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.named import notOverloaded # _MODS

30# from pygeodesy.namedTuples import Vector3Tuple # _MODS

31 from pygeodesy.props import deprecated_method, deprecated_property_RO, \

32 Property_RO, property_doc_, property_RO, _update_all

33# from pygeodesy.trf import _eT0Ds4 # _MODS

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

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

36

37# from math import fabs # from .latlonBase

38

39__all__ = _ALL_LAZY.ellipsoidalBase

40__version__ = '24.03.09'

41

42

43 class CartesianEllipsoidalBase(CartesianBase):

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

45 '''

46 _datum = _WGS84 # L{Datum}

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

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

49

50 def __init__(self, x_xyz, y=None, z=None, datum=None, reframe=None,

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

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

53

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

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

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

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

58

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

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

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

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

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

64

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

66 '''

67 CartesianBase.__init__(self, x_xyz, y=y, z=z, datum=datum, ll=ll, name=name)

68 if reframe:

69 self.reframe = reframe

70 self.epoch = epoch

71

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

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

74# '''

75# RefFrame = _MODS.trf.RefFrame

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

77# _NotImplemented(self, other)

78

79 @deprecated_method

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

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

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

83

84 @property_RO

85 def ellipsoidalCartesian(self):

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

87 '''

88 return type(self)

89

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

91 def epoch(self):

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

93 '''

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

95

96 @epoch.setter # PYCHOK setter!

97 def epoch(self, epoch):

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

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

100

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

102 '''

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

104

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

106 Vector=None, **Vector_kwds):

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

108 cartesian center point and a radius.

109

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

111 coordinates).

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

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

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

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

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

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

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

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

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

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

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

123

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

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

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

127

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

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

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

131

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

133

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

135

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

137

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

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

140 Intersection and function L{pygeodesy.radical2}.

141 '''

142 try:

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

144 center2, Radius_(radius2=radius2),

145 sphere=sphere, clas=self.classof,

146 Vector=Vector, **Vector_kwds)

147 except (TypeError, ValueError) as x:

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

149

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

151 def reframe(self):

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

153 '''

154 return self._reframe

155

156 @reframe.setter # PYCHOK setter!

157 def reframe(self, reframe):

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

159

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

161 '''

162 _set_reframe(self, reframe)

163

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

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

166

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

168 for further details.

169 '''

170 kwds = LatLon_and_kwds

171 if kwds:

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

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

174

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

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

177

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

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

180 overriding this point's reference frame.

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

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

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

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

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

186

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

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

189 is non-empty.

190

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

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

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

194

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

196 '''

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

198 epoch2=epoch2, name=name)

199

200 @deprecated_method

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

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

203 r = self

204 for t in transforms:

205 r = r.toTransform(t)

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

207

208

209 class LatLonEllipsoidalBase(LatLonBase):

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

211 '''

212 _datum = _WGS84 # L{Datum}

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

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

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

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

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

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

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

220

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

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

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

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

225

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

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

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

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

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

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

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

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

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

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

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

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

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

239 (C{bool}).

240 @kwarg name: Optional name (C{str}).

241

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

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

244

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

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

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

248

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

250 '''

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

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

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

254 if reframe:

255 self.reframe = reframe

256 self.epoch = epoch

257

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

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

260# '''

261# RefFrame = _MODS.trf.RefFrame

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

263# _NotImplemented(self, other)

264

265 def antipode(self, height=None):

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

267 to this point.

268

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

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

271

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

273 '''

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

275 if lla.datum != self.datum:

276 lla.datum = self.datum

277 return lla

278

279 @deprecated_property_RO

280 def convergence(self):

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

282 return self.gamma

283

284 @deprecated_method

285 def convertDatum(self, datum2):

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

287 return self.toDatum(datum2)

288

289 @deprecated_method

290 def convertRefFrame(self, reframe2):

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

292 return self.toRefFrame(reframe2)

293

294 @Property_RO

295 def _css(self):

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

297 '''

298 css = _MODS.css

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

300

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

302 def datum(self):

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

304 '''

305 return self._datum

306

307 @datum.setter # PYCHOK setter!

