1

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

3

4 u'''Classes L{Intersectool} and L{Intersector} to find the intersections of two geodesic lines or line segments.

5

6 Class L{Intersector} is a pure Python version of I{Karney}'s C++ class U{Intersect

7<https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1Intersect.html>}.

8

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

10<https://GeographicLib.SourceForge.io/C++/doc/IntersectTool.1.html>} utility, but intended I{for testing purposes only}.

11

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

13 and some examples run C{"env PYGEODESY_INTERSECTTOOL=<IntersectTool-path> python3 -m pygeodesy.geodesici --help"}.

14

15 Both L{Intersectool} and L{Intersector} provide methods C{All}, C{Closest}, C{Next} and C{Segment} and produce

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

17 or yield L{Intersectool5Tuple} or L{Intersector5Tuple}s with the lat-, longitude and azimuth of each intersection

18 as an extended, geodesic C{Position}-like L{GDict} instance.

19

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

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

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

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

24'''

25# make sure int/int division yields float quotient

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

27

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

29 _xinstanceof, _xor, typename

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

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

32 _45_0, _64_0, _90_0, isfinite, \

33 _EPSjam # PYCHOK used!

34 from pygeodesy.ellipsoids import _EWGS84, Fmt, unstr

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

36 _xgeodesics, _xkwds_get, _xkwds_kwds, \

37 _xkwds_pop2

38# from pygeodesy.errors import exception_chaining # _MODS

39 from pygeodesy.fmath import euclid, fdot

40 from pygeodesy.fsums import Fsum, fsum1_, _ceil

41# from pygeodesy.internals import typename # from .basics

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

43 _HASH_, _M_, _not_, _SPACE_, _too_

44 from pygeodesy.karney import Caps, _diff182, GDict, _sincos2de, _Xables

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

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

47# from pygeodesy.namedTuples import _LL4Tuple # _MODS

48 from pygeodesy.props import deprecated_method, Property, \

49 Property_RO, property_RO, property_ROver

50 from pygeodesy.solveBase import _SolveCapsBase, pairs

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

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

53 from pygeodesy.units import Azimuth as Azi, Degrees, Float, Int, \

54 _isDegrees, Lat, Lon, Meter, Meter_

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

56

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

58

59__all__ = _ALL_LAZY.geodesici

60__version__ = '25.04.14'

61

62_0t = 0, # int

63_1_1t = -1, +1

64_1_0_1t = -1, 0, +1

65_aAB_ = 'aAB'

66_c__ = '-c' # PYCHOK used!

67_cWGS84 = _EWGS84.a * PI2 # outer circumference

68_EPS3 = EPS * _3_0

69_EPSr5 = pow(EPS, 0.2) # PYCHOK used! 7.4e-4 or ~3"

70_i__ = '-i' # PYCHOK used!

71_latA_ = 'latA'

72_lonA_ = 'lonA'

73_n__ = '-n' # PYCHOK used!

74_o__ = '-o' # PYCHOK used!

75_R__ = '-R'

76_sAB_ = 'sAB'

77_sX0_ = 'sX0'

78_TRIPS = 128

79

80

81 class XDict(ADict):

82 '''4+Item result from L{Intersectool} and L{Intersector} methods

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

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

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

86 or 0 otherwise.

87

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

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

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

91

92 If present, distance C{sAB} and angular distance C{aAB} represent

93 the difference between the intersection point on geodesic lines

94 C{glA} and C{glB} in C{meter} respectively C{degrees}, typically

95 below C{5e-9 meter} or C{5 nm} and C{5e-14 degrees} or C{1 n"}.

96

97 For segments, indicators C{kA} and C{kB} are C{0} if the segments

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

99 start, respectively I{after} the end of the segment, similar to

100 L{Intersection3Tuple<Intersection3Tuple>}. Segment indicator

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

102 '''

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

104

105 def __add__(self, other):

106 X = _copy(self)

107 X += other

108 return X

109

110 def __eq__(self, other):

111 return not self.__ne__(other)

112

113 def __iadd__(self, other):

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

115 a, b = other

116 else:

117 # _xinstanceof(XDict, other=other)

118 a = other.sA

119 b = other.sB

120 if other.c:

121 self.c = other.c

122 self.sA += a # PYCHOK sA

123 self.sB += b # PYCHOK sB

124 return self

125

126 def __le__(self, other):

127 # _xinstanceof(XDict, other=other)

128 return self == other or self < other

129

130 def __lt__(self, other):

131 # _xinstanceof(XDict, other=other)

