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

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

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

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

10'''

11

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

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

14 _0_0, _0_5, _1_0

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

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

17# from pygeodesy.ecef import EcefKarney # _MODS

18 from pygeodesy.errors import _incompatible, IntersectionError, _IsnotError, \

19 _TypeError, _ValueError, _xdatum, _xError, \

20 _xkwds, _xkwds_not

21# from pygeodesy.fmath import favg # _MODS

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

23 cosineForsytheAndoyerLambert_, cosineLaw, \

24 equirectangular, euclidean, flatLocal_, \

25 flatPolar, hartzell, haversine, isantipode, \

26 _isequalTo, isnormal, normal, philam2n_xyz, \

27 thomas_, vincentys, _spherical_datum

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

29 _intersection_, _m_, _LatLon_, _no_, \

30 _overlap_, _point_ # PYCHOK used!

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

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

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

34 from pygeodesy.named import _NamedBase, notOverloaded, Fmt

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

36 Trilaterate5Tuple, Vector3Tuple

37# from pygeodesy.nvectorBase import _N_vector_ # _MODS

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

39 property_RO, _update_all

40# from pygeodesy.rhumbx import Caps, Rhumb # _MODS

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

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

43 Scalar, Scalar_

44 from pygeodesy.utily import _unrollon, _unrollon3, _Wrap

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

46 Circum3Tuple, _radii11ABC

47 from pygeodesy.vector3d import nearestOn6, Vector3d, PointsIter

48

49 from contextlib import contextmanager

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

51

52__all__ = _ALL_LAZY.latlonBase

53__version__ = '23.07.14'

54

55

56 class LatLonBase(_NamedBase):

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

58 ellipsoidal earth models.

59 '''

60 _clipid = INT0 # polygonal clip, see .booleans

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

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

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

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

65

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

67 '''New C{LatLon}.

68

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

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

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

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

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

74 (C{meter}, conventionally).

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

76 (C{bool}).

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

78

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

80

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

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

83

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

85

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

87

88 @example:

89

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

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

92 >>> r = LatLon(p)

93 '''

94 if name:

95 self.name = name

96

97 if lon is None:

98 try:

99 lat, lon = latlonh.lat, latlonh.lon

100 height = latlonh.get(_height_, height)

101 except AttributeError:

102 raise _IsnotError(_LatLon_, latlonh=latlonh)

103 if wrap:

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

105 elif wrap:

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

107 else:

108 lat = latlonh

109

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

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

112 if height: # elevation

113 self._height = Height(height)

114

115 def __eq__(self, other):

116 return self.isequalTo(other)

117

118 def __ne__(self, other):

119 return not self.isequalTo(other)

120

121 def __str__(self):

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

123

124 def antipode(self, height=None):

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

126 to this point.

127

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

129 this point's height otherwise.

130

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

132 '''

133 h = self._heigHt(height)

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

135

136 @deprecated_method

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

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

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

140

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

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

143 bounding box centered at this location.

144

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

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

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

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

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

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

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

152 overriding the point's height.

153

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

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

156

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

158 '''

159 w = Scalar_(wide=wide) * _0_5

160 t = Scalar_(tall=tall) * _0_5

161 if radius is not None:

162 r = Radius_(radius)

163 c = cos(self.phi)

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

165 t = degrees(t / r)

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

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

168

169 h = self._heigHt(height)

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

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

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

173

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

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

176 this and an other point.

177

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

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

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

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

182 point (C{bool}).

183

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

185

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

187 '''

188 def _v3d(ll):

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

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

191

192 p = self.others(other)

193 if wrap:

194 p = _Wrap.point(p)

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

196

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

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

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

200

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

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

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

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

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

206

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

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

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

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

211

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

213 than version 1.10.

214

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

216 a trilateration or C{numpy} issue.

217

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

219

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

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

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

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

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

225 height)} representing the differences between both results from

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

227

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

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

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

231 '''

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

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

234 datum=self.datum) # PYCHOK unpack

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

236

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

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

239 this and two other points.

240

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

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

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

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

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

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

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

248

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

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

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

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

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

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

255

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

257 version 1.10.

258

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

260 incompatible C{Ecef} classes or a trilateration

261 or C{numpy} issue.

262

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

264

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

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

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

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

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

270 height)} representing the difference between both results from

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

272

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

274 '''

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

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

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

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

279

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

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

282

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

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

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

286

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

288 an instance of this (sub-)class.

289

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

291 version 1.10.

292

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

294

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

296

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

298

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

300 '''

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

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

303 for i, p in enumerate(ps):

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

305

306 C = self._toCartesianEcef

307 c = C(point=self)

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

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

310 return t.dup(center=c)

311

312 @property

313 def clipid(self):

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

315 '''

316 return self._clipid

317

318 @clipid.setter # PYCHOK setter!

319 def clipid(self, clipid):

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

321 '''

322 self._clipid = int(clipid)

323

324 @deprecated_method

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

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

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

328

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

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

331 this and an other point.

332

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

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

335 larger distances.

336

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

338 @kwarg adjust_wrap: Optional keyword arguments for function

339 L{pygeodesy.compassAngle}.

340

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

342

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

344

345 @note: Courtesy of Martin Schultz.

346

347 @see: U{Local, flat earth approximation

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

349 '''

350 p = self.others(other)

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

352

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

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

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

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

357

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

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

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

361

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

363 point's datum ellipsoid).

364

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

366

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

368 L{cosineForsytheAndoyerLambertTo}, L{cosineLawTo},

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

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

371 L{thomasTo} and L{vincentysTo}.

372 '''

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

374

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

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

377 the U{Forsythe-Andoyer-Lambert correction

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

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

380 formula.

