Coverage for pygeodesy/ellipsoidalBase.py: 94%

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1 

2# -*- coding: utf-8 -*- 

3 

4u'''(INTERNAL) Private ellipsoidal base classes C{CartesianEllipsoidalBase} 

5and C{LatLonEllipsoidalBase}. 

6 

7A pure Python implementation of geodesy tools for ellipsoidal earth models, 

8transcoded in part from JavaScript originals by I{(C) Chris Veness 2005-2024} 

9and published under the same MIT Licence**, see for example U{latlon-ellipsoidal 

10<https://www.Movable-Type.co.UK/scripts/geodesy/docs/latlon-ellipsoidal.js.html>}. 

11''' 

12# make sure int/int division yields float quotient, see .basics 

13from __future__ import division as _; del _ # PYCHOK semicolon 

14 

15# from pygeodesy.basics import _xinstanceof # from .datums 

16from pygeodesy.constants import EPS, EPS0, EPS1, _0_0, _0_5 

17from pygeodesy.cartesianBase import CartesianBase # PYCHOK used! 

18from pygeodesy.datums import Datum, Datums, _earth_ellipsoid, _ellipsoidal_datum, \ 

19 Transform, _WGS84, _EWGS84, _xinstanceof # _spherical_datum 

20# from pygeodesy.ellipsoids import _EWGS84 # from .datums 

21from pygeodesy.errors import _IsnotError, RangeError, _TypeError, _xattr, _xellipsoidal, \ 

22 _xellipsoids, _xError, _xkwds, _xkwds_not 

23# from pygeodesy.fmath import favg # _MODS 

24from pygeodesy.interns import NN, _COMMA_, _ellipsoidal_ 

25from pygeodesy.latlonBase import LatLonBase, _trilaterate5, fabs, _Wrap 

26from pygeodesy.lazily import _ALL_DOCS, _ALL_LAZY, _ALL_MODS as _MODS 

27# from pygeodesy.lcc import toLcc # _MODS 

28# from pygeodesy.namedTuples import Vector3Tuple # _MODS 

29from pygeodesy.props import deprecated_method, deprecated_property_RO, \ 

30 Property_RO, property_doc_, property_RO, _update_all 

31# from pygeodesy.trf import _eT0Ds4 # _MODS 

32from pygeodesy.units import Epoch, _isDegrees, Radius_, _1mm as _TOL_M 

33# from pygeodesy.utily import _Wrap # from .latlonBase 

34 

35# from math import fabs # from .latlonBase 

36 

37__all__ = _ALL_LAZY.ellipsoidalBase 

38__version__ = '24.12.04' 

39 

40 

41class CartesianEllipsoidalBase(CartesianBase): 

42 '''(INTERNAL) Base class for ellipsoidal C{Cartesian}s. 

43 ''' 

44 _datum = _WGS84 # L{Datum} 

45 _epoch = None # overriding .reframe.epoch (C{float}) 

46 _reframe = None # reference frame (L{RefFrame}) 

47 

48 def __init__(self, x_xyz, y=None, z=None, reframe=None, epoch=None, 

49 **datum_ll_name): 

50 '''New ellispoidal C{Cartesian...}. 

51 

52 @kwarg reframe: Optional reference frame (L{RefFrame}). 

53 @kwarg epoch: Optional epoch to observe for B{C{reframe}} (C{scalar}), 

54 a non-zero, fractional calendar year; silently ignored 

55 if C{B{reframe}=None}. 

56 

57 @raise TypeError: Non-scalar B{C{x_xyz}}, B{C{y}} or B{C{z}} coordinate 

58 or B{C{x_xyz}} not a C{Cartesian} L{Ecef9Tuple}, 

59 L{Vector3Tuple} or L{Vector4Tuple} or B{C{datum}} is 

60 not a L{Datum}, B{C{reframe}} is not a L{RefFrame} or 

61 B{C{epoch}} is not C{scalar} non-zero. 

62 

63 @see: Class L{CartesianBase<CartesianBase.__init__>} for more details. 

64 ''' 

65 CartesianBase.__init__(self, x_xyz, y=y, z=z, **datum_ll_name) 

66 if reframe: 

67 self.reframe = reframe 

68 self.epoch = epoch 

69 

70# def __matmul__(self, other): # PYCHOK Python 3.5+ 

71# '''Return C{NotImplemented} for C{c_ = c @ datum}, C{c_ = c @ reframe} and C{c_ = c @ Transform}. 

72# ''' 

73# RefFrame = _MODS.trf.RefFrame 

74# return NotImplemented if isinstance(other, (Datum, RefFrame, Transform)) else \ 

75# _NotImplemented(self, other) 

76 

77 @deprecated_method 

78 def convertRefFrame(self, reframe2, reframe, epoch=None): 

79 '''DEPRECATED, use method L{toRefFrame}.''' 

80 return self.toRefFrame(reframe2, reframe=reframe, epoch=epoch) # PYCHOK no cover 

81 

82 @property_RO 

83 def ellipsoidalCartesian(self): 

84 '''Get this C{Cartesian}'s ellipsoidal class. 

85 ''' 

86 return type(self) 

87 

88 @property_doc_(''' this cartesian's observed or C{reframe} epoch (C{float}).''') 

89 def epoch(self): 

90 '''Get this cartesian's observed or C{reframe} epoch (C{Epoch}) or C{None}. 

91 ''' 

92 return self._epoch or (self.reframe.epoch if self.reframe else None) 

93 

94 @epoch.setter # PYCHOK setter! 

95 def epoch(self, epoch): 

96 '''Set or clear this cartesian's observed epoch, a fractional 

97 calendar year (L{Epoch}, C{scalar} or C{str}) or C{None}. 

98 

99 @raise TRFError: Invalid B{C{epoch}}. 

100 ''' 

101 self._epoch = None if epoch is None else Epoch(epoch) 

102 

103 def intersections2(self, radius, center2, radius2, sphere=True, 

104 Vector=None, **Vector_kwds): 

105 '''Compute the intersection of two spheres or circles, each defined by a 

106 cartesian center point and a radius. 

107 

108 @arg radius: Radius of this sphere or circle (same units as this point's 

109 coordinates). 

110 @arg center2: Center of the second sphere or circle (C{Cartesian}, L{Vector3d}, 

111 C{Vector3Tuple} or C{Vector4Tuple}). 

112 @arg radius2: Radius of the second sphere or circle (same units as this and 

113 the B{C{other}} point's coordinates). 

114 @kwarg sphere: If C{True}, compute the center and radius of the intersection 

115 of two I{spheres}. If C{False}, ignore the C{z}-component and 

116 compute the intersection of two I{circles} (C{bool}). 

117 @kwarg Vector: Class to return intersections (C{Cartesian}, L{Vector3d} or 

118 C{Vector3Tuple}) or C{None} for an instance of this (sub-)class. 

119 @kwarg Vector_kwds: Optional, additional B{C{Vector}} keyword arguments, 

120 ignored if C{B{Vector} is None}. 

