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# -*- coding: utf-8 -*- 

 

u'''Ellipsoidal classes geodetic (lat-/longitude) L{LatLon} and 

geocentric (ECEF) L{Cartesian} and functions L{areaOf}, L{isclockwise} 

and L{perimeterOf}, all based on I{Charles Karney's} Python implementation 

of U{GeographicLib<https://PyPI.org/project/geographiclib>}. 

 

Here's an example usage of C{ellipsoidalKarney}: 

 

>>> from pygeodesy.ellipsoidalKarney import LatLon 

>>> Newport_RI = LatLon(41.49008, -71.312796) 

>>> Cleveland_OH = LatLon(41.499498, -81.695391) 

>>> Newport_RI.distanceTo(Cleveland_OH) 

866,455.4329098687 # meter 

 

You can change the ellipsoid model used by the Karney formulae 

as follows: 

 

>>> from pygeodesy import Datums 

>>> from pygeodesy.ellipsoidalKarney import LatLon 

>>> p = LatLon(0, 0, datum=Datums.OSGB36) 

 

or by converting to anothor datum: 

 

>>> p = p.convertDatum(Datums.OSGB36) 

 

@newfield example: Example, Examples 

''' 

 

from pygeodesy.basics import property_RO, _xkwds 

from pygeodesy.datum import Datums 

from pygeodesy.ecef import EcefKarney 

from pygeodesy.ellipsoidalBase import CartesianEllipsoidalBase, \ 

LatLonEllipsoidalBase 

from pygeodesy.errors import _ValueError 

from pygeodesy.formy import points2 

from pygeodesy.lazily import _ALL_LAZY 

from pygeodesy.named import Bearing2Tuple, Destination2Tuple 

from pygeodesy.points import _areaError, ispolar # PYCHOK exported 

from pygeodesy.utily import unroll180, wrap90, wrap180, wrap360 

 

# all public contants, classes and functions 

__all__ = _ALL_LAZY.ellipsoidalKarney + ( 

'Cartesian', 'LatLon', # classes 

'areaOf', 'isclockwise', 'ispolar', 'perimeterOf') # functions 

__version__ = '20.06.16' 

 

 

class Cartesian(CartesianEllipsoidalBase): 

'''Extended to convert C{Karney}-based L{Cartesian} to 

C{Karney}-based L{LatLon} points. 

''' 

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

 

def toLatLon(self, **LatLon_datum_kwds): # PYCHOK LatLon=LatLon, datum=None 

'''Convert this cartesian point to a C{Karney}-based 

geodetic point. 

 

@kwarg LatLon_datum_kwds: Optional L{LatLon}, B{C{datum}} and 

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

Use B{C{LatLon=...}} to override this L{LatLon} class 

or specify B{C{LatLon=None}}. 

 

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

is C{None}, an L{Ecef9Tuple}C{(x, y, z, lat, lon, 

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

 

@raise TypeError: Invalid B{C{LatLon}}, B{C{datum}} or other 

B{C{LatLon_datum_kwds}}. 

''' 

kwds = _xkwds(LatLon_datum_kwds, LatLon=LatLon, datum=self.datum) 

return CartesianEllipsoidalBase.toLatLon(self, **kwds) 

 

 

class LatLon(LatLonEllipsoidalBase): 

'''An ellipsoidal L{LatLon} similar to L{ellipsoidalVincenty.LatLon} 

but using I{Charles F. F. Karney's} Python U{GeographicLib 

<https://PyPI.org/project/geographiclib>} to compute the geodesic 

distance, initial and final bearing (azimuths) between two given 

points or the destination point given a start point and an initial 

bearing. 

 

@note: This L{LatLon}'s methods require the U{GeographicLib 

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

''' 

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

 

def bearingTo(self, other, wrap=False): # PYCHOK no cover 

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

''' 

return self.initialBearingTo(other, wrap=wrap) 

 

def bearingTo2(self, other, wrap=False): 

'''Compute the initial and final bearing (forward and reverse 

azimuth) from this to an other point, using Karney's 

C{Inverse} method. See methods L{initialBearingTo} and 

L{finalBearingTo} for more details. 

 

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

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

 

@return: A L{Bearing2Tuple}C{(initial, final)}. 

