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.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 _IsnotError, RangeError, _TypeError, _xattr, _xellipsoidal, \

22 _xellipsoids, _xError, _xkwds, _xkwds_not

23# from pygeodesy.fmath import favg # _MODS

24 from pygeodesy.interns import NN, _COMMA_, _ellipsoidal_

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

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

27# from pygeodesy.lcc import toLcc # _MODS

28# from pygeodesy.namedTuples import Vector3Tuple # _MODS

29 from pygeodesy.props import deprecated_method, deprecated_property_RO, \

30 Property_RO, property_doc_, property_RO, _update_all

31# from pygeodesy.trf import _eT0Ds4 # _MODS

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

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

34

35# from math import fabs # from .latlonBase

36

37__all__ = _ALL_LAZY.ellipsoidalBase

38__version__ = '24.11.07'

39

40

41 class CartesianEllipsoidalBase(CartesianBase):

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

43 '''

44 _datum = _WGS84 # L{Datum}

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

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

47

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

49 **datum_ll_name):

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

51

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

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

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

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

56

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

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

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

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

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

62

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

64 '''

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

66 if reframe:

67 self.reframe = reframe

68 self.epoch = epoch

69

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

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

72# '''

73# RefFrame = _MODS.trf.RefFrame

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

75# _NotImplemented(self, other)

76

77 @deprecated_method

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

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

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

81

82 @property_RO

83 def ellipsoidalCartesian(self):

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

85 '''

86 return type(self)

87

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

89 def epoch(self):

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

91 '''

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

93

94 @epoch.setter # PYCHOK setter!

95 def epoch(self, epoch):

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

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

98

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

100 '''

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

102

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

104 Vector=None, **Vector_kwds):

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

106 cartesian center point and a radius.

107

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

109 coordinates).

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

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

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

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

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

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

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

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

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

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

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

121

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

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

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

125

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

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

128 instance, aka the I{radical center}.

129

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

131

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

133

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

135

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

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

138 Intersection and function L{pygeodesy.radical2}.

139 '''

140 try:

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

142 center2, Radius_(radius2=radius2),

143 sphere=sphere, clas=self.classof,

144 Vector=Vector, **Vector_kwds)

145 except (TypeError, ValueError) as x:

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

147

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

149 def reframe(self):

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

151 '''

152 return self._reframe

153

154 @reframe.setter # PYCHOK setter!

155 def reframe(self, reframe):

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

157

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

159 '''

160 _set_reframe(self, reframe)

161

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

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

164

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

166 for further details.

167 '''

168 kwds = LatLon_and_kwds

169 if kwds:

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

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

172

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

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

175

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

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

178 overriding this point's reference frame.

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

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

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

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

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

184

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

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

187 is non-empty.

188

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

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

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

192

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

194 '''

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

196 epoch2=epoch2, **name)

197

198 @deprecated_method

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

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

201 r = self

202 for t in transforms:

203 r = r.toTransform(t)

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

205

206

207 class LatLonEllipsoidalBase(LatLonBase):

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

209 '''

210 _datum = _WGS84 # L{Datum}

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

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

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

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

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

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

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

218

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

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

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

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

223

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

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

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

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

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

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

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

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

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

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

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

235 C{B{reframe}=None}.

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

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

238

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

240 L{rangerrors} set to C{True}.

241

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

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

244 is not C{scalar} non-zero.

245

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

247 '''

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

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

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

251 if reframe:

252 self.reframe = reframe

253 self.epoch = epoch

254

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

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

257# '''

258# RefFrame = _MODS.trf.RefFrame

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

260# _NotImplemented(self, other)

261

262 def antipode(self, height=None):

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

264 to this point.

265

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

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

268

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

270 '''

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

272 if lla.datum != self.datum:

273 lla.datum = self.datum

274 return lla

275

276 @deprecated_property_RO

277 def convergence(self):

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

279 return self.gamma # PYCHOK no cover

280

281 @deprecated_method

282 def convertDatum(self, datum2):

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

284 return self.toDatum(datum2)

285

286 @deprecated_method

287 def convertRefFrame(self, reframe2):

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

289 return self.toRefFrame(reframe2)

290

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

292 def datum(self):

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

294 '''

295 return self._datum

296

297 @datum.setter # PYCHOK setter!

