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 isstr, map1, _xinstanceof, _passarg

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

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, IntersectionError, \

21 _incompatible, _IsnotError, _TypeError, \

22 _ValueError, _xattr, _xdatum, _xError, \

23 _xkwds, _xkwds_item2, _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 # as _formy

31# from pygeodesy.internals import _passarg # from .basics

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

33 _intersection_, _LatLon_, _m_, _negative_, \

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

35# from pygeodesy.iters import PointsIter, points2 # _MODS

36# from pygeodesy.karney import Caps # _MODS

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

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

39 from pygeodesy.named import _name2__, _NamedBase, Fmt

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

41 Trilaterate5Tuple

42# from pygeodesy.nvectorBase import _N_vector_ # _MODS

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

44 property_RO, _update_all

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

46 from pygeodesy.units import _isDegrees, _isRadius, Distance_, Lat, Lon, \

47 Height, Radius, Radius_, Scalar, Scalar_

48 from pygeodesy.utily import _unrollon, _unrollon3, _Wrap

49# from pygeodesy.vector2d import _circin6, Circin6Tuple, _circum3, circum4_, \

50# Circum3Tuple, _radii11ABC # _MODS

51# from pygeodesy.vector3d import nearestOn6, Vector3d # _MODS

52

53 from contextlib import contextmanager

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

55

56__all__ = _ALL_LAZY.latlonBase

57__version__ = '24.06.07'

58

59_formy = _MODS.into(formy=__name__)

60

61

62 class LatLonBase(_NamedBase):

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

64 ellipsoidal earth models.

65 '''

66 _clipid = INT0 # polygonal clip, see .booleans

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

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

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

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

71

72 def __init__(self, latlonh, lon=None, height=0, datum=None, **wrap_name):

73 '''New C{LatLon}.

74

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

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

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

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

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

80 (C{meter}, conventionally).

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

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

83 @kwarg wrap_name: Optional C{B{name}=NN} (C{str}) and optional keyword

84 argument C{B{wrap}=False}, if C{True}, wrap or I{normalize}

85 B{C{lat}} and B{C{lon}} (C{bool}).

86

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

88

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

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

91

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

93

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

95 '''

96 w, n = self._wrap_name2(**wrap_name)

97 if n:

98 self.name = n

99

100 if lon is None:

101 lat, lon, height = _latlonheight3(latlonh, height, w)

102 elif w:

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

104 else:

105 lat = latlonh

106

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

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

109 if height: # elevation

110 self._height = Height(height)

111 if datum is not None:

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

113

114 def __eq__(self, other):

115 return self.isequalTo(other)

116

117 def __ne__(self, other):

118 return not self.isequalTo(other)

119

120 def __str__(self):

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

122

123 def antipode(self, height=None):

124 '''Return the antipode, the point diametrically opposite to

125 this point.

126

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

128 this point's height otherwise.

129

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

131 '''

132 a = _formy.antipode(*self.latlon)

133 h = self._heigHt(height)

134 return self.classof(*a, height=h)

135

136 @deprecated_method

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

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

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

140

141 def boundsOf(self, wide, tall, radius=R_M, height=None, **name):

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

143 bounding box centered at this location.

144

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

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

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

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

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

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

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

152 overriding the point's height.

153 @kwarg name: Optional C{B{name}=NN} (C{str}).

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__(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 if C{None}, use 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, V3d=_MODS.vector3d.Vector3d):

190 t = ll.toEcef(height=height) # .toVector(Vector=V3d)

191 return V3d(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_name):

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_name: Optional C{B{name}=NN} (C{str}) and optional keyword

206 argument C{B{wrap}=False}, if C{True}, wrap or I{normalize}

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

208

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

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

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

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

213

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

215 than version 1.10.

216

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

218 a trilateration or C{numpy} issue.

219

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

221

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

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

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

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

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

227 height)} representing the differences between both results from

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

229

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

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

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

233 '''

234 w, n = self._wrap_name2(**wrap_name)

235

236 with _toCartesian3(self, point2, point3, w) as cs:

237 m = _MODS.vector2d

238 r, c, d, A, B, C = m._circin6(*cs, eps=eps, useZ=True, dLL3=True,

239 datum=self.datum) # PYCHOK unpack

240 return m.Circin6Tuple(r, c.toLatLon(), d, A.toLatLon(),

241 B.toLatLon(),

242 C.toLatLon(), name=n)

243

244 def circum3(self, point2, point3, circum=True, eps=EPS4, **wrap_name):

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

246 this and two other points.

247

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

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

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

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

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

253 @kwarg wrap_name: Optional C{B{name}=NN} (C{str}) and optional keyword

254 argument C{B{wrap}=False}, if C{True}, wrap or I{normalize}

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

256

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

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

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

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

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

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

263

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

265 version 1.10.

266

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

268 incompatible C{Ecef} classes or a trilateration

269 or C{numpy} issue.

270

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

272

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

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

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

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

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

278 height)} representing the difference between both results from

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

280

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

282 '''

283 w, n = self._wrap_name2(**wrap_name)

284

285 with _toCartesian3(self, point2, point3, w, circum=circum) as cs:

286 m = _MODS.vector2d

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

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

289 return m.Circum3Tuple(r, c.toLatLon(), d, name=n)

290

291 def circum4_(self, *points, **wrap_name):

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

293

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

295 @kwarg wrap_name: Optional C{B{name}=NN} (C{str}) and optional keyword argument

296 C{B{wrap}=False}, if C{True}, wrap or I{normalize} the B{C{points}}

297 (C{bool}).

298

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

300 instance of this (sub-)class.

301

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

303 version 1.10.

304

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

306

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

308

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

310

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

312 '''

313 w, n = self._wrap_name2(**wrap_name)

314

315 def _cs(ps, C, w):

316 _wp = _Wrap.point if w else _passarg

317 for i, p in enumerate(ps):

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

319

320 C = self._toCartesianEcef

321 c = C(point=self)

322 t = _MODS.vector2d.circum4_(c, Vector=c.classof, *_cs(points, C, w))

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

324 return t.dup(center=c, name=n)

325

326 @property

327 def clipid(self):

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

329 '''

330 return self._clipid

331

332 @clipid.setter # PYCHOK setter!

333 def clipid(self, clipid):

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

335 '''

336 self._clipid = int(clipid)

337

338 @deprecated_method

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

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

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

342

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

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

345 this and an other point.

346

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

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

349 larger distances.

350

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

352 @kwarg adjust_wrap: Optional keyword arguments for function

353 L{pygeodesy.compassAngle}.

354

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

356

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

358

359 @note: Courtesy of Martin Schultz.

360

361 @see: U{Local, flat earth approximation

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

363 '''

364 p = self.others(other)

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

366

367 def cosineAndoyerLambertTo(self, other, **wrap):

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

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

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

371

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

373 @kwarg wrap: Optional keyword argument C{B{wrap}=False}, if C{True}, wrap

374 or I{normalize} and unroll the B{C{other}} point (C{bool}).

375

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

377 ellipsoid).