308 def datum(self, datum):

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

310

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

312 or not ellipsoidal.

313 '''

314 _xinstanceof(Datum, datum=datum)

315 if not datum.isEllipsoidal:

316 raise _IsnotError(_ellipsoidal_, datum=datum)

317 if self._datum != datum:

318 _update_all(self)

319 self._datum = datum

320

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

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

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

324

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

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

327

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

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

330 point (C{bool}).

331

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

333

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

335

336 @raise ValueError: Incompatible datum ellipsoids.

337

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

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

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

341 formula.

342 '''

343 p = self.others(other)

344 if wrap:

345 p = _Wrap.point(p)

346 E = self.ellipsoids(other)

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

348

349 @Property_RO

350 def _elevation2(self):

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

352 '''

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

354 timeout=self._elevation2to)

355

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

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

358 or sphere.

359

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

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

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

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

364 radius).

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

366

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

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

369

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

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

372 L{elevations.elevation2} is based.

373

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

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

376

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

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

379 '''

380 if self._elevation2to != timeout:

381 self._elevation2to = timeout

382 LatLonEllipsoidalBase._elevation2._update(self)

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

384

385 def ellipsoid(self, datum=_WGS84):

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

387

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

389

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

391 '''

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

393

394 @property_RO

395 def ellipsoidalLatLon(self):

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

397 '''

398 return type(self)

399

400 def ellipsoids(self, other):

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

402

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

404

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

406

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

408

409 @raise ValueError: Incompatible datum ellipsoids.

410 '''

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

412

413 E = self.ellipsoid()

414 try: # other may be Sphere, etc.

415 e = other.ellipsoid()

416 except AttributeError:

417 try: # no ellipsoid method, try datum

418 e = other.datum.ellipsoid

419 except AttributeError:

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

421 if e != E:

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

423 return E

424

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

426 def epoch(self):

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

428 '''

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

430

431 @epoch.setter # PYCHOK setter!

432 def epoch(self, epoch):

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

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

435

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

437 '''

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

439

440 @Property_RO

441 def Equidistant(self):

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

443 '''

444 try:

445 _ = self.datum.ellipsoid.geodesic

446 return _MODS.azimuthal.EquidistantKarney

447 except ImportError: # no geographiclib

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

449

450 @Property_RO

451 def _etm(self):

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

453 '''

454 etm = _MODS.etm

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

456

457 @property_RO

458 def gamma(self):

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

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

461 '''

462 return self._gamma

463

464 @Property_RO

465 def _geoidHeight2(self):

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

467 '''

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

469 timeout=self._geoidHeight2to)

470

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

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

473 or sphere.

474

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

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

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

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

479 radius).

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

481

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

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

484

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

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

487 the L{elevations.geoidHeight2} is based.

488

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

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

491

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

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

494 '''

495 if self._geoidHeight2to != timeout:

496 self._geoidHeight2to = timeout

497 LatLonEllipsoidalBase._geoidHeight2._update(self)

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

499

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

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

502 _MODS.named.notOverloaded(self, other, fraction, height=height, wrap=wrap)

503

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

505 equidistant=None, tol=_TOL_M):

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

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

508

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

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

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

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

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

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

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

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

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

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

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

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

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

522 length (C{meter}, conventionally).

523

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

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

526

527 @raise ImportError: Package U{geographiclib

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

529 not installed or not found, but only if

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

531

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

533 non-intersecting lines or no convergence

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

535

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

537 is not C{LatLon}.

538

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

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

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

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

543 of the authalic earth perimeter).

544

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

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

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

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

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

550 '''

551 try:

552 s2 = self.others(other)

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

554 s2, end2,

555 height=height, wrap=wrap,

556 equidistant=equidistant, tol=tol,

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

558 except (TypeError, ValueError) as x:

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

560 height=height, wrap=wrap, tol=tol)

561

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

563 equidistant=None, tol=_TOL_M):

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

565 each defined by a center point and a radius.

