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, TRFError, \ 

22 _TypeError, _ValueError, _xattr, _xellipsoidal, \ 

23 _xError, _xkwds, _xkwds_get, _xkwds_not 

24# from pygeodesy.fmath import favg # _MODS 

25from pygeodesy.interns import MISSING, NN, _COMMA_, _conversion_, _DOT_, \ 

26 _ellipsoidal_, _no_, _reframe_, _SPACE_ 

27from pygeodesy.latlonBase import LatLonBase, _trilaterate5, fabs, _Wrap 

28from pygeodesy.lazily import _ALL_DOCS, _ALL_LAZY, _ALL_MODS as _MODS 

29# from pygeodesy.lcc import toLcc # _MODS 

30# from pygeodesy.named import notOverloaded # _MODS 

31# from pygeodesy.namedTuples import Vector3Tuple # _MODS 

32from pygeodesy.props import deprecated_method, deprecated_property_RO, \ 

33 Property_RO, property_doc_, property_RO, _update_all 

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__ = '23.12.18' 

41 

42 

43class CartesianEllipsoidalBase(CartesianBase): 

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

45 ''' 

46 _datum = _WGS84 # L{Datum} 

47 _reframe = None 

48 

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

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

51# ''' 

52# RefFrame = _MODS.trf.RefFrame 

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

54# _NotImplemented(self, other) 

55 

56 @deprecated_method 

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

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

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

60 

61 @property_RO 

62 def ellipsoidalCartesian(self): 

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

64 ''' 

65 return type(self) 

66 

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

68 Vector=None, **Vector_kwds): 

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

70 cartesian center point and a radius. 

71 

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

73 coordinates). 

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

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

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

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

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

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

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

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

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

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

84 ignored if C{B{Vector} is None}. 

85 

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

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

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

89 

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

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

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

93 

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

95 

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

97 

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

99 

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

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

102 Intersection and function L{pygeodesy.radical2}. 

103 ''' 

104 try: 

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

106 center2, Radius_(radius2=radius2), 

107 sphere=sphere, clas=self.classof, 

108 Vector=Vector, **Vector_kwds) 

109 except (TypeError, ValueError) as x: 

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

111 

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

113 def reframe(self): 

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

115 ''' 

116 return self._reframe 

117 

118 @reframe.setter # PYCHOK setter! 

119 def reframe(self, reframe): 

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

121 

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

123 ''' 

124 _set_reframe(self, reframe) 

125 

126 def toRefFrame(self, reframe2, reframe=None, epoch=None): 

127 '''Convert this cartesian point from one to an other reference frame. 

128 

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

130 @arg reframe: Reference frame to convert I{from} (L{RefFrame}), 

131 overriding this cartesian's C{reframe}. 

132 @kwarg epoch: Optional epoch to observe (C{scalar}, fractional 

133 calendar year), overriding B{C{reframe}}'s epoch. 

134 

135 @return: The converted point (C{Cartesian}) or this point if 

136 conversion is C{nil}. 

137 

138 @raise TRFError: No conversion available from B{C{reframe}} 

139 to B{C{reframe2}} or invalid B{C{epoch}}. 

140 

141 @raise TypeError: B{C{reframe2}} or B{C{reframe}} not a 

142 L{RefFrame}. 

143 ''' 

144 r = self.reframe if reframe is None else reframe 

145 if r in (None, reframe2): 

146 xs = None # XXX _set_reframe(self, reframe2)? 

147 else: 

148 trf = _MODS.trf 

149 _xinstanceof(trf.RefFrame, reframe2=reframe2, reframe=r) 

150 _, xs = trf._reframeTransforms2(reframe2, r, epoch) 

151 return self.toTransforms_(*xs) if xs else self 

152 

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

154 '''Apply none, one or several Helmert transforms. 

155 

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

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

158 overriding this point's datum. 

159 

160 @return: The transformed point (C{Cartesian}) or this point 

161 if the B{C{transforms}} produce the same point. 

162 ''' 

163 r = self 

164 if transforms: 

165 xyz = r.xyz 

166 for t in transforms: 

167 xyz = t.transform(*xyz) 

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

169 if d != r.datum or xyz != r.xyz: 

170 r = r.classof(xyz, datum=d) 

171 return r 

172 

173 

174class LatLonEllipsoidalBase(LatLonBase): 

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

176 ''' 

177 _datum = _WGS84 # L{Datum} 

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

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

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

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

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

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

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

185 

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

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

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

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

190 

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

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

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

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

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

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

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

198 L{Ellipsoid2} or L{a_f2Tuple}). 

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

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

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

202 if C{B{reframe}=None}. 

