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 2005-2016}

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.basics import _xinstanceof # from .datums

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

17 from pygeodesy.cartesianBase import CartesianBase # PYCHOK used!

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

19 Transform, _WGS84, _EWGS84, _xinstanceof # _spherical_datum

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

21 from pygeodesy.errors import _incompatible, _IsnotError, RangeError, _TypeError, \

22 _ValueError, _xattr, _xellipsoidal, _xError, _xkwds, \

23 _xkwds_not

24# from pygeodesy.fmath import favg # _MODS

25 from pygeodesy.interns import NN, _COMMA_, _ellipsoidal_

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

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

28# from pygeodesy.lcc import toLcc # _MODS

29# from pygeodesy.namedTuples import Vector3Tuple # _MODS

30 from pygeodesy.props import deprecated_method, deprecated_property_RO, \

31 Property_RO, property_doc_, property_RO, _update_all

32# from pygeodesy.trf import _eT0Ds4 # _MODS

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

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

35

36# from math import fabs # from .latlonBase

37

38__all__ = _ALL_LAZY.ellipsoidalBase

39__version__ = '24.06.06'

40

41

42 class CartesianEllipsoidalBase(CartesianBase):

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

44 '''

45 _datum = _WGS84 # L{Datum}

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

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

48

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

50 **datum_ll_name):

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

52

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

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

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

56 if C{B{reframe}=None}.

57

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

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

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

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

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

63

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

65 '''

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

67 if reframe:

68 self.reframe = reframe

69 self.epoch = epoch

70

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

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

73# '''

74# RefFrame = _MODS.trf.RefFrame

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

76# _NotImplemented(self, other)

77

78 @deprecated_method

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

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

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

82

83 @property_RO

84 def ellipsoidalCartesian(self):

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

86 '''

87 return type(self)

88

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

90 def epoch(self):

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

92 '''

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

94

95 @epoch.setter # PYCHOK setter!

96 def epoch(self, epoch):

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

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

99

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

101 '''

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

103

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

105 Vector=None, **Vector_kwds):

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

107 cartesian center point and a radius.

108

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

110 coordinates).

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

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

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

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

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

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

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

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

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

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

121 ignored if C{B{Vector} is None}.

122

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

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

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

126

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

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

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

130

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

132

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

134

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

136

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

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

139 Intersection and function L{pygeodesy.radical2}.

140 '''

141 try:

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

143 center2, Radius_(radius2=radius2),

144 sphere=sphere, clas=self.classof,

145 Vector=Vector, **Vector_kwds)

146 except (TypeError, ValueError) as x:

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

148

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

150 def reframe(self):

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

152 '''

153 return self._reframe

154

155 @reframe.setter # PYCHOK setter!

156 def reframe(self, reframe):

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

158

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

160 '''

161 _set_reframe(self, reframe)

162

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

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

165

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

167 for further details.

168 '''

169 kwds = LatLon_and_kwds

170 if kwds:

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

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

173

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

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

176

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

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

179 overriding this point's reference frame.

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

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

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

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

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

185

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

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

188 is non-empty.

189

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

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

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

193

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

195 '''

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

197 epoch2=epoch2, **name)

198

199 @deprecated_method

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

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

202 r = self

203 for t in transforms:

204 r = r.toTransform(t)

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

206

207

208 class LatLonEllipsoidalBase(LatLonBase):

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

210 '''

211 _datum = _WGS84 # L{Datum}

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

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

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

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

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

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

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

219

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

221 epoch=None, wrap=False, **name):

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

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

224

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

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

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

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

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

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

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

232 L{Ellipsoid2} or L{a_f2Tuple}).

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

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

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

236 if C{B{reframe}=None}.

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

238 (C{bool}).

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

240

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

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

243

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

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

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

247

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

249 '''

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

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

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

253 if reframe:

254 self.reframe = reframe

255 self.epoch = epoch

256

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

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

259# '''

260# RefFrame = _MODS.trf.RefFrame

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

262# _NotImplemented(self, other)

263

264 def antipode(self, height=None):

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

266 to this point.

267

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

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

270

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

272 '''

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

274 if lla.datum != self.datum:

275 lla.datum = self.datum

276 return lla

277

278 @deprecated_property_RO

279 def convergence(self):

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

281 return self.gamma

282

283 @deprecated_method

284 def convertDatum(self, datum2):

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

286 return self.toDatum(datum2)

287

288 @deprecated_method

289 def convertRefFrame(self, reframe2):

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

291 return self.toRefFrame(reframe2)

292

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

294 def datum(self):

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

296 '''

297 return self._datum

298

299 @datum.setter # PYCHOK setter!

