitude (C{degrees}) 

 

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

'''New C{LatLon}. 

 

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

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

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

@kwarg 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 UnitError: Invalid B{C{lat}}, B{C{lon}} or B{C{height}}. 

 

@example: 

 

>>> p = LatLon(50.06632, -5.71475) 

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

''' 

if name: 

self.name = name 

 

self._lat = Lat(lat) # parseDMS2(lat, lon) 

self._lon = Lon(lon) # PYCHOK LatLon2Tuple 

if height: # elevation 

self._height = Height(height) 

 

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 antipode(self, height=None): 

'''Return the antipode, the point diametrically opposite 

to this point. 

 

@kwarg height: Optional height of the antipode (C{meter}), 

this point's height otherwise. 

 

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

''' 

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

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

return self.classof(a, b, height=h) 

 

@deprecated_method 

def bounds(self, wide, tall, radius=R_M): # PYCHOK no cover 

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

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

 

def boundsOf(self, wide, tall, radius=R_M, height=None): 

'''Return the SW and NE lat-/longitude of a great circle 

bounding box centered at this location. 

 

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

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

@arg tall: Latitudinal box size (C{meter}, same units as 

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

@kwarg radius: Mean earth radius (C{meter}). 

@kwarg height: Height for C{latlonSW} and C{latlonNE} (C{meter}), 

overriding the point's height. 

 

@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} 

''' 

x = Scalar_(wide=wide) * _0_5 

y = Scalar_(tall=tall) * _0_5 

if radius is not None: 

r = Radius_(radius) 

c = cos(self.phi) 

x = degrees(asin(x / r) / c) if abs(c) > EPS0 else _0_0 # XXX 

y = degrees(y / r) 

x, y = abs(x), abs(y) 

 

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

sw = self.classof(self.lat - y, self.lon - x, height=h) 

ne = self.classof(self.lat + y, self.lon + x, height=h) 

return Bounds2Tuple(sw, ne, name=self.name) 

 

def chordTo(self, other, height=None): 

'''Compute the length of the chord through the earth between 

this and an other point. 

 

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

@kwarg height: Overriding height for both points (C{meter}) 

or C{None} for each point's height. 

 

@return: The chord length (conventionally C{meter}). 

 

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

''' 

def _v3d(ll): 

t = ll.toEcef(height=height) # .toVector(Vector=Vector3d) 

return Vector3d(t.x, t.y, t.z) 

 

self.others(other) 

return _v3d(self).minus(_v3d(other)).length 

 

def circin6(self, point2, point3, eps=EPS4): 

'''Return the radius and center of the I{inscribed} aka I{In-}circle 

of the (planar) triangle formed by this and two other points. 

 

@arg point2: Second point (C{LatLon}). 

@arg point3: Third point (C{LatLon}). 

@kwarg eps: Tolerance for function L{pygeodesy.trilaterate3d2}. 

 

@return: L{Circin6Tuple}C{(radius, center, deltas, cA, cB, cC)}. The 

C{center} and contact points C{cA}, C{cB} and C{cC}, each an 

instance of this (sub-)class, are co-planar with this and the 

two given points, see the B{Note} below. 

 

@raise ImportError: Package C{numpy} not found, not installed or older 

than version 1.10. 

 

@raise IntersectionError: Near-coincident or -colinear points or 

a trilateration or C{numpy} issue. 

 

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

 

@note: The C{center} is trilaterated in cartesian (ECEF) space and converted 

back to geodetic lat-, longitude and height. The latter, conventionally 

in C{meter} indicates whether the C{center} is above, below or on the 

surface of the earth model. If C{deltas} is C{None}, the C{center} is 

I{un}ambigous. Otherwise C{deltas} is a L{LatLon3Tuple}C{(lat, lon, 

height)} representing the differences between both results from 

L{pygeodesy.trilaterate3d2} and C{center} is the mean thereof. 

 

@see: Function L{pygeodesy.circin6}, method L{circum3}, U{Incircle 

<https://MathWorld.Wolfram.com/Incircle.html>} and U{Contact Triangle 

<https://MathWorld.Wolfram.com/ContactTriangle.html>}. 

''' 

try: 

cs = self._toCartesian3(point2, point3) 

r, c, d, cA, cB, cC = _circin6(*cs, eps=eps, useZ=True, dLL3=True, 

datum=self.datum) # PYCHOK unpack 

return Circin6Tuple(r, c.toLatLon(), d, cA.toLatLon(), cB.toLatLon(), cC.toLatLon()) 

except (AssertionError, TypeError, ValueError) as x: 

raise _xError(x, point=self, point2=point2, point3=point3) 

 

def circum3(self, point2, point3, circum=True, eps=EPS4): 

'''Return the radius and center of the smallest circle I{through} or I{containing} 

this and two other points. 

 

@arg point2: Second point (C{LatLon}). 

@arg point3: Third point (C{LatLon}). 

