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# -*- coding: utf-8 -*- 

 

u'''(INTERNAL) Ellipsoidal geodesy base classes C{CartesianEllipsoidalBase} 

and C{LatLonEllipsoidalBase}. 

 

Pure Python implementation of geodesy tools for ellipsoidal earth models, 

transcoded in part from JavaScript originals by I{(C) Chris Veness 2005-2016} 

and published under the same MIT Licence**, see for example U{latlon-ellipsoidal 

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

''' 

# make sure int/int division yields float quotient, see .basics 

from __future__ import division as _; del _ # PYCHOK semicolon 

 

# from pygeodesy.basics import _xinstanceof # from .datums 

from pygeodesy.cartesianBase import CartesianBase, Vector3Tuple 

from pygeodesy.datums import Datum, Datums, _ellipsoidal_datum, \ 

_spherical_datum, _WGS84, _xinstanceof 

from pygeodesy.errors import _incompatible, _IsnotError, RangeError, TRFError, \ 

_ValueError, _xellipsoidal, _xError, _xkwds, \ 

_xkwds_get, _xkwds_not 

from pygeodesy.interns import _ellipsoidal_ # PYCHOK used! 

from pygeodesy.interns import EPS, EPS0, EPS1, MISSING, NN, _COMMA_, \ 

_conversion_, _datum_, _DOT_, _N_, _no_, \ 

_reframe_, _SPACE_, _0_0 

from pygeodesy.latlonBase import LatLonBase, _trilaterate5 

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

# from pygeodesy.namedTuples import Vector3Tuple # from .cartesianBase 

from pygeodesy.props import deprecated_method, Property_RO, \ 

property_doc_, property_RO 

from pygeodesy.units import Epoch, _1mm as _TOL_M, Radius_ 

 

__all__ = _ALL_LAZY.ellipsoidalBase 

__version__ = '22.05.04' 

 

 

class CartesianEllipsoidalBase(CartesianBase): 

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

''' 

_datum = _WGS84 # L{Datum} 

_reframe = None 

 

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

# '''Return C{NotImplemented} for C{c_ = c @ datum}, C{c_ = c @ reframe} and C{c_ = c @ Transform}. 

# ''' 

# from pygeodesy.trf import RefFrame 

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

# _NotImplemented(self, other) 

 

@deprecated_method 

def convertRefFrame(self, reframe2, reframe, epoch=None): 

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

return self.toRefFrame(reframe2, reframe, epoch=epoch) 

 

def intersections2(self, radius, center2, radius2, sphere=True, 

Vector=None, **Vector_kwds): 

'''Compute the intersection of two spheres or circles, each defined by a 

cartesian center point and a radius. 

 

@arg radius: Radius of this sphere or circle (same units as this point's 

coordinates). 

@arg center2: Center of the second sphere or circle (C{Cartesian}, L{Vector3d}, 

C{Vector3Tuple} or C{Vector4Tuple}). 

@arg radius2: Radius of the second sphere or circle (same units as this and 

the B{C{other}} point's coordinates). 

@kwarg sphere: If C{True} compute the center and radius of the intersection 

of two I{spheres}. If C{False}, ignore the C{z}-component and 

compute the intersection of two I{circles} (C{bool}). 

@kwarg Vector: Class to return intersections (C{Cartesian}, L{Vector3d} or 

C{Vector3Tuple}) or C{None} for an instance of this (sub-)class. 

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

ignored if C{B{Vector} is None}. 

 

@return: If B{C{sphere}} is C{True}, a 2-tuple of the C{center} and C{radius} 

of the intersection of the I{spheres}. The C{radius} is C{0.0} for 

abutting spheres (and the C{center} is aka I{radical center}). 

 

If B{C{sphere}} is C{False}, a 2-tuple with the two intersection 

points of the I{circles}. For abutting circles, both points are 

the same instance, aka I{radical center}. 

 

@raise IntersectionError: Concentric, invalid or non-intersecting spheres or circles. 

 

@raise TypeError: Invalid B{C{center2}}. 

 

@raise UnitError: Invalid B{C{radius}} or B{C{radius2}}. 

 

@see: U{Sphere-Sphere<https://MathWorld.Wolfram.com/Sphere-SphereIntersection.html>}, 

U{Circle-Circle<https://MathWorld.Wolfram.com/Circle-CircleIntersection.html>} 

Intersection and function L{pygeodesy.radical2}. 

''' 

try: 

return _MODS.vector3d._intersects2(self, Radius_(radius=radius), 

center2, Radius_(radius2=radius2), 

sphere=sphere, clas=self.classof, 

Vector=Vector, **Vector_kwds) 

except (TypeError, ValueError) as x: 

raise _xError(x, center=self, radius=radius, center2=center2, radius2=radius2) 

 

@property_doc_(''' this cartesian's reference frame (L{RefFrame}).''') 

def reframe(self): 

'''Get this cartesian's reference frame (L{RefFrame}) or C{None}. 

''' 

return self._reframe 

 

@reframe.setter # PYCHOK setter! 

def reframe(self, reframe): 

'''Set or clear this cartesian's reference frame. 

 

@arg reframe: Reference frame (L{RefFrame}) or C{None}. 

 

@raise TypeError: The B{C{reframe}} is not a L{RefFrame}. 

''' 

_set_reframe(self, reframe) 

 

def toRefFrame(self, reframe2, reframe=None, epoch=None): 

'''Convert this cartesian point from one to an other reference frame. 

 

@arg reframe2: Reference frame to convert I{to} (L{RefFrame}). 

