Coverage for pygeodesy/geodesici.py: 90%

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1 

2# -*- coding: utf-8 -*- 

3 

4u'''Classes L{Intersectool} and L{Intersector}, a pure Python version of I{Karney}'s C++ class 

5U{Intersect<https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1Intersect.html>} 

6to find the intersections of two geodesic lines or line segments. 

7 

8L{Intersectool} and L{Intersector} methods C{All}, C{Closest}, C{Next} and C{Segment} produce 

9 

10L{XDict} instances with 4 or more items. Adjacent methods C{All5}, C{Closest5}, C{Next5} and 

11C{Segment} return or yield L{Intersectool5Tuple} or L{Intersector5Tuple}s with the lat-, longitude 

12azimuth of each intersection as an extended or C{Position}-like L{GDict}. 

13 

14Class L{Intersectool} is a wrapper to invoke I{Karney}'s U{IntersectTool 

15<https://GeographicLib.SourceForge.io/C++/doc/IntersectTool.1.html>} utility like class L{Intersector}, 

16but intended I{for testing purposes only}. 

17 

18Set env variable C{PYGEODESY_INTERSECTTOOL} to the (fully qualified) path of the C{IntersectTool} executable. 

19 

20For more details, see the C++ U{GeographicLib<https://GeographicLib.SourceForge.io/C++/doc/index.html>} 

21documentation, I{Charles F.F. Karney}'s paper U{Geodesics intersections<https://arxiv.org/abs/2308.00495>} 

22and I{S. Baselga Moreno & J.C. Martinez-Llario}'s U{Intersection and point-to-line solutions for geodesics 

23on the ellipsoid<https://riunet.UPV.ES/bitstream/handle/10251/122902/Revised_Manuscript.pdf>}. 

24''' 

25# make sure int/int division yields float quotient 

26from __future__ import division as _; del _ # PYCHOK semicolon 

27 

28from pygeodesy.basics import _copy, _enumereverse, map1, \ 

29 _xinstanceof, _xor 

30from pygeodesy.constants import EPS, INF, INT0, PI, PI2, PI_4, \ 

31 _0_0, _0_5, _1_0, _1_5, _2_0, _3_0, \ 

32 _90_0, isfinite 

33from pygeodesy.ellipsoids import _EWGS84, Fmt, unstr 

34from pygeodesy.errors import GeodesicError, IntersectionError, _an, \ 

35 _xgeodesics, _xkwds_get, _xkwds_kwds 

36# from pygeodesy.errors import exception_chaining # _MODS 

37from pygeodesy.fmath import euclid, fdot 

38from pygeodesy.fsums import Fsum, fsum1_, _ceil 

39from pygeodesy.interns import NN, _A_, _B_, _c_, _COMMASPACE_, \ 

40 _HASH_, _M_, _not_, _SPACE_, _too_ 

41from pygeodesy.interns import _m_ # PYCHOK used! 

42from pygeodesy.karney import Caps, _diff182, GDict, _sincos2de 

43from pygeodesy.lazily import _ALL_LAZY, _ALL_MODS as _MODS, \ 

44 _getenv, _PYGEODESY_INTERSECTTOOL_ 

45from pygeodesy.named import ADict, _NamedBase, _NamedTuple, _Pass 

46from pygeodesy.props import deprecated_method, Property, \ 

47 Property_RO, property_RO 

48from pygeodesy.solveBase import _SolveCapsBase, pairs 

49# from pygeodesy.streprs import pairs # from .solveBase 

50# from pygeodesy.streprs import Fmt, unstr # from .ellipsoids 

51from pygeodesy.units import Degrees, Float, Int, Lat, Lon, \ 

52 Meter, Meter_ 

53from pygeodesy.utily import sincos2, atan2, fabs, radians 

54 

55# from math import atan2, ceil as _ceil, fabs, radians # .fsums, .utily 

56 

57__all__ = _ALL_LAZY.geodesici 

58__version__ = '24.07.09' 

59 

60_0t = 0, # int 

61_1_1t = -1, +1 

62_1_0_1t = -1, 0, +1 

63_c__ = '-c' # PYCHOK used! 

64_C__ = '-C' # PYCHOK used! 

65_EPS3 = EPS * _3_0 

66_EPSr5 = pow(EPS, 0.2) # PYCHOK used! 7.4e-4 or ~3" 

67_i__ = '-i' # PYCHOK used! 

68_latA_ = 'latA' 

69_lonA_ = 'lonA' 

70_n__ = '-n' # PYCHOK used! 

71_o__ = '-o' # PYCHOK used! 

72_R__ = '-R' 

73_sAB_ = 'sAB' 

74_sX0_ = 'sX0' 

75_TRIPS = 128 

76 

77 

78class Azi(Degrees): 

79 '''(INTERNAL) Azimuth C{Unit}. 

80 ''' 

81 pass 

82 

83 

84class XDict(ADict): 

85 '''4+Item result from L{Intersectool} and L{Intersector} methods 

86 C{All}, C{Closest}, C{Next} and C{Segment} with the intersection 

87 offsets C{sA}, C{sB} and C{sX0} in C{meter} and the coincidence 

88 indicator C{c}, an C{int}, +1 for parallel, -1 for anti-parallel 

89 or 0 otherwise. 

90 

91 Offsets C{sA} and C{sB} are distances measured I{along} geodesic 

92 line C{glA} respectively C{glB}, but C{sX0} is the I{L1-distance} 

93 between the intersection and the I{origin} C{X0}. 

94 

95 Segment indicators C{kA} and C{kB} are C{0} if the segments 

96 intersect or C{-1} or C{+1} if the intersection is I{before} 

97 the start, respectively I{after} the end of the segment, like 

98 L{Intersection3Tuple<Intersection3Tuple>}. Segment indicator 

99 C{k} is I{Karney}'s C{segmode}, equal C{kA * 3 + kB}. 

100 ''' 

101 _Delta = EPS # default margin, see C{Intersector._Delto} 

102 

103 def __add__(self, other): 

104 X = _copy(self) 

105 X += other 

106 return X 

107 

108 def __eq__(self, other): 

109 return not self.__ne__(other) 

110 

111 def __iadd__(self, other): 

112 if isinstance(other, tuple): # and len(other) == 2: 

113 a, b = other 

114 else: 

115 # _xinstanceof(XDict, other=other) 

116 a = other.sA 

117 b = other.sB 

118 if other.c: 

119 self.c = other.c 

120 self.sA += a # PYCHOK sA 

121 self.sB += b # PYCHOK sB 

122 return self 

123 

124 def __le__(self, other): 

125 # _xinstanceof(XDict, other=other) 

126 return self == other or self < other 

127 

128 def __lt__(self, other): 

129 # _xinstanceof(XDict, other=other) 

130 return (self.sA < other.sA or (self.sA == other.sA and # PYCHOK sA 

131 self.sB < other.sB) and self != other) # PYCHOK sB 

132 

133 def __ne__(self, other): 

134 # _xinstanceof(XDict, other=other) 

135 return self is not other and self.L1(other) > self._Delta 

136 

137 def _corners(self, sA, sB, T2): 

138 # yield all corners further than C{T2} 

139 a, b = self.sA, self.sB # PYCHOK sA, sB 

140 for x in (0, sA): 

141 for y in (0, sB): 

142 if _L1(x - a, y - b) >= T2: 

143 yield XDict_(x, y) 

144 

145 def _fixCoincident(self, X, c0=0): 

146 # return the mid-point if C{X} is anti-/parallel 

147 c = c0 or X.c 

148 if c: 

149 s = (self.sA - X.sA + # PYCHOK sA 

150 (self.sB - X.sB) * c) * _0_5 # PYCHOK sB 

151 X = X + (s, s * c) # NOT += 

152 return X 

153 

154 def _fixSegment(self, sA, sB): # PYCHOK no cover 

155 # modify this anti-/parallel C{XDict} 

156 a, b, c = self.sA, self.sB, self.c # PYCHOK sA, sB, c 

157 

158 def _g(): # intersection in smallest gap 

159 if c > 0: # distance to [A, B] is |(a - b) - (A - B)| 

160 t = a - b # consider corners [0, sB] and [sA, 0] 

161 t = fabs(t + sB) < fabs(t - sA) 

162 s = a + b 

163 else: # distance to [A, B] is |(a + b) - (A + B)| 

164 t = a + b # consider corner [0, 0] and [sA, sB] 

165 t = fabs(t) < fabs(t - (sA + sB)) 

166 s = sB + (a - b) 

167 return (sB if t else sA) - s 

168 

169 ta = -a 

170 tb = sA - a 

171 tc = -c * b 

172 td = -c * (b - sB) 

173 

174 ga = 0 <= (b + c * ta) <= sB 

175 gb = 0 <= (b + c * tb) <= sB 

176 gc = 0 <= (a + tc) <= sA 

177 gd = 0 <= (a + td) <= sA 

178 

179 # test opposite rectangle sides first 

180 s = ((ta + tb) if ga and gb else ( 

181 (tc + td) if gc and gd else ( 

182 (ta + tc) if ga and gc else ( 

183 (ta + td) if ga and gd else ( 

184 (tb + tc) if gb and gc else ( 

185 (tb + td) if gb and gd else _g())))))) * _0_5 

186 self += s, s * c 

187 

188 @property_RO 

189 def _is00(self): 

190 return not (self.sA or self.sB) # PYCHOK sA, sB 

191 

192 def L1(self, other=None): 

193 '''Return the C{L1} distance. 

194 ''' 

195 a, b = self.sA, self.sB # PYCHOK sA, sB 

196 if other is not None: 

197 # _xinstanceof(XDict, other=other) 

198 a -= other.sA 

199 b -= other.sB 

200 return _L1(a, b) 

201 

202 def _nD1(self, D1): 

203 # yield the C{Closest} starts 

204 D_ = 0, D1, -D1 

205 for a, b in zip((0, 1, -1, 0, 0), 

206 (0, 0, 0, 1, -1)): 

207 yield self + (D_[a], D_[b]) 

208 

209 def _nD2(self, D2): 

210 # yield the C{Next} starts 

211 D22 = D2 * _2_0 

212 D_ = 0, D2, D22, -D22, -D2 

213 for a, b in zip((-1, -1, 1, 1, -2, 0, 2, 0), 

214 (-1, 1, -1, 1, 0, 2, 0, -2)): 

215 yield self + (D_[a], D_[b]) 

216 

217 def _nmD3(self, n, m, D3): # d3 / 2 

218 # yield the C{All} starts 

219 yield self 

220 for i in range(n, m, 2): 

221 for j in range(n, m, 2): 

222 if i or j: # skip self 

223 yield self + ((i + j) * D3, 

224 (i - j) * D3) 

225 

226 def _outSide(self, sA, sB): 

227 # is this C{Xdist} outside one or both segments? 