378

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

380

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

382 L{cosineForsytheAndoyerLambertTo}, L{cosineLawTo},

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

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

385 L{thomasTo} and L{vincentysTo}.

386 '''

387 return self._distanceTo_(_formy.cosineAndoyerLambert_, other, **wrap)

388

389 def cosineForsytheAndoyerLambertTo(self, other, **wrap):

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

391 the U{Forsythe-Andoyer-Lambert correction

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

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

394 formula.

395

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

397 @kwarg wrap: Optional keyword argument C{B{wrap}=False}, if C{True}, wrap

398 or I{normalize} and unroll the B{C{other}} point (C{bool}).

399

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

401 ellipsoid).

402

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

404

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

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

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

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

409 '''

410 return self._distanceTo_(_formy.cosineForsytheAndoyerLambert_, other, **wrap)

411

412 def cosineLawTo(self, other, radius=None, **wrap):

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

414 U{spherical Law of Cosines

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

416 formula.

417

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

419 @kwarg radius: Mean earth radius (C{meter}) or C{None} for the mean radius

420 of this point's datum ellipsoid.

421 @kwarg wrap: Optional keyword argument C{B{wrap}=False}, if C{True}, wrap

422 or I{normalize} and unroll the B{C{other}} point (C{bool}).

423

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

425

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

427

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

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

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

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

432 '''

433 return self._distanceTo(_formy.cosineLaw, other, radius, **wrap)

434

435 @property_RO

436 def datum(self): # PYCHOK no cover

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

438 self._notOverloaded()

439

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

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

442

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

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

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

446 or C{None}.

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

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

449

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

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

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

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

454 is un-/specified.

455

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

457 '''

458 t = self._Ltp._local2ecef(delta, nine=True)

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

460

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

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

463 '''

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

465 if r is None:

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

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

468

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

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

471 '''

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

473 D = self.datum

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

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

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

477

478 @property_RO

479 def Ecef(self):

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

481 '''

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

483 return E

484

485 @Property_RO

486 def _Ecef_forward(self):

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

488 '''

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

490

491 @Property_RO

492 def _ecef9(self):

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

494 '''

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

496

497 @property_RO

498 def ellipsoidalLatLon(self):

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

500 '''

501 return False

502

503 @deprecated_method

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

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

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

507

508 @deprecated_method

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

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

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

512

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

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

515 using the U{Equirectangular Approximation / Projection

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

517

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

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

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

521

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

523 @kwarg radius_adjust_limit_wrap: Optional keyword arguments

524 for function L{pygeodesy.equirectangular},

525 overriding the default mean C{radius} of this

526 point's datum ellipsoid.

527

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

529

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

531

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

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

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

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

536 '''

537 return self._distanceTo(_formy.equirectangular, other, **radius_adjust_limit_wrap)

538

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

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

541 an other point.

542

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

544

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

546 @kwarg radius_adjust_wrap: Optional keyword arguments for function

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

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

549

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

551

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

553

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

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

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

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

558 '''

559 return self._distanceTo(_formy.euclidean, other, **radius_adjust_wrap)

560

561 def flatLocalTo(self, other, radius=None, **wrap):

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

563 U{ellipsoidal Earth to plane projection

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

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

566

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

568 @kwarg radius: Mean earth radius (C{meter}) or C{None} for the I{equatorial

569 radius} of this point's datum ellipsoid.

570 @kwarg wrap: Optional keyword argument C{B{wrap}=False}, if C{True}, wrap

571 or I{normalize} and unroll the B{C{other}} point (C{bool}).

572

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

574

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

576

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

578

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

580 L{cosineAndoyerLambertTo}, L{cosineForsytheAndoyerLambertTo},

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

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

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

584 '''

585 r = radius if radius in (None, R_M, _1_0, 1) else Radius(radius)

586 return self._distanceTo_(_formy.flatLocal_, other, radius=r, **wrap) # PYCHOK kwargs

587

588 hubenyTo = flatLocalTo # for Karl Hubeny

589

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

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

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

593 Geographical_distance#Polar_coordinate_flat-Earth_formula>} formula.

594

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

596 @kwarg radius_wrap: Optional keyword arguments for function

597 L{pygeodesy.flatPolar}, overriding the

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

599 datum ellipsoid.

600

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

602

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

604

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

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

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

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

609 '''

610 return self._distanceTo(_formy.flatPolar, other, **radius_wrap)

611

612 def hartzell(self, los=False, earth=None):

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

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

615

616 @kwarg los: Line-Of-Sight, I{direction} to the ellipsoid (L{Los}, L{Vector3d}),

617 C{True} for the I{normal, plumb} onto the surface or I{False} or

618 C{None} to point to the center of the ellipsoid.

619 @kwarg earth: The earth model (L{Datum}, L{Ellipsoid}, L{Ellipsoid2}, L{a_f2Tuple}

620 or C{scalar} radius in C{meter}), overriding this point's C{datum}

621 ellipsoid.

622

623 @return: The intersection (C{LatLon}) with C{.height} set to the distance to

624 this C{pov}.

625

626 @raise IntersectionError: Null or bad C{pov} or B{C{los}}, this C{pov} is inside

627 the ellipsoid or B{C{los}} points outside or away from

628 the ellipsoid.

629

630 @raise TypeError: Invalid B{C{los}} or invalid or undefined B{C{earth}} or C{datum}.

631

632 @see: Function L{hartzell<pygeodesy.formy.hartzell>} for further details.

633 '''

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

635

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

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

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

639 formula.

640

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

642 @kwarg radius_wrap: Optional keyword arguments for function

643 L{pygeodesy.haversine}, overriding the

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

645 datum ellipsoid.

646

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

648

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

650

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

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

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

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

655 '''

656 return self._distanceTo(_formy.haversine, other, **radius_wrap)

657

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

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

660

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

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

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

664

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

666 the overriding height B{C{h}} (C{Height}).

667 '''

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

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

670

671 @Property

672 def height(self):

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

674 '''

675 return self._height

676

677 @height.setter # PYCHOK setter!

678 def height(self, height):

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

680

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

682

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

684 '''

685 h = Height(height)

686 if self._height != h:

687 _update_all(self)

688 self._height = h

689

690 def _heigHt(self, height):

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

692 '''

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

694

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

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

697 this datum's ellipsoid surface.

698

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

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

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

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

703 @kwarg normal: If C{True} the projection is the normal to this

704 ellipsoid's surface, otherwise the intersection of the

705 I{radial} line to this ellipsoid's center (C{bool}).

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

707 datum (C{LatLon}) or C{None}.

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

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

710

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

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

713

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

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

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

717

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

719

720 @raise TypeError: Invalid B{C{earth}} or triaxial B{C{earth}} couldn't be

721 converted to biaxial B{C{LatLon}} datum.

722

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

724 '''

725 c = self.toCartesian()

726 if LatLon is None:

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

728 else:

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

730 r = c.toLatLon(LatLon=LatLon, **_xkwds(LatLon_kwds, datum=c.datum, height=c.height))

731 if r.datum != c.datum:

732 raise _TypeError(earth=earth, datum=r.datum)

733 return r

734

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

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

737

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

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

740

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

742 '''

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

744

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

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

747 self._notImplemented(*args, **kwds)

748

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

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

751 line and return the 2 intercant points accordingly.

