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__ = '23.05.12' 

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

131 B{C{points}} (C{bool}). 

132 

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

134 ellipsoid axes, I{squared}). 

135 

136 @raise ImportError: Package U{geographiclib 

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

138 not installed or not found. 

139 

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

141 

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

143 

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

145 longitudes not supported. 

146 

147 @note: This function requires the U{geographiclib 

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

149 

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

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

152 and L{sphericalTrigonometry.areaOf}. 

153 

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

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

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

157 ''' 

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

159 

160 

161def intersection3(start1, end1, start2, end2, height=None, wrap=False, # was=True 

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

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

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

165 (initial) bearing from North. 

166 

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

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

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

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

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

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

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

174 or C{None} for the mean height. 

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

176 and B{C{end*}} points (C{bool}). 

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

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

179 C{B{start1}.Equidistant}. 

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

181 (C{meter}, conventionally). 

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

183 or C{None}. 

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

185 ignored if C{B{LatLon} is None}. 

186 

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

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

189 lon, height, datum)}. 

190 

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

192 non-intersecting lines or no convergence 

193 for the given B{C{tol}}. 

194 

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

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

197 

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

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

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

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

202 earth perimeter). 

203 

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

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

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

207 BOUNDARIES} for more details about the iteration algorithm. 

208 ''' 

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

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

211 

212 

213def intersections2(center1, radius1, center2, radius2, height=None, wrap=False, # was=True 

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

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

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

217 

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

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

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

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

222 B{C{radius1}}). 

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

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

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

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

227 (C{bool}). 

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

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

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

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

232 and B{C{radius2}}). 

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

234 or C{None}. 

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

236 ignored if C{B{LatLon} is None}. 

237 

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

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

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

241 aka the I{radical center}. 

242 

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

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

245 

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

247 or invalid B{C{equidistant}}. 

248 

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

250 

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

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

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

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

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

256 intersections. 

257 ''' 

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

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

260 

261 

262def isclockwise(points, datum=_WGS84, wrap=True): 

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

264 

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

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

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

268 B{C{points}} (C{bool}). 

269 

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

271 

272 @raise ImportError: Package U{geographiclib 

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

274 not installed or not found. 

275 

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

277 

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

279 

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

281 area. 

282 

283 @note: This function requires the U{geographiclib 

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

285 

286 @see: L{pygeodesy.isclockwise}. 

287 ''' 

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

289 if a < 0: 

290 return True 

291 elif a > 0: 

292 return False 

293 raise _areaError(points) 

294 

295 

296def nearestOn(point, point1, point2, within=True, height=None, wrap=False, 

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

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

299 two other (ellipsoidal) points. 

300 

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

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

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

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

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

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

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

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

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

310 takes the heights of the points into account. 

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

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

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

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

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

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

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

318 (L{LatLon}) or C{None}. 

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

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

321 

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

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

324 

325 @raise ImportError: Package U{geographiclib 

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

327 not installed or not found. 

328 

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

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

331 

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

333 

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

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

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

337 BOUNDARIES} for more details about the iteration algorithm. 

338 ''' 

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

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

341 

342 

343def perimeterOf(points, closed=False, datum=_WGS84, wrap=True): 

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

345 

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

347 L{BooleanGH}). 

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

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

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

351 B{C{points}} (C{bool}). 

352 

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

354 ellipsoid axes). 

355 

356 @raise ImportError: Package U{geographiclib 

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

358 not installed or not found. 

359 

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

361 

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

363 with B{C{points}} a composite. 

364 

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

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

367 with C{B{points}} a composite. 

368 

369 @note: This function requires the U{geographiclib 

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

371 

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

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

374 and L{sphericalTrigonometry.perimeterOf}. 

375 ''' 

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

377 

378 

379__all__ += _ALL_OTHER(Cartesian, LatLon, # classes 

380 areaOf, # functions 

381 intersection3, intersections2, isclockwise, ispolar, 

382 nearestOn, perimeterOf) 

383 

384# **) MIT License 

385# 

386# Copyright (C) 2016-2023 -- mrJean1 at Gmail -- All Rights Reserved. 

387# 

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

394# 

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397# 

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