1

2# -*- coding: utf-8 -*-

3

4 u'''(INTERNAL) Private base class L{LatLonBase} for elliposiodal, spherical

5 and N-vectorial C{LatLon}s.

6

7 After I{(C) Chris Veness 2011-2015} published under the same MIT Licence**,

8 see U{https://www.Movable-Type.co.UK/scripts/latlong.html},

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

10 and U{https://www.Movable-Type.co.UK/scripts/latlong-vectors.html}.

11'''

12

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

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

15 _0_0, _0_5, _1_0

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

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

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

19 _TypeError, _ValueError, _xdatum, _xError, \

20 _xkwds, _xkwds_not

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

22 cosineForsytheAndoyerLambert_, cosineLaw, \

23 equirectangular, euclidean, flatLocal_, \

24 flatPolar, hartzell, haversine, isantipode, \

25 _isequalTo, isnormal, normal, philam2n_xyz, \

26 _spherical_datum, thomas_, vincentys

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

28 _intersection_, _m_, _LatLon_, _no_, \

29 _overlap_, _point_ # PYCHOK used!

30 from pygeodesy.iters import PointsIter, points2

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

32 from pygeodesy.named import _NamedBase, notOverloaded

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

34 Trilaterate5Tuple, Vector3Tuple

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

36 property_RO, _update_all

37 from pygeodesy.streprs import Fmt, hstr

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

39 Scalar, Scalar_

40 from pygeodesy.utily import _unrollon, _unrollon3, _Wrap

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

42 Circum3Tuple, _radii11ABC

43 from pygeodesy.vector3d import nearestOn6, Vector3d

44

45 from contextlib import contextmanager

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

47

48__all__ = _ALL_LAZY.latlonBase

49__version__ = '23.05.12'

50

51

52 class LatLonBase(_NamedBase):

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

54 ellipsoidal earth models.

55 '''

56 _clipid = INT0 # polygonal clip, see .booleans

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

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

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

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

61

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

63 '''New C{LatLon}.

64

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

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

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

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

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

70 (C{meter}, conventionally).

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

72 (C{bool}).

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

74

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

76

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

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

79

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

81

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

83

84 @example:

85

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

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

88 >>> r = LatLon(p)

89 '''

90 if name:

91 self.name = name

92

93 if lon is None:

94 try:

95 lat, lon = latlonh.lat, latlonh.lon

96 height = latlonh.get(_height_, height)

97 except AttributeError:

98 raise _IsnotError(_LatLon_, latlonh=latlonh)

99 if wrap:

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

101 elif wrap:

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

103 else:

104 lat = latlonh

105

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

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

108 if height: # elevation

109 self._height = Height(height)

110

111 def __eq__(self, other):

112 return self.isequalTo(other)

113

114 def __ne__(self, other):

115 return not self.isequalTo(other)

116

117 def __str__(self):

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

119

120 def antipode(self, height=None):

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

122 to this point.

123

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

125 this point's height otherwise.

126

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

128 '''

129 h = self._heigHt(height)

130 return self.classof(*antipode(*self.latlon), 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 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_(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_(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(cosineLaw, other, radius, wrap=wrap)

417

418 @property_RO

419 def datum(self): # PYCHOK no cover

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

421 '''

422 notOverloaded(self)

423

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

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

426

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

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

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

430 or C{None}.

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

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

433

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

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

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

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

438 is un-/specified.

439

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

441 '''

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

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

444

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

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

447 '''

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

449 if r is None:

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

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

452

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

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

455 '''

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

457 D = self.datum

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

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

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

461

462 @Property_RO

463 def Ecef(self):

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

465 '''

466 return _MODS.ecef.EcefKarney # default

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 @deprecated_method

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

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

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

484

485 @deprecated_method

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

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

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

489

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

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

492 using the U{Equirectangular Approximation / Projection

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

494

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

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

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

498

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

500 @kwarg radius_adjust_limit_wrap: Optional keyword arguments

501 for function L{pygeodesy.equirectangular},

502 overriding the default mean C{radius} of this

503 point's datum ellipsoid.

504

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

506

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

508

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

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

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

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

513 '''

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

515

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

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

518 an other point.

519

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

521

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

523 @kwarg radius_adjust_wrap: Optional keyword arguments for function

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

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

526

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

528

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

530

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

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

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

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

535 '''

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

537

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

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

540 U{ellipsoidal Earth to plane projection

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

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

543

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

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

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

547 datum ellipsoid.

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

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

550

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

552

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

554

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

556

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

558 L{cosineAndoyerLambertTo}, L{cosineForsytheAndoyerLambertTo},

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

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

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

562 '''

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

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

565

566 hubenyTo = flatLocalTo # for Karl Hubeny

567

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

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

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

571 Geographical_distance#Polar_coordinate_flat-Earth_formula>}formula.

572

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

574 @kwarg radius_wrap: Optional keyword arguments for function

575 L{pygeodesy.flatPolar}, overriding the

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

577 datum ellipsoid.

578

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

580

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

582

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

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

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

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

587 '''

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

589

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

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

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

593

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

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

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

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

598 this point's C{datum} ellipsoid.

599

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

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

602

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

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

605 points outside the ellipsoid or in an

606 opposite direction.