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

204 (C{bool}). 

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

206 

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

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

209 

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

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

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

213 

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

215 ''' 

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

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

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

219 if reframe: 

220 self.reframe = reframe 

221 self.epoch = epoch 

222 

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

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

225# ''' 

226# RefFrame = _MODS.trf.RefFrame 

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

228# _NotImplemented(self, other) 

229 

230 def antipode(self, height=None): 

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

232 to this point. 

233 

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

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

236 

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

238 ''' 

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

240 if lla.datum != self.datum: 

241 lla.datum = self.datum 

242 return lla 

243 

244 @deprecated_property_RO 

245 def convergence(self): 

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

247 return self.gamma 

248 

249 @deprecated_method 

250 def convertDatum(self, datum2): 

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

252 return self.toDatum(datum2) 

253 

254 @deprecated_method 

255 def convertRefFrame(self, reframe2): 

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

257 return self.toRefFrame(reframe2) 

258 

259 @Property_RO 

260 def _css(self): 

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

262 ''' 

263 css = _MODS.css 

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

265 

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

267 def datum(self): 

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

269 ''' 

270 return self._datum 

271 

272 @datum.setter # PYCHOK setter! 

273 def datum(self, datum): 

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

275 

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

277 or not ellipsoidal. 

278 ''' 

279 _xinstanceof(Datum, datum=datum) 

280 if not datum.isEllipsoidal: 

281 raise _IsnotError(_ellipsoidal_, datum=datum) 

282 if self._datum != datum: 

283 _update_all(self) 

284 self._datum = datum 

285 

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

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

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

289 

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

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

292 

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

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

295 point (C{bool}). 

296 

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

298 

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

300 

301 @raise ValueError: Incompatible datum ellipsoids. 

302 

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

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

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

306 formula. 

307 ''' 

308 p = self.others(other) 

309 if wrap: 

310 p = _Wrap.point(p) 

311 E = self.ellipsoids(other) 

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

313 

314 @Property_RO 

315 def _elevation2(self): 

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

317 ''' 

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

319 timeout=self._elevation2to) 

320 

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

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

323 or sphere. 

324 

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

326 C{NAD83} (C{bool}). 

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

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

329 radius). 

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

331 

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

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

334 

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

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

337 L{elevations.elevation2} is based. 

338 

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

340 U{Conterminous US (CONUS) 

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

342 

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

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

345 ''' 

346 if self._elevation2to != timeout: 

347 self._elevation2to = timeout 

348 LatLonEllipsoidalBase._elevation2._update(self) 

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

350 

351 def ellipsoid(self, datum=_WGS84): 

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

353 

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

355 

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

357 ''' 

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

359 

360 @property_RO 

361 def ellipsoidalLatLon(self): 

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

363 ''' 

364 return type(self) 

365 

366 def ellipsoids(self, other): 

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

368 

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

370 

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

372 

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

374 

375 @raise ValueError: Incompatible datum ellipsoids. 

376 ''' 

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

378 

379 E = self.ellipsoid() 

380 try: # other may be Sphere, etc. 

381 e = other.ellipsoid() 

382 except AttributeError: 

383 try: # no ellipsoid method, try datum 

384 e = other.datum.ellipsoid 

385 except AttributeError: 

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

387 if e != E: 

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

389 return E 

390 

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

392 def epoch(self): 

393 '''Get this point's observed or C{reframe} epoch (C{float}) or C{None}. 

394 ''' 

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

396 

397 @epoch.setter # PYCHOK setter! 

398 def epoch(self, epoch): 

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

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

401 

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

403 ''' 

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

405 

406 @Property_RO 

407 def Equidistant(self): 

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

409 ''' 

410 try: 

411 _ = self.datum.ellipsoid.geodesic 

412 return _MODS.azimuthal.EquidistantKarney 

413 except ImportError: # no geographiclib 

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

415 

416 @Property_RO 

417 def _etm(self): 

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

419 ''' 

420 etm = _MODS.etm 

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

422 

423 @property_RO 

424 def gamma(self): 

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

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

427 ''' 

428 return self._gamma 

429 

430 @Property_RO 

431 def _geoidHeight2(self): 

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

433 ''' 

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

435 timeout=self._geoidHeight2to) 

436 

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

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

439 or sphere. 

