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 2005-2016} 

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 _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_get, _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.named import notOverloaded # _MODS 

30# from pygeodesy.namedTuples import Vector3Tuple # _MODS 

31from pygeodesy.props import deprecated_method, deprecated_property_RO, \ 

32 Property_RO, property_doc_, property_RO, _update_all 

33# from pygeodesy.trf import _eT0Ds4 # _MODS 

34from pygeodesy.units import Epoch, _isDegrees, Radius_, _1mm as _TOL_M 

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

36 

37# from math import fabs # from .latlonBase 

38 

39__all__ = _ALL_LAZY.ellipsoidalBase 

40__version__ = '24.02.04' 

41 

42 

43class CartesianEllipsoidalBase(CartesianBase): 

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

45 ''' 

46 _datum = _WGS84 # L{Datum} 

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

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

49 

50 def __init__(self, x_xyz, y=None, z=None, datum=None, reframe=None, 

51 epoch=None, ll=None, name=NN): 

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

53 

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

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

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

57 if C{B{reframe}=None}. 

58 

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

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

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

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

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

64 

65 @see: Super-class L{CartesianBase<CartesianBase.__init__>} for more details. 

66 ''' 

67 CartesianBase.__init__(self, x_xyz, y=y, z=z, datum=datum, ll=ll, name=name) 

68 if reframe: 

69 self.reframe = reframe 

70 self.epoch = epoch 

71 

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

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

74# ''' 

75# RefFrame = _MODS.trf.RefFrame 

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

77# _NotImplemented(self, other) 

78 

79 @deprecated_method 

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

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

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

83 

84 @property_RO 

85 def ellipsoidalCartesian(self): 

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

87 ''' 

88 return type(self) 

89 

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

91 def epoch(self): 

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

93 ''' 

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

95 

96 @epoch.setter # PYCHOK setter! 

97 def epoch(self, epoch): 

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

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

100 

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

102 ''' 

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

104 

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

106 Vector=None, **Vector_kwds): 

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

108 cartesian center point and a radius. 

109 

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

111 coordinates). 

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

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

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

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

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

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

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

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

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

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

122 ignored if C{B{Vector} is None}. 

123 

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

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

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

127 

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

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

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

131 

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

133 

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

135 

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

137 

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

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

140 Intersection and function L{pygeodesy.radical2}. 

141 ''' 

142 try: 

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

144 center2, Radius_(radius2=radius2), 

145 sphere=sphere, clas=self.classof, 

146 Vector=Vector, **Vector_kwds) 

147 except (TypeError, ValueError) as x: 

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

149 

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

151 def reframe(self): 

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

153 ''' 

154 return self._reframe 

155 

156 @reframe.setter # PYCHOK setter! 

157 def reframe(self, reframe): 

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

159 

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

161 ''' 

162 _set_reframe(self, reframe) 

163 

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

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

166 

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

168 for further details. 

169 ''' 

170 kwds = LatLon_and_kwds 

171 if kwds: 

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

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

174 

175 def toRefFrame(self, reframe2, reframe=None, epoch=None, epoch2=None, name=NN): 

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

177 

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

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

180 point's reference frame. 

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

182 this point's epoch. 

183 @kwarg epoch2: Optional epoch to observe I{to} (L{Epoch}, C{scalar} or 

184 C{str}). 

185 @kwarg name: Optional name (C{str}), iff converted. 

186 

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

188 is C{nil}, this point or a copy of this point if the B{C{name}} 

189 is non-empty. 

190 

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

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

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

194 

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

196 ''' 

197 e, t0, d, d2 = _MODS.trf._eT0Ds4(self, reframe, epoch, reframe2, epoch2) 

198 if t0: 

199 r = self.toDatum(d).toTransforms_(t0).toDatum(d2).toDatum(self.datum) 

200 r.reframe, r.epoch = reframe2, e 

201 if name: 

202 r.rename(name) 

203 else: 

204 r = self.copy(name=name) if name else self 

205 return r 

206 

207 def toTransforms_(self, *transforms, **datum): 

208 '''Apply none, one or several Helmert transforms to this point. 

209 

210 @arg transforms: Transforms to apply, in order (L{Transform}s). 

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

212 this point's datum. 