752 '''

753 if height is None:

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

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

756 if h != hp:

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

758 if s: # fmath.fidw?

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

760 hq += s * Q.s12

761 hp += s * P.s12

762 else:

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

764 else:

765 hp = hq = Height(height)

766

767# n = self.name or unused.__name__

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

769 p._iteration = P.iteration

770 if P is not Q:

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

772 q._iteration = Q.iteration

773 return p, q

774

775 @deprecated_method

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

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

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

779

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

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

782 on diametrically opposite sides of the earth.

783

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

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

786

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

788 tolerance, C{False} otherwise.

789 '''

790 p = self.others(other)

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

792

793 @Property_RO

794 def isEllipsoidal(self):

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

796 '''

797 return _xattr(self.datum, isEllipsoidal=None)

798

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

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

801

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

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

804

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

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

807

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

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

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

811

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

813

814 @see: Method L{isequalTo3}.

815 '''

816 return _formy._isequalTo(self, self.others(other), eps=eps)

817

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

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

820

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

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

823

824 @return: C{True} if both points are identical I{including}

825 height, C{False} otherwise.

826

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

828 or mismatch of the B{C{other}} and this

829 C{class} or C{type}.

830

831 @see: Method L{isequalTo}.

832 '''

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

834 _formy._isequalTo(self, other, eps=eps)

835

836 @Property_RO

837 def isnormal(self):

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

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

840

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

842 <pygeodesy.isnormal>} and L{normal<pygeodesy.normal>}.

843 '''

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

845

846 @Property_RO

847 def isSpherical(self):

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

849 '''

850 return _xattr(self.datum, isSpherical=None)

851

852 @Property_RO

853 def lam(self):

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

855 '''

856 return radians(self.lon)

857

858 @Property

859 def lat(self):

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

861 '''

862 return self._lat

863

864 @lat.setter # PYCHOK setter!

865 def lat(self, lat):

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

867

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

869 '''

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

871 if self._lat != lat:

872 _update_all(self)

873 self._lat = lat

874

875 @Property

876 def latlon(self):

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

878 '''

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

880

881 @latlon.setter # PYCHOK setter!

882 def latlon(self, latlonh):

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

884 (2- or 3-tuple or comma- or space-separated C{str}

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

886

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

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

889

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

891

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

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

894 '''

895 if isstr(latlonh):

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

897 else:

898 _xinstanceof(list, tuple, latlonh=latlonh)

899 if len(latlonh) == 3:

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

901 elif len(latlonh) != 2:

902 raise _ValueError(latlonh=latlonh)

903 else:

904 h = self.height

905

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

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

908 _update_all(self)

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

910

911 def latlon2(self, ndigits=0):

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

913

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

915

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

917 and rounded away from zero.

918

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

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

921 '''

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

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

924

925 @deprecated_method

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

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

928 return self.latlon2(ndigits=ndigits)

929

930 latlon2round = latlon_ # PYCHOK no cover

931

932 @Property

933 def latlonheight(self):

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

935 '''

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

937

938 @latlonheight.setter # PYCHOK setter!

939 def latlonheight(self, latlonh):

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

941 (2- or 3-tuple or comma- or space-separated C{str} of

942 C{degrees90}, C{degrees180} and C{meter}).

943

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

945 '''

946 self.latlon = latlonh

947

948 @Property

949 def lon(self):

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

951 '''

952 return self._lon

953

954 @lon.setter # PYCHOK setter!

955 def lon(self, lon):

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

957

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

959 '''

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

961 if self._lon != lon:

962 _update_all(self)

963 self._lon = lon

964

965 @Property_RO

966 def _Ltp(self):

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

968 '''

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

970

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

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

973

974 Points are converted to and distances are computed in

975 I{geocentric}, cartesian space.

976

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

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

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

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

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

982 account for distances.

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

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

985

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

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

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

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

990 units as the cartesian axes.

991

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

993

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

995 C{Ecef} invalid.

996

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

998

999 @see: Function L{nearestOn6<pygeodesy.nearestOn6>}.

1000 '''

1001 def _cs(Ps, h, w, C):

1002 p = None # not used

1003 for i, q in Ps.enumerate():

1004 if w and i:

1005 q = _unrollon(p, q)

1006 yield C(height=h, i=i, up=3, points=q)

1007 p = q

1008

1009 C = self._toCartesianEcef # to verify datum and Ecef

1010 Ps = self.PointsIter(points, wrap=wrap)

1011

1012 c = C(height=height, this=self) # this Cartesian

1013 t = _MODS.vector3d.nearestOn6(c, _cs(Ps, height, wrap, C), closed=closed)

1014 c, s, e = t.closest, t.start, t.end

1015

1016 kwds = _xkwds_not(None, LatLon=self.classof, # this LatLon

1017 height=height)

1018 _r = self.Ecef(self.datum).reverse

1019 p = _r(c).toLatLon(**kwds)

1020 s = _r(s).toLatLon(**kwds) if s is not c else p

1021 e = _r(e).toLatLon(**kwds) if e is not c else p

1022 return t.dup(closest=p, start=s, end=e)

1023

1024 def nearestTo(self, *args, **kwds): # PYCHOK no cover

1025 '''B{Not implemented}, throws a C{NotImplementedError} always.'''

1026 self._notImplemented(*args, **kwds)

1027

1028 def normal(self):

1029 '''Normalize this point I{in-place} to C{abs(lat) <= 90} and

1030 C{abs(lon) <= 180}.

1031

1032 @return: C{True} if this point was I{normal}, C{False} if it

1033 wasn't (but is now).

1034

1035 @see: Property L{isnormal} and method L{toNormal}.

1036 '''

1037 n = self.isnormal

1038 if not n:

1039 self.latlon = _formy.normal(*self.latlon)

1040 return n

1041

1042 @property_RO

1043 def _N_vector(self):

1044 '''(INTERNAL) Get the C{Nvector} (C{nvectorBase._N_vector_})

1045 '''

1046 _N = _MODS.nvectorBase._N_vector_

1047 return _N(*self._n_xyz3, h=self.height, name=self.name)

1048

1049 @Property_RO

1050 def _n_xyz3(self):

1051 '''(INTERNAL) Get the n-vector components as L{Vector3Tuple}.

1052 '''

1053 return _formy.philam2n_xyz(self.phi, self.lam, name=self.name)

1054

1055 @Property_RO

1056 def phi(self):

1057 '''Get the latitude (B{C{radians}}).

1058 '''

1059 return radians(self.lat)

1060

1061 @Property_RO

1062 def philam(self):

1063 '''Get the lat- and longitude (L{PhiLam2Tuple}C{(phi, lam)}).

1064 '''

1065 return PhiLam2Tuple(self.phi, self.lam, name=self.name)

1066

1067 def philam2(self, ndigits=0):

1068 '''Return this point's lat- and longitude in C{radians}, rounded.

1069

1070 @kwarg ndigits: Number of (decimal) digits (C{int}).

1071

1072 @return: A L{PhiLam2Tuple}C{(phi, lam)}, both C{float}

1073 and rounded away from zero.