440 

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

442 C{NAD83/NADV88} (C{bool}). 

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

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

445 radius). 

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

447 

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

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

450 

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

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

453 the L{elevations.geoidHeight2} is based. 

454 

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

456 U{Conterminous US (CONUS) 

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

458 

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

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

461 ''' 

462 if self._geoidHeight2to != timeout: 

463 self._geoidHeight2to = timeout 

464 LatLonEllipsoidalBase._geoidHeight2._update(self) 

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

466 

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

468 '''I{Must be overloaded}.''' 

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

470 

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

472 equidistant=None, tol=_TOL_M): 

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

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

475 

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

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

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

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

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

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

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

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

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

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

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

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

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

489 length (C{meter}, conventionally). 

490 

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

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

493 

494 @raise ImportError: Package U{geographiclib 

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

496 not installed or not found, but only if 

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

498 

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

500 non-intersecting lines or no convergence 

501 for the given B{C{tol}}. 

502 

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

504 is not C{LatLon}. 

505 

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

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

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

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

510 of the authalic earth perimeter). 

511 

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

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

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

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

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

517 ''' 

518 try: 

519 s2 = self.others(other) 

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

521 s2, end2, 

522 height=height, wrap=wrap, 

523 equidistant=equidistant, tol=tol, 

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

525 except (TypeError, ValueError) as x: 

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

527 height=height, wrap=wrap, tol=tol) 

528 

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

530 equidistant=None, tol=_TOL_M): 

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

532 each defined by a center point and a radius. 

533 

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

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

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

537 B{C{radius1}}). 

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

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

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

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

542 center (C{bool}). 

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

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

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

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

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

548 

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

550 instance. For abutting circles, both intersection 

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

552 

553 @raise ImportError: Package U{geographiclib 

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

555 not installed or not found, but only if 

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

557 

558 @raise IntersectionError: Concentric, antipodal, invalid or 

559 non-intersecting circles or no 

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

561 

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

563 

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

565 

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

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

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

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

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

571 intersections. 

572 ''' 

573 try: 

574 c2 = self.others(other) 

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

576 c2, radius2, 

577 height=height, wrap=wrap, 

578 equidistant=equidistant, tol=tol, 

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

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

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

582 height=height, wrap=wrap, tol=tol) 

583 

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

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

586 

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

588 L{BooleanFHP} or L{BooleanGH}). 

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

590 B{C{points}} (C{bool}). 

591 

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

593 C{False} otherwise. 

594 

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

596 

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

598 

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

600 

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

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

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

604 ''' 

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

606 

607 @property_RO 

608 def iteration(self): 

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

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

611 ''' 

612 return self._iteration 

613 

614 @Property_RO 

615 def _lcc(self): 

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

617 ''' 

618 lcc = _MODS.lcc 

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

620 

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

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

623 

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

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

626 mean height (C{meter}). 

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

628 may be negative or greater than 1.0. 

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

630 B{C{other}} point (C{bool}). 

631 

632 @return: Midpoint (C{LatLon}). 

633 

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

635 

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

637 

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

639 ''' 

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

641 

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

643 equidistant=None, tol=_TOL_M): 

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

645 two other (ellipsoidal) points. 

646 

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

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

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

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

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

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

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

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

655 takes the heights of the points into account. 

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

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

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

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

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

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

662 

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

664 

665 @raise ImportError: Package U{geographiclib 

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

667 not installed or not found, but only if 

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

669 

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

671 B{C{equidistant}}. 

672 

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

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

675 

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

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

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

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

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

681 ''' 

682 try: 

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

684 height=height, wrap=wrap, 

685 equidistant=equidistant, 

686 tol=tol, LatLon=self.classof) 

687 except (TypeError, ValueError) as x: 

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

689 height=height, wrap=wrap, tol=tol) 

690 return t.closest 

691 

692 @Property_RO 

693 def _osgr(self): 

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

695 based on the OS recommendation. 

696 ''' 

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

698 

699 @Property_RO 

700 def _osgrTM(self): 

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

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

703 ''' 

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

705 

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

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

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

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

710 

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

712 see function L{pygeodesy.parse3llh}. 

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

714 C{None}). 

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

716 datum I{without conversion}. 

