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__ = '23.11.08'

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}.

469 '''

470 return _MODS.ecef.EcefKarney # default

471

472 @Property_RO

473 def _Ecef_forward(self):

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

475 '''

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

477

478 @Property_RO

479 def _ecef9(self):

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

481 '''

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

483

484 @property_RO

485 def ellipsoidalLatLon(self):

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

487 '''

488 return False

489

490 @deprecated_method

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

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

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

494

495 @deprecated_method

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

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

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

499

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

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

502 using the U{Equirectangular Approximation / Projection

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

504

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

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

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

508

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

510 @kwarg radius_adjust_limit_wrap: Optional keyword arguments

511 for function L{pygeodesy.equirectangular},

512 overriding the default mean C{radius} of this

513 point's datum ellipsoid.

514

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

516

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

518

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

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

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

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

523 '''

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

525

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

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

528 an other point.

529

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

531

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

533 @kwarg radius_adjust_wrap: Optional keyword arguments for function

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

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

536

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

538

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

540

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

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

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

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

545 '''

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

547

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

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

550 U{ellipsoidal Earth to plane projection

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

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

553

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

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

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

557 datum ellipsoid.

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

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

560

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

562

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

564

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

566

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

568 L{cosineAndoyerLambertTo}, L{cosineForsytheAndoyerLambertTo},

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

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

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

572 '''

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

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

575

576 hubenyTo = flatLocalTo # for Karl Hubeny

577

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

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

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

581 Geographical_distance#Polar_coordinate_flat-Earth_formula>} formula.

582

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

584 @kwarg radius_wrap: Optional keyword arguments for function

585 L{pygeodesy.flatPolar}, overriding the

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

587 datum ellipsoid.

588

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

590

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

592

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

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

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

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

597 '''

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

599

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

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

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

603

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

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

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

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

608 this point's C{datum} ellipsoid.

609

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

611 to the distance to this C{pov}.

612

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

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

615 outside or away from the ellipsoid.

616

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

618

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

620 '''

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

622

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

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

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

626 formula.

627

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

629 @kwarg radius_wrap: Optional keyword arguments for function

630 L{pygeodesy.haversine}, overriding the

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

632 datum ellipsoid.

633

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

635

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

637

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

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

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

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

642 '''

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

644

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

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

647

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

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

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

651

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

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

654 '''

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

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

657

658 @Property

659 def height(self):

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

661 '''

662 return self._height

663

664 @height.setter # PYCHOK setter!

665 def height(self, height):

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

667

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

669

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

671 '''

672 h = Height(height)

673 if self._height != h:

674 _update_all(self)

675 self._height = h

676

677 def _heigHt(self, height):

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

679 '''

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

681

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

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

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

685

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

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

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

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

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

691 ellipsoid's surface, otherwise the intersection of the

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

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

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

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

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

697

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

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

700

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

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

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

704

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

706

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

708

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

710 '''

711 c = self.toCartesian()

712 if LatLon is None:

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

714 else:

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

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

717 return r

718

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

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

721

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

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

724

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

726 '''

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

728

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

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

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

732

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

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

735 line and return the 2 intercant points accordingly.

736 '''

737 if height is None:

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

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

740 if h != hp:

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

742 if s: # fmath.fidw?

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

744 hq += s * Q.s12

745 hp += s * P.s12

746 else:

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

748 else:

749 hp = hq = Height(height)

750

751# n = self.name or unused.__name__

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

753 p._iteration = P.iteration

754 if P is not Q:

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

756 q._iteration = Q.iteration

757 return p, q

758

759 @deprecated_method

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

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

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

763

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

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

766 on diametrically opposite sides of the earth.

767

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

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

770

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

772 tolerance, C{False} otherwise.

773 '''

774 p = self.others(other)

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

776

777 @Property_RO

778 def isEllipsoidal(self):

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

780 '''

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

782

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

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

785

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

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

788

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

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

791

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

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

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

795

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

797

798 @see: Method L{isequalTo3}.

799 '''

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

801

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

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

804

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

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

807

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

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

810

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

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

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

814

815 @see: Method L{isequalTo}.

816 '''

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

818 _isequalTo(self, other, eps=eps)

819

820 @Property_RO

821 def isnormal(self):

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

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

824

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

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

827 '''

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

829

830 @Property_RO

831 def isSpherical(self):

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

833 '''

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

835

836 @Property_RO

837 def lam(self):

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

839 '''

840 return radians(self.lon)

841

842 @Property

843 def lat(self):

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

845 '''

846 return self._lat

847

848 @lat.setter # PYCHOK setter!

849 def lat(self, lat):

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

851

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

853 '''

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

855 if self._lat != lat:

856 _update_all(self)

857 self._lat = lat

858

859 @Property

860 def latlon(self):

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

862 '''

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

864

865 @latlon.setter # PYCHOK setter!