298 def datum(self, datum):

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

300

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

302 '''

303 _xinstanceof(Datum, datum=datum)

304 if not datum.isEllipsoidal:

305 raise _IsnotError(_ellipsoidal_, datum=datum)

306 if self._datum != datum:

307 _update_all(self)

308 self._datum = datum

309

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

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

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

313

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

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

316

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

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

319 point (C{bool}).

320

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

322

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

324

325 @raise ValueError: Incompatible datum ellipsoids.

326

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

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

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

330 formula.

331 '''

332 p = self.others(other)

333 if wrap: # PYCHOK no cover

334 p = _Wrap.point(p)

335 E = self.ellipsoids(other)

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

337

338 @Property_RO

339 def _elevation2(self):

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

341 '''

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

343 timeout=self._elevation2to)

344

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

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

347 or sphere.

348

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

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

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

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

353 radius).

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

355

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

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

358

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

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

361 L{elevations.elevation2} is based.

362

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

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

365

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

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

368 '''

369 if self._elevation2to != timeout:

370 self._elevation2to = timeout

371 LatLonEllipsoidalBase._elevation2._update(self)

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

373

374 def ellipsoid(self, datum=_WGS84):

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

376

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

378

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

380 '''

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

382

383 @property_RO

384 def ellipsoidalLatLon(self):

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

386 '''

387 return type(self)

388

389 def ellipsoids(self, other):

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

391

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

393

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

395

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

397

398 @raise ValueError: Incompatible datum ellipsoids.

399 '''

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

401

402 E = self.ellipsoid()

403 try: # other may be Sphere, etc.

404 e = other.ellipsoid()

405 except AttributeError:

406 try: # no ellipsoid method, try datum

407 e = other.datum.ellipsoid

408 except AttributeError:

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

410 return _xellipsoids(E, e)

411

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

413 def epoch(self):

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

415 '''

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

417

418 @epoch.setter # PYCHOK setter!

419 def epoch(self, epoch):

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

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

422

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

424 '''

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

426

427 @Property_RO

428 def Equidistant(self):

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

430 '''

431 try:

432 _ = self.datum.ellipsoid.geodesic

433 return _MODS.azimuthal.EquidistantKarney

434 except ImportError: # no geographiclib

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

436

437 @Property_RO

438 def _etm(self):

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

440 '''

441 etm = _MODS.etm

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

443

444 @property_RO

445 def gamma(self):

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

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

448 '''

449 return self._gamma

450

451 @Property_RO

452 def _geoidHeight2(self):

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

454 '''

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

456 timeout=self._geoidHeight2to)

457

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

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

460 or sphere.

461

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

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

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

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

466 radius).

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

468

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

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

471

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

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

474 the L{elevations.geoidHeight2} is based.

475

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

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

478

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

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

481 '''

482 if self._geoidHeight2to != timeout:

483 self._geoidHeight2to = timeout

484 LatLonEllipsoidalBase._geoidHeight2._update(self)

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

486

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

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

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

490

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

492 equidistant=None, tol=_TOL_M):

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

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

495

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

497 this point (compass C{degrees360}).

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

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

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

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

502 or C{None} for the mean height.

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

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

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

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

507 preferred C{.Equidistant}.

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

509 (C{meter}, conventionally).

510

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

512 a C{LatLon} instance.

513

514 @raise ImportError: Package U{geographiclib

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

516 installed or not found, but only in case

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

518

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

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

521

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

523

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

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

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

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

528

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

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

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

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

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

534 '''

535 try:

536 s2 = self.others(start2=start2)

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

538 s2, end2,

539 height=height, wrap=wrap,

540 equidistant=equidistant, tol=tol,

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

542 except (TypeError, ValueError) as x:

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

544 height=height, wrap=wrap, tol=tol)

545

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

547 equidistant=None, tol=_TOL_M):

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

549 defined by a center point and a radius.

550

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

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

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

554 B{C{radius1}}).

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

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

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

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

559 (C{bool}).

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

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

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

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

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

565

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

567 instance. For abutting circles, both intersection

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

569

570 @raise ImportError: Package U{geographiclib

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

572 not installed or not found, but only if

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

574

575 @raise IntersectionError: Concentric, antipodal, invalid or

576 non-intersecting circles or no

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

578

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

580

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

582

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

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

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

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

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

588 intersections.

589 '''

590 try:

591 c2 = self.others(center2=center2)

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

593 c2, radius2,

594 height=height, wrap=wrap,

595 equidistant=equidistant, tol=tol,

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

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

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

599 height=height, wrap=wrap, tol=tol)

600

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

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

603

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

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

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

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

608

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

610 C{False} otherwise.

611

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

613

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

615

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

617

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

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

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

621 '''

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

623

624 @property_RO

625 def iteration(self):

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

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

628 '''

629 return self._iteration

630

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

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

633

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

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

636 mean height (C{meter}).

