1

2# -*- coding: utf-8 -*-

3

4 u'''(INTERNAL) Base class L{LatLonBase} for all elliposiodal, spherical and N-vectorial C{LatLon} classes.

5

6@see: I{(C) Chris Veness}' U{latlong<https://www.Movable-Type.co.UK/scripts/latlong.html>},

7 U{-ellipsoidal<https://www.Movable-Type.co.UK/scripts/geodesy/docs/latlon-ellipsoidal.js.html>} and

8 U{-vectors<https://www.Movable-Type.co.UK/scripts/latlong-vectors.html>} and I{Charles Karney}'s

9 U{Rhumb<https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1Rhumb.html>} and

10 U{RhumbLine<https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1RhumbLine.html>} classes.

11'''

12

13 from pygeodesy.basics import isscalar, isstr, map1, _xinstanceof

14 from pygeodesy.constants import EPS, EPS0, EPS1, EPS4, INT0, R_M, \

15 _EPSqrt as _TOL, _0_0, _0_5, _1_0, \

16 _360_0, _umod_360

17# from pygeodesy.datums import _spherical_datum # from .formy

18 from pygeodesy.dms import F_D, F_DMS, latDMS, lonDMS, parse3llh

19# from pygeodesy.ecef import EcefKarney # _MODS

20 from pygeodesy.errors import _AttributeError, _incompatible, \

21 _IsnotError, IntersectionError, \

22 _ValueError, _xattr, _xdatum, \

23 _xError, _xkwds, _xkwds_not

24# from pygeodesy.fmath import favg # _MODS

25 from pygeodesy.formy import antipode, compassAngle, cosineAndoyerLambert_, \

26 cosineForsytheAndoyerLambert_, cosineLaw, \

27 equirectangular, euclidean, flatLocal_, \

28 flatPolar, _hartzell, haversine, isantipode, \

29 _isequalTo, isnormal, normal, philam2n_xyz, \

30 thomas_, vincentys, _spherical_datum

31 from pygeodesy.interns import NN, _COMMASPACE_, _concentric_, _height_, \

32 _intersection_, _LatLon_, _m_, _negative_, \

33 _no_, _overlap_, _too_, _point_ # PYCHOK used!

34# from pygeodesy.iters import PointsIter, points2 # from .vector3d, _MODS

35# from pygeodesy.karney import Caps # _MODS

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

37# from pygeodesy.ltp import Ltp, _xLtp # _MODS

38 from pygeodesy.named import _NamedBase, notImplemented, notOverloaded, Fmt

39 from pygeodesy.namedTuples import Bounds2Tuple, LatLon2Tuple, PhiLam2Tuple, \

40 Trilaterate5Tuple, Vector3Tuple

41# from pygeodesy.nvectorBase import _N_vector_ # _MODS

42 from pygeodesy.props import deprecated_method, Property, Property_RO, \

43 property_RO, _update_all

44# from pygeodesy.streprs import Fmt, hstr # from .named, _MODS

45 from pygeodesy.units import Distance_, Lat, Lon, Height, Radius, Radius_, \

46 Scalar, Scalar_

47 from pygeodesy.utily import _unrollon, _unrollon3, _Wrap

48 from pygeodesy.vector2d import _circin6, Circin6Tuple, _circum3, circum4_, \

49 Circum3Tuple, _radii11ABC

50 from pygeodesy.vector3d import nearestOn6, Vector3d, PointsIter

51

52 from contextlib import contextmanager

53 from math import asin, cos, degrees, fabs, radians

54

55__all__ = _ALL_LAZY.latlonBase

56__version__ = '23.12.02'

57

58

59 class LatLonBase(_NamedBase):

60 '''(INTERNAL) Base class for C{LatLon} points on spherical or

61 ellipsoidal earth models.

62 '''

63 _clipid = INT0 # polygonal clip, see .booleans

64 _datum = None # L{Datum}, to be overriden

65 _height = INT0 # height (C{meter}), default

66 _lat = 0 # latitude (C{degrees})

67 _lon = 0 # longitude (C{degrees})

68

69 def __init__(self, latlonh, lon=None, height=0, wrap=False, name=NN, datum=None):

70 '''New C{LatLon}.

71

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

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

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

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

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

77 (C{meter}, conventionally).

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

79 (C{bool}).

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

81 @kwarg datum: Optional datum (L{Datum}, L{Ellipsoid}, L{Ellipsoid2},

82 L{a_f2Tuple} or I{scalar} radius) or C{None}.

83

84 @return: New instance (C{LatLon}).

85

86 @raise RangeError: A B{C{lon}} or C{lat} value outside the valid

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

88

89 @raise TypeError: If B{C{latlonh}} is not a C{LatLon}.

90

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

92

93 @example:

94

95 >>> p = LatLon(50.06632, -5.71475)

96 >>> q = LatLon('50°03′59″N', """005°42'53"W""")

97 >>> r = LatLon(p)

98 '''

99 if name:

100 self.name = name

101

102 if lon is None:

103 lat, lon, height = _latlonheight3(latlonh, height, wrap)

104 elif wrap:

105 lat, lon = _Wrap.latlonDMS2(latlonh, lon)

106 else:

107 lat = latlonh

108

109 self._lat = Lat(lat) # parseDMS2(lat, lon)

110 self._lon = Lon(lon) # PYCHOK LatLon2Tuple

111 if height: # elevation

112 self._height = Height(height)

113 if datum:

114 self._datum = _spherical_datum(datum, name=self.name)

115

116 def __eq__(self, other):

117 return self.isequalTo(other)

118

119 def __ne__(self, other):

120 return not self.isequalTo(other)

121

122 def __str__(self):

123 return self.toStr(form=F_D, prec=6)

124

125 def antipode(self, height=None):

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

127 to this point.

128

129 @kwarg height: Optional height of the antipode (C{meter}),

130 this point's height otherwise.

131

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

133 '''

134 h = self._heigHt(height)

135 return self.classof(*antipode(*self.latlon), height=h)

136

137 @deprecated_method

138 def bounds(self, wide, tall, radius=R_M): # PYCHOK no cover

139 '''DEPRECATED, use method C{boundsOf}.'''

140 return self.boundsOf(wide, tall, radius=radius)

141

142 def boundsOf(self, wide, tall, radius=R_M, height=None):

143 '''Return the SW and NE lat-/longitude of a great circle

144 bounding box centered at this location.

145

146 @arg wide: Longitudinal box width (C{meter}, same units as

147 B{C{radius}} or C{degrees} if B{C{radius}} is C{None}).

148 @arg tall: Latitudinal box size (C{meter}, same units as

149 B{C{radius}} or C{degrees} if B{C{radius}} is C{None}).

150 @kwarg radius: Mean earth radius (C{meter}) or C{None} if I{both}

151 B{C{wide}} and B{C{tall}} are in C{degrees}.

152 @kwarg height: Height for C{latlonSW} and C{latlonNE} (C{meter}),

153 overriding the point's height.

154

155 @return: A L{Bounds2Tuple}C{(latlonSW, latlonNE)}, the

156 lower-left and upper-right corner (C{LatLon}).

157

158 @see: U{https://www.Movable-Type.co.UK/scripts/latlong-db.html}

159 '''

160 w = Scalar_(wide=wide) * _0_5

161 t = Scalar_(tall=tall) * _0_5

162 if radius is not None:

163 r = Radius_(radius)

164 c = cos(self.phi)

165 w = degrees(asin(w / r) / c) if fabs(c) > EPS0 else _0_0 # XXX

166 t = degrees(t / r)

167 y, t = self.lat, fabs(t)

168 x, w = self.lon, fabs(w)

169

170 h = self._heigHt(height)

171 sw = self.classof(y - t, x - w, height=h)

172 ne = self.classof(y + t, x + w, height=h)

173 return Bounds2Tuple(sw, ne, name=self.name)

174

175 def chordTo(self, other, height=None, wrap=False):

176 '''Compute the length of the chord through the earth between

177 this and an other point.

178

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

180 @kwarg height: Overriding height for both points (C{meter})

181 or C{None} for each point's height.

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

183 point (C{bool}).

184

185 @return: The chord length (conventionally C{meter}).

186

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

188 '''

189 def _v3d(ll):

190 t = ll.toEcef(height=height) # .toVector(Vector=Vector3d)

191 return Vector3d(t.x, t.y, t.z)

192

193 p = self.others(other)

194 if wrap:

195 p = _Wrap.point(p)

196 return _v3d(self).minus(_v3d(p)).length

197

198 def circin6(self, point2, point3, eps=EPS4, wrap=False):

199 '''Return the radius and center of the I{inscribed} aka I{In-}circle

200 of the (planar) triangle formed by this and two other points.

201

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

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

204 @kwarg eps: Tolerance for function L{pygeodesy.trilaterate3d2}.

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

206 B{C{point3}} (C{bool}).

207

208 @return: L{Circin6Tuple}C{(radius, center, deltas, cA, cB, cC)}. The

209 C{center} and contact points C{cA}, C{cB} and C{cC}, each an

210 instance of this (sub-)class, are co-planar with this and the

211 two given points, see the B{Note} below.

212

213 @raise ImportError: Package C{numpy} not found, not installed or older

214 than version 1.10.

215

216 @raise IntersectionError: Near-coincident or -colinear points or

217 a trilateration or C{numpy} issue.

218

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

220

221 @note: The C{center} is trilaterated in cartesian (ECEF) space and converted

222 back to geodetic lat-, longitude and height. The latter, conventionally

223 in C{meter} indicates whether the C{center} is above, below or on the

224 surface of the earth model. If C{deltas} is C{None}, the C{center} is

225 I{un}ambigous. Otherwise C{deltas} is a L{LatLon3Tuple}C{(lat, lon,

226 height)} representing the differences between both results from

227 L{pygeodesy.trilaterate3d2} and C{center} is the mean thereof.

228

229 @see: Function L{pygeodesy.circin6}, method L{circum3}, U{Incircle

230 <https://MathWorld.Wolfram.com/Incircle.html>} and U{Contact Triangle

231 <https://MathWorld.Wolfram.com/ContactTriangle.html>}.

