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, _incompatible, \

21 _IsnotError, IntersectionError, \

22 _ValueError, _xattr, _xdatum, \

23 _xError, _xkwds, _xkwds_not

24# from pygeodesy.fmath import favg # _MODS

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

26# cosineForsytheAndoyerLambert_, cosineLaw, \

27# equirectangular, euclidean, flatLocal_, \

28# flatPolar, _hartzell, haversine, isantipode, \

29# _isequalTo, isnormal, normal, philam2n_xyz, \

30# thomas_, vincentys # 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__ = '23.12.14'

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=None, earth=None):

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

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

607

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

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

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

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

612 this point's C{datum} ellipsoid.

613

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

615 to the distance to this C{pov}.

616

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

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

619 outside or away from the ellipsoid.

620

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

622

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

624 '''

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

626

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

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

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

630 formula.

631

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

633 @kwarg radius_wrap: Optional keyword arguments for function

634 L{pygeodesy.haversine}, overriding the

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

636 datum ellipsoid.

637

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

639

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

641

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

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

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

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

646 '''

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

648

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

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

651

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

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

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

655

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

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

658 '''

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

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

661

662 @Property

663 def height(self):

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

665 '''

666 return self._height

667

668 @height.setter # PYCHOK setter!

669 def height(self, height):

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

671

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

673

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

675 '''

676 h = Height(height)

677 if self._height != h:

678 _update_all(self)

679 self._height = h

680

681 def _heigHt(self, height):

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

683 '''

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

685

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

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

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

689

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

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

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

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

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

695 ellipsoid's surface, otherwise the intersection of the

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

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

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

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

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

701

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

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

704

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

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

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

708

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

710

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

712

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

714 '''

715 c = self.toCartesian()

716 if LatLon is None:

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

718 else:

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

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

721 return r

722

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

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

725

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

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

728

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

730 '''

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

732

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

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

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

736

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

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

739 line and return the 2 intercant points accordingly.

740 '''

741 if height is None:

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

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

744 if h != hp:

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

746 if s: # fmath.fidw?

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

748 hq += s * Q.s12

749 hp += s * P.s12

750 else:

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

752 else:

753 hp = hq = Height(height)

754

755# n = self.name or unused.__name__

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

757 p._iteration = P.iteration

758 if P is not Q:

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

760 q._iteration = Q.iteration

761 return p, q

762

763 @deprecated_method

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

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

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

767

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

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

770 on diametrically opposite sides of the earth.

771

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

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

774

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

776 tolerance, C{False} otherwise.

777 '''

778 p = self.others(other)

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

780

781 @Property_RO

782 def isEllipsoidal(self):

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

784 '''

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

786

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

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

789

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

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

792

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

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

795

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

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

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

799

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

801

802 @see: Method L{isequalTo3}.

803 '''

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

805

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

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

808

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

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

811

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

813 height, C{False} otherwise.

814

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

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

817 C{class} or C{type}.

818

819 @see: Method L{isequalTo}.

820 '''

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

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

823

824 @Property_RO

825 def isnormal(self):

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

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

828

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

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

831 '''

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

833

834 @Property_RO

835 def isSpherical(self):

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

837 '''

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

839

840 @Property_RO

841 def lam(self):

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

843 '''

844 return radians(self.lon)

845

846 @Property

847 def lat(self):

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

849 '''

850 return self._lat

851

852 @lat.setter # PYCHOK setter!

853 def lat(self, lat):

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

855

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

857 '''

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

859 if self._lat != lat:

860 _update_all(self)

861 self._lat = lat

862

863 @Property

864 def latlon(self):

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

866 '''

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

868

869 @latlon.setter # PYCHOK setter!

870 def latlon(self, latlonh):

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

872 (2- or 3-tuple or comma- or space-separated C{str}

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

874

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

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

877

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

879

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

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

882 '''

883 if isstr(latlonh):

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

885 else:

886 _xinstanceof(list, tuple, latlonh=latlonh)

887 if len(latlonh) == 3:

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

889 elif len(latlonh) != 2:

890 raise _ValueError(latlonh=latlonh)

891 else:

892 h = self.height

893

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

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

896 _update_all(self)

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

898

899 def latlon2(self, ndigits=0):

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

901

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

903

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

905 and rounded away from zero.

906

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

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

909 '''

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

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

912

913 @deprecated_method

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

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

916 return self.latlon2(ndigits=ndigits)

917

918 latlon2round = latlon_ # PYCHOK no cover

919

920 @Property

921 def latlonheight(self):

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

923 '''

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

925

926 @latlonheight.setter # PYCHOK setter!

927 def latlonheight(self, latlonh):

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

929 (2- or 3-tuple or comma- or space-separated C{str} of

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

931

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

933 '''

934 self.latlon = latlonh

935

936 @Property

937 def lon(self):

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

939 '''

940 return self._lon

941

942 @lon.setter # PYCHOK setter!

943 def lon(self, lon):

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

945

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

947 '''

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

949 if self._lon != lon:

950 _update_all(self)

951 self._lon = lon

952

953 @property_RO

954 def _ltp(self):

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

956 '''

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

958 return m

959

960 @Property_RO

961 def _Ltp(self):

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

963 '''

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

965

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

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

968

969 Points are converted to and distances are computed in

970 I{geocentric}, cartesian space.

971

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

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

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

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

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

977 account for distances.

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

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

980

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

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

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

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

985 units as the cartesian axes.

