1

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

3

4 u'''Class L{Intersector}, a pure Python version of parts of I{Karney}'s C++ class U{Intersect

5<https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1Intersect.html>} to intersect

6 geodesic lines.

7

8 Only C++ member functions C{All}, C{Closest} and C{All} have been transcoded into Python as methods

9 L{Intersector.All}, L{Intersector.Closest} and L{Intersector.Next} producing 4-item L{XDist}s.

10

11 Adjacent methods L{Intersector.All5}, L{Intersector.Closest5}, L{Intersector.Next5} and

12 L{Intersector.Next5s} return or yield L{Intersector5Tuple}s with the lat-, longitude, azimuth of

13 each intersection as a C{Position} L{GDict} on each geodesic line.

14

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

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

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

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

19'''

20# make sure int/int division yields float quotient

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

22

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

24 _xinstanceof, _xor

25 from pygeodesy.constants import EPS, INF, INT0, PI, PI2, PI_4, _0_0, \

26 _0_5, _1_0, _1_5, _2_0, _3_0, _90_0

27 from pygeodesy.ellipsoids import _EWGS84, Fmt

28 from pygeodesy.errors import GeodesicError, IntersectionError, \

29 _xgeodesics, _xkwds_get

30 from pygeodesy.fmath import euclid, favg, fdot

31 from pygeodesy.fsums import Fsum, fsum1_, _ceil

32 from pygeodesy.interns import _A_, _B_, _c_, _SPACE_, _too_

33 from pygeodesy.karney import Caps, _diff182, _sincos2de

34 from pygeodesy.lazily import _ALL_LAZY # _ALL_MODS as _MODS

35 from pygeodesy.named import ADict, _NamedBase, _NamedTuple

36 from pygeodesy.namedTuples import Degrees, Int, Meter, _Pass

37 from pygeodesy.props import Property, Property_RO, property_RO

38# from pygeodesy.streprs import Fmt # from .ellipsoids

39# from pygeodesy.units import Degrees, Int, Meter # from .namedTuples

40 from pygeodesy.utily import sincos2, atan2, fabs

41

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

43

44__all__ = _ALL_LAZY.geodesici

45__version__ = '24.06.27'

46

47_0t = 0, # int

48_1_1t = -1, +1

49_1_0_1t = -1, 0, +1

50_EPS3 = EPS * _3_0

51_EPSr5 = pow(EPS, 0.2) # PYCHOK used!

52_TRIPS = 128

53

54

55 def _L1(a, b):

56 return fabs(a) + fabs(b)

57

58

59 class XDist(ADict):

60 '''4-Item result from L{Intersector.All}, L{Intersector.Closest} and

61 L{Intersector.Next} with the intersection offsets C{sA}, C{sB} and

62 C{sX0} in C{meter} and the coincidence indicator C{c}, an C{int},

63 +1 for parallel, -1 for anti-parallel, 0 otherwise.

64 '''

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

66

67 def __init__(self, sA=0, sB=0, c=0, sX0=INT0):

68 '''New L{XDist}.

69

70 @kwarg sA: Offset on geodesic line A (C{meter}).

71 @kwarg sB: Offset on geodesic line B (C{meter}).

72 @kwarg c: Coincidence indicator (C{int}, +1 for parallel

73 -1 for anti-parallel, 0 otherwise.

74 @kwarg sX0: Offset to C{X0} ({Cmeter}) or L{INT0}.

75 '''

76 self.set_(sA=sA, sB=sB, c=c, sX0=sX0)

77

78 def __add__(self, other):

79 X = _copy(self)

80 X += other

81 return X

82

83 def __eq__(self, other):

84 return not self.__ne__(other)

85

86 def __iadd__(self, other):

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

88 a, b = other

89 else:

90 # _xinstanceof(XDist, other=other)

91 a = other.sA

92 b = other.sB

93 if other.c:

94 self.c = other.c

95 self.sA += a # PYCHOK sA

96 self.sB += b # PYCHOK sB

97 return self

98

99 def __le__(self, other):

100 # _xinstanceof(XDist, other=other)

101 return self == other or self < other

102

103 def __lt__(self, other):

104 # _xinstanceof(XDist, other=other)

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

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

107

108 def __ne__(self, other):

109 # _xinstanceof(XDist, other=other)

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

111

112 def _fixCoincident(self, X, *c0):

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

114 c = c0[0] if c0 else X.c

115 if c:

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

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

118 X = X + (s, s * c) # NOT +=

119 return X

120

121 def L1(self, other=None):

122 '''Return the C{L1} distance.

