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__ = '24.04.07'

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, datum=None, reframe=None,

50 epoch=None, ll=None, name=NN):

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: Super-class L{CartesianBase<CartesianBase.__init__>} for more details.

65 '''

66 CartesianBase.__init__(self, x_xyz, y=y, z=z, datum=datum, ll=ll, name=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=NN):

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 name (C{str}), C{B{reframe2}.name} iff converted.

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=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=None, reframe=None,

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

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 name (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=name)

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

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

294 def _css(self):

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

296 '''

297 css = _MODS.css

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

299

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

301 def datum(self):

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

303 '''

304 return self._datum

305

306 @datum.setter # PYCHOK setter!

307 def datum(self, datum):

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

309

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

311 or not ellipsoidal.

312 '''

313 _xinstanceof(Datum, datum=datum)

314 if not datum.isEllipsoidal:

315 raise _IsnotError(_ellipsoidal_, datum=datum)

316 if self._datum != datum:

317 _update_all(self)

318 self._datum = datum

319

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

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

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

323

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

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

326

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

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

329 point (C{bool}).

330

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

332

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

334

335 @raise ValueError: Incompatible datum ellipsoids.

336

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

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

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

340 formula.

341 '''

342 p = self.others(other)

343 if wrap:

344 p = _Wrap.point(p)

345 E = self.ellipsoids(other)

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

347

348 @Property_RO

349 def _elevation2(self):

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

351 '''

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

353 timeout=self._elevation2to)

354

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

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

357 or sphere.

358

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

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

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

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

363 radius).

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

365

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

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

368

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

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

371 L{elevations.elevation2} is based.

372

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

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

375

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

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

378 '''

379 if self._elevation2to != timeout:

380 self._elevation2to = timeout

381 LatLonEllipsoidalBase._elevation2._update(self)

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

383

384 def ellipsoid(self, datum=_WGS84):

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

386

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

388

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

390 '''

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

392

393 @property_RO

394 def ellipsoidalLatLon(self):

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

396 '''

397 return type(self)

398

399 def ellipsoids(self, other):

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

401

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

403

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

405

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

407

408 @raise ValueError: Incompatible datum ellipsoids.

409 '''

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

411

412 E = self.ellipsoid()

413 try: # other may be Sphere, etc.

414 e = other.ellipsoid()

415 except AttributeError:

416 try: # no ellipsoid method, try datum

417 e = other.datum.ellipsoid

418 except AttributeError:

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

420 if e != E:

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

422 return E

423

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

425 def epoch(self):

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

427 '''

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

429

430 @epoch.setter # PYCHOK setter!

431 def epoch(self, epoch):

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

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

434

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

436 '''

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

438

439 @Property_RO

440 def Equidistant(self):

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

442 '''

443 try:

444 _ = self.datum.ellipsoid.geodesic

445 return _MODS.azimuthal.EquidistantKarney

446 except ImportError: # no geographiclib

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

448

449 @Property_RO

450 def _etm(self):

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

452 '''

453 etm = _MODS.etm

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

455

456 @property_RO

457 def gamma(self):

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

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

460 '''

461 return self._gamma

462

463 @Property_RO

464 def _geoidHeight2(self):

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

466 '''

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

468 timeout=self._geoidHeight2to)

469

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

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

472 or sphere.

473

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

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

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

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

478 radius).

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

480

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

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

483

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

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

486 the L{elevations.geoidHeight2} is based.

487

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

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

490

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

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

493 '''

494 if self._geoidHeight2to != timeout:

495 self._geoidHeight2to = timeout

496 LatLonEllipsoidalBase._geoidHeight2._update(self)

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

498

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

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

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

502

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

504 equidistant=None, tol=_TOL_M):

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

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

507

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

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

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

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

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

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

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

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

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

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

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

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

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

521 length (C{meter}, conventionally).

522

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

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

525

526 @raise ImportError: Package U{geographiclib

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

528 not installed or not found, but only if

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

530

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

532 non-intersecting lines or no convergence

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

534

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

536 is not C{LatLon}.

537

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

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

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

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

542 of the authalic earth perimeter).