@arg reframe: Reference frame to convert I{from} (L{RefFrame}), 

overriding this cartesian's C{reframe}. 

@kwarg epoch: Optional epoch to observe (C{scalar}, fractional 

calendar year), overriding B{C{reframe}}'s epoch. 

 

@return: The converted point (C{Cartesian}) or this point if 

conversion is C{nil}. 

 

@raise TRFError: No conversion available from B{C{reframe}} 

to B{C{reframe2}} or invalid B{C{epoch}}. 

 

@raise TypeError: B{C{reframe2}} or B{C{reframe}} not a 

L{RefFrame}. 

''' 

r = self.reframe if reframe is None else reframe 

if r in (None, reframe2): 

xs = None # XXX _set_reframe(self, reframe2)? 

else: 

trf = _MODS.trf 

_xinstanceof(trf.RefFrame, reframe2=reframe2, reframe=r) 

_, xs = trf._reframeTransforms2(reframe2, r, epoch) 

return self.toTransforms_(*xs) if xs else self 

 

def toTransforms_(self, *transforms, **datum): 

'''Apply none, one or several Helmert transforms. 

 

@arg transforms: Transforms to apply, in order (L{Transform}s). 

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

overriding this point's datum. 

 

@return: The transformed point (C{Cartesian}) or this point 

if the B{C{transforms}} produce the same point. 

''' 

r = self 

if transforms: 

xyz = r.xyz 

for t in transforms: 

xyz = t.transform(*xyz) 

d = _xkwds_get(datum, datum=r.datum) 

if d != r.datum or xyz != r.xyz: 

r = r.classof(xyz, datum=d) 

return r 

 

 

class LatLonEllipsoidalBase(LatLonBase): 

'''(INTERNAL) Base class for ellipsoidal C{LatLon}s. 

''' 

_convergence = None # UTM/UPS meridian convergence (C{degrees}) 

_datum = _WGS84 # L{Datum} 

_elevation2to = None # _elevation2 timeout (C{secs}) 

_epoch = None # overriding .reframe.epoch (C{float}) 

_geoidHeight2to = None # _geoidHeight2 timeout (C{secs}) 

_reframe = None # reference frame (L{RefFrame}) 

_scale = None # UTM/UPS scale factor (C{float}) 

_toLLEB_args = () # Etm/Utm/Ups._toLLEB arguments 

 

def __init__(self, lat, lon, height=0, datum=None, reframe=None, 

epoch=None, name=NN): 

'''Create an ellipsoidal C{LatLon} point frome the given 

lat-, longitude and height on the given datum and with 

the given reference frame and epoch. 

 

@arg lat: Latitude (C{degrees} or DMS C{[N|S]}). 

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

@kwarg height: Optional elevation (C{meter}, the same units 

as the datum's half-axes). 

@kwarg datum: Optional, ellipsoidal datum to use (L{Datum}, 

L{Ellipsoid}, L{Ellipsoid2} or L{a_f2Tuple}). 

@kwarg reframe: Optional reference frame (L{RefFrame}). 

@kwarg epoch: Optional epoch to observe for B{C{reframe}} 

(C{scalar}), a non-zero, fractional calendar 

year; silently ignored if C{B{reframe} is None}. 

@kwarg name: Optional name (string). 

 

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

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

 

@raise TypeError: B{C{datum}} is not a L{Datum}, B{C{reframe}} 

is not a L{RefFrame} or B{C{epoch}} is not 

C{scalar} non-zero. 

 

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

 

@example: 

 

>>> p = LatLon(51.4778, -0.0016) # height=0, datum=Datums.WGS84 

''' 

LatLonBase.__init__(self, lat, lon, height=height, name=name) 

if datum not in (None, self._datum): 

self.datum = _ellipsoidal_datum(datum, name=name) 

if reframe: 

self.reframe = reframe 

self.epoch = epoch 

 

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

# '''Return C{NotImplemented} for C{ll_ = ll @ datum} and C{ll_ = ll @ reframe}. 

# ''' 

# from pygeodesy.trf import RefFrame 

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

# _NotImplemented(self, other) 

 

def antipode(self, height=None): 

'''Return the antipode, the point diametrically opposite 

to this point. 

 

@kwarg height: Optional height of the antipode, height 

of this point otherwise (C{meter}). 

 

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

''' 

lla = LatLonBase.antipode(self, height=height) 

if lla.datum != self.datum: 

lla.datum = self.datum 

return lla 

 

@property_RO 

def convergence(self): 

'''Get this point's UTM or UPS meridian convergence (C{degrees}) or 

C{None} if not available or not converted from L{Utm} or L{Ups}. 

''' 

return self._convergence 

 

@deprecated_method 

def convertDatum(self, datum2): 

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

return self.toDatum(datum2) 

 

@deprecated_method 

def convertRefFrame(self, reframe2): 

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

return self.toRefFrame(reframe2) 

 

@Property_RO 

def _css(self): 

'''(INTERNAL) Get this C{LatLon} point as a Cassini-Soldner location (L{Css}). 

''' 

css = _MODS.css 

return css.toCss(self, height=self.height, Css=css.Css, name=self.name) 

 

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

def datum(self): 

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

''' 

return self._datum 

 

@datum.setter # PYCHOK setter! 

def datum(self, datum): 

'''Set this point's datum I{without conversion}. 

 

@arg datum: New datum (L{Datum}). 

 

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

or not ellipsoidal. 