121 

122 @return: If C{B{sphere} is True}, a 2-tuple of the C{center} and C{radius} of 

123 the intersection of the I{spheres}. The C{radius} is C{0.0} for 

124 abutting spheres (and the C{center} is aka the I{radical center}). 

125 

126 If C{B{sphere} is False}, a 2-tuple with the two intersection points 

127 of the I{circles}. For abutting circles, both points are the same 

128 instance, aka the I{radical center}. 

129 

130 @raise IntersectionError: Concentric, invalid or non-intersecting spheres or circles. 

131 

132 @raise TypeError: Invalid B{C{center2}}. 

133 

134 @raise UnitError: Invalid B{C{radius}} or B{C{radius2}}. 

135 

136 @see: U{Sphere-Sphere<https://MathWorld.Wolfram.com/Sphere-SphereIntersection.html>}, 

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

138 Intersection and function L{pygeodesy.radical2}. 

139 ''' 

140 try: 

141 return _MODS.vector3d._intersects2(self, Radius_(radius=radius), 

142 center2, Radius_(radius2=radius2), 

143 sphere=sphere, clas=self.classof, 

144 Vector=Vector, **Vector_kwds) 

145 except (TypeError, ValueError) as x: 

146 raise _xError(x, center=self, radius=radius, center2=center2, radius2=radius2) 

147 

148 @property_doc_(''' this cartesian's reference frame (L{RefFrame}).''') 

149 def reframe(self): 

150 '''Get this cartesian's reference frame (L{RefFrame}) or C{None}. 

151 ''' 

152 return self._reframe 

153 

154 @reframe.setter # PYCHOK setter! 

155 def reframe(self, reframe): 

156 '''Set or clear this cartesian's reference frame (L{RefFrame}) or C{None}. 

157 

158 @raise TypeError: The B{C{reframe}} is not a L{RefFrame}. 

159 ''' 

160 _set_reframe(self, reframe) 

161 

162 def toLatLon(self, datum=None, height=None, **LatLon_and_kwds): # PYCHOK signature 

163 '''Convert this cartesian to a I{geodetic} (lat-/longitude) point. 

164 

165 @see: Method L{toLatLon<cartesianBase.CartesianBase.toLatLon>} 

166 for further details. 

167 ''' 

168 kwds = LatLon_and_kwds 

169 if kwds: 

170 kwds = _xkwds(kwds, reframe=self.reframe, epoch=self.epoch) 

171 return CartesianBase.toLatLon(self, datum=datum, height=height, **kwds) 

172 

173 def toRefFrame(self, reframe2, reframe=None, epoch=None, epoch2=None, **name): 

174 '''Convert this point to an other reference frame and epoch. 

175 

176 @arg reframe2: Reference frame to convert I{to} (L{RefFrame}). 

177 @kwarg reframe: Optional reference frame to convert I{from} (L{RefFrame}), 

178 overriding this point's reference frame. 

179 @kwarg epoch: Optional epoch (L{Epoch}, C{scalar} or C{str}), overriding 

180 this point's C{epoch or B{reframe}.epoch}. 

181 @kwarg epoch2: Optional epoch to observe for the converted point (L{Epoch}, 

182 C{scalar} or C{str}), otherwise B{C{epoch}}. 

183 @kwarg name: Optional C{B{name}=NN} (C{str}), overriding C{B{reframe2}.name}. 

184 

185 @return: The converted point (ellipsoidal C{Cartesian}) or if conversion 

186 C{isunity}, this point or a copy of this point if the B{C{name}} 

187 is non-empty. 

188 

189 @raise TRFError: This point's C{reframe} is not defined, invalid B{C{epoch}} 

190 or B{C{epoch2}} or conversion from this point's C{reframe} 

191 to B{C{reframe2}} is not available. 

192 

193 @raise TypeError: B{C{reframe2}} or B{C{reframe}} not a L{RefFrame}. 

194 ''' 

195 return _MODS.trf._toRefFrame(self, reframe2, reframe=reframe, epoch=epoch, 

196 epoch2=epoch2, **name) 

197 

198 @deprecated_method 

199 def toTransforms_(self, *transforms, **datum): # PYCHOK no cover 

200 '''DEPRECATED on 2024.02.14, use method C{toTransform}.''' 

201 r = self 

202 for t in transforms: 

203 r = r.toTransform(t) 

204 return r.dup(**datum) if datum else r 

205 

206 

207class LatLonEllipsoidalBase(LatLonBase): 

208 '''(INTERNAL) Base class for ellipsoidal C{LatLon}s. 

209 ''' 

210 _datum = _WGS84 # L{Datum} 

211 _elevation2to = None # _elevation2 timeout (C{secs}) 

212 _epoch = None # overriding .reframe.epoch (C{float}) 

213 _gamma = None # UTM/UPS meridian convergence (C{degrees}) 

214 _geoidHeight2to = None # _geoidHeight2 timeout (C{secs}) 

215 _reframe = None # reference frame (L{RefFrame}) 

216 _scale = None # UTM/UPS scale factor (C{float}) 

217 _toLLEB_args = () # Etm/Utm/Ups._toLLEB arguments 

218 

219 def __init__(self, latlonh, lon=None, height=0, datum=_WGS84, reframe=None, 

220 epoch=None, wrap=False, **name): 

221 '''Create an ellipsoidal C{LatLon} point from the given lat-, longitude 

222 and height on the given datum, reference frame and epoch. 

223 

224 @arg latlonh: Latitude (C{degrees} or DMS C{str} with N or S suffix) or 

225 a previous C{LatLon} instance provided C{B{lon}=None}. 

226 @kwarg lon: Longitude (C{degrees} or DMS C{str} with E or W suffix) or C(None), 

227 indicating B{C{latlonh}} is a C{LatLon}. 

228 @kwarg height: Optional height above (or below) the earth surface (C{meter}, 

229 same units as the datum's ellipsoid axes). 

230 @kwarg datum: Optional, ellipsoidal datum to use (L{Datum}, L{Ellipsoid}, 

231 L{Ellipsoid2} or L{a_f2Tuple}). 

232 @kwarg reframe: Optional reference frame (L{RefFrame}). 

233 @kwarg epoch: Optional epoch to observe for B{C{reframe}} (C{scalar}), a 

234 non-zero, fractional calendar year, but silently ignored if 

235 C{B{reframe}=None}. 

236 @kwarg wrap: If C{True}, wrap or I{normalize} B{C{lat}} and B{C{lon}} (C{bool}). 

237 @kwarg name: Optional C{B{name}=NN} (C{str}). 

238 

239 @raise RangeError: Value of C{lat} or B{C{lon}} outside the valid range and 

240 L{rangerrors} set to C{True}. 

241 

242 @raise TypeError: If B{C{latlonh}} is not a C{LatLon}, B{C{datum}} is not a 

243 L{Datum}, B{C{reframe}} is not a L{RefFrame} or B{C{epoch}} 

244 is not C{scalar} non-zero. 

245 

246 @raise UnitError: Invalid B{C{lat}}, B{C{lon}} or B{C{height}}. 

