1

2# -*- coding: utf-8 -*-

3

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

5 and C{LatLonEllipsoidalBase}.

6

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

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

9 and 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

13 from __future__ import division as _; del _ # PYCHOK semicolon

14

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

16 from pygeodesy.basics import _isin, _xinstanceof

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

18 from pygeodesy.cartesianBase import CartesianBase # PYCHOK used!

19# from pygeodesy.css import toCss # _MODS

20 from 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

26 from 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

30 from pygeodesy.interns import NN, _COMMA_, _ellipsoidal_

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

32 from 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

37 from 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

40 from 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__ = '25.04.14'

50

51

52 class 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

218 class 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 etm = _MODS.etm

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

454

455 @property_RO

456 def gamma(self):

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

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

459 '''

460 return self._gamma

461

462 @Property_RO

463 def _geoidHeight2(self):

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

465 '''

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

467 timeout=self._geoidHeight2to)

468

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

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

471 or sphere.

472

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

474 C{NAD83/NADV88} (C{bool}).

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

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

477 radius).

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

479

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

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

482

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

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

485 the L{elevations.geoidHeight2} is based.

486

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

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

489

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

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

492 '''

493 if self._geoidHeight2to != timeout:

494 self._geoidHeight2to = timeout

495 LatLonEllipsoidalBase._geoidHeight2._update(self)

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

497

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

499 '''I{Must be overloaded}.'''

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

501

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

503 equidistant=None, tol=_TOL_M):

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

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

506

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

508 this point (compass C{degrees360}).

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

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

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

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

513 or C{None} for the mean height.

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

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

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

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

518 preferred C{.Equidistant}.

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

520 (C{meter}, conventionally).

521

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

523 a C{LatLon} instance.

524

525 @raise ImportError: Package U{geographiclib

526 <https://PyPI.org/project/geographiclib>} not

527 installed or not found, but only in case

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

529

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

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

532

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

534

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

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

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

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

539

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

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

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

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

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

545 '''

546 try:

547 s2 = self.others(start2=start2)

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

549 s2, end2,

550 height=height, wrap=wrap,

551 equidistant=equidistant, tol=tol,

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

553 except (TypeError, ValueError) as x:

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

555 height=height, wrap=wrap, tol=tol)

556

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

558 equidistant=None, tol=_TOL_M):

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

560 defined by a center point and a radius.

561

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

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

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

565 B{C{radius1}}).

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

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

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

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

570 (C{bool}).

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

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

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

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

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

576

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

578 instance. For abutting circles, both intersection

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

580

581 @raise ImportError: Package U{geographiclib

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

583 not installed or not found, but only if

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

585

586 @raise IntersectionError: Concentric, antipodal, invalid or

587 non-intersecting circles or no

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

589

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

591

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

593

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

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

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

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

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

599 intersections.

600 '''

601 try:

602 c2 = self.others(center2=center2)

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

604 c2, radius2,

605 height=height, wrap=wrap,

606 equidistant=equidistant, tol=tol,

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

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

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

610 height=height, wrap=wrap, tol=tol)

611

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

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

614

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

616 L{BooleanFHP} or L{BooleanGH}).

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

618 B{C{points}} (C{bool}).

619

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

621 C{False} otherwise.

622

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

624

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

626

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

628

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

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

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

632 '''

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

634

635 @property_RO

636 def iteration(self):

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

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

639 '''

640 return self._iteration

641

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

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

644

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

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

647 mean height (C{meter}).

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

649 may be negative or greater than 1.0.

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

651 B{C{other}} point (C{bool}).

652

653 @return: Midpoint (C{LatLon}).

654

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

656

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

658

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

660 '''

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

662

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

664 equidistant=None, tol=_TOL_M):

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

666 between two other (ellipsoidal) points.

667

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

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

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

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

672 (C{bool}).

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

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

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

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

677 B{C{point2}} (C{bool}).

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

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

680 C{Equidistant}, like L{Equidistant<LatLonEllipsoidalBase.Equidistant>}.

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

682

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

684

685 @raise ImportError: Package U{geographiclib

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

687 not installed or not found, but only if

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

689

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

691

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

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

694

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

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

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

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

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

700 '''

701 try:

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

703 height=height, wrap=wrap,

704 equidistant=equidistant,

705 tol=tol, LatLon=self.classof)

706 except (TypeError, ValueError) as x:

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

708 height=height, wrap=wrap, tol=tol)

709 return t.closest

710

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

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

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

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

715

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

717 L{pygeodesy.parse3llh}.

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

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

720 I{without conversion}.

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

722 I{without conversion}.

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

724 this reframe I{without conversion}.