''' 

_xinstanceof(Datum, datum=datum) 

if not datum.isEllipsoidal: 

raise _IsnotError(_ellipsoidal_, datum=datum) 

self._update(datum != self._datum) 

self._datum = datum 

 

def distanceTo2(self, other): 

'''I{Approximate} the distance and (initial) bearing between this 

and an other (ellipsoidal) point based on the radii of curvature. 

 

I{Suitable only for short distances up to a few hundred Km 

or Miles and only between points not near-polar}. 

 

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

 

@return: An L{Distance2Tuple}C{(distance, initial)}. 

 

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

 

@raise ValueError: Incompatible datum ellipsoids. 

 

@see: Method L{Ellipsoid.distance2} and U{Local, flat earth 

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

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

formula. 

''' 

return self.ellipsoids(other).distance2(self.lat, self.lon, 

other.lat, other.lon) 

 

@Property_RO 

def _elevation2(self): 

'''(INTERNAL) Get elevation and data source. 

''' 

return _MODS.elevations.elevation2(self.lat, self.lon, 

timeout=self._elevation2to) 

 

def elevation2(self, adjust=True, datum=None, timeout=2): 

'''Return elevation of this point for its or the given datum, ellipsoid 

or sphere. 

 

@kwarg adjust: Adjust the elevation for a B{C{datum}} other than 

C{NAD83} (C{bool}). 

@kwarg datum: Optional datum overriding this point's datum (L{Datum}, 

L{Ellipsoid}, L{Ellipsoid2}, L{a_f2Tuple} or C{scalar} 

radius). 

@kwarg timeout: Optional query timeout (C{seconds}). 

 

@return: An L{Elevation2Tuple}C{(elevation, data_source)} or 

C{(None, error)} in case of errors. 

 

@note: The adjustment applied is the difference in geocentric earth 

radius between the B{C{datum}} and C{NAV83} upon which the 

L{elevations.elevation2} is based. 

 

@note: NED elevation is only available for locations within the 

U{Conterminous US (CONUS) 

<https://WikiPedia.org/wiki/Contiguous_United_States>}. 

 

@see: Function L{elevations.elevation2} and method C{Ellipsoid.Rgeocentric} 

for further details and possible C{error}s. 

''' 

if self._elevation2to != timeout: 

self._elevation2to = timeout 

LatLonEllipsoidalBase._elevation2._update(self) 

return self._Radjust2(adjust, datum, self._elevation2) 

 

def ellipsoid(self, datum=_WGS84): 

'''Return the ellipsoid of this point's datum or the given datum. 

 

@kwarg datum: Default datum (L{Datum}). 

 

@return: The ellipsoid (L{Ellipsoid} or L{Ellipsoid2}). 

''' 

return getattr(self, _datum_, datum).ellipsoid 

 

def ellipsoids(self, other): 

'''Check the type and ellipsoid of this and an other point's datum. 

 

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

 

@return: This point's datum ellipsoid (L{Ellipsoid} or L{Ellipsoid2}). 

 

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

 

@raise ValueError: Incompatible datum ellipsoids. 

''' 

self.others(other, up=2) # ellipsoids' caller 

 

E = self.ellipsoid() 

try: # other may be Sphere, etc. 

e = other.ellipsoid() 

except AttributeError: 

try: # no ellipsoid method, try datum 

e = other.datum.ellipsoid 

except AttributeError: 

e = E # no datum, XXX assume equivalent? 

if e != E: 

raise _ValueError(e.named2, txt=_incompatible(E.named2)) 

return E 

 

@property_doc_(''' this point's observed or C{reframe} epoch (C{float}).''') 

def epoch(self): 

'''Get this point's observed or C{reframe} epoch (C{float}) or C{None}. 

''' 

return self._epoch or (self.reframe.epoch if self.reframe else None) 

 

@epoch.setter # PYCHOK setter! 

def epoch(self, epoch): 

'''Set or clear this point's observed epoch. 

 

@arg epoch: Observed epoch, a fractional calendar year 

(L{Epoch}, C{scalar}) or C{None}. 

 

@raise TRFError: Invalid B{C{epoch}}. 

''' 

self._epoch = None if epoch is None else Epoch(epoch) 

 

@Property_RO 

def Equidistant(self): 

'''Get the prefered azimuthal equidistant projection I{class} (L{EquidistantKarney} or L{EquidistantExact}). 

''' 

try: 

_ = self.datum.ellipsoid.geodesic 

return _MODS.azimuthal.EquidistantKarney 

except ImportError: # no geographiclib 

return _MODS.azimuthal.EquidistantExact # XXX no longer L{azimuthal.Equidistant} 

 

@Property_RO 

def _etm(self): 

'''(INTERNAL) Get this C{LatLon} point as an ETM coordinate (L{pygeodesy.toEtm8}). 

''' 

etm = _MODS.etm 

return etm.toEtm8(self, datum=self.datum, Etm=etm.Etm) 

 

@Property_RO 

def _geoidHeight2(self): 

'''(INTERNAL) Get geoid height and model. 

''' 

return _MODS.elevations.geoidHeight2(self.lat, self.lon, model=0, 

timeout=self._geoidHeight2to) 

 

def geoidHeight2(self, adjust=False, datum=None, timeout=2): 

'''Return geoid height of this point for its or the given datum, ellipsoid 

or sphere. 

 

@kwarg adjust: Adjust the geoid height for a B{C{datum}} other than 

C{NAD83/NADV88} (C{bool}). 