@kwarg circum: If C{True} return the C{circumradius} and C{circumcenter}, 

always, ignoring the I{Meeus}' Type I case (C{bool}). 

@kwarg eps: Tolerance for function L{pygeodesy.trilaterate3d2}. 

 

@return: A L{Circum3Tuple}C{(radius, center, deltas)}. The C{center}, an 

instance of this (sub-)class, is co-planar with this and the two 

given points. If C{deltas} is C{None}, the C{center} is 

I{un}ambigous. Otherwise C{deltas} is a L{LatLon3Tuple}C{(lat, 

lon, height)} representing the difference between both results 

from L{pygeodesy.trilaterate3d2} and C{center} is the mean thereof. 

 

@raise ImportError: Package C{numpy} not found, not installed or older than 

version 1.10. 

 

@raise IntersectionError: Near-concentric, -coincident or -colinear points, 

incompatible C{Ecef} classes or a trilateration 

or C{numpy} issue. 

 

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

 

@note: The C{center} is trilaterated in cartesian (ECEF) space and converted 

back to geodetic lat-, longitude and height. The latter, conventionally 

in C{meter} indicates whether the C{center} is above, below or on the 

surface of the earth model. If C{deltas} is C{None}, the C{center} is 

I{un}ambigous. Otherwise C{deltas} is a L{LatLon3Tuple}C{(lat, lon, 

height)} representing the difference between both results from 

L{pygeodesy.trilaterate3d2} and C{center} is the mean thereof. 

 

@see: Function L{pygeodesy.circum3} and methods L{circin6} and L{circum4_}. 

''' 

try: 

cs = self._toCartesian3(point2, point3) 

r, c, d = _circum3(*cs, circum=circum, eps=eps, useZ=True, dLL3=True, # XXX -3d2 

clas=cs[0].classof, datum=self.datum) # PYCHOK unpack 

return Circum3Tuple(r, c.toLatLon(), d) 

except (AssertionError, TypeError, ValueError) as x: 

raise _xError(x, point=self, point2=point2, point3=point3, circum=circum) 

 

def circum4_(self, *points): 

'''Best-fit a sphere through this and two or more other points. 

 

@arg points: The other points (each a C{LatLon}). 

 

@return: L{Circum4Tuple}C{(radius, center, rank, residuals)} with C{center} 

an instance of this (sub-)class. 

 

@raise ImportError: Package C{numpy} not found, not installed or older than 

version 1.10. 

 

@raise NumPyError: Some C{numpy} issue. 

 

@raise TypeError: One of the B{C{points}} invalid. 

 

@raise ValueError: Too few B{C{points}}. 

 

@see: Function L{pygeodesy.circum4_} and L{circum3}. 

''' 

C = self._toCartesianEcef 

c = C(point=self) 

t = circum4_(c, Vector=c.classof, *(C(i=i, points=p) for i, p in enumerate(points))) 

c = t.center.toLatLon(LatLon=self.classof, name=t.name) 

return Circum4Tuple(t.radius, c, t.rank, t.residuals, name=c.name) 

 

@deprecated_method 

def compassAngle(self, other, adjust=True, wrap=False): # PYCHOK no cover 

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

return self.compassAngleTo(other, adjust=adjust, wrap=wrap) 

 

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. 

 

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

@kwarg adjust: Adjust the longitudinal delta by the 

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

@kwarg wrap: Wrap and L{pygeodesy.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 of 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 cosineAndoyerLambertTo(self, other, wrap=False): 

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

the U{Andoyer-Lambert correction<https://navlib.net/wp-content/uploads/ 

2013/10/admiralty-manual-of-navigation-vol-1-1964-english501c.pdf>} of 

the U{Law of Cosines<https://www.Movable-Type.co.UK/scripts/latlong.html#cosine-law>} 

formula. 

 

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

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

 

@return: Distance (C{meter}, same units as the axes of 

this point's datum ellipsoid). 

 

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

 

@see: Function L{pygeodesy.cosineAndoyerLambert} and methods 

L{cosineForsytheAndoyerLambertTo}, L{cosineLawTo}, 

C{distanceTo*}, L{equirectangularTo}, L{euclideanTo}, 

L{flatLocalTo}/L{hubenyTo}, L{flatPolarTo}, L{haversineTo}, 

L{thomasTo} and L{vincentysTo}. 

''' 

return self._distanceTo_(cosineAndoyerLambert_, other, wrap=wrap) 

 

def cosineForsytheAndoyerLambertTo(self, other, wrap=False): 

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

the U{Forsythe-Andoyer-Lambert correction 

<https://www2.UNB.Ca/gge/Pubs/TR77.pdf>} of the U{Law of Cosines 

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

formula. 

 

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

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

 

@return: Distance (C{meter}, same units as the axes of 

this point's datum ellipsoid). 

