Coverage for pygeodesy/ellipsoidalKarney.py: 100%
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« prev ^ index » next coverage.py v7.2.2, created at 2023-11-12 13:23 -0500
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 fabs, _polygon, _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__ = '23.11.08'
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 the geodesic
76 distance, initial and final bearing (azimuths) between two given
77 points or the destination point given a start point and an (initial)
78 bearing.
80 @note: This L{LatLon} require the U{geographiclib
81 <https://PyPI.org/project/geographiclib>} package.
82 '''
84 @deprecated_method
85 def bearingTo(self, other, wrap=False): # PYCHOK no cover
86 '''DEPRECATED, use method L{initialBearingTo}.
87 '''
88 return self.initialBearingTo(other, wrap=wrap)
90 @Property_RO
91 def Equidistant(self):
92 '''Get the prefered azimuthal equidistant projection I{class} (L{EquidistantKarney}).
93 '''
94 return _MODS.azimuthal.EquidistantKarney
96 @Property_RO
97 def geodesic(self):
98 '''Get this C{LatLon}'s I{wrapped} U{geodesic.Geodesic
99 <https://GeographicLib.SourceForge.io/Python/doc/code.html>}, provided
100 I{Karney}'s U{geographiclib<https://PyPI.org/project/geographiclib>}
101 package is installed.
102 '''
103 return self.datum.ellipsoid.geodesic
105 def toCartesian(self, **Cartesian_datum_kwds): # PYCHOK Cartesian=Cartesian, datum=None
106 '''Convert this point to C{Karney}-based cartesian (ECEF) coordinates.
108 @kwarg Cartesian_datum_kwds: Optional L{Cartesian}, B{C{datum}}
109 and other keyword arguments, ignored if C{B{Cartesian} is None}.
110 Use C{B{Cartesian}=...} to override this L{Cartesian} class
111 or set C{B{Cartesian} is None}.
113 @return: The cartesian (ECEF) coordinates (L{Cartesian}) or if
114 B{C{Cartesian}} is C{None}, an L{Ecef9Tuple}C{(x, y, z,
115 lat, lon, height, C, M, datum)} with C{C} and C{M} if
116 available.
118 @raise TypeError: Invalid B{C{Cartesian}}, B{C{datum}} or other
119 B{C{Cartesian_datum_kwds}}.
120 '''
121 kwds = _xkwds(Cartesian_datum_kwds, Cartesian=Cartesian, datum=self.datum)
122 return LatLonEllipsoidalBaseDI.toCartesian(self, **kwds)
125def areaOf(points, datum=_WGS84, wrap=True):
126 '''Compute the area of an (ellipsoidal) polygon or composite.
128 @arg points: The polygon points (L{LatLon}[], L{BooleanFHP}
129 or L{BooleanGH}).
130 @kwarg datum: Optional datum (L{Datum}).
131 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the
132 B{C{points}} (C{bool}).
134 @return: Area (C{meter}, same as units of the B{C{datum}}'s
135 ellipsoid axes, I{squared}).
137 @raise ImportError: Package U{geographiclib
138 <https://PyPI.org/project/geographiclib>}
139 not installed or not found.
141 @raise PointsError: Insufficient number of B{C{points}}.
143 @raise TypeError: Some B{C{points}} are not L{LatLon}.
145 @raise ValueError: Invalid C{B{wrap}=False}, unwrapped, unrolled
146 longitudes not supported.
148 @note: This function requires the U{geographiclib
149 <https://PyPI.org/project/geographiclib>} package.
151 @see: Functions L{pygeodesy.areaOf}, L{ellipsoidalExact.areaOf},
152 L{ellipsoidalGeodSolve.areaOf}, L{sphericalNvector.areaOf}
153 and L{sphericalTrigonometry.areaOf}.
155 @note: The U{area of a polygon enclosing a pole<https://GeographicLib.SourceForge.io/
156 C++/doc/classGeographicLib_1_1GeodesicExact.html#a3d7a9155e838a09a48dc14d0c3fac525>}
157 can be found by adding half the datum's ellipsoid surface area to the polygon's area.