607

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

609

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

611 '''

612 h = self.height

613 if not h:

614 r = self

615 elif h < 0:

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

617 elif los is None:

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

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

620 else:

621 c = self.toCartesian()

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

623 return r

624

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

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

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

628 formula.

629

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

631 @kwarg radius_wrap: Optional keyword arguments for function

632 L{pygeodesy.haversine}, overriding the

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

634 datum ellipsoid.

635

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

637

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

639

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

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

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

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

644 '''

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

646

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

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

649

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

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

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

653

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

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

656 '''

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

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

659

660 def _heigHt(self, height):

661 '''(INTERNAL) Overriding C{height}.

662 '''

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

664

665 @Property

666 def height(self):

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

668 '''

669 return self._height

670

671 @height.setter # PYCHOK setter!

672 def height(self, height):

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

674

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

676

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

678 '''

679 h = Height(height)

680 if self._height != h:

681 _update_all(self)

682 self._height = h

683

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

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

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

687

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

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

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

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

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

693 ellipsoid's surface, otherwise the intersection of the

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

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

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

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

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

699

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

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

702

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

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

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

706

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

708

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

710

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

712 '''

713 c = self.toCartesian()

714 if LatLon is None:

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

716 else:

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

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

719 return r

720

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

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

723

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

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

726

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

728 '''

729 return hstr(self.height, prec=prec, m=m)

730

731 @deprecated_method

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

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

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

735

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

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

738 on diametrically opposite sides of the earth.

739

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

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

742

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

744 tolerance, C{False} otherwise.

745 '''

746 p = self.others(other)

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

748

749 @Property_RO

750 def isEllipsoidal(self):

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

752 '''

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

754

755 @Property_RO

756 def isEllipsoidalLatLon(self):

757 '''Get C{LatLon} base.

758 '''

759 return False

760

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

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

763

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

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

766

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

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

769

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

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

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

773

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

775

776 @see: Method L{isequalTo3}.

777 '''

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

779

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

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

782

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

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

785

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

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

788

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

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

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

792

793 @see: Method L{isequalTo}.

794 '''

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

796 _isequalTo(self, other, eps=eps)

797

798 @Property_RO

799 def isnormal(self):

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

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

802

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

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

805 '''

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

807

808 @Property_RO

809 def isSpherical(self):

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

811 '''

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

813

814 @Property_RO

815 def lam(self):

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

817 '''

818 return radians(self.lon)

819

820 @Property

821 def lat(self):

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

823 '''

824 return self._lat

825

826 @lat.setter # PYCHOK setter!

827 def lat(self, lat):

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

829

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

831 '''

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

833 if self._lat != lat:

834 _update_all(self)

835 self._lat = lat

836

837 @Property

838 def latlon(self):

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

840 '''

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

842

843 @latlon.setter # PYCHOK setter!

844 def latlon(self, latlonh):

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

846 (2- or 3-tuple or comma- or space-separated C{str}

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

848

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

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

851

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

853

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

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

856 '''

857 if isstr(latlonh):

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

859 else:

860 _xinstanceof(list, tuple, latlonh=latlonh)

861 if len(latlonh) == 3:

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

863 elif len(latlonh) != 2:

864 raise _ValueError(latlonh=latlonh)

865 else:

866 h = self.height

867

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

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

870 _update_all(self)

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

872

873 def latlon2(self, ndigits=0):

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

875

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

877

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

879 and rounded away from zero.

880

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

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

883 '''

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

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

886

887 @deprecated_method

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

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

890 return self.latlon2(ndigits=ndigits)

891

892 latlon2round = latlon_ # PYCHOK no cover

893

894 @Property

895 def latlonheight(self):

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

897 '''

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

899

900 @latlonheight.setter # PYCHOK setter!

901 def latlonheight(self, latlonh):

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

903 (2- or 3-tuple or comma- or space-separated C{str}

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

905

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

907 '''

908 self.latlon = latlonh

909

910 @Property

911 def lon(self):

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

913 '''

914 return self._lon

915

916 @lon.setter # PYCHOK setter!

917 def lon(self, lon):

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

919

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

921 '''

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

923 if self._lon != lon:

924 _update_all(self)

925 self._lon = lon

926

927 @Property_RO

928 def _ltp(self):

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

930 '''

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

932

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

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

935

936 Points are converted to and distances are computed in

937 I{geocentric}, cartesian space.

938

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

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

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

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

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

944 account for distances.

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

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

947

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

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

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

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

952 units as the cartesian axes.

953

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

955

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

957 C{Ecef} invalid.

958

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

960

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

962 '''

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

964 p = None # not used

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

966 if w and i:

967 q = _unrollon(p, q)

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

969 p = q

970

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

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

973

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

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

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

977

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

979 height=height)

980 r = self.Ecef(self.datum).reverse

981 p = r(c).toLatLon(**kwds)

982 s = r(s).toLatLon(**kwds) if s is not c else p

983 e = r(e).toLatLon(**kwds) if e is not c else p

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

985

986 def normal(self):

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

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

989

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

991 wasn't (but is now).