866 def latlon(self, latlonh):

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

868 (2- or 3-tuple or comma- or space-separated C{str}

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

870

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

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

873

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

875

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

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

878 '''

879 if isstr(latlonh):

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

881 else:

882 _xinstanceof(list, tuple, latlonh=latlonh)

883 if len(latlonh) == 3:

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

885 elif len(latlonh) != 2:

886 raise _ValueError(latlonh=latlonh)

887 else:

888 h = self.height

889

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

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

892 _update_all(self)

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

894

895 def latlon2(self, ndigits=0):

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

897

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

899

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

901 and rounded away from zero.

902

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

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

905 '''

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

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

908

909 @deprecated_method

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

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

912 return self.latlon2(ndigits=ndigits)

913

914 latlon2round = latlon_ # PYCHOK no cover

915

916 @Property

917 def latlonheight(self):

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

919 '''

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

921

922 @latlonheight.setter # PYCHOK setter!

923 def latlonheight(self, latlonh):

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

925 (2- or 3-tuple or comma- or space-separated C{str}

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

927

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

929 '''

930 self.latlon = latlonh

931

932 @Property

933 def lon(self):

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

935 '''

936 return self._lon

937

938 @lon.setter # PYCHOK setter!

939 def lon(self, lon):

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

941

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

943 '''

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

945 if self._lon != lon:

946 _update_all(self)

947 self._lon = lon

948

949 @Property_RO

950 def _ltp(self):

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

952 '''

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

954

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

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

957

958 Points are converted to and distances are computed in

959 I{geocentric}, cartesian space.

960

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

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

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

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

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

966 account for distances.

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

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

969

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

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

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

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

974 units as the cartesian axes.

975

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

977

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

979 C{Ecef} invalid.

980

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

982

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

984 '''

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

986 p = None # not used

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

988 if w and i:

989 q = _unrollon(p, q)

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

991 p = q

992

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

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

995

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

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

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

999

1000 kwds = _xkwds_not(None, LatLon=self.classof, # this LatLon

1001 height=height)

1002 _r = self.Ecef(self.datum).reverse

1003 p = _r(c).toLatLon(**kwds)

1004 s = _r(s).toLatLon(**kwds) if s is not c else p

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

1006 return t.dup(closest=p, start=s, end=e)

1007

1008 def nearestTo(self, *args, **kwds): # PYCHOK no cover

1009 '''B{Not implemented}, throws a C{NotImplementedError} always.'''

1010 notImplemented(self, *args, **kwds)

1011

1012 def normal(self):

1013 '''Normalize this point I{in-place} to C{abs(lat) <= 90} and

1014 C{abs(lon) <= 180}.

1015

1016 @return: C{True} if this point was I{normal}, C{False} if it

1017 wasn't (but is now).

1018

1019 @see: Property L{isnormal} and method L{toNormal}.

1020 '''

1021 n = self.isnormal

1022 if not n:

1023 self.latlon = normal(*self.latlon)

1024 return n

1025

1026 @Property_RO

1027 def _N_vector(self):

1028 '''(INTERNAL) Get the (C{nvectorBase._N_vector_})

1029 '''

1030 return _MODS.nvectorBase._N_vector_(*self.xyzh)

1031

1032 @Property_RO

1033 def phi(self):

1034 '''Get the latitude (B{C{radians}}).

1035 '''

1036 return radians(self.lat)

1037

1038 @Property_RO

1039 def philam(self):

1040 '''Get the lat- and longitude (L{PhiLam2Tuple}C{(phi, lam)}).

1041 '''

1042 return PhiLam2Tuple(self.phi, self.lam, name=self.name)

1043

1044 def philam2(self, ndigits=0):

1045 '''Return this point's lat- and longitude in C{radians}, rounded.

1046

1047 @kwarg ndigits: Number of (decimal) digits (C{int}).

1048

1049 @return: A L{PhiLam2Tuple}C{(phi, lam)}, both C{float}

1050 and rounded away from zero.

1051

1052 @note: The C{round}ed values are always C{float}, also

1053 if B{C{ndigits}} is omitted.

1054 '''

1055 return PhiLam2Tuple(round(self.phi, ndigits),

1056 round(self.lam, ndigits), name=self.name)

1057

1058 @Property_RO

1059 def philamheight(self):

1060 '''Get the lat-, longitude in C{radians} and height (L{PhiLam3Tuple}C{(phi, lam, height)}).

1061 '''

1062 return self.philam.to3Tuple(self.height)

1063

1064 @deprecated_method

1065 def points(self, points, closed=True): # PYCHOK no cover

1066 '''DEPRECATED, use method L{points2}.'''