381

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

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

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

385

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

387 this point's datum ellipsoid).

388

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

390

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

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

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

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

395 '''

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

397

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

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

400 U{spherical Law of Cosines

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

402 formula.

403

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

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

406 for the mean radius of this point's datum

407 ellipsoid.

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

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

410

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

412

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

414

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

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

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

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

419 '''

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

421

422 @property_RO

423 def datum(self): # PYCHOK no cover

424 '''(INTERNAL) I{Must be overloaded}, see function C{notOverloaded}.

425 '''

426 notOverloaded(self)

427

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

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

430

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

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

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

434 or C{None}.

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

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

437

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

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

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

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

442 is un-/specified.

443

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

445 '''

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

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

448

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

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

451 '''

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

453 if r is None:

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

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

456

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

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

459 '''

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

461 D = self.datum

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

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

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

465

466 @Property_RO

467 def Ecef(self):

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

469 '''

470 return _MODS.ecef.EcefKarney # default

471

472 @Property_RO

473 def _Ecef_forward(self):

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

475 '''

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

477

478 @Property_RO

479 def _ecef9(self):

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

481 '''

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

483

484 @deprecated_method

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

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

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

488

489 @deprecated_method

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

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

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

493

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

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

496 using the U{Equirectangular Approximation / Projection

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

498

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

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

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

502

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

504 @kwarg radius_adjust_limit_wrap: Optional keyword arguments

505 for function L{pygeodesy.equirectangular},

506 overriding the default mean C{radius} of this

507 point's datum ellipsoid.

508

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

510

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

512

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

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

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

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

517 '''

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

519

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

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

522 an other point.

523

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

525

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

527 @kwarg radius_adjust_wrap: Optional keyword arguments for function

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

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

530

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

532

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

534

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

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

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

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

539 '''

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

541

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

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

544 U{ellipsoidal Earth to plane projection

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

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

547

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

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

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

551 datum ellipsoid.

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

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

554

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

556

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

558

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

560

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

562 L{cosineAndoyerLambertTo}, L{cosineForsytheAndoyerLambertTo},

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

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

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

566 '''

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

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

569

570 hubenyTo = flatLocalTo # for Karl Hubeny

571

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

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

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

575 Geographical_distance#Polar_coordinate_flat-Earth_formula>} formula.

576

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

578 @kwarg radius_wrap: Optional keyword arguments for function

579 L{pygeodesy.flatPolar}, overriding the

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

581 datum ellipsoid.

582

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

584

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

586

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

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

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

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

591 '''

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

593

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

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

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

597

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

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

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

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

602 this point's C{datum} ellipsoid.

603

604 @return: The ellipsoid intersection (C{LatLon}) or this very instance

605 if this C{pov's height} is C{0}.

606

607 @raise IntersectionError: Null C{pov} or B{C{los}} vector, this

608 C{pov's height} is negative or B{C{los}}

609 points outside the ellipsoid or in an

610 opposite direction.

611

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

613

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

615 '''

616 h = self.height

617 if not h:

618 r = self

619 elif h < 0:

620 raise IntersectionError(pov=self, los=los, height=h, txt=_no_(_height_))

621 elif los is None:

622 d = self.datum if earth is None else _spherical_datum(earth)

623 r = self.dup(datum=d, height=0, name=self.hartzell.__name__)

624 else:

625 c = self.toCartesian()

626 r = hartzell(c, los=los, earth=earth or self.datum, LatLon=self.classof)

627 return r

628

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

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

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

632 formula.

633

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

635 @kwarg radius_wrap: Optional keyword arguments for function

636 L{pygeodesy.haversine}, overriding the

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

638 datum ellipsoid.

639

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

641

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

643

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

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

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

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

648 '''

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

650

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

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

653

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

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

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

657

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

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

660 '''

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

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

663

664 @Property

665 def height(self):

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

667 '''

668 return self._height

669

670 @height.setter # PYCHOK setter!

671 def height(self, height):

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

673

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

675

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

677 '''

678 h = Height(height)

679 if self._height != h:

680 _update_all(self)

681 self._height = h

682

683 def _heigHt(self, height):

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

685 '''

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

687

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

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

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

691

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

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

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

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

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

697 ellipsoid's surface, otherwise the intersection of the

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

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

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

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

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

703

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

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

706

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

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

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

710

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

712

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

714

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

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

723 return r

724

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

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

727

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

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

730

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

732 '''

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

734

735 @deprecated_method

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

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

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

739

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

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

742 on diametrically opposite sides of the earth.

743

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

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

746

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

748 tolerance, C{False} otherwise.

749 '''

750 p = self.others(other)

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

752

753 @Property_RO

754 def isEllipsoidal(self):

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

756 '''

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

758

759 @Property_RO

760 def isEllipsoidalLatLon(self):

761 '''Get C{LatLon} base.

762 '''

763 return False

764

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

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

767

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

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

770

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

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

773

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

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

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

777

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

779

780 @see: Method L{isequalTo3}.

781 '''

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

783

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

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

786

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

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

789

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

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

792

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

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

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

796

797 @see: Method L{isequalTo}.

798 '''

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

800 _isequalTo(self, other, eps=eps)

801

802 @Property_RO

803 def isnormal(self):

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

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

806

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

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

809 '''

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

811

812 @Property_RO

813 def isSpherical(self):

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

815 '''

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

817

818 @Property_RO

819 def lam(self):

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

821 '''

822 return radians(self.lon)

823

824 @Property

825 def lat(self):

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

827 '''

828 return self._lat

829

830 @lat.setter # PYCHOK setter!

831 def lat(self, lat):

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

833

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

835 '''

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

837 if self._lat != lat:

838 _update_all(self)

839 self._lat = lat

840

841 @Property

842 def latlon(self):

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

844 '''

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

846

847 @latlon.setter # PYCHOK setter!