123 '''

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

125 if other is not None:

126 # _xinstanceof(XDist, other=other)

127 a -= other.sA

128 b -= other.sB

129 return _L1(a, b)

130

131 def _nD1(self, D1):

132 # yield the C{Closest} starts

133 D_ = 0, D1, -D1

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

135 (0, 0, 0, 1, -1)):

136 yield self + (D_[a], D_[b])

137

138 def _nD2(self, D2):

139 # yield the C{Next} starts

140 D22 = D2 * _2_0

141 D_ = 0, D2, D22, -D22, -D2

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

143 (-1, 1, -1, 1, 0, 2, 0, -2)):

144 yield self + (D_[a], D_[b])

145

146 def _nmD3(self, n, m, D3):

147 # yield the C{All} starts

148 for i in range(n, m, 2):

149 for j in range(n, m, 2):

150 if i or j:

151 yield self + ((i + j) * D3,

152 (i - j) * D3)

153

154 def _skip(self, S_, T1_Delta):

155 # remove starts from C{S_} near this C{XDist}

156 for j, S in _enumereverse(S_):

157 if S.L1(self) < T1_Delta:

158 S_.pop(j)

159

160_X000 = XDist() # PYCHOK origin

161_XINF = XDist(INF)

162

163

164 class Intersector(_NamedBase):

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

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

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

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

169

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

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

172 '''

173 # _D1 = 0

174 # _D2 = 0

175 # _g = None

176 # _T1 = 0

177 # _T5 = 0

178

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

180 '''New L{Intersector}.

181

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

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

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

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

186

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

188 large or no initial convergence.

189

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

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

192 '''

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

194 self._g = geodesic

195 if name:

196 self.name = name

197 E = self.ellipsoid

198

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

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

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

202 if self.f > 0:

203 t3 = self._obliqDist4()[0]

204 t4 = t1

205 else: # PYCHOK no cover

206 t1, t2, t3 = t2, t1, t5

207 t4 = self._polarB3()[0]

208 d1 = t2 * _0_5

209 d2 = t3 / _1_5

210 d3 = t4 - self.Delta

211 t2 = t1 * _2_0

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

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

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

215 self._D1 = d1 # tile spacing for Closest

216 self._D2 = d2 # tile spacing for Next

217 self._D3 = d3 # tile spacing for All

218 self._T1 = t1 # min distance between intersects

219 self._T2 = t2

220# self._T5 = t5

221

222 @Property_RO

223 def a(self):

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

225 '''

226 return self.ellipsoid.a

227

228 equatoradius = a # = Requatorial

229

230 def All(self, glA, glB, X0=_X000, **sMax):

231 '''Find all intersection of two geodesic lines up to a limit.

232

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

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

235 @kwarg X0: Optional offsets along the geodesic lines (L{XDist}).

236 @kwarg sMax: Optional, upper limit C{B{sMax}=2*PI*R} for the

237 distance (C{meter}).

238

239 @return: Yield an L{XDist} for each intersection found.

240

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

242 invalid, incompatible or ill-configured.

243

244 @raise IntersectionError: No convergence.

245 '''

246 self._xLines(glA, glB)

247 sMax = _xkwds_get(sMax, sMax=self.R * PI2)

248 if sMax < _EPS3:

249 sMax = _EPS3 # raise GeodesicError(sMax=sMax)

250

251 D, _D = self.Delta, self._C_2

252 xMax = sMax + D

253 m = int(_ceil(xMax / self._D3)) # m x m tiles

254 d3 = xMax / m

255 T2d3D = self._T2d3Delta(d3)

256 _X0fx = X0._fixCoincident

257

258 c0 = 0

259 C_ = _List(D) # closest coincident

260 X_ = _List(D) # intersections found

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

262 # assert len(s_) + 1 == m * m + (m - 1) % 2

263 while S_:

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

265 if Q in X_:

266 continue

267 # assert Q.c == c0 or not c0

268 a, c0 = len(X_), Q.c

269 if c0: # coincident intersection

270 Q = _X0fx(Q)

271 if Q in C_:

272 continue

273 C_.addend(Q)

274 # elimate all existing intersections

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

276 for j, X in _enumereverse(X_):

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

278 X_.pop(j)

279

280 a, s0 = len(X_), Q.sA

281 args = self._m12_M12_M21(glA, s0)

282 _cjD = self._conjDist

283 for s in (-_D, _D):

284 s += s0

285 sa = 0

286 while True:

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

288 X = Q + (sa, sa * c0)

289 i += 1

290 if X_.addend(X, X0.L1(X), i) > xMax:

291 break

292

293 X_.addend(Q, X0.L1(Q), i + 1)

294 for X in X_[a:]: # addended Xs

295 X._skip(S_, T2d3D)

296

297 return X_.sortrim(X0, sMax) # generator!

