Coverage for pygeodesy/ellipsoidalKarney.py: 100%

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1 

2# -*- coding: utf-8 -*- 

3 

4u'''Ellipsoidal, I{Karney}-based geodesy. 

5 

6Ellipsoidal geodetic (lat-/longitude) L{LatLon} and geocentric (ECEF) L{Cartesian} 

7classes and functions L{areaOf}, L{intersection3}, L{intersections2}, L{isclockwise}, 

8L{nearestOn} and L{perimeterOf}, requiring I{Charles F.F. Karney}'s U{geographiclib 

9<https://PyPI.org/project/geographiclib>} Python package to be installed. 

10 

11A usage example of C{ellipsoidalKarney}: 

12 

13 >>> from pygeodesy.ellipsoidalKarney import LatLon 

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

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

16 >>> Newport_RI.distanceTo(Cleveland_OH) 

17 866,455.4329098687 # meter 

18 

19You can change the ellipsoid model used by the I{Karney} formulae 

20as follows: 

21 

22 >>> from pygeodesy import Datums 

23 >>> from pygeodesy.ellipsoidalKarney import LatLon 

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

25 

26or by converting to anothor datum: 

27 

28 >>> p = p.toDatum(Datums.OSGB36) 

29''' 

30 

31from pygeodesy.datums import _WGS84 

32from pygeodesy.ellipsoidalBase import CartesianEllipsoidalBase, _nearestOn 

33from pygeodesy.ellipsoidalBaseDI import LatLonEllipsoidalBaseDI, \ 

34 _intersection3, _intersections2, \ 

35 _TOL_M, intersecant2 

36# from pygeodesy.errors import _xkwds # from .karney 

37from pygeodesy.karney import _polygon, fabs, _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 

41 

42# from math import fabs # from .karney 

43 

44__all__ = _ALL_LAZY.ellipsoidalKarney 

45__version__ = '24.08.13' 

46 

47 

48class Cartesian(CartesianEllipsoidalBase): 

49 '''Extended to convert C{Karney}-based L{Cartesian} to C{Karney}-based L{LatLon} points. 

50 ''' 

51 

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

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

54 

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

56 as C{datum}. Use C{B{LatLon}=..., B{datum}=...} to override 

57 this L{LatLon} class or specify C{B{LatLon}=None}. 

58 

59 @return: The geodetic point (L{LatLon}) or if C{B{LatLon} is None}, an 

60 L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M, datum)} with C{C} 

61 and C{M} if available. 

62 

63 @raise TypeError: Invalid B{C{LatLon_and_kwds}} argument. 

64 ''' 

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

66 return CartesianEllipsoidalBase.toLatLon(self, **kwds) 

67 

68 

69class LatLon(LatLonEllipsoidalBaseDI): 

70 '''An ellipsoidal L{LatLon} similar to L{ellipsoidalVincenty.LatLon} but using 

71 I{Karney}'s Python U{geographiclib<https://PyPI.org/project/geographiclib>} 

72 to compute geodesic distances, bearings (azimuths), etc. 

73 ''' 

74 

75 @deprecated_method 

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

77 '''DEPRECATED, use method L{initialBearingTo}. 

78 ''' 

79 return self.initialBearingTo(other, wrap=wrap) 

80 

81 @Property_RO 

82 def Equidistant(self): 

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

84 ''' 

85 return _MODS.azimuthal.EquidistantKarney 

86 

87 @Property_RO 

88 def geodesic(self): 

89 '''Get this C{LatLon}'s I{wrapped} U{geodesic.Geodesic 

90 <https://GeographicLib.SourceForge.io/Python/doc/code.html>}, provided 

91 I{Karney}'s U{geographiclib<https://PyPI.org/project/geographiclib>} 

92 package is installed. 

93 ''' 

94 return self.datum.ellipsoid.geodesic 

95 

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

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

98 

99 @kwarg Cartesian_datum_kwds: Optional L{Cartesian}, B{C{datum}} and other keyword 

100 arguments, ignored if C{B{Cartesian} is None}. Use C{B{Cartesian}=...} to 

101 override this L{Cartesian} class or set C{B{Cartesian}=None}. 