247 ''' 

248 LatLonBase.__init__(self, latlonh, lon=lon, height=height, wrap=wrap, **name) 

249 if datum not in (None, self._datum, _EWGS84): 

250 self.datum = _ellipsoidal_datum(datum, name=self.name) 

251 if reframe: 

252 self.reframe = reframe 

253 self.epoch = epoch 

254 

255# def __matmul__(self, other): # PYCHOK Python 3.5+ 

256# '''Return C{NotImplemented} for C{ll_ = ll @ datum} and C{ll_ = ll @ reframe}. 

257# ''' 

258# RefFrame = _MODS.trf.RefFrame 

259# return NotImplemented if isinstance(other, (Datum, RefFrame)) else \ 

260# _NotImplemented(self, other) 

261 

262 def antipode(self, height=None): 

263 '''Return the antipode, the point diametrically opposite 

264 to this point. 

265 

266 @kwarg height: Optional height of the antipode, height 

267 of this point otherwise (C{meter}). 

268 

269 @return: The antipodal point (C{LatLon}). 

270 ''' 

271 lla = LatLonBase.antipode(self, height=height) 

272 if lla.datum != self.datum: 

273 lla.datum = self.datum 

274 return lla 

275 

276 @deprecated_property_RO 

277 def convergence(self): 

278 '''DEPRECATED, use property C{gamma}.''' 

279 return self.gamma # PYCHOK no cover 

280 

281 @deprecated_method 

282 def convertDatum(self, datum2): 

283 '''DEPRECATED, use method L{toDatum}.''' 

284 return self.toDatum(datum2) 

285 

286 @deprecated_method 

287 def convertRefFrame(self, reframe2): 

288 '''DEPRECATED, use method L{toRefFrame}.''' 

289 return self.toRefFrame(reframe2) 

290 

291 @property_doc_(''' this points's datum (L{Datum}).''') 

292 def datum(self): 

293 '''Get this point's datum (L{Datum}). 

294 ''' 

295 return self._datum 

296 

297 @datum.setter # PYCHOK setter! 

298 def datum(self, datum): 

299 '''Set this point's datum I{without conversion} (L{Datum}). 

300 

301 @raise TypeError: The B{C{datum}} is not a L{Datum} or not ellipsoidal. 

302 ''' 

303 _xinstanceof(Datum, datum=datum) 

304 if not datum.isEllipsoidal: 

305 raise _IsnotError(_ellipsoidal_, datum=datum) 

306 if self._datum != datum: 

307 _update_all(self) 

308 self._datum = datum 

309 

310 def distanceTo2(self, other, wrap=False): 

311 '''I{Approximate} the distance and (initial) bearing between this 

312 and an other (ellipsoidal) point based on the radii of curvature. 

313 

314 I{Suitable only for short distances up to a few hundred Km 

315 or Miles and only between points not near-polar}. 

316 

317 @arg other: The other point (C{LatLon}). 

318 @kwarg wrap: If C{True}, wrap or I{normalize} the B{C{other}} 

319 point (C{bool}). 

320 

321 @return: An L{Distance2Tuple}C{(distance, initial)}. 

322 

323 @raise TypeError: The B{C{other}} point is not C{LatLon}. 

324 

325 @raise ValueError: Incompatible datum ellipsoids. 

326 

327 @see: Method L{Ellipsoid.distance2} and U{Local, flat earth 

328 approximation<https://www.EdWilliams.org/avform.htm#flat>} 

329 aka U{Hubeny<https://www.OVG.AT/de/vgi/files/pdf/3781/>} 

330 formula. 

331 ''' 

332 p = self.others(other) 

333 if wrap: # PYCHOK no cover 

334 p = _Wrap.point(p) 

335 E = self.ellipsoids(other) 

336 return E.distance2(*(self.latlon + p.latlon)) 

337 

338 @Property_RO 

339 def _elevation2(self): 

340 '''(INTERNAL) Get elevation and data source. 

341 ''' 

342 return _MODS.elevations.elevation2(self.lat, self.lon, 

343 timeout=self._elevation2to) 

344 

345 def elevation2(self, adjust=True, datum=None, timeout=2): 

346 '''Return elevation of this point for its or the given datum, ellipsoid 

347 or sphere. 

348 

349 @kwarg adjust: Adjust the elevation for a B{C{datum}} other than 

350 C{NAD83} (C{bool}). 

351 @kwarg datum: Optional datum overriding this point's datum (L{Datum}, 

352 L{Ellipsoid}, L{Ellipsoid2}, L{a_f2Tuple} or C{scalar} 

353 radius). 

354 @kwarg timeout: Optional query timeout (C{seconds}). 

355 

356 @return: An L{Elevation2Tuple}C{(elevation, data_source)} or 

357 C{(None, error)} in case of errors. 

358 

359 @note: The adjustment applied is the difference in geocentric earth 

360 radius between the B{C{datum}} and C{NAV83} upon which the 

361 L{elevations.elevation2} is based. 

362 

363 @note: NED elevation is only available for locations within the U{Conterminous 

364 US (CONUS)<https://WikiPedia.org/wiki/Contiguous_United_States>}. 

365 

366 @see: Function L{elevations.elevation2} and method C{Ellipsoid.Rgeocentric} 

367 for further details and possible C{error}s. 

368 ''' 

369 if self._elevation2to != timeout: 

370 self._elevation2to = timeout 

371 LatLonEllipsoidalBase._elevation2._update(self) 

372 return self._Radjust2(adjust, datum, self._elevation2) 

373 

374 def ellipsoid(self, datum=_WGS84): 

375 '''Return the ellipsoid of this point's datum or the given datum. 

376 

377 @kwarg datum: Default datum (L{Datum}). 

378 

379 @return: The ellipsoid (L{Ellipsoid} or L{Ellipsoid2}). 

380 ''' 

381 return _xattr(self, datum=datum).ellipsoid 

382 

383 @property_RO 

384 def ellipsoidalLatLon(self): 

385 '''Get this C{LatLon}'s ellipsoidal class. 

386 ''' 

387 return type(self) 

388 

389 def ellipsoids(self, other): 

390 '''Check the type and ellipsoid of this and an other point's datum. 

391 

392 @arg other: The other point (C{LatLon}). 

393 

394 @return: This point's datum ellipsoid (L{Ellipsoid} or L{Ellipsoid2}). 

395 

396 @raise TypeError: The B{C{other}} point is not C{LatLon}. 

397 

398 @raise ValueError: Incompatible datum ellipsoids. 

399 ''' 

400 self.others(other, up=2) # ellipsoids' caller 

401 

402 E = self.ellipsoid() 

403 try: # other may be Sphere, etc. 

404 e = other.ellipsoid() 

405 except AttributeError: 

406 try: # no ellipsoid method, try datum 

407 e = other.datum.ellipsoid 

408 except AttributeError: 

409 e = E # no datum, XXX assume equivalent? 

410 return _xellipsoids(E, e) 

411 

412 @property_doc_(''' this point's observed or C{reframe} epoch (C{float}).''') 

413 def epoch(self): 

414 '''Get this point's observed or C{reframe} epoch (L{Epoch}) or C{None}. 

415 ''' 

416 return self._epoch or (self.reframe.epoch if self.reframe else None) 

417 

418 @epoch.setter # PYCHOK setter! 