848 def latlon(self, latlonh):

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

850 (2- or 3-tuple or comma- or space-separated C{str}

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

852

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

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

855

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

857

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

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

860 '''

861 if isstr(latlonh):

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

863 else:

864 _xinstanceof(list, tuple, latlonh=latlonh)

865 if len(latlonh) == 3:

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

867 elif len(latlonh) != 2:

868 raise _ValueError(latlonh=latlonh)

869 else:

870 h = self.height

871

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

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

874 _update_all(self)

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

876

877 def latlon2(self, ndigits=0):

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

879

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

881

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

883 and rounded away from zero.

884

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

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

887 '''

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

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

890

891 @deprecated_method

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

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

894 return self.latlon2(ndigits=ndigits)

895

896 latlon2round = latlon_ # PYCHOK no cover

897

898 @Property

899 def latlonheight(self):

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

901 '''

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

903

904 @latlonheight.setter # PYCHOK setter!

905 def latlonheight(self, latlonh):

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

907 (2- or 3-tuple or comma- or space-separated C{str}

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

909

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

911 '''

912 self.latlon = latlonh

913

914 @Property

915 def lon(self):

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

917 '''

918 return self._lon

919

920 @lon.setter # PYCHOK setter!

921 def lon(self, lon):

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

923

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

925 '''

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

927 if self._lon != lon:

928 _update_all(self)

929 self._lon = lon

930

931 @Property_RO

932 def _ltp(self):

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

934 '''

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

936

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

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

939

940 Points are converted to and distances are computed in

941 I{geocentric}, cartesian space.

942

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

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

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

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

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

948 account for distances.

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

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

951

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

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

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

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

956 units as the cartesian axes.

957

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

959

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

961 C{Ecef} invalid.

962

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

964

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

966 '''

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

968 p = None # not used

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

970 if w and i:

971 q = _unrollon(p, q)

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

973 p = q

974

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

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

977

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

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

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

981

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

983 height=height)

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

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

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

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

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

989

990 def normal(self):

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

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

993

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

995 wasn't (but is now).

996

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

998 '''

999 n = self.isnormal

1000 if not n:

1001 self.latlon = normal(*self.latlon)

1002 return n

1003

1004 @Property_RO

1005 def _N_vector(self):

1006 '''(INTERNAL) Get the (C{nvectorBase._N_vector_})

1007 '''

1008 return _MODS.nvectorBase._N_vector_(*self.xyzh)

1009

1010 @Property_RO

1011 def phi(self):

1012 '''Get the latitude (B{C{radians}}).

1013 '''

1014 return radians(self.lat)

1015

1016 @Property_RO

1017 def philam(self):

1018 '''Get the lat- and longitude (L{PhiLam2Tuple}C{(phi, lam)}).

1019 '''

1020 return PhiLam2Tuple(self.phi, self.lam, name=self.name)

1021

1022 def philam2(self, ndigits=0):

1023 '''Return this point's lat- and longitude in C{radians}, rounded.

1024

1025 @kwarg ndigits: Number of (decimal) digits (C{int}).

1026

1027 @return: A L{PhiLam2Tuple}C{(phi, lam)}, both C{float}

1028 and rounded away from zero.

1029

1030 @note: The C{round}ed values are always C{float}, also

1031 if B{C{ndigits}} is omitted.

1032 '''

1033 return PhiLam2Tuple(round(self.phi, ndigits),

1034 round(self.lam, ndigits), name=self.name)

1035

1036 @Property_RO

1037 def philamheight(self):

1038 '''Get the lat-, longitude in C{radians} and height (L{PhiLam3Tuple}C{(phi, lam, height)}).

1039 '''

1040 return self.philam.to3Tuple(self.height)

1041

1042 @deprecated_method

1043 def points(self, points, closed=True): # PYCHOK no cover

1044 '''DEPRECATED, use method L{points2}.'''

1045 return self.points2(points, closed=closed)

1046

1047 def points2(self, points, closed=True):

1048 '''Check a path or polygon represented by points.

1049

1050 @arg points: The path or polygon points (C{LatLon}[])

1051 @kwarg closed: Optionally, consider the polygon closed,

1052 ignoring any duplicate or closing final

1053 B{C{points}} (C{bool}).

1054

1055 @return: A L{Points2Tuple}C{(number, points)}, an C{int}

1056 and C{list} or C{tuple}.

1057

1058 @raise PointsError: Insufficient number of B{C{points}}.

1059

1060 @raise TypeError: Some B{C{points}} are not C{LatLon}.

1061 '''

1062 return _MODS.iters.points2(points, closed=closed, base=self)

1063

1064 def PointsIter(self, points, loop=0, dedup=False, wrap=False):

1065 '''Return a C{PointsIter} iterator.

1066

1067 @arg points: The path or polygon points (C{LatLon}[])

1068 @kwarg loop: Number of loop-back points (non-negative C{int}).

1069 @kwarg dedup: Skip duplicate points (C{bool}).

1070 @kwarg wrap: If C{True}, wrap or I{normalize} the

1071 enum-/iterated B{C{points}} (C{bool}).

1072

1073 @return: A new C{PointsIter} iterator.

1074

1075 @raise PointsError: Insufficient number of B{C{points}}.

1076 '''

1077 return PointsIter(points, base=self, loop=loop, dedup=dedup, wrap=wrap)

1078

1079 def radii11(self, point2, point3, wrap=False):

1080 '''Return the radii of the C{Circum-}, C{In-}, I{Soddy} and C{Tangent}

1081 circles of a (planar) triangle formed by this and two other points.