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

638 may be negative or greater than 1.0.

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

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

641

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

643

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

645

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

647

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

649 '''

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

651

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

653 equidistant=None, tol=_TOL_M):

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

655 between two other (ellipsoidal) points.

656

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

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

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

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

661 (C{bool}).

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

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

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

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

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

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

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

669 C{Equidistant}, like L{Equidistant<LatLonEllipsoidalBase.Equistant>}.

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

671

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

673

674 @raise ImportError: Package U{geographiclib

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

676 not installed or not found, but only if

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

678

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

680

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

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

683

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

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

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

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

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

689 '''

690 try:

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

692 height=height, wrap=wrap,

693 equidistant=equidistant,

694 tol=tol, LatLon=self.classof)

695 except (TypeError, ValueError) as x:

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

697 height=height, wrap=wrap, tol=tol)

698 return t.closest

699

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

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

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

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

704

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

706 L{pygeodesy.parse3llh}.

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

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

709 I{without conversion}.

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

711 I{without conversion}.

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

713 this reframe I{without conversion}.

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

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

716 longitude (C{bool}).

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

718

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

720

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

722 '''

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

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

725 epoch=epoch or self.epoch,

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

727

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

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

730 difference in Gaussian radii of curvature of the given

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

732

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

734 '''

735 if adjust: # Elevation2Tuple or GeoidHeight2Tuple

736 m, t = meter_text2

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

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

739 if n > EPS0:

740 # use ratio, datum and NAD83 units may differ

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

742 _earth_ellipsoid(datum)

743 r = E.rocGauss(self.lat)

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

745 m *= r / n

746 meter_text2 = meter_text2.classof(m, t)

747 return self._xnamed(meter_text2)

748

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

750 def reframe(self):

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

752 '''

753 return self._reframe

754

755 @reframe.setter # PYCHOK setter!

756 def reframe(self, reframe):

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

758

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

760 '''

761 _set_reframe(self, reframe)

762

763 @Property_RO

764 def scale(self):

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

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

767 '''

768 return self._scale

769

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

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

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

773

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

775 for further details.

776 '''

777 kwds = Cartesian_and_kwds

778 if kwds:

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

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

781

782 def toCss(self, **toCss_kwds):

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

784

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

786

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

788

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

790 '''

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

792

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

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

795

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

797 @kwarg height: Optional height, overriding the

798 converted height (C{meter}).

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

800

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

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

803 point's C{datum}.

804

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

806 '''

807 n = self._name__(name)

808 d2 = _ellipsoidal_datum(datum2, name=n)

809 if self.datum == d2:

810 r = self.copy(name=n)

811 else:

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

813 epoch=self.epoch, reframe=self.reframe)

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

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

816 return r

817

818 def toEtm(self, **toEtm8_kwds):

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

820

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

822

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

824

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

826 '''

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

828

829 def toLcc(self, **toLcc_kwds):

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

831

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

833

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

835

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

837 '''

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

839

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

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

842

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

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

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

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

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

848

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

850

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

852 '''

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

854

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

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

857

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

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

860 formulation (C{bool}).

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

862

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

864

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

866 '''

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

868

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

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

871

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

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

874 overriding this point's reference frame.

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

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

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

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

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

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

881

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

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

884 is non-empty.

885

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

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

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

889

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

891 '''

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

893 epoch2=epoch2, height=height, **name)

894

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

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

897

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

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

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

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

902 @kwarg LatLon_kwds: Optional keyword arguments for the transformed

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

904

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

906 C{B{transform}.isunity}.

907

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

909 '''

910 _xinstanceof(Transform, transform=transform)

911 d = datum or self.datum

912 if transform.isunity:

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

914 else:

915 c = self.toCartesian()

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

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

918 return r

919

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

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

922

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

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

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

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

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

928 meter} (C{scalar}).

929

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

931

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

933 '''

934 if self._upsOK(pole, falsed):

935 u = self._ups

936 else:

937 ups = _MODS.ups

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

939 pole=pole, falsed=falsed)

940 return _lowerleft(u, center)

941

942 def toUtm(self, center=False):

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

944

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

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

947 meter} (C{scalar}).

