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 _WGS84, _xinstanceof # _spherical_datum

20 from pygeodesy.errors import _incompatible, _IsnotError, RangeError, TRFError, \

21 _ValueError, _xattr, _xellipsoidal, _xError, \

22 _xkwds, _xkwds_get, _xkwds_not

23# from pygeodesy.fmath import favg # _MODS

24 from pygeodesy.interns import MISSING, NN, _COMMA_, _conversion_, _DOT_, \

25 _ellipsoidal_, _no_, _reframe_, _SPACE_

26 from pygeodesy.latlonBase import LatLonBase, _trilaterate5, \

27 fabs, Vector3Tuple, _Wrap

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

29# from pygeodesy.lcc import toLcc # _MODS

30# from pygeodesy.named import notOverloaded # _MODS

31# from pygeodesy.namedTuples import Vector3Tuple # from .latlonBase

32 from pygeodesy.props import deprecated_method, deprecated_property_RO, \

33 Property_RO, property_doc_, property_RO, _update_all

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

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

36

37# from math import fabs # from .latlonBase

38

39__all__ = _ALL_LAZY.ellipsoidalBase

40__version__ = '23.11.08'

41

42

43 class CartesianEllipsoidalBase(CartesianBase):

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

45 '''

46 _datum = _WGS84 # L{Datum}

47 _reframe = None

48

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

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

51# '''

52# RefFrame = _MODS.trf.RefFrame

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

54# _NotImplemented(self, other)

55

56 @deprecated_method

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

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

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

60

61 @property_RO

62 def ellipsoidalCartesian(self):

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

64 '''

65 return type(self)

66

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

68 Vector=None, **Vector_kwds):

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

70 cartesian center point and a radius.

71

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

73 coordinates).

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

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

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

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

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

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

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

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

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

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

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

85

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

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

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

89

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

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

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

93

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

95

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

97

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

99

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

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

102 Intersection and function L{pygeodesy.radical2}.

103 '''

104 try:

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

106 center2, Radius_(radius2=radius2),

107 sphere=sphere, clas=self.classof,

108 Vector=Vector, **Vector_kwds)

109 except (TypeError, ValueError) as x:

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

111

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

113 def reframe(self):

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

115 '''

116 return self._reframe

117

118 @reframe.setter # PYCHOK setter!

119 def reframe(self, reframe):

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

121

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

123 '''

124 _set_reframe(self, reframe)

125

126 def toRefFrame(self, reframe2, reframe=None, epoch=None):

127 '''Convert this cartesian point from one to an other reference frame.

128

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

130 @arg reframe: Reference frame to convert I{from} (L{RefFrame}),

131 overriding this cartesian's C{reframe}.

132 @kwarg epoch: Optional epoch to observe (C{scalar}, fractional

133 calendar year), overriding B{C{reframe}}'s epoch.

134

135 @return: The converted point (C{Cartesian}) or this point if

136 conversion is C{nil}.

137

138 @raise TRFError: No conversion available from B{C{reframe}}

139 to B{C{reframe2}} or invalid B{C{epoch}}.

140

141 @raise TypeError: B{C{reframe2}} or B{C{reframe}} not a

142 L{RefFrame}.

143 '''

144 r = self.reframe if reframe is None else reframe

145 if r in (None, reframe2):

146 xs = None # XXX _set_reframe(self, reframe2)?

147 else:

148 trf = _MODS.trf

149 _xinstanceof(trf.RefFrame, reframe2=reframe2, reframe=r)

150 _, xs = trf._reframeTransforms2(reframe2, r, epoch)

151 return self.toTransforms_(*xs) if xs else self

152

153 def toTransforms_(self, *transforms, **datum):

154 '''Apply none, one or several Helmert transforms.

155

156 @arg transforms: Transforms to apply, in order (L{Transform}s).

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

158 overriding this point's datum.

159

160 @return: The transformed point (C{Cartesian}) or this point

161 if the B{C{transforms}} produce the same point.