1082

1083 @arg point2: Second point (C{LatLon}).

1084 @arg point3: Third point (C{LatLon}).

1085 @kwarg wrap: If C{True}, wrap or I{normalize} B{C{point2}} and

1086 B{C{point3}} (C{bool}).

1087

1088 @return: L{Radii11Tuple}C{(rA, rB, rC, cR, rIn, riS, roS, a, b, c, s)}.

1089

1090 @raise IntersectionError: Near-coincident or -colinear points.

1091

1092 @raise TypeError: Invalid B{C{point2}} or B{C{point3}}.

1093

1094 @see: Function L{pygeodesy.radii11}, U{Incircle

1095 <https://MathWorld.Wolfram.com/Incircle.html>}, U{Soddy Circles

1096 <https://MathWorld.Wolfram.com/SoddyCircles.html>} and U{Tangent

1097 Circles<https://MathWorld.Wolfram.com/TangentCircles.html>}.

1098 '''

1099 with _toCartesian3(self, point2, point3, wrap) as cs:

1100 return _radii11ABC(*cs, useZ=True)[0]

1101

1102 def _rhumb3(self, exact, radius): # != .sphericalBase._rhumbs3

1103 '''(INTERNAL) Get the C{rhumb} for this point's datum or for

1104 the B{C{radius}}' earth model iff non-C{None}.

1105 '''

1106 try:

1107 t = self._rhumb33[(exact, radius)]

1108 except KeyError:

1109 D = self.datum if radius is None else _spherical_datum(radius) # ellipsoidal OK

1110 r = D.ellipsoid.rhumb_(exact=exact) # or D.isSpherical)

1111 t = r, D, _MODS.karney.Caps

1112 d = self._rhumb33

1113 while d:

1114 d.popitem()

1115 d[(exact, radius)] = t # cache 3-tuple

1116 return t

1117

1118 @Property_RO

1119 def _rhumb33(self):

1120 return {} # single-item cache

1121

1122 def rhumbAzimuthTo(self, other, exact=False, radius=None, wrap=False):

1123 '''Return the azimuth (bearing) of a rhumb line (loxodrome)

1124 between this and an other (ellipsoidal) point.

1125

1126 @arg other: The other point (C{LatLon}).

1127 @kwarg exact: Exact C{Rhumb...} to use (C{bool} or C{Rhumb...}),

1128 see method L{Ellipsoid.rhumb_}.

1129 @kwarg radius: Optional earth radius (C{meter}) or earth model

1130 (L{Datum}, L{Ellipsoid}, L{Ellipsoid2} or

1131 L{a_f2Tuple}), overriding this point's datum.

1132 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the

1133 B{C{other}} point (C{bool}).

1134

1135 @return: Rhumb azimuth (compass C{degrees360}).

1136

1137 @raise TypeError: The B{C{other}} point is incompatible or

1138 B{C{radius}} is invalid.

1139 '''

1140 r, _, Cs = self._rhumb3(exact, radius)

1141 return r._Inverse(self, other, wrap, outmask=Cs.AZIMUTH).azi12

1142

1143 def rhumbDestination(self, distance, azimuth, exact=False, radius=None, height=None):

1144 '''Return the destination point having travelled the given distance

1145 from this point along a rhumb line (loxodrome) at the given azimuth.

1146

1147 @arg distance: Distance travelled (C{meter}, same units as this

1148 point's datum (ellipsoid) axes or B{C{radius}},

1149 may be negative.

1150 @arg azimuth: Azimuth (bearing) at this point (compass C{degrees}).

1151 @kwarg exact: Exact C{Rhumb...} to use (C{bool} or C{Rhumb...}),

1152 see method L{Ellipsoid.rhumb_}.

1153 @kwarg radius: Optional earth radius (C{meter}) or earth model

1154 (L{Datum}, L{Ellipsoid}, L{Ellipsoid2} or

1155 L{a_f2Tuple}), overriding this point's datum.

1156 @kwarg height: Optional height, overriding the default height

1157 (C{meter}).

1158

1159 @return: The destination point (ellipsoidal C{LatLon}).

1160

1161 @raise TypeError: Invalid B{C{radius}}.

1162

1163 @raise ValueError: Invalid B{C{distance}}, B{C{azimuth}},

1164 B{C{radius}} or B{C{height}}.

1165 '''

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

1167 d = r._Direct(self, azimuth, distance)

1168 h = self._heigHt(height)

1169 return self.classof(d.lat2, d.lon2, datum=D, height=h)

1170

1171 def rhumbDistanceTo(self, other, exact=False, radius=None, wrap=False):

1172 '''Return the distance from this to an other point along

1173 a rhumb line (loxodrome).

1174

1175 @arg other: The other point (C{LatLon}).

1176 @kwarg exact: Exact C{Rhumb...} to use (C{bool} or C{Rhumb...}),

1177 see method L{Ellipsoid.rhumb_}.

1178 @kwarg radius: Optional earth radius (C{meter}) or earth model

1179 (L{Datum}, L{Ellipsoid}, L{Ellipsoid2} or

1180 L{a_f2Tuple}), overriding this point's datum.

1181 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the

1182 B{C{other}} point (C{bool}).

1183

1184 @return: Distance (C{meter}, the same units as this point's

1185 datum (ellipsoid) axes or B{C{radius}}.

1186

1187 @raise TypeError: The B{C{other}} point is incompatible or

1188 B{C{radius}} is invalid.

1189

1190 @raise ValueError: Invalid B{C{radius}}.

1191 '''

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

1193 return r._Inverse(self, other, wrap, outmask=Cs.DISTANCE).s12

1194

1195 def rhumbLine(self, azimuth_other, exact=False, radius=None, wrap=False,

1196 **name_caps):

1197 '''Get a rhumb line through this point at a given azimuth or

1198 through this and an other point.