992

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

994 '''

995 n = self.isnormal

996 if not n:

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

998 return n

999

1000 @Property_RO

1001 def _N_vector(self):

1002 '''(INTERNAL) Get the (C{nvectorBase._N_vector_})

1003 '''

1004 return _MODS.nvectorBase._N_vector_(*self.xyzh)

1005

1006 @Property_RO

1007 def phi(self):

1008 '''Get the latitude (B{C{radians}}).

1009 '''

1010 return radians(self.lat)

1011

1012 @Property_RO

1013 def philam(self):

1014 '''Get the lat- and longitude (L{PhiLam2Tuple}C{(phi, lam)}).

1015 '''

1016 return PhiLam2Tuple(self.phi, self.lam, name=self.name)

1017

1018 def philam2(self, ndigits=0):

1019 '''Return this point's lat- and longitude in C{radians}, rounded.

1020

1021 @kwarg ndigits: Number of (decimal) digits (C{int}).

1022

1023 @return: A L{PhiLam2Tuple}C{(phi, lam)}, both C{float}

1024 and rounded away from zero.

1025

1026 @note: The C{round}ed values are always C{float}, also

1027 if B{C{ndigits}} is omitted.

1028 '''

1029 return PhiLam2Tuple(round(self.phi, ndigits),

1030 round(self.lam, ndigits), name=self.name)

1031

1032 @Property_RO

1033 def philamheight(self):

1034 '''Get the lat-, longitude in C{radians} and height (L{PhiLam3Tuple}C{(phi, lam, height)}).

1035 '''

1036 return self.philam.to3Tuple(self.height)

1037

1038 @deprecated_method

1039 def points(self, points, closed=True): # PYCHOK no cover

1040 '''DEPRECATED, use method L{points2}.'''

1041 return self.points2(points, closed=closed)

1042

1043 def points2(self, points, closed=True):

1044 '''Check a path or polygon represented by points.

1045

1046 @arg points: The path or polygon points (C{LatLon}[])

1047 @kwarg closed: Optionally, consider the polygon closed,

1048 ignoring any duplicate or closing final

1049 B{C{points}} (C{bool}).

1050

1051 @return: A L{Points2Tuple}C{(number, points)}, an C{int}

1052 and C{list} or C{tuple}.

1053

1054 @raise PointsError: Insufficient number of B{C{points}}.

1055

1056 @raise TypeError: Some B{C{points}} are not C{LatLon}.

1057 '''

1058 return points2(points, closed=closed, base=self)

1059

1060 def PointsIter(self, points, loop=0, dedup=False, wrap=False):

1061 '''Return a C{PointsIter} iterator.

1062

1063 @arg points: The path or polygon points (C{LatLon}[])

1064 @kwarg loop: Number of loop-back points (non-negative C{int}).

1065 @kwarg dedup: Skip duplicate points (C{bool}).

1066 @kwarg wrap: If C{True}, wrap or I{normalize} the

1067 enum-/iterated B{C{points}} (C{bool}).

1068

1069 @return: A new C{PointsIter} iterator.

1070

1071 @raise PointsError: Insufficient number of B{C{points}}.

1072 '''

1073 return PointsIter(points, base=self, loop=loop, dedup=dedup, wrap=wrap)

1074

1075 def radii11(self, point2, point3, wrap=False):

1076 '''Return the radii of the C{Circum-}, C{In-}, I{Soddy} and C{Tangent}

1077 circles of a (planar) triangle formed by this and two other points.

1078

1079 @arg point2: Second point (C{LatLon}).

1080 @arg point3: Third point (C{LatLon}).

1081 @kwarg wrap: If C{True}, wrap or I{normalize} B{C{point2}} and

1082 B{C{point3}} (C{bool}).

1083

1084 @return: L{Radii11Tuple}C{(rA, rB, rC, cR, rIn, riS, roS, a, b, c, s)}.

1085

1086 @raise IntersectionError: Near-coincident or -colinear points.

1087

1088 @raise TypeError: Invalid B{C{point2}} or B{C{point3}}.

1089

1090 @see: Function L{pygeodesy.radii11}, U{Incircle

1091 <https://MathWorld.Wolfram.com/Incircle.html>}, U{Soddy Circles

1092 <https://MathWorld.Wolfram.com/SoddyCircles.html>} and U{Tangent

1093 Circles<https://MathWorld.Wolfram.com/TangentCircles.html>}.

1094 '''

1095 with _toCartesian3(self, point2, point3, wrap) as cs:

1096 return _radii11ABC(*cs, useZ=True)[0]

1097

1098 def _rhumbx3(self, exact, radius): # != .sphericalBase._rhumbs3

1099 '''(INTERNAL) Get the C{rhumb} for this point's datum or for

1100 the earth model or earth B{C{radius}} if not C{None}.

1101 '''

1102 D = self.datum if radius is None else _spherical_datum(radius) # ellipsoidal OK

1103 x = _MODS.rhumbx # XXX Property_RO?

1104 r = D.ellipsoid.rhumbx if exact else \

1105 x.Rhumb(D, exact=False, name=D.name)

1106 return r, D, x.Caps

1107

1108 def rhumbAzimuthTo(self, other, exact=False, radius=None, wrap=False):

1109 '''Return the azimuth (bearing) of a rhumb line (loxodrome)

1110 between this and an other (ellipsoidal) point.