986

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

988

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

990 C{Ecef} invalid.

991

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

993

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

995 '''

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

997 p = None # not used

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

999 if w and i:

1000 q = _unrollon(p, q)

1001 yield C(height=h, i=i, up=3, points=q)

1002 p = q

1003

1004 C = self._toCartesianEcef # to verify datum and Ecef

1005 Ps = self.PointsIter(points, wrap=wrap)

1006

1007 c = C(height=height, this=self) # this Cartesian

1008 t = nearestOn6(c, _cs(Ps, height, wrap, C), closed=closed)

1009 c, s, e = t.closest, t.start, t.end

1010

1011 kwds = _xkwds_not(None, LatLon=self.classof, # this LatLon

1012 height=height)

1013 _r = self.Ecef(self.datum).reverse

1014 p = _r(c).toLatLon(**kwds)

1015 s = _r(s).toLatLon(**kwds) if s is not c else p

1016 e = _r(e).toLatLon(**kwds) if e is not c else p

1017 return t.dup(closest=p, start=s, end=e)

1018

1019 def nearestTo(self, *args, **kwds): # PYCHOK no cover

1020 '''B{Not implemented}, throws a C{NotImplementedError} always.'''

1021 notImplemented(self, *args, **kwds)

1022

1023 def normal(self):

1024 '''Normalize this point I{in-place} to C{abs(lat) <= 90} and

1025 C{abs(lon) <= 180}.

1026

1027 @return: C{True} if this point was I{normal}, C{False} if it

1028 wasn't (but is now).

1029

1030 @see: Property L{isnormal} and method L{toNormal}.

1031 '''

1032 n = self.isnormal

1033 if not n:

1034 self.latlon = self._formy.normal(*self.latlon)

1035 return n

1036

1037 @property_RO

1038 def _N_vector(self):

1039 '''(INTERNAL) Get the C{Nvector} (C{nvectorBase._N_vector_})

1040 '''

1041 x, y, z = self._n_xyz3

1042 return _MODS.nvectorBase._N_vector_(x, y, z, h=self.height, name=self.name)

1043

1044 @Property_RO

1045 def _n_xyz3(self):

1046 '''(INTERNAL) Get the n-vector components as L{Vector3Tuple}.

1047 '''

1048 return self._formy.philam2n_xyz(self.phi, self.lam, name=self.name)

1049

1050 @Property_RO

1051 def phi(self):

1052 '''Get the latitude (B{C{radians}}).

1053 '''

1054 return radians(self.lat)

1055

1056 @Property_RO

1057 def philam(self):

1058 '''Get the lat- and longitude (L{PhiLam2Tuple}C{(phi, lam)}).

1059 '''

1060 return PhiLam2Tuple(self.phi, self.lam, name=self.name)

1061

1062 def philam2(self, ndigits=0):

1063 '''Return this point's lat- and longitude in C{radians}, rounded.

1064

1065 @kwarg ndigits: Number of (decimal) digits (C{int}).

1066

1067 @return: A L{PhiLam2Tuple}C{(phi, lam)}, both C{float}

1068 and rounded away from zero.

1069

1070 @note: The C{round}ed values are always C{float}, also

1071 if B{C{ndigits}} is omitted.

1072 '''

1073 return PhiLam2Tuple(round(self.phi, ndigits),

1074 round(self.lam, ndigits), name=self.name)

1075

1076 @Property_RO

1077 def philamheight(self):

1078 '''Get the lat-, longitude in C{radians} and height (L{PhiLam3Tuple}C{(phi, lam, height)}).

1079 '''

1080 return self.philam.to3Tuple(self.height)

1081

1082 @deprecated_method

1083 def points(self, points, closed=True): # PYCHOK no cover

1084 '''DEPRECATED, use method L{points2}.'''

1085 return self.points2(points, closed=closed)

1086

1087 def points2(self, points, closed=True):

1088 '''Check a path or polygon represented by points.

1089

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

1091 @kwarg closed: Optionally, consider the polygon closed,

1092 ignoring any duplicate or closing final

1093 B{C{points}} (C{bool}).

1094

1095 @return: A L{Points2Tuple}C{(number, points)}, an C{int}

1096 and C{list} or C{tuple}.

1097

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

1099

1100 @raise TypeError: Some B{C{points}} are not C{LatLon}.

1101 '''

1102 return _MODS.iters.points2(points, closed=closed, base=self)

1103

1104 def PointsIter(self, points, loop=0, dedup=False, wrap=False):

1105 '''Return a C{PointsIter} iterator.

1106

1107 @arg points: The path or polygon points (C{LatLon}[])

1108 @kwarg loop: Number of loop-back points (non-negative C{int}).

1109 @kwarg dedup: Skip duplicate points (C{bool}).

1110 @kwarg wrap: If C{True}, wrap or I{normalize} the

1111 enum-/iterated B{C{points}} (C{bool}).

1112

1113 @return: A new C{PointsIter} iterator.

1114

1115 @raise PointsError: Insufficient number of B{C{points}}.

1116 '''

1117 return PointsIter(points, base=self, loop=loop, dedup=dedup, wrap=wrap)

1118

1119 def radii11(self, point2, point3, wrap=False):

1120 '''Return the radii of the C{Circum-}, C{In-}, I{Soddy} and C{Tangent}

1121 circles of a (planar) triangle formed by this and two other points.

1122

1123 @arg point2: Second point (C{LatLon}).

1124 @arg point3: Third point (C{LatLon}).