1199

1200 @arg azimuth_other: The azimuth of the rhumb line (compass

1201 C{degrees}) or the other point (C{LatLon}).

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

1203 see method L{Ellipsoid.rhumb_}.

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

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

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

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

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

1209 @kwarg name_caps: Optional C{B{name}=str} and C{caps}, see

1210 L{RhumbLine} C{B{caps}}.

1211

1212 @return: A C{RhumbLine} instance.

1213

1214 @raise TypeError: Invalid B{C{radius}} or BC{C{azimuth_other}}

1215 not a C{scalar} nor a C{LatLon}.

1216

1217 @see: Modules L{rhumbaux} and L{rhumbx}.

1218 '''

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

1220 a, kwds = azimuth_other, _xkwds(name_caps, name=self.name)

1221 if isscalar(a):

1222 r = r._DirectLine(self, a, **kwds)

1223 elif isinstance(a, LatLonBase):

1224 r = r._InverseLine(self, a, wrap, **kwds)

1225 else:

1226 raise _TypeError(azimuth_other=a)

1227 return r

1228

1229 def rhumbMidpointTo(self, other, exact=False, radius=None,

1230 height=None, fraction=_0_5, wrap=False):

1231 '''Return the (loxodromic) midpoint on the rhumb line between

1232 this and an other point.

1233

1234 @arg other: The other point (C{LatLon}).

1235 @kwarg exact: Exact C{Rhumb...} to use (C{bool} or C{Rhumb...}),

1236 see method L{Ellipsoid.rhumb_}.

1237 @kwarg radius: Optional earth radius (C{meter}) or earth model

1238 (L{Datum}, L{Ellipsoid}, L{Ellipsoid2} or

1239 L{a_f2Tuple}), overriding this point's datum.

1240 @kwarg height: Optional height, overriding the mean height

1241 (C{meter}).

1242 @kwarg fraction: Midpoint location from this point (C{scalar}),

1243 may be negative or greater than 1.0.

1244 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the

1245 B{C{other}} point (C{bool}).

1246

1247 @return: The midpoint at the given B{C{fraction}} along the

1248 rhumb line (C{LatLon}).

1249

1250 @raise TypeError: The B{C{other}} point is incompatible or

1251 B{C{radius}} is invalid.

1252

1253 @raise ValueError: Invalid B{C{height}} or B{C{fraction}}.

1254 '''

1255 r, D, _ = self._rhumb3(exact, radius)

1256 f = Scalar(fraction=fraction)

1257 d = r._Inverse(self, other, wrap) # C.AZIMUTH_DISTANCE

1258 d = r._Direct( self, d.azi12, d.s12 * f)

1259 h = self._havg(other, f=f, h=height)

1260 return self.classof(d.lat2, d.lon2, datum=D, height=h)

1261

1262 def thomasTo(self, other, wrap=False):

1263 '''Compute the distance between this and an other point using

1264 U{Thomas'<https://apps.DTIC.mil/dtic/tr/fulltext/u2/703541.pdf>}

1265 formula.

1266

1267 @arg other: The other point (C{LatLon}).

1268 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll

1269 the B{C{other}} point (C{bool}).

1270

1271 @return: Distance (C{meter}, same units as the axes of

1272 this point's datum ellipsoid).

1273

1274 @raise TypeError: The B{C{other}} point is not C{LatLon}.

1275

1276 @see: Function L{pygeodesy.thomas} and methods L{cosineAndoyerLambertTo},

1277 L{cosineForsytheAndoyerLambertTo}, L{cosineLawTo}, C{distanceTo*},

1278 L{equirectangularTo}, L{euclideanTo}, L{flatLocalTo}/L{hubenyTo},

1279 L{flatPolarTo}, L{haversineTo} and L{vincentysTo}.

1280 '''

1281 return self._distanceTo_(thomas_, other, wrap=wrap)

1282

1283 @deprecated_method

1284 def to2ab(self): # PYCHOK no cover

1285 '''DEPRECATED, use property L{philam}.'''

1286 return self.philam

1287

1288 def toCartesian(self, height=None, Cartesian=None, **Cartesian_kwds):

1289 '''Convert this point to cartesian, I{geocentric} coordinates,

1290 also known as I{Earth-Centered, Earth-Fixed} (ECEF).

1291

1292 @kwarg height: Optional height, overriding this point's height

1293 (C{meter}, conventionally).

1294 @kwarg Cartesian: Optional class to return the geocentric

1295 coordinates (C{Cartesian}) or C{None}.

1296 @kwarg Cartesian_kwds: Optional, additional B{C{Cartesian}}

1297 keyword arguments, ignored if

1298 C{B{Cartesian} is None}.

1299

1300 @return: A B{C{Cartesian}} or if B{C{Cartesian}} is C{None},

1301 an L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M,

1302 datum)} with C{C=0} and C{M} if available.

1303

1304 @raise TypeError: Invalid B{C{Cartesian}} or B{C{Cartesian_kwds}}.

1305 '''

1306 r = self._ecef9 if height is None else self.toEcef(height=height)

1307 if Cartesian is not None: # class or .classof

1308 r = self._xnamed(Cartesian(r, **Cartesian_kwds))

1309 _xdatum(r.datum, self.datum)

1310 return r

1311

1312 def _toCartesianEcef(self, height=None, i=None, up=2, **name_point):

1313 '''(INTERNAL) Convert to cartesian and check Ecef's before and after.

