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

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_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.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

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 _isDegrees, _isRadius, Distance_, Lat, Lon, \

46 Height, Radius, Radius_, 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__ = '24.01.18'

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 if name:

94 self.name = name

95

96 if lon is None:

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

98 elif wrap:

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

100 else:

101 lat = latlonh

102

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

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

105 if height: # elevation

106 self._height = Height(height)

107 if datum is not None:

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

109

110 def __eq__(self, other):

111 return self.isequalTo(other)

112

113 def __ne__(self, other):

114 return not self.isequalTo(other)

115

116 def __str__(self):

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

118

119 def antipode(self, height=None):

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

121 this point.

122

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

124 this point's height otherwise.

125

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

127 '''

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

129 h = self._heigHt(height)

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

131

132 @deprecated_method

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

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

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

136

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

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

139 bounding box centered at this location.

140

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

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

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

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

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

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

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

148 overriding the point's height.

149

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

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

152

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

154 '''

155 w = Scalar_(wide=wide) * _0_5

156 t = Scalar_(tall=tall) * _0_5

157 if radius is not None:

158 r = Radius_(radius)

159 c = cos(self.phi)

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

161 t = degrees(t / r)

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

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

164

165 h = self._heigHt(height)

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

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

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

169

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

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

172 this and an other point.

173

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

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

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

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

178 point (C{bool}).

179

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

181

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

183 '''

184 def _v3d(ll):

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

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

187

188 p = self.others(other)

189 if wrap:

190 p = _Wrap.point(p)

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

192

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

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

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

196

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

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

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

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

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

202

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

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

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

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

207

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

209 than version 1.10.

210

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

212 a trilateration or C{numpy} issue.

213

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

215

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

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

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

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

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

221 height)} representing the differences between both results from

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

223

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

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

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

227 '''

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

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

230 datum=self.datum) # PYCHOK unpack

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

232

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

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

235 this and two other points.

236

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

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

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

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

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

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

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

244

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

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

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

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

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

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

251

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

253 version 1.10.

254

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

256 incompatible C{Ecef} classes or a trilateration

257 or C{numpy} issue.

258

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

260

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

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

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

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

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

266 height)} representing the difference between both results from

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

268

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

270 '''

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

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

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

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

275

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

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

278

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

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

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

282

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

284 an instance of this (sub-)class.

285

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

287 version 1.10.

288

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

290

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

292

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

294

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

296 '''

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

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

299 for i, p in enumerate(ps):

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

301

302 C = self._toCartesianEcef

303 c = C(point=self)

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

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

306 return t.dup(center=c)

307

308 @property

309 def clipid(self):

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

311 '''

312 return self._clipid

313

314 @clipid.setter # PYCHOK setter!

315 def clipid(self, clipid):

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

317 '''

318 self._clipid = int(clipid)

319

320 @deprecated_method

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

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

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

324

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

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

327 this and an other point.

328

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

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

331 larger distances.

332

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

334 @kwarg adjust_wrap: Optional keyword arguments for function

335 L{pygeodesy.compassAngle}.

336

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

338

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

340

341 @note: Courtesy of Martin Schultz.

342

343 @see: U{Local, flat earth approximation

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

345 '''

346 p = self.others(other)

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

348

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

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

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

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

353

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

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

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

357

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

359 point's datum ellipsoid).

360

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

362

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

364 L{cosineForsytheAndoyerLambertTo}, L{cosineLawTo},

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

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

367 L{thomasTo} and L{vincentysTo}.

368 '''

369 return self._distanceTo_(self._formy.cosineAndoyerLambert_, other, wrap=wrap)

370

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

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

373 the U{Forsythe-Andoyer-Lambert correction

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

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

376 formula.

377

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

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

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

381

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

383 this point's datum ellipsoid).

384

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

386

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

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

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

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

391 '''

392 return self._distanceTo_(self._formy.cosineForsytheAndoyerLambert_, other, wrap=wrap)

393

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

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

396 U{spherical Law of Cosines

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

398 formula.

399

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

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

402 for the mean radius of this point's datum

403 ellipsoid.

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

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

406

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

408

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

410

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

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

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

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

415 '''

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

417

418 @property_RO

419 def datum(self): # PYCHOK no cover

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

421 notOverloaded(self)

422

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

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

425

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

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

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

429 or C{None}.

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

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

432

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

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

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

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

437 is un-/specified.

438

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

440 '''

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

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

443

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

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

446 '''

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

448 if r is None:

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

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

451

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

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

454 '''

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

456 D = self.datum

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

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

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

460

461 @property_RO

462 def Ecef(self):

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

464 '''

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

466 return E

467

468 @Property_RO

469 def _Ecef_forward(self):

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

471 '''

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

473

474 @Property_RO

475 def _ecef9(self):

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

477 '''

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

479

480 @property_RO

481 def ellipsoidalLatLon(self):

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

483 '''

484 return False

485

486 @deprecated_method

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

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

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

490

491 @deprecated_method

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

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

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

495

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

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

498 using the U{Equirectangular Approximation / Projection

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

500

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

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

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

504

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

506 @kwarg radius_adjust_limit_wrap: Optional keyword arguments

507 for function L{pygeodesy.equirectangular},

508 overriding the default mean C{radius} of this

509 point's datum ellipsoid.

510

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

512

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

514

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

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

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

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

519 '''

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

521

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

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

524 an other point.

525

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

527

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

529 @kwarg radius_adjust_wrap: Optional keyword arguments for function

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

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

532

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

534

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

536

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

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

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

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

541 '''

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

543

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

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

546 U{ellipsoidal Earth to plane projection

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

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

549

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

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

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

553 datum ellipsoid.

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

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

556

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

558

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

560

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

562

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

564 L{cosineAndoyerLambertTo}, L{cosineForsytheAndoyerLambertTo},

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

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

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

568 '''

569 return self._distanceTo_(self._formy.flatLocal_, other, wrap=wrap, radius=

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

571

572 hubenyTo = flatLocalTo # for Karl Hubeny

573

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

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

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

577 Geographical_distance#Polar_coordinate_flat-Earth_formula>} formula.

578

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

580 @kwarg radius_wrap: Optional keyword arguments for function

581 L{pygeodesy.flatPolar}, overriding the

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

583 datum ellipsoid.