1074

1075 @note: The C{round}ed values are always C{float}, also

1076 if B{C{ndigits}} is omitted.

1077 '''

1078 return PhiLam2Tuple(round(self.phi, ndigits),

1079 round(self.lam, ndigits), name=self.name)

1080

1081 @Property_RO

1082 def philamheight(self):

1083 '''Get the lat-, longitude in C{radians} and height (L{PhiLam3Tuple}C{(phi, lam, height)}).

1084 '''

1085 return self.philam.to3Tuple(self.height)

1086

1087 @deprecated_method

1088 def points(self, points, **closed): # PYCHOK no cover

1089 '''DEPRECATED, use method L{points2}.'''

1090 return self.points2(points, **closed)

1091

1092 def points2(self, points, closed=True):

1093 '''Check a path or polygon represented by points.

1094

1095 @arg points: The path or polygon points (C{LatLon}[])

1096 @kwarg closed: Optionally, consider the polygon closed,

1097 ignoring any duplicate or closing final

1098 B{C{points}} (C{bool}).

1099

1100 @return: A L{Points2Tuple}C{(number, points)}, an C{int}

1101 and C{list} or C{tuple}.

1102

1103 @raise PointsError: Insufficient number of B{C{points}}.

1104

1105 @raise TypeError: Some B{C{points}} are not C{LatLon}.

1106 '''

1107 return _MODS.iters.points2(points, closed=closed, base=self)

1108

1109 def PointsIter(self, points, loop=0, dedup=False, wrap=False):

1110 '''Return a C{PointsIter} iterator.

1111

1112 @arg points: The path or polygon points (C{LatLon}[])

1113 @kwarg loop: Number of loop-back points (non-negative C{int}).

1114 @kwarg dedup: If C{True}, skip duplicate points (C{bool}).

1115 @kwarg wrap: If C{True}, wrap or I{normalize} the

1116 enum-/iterated B{C{points}} (C{bool}).

1117

1118 @return: A new C{PointsIter} iterator.

1119

1120 @raise PointsError: Insufficient number of B{C{points}}.

1121 '''

1122 return _MODS.iters.PointsIter(points, base=self, loop=loop,

1123 dedup=dedup, wrap=wrap)

1124

1125 def radii11(self, point2, point3, wrap=False):

1126 '''Return the radii of the C{Circum-}, C{In-}, I{Soddy} and C{Tangent}

1127 circles of a (planar) triangle formed by this and two other points.

1128

1129 @arg point2: Second point (C{LatLon}).

1130 @arg point3: Third point (C{LatLon}).

1131 @kwarg wrap: If C{True}, wrap or I{normalize} B{C{point2}} and

1132 B{C{point3}} (C{bool}).

1133

1134 @return: L{Radii11Tuple}C{(rA, rB, rC, cR, rIn, riS, roS, a, b, c, s)}.

1135

1136 @raise IntersectionError: Near-coincident or -colinear points.

1137

1138 @raise TypeError: Invalid B{C{point2}} or B{C{point3}}.

1139

1140 @see: Function L{pygeodesy.radii11}, U{Incircle

1141 <https://MathWorld.Wolfram.com/Incircle.html>}, U{Soddy Circles

1142 <https://MathWorld.Wolfram.com/SoddyCircles.html>} and U{Tangent

1143 Circles<https://MathWorld.Wolfram.com/TangentCircles.html>}.

1144 '''

1145 with _toCartesian3(self, point2, point3, wrap) as cs:

1146 return _MODS.vector2d._radii11ABC(*cs, useZ=True)[0]

1147

1148 def _rhumb3(self, exact, radius): # != .sphericalBase._rhumbs3

1149 '''(INTERNAL) Get the C{rhumb} for this point's datum or for

1150 the B{C{radius}}' earth model iff non-C{None}.

1151 '''

1152 try:

1153 d = self._rhumb3dict

1154 t = d[(exact, radius)]

1155 except KeyError:

1156 D = self.datum if radius is None else \

1157 _spherical_datum(radius) # ellipsoidal OK

1158 try:

1159 r = D.ellipsoid.rhumb_(exact=exact) # or D.isSpherical

1160 except AttributeError as x:

1161 raise _AttributeError(datum=D, radius=radius, cause=x)

1162 t = r, D, _MODS.karney.Caps

1163 if len(d) > 2:

1164 d.clear() # d[:] = {}

1165 d[(exact, radius)] = t # cache 3-tuple

1166 return t

1167

1168 @Property_RO

1169 def _rhumb3dict(self): # in ._update

1170 return {} # 3-item cache

1171

1172 def rhumbAzimuthTo(self, other, exact=False, radius=None, wrap=False, b360=False):

1173 '''Return the azimuth (bearing) of a rhumb line (loxodrome) between this

1174 and an other (ellipsoidal) point.

1175

1176 @arg other: The other point (C{LatLon}).

1177 @kwarg exact: Exact C{Rhumb...} to use (C{bool} or C{Rhumb...}), see

1178 method L{Ellipsoid.rhumb_}.

1179 @kwarg radius: Optional earth radius (C{meter}) or earth model (L{Datum},

1180 L{Ellipsoid}, L{Ellipsoid2} or L{a_f2Tuple}), overriding

1181 this point's datum.

1182 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the B{C{other}}

1183 point (C{bool}).

1184 @kwarg b360: If C{True}, return the azimuth as bearing in compass

1185 degrees (C{bool}).

1186

1187 @return: Rhumb azimuth (C{degrees180} or compass C{degrees360}).

1188

1189 @raise TypeError: The B{C{other}} point is incompatible or B{C{radius}}

1190 is invalid.

1191 '''

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

1193 z = r._Inverse(self, other, wrap, outmask=Cs.AZIMUTH).azi12

1194 return _umod_360(z + _360_0) if b360 else z

1195

1196 def rhumbDestination(self, distance, azimuth, radius=None, height=None,

1197 exact=False, **name):

1198 '''Return the destination point having travelled the given distance from

1199 this point along a rhumb line (loxodrome) of the given azimuth.

1200

1201 @arg distance: Distance travelled (C{meter}, same units as this point's

1202 datum (ellipsoid) axes or B{C{radius}}, may be negative.

1203 @arg azimuth: Azimuth (bearing) of the rhumb line (compass C{degrees}).

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

1208 @kwarg exact: Exact C{Rhumb...} to use (C{bool} or C{Rhumb...}), see

1209 method L{Ellipsoid.rhumb_}.

1210 @kwarg name: Optional C{B{name}=NN} (C{str}).

1211

1212 @return: The destination point (ellipsoidal C{LatLon}).

1213

1214 @raise TypeError: Invalid B{C{radius}}.

1215

1216 @raise ValueError: Invalid B{C{distance}}, B{C{azimuth}}, B{C{radius}}

1217 or B{C{height}}.

1218 '''

1219 r, D, _ = self._rhumb3(exact, radius)

1220 d = r._Direct(self, azimuth, distance)

1221 h = self._heigHt(height)

1222 return self.classof(d.lat2, d.lon2, datum=D, height=h, **name)

1223

1224 def rhumbDistanceTo(self, other, exact=False, radius=None, wrap=False):

1225 '''Return the distance from this to an other point along a rhumb line

1226 (loxodrome).