1067 return self.points2(points, closed=closed)

1068

1069 def points2(self, points, closed=True):

1070 '''Check a path or polygon represented by points.

1071

1072 @arg points: The path or polygon points (C{LatLon}[])

1073 @kwarg closed: Optionally, consider the polygon closed,

1074 ignoring any duplicate or closing final

1075 B{C{points}} (C{bool}).

1076

1077 @return: A L{Points2Tuple}C{(number, points)}, an C{int}

1078 and C{list} or C{tuple}.

1079

1080 @raise PointsError: Insufficient number of B{C{points}}.

1081

1082 @raise TypeError: Some B{C{points}} are not C{LatLon}.

1083 '''

1084 return _MODS.iters.points2(points, closed=closed, base=self)

1085

1086 def PointsIter(self, points, loop=0, dedup=False, wrap=False):

1087 '''Return a C{PointsIter} iterator.

1088

1089 @arg points: The path or polygon points (C{LatLon}[])

1090 @kwarg loop: Number of loop-back points (non-negative C{int}).

1091 @kwarg dedup: Skip duplicate points (C{bool}).

1092 @kwarg wrap: If C{True}, wrap or I{normalize} the

1093 enum-/iterated B{C{points}} (C{bool}).

1094

1095 @return: A new C{PointsIter} iterator.

1096

1097 @raise PointsError: Insufficient number of B{C{points}}.

1098 '''

1099 return PointsIter(points, base=self, loop=loop, dedup=dedup, wrap=wrap)

1100

1101 def radii11(self, point2, point3, wrap=False):

1102 '''Return the radii of the C{Circum-}, C{In-}, I{Soddy} and C{Tangent}

1103 circles of a (planar) triangle formed by this and two other points.

1104

1105 @arg point2: Second point (C{LatLon}).

1106 @arg point3: Third point (C{LatLon}).

1107 @kwarg wrap: If C{True}, wrap or I{normalize} B{C{point2}} and

1108 B{C{point3}} (C{bool}).

1109

1110 @return: L{Radii11Tuple}C{(rA, rB, rC, cR, rIn, riS, roS, a, b, c, s)}.

1111

1112 @raise IntersectionError: Near-coincident or -colinear points.

1113

1114 @raise TypeError: Invalid B{C{point2}} or B{C{point3}}.

1115

1116 @see: Function L{pygeodesy.radii11}, U{Incircle

1117 <https://MathWorld.Wolfram.com/Incircle.html>}, U{Soddy Circles

1118 <https://MathWorld.Wolfram.com/SoddyCircles.html>} and U{Tangent

1119 Circles<https://MathWorld.Wolfram.com/TangentCircles.html>}.

1120 '''

1121 with _toCartesian3(self, point2, point3, wrap) as cs:

1122 return _radii11ABC(*cs, useZ=True)[0]

1123

1124 def _rhumb3(self, exact, radius): # != .sphericalBase._rhumbs3

1125 '''(INTERNAL) Get the C{rhumb} for this point's datum or for

1126 the B{C{radius}}' earth model iff non-C{None}.

1127 '''

1128 try:

1129 d = self._rhumb3dict

1130 t = d[(exact, radius)]

1131 except KeyError:

1132 D = self.datum if radius is None else _spherical_datum(radius) # ellipsoidal OK

1133 try:

1134 r = D.ellipsoid.rhumb_(exact=exact) # or D.isSpherical

1135 except AttributeError as x:

1136 raise _AttributeError(datum=D, radius=radius, cause=x)

1137 t = r, D, _MODS.karney.Caps

1138 while d:

1139 d.popitem()

1140 d[(exact, radius)] = t # cache 3-tuple

1141 return t

1142

1143 @Property_RO

1144 def _rhumb3dict(self): # in rhumbIntersecant2 below

1145 return {} # single-item cache

1146

1147 def rhumbAzimuthTo(self, other, exact=False, radius=None, wrap=False, b360=False):

1148 '''Return the azimuth (bearing) of a rhumb line (loxodrome) between

1149 this and an other (ellipsoidal) point.

1150

1151 @arg other: The other point (C{LatLon}).

1152 @kwarg exact: Exact C{Rhumb...} to use (C{bool} or C{Rhumb...}),

1153 see method L{Ellipsoid.rhumb_}.

1154 @kwarg radius: Optional earth radius (C{meter}) or earth model

1155 (L{Datum}, L{Ellipsoid}, L{Ellipsoid2} or

1156 L{a_f2Tuple}), overriding this point's datum.

1157 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the

1158 B{C{other}} point (C{bool}).

1159 @kwarg b360: If C{True}, return the azimuth in the bearing range.

1160

1161 @return: Rhumb azimuth (compass C{degrees180} or C{degrees360}).