584

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

586

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

588

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

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

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

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

593 '''

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

595

596 @property_RO

597 def _formy(self):

598 '''(INTERNAL) Import module C{distance.formy}, I{once} and I{lazily}

599 to avoid circular imports.

600 '''

601 LatLonBase._formy = f = _MODS.formy # overwrite property_RO

602 return f

603

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

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

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

607

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

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

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

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

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

613 ellipsoid.

614

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

616 this C{pov}.

617

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

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

620 the ellipsoid.

621

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

623

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

625 '''

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

627

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

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

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

631 formula.

632

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

634 @kwarg radius_wrap: Optional keyword arguments for function

635 L{pygeodesy.haversine}, overriding the

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

637 datum ellipsoid.

638

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

640

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

642

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

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

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

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

647 '''

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

649

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

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

652

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

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

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

656

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

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

659 '''

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

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

662

663 @Property

664 def height(self):

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

666 '''

667 return self._height

668

669 @height.setter # PYCHOK setter!

670 def height(self, height):

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

672

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

674

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

676 '''

677 h = Height(height)

678 if self._height != h:

679 _update_all(self)

680 self._height = h

681

682 def _heigHt(self, height):

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

684 '''

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

686

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

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

689 this datum's ellipsoid surface.

690

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

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

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

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

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

696 ellipsoid's surface, otherwise the intersection of the

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

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

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

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

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

702

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

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

705

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

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

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

709

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

711

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

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

714

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

716 '''

717 c = self.toCartesian()

718 if LatLon is None:

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

720 else:

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

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

723 if r.datum != c.datum:

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

725 return r

726

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

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

729

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

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

732

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

734 '''

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

736

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

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

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

740

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

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

743 line and return the 2 intercant points accordingly.

744 '''

745 if height is None:

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

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

748 if h != hp:

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

750 if s: # fmath.fidw?

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

752 hq += s * Q.s12

753 hp += s * P.s12

754 else:

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

756 else:

757 hp = hq = Height(height)

758

759# n = self.name or unused.__name__

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

761 p._iteration = P.iteration

762 if P is not Q:

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

764 q._iteration = Q.iteration

765 return p, q

766

767 @deprecated_method

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

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

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

771

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

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

774 on diametrically opposite sides of the earth.

775

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

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

778

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

780 tolerance, C{False} otherwise.

781 '''

782 p = self.others(other)

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

784

785 @Property_RO

786 def isEllipsoidal(self):

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

788 '''

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

790

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

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

793

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

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

796

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

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

799

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

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

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

803

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

805

806 @see: Method L{isequalTo3}.

807 '''

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

809

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

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

812

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

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

815

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

817 height, C{False} otherwise.

818

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

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

821 C{class} or C{type}.

822

823 @see: Method L{isequalTo}.

824 '''

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

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

827

828 @Property_RO

829 def isnormal(self):

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

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

832

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

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

835 '''

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

837

838 @Property_RO

839 def isSpherical(self):

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

841 '''

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

843

844 @Property_RO

845 def lam(self):

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

847 '''

848 return radians(self.lon)

849

850 @Property

851 def lat(self):

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

853 '''

854 return self._lat

855

856 @lat.setter # PYCHOK setter!

857 def lat(self, lat):

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

859

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

861 '''

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

863 if self._lat != lat:

864 _update_all(self)

865 self._lat = lat

866

867 @Property

868 def latlon(self):

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

870 '''

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

872

873 @latlon.setter # PYCHOK setter!

874 def latlon(self, latlonh):

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

876 (2- or 3-tuple or comma- or space-separated C{str}

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

878

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

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

881

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

883

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

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

886 '''

887 if isstr(latlonh):

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

889 else:

890 _xinstanceof(list, tuple, latlonh=latlonh)

891 if len(latlonh) == 3:

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

893 elif len(latlonh) != 2:

894 raise _ValueError(latlonh=latlonh)

895 else:

896 h = self.height

897

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

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

900 _update_all(self)

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

902

903 def latlon2(self, ndigits=0):

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

905

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

907

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

909 and rounded away from zero.

910

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

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

913 '''

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

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

916

917 @deprecated_method

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

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

920 return self.latlon2(ndigits=ndigits)

921

922 latlon2round = latlon_ # PYCHOK no cover

923

924 @Property

925 def latlonheight(self):

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

927 '''

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

929

930 @latlonheight.setter # PYCHOK setter!

931 def latlonheight(self, latlonh):

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

933 (2- or 3-tuple or comma- or space-separated C{str} of

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

935

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

937 '''

938 self.latlon = latlonh

939

940 @Property

941 def lon(self):

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

943 '''

944 return self._lon

945

946 @lon.setter # PYCHOK setter!

947 def lon(self, lon):

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

949

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

951 '''

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

953 if self._lon != lon:

954 _update_all(self)

955 self._lon = lon

956

957 @property_RO

958 def _ltp(self):

959 '''(INTERNAL) Get the C{.ltp} module, I{once}.

960 '''

961 LatLonBase._ltp = m = _MODS.ltp # overwrite property_RO

962 return m

963

964 @Property_RO

965 def _Ltp(self):

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

967 '''

968 return self._ltp.Ltp(self, ecef=self.Ecef(self.datum), name=self.name)

969

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

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

972

973 Points are converted to and distances are computed in

974 I{geocentric}, cartesian space.

975

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

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

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

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

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

981 account for distances.

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

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

984

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

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

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

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

989 units as the cartesian axes.

990

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

992

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

994 C{Ecef} invalid.

995

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

997

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

999 '''

1000 def _cs(Ps, h, w, C):

1001 p = None # not used

1002 for i, q in Ps.enumerate():

1003 if w and i:

1004 q = _unrollon(p, q)

1005 yield C(height=h, i=i, up=3, points=q)

1006 p = q

1007

1008 C = self._toCartesianEcef # to verify datum and Ecef

1009 Ps = self.PointsIter(points, wrap=wrap)

1010

1011 c = C(height=height, this=self) # this Cartesian

1012 t = nearestOn6(c, _cs(Ps, height, wrap, C), closed=closed)

1013 c, s, e = t.closest, t.start, t.end

1014

1015 kwds = _xkwds_not(None, LatLon=self.classof, # this LatLon

1016 height=height)

1017 _r = self.Ecef(self.datum).reverse

1018 p = _r(c).toLatLon(**kwds)

1019 s = _r(s).toLatLon(**kwds) if s is not c else p

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

1021 return t.dup(closest=p, start=s, end=e)

1022

1023 def nearestTo(self, *args, **kwds): # PYCHOK no cover

1024 '''B{Not implemented}, throws a C{NotImplementedError} always.'''

