Coverage for pygeodesy/ellipsoidalBase.py: 95%

289 statements  

« prev     ^ index     » next       coverage.py v7.2.2, created at 2023-04-11 14:35 -0400

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, _ellipsoidal_ # PYCHOK used! 

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

19 _spherical_datum, _WGS84, _xinstanceof 

20from pygeodesy.errors import _incompatible, _IsnotError, RangeError, TRFError, \ 

21 _ValueError, _xellipsoidal, _xError, _xkwds, \ 

22 _xkwds_get, _xkwds_not 

23# from pygeodesy.interns import _ellipsoidal_ # from .cartesianBase 

24from pygeodesy.interns import MISSING, NN, _COMMA_, _conversion_, _datum_, \ 

25 _DOT_, _no_, _reframe_, _SPACE_ 

26from pygeodesy.latlonBase import fabs, LatLonBase, _trilaterate5, Vector3Tuple 

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

28# from pygeodesy.lcc import toLcc # from ._MODS 

29# from pygeodesy.named import notOverloaded # from ._MODS 

30# from pygeodesy.namedTuples import Vector3Tuple # from .latlonBase 

31from pygeodesy.props import deprecated_method, deprecated_property_RO, \ 

32 Property_RO, property_doc_, property_RO, _update_all 

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

34 

35# from math import fabs # from .karney 

36 

37__all__ = _ALL_LAZY.ellipsoidalBase 

38__version__ = '23.04.11' 

39 

40 

41class CartesianEllipsoidalBase(CartesianBase): 

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

43 ''' 

44 _datum = _WGS84 # L{Datum} 

45 _reframe = None 

46 

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

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

49# ''' 

50# RefFrame = _MODS.trf.RefFrame 

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

52# _NotImplemented(self, other) 

53 

54 @deprecated_method 

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

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

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

58 

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

60 Vector=None, **Vector_kwds): 

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

62 cartesian center point and a radius. 

63 

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

65 coordinates). 

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

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

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

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

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

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

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

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

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

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

76 ignored if C{B{Vector} is None}. 

77 

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

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

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

81 

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

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

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

85 

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

87 

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

89 

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

91 

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

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

94 Intersection and function L{pygeodesy.radical2}. 

95 ''' 

96 try: 

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

98 center2, Radius_(radius2=radius2), 

99 sphere=sphere, clas=self.classof, 

100 Vector=Vector, **Vector_kwds) 

101 except (TypeError, ValueError) as x: 

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

103 

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

105 def reframe(self): 

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

107 ''' 

108 return self._reframe 

109 

110 @reframe.setter # PYCHOK setter! 

111 def reframe(self, reframe): 

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

113 

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

115 ''' 

116 _set_reframe(self, reframe) 

117 

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

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

120 

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

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

123 overriding this cartesian's C{reframe}. 

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

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

126 

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

128 conversion is C{nil}. 

129 

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

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

132 

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

134 L{RefFrame}. 

135 ''' 

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

137 if r in (None, reframe2): 

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

139 else: 

140 trf = _MODS.trf 

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

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

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

144 

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

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

147 

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

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

150 overriding this point's datum. 

151 

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

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

154 ''' 

155 r = self 

156 if transforms: 

157 xyz = r.xyz 

158 for t in transforms: 

159 xyz = t.transform(*xyz) 

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

161 if d != r.datum or xyz != r.xyz: 

162 r = r.classof(xyz, datum=d) 

163 return r 

164 

165 

166class LatLonEllipsoidalBase(LatLonBase): 

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

168 ''' 

169 _datum = _WGS84 # L{Datum} 

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

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

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

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

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

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

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

177 

178 def __init__(self, lat, lon, height=0, datum=None, reframe=None, 

179 epoch=None, name=NN): 

180 '''Create an ellipsoidal C{LatLon} point frome the given 

181 lat-, longitude and height on the given datum and with 

182 the given reference frame and epoch. 

