Coverage for pygeodesy/ellipsoidalKarney.py: 100%
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2# -*- coding: utf-8 -*-
4u'''Ellipsoidal, I{Karney}-based geodesy.
6Ellipsoidal geodetic (lat-/longitude) L{LatLon} and geocentric
7(ECEF) L{Cartesian} classes and functions L{areaOf}, L{intersections2},
8L{isclockwise}, L{nearestOn} and L{perimeterOf}, all requiring I{Charles
9Karney}'s U{geographiclib <https://PyPI.org/project/geographiclib>}
10Python package to be installed.
12Here's an example usage of C{ellipsoidalKarney}:
14 >>> from pygeodesy.ellipsoidalKarney import LatLon
15 >>> Newport_RI = LatLon(41.49008, -71.312796)
16 >>> Cleveland_OH = LatLon(41.499498, -81.695391)
17 >>> Newport_RI.distanceTo(Cleveland_OH)
18 866,455.4329098687 # meter
20You can change the ellipsoid model used by the I{Karney} formulae
21as follows:
23 >>> from pygeodesy import Datums
24 >>> from pygeodesy.ellipsoidalKarney import LatLon
25 >>> p = LatLon(0, 0, datum=Datums.OSGB36)
27or by converting to anothor datum:
29 >>> p = p.toDatum(Datums.OSGB36)
30'''
32from pygeodesy.datums import _WGS84
33from pygeodesy.ellipsoidalBase import CartesianEllipsoidalBase, _nearestOn
34from pygeodesy.ellipsoidalBaseDI import LatLonEllipsoidalBaseDI, \
35 _intersection3, _intersections2, \
36 _TOL_M, intersecant2
37# from pygeodesy.errors import _xkwds # from .karney
38from pygeodesy.karney import _polygon, fabs, _xkwds
39from pygeodesy.lazily import _ALL_LAZY, _ALL_MODS as _MODS, _ALL_OTHER
40from pygeodesy.points import _areaError, ispolar # PYCHOK exported
41from pygeodesy.props import deprecated_method, Property_RO
43# from math import fabs # from .karney
45__all__ = _ALL_LAZY.ellipsoidalKarney
46__version__ = '24.02.21'
49class Cartesian(CartesianEllipsoidalBase):
50 '''Extended to convert C{Karney}-based L{Cartesian} to
51 C{Karney}-based L{LatLon} points.
52 '''
54 def toLatLon(self, **LatLon_and_kwds): # PYCHOK LatLon=LatLon, datum=None
55 '''Convert this cartesian point to a C{Karney}-based geodetic point.
57 @kwarg LatLon_and_kwds: Optional L{LatLon} and L{LatLon} keyword
58 arguments as C{datum}. Use C{B{LatLon}=...,
59 B{datum}=...} to override this L{LatLon}
60 class or specify C{B{LatLon}=None}.
62 @return: The geodetic point (L{LatLon}) or if B{C{LatLon}} is C{None},
63 an L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M, datum)}
64 with C{C} and C{M} if available.
66 @raise TypeError: Invalid B{C{LatLon_and_kwds}} argument.
67 '''
68 kwds = _xkwds(LatLon_and_kwds, LatLon=LatLon, datum=self.datum)
69 return CartesianEllipsoidalBase.toLatLon(self, **kwds)
72class LatLon(LatLonEllipsoidalBaseDI):
73 '''An ellipsoidal L{LatLon} similar to L{ellipsoidalVincenty.LatLon}
74 but using I{Charles F. F. Karney}'s Python U{geographiclib
75 <https://PyPI.org/project/geographiclib>} to compute geodesic
76 distances, bearings (azimuths), etc.
78 @note: This L{LatLon} class requires the U{geographiclib
79 <https://PyPI.org/project/geographiclib>} package.
80 '''
82 @deprecated_method
83 def bearingTo(self, other, wrap=False): # PYCHOK no cover
84 '''DEPRECATED, use method L{initialBearingTo}.
