Coverage for pygeodesy/ellipsoidalBase.py: 94%

1 

2# -*- coding: utf-8 -*- 

3 

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

5and C{LatLonEllipsoidalBase}. 

6 

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

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

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

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

11''' 

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

13from __future__ import division as _; del _ # noqa: E702 ; 

14 

15# from pygeodesy.azimuthal import EquidistantExact, EquidistantKarney # _MODS 

16from pygeodesy.basics import _isin, _xinstanceof 

17from pygeodesy.constants import EPS, EPS0, EPS1, _0_0, _0_5 

18from pygeodesy.cartesianBase import CartesianBase # PYCHOK used! 

19# from pygeodesy.css import toCss # _MODS 

20from pygeodesy.datums import Datum, Datums, _earth_ellipsoid, _ellipsoidal_datum, \ 

21 Transform, _WGS84, _EWGS84 # _spherical_datum 

22# from pygeodesy.dms import parse3llh # _MODS 

23# from pygeodesy.elevations import elevation2, geoidHeight2 # _MODS 

24# from pygeodesy.ellipsoidalBaseDI import _intersect3, _intersections2, _nearestOn2 # _MODS 

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

26from pygeodesy.errors import _IsnotError, RangeError, _TypeError, _xattr, _xellipsoidal, \ 

27 _xellipsoids, _xError, _xkwds, _xkwds_not 

28# from pygeodesy.etm import etm, toEtm8 # _MODS 

29# from pygeodesy.fmath import favg # _MODS 

30from pygeodesy.interns import NN, _COMMA_, _ellipsoidal_ 

31from pygeodesy.latlonBase import LatLonBase, _trilaterate5, fabs, _Wrap 

32from pygeodesy.lazily import _ALL_DOCS, _ALL_LAZY, _ALL_MODS as _MODS 

33# from pygeodesy.lcc import toLcc # _MODS 

34# from pygeodesy.namedTuples import Vector3Tuple # _MODS 

35# from pygeodesy.osgr import toOsgr # _MODS 

36# from pygeodesy.points import isenclosedBy # _MODS 

37from pygeodesy.props import deprecated_method, deprecated_property_RO, \ 

38 Property_RO, property_doc_, property_RO, _update_all 

39# from pygeodesy.trf import RefFrame, _toRefFrame # _MODS 

40from pygeodesy.units import Epoch, _isDegrees, Radius_, _1mm as _TOL_M 

41# from pygeodesy import ups, utm, utmups # MODS 

42# from pygeodesy.utmupsBase import _lowerleft # MODS 

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

44# from pygeodesy.vector3d import _intersects2 # _MODS 

45 

46# from math import fabs # from .latlonBase 

47 

48__all__ = _ALL_LAZY.ellipsoidalBase 

49__version__ = '25.07.21' 

50 

51 

52class CartesianEllipsoidalBase(CartesianBase): 

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

54 ''' 

55 _datum = _WGS84 # L{Datum} 

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

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

58 

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

60 **datum_ll_name): 

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

62 

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

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

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

66 if C{B{reframe}=None}. 

67 

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

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

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

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

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

73 

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

75 ''' 

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

77 if reframe: 

78 self.reframe = reframe 

79 self.epoch = epoch 

80 

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

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

83# ''' 

84# RefFrame = _MODS.trf.RefFrame 

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

86# _NotImplemented(self, other) 

87 

88 @deprecated_method 

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

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

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

92 

93 @property_RO 

94 def ellipsoidalCartesian(self): 

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

96 ''' 

97 return type(self) 

98 

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

100 def epoch(self): 

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

102 ''' 

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

104 

105 @epoch.setter # PYCHOK setter! 

106 def epoch(self, epoch): 

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

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

109 

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

111 ''' 

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

113 

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

115 Vector=None, **Vector_kwds): 

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

117 cartesian center point and a radius. 

118 

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

120 coordinates). 

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

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

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

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

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

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

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

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

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

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

131 ignored if C{B{Vector} is None}. 

132 

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

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

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

136 

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

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

139 instance (aka the I{radical center}). 

140 

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

142 

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

144 

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

146 

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

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

149 Intersection and function L{pygeodesy.radical2}. 

150 ''' 

151 try: 

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

153 center2, Radius_(radius2=radius2), 

154 sphere=sphere, clas=self.classof, 

155 Vector=Vector, **Vector_kwds) 

156 except (TypeError, ValueError) as x: 

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

158 

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

160 def reframe(self): 

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

162 ''' 

163 return self._reframe 

164 

165 @reframe.setter # PYCHOK setter! 

166 def reframe(self, reframe): 

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

168 

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

170 ''' 

171 _set_reframe(self, reframe) 

172 

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

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

175 

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

177 for further details. 