232 '''

233 with _toCartesian3(self, point2, point3, wrap) as cs:

234 r, c, d, cA, cB, cC = _circin6(*cs, eps=eps, useZ=True, dLL3=True,

235 datum=self.datum) # PYCHOK unpack

236 return Circin6Tuple(r, c.toLatLon(), d, cA.toLatLon(), cB.toLatLon(), cC.toLatLon())

237

238 def circum3(self, point2, point3, circum=True, eps=EPS4, wrap=False):

239 '''Return the radius and center of the smallest circle I{through} or I{containing}

240 this and two other points.

241

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

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

244 @kwarg circum: If C{True} return the C{circumradius} and C{circumcenter},

245 always, ignoring the I{Meeus}' Type I case (C{bool}).

246 @kwarg eps: Tolerance for function L{pygeodesy.trilaterate3d2}.

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

248 B{C{point3}} (C{bool}).

249

250 @return: A L{Circum3Tuple}C{(radius, center, deltas)}. The C{center}, an

251 instance of this (sub-)class, is co-planar with this and the two

252 given points. If C{deltas} is C{None}, the C{center} is

253 I{un}ambigous. Otherwise C{deltas} is a L{LatLon3Tuple}C{(lat,

254 lon, height)} representing the difference between both results

255 from L{pygeodesy.trilaterate3d2} and C{center} is the mean thereof.

256

257 @raise ImportError: Package C{numpy} not found, not installed or older than

258 version 1.10.

259

260 @raise IntersectionError: Near-concentric, -coincident or -colinear points,

261 incompatible C{Ecef} classes or a trilateration

262 or C{numpy} issue.

263

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

265

266 @note: The C{center} is trilaterated in cartesian (ECEF) space and converted

267 back to geodetic lat-, longitude and height. The latter, conventionally

268 in C{meter} indicates whether the C{center} is above, below or on the

269 surface of the earth model. If C{deltas} is C{None}, the C{center} is

270 I{un}ambigous. Otherwise C{deltas} is a L{LatLon3Tuple}C{(lat, lon,

271 height)} representing the difference between both results from

272 L{pygeodesy.trilaterate3d2} and C{center} is the mean thereof.

273

274 @see: Function L{pygeodesy.circum3} and methods L{circin6} and L{circum4_}.

275 '''

276 with _toCartesian3(self, point2, point3, wrap, circum=circum) as cs:

277 r, c, d = _circum3(*cs, circum=circum, eps=eps, useZ=True, dLL3=True, # XXX -3d2

278 clas=cs[0].classof, datum=self.datum) # PYCHOK unpack

279 return Circum3Tuple(r, c.toLatLon(), d)

280

281 def circum4_(self, *points, **wrap):

282 '''Best-fit a sphere through this and two or more other points.

283

284 @arg points: The other points (each a C{LatLon}).

285 @kwarg wrap: If C{True}, wrap or I{normalize} the B{C{points}}

286 (C{bool}), default C{False}.

287

288 @return: L{Circum4Tuple}C{(radius, center, rank, residuals)} with C{center}

289 an instance of this (sub-)class.

290

291 @raise ImportError: Package C{numpy} not found, not installed or older than

292 version 1.10.

293

294 @raise NumPyError: Some C{numpy} issue.

295

296 @raise TypeError: One of the B{C{points}} invalid.

297

298 @raise ValueError: Too few B{C{points}}.

299

300 @see: Function L{pygeodesy.circum4_} and L{circum3}.

301 '''

302 def _cs(ps, C, wrap=False):

303 _wp = _Wrap.point if wrap else (lambda p: p)

304 for i, p in enumerate(ps):

305 yield C(i=i, points=_wp(p))

306

307 C = self._toCartesianEcef

308 c = C(point=self)

309 t = circum4_(c, Vector=c.classof, *_cs(points, C, **wrap))

310 c = t.center.toLatLon(LatLon=self.classof)

311 return t.dup(center=c)

312

313 @property

314 def clipid(self):

315 '''Get the (polygonal) clip (C{int}).

316 '''

317 return self._clipid

318

319 @clipid.setter # PYCHOK setter!

320 def clipid(self, clipid):

321 '''Get the (polygonal) clip (C{int}).

322 '''

323 self._clipid = int(clipid)

324

325 @deprecated_method

326 def compassAngle(self, other, **adjust_wrap): # PYCHOK no cover

327 '''DEPRECATED, use method L{compassAngleTo}.'''

328 return self.compassAngleTo(other, **adjust_wrap)

329

330 def compassAngleTo(self, other, **adjust_wrap):

331 '''Return the angle from North for the direction vector between

332 this and an other point.

333

334 Suitable only for short, non-near-polar vectors up to a few

335 hundred Km or Miles. Use method C{initialBearingTo} for

336 larger distances.

337

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

339 @kwarg adjust_wrap: Optional keyword arguments for function

340 L{pygeodesy.compassAngle}.

341

342 @return: Compass angle from North (C{degrees360}).

343

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

345

346 @note: Courtesy of Martin Schultz.

347

348 @see: U{Local, flat earth approximation

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

350 '''

351 p = self.others(other)

352 return compassAngle(self.lat, self.lon, p.lat, p.lon, **adjust_wrap)

353

354 def cosineAndoyerLambertTo(self, other, wrap=False):

355 '''Compute the distance between this and an other point using the U{Andoyer-Lambert correction<https://

356 navlib.net/wp-content/uploads/2013/10/admiralty-manual-of-navigation-vol-1-1964-english501c.pdf>}

357 of the U{Law of Cosines<https://www.Movable-Type.co.UK/scripts/latlong.html#cosine-law>} formula.

358

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

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

361 the B{C{other}} point (C{bool}).

362

363 @return: Distance (C{meter}, same units as the axes of this

364 point's datum ellipsoid).

365

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

367

368 @see: Function L{pygeodesy.cosineAndoyerLambert} and methods

369 L{cosineForsytheAndoyerLambertTo}, L{cosineLawTo},

370 C{distanceTo*}, L{equirectangularTo}, L{euclideanTo},

371 L{flatLocalTo}/L{hubenyTo}, L{flatPolarTo}, L{haversineTo},

372 L{thomasTo} and L{vincentysTo}.

373 '''

374 return self._distanceTo_(cosineAndoyerLambert_, other, wrap=wrap)

375

376 def cosineForsytheAndoyerLambertTo(self, other, wrap=False):

377 '''Compute the distance between this and an other point using

378 the U{Forsythe-Andoyer-Lambert correction

379 <https://www2.UNB.Ca/gge/Pubs/TR77.pdf>} of the U{Law of Cosines

380 <https://www.Movable-Type.co.UK/scripts/latlong.html#cosine-law>}

381 formula.

382

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

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

385 the B{C{other}} point (C{bool}).

386

387 @return: Distance (C{meter}, same units as the axes of

388 this point's datum ellipsoid).

389

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

391

392 @see: Function L{pygeodesy.cosineForsytheAndoyerLambert} and methods

393 L{cosineAndoyerLambertTo}, L{cosineLawTo}, C{distanceTo*},

394 L{equirectangularTo}, L{euclideanTo}, L{flatLocalTo}/L{hubenyTo},

395 L{flatPolarTo}, L{haversineTo}, L{thomasTo} and L{vincentysTo}.

396 '''

397 return self._distanceTo_(cosineForsytheAndoyerLambert_, other, wrap=wrap)

398

399 def cosineLawTo(self, other, radius=None, wrap=False):

400 '''Compute the distance between this and an other point using the

401 U{spherical Law of Cosines

402 <https://www.Movable-Type.co.UK/scripts/latlong.html#cosine-law>}

403 formula.

404

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

406 @kwarg radius: Mean earth radius (C{meter}) or C{None}

407 for the mean radius of this point's datum

408 ellipsoid.

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

410 the B{C{other}} point (C{bool}).

411

412 @return: Distance (C{meter}, same units as B{C{radius}}).

413

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

415

416 @see: Function L{pygeodesy.cosineLaw} and methods L{cosineAndoyerLambertTo},

417 L{cosineForsytheAndoyerLambertTo}, C{distanceTo*}, L{equirectangularTo},

418 L{euclideanTo}, L{flatLocalTo}/L{hubenyTo}, L{flatPolarTo},

419 L{haversineTo}, L{thomasTo} and L{vincentysTo}.

420 '''

421 return self._distanceTo(cosineLaw, other, radius, wrap=wrap)

422

423 @property_RO

424 def datum(self): # PYCHOK no cover

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

426 notOverloaded(self)

427

428 def destinationXyz(self, delta, LatLon=None, **LatLon_kwds):

429 '''Calculate the destination using a I{local} delta from this point.

430

431 @arg delta: Local delta to the destination (L{XyzLocal}, L{Enu},

432 L{Ned} or L{Local9Tuple}).

433 @kwarg LatLon: Optional (geodetic) class to return the destination

434 or C{None}.

435 @kwarg LatLon_kwds: Optional, additional B{C{LatLon}} keyword

436 arguments, ignored if C{B{LatLon} is None}.

437

438 @return: Destination as a C{B{LatLon}(lat, lon, **B{LatLon_kwds})}

439 instance or if C{B{LatLon} is None}, a L{LatLon3Tuple}C{(lat,

440 lon, height)} respectively L{LatLon4Tuple}C{(lat, lon,

441 height, datum)} depending on whether a C{datum} keyword

442 is un-/specified.

443

444 @raise TypeError: Invalid B{C{delta}}, B{C{LatLon}} or B{C{LatLon_kwds}}.

445 '''

446 t = self._ltp._local2ecef(delta, nine=True)

447 return t.toLatLon(LatLon=LatLon, **_xkwds(LatLon_kwds, name=self.name))

448

449 def _distanceTo(self, func, other, radius=None, **kwds):

450 '''(INTERNAL) Helper for distance methods C{<func>To}.

