Coverage for pygeodesy/ellipsoidalBase.py: 90%

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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 2005-2016} 

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 _incompatible, _IsnotError, RangeError, _TypeError, \ 

22 _ValueError, _xattr, _xellipsoidal, _xError, _xkwds, \ 

23 _xkwds_not 

24# from pygeodesy.fmath import favg # _MODS 

25from pygeodesy.interns import NN, _COMMA_, _ellipsoidal_ 

26from pygeodesy.latlonBase import LatLonBase, _trilaterate5, fabs, _Wrap 

27from pygeodesy.lazily import _ALL_DOCS, _ALL_LAZY, _ALL_MODS as _MODS 

28# from pygeodesy.lcc import toLcc # _MODS 

29# from pygeodesy.namedTuples import Vector3Tuple # _MODS 

30from pygeodesy.props import deprecated_method, deprecated_property_RO, \ 

31 Property_RO, property_doc_, property_RO, _update_all 

32# from pygeodesy.trf import _eT0Ds4 # _MODS 

33from pygeodesy.units import Epoch, _isDegrees, Radius_, _1mm as _TOL_M 

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

35 

36# from math import fabs # from .latlonBase 

37 

38__all__ = _ALL_LAZY.ellipsoidalBase 

39__version__ = '24.06.06' 

40 

41 

42class CartesianEllipsoidalBase(CartesianBase): 

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

44 ''' 

45 _datum = _WGS84 # L{Datum} 

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

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

48 

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

50 **datum_ll_name): 

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

52 

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

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

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

56 if C{B{reframe}=None}. 

57 

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

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

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

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

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

63 

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

65 ''' 

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

67 if reframe: 

68 self.reframe = reframe 

69 self.epoch = epoch 

70 

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

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

73# ''' 

74# RefFrame = _MODS.trf.RefFrame 

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

76# _NotImplemented(self, other) 

77 

78 @deprecated_method 

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

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

81 return self.toRefFrame(reframe2, reframe=reframe, epoch=epoch) 

82 

83 @property_RO 

84 def ellipsoidalCartesian(self): 

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

86 ''' 

87 return type(self) 

88 

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

90 def epoch(self): 

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

92 ''' 

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

94 

95 @epoch.setter # PYCHOK setter! 

96 def epoch(self, epoch): 

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

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

99 

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

101 ''' 

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

103 

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

105 Vector=None, **Vector_kwds): 

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

107 cartesian center point and a radius. 

108 

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

110 coordinates). 

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

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

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

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

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

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

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

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

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

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

121 ignored if C{B{Vector} is None}. 

122 

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

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

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

126 

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

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

129 the same instance, aka the I{radical center}. 

130 

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

132 

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

134 

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

136 

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

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

139 Intersection and function L{pygeodesy.radical2}. 

140 ''' 

141 try: 

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

143 center2, Radius_(radius2=radius2), 

144 sphere=sphere, clas=self.classof, 

145 Vector=Vector, **Vector_kwds) 

146 except (TypeError, ValueError) as x: 

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

148 

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

150 def reframe(self): 

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

152 ''' 

153 return self._reframe 

154 

155 @reframe.setter # PYCHOK setter! 

156 def reframe(self, reframe): 

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

158 

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

160 ''' 

161 _set_reframe(self, reframe) 

162 

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

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

165 

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

167 for further details. 

168 ''' 

169 kwds = LatLon_and_kwds 

170 if kwds: 

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

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

173 

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

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

176 

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

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

179 overriding this point's reference frame. 

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

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

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

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

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

185 

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

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

188 is non-empty. 

189 

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

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

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

193 

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

195 ''' 

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

197 epoch2=epoch2, **name) 

198 

199 @deprecated_method 

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

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

202 r = self 

203 for t in transforms: 

204 r = r.toTransform(t) 

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

206 

207 

208class LatLonEllipsoidalBase(LatLonBase): 

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

210 ''' 

211 _datum = _WGS84 # L{Datum} 

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

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

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

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

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

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

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

219 

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

221 epoch=None, wrap=False, **name): 

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

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

224 

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

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

227 @kwarg lon: Longitude (C{degrees} or DMS C{str} with E or W suffix) or 

228 C(None), indicating B{C{latlonh}} is a C{LatLon}. 

229 @kwarg height: Optional height above (or below) the earth surface 

230 (C{meter}, same units as the datum's ellipsoid axes). 