566

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

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

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

570 B{C{radius1}}).

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

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

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

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

575 center (C{bool}).

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

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

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

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

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

581

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

583 instance. For abutting circles, both intersection

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

585

586 @raise ImportError: Package U{geographiclib

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

588 not installed or not found, but only if

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

590

591 @raise IntersectionError: Concentric, antipodal, invalid or

592 non-intersecting circles or no

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

594

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

596

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

598

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

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

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

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

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

604 intersections.

605 '''

606 try:

607 c2 = self.others(other)

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

609 c2, radius2,

610 height=height, wrap=wrap,

611 equidistant=equidistant, tol=tol,

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

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

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

615 height=height, wrap=wrap, tol=tol)

616

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

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

619

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

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

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

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

624

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

626 C{False} otherwise.

627

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

629

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

631

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

633

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

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

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

637 '''

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

639

640 @property_RO

641 def iteration(self):

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

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

644 '''

645 return self._iteration

646

647 @Property_RO

648 def _lcc(self):

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

650 '''

651 lcc = _MODS.lcc

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

653

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

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

656

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

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

659 mean height (C{meter}).

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

661 may be negative or greater than 1.0.

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

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

664

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

666

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

668

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

670

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

672 '''

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

674

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

676 equidistant=None, tol=_TOL_M):

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

678 two other (ellipsoidal) points.

679

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

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

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

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

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

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

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

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

688 takes the heights of the points into account.

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

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

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

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

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

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

695

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

697

698 @raise ImportError: Package U{geographiclib

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

700 not installed or not found, but only if

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

702

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

704 B{C{equidistant}}.

705

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

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

708

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

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

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

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

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

714 '''

715 try:

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

717 height=height, wrap=wrap,

718 equidistant=equidistant,

719 tol=tol, LatLon=self.classof)

720 except (TypeError, ValueError) as x:

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

722 height=height, wrap=wrap, tol=tol)

723 return t.closest

724

725 @Property_RO

726 def _osgr(self):

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

728 based on the OS recommendation.

729 '''

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

731

732 @Property_RO

733 def _osgrTM(self):

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

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

736 '''

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

738

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

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

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

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

743

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

745 see function L{pygeodesy.parse3llh}.

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

747 C{None}).

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

749 datum I{without conversion}.

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

751 epoch I{without conversion}.

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

753 this reframe I{without conversion}.

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

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

756 and longitude (C{bool}).

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

758 this name.

759

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

761

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

763 '''

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

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

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

767 r.datum = datum

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

769 r.epoch = epoch

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

771 r.reframe = reframe

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

773

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

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

776 difference in Gaussian radii of curvature of the given

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

778

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

780 '''

781 if adjust: # Elevation2Tuple or GeoidHeight2Tuple

782 m, t = meter_text2

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

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

785 if n > EPS0:

786 # use ratio, datum and NAD83 units may differ

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

788 _earth_ellipsoid(datum)

789 r = E.rocGauss(self.lat)

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

791 m *= r / n

792 meter_text2 = meter_text2.classof(m, t)

793 return self._xnamed(meter_text2)

794

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

796 def reframe(self):

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

798 '''

799 return self._reframe

800

801 @reframe.setter # PYCHOK setter!

802 def reframe(self, reframe):

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

804

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

806 '''

807 _set_reframe(self, reframe)

808

809 @Property_RO

810 def scale(self):

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

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

813 '''

814 return self._scale

815

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

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

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

819

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

821 for further details.

822 '''

823 kwds = Cartesian_and_kwds

824 if kwds:

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

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

827

828 def toCss(self, **toCss_kwds):

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

830

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

832

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

834

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

836 '''

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

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

839

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

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

842

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

844 @kwarg height: Optional height, overriding the

845 converted height (C{meter}).

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

847

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

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

850 matches this point's C{datum}.

