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 

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. 

11 

12Here's an example usage of C{ellipsoidalKarney}: 

13 

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 

19 

20You can change the ellipsoid model used by the I{Karney} formulae 

21as follows: 

22 

23 >>> from pygeodesy import Datums 

24 >>> from pygeodesy.ellipsoidalKarney import LatLon 

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

26 

27or by converting to anothor datum: 

28 

29 >>> p = p.toDatum(Datums.OSGB36) 

30''' 

31 

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 

41 

42# from math import fabs # from .karney 

43 

44__all__ = _ALL_LAZY.ellipsoidalKarney 

45__version__ = '23.04.11' 

46 

47 

48class Cartesian(CartesianEllipsoidalBase): 

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

50 C{Karney}-based L{LatLon} points. 

51 ''' 

52 

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

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

55 

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}. 

60 

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. 

64 

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) 

69 

70 

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. 

78 

79 @note: This L{LatLon} require the U{geographiclib 

80 <https://PyPI.org/project/geographiclib>} package. 

81 ''' 

82 

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) 

88 

89 @Property_RO 

90 def Equidistant(self): 

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

92 ''' 

93 return _MODS.azimuthal.EquidistantKarney 

94 

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 

103 

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

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

106 

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}. 

111 

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. 

116 

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) 

122 

123 

124def areaOf(points, datum=_WGS84, wrap=True): 

125 '''Compute the area of an (ellipsoidal) polygon or composite. 

126 

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}). 

131 

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

133 ellipsoid axes, I{squared}). 

134 

135 @raise ImportError: Package U{geographiclib 

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

137 not installed or not found. 

138 

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

140 

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

142 

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

144 longitudes not supported. 

145 

146 @note: This function requires the U{geographiclib 

147 <https://PyPI.org/project/geographiclib>} package. 

148 

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

150 L{ellipsoidalGeodSolve.areaOf}, L{sphericalNvector.areaOf} 

151 and L{sphericalTrigonometry.areaOf}. 

152 

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)) 

158 

159 

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. 

165 

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}. 

184 

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)}. 

188 

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

190 non-intersecting lines or no convergence 

191 for the given B{C{tol}}. 

192 

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}}. 

195 

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). 

201 

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) 

209 

210 

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. 

215 

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}. 

234 

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}. 

239 

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

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

242 

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

244 or invalid B{C{equidistant}}. 

245 

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

247 

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) 

257 

258 

259def isclockwise(points, datum=_WGS84, wrap=True): 

260 '''Determine the direction of a path or polygon. 

261 

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}). 

265 

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

267 

268 @raise ImportError: Package U{geographiclib 

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

270 not installed or not found. 

271 

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

273 

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

275 

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

277 area. 

278 

279 @note: This function requires the U{geographiclib 

280 <https://PyPI.org/project/geographiclib>} package. 

281 

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) 

290 

291 

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. 

296 

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}. 

316 

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)}. 

319 

320 @raise ImportError: Package U{geographiclib 

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

322 not installed or not found. 

323 

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

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

326 

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

328 

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) 

336 

337 

338def perimeterOf(points, closed=False, datum=_WGS84, wrap=True): 

339 '''Compute the perimeter of an (ellipsoidal) polygon or composite. 

340 

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}). 

346 

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

348 ellipsoid axes). 

349 

350 @raise ImportError: Package U{geographiclib 

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

352 not installed or not found. 

353 

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

355 

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

357 with B{C{points}} a composite. 

358 

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. 

362 

363 @note: This function requires the U{geographiclib 

364 <https://PyPI.org/project/geographiclib>} package. 

365 

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) 

371 

372 

373__all__ += _ALL_OTHER(Cartesian, LatLon, # classes 

374 areaOf, # functions 

375 intersection3, intersections2, isclockwise, ispolar, 

376 nearestOn, perimeterOf) 

377 

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 

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

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

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 

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

391# 

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

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

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

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