1025 notImplemented(self, *args, **kwds)

1026

1027 def normal(self):

1028 '''Normalize this point I{in-place} to C{abs(lat) <= 90} and

1029 C{abs(lon) <= 180}.

1030

1031 @return: C{True} if this point was I{normal}, C{False} if it

1032 wasn't (but is now).

1033

1034 @see: Property L{isnormal} and method L{toNormal}.

1035 '''

1036 n = self.isnormal

1037 if not n:

1038 self.latlon = self._formy.normal(*self.latlon)

1039 return n

1040

1041 @property_RO

1042 def _N_vector(self):

1043 '''(INTERNAL) Get the C{Nvector} (C{nvectorBase._N_vector_})

1044 '''

1045 x, y, z = self._n_xyz3

1046 return _MODS.nvectorBase._N_vector_(x, y, z, h=self.height, name=self.name)

1047

1048 @Property_RO

1049 def _n_xyz3(self):

1050 '''(INTERNAL) Get the n-vector components as L{Vector3Tuple}.

1051 '''

1052 return self._formy.philam2n_xyz(self.phi, self.lam, name=self.name)

1053

1054 @Property_RO

1055 def phi(self):

1056 '''Get the latitude (B{C{radians}}).

1057 '''

1058 return radians(self.lat)

1059

1060 @Property_RO

1061 def philam(self):

1062 '''Get the lat- and longitude (L{PhiLam2Tuple}C{(phi, lam)}).

1063 '''

1064 return PhiLam2Tuple(self.phi, self.lam, name=self.name)

1065

1066 def philam2(self, ndigits=0):

1067 '''Return this point's lat- and longitude in C{radians}, rounded.

1068

1069 @kwarg ndigits: Number of (decimal) digits (C{int}).

1070

1071 @return: A L{PhiLam2Tuple}C{(phi, lam)}, both C{float}

1072 and rounded away from zero.

1073

1074 @note: The C{round}ed values are always C{float}, also

1075 if B{C{ndigits}} is omitted.

1076 '''

1077 return PhiLam2Tuple(round(self.phi, ndigits),

1078 round(self.lam, ndigits), name=self.name)

1079

1080 @Property_RO

1081 def philamheight(self):

1082 '''Get the lat-, longitude in C{radians} and height (L{PhiLam3Tuple}C{(phi, lam, height)}).

1083 '''

1084 return self.philam.to3Tuple(self.height)

1085

1086 @deprecated_method

1087 def points(self, points, closed=True): # PYCHOK no cover

1088 '''DEPRECATED, use method L{points2}.'''

1089 return self.points2(points, closed=closed)

1090

1091 def points2(self, points, closed=True):

1092 '''Check a path or polygon represented by points.

1093

1094 @arg points: The path or polygon points (C{LatLon}[])

1095 @kwarg closed: Optionally, consider the polygon closed,

1096 ignoring any duplicate or closing final

1097 B{C{points}} (C{bool}).

1098

1099 @return: A L{Points2Tuple}C{(number, points)}, an C{int}

1100 and C{list} or C{tuple}.

1101

1102 @raise PointsError: Insufficient number of B{C{points}}.

1103

1104 @raise TypeError: Some B{C{points}} are not C{LatLon}.

1105 '''

1106 return _MODS.iters.points2(points, closed=closed, base=self)

1107

1108 def PointsIter(self, points, loop=0, dedup=False, wrap=False):

1109 '''Return a C{PointsIter} iterator.

1110

1111 @arg points: The path or polygon points (C{LatLon}[])

1112 @kwarg loop: Number of loop-back points (non-negative C{int}).

1113 @kwarg dedup: Skip duplicate points (C{bool}).

1114 @kwarg wrap: If C{True}, wrap or I{normalize} the

1115 enum-/iterated B{C{points}} (C{bool}).

1116

1117 @return: A new C{PointsIter} iterator.

1118

1119 @raise PointsError: Insufficient number of B{C{points}}.

1120 '''

1121 return PointsIter(points, base=self, loop=loop, dedup=dedup, wrap=wrap)

1122

1123 def radii11(self, point2, point3, wrap=False):

1124 '''Return the radii of the C{Circum-}, C{In-}, I{Soddy} and C{Tangent}

1125 circles of a (planar) triangle formed by this and two other points.

1126

1127 @arg point2: Second point (C{LatLon}).

1128 @arg point3: Third point (C{LatLon}).

1129 @kwarg wrap: If C{True}, wrap or I{normalize} B{C{point2}} and

1130 B{C{point3}} (C{bool}).

1131

1132 @return: L{Radii11Tuple}C{(rA, rB, rC, cR, rIn, riS, roS, a, b, c, s)}.

1133

1134 @raise IntersectionError: Near-coincident or -colinear points.

1135

1136 @raise TypeError: Invalid B{C{point2}} or B{C{point3}}.

1137

1138 @see: Function L{pygeodesy.radii11}, U{Incircle

1139 <https://MathWorld.Wolfram.com/Incircle.html>}, U{Soddy Circles

1140 <https://MathWorld.Wolfram.com/SoddyCircles.html>} and U{Tangent

1141 Circles<https://MathWorld.Wolfram.com/TangentCircles.html>}.

1142 '''

1143 with _toCartesian3(self, point2, point3, wrap) as cs:

1144 return _radii11ABC(*cs, useZ=True)[0]

1145

1146 def _rhumb3(self, exact, radius): # != .sphericalBase._rhumbs3

1147 '''(INTERNAL) Get the C{rhumb} for this point's datum or for

1148 the B{C{radius}}' earth model iff non-C{None}.