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

232 L{Ellipsoid2} or L{a_f2Tuple}). 

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

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

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

236 if C{B{reframe}=None}. 

237 @kwarg wrap: If C{True}, wrap or I{normalize} B{C{lat}} and B{C{lon}} 

238 (C{bool}). 

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

240 

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

242 range and L{rangerrors} set to C{True}. 

243 

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

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

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

247 

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

249 ''' 

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

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

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

253 if reframe: 

254 self.reframe = reframe 

255 self.epoch = epoch 

256 

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

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

259# ''' 

260# RefFrame = _MODS.trf.RefFrame 

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

262# _NotImplemented(self, other) 

263 

264 def antipode(self, height=None): 

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

266 to this point. 

267 

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

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

270 

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

272 ''' 

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

274 if lla.datum != self.datum: 

275 lla.datum = self.datum 

276 return lla 

277 

278 @deprecated_property_RO 

279 def convergence(self): 

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

281 return self.gamma 

282 

283 @deprecated_method 

284 def convertDatum(self, datum2): 

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

286 return self.toDatum(datum2) 

287 

288 @deprecated_method 

289 def convertRefFrame(self, reframe2): 

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

291 return self.toRefFrame(reframe2) 

292 

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

294 def datum(self): 

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

296 ''' 

297 return self._datum 

298 

299 @datum.setter # PYCHOK setter! 

300 def datum(self, datum): 

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

302 

303 @raise TypeError: The B{C{datum}} is not a L{Datum} 

304 or not ellipsoidal. 

305 ''' 

306 _xinstanceof(Datum, datum=datum) 

307 if not datum.isEllipsoidal: 

308 raise _IsnotError(_ellipsoidal_, datum=datum) 

309 if self._datum != datum: 

310 _update_all(self) 

311 self._datum = datum 

312 

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

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

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

316 

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

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

319 

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

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

322 point (C{bool}). 

323 

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

325 

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

327 

328 @raise ValueError: Incompatible datum ellipsoids. 

329 

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

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

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

333 formula. 

334 ''' 

335 p = self.others(other) 

336 if wrap: 

337 p = _Wrap.point(p) 

338 E = self.ellipsoids(other) 

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

340 

341 @Property_RO 

342 def _elevation2(self): 

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

344 ''' 

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

346 timeout=self._elevation2to) 

347 

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

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

350 or sphere. 

351 

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

353 C{NAD83} (C{bool}). 

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

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

356 radius). 

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

358 

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

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

361 

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

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

364 L{elevations.elevation2} is based. 

365 

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

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

368 

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

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

371 ''' 

372 if self._elevation2to != timeout: 

373 self._elevation2to = timeout 

374 LatLonEllipsoidalBase._elevation2._update(self) 

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

376 

377 def ellipsoid(self, datum=_WGS84): 

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

379 

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

381 

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

383 ''' 

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

385 

386 @property_RO 

387 def ellipsoidalLatLon(self): 

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

389 ''' 

390 return type(self) 

391 

392 def ellipsoids(self, other): 

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

394 

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

396 

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

398 

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

400 

401 @raise ValueError: Incompatible datum ellipsoids. 

402 ''' 

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

404 

405 E = self.ellipsoid() 

406 try: # other may be Sphere, etc. 

407 e = other.ellipsoid() 

408 except AttributeError: 

409 try: # no ellipsoid method, try datum 

410 e = other.datum.ellipsoid 

411 except AttributeError: 

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

413 if e != E: 

414 raise _ValueError(e.named2, txt=_incompatible(E.named2)) 

415 return E 

416 

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

418 def epoch(self): 

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

420 ''' 

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

422 

423 @epoch.setter # PYCHOK setter! 