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

718 epoch I{without conversion}. 

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

720 this reframe I{without conversion}. 

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

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

723 and longitude (C{bool}). 

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

725 this name. 

726 

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

728 

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

730 ''' 

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

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

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

734 r.datum = datum 

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

736 r.epoch = epoch 

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

738 r.reframe = reframe 

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

740 

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

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

743 difference in Gaussian radii of curvature of the given 

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

745 

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

747 ''' 

748 if adjust: # Elevation2Tuple or GeoidHeight2Tuple 

749 m, t = meter_text2 

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

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

752 if n > EPS0: 

753 # use ratio, datum and NAD83 units may differ 

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

755 _earth_ellipsoid(datum) 

756 r = E.rocGauss(self.lat) 

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

758 m *= r / n 

759 meter_text2 = meter_text2.classof(m, t) 

760 return self._xnamed(meter_text2) 

761 

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

763 def reframe(self): 

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

765 ''' 

766 return self._reframe 

767 

768 @reframe.setter # PYCHOK setter! 

769 def reframe(self, reframe): 

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

771 

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

773 ''' 

774 _set_reframe(self, reframe) 

775 

776 @Property_RO 

777 def scale(self): 

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

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

780 ''' 

781 return self._scale 

782 

783 def toCss(self, **toCss_kwds): 

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

785 

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

787 

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

789 

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

791 ''' 

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

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

794 

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

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

797 

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

799 @kwarg height: Optional height, overriding the 

800 converted height (C{meter}). 

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

802 

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

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

805 matches this point's C{datum}. 

806 

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

808 ''' 

809 n = name or self.name 

810 d2 = _ellipsoidal_datum(datum2, name=n) 

811 if self.datum == d2: 

812 r = self.copy(name=name) 

813 else: 

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

815 epoch=self.epoch, reframe=self.reframe) 

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

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

818 return r 

819 

820 def toEtm(self, **toEtm8_kwds): 

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

822 

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

824 

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

826 

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

828 ''' 

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

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

831 

832 def toLcc(self, **toLcc_kwds): 

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

834 

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

836 

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

838 

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

840 ''' 

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

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

843 

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

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

846 

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

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

849 C{B{center} meter} (C{scalar}). 

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

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

852 

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

854 

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

856 ''' 

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

858 

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

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

861 

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

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

864 formulation (C{bool}). 

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

866 

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

868 

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

870 ''' 

871 if toOsgr_kwds: 

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

873 else: 

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

875 return r 

876 

877 def toRefFrame(self, reframe2, height=None, name=NN): 

878 '''Convert this point to an other reference frame. 

879 

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

881 @kwarg height: Optional height, overriding the converted 

882 height (C{meter}). 

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

884 

885 @return: The converted point (ellipsoidal C{LatLon}) or this 

886 point if conversion is C{nil}, or a copy of this 

887 point if the B{C{name}} is non-empty. 

888 

889 @raise TRFError: This point's C{reframe} is not defined or 

890 conversion from this point's C{reframe} to 

891 B{C{reframe2}} is not available. 

892 

893 @raise TypeError: Invalid B{C{reframe2}}, not a L{RefFrame}. 

894 ''' 

895 if not self.reframe: 

896 t = _SPACE_(_DOT_(repr(self), _reframe_), MISSING) 

897 raise TRFError(_no_(_conversion_), txt=t) 

898 

899 trf = _MODS.trf 

900 trf._xinstanceof(trf.RefFrame, reframe2=reframe2) 

901 

902 e, xs = trf._reframeTransforms2(reframe2, self.reframe, self.epoch) 

903 if xs: 

904 c = self.toCartesian().toTransforms_(*xs) 

905 n = name or self.name 

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

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

908 else: 

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

910 return ll 

911 

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

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

914 

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

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

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

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

919 to its C{lowerleft} (C{bool}) or 

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

921 

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

923 

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

925 ''' 

926 if self._upsOK(pole, falsed): 

927 u = self._ups 

928 else: 

929 ups = _MODS.ups 

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

931 pole=pole, falsed=falsed) 

932 return _lowerleft(u, center) 

933 

934 def toUtm(self, center=False): 

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

936 

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

938 to its C{lowerleft} (C{bool}) or 

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

940 

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

942 

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

944 ''' 

945 return _lowerleft(self._utm, center) 

946 

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

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

949 

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

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

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

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

954 meter} (C{scalar}). 