213 

214 @return: The transformed point (C{Cartesian}) or this point if the 

215 B{C{transforms}} produce the same point. 

216 ''' 

217 r = self 

218 if transforms: 

219 xyz = r.xyz 

220 for t in transforms: 

221 xyz = t.transform(*xyz) 

222 d = _xkwds_get(datum, datum=r.datum) 

223 if d != r.datum or xyz != r.xyz: 

224 r = r.classof(xyz, datum=d) 

225 return r 

226 

227 

228class LatLonEllipsoidalBase(LatLonBase): 

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

230 ''' 

231 _datum = _WGS84 # L{Datum} 

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

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

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

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

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

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

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

239 

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

241 epoch=None, wrap=False, name=NN): 

242 '''Create an ellipsoidal C{LatLon} point from the givenlat-, longitude 

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

244 

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

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

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

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

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

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

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

252 L{Ellipsoid2} or L{a_f2Tuple}). 

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

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

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

256 if C{B{reframe}=None}. 

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

258 (C{bool}). 

259 @kwarg name: Optional name (C{str}). 

260 

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

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

263 

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

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

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

267 

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

269 ''' 

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

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

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

273 if reframe: 

274 self.reframe = reframe 

275 self.epoch = epoch 

276 

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

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

279# ''' 

280# RefFrame = _MODS.trf.RefFrame 

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

282# _NotImplemented(self, other) 

283 

284 def antipode(self, height=None): 

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

286 to this point. 

287 

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

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

290 

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

292 ''' 

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

294 if lla.datum != self.datum: 

295 lla.datum = self.datum 

296 return lla 

297 

298 @deprecated_property_RO 

299 def convergence(self): 

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

301 return self.gamma 

302 

303 @deprecated_method 

304 def convertDatum(self, datum2): 

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

306 return self.toDatum(datum2) 

307 

308 @deprecated_method 

309 def convertRefFrame(self, reframe2): 

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

311 return self.toRefFrame(reframe2) 

312 

313 @Property_RO 

314 def _css(self): 

315 '''(INTERNAL) Get this C{LatLon} point as a Cassini-Soldner location (L{Css}). 

316 ''' 

317 css = _MODS.css 

318 return css.toCss(self, height=self.height, Css=css.Css, name=self.name) 

319 

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

321 def datum(self): 

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

323 ''' 

324 return self._datum 

325 

326 @datum.setter # PYCHOK setter! 

327 def datum(self, datum): 

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

329 

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

331 or not ellipsoidal. 

332 ''' 

333 _xinstanceof(Datum, datum=datum) 

334 if not datum.isEllipsoidal: 

335 raise _IsnotError(_ellipsoidal_, datum=datum) 

336 if self._datum != datum: 

337 _update_all(self) 

338 self._datum = datum 

339 

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

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

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

343 

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

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

346 

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

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

349 point (C{bool}). 

350 

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

352 

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

354 

355 @raise ValueError: Incompatible datum ellipsoids. 

356 

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

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

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

360 formula. 

361 ''' 

362 p = self.others(other) 

363 if wrap: 

364 p = _Wrap.point(p) 

365 E = self.ellipsoids(other) 

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

367 

368 @Property_RO 

369 def _elevation2(self): 

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

371 ''' 

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

373 timeout=self._elevation2to) 

374 

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

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

377 or sphere. 

378 

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

380 C{NAD83} (C{bool}). 

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

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

383 radius). 

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

385 

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

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

388 

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

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

391 L{elevations.elevation2} is based. 

392 

393 @note: NED elevation is only available for locations within the 

394 U{Conterminous US (CONUS) 

395 <https://WikiPedia.org/wiki/Contiguous_United_States>}. 

396 

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

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

399 ''' 

400 if self._elevation2to != timeout: 

401 self._elevation2to = timeout 

402 LatLonEllipsoidalBase._elevation2._update(self) 

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

404 

405 def ellipsoid(self, datum=_WGS84): 

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

407 

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

409 

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

411 ''' 

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

413 

414 @property_RO 

415 def ellipsoidalLatLon(self): 

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

417 ''' 

418 return type(self) 

419 

420 def ellipsoids(self, other): 

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

422 

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

424 

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

426 

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

428 

429 @raise ValueError: Incompatible datum ellipsoids. 

430 ''' 

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

432 

433 E = self.ellipsoid() 

434 try: # other may be Sphere, etc. 

435 e = other.ellipsoid() 

436 except AttributeError: 

437 try: # no ellipsoid method, try datum 

438 e = other.datum.ellipsoid 

439 except AttributeError: 

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

441 if e != E: 

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

443 return E 

444 

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

446 def epoch(self): 

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

448 ''' 

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

450 

451 @epoch.setter # PYCHOK setter! 