298

299 def All5(self, glA, glB, X0=_X000, aMax=0, **sMax):

300 '''Find all intersection of two geodesic lines up to a limit.

301

302 @kwarg aMax: Upper limit for the angular distance (C{degrees})

303 or C{None} or C{0} for unlimited.

304

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

306 for each intersection found.

307

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

309 '''

310 aA = aB = _0_0

311 for X in self.All(glA, glB, X0=X0, **sMax):

312 r = self._In5T(glA, glB, X, X)

313 yield r

314 if aMax:

315 aA += r.A.a12

316 aB += r.B.a12

317 if fabs(aA) > aMax or fabs(aB) > aMax:

318 break

319

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

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

322 '''

323 X = _copy(S)

324 for _ in range(_TRIPS):

325 S = self._Spherical(glA, glB, X)

326 X += S

327 i += 1

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

329 return self._Delto(X), i

330

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

332

333 @Property_RO

334 def _C_2(self): # normalizer, semi-circumference, C++ _d

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

336

337 def Closest(self, glA, glB, X0=_X000):

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

339

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

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

342 @kwarg X0: Optional offsets along the geodesic lines (L{XDist}).

343

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

345

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

347 invalid, incompatible or ill-configured.

348

349 @raise IntersectionError: No convergence.

350 '''

351 self._xLines(glA, glB)

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

353 while S_:

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

355 X = X0._fixCoincident(X)

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

357 d0 = X.L1(X0)

358 if d0 < self._T1:

359 Q, d, q = X, d0, i

360 break

361 if d0 < d or Q is X0:

362 Q, d, q = X, d0, i

363 X._skip(S_, self._T2D1Delta)

364

365 return None if Q is X0 else Q.set_(sX0=d, iteration=q)

366

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

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

369

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

371 or C{None} if none found.

372

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

374 '''

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

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

377

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

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

380 # if semi:

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

382 # else:

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

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

385 for _ in range(_TRIPS):

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

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

388 m23 = m13 * M12

389 M32 = M31 * M12

390 if m12:

391 m23 -= m12 * M13

392 if m13:

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

394 if semi:

395 M23 = M13 * M21

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

397 if m12 and m13:

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

399 d = m23 * M23 / (_1 - M23 * M32)

400 else:

401 d = -m23 / M32

402 s, d = _S2(d)

403 if _abs(d) <= self._Tol:

404 break

405 return s

406

407 _gl3 = None

408

409 @Property

410 def _conjDist3s(self):

411 gl, self._gl3, _D = self._gl3, None, self._C_2

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

413

414 @_conjDist3s.setter # PYCHOK setter!

415 def _conjDist3(self, gl):

416 # _XLines(gl, gl)

417 self._gl3 = gl

418

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

420 for s in self._conjDist3s:

421 T = XDist(s, s * c, c)

422 yield self._Delto(T), T.L1(X0)

423

424 def _conjDist5(self, azi):

425 gl = self._Line(azi1=azi)

426 s = self._conjDist(gl, self._C_2)

427 X, _ = self._Basic2(gl, gl, XDist(s * _0_5, -s * _1_5))

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

429

430 @Property_RO

431 def Delta(self):

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

433 '''

434 return self._C_2 * _EPSr5 # ~15 Km WGS84

435

436 def _Delto(self, X):

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

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

439 return X

440

441 @Property_RO

442 def ellipsoid(self):

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

444 '''

445 return self.geodesic.datum.ellipsoid

446

447 @Property_RO

448 def _EPS3R(self):

449 return _EPS3 * self.R

450

451 @Property_RO

452 def f(self):

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

454 '''

455 return self.ellipsoid.f

456

457 flattening = f

458

459 @Property_RO

460 def _faPI_4(self):

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

462

463 @property_RO

464 def geodesic(self):

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

466 '''

467 return self._g

468

469 @Property_RO

470 def _GeodesicLines(self):

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

472 '''

473 return type(self._Line()),

474

475 def _In5T(self, glA, glB, S, X):

476 # Return an intersection as C{Intersector5Tuple}.