1162

1163 @raise TypeError: The B{C{other}} point is incompatible or

1164 B{C{radius}} is invalid.

1165 '''

1166 r, _, Cs = self._rhumb3(exact, radius)

1167 z = r._Inverse(self, other, wrap, outmask=Cs.AZIMUTH).azi12

1168 return _umod_360(z + _360_0) if b360 else z

1169

1170 def rhumbDestination(self, distance, azimuth, exact=False, radius=None, height=None):

1171 '''Return the destination point having travelled the given distance from

1172 this point along a rhumb line (loxodrome) of the given azimuth.

1173

1174 @arg distance: Distance travelled (C{meter}, same units as this

1175 point's datum (ellipsoid) axes or B{C{radius}},

1176 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

1181 (L{Datum}, L{Ellipsoid}, L{Ellipsoid2} or

1182 L{a_f2Tuple}), overriding 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

1199 a rhumb line (loxodrome).

1200

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

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

1203 see method L{Ellipsoid.rhumb_}.

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

1205 (L{Datum}, L{Ellipsoid}, L{Ellipsoid2} or

1206 L{a_f2Tuple}), overriding this point's datum.

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

1208 B{C{other}} point (C{bool}).

1209

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

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

1212

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

1214 B{C{radius}} 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{rhumbaux} and L{rhumbx}.

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

1302 this and 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...}),

1306 see method L{Ellipsoid.rhumb_}.

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

1308 (L{Datum}, L{Ellipsoid}, L{Ellipsoid2} or

1309 L{a_f2Tuple}), overriding this point's datum.

1310 @kwarg height: Optional height, overriding the mean height

1311 (C{meter}).

1312 @kwarg fraction: Midpoint location from this point (C{scalar}), 0

1313 for this, 1 for the B{C{other}}, 0.5 for halfway

1314 between this and the B{C{other}} point, may be

1315 negative or greater than 1.

1316 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the

1317 B{C{other}} point (C{bool}).

1318

1319 @return: The midpoint at the given B{C{fraction}} along the

1320 rhumb line (this C{LatLon}).

1321

1322 @raise TypeError: The B{C{other}} point is incompatible or

1323 B{C{radius}} is invalid.

1324

1325 @raise ValueError: Invalid B{C{height}} or B{C{fraction}}.

1326 '''

1327 r, D, _ = self._rhumb3(exact, radius)

1328 f = Scalar(fraction=fraction)

1329 d = r._Inverse(self, self.others(other), wrap) # C.AZIMUTH_DISTANCE

1330 d = r._Direct( self, d.azi12, d.s12 * f)

1331 h = self._havg(other, f=f, h=height)

1332 return self.classof(d.lat2, d.lon2, datum=D, height=h)

1333

1334 @property_RO

1335 def sphericalLatLon(self):

1336 '''Get the C{LatLon type} iff spherical, overloaded in L{LatLonSphericalBase}.

1337 '''

1338 return False

1339

1340 def thomasTo(self, other, wrap=False):

1341 '''Compute the distance between this and an other point using

1342 U{Thomas'<https://apps.DTIC.mil/dtic/tr/fulltext/u2/703541.pdf>}

1343 formula.

1344

1345 @arg other: The other point (C{LatLon}).

1346 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll

1347 the B{C{other}} point (C{bool}).

1348

1349 @return: Distance (C{meter}, same units as the axes of

1350 this point's datum ellipsoid).

1351

1352 @raise TypeError: The B{C{other}} point is not C{LatLon}.

1353

1354 @see: Function L{pygeodesy.thomas} and methods L{cosineAndoyerLambertTo},

1355 L{cosineForsytheAndoyerLambertTo}, L{cosineLawTo}, C{distanceTo*},

1356 L{equirectangularTo}, L{euclideanTo}, L{flatLocalTo}/L{hubenyTo},

1357 L{flatPolarTo}, L{haversineTo} and L{vincentysTo}.

1358 '''

1359 return self._distanceTo_(thomas_, other, wrap=wrap)

1360

1361 @deprecated_method

1362 def to2ab(self): # PYCHOK no cover

1363 '''DEPRECATED, use property L{philam}.'''

1364 return self.philam

1365

1366 def toCartesian(self, height=None, Cartesian=None, **Cartesian_kwds):

1367 '''Convert this point to cartesian, I{geocentric} coordinates,

1368 also known as I{Earth-Centered, Earth-Fixed} (ECEF).

1369

1370 @kwarg height: Optional height, overriding this point's height

1371 (C{meter}, conventionally).

1372 @kwarg Cartesian: Optional class to return the geocentric

1373 coordinates (C{Cartesian}) or C{None}.