85 '''
86 return self.initialBearingTo(other, wrap=wrap)
88 @Property_RO
89 def Equidistant(self):
90 '''Get the prefered azimuthal equidistant projection I{class} (L{EquidistantKarney}).
91 '''
92 return _MODS.azimuthal.EquidistantKarney
94 @Property_RO
95 def geodesic(self):
96 '''Get this C{LatLon}'s I{wrapped} U{geodesic.Geodesic
97 <https://GeographicLib.SourceForge.io/Python/doc/code.html>}, provided
98 I{Karney}'s U{geographiclib<https://PyPI.org/project/geographiclib>}
99 package is installed.
100 '''
101 return self.datum.ellipsoid.geodesic
103 def toCartesian(self, **Cartesian_datum_kwds): # PYCHOK Cartesian=Cartesian, datum=None
104 '''Convert this point to C{Karney}-based cartesian (ECEF) coordinates.
106 @kwarg Cartesian_datum_kwds: Optional L{Cartesian}, B{C{datum}}
107 and other keyword arguments, ignored if C{B{Cartesian} is None}.
108 Use C{B{Cartesian}=...} to override this L{Cartesian} class
109 or set C{B{Cartesian} is None}.
111 @return: The cartesian (ECEF) coordinates (L{Cartesian}) or if
112 B{C{Cartesian}} is C{None}, an L{Ecef9Tuple}C{(x, y, z,
113 lat, lon, height, C, M, datum)} with C{C} and C{M} if
114 available.
116 @raise TypeError: Invalid B{C{Cartesian}}, B{C{datum}} or other
117 B{C{Cartesian_datum_kwds}}.
118 '''
119 kwds = _xkwds(Cartesian_datum_kwds, Cartesian=Cartesian, datum=self.datum)
120 return LatLonEllipsoidalBaseDI.toCartesian(self, **kwds)
123def areaOf(points, datum=_WGS84, wrap=True):
124 '''Compute the area of an (ellipsoidal) polygon or composite.
126 @arg points: The polygon points (L{LatLon}[], L{BooleanFHP}
127 or L{BooleanGH}).
128 @kwarg datum: Optional datum (L{Datum}).
129 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the
130 B{C{points}} (C{bool}).
132 @return: Area (C{meter}, same as units of the B{C{datum}}'s
133 ellipsoid axes, I{squared}).
135 @raise ImportError: Package U{geographiclib
136 <https://PyPI.org/project/geographiclib>}
137 not installed or not found.
139 @raise PointsError: Insufficient number of B{C{points}}.
141 @raise TypeError: Some B{C{points}} are not L{LatLon}.
143 @raise ValueError: Invalid C{B{wrap}=False}, unwrapped, unrolled
144 longitudes not supported.
146 @note: This function requires the U{geographiclib
147 <https://PyPI.org/project/geographiclib>} package.
149 @see: Functions L{pygeodesy.areaOf}, L{ellipsoidalExact.areaOf},
150 L{ellipsoidalGeodSolve.areaOf}, L{sphericalNvector.areaOf}
151 and L{sphericalTrigonometry.areaOf}.
153 @note: The U{area of a polygon enclosing a pole<https://GeographicLib.SourceForge.io/
154 C++/doc/classGeographicLib_1_1GeodesicExact.html#a3d7a9155e838a09a48dc14d0c3fac525>}
155 can be found by adding half the datum's ellipsoid surface area to the polygon's area.
156 '''
157 return fabs(_polygon(datum.ellipsoid.geodesic, points, True, False, wrap))
160def intersection3(start1, end1, start2, end2, height=None, wrap=False, # was=True
161 equidistant=None, tol=_TOL_M, LatLon=LatLon, **LatLon_kwds):
162 '''I{Iteratively} compute the intersection point of two lines, each defined
163 by two (ellipsoidal) points or by an (ellipsoidal) start point and an
164 (initial) bearing from North.
