Coverage for pygeodesy/ellipsoidalKarney.py: 100%
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« prev ^ index » next coverage.py v7.2.2, created at 2023-04-12 11:45 -0400
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, _TOL_M, \
35 _intersection3, _intersections2
36# from pygeodesy.errors import _xkwds # from .karney
37from pygeodesy.karney import fabs, _polygon, _xkwds
38from pygeodesy.lazily import _ALL_LAZY, _ALL_MODS as _MODS, _ALL_OTHER
39from pygeodesy.points import _areaError, ispolar # PYCHOK exported
40from pygeodesy.props import deprecated_method, Property_RO
42# from math import fabs # from .karney
44__all__ = _ALL_LAZY.ellipsoidalKarney
45__version__ = '23.04.11'
48class Cartesian(CartesianEllipsoidalBase):
49 '''Extended to convert C{Karney}-based L{Cartesian} to
50 C{Karney}-based L{LatLon} points.
51 '''
53 def toLatLon(self, **LatLon_and_kwds): # PYCHOK LatLon=LatLon, datum=None
54 '''Convert this cartesian point to a C{Karney}-based geodetic point.
56 @kwarg LatLon_and_kwds: Optional L{LatLon} and L{LatLon} keyword
57 arguments as C{datum}. Use C{B{LatLon}=...,
58 B{datum}=...} to override this L{LatLon}
59 class or specify C{B{LatLon}=None}.
61 @return: The geodetic point (L{LatLon}) or if B{C{LatLon}} is C{None},
62 an L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M, datum)}
63 with C{C} and C{M} if available.
65 @raise TypeError: Invalid B{C{LatLon_and_kwds}} argument.
66 '''
67 kwds = _xkwds(LatLon_and_kwds, LatLon=LatLon, datum=self.datum)
68 return CartesianEllipsoidalBase.toLatLon(self, **kwds)
71class LatLon(LatLonEllipsoidalBaseDI):
72 '''An ellipsoidal L{LatLon} similar to L{ellipsoidalVincenty.LatLon}
73 but using I{Charles F. F. Karney}'s Python U{geographiclib
74 <https://PyPI.org/project/geographiclib>} to compute the geodesic
75 distance, initial and final bearing (azimuths) between two given
76 points or the destination point given a start point and an (initial)
77 bearing.
79 @note: This L{LatLon} require the U{geographiclib
80 <https://PyPI.org/project/geographiclib>} package.
81 '''
83 @deprecated_method
84 def bearingTo(self, other, wrap=False): # PYCHOK no cover
85 '''DEPRECATED, use method L{initialBearingTo}.
86 '''
87 return self.initialBearingTo(other, wrap=wrap)
89 @Property_RO
90 def Equidistant(self):
91 '''Get the prefered azimuthal equidistant projection I{class} (L{EquidistantKarney}).
92 '''
93 return _MODS.azimuthal.EquidistantKarney
95 @Property_RO
96 def geodesic(self):
97 '''Get this C{LatLon}'s I{wrapped} U{geodesic.Geodesic
98 <https://GeographicLib.SourceForge.io/Python/doc/code.html>}, provided
99 I{Karney}'s U{geographiclib<https://PyPI.org/project/geographiclib>}
100 package is installed.
101 '''
102 return self.datum.ellipsoid.geodesic
104 def toCartesian(self, **Cartesian_datum_kwds): # PYCHOK Cartesian=Cartesian, datum=None
105 '''Convert this point to C{Karney}-based cartesian (ECEF) coordinates.
107 @kwarg Cartesian_datum_kwds: Optional L{Cartesian}, B{C{datum}}
108 and other keyword arguments, ignored if C{B{Cartesian} is None}.
109 Use C{B{Cartesian}=...} to override this L{Cartesian} class
110 or set C{B{Cartesian} is None}.