 

@raise ImportError: Package U{geographiclib 

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

not installed or not found. 

 

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

 

@raise ValueError: If this and the B{C{other}} point's L{Datum} 

ellipsoids are not compatible. 

''' 

r = self._inverse(other, wrap) 

return self._xnamed(Bearing2Tuple(r.initial, r.final)) 

 

def destination(self, distance, bearing, height=None): 

'''Compute the destination point after having travelled 

for the given distance from this point along a geodesic 

given by an initial bearing, using Karney's C{Direct} 

method. See method L{destination2} for more details. 

 

@arg distance: Distance (C{meter}). 

@arg bearing: Initial bearing in (compass C{degrees360}). 

@kwarg height: Optional height, overriding the default 

height (C{meter}, same units as C{distance}). 

 

@return: The destination point (L{LatLon}). 

 

@raise ImportError: Package U{geographiclib 

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

not installed or not found. 

 

@example: 

 

>>> p = LatLon(-37.95103, 144.42487) 

>>> d = p.destination(54972.271, 306.86816) 

>>> d 

LatLon(37°39′10.14″S, 143°55′35.39″E) # 37.652818°S, 143.926498°E 

''' 

r = self._direct(distance, bearing, self.classof, height) 

return r.destination 

 

def destination2(self, distance, bearing, height=None): 

'''Compute the destination point and the final bearing (reverse 

azimuth) after having travelled for the given distance from 

this point along a geodesic given by an initial bearing, 

using Karney's C{Direct} method. 

 

The distance must be in the same units as this point's datum 

axes, conventionally C{meter}. The distance is measured on 

the surface of the ellipsoid, ignoring this point's height. 

 

The initial and final bearing (forward and reverse azimuth) 

are in compass C{degrees360}. 

 

The destination point's height and datum are set to this 

point's height and datum, unless the former is overridden. 

 

@arg distance: Distance (C{meter}). 

@arg bearing: Initial bearing (compass C{degrees360}). 

@kwarg height: Optional height, overriding the default 

height (C{meter}, same units as C{distance}). 

 

@return: A L{Destination2Tuple}C{(destination, final)}. 

 

@raise ImportError: Package U{geographiclib 

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

not installed or not found. 

 

@example: 

 

>>> p = LatLon(-37.95103, 144.42487) 

>>> d, f = p.destination2(54972.271, 306.86816) 

>>> d 

LatLon(37°39′10.14″S, 143°55′35.39″E) # 37.652818°S, 143.926498°E 

>>> f 

307.1736313846665 

''' 

r = self._direct(distance, bearing, self.classof, height) 

return self._xnamed(r) 

 

def distanceTo(self, other, wrap=False, **unused): # for -DistanceTo 

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

along a geodesic, using Karney's C{Inverse} method. 

See method L{distanceTo3} for more details. 

 

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

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

 

@return: Distance (C{meter}). 

 

@raise ImportError: Package U{geographiclib 

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

not installed or not found. 

 

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

 

@raise ValueError: If this and the B{C{other}} point's L{Datum} 

ellipsoids are not compatible. 

 

@example: 

 

>>> p = LatLon(50.06632, -5.71475) 

>>> q = LatLon(58.64402, -3.07009) 

>>> d = p.distanceTo(q) # 969,954.1663142084 m 

''' 

return self._inverse(other, wrap).distance 

 

def distanceTo3(self, other, wrap=False): 

'''Compute the distance, the initial and final bearing along a 

geodesic between this and an other point, using Karney's 

C{Inverse} method. 

 

The distance is in the same units as this point's datum axes, 

conventionally meter. The distance is measured on the surface 

of the ellipsoid, ignoring this point's height. 

 

The initial and final bearing (forward and reverse azimuth) 

are in compass C{degrees360} from North. 

 

@arg other: Destination point (L{LatLon}). 

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

 

@return: A L{Distance3Tuple}C{(distance, initial, final)}. 

 

@raise ImportError: Package U{geographiclib 

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

not installed or not found. 

 

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

 

@raise ValueError: If this and the B{C{other}} point's L{Datum} 

ellipsoids are not compatible. 