166 @arg start1: Start point of the first line (L{LatLon}).
167 @arg end1: End point of the first line (L{LatLon}) or the initial bearing
168 at the first point (compass C{degrees360}).
169 @arg start2: Start point of the second line (L{LatLon}).
170 @arg end2: End point of the second line (L{LatLon}) or the initial bearing
171 at the second point (compass C{degrees360}).
172 @kwarg height: Optional height at the intersection (C{meter}, conventionally)
173 or C{None} for the mean height.
174 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the B{C{start2}}
175 and B{C{end*}} points (C{bool}).
176 @kwarg equidistant: An azimuthal equidistant projection (I{class} or function
177 L{pygeodesy.equidistant}) or C{None} for the preferred
178 C{B{start1}.Equidistant}.
179 @kwarg tol: Tolerance for convergence and for skew line distance and length
180 (C{meter}, conventionally).
181 @kwarg LatLon: Optional class to return the intersection points (L{LatLon})
182 or C{None}.
183 @kwarg LatLon_kwds: Optional, additional B{C{LatLon}} keyword arguments,
184 ignored if C{B{LatLon} is None}.
186 @return: An L{Intersection3Tuple}C{(point, outside1, outside2)} with C{point}
187 a B{C{LatLon}} or if C{B{LatLon} is None}, a L{LatLon4Tuple}C{(lat,
188 lon, height, datum)}.
190 @raise IntersectionError: Skew, colinear, parallel or otherwise
191 non-intersecting lines or no convergence
192 for the given B{C{tol}}.
194 @raise TypeError: Invalid or non-ellipsoidal B{C{start1}}, B{C{end1}},
195 B{C{start2}} or B{C{end2}} or invalid B{C{equidistant}}.
197 @note: For each line specified with an initial bearing, a pseudo-end point
198 is computed as the C{destination} along that bearing at about 1.5
199 times the distance from the start point to an initial gu-/estimate
200 of the intersection point (and between 1/8 and 3/8 of the authalic
201 earth perimeter).
203 @see: U{The B{ellipsoidal} case<https://GIS.StackExchange.com/questions/48937/
204 calculating-intersection-of-two-circles>} and U{Karney's paper
205 <https://ArXiv.org/pdf/1102.1215.pdf>}, pp 20-21, section B{14. MARITIME
206 BOUNDARIES} for more details about the iteration algorithm.
207 '''
208 return _intersection3(start1, end1, start2, end2, height=height, wrap=wrap,
209 equidistant=equidistant, tol=tol, LatLon=LatLon, **LatLon_kwds)
212def intersections2(center1, radius1, center2, radius2, height=None, wrap=False, # was=True
213 equidistant=None, tol=_TOL_M, LatLon=LatLon, **LatLon_kwds):
214 '''I{Iteratively} compute the intersection points of two circles, each defined
215 by an (ellipsoidal) center point and a radius.
217 @arg center1: Center of the first circle (L{LatLon}).
218 @arg radius1: Radius of the first circle (C{meter}, conventionally).
219 @arg center2: Center of the second circle (L{LatLon}).
220 @arg radius2: Radius of the second circle (C{meter}, same units as
221 B{C{radius1}}).
222 @kwarg height: Optional height for the intersection points (C{meter},
223 conventionally) or C{None} for the I{"radical height"}
224 at the I{radical line} between both centers.
225 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll B{C{center2}}
226 (C{bool}).
227 @kwarg equidistant: An azimuthal equidistant projection (I{class} or
228 function L{pygeodesy.equidistant}) or C{None} for
229 the preferred C{B{center1}.Equidistant}.
230 @kwarg tol: Convergence tolerance (C{meter}, same units as B{C{radius1}}
231 and B{C{radius2}}).
232 @kwarg LatLon: Optional class to return the intersection points (L{LatLon})
233 or C{None}.