477 A = self._Position(glA, S.sA, S.sX0)

478 B = self._Position(glB, S.sB, S.sX0)

479 s, a = self._Inversa12(A, B)

480 r = Intersector5Tuple(A, B, s, a, X.c, iteration=X.iteration)

481 return r

482

483 def _Inversa12(self, A, B=None):

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

485 B.lat2, B.lon2)

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

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

488

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

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

491

492 def Line(self, lat1, lon1, azi_lat2, *lon2, **name):

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

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

495

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

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

498 @arg azi_lat2: Azimuth at the first point (compass C{degrees}) if no

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

500 the second point (C{degrees}).

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

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

503

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

505 C{-.InverseLine}), properly configured for L{Intersector}.

506 '''

507 args = (lat1, lon1, azi_lat2) + lon2

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

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

510 if name:

511 gl.name= name

512 return gl

513

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

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

516

517 def _m12_M12_M21(self, gl, s):

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

519 return P.m12, P.M12, P.M21

520

521 def Next(self, glA, glB, **eps):

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

523

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

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

526 @kwarg eps: Optional equality margin C{B{eps}=Delta} (C{degrees}).

527

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

529

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

531 invalid, incompatible, ill-configured or

532 C{(lat1, lon1)} not B{C{eps}}-equal.

533

534 @raise IntersectionError: No convergence.

535

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

537 '''

538 self._xLines(glA, glB)

539 e = _xkwds_get(eps, eps=self.Delta)

540 a = glA.lat1 - glB.lat1

541 b = glA.lon1 - glB.lon1

542 if fabs(a) > e or fabs(b) > e:

543 raise GeodesicError(lat1=a, lon1=b, eps=e)

544 return self._Next(glA, glB)

545

546 def Next5(self, glA, glB, eps=_EPS3):

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

548

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

550 if none found.

551

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

553 '''

554 X = self.Next(glA, glB, eps=eps)

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

556

557 def Next5s(self, glA, glB, X0=_X000, aMax=1801, sMax=0, avg=False, **Delta):

558 '''Yield C{Next} intersections up to a maximal (angular) distance.

559

560 @kwarg aMax: Upper limit for the angular distance (C{degrees}) or

561 C{None} or C{0} for unlimited.

562 @kwarg sMax: Upper limit for the distance (C{meter}) or C{None} or

563 C{0} for unlimited.

564 @kwarg avg: If C{True}, set the next intersection lat- and longitude

565 to the mid-point of the previous ones (C{bool}).

566 @kwarg Delta: Optional, margin overrding this margin (C{meter}), see

567 prpoerty L{Delta<Intersector.Delta>}.

568

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

570 every intersection found.

571

572 @see: Methods L{Next5} for further details.

573 '''

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

575 if X is not None:

576 D = _xkwds_get(Delta, Delta=self.Delta)

577 S, _L, _abs = X, self._Line, fabs

578 while True:

579 A, B, _, _, _ = r = self._In5T(glA, glB, S, X)

580 yield r

581 if (aMax and (_abs(A.a12) > aMax or _abs(B.a12) > aMax)) or \

582 (sMax and (_abs(A.s12) > sMax or _abs(B.s12) > sMax)):

583 break

584 latA, lonA = A.lat2, A.lon2

585 latB, lonB = B.lat2, B.lon2

586 if avg:

587 latA = latB = favg(latA, latB)

588 lonA = lonB = favg(lonA, lonB)

589 X = self._Next(_L(latA, lonA, A.azi2),

590 _L(latB, lonB, B.azi2))

591 if X is None or X.L1() < D:

592 break

593 S += X.sA, X.sB

594 S.set_(sX0=X.sX0 + S.sX0)

595

596 def _Next(self, glA, glB):

597 '''(INTERNAL) Find the next intersection.