1374 @kwarg Cartesian_kwds: Optional, additional B{C{Cartesian}}

1375 keyword arguments, ignored if

1376 C{B{Cartesian} is None}.

1377

1378 @return: A B{C{Cartesian}} or if B{C{Cartesian}} is C{None},

1379 an L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M,

1380 datum)} with C{C=0} and C{M} if available.

1381

1382 @raise TypeError: Invalid B{C{Cartesian}} or B{C{Cartesian_kwds}}.

1383 '''

1384 r = self._ecef9 if height is None else self.toEcef(height=height)

1385 if Cartesian is not None: # class or .classof

1386 r = self._xnamed(Cartesian(r, **Cartesian_kwds))

1387 _xdatum(r.datum, self.datum)

1388 return r

1389

1390 def _toCartesianEcef(self, height=None, i=None, up=2, **name_point):

1391 '''(INTERNAL) Convert to cartesian and check Ecef's before and after.

1392 '''

1393 p = self.others(up=up, **name_point)

1394 c = p.toCartesian(height=height)

1395 E = self.Ecef

1396 if E:

1397 for p in (p, c):

1398 e = getattr(p, LatLonBase.Ecef.name, None)

1399 if e not in (None, E): # PYCHOK no cover

1400 n, _ = name_point.popitem()

1401 if i is not None:

1402 Fmt.SQUARE(n, i)

1403 raise _ValueError(n, e, txt=_incompatible(E.__name__))

1404 return c

1405

1406 def toDatum(self, datum2, height=None, name=NN):

1407 '''I{Must be overloaded}.'''

1408 notOverloaded(self, datum2, height=height, name=name)

1409

1410 def toEcef(self, height=None, M=False):

1411 '''Convert this point to I{geocentric} coordinates, also known as

1412 I{Earth-Centered, Earth-Fixed} (U{ECEF<https://WikiPedia.org/wiki/ECEF>}).

1413

1414 @kwarg height: Optional height, overriding this point's height

1415 (C{meter}, conventionally).

1416 @kwarg M: Optionally, include the rotation L{EcefMatrix} (C{bool}).

1417

1418 @return: An L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M, datum)}

1419 with C{C=0} and C{M} if available.

1420

1421 @raise EcefError: A C{.datum} or an ECEF issue.

1422 '''

1423 return self._ecef9 if height in (None, self.height) else \

1424 self._Ecef_forward(self.lat, self.lon, height=height, M=M)

1425

1426 @deprecated_method

1427 def to3llh(self, height=None): # PYCHOK no cover

1428 '''DEPRECATED, use property L{latlonheight} or C{latlon.to3Tuple(B{height})}.'''

1429 return self.latlonheight if height in (None, self.height) else \

1430 self.latlon.to3Tuple(height)

1431

1432 def toLocal(self, Xyz=None, ltp=None, **Xyz_kwds):

1433 '''Convert this I{geodetic} point to I{local} C{X}, C{Y} and C{Z}.

1434

1435 @kwarg Xyz: Optional class to return C{X}, C{Y} and C{Z}

1436 (L{XyzLocal}, L{Enu}, L{Ned}) or C{None}.

1437 @kwarg ltp: The I{local tangent plane} (LTP) to use,

1438 overriding this point's LTP (L{Ltp}).

1439 @kwarg Xyz_kwds: Optional, additional B{C{Xyz}} keyword

1440 arguments, ignored if C{B{Xyz} is None}.

1441

1442 @return: An B{C{Xyz}} instance or if C{B{Xyz} is None},

1443 a L{Local9Tuple}C{(x, y, z, lat, lon, height,

1444 ltp, ecef, M)} with C{M=None}, always.

1445

1446 @raise TypeError: Invalid B{C{ltp}}.

1447 '''

1448 p = _MODS.ltp._xLtp(ltp, self._ltp)

1449 return p._ecef2local(self._ecef9, Xyz, Xyz_kwds)

1450

1451 def toLtp(self, Ecef=None):

1452 '''Return the I{local tangent plane} (LTP) for this point.

1453

1454 @kwarg Ecef: Optional ECEF I{class} (L{EcefKarney}, ...

1455 L{EcefYou}), overriding this point's C{Ecef}.

1456 '''

1457 return self._ltp if Ecef in (None, self.Ecef) else _MODS.ltp.Ltp(

1458 self, ecef=Ecef(self.datum), name=self.name)

1459

1460 def toNormal(self, deep=False, name=NN):

1461 '''Get this point I{normalized} to C{abs(lat) <= 90}

1462 and C{abs(lon) <= 180}.

1463

1464 @kwarg deep: If C{True} make a deep, otherwise a

1465 shallow copy (C{bool}).

1466 @kwarg name: Optional name of the copy (C{str}).