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

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

727 longitude (C{bool}).

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

729

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

731

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

733 '''

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

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

736 epoch=epoch or self.epoch,

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

738

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

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

741 difference in Gaussian radii of curvature of the given

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

743

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

745 '''

746 if adjust: # Elevation2Tuple or GeoidHeight2Tuple

747 m, t = meter_text2

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

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

750 if n > EPS0:

751 # use ratio, datum and NAD83 units may differ

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

753 _earth_ellipsoid(datum)

754 r = E.rocGauss(self.lat)

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

756 m *= r / n

757 meter_text2 = meter_text2.classof(m, t)

758 return self._xnamed(meter_text2)

759

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

761 def reframe(self):

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

763 '''

764 return self._reframe

765

766 @reframe.setter # PYCHOK setter!

767 def reframe(self, reframe):

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

769

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

771 '''

772 _set_reframe(self, reframe)

773

774 @Property_RO

775 def scale(self):

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

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

778 '''

779 return self._scale

780

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

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

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

784

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

786 for further details.

787 '''

788 kwds = Cartesian_and_kwds

789 if kwds:

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

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

792

793 def toCss(self, **toCss_kwds):

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

795

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

797

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

799

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

801 '''

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

803

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

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

806

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

808 @kwarg height: Optional height, overriding the

809 converted height (C{meter}).

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

811

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

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

814 point's C{datum}.

815

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

817 '''

818 n = self._name__(name)

819 d2 = _ellipsoidal_datum(datum2, name=n)

820 if self.datum == d2:

821 r = self.copy(name=n)

822 else:

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

824 epoch=self.epoch, reframe=self.reframe)

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

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

827 return r

828

829 def toEtm(self, **toEtm8_kwds):

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

831

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

833

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

835

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

837 '''

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

839

840 def toLcc(self, **toLcc_kwds):

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

842

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

844

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

846

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

848 '''

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

850

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

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

853

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

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

856 C{B{center} meter} (C{scalar}).

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

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

859

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

861

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

863 '''

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

865

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

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

868

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

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

871 formulation (C{bool}).

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

873

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

875

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

877 '''

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

879

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

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

882

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

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

885 overriding this point's reference frame.

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

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

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

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

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

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

892

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

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

895 is non-empty.

896

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

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

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

900

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

902 '''

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

904 epoch2=epoch2, height=height, **name)

905

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

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

908

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

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

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

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

913 @kwarg LatLon_kwds: Optional keyword arguments for the transformed

914 point, like C{B{height}=...}.

915

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

917 C{B{transform}.isunity}.

918

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

920 '''

921 _xinstanceof(Transform, transform=transform)

922 d = datum or self.datum

923 if transform.isunity:

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

925 else:

926 c = self.toCartesian()

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

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

929 return r

930

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

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

933

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

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

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

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

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

939 meter} (C{scalar}).

940

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

942

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

944 '''

945 if self._upsOK(pole, falsed):

946 u = self._ups

947 else:

948 ups = _MODS.ups

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

950 pole=pole, falsed=falsed)

951 return _lowerleft(u, center)

952

953 def toUtm(self, center=False):

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

955

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

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

958 meter} (C{scalar}).

959

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

961

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

963 '''

964 return _lowerleft(self._utm, center)

965

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

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

968

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

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

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

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

973 meter} (C{scalar}).

974

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

976

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

978 '''

979 if self._utmOK():

980 u = self._utm

981 elif self._upsOK(pole):

982 u = self._ups

983 else: # no cover

984 utmups = _MODS.utmups

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

986 Utm=utmups.Utm, Ups=utmups.Ups)

987 if isinstance(u, utmups.Utm):

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

989 elif isinstance(u, utmups.Ups):

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

991 else:

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

993 return _lowerleft(u, center)

994

995 @deprecated_method

996 def to3xyz(self): # PYCHOK no cover

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

998

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

1000

1001 @note: Overloads C{LatLonBase.to3xyz}

1002 '''

1003 r = self.toEcef()

1004 return _MODS.namedTuples.Vector3Tuple(r.x, r.y, r.z, name=self.name)

1005

1006 def triangulate(self, bearing1, other, bearing2, **height_wrap_tol):

1007 '''I{Iteratively} locate a point given this, an other point and a bearing

1008 from North at each point.