543

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

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

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

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

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

549 '''

550 try:

551 s2 = self.others(other)

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

553 s2, end2,

554 height=height, wrap=wrap,

555 equidistant=equidistant, tol=tol,

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

557 except (TypeError, ValueError) as x:

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

559 height=height, wrap=wrap, tol=tol)

560

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

562 equidistant=None, tol=_TOL_M):

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

564 each defined by a center point and a radius.

565

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

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

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

569 B{C{radius1}}).

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

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

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

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

574 center (C{bool}).

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

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

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

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

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

580

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

582 instance. For abutting circles, both intersection

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

584

585 @raise ImportError: Package U{geographiclib

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

587 not installed or not found, but only if

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

589

590 @raise IntersectionError: Concentric, antipodal, invalid or

591 non-intersecting circles or no

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

593

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

595

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

597

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

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

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

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

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

603 intersections.

604 '''

605 try:

606 c2 = self.others(other)

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

608 c2, radius2,

609 height=height, wrap=wrap,

610 equidistant=equidistant, tol=tol,

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

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

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

614 height=height, wrap=wrap, tol=tol)

615

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

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

618

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

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

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

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

623

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

625 C{False} otherwise.

626

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

628

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

630

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

632

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

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

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

636 '''

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

638

639 @property_RO

640 def iteration(self):

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

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

643 '''

644 return self._iteration

645

646 @Property_RO

647 def _lcc(self):

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

649 '''

650 lcc = _MODS.lcc

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

652

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

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

655

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

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

658 mean height (C{meter}).

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

660 may be negative or greater than 1.0.

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

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

663

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

665

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

667

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

669

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

671 '''

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

673

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

675 equidistant=None, tol=_TOL_M):

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

677 two other (ellipsoidal) points.

678

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

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

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

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

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

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

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

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

687 takes the heights of the points into account.

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

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

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

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

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

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

694

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

696

697 @raise ImportError: Package U{geographiclib

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

699 not installed or not found, but only if

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

701

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

703 B{C{equidistant}}.

704

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

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

707

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

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

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

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

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

713 '''

714 try:

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

716 height=height, wrap=wrap,

717 equidistant=equidistant,

718 tol=tol, LatLon=self.classof)

719 except (TypeError, ValueError) as x:

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

721 height=height, wrap=wrap, tol=tol)

722 return t.closest

723

724 @Property_RO

725 def _osgr(self):

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

727 based on the OS recommendation.

728 '''

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

730

731 @Property_RO

732 def _osgrTM(self):

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

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

735 '''

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

737

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

739 sep=_COMMA_, wrap=False, name=NN):

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

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

742

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

744 see function L{pygeodesy.parse3llh}.

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

746 C{None}).

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

748 datum I{without conversion}.

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

750 epoch I{without conversion}.

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

752 this reframe I{without conversion}.

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

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

755 and longitude (C{bool}).

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

757 this name.

758

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

760

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

762 '''

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

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

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

766 r.datum = datum

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

768 r.epoch = epoch

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

770 r.reframe = reframe

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

772

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

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

775 difference in Gaussian radii of curvature of the given

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

777

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

779 '''

780 if adjust: # Elevation2Tuple or GeoidHeight2Tuple

781 m, t = meter_text2

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

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

784 if n > EPS0:

785 # use ratio, datum and NAD83 units may differ

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

787 _earth_ellipsoid(datum)

788 r = E.rocGauss(self.lat)

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

790 m *= r / n

791 meter_text2 = meter_text2.classof(m, t)

792 return self._xnamed(meter_text2)

793

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

795 def reframe(self):

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

797 '''

798 return self._reframe

799

800 @reframe.setter # PYCHOK setter!

801 def reframe(self, reframe):

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

803

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

805 '''

806 _set_reframe(self, reframe)

807

808 @Property_RO

809 def scale(self):

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

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

812 '''

813 return self._scale

814

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

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

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

818

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

820 for further details.

821 '''

822 kwds = Cartesian_and_kwds

823 if kwds:

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

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

826

827 def toCss(self, **toCss_kwds):

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

829

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

831

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

833

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

835 '''

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

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

838

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

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

841

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

843 @kwarg height: Optional height, overriding the

844 converted height (C{meter}).