102 

103 @return: The cartesian (ECEF) coordinates (L{Cartesian}) or if C{B{Cartesian} is 

104 None}, an L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M, datum)} with 

105 C{C} and C{M} if available. 

106 

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

108 ''' 

109 kwds = _xkwds(Cartesian_datum_kwds, Cartesian=Cartesian, datum=self.datum) 

110 return LatLonEllipsoidalBaseDI.toCartesian(self, **kwds) 

111 

112 

113def areaOf(points, datum=_WGS84, wrap=True): 

114 '''Compute the area of an (ellipsoidal) polygon or composite using I{Karney}'s 

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

116 

117 @arg points: The polygon points (L{LatLon}[], L{BooleanFHP} or L{BooleanGH}). 

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

119 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the B{C{points}} (C{bool}). 

120 

121 @return: Area (C{meter}, same as units of the B{C{datum}}'s ellipsoid axes, I{squared}). 

122 

123 @raise ImportError: Package U{geographiclib<https://PyPI.org/project/geographiclib>} 

124 not installed or not found. 

125 

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

127 

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

129 

130 @raise ValueError: Invalid C{B{wrap}=False}, unwrapped, unrolled longitudes not supported. 

131 

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

133 L{sphericalNvector.areaOf} and L{sphericalTrigonometry.areaOf}. 

134 

135 @note: The U{area of a polygon enclosing a pole<https://GeographicLib.SourceForge.io/ 

136 C++/doc/classGeographicLib_1_1GeodesicExact.html#a3d7a9155e838a09a48dc14d0c3fac525>} 

137 can be found by adding half the datum's ellipsoid surface area to the polygon's area. 

138 ''' 

139 return fabs(_polygon(datum.ellipsoid.geodesic, points, True, False, wrap)) 

140 

141 

142def intersection3(start1, end1, start2, end2, height=None, wrap=False, # was=True 

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

144 '''I{Iteratively} compute the intersection point of two lines, each defined 

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

146 (initial) bearing from North. 

147 

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

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

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

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

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

153 at the second point (compass C{degrees360}). 

154 @kwarg height: Optional height at the intersection (C{meter}, conventionally) 

155 or C{None} for the mean height. 

156 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the B{C{start2}} 

157 and B{C{end*}} points (C{bool}). 

158 @kwarg equidistant: An azimuthal equidistant projection (I{class} or function 

159 L{pygeodesy.equidistant}) or C{None} for the preferred 

160 C{B{start1}.Equidistant}. 

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

162 (C{meter}, conventionally). 

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

164 or C{None}. 

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

166 ignored if C{B{LatLon} is None}. 

167 

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

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

170 lon, height, datum)}. 

171 

172 @raise IntersectionError: Skew, colinear, parallel or otherwise 

173 non-intersecting lines or no convergence 

174 for the given B{C{tol}}. 

175 

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

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

178 

179 @note: For each line specified with an initial bearing, a pseudo-end point 

180 is computed as the C{destination} along that bearing at about 1.5 

181 times the distance from the start point to an initial gu-/estimate 

182 of the intersection point (and between 1/8 and 3/8 of the authalic 

183 earth perimeter). 

184 

185 @see: U{The B{ellipsoidal} case<https://GIS.StackExchange.com/questions/48937/ 

186 calculating-intersection-of-two-circles>} and U{Karney's paper 

187 <https://ArXiv.org/pdf/1102.1215.pdf>}, pp 20-21, section B{14. MARITIME 

188 BOUNDARIES} for more details about the iteration algorithm. 

189 ''' 

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

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

192 

193 

194def intersections2(center1, radius1, center2, radius2, height=None, wrap=False, # was=True 

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

196 '''I{Iteratively} compute the intersection points of two circles, each defined 

197 by an (ellipsoidal) center point and a radius. 

198 

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

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

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

202 @arg radius2: Radius of the second circle (C{meter}, same units as 

203 B{C{radius1}}). 

204 @kwarg height: Optional height for the intersection points (C{meter}, 

205 conventionally) or C{None} for the I{"radical height"} 

206 at the I{radical line} between both centers. 

207 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll B{C{center2}} 

208 (C{bool}). 

209 @kwarg equidistant: An azimuthal equidistant projection (I{class} or 

210 function L{pygeodesy.equidistant}) or C{None} for 

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

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

213 and B{C{radius2}}). 

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

215 or C{None}. 

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

217 ignored if C{B{LatLon} is None}. 

218 

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

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

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

222 aka the I{radical center}. 

223 

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

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

226 

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

228 or invalid B{C{equidistant}}. 

229 

230 @raise UnitError: Invalid B{C{radius1}}, B{C{radius2}} or B{C{height}}. 