1111

1112 @arg other: The other point (C{LatLon}).

1113 @kwarg exact: If C{True}, use the I{exact} L{Rhumb} (C{bool}),

1114 default C{False}.

1115 @kwarg radius: Optional earth radius (C{meter}) or earth model

1116 (L{Datum}, L{Ellipsoid}, L{Ellipsoid2} or

1117 L{a_f2Tuple}), overriding this point's datum.

1118 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the

1119 B{C{other}} point (C{bool}).

1120

1121 @return: Rhumb azimuth (compass C{degrees360}).

1122

1123 @raise TypeError: The B{C{other}} point is incompatible or

1124 B{C{radius}} is invalid.

1125 '''

1126 r, _, C = self._rhumbx3(exact, radius)

1127 return r._Inverse(self, other, wrap, outmask=C.AZIMUTH).azi12

1128

1129 def rhumbDestination(self, distance, azimuth, exact=False, radius=None, height=None):

1130 '''Return the destination point having travelled the given distance

1131 from this point along a rhumb line (loxodrome) at the given azimuth.

1132

1133 @arg distance: Distance travelled (C{meter}, same units as this

1134 point's datum (ellipsoid) axes or B{C{radius}},

1135 may be negative.

1136 @arg azimuth: Azimuth (bearing) at this point (compass C{degrees}).

1137 @kwarg exact: If C{True}, use the I{exact} L{Rhumb} (C{bool}),

1138 default C{False}.

1139 @kwarg radius: Optional earth radius (C{meter}) or earth model

1140 (L{Datum}, L{Ellipsoid}, L{Ellipsoid2} or

1141 L{a_f2Tuple}), overriding this point's datum.

1142 @kwarg height: Optional height, overriding the default height

1143 (C{meter}).

1144

1145 @return: The destination point (ellipsoidal C{LatLon}).

1146

1147 @raise TypeError: Invalid B{C{radius}}.

1148

1149 @raise ValueError: Invalid B{C{distance}}, B{C{azimuth}},

1150 B{C{radius}} or B{C{height}}.

1151 '''

1152 r, D, _ = self._rhumbx3(exact, radius)

1153 d = r._Direct(self, azimuth, distance)

1154 h = self._heigHt(height)

1155 return self.classof(d.lat2, d.lon2, datum=D, height=h)

1156

1157 def rhumbDistanceTo(self, other, exact=False, radius=None, wrap=False):

1158 '''Return the distance from this to an other point along

1159 a rhumb line (loxodrome).

1160

1161 @arg other: The other point (C{LatLon}).

1162 @kwarg exact: If C{True}, use the I{exact} L{Rhumb} (C{bool}),

1163 default C{False}.

1164 @kwarg radius: Optional earth radius (C{meter}) or earth model

1165 (L{Datum}, L{Ellipsoid}, L{Ellipsoid2} or

1166 L{a_f2Tuple}), overriding this point's datum.

1167 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the

1168 B{C{other}} point (C{bool}).

1169

1170 @return: Distance (C{meter}, the same units as this point's

1171 datum (ellipsoid) axes or B{C{radius}}.

1172

1173 @raise TypeError: The B{C{other}} point is incompatible or

1174 B{C{radius}} is invalid.

1175

1176 @raise ValueError: Invalid B{C{radius}}.

1177 '''

1178 r, _, C = self._rhumbx3(exact, radius)

1179 return r._Inverse(self, other, wrap, outmask=C.DISTANCE).s12

1180

1181 def rhumbLine(self, azimuth_other, exact=False, radius=None, wrap=False,

1182 **name_caps):

1183 '''Get a rhumb line through this point at a given azimuth or

1184 through this and an other point.

1185

1186 @arg azimuth_other: The azimuth of the rhumb line (compass

1187 C{degrees}) or the other point (C{LatLon}).

1188 @kwarg exact: If C{True}, use the I{exact} L{Rhumb} (C{bool}),

1189 default C{False}.

1190 @kwarg radius: Optional earth radius (C{meter}) or earth model

1191 (L{Datum}, L{Ellipsoid}, L{Ellipsoid2} or

1192 L{a_f2Tuple}), overriding this point's datum.

1193 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the

1194 C{azimuth_B{other}} point (C{bool}).

1195 @kwarg name_caps: Optional C{B{name}=str} and C{caps}, see

1196 L{RhumbLine} C{B{caps}}.

1197

1198 @return: A L{RhumbLine} instance.

1199

1200 @raise TypeError: Invalid B{C{radius}} or BC{C{azimuth_other}}

1201 not a C{scalar} nor a C{LatLon}.

1202

1203 @see: Classes L{RhumbLine} and L{Rhumb}, property L{Rhumb.exact}

1204 and methods L{Rhumb.DirectLine} and L{Rhumb.InverseLine}.

1205 '''

1206 r, _, _ = self._rhumbx3(exact, radius)

1207 a, kwds = azimuth_other, _xkwds(name_caps, name=self.name)

1208 if isscalar(a):

1209 r = r._DirectLine(self, a, **kwds)

1210 elif isinstance(a, LatLonBase):

1211 r = r._InverseLine(self, a, wrap, **kwds)

1212 else:

1213 raise _TypeError(azimuth_other=a)

1214 return r

1215

1216 def rhumbMidpointTo(self, other, exact=False, radius=None,

1217 height=None, fraction=_0_5, wrap=False):

1218 '''Return the (loxodromic) midpoint on the rhumb line between

1219 this and an other point.