452 def epoch(self, epoch): 

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

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

455 

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

457 ''' 

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

459 

460 @Property_RO 

461 def Equidistant(self): 

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

463 ''' 

464 try: 

465 _ = self.datum.ellipsoid.geodesic 

466 return _MODS.azimuthal.EquidistantKarney 

467 except ImportError: # no geographiclib 

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

469 

470 @Property_RO 

471 def _etm(self): 

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

473 ''' 

474 etm = _MODS.etm 

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

476 

477 @property_RO 

478 def gamma(self): 

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

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

481 ''' 

482 return self._gamma 

483 

484 @Property_RO 

485 def _geoidHeight2(self): 

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

487 ''' 

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

489 timeout=self._geoidHeight2to) 

490 

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

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

493 or sphere. 

494 

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

496 C{NAD83/NADV88} (C{bool}). 

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

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

499 radius). 

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

501 

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

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

504 

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

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

507 the L{elevations.geoidHeight2} is based. 

508 

509 @note: The geoid height is only available for locations within the 

510 U{Conterminous US (CONUS) 

511 <https://WikiPedia.org/wiki/Contiguous_United_States>}. 

512 

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

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

515 ''' 

516 if self._geoidHeight2to != timeout: 

517 self._geoidHeight2to = timeout 

518 LatLonEllipsoidalBase._geoidHeight2._update(self) 

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

520 

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

522 '''I{Must be overloaded}.''' 

523 _MODS.named.notOverloaded(self, other, fraction, height=height, wrap=wrap) 

524 

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

526 equidistant=None, tol=_TOL_M): 

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

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

529 

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

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

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

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

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

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

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

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

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

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

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

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

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

543 length (C{meter}, conventionally). 

544 

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

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

547 

548 @raise ImportError: Package U{geographiclib 

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

550 not installed or not found, but only if 

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

552 

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

554 non-intersecting lines or no convergence 

555 for the given B{C{tol}}. 

556 

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

558 is not C{LatLon}. 

559 

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

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

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

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

564 of the authalic earth perimeter). 

565 

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

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

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

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

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

571 ''' 

572 try: 

573 s2 = self.others(other) 

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

575 s2, end2, 

576 height=height, wrap=wrap, 

577 equidistant=equidistant, tol=tol, 

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

579 except (TypeError, ValueError) as x: 

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

581 height=height, wrap=wrap, tol=tol) 

582 

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

584 equidistant=None, tol=_TOL_M): 

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

586 each defined by a center point and a radius. 

587 

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

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

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

591 B{C{radius1}}). 

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

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

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

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

596 center (C{bool}). 

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

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

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

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

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

602 

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

604 instance. For abutting circles, both intersection 

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

606 

607 @raise ImportError: Package U{geographiclib 

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

609 not installed or not found, but only if 

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

611 

612 @raise IntersectionError: Concentric, antipodal, invalid or 

613 non-intersecting circles or no 

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

615 

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

617 

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

619 

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

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

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

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

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

625 intersections. 

626 ''' 

627 try: 

628 c2 = self.others(other) 

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

630 c2, radius2, 

631 height=height, wrap=wrap, 

632 equidistant=equidistant, tol=tol, 

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

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

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

636 height=height, wrap=wrap, tol=tol) 

637 

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

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

640 

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

642 L{BooleanFHP} or L{BooleanGH}). 

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

644 B{C{points}} (C{bool}). 

645 

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

647 C{False} otherwise. 

648 

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

650 

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

652 

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

654 

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

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

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

658 ''' 

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

660 

661 @property_RO 

662 def iteration(self): 

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

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

665 ''' 

666 return self._iteration 

667 

668 @Property_RO 

669 def _lcc(self): 

670 '''(INTERNAL) Get this C{LatLon} point as a Lambert location (L{Lcc}). 

671 ''' 

672 lcc = _MODS.lcc 

673 return lcc.toLcc(self, height=self.height, Lcc=lcc.Lcc, name=self.name) 

674 

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

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

677 

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

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

680 mean height (C{meter}). 

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

682 may be negative or greater than 1.0. 

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

684 B{C{other}} point (C{bool}). 

685 

686 @return: Midpoint (C{LatLon}). 