 

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

 

@see: Function L{pygeodesy.cosineForsytheAndoyerLambert} and methods 

L{cosineAndoyerLambertTo}, L{cosineLawTo}, C{distanceTo*}, 

L{equirectangularTo}, L{euclideanTo}, L{flatLocalTo}/L{hubenyTo}, 

L{flatPolarTo}, L{haversineTo}, L{thomasTo} and L{vincentysTo}. 

''' 

return self._distanceTo_(cosineForsytheAndoyerLambert_, other, wrap=wrap) 

 

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

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

U{spherical Law of Cosines 

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

formula. 

 

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

@kwarg radius: Mean earth radius (C{meter}) or C{None} 

for the mean radius of this point's datum 

ellipsoid. 

@kwarg wrap: Wrap and L{pygeodesy.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{pygeodesy.cosineLaw} and methods L{cosineAndoyerLambertTo}, 

L{cosineForsytheAndoyerLambertTo}, C{distanceTo*}, L{equirectangularTo}, 

L{euclideanTo}, L{flatLocalTo}/L{hubenyTo}, L{flatPolarTo}, 

L{haversineTo}, L{thomasTo} and L{vincentysTo}. 

''' 

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

 

@property_RO 

def datum(self): # PYCHOK no cover 

'''(INTERNAL) I{Must be overloaded}, see function C{notOverloaded}. 

''' 

notOverloaded(self) 

 

def destinationXyz(self, delta, LatLon=None, **LatLon_kwds): 

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

 

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

L{Ned} or L{Local9Tuple}). 

@kwarg LatLon: Optional (geodetic) class to return the destination 

or C{None}. 

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

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

 

@return: Destination as a C{B{LatLon}(lat, lon, **B{LatLon_kwds})} 

instance or if C{B{LatLon} is None}, a L{LatLon3Tuple}C{(lat, 

lon, height)} respectively L{LatLon4Tuple}C{(lat, lon, 

height, datum)} depending on whether a C{datum} keyword 

is un-/specified. 

 

@raise TypeError: Invalid B{C{delta}}, B{C{LatLon}} or B{C{LatLon_kwds}}. 

''' 

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

return t.toLatLon(LatLon=LatLon, **_xkwds(LatLon_kwds, name=self.name)) 

 

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

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

''' 

self.others(other) # up=2 

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) 

 

def _distanceTo_(self, func_, other, wrap=False): 

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

''' 

self.others(other) # up=2 

r, _ = unrollPI(self.lam, other.lam, wrap=wrap) 

r = func_(other.phi, self.phi, r, datum=self.datum) 

return r * self.datum.ellipsoid.a 

 

@Property_RO 

def Ecef(self): 

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

''' 

return _MODS.ecef.EcefKarney # default 

 

@Property_RO 

def _Ecef_forward(self): 

'''(INTERNAL) Helper for L{_ecef9} and L{toEcef} (C{callable}). 

''' 

return self.Ecef(self.datum, name=self.name).forward 

 

@Property_RO 

def _ecef9(self): 

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

''' 

return self._Ecef_forward(self, M=True) 

 

@deprecated_method 

def equals(self, other, eps=None): # PYCHOK no cover 

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

return self.isequalTo(other, eps=eps) 

 

@deprecated_method 

def equals3(self, other, eps=None): # PYCHOK no cover 

'''DEPRECATED, use method L{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#equirectangular>}. 

 

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

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

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

 

See function L{pygeodesy.equirectangular_} for more details, 

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

 

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

@kwarg radius: Mean earth radius (C{meter}) or C{None} for 

the mean radius of this point's datum ellipsoid. 

@kwarg options: Optional keyword arguments for function 

L{pygeodesy.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{pygeodesy.equirectangular} and methods L{cosineAndoyerLambertTo}, 

L{cosineForsytheAndoyerLambertTo}, L{cosineLawTo}, C{distanceTo*}, 

C{euclideanTo}, L{flatLocalTo}/L{hubenyTo}, L{flatPolarTo}, 

L{haversineTo}, L{thomasTo} and L{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{pygeodesy.euclidean} for the available B{C{options}}. 

 

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

@kwarg radius: Mean earth radius (C{meter}) or C{None} for 

the mean radius of this point's datum ellipsoid. 

@kwarg options: Optional keyword arguments for function 

L{pygeodesy.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{pygeodesy.euclidean} and methods L{cosineAndoyerLambertTo}, 

L{cosineForsytheAndoyerLambertTo}, L{cosineLawTo}, C{distanceTo*}, 

L{equirectangularTo}, L{flatLocalTo}/L{hubenyTo}, L{flatPolarTo}, 

L{haversineTo}, L{thomasTo} and L{vincentysTo}. 

''' 

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

 

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

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

U{ellipsoidal Earth to plane projection 

<https://WikiPedia.org/wiki/Geographical_distance#Ellipsoidal_Earth_projected_to_a_plane>} 

aka U{Hubeny<https://www.OVG.AT/de/vgi/files/pdf/3781/>} formula. 

 

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

@kwarg radius: Mean earth radius (C{meter}) or C{None} for the 

major radius of this point's datum/ellipsoid. 