158 '''
159 return fabs(_polygon(datum.ellipsoid.geodesic, points, True, False, wrap))
162def intersection3(start1, end1, start2, end2, height=None, wrap=False, # was=True
163 equidistant=None, tol=_TOL_M, LatLon=LatLon, **LatLon_kwds):
164 '''I{Iteratively} compute the intersection point of two lines, each defined
165 by two (ellipsoidal) points or by an (ellipsoidal) start point and an
166 (initial) bearing from North.
168 @arg start1: Start point of the first line (L{LatLon}).
169 @arg end1: End point of the first line (L{LatLon}) or the initial bearing
170 at the first point (compass C{degrees360}).
171 @arg start2: Start point of the second line (L{LatLon}).
172 @arg end2: End point of the second line (L{LatLon}) or the initial bearing
173 at the second point (compass C{degrees360}).
174 @kwarg height: Optional height at the intersection (C{meter}, conventionally)
175 or C{None} for the mean height.
176 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the B{C{start2}}
177 and B{C{end*}} points (C{bool}).
178 @kwarg equidistant: An azimuthal equidistant projection (I{class} or function
179 L{pygeodesy.equidistant}) or C{None} for the preferred
180 C{B{start1}.Equidistant}.
181 @kwarg tol: Tolerance for convergence and for skew line distance and length
182 (C{meter}, conventionally).
183 @kwarg LatLon: Optional class to return the intersection points (L{LatLon})
184 or C{None}.
185 @kwarg LatLon_kwds: Optional, additional B{C{LatLon}} keyword arguments,
186 ignored if C{B{LatLon} is None}.
188 @return: An L{Intersection3Tuple}C{(point, outside1, outside2)} with C{point}
189 a B{C{LatLon}} or if C{B{LatLon} is None}, a L{LatLon4Tuple}C{(lat,
190 lon, height, datum)}.
192 @raise IntersectionError: Skew, colinear, parallel or otherwise
193 non-intersecting lines or no convergence
194 for the given B{C{tol}}.
196 @raise TypeError: Invalid or non-ellipsoidal B{C{start1}}, B{C{end1}},
197 B{C{start2}} or B{C{end2}} or invalid B{C{equidistant}}.
199 @note: For each line specified with an initial bearing, a pseudo-end point
200 is computed as the C{destination} along that bearing at about 1.5
201 times the distance from the start point to an initial gu-/estimate
202 of the intersection point (and between 1/8 and 3/8 of the authalic
203 earth perimeter).
205 @see: U{The B{ellipsoidal} case<https://GIS.StackExchange.com/questions/48937/
206 calculating-intersection-of-two-circles>} and U{Karney's paper
207 <https://ArXiv.org/pdf/1102.1215.pdf>}, pp 20-21, section B{14. MARITIME
208 BOUNDARIES} for more details about the iteration algorithm.
209 '''
210 return _intersection3(start1, end1, start2, end2, height=height, wrap=wrap,
211 equidistant=equidistant, tol=tol, LatLon=LatLon, **LatLon_kwds)
214def intersections2(center1, radius1, center2, radius2, height=None, wrap=False, # was=True
215 equidistant=None, tol=_TOL_M, LatLon=LatLon, **LatLon_kwds):
216 '''I{Iteratively} compute the intersection points of two circles, each defined
217 by an (ellipsoidal) center point and a radius.
219 @arg center1: Center of the first circle (L{LatLon}).
220 @arg radius1: Radius of the first circle (C{meter}, conventionally).
221 @arg center2: Center of the second circle (L{LatLon}).
222 @arg radius2: Radius of the second circle (C{meter}, same units as
223 B{C{radius1}}).
224 @kwarg height: Optional height for the intersection points (C{meter},
225 conventionally) or C{None} for the I{"radical height"}
226 at the I{radical line} between both centers.
227 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll B{C{center2}}
228 (C{bool}).
229 @kwarg equidistant: An azimuthal equidistant projection (I{class} or
230 function L{pygeodesy.equidistant}) or C{None} for
231 the preferred C{B{center1}.Equidistant}.