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

846

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

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

849 matches this point's C{datum}.

850

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

852 '''

853 n = name or self.name

854 d2 = _ellipsoidal_datum(datum2, name=n)

855 if self.datum == d2:

856 r = self.copy(name=name)

857 else:

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

859 epoch=self.epoch, reframe=self.reframe)

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

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

862 return r

863

864 def toEtm(self, **toEtm8_kwds):

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

866

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

868

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

870

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

872 '''

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

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

875

876 def toLcc(self, **toLcc_kwds):

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

878

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

880

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

882

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

884 '''

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

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

887

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

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

890

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

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

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

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

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

896

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

898

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

900 '''

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

902

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

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

905

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

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

908 formulation (C{bool}).

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

910

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

912

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

914 '''

915 if toOsgr_kwds:

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

917 else:

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

919 return r

920

921 def toRefFrame(self, reframe2, reframe=None, epoch=None, epoch2=None, height=None, name=NN):

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

923

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

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

926 overriding this point's reference frame.

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

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

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

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

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

932 @kwarg name: Optional name (C{str}), C{B{reframe2}.name} iff converted.

933

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

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

936 is non-empty.

937

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

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

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

941

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

943 '''

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

945 epoch2=epoch2, name=name, height=height)

946

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

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

949

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

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

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

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

954 @kwarg LatLon_kwds: Optional keyword arguments for the transformed

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

956

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

958 C{B{transform}.isunity}.

959

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

961 '''

962 _xinstanceof(Transform, transform=transform)

963 d = datum or self.datum

964 if transform.isunity:

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

966 else:

967 c = self.toCartesian()

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

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

970 return r

971

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

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

974

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

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

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

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

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

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

981

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

983

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

985 '''

986 if self._upsOK(pole, falsed):

987 u = self._ups

988 else:

989 ups = _MODS.ups

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

991 pole=pole, falsed=falsed)

992 return _lowerleft(u, center)

993

994 def toUtm(self, center=False):

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

996

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

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

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

1000

1001 @return: The UTM coordinate (L{Utm}).

1002

1003 @see: Method L{Mgrs.toUtm} and function L{pygeodesy.toUtm8}.

1004 '''

1005 return _lowerleft(self._utm, center)

1006

1007 def toUtmUps(self, pole=NN, center=False):

1008 '''Convert this C{LatLon} point to a UTM or UPS coordinate.

1009

1010 @kwarg pole: Optional top/center of UPS (stereographic)

1011 projection (C{str}, 'N[orth]' or 'S[outh]').

1012 @kwarg center: If C{True}, I{un}-center the UTM or UPS to

1013 its C{lowerleft} (C{bool}) or by C{B{center}

1014 meter} (C{scalar}).

1015

1016 @return: The UTM or UPS coordinate (L{Utm} or L{Ups}).

1017

1018 @see: Function L{pygeodesy.toUtmUps8}.

1019 '''

1020 if self._utmOK():

1021 u = self._utm

1022 elif self._upsOK(pole):

1023 u = self._ups

1024 else: # no cover

1025 utmups = _MODS.utmups

1026 u = utmups.toUtmUps8(self, datum=self.datum, pole=pole, name=self.name,

1027 Utm=utmups.Utm, Ups=utmups.Ups)

1028 if isinstance(u, utmups.Utm):

1029 self._update(False, _utm=u) # PYCHOK kwds

1030 elif isinstance(u, utmups.Ups):

1031 self._update(False, _ups=u) # PYCHOK kwds

1032 else:

1033 _xinstanceof(utmups.Utm, utmups.Ups, toUtmUps8=u)

1034 return _lowerleft(u, center)

1035

1036 @deprecated_method

1037 def to3xyz(self): # PYCHOK no cover

1038 '''DEPRECATED, use method C{toEcef}.

1039

1040 @return: A L{Vector3Tuple}C{(x, y, z)}.