424 def epoch(self, epoch): 

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

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

427 

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

429 ''' 

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

431 

432 @Property_RO 

433 def Equidistant(self): 

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

435 ''' 

436 try: 

437 _ = self.datum.ellipsoid.geodesic 

438 return _MODS.azimuthal.EquidistantKarney 

439 except ImportError: # no geographiclib 

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

441 

442 @Property_RO 

443 def _etm(self): 

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

445 ''' 

446 etm = _MODS.etm 

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

448 

449 @property_RO 

450 def gamma(self): 

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

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

453 ''' 

454 return self._gamma 

455 

456 @Property_RO 

457 def _geoidHeight2(self): 

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

459 ''' 

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

461 timeout=self._geoidHeight2to) 

462 

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

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

465 or sphere. 

466 

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

468 C{NAD83/NADV88} (C{bool}). 

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

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

471 radius). 

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

473 

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

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

476 

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

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

479 the L{elevations.geoidHeight2} is based. 

480 

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

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

483 

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

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

486 ''' 

487 if self._geoidHeight2to != timeout: 

488 self._geoidHeight2to = timeout 

489 LatLonEllipsoidalBase._geoidHeight2._update(self) 

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

491 

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

493 '''I{Must be overloaded}.''' 

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

495 

496 def intersection3(self, end1, other, end2, height=None, wrap=False, # was=True 

497 equidistant=None, tol=_TOL_M): 

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

499 defined by two points or a start point and bearing from North. 

500 

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

502 bearing at this point (compass C{degrees360}). 

503 @arg other: Start point of the other line (C{LatLon}). 

504 @arg end2: End point of the other line (C{LatLon}) or the initial 

505 bearing at the other point (compass C{degrees360}). 

506 @kwarg height: Optional height at the intersection (C{meter}, 

507 conventionally) or C{None} for the mean height. 

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

509 B{C{other}} and B{C{end*}} points (C{bool}). 

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

511 function L{pygeodesy.equidistant}), or C{None} 

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

513 @kwarg tol: Tolerance for convergence and skew line distance and 

514 length (C{meter}, conventionally). 

515 

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

517 with C{point} a C{LatLon} instance. 

518 

519 @raise ImportError: Package U{geographiclib 

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

521 not installed or not found, but only if 

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

523 

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

525 non-intersecting lines or no convergence 

526 for the given B{C{tol}}. 

527 

528 @raise TypeError: If B{C{end1}}, B{C{other}} or B{C{end2}} point 

529 is not C{LatLon}. 

530 

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

532 point is computed as the C{destination} along that bearing at 

533 about 1.5 times the distance from the start point to an initial 

534 gu-/estimate of the intersection point (and between 1/8 and 3/8 

535 of the authalic earth perimeter). 

536 

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

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

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

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

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

542 ''' 

543 try: 

544 s2 = self.others(other) 

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

546 s2, end2, 

547 height=height, wrap=wrap, 

548 equidistant=equidistant, tol=tol, 

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

550 except (TypeError, ValueError) as x: 

551 raise _xError(x, start1=self, end1=end1, other=other, end2=end2, 

552 height=height, wrap=wrap, tol=tol) 

553 

554 def intersections2(self, radius1, other, radius2, height=None, wrap=False, # was=True 

555 equidistant=None, tol=_TOL_M): 

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

557 each defined by a center point and a radius. 

558 

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

560 @arg other: Center of the other circle (C{LatLon}). 

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

562 B{C{radius1}}). 

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

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

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

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

567 center (C{bool}). 

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

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

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

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

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

573 

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

575 instance. For abutting circles, both intersection 

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

577 

578 @raise ImportError: Package U{geographiclib 

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

580 not installed or not found, but only if 

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

582 

583 @raise IntersectionError: Concentric, antipodal, invalid or 

584 non-intersecting circles or no 

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

586 

587 @raise TypeError: Invalid B{C{other}} or B{C{equidistant}}. 

588 

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

590 

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

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

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

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

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

596 intersections. 