183 

184 @arg lat: Latitude (C{degrees} or DMS C{[N|S]}). 

185 @arg lon: Longitude (C{degrees} or DMS C{str[E|W]}). 

186 @kwarg height: Optional elevation (C{meter}, the same units 

187 as the datum's half-axes). 

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

189 L{Ellipsoid}, L{Ellipsoid2} or L{a_f2Tuple}). 

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

191 @kwarg epoch: Optional epoch to observe for B{C{reframe}} 

192 (C{scalar}), a non-zero, fractional calendar 

193 year; silently ignored if C{B{reframe} is None}. 

194 @kwarg name: Optional name (string). 

195 

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

197 range and C{rangerrors} set to C{True}. 

198 

199 @raise TypeError: B{C{datum}} is not a L{Datum}, B{C{reframe}} 

200 is not a L{RefFrame} or B{C{epoch}} is not 

201 C{scalar} non-zero. 

202 

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

204 

205 @example: 

206 

207 >>> p = LatLon(51.4778, -0.0016) # height=0, datum=Datums.WGS84 

208 ''' 

209 LatLonBase.__init__(self, lat, lon, height=height, name=name) 

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

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

212 if reframe: 

213 self.reframe = reframe 

214 self.epoch = epoch 

215 

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

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

218# ''' 

219# RefFrame = _MODS.trf.RefFrame 

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

221# _NotImplemented(self, other) 

222 

223 def antipode(self, height=None): 

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

225 to this point. 

226 

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

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

229 

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

231 ''' 

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

233 if lla.datum != self.datum: 

234 lla.datum = self.datum 

235 return lla 

236 

237 @deprecated_property_RO 

238 def convergence(self): 

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

240 return self.gamma 

241 

242 @deprecated_method 

243 def convertDatum(self, datum2): 

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

245 return self.toDatum(datum2) 

246 

247 @deprecated_method 

248 def convertRefFrame(self, reframe2): 

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

250 return self.toRefFrame(reframe2) 

251 

252 @Property_RO 

253 def _css(self): 

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

255 ''' 

256 css = _MODS.css 

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

258 

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

260 def datum(self): 

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

262 ''' 

263 return self._datum 

264 

265 @datum.setter # PYCHOK setter! 

266 def datum(self, datum): 

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

268 

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

270 or not ellipsoidal. 

271 ''' 

272 _xinstanceof(Datum, datum=datum) 

273 if not datum.isEllipsoidal: 

274 raise _IsnotError(_ellipsoidal_, datum=datum) 

275 if self._datum != datum: 

276 _update_all(self) 

277 self._datum = datum 

278 

279 def distanceTo2(self, other): 

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

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

282 

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

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

285 

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

287 

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

289 

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

291 

292 @raise ValueError: Incompatible datum ellipsoids. 

293 

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

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

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

297 formula. 

298 ''' 

299 return self.ellipsoids(other).distance2(self.lat, self.lon, 

300 other.lat, other.lon) 

301 

302 @Property_RO 

303 def _elevation2(self): 

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

305 ''' 

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

307 timeout=self._elevation2to) 

308 

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

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

311 or sphere. 

312 

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

314 C{NAD83} (C{bool}). 

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

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

317 radius). 

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

319 

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

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

322 

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

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

325 L{elevations.elevation2} is based. 

326 

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

328 U{Conterminous US (CONUS) 

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

330 

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

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

333 ''' 

334 if self._elevation2to != timeout: 

335 self._elevation2to = timeout 

336 LatLonEllipsoidalBase._elevation2._update(self) 

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

338 

339 def ellipsoid(self, datum=_WGS84): 

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

341 

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

343 

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

345 ''' 

346 return getattr(self, _datum_, datum).ellipsoid 

347 

348 def ellipsoids(self, other): 

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

350 

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

352 

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

354 

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

356 

357 @raise ValueError: Incompatible datum ellipsoids. 

358 ''' 

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

360 

361 E = self.ellipsoid() 

362 try: # other may be Sphere, etc. 