162 '''

163 r = self

164 if transforms:

165 xyz = r.xyz

166 for t in transforms:

167 xyz = t.transform(*xyz)

168 d = _xkwds_get(datum, datum=r.datum)

169 if d != r.datum or xyz != r.xyz:

170 r = r.classof(xyz, datum=d)

171 return r

172

173

174 class LatLonEllipsoidalBase(LatLonBase):

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

176 '''

177 _datum = _WGS84 # L{Datum}

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

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

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

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

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

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

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

185

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

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

188 '''Create an ellipsoidal C{LatLon} point frome the given

189 lat-, longitude and height on the given datum and with

190 the given reference frame and epoch.

191

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

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

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

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

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

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

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

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

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

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

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

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

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

205 (C{bool}).

206 @kwarg name: Optional name (string).

207

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

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

210

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

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

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

214

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

216

217 @example:

218

219 >>> p = LatLon(51.4778, -0.0016) # height=0, datum=Datums.WGS84

220 '''

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

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

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

224 if reframe:

225 self.reframe = reframe

226 self.epoch = epoch

227

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

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

230# '''

231# RefFrame = _MODS.trf.RefFrame

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

233# _NotImplemented(self, other)

234

235 def antipode(self, height=None):

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

237 to this point.

238

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

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

241

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

243 '''

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

245 if lla.datum != self.datum:

246 lla.datum = self.datum

247 return lla

248

249 @deprecated_property_RO

250 def convergence(self):

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

252 return self.gamma

253

254 @deprecated_method

255 def convertDatum(self, datum2):

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

257 return self.toDatum(datum2)

258

259 @deprecated_method

260 def convertRefFrame(self, reframe2):

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

262 return self.toRefFrame(reframe2)

263

264 @Property_RO

265 def _css(self):

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

267 '''

268 css = _MODS.css

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

270

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

272 def datum(self):

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

274 '''

275 return self._datum

276

277 @datum.setter # PYCHOK setter!

278 def datum(self, datum):

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

280

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

282 or not ellipsoidal.

283 '''

284 _xinstanceof(Datum, datum=datum)

285 if not datum.isEllipsoidal:

286 raise _IsnotError(_ellipsoidal_, datum=datum)

287 if self._datum != datum:

288 _update_all(self)

289 self._datum = datum

290

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

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

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

294

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

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

297

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

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

300 point (C{bool}).

301

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

303

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

305

306 @raise ValueError: Incompatible datum ellipsoids.

307

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

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

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

311 formula.

312 '''

313 p = self.others(other)

314 if wrap:

315 p = _Wrap.point(p)

316 E = self.ellipsoids(other)

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

318

319 @Property_RO

320 def _elevation2(self):

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

322 '''

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

324 timeout=self._elevation2to)

325

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

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

328 or sphere.

329

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

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

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

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

334 radius).

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

336

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

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

339

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

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

342 L{elevations.elevation2} is based.

343

344 @note: NED elevation is only available for locations within the

345 U{Conterminous US (CONUS)

346 <https://WikiPedia.org/wiki/Contiguous_United_States>}.

347

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

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

350 '''

351 if self._elevation2to != timeout:

352 self._elevation2to = timeout

353 LatLonEllipsoidalBase._elevation2._update(self)

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

355

356 def ellipsoid(self, datum=_WGS84):

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

358

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

360

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

362 '''

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

364

365 @property_RO

366 def ellipsoidalLatLon(self):

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

368 '''

369 return type(self)

370

371 def ellipsoids(self, other):

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

373

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

375

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

377

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

379

380 @raise ValueError: Incompatible datum ellipsoids.

381 '''

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

383

384 E = self.ellipsoid()

385 try: # other may be Sphere, etc.

386 e = other.ellipsoid()

387 except AttributeError:

388 try: # no ellipsoid method, try datum

389 e = other.datum.ellipsoid

390 except AttributeError:

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

392 if e != E:

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

394 return E

395

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

397 def epoch(self):

398 '''Get this point's observed or C{reframe} epoch (C{float}) or C{None}.

399 '''

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

401

402 @epoch.setter # PYCHOK setter!