@kwarg wrap: Wrap and L{pygeodesy.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}. 

 

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

 

@see: Function L{pygeodesy.flatLocal}/L{pygeodesy.hubeny}, methods 

L{cosineAndoyerLambertTo}, L{cosineForsytheAndoyerLambertTo}, 

L{cosineLawTo}, C{distanceTo*}, L{equirectangularTo}, L{euclideanTo}, 

L{flatPolarTo}, L{haversineTo}, L{thomasTo} and L{vincentysTo} and 

U{local, flat Earth approximation<https://www.edwilliams.org/avform.htm#flat>}. 

''' 

E = self.datum.ellipsoid 

r = self._distanceTo_(flatLocal_, other, wrap=wrap) * E.a2_ 

a = E.a if radius in (None, 1, _1_0) else Radius(radius) 

return r * a 

 

hubenyTo = flatLocalTo # for Karl Hubeny 

 

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

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

the U{polar coordinate flat-Earth<https://WikiPedia.org/wiki/ 

Geographical_distance#Polar_coordinate_flat-Earth_formula>}formula. 

 

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

@kwarg radius: Mean earth radius (C{meter}) or C{None} 

for the mean radius of this point's datum 

ellipsoid. 

@kwarg wrap: Wrap and L{pygeodesy.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{pygeodesy.flatPolar} and methods L{cosineAndoyerLambertTo}, 

L{cosineForsytheAndoyerLambertTo}, L{cosineLawTo}, C{distanceTo*}, 

L{equirectangularTo}, L{euclideanTo}, L{flatLocalTo}/L{hubenyTo}, 

L{haversineTo}, L{thomasTo} and L{vincentysTo}. 

''' 

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

 

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

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

(pov) with this point'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 point's C{datum} ellipsoid. 

 

@return: The ellipsoid intersection (C{LatLon}) or this very instance 

if this C{pov's height} is C{0}. 

 

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

C{pov's height} is negative or B{C{los}} 

points outside the ellipsoid or in an 

opposite direction. 

 

@raise TypeError: Invalid B{C{los}}. 

 

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

''' 

h = self.height 

if not h: 

r = self 

elif h < 0: 

raise IntersectionError(pov=self, los=los, height=h, txt=_no_(_height_)) 

elif los is None: 

d = self.datum if earth is None else _spherical_datum(earth) 

r = self.dup(datum=d, height=0, name=self.hartzell.__name__) 

else: 

c = self.toCartesian() 

r = hartzell(c, los=los, earth=earth or self.datum, LatLon=self.classof) 

return r 

 

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. 

 

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

@kwarg radius: Mean earth radius (C{meter}) or C{None} for 

the mean radius of this point's datum ellipsoid. 

@kwarg wrap: Wrap and L{pygeodesy.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{pygeodesy.haversine} and methods L{cosineAndoyerLambertTo}, 

L{cosineForsytheAndoyerLambertTo}, L{cosineLawTo}, C{distanceTo*}, 

L{equirectangularTo}, L{euclideanTo}, L{flatLocalTo}/L{hubenyTo}, 

L{flatPolarTo}, L{thomasTo} and L{vincentysTo}. 

''' 

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

 

def _havg(self, other, f=_0_5): 

'''(INTERNAL) Weighted, average height. 

 

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

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

 

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

''' 

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

 

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

def height(self): 

'''Get the height (C{meter}). 

''' 

return self._height 

 

@height.setter # PYCHOK setter! 

def height(self, height): 

'''Set the height. 

 

@arg height: New height (C{meter}). 

 

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

 

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

''' 

h = Height(height) 

self._update(h != self.height) 

self._height = h 

 

def height4(self, earth=None, normal=True, LatLon=None, **LatLon_kwds): 

'''Compute the height 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 LatLon: Optional class to return the height and projection 

(C{LatLon}) or C{None}. 

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

ignored if C{B{LatLon} is None}. 

 

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

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

 

@return: An instance of B{C{LatLon}} or if C{B{LatLon} 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. 

''' 

if LatLon is None: 

r = self.toCartesian().height4(earth=earth, normal=normal) 

else: 

c = self.toCartesian() 

r = c.height4(earth=earth, normal=normal, Cartesian=c.classof, height=0) 

r = r.toLatLon(LatLon=LatLon, **_xkwds(LatLon_kwds, height=r.height)) 

return r 

 

def heightStr(self, prec=-2, m=_m_): 

'''Return this B{C{height}} as C{str}ing. 

 

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

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

 

@see: Function L{pygeodesy.hstr}. 

''' 

return hstr(self.height, prec=prec, m=m) 

 

@deprecated_method 

def isantipode(self, other, eps=EPS): # PYCHOK no cover 

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

return self.isantipodeTo(other, eps=eps) 

 

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

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

on diametrically opposite sides of the earth. 