1227

1228 @arg other: The other point (C{LatLon}).

1229 @kwarg exact: Exact C{Rhumb...} to use (C{bool} or C{Rhumb...}), see

1230 method L{Ellipsoid.rhumb_}.

1231 @kwarg radius: Optional earth radius (C{meter}) or earth model (L{Datum},

1232 L{Ellipsoid}, L{Ellipsoid2} or L{a_f2Tuple}), overriding

1233 this point's datum.

1234 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the B{C{other}}

1235 point (C{bool}).

1236

1237 @return: Distance (C{meter}, the same units as this point's datum

1238 (ellipsoid) axes or B{C{radius}}.

1239

1240 @raise TypeError: The B{C{other}} point is incompatible or B{C{radius}}

1241 is invalid.

1242

1243 @raise ValueError: Invalid B{C{radius}}.

1244 '''

1245 r, _, Cs = self._rhumb3(exact, radius)

1246 return r._Inverse(self, other, wrap, outmask=Cs.DISTANCE).s12

1247

1248 def rhumbIntersecant2(self, circle, point, other, height=None,

1249 **exact_radius_wrap_eps_tol):

1250 '''Compute the intersections of a circle and a rhumb line given as two

1251 points or as a point and azimuth.

1252

1253 @arg circle: Radius of the circle centered at this location (C{meter}),

1254 or a point on the circle (this C{LatLon}).

1255 @arg point: The start point of the rhumb line (this C{LatLon}).

1256 @arg other: An other point I{on} (this C{LatLon}) or the azimuth I{of}

1257 (compass C{degrees}) the rhumb line.

1258 @kwarg height: Optional height for the intersection points (C{meter},

1259 conventionally) or C{None} for interpolated heights.

1260 @kwarg exact_radius_wrap_eps_tol: Optional keyword arguments, see

1261 methods L{rhumbLine} and L{RhumbLineAux.Intersecant2}

1262 or L{RhumbLine.Intersecant2}.

1263

1264 @return: 2-Tuple of the intersection points (representing a chord),

1265 each an instance of this class. Both points are the same

1266 instance if the rhumb line is tangent to the circle.

1267

1268 @raise IntersectionError: The circle and rhumb line do not intersect.

1269

1270 @raise TypeError: If B{C{point}} is not this C{LatLon} or B{C{circle}}

1271 or B{C{other}} invalid.

1272

1273 @raise ValueError: Invalid B{C{circle}}, B{C{other}}, B{C{height}}

1274 or B{C{exact_radius_wrap}}.

1275

1276 @see: Methods L{RhumbLineAux.Intersecant2} and L{RhumbLine.Intersecant2}.

1277 '''

1278 def _kwds3(eps=EPS, tol=_TOL, wrap=False, **kwds):

1279 return kwds, wrap, dict(eps=eps, tol=tol)

1280

1281 exact_radius, w, eps_tol = _kwds3(**exact_radius_wrap_eps_tol)

1282

1283 p = _unrollon(self, self.others(point=point), wrap=w)

1284 try:

1285 r = Radius_(circle=circle) if _isRadius(circle) else \

1286 self.rhumbDistanceTo(self.others(circle=circle), wrap=w, **exact_radius)

1287 rl = p.rhumbLine(other, wrap=w, **exact_radius)

1288 P, Q = rl.Intersecant2(self.lat, self.lon, r, **eps_tol)

1289

1290 return self._intersecend2(p, other, w, height, rl.rhumb, P, Q,

1291 self.rhumbIntersecant2)

1292 except (TypeError, ValueError) as x:

1293 raise _xError(x, center=self, circle=circle, point=point, other=other,

1294 **exact_radius_wrap_eps_tol)

1295

1296 def rhumbLine(self, other, exact=False, radius=None, wrap=False, **name_caps):

1297 '''Get a rhumb line through this point at a given azimuth or through

1298 this and an other point.

1299

1300 @arg other: The azimuth I{of} (compass C{degrees}) or an other point

1301 I{on} (this C{LatLon}) the rhumb line.

1302 @kwarg exact: Exact C{Rhumb...} to use (C{bool} or C{Rhumb...}), see

1303 method L{Ellipsoid.rhumb_}.

1304 @kwarg radius: Optional earth radius (C{meter}) or earth model

1305 (L{Datum}, L{Ellipsoid}, L{Ellipsoid2} or L{a_f2Tuple}),

1306 overriding this point's datum.

1307 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the B{C{other}}

1308 point (C{bool}).

1309 @kwarg name_caps: Optional C{B{name}=str} and C{caps}, see L{RhumbLine}

1310 or L{RhumbLineAux} C{B{caps}}.

1311

1312 @return: A C{RhumbLine} instance.

1313

1314 @raise TypeError: Invalid B{C{radius}} or B{C{other}} not C{scalar} nor

1315 this C{LatLon}.

1316

1317 @see: Modules L{rhumb.aux_} and L{rhumb.ekx}.

1318 '''

1319 r, _, Cs = self._rhumb3(exact, radius)

1320 kwds = _xkwds(name_caps, name=self.name, caps=Cs.LINE_OFF)

1321 rl = r._DirectLine( self, other, **kwds) if _isDegrees(other) else \

1322 r._InverseLine(self, self.others(other), wrap, **kwds)

1323 return rl

1324

1325 def rhumbMidpointTo(self, other, exact=False, radius=None,

1326 height=None, fraction=_0_5, **wrap_name):

1327 '''Return the (loxodromic) midpoint on the rhumb line between this and

1328 an other point.

1329

1330 @arg other: The other point (this C{LatLon}).

1331 @kwarg exact: Exact C{Rhumb...} to use (C{bool} or C{Rhumb...}), see

1332 method L{Ellipsoid.rhumb_}.

1333 @kwarg radius: Optional earth radius (C{meter}) or earth model (L{Datum},

1334 L{Ellipsoid}, L{Ellipsoid2} or L{a_f2Tuple}), overriding

1335 this point's datum.

1336 @kwarg height: Optional height, overriding the mean height (C{meter}).

1337 @kwarg fraction: Midpoint location from this point (C{scalar}), 0 for this,

1338 1 for the B{C{other}}, 0.5 for halfway between this and

1339 the B{C{other}} point, may be negative or greater than 1.

1340 @kwarg wrap_name: Optional C{B{name}=NN} (C{str}) and optional keyword

1341 argument C{B{wrap}=False}, if C{True}, wrap or I{normalize}

1342 and unroll the B{C{other}} point (C{bool}).

1343

1344 @return: The midpoint at the given B{C{fraction}} along the rhumb line

1345 (this C{LatLon}).

1346

1347 @raise TypeError: The B{C{other}} point is incompatible or B{C{radius}}

1348 is invalid.

1349

1350 @raise ValueError: Invalid B{C{height}} or B{C{fraction}}.