451 '''

452 p, r = self.others(other, up=2), radius

453 if r is None:

454 r = self._datum.ellipsoid.R1 if self._datum else R_M

455 return func(self.lat, self.lon, p.lat, p.lon, radius=r, **kwds)

456

457 def _distanceTo_(self, func_, other, wrap=False, radius=None):

458 '''(INTERNAL) Helper for (ellipsoidal) methods C{<func>To}.

459 '''

460 p = self.others(other, up=2)

461 D = self.datum

462 lam21, phi2, _ = _Wrap.philam3(self.lam, p.phi, p.lam, wrap)

463 r = func_(phi2, self.phi, lam21, datum=D)

464 return r * (D.ellipsoid.a if radius is None else radius)

465

466 @property_RO

467 def Ecef(self):

468 '''Get the ECEF I{class} (L{EcefKarney}), I{lazily, once}.

469 '''

470 LatLonBase.Ecef = E = _MODS.ecef.EcefKarney # overwrite property_RO

471 return E

472

473 @Property_RO

474 def _Ecef_forward(self):

475 '''(INTERNAL) Helper for L{_ecef9} and L{toEcef} (C{callable}).

476 '''

477 return self.Ecef(self.datum, name=self.name).forward

478

479 @Property_RO

480 def _ecef9(self):

481 '''(INTERNAL) Helper for L{toCartesian}, L{toEcef} and L{toCartesian} (L{Ecef9Tuple}).

482 '''

483 return self._Ecef_forward(self, M=True)

484

485 @property_RO

486 def ellipsoidalLatLon(self):

487 '''Get the C{LatLon type} iff ellipsoidal, overloaded in L{LatLonEllipsoidalBase}.

488 '''

489 return False

490

491 @deprecated_method

492 def equals(self, other, eps=None): # PYCHOK no cover

493 '''DEPRECATED, use method L{isequalTo}.'''

494 return self.isequalTo(other, eps=eps)

495

496 @deprecated_method

497 def equals3(self, other, eps=None): # PYCHOK no cover

498 '''DEPRECATED, use method L{isequalTo3}.'''

499 return self.isequalTo3(other, eps=eps)

500

501 def equirectangularTo(self, other, **radius_adjust_limit_wrap):

502 '''Compute the distance between this and an other point

503 using the U{Equirectangular Approximation / Projection

504 <https://www.Movable-Type.co.UK/scripts/latlong.html#equirectangular>}.

505

506 Suitable only for short, non-near-polar distances up to a

507 few hundred Km or Miles. Use method L{haversineTo} or

508 C{distanceTo*} for more accurate and/or larger distances.

509

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

511 @kwarg radius_adjust_limit_wrap: Optional keyword arguments

512 for function L{pygeodesy.equirectangular},

513 overriding the default mean C{radius} of this

514 point's datum ellipsoid.

515

516 @return: Distance (C{meter}, same units as B{C{radius}}).

517

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

519

520 @see: Function L{pygeodesy.equirectangular} and methods L{cosineAndoyerLambertTo},

521 L{cosineForsytheAndoyerLambertTo}, L{cosineLawTo}, C{distanceTo*},

522 C{euclideanTo}, L{flatLocalTo}/L{hubenyTo}, L{flatPolarTo},

523 L{haversineTo}, L{thomasTo} and L{vincentysTo}.

524 '''

525 return self._distanceTo(equirectangular, other, **radius_adjust_limit_wrap)

526

527 def euclideanTo(self, other, **radius_adjust_wrap):

528 '''Approximate the C{Euclidian} distance between this and

529 an other point.

530

531 See function L{pygeodesy.euclidean} for the available B{C{options}}.

532

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

534 @kwarg radius_adjust_wrap: Optional keyword arguments for function

535 L{pygeodesy.euclidean}, overriding the default mean

536 C{radius} of this point's datum ellipsoid.

537

538 @return: Distance (C{meter}, same units as B{C{radius}}).

539

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

541

542 @see: Function L{pygeodesy.euclidean} and methods L{cosineAndoyerLambertTo},

543 L{cosineForsytheAndoyerLambertTo}, L{cosineLawTo}, C{distanceTo*},

544 L{equirectangularTo}, L{flatLocalTo}/L{hubenyTo}, L{flatPolarTo},

545 L{haversineTo}, L{thomasTo} and L{vincentysTo}.

546 '''

547 return self._distanceTo(euclidean, other, **radius_adjust_wrap)

548

549 def flatLocalTo(self, other, radius=None, wrap=False):

550 '''Compute the distance between this and an other point using the

551 U{ellipsoidal Earth to plane projection

552 <https://WikiPedia.org/wiki/Geographical_distance#Ellipsoidal_Earth_projected_to_a_plane>}

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

554

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

556 @kwarg radius: Mean earth radius (C{meter}) or C{None} for

557 the I{equatorial radius} of this point's

558 datum ellipsoid.

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

560 the B{C{other}} point (C{bool}).

561

562 @return: Distance (C{meter}, same units as B{C{radius}}).

563

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

565

566 @raise ValueError: Invalid B{C{radius}}.

567

568 @see: Function L{pygeodesy.flatLocal}/L{pygeodesy.hubeny}, methods

569 L{cosineAndoyerLambertTo}, L{cosineForsytheAndoyerLambertTo},

570 L{cosineLawTo}, C{distanceTo*}, L{equirectangularTo}, L{euclideanTo},

571 L{flatPolarTo}, L{haversineTo}, L{thomasTo} and L{vincentysTo} and

572 U{local, flat Earth approximation<https://www.edwilliams.org/avform.htm#flat>}.

573 '''

574 return self._distanceTo_(flatLocal_, other, wrap=wrap, radius=

575 radius if radius in (None, R_M, _1_0, 1) else Radius(radius)) # PYCHOK kwargs

576

577 hubenyTo = flatLocalTo # for Karl Hubeny

578

579 def flatPolarTo(self, other, **radius_wrap):

580 '''Compute the distance between this and an other point using

581 the U{polar coordinate flat-Earth<https://WikiPedia.org/wiki/

582 Geographical_distance#Polar_coordinate_flat-Earth_formula>} formula.

583

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

585 @kwarg radius_wrap: Optional keyword arguments for function

586 L{pygeodesy.flatPolar}, overriding the

587 default mean C{radius} of this point's

588 datum ellipsoid.

589

590 @return: Distance (C{meter}, same units as B{C{radius}}).

591

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

593

594 @see: Function L{pygeodesy.flatPolar} and methods L{cosineAndoyerLambertTo},

595 L{cosineForsytheAndoyerLambertTo}, L{cosineLawTo}, C{distanceTo*},

596 L{equirectangularTo}, L{euclideanTo}, L{flatLocalTo}/L{hubenyTo},

597 L{haversineTo}, L{thomasTo} and L{vincentysTo}.

598 '''

599 return self._distanceTo(flatPolar, other, **radius_wrap)

600

601 def hartzell(self, los=None, earth=None):

602 '''Compute the intersection of a Line-Of-Sight (los) from this Point-Of-View

603 (pov) with this point's ellipsoid surface.

604

605 @kwarg los: Line-Of-Sight, I{direction} to earth (L{Los}, L{Vector3d})

606 or C{None} to point to the ellipsoid's center.

607 @kwarg earth: The earth model (L{Datum}, L{Ellipsoid}, L{Ellipsoid2},

608 L{a_f2Tuple} or C{scalar} radius in C{meter}) overriding

609 this point's C{datum} ellipsoid.

610

611 @return: The ellipsoid intersection (C{LatLon}) with C{.height} set

612 to the distance to this C{pov}.

613

614 @raise IntersectionError: Null or bad C{pov} or B{C{los}}, this C{pov}

615 is inside the ellipsoid or B{C{los}} points

616 outside or away from the ellipsoid.

617

618 @raise TypeError: Invalid B{C{los}}.

619

620 @see: Function C{hartzell} for further details.

621 '''

622 return _hartzell(self, los, earth, LatLon=self.classof)

623

624 def haversineTo(self, other, **radius_wrap):

625 '''Compute the distance between this and an other point using the

626 U{Haversine<https://www.Movable-Type.co.UK/scripts/latlong.html>}

627 formula.

628

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

630 @kwarg radius_wrap: Optional keyword arguments for function

631 L{pygeodesy.haversine}, overriding the

632 default mean C{radius} of this point's

633 datum ellipsoid.

634

635 @return: Distance (C{meter}, same units as B{C{radius}}).

636

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

638

639 @see: Function L{pygeodesy.haversine} and methods L{cosineAndoyerLambertTo},

640 L{cosineForsytheAndoyerLambertTo}, L{cosineLawTo}, C{distanceTo*},

641 L{equirectangularTo}, L{euclideanTo}, L{flatLocalTo}/L{hubenyTo},

642 L{flatPolarTo}, L{thomasTo} and L{vincentysTo}.

643 '''

644 return self._distanceTo(haversine, other, **radius_wrap)

645

646 def _havg(self, other, f=_0_5, h=None):

647 '''(INTERNAL) Weighted, average height.

648

649 @arg other: An other point (C{LatLon}).

650 @kwarg f: Optional fraction (C{float}).

651 @kwarg h: Overriding height (C{meter}).

652

653 @return: Average, fractional height (C{float}) or

654 the overriding B{C{height}} (C{Height}).

655 '''

656 return Height(h) if h is not None else \

657 _MODS.fmath.favg(self.height, other.height, f=f)

658

659 @Property

660 def height(self):

661 '''Get the height (C{meter}).

662 '''

663 return self._height

664

665 @height.setter # PYCHOK setter!

666 def height(self, height):

667 '''Set the height (C{meter}).

668

669 @raise TypeError: Invalid B{C{height}} C{type}.

670

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

672 '''

673 h = Height(height)

674 if self._height != h:

675 _update_all(self)

676 self._height = h

677

678 def _heigHt(self, height):

679 '''(INTERNAL) Overriding this C{height}.