687 

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

689 

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

691 

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

693 ''' 

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

695 

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

697 equidistant=None, tol=_TOL_M): 

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

699 two other (ellipsoidal) points. 

700 

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

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

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

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

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

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

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

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

709 takes the heights of the points into account. 

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

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

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

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

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

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

716 

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

718 

719 @raise ImportError: Package U{geographiclib 

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

721 not installed or not found, but only if 

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

723 

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

725 B{C{equidistant}}. 

726 

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

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

729 

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

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

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

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

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

735 ''' 

736 try: 

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

738 height=height, wrap=wrap, 

739 equidistant=equidistant, 

740 tol=tol, LatLon=self.classof) 

741 except (TypeError, ValueError) as x: 

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

743 height=height, wrap=wrap, tol=tol) 

744 return t.closest 

745 

746 @Property_RO 

747 def _osgr(self): 

748 '''(INTERNAL) Get this C{LatLon} point as an OSGR coordinate (L{Osgr}), 

749 based on the OS recommendation. 

750 ''' 

751 return _MODS.osgr.toOsgr(self, kTM=False, name=self.name) # datum=self.datum 

752 

753 @Property_RO 

754 def _osgrTM(self): 

755 '''(INTERNAL) Get this C{LatLon} point as an OSGR coordinate (L{Osgr}) 

756 based on I{Karney}'s Krüger implementation. 

757 ''' 

758 return _MODS.osgr.toOsgr(self, kTM=True, name=self.name) # datum=self.datum 

759 

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

761 sep=_COMMA_, wrap=False, name=NN): 

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

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

764 

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

766 see function L{pygeodesy.parse3llh}. 

767 @kwarg height: Optional, default height (C{meter} or 

768 C{None}). 

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

770 datum I{without conversion}. 

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

772 epoch I{without conversion}. 

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

774 this reframe I{without conversion}. 

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

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

777 and longitude (C{bool}). 

778 @kwarg name: Optional instance name (C{str}), overriding 

779 this name. 

780 

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

782 

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

784 ''' 

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

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

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

788 r.datum = datum 

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

790 r.epoch = epoch 

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

792 r.reframe = reframe 

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

794 

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

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

797 difference in Gaussian radii of curvature of the given 

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

799 

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

801 ''' 

802 if adjust: # Elevation2Tuple or GeoidHeight2Tuple 

803 m, t = meter_text2 

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

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

806 if n > EPS0: 

807 # use ratio, datum and NAD83 units may differ 

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

809 _earth_ellipsoid(datum) 

810 r = E.rocGauss(self.lat) 

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

812 m *= r / n 

813 meter_text2 = meter_text2.classof(m, t) 

814 return self._xnamed(meter_text2) 

815 

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

817 def reframe(self): 

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

819 ''' 

820 return self._reframe 

821 

822 @reframe.setter # PYCHOK setter! 

823 def reframe(self, reframe): 

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

825 

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

827 ''' 

828 _set_reframe(self, reframe) 

829 

830 @Property_RO 

831 def scale(self): 

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

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

834 ''' 

835 return self._scale 

836 

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

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

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

840 

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

842 for further details. 

843 ''' 

844 kwds = Cartesian_and_kwds 

845 if kwds: 

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

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

848 

849 def toCss(self, **toCss_kwds): 

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

851 

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

853 

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

855 

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

857 ''' 

858 return self._css if not toCss_kwds else _MODS.css.toCss( 

859 self, **_xkwds(toCss_kwds, name=self.name)) 

860 

861 def toDatum(self, datum2, height=None, name=NN): 

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

863 

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

865 @kwarg height: Optional height, overriding the 

866 converted height (C{meter}). 

867 @kwarg name: Optional name (C{str}), iff converted. 

868 

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

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

871 matches this point's C{datum}. 

872 

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

874 ''' 

875 n = name or self.name 

876 d2 = _ellipsoidal_datum(datum2, name=n) 

877 if self.datum == d2: 

878 r = self.copy(name=name) 

879 else: 

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

881 epoch=self.epoch, reframe=self.reframe) 

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

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

884 return r 

885 

886 def toEtm(self, **toEtm8_kwds): 

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

888 

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

890 

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

892 

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

894 ''' 

895 return self._etm if not toEtm8_kwds else _MODS.etm.toEtm8( 

896 self, **_xkwds(toEtm8_kwds, name=self.name)) 

897 

898 def toLcc(self, **toLcc_kwds): 

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

900 

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

902 

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

904 

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

906 ''' 

907 return self._lcc if not toLcc_kwds else _MODS.lcc.toLcc( 

908 self, **_xkwds(toLcc_kwds, name=self.name)) 

909 

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

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

912 

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

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

915 C{B{center} meter} (C{scalar}). 

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

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

918 

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

920 

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

922 ''' 

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

924 

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

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

927 

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

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

930 formulation (C{bool}). 