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

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

134

135 def __ne__(self, other):

136 # _xinstanceof(XDict, other=other)

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

138

139 def _corners(self, sA, sB, T2):

140 # yield all corners further than C{T2}

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

142 for x in (0, sA):

143 for y in (0, sB):

144 if _L1(x - a, y - b) >= T2:

145 yield XDict_(x, y)

146

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

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

149 c = c0 or X.c

150 if c:

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

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

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

154 return X

155

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

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

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

159

160 def _g(): # intersection in smallest gap

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

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

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

164 s = a + b

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

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

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

168 s = sB + (a - b)

169 return (sB if t else sA) - s

170

171 ta = -a

172 tb = sA - a

173 tc = -c * b

174 td = -c * (b - sB)

175

176 ga = 0 <= (b + c * ta) <= sB

177 gb = 0 <= (b + c * tb) <= sB

178 gc = 0 <= (a + tc) <= sA

179 gd = 0 <= (a + td) <= sA

180

181 # test opposite rectangle sides first

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

183 (tc + td) if gc and gd else (

184 (ta + tc) if ga and gc else (

185 (ta + td) if ga and gd else (

186 (tb + tc) if gb and gc else (

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

188 self += s, s * c

189

190 @property_RO

191 def _is00(self):

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

193

194 def L1(self, other=None):

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

196 '''

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

198 if other is not None:

199 # _xinstanceof(XDict, other=other)

200 a -= other.sA

201 b -= other.sB

202 return _L1(a, b)

203

204 def _nD1(self, D1):

205 # yield the C{Closest} starts

206 D_ = 0, D1, -D1

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

208 (0, 0, 0, 1, -1)):

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

210

211 def _nD2(self, D2):

212 # yield the C{Next} starts

213 D22 = D2 * _2_0

214 D_ = 0, D2, D22, -D22, -D2

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

216 (-1, 1, -1, 1, 0, 2, 0, -2)):

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

218

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

220 # yield the C{All} starts

221 yield self

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

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

224 if i or j: # skip self

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

226 (i - j) * D3)

227

228 def _outSide(self, sA, sB):

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

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

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

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

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

234 return bool(kA or kB)

235

236 def _skip(self, S_, T1_Delta):

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

238 for j, S in _enumereverse(S_):

239 if S.L1(self) < T1_Delta:

240 S_.pop(j)

241

242

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

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

245 '''

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

247

248_X000 = XDict_() # PYCHOK origin

249_XINF = XDict_(INF)

250

251

252 class _IntersectBase(_NamedBase):

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

254 '''

255 # _g = None

256

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

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

259 self._g = geodesic

260 if name:

261 self.name = name

262

263 @Property_RO

264 def a(self):

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

266 '''

267 return self.ellipsoid.a

268

269 equatoradius = a # = Requatorial

270

271 def All(self, glA, glB, **kwds): # PYCHOK no cover

272 '''(INTERNAL) I{Must be overloaded}.'''

273 self._notOverloaded(glA, glB, **kwds)

274

275 @Property_RO

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

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

278

279 @Property_RO

280 def _cMax(self): # outer circumference

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

282

283 @property_RO

284 def datum(self):

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

286 '''

287 return self.geodesic.datum

288

289 @Property_RO

290 def ellipsoid(self):

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

292 '''

293 return self.geodesic.datum.ellipsoid

294

295 @Property_RO

296 def f(self):

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

298 '''

299 return self.ellipsoid.f

300

301 flattening = f

302

303 @property_RO

304 def geodesic(self):

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

306 '''

307 return self._g

308

309 def _illz2G(self, G, il):

310 '''(INTERNAL) Set C{InverseLine} 1-/2-attrs into C{G}, a C{GDict}.

311 '''

312 try:

313 G.set_(lat1=il.lat1, lon1=il.lon1, azi1=il.azi1, a12=il.a13, # .Arc()

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

315 except AttributeError:

316 r = il.Position(il.s13, outmask=Caps.STANDARD_LINE) # isfinite(il.s13)

317 G.set_(**r)

318# for n, v in r.items():

319# if not hasattr(il, n):

320# setattr(il, n, v)

321 return G

322

323 def intersect7(self, start1, end1, start2, end2, X0=_X000, aMaX0=0, sMaX0=_cWGS84,

324 **LatLon_and_kwds):

325 '''Yield the intersection points of two lines, each defined by two (ellipsoidal)

326 points or by an (ellipsoidal) start point and an azimuth from North.

327

328 @arg start1: Start point of the first line (C{LatLon}).