112 @return: The cartesian (ECEF) coordinates (L{Cartesian}) or if
113 B{C{Cartesian}} is C{None}, an L{Ecef9Tuple}C{(x, y, z,
114 lat, lon, height, C, M, datum)} with C{C} and C{M} if
115 available.
117 @raise TypeError: Invalid B{C{Cartesian}}, B{C{datum}} or other
118 B{C{Cartesian_datum_kwds}}.
119 '''
120 kwds = _xkwds(Cartesian_datum_kwds, Cartesian=Cartesian, datum=self.datum)
121 return LatLonEllipsoidalBaseDI.toCartesian(self, **kwds)
124def areaOf(points, datum=_WGS84, wrap=True):
125 '''Compute the area of an (ellipsoidal) polygon or composite.
127 @arg points: The polygon points (L{LatLon}[], L{BooleanFHP}
128 or L{BooleanGH}).
129 @kwarg datum: Optional datum (L{Datum}).
130 @kwarg wrap: Wrap and unroll longitudes (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=True,
161 equidistant=None, tol=_TOL_M, LatLon=LatLon, **LatLon_kwds):
162 '''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: Wrap and unroll longitudes (C{bool}).
175 @kwarg equidistant: An azimuthal equidistant projection (I{class} or function
176 L{pygeodesy.equidistant}) or C{None} for the preferred
177 C{B{start1}.Equidistant}.
178 @kwarg tol: Tolerance for convergence and for skew line distance and length
179 (C{meter}, conventionally).
180 @kwarg LatLon: Optional class to return the intersection points (L{LatLon})
181 or C{None}.
182 @kwarg LatLon_kwds: Optional, additional B{C{LatLon}} keyword arguments,
183 ignored if C{B{LatLon} is None}.
185 @return: An L{Intersection3Tuple}C{(point, outside1, outside2)} with C{point}
186 a B{C{LatLon}} or if C{B{LatLon} is None}, a L{LatLon4Tuple}C{(lat,
187 lon, height, datum)}.
189 @raise IntersectionError: Skew, colinear, parallel or otherwise
190 non-intersecting lines or no convergence
191 for the given B{C{tol}}.
193 @raise TypeError: Invalid or non-ellipsoidal B{C{start1}}, B{C{end1}},
194 B{C{start2}} or B{C{end2}} or invalid B{C{equidistant}}.
196 @note: For each line specified with an initial bearing, a pseudo-end point
197 is computed as the C{destination} along that bearing at about 1.5
198 times the distance from the start point to an initial gu-/estimate
199 of the intersection point (and between 1/8 and 3/8 of the authalic
200 earth perimeter).
202 @see: U{The B{ellipsoidal} case<https://GIS.StackExchange.com/questions/48937/
203 calculating-intersection-of-two-circles>} and U{Karney's paper
204 <https://ArXiv.org/pdf/1102.1215.pdf>}, pp 20-21, section B{14. MARITIME
205 BOUNDARIES} for more details about the iteration algorithm.
206 '''
207 return _intersection3(start1, end1, start2, end2, height=height, wrap=wrap,
208 equidistant=equidistant, tol=tol, LatLon=LatLon, **LatLon_kwds)
211def intersections2(center1, radius1, center2, radius2, height=None, wrap=True,
212 equidistant=None, tol=_TOL_M, LatLon=LatLon, **LatLon_kwds):
213 '''Iteratively compute the intersection points of two circles, each defined
214 by an (ellipsoidal) center point and a radius.
216 @arg center1: Center of the first circle (L{LatLon}).
217 @arg radius1: Radius of the first circle (C{meter}, conventionally).
218 @arg center2: Center of the second circle (L{LatLon}).
219 @arg radius2: Radius of the second circle (C{meter}, same units as
220 B{C{radius1}}).
221 @kwarg height: Optional height for the intersection points (C{meter},
222 conventionally) or C{None} for the I{"radical height"}
223 at the I{radical line} between both centers.
224 @kwarg wrap: Wrap and unroll longitudes (C{bool}).