''' 

return self._xnamed(self._inverse(other, wrap)) 

 

def finalBearingOn(self, distance, bearing): 

'''Compute the final bearing (reverse azimuth) after having 

travelled for the given distance along a geodesic given 

by an initial bearing from this point, using Karney's 

C{Direct} method. See method L{destination2} for more details. 

 

@arg distance: Distance (C{meter}). 

@arg bearing: Initial bearing (compass C{degrees360}). 

 

@return: Final bearing (compass C{degrees360}). 

 

@raise ImportError: Package U{geographiclib 

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

not installed or not found. 

 

@example: 

 

>>> p = LatLon(-37.95103, 144.42487) 

>>> b = 306.86816 

>>> f = p.finalBearingOn(54972.271, b) # 307.1736313846665° 

''' 

return self._direct(distance, bearing, None, None).final 

 

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

'''Compute the final bearing (reverse azimuth) after having 

travelled along a geodesic from this point to an other 

point, using Karney's C{Inverse} method. See method 

L{distanceTo3} for more details. 

 

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

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

 

@return: Final bearing (compass C{degrees360}). 

 

@raise ImportError: Package U{geographiclib 

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

not installed or not found. 

 

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

 

@raise ValueError: If this and the B{C{other}} point's L{Datum} 

ellipsoids are not compatible. 

 

@example: 

 

>>> p = new LatLon(50.06632, -5.71475) 

>>> q = new LatLon(58.64402, -3.07009) 

>>> f = p.finalBearingTo(q) # 11.297220414306684° 

 

>>> p = LatLon(52.205, 0.119) 

>>> q = LatLon(48.857, 2.351) 

>>> f = p.finalBearingTo(q) # 157.83449958372714° 

''' 

return self._inverse(other, wrap).final 

 

@property_RO 

def geodesic(self): 

'''Get this C{LatLon}'s I{wrapped} U{Karney Geodesic 

<https://GeographicLib.SourceForge.io/html/python/code.html>}, 

provided package U{geographiclib 

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

''' 

return self.datum.ellipsoid.geodesic 

 

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

'''Compute the initial bearing (forward azimuth) to travel 

along a geodesic from this point to an other point, 

using Karney's C{Inverse} method. See method 

L{distanceTo3} for more details. 

 

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

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

 

@return: Initial bearing (compass C{degrees360}). 

 

@raise ImportError: Package U{geographiclib 

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

not installed or not found. 

 

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

 

@raise ValueError: If this and the B{C{other}} point's L{Datum} 

ellipsoids are not compatible. 

 

@example: 

 

>>> p = LatLon(50.06632, -5.71475) 

>>> q = LatLon(58.64402, -3.07009) 

>>> b = p.initialBearingTo(q) # 9.141877488906045° 

 

>>> p = LatLon(52.205, 0.119) 

>>> q = LatLon(48.857, 2.351) 

>>> b = p.initialBearingTo(q) # 156.1106404059787° 

 

@JSname: I{bearingTo}. 

''' 

return self._inverse(other, wrap).initial 

 

def toCartesian(self, **Cartesian_datum_kwds): # PYCHOK Cartesian=Cartesian, datum=None 

'''Convert this point to C{Karney}-based cartesian (ECEF) coordinates. 

 

@kwarg Cartesian_datum_kwds: Optional L{Cartesian}, B{C{datum}} 

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

Use B{C{Cartesian=...}} to override this L{Cartesian} class 

or set B{C{Cartesian=None}}. 

 

@return: The cartesian (ECEF) coordinates (L{Cartesian}) or if 

B{C{Cartesian}} is C{None}, an L{Ecef9Tuple}C{(x, y, z, 

lat, lon, height, C, M, datum)} with C{C} and C{M} if 

available. 

 

@raise TypeError: Invalid B{C{Cartesian}}, B{C{datum}} or other 

B{C{Cartesian_datum_kwds}}. 

''' 

kwds = _xkwds(Cartesian_datum_kwds, Cartesian=Cartesian, 

datum=self.datum) 

return LatLonEllipsoidalBase.toCartesian(self, **kwds) 

 

def _direct(self, distance, bearing, LL, height): 

'''(INTERNAL) Karney's C{Direct} method. 