403 def epoch(self, epoch):

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

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

406

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

408 '''

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

410

411 @Property_RO

412 def Equidistant(self):

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

414 '''

415 try:

416 _ = self.datum.ellipsoid.geodesic

417 return _MODS.azimuthal.EquidistantKarney

418 except ImportError: # no geographiclib

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

420

421 @Property_RO

422 def _etm(self):

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

424 '''

425 etm = _MODS.etm

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

427

428 @property_RO

429 def gamma(self):

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

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

432 '''

433 return self._gamma

434

435 @Property_RO

436 def _geoidHeight2(self):

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

438 '''

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

440 timeout=self._geoidHeight2to)

441

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

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

444 or sphere.

445

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

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

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

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

450 radius).

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

452

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

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

455

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

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

458 the L{elevations.geoidHeight2} is based.

459

460 @note: The geoid height is only available for locations within the

461 U{Conterminous US (CONUS)

462 <https://WikiPedia.org/wiki/Contiguous_United_States>}.

463

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

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

466 '''

467 if self._geoidHeight2to != timeout:

468 self._geoidHeight2to = timeout

469 LatLonEllipsoidalBase._geoidHeight2._update(self)

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

471

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

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

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

475

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

477 equidistant=None, tol=_TOL_M):

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

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

480

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

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

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

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

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

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

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

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

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

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

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

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

493 @kwarg tol: Tolerance for skew line distance and length and for

494 convergence (C{meter}, conventionally).

495

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

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

498

499 @raise ImportError: Package U{geographiclib

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

501 not installed or not found, but only if

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

503

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

505 non-intersecting lines or no convergence

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

507

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

509 is not C{LatLon}.

510

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

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

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

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

515 of the authalic earth perimeter).

516

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

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

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

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

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

522 '''

523 try:

524 s2 = self.others(other)

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

526 s2, end2,

527 height=height, wrap=wrap,

528 equidistant=equidistant, tol=tol,

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

530 except (TypeError, ValueError) as x:

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

532 height=height, wrap=wrap, tol=tol)

533

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

535 equidistant=None, tol=_TOL_M):

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

537 each defined by a center point and a radius.

538

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

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

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

542 B{C{radius1}}).

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

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

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

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

547 center (C{bool}).

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

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

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

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

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

553

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

555 instance. For abutting circles, both intersection

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

557

558 @raise ImportError: Package U{geographiclib

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

560 not installed or not found, but only if

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

562

563 @raise IntersectionError: Concentric, antipodal, invalid or

564 non-intersecting circles or no

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

566

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

568

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

570

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

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

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

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

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

576 intersections.

577 '''

578 try:

579 c2 = self.others(other)

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

581 c2, radius2,

582 height=height, wrap=wrap,

583 equidistant=equidistant, tol=tol,

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

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

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

587 height=height, wrap=wrap, tol=tol)

588

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

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

591

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

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

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

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

596

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

598 C{False} otherwise.

599

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

601

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

603

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

605

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

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

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

609 '''

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

611

612 @property_RO

613 def iteration(self):

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

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

616 '''

617 return self._iteration

618

619 @Property_RO

620 def _lcc(self):

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

622 '''

623 lcc = _MODS.lcc

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

625

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

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

628

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

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

631 mean height (C{meter}).

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

633 may be negative or greater than 1.0.

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

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

636

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

638

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

640

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

642

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

644 '''

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

646

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

648 equidistant=None, tol=_TOL_M):

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

650 two other (ellipsoidal) points.

651

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

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

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

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

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

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

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

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

660 takes the heights of the points into account.

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

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

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

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

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

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

667

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

669

670 @raise ImportError: Package U{geographiclib

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

672 not installed or not found, but only if

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

674

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

676 B{C{equidistant}}.

677

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

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

680

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

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

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

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

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

686 '''

687 try:

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

689 height=height, wrap=wrap,

690 equidistant=equidistant,

691 tol=tol, LatLon=self.classof)

692 except (TypeError, ValueError) as x:

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

694 height=height, wrap=wrap, tol=tol)

695 return t.closest

696

697 @Property_RO

698 def _osgr(self):

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

700 based on the OS recommendation.

701 '''

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

703

704 @Property_RO

705 def _osgrTM(self):

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

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

708 '''

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

710

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

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

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

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

715

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

717 see function L{pygeodesy.parse3llh}.

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

719 C{None}).

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

721 datum I{without conversion}.

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

723 epoch I{without conversion}.