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

932 

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

934 

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

936 ''' 

937 if toOsgr_kwds: 

938 r = _MODS.osgr.toOsgr(self, kTM=kTM, **_xkwds(toOsgr_kwds, name=self.name)) 

939 else: 

940 r = self._osgrTM if kTM else self._osgr 

941 return r 

942 

943 def toRefFrame(self, reframe2, reframe=None, epoch=None, epoch2=None, height=None, name=NN): 

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

945 

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

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

948 point's reference frame. 

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

950 this point's epoch. 

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

952 C{scalar} or C{str}). 

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

954 @kwarg name: Optional name (C{str}), iff converted. 

955 

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

957 C{nil}, this point or a copy of this point if the B{C{name}} is 

958 non-empty. 

959 

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

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

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

963 

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

965 ''' 

966 e, t0, d, d2 = _MODS.trf._eT0Ds4(self, reframe, epoch, reframe2, epoch2) 

967 if t0: 

968 c = self.toCartesian().toDatum(d).toTransforms_(t0).toDatum(d2) 

969 n = name or self.name 

970 ll = c.toLatLon(datum=self.datum, epoch=e, height=height, 

971 LatLon=self.classof, name=n, reframe=reframe2) 

972 else: 

973 ll = self.copy(name=name) if name else self 

974 return ll 

975 

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

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

978 

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

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

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

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

983 to its C{lowerleft} (C{bool}) or 

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

985 

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

987 

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

989 ''' 

990 if self._upsOK(pole, falsed): 

991 u = self._ups 

992 else: 

993 ups = _MODS.ups 

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

995 pole=pole, falsed=falsed) 

996 return _lowerleft(u, center) 

997 

998 def toUtm(self, center=False): 

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

1000 

1001 @kwarg center: If C{True}, I{un}-center the UTM 

1002 to its C{lowerleft} (C{bool}) or 

1003 by C{B{center} meter} (C{scalar}). 

1004 

1005 @return: The UTM coordinate (L{Utm}). 

1006 

1007 @see: Method L{Mgrs.toUtm} and function L{pygeodesy.toUtm8}. 

1008 ''' 

1009 return _lowerleft(self._utm, center) 

1010 

1011 def toUtmUps(self, pole=NN, center=False): 

1012 '''Convert this C{LatLon} point to a UTM or UPS coordinate. 

1013 

1014 @kwarg pole: Optional top/center of UPS (stereographic) 

1015 projection (C{str}, 'N[orth]' or 'S[outh]'). 

1016 @kwarg center: If C{True}, I{un}-center the UTM or UPS to 

1017 its C{lowerleft} (C{bool}) or by C{B{center} 

1018 meter} (C{scalar}). 

1019 

1020 @return: The UTM or UPS coordinate (L{Utm} or L{Ups}). 

1021 

1022 @see: Function L{pygeodesy.toUtmUps8}. 

1023 ''' 

1024 if self._utmOK(): 

1025 u = self._utm 

1026 elif self._upsOK(pole): 

1027 u = self._ups 

1028 else: # no cover 

1029 utmups = _MODS.utmups 

1030 u = utmups.toUtmUps8(self, datum=self.datum, pole=pole, name=self.name, 

1031 Utm=utmups.Utm, Ups=utmups.Ups) 

1032 if isinstance(u, utmups.Utm): 

1033 self._update(False, _utm=u) # PYCHOK kwds 

1034 elif isinstance(u, utmups.Ups): 

1035 self._update(False, _ups=u) # PYCHOK kwds 

1036 else: 

1037 _xinstanceof(utmups.Utm, utmups.Ups, toUtmUps8=u) 

1038 return _lowerleft(u, center) 

1039 

1040 @deprecated_method 

1041 def to3xyz(self): # PYCHOK no cover 

1042 '''DEPRECATED, use method C{toEcef}. 

1043 

1044 @return: A L{Vector3Tuple}C{(x, y, z)}. 