329 @arg end1: End point of the first line (C{LatLon}) or the azimuth at the

330 B{C{start1}} point (compass C{degrees360}).

331 @arg start2: Start point of the second line (C{LatLon}).

332 @arg end2: End point of the second line (C{LatLon}) or the azimuth at the

333 B{C{start2}} point (compass C{degrees360}).

334 @kwarg X0: Optional I{origin} for I{L1-distances} (L{XDict}) or C{None} for

335 the L{Middle<Intersector.Middle>}, otherwise C{XDiff_(0, 0)}.

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

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

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

339 I{L1-distance} to B{C{X0}} (C{meter}).

340 @kwarg LatLon_and_kwds: Optional class C{B{LatLon}=None} to return intersection

341 points and optional, additional B{C{LatLon}} keyword arguments.

342

343 @note: The C{lat} and C{lon} attr of B{C{start1}}, B{C{end1}}, B{C{start2}} and

344 B{C{end2}} are used I{verbatim}, ignoring C{datum} or C{ellipsoid}.

345

346 @return: Yield an L{Intersect7Tuple}C{(A, B, sAB, aAB, c, kA, kB)} for every

347 intersection found, with C{A} and C{B} each a B{C{LatLon}} or if

348 C{B{LatLon} is None} or not specified, a L{LatLon4Tuple}C{(lat, lon,

349 height, datum)} with C{height 0} and this C{datum}.

350

351 @raise GeodesicError: Invalid B{C{start1}}, B{C{end1}}, B{C{start2}} or

352 B{C{end2}} or B{C{end1}} and B{C{end2}} differ in type.

353

354 @raise IntersectionError: No convergence.

355 '''

356

357 def _args(s, e):

358 t = (e,) if _isDegrees(e) else (e.lat, e.lon)

359 return (s.lat, s.lon) + t

360

361 try:

362 glA = self.Line(*_args(start1, end1))

363 glB = self.Line(*_args(start2, end2))

364 except Exception as x:

365 raise GeodesicError(start1=start1, end1=end1, start2=start2, end2=end2, cause=x)

366

367 LL, kwds = _xkwds_pop2(LatLon_and_kwds, LatLon=None)

368 d, kwds = _xkwds_pop2(kwds, datum=self.datum)

369 h, kwds = _xkwds_pop2(kwds, height=0)

370

371 _LL4T = _MODS.namedTuples._LL4Tuple

372 for X in self.All(glA, glB, X0=X0, aMaX0=aMaX0, sMaX0=sMaX0, _C=True):

373 A = B = _LL4T(X.latA, X.lonA, h, d, LL, kwds, iteration=X.iteration)

374 if X.sAB or X.latA != X.latB or X.lonA != X.lonB:

375 B = _LL4T(X.latB, X.lonB, h, d, LL, kwds, iteration=X.iteration)

376 yield Intersect7Tuple(A, B, X.sAB, X.aAB, X.c, _xkwds_get(X, kA=0),

377 _xkwds_get(X, kB=0))

378

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

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

381 B.lat2, B.lon2)

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

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

384

385 def k2kAkB(self, k):

386 '''Unravel C{k} into C{kA} and C{kB}.

387

388 @arg k: Segment indicator C{kA * 3 + kB} (C{int}).

389

390 @return: An C{ADict(k=k, kA=kA, kB=kB)}.

391

392 @raise GeodesicError: Invalid B{C{k}}.

393 '''

394 for kA in range(-1, 2):

395 for kB in range(-1, 2):

396 if (kA * 3 + kB) == k:

397 return ADict(k=k, kA=kA, kB=kB)

398 raise GeodesicError(k=k)

399

400# def k2kAkB(self, k):

401# # unravel C{k} into C{kA} and C{kB}.

402# kA, kB = divmod(k, 3)

403# if kB > 1:

404# kA += 1

405# kB -= 3

406# return kA, kB

407

408 def Line(self, lat1, lon1, azi1_lat2, *lon2, **name): # PYCHOK no cover

409 '''(INTERNAL) I{Must be overloaded}.'''

410 self._notOverloaded(lat1, lon1, azi1_lat2, *lon2, **name)

411

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

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

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

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

416 else:

417 t += Azi(azi1=azi1_lat2),

418 return t

419

420 @deprecated_method

421 def Next5s(self, glA, glB, X0=_X000, aMax=1801, sMax=0, **unused): # PYCHOK no cover

422 '''DEPRECATED on 2024.07.02, use method C{All5}.'''