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

725 this reframe I{without conversion}.

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

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

728 and longitude (C{bool}).

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

730 this name.

731

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

733

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

735 '''

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

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

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

739 r.datum = datum

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

741 r.epoch = epoch

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

743 r.reframe = reframe

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

745

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

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

748 difference in Gaussian radii of curvature of the given

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

750

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

752 '''

753 if adjust: # Elevation2Tuple or GeoidHeight2Tuple

754 m, t = meter_text2

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

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

757 if n > EPS0:

758 # use ratio, datum and NAD83 units may differ

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

760 _earth_ellipsoid(datum)

761 r = E.rocGauss(self.lat)

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

763 m *= r / n

764 meter_text2 = meter_text2.classof(m, t)

765 return self._xnamed(meter_text2)

766

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

768 def reframe(self):

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

770 '''

771 return self._reframe

772

773 @reframe.setter # PYCHOK setter!

774 def reframe(self, reframe):

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

776

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

778 '''

779 _set_reframe(self, reframe)

780

781 @Property_RO

782 def scale(self):

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

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

785 '''

786 return self._scale

787

788 def toCss(self, **toCss_kwds):

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

790

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

792

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

794

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

796 '''

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

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

799

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

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

802

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

804 @kwarg height: Optional height, overriding the

805 converted height (C{meter}).

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

807

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

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

810 matches this point's C{datum}.

811

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

813

814 @example:

815

816 >>> p = LatLon(51.4778, -0.0016) # default Datums.WGS84

817 >>> p.toDatum(Datums.OSGB36) # 51.477284°N, 000.00002°E

818 '''

819 n = name or self.name

820 d2 = _ellipsoidal_datum(datum2, name=n)

821 if self.datum == d2:

822 r = self.copy(name=name)

823 else:

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

825 epoch=self.epoch, reframe=self.reframe)

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

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

828 return r

829

830 def toEtm(self, **toEtm8_kwds):

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

832

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

834

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

836

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

838 '''

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

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

841

842 def toLcc(self, **toLcc_kwds):

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

844

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

846

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

848

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

850 '''

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

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

853

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

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

856

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

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

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

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

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

862

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

864

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

866 '''

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

868

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

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

871

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

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

874 formulation (C{bool}).

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

876

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

878

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

880 '''

881 if toOsgr_kwds:

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

883 else:

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

885 return r

886

887 def toRefFrame(self, reframe2, height=None, name=NN):

888 '''Convert this point to an other reference frame.

889

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

891 @kwarg height: Optional height, overriding the converted

892 height (C{meter}).

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

894

895 @return: The converted point (ellipsoidal C{LatLon}) or this

896 point if conversion is C{nil}, or a copy of this

897 point if the B{C{name}} is non-empty.

898

899 @raise TRFError: This point's C{reframe} is not defined or

900 conversion from this point's C{reframe} to

901 B{C{reframe2}} is not available.

902

903 @raise TypeError: Invalid B{C{reframe2}}, not a L{RefFrame}.

904

905 @example:

906

907 >>> p = LatLon(51.4778, -0.0016, reframe=RefFrames.ETRF2000) # default Datums.WGS84

908 >>> p.toRefFrame(RefFrames.ITRF2014) # 51.477803°N, 000.001597°W, +0.01m

909 >>> p.toRefFrame(RefFrames.ITRF2014, height=0) # 51.477803°N, 000.001597°W

910 '''

911 if not self.reframe:

912 t = _SPACE_(_DOT_(repr(self), _reframe_), MISSING)

913 raise TRFError(_no_(_conversion_), txt=t)

914

915 trf = _MODS.trf

916 trf._xinstanceof(trf.RefFrame, reframe2=reframe2)

917

918 e, xs = trf._reframeTransforms2(reframe2, self.reframe, self.epoch)

919 if xs:

920 c = self.toCartesian().toTransforms_(*xs)

921 n = name or self.name

922 ll = c.toLatLon(datum=self.datum, epoch=e, height=height,

923 LatLon=self.classof, name=n, reframe=reframe2)

924 else:

925 ll = self.copy(name=name) if name else self

926 return ll

927

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

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

930

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

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

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

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

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

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

937

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

939

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

941 '''

942 if self._upsOK(pole, falsed):

943 u = self._ups

944 else:

945 ups = _MODS.ups

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

947 pole=pole, falsed=falsed)

948 return _lowerleft(u, center)

949

950 def toUtm(self, center=False):

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

952

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

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

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

956

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

958

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

960 '''

961 return _lowerleft(self._utm, center)

962

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

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

965

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

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

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

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

970 meter} (C{scalar}).