419 def epoch(self, epoch): 

420 '''Set or clear this point's observed epoch, a fractional 

421 calendar year (L{Epoch}, C{scalar} or C{str}) or C{None}. 

422 

423 @raise TRFError: Invalid B{C{epoch}}. 

424 ''' 

425 self._epoch = None if epoch is None else Epoch(epoch) 

426 

427 @Property_RO 

428 def Equidistant(self): 

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

430 ''' 

431 try: 

432 _ = self.datum.ellipsoid.geodesic 

433 return _MODS.azimuthal.EquidistantKarney 

434 except ImportError: # no geographiclib 

435 return _MODS.azimuthal.EquidistantExact # XXX no longer L{azimuthal.Equidistant} 

436 

437 @Property_RO 

438 def _etm(self): 

439 '''(INTERNAL) Get this C{LatLon} point as an ETM coordinate (L{pygeodesy.toEtm8}). 

440 ''' 

441 etm = _MODS.etm 

442 return etm.toEtm8(self, datum=self.datum, Etm=etm.Etm) 

443 

444 @property_RO 

445 def gamma(self): 

446 '''Get this point's UTM or UPS meridian convergence (C{degrees}) or 

447 C{None} if not available or not converted from L{Utm} or L{Ups}. 

448 ''' 

449 return self._gamma 

450 

451 @Property_RO 

452 def _geoidHeight2(self): 

453 '''(INTERNAL) Get geoid height and model. 

454 ''' 

455 return _MODS.elevations.geoidHeight2(self.lat, self.lon, model=0, 

456 timeout=self._geoidHeight2to) 

457 

458 def geoidHeight2(self, adjust=False, datum=None, timeout=2): 

459 '''Return geoid height of this point for its or the given datum, ellipsoid 

460 or sphere. 

461 

462 @kwarg adjust: Adjust the geoid height for a B{C{datum}} other than 

463 C{NAD83/NADV88} (C{bool}). 

464 @kwarg datum: Optional datum overriding this point's datum (L{Datum}, 

465 L{Ellipsoid}, L{Ellipsoid2}, L{a_f2Tuple} or C{scalar} 

466 radius). 

467 @kwarg timeout: Optional query timeout (C{seconds}). 

468 

469 @return: A L{GeoidHeight2Tuple}C{(height, model_name)} or 

470 C{(None, error)} in case of errors. 

471 

472 @note: The adjustment applied is the difference in geocentric earth 

473 radius between the B{C{datum}} and C{NAV83/NADV88} upon which 

474 the L{elevations.geoidHeight2} is based. 

475 

476 @note: The geoid height is only available for locations within the U{Conterminous 

477 US (CONUS)<https://WikiPedia.org/wiki/Contiguous_United_States>}. 

478 

479 @see: Function L{elevations.geoidHeight2} and method C{Ellipsoid.Rgeocentric} 

480 for further details and possible C{error}s. 

481 ''' 

482 if self._geoidHeight2to != timeout: 

483 self._geoidHeight2to = timeout 

484 LatLonEllipsoidalBase._geoidHeight2._update(self) 

485 return self._Radjust2(adjust, datum, self._geoidHeight2) 

486 

487 def intermediateTo(self, other, fraction, height=None, wrap=False): # PYCHOK no cover 

488 '''I{Must be overloaded}.''' 

489 self._notOverloaded(other, fraction, height=height, wrap=wrap) 

490 

491 def intersection3(self, end1, start2, end2, height=None, wrap=False, # was=True 

492 equidistant=None, tol=_TOL_M): 

493 '''I{Iteratively} compute the intersection point of two geodesic lines, each 

494 given as two points or as a start point and a bearing from North. 

495 

496 @arg end1: End point of this line (C{LatLon}) or the initial bearing at 

497 this point (compass C{degrees360}). 

498 @arg start2: Start point of the second line (this C{LatLon}). 

499 @arg end2: End point of the second line (this C{LatLon}) or the initial 

500 bearing at B{C{start2}} (compass C{degrees360}). 

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

502 or C{None} for the mean height. 

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

504 both B{C{end*}} points (C{bool}). 

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

506 L{pygeodesy.equidistant}), or C{None} for this point's 

507 preferred C{.Equidistant}. 

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

509 (C{meter}, conventionally). 

510 

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

512 a C{LatLon} instance. 

513 

514 @raise ImportError: Package U{geographiclib 

515 <https://PyPI.org/project/geographiclib>} not 

516 installed or not found, but only in case 

517 C{B{equidistant}=}L{EquidistantKarney}. 

518 

519 @raise IntersectionError: Skew, colinear, parallel or otherwise non-intersecting 

520 lines or no convergence for the given B{C{tol}}. 

521 

522 @raise TypeError: Invalid B{C{end1}}, B{C{start2}} or B{C{end2}}. 

523 

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

525 computed as the C{destination} along that bearing at about 1.5 times the 

526 distance from the start point to an initial gu-/estimate of the intersection 

527 point (and between 1/8 and 3/8 of the C{authalic} earth perimeter). 

528 

529 @see: I{Karney's} U{intersect.cpp<https://SourceForge.net/p/geographiclib/ 

530 discussion/1026621/thread/21aaff9f/>}, U{The B{ellipsoidal} case<https:// 

531 GIS.StackExchange.com/questions/48937/calculating-intersection-of-two-circles>} 

532 and U{Karney's paper<https://ArXiv.org/pdf/1102.1215.pdf>}, pp 20-21, section 

533 B{14. MARITIME BOUNDARIES} for more details about the iteration algorithm. 

534 ''' 

535 try: 

536 s2 = self.others(start2=start2) 

537 return _MODS.ellipsoidalBaseDI._intersect3(self, end1, 

538 s2, end2, 

539 height=height, wrap=wrap, 

540 equidistant=equidistant, tol=tol, 

541 LatLon=self.classof, datum=self.datum) 

542 except (TypeError, ValueError) as x: 

543 raise _xError(x, start1=self, end1=end1, start2=start2, end2=end2, 

544 height=height, wrap=wrap, tol=tol) 

545 

546 def intersections2(self, radius1, center2, radius2, height=None, wrap=False, # was=True 

547 equidistant=None, tol=_TOL_M): 

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

549 defined by a center point and a radius. 

550 

551 @arg radius1: Radius of this circle (C{meter}, conventionally). 

552 @arg center2: Center of the other circle (this C{LatLon}). 

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

554 B{C{radius1}}). 

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

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

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

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

559 (C{bool}). 

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

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

562 for this point's preferred C{.Equidistant}. 

563 @kwarg tol: Convergence tolerance (C{meter}, same units as 

564 B{C{radius1}} and B{C{radius2}}). 

565 

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

567 instance. For abutting circles, both intersection 

568 points are the same instance, aka the I{radical center}. 

569 

570 @raise ImportError: Package U{geographiclib 

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

572 not installed or not found, but only if 

573 C{B{equidistant}=}L{EquidistantKarney}. 

574 

575 @raise IntersectionError: Concentric, antipodal, invalid or 

576 non-intersecting circles or no 

577 convergence for the given B{C{tol}}. 