 

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

@kwarg 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) 

 

@Property_RO 

def isEllipsoidal(self): 

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

''' 

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

 

@Property_RO 

def isEllipsoidalLatLon(self): 

'''Get C{LatLon} base. 

''' 

return False 

 

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

'''Compare this point with an other point, I{ignoring} height. 

 

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

@kwarg 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} 

or mismatch of the B{C{other}} and 

this C{class} or C{type}. 

 

@raise UnitError: Invalid B{C{eps}}. 

 

@see: Method L{isequalTo3}. 

''' 

self.others(other) 

 

return _isequalTo(self, other, eps=Scalar_(eps=eps)) if eps else \ 

(self.lat == other.lat and self.lon == other.lon) 

 

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

'''Compare this point with an other point, I{including} height. 

 

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

@kwarg 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} 

or mismatch of the B{C{other}} and 

this C{class} or C{type}. 

 

@see: Method L{isequalTo}. 

''' 

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

 

@Property_RO 

def isSpherical(self): 

'''Check whether this point 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 longitude (B{C{radians}}). 

''' 

return self.philam.lam 

 

@property_doc_(''' the latitude (C{degrees90}).''') 

def lat(self): 

'''Get the latitude (C{degrees90}). 

''' 

return self._lat 

 

@lat.setter # PYCHOK setter! 

def lat(self, lat): 

'''Set the latitude. 

 

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

 

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

''' 

lat = 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}C{(lat, lon)}). 

''' 

return LatLon2Tuple(self._lat, self._lon, name=self.name) 

 

@latlon.setter # PYCHOK setter! 

def latlon(self, latlonh): 

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

 

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

3-tuple or comma- or space-separated C{str} 

of C{degrees90}, C{degrees180} 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{pygeodesy.parse3llh} to parse a B{C{latlonh}} 

string into a 3-tuple (lat, lon, h). 

''' 

if isstr(latlonh): 

latlonh = parse3llh(latlonh, height=self.height) 

else: 

_xinstanceof(list, tuple, latlonh=latlonh) 

if len(latlonh) == 3: 

h = Height(latlonh[2], name=Fmt.SQUARE(latlonh=2)) 

elif len(latlonh) != 2: 

raise _ValueError(latlonh=latlonh) 

else: 

h = self.height 

 

lat = Lat(latlonh[0]) # parseDMS2(latlonh[0], latlonh[1]) 

lon = Lon(latlonh[1]) 

self._update(lat != self._lat or 

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

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

 

def latlon2(self, ndigits=0): 

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

 

@kwarg 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. 

''' 

return LatLon2Tuple(round(self.lat, ndigits), 

round(self.lon, ndigits), name=self.name) 

 

@deprecated_method 

def latlon_(self, ndigits=0): # PYCHOK no cover 

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

return self.latlon2(ndigits=ndigits) 

 

latlon2round = latlon_ # PYCHOK no cover 

 

@Property_RO 

def latlonheight(self): 

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

''' 

return self.latlon.to3Tuple(self.height) 

 

@property_doc_(''' the longitude (C{degrees180}).''') 

def lon(self): 

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

''' 

return self._lon 

 

@lon.setter # PYCHOK setter! 

def lon(self, lon): 

'''Set the longitude. 

 

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

 

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

''' 

lon = Lon(lon) # parseDMS(lon, suffix=_EW_, clip=180) 

self._update(lon != self._lon) 

self._lon = lon 

 

@Property_RO 

def _ltp(self): 

'''(INTERNAL) Cache for L{toLtp}. 

''' 

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

 

def nearestOn6(self, points, closed=False, height=None, wrap=False): 

'''Locate the point on a path or polygon closest to this point. 

 

Points are converted to and distances are computed in 

I{geocentric}, cartesian space. 

 

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

@kwarg closed: Optionally, close the polygon (C{bool}). 

@kwarg height: Optional height, overriding the height of 

this and all other points (C{meter}). If 

C{None}, take the height of points into 

account for distances. 

@kwarg wrap: Wrap and L{pygeodesy.unroll180} longitudes 

(C{bool}). 

 

@return: A L{NearestOn6Tuple}C{(closest, distance, fi, j, 

start, end)} with the C{closest}, the C{start} 

and the C{end} point each an instance of this 

C{LatLon} and C{distance} in C{meter}, same 

units as the cartesian axes. 

 

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

 

@raise TypeError: Some B{C{points}} or some B{C{points}}' 

C{Ecef} invalid. 

 

@raise ValueError: Some B{C{points}}' C{Ecef} is incompatible. 

 

@see: Function L{pygeodesy.nearestOn6}. 