971

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

973

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

975 '''

976 if self._utmOK():

977 u = self._utm

978 elif self._upsOK(pole):

979 u = self._ups

980 else: # no cover

981 utmups = _MODS.utmups

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

983 Utm=utmups.Utm, Ups=utmups.Ups)

984 if isinstance(u, utmups.Utm):

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

986 elif isinstance(u, utmups.Ups):

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

988 else:

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

990 return _lowerleft(u, center)

991

992 @deprecated_method

993 def to3xyz(self): # PYCHOK no cover

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

995

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

997

998 @note: Overloads C{LatLonBase.to3xyz}

999 '''

1000 r = self.toEcef()

1001 return Vector3Tuple(r.x, r.y, r.z, name=self.name)

1002

1003 def trilaterate5(self, distance1, point2, distance2, point3, distance3,

1004 area=True, eps=EPS1, wrap=False):

1005 '''Trilaterate three points by I{area overlap} or I{perimeter

1006 intersection} of three intersecting circles.

1007

1008 @arg distance1: Distance to this point (C{meter}), same units

1009 as B{C{eps}}).

1010 @arg point2: Second center point (C{LatLon}).

1011 @arg distance2: Distance to point2 (C{meter}, same units as

1012 B{C{eps}}).

1013 @arg point3: Third center point (C{LatLon}).

1014 @arg distance3: Distance to point3 (C{meter}, same units as

1015 B{C{eps}}).

1016 @kwarg area: If C{True} compute the area overlap, otherwise the

1017 perimeter intersection of the circles (C{bool}).

1018 @kwarg eps: The required I{minimal overlap} for C{B{area}=True}

1019 or the I{intersection margin} for C{B{area}=False}

1020 (C{meter}, conventionally).

1021 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll

1022 B{C{point2}} and B{C{point3}} (C{bool}).

1023

1024 @return: A L{Trilaterate5Tuple}C{(min, minPoint, max, maxPoint, n)}

1025 with C{min} and C{max} in C{meter}, same units as B{C{eps}},

1026 the corresponding trilaterated points C{minPoint} and

1027 C{maxPoint} as I{ellipsoidal} C{LatLon} and C{n}, the number

1028 of trilatered points found for the given B{C{eps}}.

1029

1030 If only a single trilaterated point is found, C{min I{is}

1031 max}, C{minPoint I{is} maxPoint} and C{n = 1}.

1032

1033 For C{B{area}=True}, C{min} and C{max} are the smallest

1034 respectively largest I{radial} overlap found.

1035

1036 For C{B{area}=False}, C{min} and C{max} represent the

1037 nearest respectively farthest intersection margin.

1038

1039 If C{B{area}=True} and all 3 circles are concentric, C{n=0}

1040 and C{minPoint} and C{maxPoint} are the B{C{point#}} with

1041 the smallest B{C{distance#}} C{min} respectively C{max} the

1042 largest B{C{distance#}}.

1043

1044 @raise IntersectionError: Trilateration failed for the given B{C{eps}},

1045 insufficient overlap for C{B{area}=True}, no

1046 circle intersections for C{B{area}=False} or

1047 all circles are (near-)concentric.

1048

1049 @raise TypeError: Invalid B{C{point2}} or B{C{point3}}.

1050

1051 @raise ValueError: Coincident B{C{points}} or invalid B{C{distance1}},

1052 B{C{distance2}} or B{C{distance3}}.

1053

1054 @note: Ellipsoidal trilateration invokes methods C{LatLon.intersections2}

1055 and C{LatLon.nearestOn} based on I{Karney}'s Python U{geographiclib

1056 <https://PyPI.org/project/geographiclib>} if installed, otherwise

1057 the accurate (but slower) C{ellipsoidalExact.LatLon} methods.