598 '''

599 X0, self._conjDist3s = _X000, glA

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

601 while S_:

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

603 X = X0._fixCoincident(X)

604 t = X.L1(X0) # == X.L1()

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

606 if z:

607 if not c:

608 continue

609 Tt_ = self._conjDist3Tt_(c, X0)

610 else:

611 Tt_ = (X, t),

612

613 for T, t in Tt_:

614 if t < d or Q is _XINF:

615 Q, d, q = T, t, i

616 i += 1

617

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

619 if c else _0t):

620 T = X

621 if s and c:

622 s *= self._D2

623 T = X + (s, s * c) # NOT +=

624 T._skip(S_, self._T2D2Delta)

625

626 return None if Q is _XINF else Q.set_(sX0=d, iteration=q)

627

628 def _obliqDist4(self):

629 zx = 45.0

630 if self.f:

631 _abs, _cjD5 = fabs, self._conjDist5

632

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

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

635 sx, dsx, zx = s1, _abs(ds1), z1

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

637 for _ in range(16):

638 if ds1 == ds0:

639 break

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

641 _, ds0, z0 = s1, ds1, z1

642 s1, ds1, z1, a, b = _cjD5(z)

643 if _abs(ds1) < dsx:

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

645 if not dsx:

646 break

647 else:

648 sx, sAx, sBx = self._C_2, _0_5, -_1_5

649 return sx, zx, sAx, sBx

650

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

652 latx = 64.0

653 lat = _90_0 - latx

654 if self.f:

655 _d, _pD2 = fdot, self._polarDist2

656

657 s0, lat0 = _pD2(latx - _1_0)

658 s1, lat1 = _pD2(latx + _1_0)

659 s2, lat2 = \

660 sx, latx = _pD2(latx)

661 prolate = self.f < 0

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

663 for _ in range(_TRIPS):

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

665 d = _d(t, s2, s1, s0) * _2_0

666 if not d: # or isnan(d)

667 break

668 lat = _d(t, (lat1 + lat0) * s2,

669 (lat0 + lat2) * s1,

670 (lat2 + lat1) * s0) / d

671 s0, lat0 = s1, lat1

672 s1, lat1 = s2, lat2

673 s2, lat2 = _pD2(lat)

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

675 sx, latx = s2, lat2

676 if lats:

677 _, lat = _pD2(latx, lat2=True)

678 sx += sx

679 else:

680 sx = self._C_2

681 return sx, latx, lat

682

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

684 gl = self._Line(lat1=lat1)

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

686 if lat2:

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

688 return s, lat1

689

690 def _Position(self, gl, s, *sX0):

691 P = gl.Position(s, outmask=Caps._STD_LINE)

692 if sX0:

693 X = gl.Position(*sX0, outmask=Caps._STD_LINE)

694 P.set_(lat0=X.lat2, lon0=X.lon2,

695 azi0=X.azi2, s10=X.s12, a10=X.a12)

696 return P

697

698 @Property_RO

699 def R(self):

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

701 '''

702 return self.ellipsoid.R2

703

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

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

706 '''

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

708 A = self._Position(glA, S.sA)

709 B = self._Position(glB, S.sB)

710 D = self._Inverse(A, B)

711

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

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

714 c, dc = _diff182(a, b)

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

716 a, da = -a, -da

717 b, db = -b, -db

718 sa, ca = _sincos2de(a, da)

719 sb, cb = _sincos2de(b, db)

720

721 e, z, _abs = _EPS3, D.s12, fabs

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

723 sA = sB = 0 # at intersection

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

725 -1 if _abs(sa + sb) <= e and _abs(ca + cb) <= e else 0)

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

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

728 sB = -cb * z * _0_5

729 c = 1 if (ca * cb) > 0 else -1

730 # alt1: sA = ca * z; sB = 0

731 # alt2: sB = -cb * z; sA = 0

732 else: # general case

733 sz, cz = sincos2(z / self.R)

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

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

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

737 # order to avoid some convergence failures in _Basic2.

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

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

740 c = 0

741 return XDist(sA, sB, c) # no ._Delto

742

743 @Property_RO

744 def _T2D1Delta(self):

745 return self._T2d3Delta(self._D1)

746

747 @Property_RO

748 def _T2D2Delta(self):

749 return self._T2d3Delta(self._D2)

750

751 def _T2d3Delta(self, d3):

752 return self._T2 - d3 - self.Delta

753

754 @Property_RO

755 def _Tol(self): # convergence tolerance

756 return self._C_2 * pow(EPS, 0.75) # _0_75

757

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

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

760

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

762 for further details.