1125 @kwarg wrap: If C{True}, wrap or I{normalize} B{C{point2}} and

1126 B{C{point3}} (C{bool}).

1127

1128 @return: L{Radii11Tuple}C{(rA, rB, rC, cR, rIn, riS, roS, a, b, c, s)}.

1129

1130 @raise IntersectionError: Near-coincident or -colinear points.

1131

1132 @raise TypeError: Invalid B{C{point2}} or B{C{point3}}.

1133

1134 @see: Function L{pygeodesy.radii11}, U{Incircle

1135 <https://MathWorld.Wolfram.com/Incircle.html>}, U{Soddy Circles

1136 <https://MathWorld.Wolfram.com/SoddyCircles.html>} and U{Tangent

1137 Circles<https://MathWorld.Wolfram.com/TangentCircles.html>}.

1138 '''

1139 with _toCartesian3(self, point2, point3, wrap) as cs:

1140 return _radii11ABC(*cs, useZ=True)[0]

1141

1142 def _rhumb3(self, exact, radius): # != .sphericalBase._rhumbs3

1143 '''(INTERNAL) Get the C{rhumb} for this point's datum or for

1144 the B{C{radius}}' earth model iff non-C{None}.

1145 '''

1146 try:

1147 d = self._rhumb3dict

1148 t = d[(exact, radius)]

1149 except KeyError:

1150 D = self.datum if radius is None else \

1151 _spherical_datum(radius) # ellipsoidal OK

1152 try:

1153 r = D.ellipsoid.rhumb_(exact=exact) # or D.isSpherical

1154 except AttributeError as x:

1155 raise _AttributeError(datum=D, radius=radius, cause=x)

1156 t = r, D, _MODS.karney.Caps

1157 while d:

1158 d.popitem()

1159 d[(exact, radius)] = t # cache 3-tuple

1160 return t

1161

1162 @Property_RO

1163 def _rhumb3dict(self): # in rhumbIntersecant2 below

1164 return {} # single-item cache

1165

1166 def rhumbAzimuthTo(self, other, exact=False, radius=None, wrap=False, b360=False):

1167 '''Return the azimuth (bearing) of a rhumb line (loxodrome) between this

1168 and an other (ellipsoidal) point.

1169

1170 @arg other: The other point (C{LatLon}).

1171 @kwarg exact: Exact C{Rhumb...} to use (C{bool} or C{Rhumb...}), see

1172 method L{Ellipsoid.rhumb_}.

1173 @kwarg radius: Optional earth radius (C{meter}) or earth model (L{Datum},

1174 L{Ellipsoid}, L{Ellipsoid2} or L{a_f2Tuple}), overriding

1175 this point's datum.

1176 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the B{C{other}}

1177 point (C{bool}).

1178 @kwarg b360: If C{True}, return the azimuth in the bearing range.

1179

1180 @return: Rhumb azimuth (compass C{degrees180} or C{degrees360}).

1181

1182 @raise TypeError: The B{C{other}} point is incompatible or B{C{radius}}

1183 is invalid.

1184 '''

1185 r, _, Cs = self._rhumb3(exact, radius)

1186 z = r._Inverse(self, other, wrap, outmask=Cs.AZIMUTH).azi12

1187 return _umod_360(z + _360_0) if b360 else z

1188

1189 def rhumbDestination(self, distance, azimuth, exact=False, radius=None, height=None):

1190 '''Return the destination point having travelled the given distance from

1191 this point along a rhumb line (loxodrome) of the given azimuth.

1192

1193 @arg distance: Distance travelled (C{meter}, same units as this point's

1194 datum (ellipsoid) axes or B{C{radius}}, may be negative.

1195 @arg azimuth: Azimuth (bearing) of the rhumb line (compass C{degrees}).

1196 @kwarg exact: Exact C{Rhumb...} to use (C{bool} or C{Rhumb...}), see

1197 method L{Ellipsoid.rhumb_}.

1198 @kwarg radius: Optional earth radius (C{meter}) or earth model (L{Datum},

1199 L{Ellipsoid}, L{Ellipsoid2} or L{a_f2Tuple}), overriding

1200 this point's datum.

1201 @kwarg height: Optional height, overriding the default height (C{meter}).

1202

1203 @return: The destination point (ellipsoidal C{LatLon}).

1204

1205 @raise TypeError: Invalid B{C{radius}}.

1206

1207 @raise ValueError: Invalid B{C{distance}}, B{C{azimuth}}, B{C{radius}}

1208 or B{C{height}}.

1209 '''

1210 r, D, _ = self._rhumb3(exact, radius)

1211 d = r._Direct(self, azimuth, distance)

1212 h = self._heigHt(height)

1213 return self.classof(d.lat2, d.lon2, datum=D, height=h)

1214

1215 def rhumbDistanceTo(self, other, exact=False, radius=None, wrap=False):

1216 '''Return the distance from this to an other point along a rhumb line

1217 (loxodrome).

1218

1219 @arg other: The other point (C{LatLon}).

1220 @kwarg exact: Exact C{Rhumb...} to use (C{bool} or C{Rhumb...}), see

1221 method L{Ellipsoid.rhumb_}.

1222 @kwarg radius: Optional earth radius (C{meter}) or earth model (L{Datum},

1223 L{Ellipsoid}, L{Ellipsoid2} or L{a_f2Tuple}), overriding

1224 this point's datum.

1225 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the B{C{other}}

1226 point (C{bool}).

