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, \ 

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 

42 

43# from math import fabs # from .karney 

44 

45__all__ = _ALL_LAZY.ellipsoidalKarney 

46__version__ = '24.02.21' 

47 

48 

49class Cartesian(CartesianEllipsoidalBase): 

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

51 C{Karney}-based L{LatLon} points. 

52 ''' 

53 

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

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

56 

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}. 

61 

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. 

65 

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) 

70 

71 

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. 

77 

78 @note: This L{LatLon} class requires the U{geographiclib 

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

80 ''' 

81 

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) 

87 

88 @Property_RO 

89 def Equidistant(self): 

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

91 ''' 

92 return _MODS.azimuthal.EquidistantKarney 

93 

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 

102 

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

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

105 

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}. 

110 

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. 

115 

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) 

121 

122 

123def areaOf(points, datum=_WGS84, wrap=True): 

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

125 

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}). 

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=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. 

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: 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}. 

185 

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)}. 

189 

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

191 non-intersecting lines or no convergence 

192 for the given B{C{tol}}. 

193 

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}}. 

196 

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). 

202 

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) 

210 

211 

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. 

216 

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}. 

236 

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}. 

241 

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

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

244 

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

246 or invalid B{C{equidistant}}. 

247 

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

249 

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) 

259 

260 

261def isclockwise(points, datum=_WGS84, wrap=True): 

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

263 

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}). 

268 

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

270 

271 @raise ImportError: Package U{geographiclib 

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

273 not installed or not found. 

274 

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

276 

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

278 

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

280 area. 

281 

282 @note: This function requires the U{geographiclib 

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

284 

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) 

293 

294 

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. 

299 

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}. 

320 

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)}. 

323 

324 @raise ImportError: Package U{geographiclib 

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

326 not installed or not found. 

327 

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

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

330 

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

332 

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) 

340 

341 

342def perimeterOf(points, closed=False, datum=_WGS84, wrap=True): 

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

344 

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}). 

351 

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

353 ellipsoid axes). 

354 

355 @raise ImportError: Package U{geographiclib 

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

357 not installed or not found. 

358 

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

360 

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

362 with B{C{points}} a composite. 

363 

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. 

367 

368 @note: This function requires the U{geographiclib 

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

370 

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) 

376 

377 

378__all__ += _ALL_OTHER(Cartesian, LatLon, # classes 

379 areaOf, intersecant2, # from .ellipsoidalBase 

380 intersection3, intersections2, isclockwise, ispolar, 

381 nearestOn, perimeterOf) 

382 

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 

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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 

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