300 def datum(self, datum):

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

302

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

304 or not ellipsoidal.

305 '''

306 _xinstanceof(Datum, datum=datum)

307 if not datum.isEllipsoidal:

308 raise _IsnotError(_ellipsoidal_, datum=datum)

309 if self._datum != datum:

310 _update_all(self)

311 self._datum = datum

312

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

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

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

316

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

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

319

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

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

322 point (C{bool}).

323

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

325

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

327

328 @raise ValueError: Incompatible datum ellipsoids.

329

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

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

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

333 formula.

334 '''

335 p = self.others(other)

336 if wrap:

337 p = _Wrap.point(p)

338 E = self.ellipsoids(other)

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

340

341 @Property_RO

342 def _elevation2(self):

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

344 '''

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

346 timeout=self._elevation2to)

347

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

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

350 or sphere.

351

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

353 C{NAD83} (C{bool}).

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

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

356 radius).

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

358

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

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

361

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

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

364 L{elevations.elevation2} is based.

365

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

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

368

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

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

371 '''

372 if self._elevation2to != timeout:

373 self._elevation2to = timeout

374 LatLonEllipsoidalBase._elevation2._update(self)

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

376

377 def ellipsoid(self, datum=_WGS84):

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

379

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

381

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

383 '''

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

385

386 @property_RO

387 def ellipsoidalLatLon(self):

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

389 '''

390 return type(self)

391

392 def ellipsoids(self, other):

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

394

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

396

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

398

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

400

401 @raise ValueError: Incompatible datum ellipsoids.

402 '''

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

404

405 E = self.ellipsoid()

406 try: # other may be Sphere, etc.

407 e = other.ellipsoid()

408 except AttributeError:

409 try: # no ellipsoid method, try datum

410 e = other.datum.ellipsoid

411 except AttributeError:

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

413 if e != E:

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

415 return E

416

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

418 def epoch(self):

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

420 '''

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

422

423 @epoch.setter # PYCHOK setter!

424 def epoch(self, epoch):

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

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

427

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

429 '''

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

431

432 @Property_RO

433 def Equidistant(self):

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

435 '''

436 try:

437 _ = self.datum.ellipsoid.geodesic

438 return _MODS.azimuthal.EquidistantKarney

439 except ImportError: # no geographiclib

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

441

442 @Property_RO

443 def _etm(self):

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

445 '''

446 etm = _MODS.etm

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

448

449 @property_RO

450 def gamma(self):

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

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

453 '''

454 return self._gamma

455

456 @Property_RO

457 def _geoidHeight2(self):

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

459 '''

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

461 timeout=self._geoidHeight2to)

462

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

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

465 or sphere.

466

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

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

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

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

471 radius).

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

473

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

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

476

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

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

479 the L{elevations.geoidHeight2} is based.

480

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

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

483

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

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

486 '''

487 if self._geoidHeight2to != timeout:

488 self._geoidHeight2to = timeout

489 LatLonEllipsoidalBase._geoidHeight2._update(self)

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

491

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

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

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

495

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

497 equidistant=None, tol=_TOL_M):

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

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

500

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

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

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

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

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

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

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

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

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

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

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

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

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

514 length (C{meter}, conventionally).

515

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

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

518

519 @raise ImportError: Package U{geographiclib

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

521 not installed or not found, but only if

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

523

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

525 non-intersecting lines or no convergence

526 for the given B{C{tol}}.

527

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

529 is not C{LatLon}.

530

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

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

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

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

535 of the authalic earth perimeter).

536

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

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

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

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

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

542 '''

543 try:

544 s2 = self.others(other)

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

546 s2, end2,

547 height=height, wrap=wrap,

548 equidistant=equidistant, tol=tol,

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

550 except (TypeError, ValueError) as x:

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

552 height=height, wrap=wrap, tol=tol)

553

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

555 equidistant=None, tol=_TOL_M):

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

557 each defined by a center point and a radius.

558

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

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

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

562 B{C{radius1}}).

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

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

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

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

567 center (C{bool}).

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

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

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

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

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

573

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

575 instance. For abutting circles, both intersection

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

577

578 @raise ImportError: Package U{geographiclib

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

580 not installed or not found, but only if

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

582

583 @raise IntersectionError: Concentric, antipodal, invalid or

584 non-intersecting circles or no

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

586

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

588

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

590

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

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

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

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

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

596 intersections.