1467

1468 @return: A copy of this point, I{normalized} and

1469 optionally renamed (C{LatLon}).

1470

1471 @see: Property L{isnormal}, method L{normal} and function

1472 L{pygeodesy.normal}.

1473 '''

1474 ll = self.copy(deep=deep)

1475 _ = ll.normal()

1476 if name:

1477 ll.rename(name)

1478 return ll

1479

1480 def toNvector(self, h=None, Nvector=None, **Nvector_kwds):

1481 '''Convert this point to C{n-vector} (normal to the earth's surface)

1482 components, I{including height}.

1483

1484 @kwarg h: Optional height, overriding this point's

1485 height (C{meter}).

1486 @kwarg Nvector: Optional class to return the C{n-vector}

1487 components (C{Nvector}) or C{None}.

1488 @kwarg Nvector_kwds_wrap: Optional, additional B{C{Nvector}}

1489 keyword arguments, ignored if C{B{Nvector}

1490 is None}.

1491

1492 @return: A B{C{Nvector}} or a L{Vector4Tuple}C{(x, y, z, h)}

1493 if B{C{Nvector}} is C{None}.

1494

1495 @raise TypeError: Invalid B{C{Nvector}} or B{C{Nvector_kwds}}.

1496 '''

1497 return self.toVector(Vector=Nvector, h=self.height if h is None else h,

1498 ll=self, **Nvector_kwds)

1499

1500 def toStr(self, form=F_DMS, joined=_COMMASPACE_, m=_m_, **prec_sep_s_D_M_S): # PYCHOK expected

1501 '''Convert this point to a "lat, lon[, +/-height]" string, formatted

1502 in the given C{B{form}at}.

1503

1504 @kwarg form: The lat-/longitude C{B{form}at} to use (C{str}), see

1505 functions L{pygeodesy.latDMS} or L{pygeodesy.lonDMS}.

1506 @kwarg joined: Separator to join the lat-, longitude and heigth

1507 strings (C{str} or C{None} or C{NN} for non-joined).

1508 @kwarg m: Optional unit of the height (C{str}), use C{None} to

1509 exclude height from the returned string.

1510 @kwarg prec_sep_s_D_M_S: Optional C{B{prec}ision}, C{B{sep}arator},

1511 B{C{s_D}}, B{C{s_M}}, B{C{s_S}} and B{C{s_DMS}} keyword

1512 arguments, see function L{pygeodesy.latDMS} or

1513 L{pygeodesy.lonDMS}.

1514

1515 @return: This point in the specified C{B{form}at}, etc. (C{str} or

1516 a 2- or 3-tuple C{(lat_str, lon_str[, height_str])} if

1517 C{B{joined}=NN} or C{B{joined}=None}).

1518

1519 @see: Function L{pygeodesy.latDMS} or L{pygeodesy.lonDMS} for more

1520 details about keyword arguments C{B{form}at}, C{B{prec}ision},

1521 C{B{sep}arator}, B{C{s_D}}, B{C{s_M}}, B{C{s_S}} and B{C{s_DMS}}.

1522

1523 @example:

1524

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

1526 >>> LatLon(51.4778, -0.0016).toStr(F_D) # 51.4778°N, 000.0016°W

1527 >>> LatLon(51.4778, -0.0016, 42).toStr() # 51°28′40″N, 000°00′06″W, +42.00m

1528 '''

1529 t = (latDMS(self.lat, form=form, **prec_sep_s_D_M_S),

1530 lonDMS(self.lon, form=form, **prec_sep_s_D_M_S))

1531 if self.height and m is not None:

1532 t += (self.heightStr(m=m),)

1533 return joined.join(t) if joined else t

1534

1535 def toVector(self, Vector=None, **Vector_kwds):

1536 '''Convert this point to C{n-vector} (normal to the earth's

1537 surface) components, I{ignoring height}.

1538

1539 @kwarg Vector: Optional class to return the C{n-vector}

1540 components (L{Vector3d}) or C{None}.

1541 @kwarg Vector_kwds: Optional, additional B{C{Vector}}

1542 keyword arguments, ignored if

1543 C{B{Vector} is None}.

1544

1545 @return: A B{C{Vector}} or a L{Vector3Tuple}C{(x, y, z)}

1546 if B{C{Vector}} is C{None}.

1547

1548 @raise TypeError: Invalid B{C{Vector}} or B{C{kwds}}.

1549

1550 @note: These are C{n-vector} x, y and z components,

1551 I{NOT} geocentric (ECEF) x, y and z coordinates!

1552 '''

1553 r = self._vector3tuple

1554 if Vector is not None:

1555 r = Vector(*r, **_xkwds(Vector_kwds, name=self.name))

1556 return r

1557

1558 def toVector3d(self):

1559 '''Convert this point to C{n-vector} (normal to the earth's

1560 surface) components, I{ignoring height}.