363 e = other.ellipsoid() 

364 except AttributeError: 

365 try: # no ellipsoid method, try datum 

366 e = other.datum.ellipsoid 

367 except AttributeError: 

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

369 if e != E: 

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

371 return E 

372 

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

374 def epoch(self): 

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

376 ''' 

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

378 

379 @epoch.setter # PYCHOK setter! 

380 def epoch(self, epoch): 

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

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

383 

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

385 ''' 

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

387 

388 @Property_RO 

389 def Equidistant(self): 

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

391 ''' 

392 try: 

393 _ = self.datum.ellipsoid.geodesic 

394 return _MODS.azimuthal.EquidistantKarney 

395 except ImportError: # no geographiclib 

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

397 

398 @Property_RO 

399 def _etm(self): 

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

401 ''' 

402 etm = _MODS.etm 

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

404 

405 @property_RO 

406 def gamma(self): 

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

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

409 ''' 

410 return self._gamma 

411 

412 @Property_RO 

413 def _geoidHeight2(self): 

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

415 ''' 

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

417 timeout=self._geoidHeight2to) 

418 

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

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

421 or sphere. 

422 

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

424 C{NAD83/NADV88} (C{bool}). 

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

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

427 radius). 

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

429 

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

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

432 

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

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

435 the L{elevations.geoidHeight2} is based. 

436 

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

438 U{Conterminous US (CONUS) 

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

440 

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

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

443 ''' 

444 if self._geoidHeight2to != timeout: 

445 self._geoidHeight2to = timeout 

446 LatLonEllipsoidalBase._geoidHeight2._update(self) 

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

448 

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

450 '''(INTERNAL) I{Must be overloaded}, see function C{notOverloaded}. 

451 ''' 

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

453 

454 def intersection3(self, end1, other, end2, height=None, wrap=True, 

455 equidistant=None, tol=_TOL_M): 

456 '''Iteratively compute the intersection point of two lines, each 

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

458 

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

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

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

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

463 initial bearing at the other point (compass 

464 C{degrees360}). 

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

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

467 @kwarg wrap: Wrap and unroll longitudes (C{bool}). 

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

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

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

471 @kwarg tol: Tolerance for skew line distance and length and for 

472 convergence (C{meter}, conventionally). 

473 

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

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

476 

477 @raise ImportError: Package U{geographiclib 

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

479 not installed or not found, but only if 

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

481 

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

483 non-intersecting lines or no convergence 

484 for the given B{C{tol}}. 

485 

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

487 is not C{LatLon}. 

488 

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

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

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

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

493 of the authalic earth perimeter). 

494 

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

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

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

498 BOUNDARIES} for more details about the iteration algorithm. 

499 ''' 

500 try: 

501 s2 = self.others(other) 

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

503 s2, end2, 

504 height=height, wrap=wrap, 

505 equidistant=equidistant, tol=tol, 

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

507 except (TypeError, ValueError) as x: 

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

509 height=height, wrap=wrap, tol=tol) 

510 

511 def intersections2(self, radius1, other, radius2, height=None, wrap=True, 

512 equidistant=None, tol=_TOL_M): 

513 '''Iteratively compute the intersection points of two circles, 

514 each defined by a center point and a radius. 

515 

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

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

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

519 B{C{radius1}}). 

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

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

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

523 @kwarg wrap: Wrap and unroll longitudes (C{bool}). 

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

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

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

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

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

529 

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

531 instance. For abutting circles, both intersection 

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

533 

534 @raise ImportError: Package U{geographiclib 

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

536 not installed or not found, but only if 

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

538 

539 @raise IntersectionError: Concentric, antipodal, invalid or 

540 non-intersecting circles or no 

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

542 

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

544 

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

546 

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

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

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

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

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

552 intersections. 

