Coverage for pygeodesy/latlonBase.py: 93%

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1 

2# -*- coding: utf-8 -*- 

3 

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

5and N-vectorial C{LatLon}s. 

6 

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

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

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

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

11''' 

12 

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

14from 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 

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

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

19 _TypeError, _ValueError, _xdatum, _xError, \ 

20 _xkwds, _xkwds_not 

21from 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 

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

28 _intersection_, _m_, _LatLon_, _no_, \ 

29 _overlap_, _point_ # PYCHOK used! 

30from pygeodesy.iters import PointsIter, points2 

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

32from pygeodesy.named import _NamedBase, notOverloaded 

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

34 Trilaterate5Tuple, Vector3Tuple 

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

36 property_RO, _update_all 

37from pygeodesy.streprs import Fmt, hstr 

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

39 Scalar, Scalar_ 

40from pygeodesy.utily import _unrollon, _unrollon3, _Wrap 

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

42 Circum3Tuple, _radii11ABC 

43from pygeodesy.vector3d import nearestOn6, Vector3d 

44 

45from contextlib import contextmanager 

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

47 

48__all__ = _ALL_LAZY.latlonBase 

49__version__ = '23.05.12' 

50 

51 

52class 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 

1533class _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 

1551def _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.