178 ''' 

179 kwds = LatLon_and_kwds 

180 if kwds: 

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

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

183 

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

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

186 

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

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

189 overriding this point's reference frame. 

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

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

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

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

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

195 

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

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

198 is non-empty. 

199 

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

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

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

203 

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

205 ''' 

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

207 epoch2=epoch2, **name) 

208 

209 @deprecated_method 

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

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

212 r = self 

213 for t in transforms: 

214 r = r.toTransform(t) 

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

216 

217 

218class LatLonEllipsoidalBase(LatLonBase): 

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

220 ''' 

221 _datum = _WGS84 # L{Datum} 

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

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

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

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

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

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

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

229 

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

231 epoch=None, wrap=False, **name): 

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

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

234 

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

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

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

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

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

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

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

242 L{Ellipsoid2} or L{a_f2Tuple}). 

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

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

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

246 C{B{reframe}=None}. 

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

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

249 

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

251 L{rangerrors} set to C{True}. 

252 

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

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

255 is not C{scalar} non-zero. 

256 

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

258 ''' 

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

260 if not _isin(datum, None, self._datum, _EWGS84): 

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

262 if reframe: 

263 self.reframe = reframe 

264 self.epoch = epoch 

265 

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

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

268# ''' 

269# RefFrame = _MODS.trf.RefFrame 

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

271# _NotImplemented(self, other) 

272 

273 def antipode(self, height=None): 

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

275 to this point. 

276 

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

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

279 

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

281 ''' 

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

283 if lla.datum != self.datum: 

284 lla.datum = self.datum 

285 return lla 

286 

287 @deprecated_property_RO 

288 def convergence(self): 

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

290 return self.gamma # PYCHOK no cover 

291 

292 @deprecated_method 

293 def convertDatum(self, datum2): 

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

295 return self.toDatum(datum2) 

296 

297 @deprecated_method 

298 def convertRefFrame(self, reframe2): 

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

300 return self.toRefFrame(reframe2) 

301 

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

303 def datum(self): 

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

305 ''' 

306 return self._datum 

307 

308 @datum.setter # PYCHOK setter! 

309 def datum(self, datum): 

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

311 

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

313 ''' 

314 _xinstanceof(Datum, datum=datum) 

315 if not datum.isEllipsoidal: 

316 raise _IsnotError(_ellipsoidal_, datum=datum) 

317 if self._datum != datum: 

318 _update_all(self) 

319 self._datum = datum 

320 

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

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

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

324 

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

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

327 

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

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

330 point (C{bool}). 

331 

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

333 

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

335 

336 @raise ValueError: Incompatible datum ellipsoids. 

337 

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

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

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

341 formula. 

342 ''' 

343 p = self.others(other) 

344 if wrap: # PYCHOK no cover 

345 p = _Wrap.point(p) 

346 E = self.ellipsoids(other) 

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

348 

349 @Property_RO 

350 def _elevation2(self): 

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

352 ''' 

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

354 timeout=self._elevation2to) 

355 

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

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

358 or sphere. 

359 

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

361 C{NAD83} (C{bool}). 

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

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

364 radius). 

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

366 

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

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

369 

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

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

372 L{elevations.elevation2} is based. 

373 

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

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

376 

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

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

379 ''' 

380 if self._elevation2to != timeout: 

381 self._elevation2to = timeout 

382 LatLonEllipsoidalBase._elevation2._update(self) 

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

384 

385 def ellipsoid(self, datum=_WGS84): 

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

387 

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

389 

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

391 ''' 

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

393 

394 @property_RO 

395 def ellipsoidalLatLon(self): 

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

397 ''' 

398 return type(self) 

399 

400 def ellipsoids(self, other): 

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

402 

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

404 

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

406 

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

408 

409 @raise ValueError: Incompatible datum ellipsoids. 

410 ''' 

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

412 

413 E = self.ellipsoid() 

414 try: # other may be Sphere, etc. 

415 e = other.ellipsoid() 

416 except AttributeError: 

417 try: # no ellipsoid method, try datum 

418 e = other.datum.ellipsoid 

419 except AttributeError: 

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

421 return _xellipsoids(E, e) 

422 

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

424 def epoch(self): 

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

426 ''' 

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

428 

429 @epoch.setter # PYCHOK setter! 

430 def epoch(self, epoch): 

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

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

433 

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

435 ''' 

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

437 

438 @Property_RO 

439 def Equidistant(self): 

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

441 ''' 

442 try: 

443 _ = self.datum.ellipsoid.geodesic 

444 return _MODS.azimuthal.EquidistantKarney 

445 except ImportError: # no geographiclib 

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

447 

448 @Property_RO 

449 def _etm(self): 

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

451 ''' 

452 return self._toX8(_MODS.etm.toEtm8) 

453 

454 @property_RO 

455 def gamma(self): 

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

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

458 ''' 

459 return self._gamma 

460 

461 @Property_RO 

462 def _geoidHeight2(self): 

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

464 ''' 

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

466 timeout=self._geoidHeight2to) 

467 

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

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

470 or sphere. 