553 ''' 

554 try: 

555 c2 = self.others(other) 

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

557 c2, radius2, 

558 height=height, wrap=wrap, 

559 equidistant=equidistant, tol=tol, 

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

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

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

563 height=height, wrap=wrap, tol=tol) 

564 

565 @Property_RO 

566 def isEllipsoidalLatLon(self): 

567 '''Get C{LatLon} base. 

568 ''' 

569 return True 

570 

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

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

573 

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

575 L{BooleanFHP} or L{BooleanGH}). 

576 @kwarg wrap: Wrap lat-, wrap and unroll longitudes (C{bool}). 

577 

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

579 C{False} otherwise. 

580 

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

582 

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

584 

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

586 

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

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

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

590 ''' 

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

592 

593 @property_RO 

594 def iteration(self): 

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

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

597 ''' 

598 return self._iteration 

599 

600 @Property_RO 

601 def _lcc(self): 

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

603 ''' 

604 lcc = _MODS.lcc 

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

606 

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

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

609 

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

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

612 mean height (C{meter}). 

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

614 may be negative or greater than 1.0. 

615 @kwarg wrap: Wrap and unroll longitudes (C{bool}). 

616 

617 @return: Midpoint (C{LatLon}). 

618 

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

620 

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

622 

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

624 ''' 

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

626 

627 def nearestOn(self, point1, point2, within=True, height=None, wrap=True, 

628 equidistant=None, tol=_TOL_M): 

629 '''Iteratively locate the closest point on the geodesic between 

630 two other (ellipsoidal) points. 

631 

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

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

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

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

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

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

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

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

640 takes the heights of the points into account. 

641 @kwarg wrap: Wrap and unroll longitudes (C{bool}). 

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

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

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

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

646 

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

648 

649 @raise ImportError: Package U{geographiclib 

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

651 not installed or not found, but only if 

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

653 

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

655 B{C{equidistant}}. 

656 

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

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

659 

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

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

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

663 BOUNDARIES} for details about the iteration algorithm. 

664 ''' 

665 try: 

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

667 height=height, wrap=wrap, 

668 equidistant=equidistant, 

669 tol=tol, LatLon=self.classof) 

670 except (TypeError, ValueError) as x: 

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

672 height=height, wrap=wrap, tol=tol) 

673 return t.closest 

674 

675 @Property_RO 

676 def _osgr(self): 

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

678 based on the OS recommendation. 

679 ''' 

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

681 

682 @Property_RO 

683 def _osgrTM(self): 

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

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

686 ''' 

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

688 

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

690 sep=_COMMA_, name=NN): 

691 '''Parse a string representing a similar, ellipsoidal C{LatLon} 

692 point, consisting of C{"lat, lon[, height]"}. 

693 

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

695 see function L{pygeodesy.parse3llh}. 

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

697 C{None}). 

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

699 datum I{without conversion}. 

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

701 epoch I{without conversion}. 

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

703 this reframe I{without conversion}. 

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

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

706 this name. 

707 

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

709 

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

711 ''' 

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

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

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

715 r.datum = datum 

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

717 r.epoch = epoch 

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

719 r.reframe = reframe 

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

721 

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

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

724 difference in Gaussian radii of curvature of the given 

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

726 

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

728 ''' 

729 if adjust: # Elevation2Tuple or GeoidHeight2Tuple 

730 m, t = meter_text2 

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

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

733 if n > EPS0: 

734 # use ratio, datum and NAD83 units may differ 

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

736 _spherical_datum(datum).ellipsoid 

737 r = E.rocGauss(self.lat) 

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

739 m *= r / n 

740 meter_text2 = meter_text2.classof(m, t) 

741 return self._xnamed(meter_text2) 

742 

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

744 def reframe(self): 

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

746 ''' 

747 return self._reframe 

748 

749 @reframe.setter # PYCHOK setter! 