597 ''' 

598 try: 

599 c2 = self.others(other) 

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

601 c2, radius2, 

602 height=height, wrap=wrap, 

603 equidistant=equidistant, tol=tol, 

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

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

606 raise _xError(x, center=self, radius1=radius1, other=other, radius2=radius2, 

607 height=height, wrap=wrap, tol=tol) 

608 

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

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

611 

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

613 L{BooleanFHP} or L{BooleanGH}). 

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

615 B{C{points}} (C{bool}). 

616 

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

618 C{False} otherwise. 

619 

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

621 

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

623 

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

625 

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

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

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

629 ''' 

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

631 

632 @property_RO 

633 def iteration(self): 

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

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

636 ''' 

637 return self._iteration 

638 

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

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

641 

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

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

644 mean height (C{meter}). 

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

646 may be negative or greater than 1.0. 

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

648 B{C{other}} point (C{bool}). 

649 

650 @return: Midpoint (C{LatLon}). 

651 

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

653 

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

655 

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

657 ''' 

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

659 

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

661 equidistant=None, tol=_TOL_M): 

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

663 two other (ellipsoidal) points. 

664 

665 @arg point1: Start point (C{LatLon}). 

666 @arg point2: End point (C{LatLon}). 

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

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

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

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

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

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

673 takes the heights of the points into account. 

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

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

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

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

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

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

680 

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

682 

683 @raise ImportError: Package U{geographiclib 

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

685 not installed or not found, but only if 

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

687 

688 @raise TypeError: Invalid B{C{point1}}, B{C{point2}} or 

689 B{C{equidistant}}. 

690 

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

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

693 

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

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

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

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

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

699 ''' 

700 try: 

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

702 height=height, wrap=wrap, 

703 equidistant=equidistant, 

704 tol=tol, LatLon=self.classof) 

705 except (TypeError, ValueError) as x: 

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

707 height=height, wrap=wrap, tol=tol) 

708 return t.closest 

709 

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

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

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

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

714 

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

716 L{pygeodesy.parse3llh}. 

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

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

719 I{without conversion}. 

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

721 I{without conversion}. 

722 @kwarg reframe: Optional datum (L{RefFrame}), overriding this 

723 reframe I{without conversion}. 

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

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

726 longitude (C{bool}). 

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

728 

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

730 

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

732 ''' 

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

734 r = self.classof(a, b, height=h, datum=self.datum) 

735 if datum not in (None, self.datum): 

736 r.datum = datum 

737 if epoch not in (None, self.epoch): 

738 r.epoch = epoch 

739 if reframe not in (None, self.reframe): 

740 r.reframe = reframe 

741 return self._xnamed(r, force=True, **name) if name else r 

742 

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

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

745 difference in Gaussian radii of curvature of the given 

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

747 

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

749 ''' 

750 if adjust: # Elevation2Tuple or GeoidHeight2Tuple 

751 m, t = meter_text2 

752 if isinstance(m, float) and fabs(m) > EPS: 

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

754 if n > EPS0: 

755 # use ratio, datum and NAD83 units may differ 

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

757 _earth_ellipsoid(datum) 

758 r = E.rocGauss(self.lat) 

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

760 m *= r / n 

761 meter_text2 = meter_text2.classof(m, t) 

762 return self._xnamed(meter_text2) 

763 

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

765 def reframe(self): 

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

767 ''' 

768 return self._reframe 

769 

770 @reframe.setter # PYCHOK setter! 

771 def reframe(self, reframe): 

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

773 

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

775 ''' 

776 _set_reframe(self, reframe) 

777 

778 @Property_RO 

779 def scale(self): 

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

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

782 ''' 

783 return self._scale 

784 

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

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

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

788 

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

790 for further details. 

791 ''' 

792 kwds = Cartesian_and_kwds 

793 if kwds: 

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

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

796 

797 def toCss(self, **toCss_kwds): 

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

799 

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

801 

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

803 

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

805 ''' 

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

807 

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

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

810 

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

812 @kwarg height: Optional height, overriding the 

813 converted height (C{meter}). 