1220

1221 @arg other: The other point (C{LatLon}).

1222 @kwarg exact: If C{True}, use the I{exact} L{Rhumb} (C{bool}),

1223 default C{False}.

1224 @kwarg radius: Optional earth radius (C{meter}) or earth model

1225 (L{Datum}, L{Ellipsoid}, L{Ellipsoid2} or

1226 L{a_f2Tuple}), overriding this point's datum.

1227 @kwarg height: Optional height, overriding the mean height

1228 (C{meter}).

1229 @kwarg fraction: Midpoint location from this point (C{scalar}),

1230 may be negative or greater than 1.0.

1231 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the

1232 B{C{other}} point (C{bool}).

1233

1234 @return: The midpoint at the given B{C{fraction}} along the

1235 rhumb line (C{LatLon}).

1236

1237 @raise TypeError: The B{C{other}} point is incompatible or

1238 B{C{radius}} is invalid.

1239

1240 @raise ValueError: Invalid B{C{height}} or B{C{fraction}}.

1241 '''

1242 r, D, _ = self._rhumbx3(exact, radius)

1243 f = Scalar(fraction=fraction)

1244 d = r._Inverse(self, other, wrap) # C.AZIMUTH_DISTANCE

1245 d = r._Direct( self, d.azi12, d.s12 * f)

1246 h = self._havg(other, f=f, h=height)

1247 return self.classof(d.lat2, d.lon2, datum=D, height=h)

1248

1249 def thomasTo(self, other, wrap=False):

1250 '''Compute the distance between this and an other point using

1251 U{Thomas'<https://apps.DTIC.mil/dtic/tr/fulltext/u2/703541.pdf>}

1252 formula.

1253

1254 @arg other: The other point (C{LatLon}).

1255 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll

1256 the B{C{other}} point (C{bool}).

1257

1258 @return: Distance (C{meter}, same units as the axes of

1259 this point's datum ellipsoid).

1260

1261 @raise TypeError: The B{C{other}} point is not C{LatLon}.

1262

1263 @see: Function L{pygeodesy.thomas} and methods L{cosineAndoyerLambertTo},

1264 L{cosineForsytheAndoyerLambertTo}, L{cosineLawTo}, C{distanceTo*},

1265 L{equirectangularTo}, L{euclideanTo}, L{flatLocalTo}/L{hubenyTo},

1266 L{flatPolarTo}, L{haversineTo} and L{vincentysTo}.

1267 '''

1268 return self._distanceTo_(thomas_, other, wrap=wrap)

1269

1270 @deprecated_method

1271 def to2ab(self): # PYCHOK no cover

1272 '''DEPRECATED, use property L{philam}.'''

1273 return self.philam

1274

1275 def toCartesian(self, height=None, Cartesian=None, **Cartesian_kwds):

1276 '''Convert this point to cartesian, I{geocentric} coordinates,

1277 also known as I{Earth-Centered, Earth-Fixed} (ECEF).

1278

1279 @kwarg height: Optional height, overriding this point's height

1280 (C{meter}, conventionally).

1281 @kwarg Cartesian: Optional class to return the geocentric

1282 coordinates (C{Cartesian}) or C{None}.

1283 @kwarg Cartesian_kwds: Optional, additional B{C{Cartesian}}

1284 keyword arguments, ignored if

1285 C{B{Cartesian} is None}.

1286

1287 @return: A B{C{Cartesian}} or if B{C{Cartesian}} is C{None},

1288 an L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M,

1289 datum)} with C{C=0} and C{M} if available.

1290

1291 @raise TypeError: Invalid B{C{Cartesian}} or B{C{Cartesian_kwds}}.

1292 '''

1293 r = self._ecef9 if height is None else self.toEcef(height=height)

1294 if Cartesian is not None: # class or .classof

1295 r = self._xnamed(Cartesian(r, **Cartesian_kwds))

1296 _xdatum(r.datum, self.datum)

1297 return r

1298

1299 def _toCartesianEcef(self, height=None, i=None, up=2, **name_point):

1300 '''(INTERNAL) Convert to cartesian and check Ecef's before and after.

1301 '''

1302 p = self.others(up=up, **name_point)

1303 c = p.toCartesian(height=height)

1304 E = self.Ecef

1305 if E:

1306 for p in (p, c):

1307 e = getattr(p, LatLonBase.Ecef.name, None)

1308 if e not in (None, E): # PYCHOK no cover

1309 n, _ = name_point.popitem()

1310 if i is not None:

1311 Fmt.SQUARE(n, i)

1312 raise _ValueError(n, e, txt=_incompatible(E.__name__))

1313 return c

1314

1315 def toEcef(self, height=None, M=False):

1316 '''Convert this point to I{geocentric} coordinates, also known as

1317 I{Earth-Centered, Earth-Fixed} (U{ECEF<https://WikiPedia.org/wiki/ECEF>}).

1318

1319 @kwarg height: Optional height, overriding this point's height

1320 (C{meter}, conventionally).