578 

579 @raise TypeError: Invalid B{C{center2}} or B{C{equidistant}}. 

580 

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

582 

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

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

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

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

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

588 intersections. 

589 ''' 

590 try: 

591 c2 = self.others(center2=center2) 

592 return _MODS.ellipsoidalBaseDI._intersections2(self, radius1, 

593 c2, radius2, 

594 height=height, wrap=wrap, 

595 equidistant=equidistant, tol=tol, 

596 LatLon=self.classof, datum=self.datum) 

597 except (AssertionError, TypeError, ValueError) as x: 

598 raise _xError(x, center=self, radius1=radius1, center2=center2, radius2=radius2, 

599 height=height, wrap=wrap, tol=tol) 

600 

601 def isenclosedBy(self, points, wrap=False): 

602 '''Check whether a polygon or composite encloses this point. 

603 

604 @arg points: The polygon points or clips (C{LatLon}[], 

605 L{BooleanFHP} or L{BooleanGH}). 

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

607 B{C{points}} (C{bool}). 

608 

609 @return: C{True} if this point is inside the polygon or composite, 

610 C{False} otherwise. 

611 

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

613 

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

615 

616 @raise ValueError: Invalid B{C{point}}, lat- or longitude. 

617 

618 @see: Functions L{pygeodesy.isconvex}, L{pygeodesy.isenclosedBy} 

619 and L{pygeodesy.ispolar} especially if the B{C{points}} may 

620 enclose a pole or wrap around the earth I{longitudinally}. 

621 ''' 

622 return _MODS.points.isenclosedBy(self, points, wrap=wrap) 

623 

624 @property_RO 

625 def iteration(self): 

626 '''Get the most recent C{intersections2} or C{nearestOn} iteration 

627 number (C{int}) or C{None} if not available/applicable. 

628 ''' 

629 return self._iteration 

630 

631 def midpointTo(self, other, height=None, fraction=_0_5, wrap=False): 

632 '''Find the midpoint on a geodesic between this and an other point. 

633 

634 @arg other: The other point (C{LatLon}). 

635 @kwarg height: Optional height for midpoint, overriding the 

636 mean height (C{meter}). 

637 @kwarg fraction: Midpoint location from this point (C{scalar}), 

638 may be negative or greater than 1.0. 

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

640 B{C{other}} point (C{bool}). 

641 

642 @return: Midpoint (C{LatLon}). 

643 

644 @raise TypeError: The B{C{other}} point is not C{LatLon}. 

645 

646 @raise ValueError: Invalid B{C{height}}. 

647 

648 @see: Methods C{intermediateTo} and C{rhumbMidpointTo}. 

649 ''' 

650 return self.intermediateTo(other, fraction, height=height, wrap=wrap) 

651 

652 def nearestOn(self, point1, point2, within=True, height=None, wrap=False, # was=True 

653 equidistant=None, tol=_TOL_M): 

654 '''I{Iteratively} locate the closest point on the geodesic (line) 

655 between two other (ellipsoidal) points. 

656 

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

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

659 @kwarg within: If C{True}, return the closest point I{between} B{C{point1}} and 

660 B{C{point2}}, otherwise the closest point elsewhere on the geodesic 

661 (C{bool}). 

662 @kwarg height: Optional height for the closest point (C{meter}, conventionally) 

663 or C{None} or C{False} for the interpolated height. If C{False}, 

664 the closest takes the heights of the points into account. 

665 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll both B{C{point1}} and 

666 B{C{point2}} (C{bool}). 

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

668 L{pygeodesy.equidistant}) or C{None} for this point's preferred 

669 C{Equidistant}, like L{Equidistant<LatLonEllipsoidalBase.Equidistant>}. 

670 @kwarg tol: Convergence tolerance (C{meter}, conventionally). 

671 

672 @return: Closest point (C{LatLon}). 

673 

674 @raise ImportError: Package U{geographiclib 

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

676 not installed or not found, but only if 

677 C{B{equidistant}=}L{EquidistantKarney}. 

678 

679 @raise TypeError: Invalid B{C{point1}}, B{C{point2}} or B{C{equidistant}}. 

680 

681 @raise ValueError: Datum or ellipsoid of B{C{point1}} or B{C{point2}} is incompatible 

682 or no convergence for the given B{C{tol}}. 

683 

684 @see: I{Karney}'s U{intercept.cpp<https://SourceForge.net/p/geographiclib/ 

685 discussion/1026621/thread/21aaff9f/>}, U{The B{ellipsoidal} case<https:// 

686 GIS.StackExchange.com/questions/48937/calculating-intersection-of-two-circles>} 

687 and U{Karney's paper<https://ArXiv.org/pdf/1102.1215.pdf>}, pp 20-21, section 

688 B{14. MARITIME BOUNDARIES} for details about the iteration algorithm. 

689 ''' 

690 try: 

691 t = _MODS.ellipsoidalBaseDI._nearestOn2(self, point1, point2, within=within, 

692 height=height, wrap=wrap, 

693 equidistant=equidistant, 

694 tol=tol, LatLon=self.classof) 

695 except (TypeError, ValueError) as x: 

696 raise _xError(x, point=self, point1=point1, point2=point2, within=within, 

697 height=height, wrap=wrap, tol=tol) 

698 return t.closest 

699 

700 def parse(self, strllh, height=0, datum=None, epoch=None, reframe=None, 

701 sep=_COMMA_, wrap=False, **name): 

702 '''Parse a string consisting of C{"lat, lon[, height]"}, 

703 representing a similar, ellipsoidal C{LatLon} point. 

704 

705 @arg strllh: Lat, lon and optional height (C{str}), see function 

706 L{pygeodesy.parse3llh}. 

707 @kwarg height: Optional, default height (C{meter} or C{None}). 

708 @kwarg datum: Optional datum (L{Datum}), overriding this datum 

709 I{without conversion}. 

710 @kwarg epoch: Optional datum (L{Epoch}), overriding this epoch 

711 I{without conversion}. 

712 @kwarg reframe: Optional reference frame (L{RefFrame}), overriding 

713 this reframe I{without conversion}. 

714 @kwarg sep: Optional separator (C{str}). 

715 @kwarg wrap: If C{True}, wrap or I{normalize} the lat- and 

716 longitude (C{bool}). 

717 @kwarg name: Optional C{B{name}=NN} (C{str}), overriding this name. 

718 

719 @return: The similar point (ellipsoidal C{LatLon}). 

720 

721 @raise ParseError: Invalid B{C{strllh}}. 

722 ''' 

723 a, b, h = _MODS.dms.parse3llh(strllh, height=height, sep=sep, wrap=wrap) 

724 return self.classof(a, b, height=h, datum=datum or self.datum, 

725 epoch=epoch or self.epoch, 

726 reframe=reframe or self.reframe, **name) 

727 

728 def _Radjust2(self, adjust, datum, meter_text2): 

729 '''(INTERNAL) Adjust an C{elevation} or C{geoidHeight} with 

730 difference in Gaussian radii of curvature of the given 

731 datum and NAD83 ellipsoids at this point's latitude. 