228 a, b = self.sA, self.sB # PYCHOK sA, sB 

229 kA = -1 if a < 0 else (+1 if a > sA else INT0) 

230 kB = -1 if b < 0 else (+1 if b > sB else INT0) 

231 self.set_(kA=kA, kB=kB, k=(kA * 3 + kB) or INT0) 

232 return bool(kA or kB) 

233 

234 def _skip(self, S_, T1_Delta): 

235 # remove starts from list C{S_} near this C{XDict} 

236 for j, S in _enumereverse(S_): 

237 if S.L1(self) < T1_Delta: 

238 S_.pop(j) 

239 

240 

241def XDict_(sA=_0_0, sB=_0_0, c=INT0, sX0=_0_0): 

242 '''(INTERNAL) New L{XDict} from positionals. 

243 ''' 

244 return XDict(sA=sA, sB=sB, c=c, sX0=sX0) 

245 

246_X000 = XDict_() # PYCHOK origin 

247_XINF = XDict_(INF) 

248 

249 

250class _IntersectBase(_NamedBase): 

251 '''(INTERNAL) Base class for L{Intersectool} and L{Intersector}. 

252 ''' 

253 # _g = None 

254 

255 def __init__(self, geodesic, **name): 

256 _xinstanceof(*_EWGS84._Geodesics, geodesic=geodesic) 

257 self._g = geodesic 

258 if name: 

259 self.name = name 

260 

261 @Property_RO 

262 def a(self): 

263 '''Get the I{equatorial} radius, semi-axis (C{meter}). 

264 ''' 

265 return self.ellipsoid.a 

266 

267 equatoradius = a # = Requatorial 

268 

269 @Property_RO 

270 def _cHalf(self): # normalizer, semi-circumference 

271 return self.R * PI # ~20K Km WGS84 

272 

273 @Property_RO 

274 def _cMax(self): # outer circumference 

275 return max(self.a, self.ellipsoid.b, self.R) * PI2 

276 

277 @property_RO 

278 def datum(self): 

279 '''Get the geodesic's datum (C{Datum}). 

280 ''' 

281 return self.geodesic.datum 

282 

283 @Property_RO 

284 def ellipsoid(self): 

285 '''Get the C{geodesic}'s ellipsoid (C{Ellipsoid}). 

286 ''' 

287 return self.geodesic.datum.ellipsoid 

288 

289 @Property_RO 

290 def f(self): 

291 '''Get the I{flattening} (C{scalar}), C{0} for spherical, negative for prolate. 

292 ''' 

293 return self.ellipsoid.f 

294 

295 flattening = f 

296 

297 @property_RO 

298 def geodesic(self): 

299 '''Get the C{geodesic} (C{Geodesic...}). 

300 ''' 

301 return self._g 

302 

303 def _Inversa12(self, A, B=None): 

304 lls = (0, 0, A, 0) if B is None else (A.lat2, A.lon2, 

305 B.lat2, B.lon2) 

306 r = self._g.Inverse(*lls, outmask=Caps.DISTANCE) 

307 return r.s12, r.a12 # .a12 always in r 

308 

309 def _ll3z4ll(self, lat1, lon1, azi1_lat2, *lon2): 

310 t = Lat(lat1=lat1), Lon(lon1=lon1) 

311 if lon2: # get azis for All, keep lat-/lons 

312 t += Lat(lat2=azi1_lat2), Lon(lon2=lon2[0]) 

313 else: 

314 t += Azi(azi1=azi1_lat2), 

315 return t 

316 

317 @deprecated_method 

318 def Next5s(self, glA, glB, X0=_X000, aMax=1801, sMax=0, **unused): 

319 '''DEPRECATED on 2024.07.02, use method L{All5}.''' 

320 return self.All5(glA, glB, X0=X0, aMaX0=aMax, sMaX0=sMax) # PYCHOK attr 

321 

322 @Property_RO 

323 def R(self): 

324 '''Get the I{authalic} earth radius (C{meter}). 

325 ''' 

326 return self.ellipsoid.R2 

327 

328 def _sMaX0_C2(self, aMaX0, **sMaX0_C): 

329 _g = _xkwds_get 

330 s = _g(sMaX0_C, sMaX0=self._cMax) 

331 s = _g(sMaX0_C, sMax=s) # for backward ... 

332 a = _g(sMaX0_C, aMax=aMaX0) # ... compatibility 

333 if a: # degrees to meter, approx. 

334 s = max(s, self.R * radians(a)) # ellipsoid.degrees2m(a) 

335 s = _g(sMaX0_C, _R=s) 

336 if s < _EPS3: 

337 s = _EPS3 # raise GeodesicError(sMaX0=s) 

338 return s, _xkwds_kwds(sMaX0_C, _C=False) 

339 

340 def _xNext(self, glA, glB, eps1, **eps_C): # PYCHOK no cover 

341 eps1 = _xkwds_get(eps_C, eps=eps1) # eps for backward compatibility 

342 if eps1 is not None: 

343 a = glA.lat1 - glB.lat1 

344 b = glA.lon1 - glB.lon1 

345 if euclid(a, b) > eps1: 

346 raise GeodesicError(lat=a, lon=b, eps1=eps1) 

347 return _xkwds_kwds(eps_C, _C=False) 

348 

349 

350class Intersectool(_IntersectBase, _SolveCapsBase): 

351 '''Wrapper to invoke I{Karney}'s utility U{IntersectTool 

352 <https://GeographicLib.SourceForge.io/C++/doc/IntersectTool.1.html>} 

353 similar to class L{Intersector<geodesici.Intersector>}. 

354 

355 @note: Use property C{IntersectTool} or env variable C{PYGEODESY_INTERSECTTOOL} 

356 to specify the (fully qualified) path to the C{IntersectTool} executable. 

357 

358 @note: This C{Intersectool} is intended I{for testing purposes only}, it invokes 

359 the C{IntersectTool} executable for I{every} method call. 

360 ''' 

361 _Error = GeodesicError 

362 _linelimit = 1200 # line printer width X 10 

363 _Names_ABs = _latA_, _lonA_, 'latB', 'lonB', _sAB_ # -C to stderr 

364 _Names_XDict = 'sA', 'sB', _c_ # plus 'k' from -i or 'sX0' from -R 

365 _Xable_name = 'IntersectTool' 

366 _Xable_path = _getenv(_PYGEODESY_INTERSECTTOOL_, _PYGEODESY_INTERSECTTOOL_) 

367 

368 def __init__(self, a_geodesic=None, f=None, **name): 

369 '''New L{IntersectTool}. 

370 

371 @arg a_geodesic: Earth' equatorial axis (C{meter}) or a geodesic 

372 (L{GeodesicExact<pygeodesy.geodesicx.GeodesicExact>}, 

373 wrapped L{Geodesic<pygeodesy.geodesicw.Geodesic>} or 

374 L{GeodesicSolve<pygeodesy.geodsolve.GeodesicSolve>}). 

375 @kwarg f: Earth' flattening (C{scalar}), required if B{C{a_geodesic}} 

376 is in C{meter}, ignored otherwise. 

377 @kwarg name: Optional C{B{name}=NN} (C{str}). 

378 

379 @raise GeodesicError: The eccentricity of the B{C{geodesic}}'s ellipsoid is too 

380 large or no initial convergence. 

381 

382 @see: The B{Note} at I{Karney}'s C++ U{Intersect<https://GeographicLib.sourceforge.io/ 

383 C++/doc/classGeographicLib_1_1Intersect.html#ae41f54c9a44836f6c8f140f6994930cf>}. 

384 ''' 

385 g = self._GeodesicExact() if a_geodesic is None else (a_geodesic if f is None else 

386 self._GeodesicExact(a_geodesic, f)) 

387 _IntersectBase.__init__(self, g, **name) 

388 

389 def All(self, glA, glB, X0=_X000, eps1=_0_0, aMaX0=0, **sMaX0_C): 

390 '''Yield all intersection of two geodesic lines up to a limit. 

391 

392 @kwarg eps1: Optional margin for the L{euclid<pygeodesy.euclid>}ean distance 

393 (C{degrees}) between the C{(lat1, lon1)} points of both lines for 

394 using the L{IntersectTool<Intersectool.IntersectTool>}'s C{"-n"} 

395 option, unless C{B{eps1}=None}. 

396 

397 @return: An L{XDict} for each intersection. 

398 ''' 

399 def _xz2(**gl): 

400 try: 

401 n, gl = gl.popitem() # _xkwds_item2(gl) 

402 try: 

403 return self._c_alt, (gl.azi1,) 

404 except (AttributeError, KeyError): 

405 return self._i_alt, (gl.lat2, gl.lon2) 

406 except Exception as x: 

407 raise GeodesicError(n, gl, cause=x) 

408 

409 _t, a = _xz2(glA=glA) 

410 _x, b = _xz2(glB=glB) 

411 if _x is not _t: 

412 raise GeodesicError(glA=glA, glB=glB) 

413 

414 A = glA.lat1, glA.lon1 

415 B = glB.lat1, glB.lon1 

416 if _x is self._c_alt: 

417 if X0 is _X000 or X0._is00: 

418 if eps1 is not None and \ 

419 euclid(glA.lat1 - glB.lat1, 

420 glA.lon1 - glB.lon1) <= eps1: 

421 _x, B = self._n_alt, () 

422 else: # non-zero offset 

423 _x = self._o_alt 

424 b += X0.sA, X0.sB 

425 

426 sMaX0, _C = self._sMaX0_C2(aMaX0, **sMaX0_C) 

427 for X in self._XDictInvoke(_x, _sX0_, (A + a + B + b), 

428 _R=sMaX0, **_C): 

429 yield X.set_(c=int(X.c)) 

430 

431 def All5(self, glA, glB, X0=_X000, **aMaX0_sMaX0): 

432 '''Yield all intersection of two geodesic lines up to a limit. 

433 

434 @return: An L{Intersectool5Tuple} for each intersection. 

435 ''' 

436 for X in self.All(glA, glB, X0=X0, _C=True, **aMaX0_sMaX0): 

437 yield self._In5T(glA, glB, X, X) 

438 

439 @Property_RO 

440 def _C_option(self): 

441 return (_C__,) 

442 

443 @Property_RO 

444 def _cmdBasic(self): 

445 '''(INTERNAL) Get the basic C{IntersectTool} cmd (C{tuple}). 

446 ''' 

447 return (self.IntersectTool,) + (self._e_option + 

448 self._E_option + 

449 self._p_option) 

450 

451 @Property_RO 

452 def _c_alt(self): 

453 '''(INTERNAL) Get the C{Closest} format (C{tuple}). 

454 ''' 

455 return _c__, # latA lonA aziA latB lonB aziB 

456 

457 def Closest(self, glA, glB, X0=_X000, _C=False): 

458 '''Find the closest intersection of two geodesic lines. 

459 

460 @kwarg _C: Use C{B{_C}=True} to include the C{"-C"} results (C{bool}). 

461 

462 @return: An L{XDict}. 