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

815 

816 @return: The converted point (ellipsoidal C{LatLon}) 

817 or a copy of this point if B{C{datum2}} 

818 matches this point's C{datum}. 

819 

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

821 ''' 

822 n = self._name__(name) 

823 d2 = _ellipsoidal_datum(datum2, name=n) 

824 if self.datum == d2: 

825 r = self.copy(name=n) 

826 else: 

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

828 epoch=self.epoch, reframe=self.reframe) 

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

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

831 return r 

832 

833 def toEtm(self, **toEtm8_kwds): 

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

835 

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

837 

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

839 

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

841 ''' 

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

843 

844 def toLcc(self, **toLcc_kwds): 

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

846 

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

848 

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

850 

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

852 ''' 

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

854 

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

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

857 

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

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

860 C{B{center} meter} (C{scalar}). 

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

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

863 

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

865 

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

867 ''' 

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

869 

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

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

872 

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

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

875 formulation (C{bool}). 

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

877 

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

879 

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

881 ''' 

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

883 

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

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

886 

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

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

889 overriding this point's reference frame. 

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

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

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

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

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

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

896 

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

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

899 is non-empty. 

900 

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

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

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

904 

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

906 ''' 

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

908 epoch2=epoch2, height=height, **name) 

909 

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

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

912 

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

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

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

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

917 @kwarg LatLon_kwds: Optional keyword arguments for the transformed 

918 point, like C{B{height}=...}. 

919 

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

921 C{B{transform}.isunity}. 

922 

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

924 ''' 

925 _xinstanceof(Transform, transform=transform) 

926 d = datum or self.datum 

927 if transform.isunity: 

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

929 else: 

930 c = self.toCartesian() 

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

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

933 return r 

934 

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

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

937 

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

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

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

941 @kwarg center: If C{True}, I{un}-center the UPS 

942 to its C{lowerleft} (C{bool}) or 

943 by C{B{center} meter} (C{scalar}). 

944 

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

946 

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

948 ''' 

949 if self._upsOK(pole, falsed): 

950 u = self._ups 

951 else: 

952 ups = _MODS.ups 

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

954 pole=pole, falsed=falsed) 

955 return _lowerleft(u, center) 

956 

957 def toUtm(self, center=False): 

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

959 

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

961 to its C{lowerleft} (C{bool}) or 

962 by C{B{center} meter} (C{scalar}). 

963 

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

965 

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

967 ''' 

968 return _lowerleft(self._utm, center) 

969 

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

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

972 

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

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

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

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

977 meter} (C{scalar}). 

978 

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

980 

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

982 ''' 

983 if self._utmOK(): 

984 u = self._utm 

985 elif self._upsOK(pole): 

986 u = self._ups 

987 else: # no cover 

988 utmups = _MODS.utmups 

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

990 Utm=utmups.Utm, Ups=utmups.Ups) 

991 if isinstance(u, utmups.Utm): 

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

993 elif isinstance(u, utmups.Ups): 

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

995 else: 

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

997 return _lowerleft(u, center) 

998 

999 @deprecated_method 

1000 def to3xyz(self): # PYCHOK no cover 

1001 '''DEPRECATED, use method C{toEcef}. 

1002 

1003 @return: A L{Vector3Tuple}C{(x, y, z)}. 

1004 

1005 @note: Overloads C{LatLonBase.to3xyz} 

1006 ''' 

1007 r = self.toEcef() 

1008 return _MODS.namedTuples.Vector3Tuple(r.x, r.y, r.z, name=self.name) 

1009 

1010 def triangulate(self, bearing1, other, bearing2, **height_wrap_tol): 

1011 '''I{Iteratively} locate a point given this, an other point and the (initial) 

1012 bearing at this and at the other point. 

1013 

1014 @arg bearing1: Bearing at this point (compass C{degrees360}). 

1015 @arg other: Start point of the other line (C{LatLon}). 

1016 @arg bearing2: Bearing at the other point (compass C{degrees360}). 