955 

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

957 

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

959 ''' 

960 if self._utmOK(): 

961 u = self._utm 

962 elif self._upsOK(pole): 

963 u = self._ups 

964 else: # no cover 

965 utmups = _MODS.utmups 

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

967 Utm=utmups.Utm, Ups=utmups.Ups) 

968 if isinstance(u, utmups.Utm): 

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

970 elif isinstance(u, utmups.Ups): 

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

972 else: 

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

974 return _lowerleft(u, center) 

975 

976 @deprecated_method 

977 def to3xyz(self): # PYCHOK no cover 

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

979 

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

981 

982 @note: Overloads C{LatLonBase.to3xyz} 

983 ''' 

984 r = self.toEcef() 

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

986 

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

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

989 bearing at this and at the other point. 

990 

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

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

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

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

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

996 

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

998 

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

1000 ''' 

1001 if _isDegrees(bearing1) and _isDegrees(bearing2): 

1002 r = self.intersection3(bearing1, other, bearing2, **height_wrap_tol) 

1003 return r.point 

1004 raise _TypeError(bearing1=bearing1, bearing2=bearing2 **height_wrap_tol) 

1005 

1006 def trilaterate5(self, distance1, point2, distance2, point3, distance3, 

1007 area=True, eps=EPS1, wrap=False): 

1008 '''Trilaterate three points by I{area overlap} or I{perimeter 

1009 intersection} of three intersecting circles. 

1010 

1011 @arg distance1: Distance to this point (C{meter}), same units 

1012 as B{C{eps}}). 

1013 @arg point2: Second center point (C{LatLon}). 

1014 @arg distance2: Distance to point2 (C{meter}, same units as 

1015 B{C{eps}}). 

1016 @arg point3: Third center point (C{LatLon}). 

1017 @arg distance3: Distance to point3 (C{meter}, same units as 

1018 B{C{eps}}). 

1019 @kwarg area: If C{True} compute the area overlap, otherwise the 

1020 perimeter intersection of the circles (C{bool}). 

1021 @kwarg eps: The required I{minimal overlap} for C{B{area}=True} 

1022 or the I{intersection margin} for C{B{area}=False} 

1023 (C{meter}, conventionally). 

1024 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll 

1025 B{C{point2}} and B{C{point3}} (C{bool}). 

1026 

1027 @return: A L{Trilaterate5Tuple}C{(min, minPoint, max, maxPoint, n)} 

1028 with C{min} and C{max} in C{meter}, same units as B{C{eps}}, 

1029 the corresponding trilaterated points C{minPoint} and 

1030 C{maxPoint} as I{ellipsoidal} C{LatLon} and C{n}, the number 

1031 of trilatered points found for the given B{C{eps}}. 

1032 

1033 If only a single trilaterated point is found, C{min I{is} 

1034 max}, C{minPoint I{is} maxPoint} and C{n = 1}. 

1035 

1036 For C{B{area}=True}, C{min} and C{max} are the smallest 

1037 respectively largest I{radial} overlap found. 

1038 

1039 For C{B{area}=False}, C{min} and C{max} represent the 

1040 nearest respectively farthest intersection margin. 

1041 

1042 If C{B{area}=True} and all 3 circles are concentric, C{n=0} 

1043 and C{minPoint} and C{maxPoint} are the B{C{point#}} with 

1044 the smallest B{C{distance#}} C{min} respectively C{max} the 

1045 largest B{C{distance#}}. 

1046 

1047 @raise IntersectionError: Trilateration failed for the given B{C{eps}}, 

1048 insufficient overlap for C{B{area}=True}, no 

1049 circle intersections for C{B{area}=False} or 

1050 all circles are (near-)concentric. 

1051 

1052 @raise TypeError: Invalid B{C{point2}} or B{C{point3}}. 

1053 

1054 @raise ValueError: Coincident B{C{points}} or invalid B{C{distance1}}, 

1055 B{C{distance2}} or B{C{distance3}}. 

1056 

1057 @note: Ellipsoidal trilateration invokes methods C{LatLon.intersections2} 

1058 and C{LatLon.nearestOn} based on I{Karney}'s Python U{geographiclib 

1059 <https://PyPI.org/project/geographiclib>} if installed, otherwise 

1060 the accurate (but slower) C{ellipsoidalExact.LatLon} methods. 