1227

1228 @return: Distance (C{meter}, the same units as this point's datum

1229 (ellipsoid) axes or B{C{radius}}.

1230

1231 @raise TypeError: The B{C{other}} point is incompatible or B{C{radius}}

1232 is invalid.

1233

1234 @raise ValueError: Invalid B{C{radius}}.

1235 '''

1236 r, _, Cs = self._rhumb3(exact, radius)

1237 return r._Inverse(self, other, wrap, outmask=Cs.DISTANCE).s12

1238

1239 def rhumbIntersecant2(self, circle, point, other, height=None,

1240 **exact_radius_wrap_eps_tol):

1241 '''Compute the intersections of a circle and a rhumb line given as two

1242 points or as a point and azimuth.

1243

1244 @arg circle: Radius of the circle centered at this location (C{meter}),

1245 or a point on the circle (this C{LatLon}).

1246 @arg point: The start point of the rhumb line (this C{LatLon}).

1247 @arg other: An other point I{on} (this C{LatLon}) or the azimuth I{of}

1248 (compass C{degrees}) the rhumb line.

1249 @kwarg height: Optional height for the intersection points (C{meter},

1250 conventionally) or C{None} for interpolated heights.

1251 @kwarg exact_radius_wrap_eps_tol: Optional keyword arguments, see

1252 methods L{rhumbLine} and L{RhumbLineAux.Intersecant2}

1253 or L{RhumbLine.Intersecant2}.

1254

1255 @return: 2-Tuple of the intersection points (representing a chord),

1256 each an instance of this class. Both points are the same

1257 instance if the rhumb line is tangent to the circle.

1258

1259 @raise IntersectionError: The circle and rhumb line do not intersect.

1260

1261 @raise TypeError: If B{C{point}} is not this C{LatLon} or B{C{circle}}

1262 or B{C{other}} invalid.

1263

1264 @raise ValueError: Invalid B{C{circle}}, B{C{other}}, B{C{height}}

1265 or B{C{exact_radius_wrap}}.

1266

1267 @see: Methods L{RhumbLineAux.Intersecant2} and L{RhumbLine.Intersecant2}.

1268 '''

1269 def _kwds3(eps=EPS, tol=_TOL, wrap=False, **kwds):

1270 return kwds, wrap, dict(eps=eps, tol=tol)

1271

1272 exact_radius, w, eps_tol = _kwds3(**exact_radius_wrap_eps_tol)

1273

1274 p = _unrollon(self, self.others(point=point), wrap=w)

1275 try:

1276 r = Radius_(circle=circle) if _isRadius(circle) else \

1277 self.rhumbDistanceTo(self.others(circle=circle), wrap=w, **exact_radius)

1278 rl = p.rhumbLine(other, wrap=w, **exact_radius)

1279 P, Q = rl.Intersecant2(self.lat, self.lon, r, **eps_tol)

1280

1281 return self._intersecend2(p, other, w, height, rl.rhumb, P, Q,

1282 self.rhumbIntersecant2)

1283

1284 except (TypeError, ValueError) as x:

1285 raise _xError(x, center=self, circle=circle, point=point, other=other,

1286 **exact_radius_wrap_eps_tol)

1287

1288 def rhumbLine(self, other, exact=False, radius=None, wrap=False, **name_caps):

1289 '''Get a rhumb line through this point at a given azimuth or through

1290 this and an other point.

1291

1292 @arg other: The azimuth I{of} (compass C{degrees}) or an other point

1293 I{on} (this C{LatLon}) the rhumb line.

1294 @kwarg exact: Exact C{Rhumb...} to use (C{bool} or C{Rhumb...}), see

1295 method L{Ellipsoid.rhumb_}.

1296 @kwarg radius: Optional earth radius (C{meter}) or earth model

1297 (L{Datum}, L{Ellipsoid}, L{Ellipsoid2} or L{a_f2Tuple}),

1298 overriding this point's datum.

1299 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the B{C{other}}

1300 point (C{bool}).

1301 @kwarg name_caps: Optional C{B{name}=str} and C{caps}, see L{RhumbLine}

1302 or L{RhumbLineAux} C{B{caps}}.

1303

1304 @return: A C{RhumbLine} instance.

1305

1306 @raise TypeError: Invalid B{C{radius}} or B{C{other}} not C{scalar} nor

1307 this C{LatLon}.

1308

1309 @see: Modules L{rhumb.aux_} and L{rhumb.ekx}.

1310 '''

1311 r, _, Cs = self._rhumb3(exact, radius)

1312 kwds = _xkwds(name_caps, name=self.name, caps=Cs.LINE_OFF)

1313 rl = r._DirectLine( self, other, **kwds) if _isDegrees(other) else \

1314 r._InverseLine(self, self.others(other), wrap, **kwds)

1315 return rl

1316

1317 def rhumbMidpointTo(self, other, exact=False, radius=None,

1318 height=None, fraction=_0_5, wrap=False):

1319 '''Return the (loxodromic) midpoint on the rhumb line between this and

1320 an other point.

1321

1322 @arg other: The other point (this C{LatLon}).

1323 @kwarg exact: Exact C{Rhumb...} to use (C{bool} or C{Rhumb...}), see

1324 method L{Ellipsoid.rhumb_}.

1325 @kwarg radius: Optional earth radius (C{meter}) or earth model (L{Datum},

1326 L{Ellipsoid}, L{Ellipsoid2} or L{a_f2Tuple}), overriding

1327 this point's datum.