1149 '''

1150 try:

1151 d = self._rhumb3dict

1152 t = d[(exact, radius)]

1153 except KeyError:

1154 D = self.datum if radius is None else \

1155 _spherical_datum(radius) # ellipsoidal OK

1156 try:

1157 r = D.ellipsoid.rhumb_(exact=exact) # or D.isSpherical

1158 except AttributeError as x:

1159 raise _AttributeError(datum=D, radius=radius, cause=x)

1160 t = r, D, _MODS.karney.Caps

1161 while d:

1162 d.popitem()

1163 d[(exact, radius)] = t # cache 3-tuple

1164 return t

1165

1166 @Property_RO

1167 def _rhumb3dict(self): # in rhumbIntersecant2 below

1168 return {} # single-item cache

1169

1170 def rhumbAzimuthTo(self, other, exact=False, radius=None, wrap=False, b360=False):

1171 '''Return the azimuth (bearing) of a rhumb line (loxodrome) between this

1172 and an other (ellipsoidal) point.

1173

1174 @arg other: The other point (C{LatLon}).

1175 @kwarg exact: Exact C{Rhumb...} to use (C{bool} or C{Rhumb...}), see

1176 method L{Ellipsoid.rhumb_}.

1177 @kwarg radius: Optional earth radius (C{meter}) or earth model (L{Datum},

1178 L{Ellipsoid}, L{Ellipsoid2} or L{a_f2Tuple}), overriding

1179 this point's datum.

1180 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the B{C{other}}

1181 point (C{bool}).

1182 @kwarg b360: If C{True}, return the azimuth in the bearing range.

1183

1184 @return: Rhumb azimuth (compass C{degrees180} or C{degrees360}).

1185

1186 @raise TypeError: The B{C{other}} point is incompatible or B{C{radius}}

1187 is invalid.

1188 '''

1189 r, _, Cs = self._rhumb3(exact, radius)

1190 z = r._Inverse(self, other, wrap, outmask=Cs.AZIMUTH).azi12

1191 return _umod_360(z + _360_0) if b360 else z

1192

1193 def rhumbDestination(self, distance, azimuth, exact=False, radius=None, height=None):

1194 '''Return the destination point having travelled the given distance from

1195 this point along a rhumb line (loxodrome) of the given azimuth.

1196

1197 @arg distance: Distance travelled (C{meter}, same units as this point's

1198 datum (ellipsoid) axes or B{C{radius}}, may be negative.

1199 @arg azimuth: Azimuth (bearing) of the rhumb line (compass C{degrees}).

1200 @kwarg exact: Exact C{Rhumb...} to use (C{bool} or C{Rhumb...}), see

1201 method L{Ellipsoid.rhumb_}.

1202 @kwarg radius: Optional earth radius (C{meter}) or earth model (L{Datum},

1203 L{Ellipsoid}, L{Ellipsoid2} or L{a_f2Tuple}), overriding

1204 this point's datum.

1205 @kwarg height: Optional height, overriding the default height (C{meter}).

1206

1207 @return: The destination point (ellipsoidal C{LatLon}).

1208

1209 @raise TypeError: Invalid B{C{radius}}.

1210

1211 @raise ValueError: Invalid B{C{distance}}, B{C{azimuth}}, B{C{radius}}

1212 or B{C{height}}.

1213 '''

1214 r, D, _ = self._rhumb3(exact, radius)

1215 d = r._Direct(self, azimuth, distance)

1216 h = self._heigHt(height)

1217 return self.classof(d.lat2, d.lon2, datum=D, height=h)

1218

1219 def rhumbDistanceTo(self, other, exact=False, radius=None, wrap=False):

1220 '''Return the distance from this to an other point along a rhumb line

1221 (loxodrome).

1222

1223 @arg other: The other point (C{LatLon}).

1224 @kwarg exact: Exact C{Rhumb...} to use (C{bool} or C{Rhumb...}), see

1225 method L{Ellipsoid.rhumb_}.

1226 @kwarg radius: Optional earth radius (C{meter}) or earth model (L{Datum},

1227 L{Ellipsoid}, L{Ellipsoid2} or L{a_f2Tuple}), overriding

1228 this point's datum.

1229 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the B{C{other}}

1230 point (C{bool}).

1231

1232 @return: Distance (C{meter}, the same units as this point's datum

1233 (ellipsoid) axes or B{C{radius}}.

1234

1235 @raise TypeError: The B{C{other}} point is incompatible or B{C{radius}}

1236 is invalid.

1237

1238 @raise ValueError: Invalid B{C{radius}}.

1239 '''

1240 r, _, Cs = self._rhumb3(exact, radius)

1241 return r._Inverse(self, other, wrap, outmask=Cs.DISTANCE).s12

1242

1243 def rhumbIntersecant2(self, circle, point, other, height=None,

1244 **exact_radius_wrap_eps_tol):

1245 '''Compute the intersections of a circle and a rhumb line given as two

1246 points or as a point and azimuth.

1247

1248 @arg circle: Radius of the circle centered at this location (C{meter}),

1249 or a point on the circle (this C{LatLon}).

1250 @arg point: The start point of the rhumb line (this C{LatLon}).

1251 @arg other: An other point I{on} (this C{LatLon}) or the azimuth I{of}

1252 (compass C{degrees}) the rhumb line.

1253 @kwarg height: Optional height for the intersection points (C{meter},

1254 conventionally) or C{None} for interpolated heights.

1255 @kwarg exact_radius_wrap_eps_tol: Optional keyword arguments, see

1256 methods L{rhumbLine} and L{RhumbLineAux.Intersecant2}

1257 or L{RhumbLine.Intersecant2}.

1258

1259 @return: 2-Tuple of the intersection points (representing a chord),

1260 each an instance of this class. Both points are the same

1261 instance if the rhumb line is tangent to the circle.

1262

1263 @raise IntersectionError: The circle and rhumb line do not intersect.

1264

1265 @raise TypeError: If B{C{point}} is not this C{LatLon} or B{C{circle}}

1266 or B{C{other}} invalid.

1267

1268 @raise ValueError: Invalid B{C{circle}}, B{C{other}}, B{C{height}}

1269 or B{C{exact_radius_wrap}}.

1270

1271 @see: Methods L{RhumbLineAux.Intersecant2} and L{RhumbLine.Intersecant2}.