471 

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

473 C{NAD83/NADV88} (C{bool}). 

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

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

476 radius). 

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

478 

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

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

481 

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

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

484 the L{elevations.geoidHeight2} is based. 

485 

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

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

488 

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

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

491 ''' 

492 if self._geoidHeight2to != timeout: 

493 self._geoidHeight2to = timeout 

494 LatLonEllipsoidalBase._geoidHeight2._update(self) 

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

496 

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

498 '''I{Must be overloaded}.''' 

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

500 

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

502 equidistant=None, tol=_TOL_M): 

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

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

505 

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

507 this point (compass C{degrees360}). 

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

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

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

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

512 or C{None} for the mean height. 

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

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

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

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

517 preferred C{.Equidistant}. 

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

519 (C{meter}, conventionally). 

520 

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

522 a C{LatLon} instance. 

523 

524 @raise ImportError: Package U{geographiclib 

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

526 not installed or not found, but only if 

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

528 

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

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

531 

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

533 

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

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

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

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

538 

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

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

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

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

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

544 ''' 

545 try: 

546 s2 = self.others(start2=start2) 

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

548 s2, end2, 

549 height=height, wrap=wrap, 

550 equidistant=equidistant, tol=tol, 

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

552 except (TypeError, ValueError) as x: 

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

554 height=height, wrap=wrap, tol=tol) 

555 

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

557 equidistant=None, tol=_TOL_M): 

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

559 defined by a center point and a radius. 

560 

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

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

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

564 B{C{radius1}}). 

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

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

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

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

569 (C{bool}). 

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

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

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

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

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

575 

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

577 instance. For abutting circles, both intersection 

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

579 

580 @raise ImportError: Package U{geographiclib 

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

582 not installed or not found, but only if 

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

584 

585 @raise IntersectionError: Concentric, antipodal, invalid or 

586 non-intersecting circles or no 

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

588 

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

590 

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

592 

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

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

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

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

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

598 intersections. 

599 ''' 

600 try: 

601 c2 = self.others(center2=center2) 

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

603 c2, radius2, 

604 height=height, wrap=wrap, 

605 equidistant=equidistant, tol=tol, 

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

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

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

609 height=height, wrap=wrap, tol=tol) 

610 

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

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

613 

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

615 L{BooleanFHP} or L{BooleanGH}). 

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

617 B{C{points}} (C{bool}). 

618 

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

620 C{False} otherwise. 

621 

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

623 

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

625 

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

627 

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

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

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

631 ''' 

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

633 

634 @property_RO 

635 def iteration(self): 

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

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

638 ''' 

639 return self._iteration 

640 

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

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

643 

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

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

646 mean height (C{meter}). 

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

648 may be negative or greater than 1.0. 

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

650 B{C{other}} point (C{bool}). 

651 

652 @return: Midpoint (C{LatLon}). 

653 

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

655 

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

657 

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

659 ''' 

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

661 

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

663 equidistant=None, tol=_TOL_M): 

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

665 between two other (ellipsoidal) points. 

666 

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

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

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

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

671 (C{bool}). 

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

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

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

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

676 B{C{point2}} (C{bool}). 

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

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

679 preferred C{Equidistant}, like L{Equidistant}. 

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

681 

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

683 

684 @raise ImportError: Package U{geographiclib 

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

686 not installed or not found, but only if 

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

688 

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

690 

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

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

693 

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

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

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

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

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

699 ''' 

700 try: 

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

702 height=height, wrap=wrap, 

703 equidistant=equidistant, 

704 tol=tol, LatLon=self.classof) 

705 except (TypeError, ValueError) as x: 

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

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

708 return t.closest 

709 

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

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

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

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

714 

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

716 L{pygeodesy.parse3llh}. 

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

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

719 I{without conversion}. 

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

721 I{without conversion}. 

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

723 this reframe I{without conversion}. 

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

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

726 longitude (C{bool}). 

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

728 

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

730 

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

732 ''' 

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

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

735 epoch=epoch or self.epoch, 

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

737 

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

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

740 difference in Gaussian radii of curvature of the given 

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

742 

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

744 ''' 

745 if adjust: # Elevation2Tuple or GeoidHeight2Tuple 

746 m, t = meter_text2 

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

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

749 if n > EPS0: 

750 # use ratio, datum and NAD83 units may differ 

751 E = self.ellipsoid() if _isin(datum, None, self.datum) else \ 

752 _earth_ellipsoid(datum) 

753 r = E.rocGauss(self.lat) 

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

755 m *= r / n 

756 meter_text2 = meter_text2.classof(m, t) 

757 return self._xnamed(meter_text2) 

758 

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

760 def reframe(self): 

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

762 ''' 

763 return self._reframe 

764 

765 @reframe.setter # PYCHOK setter! 