1328 @kwarg height: Optional height, overriding the mean height (C{meter}).

1329 @kwarg fraction: Midpoint location from this point (C{scalar}), 0 for this,

1330 1 for the B{C{other}}, 0.5 for halfway between this and

1331 the B{C{other}} point, may be negative or greater than 1.

1332 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the B{C{other}}

1333 point (C{bool}).

1334

1335 @return: The midpoint at the given B{C{fraction}} along the rhumb line

1336 (this C{LatLon}).

1337

1338 @raise TypeError: The B{C{other}} point is incompatible or B{C{radius}}

1339 is invalid.

1340

1341 @raise ValueError: Invalid B{C{height}} or B{C{fraction}}.

1342 '''

1343 r, D, _ = self._rhumb3(exact, radius)

1344 f = Scalar(fraction=fraction)

1345 d = r._Inverse(self, self.others(other), wrap) # C.AZIMUTH_DISTANCE

1346 d = r._Direct( self, d.azi12, d.s12 * f)

1347 h = self._havg(other, f=f, h=height)

1348 return self.classof(d.lat2, d.lon2, datum=D, height=h)

1349

1350 @property_RO

1351 def sphericalLatLon(self):

1352 '''Get the C{LatLon type} iff spherical, overloaded in L{LatLonSphericalBase}.

1353 '''

1354 return False

1355

1356 def thomasTo(self, other, wrap=False):

1357 '''Compute the distance between this and an other point using

1358 U{Thomas'<https://apps.DTIC.mil/dtic/tr/fulltext/u2/703541.pdf>}

1359 formula.

1360

1361 @arg other: The other point (C{LatLon}).

1362 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll

1363 the B{C{other}} point (C{bool}).

1364

1365 @return: Distance (C{meter}, same units as the axes of

1366 this point's datum ellipsoid).

1367

1368 @raise TypeError: The B{C{other}} point is not C{LatLon}.

1369

1370 @see: Function L{pygeodesy.thomas} and methods L{cosineAndoyerLambertTo},

1371 L{cosineForsytheAndoyerLambertTo}, L{cosineLawTo}, C{distanceTo*},

1372 L{equirectangularTo}, L{euclideanTo}, L{flatLocalTo}/L{hubenyTo},

1373 L{flatPolarTo}, L{haversineTo} and L{vincentysTo}.

1374 '''

1375 return self._distanceTo_(self._formy.thomas_, other, wrap=wrap)

1376

1377 @deprecated_method

1378 def to2ab(self): # PYCHOK no cover

1379 '''DEPRECATED, use property L{philam}.'''

1380 return self.philam

1381

1382 def toCartesian(self, height=None, Cartesian=None, **Cartesian_kwds):

1383 '''Convert this point to cartesian, I{geocentric} coordinates,

1384 also known as I{Earth-Centered, Earth-Fixed} (ECEF).

1385

1386 @kwarg height: Optional height, overriding this point's height

1387 (C{meter}, conventionally).

1388 @kwarg Cartesian: Optional class to return the geocentric

1389 coordinates (C{Cartesian}) or C{None}.

1390 @kwarg Cartesian_kwds: Optional, additional B{C{Cartesian}}

1391 keyword arguments, ignored if

1392 C{B{Cartesian} is None}.

1393

1394 @return: A B{C{Cartesian}} or if B{C{Cartesian}} is C{None},

1395 an L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M,

1396 datum)} with C{C=0} and C{M} if available.

1397

1398 @raise TypeError: Invalid B{C{Cartesian}} or B{C{Cartesian_kwds}}.

1399

1400 @see: Methods C{toNvector}, C{toVector} and C{toVector3d}.

1401 '''

1402 r = self._ecef9 if height is None else self.toEcef(height=height)

1403 if Cartesian is not None: # class or .classof

1404 r = Cartesian(r, **_xkwds(Cartesian_kwds, name=self.name))

1405 _xdatum(r.datum, self.datum)

1406 return r

1407

1408 def _toCartesianEcef(self, height=None, i=None, up=2, **name_point):

1409 '''(INTERNAL) Convert to cartesian and check Ecef's before and after.

1410 '''

1411 p = self.others(up=up, **name_point)

1412 c = p.toCartesian(height=height)

1413 E = self.Ecef

1414 if E:

1415 for p in (p, c):

1416 e = _xattr(p, Ecef=None)

1417 if e not in (None, E): # PYCHOK no cover

1418 n, _ = name_point.popitem()

1419 if i is not None:

1420 n = Fmt.SQUARE(n, i)

1421 raise _ValueError(n, e, txt=_incompatible(E.__name__))

1422 return c

1423

1424 def toDatum(self, datum2, height=None, name=NN):

1425 '''I{Must be overloaded}.'''

1426 notOverloaded(self, datum2, height=height, name=name)

1427

1428 def toEcef(self, height=None, M=False):

1429 '''Convert this point to I{geocentric} coordinates, also known as

1430 I{Earth-Centered, Earth-Fixed} (U{ECEF<https://WikiPedia.org/wiki/ECEF>}).

1431

1432 @kwarg height: Optional height, overriding this point's height

1433 (C{meter}, conventionally).

1434 @kwarg M: Optionally, include the rotation L{EcefMatrix} (C{bool}).

1435

1436 @return: An L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M, datum)}

1437 with C{C=0} and C{M} if available.