680 '''

681 return self.height if height is None else Height(height)

682

683 def height4(self, earth=None, normal=True, LatLon=None, **LatLon_kwds):

684 '''Compute the height above or below and the projection of this point

685 on this datum's or on an other earth's ellipsoid surface.

686

687 @kwarg earth: A datum, ellipsoid, triaxial ellipsoid or earth radius

688 I{overriding} this datum (L{Datum}, L{Ellipsoid},

689 L{Ellipsoid2}, L{a_f2Tuple}, L{Triaxial}, L{Triaxial_},

690 L{JacobiConformal} or C{meter}, conventionally).

691 @kwarg normal: If C{True} the projection is the nearest point on the

692 ellipsoid's surface, otherwise the intersection of the

693 radial line to the center and the ellipsoid's surface.

694 @kwarg LatLon: Optional class to return the height and projection

695 (C{LatLon}) or C{None}.

696 @kwarg LatLon_kwds: Optional, additional B{C{LatLon}} keyword arguments,

697 ignored if C{B{LatLon} is None}.

698

699 @note: Use keyword argument C{height=0} to override C{B{LatLon}.height}

700 to {0} or any other C{scalar}, conventionally in C{meter}.

701

702 @return: An instance of B{C{LatLon}} or if C{B{LatLon} is None}, a

703 L{Vector4Tuple}C{(x, y, z, h)} with the I{projection} C{x}, C{y}

704 and C{z} coordinates and height C{h} in C{meter}, conventionally.

705

706 @raise TriaxialError: No convergence in triaxial root finding.

707

708 @raise TypeError: Invalid B{C{earth}}.

709

710 @see: L{Ellipsoid.height4} and L{Triaxial_.height4} for more information.

711 '''

712 c = self.toCartesian()

713 if LatLon is None:

714 r = c.height4(earth=earth, normal=normal)

715 else:

716 r = c.height4(earth=earth, normal=normal, Cartesian=c.classof, height=0)

717 r = r.toLatLon(LatLon=LatLon, **_xkwds(LatLon_kwds, height=r.height))

718 return r

719

720 def heightStr(self, prec=-2, m=_m_):

721 '''Return this point's B{C{height}} as C{str}ing.

722

723 @kwarg prec: Number of (decimal) digits, unstripped (C{int}).

724 @kwarg m: Optional unit of the height (C{str}).

725

726 @see: Function L{pygeodesy.hstr}.

727 '''

728 return _MODS.streprs.hstr(self.height, prec=prec, m=m)

729

730 def intersecant2(self, *args, **kwds): # PYCHOK no cover

731 '''B{Not implemented}, throws a C{NotImplementedError} always.'''

732 notImplemented(self, *args, **kwds)

733

734 def _intersecend2(self, p, q, wrap, height, g_or_r, P, Q, unused): # in .LatLonEllipsoidalBaseDI.intersecant2

735 '''(INTERNAL) Interpolate 2 heights along a geodesic or rhumb

736 line and return the 2 intercant points accordingly.

737 '''

738 if height is None:

739 hp = hq = _xattr(p, height=INT0)

740 h = _xattr(q, height=hp) # if isLatLon(q) else hp

741 if h != hp:

742 s = g_or_r._Inverse(p, q, wrap).s12

743 if s: # fmath.fidw?

744 s = (h - hp) / s # slope

745 hq += s * Q.s12

746 hp += s * P.s12

747 else:

748 hp = hq = _MODS.fmath.favg(hp, h)

749 else:

750 hp = hq = Height(height)

751

752# n = self.name or unused.__name__

753 p = q = self.classof(P.lat2, P.lon2, datum=g_or_r.datum, height=hp) # name=n

754 p._iteration = P.iteration

755 if P is not Q:

756 q = self.classof(Q.lat2, Q.lon2, datum=g_or_r.datum, height=hq) # name=n

757 q._iteration = Q.iteration

758 return p, q

759

760 @deprecated_method

761 def isantipode(self, other, eps=EPS): # PYCHOK no cover

762 '''DEPRECATED, use method L{isantipodeTo}.'''

763 return self.isantipodeTo(other, eps=eps)

764

765 def isantipodeTo(self, other, eps=EPS):

766 '''Check whether this and an other point are antipodal,

767 on diametrically opposite sides of the earth.

768

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

770 @kwarg eps: Tolerance for near-equality (C{degrees}).

771

772 @return: C{True} if points are antipodal within the given

773 tolerance, C{False} otherwise.

774 '''

775 p = self.others(other)

776 return isantipode(*(self.latlon + p.latlon), eps=eps)

777

778 @Property_RO

779 def isEllipsoidal(self):

780 '''Check whether this point is ellipsoidal (C{bool} or C{None} if unknown).

781 '''

782 return self.datum.isEllipsoidal if self._datum else None

783

784 def isequalTo(self, other, eps=None):

785 '''Compare this point with an other point, I{ignoring} height.

786

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

788 @kwarg eps: Tolerance for equality (C{degrees}).

789

790 @return: C{True} if both points are identical,

791 I{ignoring} height, C{False} otherwise.

792

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

794 or mismatch of the B{C{other}} and

795 this C{class} or C{type}.

796

797 @raise UnitError: Invalid B{C{eps}}.

798

799 @see: Method L{isequalTo3}.

800 '''

801 return _isequalTo(self, self.others(other), eps=eps)

802

803 def isequalTo3(self, other, eps=None):

804 '''Compare this point with an other point, I{including} height.

805

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

807 @kwarg eps: Tolerance for equality (C{degrees}).

808

809 @return: C{True} if both points are identical

810 I{including} height, C{False} otherwise.

811

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

813 or mismatch of the B{C{other}} and

814 this C{class} or C{type}.

815

816 @see: Method L{isequalTo}.

817 '''

818 return self.height == self.others(other).height and \

819 _isequalTo(self, other, eps=eps)

820

821 @Property_RO

822 def isnormal(self):

823 '''Return C{True} if this point is normal (C{bool}),

824 meaning C{abs(lat) <= 90} and C{abs(lon) <= 180}.

825

826 @see: Methods L{normal}, L{toNormal} and functions

827 L{pygeodesy.isnormal} and L{pygeodesy.normal}.

828 '''

829 return isnormal(self.lat, self.lon, eps=0)

830

831 @Property_RO

832 def isSpherical(self):

833 '''Check whether this point is spherical (C{bool} or C{None} if unknown).

834 '''

835 return self.datum.isSpherical if self._datum else None

836

837 @Property_RO

838 def lam(self):

839 '''Get the longitude (B{C{radians}}).

840 '''

841 return radians(self.lon)

842

843 @Property

844 def lat(self):

845 '''Get the latitude (C{degrees90}).

846 '''

847 return self._lat

848

849 @lat.setter # PYCHOK setter!

850 def lat(self, lat):

851 '''Set the latitude (C{str[N|S]} or C{degrees}).

852

853 @raise ValueError: Invalid B{C{lat}}.

854 '''

855 lat = Lat(lat) # parseDMS(lat, suffix=_NS_, clip=90)

856 if self._lat != lat:

857 _update_all(self)

858 self._lat = lat

859

860 @Property

861 def latlon(self):

862 '''Get the lat- and longitude (L{LatLon2Tuple}C{(lat, lon)}).

863 '''

864 return LatLon2Tuple(self._lat, self._lon, name=self.name)

865

866 @latlon.setter # PYCHOK setter!

867 def latlon(self, latlonh):

868 '''Set the lat- and longitude and optionally the height

869 (2- or 3-tuple or comma- or space-separated C{str}

870 of C{degrees90}, C{degrees180} and C{meter}).

871

872 @raise TypeError: Height of B{C{latlonh}} not C{scalar} or

873 B{C{latlonh}} not C{list} or C{tuple}.

874

875 @raise ValueError: Invalid B{C{latlonh}} or M{len(latlonh)}.

876

877 @see: Function L{pygeodesy.parse3llh} to parse a B{C{latlonh}}

878 string into a 3-tuple C{(lat, lon, h)}.

879 '''

880 if isstr(latlonh):

881 latlonh = parse3llh(latlonh, height=self.height)

882 else:

883 _xinstanceof(list, tuple, latlonh=latlonh)

884 if len(latlonh) == 3:

885 h = Height(latlonh[2], name=Fmt.SQUARE(latlonh=2))

886 elif len(latlonh) != 2:

887 raise _ValueError(latlonh=latlonh)

888 else:

889 h = self.height

890

891 llh = Lat(latlonh[0]), Lon(latlonh[1]), h # parseDMS2(latlonh[0], latlonh[1])

892 if (self._lat, self._lon, self._height) != llh:

893 _update_all(self)

894 self._lat, self._lon, self._height = llh

895

896 def latlon2(self, ndigits=0):

897 '''Return this point's lat- and longitude in C{degrees}, rounded.

898

899 @kwarg ndigits: Number of (decimal) digits (C{int}).

900

901 @return: A L{LatLon2Tuple}C{(lat, lon)}, both C{float}

902 and rounded away from zero.

903

904 @note: The C{round}ed values are always C{float}, also

905 if B{C{ndigits}} is omitted.

906 '''

907 return LatLon2Tuple(round(self.lat, ndigits),

908 round(self.lon, ndigits), name=self.name)

909

910 @deprecated_method

911 def latlon_(self, ndigits=0): # PYCHOK no cover

912 '''DEPRECATED, use method L{latlon2}.'''

913 return self.latlon2(ndigits=ndigits)

914

915 latlon2round = latlon_ # PYCHOK no cover

916

917 @Property

918 def latlonheight(self):

919 '''Get the lat-, longitude and height (L{LatLon3Tuple}C{(lat, lon, height)}).

920 '''

921 return self.latlon.to3Tuple(self.height)

922

923 @latlonheight.setter # PYCHOK setter!