1041

1042 @note: Overloads C{LatLonBase.to3xyz}

1043 '''

1044 r = self.toEcef()

1045 return _MODS.namedTuples.Vector3Tuple(r.x, r.y, r.z, name=self.name)

1046

1047 def triangulate(self, bearing1, other, bearing2, **height_wrap_tol):

1048 '''I{Iteratively} locate a point given this, an other point and the (initial)

1049 bearing at this and at the other point.

1050

1051 @arg bearing1: Bearing at this point (compass C{degrees360}).

1052 @arg other: Start point of the other line (C{LatLon}).

1053 @arg bearing2: Bearing at the other point (compass C{degrees360}).

1054 @kwarg height_wrap_tol: Optional keyword arguments C{B{height}=None},

1055 C{B{wrap}=False} and C{B{tol}}, see method L{intersection3}.

1056

1057 @return: Triangulated point (C{LatLon}).

1058

1059 @see: Method L{intersection3} for further details.

1060 '''

1061 if _isDegrees(bearing1) and _isDegrees(bearing2):

1062 r = self.intersection3(bearing1, other, bearing2, **height_wrap_tol)

1063 return r.point

1064 raise _TypeError(bearing1=bearing1, bearing2=bearing2 **height_wrap_tol)

1065

1066 def trilaterate5(self, distance1, point2, distance2, point3, distance3,

1067 area=True, eps=EPS1, wrap=False):

1068 '''Trilaterate three points by I{area overlap} or I{perimeter

1069 intersection} of three intersecting circles.

1070

1071 @arg distance1: Distance to this point (C{meter}), same units

1072 as B{C{eps}}).

1073 @arg point2: Second center point (C{LatLon}).

1074 @arg distance2: Distance to point2 (C{meter}, same units as

1075 B{C{eps}}).

1076 @arg point3: Third center point (C{LatLon}).

1077 @arg distance3: Distance to point3 (C{meter}, same units as

1078 B{C{eps}}).

1079 @kwarg area: If C{True} compute the area overlap, otherwise the

1080 perimeter intersection of the circles (C{bool}).

1081 @kwarg eps: The required I{minimal overlap} for C{B{area}=True}

1082 or the I{intersection margin} for C{B{area}=False}

1083 (C{meter}, conventionally).

1084 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll

1085 B{C{point2}} and B{C{point3}} (C{bool}).

1086

1087 @return: A L{Trilaterate5Tuple}C{(min, minPoint, max, maxPoint, n)}

1088 with C{min} and C{max} in C{meter}, same units as B{C{eps}},

1089 the corresponding trilaterated points C{minPoint} and

1090 C{maxPoint} as I{ellipsoidal} C{LatLon} and C{n}, the number

1091 of trilatered points found for the given B{C{eps}}.

1092

1093 If only a single trilaterated point is found, C{min I{is}

1094 max}, C{minPoint I{is} maxPoint} and C{n = 1}.

1095

1096 For C{B{area}=True}, C{min} and C{max} are the smallest

1097 respectively largest I{radial} overlap found.

1098

1099 For C{B{area}=False}, C{min} and C{max} represent the

1100 nearest respectively farthest intersection margin.

1101

1102 If C{B{area}=True} and all 3 circles are concentric, C{n=0}

1103 and C{minPoint} and C{maxPoint} are the B{C{point#}} with

1104 the smallest B{C{distance#}} C{min} respectively C{max} the

1105 largest B{C{distance#}}.

1106

1107 @raise IntersectionError: Trilateration failed for the given B{C{eps}},

1108 insufficient overlap for C{B{area}=True}, no

1109 circle intersections for C{B{area}=False} or

1110 all circles are (near-)concentric.

1111

1112 @raise TypeError: Invalid B{C{point2}} or B{C{point3}}.

1113

1114 @raise ValueError: Coincident B{C{points}} or invalid B{C{distance1}},

1115 B{C{distance2}} or B{C{distance3}}.

1116

1117 @note: Ellipsoidal trilateration invokes methods C{LatLon.intersections2}

1118 and C{LatLon.nearestOn} based on I{Karney}'s Python U{geographiclib

1119 <https://PyPI.org/project/geographiclib>} if installed, otherwise

1120 the accurate (but slower) C{ellipsoidalExact.LatLon} methods.