231 

232 @see: U{The B{ellipsoidal} case<https://GIS.StackExchange.com/questions/48937/ 

233 calculating-intersection-of-two-circles>}, U{Karney's paper 

234 <https://ArXiv.org/pdf/1102.1215.pdf>}, pp 20-21, section B{14. MARITIME BOUNDARIES}, 

235 U{circle-circle<https://MathWorld.Wolfram.com/Circle-CircleIntersection.html>} and 

236 U{sphere-sphere<https://MathWorld.Wolfram.com/Sphere-SphereIntersection.html>} 

237 intersections. 

238 ''' 

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

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

241 

242 

243def isclockwise(points, datum=_WGS84, wrap=True): 

244 '''Determine the direction of a path or polygon using I{Karney}'s 

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

246 

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

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

249 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the 

250 B{C{points}} (C{bool}). 

251 

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

253 

254 @raise ImportError: Package U{geographiclib 

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

256 not installed or not found. 

257 

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

259 

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

261 

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

263 

264 @see: L{pygeodesy.isclockwise}. 

265 ''' 

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

267 if a < 0: 

268 return True 

269 elif a > 0: 

270 return False 

271 raise _areaError(points) 

272 

273 

274def nearestOn(point, point1, point2, within=True, height=None, wrap=False, 

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

276 '''I{Iteratively} locate the closest point on the geodesic between 

277 two other (ellipsoidal) points. 

278 

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

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

281 @arg point2: End point of the geodesic (C{LatLon}). 

282 @kwarg within: If C{True}, return the closest point I{between} 

283 B{C{point1}} and B{C{point2}}, otherwise the 

284 closest point elsewhere on the geodesic (C{bool}). 

285 @kwarg height: Optional height for the closest point (C{meter}, 

286 conventionally) or C{None} or C{False} for the 

287 interpolated height. If C{False}, the closest 

288 takes the heights of the points into account. 

289 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll both 

290 B{C{point1}} and B{C{point2}} (C{bool}). 

291 @kwarg equidistant: An azimuthal equidistant projection (I{class} 

292 or function L{pygeodesy.equidistant}) or C{None} 

293 for the preferred C{B{point}.Equidistant}. 

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

295 @kwarg LatLon: Optional class to return the closest point 

296 (L{LatLon}) or C{None}. 

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

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

299 

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

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

302 

303 @raise ImportError: Package U{geographiclib 

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

305 not installed or not found. 

306 

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

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

309 

310 @raise ValueError: No convergence for the B{C{tol}}. 

311 

312 @see: U{The B{ellipsoidal} case<https://GIS.StackExchange.com/questions/48937/ 

313 calculating-intersection-of-two-circles>} and U{Karney's paper 

314 <https://ArXiv.org/pdf/1102.1215.pdf>}, pp 20-21, section B{14. MARITIME 

315 BOUNDARIES} for more details about the iteration algorithm. 

316 ''' 

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

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

319 

320 

321def perimeterOf(points, closed=False, datum=_WGS84, wrap=True): 

322 '''Compute the perimeter of an (ellipsoidal) polygon or composite using I{Karney}'s 

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

324 

325 @arg points: The polygon points (L{LatLon}[], L{BooleanFHP} or 

326 L{BooleanGH}). 

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

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

329 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the 

330 B{C{points}} (C{bool}). 

331 

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

333 ellipsoid axes). 

334 

335 @raise ImportError: Package U{geographiclib 

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

337 not installed or not found. 

338 

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

340 

341 @raise TypeError: Some B{C{points}} are not L{LatLon} or C{B{closed}=False} 

342 with B{C{points}} a composite. 

343 

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

345 longitudes not supported or C{B{closed}=False} 

346 with C{B{points}} a composite. 

347 

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

349 L{ellipsoidalGeodSolve.perimeterOf}, L{sphericalNvector.perimeterOf} 

350 and L{sphericalTrigonometry.perimeterOf}. 

351 ''' 

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

353 

354 

355__all__ += _ALL_OTHER(Cartesian, LatLon, # classes 

356 areaOf, intersecant2, # from .ellipsoidalBase 

357 intersection3, intersections2, isclockwise, ispolar, 

358 nearestOn, perimeterOf) 

359 

360# **) MIT License 

361# 

362# Copyright (C) 2016-2025 -- mrJean1 at Gmail -- All Rights Reserved. 

363# 

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

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

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

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

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

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

370# 

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

372# in all copies or substantial portions of the Software. 

373# 

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

375# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, 

376# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL 

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