597 '''

598 try:

599 c2 = self.others(other)

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

601 c2, radius2,

602 height=height, wrap=wrap,

603 equidistant=equidistant, tol=tol,

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

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

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

607 height=height, wrap=wrap, tol=tol)

608

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

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

611

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

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

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

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

616

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

618 C{False} otherwise.

619

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

621

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

623

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

625

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

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

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

629 '''

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

631

632 @property_RO

633 def iteration(self):

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

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

636 '''

637 return self._iteration

638

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

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

641

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

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

644 mean height (C{meter}).

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

646 may be negative or greater than 1.0.

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

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

649

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

651

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

653

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

655

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

657 '''

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

659

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

661 equidistant=None, tol=_TOL_M):

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

663 two other (ellipsoidal) points.

664

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

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

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

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

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

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

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

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

673 takes the heights of the points into account.

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

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

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

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

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

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

680

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

682

683 @raise ImportError: Package U{geographiclib

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

685 not installed or not found, but only if

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

687

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

689 B{C{equidistant}}.

690

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

692 incompatible 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 datum (L{RefFrame}), overriding this

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

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

736 r.datum = datum

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

738 r.epoch = epoch

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

740 r.reframe = reframe

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

742

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

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

745 difference in Gaussian radii of curvature of the given

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

747

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

749 '''

750 if adjust: # Elevation2Tuple or GeoidHeight2Tuple

751 m, t = meter_text2

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

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

754 if n > EPS0:

755 # use ratio, datum and NAD83 units may differ

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

757 _earth_ellipsoid(datum)

758 r = E.rocGauss(self.lat)

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

760 m *= r / n

761 meter_text2 = meter_text2.classof(m, t)

762 return self._xnamed(meter_text2)

763

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

765 def reframe(self):

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

767 '''

768 return self._reframe

769

770 @reframe.setter # PYCHOK setter!

771 def reframe(self, reframe):

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

773

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

775 '''

776 _set_reframe(self, reframe)

777

778 @Property_RO

779 def scale(self):

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

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

782 '''

783 return self._scale

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 L{pygeodesy.toCss} keyword arguments.

801

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

803

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

805 '''

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

807

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

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

810

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

812 @kwarg height: Optional height, overriding the

813 converted height (C{meter}).

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

815

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

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

818 matches this point's C{datum}.

819

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

821 '''

822 n = self._name__(name)

823 d2 = _ellipsoidal_datum(datum2, name=n)

824 if self.datum == d2:

825 r = self.copy(name=n)

826 else:

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

828 epoch=self.epoch, reframe=self.reframe)

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

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

831 return r

832

833 def toEtm(self, **toEtm8_kwds):

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

835

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

837

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

839

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

841 '''

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

843

844 def toLcc(self, **toLcc_kwds):

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

846

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

848

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

850

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

852 '''

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

854

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

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

857

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

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

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

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

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

863

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

865

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

867 '''

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

869

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

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

872

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

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

875 formulation (C{bool}).

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

877

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

879

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

881 '''

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

883

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

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

886

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

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

889 overriding this point's reference frame.

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

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

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

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

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

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

896

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

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

899 is non-empty.

900

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

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

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

904

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

906 '''

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

908 epoch2=epoch2, height=height, **name)

909

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

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

912

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

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

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

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

917 @kwarg LatLon_kwds: Optional keyword arguments for the transformed

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

919

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

921 C{B{transform}.isunity}.

922

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

924 '''

925 _xinstanceof(Transform, transform=transform)

926 d = datum or self.datum

927 if transform.isunity:

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

929 else:

930 c = self.toCartesian()

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

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

933 return r

934

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

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

937

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

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

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

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

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

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

944

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

946

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

948 '''

949 if self._upsOK(pole, falsed):

950 u = self._ups

951 else:

952 ups = _MODS.ups

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

954 pole=pole, falsed=falsed)

955 return _lowerleft(u, center)

956

957 def toUtm(self, center=False):

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

959

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

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

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

963

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

965

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

967 '''

968 return _lowerleft(self._utm, center)

969

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

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

972

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

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

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

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

977 meter} (C{scalar}).