732 

733 @note: This is an arbitrary, possibly incorrect adjustment. 

734 ''' 

735 if adjust: # Elevation2Tuple or GeoidHeight2Tuple 

736 m, t = meter_text2 

737 if isinstance(m, float) and fabs(m) > EPS: # PYCHOK no cover 

738 n = Datums.NAD83.ellipsoid.rocGauss(self.lat) 

739 if n > EPS0: 

740 # use ratio, datum and NAD83 units may differ 

741 E = self.ellipsoid() if datum in (None, self.datum) else \ 

742 _earth_ellipsoid(datum) 

743 r = E.rocGauss(self.lat) 

744 if r > EPS0 and fabs(r - n) > EPS: # EPS1 

745 m *= r / n 

746 meter_text2 = meter_text2.classof(m, t) 

747 return self._xnamed(meter_text2) 

748 

749 @property_doc_(''' this point's reference frame (L{RefFrame}).''') 

750 def reframe(self): 

751 '''Get this point's reference frame (L{RefFrame}) or C{None}. 

752 ''' 

753 return self._reframe 

754 

755 @reframe.setter # PYCHOK setter! 

756 def reframe(self, reframe): 

757 '''Set or clear this point's reference frame (L{RefFrame}) or C{None}. 

758 

759 @raise TypeError: The B{C{reframe}} is not a L{RefFrame}. 

760 ''' 

761 _set_reframe(self, reframe) 

762 

763 @Property_RO 

764 def scale(self): 

765 '''Get this point's UTM grid or UPS point scale factor (C{float}) 

766 or C{None} if not converted from L{Utm} or L{Ups}. 

767 ''' 

768 return self._scale 

769 

770 def toCartesian(self, height=None, **Cartesian_and_kwds): # PYCHOK signature 

771 '''Convert this point to cartesian, I{geocentric} coordinates, 

772 also known as I{Earth-Centered, Earth-Fixed} (ECEF). 

773 

774 @see: Method L{toCartesian<latlonBase.LatLonBase.toCartesian>} 

775 for further details. 

776 ''' 

777 kwds = Cartesian_and_kwds 

778 if kwds: 

779 kwds = _xkwds(kwds, reframe=self.reframe, epoch=self.epoch) 

780 return LatLonBase.toCartesian(self, height=height, **kwds) 

781 

782 def toCss(self, **toCss_kwds): 

783 '''Convert this C{LatLon} point to a Cassini-Soldner location. 

784 

785 @kwarg toCss_kwds: Optional L{pygeodesy.toCss} keyword arguments. 

786 

787 @return: The Cassini-Soldner location (L{Css}). 

788 

789 @see: Function L{pygeodesy.toCss}. 

790 ''' 

791 return _MODS.css.toCss(self, **self._name1__(toCss_kwds)) 

792 

793 def toDatum(self, datum2, height=None, **name): 

794 '''Convert this point to an other datum. 

795 

796 @arg datum2: Datum to convert I{to} (L{Datum}). 

797 @kwarg height: Optional height, overriding the 

798 converted height (C{meter}). 

799 @kwarg name: Optional C{B{name}=NN} (C{str}). 

800 

801 @return: The converted point (this C{LatLon}) or a copy 

802 of this point if B{C{datum2}} matches this 

803 point's C{datum}. 

804 

805 @raise TypeError: Invalid B{C{datum2}}. 

806 ''' 

807 n = self._name__(name) 

808 d2 = _ellipsoidal_datum(datum2, name=n) 

809 if self.datum == d2: 

810 r = self.copy(name=n) 

811 else: 

812 kwds = _xkwds_not(None, LatLon=self.classof, name=n, 

813 epoch=self.epoch, reframe=self.reframe) 

814 c = self.toCartesian().toDatum(d2) 

815 r = c.toLatLon(datum=d2, height=height, **kwds) 

816 return r 

817 

818 def toEtm(self, **toEtm8_kwds): 

819 '''Convert this C{LatLon} point to an ETM coordinate. 

820 

821 @kwarg toEtm8_kwds: Optional L{pygeodesy.toEtm8} keyword arguments. 

822 

823 @return: The ETM coordinate (L{Etm}). 

824 

825 @see: Function L{pygeodesy.toEtm8}. 

826 ''' 

827 return _MODS.etm.toEtm8(self, **self._name1__(toEtm8_kwds)) if toEtm8_kwds else self._etm 

828 

829 def toLcc(self, **toLcc_kwds): 

830 '''Convert this C{LatLon} point to a Lambert location. 

831 

832 @kwarg toLcc_kwds: Optional L{pygeodesy.toLcc} keyword arguments. 

833 

834 @return: The Lambert location (L{Lcc}). 

835 

836 @see: Function L{pygeodesy.toLcc}. 

837 ''' 

838 return _MODS.lcc.toLcc(self, **self._name1__(toLcc_kwds)) 

839 

840 def toMgrs(self, center=False, pole=NN): 

841 '''Convert this C{LatLon} point to an MGRS coordinate. 

842 

843 @kwarg center: If C{True}, try to I{un}-center MGRS 

844 to its C{lowerleft} (C{bool}) or by 

845 C{B{center} meter} (C{scalar}). 

846 @kwarg pole: Optional top/center for the MGRS UPS 

847 projection (C{str}, 'N[orth]' or 'S[outh]'). 

848 

849 @return: The MGRS coordinate (L{Mgrs}). 

850 

851 @see: Method L{toUtmUps} and L{Mgrs.toLatLon}. 

852 ''' 

853 return self.toUtmUps(center=center, pole=pole).toMgrs(center=False) 

854 

855 def toOsgr(self, kTM=False, **toOsgr_kwds): 

856 '''Convert this C{LatLon} point to an OSGR coordinate. 

857 

858 @kwarg kTM: If C{True}, use I{Karney}'s Krüger method from module 

859 L{ktm}, otherwise I{Ordinance Survery}'s recommended 

860 formulation (C{bool}). 

861 @kwarg toOsgr_kwds: Optional L{pygeodesy.toOsgr} keyword arguments. 

862 

863 @return: The OSGR coordinate (L{Osgr}). 

864 

865 @see: Function L{pygeodesy.toOsgr}. 

866 ''' 

867 return _MODS.osgr.toOsgr(self, kTM=kTM, **self._name1__(toOsgr_kwds)) 

868 

869 def toRefFrame(self, reframe2, reframe=None, epoch=None, epoch2=None, height=None, **name): 

870 '''Convert this point to an other reference frame and epoch. 

871 

872 @arg reframe2: Reference frame to convert I{to} (L{RefFrame}). 

873 @kwarg reframe: Optional reference frame to convert I{from} (L{RefFrame}), 

874 overriding this point's reference frame. 

875 @kwarg epoch: Optional epoch (L{Epoch}, C{scalar} or C{str}), overriding 

876 this point's C{epoch or B{reframe}.epoch}. 

877 @kwarg epoch2: Optional epoch to observe for the converted point (L{Epoch}, 

878 C{scalar} or C{str}), otherwise B{C{epoch}}. 

879 @kwarg height: Optional height, overriding the converted height (C{meter}). 