750 def reframe(self, reframe): 

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

752 

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

754 ''' 

755 _set_reframe(self, reframe) 

756 

757 @Property_RO 

758 def scale(self): 

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

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

761 ''' 

762 return self._scale 

763 

764 def toCss(self, **toCss_kwds): 

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

766 

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

768 

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

770 

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

772 ''' 

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

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

775 

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

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

778 

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

780 @kwarg height: Optional height, overriding the 

781 converted height (C{meter}). 

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

783 

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

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

786 matches this point's C{datum}. 

787 

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

789 

790 @example: 

791 

792 >>> p = LatLon(51.4778, -0.0016) # default Datums.WGS84 

793 >>> p.toDatum(Datums.OSGB36) # 51.477284°N, 000.00002°E 

794 ''' 

795 n = name or self.name 

796 d2 = _ellipsoidal_datum(datum2, name=n) 

797 if self.datum == d2: 

798 r = self.copy(name=name) 

799 else: 

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

801 epoch=self.epoch, reframe=self.reframe) 

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

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

804 return r 

805 

806 def toEtm(self, **toEtm8_kwds): 

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

808 

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

810 

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

812 

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

814 ''' 

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

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

817 

818 def toLcc(self, **toLcc_kwds): 

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

820 

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

822 

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

824 

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

826 ''' 

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

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

829 

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

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

832 

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

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

835 C{B{center} meter} (C{scalar}). 

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

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

838 

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

840 

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

842 ''' 

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

844 

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

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

847 

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

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

850 formulation (C{bool}). 

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

852 

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

854 

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

856 ''' 

857 if toOsgr_kwds: 

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

859 else: 

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

861 return r 

862 

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

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

865 

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

867 @kwarg height: Optional height, overriding the converted 

868 height (C{meter}). 

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

870 

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

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

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

874 

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

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

877 B{C{reframe2}} is not available. 

878 

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

880 

881 @example: 

882 

883 >>> p = LatLon(51.4778, -0.0016, reframe=RefFrames.ETRF2000) # default Datums.WGS84 

884 >>> p.toRefFrame(RefFrames.ITRF2014) # 51.477803°N, 000.001597°W, +0.01m 

885 >>> p.toRefFrame(RefFrames.ITRF2014, height=0) # 51.477803°N, 000.001597°W 

886 ''' 

887 if not self.reframe: 

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

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

890 

891 trf = _MODS.trf 

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

893 

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

895 if xs: 

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

897 n = name or self.name 

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

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

900 else: 

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

902 return ll 

903 

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

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

906 

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

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

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

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

911 to its C{lowerleft} (C{bool}) or 

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

913 

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

915 

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

917 ''' 

918 if self._upsOK(pole, falsed): 

919 u = self._ups 

920 else: 

921 ups = _MODS.ups 

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

923 pole=pole, falsed=falsed) 

924 return _lowerleft(u, center) 

925 

926 def toUtm(self, center=False): 

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

928 

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

930 to its C{lowerleft} (C{bool}) or 

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

932 

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

934 

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

936 ''' 

937 return _lowerleft(self._utm, center) 

938 

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

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

941 

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

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

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

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

946 meter} (C{scalar}). 

947 

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

949 

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

951 ''' 

952 if self._utmOK(): 

953 u = self._utm 

954 elif self._upsOK(pole): 

955 u = self._ups 

956 else: # no cover 

957 utmups = _MODS.utmups 

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

959 Utm=utmups.Utm, Ups=utmups.Ups) 

960 if isinstance(u, utmups.Utm): 

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

962 elif isinstance(u, utmups.Ups): 

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

964 else: 

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

966 return _lowerleft(u, center) 

967 

968 def toWm(self, **toWm_kwds): 

969 '''Convert this C{LatLon} point to a WM coordinate. 

970 

971 @kwarg toWm_kwds: Optional L{pygeodesy.toWm} keyword arguments. 

972 

973 @return: The WM coordinate (L{Wm}). 

974 

975 @see: Function L{pygeodesy.toWm}. 