1009

1010 @arg bearing1: Bearing at this point (compass C{degrees360}).

1011 @arg other: The other point (C{LatLon}).

1012 @arg bearing2: Bearing at the B{C{other}} point (compass C{degrees360}).

1013 @kwarg height_wrap_tol: Optional keyword arguments C{B{height}=None},

1014 C{B{wrap}=False} and C{B{tol}}, see method L{intersection3

1015 <pygeodesy.ellipsoidalBase.LatLonEllipsoidalBase>}.

1016

1017 @return: Triangulated point (C{LatLon}).

1018

1019 @see: Method L{intersection3<pygeodesy.ellipsoidalBase.LatLonEllipsoidalBase>}

1020 for further details.

1021 '''

1022 if _isDegrees(bearing1) and _isDegrees(bearing2):

1023 r = self.intersection3(bearing1, other, bearing2, **height_wrap_tol)

1024 return r.point

1025 raise _TypeError(bearing1=bearing1, bearing2=bearing2 **height_wrap_tol)

1026

1027 def trilaterate5(self, distance1, point2, distance2, point3, distance3,

1028 area=True, eps=EPS1, wrap=False):

1029 '''Trilaterate three points by I{area overlap} or I{perimeter intersection}

1030 of three intersecting circles.

1031

1032 @arg distance1: Distance to this point (C{meter}), same units as B{C{eps}}).

1033 @arg point2: Second center point (C{LatLon}).

1034 @arg distance2: Distance to point2 (C{meter}, same units as B{C{eps}}).

1035 @arg point3: Third center point (C{LatLon}).

1036 @arg distance3: Distance to point3 (C{meter}, same units as B{C{eps}}).

1037 @kwarg area: If C{True}, compute the area overlap, otherwise the perimeter

1038 intersection of the circles (C{bool}).

1039 @kwarg eps: The required I{minimal overlap} for C{B{area}=True} or the

1040 I{intersection margin} for C{B{area}=False} (C{meter},

1041 conventionally).

1042 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll B{C{point2}}

1043 and B{C{point3}} (C{bool}).

1044

1045 @return: A L{Trilaterate5Tuple}C{(min, minPoint, max, maxPoint, n)} with

1046 C{min} and C{max} in C{meter}, same units as B{C{eps}}, the

1047 corresponding trilaterated points C{minPoint} and C{maxPoint}

1048 as I{ellipsoidal} C{LatLon} and C{n}, the number of trilatered

1049 points found for the given B{C{eps}}.

1050

1051 If only a single trilaterated point is found, C{min I{is} max},

1052 C{minPoint I{is} maxPoint} and C{n=1}.

1053

1054 If C{B{area}=False}, C{min} and C{max} represent the nearest

1055 respectively farthest intersection margin.

1056

1057 If C{B{area}=True}, C{min} and C{max} are the smallest respectively

1058 largest I{radial} overlap found.

1059

1060 If C{B{area}=True} and all 3 circles are concentric, C{n=0} and

1061 C{minPoint} and C{maxPoint} are the B{C{point#}} with the smallest

1062 B{C{distance#}} C{min} respectively largest B{C{distance#}} C{max}.

1063

1064 @raise IntersectionError: Trilateration failed for the given B{C{eps}},

1065 insufficient overlap for C{B{area}=True}, no

1066 circle intersections for C{B{area}=False} or

1067 all circles are (near-)concentric.

1068

1069 @raise TypeError: Invalid B{C{point2}} or B{C{point3}}.

1070

1071 @raise ValueError: Coincident B{C{points}} or invalid B{C{distance1}},

1072 B{C{distance2}} or B{C{distance3}}.

1073

1074 @note: Ellipsoidal trilateration invokes methods C{LatLon.intersections2}

1075 and C{LatLon.nearestOn} based on I{Karney}'s Python U{geographiclib

1076 <https://PyPI.org/project/geographiclib>} if installed, otherwise

1077 the accurate (but slower) C{ellipsoidalExact.LatLon} methods.

