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# -*- coding: utf-8 -*- 

 

u'''Exact ellipsoidal geodesy, intended I{for testing purposes only}. 

 

Ellipsoidal geodetic (lat-/longitude) L{LatLon} and geocentric 

(ECEF) L{Cartesian} classes and functions L{areaOf}, L{intersections2}, 

L{isclockwise}, L{nearestOn} and L{perimeterOf} based on module 

L{geodsolve}, a wrapper invoking I{Karney}'s U{GeodSolve 

<https://GeographicLib.SourceForge.io/html/GeodSolve.1.html>} utility. 

''' 

 

# from pygeodesy.datums import _WGS84 # from .ellipsoidalBase 

from pygeodesy.ellipsoidalBase import CartesianEllipsoidalBase, \ 

_nearestOn, _WGS84 

from pygeodesy.ellipsoidalBaseDI import LatLonEllipsoidalBaseDI, _TOL_M, \ 

_intersection3, _intersections2 

# from pygeodesy.errors import _xkwds # from .karney 

from pygeodesy.karney import _polygon, Property_RO, _xkwds 

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

from pygeodesy.points import _areaError, ispolar # PYCHOK exported 

# from pygeodesy.props import Property_RO # from .karney 

 

__all__ = _ALL_LAZY.ellipsoidalGeodSolve 

__version__ = '22.01.17' 

 

 

class Cartesian(CartesianEllipsoidalBase): 

'''Extended to convert exact L{Cartesian} to exact L{LatLon} points. 

''' 

 

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

'''Convert this cartesian point to an exact geodetic point. 

 

@kwarg LatLon_and_kwds: Optional L{LatLon} and L{LatLon} keyword 

arguments as C{datum}. Use C{B{LatLon}=..., 

B{datum}=...} to override this L{LatLon} 

class or specify C{B{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_and_kwds}} argument. 

''' 

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

return CartesianEllipsoidalBase.toLatLon(self, **kwds) 

 

 

class LatLon(LatLonEllipsoidalBaseDI): 

'''An ellipsoidal L{LatLon} like L{ellipsoidalKarney.LatLon} but using (exact) 

geodesic I{wrapper} L{GeodesicSolve} 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. 

''' 

 

@Property_RO 

def Equidistant(self): 

'''Get the prefered azimuthal equidistant projection I{class} (L{EquidistantGeodSolve}). 

''' 

return _MODS.azimuthal.EquidistantGeodSolve 

 

@Property_RO 

def geodesicx(self): 

'''Get this C{LatLon}'s (exact) geodesic (L{GeodesicSolve}). 

''' 

return self.datum.ellipsoid.geodsolve 

 

geodesic = geodesicx # for C{._Direct} and C{._Inverse} 

 

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

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

 

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

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

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

or set C{B{Cartesian} is 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 LatLonEllipsoidalBaseDI.toCartesian(self, **kwds) 

 

 

def areaOf(points, datum=_WGS84, wrap=True): 

'''Compute the area of an (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}}'s ellipsoid axes, I{squared}). 

 

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

 

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

 

@raise ValueError: Invalid C{B{wrap}=False}, unwrapped, 

unrolled longitudes not supported. 

 

@see: Functions L{pygeodesy.areaOf}, L{ellipsoidalExact.areaOf}, 

L{ellipsoidalKarney.areaOf}, L{sphericalNvector.areaOf} 

and L{sphericalTrigonometry.areaOf}. 

''' 

return abs(_polygon(datum.ellipsoid.geodsolve, points, True, False, wrap)) 

 

 

def intersection3(start1, end1, start2, end2, height=None, wrap=True, 

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

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

by two (ellipsoidal) points or by an (ellipsoidal) start point and a 

bearing from North. 

 

@arg start1: Start point of the first path (L{LatLon}). 

@arg end1: End point of the first path (L{LatLon}) or the initial bearing 

at the first point (compass C{degrees360}). 

@arg start2: Start point of the second path (L{LatLon}). 

@arg end2: End point of the second path (L{LatLon}) or the initial bearing 

at the second 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 the preferred 

C{B{start1}.Equidistant}. 

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

(C{meter}, conventionally). 

@kwarg LatLon: Optional class to return the intersection points (L{LatLon}) 

or C{None}. 

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

ignored if C{B{LatLon} is None}. 