976 ''' 

977 return self._wm if not toWm_kwds else _MODS.webmercator.toWm( 

978 self, **_xkwds(toWm_kwds, name=self.name)) 

979 

980 @deprecated_method 

981 def to3xyz(self): # PYCHOK no cover 

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

983 

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

985 

986 @note: Overloads C{LatLonBase.to3xyz} 

987 ''' 

988 r = self.toEcef() 

989 return Vector3Tuple(r.x, r.y, r.z, name=self.name) 

990 

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

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

993 '''Trilaterate three points by area overlap or perimeter intersection 

994 of three intersecting circles. 

995 

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

997 as B{C{eps}}). 

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

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

1000 B{C{eps}}). 

1001 @arg point3: Third center point (C{LatLon}). 

1002 @arg distance3: Distance to point3 (C{meter}, same units as 

1003 B{C{eps}}). 

1004 @kwarg area: If C{True} compute the area overlap, otherwise the 

1005 perimeter intersection of the circles (C{bool}). 

1006 @kwarg eps: The required I{minimal overlap} for C{B{area}=True} 

1007 or the I{intersection margin} for C{B{area}=False} 

1008 (C{meter}, conventionally). 

1009 @kwarg wrap: Wrap/unroll angular distances (C{bool}). 

1010 

1011 @return: A L{Trilaterate5Tuple}C{(min, minPoint, max, maxPoint, n)} 

1012 with C{min} and C{max} in C{meter}, same units as B{C{eps}}, 

1013 the corresponding trilaterated points C{minPoint} and 

1014 C{maxPoint} as I{ellipsoidal} C{LatLon} and C{n}, the number 

1015 of trilatered points found for the given B{C{eps}}. 

1016 

1017 If only a single trilaterated point is found, C{min I{is} 

1018 max}, C{minPoint I{is} maxPoint} and C{n = 1}. 

1019 

1020 For C{B{area}=True}, C{min} and C{max} are the smallest 

1021 respectively largest I{radial} overlap found. 

1022 

1023 For C{B{area}=False}, C{min} and C{max} represent the 

1024 nearest respectively farthest intersection margin. 

1025 

1026 If C{B{area}=True} and all 3 circles are concentric, C{n=0} 

1027 and C{minPoint} and C{maxPoint} are the B{C{point#}} with 

1028 the smallest B{C{distance#}} C{min} respectively C{max} the 

1029 largest B{C{distance#}}. 

1030 

1031 @raise IntersectionError: Trilateration failed for the given B{C{eps}}, 

1032 insufficient overlap for C{B{area}=True} or 

1033 no intersection or all (near-)concentric for 

1034 C{B{area}=False}. 

1035 

1036 @raise TypeError: Invalid B{C{point2}} or B{C{point3}}. 

1037 

1038 @raise ValueError: Coincident B{C{points}} or invalid B{C{distance1}}, 

1039 B{C{distance2}} or B{C{distance3}}. 

1040 

1041 @note: Ellipsoidal trilateration invokes methods C{LatLon.intersections2} 

1042 and C{LatLon.nearestOn} based on I{Karney}'s Python U{geographiclib 

1043 <https://PyPI.org/project/geographiclib>} if installed, otherwise 

1044 uses the accurate (but slower) C{ellipsoidalExact.LatLon} methods. 

1045 ''' 

1046 return _trilaterate5(self, distance1, 

1047 self.others(point2=point2), distance2, 

1048 self.others(point3=point3), distance3, 

1049 area=area, eps=eps, wrap=wrap) 

1050 

1051 @Property_RO 

1052 def _ups(self): # __dict__ value overwritten by method C{toUtmUps} 

1053 '''(INTERNAL) Get this C{LatLon} point as UPS coordinate (L{Ups}), 

1054 see L{pygeodesy.toUps8}. 

1055 ''' 

1056 ups = _MODS.ups 

1057 return ups.toUps8(self, datum=self.datum, Ups=ups.Ups, 

1058 pole=NN, falsed=True, name=self.name) 

1059 

1060 def _upsOK(self, pole=NN, falsed=True): 

1061 '''(INTERNAL) Check matching C{Ups}. 