@kwarg datum: Optional datum overriding this point's datum (L{Datum}, 

L{Ellipsoid}, L{Ellipsoid2}, L{a_f2Tuple} or C{scalar} 

radius). 

@kwarg timeout: Optional query timeout (C{seconds}). 

 

@return: A L{GeoidHeight2Tuple}C{(height, model_name)} or 

C{(None, error)} in case of errors. 

 

@note: The adjustment applied is the difference in geocentric earth 

radius between the B{C{datum}} and C{NAV83/NADV88} upon which 

the L{elevations.geoidHeight2} is based. 

 

@note: The geoid height is only available for locations within the 

U{Conterminous US (CONUS) 

<https://WikiPedia.org/wiki/Contiguous_United_States>}. 

 

@see: Function L{elevations.geoidHeight2} and method C{Ellipsoid.Rgeocentric} 

for further details and possible C{error}s. 

''' 

if self._geoidHeight2to != timeout: 

self._geoidHeight2to = timeout 

LatLonEllipsoidalBase._geoidHeight2._update(self) 

return self._Radjust2(adjust, datum, self._geoidHeight2) 

 

def intersection3(self, end1, other, end2, height=None, wrap=True, 

equidistant=None, tol=_TOL_M): 

'''Interatively compute the intersection point of two paths, each 

defined by two points or a start point and bearing from North. 

 

@arg end1: End point of this path (C{LatLon}) or the initial 

bearing at this point (compass C{degrees360}). 

@arg other: Start point of the other path (C{LatLon}). 

@arg end2: End point of the other path (C{LatLon}) or the 

initial bearing at the other point (compass 

C{degrees360}). 

@kwarg height: Optional height at the intersection (C{meter}, 

conventionally) or C{None} for the mean height. 

@kwarg wrap: Wrap and unroll longitudes (C{bool}). 

@kwarg equidistant: An azimuthal equidistant projection (I{class} or 

function L{pygeodesy.equidistant}), or C{None} 

for this point's preferred C{.Equidistant}. 

@kwarg tol: Tolerance for skew line distance and length and for 

convergence (C{meter}, conventionally). 

 

@return: An L{Intersection3Tuple}C{(point, outside1, outside2)} 

with C{point} a C{LatLon} instance. 

 

@raise ImportError: Package U{geographiclib 

<https://PyPI.org/project/geographiclib>} 

not installed or not found, but only if 

C{B{equidistant}=}L{EquidistantKarney}. 

 

@raise IntersectionError: Skew, colinear, parallel or otherwise 

non-intersecting paths or no convergence 

for the given B{C{tol}}. 

 

@raise TypeError: If B{C{end1}}, B{C{other}} or B{C{end2}} point 

is not C{LatLon}. 

 

@note: For each path specified with an initial bearing, a pseudo-end 

point is computed as the C{destination} along that bearing at 

about 1.5 times the distance from the start point to an initial 

gu-/estimate of the intersection point (and between 1/8 and 3/8 

of the authalic earth perimeter). 

 

@see: U{The B{ellipsoidal} case<https://GIS.StackExchange.com/questions/48937/ 

calculating-intersection-of-two-circles>} and U{Karney's paper 

<https://ArXiv.org/pdf/1102.1215.pdf>}, pp 20-21, section B{14. MARITIME 

BOUNDARIES} for more details about the iteration algorithm. 

''' 

try: 

s2 = self.others(other) 

return _MODS.ellipsoidalBaseDI._intersect3(self, end1, 

s2, end2, 

height=height, wrap=wrap, 

equidistant=equidistant, tol=tol, 

LatLon=self.classof, datum=self.datum) 

except (TypeError, ValueError) as x: 

raise _xError(x, start1=self, end1=end1, other=other, end2=end2, 

height=height, wrap=wrap, tol=tol) 

 

def intersections2(self, radius1, other, radius2, height=None, wrap=True, 

equidistant=None, tol=_TOL_M): 

'''Interatively compute the intersection points of two circles, 

each defined by a center point and a radius. 

 

@arg radius1: Radius of this circle (C{meter}, conventionally). 

@arg other: Center of the other circle (C{LatLon}). 

@arg radius2: Radius of the other circle (C{meter}, same units as 

B{C{radius1}}). 

@kwarg height: Optional height for the intersection points (C{meter}, 

conventionally) or C{None} for the I{"radical height"} 

at the I{radical line} between both centers. 

@kwarg wrap: Wrap and unroll longitudes (C{bool}). 

@kwarg equidistant: An azimuthal equidistant projection (I{class} or 

function L{pygeodesy.equidistant}), or C{None} 

for this point's preferred C{.Equidistant}. 

@kwarg tol: Convergence tolerance (C{meter}, same units as 

B{C{radius1}} and B{C{radius2}}). 

 

@return: 2-Tuple of the intersection points, each a C{LatLon} 

instance. For abutting circles, both intersection 

points are the same instance, aka I{radical center}. 

 

@raise ImportError: Package U{geographiclib 

<https://PyPI.org/project/geographiclib>} 

not installed or not found, but only if 

C{B{equidistant}=}L{EquidistantKarney}. 

 

@raise IntersectionError: Concentric, antipodal, invalid or 

non-intersecting circles or no 

convergence for the given B{C{tol}}. 

 

@raise TypeError: Invalid B{C{other}} or B{C{equidistant}}. 

 

@raise UnitError: Invalid B{C{radius1}}, B{C{radius2}} or B{C{height}}. 