''' 

def _cs(Ps, h, w, C): 

p = None # not used 

for i, q in Ps.enumerate(): 

if w and i != 0: 

q = _unrollon(p, q) 

yield C(height=h, i=i, up=3, points=q) 

p = q 

 

C = self._toCartesianEcef # to verify datum and Ecef 

Ps = self.PointsIter(points) 

 

c = C(height=height, this=self) # this Cartesian 

t = nearestOn6(c, _cs(Ps, height, wrap, C), closed=closed) 

c, s, e = t.closest, t.start, t.end 

 

kwds = _xkwds_not(None, LatLon=self.classof, # this LatLon 

height=height) 

r = self.Ecef(self.datum).reverse 

p = r(c).toLatLon(**kwds) 

s = r(s).toLatLon(**kwds) if s is not c else p 

e = r(e).toLatLon(**kwds) if e is not c else p 

return t.dup(closest=p, start=s, end=e) 

 

@Property_RO 

def _N_vector(self): 

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

''' 

return _MODS.nvectorBase._N_vector_(*self.xyzh) 

 

@Property_RO 

def phi(self): 

'''Get the latitude (B{C{radians}}). 

''' 

return self.philam.phi 

 

@Property_RO 

def philam(self): 

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

''' 

return PhiLam2Tuple(radians(self.lat), 

radians(self.lon), name=self.name) 

 

def philam2(self, ndigits=0): 

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

 

@kwarg 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. 

''' 

return PhiLam2Tuple(round(self.phi, ndigits), 

round(self.lam, ndigits), name=self.name) 

 

@Property_RO 

def philamheight(self): 

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

''' 

return self.philam.to3Tuple(self.height) 

 

@deprecated_method 

def points(self, points, closed=True): # PYCHOK no cover 

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

return self.points2(points, closed=closed) 

 

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

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

 

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

@kwarg 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 PointsError: Insufficient number of B{C{points}}. 

 

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

''' 

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

 

def PointsIter(self, points, loop=0, dedup=False): 

'''Return a C{PointsIter} iterator. 

 

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

@kwarg loop: Number of loop-back points (non-negative C{int}). 

@kwarg dedup: Skip duplicate points (C{bool}). 

 

@return: A new C{PointsIter} iterator. 

 

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

''' 

return PointsIter(points, base=self, loop=loop, dedup=dedup) 

 

def radii11(self, point2, point3): 

'''Return the radii of the C{Circum-}, C{In-}, I{Soddy} and C{Tangent} 

circles of a (planar) triangle formed by this and two other points. 

 

@arg point2: Second point (C{LatLon}). 

@arg point3: Third point (C{LatLon}). 

 

@return: L{Radii11Tuple}C{(rA, rB, rC, cR, rIn, riS, roS, a, b, c, s)}. 

 

@raise IntersectionError: Near-coincident or -colinear points. 

 

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

 

@see: Function L{pygeodesy.radii11}, U{Incircle 

<https://MathWorld.Wolfram.com/Incircle.html>}, U{Soddy Circles 

<https://MathWorld.Wolfram.com/SoddyCircles.html>} and U{Tangent 

Circles<https://MathWorld.Wolfram.com/TangentCircles.html>}. 

''' 

try: 

cs = self._toCartesian3(point2, point3) 

return _radii11ABC(*cs, useZ=True)[0] 

except (TypeError, ValueError) as x: 

raise _xError(x, point=self, point2=point2, point3=point3) 

 

def thomasTo(self, other, wrap=False): 

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

U{Thomas'<https://apps.DTIC.mil/dtic/tr/fulltext/u2/703541.pdf>} 

formula. 

 

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

@kwarg wrap: Wrap and L{pygeodesy.unrollPI} longitudes (C{bool}). 

 

@return: Distance (C{meter}, same units as the axes of 

this point's datum ellipsoid). 

 

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

 

@see: Function L{pygeodesy.thomas} and methods L{cosineAndoyerLambertTo}, 

L{cosineForsytheAndoyerLambertTo}, L{cosineLawTo}, C{distanceTo*}, 

L{equirectangularTo}, L{euclideanTo}, L{flatLocalTo}/L{hubenyTo}, 

L{flatPolarTo}, L{haversineTo} and L{vincentysTo}. 

''' 

return self._distanceTo_(thomas_, other, wrap=wrap) 

 

@deprecated_method 

def to2ab(self): # PYCHOK no cover 

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

return self.philam 

 

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

'''Convert this point to cartesian, I{geocentric} coordinates, 

also known as I{Earth-Centered, Earth-Fixed} (ECEF). 

 

@kwarg height: Optional height, overriding this point's height 

(C{meter}, conventionally). 

@kwarg Cartesian: Optional class to return the geocentric 

coordinates (C{Cartesian}) or C{None}. 

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

keyword arguments, ignored if 

C{B{Cartesian} is None}. 

 

@return: A 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=0} and C{M} if available. 

 

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

''' 

r = self._ecef9 if height is None else self.toEcef(height=height) 

if Cartesian is not None: # class or .classof 

r = self._xnamed(Cartesian(r, **Cartesian_kwds)) 

_xdatum(r.datum, self.datum) 

return r 

 

def _toCartesian3(self, point2, point3): 

'''(INTERNAL) Convert this and 2 other points. 