1062 ''' 

1063 try: 

1064 u = self._ups 

1065 except RangeError: 

1066 return False 

1067 return falsed and (u.pole == pole[:1].upper() or not pole) 

1068 

1069 @Property_RO 

1070 def _utm(self): # __dict__ value overwritten by method C{toUtmUps} 

1071 '''(INTERNAL) Get this C{LatLon} point as UTM coordinate (L{Utm}), 

1072 see L{pygeodesy.toUtm8}. 

1073 ''' 

1074 utm = _MODS.utm 

1075 return utm.toUtm8(self, datum=self.datum, Utm=utm.Utm, name=self.name) 

1076 

1077 def _utmOK(self): 

1078 '''(INTERNAL) Check C{Utm}. 

1079 ''' 

1080 try: 

1081 _ = self._utm 

1082 except RangeError: 

1083 return False 

1084 return True 

1085 

1086 @Property_RO 

1087 def _wm(self): 

1088 '''(INTERNAL) Get this C{LatLon} point as webmercator (L{Wm}). 

1089 ''' 

1090 return _MODS.webmercator.toWm(self) 

1091 

1092 

1093def _lowerleft(utmups, center): 

1094 '''(INTERNAL) Optionally I{un}-center C{utmups}. 

1095 ''' 

1096 if center in (False, 0, _0_0): 

1097 u = utmups 

1098 elif center in (True,): 

1099 u = utmups._lowerleft 

1100 else: 

1101 u = _MODS.utmupsBase._lowerleft(utmups, center) 

1102 return u 

1103 

1104 

1105def _nearestOn(point, point1, point2, within=True, height=None, wrap=True, 

1106 equidistant=None, tol=_TOL_M, LatLon=None, **LatLon_kwds): 

1107 '''(INTERNAL) Get closest point, imported by .ellipsoidalExact, 

1108 -GeodSolve, -Karney and -Vincenty to embellish exceptions. 

1109 ''' 

1110 try: 

1111 p = _xellipsoidal(point=point) 

1112 t = _MODS.ellipsoidalBaseDI._nearestOn2(p, point1, point2, within=within, 

1113 height=height, wrap=wrap, 

1114 equidistant=equidistant, tol=tol, 

1115 LatLon=LatLon, **LatLon_kwds) 

1116 except (TypeError, ValueError) as x: 

1117 raise _xError(x, point=point, point1=point1, point2=point2) 

1118 return t.closest 

1119 

1120 

1121def _set_reframe(inst, reframe): 

1122 '''(INTERNAL) Set or clear an instance's reference frame. 

1123 ''' 

1124 if reframe is not None: 

1125 _xinstanceof(_MODS.trf.RefFrame, reframe=reframe) 

1126 inst._reframe = reframe 

1127 elif inst.reframe is not None: 

1128 inst._reframe = None 

1129 

1130 

1131__all__ += _ALL_DOCS(CartesianEllipsoidalBase, LatLonEllipsoidalBase) 

1132 

1133# **) MIT License 

1134# 

1135# Copyright (C) 2016-2023 -- mrJean1 at Gmail -- All Rights Reserved. 

1136# 

1137# Permission is hereby granted, free of charge, to any person obtaining a 

1138# copy of this software and associated documentation files (the "Software"), 

1139# to deal in the Software without restriction, including without limitation 

1140# the rights to use, copy, modify, merge, publish, distribute, sublicense, 

1141# and/or sell copies of the Software, and to permit persons to whom the 

1142# Software is furnished to do so, subject to the following conditions: 

1143# 

1144# The above copyright notice and this permission notice shall be included 

1145# in all copies or substantial portions of the Software. 

1146# 

1147# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS 

1148# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, 

1149# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL 

1150# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR 

1151# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, 

1152# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR 

1153# OTHER DEALINGS IN THE SOFTWARE.