924 def latlonheight(self, latlonh):

925 '''Set the lat- and longitude and optionally the height

926 (2- or 3-tuple or comma- or space-separated C{str}

927 of C{degrees90}, C{degrees180} and C{meter}).

928

929 @see: Property L{latlon} for more details.

930 '''

931 self.latlon = latlonh

932

933 @Property

934 def lon(self):

935 '''Get the longitude (C{degrees180}).

936 '''

937 return self._lon

938

939 @lon.setter # PYCHOK setter!

940 def lon(self, lon):

941 '''Set the longitude (C{str[E|W]} or C{degrees}).

942

943 @raise ValueError: Invalid B{C{lon}}.

944 '''

945 lon = Lon(lon) # parseDMS(lon, suffix=_EW_, clip=180)

946 if self._lon != lon:

947 _update_all(self)

948 self._lon = lon

949

950 @Property_RO

951 def _ltp(self):

952 '''(INTERNAL) Cache for L{toLtp}.

953 '''

954 return _MODS.ltp.Ltp(self, ecef=self.Ecef(self.datum), name=self.name)

955

956 def nearestOn6(self, points, closed=False, height=None, wrap=False):

957 '''Locate the point on a path or polygon closest to this point.

958

959 Points are converted to and distances are computed in

960 I{geocentric}, cartesian space.

961

962 @arg points: The path or polygon points (C{LatLon}[]).

963 @kwarg closed: Optionally, close the polygon (C{bool}).

964 @kwarg height: Optional height, overriding the height of

965 this and all other points (C{meter}). If

966 C{None}, take the height of points into

967 account for distances.

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

969 the B{C{points}} (C{bool}).

970

971 @return: A L{NearestOn6Tuple}C{(closest, distance, fi, j,

972 start, end)} with the C{closest}, the C{start}

973 and the C{end} point each an instance of this

974 C{LatLon} and C{distance} in C{meter}, same

975 units as the cartesian axes.

976

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

978

979 @raise TypeError: Some B{C{points}} or some B{C{points}}'

980 C{Ecef} invalid.

981

982 @raise ValueError: Some B{C{points}}' C{Ecef} is incompatible.

983

984 @see: Function L{pygeodesy.nearestOn6}.

985 '''

986 def _cs(Ps, h, w, C):

987 p = None # not used

988 for i, q in Ps.enumerate():

989 if w and i:

990 q = _unrollon(p, q)

991 yield C(height=h, i=i, up=3, points=q)

992 p = q

993

994 C = self._toCartesianEcef # to verify datum and Ecef

995 Ps = self.PointsIter(points, wrap=wrap)

996

997 c = C(height=height, this=self) # this Cartesian

998 t = nearestOn6(c, _cs(Ps, height, wrap, C), closed=closed)

999 c, s, e = t.closest, t.start, t.end

1000

1001 kwds = _xkwds_not(None, LatLon=self.classof, # this LatLon

1002 height=height)

1003 _r = self.Ecef(self.datum).reverse

1004 p = _r(c).toLatLon(**kwds)

1005 s = _r(s).toLatLon(**kwds) if s is not c else p

1006 e = _r(e).toLatLon(**kwds) if e is not c else p

1007 return t.dup(closest=p, start=s, end=e)

1008

1009 def nearestTo(self, *args, **kwds): # PYCHOK no cover

1010 '''B{Not implemented}, throws a C{NotImplementedError} always.'''

1011 notImplemented(self, *args, **kwds)

1012

1013 def normal(self):

1014 '''Normalize this point I{in-place} to C{abs(lat) <= 90} and

1015 C{abs(lon) <= 180}.

1016

1017 @return: C{True} if this point was I{normal}, C{False} if it

1018 wasn't (but is now).

1019

1020 @see: Property L{isnormal} and method L{toNormal}.

1021 '''

1022 n = self.isnormal

1023 if not n:

1024 self.latlon = normal(*self.latlon)

1025 return n

1026

1027 @Property_RO

1028 def _N_vector(self):

1029 '''(INTERNAL) Get the (C{nvectorBase._N_vector_})

1030 '''

1031 return _MODS.nvectorBase._N_vector_(*self.xyzh)

1032

1033 @Property_RO

1034 def phi(self):

1035 '''Get the latitude (B{C{radians}}).

1036 '''

1037 return radians(self.lat)

1038

1039 @Property_RO

1040 def philam(self):

1041 '''Get the lat- and longitude (L{PhiLam2Tuple}C{(phi, lam)}).

1042 '''

1043 return PhiLam2Tuple(self.phi, self.lam, name=self.name)

1044

1045 def philam2(self, ndigits=0):

1046 '''Return this point's lat- and longitude in C{radians}, rounded.

1047

1048 @kwarg ndigits: Number of (decimal) digits (C{int}).

1049

1050 @return: A L{PhiLam2Tuple}C{(phi, lam)}, both C{float}

1051 and rounded away from zero.

1052

1053 @note: The C{round}ed values are always C{float}, also

1054 if B{C{ndigits}} is omitted.

1055 '''

1056 return PhiLam2Tuple(round(self.phi, ndigits),

1057 round(self.lam, ndigits), name=self.name)

1058

1059 @Property_RO

1060 def philamheight(self):

1061 '''Get the lat-, longitude in C{radians} and height (L{PhiLam3Tuple}C{(phi, lam, height)}).

1062 '''

1063 return self.philam.to3Tuple(self.height)

1064

1065 @deprecated_method

1066 def points(self, points, closed=True): # PYCHOK no cover

1067 '''DEPRECATED, use method L{points2}.'''

1068 return self.points2(points, closed=closed)

1069

1070 def points2(self, points, closed=True):

1071 '''Check a path or polygon represented by points.

1072

1073 @arg points: The path or polygon points (C{LatLon}[])

1074 @kwarg closed: Optionally, consider the polygon closed,

1075 ignoring any duplicate or closing final

1076 B{C{points}} (C{bool}).

1077

1078 @return: A L{Points2Tuple}C{(number, points)}, an C{int}

1079 and C{list} or C{tuple}.

1080

1081 @raise PointsError: Insufficient number of B{C{points}}.

1082

1083 @raise TypeError: Some B{C{points}} are not C{LatLon}.

1084 '''

1085 return _MODS.iters.points2(points, closed=closed, base=self)

1086

1087 def PointsIter(self, points, loop=0, dedup=False, wrap=False):

1088 '''Return a C{PointsIter} iterator.

1089

1090 @arg points: The path or polygon points (C{LatLon}[])

1091 @kwarg loop: Number of loop-back points (non-negative C{int}).

1092 @kwarg dedup: Skip duplicate points (C{bool}).

1093 @kwarg wrap: If C{True}, wrap or I{normalize} the

1094 enum-/iterated B{C{points}} (C{bool}).

1095

1096 @return: A new C{PointsIter} iterator.

1097

1098 @raise PointsError: Insufficient number of B{C{points}}.

1099 '''

1100 return PointsIter(points, base=self, loop=loop, dedup=dedup, wrap=wrap)

1101

1102 def radii11(self, point2, point3, wrap=False):

1103 '''Return the radii of the C{Circum-}, C{In-}, I{Soddy} and C{Tangent}

1104 circles of a (planar) triangle formed by this and two other points.

1105

1106 @arg point2: Second point (C{LatLon}).

1107 @arg point3: Third point (C{LatLon}).

1108 @kwarg wrap: If C{True}, wrap or I{normalize} B{C{point2}} and

1109 B{C{point3}} (C{bool}).

1110

1111 @return: L{Radii11Tuple}C{(rA, rB, rC, cR, rIn, riS, roS, a, b, c, s)}.

1112

1113 @raise IntersectionError: Near-coincident or -colinear points.

1114

1115 @raise TypeError: Invalid B{C{point2}} or B{C{point3}}.

1116

1117 @see: Function L{pygeodesy.radii11}, U{Incircle

1118 <https://MathWorld.Wolfram.com/Incircle.html>}, U{Soddy Circles

1119 <https://MathWorld.Wolfram.com/SoddyCircles.html>} and U{Tangent

1120 Circles<https://MathWorld.Wolfram.com/TangentCircles.html>}.

1121 '''

1122 with _toCartesian3(self, point2, point3, wrap) as cs:

1123 return _radii11ABC(*cs, useZ=True)[0]

1124

1125 def _rhumb3(self, exact, radius): # != .sphericalBase._rhumbs3

1126 '''(INTERNAL) Get the C{rhumb} for this point's datum or for the B{C{radius}}'

1127 earth model iff non-C{None}.

1128 '''

1129 try:

1130 d = self._rhumb3dict

1131 t = d[(exact, radius)]

1132 except KeyError:

1133 D = self.datum if radius is None else _spherical_datum(radius) # ellipsoidal OK

1134 try:

1135 r = D.ellipsoid.rhumb_(exact=exact) # or D.isSpherical

1136 except AttributeError as x:

1137 raise _AttributeError(datum=D, radius=radius, cause=x)

1138 t = r, D, _MODS.karney.Caps

1139 while d:

1140 d.popitem()

1141 d[(exact, radius)] = t # cache 3-tuple

1142 return t

1143

1144 @Property_RO

1145 def _rhumb3dict(self): # in rhumbIntersecant2 below

1146 return {} # single-item cache

1147

1148 def rhumbAzimuthTo(self, other, exact=False, radius=None, wrap=False, b360=False):

1149 '''Return the azimuth (bearing) of a rhumb line (loxodrome) between this

1150 and an other (ellipsoidal) point.

1151

1152 @arg other: The other point (C{LatLon}).

1153 @kwarg exact: Exact C{Rhumb...} to use (C{bool} or C{Rhumb...}), see

1154 method L{Ellipsoid.rhumb_}.

1155 @kwarg radius: Optional earth radius (C{meter}) or earth model (L{Datum},

1156 L{Ellipsoid}, L{Ellipsoid2} or L{a_f2Tuple}), overriding

1157 this point's datum.

1158 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the B{C{other}}

1159 point (C{bool}).