1078 '''

1079 return _trilaterate5(self, distance1,

1080 self.others(point2=point2), distance2,

1081 self.others(point3=point3), distance3,

1082 area=area, eps=eps, wrap=wrap)

1083

1084 @Property_RO

1085 def _ups(self): # __dict__ value overwritten by method C{toUtmUps}

1086 '''(INTERNAL) Get this C{LatLon} point as UPS coordinate (L{Ups}),

1087 see L{pygeodesy.toUps8}.

1088 '''

1089 ups = _MODS.ups

1090 return ups.toUps8(self, datum=self.datum, Ups=ups.Ups,

1091 pole=NN, falsed=True, name=self.name)

1092

1093 def _upsOK(self, pole=NN, falsed=True):

1094 '''(INTERNAL) Check matching C{Ups}.

1095 '''

1096 try:

1097 u = self._ups

1098 except RangeError:

1099 return False

1100 return falsed and (u.pole == pole[:1].upper() or not pole)

1101

1102 @Property_RO

1103 def _utm(self): # __dict__ value overwritten by method C{toUtmUps}

1104 '''(INTERNAL) Get this C{LatLon} point as UTM coordinate (L{Utm}),

1105 see L{pygeodesy.toUtm8}.

1106 '''

1107 utm = _MODS.utm

1108 return utm.toUtm8(self, datum=self.datum, Utm=utm.Utm, name=self.name)

1109

1110 def _utmOK(self):

1111 '''(INTERNAL) Check C{Utm}.

1112 '''

1113 try:

1114 _ = self._utm

1115 except RangeError:

1116 return False

1117 return True

1118

1119

1120 def _lowerleft(utmups, center):

1121 '''(INTERNAL) Optionally I{un}-center C{utmups}.

1122 '''

1123 if _isin(center, False, 0, _0_0):

1124 u = utmups

1125 elif _isin(center, True):

1126 u = utmups._lowerleft

1127 else:

1128 u = _MODS.utmupsBase._lowerleft(utmups, center)

1129 return u

1130

1131

1132 def _nearestOn(point, point1, point2, within=True, height=None, wrap=False, # was=True

1133 equidistant=None, tol=_TOL_M, **LatLon_and_kwds):

1134 '''(INTERNAL) Get closest point, imported by .ellipsoidalExact,

1135 -GeodSolve, -Karney and -Vincenty to embellish exceptions.

1136 '''

1137 try:

1138 p = _xellipsoidal(point=point)

1139 t = _MODS.ellipsoidalBaseDI._nearestOn2(p, point1, point2, within=within,

1140 height=height, wrap=wrap,

1141 equidistant=equidistant,

1142 tol=tol, **LatLon_and_kwds)

1143 except (TypeError, ValueError) as x:

1144 raise _xError(x, point=point, point1=point1, point2=point2)

1145 return t.closest

1146

1147

1148 def _set_reframe(inst, reframe):

1149 '''(INTERNAL) Set or clear an instance's reference frame.

1150 '''

1151 if reframe is not None:

1152 _xinstanceof(_MODS.trf.RefFrame, reframe=reframe)

1153 inst._reframe = reframe

1154 elif inst.reframe is not None:

1155 inst._reframe = None

1156

1157

1158__all__ += _ALL_DOCS(CartesianEllipsoidalBase, LatLonEllipsoidalBase)

1159

1160# **) MIT License

1161#

1162# Copyright (C) 2016-2025 -- mrJean1 at Gmail -- All Rights Reserved.

1163#

1164# Permission is hereby granted, free of charge, to any person obtaining a

1165# copy of this software and associated documentation files (the "Software"),

1166# to deal in the Software without restriction, including without limitation

1167# the rights to use, copy, modify, merge, publish, distribute, sublicense,

1168# and/or sell copies of the Software, and to permit persons to whom the

1169# Software is furnished to do so, subject to the following conditions:

1170#

1171# The above copyright notice and this permission notice shall be included

1172# in all copies or substantial portions of the Software.

1173#

1174# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS

1175# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,

1176# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL

1177# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR

1178# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,

1179# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR

1180# OTHER DEALINGS IN THE SOFTWARE.