1058 '''

1059 return _trilaterate5(self, distance1,

1060 self.others(point2=point2), distance2,

1061 self.others(point3=point3), distance3,

1062 area=area, eps=eps, wrap=wrap)

1063

1064 @Property_RO

1065 def _ups(self): # __dict__ value overwritten by method C{toUtmUps}

1066 '''(INTERNAL) Get this C{LatLon} point as UPS coordinate (L{Ups}),

1067 see L{pygeodesy.toUps8}.

1068 '''

1069 ups = _MODS.ups

1070 return ups.toUps8(self, datum=self.datum, Ups=ups.Ups,

1071 pole=NN, falsed=True, name=self.name)

1072

1073 def _upsOK(self, pole=NN, falsed=True):

1074 '''(INTERNAL) Check matching C{Ups}.

1075 '''

1076 try:

1077 u = self._ups

1078 except RangeError:

1079 return False

1080 return falsed and (u.pole == pole[:1].upper() or not pole)

1081

1082 @Property_RO

1083 def _utm(self): # __dict__ value overwritten by method C{toUtmUps}

1084 '''(INTERNAL) Get this C{LatLon} point as UTM coordinate (L{Utm}),

1085 see L{pygeodesy.toUtm8}.

1086 '''

1087 utm = _MODS.utm

1088 return utm.toUtm8(self, datum=self.datum, Utm=utm.Utm, name=self.name)

1089

1090 def _utmOK(self):

1091 '''(INTERNAL) Check C{Utm}.

1092 '''

1093 try:

1094 _ = self._utm

1095 except RangeError:

1096 return False

1097 return True

1098

1099

1100 def _lowerleft(utmups, center):

1101 '''(INTERNAL) Optionally I{un}-center C{utmups}.

1102 '''

1103 if center in (False, 0, _0_0):

1104 u = utmups

1105 elif center in (True,):

1106 u = utmups._lowerleft

1107 else:

1108 u = _MODS.utmupsBase._lowerleft(utmups, center)

1109 return u

1110

1111

1112 def _nearestOn(point, point1, point2, within=True, height=None, wrap=False, # was=True

1113 equidistant=None, tol=_TOL_M, **LatLon_and_kwds):

1114 '''(INTERNAL) Get closest point, imported by .ellipsoidalExact,

1115 -GeodSolve, -Karney and -Vincenty to embellish exceptions.

1116 '''

1117 try:

1118 p = _xellipsoidal(point=point)

1119 t = _MODS.ellipsoidalBaseDI._nearestOn2(p, point1, point2, within=within,

1120 height=height, wrap=wrap,

1121 equidistant=equidistant,

1122 tol=tol, **LatLon_and_kwds)

1123 except (TypeError, ValueError) as x:

1124 raise _xError(x, point=point, point1=point1, point2=point2)

1125 return t.closest

1126

1127

1128 def _set_reframe(inst, reframe):

1129 '''(INTERNAL) Set or clear an instance's reference frame.

1130 '''

1131 if reframe is not None:

1132 _xinstanceof(_MODS.trf.RefFrame, reframe=reframe)

1133 inst._reframe = reframe

1134 elif inst.reframe is not None:

1135 inst._reframe = None

1136

1137

1138__all__ += _ALL_DOCS(CartesianEllipsoidalBase, LatLonEllipsoidalBase)

1139

1140# **) MIT License

1141#

1142# Copyright (C) 2016-2023 -- mrJean1 at Gmail -- All Rights Reserved.

1143#

1144# Permission is hereby granted, free of charge, to any person obtaining a

1145# copy of this software and associated documentation files (the "Software"),

1146# to deal in the Software without restriction, including without limitation

1147# the rights to use, copy, modify, merge, publish, distribute, sublicense,

1148# and/or sell copies of the Software, and to permit persons to whom the

1149# Software is furnished to do so, subject to the following conditions:

1150#

1151# The above copyright notice and this permission notice shall be included

1152# in all copies or substantial portions of the Software.

1153#

1154# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS

1155# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,

1156# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL

1157# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR

1158# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,

1159# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR

1160# OTHER DEALINGS IN THE SOFTWARE.