1160 @kwarg b360: If C{True}, return the azimuth in the bearing range.

1161

1162 @return: Rhumb azimuth (compass C{degrees180} or C{degrees360}).

1163

1164 @raise TypeError: The B{C{other}} point is incompatible or B{C{radius}}

1165 is invalid.

1166 '''

1167 r, _, Cs = self._rhumb3(exact, radius)

1168 z = r._Inverse(self, other, wrap, outmask=Cs.AZIMUTH).azi12

1169 return _umod_360(z + _360_0) if b360 else z

1170

1171 def rhumbDestination(self, distance, azimuth, exact=False, radius=None, height=None):

1172 '''Return the destination point having travelled the given distance from

1173 this point along a rhumb line (loxodrome) of the given azimuth.

1174

1175 @arg distance: Distance travelled (C{meter}, same units as this point's

1176 datum (ellipsoid) axes or B{C{radius}}, may be negative.

1177 @arg azimuth: Azimuth (bearing) of the rhumb line (compass C{degrees}).

1178 @kwarg exact: Exact C{Rhumb...} to use (C{bool} or C{Rhumb...}), see

1179 method L{Ellipsoid.rhumb_}.

1180 @kwarg radius: Optional earth radius (C{meter}) or earth model (L{Datum},

1181 L{Ellipsoid}, L{Ellipsoid2} or L{a_f2Tuple}), overriding

1182 this point's datum.

1183 @kwarg height: Optional height, overriding the default height (C{meter}).

1184

1185 @return: The destination point (ellipsoidal C{LatLon}).

1186

1187 @raise TypeError: Invalid B{C{radius}}.

1188

1189 @raise ValueError: Invalid B{C{distance}}, B{C{azimuth}}, B{C{radius}}

1190 or B{C{height}}.

1191 '''

1192 r, D, _ = self._rhumb3(exact, radius)

1193 d = r._Direct(self, azimuth, distance)

1194 h = self._heigHt(height)

1195 return self.classof(d.lat2, d.lon2, datum=D, height=h)

1196

1197 def rhumbDistanceTo(self, other, exact=False, radius=None, wrap=False):

1198 '''Return the distance from this to an other point along a rhumb line

1199 (loxodrome).

1200

1201 @arg other: The other point (C{LatLon}).

1202 @kwarg exact: Exact C{Rhumb...} to use (C{bool} or C{Rhumb...}), see

1203 method L{Ellipsoid.rhumb_}.

1204 @kwarg radius: Optional earth radius (C{meter}) or earth model (L{Datum},

1205 L{Ellipsoid}, L{Ellipsoid2} or L{a_f2Tuple}), overriding

1206 this point's datum.

1207 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the B{C{other}}

1208 point (C{bool}).

1209

1210 @return: Distance (C{meter}, the same units as this point's datum

1211 (ellipsoid) axes or B{C{radius}}.

1212

1213 @raise TypeError: The B{C{other}} point is incompatible or B{C{radius}}

1214 is invalid.

1215

1216 @raise ValueError: Invalid B{C{radius}}.

1217 '''

1218 r, _, Cs = self._rhumb3(exact, radius)

1219 return r._Inverse(self, other, wrap, outmask=Cs.DISTANCE).s12

1220

1221 def rhumbIntersecant2(self, circle, point, other, height=None,

1222 **exact_radius_wrap_eps_tol):

1223 '''Compute the intersections of a circle and a rhumb line given as two

1224 points or as a point and azimuth.

1225

1226 @arg circle: Radius of the circle centered at this location (C{meter}),

1227 or a point on the circle (this C{LatLon}).

1228 @arg point: The start point of the rhumb line (this C{LatLon}).

1229 @arg other: An other point I{on} (this C{LatLon}) or the azimuth I{of}

1230 (compass C{degrees}) the rhumb line.

1231 @kwarg height: Optional height for the intersection points (C{meter},

1232 conventionally) or C{None} for interpolated heights.

1233 @kwarg exact_radius_wrap_eps_tol: Optional keyword arguments, see

1234 methods L{rhumbLine} and L{RhumbLineAux.Intersecant2}

1235 or L{RhumbLine.Intersecant2}.

1236

1237 @return: 2-Tuple of the intersection points (representing a chord),

1238 each an instance of this class. Both points are the same

1239 instance if the rhumb line is tangent to the circle.

1240

1241 @raise IntersectionError: The circle and rhumb line do not intersect.

1242

1243 @raise TypeError: If B{C{point}} is not this C{LatLon} or B{C{circle}}

1244 or B{C{other}} invalid.

1245

1246 @raise ValueError: Invalid B{C{circle}}, B{C{other}}, B{C{height}}

1247 or B{C{exact_radius_wrap}}.

1248

1249 @see: Methods L{RhumbLineAux.Intersecant2} and L{RhumbLine.Intersecant2}.

1250 '''

1251 def _kwds3(eps=EPS, tol=_TOL, wrap=False, **kwds):

1252 return kwds, wrap, dict(eps=eps, tol=tol)

1253

1254 exact_radius, w, eps_tol = _kwds3(**exact_radius_wrap_eps_tol)

1255

1256 p = _unrollon(self, self.others(point=point), wrap=w)

1257 try:

1258 r = Radius_(circle=circle) if isscalar(circle) else \

1259 self.rhumbDistanceTo(self.others(circle=circle), wrap=w, **exact_radius)

1260 rl = p.rhumbLine(other, wrap=w, **exact_radius)

1261 P, Q = rl.Intersecant2(self.lat, self.lon, r, **eps_tol)

1262

1263 return self._intersecend2(p, other, w, height, rl.rhumb, P, Q,

1264 self.rhumbIntersecant2)

1265

1266 except (TypeError, ValueError) as x:

1267 raise _xError(x, center=self, circle=circle, point=point, other=other,

1268 **exact_radius_wrap_eps_tol)

1269

1270 def rhumbLine(self, other, exact=False, radius=None, wrap=False, **name_caps):

1271 '''Get a rhumb line through this point at a given azimuth or through

1272 this and an other point.

1273

1274 @arg other: The azimuth I{of} (compass C{degrees}) or an other point

1275 I{on} (this C{LatLon}) the rhumb line.

1276 @kwarg exact: Exact C{Rhumb...} to use (C{bool} or C{Rhumb...}), see

1277 method L{Ellipsoid.rhumb_}.

1278 @kwarg radius: Optional earth radius (C{meter}) or earth model

1279 (L{Datum}, L{Ellipsoid}, L{Ellipsoid2} or L{a_f2Tuple}),

1280 overriding this point's datum.

1281 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the B{C{other}}

1282 point (C{bool}).

1283 @kwarg name_caps: Optional C{B{name}=str} and C{caps}, see L{RhumbLine}

1284 or L{RhumbLineAux} C{B{caps}}.

1285

1286 @return: A C{RhumbLine} instance.

1287

1288 @raise TypeError: Invalid B{C{radius}} or B{C{other}} not C{scalar} nor

1289 this C{LatLon}.

1290

1291 @see: Modules L{rhumb.aux_} and L{rhumb.ekx}.

1292 '''

1293 r, _, Cs = self._rhumb3(exact, radius)

1294 kwds = _xkwds(name_caps, name=self.name, caps=Cs.LINE_OFF)

1295 rl = r._DirectLine( self, other, **kwds) if isscalar(other) else \

1296 r._InverseLine(self, self.others(other), wrap, **kwds)

1297 return rl

1298

1299 def rhumbMidpointTo(self, other, exact=False, radius=None,

1300 height=None, fraction=_0_5, wrap=False):

1301 '''Return the (loxodromic) midpoint on the rhumb line between this and

1302 an other point.

1303

1304 @arg other: The other point (this C{LatLon}).

1305 @kwarg exact: Exact C{Rhumb...} to use (C{bool} or C{Rhumb...}), see

1306 method L{Ellipsoid.rhumb_}.

1307 @kwarg radius: Optional earth radius (C{meter}) or earth model (L{Datum},

1308 L{Ellipsoid}, L{Ellipsoid2} or L{a_f2Tuple}), overriding

1309 this point's datum.

1310 @kwarg height: Optional height, overriding the mean height (C{meter}).

1311 @kwarg fraction: Midpoint location from this point (C{scalar}), 0 for this,

1312 1 for the B{C{other}}, 0.5 for halfway between this and

1313 the B{C{other}} point, may be negative or greater than 1.

1314 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the B{C{other}}

1315 point (C{bool}).

1316

1317 @return: The midpoint at the given B{C{fraction}} along the rhumb line

1318 (this C{LatLon}).

1319

1320 @raise TypeError: The B{C{other}} point is incompatible or B{C{radius}}

1321 is invalid.

1322

1323 @raise ValueError: Invalid B{C{height}} or B{C{fraction}}.

1324 '''

1325 r, D, _ = self._rhumb3(exact, radius)

1326 f = Scalar(fraction=fraction)

1327 d = r._Inverse(self, self.others(other), wrap) # C.AZIMUTH_DISTANCE

1328 d = r._Direct( self, d.azi12, d.s12 * f)

1329 h = self._havg(other, f=f, h=height)

1330 return self.classof(d.lat2, d.lon2, datum=D, height=h)

1331

1332 @property_RO

1333 def sphericalLatLon(self):

1334 '''Get the C{LatLon type} iff spherical, overloaded in L{LatLonSphericalBase}.

1335 '''

1336 return False

1337

1338 def thomasTo(self, other, wrap=False):

1339 '''Compute the distance between this and an other point using

1340 U{Thomas'<https://apps.DTIC.mil/dtic/tr/fulltext/u2/703541.pdf>}

1341 formula.

1342

1343 @arg other: The other point (C{LatLon}).

1344 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll

1345 the B{C{other}} point (C{bool}).

1346

1347 @return: Distance (C{meter}, same units as the axes of

1348 this point's datum ellipsoid).

1349

1350 @raise TypeError: The B{C{other}} point is not C{LatLon}.