1438

1439 @raise EcefError: A C{.datum} or an ECEF issue.

1440 '''

1441 return self._ecef9 if height in (None, self.height) else \

1442 self._Ecef_forward(self.lat, self.lon, height=height, M=M)

1443

1444 @deprecated_method

1445 def to3llh(self, height=None): # PYCHOK no cover

1446 '''DEPRECATED, use property L{latlonheight} or C{latlon.to3Tuple(B{height})}.'''

1447 return self.latlonheight if height in (None, self.height) else \

1448 self.latlon.to3Tuple(height)

1449

1450 def toLocal(self, Xyz=None, ltp=None, **Xyz_kwds):

1451 '''Convert this I{geodetic} point to I{local} C{X}, C{Y} and C{Z}.

1452

1453 @kwarg Xyz: Optional class to return C{X}, C{Y} and C{Z}

1454 (L{XyzLocal}, L{Enu}, L{Ned}) or C{None}.

1455 @kwarg ltp: The I{local tangent plane} (LTP) to use,

1456 overriding this point's LTP (L{Ltp}).

1457 @kwarg Xyz_kwds: Optional, additional B{C{Xyz}} keyword

1458 arguments, ignored if C{B{Xyz} is None}.

1459

1460 @return: An B{C{Xyz}} instance or if C{B{Xyz} is None},

1461 a L{Local9Tuple}C{(x, y, z, lat, lon, height,

1462 ltp, ecef, M)} with C{M=None}, always.

1463

1464 @raise TypeError: Invalid B{C{ltp}}.

1465 '''

1466 p = self._ltp._xLtp(ltp, self._Ltp)

1467 return p._ecef2local(self._ecef9, Xyz, Xyz_kwds)

1468

1469 def toLtp(self, Ecef=None):

1470 '''Return the I{local tangent plane} (LTP) for this point.

1471

1472 @kwarg Ecef: Optional ECEF I{class} (L{EcefKarney}, ...

1473 L{EcefYou}), overriding this point's C{Ecef}.

1474 '''

1475 return self._Ltp if Ecef in (None, self.Ecef) else self._ltp.Ltp(

1476 self, ecef=Ecef(self.datum), name=self.name)

1477

1478 def toNormal(self, deep=False, name=NN):

1479 '''Get this point I{normalized} to C{abs(lat) <= 90}

1480 and C{abs(lon) <= 180}.

1481

1482 @kwarg deep: If C{True} make a deep, otherwise a

1483 shallow copy (C{bool}).

1484 @kwarg name: Optional name of the copy (C{str}).

1485

1486 @return: A copy of this point, I{normalized} and

1487 optionally renamed (C{LatLon}).

1488

1489 @see: Property L{isnormal}, method L{normal} and function

1490 L{pygeodesy.normal}.

1491 '''

1492 ll = self.copy(deep=deep)

1493 _ = ll.normal()

1494 if name:

1495 ll.rename(name)

1496 return ll

1497

1498 def toNvector(self, h=None, Nvector=None, **Nvector_kwds):

1499 '''Convert this point to C{n-vector} (normal to the earth's surface)

1500 components, I{including height}.

1501

1502 @kwarg h: Optional height, overriding this point's height (C{meter}).

1503 @kwarg Nvector: Optional class to return the C{n-vector} components

1504 (C{Nvector}) or C{None}.

1505 @kwarg Nvector_kwds: Optional, additional B{C{Nvector}} keyword

1506 arguments, ignored if C{B{Nvector} is None}.

1507

1508 @return: An B{C{Nvector}} or a L{Vector4Tuple}C{(x, y, z, h)} if

1509 B{C{Nvector}} is C{None}.

1510

1511 @raise TypeError: Invalid B{C{h}}, B{C{Nvector}} or B{C{Nvector_kwds}}

1512 item.

1513

1514 @see: Methods C{toCartesian}, C{toVector} and C{toVector3d}.

1515 '''

1516 h = self._heigHt(h)

1517 if Nvector is None:

1518 r = self._n_xyz3.to4Tuple(h)

1519 else:

1520 x, y, z = self._n_xyz3

1521 r = Nvector(x, y, z, h=h, ll=self, **_xkwds(Nvector_kwds, name=self.name))

1522 return r

1523

1524 def toStr(self, form=F_DMS, joined=_COMMASPACE_, m=_m_, **prec_sep_s_D_M_S): # PYCHOK expected

1525 '''Convert this point to a "lat, lon[, +/-height]" string, formatted

1526 in the given C{B{form}at}.

1527

1528 @kwarg form: The lat-/longitude C{B{form}at} to use (C{str}), see

1529 functions L{pygeodesy.latDMS} or L{pygeodesy.lonDMS}.

1530 @kwarg joined: Separator to join the lat-, longitude and heigth

1531 strings (C{str} or C{None} or C{NN} for non-joined).

1532 @kwarg m: Optional unit of the height (C{str}), use C{None} to

1533 exclude height from the returned string.