232 @kwarg tol: Convergence tolerance (C{meter}, same units as B{C{radius1}}
233 and B{C{radius2}}).
234 @kwarg LatLon: Optional class to return the intersection points (L{LatLon})
235 or C{None}.
236 @kwarg LatLon_kwds: Optional, additional B{C{LatLon}} keyword arguments,
237 ignored if C{B{LatLon} is None}.
239 @return: 2-Tuple of the intersection points, each a B{C{LatLon}} instance
240 or L{LatLon4Tuple}C{(lat, lon, height, datum)} if C{B{LatLon} is
241 None}. For abutting circles, both points are the same instance,
242 aka the I{radical center}.
244 @raise IntersectionError: Concentric, antipodal, invalid or non-intersecting
245 circles or no convergence for the B{C{tol}}.
247 @raise TypeError: Invalid or non-ellipsoidal B{C{center1}} or B{C{center2}}
248 or invalid B{C{equidistant}}.
250 @raise UnitError: Invalid B{C{radius1}}, B{C{radius2}} or B{C{height}}.
252 @see: U{The B{ellipsoidal} case<https://GIS.StackExchange.com/questions/48937/
253 calculating-intersection-of-two-circles>}, U{Karney's paper
254 <https://ArXiv.org/pdf/1102.1215.pdf>}, pp 20-21, section B{14. MARITIME BOUNDARIES},
255 U{circle-circle<https://MathWorld.Wolfram.com/Circle-CircleIntersection.html>} and
256 U{sphere-sphere<https://MathWorld.Wolfram.com/Sphere-SphereIntersection.html>}
257 intersections.
258 '''
259 return _intersections2(center1, radius1, center2, radius2, height=height, wrap=wrap,
260 equidistant=equidistant, tol=tol, LatLon=LatLon, **LatLon_kwds)
263def isclockwise(points, datum=_WGS84, wrap=True):
264 '''Determine the direction of a path or polygon.
266 @arg points: The path or polygon points (C{LatLon}[]).
267 @kwarg datum: Optional datum (L{Datum}).
268 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the
269 B{C{points}} (C{bool}).
271 @return: C{True} if B{C{points}} are clockwise, C{False} otherwise.
273 @raise ImportError: Package U{geographiclib
274 <https://PyPI.org/project/geographiclib>}
275 not installed or not found.
277 @raise PointsError: Insufficient number of B{C{points}}.
279 @raise TypeError: Some B{C{points}} are not C{LatLon}.
281 @raise ValueError: The B{C{points}} enclose a pole or zero
282 area.
284 @note: This function requires the U{geographiclib
285 <https://PyPI.org/project/geographiclib>} package.
287 @see: L{pygeodesy.isclockwise}.
288 '''
289 a = _polygon(datum.ellipsoid.geodesic, points, True, False, wrap)
290 if a < 0:
291 return True
292 elif a > 0:
293 return False
294 raise _areaError(points)
297def nearestOn(point, point1, point2, within=True, height=None, wrap=False,
298 equidistant=None, tol=_TOL_M, LatLon=LatLon, **LatLon_kwds):
299 '''I{Iteratively} locate the closest point on the geodesic between
300 two other (ellipsoidal) points.
302 @arg point: Reference point (C{LatLon}).
303 @arg point1: Start point of the geodesic (C{LatLon}).
304 @arg point2: End point of the geodesic (C{LatLon}).
305 @kwarg within: If C{True} return the closest point I{between}
306 B{C{point1}} and B{C{point2}}, otherwise the
307 closest point elsewhere on the geodesic (C{bool}).
308 @kwarg height: Optional height for the closest point (C{meter},
309 conventionally) or C{None} or C{False} for the
310 interpolated height. If C{False}, the closest
311 takes the heights of the points into account.
312 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll both
313 B{C{point1}} and B{C{point2}} (C{bool}).
314 @kwarg equidistant: An azimuthal equidistant projection (I{class}
315 or function L{pygeodesy.equidistant}) or C{None}
316 for the preferred C{B{point}.Equidistant}.