1272 '''

1273 def _kwds3(eps=EPS, tol=_TOL, wrap=False, **kwds):

1274 return kwds, wrap, dict(eps=eps, tol=tol)

1275

1276 exact_radius, w, eps_tol = _kwds3(**exact_radius_wrap_eps_tol)

1277

1278 p = _unrollon(self, self.others(point=point), wrap=w)

1279 try:

1280 r = Radius_(circle=circle) if _isRadius(circle) else \

1281 self.rhumbDistanceTo(self.others(circle=circle), wrap=w, **exact_radius)

1282 rl = p.rhumbLine(other, wrap=w, **exact_radius)

1283 P, Q = rl.Intersecant2(self.lat, self.lon, r, **eps_tol)

1284

1285 return self._intersecend2(p, other, w, height, rl.rhumb, P, Q,

1286 self.rhumbIntersecant2)

1287

1288 except (TypeError, ValueError) as x:

1289 raise _xError(x, center=self, circle=circle, point=point, other=other,

1290 **exact_radius_wrap_eps_tol)

1291

1292 def rhumbLine(self, other, exact=False, radius=None, wrap=False, **name_caps):

1293 '''Get a rhumb line through this point at a given azimuth or through

1294 this and an other point.

1295

1296 @arg other: The azimuth I{of} (compass C{degrees}) or an other point

1297 I{on} (this C{LatLon}) the rhumb line.

1298 @kwarg exact: Exact C{Rhumb...} to use (C{bool} or C{Rhumb...}), see

1299 method L{Ellipsoid.rhumb_}.

1300 @kwarg radius: Optional earth radius (C{meter}) or earth model

1301 (L{Datum}, L{Ellipsoid}, L{Ellipsoid2} or L{a_f2Tuple}),

1302 overriding this point's datum.

1303 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the B{C{other}}

1304 point (C{bool}).

1305 @kwarg name_caps: Optional C{B{name}=str} and C{caps}, see L{RhumbLine}

1306 or L{RhumbLineAux} C{B{caps}}.

1307

1308 @return: A C{RhumbLine} instance.

1309

1310 @raise TypeError: Invalid B{C{radius}} or B{C{other}} not C{scalar} nor

1311 this C{LatLon}.

1312

1313 @see: Modules L{rhumb.aux_} and L{rhumb.ekx}.

1314 '''

1315 r, _, Cs = self._rhumb3(exact, radius)

1316 kwds = _xkwds(name_caps, name=self.name, caps=Cs.LINE_OFF)

1317 rl = r._DirectLine( self, other, **kwds) if _isDegrees(other) else \

1318 r._InverseLine(self, self.others(other), wrap, **kwds)

1319 return rl

1320

1321 def rhumbMidpointTo(self, other, exact=False, radius=None,

1322 height=None, fraction=_0_5, wrap=False):

1323 '''Return the (loxodromic) midpoint on the rhumb line between this and

1324 an other point.

1325

1326 @arg other: The other point (this C{LatLon}).

1327 @kwarg exact: Exact C{Rhumb...} to use (C{bool} or C{Rhumb...}), see

1328 method L{Ellipsoid.rhumb_}.

1329 @kwarg radius: Optional earth radius (C{meter}) or earth model (L{Datum},

1330 L{Ellipsoid}, L{Ellipsoid2} or L{a_f2Tuple}), overriding

1331 this point's datum.

1332 @kwarg height: Optional height, overriding the mean height (C{meter}).

1333 @kwarg fraction: Midpoint location from this point (C{scalar}), 0 for this,

1334 1 for the B{C{other}}, 0.5 for halfway between this and

1335 the B{C{other}} point, may be negative or greater than 1.

1336 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the B{C{other}}

1337 point (C{bool}).

1338

1339 @return: The midpoint at the given B{C{fraction}} along the rhumb line

1340 (this C{LatLon}).

1341

1342 @raise TypeError: The B{C{other}} point is incompatible or B{C{radius}}

1343 is invalid.

1344

1345 @raise ValueError: Invalid B{C{height}} or B{C{fraction}}.

1346 '''

1347 r, D, _ = self._rhumb3(exact, radius)

1348 f = Scalar(fraction=fraction)

1349 d = r._Inverse(self, self.others(other), wrap) # C.AZIMUTH_DISTANCE

1350 d = r._Direct( self, d.azi12, d.s12 * f)

1351 h = self._havg(other, f=f, h=height)

1352 return self.classof(d.lat2, d.lon2, datum=D, height=h)

1353

1354 @property_RO

1355 def sphericalLatLon(self):

1356 '''Get the C{LatLon type} iff spherical, overloaded in L{LatLonSphericalBase}.

1357 '''

1358 return False

1359

1360 def thomasTo(self, other, wrap=False):

1361 '''Compute the distance between this and an other point using

1362 U{Thomas'<https://apps.DTIC.mil/dtic/tr/fulltext/u2/703541.pdf>}

1363 formula.

1364

1365 @arg other: The other point (C{LatLon}).

1366 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll

1367 the B{C{other}} point (C{bool}).

1368

1369 @return: Distance (C{meter}, same units as the axes of

1370 this point's datum ellipsoid).

1371

1372 @raise TypeError: The B{C{other}} point is not C{LatLon}.

1373

1374 @see: Function L{pygeodesy.thomas} and methods L{cosineAndoyerLambertTo},

1375 L{cosineForsytheAndoyerLambertTo}, L{cosineLawTo}, C{distanceTo*},

1376 L{equirectangularTo}, L{euclideanTo}, L{flatLocalTo}/L{hubenyTo},

1377 L{flatPolarTo}, L{haversineTo} and L{vincentysTo}.

1378 '''

1379 return self._distanceTo_(self._formy.thomas_, other, wrap=wrap)

1380

1381 @deprecated_method

1382 def to2ab(self): # PYCHOK no cover

1383 '''DEPRECATED, use property L{philam}.'''

1384 return self.philam

1385

1386 def toCartesian(self, height=None, Cartesian=None, **Cartesian_kwds):

1387 '''Convert this point to cartesian, I{geocentric} coordinates,

1388 also known as I{Earth-Centered, Earth-Fixed} (ECEF).

1389

1390 @kwarg height: Optional height, overriding this point's height

1391 (C{meter}, conventionally).