880 @kwarg name: Optional C{B{name}=NN} (C{str}), overriding C{B{reframe2}.name}. 

881 

882 @return: The converted point (ellipsoidal C{LatLon}) or if conversion 

883 C{isunity}, this point or a copy of this point if the B{C{name}} 

884 is non-empty. 

885 

886 @raise TRFError: This point's C{reframe} is not defined, invalid B{C{epoch}} 

887 or B{C{epoch2}} or conversion from this point's C{reframe} 

888 to B{C{reframe2}} is not available. 

889 

890 @raise TypeError: B{C{reframe2}} or B{C{reframe}} not a L{RefFrame}. 

891 ''' 

892 return _MODS.trf._toRefFrame(self, reframe2, reframe=reframe, epoch=epoch, 

893 epoch2=epoch2, height=height, **name) 

894 

895 def toTransform(self, transform, inverse=False, datum=None, **LatLon_kwds): 

896 '''Apply a Helmert transform to this geodetic point. 

897 

898 @arg transform: Transform to apply (L{Transform} or L{TransformXform}). 

899 @kwarg inverse: Apply the inverse of the Helmert transform (C{bool}). 

900 @kwarg datum: Datum for the transformed point (L{Datum}), overriding 

901 this point's datum but I{not} taken it into account. 

902 @kwarg LatLon_kwds: Optional keyword arguments for the transformed 

903 point, like C{B{height}=...}. 

904 

905 @return: A transformed point (C{LatLon}) or a copy of this point if 

906 C{B{transform}.isunity}. 

907 

908 @raise TypeError: Invalid B{C{transform}}. 

909 ''' 

910 _xinstanceof(Transform, transform=transform) 

911 d = datum or self.datum 

912 if transform.isunity: 

913 r = self.dup(datum=d, **LatLon_kwds) 

914 else: 

915 c = self.toCartesian() 

916 c = c.toTransform(transform, inverse=inverse, datum=d) 

917 r = c.toLatLon(LatLon=self.classof, **_xkwds(LatLon_kwds, height=self.height)) 

918 return r 

919 

920 def toUps(self, pole=NN, falsed=True, center=False): 

921 '''Convert this C{LatLon} point to a UPS coordinate. 

922 

923 @kwarg pole: Optional top/center of (stereographic) 

924 projection (C{str}, 'N[orth]' or 'S[outh]'). 

925 @kwarg falsed: False easting and northing (C{bool}). 

926 @kwarg center: If C{True}, I{un}-center the UPS to its 

927 C{lowerleft} (C{bool}) or by C{B{center} 

928 meter} (C{scalar}). 

929 

930 @return: The UPS coordinate (L{Ups}). 

931 

932 @see: Function L{pygeodesy.toUps8}. 

933 ''' 

934 if self._upsOK(pole, falsed): 

935 u = self._ups 

936 else: 

937 ups = _MODS.ups 

938 u = ups.toUps8(self, datum=self.datum, Ups=ups.Ups, 

939 pole=pole, falsed=falsed) 

940 return _lowerleft(u, center) 

941 

942 def toUtm(self, center=False): 

943 '''Convert this C{LatLon} point to a UTM coordinate. 

944 

945 @kwarg center: If C{True}, I{un}-center the UTM to its 

946 C{lowerleft} (C{bool}) or by C{B{center} 

947 meter} (C{scalar}). 

948 

949 @return: The UTM coordinate (L{Utm}). 

950 

951 @see: Method L{Mgrs.toUtm} and function L{pygeodesy.toUtm8}. 

952 ''' 

953 return _lowerleft(self._utm, center) 

954 

955 def toUtmUps(self, pole=NN, center=False): 

956 '''Convert this C{LatLon} point to a UTM or UPS coordinate. 

957 

958 @kwarg pole: Optional top/center of UPS (stereographic) 

959 projection (C{str}, 'N[orth]' or 'S[outh]'). 

960 @kwarg center: If C{True}, I{un}-center the UTM or UPS to 

961 its C{lowerleft} (C{bool}) or by C{B{center} 

962 meter} (C{scalar}). 

963 

964 @return: The UTM or UPS coordinate (L{Utm} or L{Ups}). 

965 

966 @see: Function L{pygeodesy.toUtmUps8}. 

967 ''' 

968 if self._utmOK(): 

969 u = self._utm 

970 elif self._upsOK(pole): 

971 u = self._ups 

972 else: # no cover 

973 utmups = _MODS.utmups 

974 u = utmups.toUtmUps8(self, datum=self.datum, pole=pole, name=self.name, 

975 Utm=utmups.Utm, Ups=utmups.Ups) 

976 if isinstance(u, utmups.Utm): 

977 self._update(False, _utm=u) # PYCHOK kwds 

978 elif isinstance(u, utmups.Ups): 

979 self._update(False, _ups=u) # PYCHOK kwds 

980 else: 

981 _xinstanceof(utmups.Utm, utmups.Ups, toUtmUps8=u) 

982 return _lowerleft(u, center) 

983 

984 @deprecated_method 

985 def to3xyz(self): # PYCHOK no cover 

986 '''DEPRECATED, use method C{toEcef}. 

987 

988 @return: A L{Vector3Tuple}C{(x, y, z)}. 

989 

990 @note: Overloads C{LatLonBase.to3xyz} 

991 ''' 

992 r = self.toEcef() 

993 return _MODS.namedTuples.Vector3Tuple(r.x, r.y, r.z, name=self.name) 

994 

995 def triangulate(self, bearing1, other, bearing2, **height_wrap_tol): 

996 '''I{Iteratively} locate a point given this, an other point and a bearing 

997 from North at each point. 

998 

999 @arg bearing1: Bearing at this point (compass C{degrees360}). 

1000 @arg other: The other point (C{LatLon}). 

1001 @arg bearing2: Bearing at the B{C{other}} point (compass C{degrees360}). 

1002 @kwarg height_wrap_tol: Optional keyword arguments C{B{height}=None}, 

1003 C{B{wrap}=False} and C{B{tol}}, see method L{intersection3 

1004 <pygeodesy.ellipsoidalBase.LatLonEllipsoidalBase>}. 

1005 

1006 @return: Triangulated point (C{LatLon}). 

1007 

1008 @see: Method L{intersection3<pygeodesy.ellipsoidalBase.LatLonEllipsoidalBase>} 

1009 for further details. 

1010 ''' 

1011 if _isDegrees(bearing1) and _isDegrees(bearing2): 

1012 r = self.intersection3(bearing1, other, bearing2, **height_wrap_tol) 

1013 return r.point 

1014 raise _TypeError(bearing1=bearing1, bearing2=bearing2 **height_wrap_tol) 

1015 

1016 def trilaterate5(self, distance1, point2, distance2, point3, distance3, 

1017 area=True, eps=EPS1, wrap=False): 

1018 '''Trilaterate three points by I{area overlap} or I{perimeter intersection} 

1019 of three intersecting circles. 

1020 

1021 @arg distance1: Distance to this point (C{meter}), same units as B{C{eps}}). 