1351

1352 @see: Function L{pygeodesy.thomas} and methods L{cosineAndoyerLambertTo},

1353 L{cosineForsytheAndoyerLambertTo}, L{cosineLawTo}, C{distanceTo*},

1354 L{equirectangularTo}, L{euclideanTo}, L{flatLocalTo}/L{hubenyTo},

1355 L{flatPolarTo}, L{haversineTo} and L{vincentysTo}.

1356 '''

1357 return self._distanceTo_(thomas_, other, wrap=wrap)

1358

1359 @deprecated_method

1360 def to2ab(self): # PYCHOK no cover

1361 '''DEPRECATED, use property L{philam}.'''

1362 return self.philam

1363

1364 def toCartesian(self, height=None, Cartesian=None, **Cartesian_kwds):

1365 '''Convert this point to cartesian, I{geocentric} coordinates,

1366 also known as I{Earth-Centered, Earth-Fixed} (ECEF).

1367

1368 @kwarg height: Optional height, overriding this point's height

1369 (C{meter}, conventionally).

1370 @kwarg Cartesian: Optional class to return the geocentric

1371 coordinates (C{Cartesian}) or C{None}.

1372 @kwarg Cartesian_kwds: Optional, additional B{C{Cartesian}}

1373 keyword arguments, ignored if

1374 C{B{Cartesian} is None}.

1375

1376 @return: A B{C{Cartesian}} or if B{C{Cartesian}} is C{None},

1377 an L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M,

1378 datum)} with C{C=0} and C{M} if available.

1379

1380 @raise TypeError: Invalid B{C{Cartesian}} or B{C{Cartesian_kwds}}.

1381 '''

1382 r = self._ecef9 if height is None else self.toEcef(height=height)

1383 if Cartesian is not None: # class or .classof

1384 r = self._xnamed(Cartesian(r, **Cartesian_kwds))

1385 _xdatum(r.datum, self.datum)

1386 return r

1387

1388 def _toCartesianEcef(self, height=None, i=None, up=2, **name_point):

1389 '''(INTERNAL) Convert to cartesian and check Ecef's before and after.

1390 '''

1391 p = self.others(up=up, **name_point)

1392 c = p.toCartesian(height=height)

1393 E = self.Ecef

1394 if E:

1395 for p in (p, c):

1396 e = _xattr(p, Ecef=None)

1397 if e not in (None, E): # PYCHOK no cover

1398 n, _ = name_point.popitem()

1399 if i is not None:

1400 n = Fmt.SQUARE(n, i)

1401 raise _ValueError(n, e, txt=_incompatible(E.__name__))

1402 return c

1403

1404 def toDatum(self, datum2, height=None, name=NN):

1405 '''I{Must be overloaded}.'''

1406 notOverloaded(self, datum2, height=height, name=name)

1407

1408 def toEcef(self, height=None, M=False):

1409 '''Convert this point to I{geocentric} coordinates, also known as

1410 I{Earth-Centered, Earth-Fixed} (U{ECEF<https://WikiPedia.org/wiki/ECEF>}).

1411

1412 @kwarg height: Optional height, overriding this point's height

1413 (C{meter}, conventionally).

1414 @kwarg M: Optionally, include the rotation L{EcefMatrix} (C{bool}).

1415

1416 @return: An L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M, datum)}

1417 with C{C=0} and C{M} if available.

1418

1419 @raise EcefError: A C{.datum} or an ECEF issue.

1420 '''

1421 return self._ecef9 if height in (None, self.height) else \

1422 self._Ecef_forward(self.lat, self.lon, height=height, M=M)

1423

1424 @deprecated_method

1425 def to3llh(self, height=None): # PYCHOK no cover

1426 '''DEPRECATED, use property L{latlonheight} or C{latlon.to3Tuple(B{height})}.'''

1427 return self.latlonheight if height in (None, self.height) else \

1428 self.latlon.to3Tuple(height)

1429

1430 def toLocal(self, Xyz=None, ltp=None, **Xyz_kwds):

1431 '''Convert this I{geodetic} point to I{local} C{X}, C{Y} and C{Z}.

1432

1433 @kwarg Xyz: Optional class to return C{X}, C{Y} and C{Z}

1434 (L{XyzLocal}, L{Enu}, L{Ned}) or C{None}.

1435 @kwarg ltp: The I{local tangent plane} (LTP) to use,

1436 overriding this point's LTP (L{Ltp}).

1437 @kwarg Xyz_kwds: Optional, additional B{C{Xyz}} keyword

1438 arguments, ignored if C{B{Xyz} is None}.

1439

1440 @return: An B{C{Xyz}} instance or if C{B{Xyz} is None},

1441 a L{Local9Tuple}C{(x, y, z, lat, lon, height,

1442 ltp, ecef, M)} with C{M=None}, always.

1443

1444 @raise TypeError: Invalid B{C{ltp}}.

1445 '''

1446 p = _MODS.ltp._xLtp(ltp, self._ltp)

1447 return p._ecef2local(self._ecef9, Xyz, Xyz_kwds)

1448

1449 def toLtp(self, Ecef=None):

1450 '''Return the I{local tangent plane} (LTP) for this point.

1451

1452 @kwarg Ecef: Optional ECEF I{class} (L{EcefKarney}, ...

1453 L{EcefYou}), overriding this point's C{Ecef}.

1454 '''

1455 return self._ltp if Ecef in (None, self.Ecef) else _MODS.ltp.Ltp(

1456 self, ecef=Ecef(self.datum), name=self.name)

1457

1458 def toNormal(self, deep=False, name=NN):

1459 '''Get this point I{normalized} to C{abs(lat) <= 90}

1460 and C{abs(lon) <= 180}.

1461

1462 @kwarg deep: If C{True} make a deep, otherwise a

1463 shallow copy (C{bool}).

1464 @kwarg name: Optional name of the copy (C{str}).

1465

1466 @return: A copy of this point, I{normalized} and

1467 optionally renamed (C{LatLon}).

1468

1469 @see: Property L{isnormal}, method L{normal} and function

1470 L{pygeodesy.normal}.

1471 '''

1472 ll = self.copy(deep=deep)

1473 _ = ll.normal()

1474 if name:

1475 ll.rename(name)

1476 return ll

1477

1478 def toNvector(self, h=None, Nvector=None, **Nvector_kwds):

1479 '''Convert this point to C{n-vector} (normal to the earth's surface)

1480 components, I{including height}.

1481

1482 @kwarg h: Optional height, overriding this point's

1483 height (C{meter}).

1484 @kwarg Nvector: Optional class to return the C{n-vector}

1485 components (C{Nvector}) or C{None}.

1486 @kwarg Nvector_kwds_wrap: Optional, additional B{C{Nvector}}

1487 keyword arguments, ignored if C{B{Nvector}

1488 is None}.

1489

1490 @return: A B{C{Nvector}} or a L{Vector4Tuple}C{(x, y, z, h)}

1491 if B{C{Nvector}} is C{None}.

1492

1493 @raise TypeError: Invalid B{C{Nvector}} or B{C{Nvector_kwds}}.

1494 '''

1495 return self.toVector(Vector=Nvector, h=self.height if h is None else h,

1496 ll=self, **Nvector_kwds)

1497

1498 def toStr(self, form=F_DMS, joined=_COMMASPACE_, m=_m_, **prec_sep_s_D_M_S): # PYCHOK expected

1499 '''Convert this point to a "lat, lon[, +/-height]" string, formatted

1500 in the given C{B{form}at}.

1501

1502 @kwarg form: The lat-/longitude C{B{form}at} to use (C{str}), see

1503 functions L{pygeodesy.latDMS} or L{pygeodesy.lonDMS}.

1504 @kwarg joined: Separator to join the lat-, longitude and heigth

1505 strings (C{str} or C{None} or C{NN} for non-joined).

1506 @kwarg m: Optional unit of the height (C{str}), use C{None} to

1507 exclude height from the returned string.

1508 @kwarg prec_sep_s_D_M_S: Optional C{B{prec}ision}, C{B{sep}arator},

1509 B{C{s_D}}, B{C{s_M}}, B{C{s_S}} and B{C{s_DMS}} keyword

1510 arguments, see function L{pygeodesy.latDMS} or

1511 L{pygeodesy.lonDMS}.

1512

1513 @return: This point in the specified C{B{form}at}, etc. (C{str} or

1514 a 2- or 3-tuple C{(lat_str, lon_str[, height_str])} if

1515 C{B{joined}=NN} or C{B{joined}=None}).

1516

1517 @see: Function L{pygeodesy.latDMS} or L{pygeodesy.lonDMS} for more

1518 details about keyword arguments C{B{form}at}, C{B{prec}ision},

1519 C{B{sep}arator}, B{C{s_D}}, B{C{s_M}}, B{C{s_S}} and B{C{s_DMS}}.

1520

1521 @example:

1522

1523 >>> LatLon(51.4778, -0.0016).toStr() # 51°28′40″N, 000°00′06″W

1524 >>> LatLon(51.4778, -0.0016).toStr(F_D) # 51.4778°N, 000.0016°W

1525 >>> LatLon(51.4778, -0.0016, 42).toStr() # 51°28′40″N, 000°00′06″W, +42.00m

1526 '''

1527 t = (latDMS(self.lat, form=form, **prec_sep_s_D_M_S),

1528 lonDMS(self.lon, form=form, **prec_sep_s_D_M_S))

1529 if self.height and m is not None:

1530 t += (self.heightStr(m=m),)

1531 return joined.join(t) if joined else t

1532

1533 def toVector(self, Vector=None, **Vector_kwds):

1534 '''Convert this point to C{n-vector} (normal to the earth's

1535 surface) components, I{ignoring height}.

1536

1537 @kwarg Vector: Optional class to return the C{n-vector}

1538 components (L{Vector3d}) or C{None}.