1121 '''

1122 return _trilaterate5(self, distance1,

1123 self.others(point2=point2), distance2,

1124 self.others(point3=point3), distance3,

1125 area=area, eps=eps, wrap=wrap)

1126

1127 @Property_RO

1128 def _ups(self): # __dict__ value overwritten by method C{toUtmUps}

1129 '''(INTERNAL) Get this C{LatLon} point as UPS coordinate (L{Ups}),

1130 see L{pygeodesy.toUps8}.

1131 '''

1132 ups = _MODS.ups

1133 return ups.toUps8(self, datum=self.datum, Ups=ups.Ups,

1134 pole=NN, falsed=True, name=self.name)

1135

1136 def _upsOK(self, pole=NN, falsed=True):

1137 '''(INTERNAL) Check matching C{Ups}.

1138 '''

1139 try:

1140 u = self._ups

1141 except RangeError:

1142 return False

1143 return falsed and (u.pole == pole[:1].upper() or not pole)

1144

1145 @Property_RO

1146 def _utm(self): # __dict__ value overwritten by method C{toUtmUps}

1147 '''(INTERNAL) Get this C{LatLon} point as UTM coordinate (L{Utm}),

1148 see L{pygeodesy.toUtm8}.

1149 '''

1150 utm = _MODS.utm

1151 return utm.toUtm8(self, datum=self.datum, Utm=utm.Utm, name=self.name)

1152

1153 def _utmOK(self):

1154 '''(INTERNAL) Check C{Utm}.

1155 '''

1156 try:

1157 _ = self._utm

1158 except RangeError:

1159 return False

1160 return True

1161

1162

1163 def _lowerleft(utmups, center):

1164 '''(INTERNAL) Optionally I{un}-center C{utmups}.

1165 '''

1166 if center in (False, 0, _0_0):

1167 u = utmups

1168 elif center in (True,):

1169 u = utmups._lowerleft

1170 else:

1171 u = _MODS.utmupsBase._lowerleft(utmups, center)

1172 return u

1173

1174

1175 def _nearestOn(point, point1, point2, within=True, height=None, wrap=False, # was=True

1176 equidistant=None, tol=_TOL_M, **LatLon_and_kwds):

1177 '''(INTERNAL) Get closest point, imported by .ellipsoidalExact,

1178 -GeodSolve, -Karney and -Vincenty to embellish exceptions.

1179 '''

1180 try:

1181 p = _xellipsoidal(point=point)

1182 t = _MODS.ellipsoidalBaseDI._nearestOn2(p, point1, point2, within=within,

1183 height=height, wrap=wrap,

1184 equidistant=equidistant,

1185 tol=tol, **LatLon_and_kwds)

1186 except (TypeError, ValueError) as x:

1187 raise _xError(x, point=point, point1=point1, point2=point2)

1188 return t.closest

1189

1190

1191 def _set_reframe(inst, reframe):

1192 '''(INTERNAL) Set or clear an instance's reference frame.

1193 '''

1194 if reframe is not None:

1195 _xinstanceof(_MODS.trf.RefFrame, reframe=reframe)

1196 inst._reframe = reframe

1197 elif inst.reframe is not None:

1198 inst._reframe = None

1199

1200

1201__all__ += _ALL_DOCS(CartesianEllipsoidalBase, LatLonEllipsoidalBase)

1202

1203# **) MIT License

1204#

1205# Copyright (C) 2016-2024 -- mrJean1 at Gmail -- All Rights Reserved.

1206#

1207# Permission is hereby granted, free of charge, to any person obtaining a

1208# copy of this software and associated documentation files (the "Software"),

1209# to deal in the Software without restriction, including without limitation

1210# the rights to use, copy, modify, merge, publish, distribute, sublicense,

1211# and/or sell copies of the Software, and to permit persons to whom the

1212# Software is furnished to do so, subject to the following conditions:

1213#

1214# The above copyright notice and this permission notice shall be included

1215# in all copies or substantial portions of the Software.

1216#

1217# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS

1218# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,

1219# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL

1220# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR

1221# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,

1222# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR

1223# OTHER DEALINGS IN THE SOFTWARE.