851

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

853 '''

854 n = name or self.name

855 d2 = _ellipsoidal_datum(datum2, name=n)

856 if self.datum == d2:

857 r = self.copy(name=name)

858 else:

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

860 epoch=self.epoch, reframe=self.reframe)

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

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

863 return r

864

865 def toEtm(self, **toEtm8_kwds):

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

867

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

869

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

871

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

873 '''

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

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

876

877 def toLcc(self, **toLcc_kwds):

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

879

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

881

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

883

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

885 '''

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

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

888

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

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

891

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

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

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

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

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

897

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

899

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

901 '''

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

903

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

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

906

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

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

909 formulation (C{bool}).

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

911

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

913

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

915 '''

916 if toOsgr_kwds:

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

918 else:

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

920 return r

921

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

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

924

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

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

927 overriding this point's reference frame.

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

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

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

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

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

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

934

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

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

937 is non-empty.

938

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

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

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

942

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

944 '''

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

946 epoch2=epoch2, name=name, height=height)

947

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

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

950

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

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

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

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

955 @kwarg LatLon_kwds: Optional keyword arguments for the transformed

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

957

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

959 C{B{transform}.isunity}.

960

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

962 '''

963 _xinstanceof(Transform, transform=transform)

964 d = datum or self.datum

965 if transform.isunity:

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

967 else:

968 c = self.toCartesian()

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

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

971 return r

972

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

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

975

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

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

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

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

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

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

982

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

984

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

986 '''

987 if self._upsOK(pole, falsed):

988 u = self._ups

989 else:

990 ups = _MODS.ups

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

992 pole=pole, falsed=falsed)

993 return _lowerleft(u, center)

994

995 def toUtm(self, center=False):

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

997

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

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

1000 by C{B{center} meter} (C{scalar}).

1001

1002 @return: The UTM coordinate (L{Utm}).

1003

1004 @see: Method L{Mgrs.toUtm} and function L{pygeodesy.toUtm8}.

1005 '''

1006 return _lowerleft(self._utm, center)

1007

1008 def toUtmUps(self, pole=NN, center=False):

1009 '''Convert this C{LatLon} point to a UTM or UPS coordinate.

1010

1011 @kwarg pole: Optional top/center of UPS (stereographic)

1012 projection (C{str}, 'N[orth]' or 'S[outh]').

1013 @kwarg center: If C{True}, I{un}-center the UTM or UPS to

1014 its C{lowerleft} (C{bool}) or by C{B{center}

1015 meter} (C{scalar}).

1016

1017 @return: The UTM or UPS coordinate (L{Utm} or L{Ups}).

1018

1019 @see: Function L{pygeodesy.toUtmUps8}.

1020 '''

1021 if self._utmOK():

1022 u = self._utm

1023 elif self._upsOK(pole):

1024 u = self._ups

1025 else: # no cover

1026 utmups = _MODS.utmups

1027 u = utmups.toUtmUps8(self, datum=self.datum, pole=pole, name=self.name,

1028 Utm=utmups.Utm, Ups=utmups.Ups)

1029 if isinstance(u, utmups.Utm):

1030 self._update(False, _utm=u) # PYCHOK kwds

1031 elif isinstance(u, utmups.Ups):

1032 self._update(False, _ups=u) # PYCHOK kwds

1033 else:

1034 _xinstanceof(utmups.Utm, utmups.Ups, toUtmUps8=u)

1035 return _lowerleft(u, center)

1036

1037 @deprecated_method

1038 def to3xyz(self): # PYCHOK no cover

1039 '''DEPRECATED, use method C{toEcef}.

1040

1041 @return: A L{Vector3Tuple}C{(x, y, z)}.

1042

1043 @note: Overloads C{LatLonBase.to3xyz}

1044 '''

1045 r = self.toEcef()

1046 return _MODS.namedTuples.Vector3Tuple(r.x, r.y, r.z, name=self.name)

1047

1048 def triangulate(self, bearing1, other, bearing2, **height_wrap_tol):

1049 '''I{Iteratively} locate a point given this, an other point and the (initial)

1050 bearing at this and at the other point.