234 @kwarg LatLon_kwds: Optional, additional B{C{LatLon}} keyword arguments,
235 ignored if C{B{LatLon} is None}.
237 @return: 2-Tuple of the intersection points, each a B{C{LatLon}} instance
238 or L{LatLon4Tuple}C{(lat, lon, height, datum)} if C{B{LatLon} is
239 None}. For abutting circles, both points are the same instance,
240 aka the I{radical center}.
242 @raise IntersectionError: Concentric, antipodal, invalid or non-intersecting
243 circles or no convergence for the B{C{tol}}.
245 @raise TypeError: Invalid or non-ellipsoidal B{C{center1}} or B{C{center2}}
246 or invalid B{C{equidistant}}.
248 @raise UnitError: Invalid B{C{radius1}}, B{C{radius2}} or B{C{height}}.
250 @see: U{The B{ellipsoidal} case<https://GIS.StackExchange.com/questions/48937/
251 calculating-intersection-of-two-circles>}, U{Karney's paper
252 <https://ArXiv.org/pdf/1102.1215.pdf>}, pp 20-21, section B{14. MARITIME BOUNDARIES},
253 U{circle-circle<https://MathWorld.Wolfram.com/Circle-CircleIntersection.html>} and
254 U{sphere-sphere<https://MathWorld.Wolfram.com/Sphere-SphereIntersection.html>}
255 intersections.
256 '''
257 return _intersections2(center1, radius1, center2, radius2, height=height, wrap=wrap,
258 equidistant=equidistant, tol=tol, LatLon=LatLon, **LatLon_kwds)
261def isclockwise(points, datum=_WGS84, wrap=True):
262 '''Determine the direction of a path or polygon.
264 @arg points: The path or polygon points (C{LatLon}[]).
265 @kwarg datum: Optional datum (L{Datum}).
266 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the
267 B{C{points}} (C{bool}).
269 @return: C{True} if B{C{points}} are clockwise, C{False} otherwise.
271 @raise ImportError: Package U{geographiclib
272 <https://PyPI.org/project/geographiclib>}
273 not installed or not found.
275 @raise PointsError: Insufficient number of B{C{points}}.
277 @raise TypeError: Some B{C{points}} are not C{LatLon}.
279 @raise ValueError: The B{C{points}} enclose a pole or zero
280 area.
282 @note: This function requires the U{geographiclib
283 <https://PyPI.org/project/geographiclib>} package.
285 @see: L{pygeodesy.isclockwise}.
286 '''
287 a = _polygon(datum.ellipsoid.geodesic, points, True, False, wrap)
288 if a < 0:
289 return True
290 elif a > 0:
291 return False
292 raise _areaError(points)
295def nearestOn(point, point1, point2, within=True, height=None, wrap=False,
296 equidistant=None, tol=_TOL_M, LatLon=LatLon, **LatLon_kwds):
297 '''I{Iteratively} locate the closest point on the geodesic between
298 two other (ellipsoidal) points.
300 @arg point: Reference point (C{LatLon}).
301 @arg point1: Start point of the geodesic (C{LatLon}).
302 @arg point2: End point of the geodesic (C{LatLon}).
303 @kwarg within: If C{True} return the closest point I{between}
304 B{C{point1}} and B{C{point2}}, otherwise the
305 closest point elsewhere on the geodesic (C{bool}).
306 @kwarg height: Optional height for the closest point (C{meter},
307 conventionally) or C{None} or C{False} for the
308 interpolated height. If C{False}, the closest
309 takes the heights of the points into account.
310 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll both
311 B{C{point1}} and B{C{point2}} (C{bool}).
312 @kwarg equidistant: An azimuthal equidistant projection (I{class}
313 or function L{pygeodesy.equidistant}) or C{None}
314 for the preferred C{B{point}.Equidistant}.
315 @kwarg tol: Convergence tolerance (C{meter}).