 

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

a B{C{LatLon}} or if C{B{LatLon} is None}, a L{LatLon4Tuple}C{(lat, 

lon, height, datum)}. 

 

@raise IntersectionError: Skew, colinear, parallel or otherwise 

non-intersecting paths or no convergence 

for the given B{C{tol}}. 

 

@raise TypeError: Invalid or non-ellipsoidal B{C{start1}}, B{C{end1}}, 

B{C{start2}} or B{C{end2}} or invalid B{C{equidistant}}. 

 

@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. 

''' 

return _intersection3(start1, end1, start2, end2, height=height, wrap=wrap, 

equidistant=equidistant, tol=tol, LatLon=LatLon, **LatLon_kwds) 

 

 

def intersections2(center1, radius1, center2, radius2, height=None, wrap=True, 

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

'''Iteratively compute the intersection points of two circles, each defined 

by an (ellipsoidal) center point and a radius. 

 

@arg center1: Center of the first circle (L{LatLon}). 

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

@arg center2: Center of the second circle (L{LatLon}). 

@arg radius2: Radius of the second 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 

the preferred C{B{center1}.Equidistant}. 

@kwarg tol: Convergence tolerance (C{meter}, same units as B{C{radius1}} 

and B{C{radius2}}). 

@kwarg LatLon: Optional class to return the intersection points (L{LatLon}) 

or C{None}. 

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

ignored if C{B{LatLon} is None}. 

 

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

or L{LatLon4Tuple}C{(lat, lon, height, datum)} if C{B{LatLon} is 

None}. For abutting circles, both points are the same instance, 

aka the I{radical center}. 

 

@raise IntersectionError: Concentric, antipodal, invalid or non-intersecting 

circles or no convergence for the B{C{tol}}. 

 

@raise TypeError: Invalid or non-ellipsoidal B{C{center1}} or B{C{center2}} 

or invalid 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. 

''' 

return _intersections2(center1, radius1, center2, radius2, height=height, wrap=wrap, 

equidistant=equidistant, tol=tol, LatLon=LatLon, **LatLon_kwds) 

 

 

def isclockwise(points, datum=_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 PointsError: Insufficient number of B{C{points}}. 

 

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

 

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

area. 

 

@see: L{pygeodesy.isclockwise}. 

''' 

a = _polygon(datum.ellipsoid.geodsolve, points, True, False, wrap) 

if a < 0: 

return True 

elif a > 0: 

return False 

raise _areaError(points) 

 

 

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

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

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

two other (ellipsoidal) points. 

 

@arg point: Reference point (C{LatLon}). 

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

@arg point2: End point of the geodesic (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 the preferred C{B{point}.Equidistant}. 

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

@kwarg LatLon: Optional class to return the closest point 

(L{LatLon}) or C{None}. 

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

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

 

@return: Closest point, a B{C{LatLon}} instance or if C{B{LatLon} 

is None}, a L{LatLon4Tuple}C{(lat, lon, height, datum)}. 

 

@raise TypeError: Invalid or non-ellipsoidal B{C{point}}, B{C{point1}} 

or B{C{point2}} or invalid B{C{equidistant}}. 

 

@raise ValueError: No convergence for the 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 more details about the iteration algorithm. 

''' 

return _nearestOn(point, point1, point2, within=within, height=height, wrap=wrap, 

equidistant=equidistant, tol=tol, LatLon=LatLon, **LatLon_kwds) 

 

 

def perimeterOf(points, closed=False, datum=_WGS84, wrap=True): 

'''Compute the perimeter of an (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}}'s ellipsoid axes). 

 

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

 

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

 

@raise ValueError: Invalid C{B{wrap}=False}, unwrapped, 

unrolled longitudes not supported. 

 

@see: Functions L{pygeodesy.perimeterOf}, L{ellipsoidalExact.perimeterOf}, 

L{ellipsoidalKarney.perimeterOf}, L{sphericalNvector.perimeterOf} 

and L{sphericalTrigonometry.perimeterOf}. 

''' 

return _polygon(datum.ellipsoid.geodsolve, points, closed, True, wrap) 

 

 

__all__ += _ALL_OTHER(Cartesian, LatLon, # classes 

areaOf, # functions 

intersection3, intersections2, isclockwise, ispolar, 

nearestOn, perimeterOf) 

 

# **) 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.