1561

1562 @return: Unit vector (L{Vector3d}).

1563

1564 @note: These are C{n-vector} x, y and z components,

1565 I{NOT} geocentric (ECEF) x, y and z coordinates!

1566 '''

1567 return self._vector3d # XXX .unit()

1568

1569 def toWm(self, **toWm_kwds):

1570 '''Convert this point to a WM coordinate.

1571

1572 @kwarg toWm_kwds: Optional L{pygeodesy.toWm} keyword arguments.

1573

1574 @return: The WM coordinate (L{Wm}).

1575

1576 @see: Function L{pygeodesy.toWm}.

1577 '''

1578 return self._wm if not toWm_kwds else _MODS.webmercator.toWm(

1579 self, **_xkwds(toWm_kwds, name=self.name))

1580

1581 @deprecated_method

1582 def to3xyz(self): # PYCHOK no cover

1583 '''DEPRECATED, use property L{xyz} or method L{toNvector}, L{toVector},

1584 L{toVector3d} or perhaps (geocentric) L{toEcef}.'''

1585 return self.xyz # self.toVector()

1586

1587 @Property_RO

1588 def _vector3d(self):

1589 '''(INTERNAL) Cache for L{toVector3d}.

1590 '''

1591 return self.toVector(Vector=Vector3d) # XXX .unit()

1592

1593 @Property_RO

1594 def _vector3tuple(self):

1595 '''(INTERNAL) Cache for L{toVector}.

1596 '''

1597 return philam2n_xyz(self.phi, self.lam, name=self.name)

1598

1599 def vincentysTo(self, other, **radius_wrap):

1600 '''Compute the distance between this and an other point using

1601 U{Vincenty's<https://WikiPedia.org/wiki/Great-circle_distance>}

1602 spherical formula.

1603

1604 @arg other: The other point (C{LatLon}).

1605 @kwarg radius_wrap: Optional keyword arguments for function

1606 L{pygeodesy.vincentys}, overriding the

1607 default mean C{radius} of this point's

1608 datum ellipsoid.

1609

1610 @return: Distance (C{meter}, same units as B{C{radius}}).

1611

1612 @raise TypeError: The B{C{other}} point is not C{LatLon}.

1613

1614 @see: Function L{pygeodesy.vincentys} and methods L{cosineAndoyerLambertTo},

1615 L{cosineForsytheAndoyerLambertTo}, L{cosineLawTo}, C{distanceTo*},

1616 L{equirectangularTo}, L{euclideanTo}, L{flatLocalTo}/L{hubenyTo},

1617 L{flatPolarTo}, L{haversineTo} and L{thomasTo}.

1618 '''

1619 return self._distanceTo(vincentys, other, **_xkwds(radius_wrap, radius=None))

1620

1621 @Property_RO

1622 def _wm(self):

1623 '''(INTERNAL) Get this point as webmercator (L{Wm}).

1624 '''

1625 return _MODS.webmercator.toWm(self)

1626

1627 @Property_RO

1628 def xyz(self):

1629 '''Get the C{n-vector} X, Y and Z components (L{Vector3Tuple}C{(x, y, z)})

1630

1631 @note: These are C{n-vector} x, y and z components, I{NOT}

1632 geocentric (ECEF) x, y and z coordinates!

1633 '''

1634 return self.toVector(Vector=Vector3Tuple)

1635

1636 @Property_RO

1637 def xyzh(self):

1638 '''Get the C{n-vector} X, Y, Z and H components (L{Vector4Tuple}C{(x, y, z, h)})

1639

1640 @note: These are C{n-vector} x, y and z components, I{NOT}

1641 geocentric (ECEF) x, y and z coordinates!

1642 '''

1643 return self.xyz.to4Tuple(self.height)

1644

1645

1646 class _toCartesian3(object): # see also .formy._idllmn6, .geodesicw._wargs, .vector2d._numpy

1647 '''(INTERNAL) Wrapper to convert 2 other points.

1648 '''

1649 @contextmanager # <https://www.Python.org/dev/peps/pep-0343/> Examples

1650 def __call__(self, p, p2, p3, wrap, **kwds):

1651 try:

1652 if wrap:

1653 p2, p3 = map1(_Wrap.point, p2, p3)

1654 kwds = _xkwds(kwds, wrap=wrap)

1655 yield (p. toCartesian().copy(name=_point_), # copy to rename

1656 p._toCartesianEcef(up=4, point2=p2),

1657 p._toCartesianEcef(up=4, point3=p3))

1658 except (AssertionError, TypeError, ValueError) as x: # Exception?