316 @kwarg LatLon: Optional class to return the closest point
317 (L{LatLon}) or C{None}.
318 @kwarg LatLon_kwds: Optional, additional B{C{LatLon}} keyword
319 arguments, ignored if C{B{LatLon} is None}.
321 @return: Closest point, a B{C{LatLon}} instance or if C{B{LatLon}
322 is None}, a L{LatLon4Tuple}C{(lat, lon, height, datum)}.
324 @raise ImportError: Package U{geographiclib
325 <https://PyPI.org/project/geographiclib>}
326 not installed or not found.
328 @raise TypeError: Invalid or non-ellipsoidal B{C{point}}, B{C{point1}}
329 or B{C{point2}} or invalid B{C{equidistant}}.
331 @raise ValueError: No convergence for the B{C{tol}}.
333 @see: U{The B{ellipsoidal} case<https://GIS.StackExchange.com/questions/48937/
334 calculating-intersection-of-two-circles>} and U{Karney's paper
335 <https://ArXiv.org/pdf/1102.1215.pdf>}, pp 20-21, section B{14. MARITIME
336 BOUNDARIES} for more details about the iteration algorithm.
337 '''
338 return _nearestOn(point, point1, point2, within=within, height=height, wrap=wrap,
339 equidistant=equidistant, tol=tol, LatLon=LatLon, **LatLon_kwds)
342def perimeterOf(points, closed=False, datum=_WGS84, wrap=True):
343 '''Compute the perimeter of an (ellipsoidal) polygon or composite.
345 @arg points: The polygon points (L{LatLon}[], L{BooleanFHP} or
346 L{BooleanGH}).
347 @kwarg closed: Optionally, close the polygon (C{bool}).
348 @kwarg datum: Optional datum (L{Datum}).
349 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the
350 B{C{points}} (C{bool}).
352 @return: Perimeter (C{meter}, same as units of the B{C{datum}}'s
353 ellipsoid axes).
355 @raise ImportError: Package U{geographiclib
356 <https://PyPI.org/project/geographiclib>}
357 not installed or not found.
359 @raise PointsError: Insufficient number of B{C{points}}.
361 @raise TypeError: Some B{C{points}} are not L{LatLon} or C{B{closed}=False}
362 with B{C{points}} a composite.
364 @raise ValueError: Invalid C{B{wrap}=False}, unwrapped, unrolled
365 longitudes not supported or C{B{closed}=False}
366 with C{B{points}} a composite.
368 @note: This function requires the U{geographiclib
369 <https://PyPI.org/project/geographiclib>} package.
371 @see: Functions L{pygeodesy.perimeterOf}, L{ellipsoidalExact.perimeterOf},
372 L{ellipsoidalGeodSolve.perimeterOf}, L{sphericalNvector.perimeterOf}
373 and L{sphericalTrigonometry.perimeterOf}.
374 '''
375 return _polygon(datum.ellipsoid.geodesic, points, closed, True, wrap)
378__all__ += _ALL_OTHER(Cartesian, LatLon, # classes
379 areaOf, intersecant2, # from .ellipsoidalBase
380 intersection3, intersections2, isclockwise, ispolar,
381 nearestOn, perimeterOf)
383# **) MIT License
384#
385# Copyright (C) 2016-2024 -- mrJean1 at Gmail -- All Rights Reserved.
386#
387# Permission is hereby granted, free of charge, to any person obtaining a
388# copy of this software and associated documentation files (the "Software"),
389# to deal in the Software without restriction, including without limitation
390# the rights to use, copy, modify, merge, publish, distribute, sublicense,
391# and/or sell copies of the Software, and to permit persons to whom the
392# Software is furnished to do so, subject to the following conditions:
393#
394# The above copyright notice and this permission notice shall be included
395# in all copies or substantial portions of the Software.
396#
397# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
398# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
399# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
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403# OTHER DEALINGS IN THE SOFTWARE.