978

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

980

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

982 '''

983 if self._utmOK():

984 u = self._utm

985 elif self._upsOK(pole):

986 u = self._ups

987 else: # no cover

988 utmups = _MODS.utmups

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

990 Utm=utmups.Utm, Ups=utmups.Ups)

991 if isinstance(u, utmups.Utm):

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

993 elif isinstance(u, utmups.Ups):

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

995 else:

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

997 return _lowerleft(u, center)

998

999 @deprecated_method

1000 def to3xyz(self): # PYCHOK no cover

1001 '''DEPRECATED, use method C{toEcef}.

1002

1003 @return: A L{Vector3Tuple}C{(x, y, z)}.

1004

1005 @note: Overloads C{LatLonBase.to3xyz}

1006 '''

1007 r = self.toEcef()

1008 return _MODS.namedTuples.Vector3Tuple(r.x, r.y, r.z, name=self.name)

1009

1010 def triangulate(self, bearing1, other, bearing2, **height_wrap_tol):

1011 '''I{Iteratively} locate a point given this, an other point and the (initial)

1012 bearing at this and at the other point.

1013

1014 @arg bearing1: Bearing at this point (compass C{degrees360}).

1015 @arg other: Start point of the other line (C{LatLon}).

1016 @arg bearing2: Bearing at the other point (compass C{degrees360}).

1017 @kwarg height_wrap_tol: Optional keyword arguments C{B{height}=None},

1018 C{B{wrap}=False} and C{B{tol}}, see method L{intersection3}.

1019

1020 @return: Triangulated point (C{LatLon}).

1021

1022 @see: Method L{intersection3} for further details.

1023 '''

1024 if _isDegrees(bearing1) and _isDegrees(bearing2):

1025 r = self.intersection3(bearing1, other, bearing2, **height_wrap_tol)

1026 return r.point

1027 raise _TypeError(bearing1=bearing1, bearing2=bearing2 **height_wrap_tol)

1028

1029 def trilaterate5(self, distance1, point2, distance2, point3, distance3,

1030 area=True, eps=EPS1, wrap=False):

1031 '''Trilaterate three points by I{area overlap} or I{perimeter

1032 intersection} of three intersecting circles.

1033

1034 @arg distance1: Distance to this point (C{meter}), same units

1035 as B{C{eps}}).

1036 @arg point2: Second center point (C{LatLon}).

1037 @arg distance2: Distance to point2 (C{meter}, same units as

1038 B{C{eps}}).

1039 @arg point3: Third center point (C{LatLon}).

1040 @arg distance3: Distance to point3 (C{meter}, same units as

1041 B{C{eps}}).

1042 @kwarg area: If C{True} compute the area overlap, otherwise the

1043 perimeter intersection of the circles (C{bool}).

1044 @kwarg eps: The required I{minimal overlap} for C{B{area}=True}

1045 or the I{intersection margin} for C{B{area}=False}

1046 (C{meter}, conventionally).

1047 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll

1048 B{C{point2}} and B{C{point3}} (C{bool}).

1049

1050 @return: A L{Trilaterate5Tuple}C{(min, minPoint, max, maxPoint, n)}

1051 with C{min} and C{max} in C{meter}, same units as B{C{eps}},

1052 the corresponding trilaterated points C{minPoint} and

1053 C{maxPoint} as I{ellipsoidal} C{LatLon} and C{n}, the number

1054 of trilatered points found for the given B{C{eps}}.

1055

1056 If only a single trilaterated point is found, C{min I{is}

1057 max}, C{minPoint I{is} maxPoint} and C{n = 1}.

1058

1059 For C{B{area}=True}, C{min} and C{max} are the smallest

1060 respectively largest I{radial} overlap found.

1061

1062 For C{B{area}=False}, C{min} and C{max} represent the

1063 nearest respectively farthest intersection margin.

1064

1065 If C{B{area}=True} and all 3 circles are concentric, C{n=0}

1066 and C{minPoint} and C{maxPoint} are the B{C{point#}} with

1067 the smallest B{C{distance#}} C{min} respectively C{max} the

1068 largest B{C{distance#}}.

1069

1070 @raise IntersectionError: Trilateration failed for the given B{C{eps}},

1071 insufficient overlap for C{B{area}=True}, no

1072 circle intersections for C{B{area}=False} or

1073 all circles are (near-)concentric.

1074

1075 @raise TypeError: Invalid B{C{point2}} or B{C{point3}}.