463 ''' 

464 args = glA.lat1, glA.lon1, glA.azi1, \ 

465 glB.lat1, glB.lon1, glB.azi1 

466 if X0 is _X000 or X0._is000: 

467 _x = self._c_alt 

468 else: 

469 _x = self._o_alt 

470 args += X0.sA, X0.sB 

471 return self._XDictInvoke(_x, NN, args, _C=_C) # _R=None) 

472 

473 def Closest5(self, glA, glB, **unused): 

474 '''Find the closest intersection of two geodesic lines. 

475 

476 @return: An L{Intersectool5Tuple}. 

477 ''' 

478 X = self.Closest(glA, glB, _C=True) 

479 return self._In5T(glA, glB, X, X) 

480 

481 @property_RO 

482 def _GeodesicExact(self): 

483 '''Get the I{class} L{GeodesicExact}, I{once}. 

484 ''' 

485 Intersectool._GeodesicExact = G = _MODS.geodesicx.GeodesicExact # overwrite property_RO 

486 return G 

487 

488 @Property_RO 

489 def _i_alt(self): 

490 '''(INTERNAL) Get the C{Segment} format (C{tuple}). 

491 ''' 

492 return _i__, # latA1 lonA1 latA2 lonA2 latB1 lonB1 latB2 lonB2 

493 

494 def _In5T(self, glA, glB, S, X, k2=False, **_2X): 

495 A = GDict(glA).set_(lat2=X.latA, lon2=X.lonA, s12=S.sA) 

496 B = GDict(glB).set_(lat2=X.latB, lon2=X.lonB, s12=S.sB) 

497 if k2: 

498 A.set_(k2=X.kA) 

499 B.set_(k2=X.kB) 

500 s, a = self._Inversa12(A, B) 

501 sAB = _xkwds_get(X, sAB=s) 

502 if a and s and s != sAB: 

503 a *= sAB / s # adjust a 

504 return Intersectool5Tuple(A._2X(glA, **_2X), 

505 B._2X(glB, **_2X), sAB, a, X.c) 

506 

507 @Property 

508 def IntersectTool(self): 

509 '''Get the U{IntersectTool<https://GeographicLib.SourceForge.io/C++/doc/IntersectTool.1.html>} 

510 executable (C{filename}). 

511 ''' 

512 return self._Xable_path 

513 

514 @IntersectTool.setter # PYCHOK setter! 

515 def IntersectTool(self, path): 

516 '''Set the U{IntersectTool<https://GeographicLib.SourceForge.io/C++/doc/IntersectTool.1.html>} 

517 executable (C{filename}), the (fully qualified) path to the C{IntersectTool} executable. 

518 

519 @raise GeodesicError: Invalid B{C{path}}, B{C{path}} doesn't exist or isn't the 

520 C{IntersectTool} executable. 

521 ''' 

522 self._setXable(path) 

523 

524 def Line(self, lat1, lon1, azi1_lat2, *lon2, **name): 

525 '''Return a geodesic line from this C{Intersector}'s geodesic, specified by 

526 two (goedetic) points or a (goedetic) point and an (initial) azimuth. 

527 

528 @return: A 3- or 6-item, named L{GDict}. 

529 ''' 

530 args = self._ll3z4ll(lat1, lon1, azi1_lat2, *lon2) 

531 gl = GDict((u.name, u) for u in args) 

532# if lon2: # get azis for All, use lat-/lons as given 

533# r = self._g.Inverse(outmask=Caps.AZIMUTH, *args) 

534# gl.set_(azi1=Azi(azi1=r.azi1), azi2=Azi(azi2=r.azi2)) 

535 if name: 

536 gl.name= name 

537 return gl 

538 

539 def Middle(self, glA, glB, **_C): 

540 '''Get the mid-points on two geodesic line segments. 

541 

542 @kwarg _C: Use C{B{_C}=True} to include the C{"-C"} results (C{bool}). 

543 

544 @return: An L{XDict}. 

545 ''' 

546 X, _, _, _, _ = self._middle5(glA, glB, **_C) 

547 return X 

548 

549 def _middle5(self, glA, glB, _C=False, **unused): 

550 # return intersections C{A} and C{B} and the 

551 # center C{X0} of rectangle [sA, sB] 

552 

553 def _smi4(**gl): 

554 try: 

555 n, gl = gl.popitem() 

556 il = self._g.InverseLine(gl.lat1, gl.lon1, gl.lat2, gl.lon2) 

557 except Exception as x: 

558 raise GeodesicError(n, gl, cause=x) 

559 s = il.s13 

560 m = s * _0_5 

561 return s, m, il, (il.Position(m, outmask=Caps._STD_LINE) if _C else None) 

562 

563 sA, mA, iA, A = _smi4(glA=glA) 

564 sB, mB, iB, B = _smi4(glB=glB) 

565 X = XDict_(mA, mB) # center 

566 _ = X._outSide(sA, sB) 

567 if _C: # _Names_ABs 

568 s, a = self._Inversa12(A, B) 

569 X.set_(latA=A.lat2, lonA=A.lon2, aMM=a, # assert sA == A.s12 

570 latB=B.lat2, lonB=B.lon2, sMM=s) # assert sB == B.s12 

571 return X, A, iA, B, iB 

572 

573 def Middle5(self, glA, glB, **unused): 

574 '''Get the mid-points on two geodesic line segments and their distance. 

575 

576 @return: A L{Middle5Tuple}. 

577 ''' 

578 X, A, iA, B, iB = self._middle5(glA, glB, _C=True) 

579 A, B, s, a, c = self._In5T(A, B, X, X, _2X=_M_) 

580 return Middle5Tuple(_llz2G(A, glA, iA), _llz2G(B, glB, iB), s, a, c) 

581 

582 @Property_RO 

583 def _n_alt(self): 

584 '''(INTERNAL) Get the C{Next} format (C{tuple}). 

585 ''' 

586 return _n__, # latA lonA aziA aziB 

587 

588 def Next(self, glA, glB, eps1=None, **_C): # PYCHOK no cover 

589 '''Find the next intersection of two I{intersecting} geodesic lines. 

590 

591 @kwarg _C: Use C{B{_C}=True} to include the option C{"-C"} results (C{bool}). 

592 

593 @return: An L{XDict}. 

594 ''' 

595 if eps1 or _C: 

596 _C = self._xNext(glA, glB, eps1, **_C) 

597 return self._XDictInvoke(self._n_alt, NN, 

598 (glA.lat1, glA.lon1, glA.azi1, glB.azi1), 

599 **_C) # _R=None 

600 

601 def Next5(self, glA, glB, **eps1): # PYCHOK no cover 

602 '''Find the next intersection of two I{intersecting} geodesic lines. 

603 

604 @return: An L{Intersectool5Tuple}. 

605 ''' 

606 X = self.Next(glA, glB, _C=True, **eps1) 

607 return self._In5T(glA, glB, X, X) 

608 

609 @Property_RO 

610 def _o_alt(self): 

611 '''(INTERNAL) Get the C{Offset} format (C{tuple}). 

612 ''' 

613 return _o__, # latA lonA aziA latB lonB aziB x0 y0 

614 

615 def _R_option(self, _R=None): 

616 '''(INTERNAL) Get the C{-R maxdist} option. 

617 ''' 

618 return () if _R is None else (_R__, str(_R)) # -R maxdist 

619 

620 def Segment(self, glA, glB, **_C_unused): 

621 '''Find the intersection between two geodesic line segments. 

622 

623 @kwarg _C: Use C{B{_C}=True} to include the option C{"-C"} results (C{bool}). 

624 

625 @return: An L{XDict}. 

626 ''' 

627 X = self._XDictInvoke(self._i_alt, 'k', 

628 (glA.lat1, glA.lon1, glA.lat2, glA.lon2, 

629 glB.lat1, glB.lon1, glB.lat2, glB.lon2), 

630 _C=_xkwds_get(_C_unused, _C=False)) # _R=None 

631 k = int(X.k) 

632 for kA in range(-1, 2): 

633 for kB in range(-1, 2): 

634 if (kA * 3 + kB) == k: 

635 return X.set_(k=k, kA=kA, kB=kB) 

636 raise GeodesicError(k=k, glA=glA, glB=glB, txt=repr(X)) 

637 

638 def Segment5(self, glA, glB, **unused): 

639 '''Find the next intersection of two I{intersecting} geodesic lines. 

640 

641 @return: An L{Intersectool5Tuple}. 

642 ''' 

643 X = self.Segment(glA, glB, _C=True) 

644 return self._In5T(glA, glB, X, X, k2=True) 

645 

646 def toStr(self, prec=6, sep=_COMMASPACE_, **unused): # PYCHOK signature 

647 '''Return this C{Intersectool} as string. 

648 

649 @kwarg prec_sep: Keyword argumens C{B{prec}=6} and C{B{sep}=", "} 

650 for the C{float} C{prec}ision, number of decimal digits 

651 (0..9) and the C{sep}arator string to join. Trailing 

652 zero decimals are stripped for B{C{prec}} values of 1 

653 and above, but kept for negative B{C{prec}} values. 

654 

655 @return: Intersectool items (C{str}). 

656 ''' 

657 d = dict(geodesic=self.geodesic, invokation=self.invokation, 

658 status=self.status, 

659 IntersectTool=self.IntersectTool) 

660 return sep.join(pairs(d, prec=prec)) 

661 

662 def _XDictInvoke(self, alt, _k_sX0, args, _C=False, **_R): 

663 '''(INTERNAL) Invoke C{IntersectTool}, return results as C{XDict} or 

664 a C{generator} if keyword argument C{B{_R}=sMaX0} is specified. 

665 ''' 

666 # assert len(args) == {self._c_alt: 6, 

667 # self._i_alt: 8, 

668 # self._n_alt: 4, 

669 # self._o_alt: 8}.get(alt, len(args)) 

670 cmd = self._cmdBasic 

671 Names = self._Names_XDict # has _c_ always 

672 if _k_sX0: 

673 Names += _k_sX0, 

674 if _C: 

675 cmd += self._C_option 

676 Names += self._Names_ABs 

677 if _R: 

678 cmd += self._R_option(**_R) 

679 X, _R = self._DictInvoke2(cmd + alt, Names, XDict, args, **_R) 

680 return X if _R else X.set_(c=int(X.c)) # generator or XDict 

681 

682 

683class Intersector(_IntersectBase): 

684 '''Finder of intersections between two goedesic lines, each an instance 

685 of L{GeodesicLineExact<pygeodesy.geodesicx.GeodesicLineExact>}, 

686 wrapped L{GeodesicLine<pygeodesy.geodesicw.GeodesicLine>} or 

687 L{GeodesicLineSolve<pygeodesy.geodsolve.GeodesicLineSolve>}. 

688 

689 @see: I{Karney}'s C++ class U{Intersect<https://GeographicLib.sourceforge.io/ 

690 C++/doc/classGeographicLib_1_1Intersect.html#details>} for more details. 

691 ''' 

692 # _D1 = 0 

693 # _D2 = 0 

694 # _T1 = 0 

695 # _T5 = 0 

696 

697 def __init__(self, geodesic, **name): 

698 '''New L{Intersector}. 