1392 @kwarg Cartesian: Optional class to return the geocentric

1393 coordinates (C{Cartesian}) or C{None}.

1394 @kwarg Cartesian_kwds: Optional, additional B{C{Cartesian}}

1395 keyword arguments, ignored if

1396 C{B{Cartesian} is None}.

1397

1398 @return: A B{C{Cartesian}} or if B{C{Cartesian}} is C{None},

1399 an L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M,

1400 datum)} with C{C=0} and C{M} if available.

1401

1402 @raise TypeError: Invalid B{C{Cartesian}} or B{C{Cartesian_kwds}}.

1403

1404 @see: Methods C{toNvector}, C{toVector} and C{toVector3d}.

1405 '''

1406 r = self._ecef9 if height is None else self.toEcef(height=height)

1407 if Cartesian is not None: # class or .classof

1408 r = Cartesian(r, **_xkwds(Cartesian_kwds, name=self.name))

1409 _xdatum(r.datum, self.datum)

1410 return r

1411

1412 def _toCartesianEcef(self, height=None, i=None, up=2, **name_point):

1413 '''(INTERNAL) Convert to cartesian and check Ecef's before and after.

1414 '''

1415 p = self.others(up=up, **name_point)

1416 c = p.toCartesian(height=height)

1417 E = self.Ecef

1418 if E:

1419 for p in (p, c):

1420 e = _xattr(p, Ecef=None)

1421 if e not in (None, E): # PYCHOK no cover

1422 n, _ = name_point.popitem()

1423 if i is not None:

1424 n = Fmt.SQUARE(n, i)

1425 raise _ValueError(n, e, txt=_incompatible(E.__name__))

1426 return c

1427

1428 def toDatum(self, datum2, height=None, name=NN):

1429 '''I{Must be overloaded}.'''

1430 notOverloaded(self, datum2, height=height, name=name)

1431

1432 def toEcef(self, height=None, M=False):

1433 '''Convert this point to I{geocentric} coordinates, also known as

1434 I{Earth-Centered, Earth-Fixed} (U{ECEF<https://WikiPedia.org/wiki/ECEF>}).

1435

1436 @kwarg height: Optional height, overriding this point's height

1437 (C{meter}, conventionally).

1438 @kwarg M: Optionally, include the rotation L{EcefMatrix} (C{bool}).

1439

1440 @return: An L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M, datum)}

1441 with C{C=0} and C{M} if available.

1442

1443 @raise EcefError: A C{.datum} or an ECEF issue.

1444 '''

1445 return self._ecef9 if height in (None, self.height) else \

1446 self._Ecef_forward(self.lat, self.lon, height=height, M=M)

1447

1448 @deprecated_method

1449 def to3llh(self, height=None): # PYCHOK no cover

1450 '''DEPRECATED, use property L{latlonheight} or C{latlon.to3Tuple(B{height})}.'''

1451 return self.latlonheight if height in (None, self.height) else \

1452 self.latlon.to3Tuple(height)

1453

1454 def toLocal(self, Xyz=None, ltp=None, **Xyz_kwds):

1455 '''Convert this I{geodetic} point to I{local} C{X}, C{Y} and C{Z}.

1456

1457 @kwarg Xyz: Optional class to return C{X}, C{Y} and C{Z}

1458 (L{XyzLocal}, L{Enu}, L{Ned}) or C{None}.

1459 @kwarg ltp: The I{local tangent plane} (LTP) to use,

1460 overriding this point's LTP (L{Ltp}).

1461 @kwarg Xyz_kwds: Optional, additional B{C{Xyz}} keyword

1462 arguments, ignored if C{B{Xyz} is None}.

1463

1464 @return: An B{C{Xyz}} instance or if C{B{Xyz} is None},

1465 a L{Local9Tuple}C{(x, y, z, lat, lon, height,

1466 ltp, ecef, M)} with C{M=None}, always.

1467

1468 @raise TypeError: Invalid B{C{ltp}}.

1469 '''

1470 p = self._ltp._xLtp(ltp, self._Ltp)

1471 return p._ecef2local(self._ecef9, Xyz, Xyz_kwds)

1472

1473 def toLtp(self, Ecef=None):

1474 '''Return the I{local tangent plane} (LTP) for this point.

1475

1476 @kwarg Ecef: Optional ECEF I{class} (L{EcefKarney}, ...

1477 L{EcefYou}), overriding this point's C{Ecef}.

1478 '''

1479 return self._Ltp if Ecef in (None, self.Ecef) else self._ltp.Ltp(

1480 self, ecef=Ecef(self.datum), name=self.name)

1481

1482 def toNormal(self, deep=False, name=NN):

1483 '''Get this point I{normalized} to C{abs(lat) <= 90}

1484 and C{abs(lon) <= 180}.

1485

1486 @kwarg deep: If C{True} make a deep, otherwise a

1487 shallow copy (C{bool}).

1488 @kwarg name: Optional name of the copy (C{str}).

1489

1490 @return: A copy of this point, I{normalized} and

1491 optionally renamed (C{LatLon}).

1492

1493 @see: Property L{isnormal}, method L{normal} and function

1494 L{pygeodesy.normal}.

1495 '''

1496 ll = self.copy(deep=deep)

1497 _ = ll.normal()

1498 if name:

1499 ll.rename(name)

1500 return ll

1501

1502 def toNvector(self, h=None, Nvector=None, **Nvector_kwds):

1503 '''Convert this point to C{n-vector} (normal to the earth's surface)

1504 components, I{including height}.

1505

1506 @kwarg h: Optional height, overriding this point's height (C{meter}).

1507 @kwarg Nvector: Optional class to return the C{n-vector} components

1508 (C{Nvector}) or C{None}.

1509 @kwarg Nvector_kwds: Optional, additional B{C{Nvector}} keyword

1510 arguments, ignored if C{B{Nvector} is None}.

1511

1512 @return: An B{C{Nvector}} or a L{Vector4Tuple}C{(x, y, z, h)} if

1513 B{C{Nvector}} is C{None}.

1514

1515 @raise TypeError: Invalid B{C{h}}, B{C{Nvector}} or B{C{Nvector_kwds}}

1516 item.

1517

1518 @see: Methods C{toCartesian}, C{toVector} and C{toVector3d}.