1076

1077 @raise ValueError: Coincident B{C{points}} or invalid B{C{distance1}},

1078 B{C{distance2}} or B{C{distance3}}.

1079

1080 @note: Ellipsoidal trilateration invokes methods C{LatLon.intersections2}

1081 and C{LatLon.nearestOn} based on I{Karney}'s Python U{geographiclib

1082 <https://PyPI.org/project/geographiclib>} if installed, otherwise

1083 the accurate (but slower) C{ellipsoidalExact.LatLon} methods.

1084 '''

1085 return _trilaterate5(self, distance1,

1086 self.others(point2=point2), distance2,

1087 self.others(point3=point3), distance3,

1088 area=area, eps=eps, wrap=wrap)

1089

1090 @Property_RO

1091 def _ups(self): # __dict__ value overwritten by method C{toUtmUps}

1092 '''(INTERNAL) Get this C{LatLon} point as UPS coordinate (L{Ups}),

1093 see L{pygeodesy.toUps8}.

1094 '''

1095 ups = _MODS.ups

1096 return ups.toUps8(self, datum=self.datum, Ups=ups.Ups,

1097 pole=NN, falsed=True, name=self.name)

1098

1099 def _upsOK(self, pole=NN, falsed=True):

1100 '''(INTERNAL) Check matching C{Ups}.

1101 '''

1102 try:

1103 u = self._ups

1104 except RangeError:

1105 return False

1106 return falsed and (u.pole == pole[:1].upper() or not pole)

1107

1108 @Property_RO

1109 def _utm(self): # __dict__ value overwritten by method C{toUtmUps}

1110 '''(INTERNAL) Get this C{LatLon} point as UTM coordinate (L{Utm}),

1111 see L{pygeodesy.toUtm8}.

1112 '''

1113 utm = _MODS.utm

1114 return utm.toUtm8(self, datum=self.datum, Utm=utm.Utm, name=self.name)

1115

1116 def _utmOK(self):

1117 '''(INTERNAL) Check C{Utm}.

1118 '''

1119 try:

1120 _ = self._utm

1121 except RangeError:

1122 return False

1123 return True

1124

1125

1126 def _lowerleft(utmups, center):

1127 '''(INTERNAL) Optionally I{un}-center C{utmups}.

1128 '''

1129 if center in (False, 0, _0_0):

1130 u = utmups

1131 elif center in (True,):

1132 u = utmups._lowerleft

1133 else:

1134 u = _MODS.utmupsBase._lowerleft(utmups, center)

1135 return u

1136

1137

1138 def _nearestOn(point, point1, point2, within=True, height=None, wrap=False, # was=True

1139 equidistant=None, tol=_TOL_M, **LatLon_and_kwds):

1140 '''(INTERNAL) Get closest point, imported by .ellipsoidalExact,

1141 -GeodSolve, -Karney and -Vincenty to embellish exceptions.

1142 '''

1143 try:

1144 p = _xellipsoidal(point=point)

1145 t = _MODS.ellipsoidalBaseDI._nearestOn2(p, point1, point2, within=within,

1146 height=height, wrap=wrap,

1147 equidistant=equidistant,

1148 tol=tol, **LatLon_and_kwds)

1149 except (TypeError, ValueError) as x:

1150 raise _xError(x, point=point, point1=point1, point2=point2)

1151 return t.closest

1152

1153

1154 def _set_reframe(inst, reframe):

1155 '''(INTERNAL) Set or clear an instance's reference frame.

1156 '''

1157 if reframe is not None:

1158 _xinstanceof(_MODS.trf.RefFrame, reframe=reframe)

1159 inst._reframe = reframe

1160 elif inst.reframe is not None:

1161 inst._reframe = None

1162

1163

1164__all__ += _ALL_DOCS(CartesianEllipsoidalBase, LatLonEllipsoidalBase)

1165

1166# **) MIT License

1167#

1168# Copyright (C) 2016-2024 -- mrJean1 at Gmail -- All Rights Reserved.

1169#

1170# Permission is hereby granted, free of charge, to any person obtaining a

1171# copy of this software and associated documentation files (the "Software"),

1172# to deal in the Software without restriction, including without limitation

1173# the rights to use, copy, modify, merge, publish, distribute, sublicense,

1174# and/or sell copies of the Software, and to permit persons to whom the

1175# Software is furnished to do so, subject to the following conditions:

1176#

1177# The above copyright notice and this permission notice shall be included

1178# in all copies or substantial portions of the Software.

1179#

1180# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS

1181# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,

1182# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL

1183# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR

1184# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,

1185# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR

1186# OTHER DEALINGS IN THE SOFTWARE.