699 

700 @arg geodesic: The geodesic (L{GeodesicExact<pygeodesy.geodesicx.GeodesicExact>}, 

701 wrapped L{Geodesic<pygeodesy.geodesicw.Geodesic>} or 

702 L{GeodesicSolve<pygeodesy.geodsolve.GeodesicSolve>}). 

703 @kwarg name: Optional C{B{name}=NN} (C{str}). 

704 

705 @raise GeodesicError: The eccentricity of the B{C{geodesic}}'s ellipsoid is too 

706 large or no initial convergence. 

707 

708 @see: The B{Note} at I{Karney}'s C++ U{Intersect<https://GeographicLib.sourceforge.io/ 

709 C++/doc/classGeographicLib_1_1Intersect.html#ae41f54c9a44836f6c8f140f6994930cf>}. 

710 ''' 

711 _IntersectBase.__init__(self, geodesic, **name) 

712 E = self.ellipsoid 

713 t1 = E.b * PI # min distance between intersects 

714 t2 = self._polarDist2(_90_0)[0] * _2_0 # furthest, closest intersect 

715 t5 = self._Inversa12( _90_0)[0] * _2_0 # longest, shortest geodesic 

716 if self.f > 0: 

717 t3 = self._obliqDist4()[0] 

718 t4 = t1 

719 else: # PYCHOK no cover 

720 t1, t2, t3 = t2, t1, t5 

721 t4, _, _ = self._polarB3() 

722 

723 self._D1 = d1 = t2 * _0_5 # ~E.L tile spacing for Closest 

724 self._D2 = d2 = t3 / _1_5 # tile spacing for Next 

725 self._D3 = d3 = t4 - self.Delta # tile spacing for All 

726 self._T1 = t1 # min distance between intersects 

727 self._T2 = t2 = t1 * _2_0 

728# self._T5 = t5 # not used 

729 if not (d1 < d3 and d2 < d3 and d2 < t2): 

730 t = Fmt.PARENSPACED(_too_('eccentric'), E.e) 

731 raise GeodesicError(ellipsoid=E.toStr(terse=2), txt=t) 

732 

733 def All(self, glA, glB, X0=None, aMaX0=0, **sMaX0_C): # MCCABE 13 

734 '''Yield all intersection of two geodesic lines up to a limit. 

735 

736 @arg glA: A geodesic line (L{Line<Intersector.Line>}). 

737 @arg glB: An other geodesic line (L{Line<Intersector.Line>}). 

738 @kwarg X0: Optional I{origin} for I{L1-distances} (L{XDict}) or 

739 C{None} for the L{Middle<Intersector.Middle>} of both 

740 lines if both are a 4-C{args} L{Line<Intersector.Line>} 

741 or C{InverseLine}, otherwise C{XDiff_(0, 0)}. 

742 @kwarg aMaX0: Upper limit for the I{angular L1-distance} 

743 (C{degrees}) or C{None} or C{0} for unlimited. 

744 @kwarg sMaX0_C: Optional, upper limit C{B{sMaX0}=2*PI*R} for the 

745 I{L1-distance} to B{C{X0}} (C{meter}) and option 

746 C{B{_C}=False} to include the intersection lat-/ 

747 longitudes C{latA}, C{lonA}, C{latB}, C{lonB} and 

748 distances C{sAB} and C{aSB}. 

749 

750 @return: Yield an L{XDict} for each intersection found. 

751 

752 @raise GeodesicError: Geodesic line B{C{glA}} or B{C{glB}} 

753 invalid, incompatible or ill-configured. 

754 

755 @raise IntersectionError: No convergence. 

756 ''' 

757 self._xLines(glA, glB) 

758 if X0 is None: 

759 try: # determine X0 

760 X0, _, _ = self._middle3(glA, glB, True) 

761 except GeodesicError: # no .Distance 

762 X0 = _X000 

763 sMaX0, _C = self._sMaX0_C2(aMaX0, **sMaX0_C) 

764 

765 D, _D = self.Delta, self._cHalf # C++ _d 

766 xMaX0 = sMaX0 + D 

767 m = int(_ceil(xMaX0 / self._D3)) # m x m tiles 

768 d3 = xMaX0 / m 

769 T2d3D = self._T2d3Delta(d3) 

770 

771 C_ = _List(D) # closest coincident 

772 X_ = _List(D) # intersections found 

773 c0 = 0 

774 S_ = list(X0._nmD3(1 - m, m, d3 * _0_5)) 

775 # assert len(S_) == m * m + (m - 1) % 2 

776 while S_: 

777 Q, i = self._Basic2(glA, glB, S_.pop(0)) 

778 if Q in X_: 

779 continue 

780 if Q.c: # coincident intersection # PYCHOK no cover 

781 _X0fx = X0._fixCoincident 

782 Q = _X0fx(Q) # Q = Q' 

783 if c0 and Q in C_: 

784 continue 

785 C_.addend(Q) 

786 # elimate all existing intersections 

787 # on this line (which didn't set c0) 

788 c0 = Q.c 

789 for j, X in _enumereverse(X_): 

790 if _X0fx(X, c0).L1(Q) <= D: # X' == Q 

791 X_.pop(j) 

792 

793 a, s0 = len(X_), Q.sA 

794 args = self._m12_M12_M21(glA, s0) 

795 _cjD = self._conjDist 

796 for s in (-_D, _D): 

797 s += s0 

798 sa = 0 

799 while True: 

800 i += 1 

801 sa = _cjD(glA, s + sa, *args) - s0 

802 X = Q + (sa, sa * c0) 

803 if X_.addend(X, X0.L1(X), i) > xMaX0: 

804 break 

805 

806 elif c0 and Q in C_: # Q.c == 0 

807 continue 

808 else: 

809 a = len(X_) 

810 

811 X_.addend(Q, X0.L1(Q), i + 1) 

812 for X in X_[a:]: # addended Xs 

813 X._skip(S_, T2d3D) 

814 

815 return X_.sorter(sMaX0, self._C, glA, glB, **_C) # generator 

816 

817 def All5(self, glA, glB, X0=_X000, **aMaX0_sMaX0_C): 

818 '''Yield all intersection of two geodesic lines up to a limit. 

819 

820 @return: Yield an L{Intersector5Tuple}C{(A, B, sAB, aAB, c)} 

821 for each intersection found. 

822 

823 @see: Methods L{All} for further details. 

824 ''' 

825 for X in self.All(glA, glB, X0=X0, **aMaX0_sMaX0_C): 

826 yield self._In5T(glA, glB, X, X) 

827 

828 def _Basic2(self, glA, glB, S, i=0): 

829 '''(INTERNAL) Get a basic solution. 

830 ''' 

831 X = _copy(S) 

832 for _ in range(_TRIPS): 

833 S = self._Spherical(glA, glB, X) 

834 X += S 

835 i += 1 

836 if X.c or S.L1() <= self._Tol: # or isnan 

837 return self._Delto(X), i 

838 

839 raise IntersectionError(Fmt.no_convergence(S.L1(), self._Tol)) 

840 

841 def _C(self, X, glA, glB, _C=False, _AB=True): 

842 # add the C{_C} items to C{X}, if requested. 

843 if _C: 

844 A = self._Position(glA, X.sA) 

845 B = self._Position(glB, X.sB) 

846 s, a = self._Inversa12(A, B) 

847 X.set_(latA=A.lat2, lonA=A.lon2, 

848 latB=B.lat2, lonB=B.lon2) 

849 if _AB: 

850 X.set_(sAB=s, aAB=a) 

851 else: 

852 X.set_(sMM=s, aMM=a) 

853 return X 

854 

855 def Closest(self, glA, glB, X0=_X000, **_C): 

856 '''Find the closest intersection of two geodesic lines. 

857 

858 @arg glA: A geodesic line (L{Line<Intersector.Line>}). 

859 @arg glB: An other geodesic line (L{Line<Intersector.Line>}). 

860 @kwarg X0: Optional I{origin} for I{L1-closeness} (L{XDict}). 

861 @kwarg _C: If C{True}, include the lat-/longitudes C{latA}, 

862 C{lonA}, C{latB}, C{lonB} oon and distances C{sAB} 

863 and C{aSB} between the intersections. 

864 

865 @return: The intersection (L{XDict}) or C{None} if none found. 

866 

867 @raise GeodesicError: Geodesic line B{C{glA}} or B{C{glB}} 

868 invalid, incompatible or ill-configured. 

869 

870 @raise IntersectionError: No convergence. 

871 ''' 

872 self._xLines(glA, glB) 

873 Q, d, S_, i = X0, INF, list(X0._nD1(self._D1)), 0 

874 while S_: 

875 X, i = self._Basic2(glA, glB, S_.pop(0), i) 

876 X = X0._fixCoincident(X) 

877 if X.L1(Q) > self.Delta: # X != Q 

878 d0 = X.L1(X0) 

879 if d0 < self._T1: 

880 Q, d, q = X, d0, i 

881 break 

882 if d0 < d or Q is X0: 

883 Q, d, q = X, d0, i 

884 X._skip(S_, self._T2D1Delta) 

885 

886 return None if Q is X0 else self._C(Q, glA, glB, **_C).set_(sX0=d, iteration=q) 

887 

888 def Closest5(self, glA, glB, X0=_X000): 

889 '''Find the closest intersection of two geodesic lines. 

890 

891 @return: An L{Intersector5Tuple}C{(A, B, sAB, aAB, c)} 

892 or C{None} if none found. 

893 

894 @see: Method L{Closest} for further details. 

895 ''' 

896 X = self.Closest(glA, glB, X0=X0) 

897 return X if X is None else self._In5T(glA, glB, X, X) 

898 

899 def _conjDist(self, gl, s, m12=0, M12=1, M21=1, semi=False): 

900 # Find semi-/conjugate point relative to s0 which is close to s1. 

901 # if semi: 

902 # solve for M23 = 0 using dM23 / ds3 = - (1 - M23 * M32) / m23 

903 # else: 

904 # solve for m23 = 0 using dm23 / ds3 = M32 

905 _S2, _abs, _1 = Fsum(s).fsum2_, fabs, _1_0 

906 for _ in range(_TRIPS): 

907 m13, M13, M31 = self._m12_M12_M21(gl, s) 

908 # see "Algorithms for geodesics", eqs. 31, 32, 33. 

909 m23 = m13 * M12 

910 M32 = M31 * M12 

911 if m12: # PYCHOK no cover 

912 m23 -= m12 * M13 

913 if m13: 

914 M32 += (_1 - M13 * M31) * m12 / m13 

915 if semi: 

916 M23 = M13 * M21 

917 # when m12 -> eps, (1 - M12 * M21) -> eps^2, I suppose. 

918 if m12 and m13: 

919 M23 += (_1 - M12 * M21) * m13 / m12 

920 d = m23 * M23 / (_1 - M23 * M32) 

921 else: 

922 d = -m23 / M32 

923 s, d = _S2(d) 

924 if _abs(d) <= self._Tol: 

925 break 

926 return s 

927 

928 _gl3 = None 

929 

930 @Property 

931 def _conjDist3s(self): 

932 gl, self._gl3, _D = self._gl3, None, self._cHalf 

933 return tuple(self._conjDist(gl, s) for s in (-_D, 0, _D)) 

934 

935 @_conjDist3s.setter # PYCHOK setter! 