1314 '''

1315 p = self.others(up=up, **name_point)

1316 c = p.toCartesian(height=height)

1317 E = self.Ecef

1318 if E:

1319 for p in (p, c):

1320 e = getattr(p, LatLonBase.Ecef.name, None)

1321 if e not in (None, E): # PYCHOK no cover

1322 n, _ = name_point.popitem()

1323 if i is not None:

1324 Fmt.SQUARE(n, i)

1325 raise _ValueError(n, e, txt=_incompatible(E.__name__))

1326 return c

1327

1328 def toEcef(self, height=None, M=False):

1329 '''Convert this point to I{geocentric} coordinates, also known as

1330 I{Earth-Centered, Earth-Fixed} (U{ECEF<https://WikiPedia.org/wiki/ECEF>}).

1331

1332 @kwarg height: Optional height, overriding this point's height

1333 (C{meter}, conventionally).

1334 @kwarg M: Optionally, include the rotation L{EcefMatrix} (C{bool}).

1335

1336 @return: An L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M, datum)}

1337 with C{C=0} and C{M} if available.

1338

1339 @raise EcefError: A C{.datum} or an ECEF issue.

1340 '''

1341 return self._ecef9 if height in (None, self.height) else \

1342 self._Ecef_forward(self.lat, self.lon, height=height, M=M)

1343

1344 @deprecated_method

1345 def to3llh(self, height=None): # PYCHOK no cover

1346 '''DEPRECATED, use property L{latlonheight} or C{latlon.to3Tuple(B{height})}.'''

1347 return self.latlonheight if height in (None, self.height) else \

1348 self.latlon.to3Tuple(height)

1349

1350 def toLocal(self, Xyz=None, ltp=None, **Xyz_kwds):

1351 '''Convert this I{geodetic} point to I{local} C{X}, C{Y} and C{Z}.

1352

1353 @kwarg Xyz: Optional class to return C{X}, C{Y} and C{Z}

1354 (L{XyzLocal}, L{Enu}, L{Ned}) or C{None}.

1355 @kwarg ltp: The I{local tangent plane} (LTP) to use,

1356 overriding this point's LTP (L{Ltp}).

1357 @kwarg Xyz_kwds: Optional, additional B{C{Xyz}} keyword

1358 arguments, ignored if C{B{Xyz} is None}.

1359

1360 @return: An B{C{Xyz}} instance or if C{B{Xyz} is None},

1361 a L{Local9Tuple}C{(x, y, z, lat, lon, height,

1362 ltp, ecef, M)} with C{M=None}, always.

1363

1364 @raise TypeError: Invalid B{C{ltp}}.

1365 '''

1366 p = _MODS.ltp._xLtp(ltp, self._ltp)

1367 return p._ecef2local(self._ecef9, Xyz, Xyz_kwds)

1368

1369 def toLtp(self, Ecef=None):

1370 '''Return the I{local tangent plane} (LTP) for this point.

1371

1372 @kwarg Ecef: Optional ECEF I{class} (L{EcefKarney}, ...

1373 L{EcefYou}), overriding this point's C{Ecef}.

1374 '''

1375 return self._ltp if Ecef in (None, self.Ecef) else _MODS.ltp.Ltp(

1376 self, ecef=Ecef(self.datum), name=self.name)

1377

1378 def toNormal(self, deep=False, name=NN):

1379 '''Get this point I{normalized} to C{abs(lat) <= 90}

1380 and C{abs(lon) <= 180}.

1381

1382 @kwarg deep: If C{True} make a deep, otherwise a

1383 shallow copy (C{bool}).

1384 @kwarg name: Optional name of the copy (C{str}).

1385

1386 @return: A copy of this point, I{normalized} and

1387 optionally renamed (C{LatLon}).

1388

1389 @see: Property L{isnormal}, method L{normal} and function

1390 L{pygeodesy.normal}.

1391 '''

1392 ll = self.copy(deep=deep)

1393 _ = ll.normal()

1394 if name:

1395 ll.rename(name)

1396 return ll

1397

1398 def toNvector(self, h=None, Nvector=None, **Nvector_kwds):

1399 '''Convert this point to C{n-vector} (normal to the earth's surface)

1400 components, I{including height}.

1401

1402 @kwarg h: Optional height, overriding this point's

1403 height (C{meter}).

1404 @kwarg Nvector: Optional class to return the C{n-vector}

1405 components (C{Nvector}) or C{None}.

1406 @kwarg Nvector_kwds_wrap: Optional, additional B{C{Nvector}}

1407 keyword arguments, ignored if C{B{Nvector}

1408 is None}.

1409

1410 @return: A B{C{Nvector}} or a L{Vector4Tuple}C{(x, y, z, h)}

1411 if B{C{Nvector}} is C{None}.

1412

1413 @raise TypeError: Invalid B{C{Nvector}} or B{C{Nvector_kwds}}.

1414 '''

1415 return self.toVector(Vector=Nvector, h=self.height if h is None else h,

1416 ll=self, **Nvector_kwds)

1417

1418 def toStr(self, form=F_DMS, joined=_COMMASPACE_, m=_m_, **prec_sep_s_D_M_S): # PYCHOK expected

1419 '''Convert this point to a "lat, lon[, +/-height]" string, formatted

1420 in the given C{B{form}at}.

1421

1422 @kwarg form: The lat-/longitude C{B{form}at} to use (C{str}), see

1423 functions L{pygeodesy.latDMS} or L{pygeodesy.lonDMS}.

1424 @kwarg joined: Separator to join the lat-, longitude and heigth

1425 strings (C{str} or C{None} or C{NN} for non-joined).

1426 @kwarg m: Optional unit of the height (C{str}), use C{None} to

1427 exclude height from the returned string.