1321 @kwarg M: Optionally, include the rotation L{EcefMatrix} (C{bool}).

1322

1323 @return: An L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M, datum)}

1324 with C{C=0} and C{M} if available.

1325

1326 @raise EcefError: A C{.datum} or an ECEF issue.

1327 '''

1328 return self._ecef9 if height in (None, self.height) else \

1329 self._Ecef_forward(self.lat, self.lon, height=height, M=M)

1330

1331 @deprecated_method

1332 def to3llh(self, height=None): # PYCHOK no cover

1333 '''DEPRECATED, use property L{latlonheight} or C{latlon.to3Tuple(B{height})}.'''

1334 return self.latlonheight if height in (None, self.height) else \

1335 self.latlon.to3Tuple(height)

1336

1337 def toLocal(self, Xyz=None, ltp=None, **Xyz_kwds):

1338 '''Convert this I{geodetic} point to I{local} C{X}, C{Y} and C{Z}.

1339

1340 @kwarg Xyz: Optional class to return C{X}, C{Y} and C{Z}

1341 (L{XyzLocal}, L{Enu}, L{Ned}) or C{None}.

1342 @kwarg ltp: The I{local tangent plane} (LTP) to use,

1343 overriding this point's LTP (L{Ltp}).

1344 @kwarg Xyz_kwds: Optional, additional B{C{Xyz}} keyword

1345 arguments, ignored if C{B{Xyz} is None}.

1346

1347 @return: An B{C{Xyz}} instance or if C{B{Xyz} is None},

1348 a L{Local9Tuple}C{(x, y, z, lat, lon, height,

1349 ltp, ecef, M)} with C{M=None}, always.

1350

1351 @raise TypeError: Invalid B{C{ltp}}.

1352 '''

1353 p = _MODS.ltp._xLtp(ltp, self._ltp)

1354 return p._ecef2local(self._ecef9, Xyz, Xyz_kwds)

1355

1356 def toLtp(self, Ecef=None):

1357 '''Return the I{local tangent plane} (LTP) for this point.

1358

1359 @kwarg Ecef: Optional ECEF I{class} (L{EcefKarney}, ...

1360 L{EcefYou}), overriding this point's C{Ecef}.

1361 '''

1362 return self._ltp if Ecef in (None, self.Ecef) else _MODS.ltp.Ltp(

1363 self, ecef=Ecef(self.datum), name=self.name)

1364

1365 def toNormal(self, deep=False, name=NN):

1366 '''Get this point I{normalized} to C{abs(lat) <= 90}

1367 and C{abs(lon) <= 180}.

1368

1369 @kwarg deep: If C{True} make a deep, otherwise a

1370 shallow copy (C{bool}).

1371 @kwarg name: Optional name of the copy (C{str}).

1372

1373 @return: A copy of this point, I{normalized} and

1374 optionally renamed (C{LatLon}).

1375

1376 @see: Property L{isnormal}, method L{normal} and function

1377 L{pygeodesy.normal}.

1378 '''

1379 ll = self.copy(deep=deep)

1380 _ = ll.normal()

1381 if name:

1382 ll.rename(name)

1383 return ll

1384

1385 def toNvector(self, h=None, Nvector=None, **Nvector_kwds):

1386 '''Convert this point to C{n-vector} (normal to the earth's surface)

1387 components, I{including height}.

1388

1389 @kwarg h: Optional height, overriding this point's

1390 height (C{meter}).

1391 @kwarg Nvector: Optional class to return the C{n-vector}

1392 components (C{Nvector}) or C{None}.

1393 @kwarg Nvector_kwds_wrap: Optional, additional B{C{Nvector}}

1394 keyword arguments, ignored if C{B{Nvector}

1395 is None}.

1396

1397 @return: A B{C{Nvector}} or a L{Vector4Tuple}C{(x, y, z, h)}

1398 if B{C{Nvector}} is C{None}.

1399

1400 @raise TypeError: Invalid B{C{Nvector}} or B{C{Nvector_kwds}}.

1401 '''

1402 return self.toVector(Vector=Nvector, h=self.height if h is None else h,

1403 ll=self, **Nvector_kwds)

1404

1405 def toStr(self, form=F_DMS, joined=_COMMASPACE_, m=_m_, **prec_sep_s_D_M_S): # PYCHOK expected

1406 '''Convert this point to a "lat, lon[, +/-height]" string, formatted

1407 in the given C{B{form}at}.

1408

1409 @kwarg form: The lat-/longitude C{B{form}at} to use (C{str}), see

1410 functions L{pygeodesy.latDMS} or L{pygeodesy.lonDMS}.

1411 @kwarg joined: Separator to join the lat-, longitude and heigth

1412 strings (C{str} or C{None} or C{NN} for non-joined).

1413 @kwarg m: Optional unit of the height (C{str}), use C{None} to

1414 exclude height from the returned string.