1045 

1046 @note: Overloads C{LatLonBase.to3xyz} 

1047 ''' 

1048 r = self.toEcef() 

1049 return _MODS.namedTuples.Vector3Tuple(r.x, r.y, r.z, name=self.name) 

1050 

1051 def triangulate(self, bearing1, other, bearing2, **height_wrap_tol): 

1052 '''I{Iteratively} locate a point given this, an other point and the (initial) 

1053 bearing at this and at the other point. 

1054 

1055 @arg bearing1: Bearing at this point (compass C{degrees360}). 

1056 @arg other: Start point of the other line (C{LatLon}). 

1057 @arg bearing2: Bearing at the other point (compass C{degrees360}). 

1058 @kwarg height_wrap_tol: Optional keyword arguments C{B{height}=None}, 

1059 C{B{wrap}=False} and C{B{tol}}, see method L{intersection3}. 

1060 

1061 @return: Triangulated point (C{LatLon}). 

1062 

1063 @see: Method L{intersection3} for further details. 

1064 ''' 

1065 if _isDegrees(bearing1) and _isDegrees(bearing2): 

1066 r = self.intersection3(bearing1, other, bearing2, **height_wrap_tol) 

1067 return r.point 

1068 raise _TypeError(bearing1=bearing1, bearing2=bearing2 **height_wrap_tol) 

1069 

1070 def trilaterate5(self, distance1, point2, distance2, point3, distance3, 

1071 area=True, eps=EPS1, wrap=False): 

1072 '''Trilaterate three points by I{area overlap} or I{perimeter 

1073 intersection} of three intersecting circles. 

1074 

1075 @arg distance1: Distance to this point (C{meter}), same units 

1076 as B{C{eps}}). 

1077 @arg point2: Second center point (C{LatLon}). 

1078 @arg distance2: Distance to point2 (C{meter}, same units as 

1079 B{C{eps}}). 

1080 @arg point3: Third center point (C{LatLon}). 

1081 @arg distance3: Distance to point3 (C{meter}, same units as 

1082 B{C{eps}}). 

1083 @kwarg area: If C{True} compute the area overlap, otherwise the 

1084 perimeter intersection of the circles (C{bool}). 

1085 @kwarg eps: The required I{minimal overlap} for C{B{area}=True} 

1086 or the I{intersection margin} for C{B{area}=False} 

1087 (C{meter}, conventionally). 

1088 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll 

1089 B{C{point2}} and B{C{point3}} (C{bool}). 

1090 

1091 @return: A L{Trilaterate5Tuple}C{(min, minPoint, max, maxPoint, n)} 

1092 with C{min} and C{max} in C{meter}, same units as B{C{eps}}, 

1093 the corresponding trilaterated points C{minPoint} and 

1094 C{maxPoint} as I{ellipsoidal} C{LatLon} and C{n}, the number 

1095 of trilatered points found for the given B{C{eps}}. 

1096 

1097 If only a single trilaterated point is found, C{min I{is} 

1098 max}, C{minPoint I{is} maxPoint} and C{n = 1}. 

1099 

1100 For C{B{area}=True}, C{min} and C{max} are the smallest 

1101 respectively largest I{radial} overlap found. 

1102 

1103 For C{B{area}=False}, C{min} and C{max} represent the 

1104 nearest respectively farthest intersection margin. 

1105 

1106 If C{B{area}=True} and all 3 circles are concentric, C{n=0} 

1107 and C{minPoint} and C{maxPoint} are the B{C{point#}} with 

1108 the smallest B{C{distance#}} C{min} respectively C{max} the 

1109 largest B{C{distance#}}. 

1110 

1111 @raise IntersectionError: Trilateration failed for the given B{C{eps}}, 

1112 insufficient overlap for C{B{area}=True}, no 

1113 circle intersections for C{B{area}=False} or 

1114 all circles are (near-)concentric. 

1115 

1116 @raise TypeError: Invalid B{C{point2}} or B{C{point3}}. 

1117 

1118 @raise ValueError: Coincident B{C{points}} or invalid B{C{distance1}}, 

1119 B{C{distance2}} or B{C{distance3}}. 

1120 

1121 @note: Ellipsoidal trilateration invokes methods C{LatLon.intersections2} 

1122 and C{LatLon.nearestOn} based on I{Karney}'s Python U{geographiclib 

1123 <https://PyPI.org/project/geographiclib>} if installed, otherwise 

1124 the accurate (but slower) C{ellipsoidalExact.LatLon} methods. 