936 def _conjDist3(self, gl): 

937 # _XLines(gl, gl) 

938 self._gl3 = gl 

939 

940 def _conjDist3Tt_(self, c, X0=_X000): 

941 for s in self._conjDist3s: 

942 T = XDict_(s, s * c, c) 

943 yield self._Delto(T), T.L1(X0) 

944 

945 def _conjDist5(self, azi): 

946 gl = self._Line(azi1=azi) 

947 s = self._conjDist(gl, self._cHalf) 

948 X, _ = self._Basic2(gl, gl, XDict_(s * _0_5, -s * _1_5)) 

949 return s, (X.L1() - s * _2_0), azi, X.sA, X.sB 

950 

951 @Property_RO 

952 def Delta(self): 

953 '''Get the equality and tiling margin (C{meter}). 

954 ''' 

955 return self._cHalf * _EPSr5 # ~15 Km WGS84 

956 

957 def _Delto(self, X): 

958 # copy Delta into X, overriding X's default 

959 X._Delta = self.Delta # NOT X.set_(self.Delta) 

960 return X 

961 

962 @Property_RO 

963 def _EPS3R(self): 

964 return _EPS3 * self.R 

965 

966 @Property_RO 

967 def _faPI_4(self): 

968 return (self.f + _2_0) * self.a * PI_4 

969 

970 @Property_RO 

971 def _GeodesicLines(self): 

972 '''(INTERNAL) Get the C{Geodesic...Line} class(es). 

973 ''' 

974 return type(self._Line()), 

975 

976 def _In5T(self, glA, glB, S, X, k2=False, **_2X): 

977 # Return an intersection as C{Intersector5Tuple}. 

978 A = self._Position(glA, S.sA) 

979 B = self._Position(glB, S.sB) 

980 if k2: 

981 A.set_(k2=X.kA) 

982 B.set_(k2=X.kB) 

983 s, a = self._Inversa12(A, B) 

984 return Intersector5Tuple(A._2X(glA, **_2X), 

985 B._2X(glB, **_2X), s, a, X.c, iteration=X.iteration) 

986 

987 def _Inverse(self, A, B): # caps=Caps.STANDARD 

988 return self._g.Inverse(A.lat2, A.lon2, B.lat2, B.lon2) 

989 

990 def Line(self, lat1, lon1, azi1_lat2, *lon2, **name): 

991 '''Return a geodesic line from this C{Intersector}'s geodesic, specified by 

992 two (goedetic) points or a (goedetic) point and an (initial) azimuth. 

993 

994 @arg lat1: Latitude of the first point (C{degrees}). 

995 @arg lon1: Longitude of the first point (C{degrees}). 

996 @arg azi1_lat2: Azimuth at the first point (compass C{degrees}) if no 

997 B{C{lon2}} argument is given, otherwise the latitude of 

998 the second point (C{degrees}). 

999 @arg lon2: If given, the longitude of the second point (C{degrees}). 

1000 @kwarg name: Optional C{B{name}=NN} (C{str}). 

1001 

1002 @return: A line (from L{geodesic<Intersector.geodesic>}C{.Line} or 

1003 C{.InverseLine} method) with C{LINE_CAPS}. 

1004 ''' 

1005 args = self._ll3z4ll(lat1, lon1, azi1_lat2, *lon2) 

1006 gl = self._g.InverseLine(*args, caps=Caps.LINE_CAPS) if lon2 else \ 

1007 self._g.Line( *args, caps=Caps.LINE_CAPS) 

1008 if name: 

1009 gl.name= name 

1010 return gl 

1011 

1012 def _Line(self, lat1=0, lon1=0, azi1=0): 

1013 return self._g.Line(lat1, lon1, azi1, caps=Caps.LINE_CAPS) 

1014 

1015 def Middle(self, glA, glB, raiser=True, **_C): 

1016 '''Get the mid-points on two geodesic line segments. 

1017 

1018 @arg glA: A geodesic line (L{Line<Intersector.Line>}, 4-C{args}). 

1019 @arg glB: An other geodesic line (L{Line<Intersector.Line>}, 4-C{args}). 

1020 @kwarg raiser: If C{True}, check that B{C{glA}} and B{C{glB}} are a 

1021 4-C{args} L{Line<Intersector.Line>} or C{InverseLine} 

1022 (C{bool}). 

1023 @kwarg _C: If C{True}, include the lat-/longitudes C{latA}, C{lonA}, 

1024 C{latB}, C{lonB} of the mid-points and half-lengths C{sA} 

1025 and C{sB} in C{meter} of the respective line segments. 

1026 

1027 @return: The mid-point and half-length of each segment (L{XDict}), 

1028 B{C{_C}} above. 

1029 

1030 @raise GeodesicError: Geodesic line B{C{glA}} or B{C{glB}} invalid, 

1031 incompatible, ill-configured or not a 4-C{args 

1032 Line} or other C{InverseLine}. 

1033 ''' 

1034 M, _, _ = self._middle3(glA, glB, raiser) 

1035 # _ = X._outSide(sA, sB) 

1036 return self._C(M, glA, glB, _AB=False, **_C) if _C else M 

1037 

1038 def _middle3(self, glA, glB, raiser): # in .All 

1039 # return segment length C{sA} and C{sB} and the 

1040 # center C{X0} of rectangle [sA, sB] 

1041 self._xLines(glA, glB, s13=raiser) # need .Distance 

1042 sA = glA.Distance() 

1043 sB = glB.Distance() 

1044 X = XDict_(sA * _0_5, sB * _0_5) # center 

1045 return self._Delto(X), sA, sB 

1046 

1047 def Middle5(self, glA, glB, **raiser): 

1048 '''Get the mid-points of two geodesic line segments and distances. 

1049 

1050 @return: A L{Middle5Tuple}C{(A, B, sMM, aMM, c)}. 

1051 

1052 @see: Method L{Middle} for further details. 

1053 ''' 

1054 M = self.Middle(glA, glB, _C=True, **raiser) 

1055 A, B, s, a, c = self._In5T(glA, glB, M, M, _2X=_M_) 

1056 return Middle5Tuple(_llz2G(A, glA, glA), _llz2G(B, glB, glB), s, a, c) 

1057 

1058 def _m12_M12_M21(self, gl, s): 

1059 P = gl.Position(s, outmask=Caps._REDUCEDLENGTH_GEODESICSCALE) 

1060 return P.m12, P.M12, P.M21 

1061 

1062 def Next(self, glA, glB, eps1=None, **_C): # PYCHOK no cover 

1063 '''Yield the next intersection of two I{intersecting} geodesic lines. 

1064 

1065 @arg glA: A geodesic line (L{Line<Intersector.Line>}). 

1066 @arg glB: An other geodesic line (L{Line<Intersector.Line>}). 

1067 @kwarg eps1: Optional margin for the L{euclid<pygeodesy.euclid>}ean 

1068 distance (C{degrees}) between the C{(lat1, lon1)} points 

1069 of both lines or C{None} for unchecked. 

1070 @kwarg _C: If C{True}, include the lat-/longitudes C{latA}, C{lonA}, 

1071 C{latB}, C{lonB} of and distances C{sAB} and C{aSB} 

1072 between the intersections. 

1073 

1074 @return: The intersection (L{XDict}) or C{None} if none found. 

1075 

1076 @raise GeodesicError: Geodesic line B{C{glA}} or B{C{glB}} invalid, 

1077 incompatible, ill-configured or C{(lat1, lon1)} 

1078 not B{C{eps1}}-equal. 

1079 

1080 @raise IntersectionError: No convergence. 

1081 

1082 @note: Offset C{X0} is implicit, zeros. 

1083 ''' 

1084 self._xLines(glA, glB) 

1085 if eps1 or _C: # eps 

1086 _C = self._xNext(glA, glB, eps1, **_C) 

1087 

1088 X0, self._conjDist3s = _X000, glA # reset Property 

1089 Q, d, S_, i = _XINF, INF, list(X0._nD2(self._D2)), 0 

1090 while S_: 

1091 X, i = self._Basic2(glA, glB, S_.pop(0), i) 

1092 X = X0._fixCoincident(X) 

1093 t = X.L1(X0) # == X.L1() 

1094 c, z = X.c, (t <= self.Delta) # X == X0 

1095 if z: 

1096 if not c: 

1097 continue 

1098 Tt_ = self._conjDist3Tt_(c, X0) 

1099 else: 

1100 Tt_ = (X, t), 

1101 

1102 for T, t in Tt_: 

1103 if t < d or Q is _XINF: 

1104 Q, d, q = T, t, i 

1105 i += 1 

1106 

1107 for s in ((_1_1t if z else _1_0_1t) 

1108 if c else _0t): 

1109 T = X 

1110 if s and c: 

1111 s *= self._D2 

1112 T = X + (s, s * c) # NOT += 

1113 T._skip(S_, self._T2D2Delta) 

1114 

1115 return None if Q is _XINF else self._C(Q, glA, glB, **_C).set_(sX0=d, iteration=q) 

1116 

1117 def Next5(self, glA, glB, **eps1): # PYCHOK no cover 

1118 '''Yield the next intersection of two I{intersecting} geodesic lines. 

1119 

1120 @return: An L{Intersector5Tuple}C{(A, B, sAB, aAB, c)} or C{None} 

1121 if none found. 

1122 

1123 @see: Method L{Next} for further details. 