 

@see: U{The B{ellipsoidal} case<https://GIS.StackExchange.com/questions/48937/ 

calculating-intersection-of-two-circles>}, U{Karney's paper 

<https://ArXiv.org/pdf/1102.1215.pdf>}, pp 20-21, section B{14. MARITIME BOUNDARIES}, 

U{circle-circle<https://MathWorld.Wolfram.com/Circle-CircleIntersection.html>} and 

U{sphere-sphere<https://MathWorld.Wolfram.com/Sphere-SphereIntersection.html>} 

intersections. 

''' 

try: 

c2 = self.others(other) 

return _MODS.ellipsoidalBaseDI._intersections2(self, radius1, 

c2, radius2, 

height=height, wrap=wrap, 

equidistant=equidistant, tol=tol, 

LatLon=self.classof, datum=self.datum) 

except (AssertionError, TypeError, ValueError) as x: 

raise _xError(x, center=self, radius1=radius1, other=other, radius2=radius2, 

height=height, wrap=wrap, tol=tol) 

 

@Property_RO 

def isEllipsoidalLatLon(self): 

'''Get C{LatLon} base. 

''' 

return True 

 

@property_RO 

def iteration(self): 

'''Get the most recent C{intersections2} or C{nearestOn} iteration 

number (C{int}) or C{None} if not available/applicable. 

''' 

return self._iteration 

 

@Property_RO 

def _lcc(self): 

'''(INTERNAL) Get this C{LatLon} point as a Lambert location (L{Lcc}). 

''' 

lcc = _MODS.lcc 

return lcc.toLcc(self, height=self.height, Lcc=lcc.Lcc, name=self.name) 

 

def nearestOn(self, point1, point2, within=True, height=None, wrap=True, 

equidistant=None, tol=_TOL_M): 

'''Interatively locate the closest point on the geodesic between 

two other (ellipsoidal) points. 

 

@arg point1: Start point (C{LatLon}). 

@arg point2: End point (C{LatLon}). 

@kwarg within: If C{True} return the closest point I{between} 

B{C{point1}} and B{C{point2}}, otherwise the 

closest point elsewhere on the geodesic (C{bool}). 

@kwarg height: Optional height for the closest point (C{meter}, 

conventionally) or C{None} or C{False} for the 

interpolated height. If C{False}, the closest 

takes the heights of the points into account. 

@kwarg wrap: Wrap and unroll longitudes (C{bool}). 

@kwarg equidistant: An azimuthal equidistant projection (I{class} or 

function L{pygeodesy.equidistant}), or C{None} 

for this point's preferred C{.Equidistant}. 

@kwarg tol: Convergence tolerance (C{meter}, conventionally). 

 

@return: Closest point (C{LatLon}). 

 

@raise ImportError: Package U{geographiclib 

<https://PyPI.org/project/geographiclib>} 

not installed or not found, but only if 

C{B{equidistant}=}L{EquidistantKarney}. 

 

@raise TypeError: Invalid B{C{point1}}, B{C{point2}} or 

B{C{equidistant}}. 

 

@raise ValueError: Datum or ellipsoid of B{C{point1}} or B{C{point2}} is 

incompatible or no convergence for the given B{C{tol}}. 

 

@see: U{The B{ellipsoidal} case<https://GIS.StackExchange.com/questions/48937/ 

calculating-intersection-of-two-circles>} and U{Karney's paper 

<https://ArXiv.org/pdf/1102.1215.pdf>}, pp 20-21, section B{14. MARITIME 

BOUNDARIES} for details about the iteration algorithm. 

''' 

try: 

t = _MODS.ellipsoidalBaseDI._nearestOn2(self, point1, point2, within=within, 

height=height, wrap=wrap, 

equidistant=equidistant, 

tol=tol, LatLon=self.classof) 

except (TypeError, ValueError) as x: 

raise _xError(x, point=self, point1=point1, point2=point2, within=within, 

height=height, wrap=wrap, tol=tol) 

return t.closest 

 

@Property_RO 

def _osgr(self): 

'''(INTERNAL) Get this C{LatLon} point to an OSGR coordinate (L{Osgr}). 

''' 

osgr = _MODS.osgr 

return osgr.toOsgr(self, datum=self.datum, Osgr=osgr.Osgr, name=self.name) 

 

def parse(self, strllh, height=0, datum=None, epoch=None, reframe=None, 

sep=_COMMA_, name=NN): 

'''Parse a string representing a similar, ellipsoidal C{LatLon} 

point, consisting of C{"lat, lon[, height]"}. 

 

@arg strllh: Lat, lon and optional height (C{str}), 

see function L{pygeodesy.parse3llh}. 

@kwarg height: Optional, default height (C{meter} or 

C{None}). 

@kwarg datum: Optional datum (L{Datum}), overriding this 

datum I{without conversion}. 

@kwarg epoch: Optional datum (L{Epoch}), overriding this 

epoch I{without conversion}. 

@kwarg reframe: Optional datum (L{RefFrame}), overriding 

this reframe I{without conversion}. 

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

@kwarg name: Optional instance name (C{str}), overriding 

this name. 

 

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

 

@raise ParseError: Invalid B{C{strllh}}. 

''' 

a, b, h = _MODS.dms.parse3llh(strllh, height=height, sep=sep) 

r = self.classof(a, b, height=h, datum=self.datum) 

if datum not in (None, self.datum): 

r.datum = datum 

if epoch not in (None, self.epoch): 

r.epoch = epoch 

if reframe not in (None, self.reframe): 

r.reframe = reframe 

return self._xnamed(r, name=name, force=True) if name else r 

 

def _Radjust2(self, adjust, datum, meter_text2): 

'''(INTERNAL) Adjust an C{elevation} or C{geoidHeight} with 

difference in Gaussian radii of curvature of the given 

datum and NAD83 ellipsoids at this point's latitude. 