1415 @kwarg prec_sep_s_D_M_S: Optional C{B{prec}ision}, C{B{sep}arator},

1416 B{C{s_D}}, B{C{s_M}}, B{C{s_S}} and B{C{s_DMS}} keyword

1417 arguments, see function L{pygeodesy.latDMS} or

1418 L{pygeodesy.lonDMS}.

1419

1420 @return: This point in the specified C{B{form}at}, etc. (C{str} or

1421 a 2- or 3-tuple C{(lat_str, lon_str[, height_str])} if

1422 C{B{joined}=NN} or C{B{joined}=None}).

1423

1424 @see: Function L{pygeodesy.latDMS} or L{pygeodesy.lonDMS} for more

1425 details about keyword arguments C{B{form}at}, C{B{prec}ision},

1426 C{B{sep}arator}, B{C{s_D}}, B{C{s_M}}, B{C{s_S}} and B{C{s_DMS}}.

1427

1428 @example:

1429

1430 >>> LatLon(51.4778, -0.0016).toStr() # 51°28′40″N, 000°00′06″W

1431 >>> LatLon(51.4778, -0.0016).toStr(F_D) # 51.4778°N, 000.0016°W

1432 >>> LatLon(51.4778, -0.0016, 42).toStr() # 51°28′40″N, 000°00′06″W, +42.00m

1433 '''

1434 t = (latDMS(self.lat, form=form, **prec_sep_s_D_M_S),

1435 lonDMS(self.lon, form=form, **prec_sep_s_D_M_S))

1436 if self.height and m is not None:

1437 t += (self.heightStr(m=m),)

1438 return joined.join(t) if joined else t

1439

1440 def toVector(self, Vector=None, **Vector_kwds):

1441 '''Convert this point to C{n-vector} (normal to the earth's

1442 surface) components, I{ignoring height}.

1443

1444 @kwarg Vector: Optional class to return the C{n-vector}

1445 components (L{Vector3d}) or C{None}.

1446 @kwarg Vector_kwds: Optional, additional B{C{Vector}}

1447 keyword arguments, ignored if

1448 C{B{Vector} is None}.

1449

1450 @return: A B{C{Vector}} or a L{Vector3Tuple}C{(x, y, z)}

1451 if B{C{Vector}} is C{None}.

1452

1453 @raise TypeError: Invalid B{C{Vector}} or B{C{kwds}}.

1454

1455 @note: These are C{n-vector} x, y and z components,

1456 I{NOT} geocentric (ECEF) x, y and z coordinates!

1457 '''

1458 r = self._vector3tuple

1459 if Vector is not None:

1460 r = Vector(*r, **_xkwds(Vector_kwds, name=self.name))

1461 return r

1462

1463 def toVector3d(self):

1464 '''Convert this point to C{n-vector} (normal to the earth's

1465 surface) components, I{ignoring height}.

1466

1467 @return: Unit vector (L{Vector3d}).

1468

1469 @note: These are C{n-vector} x, y and z components,

1470 I{NOT} geocentric (ECEF) x, y and z coordinates!

1471 '''

1472 return self._vector3d # XXX .unit()

1473

1474 @deprecated_method

1475 def to3xyz(self): # PYCHOK no cover

1476 '''DEPRECATED, use property L{xyz} or method L{toNvector}, L{toVector},

1477 L{toVector3d} or perhaps (geocentric) L{toEcef}.'''

1478 return self.xyz # self.toVector()

1479

1480 @Property_RO

1481 def _vector3d(self):

1482 '''(INTERNAL) Cache for L{toVector3d}.

1483 '''

1484 return self.toVector(Vector=Vector3d) # XXX .unit()

1485

1486 @Property_RO

1487 def _vector3tuple(self):

1488 '''(INTERNAL) Cache for L{toVector}.

1489 '''

1490 return philam2n_xyz(self.phi, self.lam, name=self.name)

1491

1492 def vincentysTo(self, other, **radius_wrap):

1493 '''Compute the distance between this and an other point using

1494 U{Vincenty's<https://WikiPedia.org/wiki/Great-circle_distance>}

1495 spherical formula.

1496

1497 @arg other: The other point (C{LatLon}).

1498 @kwarg radius_wrap: Optional keyword arguments for function

1499 L{pygeodesy.vincentys}, overriding the

1500 default mean C{radius} of this point's

1501 datum ellipsoid.

1502

1503 @return: Distance (C{meter}, same units as B{C{radius}}).

1504

1505 @raise TypeError: The B{C{other}} point is not C{LatLon}.

1506

1507 @see: Function L{pygeodesy.vincentys} and methods L{cosineAndoyerLambertTo},

1508 L{cosineForsytheAndoyerLambertTo}, L{cosineLawTo}, C{distanceTo*},

1509 L{equirectangularTo}, L{euclideanTo}, L{flatLocalTo}/L{hubenyTo},

1510 L{flatPolarTo}, L{haversineTo} and L{thomasTo}.

1511 '''

1512 return self._distanceTo(vincentys, other, **_xkwds(radius_wrap, radius=None))

1513

1514 @Property_RO

1515 def xyz(self):

1516 '''Get the C{n-vector} X, Y and Z components (L{Vector3Tuple}C{(x, y, z)})

1517

1518 @note: These are C{n-vector} x, y and z components, I{NOT}

1519 geocentric (ECEF) x, y and z coordinates!