1124 ''' 

1125 X = self.Next(glA, glB, **eps1) 

1126 return X if X is None else self._In5T(glA, glB, X, X) 

1127 

1128 def _obliqDist4(self): 

1129 zx = 45.0 

1130 if self.f: 

1131 _abs, _cjD5 = fabs, self._conjDist5 

1132 

1133 _, ds0, z0, _, _ = _cjD5(zx + _1_0) 

1134 s1, ds1, z1, sAx, sBx = _cjD5(zx - _1_0) 

1135 sx, dsx, zx = s1, _abs(ds1), z1 

1136 # find ds(azi) = 0 by secant method 

1137 for _ in range(16): 

1138 if ds1 == ds0: 

1139 break 

1140 z = (z0 * ds1 - z1 * ds0) / (ds1 - ds0) 

1141 _, ds0, z0 = s1, ds1, z1 

1142 s1, ds1, z1, a, b = _cjD5(z) 

1143 if _abs(ds1) < dsx: 

1144 sx, dsx, zx, sAx, sBx = s1, _abs(ds1), z, a, b 

1145 if not dsx: 

1146 break 

1147 else: 

1148 sx, sAx, sBx = self._cHalf, _0_5, -_1_5 

1149 return sx, zx, sAx, sBx 

1150 

1151 def _polarB3(self, lats=False): # PYCHOK no cover 

1152 latx = 64.0 

1153 lat = _90_0 - latx 

1154 if self.f: 

1155 _d, _pD2 = fdot, self._polarDist2 

1156 

1157 s0, lat0 = _pD2(latx - _1_0) 

1158 s1, lat1 = _pD2(latx + _1_0) 

1159 s2, lat2 = \ 

1160 sx, latx = _pD2(latx) 

1161 prolate = self.f < 0 

1162 # solve for ds(lat) / dlat = 0 with a quadratic fit 

1163 for _ in range(_TRIPS): 

1164 t = (lat1 - lat0), (lat0 - lat2), (lat2 - lat1) 

1165 d = _d(t, s2, s1, s0) * _2_0 

1166 if not d: # or isnan(d) 

1167 break 

1168 lat = _d(t, (lat1 + lat0) * s2, 

1169 (lat0 + lat2) * s1, 

1170 (lat2 + lat1) * s0) / d 

1171 s0, lat0 = s1, lat1 

1172 s1, lat1 = s2, lat2 

1173 s2, lat2 = _pD2(lat) 

1174 if (s2 < sx) if prolate else (s2 > sx): 

1175 sx, latx = s2, lat2 

1176 if lats: 

1177 _, lat = _pD2(latx, lat2=True) 

1178 sx += sx 

1179 else: 

1180 sx = self._cHalf 

1181 return sx, latx, lat 

1182 

1183 def _polarDist2(self, lat1, lat2=False): 

1184 gl = self._Line(lat1=lat1) 

1185 s = self._conjDist(gl, self._faPI_4, semi=True) 

1186 if lat2: 

1187 lat1 = gl.Position(s, outmask=Caps.LATITUDE).lat2 

1188 return s, lat1 

1189 

1190 def _Position(self, gl, s): 

1191 return gl.Position(s, outmask=Caps._STD_LINE) 

1192 

1193 def Segment(self, glA, glB, proven=None, raiser=True, **_C): 

1194 '''Find the intersection between two geodesic line segments. 

1195 

1196 @kwarg proven: Conjecture is that whenever two geodesic line 

1197 segments intersect, the intersection is the 

1198 one closest to the mid-points of segments. 

1199 If so, use C{B{proven}=True}, otherwise find 

1200 intersections on the segments and specify 

1201 C{B{proven}=None} to return the first or 

1202 C{B{proven}=False} the closest (C{bool}). 

1203 @kwarg raiser: If C{True}, check that B{C{glA}} and B{C{glB}} 

1204 are an 4-C{args} L{Line<Intersector.Line>} or 

1205 C{InverseLine} (C{bool}). 

1206 @kwarg _C: If C{True}, include the lat-/longitudes C{latA}, 

1207 C{lonA}, C{latB}, C{lonB} of and distances C{sAB} 

1208 and C{aSB} between the intersections. 

1209 

1210 @return: The intersection of the segments (L{XDict}) with 

1211 indicators C{kA}, C{kB} and C{k} set or if no 

1212 intersection is found, C{None}. 

1213 

1214 @raise GeodesicError: Geodesic line B{C{glA}} or B{C{glB}} 

1215 invalid, incompatible, ill-configured or 

1216 not an C{InverseLine} or 4-C{args Line}. 

1217 

1218 @raise IntersectionError: No convergence. 

1219 

1220 @see: Method L{Middle<Intersector.Middle>} for further details. 

1221 ''' 

1222 X0, sA, sB = self._middle3(glA, glB, raiser) 

1223 Q = self.Closest(glA, glB, X0) # to X0 

1224 if Q is not None: 

1225 if Q.c: # anti-/parallel 

1226 Q._fixSegment(sA, sB) 

1227 # are rectangle [sA, sB] corners further from X0 than Q? 

1228 d0 = X0.L1(Q) 

1229 if Q._outSide(sA, sB) and d0 <= X0.L1() and not proven: 

1230 i = Q.iteration 

1231 for T in X0._corners(sA, sB, self._T2): 

1232 X, i = self._Basic2(glA, glB, T, i) 

1233 X = T._fixCoincident(X) 

1234 if not X._outSide(sA, sB): 

1235 d = X0.L1(X) 

1236 if d < d0 or proven is None: 

1237 Q, d0 = X, d 

1238 if proven is None: 

1239 break 

1240 Q.set_(iteration=i) 

1241 

1242 Q = self._C(Q, glA, glB, **_C).set_(sX0=d0) 

1243 return Q 

1244 

1245 def Segment5(self, glA, glB, **proven_raiser): 

1246 '''Find the intersection between two geodesic line segments. 

1247 

1248 @return: An L{Intersector5Tuple}C{(A, B, sAB, aAB, c)} 

1249 or C{None} if none found. 

1250 

1251 @see: Method L{Segment} for further details. 

1252 ''' 

1253 X = self.Segment(glA, glB, **proven_raiser) 

1254 return X if X is None else self._In5T(glA, glB, X, X, k2=True) 

1255 

1256 def _Spherical(self, glA, glB, S): 

1257 '''(INTERNAL) Get solution based from a spherical triangle. 

1258 ''' 

1259 # threshold for coincident geodesics/intersections ~4.3 nm WGS84. 

1260 A = self._Position(glA, S.sA) 

1261 B = self._Position(glB, S.sB) 

1262 D = self._Inverse(A, B) 

1263 

1264 a, da = _diff182(A.azi2, D.azi1) # interior angle at A 

1265 b, db = _diff182(B.azi2, D.azi2) # exterior angle at B 

1266 c, dc = _diff182(a, b) 

1267 if fsum1_(dc, db, -da, c) < 0: # inverted triangle 

1268 a, da = -a, -da 

1269 b, db = -b, -db 

1270 sa, ca = _sincos2de(a, da) 

1271 sb, cb = _sincos2de(b, db) 

1272 

1273 e, z, _abs = _EPS3, D.s12, fabs 

1274 if _abs(z) <= self._EPS3R: # XXX z <= ... 

1275 sA = sB = 0 # at intersection 

1276 c = 1 if _abs(sa - sb) <= e and _abs(ca - cb) <= e else ( 

1277 -1 if _abs(sa + sb) <= e and _abs(ca + cb) <= e else 0) 

1278 elif _abs(sa) <= e and _abs(sb) <= e: # coincident 

1279 sA = ca * z * _0_5 # choose mid-point 

1280 sB = -cb * z * _0_5 

1281 c = 1 if (ca * cb) > 0 else -1 

1282 # alt1: sA = ca * z; sB = 0 

1283 # alt2: sB = -cb * z; sA = 0 

1284 else: # general case 

1285 sz, cz = sincos2(z / self.R) 

1286 # [SKIP: Divide args by |sz| to avoid possible underflow 

1287 # in {sa, sb} * sz; this is probably not necessary]. 

1288 # Definitely need to treat sz < 0 (z > PI*R) correctly in 

1289 # order to avoid some convergence failures in _Basic2. 

1290 sA = atan2(sb * sz, sb * ca * cz - sa * cb) * self.R 

1291 sB = atan2(sa * sz, -sa * cb * cz + sb * ca) * self.R 

1292 c = 0 

1293 return XDict_(sA, sB, c) # no ._Delto 

1294 

1295 @Property_RO 

1296 def _T2D1Delta(self): 

1297 return self._T2d3Delta(self._D1) 

1298 

1299 @Property_RO 

1300 def _T2D2Delta(self): 

1301 return self._T2d3Delta(self._D2) 

1302 

1303 def _T2d3Delta(self, d3): 

1304 return self._T2 - d3 - self.Delta 

1305 

1306 @Property_RO 

1307 def _Tol(self): # convergence tolerance 

1308 return self._cHalf * pow(EPS, 0.75) # _0_75 

1309 

1310 def toStr(self, **prec_sep_name): # PYCHOK signature 

1311 '''Return this C{Intersector} as string. 

1312 

1313 @see: L{Ellipsoid.toStr<pygeodesy.ellipsoids.Ellipsoid.toStr>} 

1314 for further details. 

1315 

1316 @return: C{Intersector} (C{str}). 

1317 ''' 

1318 return self._instr(props=(Intersector.geodesic,), **prec_sep_name) 

1319 

1320 def _xLines(self, glA, glB, s13=False): 

1321 # check two geodesic lines vs this geodesic 

1322 C, gls = Caps.LINE_CAPS, dict(glA=glA, glB=glB) 

1323 _xinstanceof(*self._GeodesicLines, **gls) 

1324 for n, gl in gls.items(): 

1325 try: 

1326 _xgeodesics(gl.geodesic, self.geodesic) 

1327 if s13 and not isfinite(gl.s13): # or not gl.caps & Caps.DISTANCE_IN 

1328 t = gl.geodesic.InverseLine.__name__ 

1329 raise TypeError(_not_(_an(t))) 

1330 c = gl.caps & C 

1331 if c != C: # not gl.caps_(C) 

1332 c, C, x = map1(bin, c, C, _xor(c, C)) 

1333 x = _SPACE_(_xor.__name__, repr(x))[1:] 

1334 raise GeodesicError(caps=c, LINE_CAPS=C, txt=x) 

1335 except Exception as x: 

1336 raise GeodesicError(n, gl, cause=x) 

1337 

1338 

1339class Intersectool5Tuple(_NamedTuple): 

1340 '''5-Tuple C{(A, B, sAB, aAB, c)} with C{A} and C{B} the C{Position} 

1341 of the intersection on each geodesic line, the distance C{sAB} 

1342 between C{A} and C{B} in C{meter}, the angular distance C{aAB} in 

1343 C{degrees} and coincidence indicator C{c} (C{int}), see L{XDict}. 

1344 

1345 @note: C{A} and C{B} are each a C{GDict} with C{lat1}, C{lon1} and 

1346 C{azi1} or C{lat2}, C{lon2} from the geodesic line C{glA} 

1347 respectively C{glB} and the intersection location in C{latX}, 

1348 C{lonX}, distance C{s1X} in C{meter} and angular distance 

1349 C{a1M} in C{degrees} and the segment indicator C{kX}. See 

1350 L{XDict} for more details. 

1351 ''' 

1352 _Names_ = (_A_, _B_, _sAB_, 'aAB', _c_) 

1353 _Units_ = (_Pass, _Pass, Meter, Degrees, Int) 

1354 

1355 

1356class Intersector5Tuple(Intersectool5Tuple): 

1357 '''5-Tuple C{(A, B, sAB, aAB, c)} with C{A} and C{B} the C{Position} 

1358 of the intersection on each geodesic line, the distance C{sAB} 

1359 between C{A} and C{B} in C{meter}, angular distance C{aAB} in 

1360 C{degrees} and coincidence indicator C{c} (C{int}), see L{XDict}. 

1361 

1362 @note: C{A} and C{B} are each a C{GeodesicLine...Position} for 

1363 C{outmask=Caps.STANDARD} with the intersection location in 

1364 C{latX}, C{lonX}, azimuth in C{aziX}, distance C{s1X} in 

1365 C{meter} and angular distance C{a1X} in C{degrees} and the 

1366 segment indicator C{kX}. See L{XDict} for more details. 