317 @kwarg tol: Convergence tolerance (C{meter}).
318 @kwarg LatLon: Optional class to return the closest point
319 (L{LatLon}) or C{None}.
320 @kwarg LatLon_kwds: Optional, additional B{C{LatLon}} keyword
321 arguments, ignored if C{B{LatLon} is None}.
323 @return: Closest point, a B{C{LatLon}} instance or if C{B{LatLon}
324 is None}, a L{LatLon4Tuple}C{(lat, lon, height, datum)}.
326 @raise ImportError: Package U{geographiclib
327 <https://PyPI.org/project/geographiclib>}
328 not installed or not found.
330 @raise TypeError: Invalid or non-ellipsoidal B{C{point}}, B{C{point1}}
331 or B{C{point2}} or invalid B{C{equidistant}}.
333 @raise ValueError: No convergence for the B{C{tol}}.
335 @see: U{The B{ellipsoidal} case<https://GIS.StackExchange.com/questions/48937/
336 calculating-intersection-of-two-circles>} and U{Karney's paper
337 <https://ArXiv.org/pdf/1102.1215.pdf>}, pp 20-21, section B{14. MARITIME
338 BOUNDARIES} for more details about the iteration algorithm.
339 '''
340 return _nearestOn(point, point1, point2, within=within, height=height, wrap=wrap,
341 equidistant=equidistant, tol=tol, LatLon=LatLon, **LatLon_kwds)
344def perimeterOf(points, closed=False, datum=_WGS84, wrap=True):
345 '''Compute the perimeter of an (ellipsoidal) polygon or composite.
347 @arg points: The polygon points (L{LatLon}[], L{BooleanFHP} or
348 L{BooleanGH}).
349 @kwarg closed: Optionally, close the polygon (C{bool}).
350 @kwarg datum: Optional datum (L{Datum}).
351 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the
352 B{C{points}} (C{bool}).
354 @return: Perimeter (C{meter}, same as units of the B{C{datum}}'s
355 ellipsoid axes).
357 @raise ImportError: Package U{geographiclib
358 <https://PyPI.org/project/geographiclib>}
359 not installed or not found.
361 @raise PointsError: Insufficient number of B{C{points}}.
363 @raise TypeError: Some B{C{points}} are not L{LatLon} or C{B{closed}=False}
364 with B{C{points}} a composite.
366 @raise ValueError: Invalid C{B{wrap}=False}, unwrapped, unrolled
367 longitudes not supported or C{B{closed}=False}
368 with C{B{points}} a composite.
370 @note: This function requires the U{geographiclib
371 <https://PyPI.org/project/geographiclib>} package.
373 @see: Functions L{pygeodesy.perimeterOf}, L{ellipsoidalExact.perimeterOf},
374 L{ellipsoidalGeodSolve.perimeterOf}, L{sphericalNvector.perimeterOf}
375 and L{sphericalTrigonometry.perimeterOf}.
376 '''
377 return _polygon(datum.ellipsoid.geodesic, points, closed, True, wrap)
380__all__ += _ALL_OTHER(Cartesian, LatLon, # classes
381 areaOf, intersecant2, # from .ellipsoidalBase
382 intersection3, intersections2, isclockwise, ispolar,
383 nearestOn, perimeterOf)
385# **) MIT License
386#
387# Copyright (C) 2016-2023 -- mrJean1 at Gmail -- All Rights Reserved.
388#
389# Permission is hereby granted, free of charge, to any person obtaining a
390# copy of this software and associated documentation files (the "Software"),
391# to deal in the Software without restriction, including without limitation
392# the rights to use, copy, modify, merge, publish, distribute, sublicense,
393# and/or sell copies of the Software, and to permit persons to whom the
394# Software is furnished to do so, subject to the following conditions:
395#
396# The above copyright notice and this permission notice shall be included
397# in all copies or substantial portions of the Software.
398#
399# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
400# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
401# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
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405# OTHER DEALINGS IN THE SOFTWARE.