1061 ''' 

1062 return _trilaterate5(self, distance1, 

1063 self.others(point2=point2), distance2, 

1064 self.others(point3=point3), distance3, 

1065 area=area, eps=eps, wrap=wrap) 

1066 

1067 @Property_RO 

1068 def _ups(self): # __dict__ value overwritten by method C{toUtmUps} 

1069 '''(INTERNAL) Get this C{LatLon} point as UPS coordinate (L{Ups}), 

1070 see L{pygeodesy.toUps8}. 

1071 ''' 

1072 ups = _MODS.ups 

1073 return ups.toUps8(self, datum=self.datum, Ups=ups.Ups, 

1074 pole=NN, falsed=True, name=self.name) 

1075 

1076 def _upsOK(self, pole=NN, falsed=True): 

1077 '''(INTERNAL) Check matching C{Ups}. 

1078 ''' 

1079 try: 

1080 u = self._ups 

1081 except RangeError: 

1082 return False 

1083 return falsed and (u.pole == pole[:1].upper() or not pole) 

1084 

1085 @Property_RO 

1086 def _utm(self): # __dict__ value overwritten by method C{toUtmUps} 

1087 '''(INTERNAL) Get this C{LatLon} point as UTM coordinate (L{Utm}), 

1088 see L{pygeodesy.toUtm8}. 

1089 ''' 

1090 utm = _MODS.utm 

1091 return utm.toUtm8(self, datum=self.datum, Utm=utm.Utm, name=self.name) 

1092 

1093 def _utmOK(self): 

1094 '''(INTERNAL) Check C{Utm}. 

1095 ''' 

1096 try: 

1097 _ = self._utm 

1098 except RangeError: 

1099 return False 

1100 return True 

1101 

1102 

1103def _lowerleft(utmups, center): 

1104 '''(INTERNAL) Optionally I{un}-center C{utmups}. 

1105 ''' 

1106 if center in (False, 0, _0_0): 

1107 u = utmups 

1108 elif center in (True,): 

1109 u = utmups._lowerleft 

1110 else: 

1111 u = _MODS.utmupsBase._lowerleft(utmups, center) 

1112 return u 

1113 

1114 

1115def _nearestOn(point, point1, point2, within=True, height=None, wrap=False, # was=True 

1116 equidistant=None, tol=_TOL_M, **LatLon_and_kwds): 

1117 '''(INTERNAL) Get closest point, imported by .ellipsoidalExact, 

1118 -GeodSolve, -Karney and -Vincenty to embellish exceptions. 

1119 ''' 

1120 try: 

1121 p = _xellipsoidal(point=point) 

1122 t = _MODS.ellipsoidalBaseDI._nearestOn2(p, point1, point2, within=within, 

1123 height=height, wrap=wrap, 

1124 equidistant=equidistant, 

1125 tol=tol, **LatLon_and_kwds) 

1126 except (TypeError, ValueError) as x: 

1127 raise _xError(x, point=point, point1=point1, point2=point2) 

1128 return t.closest 

1129 

1130 

1131def _set_reframe(inst, reframe): 

1132 '''(INTERNAL) Set or clear an instance's reference frame. 

1133 ''' 

1134 if reframe is not None: 

1135 _xinstanceof(_MODS.trf.RefFrame, reframe=reframe) 

1136 inst._reframe = reframe 

1137 elif inst.reframe is not None: 

1138 inst._reframe = None 

1139 

1140 

1141__all__ += _ALL_DOCS(CartesianEllipsoidalBase, LatLonEllipsoidalBase) 

1142 

1143# **) MIT License 

1144# 

1145# Copyright (C) 2016-2024 -- mrJean1 at Gmail -- All Rights Reserved. 

1146# 

1147# Permission is hereby granted, free of charge, to any person obtaining a 

1148# copy of this software and associated documentation files (the "Software"), 

1149# to deal in the Software without restriction, including without limitation 

1150# the rights to use, copy, modify, merge, publish, distribute, sublicense, 

1151# and/or sell copies of the Software, and to permit persons to whom the 

1152# Software is furnished to do so, subject to the following conditions: 

1153# 

1154# The above copyright notice and this permission notice shall be included 

1155# in all copies or substantial portions of the Software. 

1156# 

1157# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS 

1158# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, 

1159# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL 

1160# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR 

1161# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, 

1162# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR 

1163# OTHER DEALINGS IN THE SOFTWARE.