1367 ''' 

1368 _Names_ = Intersectool5Tuple._Names_ 

1369 

1370 

1371class Middle5Tuple(Intersectool5Tuple): 

1372 '''5-Tuple C{(A, B, sMM, aMM, c)} with C{A} and C{B} the I{line segments} 

1373 including the mid-point location in C{latM}, C{lonM}, distance C{s1M} 

1374 in C{meter} and angular distance C{a1M} in C{degrees}, the distance 

1375 between both mid-points C{sMM} in C{meter} and angular distance C{aMM} 

1376 in C{degrees} and coincidence indicator C{c} (C{int}). See L{XDict} 

1377 for more details. 

1378 ''' 

1379 _Names_ = (_A_, _B_, 'sMM', 'aMM', _c_) 

1380 

1381 

1382class _List(list): 

1383 

1384 _Delta = 0 # equality margin 

1385 

1386 def __init__(self, Delta): 

1387 self._Delta = Delta 

1388# list.__init__(self) 

1389 

1390 def __contains__(self, other): 

1391 # handle C{if X in this: ...} 

1392 a, b = other.sA, other.sB 

1393 D, _D1 = self._Delta, _L1 

1394 for X in self: 

1395 if _D1(X.sA - a, X.sB - b) <= D: 

1396 return True 

1397 return False 

1398 

1399 def addend(self, X, *d0_i): 

1400 # append an item, updated 

1401 if d0_i: 

1402 d0, i = d0_i 

1403 X.set_(sX0=d0, iteration=i) 

1404 self.append(X) 

1405 return X.sX0 

1406 

1407 def sorter(self, sMaX0, dot_C, glA, glB, **_C): 

1408 # trim and sort the X items 

1409 

1410 def _key(X): 

1411 return X.sX0 # rank of X 

1412 

1413 t = (X for X in self if X.sX0 <= sMaX0) 

1414 for X in sorted(t, key=_key): 

1415 yield dot_C(X, glA, glB, **_C) if _C else X 

1416 

1417 

1418def _L1(a, b): 

1419 '''(INTERNAL) Return the I{L1} distance. 

1420 ''' 

1421 return fabs(a) + fabs(b) 

1422 

1423 

1424def _llz2G(G, gl, il): 

1425 '''(INTERNAL) Set C{InverseLine} attrs in C{G}, a C{GDict}. 

1426 ''' 

1427 return G.set_(lat1=gl.lat1, lon1=gl.lon1, azi1=il.azi1, a12=il.a13, # .Arc() 

1428 lat2=gl.lat2, lon2=gl.lon2, azi2=il.azi2, s12=il.s13) # .Distance() 

1429 

1430 

1431if __name__ == '__main__': # MCCABE 14 

1432 

1433 from pygeodesy import printf 

1434 

1435 def _main(args): 

1436 

1437 from pygeodesy import GeodesicExact 

1438 from pygeodesy.internals import _plural, _usage 

1439 from pygeodesy.interns import _COLONSPACE_, _DASH_, _DOT_, \ 

1440 _EQUAL_, _i_, _n_, _version_, _X_ 

1441 import re 

1442 

1443 class XY0(Float): 

1444 pass 

1445 

1446 def _opts(_h): # for _usage() 

1447 ll4 = ' latA1 lonA1' 

1448 ll4 += ll4.replace('1', '2') 

1449 ll4 += ll4.replace(_A_, _B_) 

1450 llz = _SPACE_(NN, _latA_, _lonA_, 'aziA') 

1451 llz2 = llz + llz.replace(_A_, _B_) 

1452 return dict(opts='-Verbose|V--version|v--help|h--Tool|T--Check|C-R meter-', 

1453 alts=((_c_ + llz2), 

1454 (_i_ + ll4), 

1455 (_m_ + ll4), 

1456 (_M_ + ll4), 

1457 (_n_ + llz + ' aziB'), 

1458 ('o' + llz2 + ' x0 y0')), 

1459 help=_h if isinstance(_h, str) else NN) 

1460 

1461 def _starts(opt, arg, n=0): 

1462 return opt.startswith(arg) and len(arg.lstrip(_DASH_)) > n 

1463 

1464 _isopt = re.compile('^[-]+[a-z]*$', flags=re.IGNORECASE).match 

1465 

1466 I = Intersector(GeodesicExact()) # PYCHOK I 

1467 M = m = _R = None 

1468 _T = _V = _h = _C = False 

1469 

1470 while args and _isopt(args[0]): 

1471 arg = args.pop(0) 

1472 if arg == _C__ or _starts('--Check', arg): 

1473 _C = True 

1474 elif arg == _c__: 

1475 M, m = I.Closest, 6 # latA lonA aziA latB lonB aziB 

1476 elif arg == '-h' or _starts('--help', arg): 

1477 _h = args[0] if args and _isopt(args[0]) else True 

1478 elif arg == _i__: 

1479 M, m = I.Segment, 8 # latA1 lonA1 latA2 lonA2 latB1 lonB1 latB2 lonB2 

1480 elif arg == '-m': 

1481 M, m = I.Middle, 8 # latA1 lonA1 latA2 lonA2 latB1 lonB1 latB2 lonB2 

1482 _R = None 

1483 elif arg == '-M': 

1484 M, m = I.Middle5, 8 # latA1 lonA1 latA2 lonA2 latB1 lonB1 latB2 lonB2 

1485 _R = _C = None 

1486 elif arg == _n__: 

1487 M, m = I.Next, 4 # latA lonA aziA aziB 

1488 elif arg == _o__: 

1489 M, m = I.Closest, 8 # latA lonA aziA latB lonB aziB x0 y0 

1490 elif arg == _R__ and args: 

1491 _R = args.pop(0) 

1492 elif arg == '-T' or _starts('--Tool', arg): 

1493 I = Intersectool() # PYCHOK I 

1494 if _V: 

1495 I.verbose = True 

1496 if I.IntersectTool in (_PYGEODESY_INTERSECTTOOL_, None): # not set 

1497 I.IntersectTool = '/opt/local/bin/IntersectTool' # '/opt/local/Cellar/geographiclib/2.3/bin/IntersectTool' # HomeBrew 

1498 M, _T = None, True 

1499 elif arg == '-V' or _starts('--Verbose', arg): 

1500 _V = True 

1501 if _T: 

1502 I.verbose = True 

1503 elif arg == '-v' or _starts('--version', arg): 

1504 printf(_COLONSPACE_(*((_version_, I.version) if _T else 

1505 (__version__, repr(I))))) 

1506 else: 

1507 raise ValueError('invalid option %r' % (arg,)) 

1508 

1509 if _h or M is None: 

1510 printf(_usage(__file__, **_opts(_h)), nl=1) 

1511# exit(0) 

1512 else: 

1513 n = len(args) 

1514 if n < m: 

1515 n = _plural('only %s arg' % (n,), n) if n else 'no args' 

1516 raise ValueError('%s, need %s' % (n, m)) 

1517 args[:] = args[:m] 

1518 

1519 kwds = dict(_C=True) if _C else {} 

1520 if M == I.Next: # -n 

1521 # get latA lonA aziA latA lonA aziB 

1522 args[3:] = args[:2] + args[3:4] 

1523 elif M == I.Closest and m > 6: # -o 

1524 y0 = Meter(y0=args.pop()) 

1525 x0 = Meter(x0=args.pop()) 

1526 kwds.update(X0=XDict_(x0, y0)) 

1527 if _R: 

1528 m = Meter_(_R, name=_R__, low=0) 

1529 kwds.update(sMaX0=m) 

1530 M = I.All 

1531 

1532 n = len(args) // 2 

1533 glA = I.Line(*args[:n]) 

1534 glB = I.Line(*args[n:]) 

1535 

1536 m = _DOT_(I.__class__.__name__, M.__name__) 

1537 if _V: 

1538 X = _SPACE_(_X_, _EQUAL_, m) 

1539 printf(unstr(X, glA, glB, **kwds)) 

1540 

1541 X = M(glA, glB, **kwds) 

1542 if X is None or isinstance(X, (XDict, tuple)): 

1543 printf(_COLONSPACE_(m, repr(X))) 

1544 else: 

1545 for i, X in enumerate(X): 

1546 printf(_COLONSPACE_(Fmt.INDEX(m, i), repr(X))) 

1547 

1548 from sys import argv, stderr 

1549 try: 

1550 if len(argv) == 2 and argv[1] == _HASH_: 

1551 from pygeodesy.internals import _usage_argv 

1552 

1553 s = _SPACE_(*_usage_argv(__file__)) 

1554 for t in ('-h', '-h -n', 

1555 '-c 0 0 45 40 10 135', 

1556 '-C -c 0 0 45 40 10 135', 

1557 '-T -R 2.6e7 -c 0 0 45 40 10 135', 

1558 '-c 50 -4 -147.7 0 0 90', 

1559 '-C -c 50 -4 -147.7 0 0 90', 

1560 '# % echo 0 0 10 10 50 -4 50S 4W | IntersectTool -i -p 0 -C', 

1561 '# -631414 5988887 0 -3', 

1562 '# -4.05187 -4.00000 -4.05187 -4.00000 0', 

1563 '-C -m 0 0 10 10 50 -4 50S 4W', 

1564 '-M 0 0 10 10 50 -4 50S 4W', 

1565 '-i 0 0 10 10 50 -4 50S 4W', 

1566 '-T -i 0 0 10 10 50 -4 50S 4W', 

1567 '-C -i 0 0 10 10 50 -4 50S 4W', 

1568 '-T -C -i 0 0 10 10 50 -4 50S 4W', 

1569 '-V -T -i 0 0 10 10 50 -4 -50 -4', 

1570 '-C -R 4e7 -c 50 -4 -147.7 0 0 90', 

1571 '-T -C -R 4e7 -c 50 -4 -147.7 0 0 90', 

1572 '-R 4e7 -i 0 0 10 10 50 -4 -50 -4', 

1573 '-T -R 4e7 -i 0 0 10 10 50 -4 -50 -4'): 

1574 if t.startswith(_HASH_): 

1575 printf(t, nl=int(t[2] == '%')) 

1576 else: 

1577 printf(_SPACE_(_HASH_, s, t), nl=1) 

1578 argv[1:] = t = t.split() 

1579 _main(t) 

1580 else: 

1581 _main(argv[1:]) 

1582 

1583 except Exception as x: 

1584 x = _SPACE_(x, NN, _HASH_, *argv) 

1585 printf(x, file=stderr, nl=1) 

1586 if '-V' in x or _MODS.errors.exception_chaining(): 

1587 raise 

1588 exit(1) 

1589 

1590# % env PYGEODESY_INTERSECTTOOL=... python3 -m pygeodesy.geodesici -h 

1591# 

1592# usage: python3 -m ....pygeodesy.geodesici [--Verbose | -V] [--version | -v] [--help | -h] [--Tool | -T] [--Check | -C] [-R meter] 