1017 @kwarg height_wrap_tol: Optional keyword arguments C{B{height}=None}, 

1018 C{B{wrap}=False} and C{B{tol}}, see method L{intersection3}. 

1019 

1020 @return: Triangulated point (C{LatLon}). 

1021 

1022 @see: Method L{intersection3} for further details. 

1023 ''' 

1024 if _isDegrees(bearing1) and _isDegrees(bearing2): 

1025 r = self.intersection3(bearing1, other, bearing2, **height_wrap_tol) 

1026 return r.point 

1027 raise _TypeError(bearing1=bearing1, bearing2=bearing2 **height_wrap_tol) 

1028 

1029 def trilaterate5(self, distance1, point2, distance2, point3, distance3, 

1030 area=True, eps=EPS1, wrap=False): 

1031 '''Trilaterate three points by I{area overlap} or I{perimeter 

1032 intersection} of three intersecting circles. 

1033 

1034 @arg distance1: Distance to this point (C{meter}), same units 

1035 as B{C{eps}}). 

1036 @arg point2: Second center point (C{LatLon}). 

1037 @arg distance2: Distance to point2 (C{meter}, same units as 

1038 B{C{eps}}). 

1039 @arg point3: Third center point (C{LatLon}). 

1040 @arg distance3: Distance to point3 (C{meter}, same units as 

1041 B{C{eps}}). 

1042 @kwarg area: If C{True} compute the area overlap, otherwise the 

1043 perimeter intersection of the circles (C{bool}). 

1044 @kwarg eps: The required I{minimal overlap} for C{B{area}=True} 

1045 or the I{intersection margin} for C{B{area}=False} 

1046 (C{meter}, conventionally). 

1047 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll 

1048 B{C{point2}} and B{C{point3}} (C{bool}). 

1049 

1050 @return: A L{Trilaterate5Tuple}C{(min, minPoint, max, maxPoint, n)} 

1051 with C{min} and C{max} in C{meter}, same units as B{C{eps}}, 

1052 the corresponding trilaterated points C{minPoint} and 

1053 C{maxPoint} as I{ellipsoidal} C{LatLon} and C{n}, the number 

1054 of trilatered points found for the given B{C{eps}}. 

1055 

1056 If only a single trilaterated point is found, C{min I{is} 

1057 max}, C{minPoint I{is} maxPoint} and C{n = 1}. 

1058 

1059 For C{B{area}=True}, C{min} and C{max} are the smallest 

1060 respectively largest I{radial} overlap found. 

1061 

1062 For C{B{area}=False}, C{min} and C{max} represent the 

1063 nearest respectively farthest intersection margin. 

1064 

1065 If C{B{area}=True} and all 3 circles are concentric, C{n=0} 

1066 and C{minPoint} and C{maxPoint} are the B{C{point#}} with 

1067 the smallest B{C{distance#}} C{min} respectively C{max} the 

1068 largest B{C{distance#}}. 

1069 

1070 @raise IntersectionError: Trilateration failed for the given B{C{eps}}, 

1071 insufficient overlap for C{B{area}=True}, no 

1072 circle intersections for C{B{area}=False} or 

1073 all circles are (near-)concentric. 

1074 

1075 @raise TypeError: Invalid B{C{point2}} or B{C{point3}}. 

1076 

1077 @raise ValueError: Coincident B{C{points}} or invalid B{C{distance1}}, 

1078 B{C{distance2}} or B{C{distance3}}. 

1079 

1080 @note: Ellipsoidal trilateration invokes methods C{LatLon.intersections2} 

1081 and C{LatLon.nearestOn} based on I{Karney}'s Python U{geographiclib 

1082 <https://PyPI.org/project/geographiclib>} if installed, otherwise 

1083 the accurate (but slower) C{ellipsoidalExact.LatLon} methods. 

1084 ''' 

1085 return _trilaterate5(self, distance1, 

1086 self.others(point2=point2), distance2, 

1087 self.others(point3=point3), distance3, 

1088 area=area, eps=eps, wrap=wrap) 

1089 

1090 @Property_RO 

1091 def _ups(self): # __dict__ value overwritten by method C{toUtmUps} 

1092 '''(INTERNAL) Get this C{LatLon} point as UPS coordinate (L{Ups}), 

1093 see L{pygeodesy.toUps8}. 