225 @kwarg equidistant: An azimuthal equidistant projection (I{class} or
226 function L{pygeodesy.equidistant}) or C{None} for
227 the preferred C{B{center1}.Equidistant}.
228 @kwarg tol: Convergence tolerance (C{meter}, same units as B{C{radius1}}
229 and B{C{radius2}}).
230 @kwarg LatLon: Optional class to return the intersection points (L{LatLon})
231 or C{None}.
232 @kwarg LatLon_kwds: Optional, additional B{C{LatLon}} keyword arguments,
233 ignored if C{B{LatLon} is None}.
235 @return: 2-Tuple of the intersection points, each a B{C{LatLon}} instance
236 or L{LatLon4Tuple}C{(lat, lon, height, datum)} if C{B{LatLon} is
237 None}. For abutting circles, both points are the same instance,
238 aka the I{radical center}.
240 @raise IntersectionError: Concentric, antipodal, invalid or non-intersecting
241 circles or no convergence for the B{C{tol}}.
243 @raise TypeError: Invalid or non-ellipsoidal B{C{center1}} or B{C{center2}}
244 or invalid B{C{equidistant}}.
246 @raise UnitError: Invalid B{C{radius1}}, B{C{radius2}} or B{C{height}}.
248 @see: U{The B{ellipsoidal} case<https://GIS.StackExchange.com/questions/48937/
249 calculating-intersection-of-two-circles>}, U{Karney's paper
250 <https://ArXiv.org/pdf/1102.1215.pdf>}, pp 20-21, section B{14. MARITIME BOUNDARIES},
251 U{circle-circle<https://MathWorld.Wolfram.com/Circle-CircleIntersection.html>} and
252 U{sphere-sphere<https://MathWorld.Wolfram.com/Sphere-SphereIntersection.html>}
253 intersections.
254 '''
255 return _intersections2(center1, radius1, center2, radius2, height=height, wrap=wrap,
256 equidistant=equidistant, tol=tol, LatLon=LatLon, **LatLon_kwds)
259def isclockwise(points, datum=_WGS84, wrap=True):
260 '''Determine the direction of a path or polygon.
262 @arg points: The path or polygon points (C{LatLon}[]).
263 @kwarg datum: Optional datum (L{Datum}).
264 @kwarg wrap: Wrap and unroll longitudes (C{bool}).
266 @return: C{True} if B{C{points}} are clockwise, C{False} otherwise.
268 @raise ImportError: Package U{geographiclib
269 <https://PyPI.org/project/geographiclib>}
270 not installed or not found.
272 @raise PointsError: Insufficient number of B{C{points}}.
274 @raise TypeError: Some B{C{points}} are not C{LatLon}.
276 @raise ValueError: The B{C{points}} enclose a pole or zero
277 area.
279 @note: This function requires the U{geographiclib
280 <https://PyPI.org/project/geographiclib>} package.
282 @see: L{pygeodesy.isclockwise}.
283 '''
284 a = _polygon(datum.ellipsoid.geodesic, points, True, False, wrap)
285 if a < 0:
286 return True
287 elif a > 0:
288 return False
289 raise _areaError(points)
292def nearestOn(point, point1, point2, within=True, height=None, wrap=False,
293 equidistant=None, tol=_TOL_M, LatLon=LatLon, **LatLon_kwds):
294 '''Iteratively locate the closest point on the geodesic between
295 two other (ellipsoidal) points.
297 @arg point: Reference point (C{LatLon}).
298 @arg point1: Start point of the geodesic (C{LatLon}).
299 @arg point2: End point of the geodesic (C{LatLon}).
300 @kwarg within: If C{True} return the closest point I{between}
301 B{C{point1}} and B{C{point2}}, otherwise the
302 closest point elsewhere on the geodesic (C{bool}).
303 @kwarg height: Optional height for the closest point (C{meter},
304 conventionally) or C{None} or C{False} for the
305 interpolated height. If C{False}, the closest
306 takes the heights of the points into account.