 

@return: A L{Destination2Tuple}C{(destination, final)} or 

a L{Destination3Tuple}C{(lat, lon, final)} if 

B{C{LL}} is C{None}. 

''' 

g = self.datum.ellipsoid.geodesic 

r = g.Direct3(self.lat, self.lon, bearing, distance) 

if LL: 

h = self.height if height is None else height 

d = LL(wrap90(r.lat), wrap180(r.lon), height=h, datum=self.datum) 

r = Destination2Tuple(self._xnamed(d), wrap360(r.final)) 

return r 

 

def _inverse(self, other, wrap): 

'''(INTERNAL) Karney's C{Inverse} method. 

 

@return: A L{Distance3Tuple}C{(distance, initial, final)}. 

 

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

 

@raise ValueError: If this and the B{C{other}} point's 

L{Datum} ellipsoids are not compatible. 

''' 

g = self.ellipsoids(other).geodesic 

_, lon = unroll180(self.lon, other.lon, wrap=wrap) 

return g.Inverse3(self.lat, self.lon, other.lat, lon) 

 

 

def _geodesic(datum, points, closed, line, wrap): 

# Compute the area or perimeter of a polygon, 

# using the GeographicLib package, iff installed 

g = datum.ellipsoid.geodesic 

 

if not wrap: # capability LONG_UNROLL can't be off 

raise _ValueError(wrap=wrap) 

 

_, points = points2(points, closed=closed) # base=LatLonEllipsoidalBase(0, 0) 

 

g = g.Polygon(line) 

 

# note, lon deltas are unrolled, by default 

for p in points: 

g.AddPoint(p.lat, p.lon) 

if closed and line: 

p = points[0] 

g.AddPoint(p.lat, p.lon) 

 

# g.Compute returns (number_of_points, perimeter, signed area) 

return g.Compute(False, True)[1 if line else 2] 

 

 

def areaOf(points, datum=Datums.WGS84, wrap=True): 

'''Compute the area of a (n ellipsoidal) polygon. 

 

@arg points: The polygon points (L{LatLon}[]). 

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

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

 

@return: Area (C{meter}, same as units of the B{C{datum}} 

ellipsoid, squared). 

 

@raise ImportError: Package U{GeographicLib 

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

 

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

 

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

 

@raise ValueError: Invalid B{C{wrap}}, longitudes not 

wrapped, unrolled. 

 

@note: This function requires installation of the U{GeographicLib 

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

 

@see: L{pygeodesy.areaOf}, L{sphericalNvector.areaOf} and 

L{sphericalTrigonometry.areaOf}. 

''' 

return abs(_geodesic(datum, points, True, False, wrap)) 

 

 

def isclockwise(points, datum=Datums.WGS84, wrap=True): 

'''Determine the direction of a path or polygon. 

 

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

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

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

 

@return: C{True} if B{C{points}} are clockwise, C{False} otherwise. 

 

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

 

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

 

@raise ValueError: The B{C{points}} enclose a pole or zero 

area. 

 

@note: This function requires installation of the U{GeographicLib 

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

 

@see: L{pygeodesy.isclockwise}. 

''' 

a = _geodesic(datum, points, True, False, wrap) 

if a > 0: 

return True 

elif a < 0: 

return False 

raise _areaError(points) 

 

 

def perimeterOf(points, closed=False, datum=Datums.WGS84, wrap=True): 

'''Compute the perimeter of a (n ellipsoidal) polygon. 

 

@arg points: The polygon points (L{LatLon}[]). 

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

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

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

 

@return: Perimeter (C{meter}, same as units of the B{C{datum}} 

ellipsoid). 

 

@raise ImportError: Package U{GeographicLib 

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

 

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

 

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

 

@raise ValueError: Invalid B{C{wrap}}, longitudes not 

wrapped, unrolled. 

 

@note: This function requires installation of the U{GeographicLib 

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

 

@see: L{pygeodesy.perimeterOf} and L{sphericalTrigonometry.perimeterOf}. 

''' 

return _geodesic(datum, points, closed, True, wrap) 

 

# **) MIT License 

# 

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

# 

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

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

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

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

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

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

# 

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

# in all copies or substantial portions of the Software. 

# 

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

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