1125 ''' 

1126 return _trilaterate5(self, distance1, 

1127 self.others(point2=point2), distance2, 

1128 self.others(point3=point3), distance3, 

1129 area=area, eps=eps, wrap=wrap) 

1130 

1131 @Property_RO 

1132 def _ups(self): # __dict__ value overwritten by method C{toUtmUps} 

1133 '''(INTERNAL) Get this C{LatLon} point as UPS coordinate (L{Ups}), 

1134 see L{pygeodesy.toUps8}. 

1135 ''' 

1136 ups = _MODS.ups 

1137 return ups.toUps8(self, datum=self.datum, Ups=ups.Ups, 

1138 pole=NN, falsed=True, name=self.name) 

1139 

1140 def _upsOK(self, pole=NN, falsed=True): 

1141 '''(INTERNAL) Check matching C{Ups}. 

1142 ''' 

1143 try: 

1144 u = self._ups 

1145 except RangeError: 

1146 return False 

1147 return falsed and (u.pole == pole[:1].upper() or not pole) 

1148 

1149 @Property_RO 

1150 def _utm(self): # __dict__ value overwritten by method C{toUtmUps} 

1151 '''(INTERNAL) Get this C{LatLon} point as UTM coordinate (L{Utm}), 

1152 see L{pygeodesy.toUtm8}. 

1153 ''' 

1154 utm = _MODS.utm 

1155 return utm.toUtm8(self, datum=self.datum, Utm=utm.Utm, name=self.name) 

1156 

1157 def _utmOK(self): 

1158 '''(INTERNAL) Check C{Utm}. 

1159 ''' 

1160 try: 

1161 _ = self._utm 

1162 except RangeError: 

1163 return False 

1164 return True 

1165 

1166 

1167def _lowerleft(utmups, center): 

1168 '''(INTERNAL) Optionally I{un}-center C{utmups}. 

1169 ''' 

1170 if center in (False, 0, _0_0): 

1171 u = utmups 

1172 elif center in (True,): 

1173 u = utmups._lowerleft 

1174 else: 

1175 u = _MODS.utmupsBase._lowerleft(utmups, center) 

1176 return u 

1177 

1178 

1179def _nearestOn(point, point1, point2, within=True, height=None, wrap=False, # was=True 

1180 equidistant=None, tol=_TOL_M, **LatLon_and_kwds): 

1181 '''(INTERNAL) Get closest point, imported by .ellipsoidalExact, 

1182 -GeodSolve, -Karney and -Vincenty to embellish exceptions. 

1183 ''' 

1184 try: 

1185 p = _xellipsoidal(point=point) 

1186 t = _MODS.ellipsoidalBaseDI._nearestOn2(p, point1, point2, within=within, 

1187 height=height, wrap=wrap, 

1188 equidistant=equidistant, 

1189 tol=tol, **LatLon_and_kwds) 

1190 except (TypeError, ValueError) as x: 

1191 raise _xError(x, point=point, point1=point1, point2=point2) 

1192 return t.closest 

1193 

1194 

1195def _set_reframe(inst, reframe): 

1196 '''(INTERNAL) Set or clear an instance's reference frame. 

1197 ''' 

1198 if reframe is not None: 

1199 _xinstanceof(_MODS.trf.RefFrame, reframe=reframe) 

1200 inst._reframe = reframe 

1201 elif inst.reframe is not None: 

1202 inst._reframe = None 

1203 

1204 

1205__all__ += _ALL_DOCS(CartesianEllipsoidalBase, LatLonEllipsoidalBase) 

1206 

1207# **) MIT License 

1208# 

1209# Copyright (C) 2016-2024 -- mrJean1 at Gmail -- All Rights Reserved. 

1210# 

1211# Permission is hereby granted, free of charge, to any person obtaining a 

1212# copy of this software and associated documentation files (the "Software"), 

1213# to deal in the Software without restriction, including without limitation 

1214# the rights to use, copy, modify, merge, publish, distribute, sublicense, 

1215# and/or sell copies of the Software, and to permit persons to whom the 

1216# Software is furnished to do so, subject to the following conditions: 

1217# 

1218# The above copyright notice and this permission notice shall be included 

1219# in all copies or substantial portions of the Software. 

1220# 

1221# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS 

1222# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, 

1223# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL 

1224# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR 

1225# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, 

1226# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR 

1227# OTHER DEALINGS IN THE SOFTWARE.