1351 '''

1352 w, n = self._wrap_name2(**wrap_name)

1353 r, D, _ = self._rhumb3(exact, radius)

1354 f = Scalar(fraction=fraction)

1355 d = r._Inverse(self, self.others(other), w) # C.AZIMUTH_DISTANCE

1356 d = r._Direct( self, d.azi12, d.s12 * f)

1357 h = self._havg(other, f=f, h=height)

1358 return self.classof(d.lat2, d.lon2, datum=D, height=h, name=n)

1359

1360 @property_RO

1361 def sphericalLatLon(self):

1362 '''Get the C{LatLon type} iff spherical, overloaded in L{LatLonSphericalBase}.

1363 '''

1364 return False

1365

1366 def thomasTo(self, other, **wrap):

1367 '''Compute the distance between this and an other point using U{Thomas'

1368 <https://apps.DTIC.mil/dtic/tr/fulltext/u2/703541.pdf>} formula.

1369

1370 @arg other: The other point (C{LatLon}).

1371 @kwarg wrap: Optional keyword argument C{B{wrap}=False}, if C{True}, wrap

1372 or I{normalize} and unroll the B{C{other}} point (C{bool}).

1373

1374 @return: Distance (C{meter}, same units as the axes of this point's datum

1375 ellipsoid).

1376

1377 @raise TypeError: The B{C{other}} point is not C{LatLon}.

1378

1379 @see: Function L{pygeodesy.thomas} and methods L{cosineAndoyerLambertTo},

1380 L{cosineForsytheAndoyerLambertTo}, L{cosineLawTo}, C{distanceTo*},

1381 L{equirectangularTo}, L{euclideanTo}, L{flatLocalTo}/L{hubenyTo},

1382 L{flatPolarTo}, L{haversineTo} and L{vincentysTo}.

1383 '''

1384 return self._distanceTo_(_formy.thomas_, other, **wrap)

1385

1386 @deprecated_method

1387 def to2ab(self): # PYCHOK no cover

1388 '''DEPRECATED, use property L{philam}.'''

1389 return self.philam

1390

1391 def toCartesian(self, height=None, Cartesian=None, **Cartesian_kwds):

1392 '''Convert this point to cartesian, I{geocentric} coordinates,

1393 also known as I{Earth-Centered, Earth-Fixed} (ECEF).

1394

1395 @kwarg height: Optional height, overriding this point's height

1396 (C{meter}, conventionally).

1397 @kwarg Cartesian: Optional class to return the geocentric

1398 coordinates (C{Cartesian}) or C{None}.

1399 @kwarg Cartesian_kwds: Optional, additional B{C{Cartesian}}

1400 keyword arguments, ignored if

1401 C{B{Cartesian} is None}.

1402

1403 @return: A B{C{Cartesian}} or if B{C{Cartesian}} is C{None},

1404 an L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M,

1405 datum)} with C{C=0} and C{M} if available.

1406

1407 @raise TypeError: Invalid B{C{Cartesian}} or B{C{Cartesian_kwds}}.

1408

1409 @see: Methods C{toNvector}, C{toVector} and C{toVector3d}.

1410 '''

1411 r = self._ecef9 if height is None else self.toEcef(height=height)

1412 if Cartesian is not None: # class or .classof

1413 r = Cartesian(r, **self._name1__(Cartesian_kwds))

1414 _xdatum(r.datum, self.datum)

1415 return r

1416

1417 def _toCartesianEcef(self, height=None, i=None, up=2, **name_point):

1418 '''(INTERNAL) Convert to cartesian and check Ecef's before and after.

1419 '''

1420 p = self.others(up=up, **name_point)

1421 c = p.toCartesian(height=height)

1422 E = self.Ecef

1423 if E:

1424 for p in (p, c):

1425 e = _xattr(p, Ecef=None)

1426 if e not in (None, E): # PYCHOK no cover

1427 n, _ = _xkwds_item2(name_point)

1428 n = Fmt.INDEX(n, i)

1429 raise _ValueError(n, e, txt=_incompatible(E.__name__)) # txt__

1430 return c

1431

1432 def toDatum(self, datum2, height=None, **name):

1433 '''I{Must be overloaded}.'''

1434 self._notOverloaded(datum2, height=height, **name)

1435

1436 def toEcef(self, height=None, M=False):

1437 '''Convert this point to I{geocentric} coordinates, also known as

1438 I{Earth-Centered, Earth-Fixed} (U{ECEF<https://WikiPedia.org/wiki/ECEF>}).

1439

1440 @kwarg height: Optional height, overriding this point's height

1441 (C{meter}, conventionally).

1442 @kwarg M: Optionally, include the rotation L{EcefMatrix} (C{bool}).

1443

1444 @return: An L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M, datum)}

1445 with C{C=0} and C{M} if available.

1446

1447 @raise EcefError: A C{.datum} or an ECEF issue.

1448 '''

1449 return self._ecef9 if height in (None, self.height) else \

1450 self._Ecef_forward(self.lat, self.lon, height=height, M=M)

1451

1452 @deprecated_method

1453 def to3llh(self, height=None): # PYCHOK no cover

1454 '''DEPRECATED, use property L{latlonheight} or C{latlon.to3Tuple(B{height})}.'''

1455 return self.latlonheight if height in (None, self.height) else \

1456 self.latlon.to3Tuple(height)

1457

1458 def toLocal(self, Xyz=None, ltp=None, **Xyz_kwds):

1459 '''Convert this I{geodetic} point to I{local} C{X}, C{Y} and C{Z}.

1460

1461 @kwarg Xyz: Optional class to return C{X}, C{Y} and C{Z} (L{XyzLocal},

1462 L{Enu}, L{Ned}) or C{None}.

1463 @kwarg ltp: The I{local tangent plane} (LTP) to use, overriding this

1464 point's LTP (L{Ltp}).

1465 @kwarg Xyz_kwds: Optional, additional B{C{Xyz}} keyword arguments,

1466 ignored if C{B{Xyz} is None}.

1467

1468 @return: An B{C{Xyz}} instance or a L{Local9Tuple}C{(x, y, z, lat, lon,

1469 height, ltp, ecef, M)} if C{B{Xyz} is None} (with C{M=None}).

1470

1471 @raise TypeError: Invalid B{C{ltp}}.

1472 '''

1473 return _MODS.ltp._toLocal(self, ltp, Xyz, Xyz_kwds) # self._ecef9

1474

1475 def toLtp(self, Ecef=None, **name):

1476 '''Return the I{local tangent plane} (LTP) for this point.

1477

1478 @kwarg Ecef: Optional ECEF I{class} (L{EcefKarney}, ...

1479 L{EcefYou}), overriding this point's C{Ecef}.

1480 @kwarg name: Optional C{B{name}=NN} (C{str}).

1481 '''

1482 return _MODS.ltp._toLtp(self, Ecef, self, name) # self._Ltp

1483

1484 def toNormal(self, deep=False, **name):

1485 '''Get this point I{normalized} to C{abs(lat) <= 90}

1486 and C{abs(lon) <= 180}.

1487

1488 @kwarg deep: If C{True} make a deep, otherwise a

1489 shallow copy (C{bool}).