1051

1052 @arg bearing1: Bearing at this point (compass C{degrees360}).

1053 @arg other: Start point of the other line (C{LatLon}).

1054 @arg bearing2: Bearing at the other point (compass C{degrees360}).

1055 @kwarg height_wrap_tol: Optional keyword arguments C{B{height}=None},

1056 C{B{wrap}=False} and C{B{tol}}, see method L{intersection3}.

1057

1058 @return: Triangulated point (C{LatLon}).

1059

1060 @see: Method L{intersection3} for further details.

1061 '''

1062 if _isDegrees(bearing1) and _isDegrees(bearing2):

1063 r = self.intersection3(bearing1, other, bearing2, **height_wrap_tol)

1064 return r.point

1065 raise _TypeError(bearing1=bearing1, bearing2=bearing2 **height_wrap_tol)

1066

1067 def trilaterate5(self, distance1, point2, distance2, point3, distance3,

1068 area=True, eps=EPS1, wrap=False):

1069 '''Trilaterate three points by I{area overlap} or I{perimeter

1070 intersection} of three intersecting circles.

1071

1072 @arg distance1: Distance to this point (C{meter}), same units

1073 as B{C{eps}}).

1074 @arg point2: Second center point (C{LatLon}).

1075 @arg distance2: Distance to point2 (C{meter}, same units as

1076 B{C{eps}}).

1077 @arg point3: Third center point (C{LatLon}).

1078 @arg distance3: Distance to point3 (C{meter}, same units as

1079 B{C{eps}}).

1080 @kwarg area: If C{True} compute the area overlap, otherwise the

1081 perimeter intersection of the circles (C{bool}).

1082 @kwarg eps: The required I{minimal overlap} for C{B{area}=True}

1083 or the I{intersection margin} for C{B{area}=False}

1084 (C{meter}, conventionally).

1085 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll

1086 B{C{point2}} and B{C{point3}} (C{bool}).

1087

1088 @return: A L{Trilaterate5Tuple}C{(min, minPoint, max, maxPoint, n)}

1089 with C{min} and C{max} in C{meter}, same units as B{C{eps}},

1090 the corresponding trilaterated points C{minPoint} and

1091 C{maxPoint} as I{ellipsoidal} C{LatLon} and C{n}, the number

1092 of trilatered points found for the given B{C{eps}}.

1093

1094 If only a single trilaterated point is found, C{min I{is}

1095 max}, C{minPoint I{is} maxPoint} and C{n = 1}.

1096

1097 For C{B{area}=True}, C{min} and C{max} are the smallest

1098 respectively largest I{radial} overlap found.

1099

1100 For C{B{area}=False}, C{min} and C{max} represent the

1101 nearest respectively farthest intersection margin.

1102

1103 If C{B{area}=True} and all 3 circles are concentric, C{n=0}

1104 and C{minPoint} and C{maxPoint} are the B{C{point#}} with

1105 the smallest B{C{distance#}} C{min} respectively C{max} the

1106 largest B{C{distance#}}.

1107

1108 @raise IntersectionError: Trilateration failed for the given B{C{eps}},

1109 insufficient overlap for C{B{area}=True}, no

1110 circle intersections for C{B{area}=False} or

1111 all circles are (near-)concentric.

1112

1113 @raise TypeError: Invalid B{C{point2}} or B{C{point3}}.

1114

1115 @raise ValueError: Coincident B{C{points}} or invalid B{C{distance1}},

1116 B{C{distance2}} or B{C{distance3}}.

1117

1118 @note: Ellipsoidal trilateration invokes methods C{LatLon.intersections2}

1119 and C{LatLon.nearestOn} based on I{Karney}'s Python U{geographiclib

1120 <https://PyPI.org/project/geographiclib>} if installed, otherwise

1121 the accurate (but slower) C{ellipsoidalExact.LatLon} methods.