948

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

950

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

952 '''

953 return _lowerleft(self._utm, center)

954

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

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

957

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

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

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

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

962 meter} (C{scalar}).

963

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

965

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

967 '''

968 if self._utmOK():

969 u = self._utm

970 elif self._upsOK(pole):

971 u = self._ups

972 else: # no cover

973 utmups = _MODS.utmups

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

975 Utm=utmups.Utm, Ups=utmups.Ups)

976 if isinstance(u, utmups.Utm):

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

978 elif isinstance(u, utmups.Ups):

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

980 else:

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

982 return _lowerleft(u, center)

983

984 @deprecated_method

985 def to3xyz(self): # PYCHOK no cover

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

987

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

989

990 @note: Overloads C{LatLonBase.to3xyz}

991 '''

992 r = self.toEcef()

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

994

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

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

997 from North at each point.

998

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

1000 @arg other: The other point (C{LatLon}).

1001 @arg bearing2: Bearing at the B{C{other}} point (compass C{degrees360}).

1002 @kwarg height_wrap_tol: Optional keyword arguments C{B{height}=None},

1003 C{B{wrap}=False} and C{B{tol}}, see method L{intersection3

1004 <pygeodesy.ellipsoidalBase.LatLonEllipsoidalBase>}.

1005

1006 @return: Triangulated point (C{LatLon}).

1007

1008 @see: Method L{intersection3<pygeodesy.ellipsoidalBase.LatLonEllipsoidalBase>}

1009 for further details.

1010 '''

1011 if _isDegrees(bearing1) and _isDegrees(bearing2):

1012 r = self.intersection3(bearing1, other, bearing2, **height_wrap_tol)

1013 return r.point

1014 raise _TypeError(bearing1=bearing1, bearing2=bearing2 **height_wrap_tol)

1015

1016 def trilaterate5(self, distance1, point2, distance2, point3, distance3,

1017 area=True, eps=EPS1, wrap=False):

1018 '''Trilaterate three points by I{area overlap} or I{perimeter intersection}

1019 of three intersecting circles.

1020

1021 @arg distance1: Distance to this point (C{meter}), same units as B{C{eps}}).

1022 @arg point2: Second center point (C{LatLon}).

1023 @arg distance2: Distance to point2 (C{meter}, same units as B{C{eps}}).

1024 @arg point3: Third center point (C{LatLon}).

1025 @arg distance3: Distance to point3 (C{meter}, same units as B{C{eps}}).

1026 @kwarg area: If C{True}, compute the area overlap, otherwise the perimeter

1027 intersection of the circles (C{bool}).

1028 @kwarg eps: The required I{minimal overlap} for C{B{area}=True} or the

1029 I{intersection margin} for C{B{area}=False} (C{meter},

1030 conventionally).

1031 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll B{C{point2}}

1032 and B{C{point3}} (C{bool}).

1033

1034 @return: A L{Trilaterate5Tuple}C{(min, minPoint, max, maxPoint, n)} with

1035 C{min} and C{max} in C{meter}, same units as B{C{eps}}, the

1036 corresponding trilaterated points C{minPoint} and C{maxPoint}

1037 as I{ellipsoidal} C{LatLon} and C{n}, the number of trilatered

1038 points found for the given B{C{eps}}.

1039

1040 If only a single trilaterated point is found, C{min I{is} max},

1041 C{minPoint I{is} maxPoint} and C{n=1}.

1042

1043 If C{B{area}=False}, C{min} and C{max} represent the nearest

1044 respectively farthest intersection margin.

1045

1046 If C{B{area}=True}, C{min} and C{max} are the smallest respectively

1047 largest I{radial} overlap found.

1048

1049 If C{B{area}=True} and all 3 circles are concentric, C{n=0} and

1050 C{minPoint} and C{maxPoint} are the B{C{point#}} with the smallest

1051 B{C{distance#}} C{min} respectively largest B{C{distance#}} C{max}.

1052

1053 @raise IntersectionError: Trilateration failed for the given B{C{eps}},

1054 insufficient overlap for C{B{area}=True}, no

1055 circle intersections for C{B{area}=False} or

1056 all circles are (near-)concentric.

1057

1058 @raise TypeError: Invalid B{C{point2}} or B{C{point3}}.