1490 @kwarg name: Optional C{B{name}=NN} (C{str}).

1491

1492 @return: A copy of this point, I{normalized} (C{LatLon}),

1493 optionally renamed.

1494

1495 @see: Property L{isnormal}, method L{normal} and function

1496 L{pygeodesy.normal}.

1497 '''

1498 ll = self.copy(deep=deep)

1499 _ = ll.normal()

1500 if name:

1501 ll.rename(name)

1502 return ll

1503

1504 def toNvector(self, h=None, Nvector=None, **name_Nvector_kwds):

1505 '''Convert this point to C{n-vector} (normal to the earth's surface)

1506 components, I{including height}.

1507

1508 @kwarg h: Optional height, overriding this point's height (C{meter}).

1509 @kwarg Nvector: Optional class to return the C{n-vector} components

1510 (C{Nvector}) or C{None}.

1511 @kwarg name_Nvector_kwds: Optional C{B{name}=NN} (C{str}) and optional,

1512 additional B{C{Nvector}} keyword arguments, ignored if

1513 C{B{Nvector} is None}.

1514

1515 @return: An B{C{Nvector}} or a L{Vector4Tuple}C{(x, y, z, h)} if

1516 B{C{Nvector}} is C{None}.

1517

1518 @raise TypeError: Invalid B{C{h}}, B{C{Nvector}} or

1519 B{C{name_Nvector_kwds}} item.

1520

1521 @see: Methods C{toCartesian}, C{toVector} and C{toVector3d}.

1522 '''

1523 h = self._heigHt(h)

1524 if Nvector is None:

1525 r = self._n_xyz3.to4Tuple(h)

1526 n, _ = _name2__(name_Nvector_kwds, _or_nameof=self)

1527 if n:

1528 r.rename(n)

1529 else:

1530 x, y, z = self._n_xyz3

1531 r = Nvector(x, y, z, h=h, ll=self, **self._name1__(name_Nvector_kwds))

1532 return r

1533

1534 def toStr(self, form=F_DMS, joined=_COMMASPACE_, m=_m_, **prec_sep_s_D_M_S): # PYCHOK expected

1535 '''Convert this point to a "lat, lon[, +/-height]" string, formatted

1536 in the given C{B{form}at}.

1537

1538 @kwarg form: The lat-/longitude C{B{form}at} to use (C{str}), see

1539 functions L{pygeodesy.latDMS} or L{pygeodesy.lonDMS}.

1540 @kwarg joined: Separator to join the lat-, longitude and heigth

1541 strings (C{str} or C{None} or C{NN} for non-joined).

1542 @kwarg m: Optional unit of the height (C{str}), use C{None} to

1543 exclude height from the returned string.

1544 @kwarg prec_sep_s_D_M_S: Optional C{B{prec}ision}, C{B{sep}arator},

1545 B{C{s_D}}, B{C{s_M}}, B{C{s_S}} and B{C{s_DMS}} keyword

1546 arguments, see function L{pygeodesy.latDMS} or

1547 L{pygeodesy.lonDMS}.

1548

1549 @return: This point in the specified C{B{form}at}, etc. (C{str} or

1550 a 2- or 3-tuple C{(lat_str, lon_str[, height_str])} if

1551 C{B{joined}=NN} or C{B{joined}=None}).

1552

1553 @see: Function L{pygeodesy.latDMS} or L{pygeodesy.lonDMS} for more

1554 details about keyword arguments C{B{form}at}, C{B{prec}ision},

1555 C{B{sep}arator}, B{C{s_D}}, B{C{s_M}}, B{C{s_S}} and B{C{s_DMS}}.

1556 '''

1557 t = (latDMS(self.lat, form=form, **prec_sep_s_D_M_S),

1558 lonDMS(self.lon, form=form, **prec_sep_s_D_M_S))

1559 if self.height and m is not None:

1560 t += (self.heightStr(m=m),)

1561 return joined.join(t) if joined else t

1562

1563 def toVector(self, Vector=None, **Vector_kwds):

1564 '''Convert this point to a C{Vector} with the I{geocentric} C{(x,

1565 y, z)} (ECEF) coordinates, I{ignoring height}.

1566

1567 @kwarg Vector: Optional class to return the I{geocentric}

1568 components (L{Vector3d}) or C{None}.

1569 @kwarg Vector_kwds: Optional, additional B{C{Vector}} keyword

1570 arguments, ignored if C{B{Vector} is None}.

1571

1572 @return: A named B{C{Vector}} or if B{C{Vector}} is C{None} a

1573 named L{Vector3Tuple}C{(x, y, z)}.

1574

1575 @raise TypeError: Invalid B{C{Vector}} or B{C{Vector_kwds}} item.

1576

1577 @see: Methods C{toCartesian}, C{toNvector} and C{toVector3d}.

1578 '''

1579 return self._ecef9.toVector(Vector=Vector, **self._name1__(Vector_kwds))

1580

1581 def toVector3d(self, norm=True, **Vector3d_kwds):

1582 '''Convert this point to a L{Vector3d} with the I{geocentric} C{(x, y,

1583 z)} (ECEF) coordinates, I{ignoring height}.

1584

1585 @kwarg norm: If C{False}, don't normalize the coordinates (C{bool}).

1586 @kwarg Vector3d_kwds: Optional L{Vector3d} keyword arguments.

1587

1588 @return: Named, unit vector or vector (L{Vector3d}).

1589

1590 @raise TypeError: Invalid B{C{Vector3d_kwds}} item.

1591

1592 @see: Methods C{toCartesian}, C{toNvector} and C{toVector}.

1593 '''

1594 r = self.toVector(Vector=_MODS.vector3d.Vector3d, **Vector3d_kwds)

1595 if norm:

1596 r = r.unit(ll=self)

1597 return r

1598

1599 def toWm(self, **toWm_kwds):

1600 '''Convert this point to a WM coordinate.

1601

1602 @kwarg toWm_kwds: Optional L{pygeodesy.toWm} keyword arguments.

1603

1604 @return: The WM coordinate (L{Wm}).

1605

1606 @see: Function L{pygeodesy.toWm}.

1607 '''

1608 return _MODS.webmercator.toWm(self, **self._name1__(toWm_kwds))

1609

1610 @deprecated_method

1611 def to3xyz(self): # PYCHOK no cover

1612 '''DEPRECATED, use property L{xyz} or method L{toNvector}, L{toVector},

1613 L{toVector3d} or perhaps (geocentric) L{toEcef}.'''

1614 return self.xyz # self.toVector()

1615

1616# def _update(self, updated, *attrs, **setters):

1617# '''(INTERNAL) See C{_NamedBase._update}.

1618# '''

1619# if updated:

1620# self._rhumb3dict.clear()

1621# return _NamedBase._update(self, updated, *attrs, **setters)

1622

1623 def vincentysTo(self, other, **radius_wrap):

1624 '''Compute the distance between this and an other point using

1625 U{Vincenty's<https://WikiPedia.org/wiki/Great-circle_distance>}

1626 spherical formula.

1627

1628 @arg other: The other point (C{LatLon}).