1519 '''

1520 h = self._heigHt(h)

1521 if Nvector is None:

1522 r = self._n_xyz3.to4Tuple(h)

1523 else:

1524 x, y, z = self._n_xyz3

1525 r = Nvector(x, y, z, h=h, ll=self, **_xkwds(Nvector_kwds, name=self.name))

1526 return r

1527

1528 def toStr(self, form=F_DMS, joined=_COMMASPACE_, m=_m_, **prec_sep_s_D_M_S): # PYCHOK expected

1529 '''Convert this point to a "lat, lon[, +/-height]" string, formatted

1530 in the given C{B{form}at}.

1531

1532 @kwarg form: The lat-/longitude C{B{form}at} to use (C{str}), see

1533 functions L{pygeodesy.latDMS} or L{pygeodesy.lonDMS}.

1534 @kwarg joined: Separator to join the lat-, longitude and heigth

1535 strings (C{str} or C{None} or C{NN} for non-joined).

1536 @kwarg m: Optional unit of the height (C{str}), use C{None} to

1537 exclude height from the returned string.

1538 @kwarg prec_sep_s_D_M_S: Optional C{B{prec}ision}, C{B{sep}arator},

1539 B{C{s_D}}, B{C{s_M}}, B{C{s_S}} and B{C{s_DMS}} keyword

1540 arguments, see function L{pygeodesy.latDMS} or

1541 L{pygeodesy.lonDMS}.

1542

1543 @return: This point in the specified C{B{form}at}, etc. (C{str} or

1544 a 2- or 3-tuple C{(lat_str, lon_str[, height_str])} if

1545 C{B{joined}=NN} or C{B{joined}=None}).

1546

1547 @see: Function L{pygeodesy.latDMS} or L{pygeodesy.lonDMS} for more

1548 details about keyword arguments C{B{form}at}, C{B{prec}ision},

1549 C{B{sep}arator}, B{C{s_D}}, B{C{s_M}}, B{C{s_S}} and B{C{s_DMS}}.

1550 '''

1551 t = (latDMS(self.lat, form=form, **prec_sep_s_D_M_S),

1552 lonDMS(self.lon, form=form, **prec_sep_s_D_M_S))

1553 if self.height and m is not None:

1554 t += (self.heightStr(m=m),)

1555 return joined.join(t) if joined else t

1556

1557 def toVector(self, Vector=None, **Vector_kwds):

1558 '''Convert this point to a C{Vector} with the I{geocentric} C{(x,

1559 y, z)} (ECEF) coordinates, I{ignoring height}.

1560

1561 @kwarg Vector: Optional class to return the I{geocentric}

1562 components (L{Vector3d}) or C{None}.

1563 @kwarg Vector_kwds: Optional, additional B{C{Vector}} keyword

1564 arguments, ignored if C{B{Vector} is None}.

1565

1566 @return: A B{C{Vector}} or a L{Vector3Tuple}C{(x, y, z)}

1567 if B{C{Vector}} is C{None}.

1568

1569 @raise TypeError: Invalid B{C{Vector}} or B{C{Vector_kwds}} item.

1570

1571 @see: Methods C{toCartesian}, C{toNvector} and C{toVector3d}.

1572 '''

1573 return self._ecef9.toVector(Vector=Vector, **Vector_kwds)

1574

1575 def toVector3d(self, norm=True, **Vector3d_kwds):

1576 '''Convert this point to a L{Vector3d} with the I{geocentric} C{(x,

1577 y, z)} (ECEF) I{unit} coordinates, I{ignoring height}.

1578

1579 @kwarg norm: Normalize the 3-D vector (C{bool}).

1580 @kwarg Vector3d_kwds: Optional L{Vector3d} keyword arguments.

1581

1582 @return: Unit vector (L{Vector3d}).

1583

1584 @raise TypeError: Invalid B{C{Vector3d_kwds}} item.

1585

1586 @see: Methods C{toCartesian}, C{toNvector} and C{toVector}.

1587 '''

1588 r = self.toVector(Vector=Vector3d, **Vector3d_kwds)

1589 if norm:

1590 r = r.unit(ll=self)

1591 return r

1592

1593 def toWm(self, **toWm_kwds):

1594 '''Convert this point to a WM coordinate.

1595

1596 @kwarg toWm_kwds: Optional L{pygeodesy.toWm} keyword arguments.

1597

1598 @return: The WM coordinate (L{Wm}).

1599

1600 @see: Function L{pygeodesy.toWm}.

1601 '''

1602 return self._wm if not toWm_kwds else _MODS.webmercator.toWm(

1603 self, **_xkwds(toWm_kwds, name=self.name))

1604

1605 @deprecated_method

1606 def to3xyz(self): # PYCHOK no cover

1607 '''DEPRECATED, use property L{xyz} or method L{toNvector}, L{toVector},

1608 L{toVector3d} or perhaps (geocentric) L{toEcef}.'''

1609 return self.xyz # self.toVector()

1610

1611 def vincentysTo(self, other, **radius_wrap):

1612 '''Compute the distance between this and an other point using

1613 U{Vincenty's<https://WikiPedia.org/wiki/Great-circle_distance>}

1614 spherical formula.

1615

1616 @arg other: The other point (C{LatLon}).

1617 @kwarg radius_wrap: Optional keyword arguments for function

1618 L{pygeodesy.vincentys}, overriding the

1619 default mean C{radius} of this point's

1620 datum ellipsoid.

1621

1622 @return: Distance (C{meter}, same units as B{C{radius}}).

1623

1624 @raise TypeError: The B{C{other}} point is not C{LatLon}.

1625

1626 @see: Function L{pygeodesy.vincentys} and methods L{cosineAndoyerLambertTo},

1627 L{cosineForsytheAndoyerLambertTo}, L{cosineLawTo}, C{distanceTo*},

1628 L{equirectangularTo}, L{euclideanTo}, L{flatLocalTo}/L{hubenyTo},

1629 L{flatPolarTo}, L{haversineTo} and L{thomasTo}.

1630 '''

1631 return self._distanceTo(self._formy.vincentys, other, **_xkwds(radius_wrap, radius=None))

1632

1633 @Property_RO

1634 def _wm(self):

1635 '''(INTERNAL) Get this point as webmercator (L{Wm}).