1428 @kwarg prec_sep_s_D_M_S: Optional C{B{prec}ision}, C{B{sep}arator},

1429 B{C{s_D}}, B{C{s_M}}, B{C{s_S}} and B{C{s_DMS}} keyword

1430 arguments, see function L{pygeodesy.latDMS} or

1431 L{pygeodesy.lonDMS}.

1432

1433 @return: This point in the specified C{B{form}at}, etc. (C{str} or

1434 a 2- or 3-tuple C{(lat_str, lon_str[, height_str])} if

1435 C{B{joined}=NN} or C{B{joined}=None}).

1436

1437 @see: Function L{pygeodesy.latDMS} or L{pygeodesy.lonDMS} for more

1438 details about keyword arguments C{B{form}at}, C{B{prec}ision},

1439 C{B{sep}arator}, B{C{s_D}}, B{C{s_M}}, B{C{s_S}} and B{C{s_DMS}}.

1440

1441 @example:

1442

1443 >>> LatLon(51.4778, -0.0016).toStr() # 51°28′40″N, 000°00′06″W

1444 >>> LatLon(51.4778, -0.0016).toStr(F_D) # 51.4778°N, 000.0016°W

1445 >>> LatLon(51.4778, -0.0016, 42).toStr() # 51°28′40″N, 000°00′06″W, +42.00m

1446 '''

1447 t = (latDMS(self.lat, form=form, **prec_sep_s_D_M_S),

1448 lonDMS(self.lon, form=form, **prec_sep_s_D_M_S))

1449 if self.height and m is not None:

1450 t += (self.heightStr(m=m),)

1451 return joined.join(t) if joined else t

1452

1453 def toVector(self, Vector=None, **Vector_kwds):

1454 '''Convert this point to C{n-vector} (normal to the earth's

1455 surface) components, I{ignoring height}.

1456

1457 @kwarg Vector: Optional class to return the C{n-vector}

1458 components (L{Vector3d}) or C{None}.

1459 @kwarg Vector_kwds: Optional, additional B{C{Vector}}

1460 keyword arguments, ignored if

1461 C{B{Vector} is None}.

1462

1463 @return: A B{C{Vector}} or a L{Vector3Tuple}C{(x, y, z)}

1464 if B{C{Vector}} is C{None}.

1465

1466 @raise TypeError: Invalid B{C{Vector}} or B{C{kwds}}.

1467

1468 @note: These are C{n-vector} x, y and z components,

1469 I{NOT} geocentric (ECEF) x, y and z coordinates!

1470 '''

1471 r = self._vector3tuple

1472 if Vector is not None:

1473 r = Vector(*r, **_xkwds(Vector_kwds, name=self.name))

1474 return r

1475

1476 def toVector3d(self):

1477 '''Convert this point to C{n-vector} (normal to the earth's

1478 surface) components, I{ignoring height}.

1479

1480 @return: Unit vector (L{Vector3d}).

1481

1482 @note: These are C{n-vector} x, y and z components,

1483 I{NOT} geocentric (ECEF) x, y and z coordinates!

1484 '''

1485 return self._vector3d # XXX .unit()

1486

1487 def toWm(self, **toWm_kwds):

1488 '''Convert this point to a WM coordinate.

1489

1490 @kwarg toWm_kwds: Optional L{pygeodesy.toWm} keyword arguments.

1491

1492 @return: The WM coordinate (L{Wm}).

1493

1494 @see: Function L{pygeodesy.toWm}.

1495 '''

1496 return self._wm if not toWm_kwds else _MODS.webmercator.toWm(

1497 self, **_xkwds(toWm_kwds, name=self.name))

1498

1499 @deprecated_method

1500 def to3xyz(self): # PYCHOK no cover

1501 '''DEPRECATED, use property L{xyz} or method L{toNvector}, L{toVector},

1502 L{toVector3d} or perhaps (geocentric) L{toEcef}.'''

1503 return self.xyz # self.toVector()

1504

1505 @Property_RO

1506 def _vector3d(self):

1507 '''(INTERNAL) Cache for L{toVector3d}.

1508 '''

1509 return self.toVector(Vector=Vector3d) # XXX .unit()

1510

1511 @Property_RO

1512 def _vector3tuple(self):

1513 '''(INTERNAL) Cache for L{toVector}.

1514 '''

1515 return philam2n_xyz(self.phi, self.lam, name=self.name)

1516

1517 def vincentysTo(self, other, **radius_wrap):

1518 '''Compute the distance between this and an other point using

1519 U{Vincenty's<https://WikiPedia.org/wiki/Great-circle_distance>}

1520 spherical formula.

1521

1522 @arg other: The other point (C{LatLon}).

1523 @kwarg radius_wrap: Optional keyword arguments for function

1524 L{pygeodesy.vincentys}, overriding the

1525 default mean C{radius} of this point's

1526 datum ellipsoid.

1527

1528 @return: Distance (C{meter}, same units as B{C{radius}}).

1529

1530 @raise TypeError: The B{C{other}} point is not C{LatLon}.

1531

1532 @see: Function L{pygeodesy.vincentys} and methods L{cosineAndoyerLambertTo},

1533 L{cosineForsytheAndoyerLambertTo}, L{cosineLawTo}, C{distanceTo*},

1534 L{equirectangularTo}, L{euclideanTo}, L{flatLocalTo}/L{hubenyTo},

1535 L{flatPolarTo}, L{haversineTo} and L{thomasTo}.

1536 '''

1537 return self._distanceTo(vincentys, other, **_xkwds(radius_wrap, radius=None))

1538

1539 @Property_RO

1540 def _wm(self):

1541 '''(INTERNAL) Get this point as webmercator (L{Wm}).