307 @kwarg wrap: Wrap and unroll longitudes (C{bool}).
308 @kwarg equidistant: An azimuthal equidistant projection (I{class}
309 or function L{pygeodesy.equidistant}) or C{None}
310 for the preferred C{B{point}.Equidistant}.
311 @kwarg tol: Convergence tolerance (C{meter}).
312 @kwarg LatLon: Optional class to return the closest point
313 (L{LatLon}) or C{None}.
314 @kwarg LatLon_kwds: Optional, additional B{C{LatLon}} keyword
315 arguments, ignored if C{B{LatLon} is None}.
317 @return: Closest point, a B{C{LatLon}} instance or if C{B{LatLon}
318 is None}, a L{LatLon4Tuple}C{(lat, lon, height, datum)}.
320 @raise ImportError: Package U{geographiclib
321 <https://PyPI.org/project/geographiclib>}
322 not installed or not found.
324 @raise TypeError: Invalid or non-ellipsoidal B{C{point}}, B{C{point1}}
325 or B{C{point2}} or invalid B{C{equidistant}}.
327 @raise ValueError: No convergence for the B{C{tol}}.
329 @see: U{The B{ellipsoidal} case<https://GIS.StackExchange.com/questions/48937/
330 calculating-intersection-of-two-circles>} and U{Karney's paper
331 <https://ArXiv.org/pdf/1102.1215.pdf>}, pp 20-21, section B{14. MARITIME
332 BOUNDARIES} for more details about the iteration algorithm.
333 '''
334 return _nearestOn(point, point1, point2, within=within, height=height, wrap=wrap,
335 equidistant=equidistant, tol=tol, LatLon=LatLon, **LatLon_kwds)
338def perimeterOf(points, closed=False, datum=_WGS84, wrap=True):
339 '''Compute the perimeter of an (ellipsoidal) polygon or composite.
341 @arg points: The polygon points (L{LatLon}[], L{BooleanFHP} or
342 L{BooleanGH}).
343 @kwarg closed: Optionally, close the polygon (C{bool}).
344 @kwarg datum: Optional datum (L{Datum}).
345 @kwarg wrap: Wrap and unroll longitudes (C{bool}).
347 @return: Perimeter (C{meter}, same as units of the B{C{datum}}'s
348 ellipsoid axes).
350 @raise ImportError: Package U{geographiclib
351 <https://PyPI.org/project/geographiclib>}
352 not installed or not found.
354 @raise PointsError: Insufficient number of B{C{points}}.
356 @raise TypeError: Some B{C{points}} are not L{LatLon} or C{B{closed}=False}
357 with B{C{points}} a composite.
359 @raise ValueError: Invalid C{B{wrap}=False}, unwrapped, unrolled
360 longitudes not supported or C{B{closed}=False}
361 with C{B{points}} a composite.
363 @note: This function requires the U{geographiclib
364 <https://PyPI.org/project/geographiclib>} package.
366 @see: Functions L{pygeodesy.perimeterOf}, L{ellipsoidalExact.perimeterOf},
367 L{ellipsoidalGeodSolve.perimeterOf}, L{sphericalNvector.perimeterOf}
368 and L{sphericalTrigonometry.perimeterOf}.
369 '''
370 return _polygon(datum.ellipsoid.geodesic, points, closed, True, wrap)
373__all__ += _ALL_OTHER(Cartesian, LatLon, # classes
374 areaOf, # functions
375 intersection3, intersections2, isclockwise, ispolar,
376 nearestOn, perimeterOf)
378# **) MIT License
379#
380# Copyright (C) 2016-2023 -- mrJean1 at Gmail -- All Rights Reserved.
381#
382# Permission is hereby granted, free of charge, to any person obtaining a
383# copy of this software and associated documentation files (the "Software"),
384# to deal in the Software without restriction, including without limitation
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387# Software is furnished to do so, subject to the following conditions:
388#
389# The above copyright notice and this permission notice shall be included
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393# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
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