763

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

765 '''

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

767

768 def _xLines(self, glA, glB):

769 # check two geodesic lines vs this geodesic

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

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

772 for n, gl in gls.items():

773 try:

774 _xgeodesics(gl.geodesic, self.geodesic)

775 c = gl.caps & C

776 if c != C: # not gl.caps_(C)

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

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

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

780 except Exception as x:

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

782

783

784 class Intersector5Tuple(_NamedTuple):

785 '''5-Tuple C{(A, B, sAB, aAB, c)} with C{A} and C{B} the C{Position}

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

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

788 C{degrees} and coincidence indicator C{c} (C{int}), see L{XDist}.

789

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

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

792 C{lat2}, C{lon2}, azimuth in C{azi2}, the distance C{s12}

793 in C{meter} and angular distance C{a12} in C{degrees} and

794 extended with the C{X0} offset location in C{lat0}, C{lon0},

795 C{azi0}, C{s10} and C{a10}.

796 '''

797 _Names_ = (_A_, _B_, 'sAB', 'aAB', _c_)

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

799

800

801 class _List(list):

802

803 _Delta = 0 # equality margin

804

805 def __init__(self, Delta):

806 self._Delta = Delta

807# list.__init__(self)

808

809 def __contains__(self, other):

810 # handle C{if X in this: ...}

811 a, b = other.sA, other.sB

812 D, _D1 = self._Delta, _L1

813 for X in self:

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

815 return True

816 return False

817

818 def addend(self, X, *d0_i):

819 # append an item, updated

820 if d0_i:

821 d0, i = d0_i

822 X.set_(sX0=d0, iteration=i)

823 self.append(X)

824 return X.sX0

825

826 def sortrim(self, X0, sMax):

827 # trim and sort the X items

828

829 def _key(Xk):

830 _, k = Xk

831 return k # rank of X

832

833 for X, _ in sorted(self.trim(X0, sMax), key=_key):

834 yield X # de-tuple (X, k)

835

836 def trim(self, X0, sMax):

837 # trim and yield 2-tuple (X, rank)

838 a, b, _eu = X0.sA, X0.sB, euclid

839

840 for X in self:

841 k = X.sX0

842 if k <= sMax:

843 k += _eu(X.sA - a, X.sB - b)

844 yield X, k # rank of X

845

846

847 if __name__ == '__main__':

848

849 from pygeodesy import GeodesicExact, printf

850

851 I = Intersector(GeodesicExact(), name='Test') # PYCHOK I

852

853 # <https://GeographicLib.sourceforge.io/C++/doc/classGeographicLib_1_1Intersect.html>

854 a = I.Line( 0, 0, 45)

855 b = I.Line(45, 10, 135)

856 printf('Closest: %r', I.Closest(a, b))

857 printf('Closest5: %r', I.Closest5(a, b), nt=1)

858

859 for i, t in enumerate(I.Next5s(a, b)):

860 printf('Next5s %s: %r (%s)', i, t, t.iteration)

861

862 # <https://GeographicLib.sourceforge.io/C++/doc/IntersectTool.1.html>

863 a = I.Line(50, -4, -147.7)

864 b = I.Line( 0, 0, 90)

865 printf('Closest: %r', I.Closest(a, b), nl=1)

866 printf('Closest5: %r', I.Closest5(a, b), nt=1)

867

868 a = I.Line(50, -4, -147.7)

869 b = I.Line( 0, 180, 0)

870 for i, X in enumerate(I.All(a, b)):

871 printf('All %s: %r (%s)', i, X, X.iteration)

872 if i > 9:

873 break

874 printf('')

875 for i, t in enumerate(I.All5(a, b)):

876 printf('All5 %s: %r (%s)', i, t, t.iteration)

877 if i > 9:

878 break

879

880 # % echo 50N 4W 147.7W 0 0 90 | IntersectTool -e 6371e3 0 -c -p 0 -C

881 # 6077191 -3318019 0

882 # -0.00000 -29.83966 -0.00000 -29.83966 0

883 I = Intersector(GeodesicExact(6371e3, 0), name='Test') # PYCHOK I

884 a = I.Line(50, -4, -147.7)

885 b = I.Line( 0, 0, 90)

886 printf('Closest: %r', I.Closest(a, b), nl=1)

887 printf('Closest5: %r', I.Closest5(a, b))

888

889# **) MIT License

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

892#

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

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

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

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

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

899#

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

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