 

@note: This is an arbitrary, possibly incorrect adjustment. 

''' 

if adjust: # Elevation2Tuple or GeoidHeight2Tuple 

m, t = meter_text2 

if isinstance(m, float) and abs(m) > EPS: 

n = Datums.NAD83.ellipsoid.rocGauss(self.lat) 

if n > EPS0: 

# use ratio, datum and NAD83 units may differ 

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

_spherical_datum(datum).ellipsoid 

r = E.rocGauss(self.lat) 

if r > EPS0 and abs(r - n) > EPS: # EPS1 

m *= r / n 

meter_text2 = meter_text2.classof(m, t) 

return self._xnamed(meter_text2) 

 

@property_doc_(''' this point's reference frame (L{RefFrame}).''') 

def reframe(self): 

'''Get this point's reference frame (L{RefFrame}) or C{None}. 

''' 

return self._reframe 

 

@reframe.setter # PYCHOK setter! 

def reframe(self, reframe): 

'''Set or clear this point's reference frame. 

 

@arg reframe: Reference frame (L{RefFrame}) or C{None}. 

 

@raise TypeError: The B{C{reframe}} is not a L{RefFrame}. 

''' 

_set_reframe(self, reframe) 

 

@Property_RO 

def scale(self): 

'''Get this point's UTM grid or UPS point scale factor (C{float}) 

or C{None} if not converted from L{Utm} or L{Ups}. 

''' 

return self._scale 

 

def toCss(self, **toCss_kwds): 

'''Convert this C{LatLon} point to a Cassini-Soldner location. 

 

@kwarg toCss_kwds: Optional L{pygeodesy.toCss} keyword arguments. 

 

@return: The Cassini-Soldner location (L{Css}). 

 

@see: Function L{pygeodesy.toCss}. 

''' 

return self._css if not toCss_kwds else _MODS.css.toCss( 

self, **_xkwds(toCss_kwds, name=self.name)) 

 

def toDatum(self, datum2, height=None, name=NN): 

'''Convert this point to an other datum. 

 

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

@kwarg height: Optional height, overriding the 

converted height (C{meter}). 

@kwarg name: Optional name (C{str}), iff converted. 

 

@return: The converted point (ellipsoidal C{LatLon}) 

or a copy of this point if B{C{datum2}} 

matches this point's C{datum}. 

 

@raise TypeError: Invalid B{C{datum2}}. 

 

@example: 

 

>>> p = LatLon(51.4778, -0.0016) # default Datums.WGS84 

>>> p.toDatum(Datums.OSGB36) # 51.477284°N, 000.00002°E 

''' 

n = name or self.name 

d2 = _ellipsoidal_datum(datum2, name=n) 

if self.datum == d2: 

r = self.copy(name=name) 

else: 

kwds = _xkwds_not(None, LatLon=self.classof, name=n, 

epoch=self.epoch, reframe=self.reframe) 

c = self.toCartesian().toDatum(d2) 

r = c.toLatLon(datum=d2, height=height, **kwds) 

return r 

 

def toEtm(self, **toEtm8_kwds): 

'''Convert this C{LatLon} point to an ETM coordinate. 

 

@kwarg toEtm8_kwds: Optional L{pygeodesy.toEtm8} keyword arguments. 

 

@return: The ETM coordinate (L{Etm}). 

 

@see: Function L{pygeodesy.toEtm8}. 

''' 

return self._etm if not toEtm8_kwds else _MODS.etm.toEtm8( 

self, **_xkwds(toEtm8_kwds, name=self.name)) 

 

def toLcc(self, **toLcc_kwds): 

'''Convert this C{LatLon} point to a Lambert location. 

 

@kwarg toLcc_kwds: Optional L{pygeodesy.toLcc} keyword arguments. 

 

@return: The Lambert location (L{Lcc}). 

 

@see: Function L{pygeodesy.toLcc}. 

''' 

return self._lcc if not toLcc_kwds else _MODS.lcc.toLcc( 

self, **_xkwds(toLcc_kwds, name=self.name)) 

 

def toMgrs(self, center=False): 

'''Convert this C{LatLon} point to an MGRS coordinate. 

 

@kwarg center: If C{True}, try to I{un}-center MGRS 

to its C{lowerleft} (C{bool}) or by 

C{B{center} meter} (C{scalar}). 

 

@return: The MGRS coordinate (L{Mgrs}). 

 

@see: Method L{toUtm} and L{Mgrs.toLatLon}. 

''' 

return self.toUtm(center=center).toMgrs(center=False) 

 

def toOsgr(self, **toOsgr_kwds): 

'''Convert this C{LatLon} point to an OSGR coordinate. 

 

@kwarg toOsgr_kwds: Optional L{pygeodesy.toOsgr} keyword arguments. 

 

@return: The OSGR coordinate (L{Osgr}). 

 

@see: Function L{pygeodesy.toOsgr}. 

''' 

return self._osgr if not toOsgr_kwds else _MODS.osgr.toOsgr( 

self, **_xkwds(toOsgr_kwds, name=self.name)) 

 

def toRefFrame(self, reframe2, height=None, name=NN): 

'''Convert this point to an other reference frame. 

 

@arg reframe2: Reference frame to convert I{to} (L{RefFrame}). 