1542 '''

1543 return _MODS.webmercator.toWm(self)

1544

1545 @Property_RO

1546 def xyz(self):

1547 '''Get the C{n-vector} X, Y and Z components (L{Vector3Tuple}C{(x, y, z)})

1548

1549 @note: These are C{n-vector} x, y and z components, I{NOT}

1550 geocentric (ECEF) x, y and z coordinates!

1551 '''

1552 return self.toVector(Vector=Vector3Tuple)

1553

1554 @Property_RO

1555 def xyzh(self):

1556 '''Get the C{n-vector} X, Y, Z and H components (L{Vector4Tuple}C{(x, y, z, h)})

1557

1558 @note: These are C{n-vector} x, y and z components, I{NOT}

1559 geocentric (ECEF) x, y and z coordinates!

1560 '''

1561 return self.xyz.to4Tuple(self.height)

1562

1563

1564 class _toCartesian3(object): # see also .geodesicw._wargs, .vector2d._numpy

1565 '''(INTERNAL) Wrapper to convert 2 other points.

1566 '''

1567 @contextmanager # <https://www.python.org/dev/peps/pep-0343/> Examples

1568 def __call__(self, p, p2, p3, wrap, **kwds):

1569 try:

1570 if wrap:

1571 p2, p3 = map1(_Wrap.point, p2, p3)

1572 kwds = _xkwds(kwds, wrap=wrap)

1573 yield (p. toCartesian().copy(name=_point_), # copy to rename

1574 p._toCartesianEcef(up=4, point2=p2),

1575 p._toCartesianEcef(up=4, point3=p3))

1576 except (AssertionError, TypeError, ValueError) as x:

1577 raise _xError(x, point=p, point2=p2, point3=p3, **kwds)

1578

1579_toCartesian3 = _toCartesian3() # PYCHOK singleton

1580

1581

1582 def _trilaterate5(p1, d1, p2, d2, p3, d3, area=True, eps=EPS1, # MCCABE 13

1583 radius=R_M, wrap=False):

1584 '''(INTERNAL) Trilaterate three points by area overlap or by

1585 perimeter intersection of three circles.

1586

1587 @note: The B{C{radius}} is only needed for both the n-vectorial

1588 and C{sphericalTrigonometry.LatLon.distanceTo} methods and

1589 silently ignored by the C{ellipsoidalExact}, C{-GeodSolve},

1590 C{-Karney} and C{-Vincenty.LatLon.distanceTo} methods.

1591 '''

1592 p2, p3, w = _unrollon3(p1, p2, p3, wrap)

1593

1594 r1 = Distance_(distance1=d1)

1595 r2 = Distance_(distance2=d2)

1596 r3 = Distance_(distance3=d3)

1597 m = 0 if area else (r1 + r2 + r3)

1598 pc = 0

1599 t = []

1600 for _ in range(3):

1601 try: # intersection of circle (p1, r1) and (p2, r2)

1602 c1, c2 = p1.intersections2(r1, p2, r2, wrap=w)

1603

1604 if area: # check overlap

1605 if c1 is c2: # abutting

1606 c = c1

1607 else: # nearest point on radical

1608 c = p3.nearestOn(c1, c2, within=True, wrap=w)

1609 d = r3 - p3.distanceTo(c, radius=radius, wrap=w)

1610 if d > eps: # sufficient overlap

1611 t.append((d, c))

1612 m = max(m, d)

1613

1614 else: # check intersection

1615 for c in ((c1,) if c1 is c2 else (c1, c2)):

1616 d = fabs(r3 - p3.distanceTo(c, radius=radius, wrap=w))

1617 if d < eps: # below margin

1618 t.append((d, c))

1619 m = min(m, d)

1620

1621 except IntersectionError as x:

1622 if _concentric_ in str(x): # XXX ConcentricError?

1623 pc += 1

1624

1625 p1, r1, p2, r2, p3, r3 = p2, r2, p3, r3, p1, r1 # rotate

1626

1627 if t: # get min, max, points and count ...

1628 t = tuple(sorted(t))

1629 n = len(t), # as 1-tuple

1630 # ... or for a single trilaterated result,

1631 # min *is* max, min- *is* maxPoint and n=1, 2 or 3

1632 return Trilaterate5Tuple(t[0] + t[-1] + n) # *(t[0] + ...)

1633

1634 elif area and pc == 3: # all pairwise concentric ...

1635 r, p = min((r1, p1), (r2, p2), (r3, p3))

1636 m = max(r1, r2, r3)

1637 # ... return "smallest" point twice, the smallest

1638 # and largest distance and n=0 for concentric

1639 return Trilaterate5Tuple(float(r), p, float(m), p, 0)

1640

1641 n, f = (_overlap_, max) if area else (_intersection_, min)

1642 t = _COMMASPACE_(_no_(n), '%s %.3g' % (f.__name__, m))

1643 raise IntersectionError(area=area, eps=eps, wrap=wrap, txt=t)

1644

1645

1646__all__ += _ALL_DOCS(LatLonBase)

1647

1648# **) MIT License

1649#

1650# Copyright (C) 2016-2023 -- mrJean1 at Gmail -- All Rights Reserved.

1651#

1652# Permission is hereby granted, free of charge, to any person obtaining a

1653# copy of this software and associated documentation files (the "Software"),

1654# to deal in the Software without restriction, including without limitation

1655# the rights to use, copy, modify, merge, publish, distribute, sublicense,

1656# and/or sell copies of the Software, and to permit persons to whom the

1657# Software is furnished to do so, subject to the following conditions:

1658#

1659# The above copyright notice and this permission notice shall be included

1660# in all copies or substantial portions of the Software.

1661#

1662# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS

1663# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,

1664# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL

1665# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR

1666# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,

1667# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR

1668# OTHER DEALINGS IN THE SOFTWARE.