1534 @kwarg prec_sep_s_D_M_S: Optional C{B{prec}ision}, C{B{sep}arator},

1535 B{C{s_D}}, B{C{s_M}}, B{C{s_S}} and B{C{s_DMS}} keyword

1536 arguments, see function L{pygeodesy.latDMS} or

1537 L{pygeodesy.lonDMS}.

1538

1539 @return: This point in the specified C{B{form}at}, etc. (C{str} or

1540 a 2- or 3-tuple C{(lat_str, lon_str[, height_str])} if

1541 C{B{joined}=NN} or C{B{joined}=None}).

1542

1543 @see: Function L{pygeodesy.latDMS} or L{pygeodesy.lonDMS} for more

1544 details about keyword arguments C{B{form}at}, C{B{prec}ision},

1545 C{B{sep}arator}, B{C{s_D}}, B{C{s_M}}, B{C{s_S}} and B{C{s_DMS}}.

1546 '''

1547 t = (latDMS(self.lat, form=form, **prec_sep_s_D_M_S),

1548 lonDMS(self.lon, form=form, **prec_sep_s_D_M_S))

1549 if self.height and m is not None:

1550 t += (self.heightStr(m=m),)

1551 return joined.join(t) if joined else t

1552

1553 def toVector(self, Vector=None, **Vector_kwds):

1554 '''Convert this point to a C{Vector} with the I{geocentric} C{(x,

1555 y, z)} (ECEF) coordinates, I{ignoring height}.

1556

1557 @kwarg Vector: Optional class to return the I{geocentric}

1558 components (L{Vector3d}) or C{None}.

1559 @kwarg Vector_kwds: Optional, additional B{C{Vector}} keyword

1560 arguments, ignored if C{B{Vector} is None}.

1561

1562 @return: A B{C{Vector}} or a L{Vector3Tuple}C{(x, y, z)}

1563 if B{C{Vector}} is C{None}.

1564

1565 @raise TypeError: Invalid B{C{Vector}} or B{C{Vector_kwds}} item.

1566

1567 @see: Methods C{toCartesian}, C{toNvector} and C{toVector3d}.

1568 '''

1569 return self._ecef9.toVector(Vector=Vector, **Vector_kwds)

1570

1571 def toVector3d(self, norm=True, **Vector3d_kwds):

1572 '''Convert this point to a L{Vector3d} with the I{geocentric} C{(x,

1573 y, z)} (ECEF) I{unit} coordinates, I{ignoring height}.

1574

1575 @kwarg norm: Normalize the 3-D vector (C{bool}).

1576 @kwarg Vector3d_kwds: Optional L{Vector3d} keyword arguments.

1577

1578 @return: Unit vector (L{Vector3d}).

1579

1580 @raise TypeError: Invalid B{C{Vector3d_kwds}} item.

1581

1582 @see: Methods C{toCartesian}, C{toNvector} and C{toVector}.

1583 '''

1584 r = self.toVector(Vector=Vector3d, **Vector3d_kwds)

1585 if norm:

1586 r = r.unit(ll=self)

1587 return r

1588

1589 def toWm(self, **toWm_kwds):

1590 '''Convert this point to a WM coordinate.

1591

1592 @kwarg toWm_kwds: Optional L{pygeodesy.toWm} keyword arguments.

1593

1594 @return: The WM coordinate (L{Wm}).

1595

1596 @see: Function L{pygeodesy.toWm}.

1597 '''

1598 return self._wm if not toWm_kwds else _MODS.webmercator.toWm(

1599 self, **_xkwds(toWm_kwds, name=self.name))

1600

1601 @deprecated_method

1602 def to3xyz(self): # PYCHOK no cover

1603 '''DEPRECATED, use property L{xyz} or method L{toNvector}, L{toVector},

1604 L{toVector3d} or perhaps (geocentric) L{toEcef}.'''

1605 return self.xyz # self.toVector()

1606

1607 def vincentysTo(self, other, **radius_wrap):

1608 '''Compute the distance between this and an other point using

1609 U{Vincenty's<https://WikiPedia.org/wiki/Great-circle_distance>}

1610 spherical formula.

1611

1612 @arg other: The other point (C{LatLon}).

1613 @kwarg radius_wrap: Optional keyword arguments for function

1614 L{pygeodesy.vincentys}, overriding the

1615 default mean C{radius} of this point's

1616 datum ellipsoid.

1617

1618 @return: Distance (C{meter}, same units as B{C{radius}}).

1619

1620 @raise TypeError: The B{C{other}} point is not C{LatLon}.

1621

1622 @see: Function L{pygeodesy.vincentys} and methods L{cosineAndoyerLambertTo},

1623 L{cosineForsytheAndoyerLambertTo}, L{cosineLawTo}, C{distanceTo*},

1624 L{equirectangularTo}, L{euclideanTo}, L{flatLocalTo}/L{hubenyTo},

1625 L{flatPolarTo}, L{haversineTo} and L{thomasTo}.

1626 '''

1627 return self._distanceTo(self._formy.vincentys, other, **_xkwds(radius_wrap, radius=None))

1628

1629 @Property_RO

1630 def _wm(self):

1631 '''(INTERNAL) Get this point as webmercator (L{Wm}).

1632 '''

1633 return _MODS.webmercator.toWm(self)

1634

1635 @property_RO

1636 def xyz(self):

1637 '''Get the I{geocentric} C{(x, y, z)} coordinates (L{Vector3Tuple}C{(x, y, z)})

1638 '''

1639 return self._ecef9.xyz

1640

1641 @Property_RO

1642 def xyzh(self):

1643 '''Get the I{geocentric} C{(x, y, z)} coordinates and height (L{Vector4Tuple}C{(x, y, z, h)})

1644 '''

1645 return self.xyz.to4Tuple(self.height)

1646

1647

1648 class _toCartesian3(object): # see also .formy._idllmn6, .geodesicw._wargs, .vector2d._numpy

1649 '''(INTERNAL) Wrapper to convert 2 other points.