''' 

return (self. toCartesian().copy(name=_point_), # copy to rename 

self._toCartesianEcef(up=3, point2=point2), 

self._toCartesianEcef(up=3, point3=point3)) 

 

def _toCartesianEcef(self, height=None, i=None, up=2, **name_point): 

'''(INTERNAL) Convert to cartesian and check Ecef's before and after. 

''' 

p = self.others(up=up, **name_point) 

c = p.toCartesian(height=height) 

E = self.Ecef 

if E: 

for p in (p, c): 

e = getattr(p, LatLonBase.Ecef.name, None) 

if e not in (None, E): 

n, _ = name_point.popitem() 

if i is not None: 

Fmt.SQUARE(n, i) 

raise _ValueError(n, e, txt=_incompatible(E.__name__)) 

return c 

 

def toEcef(self, height=None, M=False): 

'''Convert this point to I{geocentric} coordinates, also known as 

I{Earth-Centered, Earth-Fixed} (U{ECEF<https://WikiPedia.org/wiki/ECEF>}). 

 

@kwarg height: Optional height, overriding this point's height 

(C{meter}, conventionally). 

@kwarg M: Optionally, include the rotation L{EcefMatrix} (C{bool}). 

 

@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. 

''' 

return self._ecef9 if height in (None, self.height) else \ 

self._Ecef_forward(self.lat, self.lon, height=height, M=M) 

 

@deprecated_method 

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

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

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

self.latlon.to3Tuple(height) 

 

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

'''Convert this I{geodetic} point 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 point'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 = self._ltp if ltp is None else _MODS.ltp._xLtp(ltp) 

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

 

def toLtp(self, Ecef=None): 

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

 

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

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

''' 

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

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

 

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

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

surface) components, I{including height}. 

 

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

height (C{meter}). 

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

components (C{Nvector}) or C{None}. 

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

keyword arguments, ignored if 

C{B{Nvector} is None}. 

 

@return: A B{C{Nvector}} or an 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 self.toVector(Vector=Nvector, h=self.height if h is None else h, 

ll=self, **Nvector_kwds) 

 

def toStr(self, form=F_DMS, prec=None, m=_m_, sep=_COMMASPACE_, **s_D_M_S): # PYCHOK expected 

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

formatted in the given form. 

 

@kwarg form: Format specifier (C{str} or L{F_D}, L{F_DM}, L{F_DMS}, 

L{F_DEG}, L{F_MIN}, L{F_SEC}, L{F_D60}, L{F__E}, 

L{F__F}, L{F__G}, L{F_RAD}, L{F_D_}, L{F_DM_}, L{F_DMS_}, 

L{F_DEG_}, L{F_MIN_}, L{F_SEC_}, L{F_D60_}, L{F__E_}, 

L{F__F_}, L{F__G_}, L{F_RAD_}, L{F_D__}, L{F_DM__}, 

L{F_DMS__}, L{F_DEG__}, L{F_MIN__}, L{F_SEC__}, L{F_D60__}, 

L{F__E__}, L{F__F__}, L{F__G__} or L{F_RAD__}) 

@kwarg prec: Number of decimal digits (0..9 or C{None} for default). 

Trailing zero decimals are stripped for B{C{prec}} 

values of 1 and above, but kept for negative B{C{prec}}. 

@kwarg m: Optional unit of the height (C{str}), use C{None} to 

exclude height from the returned string. 

@kwarg sep: Separator between degrees, minutes, seconds and suffix (C{str}). 

@kwarg s_D_M_S: Optional keyword arguments C{B{s_D}=str}, C{B{s_M}=str} 

and/or C{B{s_S}=str} to override the degrees, minutes 

respectively seconds symbol, defaults L{S_DEG}, L{S_MIN} 

respectively L{S_SEC}. 

 

@return: This point in the specified B{C{form}} (C{str}). 

 

@see: Function L{pygeodesy.degDMS} for B{C{form}} and B{C{s_D_M_S}}. 

 

@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, **s_D_M_S), 

lonDMS(self.lon, form=form, prec=prec, **s_D_M_S)) 

if self.height and m is not None: 

t += (self.heightStr(m=m),) 

return sep.join(t) 

 

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

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

surface) components, I{ignoring height}. 

 

@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 a L{Vector3Tuple}C{(x, y, z)} 

if B{C{Vector}} is C{None}. 

 

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

 

@note: These are C{n-vector} x, y and z components, 

I{NOT} geocentric (ECEF) x, y and z coordinates! 

''' 

r = self._vector3tuple 

if Vector is not None: 

r = self._xnamed(Vector(r.x, r.y, r.z, **Vector_kwds)) 

return 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}). 

 

@note: These are C{n-vector} x, y and z components, 

I{NOT} geocentric (ECEF) x, y and z coordinates! 