1629 @kwarg radius_wrap: Optional keyword arguments for function

1630 L{pygeodesy.vincentys}, overriding the

1631 default mean C{radius} of this point's

1632 datum ellipsoid.

1633

1634 @return: Distance (C{meter}, same units as B{C{radius}}).

1635

1636 @raise TypeError: The B{C{other}} point is not C{LatLon}.

1637

1638 @see: Function L{pygeodesy.vincentys} and methods L{cosineAndoyerLambertTo},

1639 L{cosineForsytheAndoyerLambertTo}, L{cosineLawTo}, C{distanceTo*},

1640 L{equirectangularTo}, L{euclideanTo}, L{flatLocalTo}/L{hubenyTo},

1641 L{flatPolarTo}, L{haversineTo} and L{thomasTo}.

1642 '''

1643 return self._distanceTo(_formy.vincentys, other, **_xkwds(radius_wrap, radius=None))

1644

1645 def _wrap_name2(self, wrap=False, **name):

1646 '''(INTERNAL) Return the C{wrap} and C{name} value.

1647 '''

1648 return wrap, (self._name__(name) if name else NN)

1649

1650 @property_RO

1651 def xyz(self):

1652 '''Get the I{geocentric} C{(x, y, z)} coordinates (L{Vector3Tuple}C{(x, y, z)})

1653 '''

1654 return self._ecef9.xyz

1655

1656 @Property_RO

1657 def xyzh(self):

1658 '''Get the I{geocentric} C{(x, y, z)} coordinates and height (L{Vector4Tuple}C{(x, y, z, h)})

1659 '''

1660 return self.xyz.to4Tuple(self.height)

1661

1662

1663 class _toCartesian3(object): # see also .formy._idllmn6, .geodesicw._wargs, .vector2d._numpy

1664 '''(INTERNAL) Wrapper to convert 2 other points.

1665 '''

1666 @contextmanager # <https://www.Python.org/dev/peps/pep-0343/> Examples

1667 def __call__(self, p, p2, p3, wrap, **kwds):

1668 try:

1669 if wrap:

1670 p2, p3 = map1(_Wrap.point, p2, p3)

1671 kwds = _xkwds(kwds, wrap=wrap)

1672 yield (p. toCartesian().copy(name=_point_), # copy to rename

1673 p._toCartesianEcef(up=4, point2=p2),

1674 p._toCartesianEcef(up=4, point3=p3))

1675 except (AssertionError, TypeError, ValueError) as x: # Exception?

1676 raise _xError(x, point=p, point2=p2, point3=p3, **kwds)

1677

1678_toCartesian3 = _toCartesian3() # PYCHOK singleton

1679

1680

1681 def _latlonheight3(latlonh, height, wrap): # in .points.LatLon_.__init__

1682 '''(INTERNAL) Get 3-tuple C{(lat, lon, height)}.

1683 '''

1684 try:

1685 lat, lon = latlonh.lat, latlonh.lon

1686 height = _xattr(latlonh, height=height)

1687 except AttributeError:

1688 raise _IsnotError(_LatLon_, latlonh=latlonh)

1689 if wrap:

1690 lat, lon = _Wrap.latlon(lat, lon)

1691 return lat, lon, height

1692

1693

1694 def _trilaterate5(p1, d1, p2, d2, p3, d3, area=True, eps=EPS1, # MCCABE 13

1695 radius=R_M, wrap=False):

1696 '''(INTERNAL) Trilaterate three points by I{area overlap} or by

1697 I{perimeter intersection} of three circles.

1698

1699 @note: The B{C{radius}} is only needed for the n-vectorial and

1700 C{sphericalTrigonometry.LatLon.distanceTo} methods and

1701 silently ignored by the C{ellipsoidalExact}, C{-GeodSolve},

1702 C{-Karney} and C{-Vincenty.LatLon.distanceTo} methods.

1703 '''

1704 p2, p3, w = _unrollon3(p1, p2, p3, wrap)

1705

1706 r1 = Distance_(distance1=d1)

1707 r2 = Distance_(distance2=d2)

1708 r3 = Distance_(distance3=d3)

1709 m = 0 if area else (r1 + r2 + r3)

1710 pc = 0

1711 t = []

1712 for _ in range(3):

1713 try: # intersection of circle (p1, r1) and (p2, r2)

1714 c1, c2 = p1.intersections2(r1, p2, r2, wrap=w)

1715

1716 if area: # check overlap

1717 if c1 is c2: # abutting

1718 c = c1

1719 else: # nearest point on radical

1720 c = p3.nearestOn(c1, c2, within=True, wrap=w)

1721 d = r3 - p3.distanceTo(c, radius=radius, wrap=w)

1722 if d > eps: # sufficient overlap

1723 t.append((d, c))

1724 m = max(m, d)

1725

1726 else: # check intersection

1727 for c in ((c1,) if c1 is c2 else (c1, c2)):

1728 d = fabs(r3 - p3.distanceTo(c, radius=radius, wrap=w))

1729 if d < eps: # below margin

1730 t.append((d, c))

1731 m = min(m, d)

1732

1733 except IntersectionError as x:

1734 if _concentric_ in str(x): # XXX ConcentricError?

1735 pc += 1

1736

1737 p1, r1, p2, r2, p3, r3 = p2, r2, p3, r3, p1, r1 # rotate

1738

1739 if t: # get min, max, points and count ...

1740 t = tuple(sorted(t))

1741 n = len(t), # as 1-tuple

1742 # ... or for a single trilaterated result,

1743 # min *is* max, min- *is* maxPoint and n=1, 2 or 3

1744 return Trilaterate5Tuple(t[0] + t[-1] + n) # *(t[0] + ...)

1745

1746 elif area and pc == 3: # all pairwise concentric ...

1747 r, p = min((r1, p1), (r2, p2), (r3, p3))

1748 m = max(r1, r2, r3)

1749 # ... return "smallest" point twice, the smallest

1750 # and largest distance and n=0 for concentric

1751 return Trilaterate5Tuple(float(r), p, float(m), p, 0)

1752

1753 n, f = (_overlap_, max) if area else (_intersection_, min)

1754 t = _COMMASPACE_(_no_(n), '%s %.3g' % (f.__name__, m))

1755 raise IntersectionError(area=area, eps=eps, wrap=wrap, txt=t)

1756

1757

1758__all__ += _ALL_DOCS(LatLonBase)

1759

1760# **) MIT License

1761#

1762# Copyright (C) 2016-2024 -- mrJean1 at Gmail -- All Rights Reserved.

1763#

1764# Permission is hereby granted, free of charge, to any person obtaining a

1765# copy of this software and associated documentation files (the "Software"),

1766# to deal in the Software without restriction, including without limitation

1767# the rights to use, copy, modify, merge, publish, distribute, sublicense,

1768# and/or sell copies of the Software, and to permit persons to whom the

1769# Software is furnished to do so, subject to the following conditions:

1770#

1771# The above copyright notice and this permission notice shall be included

1772# in all copies or substantial portions of the Software.

1773#

1774# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS

1775# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,

1776# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL

1777# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR

1778# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,

1779# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR

1780# OTHER DEALINGS IN THE SOFTWARE.