1593# [-c latA lonA aziA latB lonB aziB | 

1594# -i latA1 lonA1 latA2 lonA2 latB1 lonB1 latB2 lonB2 | 

1595# -m latA1 lonA1 latA2 lonA2 latB1 lonB1 latB2 lonB2 | 

1596# -M latA1 lonA1 latA2 lonA2 latB1 lonB1 latB2 lonB2 | 

1597# -n latA lonA aziA aziB | 

1598# -o latA lonA aziA latB lonB aziB x0 y0] 

1599 

1600# % python3 -m ....pygeodesy.geodesici -h -n 

1601# 

1602# usage: python3 -m ....pygeodesy.geodesici -n latA lonA aziA aziB 

1603 

1604# % python3 -m ....pygeodesy.geodesici -c 0 0 45 40 10 135 

1605# Intersector.Closest: XDict(c=0, sA=3862290.547855, sB=2339969.547699, sX0=6202260.095554) 

1606 

1607# % python3 -m ....pygeodesy.geodesici -C -c 0 0 45 40 10 135 

1608# Intersector.Closest: XDict(aAB=0.0, c=0, latA=23.875306, latB=23.875306, lonA=26.094096, lonB=26.094096, sA=3862290.547855, sAB=0.0, sB=2339969.547699, sX0=6202260.095554) 

1609 

1610# % env PYGEODESY_INTERSECTTOOL=...python3 -m ....pygeodesy.geodesici -T -R 2.6e7 -c 0 0 45 40 10 135 

1611# Intersectool.All[0]: XDict(c=0, sA=3862290.547855, sB=2339969.547699, sX0=6202260.095554) 

1612 

1613# % python3 -m ....pygeodesy.geodesici -c 50 -4 -147.7 0 0 90 

1614# Intersector.Closest: XDict(c=0, sA=6058048.653081, sB=-3311252.995823, sX0=9369301.648903) 

1615 

1616# % python3 -m ....pygeodesy.geodesici -C -c 50 -4 -147.7 0 0 90 

1617# Intersector.Closest: XDict(aAB=0.0, c=0, latA=0.0, latB=-0.0, lonA=-29.745492, lonB=-29.745492, sA=6058048.653081, sAB=0.0, sB=-3311252.995823, sX0=9369301.648903) 

1618 

1619# % echo 0 0 10 10 50 -4 50S 4W | IntersectTool -i -p 0 -C 

1620# -631414 5988887 0 -3 

1621# -4.05187 -4.00000 -4.05187 -4.00000 0 

1622 

1623# % python3 -m ....pygeodesy.geodesici -C -m 0 0 10 10 50 -4 50S 4W 

1624# Intersector.Middle: XDict(aMM=10.262308, c=0, latA=5.019509, latB=0.036282, lonA=4.961883, lonB=-4.0, sA=782554.549609, sB=5536835.161499, sMM=1138574.546746, sX0=0.0) 

1625 

1626# % python3 -m ....pygeodesy.geodesici -M 0 0 10 10 50 -4 50S 4W 

1627# Intersector.Middle5: Middle5Tuple(A=GDict(a12=14.106434, a1M=7.053396, azi1=44.75191, azi2=45.629037, aziM=44.969535, lat1=0.0, lat2=10.0, latM=5.019509, lon1=0.0, lon2=10.0, lonM=4.961883, s12=1565109.099218, s1M=782554.549609), B=GDict(a12=99.810444, a1M=49.869061, azi1=180.0, azi2=180.0, aziM=180.0, lat1=50.0, lat2=-50.0, latM=0.036282, lon1=-4.0, lon2=-4.0, lonM=-4.0, s12=11073670.322999, s1M=5536835.161499), sMM=1138574.546746, aMM=10.262308, c=0) 

1628 

1629# % python3 -m ....pygeodesy.geodesici -i 0 0 10 10 50 -4 50S 4W 

1630# Intersector.Segment: XDict(c=0, k=-3, kA=-1, kB=0, sA=-631414.26877, sB=5988887.278435, sX0=1866020.935315) 

1631 

1632# % env PYGEODESY_INTERSECTTOOL=... python3 -m ....pygeodesy.geodesici -T -i 0 0 10 10 50 -4 50S 4W 

1633# Intersectool.Segment: XDict(c=0, k=-3, kA=-1, kB=0, sA=-631414.26877, sB=5988887.278435) 

1634 

1635# % python3 -m ....pygeodesy.geodesici -C -i 0 0 10 10 50 -4 50S 4W 

1636# Intersector.Segment: XDict(aAB=0.0, c=0, k=-3, kA=-1, kB=0, latA=-4.051871, latB=-4.051871, lonA=-4.0, lonB=-4.0, sA=-631414.26877, sAB=0.0, sB=5988887.278435, sX0=1866020.935315) 

1637 

1638# % env PYGEODESY_INTERSECTTOOL=... python3 -m ....pygeodesy.geodesici -T -C -i 0 0 10 10 50 -4 50S 4W 

1639# Intersectool.Segment: XDict(c=0, k=-3, kA=-1, kB=0, latA=-4.051871, latB=-4.051871, lonA=-4.0, lonB=-4.0, sA=-631414.26877, sAB=0.0, sB=5988887.278435) 

1640 

1641# % env PYGEODESY_INTERSECTTOOL=... python3 -m ....pygeodesy.geodesici -V -T -i 0 0 10 10 50 -4 -50 -4 

1642# Intersectool@1: /opt/local/bin/IntersectTool --version (invoke) 

1643# Intersectool@1: '/opt/local/bin/IntersectTool: GeographicLib version 2.3' (0) 

1644# Intersectool@1: /opt/local/bin/IntersectTool: GeographicLib version 2.3 (0) 

1645# X = Intersectool.Segment(GDict(lat1=0.0, lat2=10.0, lon1=0.0, lon2=10.0), GDict(lat1=50.0, lat2=-50.0, lon1=-4.0, lon2=-4.0)) 

1646# Intersectool@2: /opt/local/bin/IntersectTool -E -p 10 -i \ 0.0 0.0 10.0 10.0 50.0 -4.0 -50.0 -4.0 (Segment) 

1647# Intersectool@2: '-631414.2687702414 5988887.2784352796 0 -3' (0) 

1648# Intersectool@2: sA=-631414.2687702414, sB=5988887.2784352796, c=0, k=-3 (0) 

1649# Intersectool.Segment: XDict(c=0, k=-3, kA=-1, kB=0, sA=-631414.26877, sB=5988887.278435) 

1650 

1651# % python3 -m ....pygeodesy.geodesici -C -R 4e7 -c 50 -4 -147.7 0 0 90 

1652# Intersector.All[0]: XDict(aAB=0.0, c=0, latA=0.0, latB=-0.0, lonA=-29.745492, lonB=-29.745492, sA=6058048.653081, sAB=0.0, sB=-3311252.995823, sX0=9369301.648903) 

1653# Intersector.All[1]: XDict(aAB=0.0, c=0, latA=0.0, latB=0.0, lonA=150.046964, lonB=150.046964, sA=-13941907.021445, sAB=0.0, sB=16703151.659744, sX0=30645058.681189) 

1654# Intersector.All[2]: XDict(aAB=0.0, c=0, latA=-0.0, latB=-0.0, lonA=-30.16058, lonB=-30.16058, sA=-33941862.69597, sAB=0.0, sB=-3357460.370268, sX0=37299323.066238) 

1655# Intersector.All[3]: XDict(aAB=0.0, c=0, latA=-0.0, latB=0.0, lonA=150.046964, lonB=150.046964, sA=-13941907.021445, sAB=0.0, sB=-23371865.025835, sX0=37313772.047279) 

1656 

1657# % env PYGEODESY_INTERSECTTOOL=... python3 -m ....pygeodesy.geodesici -T -C -R 4e7 -c 50 -4 -147.7 0 0 90 

1658# Intersectool.All[0]: XDict(c=0, latA=-0.0, latB=-0.0, lonA=-29.745492, lonB=-29.745492, sA=6058048.653081, sAB=0.0, sB=-3311252.995823, sX0=9369301.648903) 

1659# Intersectool.All[1]: XDict(c=0, latA=0.0, latB=0.0, lonA=150.046964, lonB=150.046964, sA=-13941907.021445, sAB=0.0, sB=16703151.659744, sX0=30645058.681189) 

1660# Intersectool.All[2]: XDict(c=0, latA=-0.0, latB=-0.0, lonA=-30.16058, lonB=-30.16058, sA=-33941862.69597, sAB=0.0, sB=-3357460.370268, sX0=37299323.066238) 

1661# Intersectool.All[3]: XDict(c=0, latA=-0.0, latB=0.0, lonA=150.046964, lonB=150.046964, sA=-13941907.021445, sAB=0.0, sB=-23371865.025835, sX0=37313772.047279) 

1662 

1663# % python3 -m ....pygeodesy.geodesici -R 4e7 -i 0 0 10 10 50 -4 -50 -4 

1664# Intersector.All[0]: XDict(c=0, sA=-631414.26877, sB=5988887.278435, sX0=1866020.935315) 

1665# Intersector.All[1]: XDict(c=0, sA=19422725.117572, sB=-14062417.105648, sX0=38239422.83511) 

1666# Intersector.All[2]: XDict(c=0, sA=19422725.117572, sB=25945445.811603, sX0=39048781.218067) 

1667# Intersector.All[3]: XDict(c=0, sA=39476927.464575, sB=5894074.699478, sX0=39051612.452944) 

1668 

1669# % env PYGEODESY_INTERSECTTOOL=... python3 -m ....pygeodesy.geodesici -T -R 4e7 -i 0 0 10 10 50 -4 -50 -4 

1670# Intersectool.All[0]: XDict(c=0, sA=-631414.26877, sB=5988887.278435, sX0=1862009.05513) 

1671# Intersectool.All[1]: XDict(c=0, sA=19422725.117572, sB=-14062417.105648, sX0=38243434.715295) 

1672# Intersectool.All[2]: XDict(c=0, sA=19422725.117572, sB=25945445.811603, sX0=39044769.337882) 

1673# Intersectool.All[3]: XDict(c=0, sA=39476927.464575, sB=5894074.699478, sX0=39047600.57276) 

1674 

1675 

1676# **) MIT License 

1677# 

1678# Copyright (C) 2024-2024 -- mrJean1 at Gmail -- All Rights Reserved. 

1679# 

1680# Permission is hereby granted, free of charge, to any person obtaining a 

1681# copy of this software and associated documentation files (the "Software"), 

1682# to deal in the Software without restriction, including without limitation 

1683# the rights to use, copy, modify, merge, publish, distribute, sublicense, 

1684# and/or sell copies of the Software, and to permit persons to whom the 

1685# Software is furnished to do so, subject to the following conditions: 

1686# 

1687# The above copyright notice and this permission notice shall be included 

1688# in all copies or substantial portions of the Software. 

1689# 

1690# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS 

1691# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, 

1692# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL 

1693# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR 

1694# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, 

1695# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR 

1696# OTHER DEALINGS IN THE SOFTWARE.