1539 @kwarg Vector_kwds: Optional, additional B{C{Vector}}

1540 keyword arguments, ignored if

1541 C{B{Vector} is None}.

1542

1543 @return: A B{C{Vector}} or a L{Vector3Tuple}C{(x, y, z)}

1544 if B{C{Vector}} is C{None}.

1545

1546 @raise TypeError: Invalid B{C{Vector}} or B{C{kwds}}.

1547

1548 @note: These are C{n-vector} x, y and z components,

1549 I{NOT} geocentric (ECEF) x, y and z coordinates!

1550 '''

1551 r = self._vector3tuple

1552 if Vector is not None:

1553 r = Vector(*r, **_xkwds(Vector_kwds, name=self.name))

1554 return r

1555

1556 def toVector3d(self):

1557 '''Convert this point to C{n-vector} (normal to the earth's

1558 surface) components, I{ignoring height}.

1559

1560 @return: Unit vector (L{Vector3d}).

1561

1562 @note: These are C{n-vector} x, y and z components,

1563 I{NOT} geocentric (ECEF) x, y and z coordinates!

1564 '''

1565 return self._vector3d # XXX .unit()

1566

1567 def toWm(self, **toWm_kwds):

1568 '''Convert this point to a WM coordinate.

1569

1570 @kwarg toWm_kwds: Optional L{pygeodesy.toWm} keyword arguments.

1571

1572 @return: The WM coordinate (L{Wm}).

1573

1574 @see: Function L{pygeodesy.toWm}.

1575 '''

1576 return self._wm if not toWm_kwds else _MODS.webmercator.toWm(

1577 self, **_xkwds(toWm_kwds, name=self.name))

1578

1579 @deprecated_method

1580 def to3xyz(self): # PYCHOK no cover

1581 '''DEPRECATED, use property L{xyz} or method L{toNvector}, L{toVector},

1582 L{toVector3d} or perhaps (geocentric) L{toEcef}.'''

1583 return self.xyz # self.toVector()

1584

1585 @Property_RO

1586 def _vector3d(self):

1587 '''(INTERNAL) Cache for L{toVector3d}.

1588 '''

1589 return self.toVector(Vector=Vector3d) # XXX .unit()

1590

1591 @Property_RO

1592 def _vector3tuple(self):

1593 '''(INTERNAL) Cache for L{toVector}.

1594 '''

1595 return philam2n_xyz(self.phi, self.lam, name=self.name)

1596

1597 def vincentysTo(self, other, **radius_wrap):

1598 '''Compute the distance between this and an other point using

1599 U{Vincenty's<https://WikiPedia.org/wiki/Great-circle_distance>}

1600 spherical formula.

1601

1602 @arg other: The other point (C{LatLon}).

1603 @kwarg radius_wrap: Optional keyword arguments for function

1604 L{pygeodesy.vincentys}, overriding the

1605 default mean C{radius} of this point's

1606 datum ellipsoid.

1607

1608 @return: Distance (C{meter}, same units as B{C{radius}}).

1609

1610 @raise TypeError: The B{C{other}} point is not C{LatLon}.

1611

1612 @see: Function L{pygeodesy.vincentys} and methods L{cosineAndoyerLambertTo},

1613 L{cosineForsytheAndoyerLambertTo}, L{cosineLawTo}, C{distanceTo*},

1614 L{equirectangularTo}, L{euclideanTo}, L{flatLocalTo}/L{hubenyTo},

1615 L{flatPolarTo}, L{haversineTo} and L{thomasTo}.

1616 '''

1617 return self._distanceTo(vincentys, other, **_xkwds(radius_wrap, radius=None))

1618

1619 @Property_RO

1620 def _wm(self):

1621 '''(INTERNAL) Get this point as webmercator (L{Wm}).

1622 '''

1623 return _MODS.webmercator.toWm(self)

1624

1625 @Property_RO

1626 def xyz(self):

1627 '''Get the C{n-vector} X, Y and Z components (L{Vector3Tuple}C{(x, y, z)})

1628

1629 @note: These are C{n-vector} x, y and z components, I{NOT}

1630 geocentric (ECEF) x, y and z coordinates!

1631 '''

1632 return self.toVector(Vector=Vector3Tuple)

1633

1634 @Property_RO

1635 def xyzh(self):

1636 '''Get the C{n-vector} X, Y, Z and H components (L{Vector4Tuple}C{(x, y, z, h)})

1637

1638 @note: These are C{n-vector} x, y and z components, I{NOT}

1639 geocentric (ECEF) x, y and z coordinates!

1640 '''

1641 return self.xyz.to4Tuple(self.height)

1642

1643

1644 class _toCartesian3(object): # see also .formy._idllmn6, .geodesicw._wargs, .vector2d._numpy

1645 '''(INTERNAL) Wrapper to convert 2 other points.

1646 '''

1647 @contextmanager # <https://www.Python.org/dev/peps/pep-0343/> Examples

1648 def __call__(self, p, p2, p3, wrap, **kwds):

1649 try:

1650 if wrap:

1651 p2, p3 = map1(_Wrap.point, p2, p3)

1652 kwds = _xkwds(kwds, wrap=wrap)

1653 yield (p. toCartesian().copy(name=_point_), # copy to rename

1654 p._toCartesianEcef(up=4, point2=p2),

1655 p._toCartesianEcef(up=4, point3=p3))

1656 except (AssertionError, TypeError, ValueError) as x: # Exception?

1657 raise _xError(x, point=p, point2=p2, point3=p3, **kwds)

1658

1659_toCartesian3 = _toCartesian3() # PYCHOK singleton

1660

1661

1662 def _latlonheight3(latlonh, height, wrap): # in .points.LatLon_.__init__

1663 '''(INTERNAL) Get 3-tuple C{(lat, lon, height)}.

1664 '''

1665 try:

1666 lat, lon = latlonh.lat, latlonh.lon

1667 height = _xattr(latlonh, height=height)

1668 except AttributeError:

1669 raise _IsnotError(_LatLon_, latlonh=latlonh)

1670 if wrap:

1671 lat, lon = _Wrap.latlon(lat, lon)

1672 return lat, lon, height

1673

1674

1675 def _trilaterate5(p1, d1, p2, d2, p3, d3, area=True, eps=EPS1, # MCCABE 13

1676 radius=R_M, wrap=False):

1677 '''(INTERNAL) Trilaterate three points by I{area overlap} or by

1678 I{perimeter intersection} of three circles.

1679

1680 @note: The B{C{radius}} is only needed for both the n-vectorial

1681 and C{sphericalTrigonometry.LatLon.distanceTo} methods and

1682 silently ignored by the C{ellipsoidalExact}, C{-GeodSolve},

1683 C{-Karney} and C{-Vincenty.LatLon.distanceTo} methods.

1684 '''

1685 p2, p3, w = _unrollon3(p1, p2, p3, wrap)

1686

1687 r1 = Distance_(distance1=d1)

1688 r2 = Distance_(distance2=d2)

1689 r3 = Distance_(distance3=d3)

1690 m = 0 if area else (r1 + r2 + r3)

1691 pc = 0

1692 t = []

1693 for _ in range(3):

1694 try: # intersection of circle (p1, r1) and (p2, r2)

1695 c1, c2 = p1.intersections2(r1, p2, r2, wrap=w)

1696

1697 if area: # check overlap

1698 if c1 is c2: # abutting

1699 c = c1

1700 else: # nearest point on radical

1701 c = p3.nearestOn(c1, c2, within=True, wrap=w)

1702 d = r3 - p3.distanceTo(c, radius=radius, wrap=w)

1703 if d > eps: # sufficient overlap

1704 t.append((d, c))

1705 m = max(m, d)

1706

1707 else: # check intersection

1708 for c in ((c1,) if c1 is c2 else (c1, c2)):

1709 d = fabs(r3 - p3.distanceTo(c, radius=radius, wrap=w))

1710 if d < eps: # below margin

1711 t.append((d, c))

1712 m = min(m, d)

1713

1714 except IntersectionError as x:

1715 if _concentric_ in str(x): # XXX ConcentricError?

1716 pc += 1

1717

1718 p1, r1, p2, r2, p3, r3 = p2, r2, p3, r3, p1, r1 # rotate

1719

1720 if t: # get min, max, points and count ...

1721 t = tuple(sorted(t))

1722 n = len(t), # as 1-tuple

1723 # ... or for a single trilaterated result,

1724 # min *is* max, min- *is* maxPoint and n=1, 2 or 3

1725 return Trilaterate5Tuple(t[0] + t[-1] + n) # *(t[0] + ...)

1726

1727 elif area and pc == 3: # all pairwise concentric ...

1728 r, p = min((r1, p1), (r2, p2), (r3, p3))

1729 m = max(r1, r2, r3)

1730 # ... return "smallest" point twice, the smallest

1731 # and largest distance and n=0 for concentric

1732 return Trilaterate5Tuple(float(r), p, float(m), p, 0)

1733

1734 n, f = (_overlap_, max) if area else (_intersection_, min)

1735 t = _COMMASPACE_(_no_(n), '%s %.3g' % (f.__name__, m))

1736 raise IntersectionError(area=area, eps=eps, wrap=wrap, txt=t)

1737

1738

1739__all__ += _ALL_DOCS(LatLonBase)

1740

1741# **) MIT License

1742#

1743# Copyright (C) 2016-2023 -- mrJean1 at Gmail -- All Rights Reserved.

1744#

1745# Permission is hereby granted, free of charge, to any person obtaining a

1746# copy of this software and associated documentation files (the "Software"),

1747# to deal in the Software without restriction, including without limitation

1748# the rights to use, copy, modify, merge, publish, distribute, sublicense,

1749# and/or sell copies of the Software, and to permit persons to whom the

1750# Software is furnished to do so, subject to the following conditions:

1751#

1752# The above copyright notice and this permission notice shall be included

1753# in all copies or substantial portions of the Software.

1754#

1755# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS

1756# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,

1757# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL

1758# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR

1759# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,

1760# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR

1761# OTHER DEALINGS IN THE SOFTWARE.