1059

1060 @raise ValueError: Coincident B{C{points}} or invalid B{C{distance1}},

1061 B{C{distance2}} or B{C{distance3}}.

1062

1063 @note: Ellipsoidal trilateration invokes methods C{LatLon.intersections2}

1064 and C{LatLon.nearestOn} based on I{Karney}'s Python U{geographiclib

1065 <https://PyPI.org/project/geographiclib>} if installed, otherwise

1066 the accurate (but slower) C{ellipsoidalExact.LatLon} methods.

1067 '''

1068 return _trilaterate5(self, distance1,

1069 self.others(point2=point2), distance2,

1070 self.others(point3=point3), distance3,

1071 area=area, eps=eps, wrap=wrap)

1072

1073 @Property_RO

1074 def _ups(self): # __dict__ value overwritten by method C{toUtmUps}

1075 '''(INTERNAL) Get this C{LatLon} point as UPS coordinate (L{Ups}),

1076 see L{pygeodesy.toUps8}.

1077 '''

1078 ups = _MODS.ups

1079 return ups.toUps8(self, datum=self.datum, Ups=ups.Ups,

1080 pole=NN, falsed=True, name=self.name)

1081

1082 def _upsOK(self, pole=NN, falsed=True):

1083 '''(INTERNAL) Check matching C{Ups}.

1084 '''

1085 try:

1086 u = self._ups

1087 except RangeError:

1088 return False

1089 return falsed and (u.pole == pole[:1].upper() or not pole)

1090

1091 @Property_RO

1092 def _utm(self): # __dict__ value overwritten by method C{toUtmUps}

1093 '''(INTERNAL) Get this C{LatLon} point as UTM coordinate (L{Utm}),

1094 see L{pygeodesy.toUtm8}.

1095 '''

1096 utm = _MODS.utm

1097 return utm.toUtm8(self, datum=self.datum, Utm=utm.Utm, name=self.name)

1098

1099 def _utmOK(self):

1100 '''(INTERNAL) Check C{Utm}.

1101 '''

1102 try:

1103 _ = self._utm

1104 except RangeError:

1105 return False

1106 return True

1107

1108

1109 def _lowerleft(utmups, center):

1110 '''(INTERNAL) Optionally I{un}-center C{utmups}.

1111 '''

1112 if center in (False, 0, _0_0):

1113 u = utmups

1114 elif center in (True,):

1115 u = utmups._lowerleft

1116 else:

1117 u = _MODS.utmupsBase._lowerleft(utmups, center)

1118 return u

1119

1120

1121 def _nearestOn(point, point1, point2, within=True, height=None, wrap=False, # was=True

1122 equidistant=None, tol=_TOL_M, **LatLon_and_kwds):

1123 '''(INTERNAL) Get closest point, imported by .ellipsoidalExact,

1124 -GeodSolve, -Karney and -Vincenty to embellish exceptions.

1125 '''

1126 try:

1127 p = _xellipsoidal(point=point)

1128 t = _MODS.ellipsoidalBaseDI._nearestOn2(p, point1, point2, within=within,

1129 height=height, wrap=wrap,

1130 equidistant=equidistant,

1131 tol=tol, **LatLon_and_kwds)

1132 except (TypeError, ValueError) as x:

1133 raise _xError(x, point=point, point1=point1, point2=point2)

1134 return t.closest

1135

1136

1137 def _set_reframe(inst, reframe):

1138 '''(INTERNAL) Set or clear an instance's reference frame.

1139 '''

1140 if reframe is not None:

1141 _xinstanceof(_MODS.trf.RefFrame, reframe=reframe)

1142 inst._reframe = reframe

1143 elif inst.reframe is not None:

1144 inst._reframe = None

1145

1146

1147__all__ += _ALL_DOCS(CartesianEllipsoidalBase, LatLonEllipsoidalBase)

1148

1149# **) MIT License

1150#

1151# Copyright (C) 2016-2024 -- mrJean1 at Gmail -- All Rights Reserved.

1152#

1153# Permission is hereby granted, free of charge, to any person obtaining a

1154# copy of this software and associated documentation files (the "Software"),

1155# to deal in the Software without restriction, including without limitation

1156# the rights to use, copy, modify, merge, publish, distribute, sublicense,

1157# and/or sell copies of the Software, and to permit persons to whom the

1158# Software is furnished to do so, subject to the following conditions:

1159#

1160# The above copyright notice and this permission notice shall be included

1161# in all copies or substantial portions of the Software.

1162#

1163# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS

1164# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,

1165# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL

1166# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR

1167# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,

1168# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR

1169# OTHER DEALINGS IN THE SOFTWARE.