1122 '''

1123 return _trilaterate5(self, distance1,

1124 self.others(point2=point2), distance2,

1125 self.others(point3=point3), distance3,

1126 area=area, eps=eps, wrap=wrap)

1127

1128 @Property_RO

1129 def _ups(self): # __dict__ value overwritten by method C{toUtmUps}

1130 '''(INTERNAL) Get this C{LatLon} point as UPS coordinate (L{Ups}),

1131 see L{pygeodesy.toUps8}.

1132 '''

1133 ups = _MODS.ups

1134 return ups.toUps8(self, datum=self.datum, Ups=ups.Ups,

1135 pole=NN, falsed=True, name=self.name)

1136

1137 def _upsOK(self, pole=NN, falsed=True):

1138 '''(INTERNAL) Check matching C{Ups}.

1139 '''

1140 try:

1141 u = self._ups

1142 except RangeError:

1143 return False

1144 return falsed and (u.pole == pole[:1].upper() or not pole)

1145

1146 @Property_RO

1147 def _utm(self): # __dict__ value overwritten by method C{toUtmUps}

1148 '''(INTERNAL) Get this C{LatLon} point as UTM coordinate (L{Utm}),

1149 see L{pygeodesy.toUtm8}.

1150 '''

1151 utm = _MODS.utm

1152 return utm.toUtm8(self, datum=self.datum, Utm=utm.Utm, name=self.name)

1153

1154 def _utmOK(self):

1155 '''(INTERNAL) Check C{Utm}.

1156 '''

1157 try:

1158 _ = self._utm

1159 except RangeError:

1160 return False

1161 return True

1162

1163

1164 def _lowerleft(utmups, center):

1165 '''(INTERNAL) Optionally I{un}-center C{utmups}.

1166 '''

1167 if center in (False, 0, _0_0):

1168 u = utmups

1169 elif center in (True,):

1170 u = utmups._lowerleft

1171 else:

1172 u = _MODS.utmupsBase._lowerleft(utmups, center)

1173 return u

1174

1175

1176 def _nearestOn(point, point1, point2, within=True, height=None, wrap=False, # was=True

1177 equidistant=None, tol=_TOL_M, **LatLon_and_kwds):

1178 '''(INTERNAL) Get closest point, imported by .ellipsoidalExact,

1179 -GeodSolve, -Karney and -Vincenty to embellish exceptions.

1180 '''

1181 try:

1182 p = _xellipsoidal(point=point)

1183 t = _MODS.ellipsoidalBaseDI._nearestOn2(p, point1, point2, within=within,

1184 height=height, wrap=wrap,

1185 equidistant=equidistant,

1186 tol=tol, **LatLon_and_kwds)

1187 except (TypeError, ValueError) as x:

1188 raise _xError(x, point=point, point1=point1, point2=point2)

1189 return t.closest

1190

1191

1192 def _set_reframe(inst, reframe):

1193 '''(INTERNAL) Set or clear an instance's reference frame.

1194 '''

1195 if reframe is not None:

1196 _xinstanceof(_MODS.trf.RefFrame, reframe=reframe)

1197 inst._reframe = reframe

1198 elif inst.reframe is not None:

1199 inst._reframe = None

1200

1201

1202__all__ += _ALL_DOCS(CartesianEllipsoidalBase, LatLonEllipsoidalBase)

1203

1204# **) MIT License

1205#

1206# Copyright (C) 2016-2024 -- mrJean1 at Gmail -- All Rights Reserved.

1207#

1208# Permission is hereby granted, free of charge, to any person obtaining a

1209# copy of this software and associated documentation files (the "Software"),

1210# to deal in the Software without restriction, including without limitation

1211# the rights to use, copy, modify, merge, publish, distribute, sublicense,

1212# and/or sell copies of the Software, and to permit persons to whom the

1213# Software is furnished to do so, subject to the following conditions:

1214#

1215# The above copyright notice and this permission notice shall be included

1216# in all copies or substantial portions of the Software.

1217#

1218# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS

1219# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,

1220# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL

1221# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR

1222# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,

1223# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR

1224# OTHER DEALINGS IN THE SOFTWARE.