1022 @arg point2: Second center point (C{LatLon}). 

1023 @arg distance2: Distance to point2 (C{meter}, same units as B{C{eps}}). 

1024 @arg point3: Third center point (C{LatLon}). 

1025 @arg distance3: Distance to point3 (C{meter}, same units as B{C{eps}}). 

1026 @kwarg area: If C{True}, compute the area overlap, otherwise the perimeter 

1027 intersection of the circles (C{bool}). 

1028 @kwarg eps: The required I{minimal overlap} for C{B{area}=True} or the 

1029 I{intersection margin} for C{B{area}=False} (C{meter}, 

1030 conventionally). 

1031 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll B{C{point2}} 

1032 and B{C{point3}} (C{bool}). 

1033 

1034 @return: A L{Trilaterate5Tuple}C{(min, minPoint, max, maxPoint, n)} with 

1035 C{min} and C{max} in C{meter}, same units as B{C{eps}}, the 

1036 corresponding trilaterated points C{minPoint} and C{maxPoint} 

1037 as I{ellipsoidal} C{LatLon} and C{n}, the number of trilatered 

1038 points found for the given B{C{eps}}. 

1039 

1040 If only a single trilaterated point is found, C{min I{is} max}, 

1041 C{minPoint I{is} maxPoint} and C{n=1}. 

1042 

1043 If C{B{area}=False}, C{min} and C{max} represent the nearest 

1044 respectively farthest intersection margin. 

1045 

1046 If C{B{area}=True}, C{min} and C{max} are the smallest respectively 

1047 largest I{radial} overlap found. 

1048 

1049 If C{B{area}=True} and all 3 circles are concentric, C{n=0} and 

1050 C{minPoint} and C{maxPoint} are the B{C{point#}} with the smallest 

1051 B{C{distance#}} C{min} respectively largest B{C{distance#}} C{max}. 

1052 

1053 @raise IntersectionError: Trilateration failed for the given B{C{eps}}, 

1054 insufficient overlap for C{B{area}=True}, no 

1055 circle intersections for C{B{area}=False} or 

1056 all circles are (near-)concentric. 

1057 

1058 @raise TypeError: Invalid B{C{point2}} or B{C{point3}}. 

1059 

1060 @raise ValueError: Coincident B{C{points}} or invalid B{C{distance1}}, 

1061 B{C{distance2}} or B{C{distance3}}. 

1062 

1063 @note: Ellipsoidal trilateration invokes methods C{LatLon.intersections2} 

1064 and C{LatLon.nearestOn} based on I{Karney}'s Python U{geographiclib 

1065 <https://PyPI.org/project/geographiclib>} if installed, otherwise 

1066 the accurate (but slower) C{ellipsoidalExact.LatLon} methods. 

1067 ''' 

1068 return _trilaterate5(self, distance1, 

1069 self.others(point2=point2), distance2, 

1070 self.others(point3=point3), distance3, 

1071 area=area, eps=eps, wrap=wrap) 

1072 

1073 @Property_RO 

1074 def _ups(self): # __dict__ value overwritten by method C{toUtmUps} 

1075 '''(INTERNAL) Get this C{LatLon} point as UPS coordinate (L{Ups}), 

1076 see L{pygeodesy.toUps8}. 

1077 ''' 

1078 ups = _MODS.ups 

1079 return ups.toUps8(self, datum=self.datum, Ups=ups.Ups, 

1080 pole=NN, falsed=True, name=self.name) 

1081 

1082 def _upsOK(self, pole=NN, falsed=True): 

1083 '''(INTERNAL) Check matching C{Ups}. 

1084 ''' 

1085 try: 

1086 u = self._ups 

1087 except RangeError: 

1088 return False 

1089 return falsed and (u.pole == pole[:1].upper() or not pole) 

1090 

1091 @Property_RO 

1092 def _utm(self): # __dict__ value overwritten by method C{toUtmUps} 

1093 '''(INTERNAL) Get this C{LatLon} point as UTM coordinate (L{Utm}), 

1094 see L{pygeodesy.toUtm8}. 

1095 ''' 

1096 utm = _MODS.utm 

1097 return utm.toUtm8(self, datum=self.datum, Utm=utm.Utm, name=self.name) 

1098 

1099 def _utmOK(self): 

1100 '''(INTERNAL) Check C{Utm}. 

1101 ''' 

1102 try: 

1103 _ = self._utm 

1104 except RangeError: 

1105 return False 

1106 return True 

1107 

1108 

1109def _lowerleft(utmups, center): 

1110 '''(INTERNAL) Optionally I{un}-center C{utmups}. 

1111 ''' 

1112 if center in (False, 0, _0_0): 

1113 u = utmups 

1114 elif center in (True,): 

1115 u = utmups._lowerleft 

1116 else: 

1117 u = _MODS.utmupsBase._lowerleft(utmups, center) 

1118 return u 

1119 

1120 

1121def _nearestOn(point, point1, point2, within=True, height=None, wrap=False, # was=True 

1122 equidistant=None, tol=_TOL_M, **LatLon_and_kwds): 

1123 '''(INTERNAL) Get closest point, imported by .ellipsoidalExact, 

1124 -GeodSolve, -Karney and -Vincenty to embellish exceptions. 

1125 ''' 

1126 try: 

1127 p = _xellipsoidal(point=point) 

1128 t = _MODS.ellipsoidalBaseDI._nearestOn2(p, point1, point2, within=within, 

1129 height=height, wrap=wrap, 

1130 equidistant=equidistant, 

1131 tol=tol, **LatLon_and_kwds) 

1132 except (TypeError, ValueError) as x: 

1133 raise _xError(x, point=point, point1=point1, point2=point2) 

1134 return t.closest 

1135 

1136 

1137def _set_reframe(inst, reframe): 

1138 '''(INTERNAL) Set or clear an instance's reference frame. 

1139 ''' 

1140 if reframe is not None: 

1141 _xinstanceof(_MODS.trf.RefFrame, reframe=reframe) 

1142 inst._reframe = reframe 

1143 elif inst.reframe is not None: 

1144 inst._reframe = None 

1145 

1146 

1147__all__ += _ALL_DOCS(CartesianEllipsoidalBase, LatLonEllipsoidalBase) 

1148 

1149# **) MIT License 

1150# 

1151# Copyright (C) 2016-2025 -- mrJean1 at Gmail -- All Rights Reserved. 

1152# 

1153# Permission is hereby granted, free of charge, to any person obtaining a 

1154# copy of this software and associated documentation files (the "Software"), 

1155# to deal in the Software without restriction, including without limitation 

1156# the rights to use, copy, modify, merge, publish, distribute, sublicense, 

1157# and/or sell copies of the Software, and to permit persons to whom the 

1158# Software is furnished to do so, subject to the following conditions: 

1159# 

1160# The above copyright notice and this permission notice shall be included 

1161# in all copies or substantial portions of the Software. 

1162# 

1163# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS 

1164# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, 

1165# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL 

1166# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR 

1167# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, 

1168# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR 

1169# OTHER DEALINGS IN THE SOFTWARE.