1636 '''

1637 return _MODS.webmercator.toWm(self)

1638

1639 @property_RO

1640 def xyz(self):

1641 '''Get the I{geocentric} C{(x, y, z)} coordinates (L{Vector3Tuple}C{(x, y, z)})

1642 '''

1643 return self._ecef9.xyz

1644

1645 @Property_RO

1646 def xyzh(self):

1647 '''Get the I{geocentric} C{(x, y, z)} coordinates and height (L{Vector4Tuple}C{(x, y, z, h)})

1648 '''

1649 return self.xyz.to4Tuple(self.height)

1650

1651

1652 class _toCartesian3(object): # see also .formy._idllmn6, .geodesicw._wargs, .vector2d._numpy

1653 '''(INTERNAL) Wrapper to convert 2 other points.

1654 '''

1655 @contextmanager # <https://www.Python.org/dev/peps/pep-0343/> Examples

1656 def __call__(self, p, p2, p3, wrap, **kwds):

1657 try:

1658 if wrap:

1659 p2, p3 = map1(_Wrap.point, p2, p3)

1660 kwds = _xkwds(kwds, wrap=wrap)

1661 yield (p. toCartesian().copy(name=_point_), # copy to rename

1662 p._toCartesianEcef(up=4, point2=p2),

1663 p._toCartesianEcef(up=4, point3=p3))

1664 except (AssertionError, TypeError, ValueError) as x: # Exception?

1665 raise _xError(x, point=p, point2=p2, point3=p3, **kwds)

1666

1667_toCartesian3 = _toCartesian3() # PYCHOK singleton

1668

1669

1670 def _latlonheight3(latlonh, height, wrap): # in .points.LatLon_.__init__

1671 '''(INTERNAL) Get 3-tuple C{(lat, lon, height)}.

1672 '''

1673 try:

1674 lat, lon = latlonh.lat, latlonh.lon

1675 height = _xattr(latlonh, height=height)

1676 except AttributeError:

1677 raise _IsnotError(_LatLon_, latlonh=latlonh)

1678 if wrap:

1679 lat, lon = _Wrap.latlon(lat, lon)

1680 return lat, lon, height

1681

1682

1683 def _trilaterate5(p1, d1, p2, d2, p3, d3, area=True, eps=EPS1, # MCCABE 13

1684 radius=R_M, wrap=False):

1685 '''(INTERNAL) Trilaterate three points by I{area overlap} or by

1686 I{perimeter intersection} of three circles.

1687

1688 @note: The B{C{radius}} is only needed for the n-vectorial and

1689 C{sphericalTrigonometry.LatLon.distanceTo} methods and

1690 silently ignored by the C{ellipsoidalExact}, C{-GeodSolve},

1691 C{-Karney} and C{-Vincenty.LatLon.distanceTo} methods.

1692 '''

1693 p2, p3, w = _unrollon3(p1, p2, p3, wrap)

1694

1695 r1 = Distance_(distance1=d1)

1696 r2 = Distance_(distance2=d2)

1697 r3 = Distance_(distance3=d3)

1698 m = 0 if area else (r1 + r2 + r3)

1699 pc = 0

1700 t = []

1701 for _ in range(3):

1702 try: # intersection of circle (p1, r1) and (p2, r2)

1703 c1, c2 = p1.intersections2(r1, p2, r2, wrap=w)

1704

1705 if area: # check overlap

1706 if c1 is c2: # abutting

1707 c = c1

1708 else: # nearest point on radical

1709 c = p3.nearestOn(c1, c2, within=True, wrap=w)

1710 d = r3 - p3.distanceTo(c, radius=radius, wrap=w)

1711 if d > eps: # sufficient overlap

1712 t.append((d, c))

1713 m = max(m, d)

1714

1715 else: # check intersection

1716 for c in ((c1,) if c1 is c2 else (c1, c2)):

1717 d = fabs(r3 - p3.distanceTo(c, radius=radius, wrap=w))

1718 if d < eps: # below margin

1719 t.append((d, c))

1720 m = min(m, d)

1721

1722 except IntersectionError as x:

1723 if _concentric_ in str(x): # XXX ConcentricError?

1724 pc += 1

1725

1726 p1, r1, p2, r2, p3, r3 = p2, r2, p3, r3, p1, r1 # rotate

1727

1728 if t: # get min, max, points and count ...

1729 t = tuple(sorted(t))

1730 n = len(t), # as 1-tuple

1731 # ... or for a single trilaterated result,

1732 # min *is* max, min- *is* maxPoint and n=1, 2 or 3

1733 return Trilaterate5Tuple(t[0] + t[-1] + n) # *(t[0] + ...)

1734

1735 elif area and pc == 3: # all pairwise concentric ...

1736 r, p = min((r1, p1), (r2, p2), (r3, p3))

1737 m = max(r1, r2, r3)

1738 # ... return "smallest" point twice, the smallest

1739 # and largest distance and n=0 for concentric

1740 return Trilaterate5Tuple(float(r), p, float(m), p, 0)

1741

1742 n, f = (_overlap_, max) if area else (_intersection_, min)

1743 t = _COMMASPACE_(_no_(n), '%s %.3g' % (f.__name__, m))

1744 raise IntersectionError(area=area, eps=eps, wrap=wrap, txt=t)

1745

1746

1747__all__ += _ALL_DOCS(LatLonBase)

1748

1749# **) MIT License

1750#

1751# Copyright (C) 2016-2024 -- mrJean1 at Gmail -- All Rights Reserved.

1752#

1753# Permission is hereby granted, free of charge, to any person obtaining a

1754# copy of this software and associated documentation files (the "Software"),

1755# to deal in the Software without restriction, including without limitation

1756# the rights to use, copy, modify, merge, publish, distribute, sublicense,

1757# and/or sell copies of the Software, and to permit persons to whom the

1758# Software is furnished to do so, subject to the following conditions:

1759#

1760# The above copyright notice and this permission notice shall be included

1761# in all copies or substantial portions of the Software.

1762#

1763# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS

1764# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,

1765# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL

1766# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR

1767# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,

1768# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR

1769# OTHER DEALINGS IN THE SOFTWARE.