766 def reframe(self, reframe): 

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

768 

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

770 ''' 

771 _set_reframe(self, reframe) 

772 

773 @Property_RO 

774 def scale(self): 

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

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

777 ''' 

778 return self._scale 

779 

780 def _toX8(self, toX8, **kwds): 

781 '''(INTERNAL) Return toX8(self, ...). 

782 ''' 

783 return toX8(self, **_xkwds(kwds, datum=self.datum, name=self.name)) 

784 

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

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

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

788 

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

790 for further details. 

791 ''' 

792 kwds = Cartesian_and_kwds 

793 if kwds: 

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

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

796 

797 def toCss(self, **toCss_kwds): 

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

799 

800 @kwarg toCss_kwds: Optional keyword arguments for function 

801 L{pygeodesy.toCss}. 

802 

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

804 ''' 

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

806 

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

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

809 

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

811 @kwarg height: Optional height, overriding the 

812 converted height (C{meter}). 

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

814 

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

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

817 point's C{datum}. 

818 

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

820 ''' 

821 n = self._name__(name) 

822 d2 = _ellipsoidal_datum(datum2, name=n) 

823 if self.datum == d2: 

824 r = self.copy(name=n) 

825 else: 

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

827 epoch=self.epoch, reframe=self.reframe) 

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

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

830 return r 

831 

832 def toEtm(self, **toEtm8_kwds): 

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

834 

835 @kwarg toEtm8_kwds: Optional keyword arguments for 

836 function L{pygeodesy.toEtm8}. 

837 

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

839 ''' 

840 return self._etm if not toEtm8_kwds else \ 

841 self._toX8(_MODS.etm.toEtm8, **toEtm8_kwds) 

842 

843 def toLcc(self, **toLcc_kwds): 

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

845 

846 @kwarg toLcc_kwds: Optional keyword arguments for 

847 function L{pygeodesy.toLcc}. 

848 

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

850 ''' 

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

852 

853 def toMgrs(self, center=False, **toUtmUps_kwds): 

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

855 

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

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

858 C{B{center} meter} (C{scalar}). 

859 @kwarg toUtmUps_kwds: Optional keyword arguments for 

860 method L{toUtmUps}. 

861 

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

863 

864 @see: Methods L{toUtmUps} and L{toMgrs<pygeodesy.utmupsBase.UtmUpsBase.toMgrs>}. 

865 ''' 

866 return self.toUtmUps(center=center, **toUtmUps_kwds).toMgrs(center=False) 

867 

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

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

870 

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

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

873 formulation (C{bool}). 

874 @kwarg toOsgr_kwds: Optional keyword arguments for function 

875 L{pygeodesy.toOsgr}. 

876 

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

878 ''' 

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

880 

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

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

883 

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

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

886 overriding this point's reference frame. 

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

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

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

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

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

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

893 

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

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

896 is non-empty. 

897 

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

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

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

901 

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

903 ''' 

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

905 epoch2=epoch2, height=height, **name) 

906 

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

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

909 

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

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

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

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

914 @kwarg LatLon_kwds: Optional keyword arguments for the transformed 

915 point, like C{B{height}=...}. 

916 

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

918 C{B{transform}.isunity}. 

919 

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

921 ''' 

922 _xinstanceof(Transform, transform=transform) 

923 d = datum or self.datum 

924 if transform.isunity: 

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

926 else: 

927 c = self.toCartesian() 

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

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

930 return r 

931 

932 def toUps(self, center=False, **toUps8_kwds): 

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

934 

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

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

937 meter} (C{scalar}). 

938 @kwarg toUps8_kwds: Optional keyword arguments for 

939 function L{pygeodesy.toUps8}. 

940 

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

942 ''' 

943 u = self._ups if (not toUps8_kwds) and self._upsOK() else \ 

944 self._toX8(_MODS.ups.toUps8, **toUps8_kwds) 

945 return _lowerleft(u, center) 

946 

947 def toUtm(self, center=False, **toUtm8_kwds): 

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

949 

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

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

952 meter} (C{scalar}). 

953 @kwarg toUtm8_kwds: Optional keyword arguments for function 

954 L{pygeodesy.toUtm8}. 

955 

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

957 

958 @note: For the highest accuracy, use method L{toEtm} and 

959 class L{pygeodesy.Etm} instead of L{pygeodesy.Utm}. 

960 ''' 

961 u = self._utm if not toUtm8_kwds else \ 

962 self._toX8(_MODS.utm.toUtm8, **toUtm8_kwds)