@kwarg height: Optional height, overriding the converted 

height (C{meter}). 

@kwarg name: Optional name (C{str}), iff converted. 

 

@return: The converted point (ellipsoidal C{LatLon}) or this 

point if conversion is C{nil}, or a copy of this 

point if the B{C{name}} is non-empty. 

 

@raise TRFError: This point's C{reframe} is not defined or 

conversion from this point's C{reframe} to 

B{C{reframe2}} is not available. 

 

@raise TypeError: Invalid B{C{reframe2}}, not a L{RefFrame}. 

 

@example: 

 

>>> p = LatLon(51.4778, -0.0016, reframe=RefFrames.ETRF2000) # default Datums.WGS84 

>>> p.toRefFrame(RefFrames.ITRF2014) # 51.477803°N, 000.001597°W, +0.01m 

>>> p.toRefFrame(RefFrames.ITRF2014, height=0) # 51.477803°N, 000.001597°W 

''' 

if not self.reframe: 

t = _SPACE_(_DOT_(repr(self), _reframe_), MISSING) 

raise TRFError(_no_(_conversion_), txt=t) 

 

trf = _MODS.trf 

trf._xinstanceof(trf.RefFrame, reframe2=reframe2) 

 

e, xs = trf._reframeTransforms2(reframe2, self.reframe, self.epoch) 

if xs: 

c = self.toCartesian().toTransforms_(*xs) 

n = name or self.name 

ll = c.toLatLon(datum=self.datum, epoch=e, height=height, 

LatLon=self.classof, name=n, reframe=reframe2) 

else: 

ll = self.copy(name=name) if name else self 

return ll 

 

def toUps(self, pole=_N_, falsed=True): 

'''Convert this C{LatLon} point to a UPS coordinate. 

 

@kwarg pole: Optional top/center of (stereographic) 

projection (C{str}, 'N[orth]' or 'S[outh]'). 

@kwarg falsed: False easting and northing (C{bool}). 

 

@return: The UPS coordinate (L{Ups}). 

 

@see: Function L{pygeodesy.toUps8}. 

''' 

if self._upsOK(pole, falsed): 

u = self._ups 

else: 

ups = _MODS.ups 

u = ups.toUps8(self, datum=self.datum, Ups=ups.Ups, 

pole=pole, falsed=falsed) 

return u 

 

def toUtm(self, center=False): 

'''Convert this C{LatLon} point to a UTM coordinate. 

 

@kwarg center: If C{True}, I{un}-center the UTM 

to its C{lowerleft} (C{bool}) or 

by C{B{center} meter} (C{scalar}). 

 

@return: The UTM coordinate (L{Utm}). 

 

@see: Method L{Mgrs.toUtm} and function L{pygeodesy.toUtm8}. 

''' 

if center in (False, 0, _0_0): 

u = self._utm 

elif center in (True,): 

u = self._utm._lowerleft 

else: 

u = _MODS.utm._lowerleft(self._utm, center) 

return u 

 

def toUtmUps(self, pole=NN): 

'''Convert this C{LatLon} point to a UTM or UPS coordinate. 

 

@kwarg pole: Optional top/center of UPS (stereographic) 

projection (C{str}, 'N[orth]' or 'S[outh]'). 

 

@return: The UTM or UPS coordinate (L{Utm} or L{Ups}). 

 

@raise TypeError: Result in L{Utm} or L{Ups}. 

 

@see: Function L{pygeodesy.toUtmUps8}. 

''' 

if self._utmOK(): 

u = self._utm 

elif self._upsOK(pole): 

u = self._ups 

else: # no cover 

from pygeodesy.utmups import toUtmUps8, Utm, Ups # utmups = _MODS.utmups 

u = toUtmUps8(self, datum=self.datum, Utm=Utm, Ups=Ups, 

pole=pole, name=self.name) 

if isinstance(u, Utm): 

self._update(False, _utm=u) # PYCHOK kwds 

elif isinstance(u, Ups): 

self._update(False, _ups=u) # PYCHOK kwds 

else: 

_xinstanceof(Utm, Ups, toUtmUps8=u) 

return u 

 

def toWm(self, **toWm_kwds): 

'''Convert this C{LatLon} point to a WM coordinate. 

 

@kwarg toWm_kwds: Optional L{pygeodesy.toWm} keyword arguments. 

 

@return: The WM coordinate (L{Wm}). 

 

@see: Function L{pygeodesy.toWm}. 

''' 

return self._wm if not toWm_kwds else _MODS.webmercator.toWm( 

self, **_xkwds(toWm_kwds, name=self.name)) 

 

@deprecated_method 

def to3xyz(self): # PYCHOK no cover 

'''DEPRECATED, use method C{toEcef}. 

 

@return: A L{Vector3Tuple}C{(x, y, z)}. 

 

@note: Overloads C{LatLonBase.to3xyz} 

''' 

r = self.toEcef() 

return Vector3Tuple(r.x, r.y, r.z, name=self.name) 

 

def trilaterate5(self, distance1, point2, distance2, point3, distance3, 

area=True, eps=EPS1, wrap=False): 

'''Trilaterate three points by area overlap or perimeter intersection 

of three intersecting circles. 

 

@arg distance1: Distance to this point (C{meter}), same units 

as B{C{eps}}). 

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

@arg distance2: Distance to point2 (C{meter}, same units as 

B{C{eps}}). 

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

@arg distance3: Distance to point3 (C{meter}, same units as 

B{C{eps}}). 

@kwarg area: If C{True} compute the area overlap, otherwise the 

perimeter intersection of the circles (C{bool}). 