1659 raise _xError(x, point=p, point2=p2, point3=p3, **kwds)

1660

1661_toCartesian3 = _toCartesian3() # PYCHOK singleton

1662

1663

1664 def _latlonheight3(latlonh, height, wrap): # in .points.LatLon_.__init__

1665 '''(INTERNAL) Get 3-tuple C{(lat, lon, height)}.

1666 '''

1667 try:

1668 lat, lon = latlonh.lat, latlonh.lon

1669 height = _xattr(latlonh, height=height)

1670 except AttributeError:

1671 raise _IsnotError(_LatLon_, latlonh=latlonh)

1672 if wrap:

1673 lat, lon = _Wrap.latlon(lat, lon)

1674 return lat, lon, height

1675

1676

1677 def _trilaterate5(p1, d1, p2, d2, p3, d3, area=True, eps=EPS1, # MCCABE 13

1678 radius=R_M, wrap=False):

1679 '''(INTERNAL) Trilaterate three points by I{area overlap} or by

1680 I{perimeter intersection} of three circles.

1681

1682 @note: The B{C{radius}} is only needed for both the n-vectorial

1683 and C{sphericalTrigonometry.LatLon.distanceTo} methods and

1684 silently ignored by the C{ellipsoidalExact}, C{-GeodSolve},

1685 C{-Karney} and C{-Vincenty.LatLon.distanceTo} methods.

1686 '''

1687 p2, p3, w = _unrollon3(p1, p2, p3, wrap)

1688

1689 r1 = Distance_(distance1=d1)

1690 r2 = Distance_(distance2=d2)

1691 r3 = Distance_(distance3=d3)

1692 m = 0 if area else (r1 + r2 + r3)

1693 pc = 0

1694 t = []

1695 for _ in range(3):

1696 try: # intersection of circle (p1, r1) and (p2, r2)

1697 c1, c2 = p1.intersections2(r1, p2, r2, wrap=w)

1698

1699 if area: # check overlap

1700 if c1 is c2: # abutting

1701 c = c1

1702 else: # nearest point on radical

1703 c = p3.nearestOn(c1, c2, within=True, wrap=w)

1704 d = r3 - p3.distanceTo(c, radius=radius, wrap=w)

1705 if d > eps: # sufficient overlap

1706 t.append((d, c))

1707 m = max(m, d)

1708

1709 else: # check intersection

1710 for c in ((c1,) if c1 is c2 else (c1, c2)):

1711 d = fabs(r3 - p3.distanceTo(c, radius=radius, wrap=w))

1712 if d < eps: # below margin

1713 t.append((d, c))

1714 m = min(m, d)

1715

1716 except IntersectionError as x:

1717 if _concentric_ in str(x): # XXX ConcentricError?

1718 pc += 1

1719

1720 p1, r1, p2, r2, p3, r3 = p2, r2, p3, r3, p1, r1 # rotate

1721

1722 if t: # get min, max, points and count ...

1723 t = tuple(sorted(t))

1724 n = len(t), # as 1-tuple

1725 # ... or for a single trilaterated result,

1726 # min *is* max, min- *is* maxPoint and n=1, 2 or 3

1727 return Trilaterate5Tuple(t[0] + t[-1] + n) # *(t[0] + ...)

1728

1729 elif area and pc == 3: # all pairwise concentric ...

1730 r, p = min((r1, p1), (r2, p2), (r3, p3))

1731 m = max(r1, r2, r3)

1732 # ... return "smallest" point twice, the smallest

1733 # and largest distance and n=0 for concentric

1734 return Trilaterate5Tuple(float(r), p, float(m), p, 0)

1735

1736 n, f = (_overlap_, max) if area else (_intersection_, min)

1737 t = _COMMASPACE_(_no_(n), '%s %.3g' % (f.__name__, m))

1738 raise IntersectionError(area=area, eps=eps, wrap=wrap, txt=t)

1739

1740

1741__all__ += _ALL_DOCS(LatLonBase)

1742

1743# **) MIT License

1744#

1745# Copyright (C) 2016-2023 -- mrJean1 at Gmail -- All Rights Reserved.

1746#

1747# Permission is hereby granted, free of charge, to any person obtaining a

1748# copy of this software and associated documentation files (the "Software"),

1749# to deal in the Software without restriction, including without limitation

1750# the rights to use, copy, modify, merge, publish, distribute, sublicense,

1751# and/or sell copies of the Software, and to permit persons to whom the

1752# Software is furnished to do so, subject to the following conditions:

1753#

1754# The above copyright notice and this permission notice shall be included

1755# in all copies or substantial portions of the Software.

1756#

1757# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS

1758# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,

1759# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL

1760# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR

1761# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,

1762# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR

1763# OTHER DEALINGS IN THE SOFTWARE.