1520 '''

1521 return self.toVector(Vector=Vector3Tuple)

1522

1523 @Property_RO

1524 def xyzh(self):

1525 '''Get the C{n-vector} X, Y, Z and H components (L{Vector4Tuple}C{(x, y, z, h)})

1526

1527 @note: These are C{n-vector} x, y and z components, I{NOT}

1528 geocentric (ECEF) x, y and z coordinates!

1529 '''

1530 return self.xyz.to4Tuple(self.height)

1531

1532

1533 class _toCartesian3(object): # see also .geodesicw._wargs, .vector2d._numpy

1534 '''(INTERNAL) Wrapper convert 2 other points.

1535 '''

1536 @contextmanager # <https://www.python.org/dev/peps/pep-0343/> Examples

1537 def __call__(self, p, p2, p3, wrap, **kwds):

1538 try:

1539 if wrap:

1540 p2, p3 = map1(_Wrap.point, p2, p3)

1541 kwds = _xkwds(kwds, wrap=wrap)

1542 yield (p. toCartesian().copy(name=_point_), # copy to rename

1543 p._toCartesianEcef(up=4, point2=p2),

1544 p._toCartesianEcef(up=4, point3=p3))

1545 except (AssertionError, TypeError, ValueError) as x:

1546 raise _xError(x, point=p, point2=p2, point3=p3, **kwds)

1547

1548_toCartesian3 = _toCartesian3() # PYCHOK singleton

1549

1550

1551 def _trilaterate5(p1, d1, p2, d2, p3, d3, area=True, eps=EPS1, # MCCABE 13

1552 radius=R_M, wrap=False):

1553 '''(INTERNAL) Trilaterate three points by area overlap or by

1554 perimeter intersection of three circles.

1555

1556 @note: The B{C{radius}} is only needed for both the n-vectorial

1557 and C{sphericalTrigonometry.LatLon.distanceTo} methods and

1558 silently ignored by the C{ellipsoidalExact}, C{-GeodSolve},

1559 C{-Karney} and C{-Vincenty.LatLon.distanceTo} methods.

1560 '''

1561 p2, p3, w = _unrollon3(p1, p2, p3, wrap)

1562

1563 r1 = Distance_(distance1=d1)

1564 r2 = Distance_(distance2=d2)

1565 r3 = Distance_(distance3=d3)

1566 m = 0 if area else (r1 + r2 + r3)

1567 pc = 0

1568 t = []

1569 for _ in range(3):

1570 try: # intersection of circle (p1, r1) and (p2, r2)

1571 c1, c2 = p1.intersections2(r1, p2, r2, wrap=w)

1572

1573 if area: # check overlap

1574 if c1 is c2: # abutting

1575 c = c1

1576 else: # nearest point on radical

1577 c = p3.nearestOn(c1, c2, within=True, wrap=w)

1578 d = r3 - p3.distanceTo(c, radius=radius, wrap=w)

1579 if d > eps: # sufficient overlap

1580 t.append((d, c))

1581 m = max(m, d)

1582

1583 else: # check intersection

1584 for c in ((c1,) if c1 is c2 else (c1, c2)):

1585 d = fabs(r3 - p3.distanceTo(c, radius=radius, wrap=w))

1586 if d < eps: # below margin

1587 t.append((d, c))

1588 m = min(m, d)

1589

1590 except IntersectionError as x:

1591 if _concentric_ in str(x): # XXX ConcentricError?

1592 pc += 1

1593

1594 p1, r1, p2, r2, p3, r3 = p2, r2, p3, r3, p1, r1 # rotate

1595

1596 if t: # get min, max, points and count ...

1597 t = tuple(sorted(t))

1598 n = (len(t),) # as 1-tuple

1599 # ... or for a single trilaterated result,

1600 # min *is* max, min- *is* maxPoint and n=1

1601 return Trilaterate5Tuple(t[0] + t[-1] + n) # *(t[0] + ...)

1602

1603 elif area and pc == 3: # all pairwise concentric ...

1604 r, p = min((r1, p1), (r2, p2), (r3, p3))

1605 m = max(r1, r2, r3)

1606 # ... return "smallest" point twice, the smallest

1607 # and largest distance and n=0 for concentric

1608 return Trilaterate5Tuple(float(r), p, float(m), p, 0)

1609

1610 n, f = (_overlap_, max) if area else (_intersection_, min)

1611 t = '%s (%s %.3f)' % (_no_(n), f.__name__, m)

1612 raise IntersectionError(area=area, eps=eps, wrap=wrap, txt=t)

1613

1614

1615__all__ += _ALL_DOCS(LatLonBase)

1616

1617# **) MIT License

1618#

1619# Copyright (C) 2016-2023 -- mrJean1 at Gmail -- All Rights Reserved.

1620#

1621# Permission is hereby granted, free of charge, to any person obtaining a

1622# copy of this software and associated documentation files (the "Software"),

1623# to deal in the Software without restriction, including without limitation

1624# the rights to use, copy, modify, merge, publish, distribute, sublicense,

1625# and/or sell copies of the Software, and to permit persons to whom the

1626# Software is furnished to do so, subject to the following conditions:

1627#

1628# The above copyright notice and this permission notice shall be included

1629# in all copies or substantial portions of the Software.

1630#

1631# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS

1632# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,

1633# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL

1634# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR

1635# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,

1636# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR

1637# OTHER DEALINGS IN THE SOFTWARE.