''' 

return self._vector3d # XXX .unit() 

 

@deprecated_method 

def to3xyz(self): # PYCHOK no cover 

'''DEPRECATED, use property L{xyz} or method L{toNvector}, L{toVector}, 

L{toVector3d} or perhaps (geocentric) L{toEcef}.''' 

return self.xyz # self.toVector() 

 

@Property_RO 

def _vector3d(self): 

'''(INTERNAL) Cache for L{toVector3d}. 

''' 

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

 

@Property_RO 

def _vector3tuple(self): 

'''(INTERNAL) Cache for L{toVector}. 

''' 

return latlon2n_xyz(self.lat, self.lon, name=self.name) 

 

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. 

 

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

@kwarg radius: Mean earth radius (C{meter}) or C{None} 

for the mean radius of this point's datum 

ellipsoid. 

@kwarg wrap: Wrap and L{pygeodesy.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{pygeodesy.vincentys} and methods L{cosineAndoyerLambertTo}, 

L{cosineForsytheAndoyerLambertTo}, L{cosineLawTo}, C{distanceTo*}, 

L{equirectangularTo}, L{euclideanTo}, L{flatLocalTo}/L{hubenyTo}, 

L{flatPolarTo}, L{haversineTo} and L{thomasTo}. 

''' 

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

 

@Property_RO 

def xyz(self): 

'''Get the C{n-vector} X, Y and Z components (L{Vector3Tuple}C{(x, y, z)}) 

 

@note: These are C{n-vector} x, y and z components, I{NOT} 

geocentric (ECEF) x, y and z coordinates! 

''' 

return self.toVector(Vector=Vector3Tuple) 

 

@Property_RO 

def xyzh(self): 

'''Get the C{n-vector} X, Y, Z and H components (L{Vector4Tuple}C{(x, y, z, h)}) 

 

@note: These are C{n-vector} x, y and z components, I{NOT} 

geocentric (ECEF) x, y and z coordinates! 

''' 

return self.xyz.to4Tuple(self.height) 

 

 

def _isequalTo(point1, point2, eps=EPS): # in .ellipsoidalBaseDI._intersect3._on 

'''(INTERNAL) Compare point lat-/lon without type. 

''' 

return max(abs(point1.lat - point2.lat), 

abs(point1.lon - point2.lon)) < eps 

 

 

def _trilaterate5(p1, d1, p2, d2, p3, d3, area=True, eps=EPS1, 

radius=R_M, wrap=False): 

'''(INTERNAL) Trilaterate three points by area overlap or by 

perimeter intersection of three circles. 

 

@note: The B{C{radius}} is only needed for both the n-vectorial 

and sphericalTrigonometry C{LatLon.distanceTo} methods and 

silently ignored by the C{ellipsoidalExact} C{-GeodSolve}, 

C{-Karney} and C{-Vincenty.LatLon.distanceTo} methods. 

''' 

r1 = Distance_(distance1=d1) 

r2 = Distance_(distance2=d2) 

r3 = Distance_(distance3=d3) 

 

m = 0 if area else (r1 + r2 + r3) 

pc = 0 

t = [] 

for _ in range(3): 

try: # intersection of circle (p1, r1) and (p2, r2) 

c1, c2 = p1.intersections2(r1, p2, r2, wrap=wrap) 

 

if area: # check overlap 

if c1 is c2: # abutting 

c = c1 

else: # nearest point on radical 

c = p3.nearestOn(c1, c2, within=True, wrap=wrap) 

d = r3 - p3.distanceTo(c, radius=radius, wrap=wrap) 

if d > eps: # sufficient overlap 

t.append((d, c)) 

m = max(m, d) 

 

else: # check intersection 

for c in ((c1,) if c1 is c2 else (c1, c2)): 

d = abs(r3 - p3.distanceTo(c, radius=radius, wrap=wrap)) 

if d < eps: # below margin 

t.append((d, c)) 

m = min(m, d) 

 

except IntersectionError as x: 

if _concentric_ in str(x): # XXX ConcentricError? 

pc += 1 

 

p1, r1, p2, r2, p3, r3 = p2, r2, p3, r3, p1, r1 # rotate 

 

if t: # get min, max, points and count ... 

t = tuple(sorted(t)) 

n = len(t), # as tuple 

# ... or for a single trilaterated result, 

# min *is* max, min- *is* maxPoint and n=1 

return Trilaterate5Tuple(t[0] + t[-1] + n) # *(t[0] + ...) 

 

elif area and pc == 3: # all pairwise concentric ... 

r, p = min((r1, p1), (r2, p2), (r3, p3)) 

m = max(r1, r2, r3) 

# ... return "smallest" point twice, the smallest 

# and largest distance and n=0 for concentric 

return Trilaterate5Tuple(float(r), p, float(m), p, 0) 

 

n, f = (_overlap_, max) if area else (_intersection_, min) 

t = '%s (%s %.3f)' % (_no_(n), f.__name__, m) 

raise IntersectionError(area=area, eps=eps, wrap=wrap, txt=t) 

 

 

__all__ += _ALL_DOCS(LatLonBase) 

 

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