@kwarg eps: The required I{minimal overlap} for C{B{area}=True} 

or the I{intersection margin} for C{B{area}=False} 

(C{meter}, conventionally). 

@kwarg wrap: Wrap/unroll angular distances (C{bool}). 

 

@return: A L{Trilaterate5Tuple}C{(min, minPoint, max, maxPoint, n)} 

with C{min} and C{max} in C{meter}, same units as B{C{eps}}, 

the corresponding trilaterated points C{minPoint} and 

C{maxPoint} as I{ellipsoidal} C{LatLon} and C{n}, the number 

of trilatered points found for the given B{C{eps}}. 

 

If only a single trilaterated point is found, C{min I{is} 

max}, C{minPoint I{is} maxPoint} and C{n = 1}. 

 

For C{B{area}=True}, C{min} and C{max} are the smallest 

respectively largest I{radial} overlap found. 

 

For C{B{area}=False}, C{min} and C{max} represent the 

nearest respectively farthest intersection margin. 

 

If C{B{area}=True} and all 3 circles are concentric, C{n=0} 

and C{minPoint} and C{maxPoint} are the B{C{point#}} with 

the smallest B{C{distance#}} C{min} respectively C{max} the 

largest B{C{distance#}}. 

 

@raise IntersectionError: Trilateration failed for the given B{C{eps}}, 

insufficient overlap for C{B{area}=True} or 

no intersection or all (near-)concentric for 

C{B{area}=False}. 

 

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

 

@raise ValueError: Coincident B{C{points}} or invalid B{C{distance1}}, 

B{C{distance2}} or B{C{distance3}}. 

 

@note: Ellipsoidal trilateration invokes methods C{LatLon.intersections2} 

and C{LatLon.nearestOn} based on I{Karney}'s Python U{geographiclib 

<https://PyPI.org/project/geographiclib>} if installed, otherwise 

uses the accurate (but slower) C{ellipsoidalExact.LatLon} methods. 

''' 

return _trilaterate5(self, distance1, 

self.others(point2=point2), distance2, 

self.others(point3=point3), distance3, 

area=area, eps=eps, wrap=wrap) 

 

@Property_RO 

def _ups(self): # __dict__ value overwritten by method C{toUtmUps} 

'''(INTERNAL) Get this C{LatLon} point as UPS coordinate (L{Ups}), 

see L{pygeodesy.toUps8}. 

''' 

ups = _MODS.ups 

return ups.toUps8(self, datum=self.datum, Ups=ups.Ups, 

pole=NN, falsed=True, name=self.name) 

 

def _upsOK(self, pole=NN, falsed=True): 

'''(INTERNAL) Check matching C{Ups}. 

''' 

try: 

u = self._ups 

except RangeError: 

return False 

return falsed and (u.pole == pole[:1].upper() or not pole) 

 

@Property_RO 

def _utm(self): # __dict__ value overwritten by method C{toUtmUps} 

'''(INTERNAL) Get this C{LatLon} point as UTM coordinate (L{Utm}), 

see L{pygeodesy.toUtm8}. 

''' 

utm = _MODS.utm 

return utm.toUtm8(self, datum=self.datum, Utm=utm.Utm, name=self.name) 

 

def _utmOK(self): 

'''(INTERNAL) Check C{Utm}. 

''' 

try: 

_ = self._utm 

except RangeError: 

return False 

return True 

 

@Property_RO 

def _wm(self): 

'''(INTERNAL) Get this C{LatLon} point as webmercator (L{Wm}). 

''' 

return _MODS.webmercator.toWm(self) 

 

 

def _nearestOn(point, point1, point2, within=True, height=None, wrap=True, 

equidistant=None, tol=_TOL_M, LatLon=None, **LatLon_kwds): 

'''(INTERNAL) Get closest point, imported by .ellipsoidalExact, 

-GeodSolve, -Karney and -Vincenty to embellish exceptions. 

''' 

try: 

p = _xellipsoidal(point=point) 

t = _MODS.ellipsoidalBaseDI._nearestOn2(p, point1, point2, within=within, 

height=height, wrap=wrap, 

equidistant=equidistant, tol=tol, 

LatLon=LatLon, **LatLon_kwds) 

except (TypeError, ValueError) as x: 

raise _xError(x, point=point, point1=point1, point2=point2) 

return t.closest 

 

 

def _set_reframe(inst, reframe): 

'''(INTERNAL) Set or clear an instance's reference frame. 

''' 

if reframe is not None: 

_xinstanceof(_MODS.trf.RefFrame, reframe=reframe) 

inst._reframe = reframe 

elif inst.reframe is not None: 

inst._reframe = None 

 

 

__all__ += _ALL_DOCS(CartesianEllipsoidalBase, LatLonEllipsoidalBase) 

 

# **) MIT License 

# 

# Copyright (C) 2016-2022 -- mrJean1 at Gmail -- All Rights Reserved. 

# 

# Permission is hereby granted, free of charge, to any person obtaining a 

# copy of this software and associated documentation files (the "Software"), 

# to deal in the Software without restriction, including without limitation 

# the rights to use, copy, modify, merge, publish, distribute, sublicense, 

# and/or sell copies of the Software, and to permit persons to whom the 

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

# 

# The above copyright notice and this permission notice shall be included 

# in all copies or substantial portions of the Software. 

# 

# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS 

# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, 

# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL 

# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR 

# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, 

# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR 

# OTHER DEALINGS IN THE SOFTWARE.