1094 ''' 

1095 ups = _MODS.ups 

1096 return ups.toUps8(self, datum=self.datum, Ups=ups.Ups, 

1097 pole=NN, falsed=True, name=self.name) 

1098 

1099 def _upsOK(self, pole=NN, falsed=True): 

1100 '''(INTERNAL) Check matching C{Ups}. 

1101 ''' 

1102 try: 

1103 u = self._ups 

1104 except RangeError: 

1105 return False 

1106 return falsed and (u.pole == pole[:1].upper() or not pole) 

1107 

1108 @Property_RO 

1109 def _utm(self): # __dict__ value overwritten by method C{toUtmUps} 

1110 '''(INTERNAL) Get this C{LatLon} point as UTM coordinate (L{Utm}), 

1111 see L{pygeodesy.toUtm8}. 

1112 ''' 

1113 utm = _MODS.utm 

1114 return utm.toUtm8(self, datum=self.datum, Utm=utm.Utm, name=self.name) 

1115 

1116 def _utmOK(self): 

1117 '''(INTERNAL) Check C{Utm}. 

1118 ''' 

1119 try: 

1120 _ = self._utm 

1121 except RangeError: 

1122 return False 

1123 return True 

1124 

1125 

1126def _lowerleft(utmups, center): 

1127 '''(INTERNAL) Optionally I{un}-center C{utmups}. 

1128 ''' 

1129 if center in (False, 0, _0_0): 

1130 u = utmups 

1131 elif center in (True,): 

1132 u = utmups._lowerleft 

1133 else: 

1134 u = _MODS.utmupsBase._lowerleft(utmups, center) 

1135 return u 

1136 

1137 

1138def _nearestOn(point, point1, point2, within=True, height=None, wrap=False, # was=True 

1139 equidistant=None, tol=_TOL_M, **LatLon_and_kwds): 

1140 '''(INTERNAL) Get closest point, imported by .ellipsoidalExact, 

1141 -GeodSolve, -Karney and -Vincenty to embellish exceptions. 

1142 ''' 

1143 try: 

1144 p = _xellipsoidal(point=point) 

1145 t = _MODS.ellipsoidalBaseDI._nearestOn2(p, point1, point2, within=within, 

1146 height=height, wrap=wrap, 

1147 equidistant=equidistant, 

1148 tol=tol, **LatLon_and_kwds) 

1149 except (TypeError, ValueError) as x: 

1150 raise _xError(x, point=point, point1=point1, point2=point2) 

1151 return t.closest 

1152 

1153 

1154def _set_reframe(inst, reframe): 

1155 '''(INTERNAL) Set or clear an instance's reference frame. 

1156 ''' 

1157 if reframe is not None: 

1158 _xinstanceof(_MODS.trf.RefFrame, reframe=reframe) 

1159 inst._reframe = reframe 

1160 elif inst.reframe is not None: 

1161 inst._reframe = None 

1162 

1163 

1164__all__ += _ALL_DOCS(CartesianEllipsoidalBase, LatLonEllipsoidalBase) 

1165 

1166# **) MIT License 

1167# 

1168# Copyright (C) 2016-2024 -- mrJean1 at Gmail -- All Rights Reserved. 

1169# 

1170# Permission is hereby granted, free of charge, to any person obtaining a 

1171# copy of this software and associated documentation files (the "Software"), 

1172# to deal in the Software without restriction, including without limitation 

1173# the rights to use, copy, modify, merge, publish, distribute, sublicense, 

1174# and/or sell copies of the Software, and to permit persons to whom the 

1175# Software is furnished to do so, subject to the following conditions: 

1176# 

1177# The above copyright notice and this permission notice shall be included 

1178# in all copies or substantial portions of the Software. 

1179# 

1180# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS 

1181# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, 

1182# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL 

1183# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR 

1184# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, 

1185# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR 

1186# OTHER DEALINGS IN THE SOFTWARE.