1650 '''

1651 @contextmanager # <https://www.Python.org/dev/peps/pep-0343/> Examples

1652 def __call__(self, p, p2, p3, wrap, **kwds):

1653 try:

1654 if wrap:

1655 p2, p3 = map1(_Wrap.point, p2, p3)

1656 kwds = _xkwds(kwds, wrap=wrap)

1657 yield (p. toCartesian().copy(name=_point_), # copy to rename

1658 p._toCartesianEcef(up=4, point2=p2),

1659 p._toCartesianEcef(up=4, point3=p3))

1660 except (AssertionError, TypeError, ValueError) as x: # Exception?

1661 raise _xError(x, point=p, point2=p2, point3=p3, **kwds)

1662

1663_toCartesian3 = _toCartesian3() # PYCHOK singleton

1664

1665

1666 def _latlonheight3(latlonh, height, wrap): # in .points.LatLon_.__init__

1667 '''(INTERNAL) Get 3-tuple C{(lat, lon, height)}.

1668 '''

1669 try:

1670 lat, lon = latlonh.lat, latlonh.lon

1671 height = _xattr(latlonh, height=height)

1672 except AttributeError:

1673 raise _IsnotError(_LatLon_, latlonh=latlonh)

1674 if wrap:

1675 lat, lon = _Wrap.latlon(lat, lon)

1676 return lat, lon, height

1677

1678

1679 def _trilaterate5(p1, d1, p2, d2, p3, d3, area=True, eps=EPS1, # MCCABE 13

1680 radius=R_M, wrap=False):

1681 '''(INTERNAL) Trilaterate three points by I{area overlap} or by

1682 I{perimeter intersection} of three circles.

1683

1684 @note: The B{C{radius}} is only needed for both the n-vectorial

1685 and C{sphericalTrigonometry.LatLon.distanceTo} methods and

1686 silently ignored by the C{ellipsoidalExact}, C{-GeodSolve},

1687 C{-Karney} and C{-Vincenty.LatLon.distanceTo} methods.

1688 '''

1689 p2, p3, w = _unrollon3(p1, p2, p3, wrap)

1690

1691 r1 = Distance_(distance1=d1)

1692 r2 = Distance_(distance2=d2)

1693 r3 = Distance_(distance3=d3)

1694 m = 0 if area else (r1 + r2 + r3)

1695 pc = 0

1696 t = []

1697 for _ in range(3):

1698 try: # intersection of circle (p1, r1) and (p2, r2)

1699 c1, c2 = p1.intersections2(r1, p2, r2, wrap=w)

1700

1701 if area: # check overlap

1702 if c1 is c2: # abutting

1703 c = c1

1704 else: # nearest point on radical

1705 c = p3.nearestOn(c1, c2, within=True, wrap=w)

1706 d = r3 - p3.distanceTo(c, radius=radius, wrap=w)

1707 if d > eps: # sufficient overlap

1708 t.append((d, c))

1709 m = max(m, d)

1710

1711 else: # check intersection

1712 for c in ((c1,) if c1 is c2 else (c1, c2)):

1713 d = fabs(r3 - p3.distanceTo(c, radius=radius, wrap=w))

1714 if d < eps: # below margin

1715 t.append((d, c))

1716 m = min(m, d)

1717

1718 except IntersectionError as x:

1719 if _concentric_ in str(x): # XXX ConcentricError?

1720 pc += 1

1721

1722 p1, r1, p2, r2, p3, r3 = p2, r2, p3, r3, p1, r1 # rotate

1723

1724 if t: # get min, max, points and count ...

1725 t = tuple(sorted(t))

1726 n = len(t), # as 1-tuple

1727 # ... or for a single trilaterated result,

1728 # min *is* max, min- *is* maxPoint and n=1, 2 or 3

1729 return Trilaterate5Tuple(t[0] + t[-1] + n) # *(t[0] + ...)

1730

1731 elif area and pc == 3: # all pairwise concentric ...

1732 r, p = min((r1, p1), (r2, p2), (r3, p3))

1733 m = max(r1, r2, r3)

1734 # ... return "smallest" point twice, the smallest

1735 # and largest distance and n=0 for concentric

1736 return Trilaterate5Tuple(float(r), p, float(m), p, 0)

1737

1738 n, f = (_overlap_, max) if area else (_intersection_, min)

1739 t = _COMMASPACE_(_no_(n), '%s %.3g' % (f.__name__, m))

1740 raise IntersectionError(area=area, eps=eps, wrap=wrap, txt=t)

1741

1742

1743__all__ += _ALL_DOCS(LatLonBase)

1744

1745# **) MIT License

1746#

1747# Copyright (C) 2016-2024 -- mrJean1 at Gmail -- All Rights Reserved.

1748#

1749# Permission is hereby granted, free of charge, to any person obtaining a

1750# copy of this software and associated documentation files (the "Software"),

1751# to deal in the Software without restriction, including without limitation

1752# the rights to use, copy, modify, merge, publish, distribute, sublicense,

1753# and/or sell copies of the Software, and to permit persons to whom the

1754# Software is furnished to do so, subject to the following conditions:

1755#

1756# The above copyright notice and this permission notice shall be included

1757# in all copies or substantial portions of the Software.

1758#

1759# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS

1760# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,

1761# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL

1762# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR

1763# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,

1764# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR

1765# OTHER DEALINGS IN THE SOFTWARE.