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

424

425 @Property_RO

426 def R(self):

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

428 '''

429 return self.ellipsoid.R2

430

431 def _sMaX0_C2(self, aMaX0=0, **sMaX0_C):

432 _g = _xkwds_get

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

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

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

436 if a: # degrees to meter, approx.

437 s = min(s, self.R * radians(a)) # ellipsoid.degrees2m(a)

438 s = _g(sMaX0_C, _R=s)

439 if s < _EPS3:

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

441 return s, _g(sMaX0_C, _C=False)

442

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

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

445 if eps1 is not None:

446 a = glA.lat1 - glB.lat1

447 b = glA.lon1 - glB.lon1

448 if euclid(a, b) > eps1:

449 raise GeodesicError(lat_=a, lon_=b, eps1=eps1)

450 return _xkwds_kwds(eps_C, _C=False)

451

452

453 class Intersectool(_IntersectBase, _SolveCapsBase):

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

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

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

457

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

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

460

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

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

463 '''

464 _c_alt = _c__, # Closest latA lonA aziA latB lonB aziB

465 _C_option = '-C',

466 _Error = GeodesicError

467 _i_alt = _i__, # Segment latA1 lonA1 latA2 lonA2 latB1 lonB1 latB2 lonB2

468 _linelimit = 1200 # line printer width X 10

469 _n_alt = _n__, # Next latA lonA aziA aziB

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

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

472 _o_alt = _o__, # Offset latA lonA aziA latB lonB aziB x0 y0

473 _Xable_name = _Xables.IntersectTool.__name__ # typename

474 _Xable_path = _Xables.IntersectTool()

475

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

477 '''New L{IntersectTool}.

478

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

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

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

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

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

484 is in C{meter}, ignored otherwise.

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

486

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

488 large or no initial convergence.

489

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

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

492 '''

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

494 self._GeodesicExact(a_geodesic, f))

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

496

497 def All(self, glA, glB, X0=_X000, eps1=_0_0, aMaX0=0, **sMaX0_C): # PYCHOK signature

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

499

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

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

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

503 option, unless C{B{eps1}=None}.

504

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

506 '''

507 for X, _ in self._All2(glA, glB, X0, eps1, aMaX0=aMaX0, **sMaX0_C):

508 yield X

509

510 def _All2(self, glA, glB, X0, eps1, **aMaX0_sMaX0_C): # MCCABE 13

511 '''(INTERNAL) Helper for methods C{.All} and C{.All5}.

512 '''

513 def _xz2(**gl):

514 try:

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

516 try:

517 return self._c_alt, (gl.azi1,)

518 except (AttributeError, KeyError):

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

520 except Exception as x:

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

522

523 _t, a = _xz2(glA=glA)

524 _x, b = _xz2(glB=glB)

525 if _x is not _t:

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

527

528 A = glA.lat1, glA.lon1

529 B = glB.lat1, glB.lon1

530 if _x is self._c_alt:

531 if X0 is _X000 or X0._is00:

532 if eps1 is not None and \

533 euclid(glA.lat1 - glB.lat1,

534 glA.lon1 - glB.lon1) <= eps1:

535 _x, B = self._n_alt, ()

536 else: # non-zero offset

537 _x = self._o_alt

538 b += X0.sA, X0.sB

539

540 sMaX0, _C = self._sMaX0_C2(**aMaX0_sMaX0_C)

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

542 _C=_C, _R=sMaX0):

543 if _C:

544 T = self._In5T(glA, glB, X, X)

545 if _aAB_ not in X:

546 X.set_(sAB=T.sAB, aAB=T.aAB)

547 else:

548 T = None

549 yield X.set_(c=int(X.c)), T

550

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

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

553

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

555 '''

556 for _, T in self._All2(glA, glB, X0, _0_0, _C=True, **aMaX0_sMaX0):

557 yield T

558

559 @Property_RO

560 def _cmdBasic(self):

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

562 '''

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

564 self._E_option +

565 self._p_option)

566

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

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

569

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

571

572 @return: An L{XDict}.

573 '''

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

575 glB.lat1, glB.lon1, glB.azi1

576 if X0 is _X000 or X0._is000:

577 _x = self._c_alt

578 else:

579 _x = self._o_alt

580 args += X0.sA, X0.sB

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

582

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

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

585

586 @return: An L{Intersectool5Tuple}.

587 '''

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

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

590

591 @property_ROver

592 def _GeodesicExact(self):

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

594 '''

595 return _MODS.geodesicx.GeodesicExact # overwrite property_ROver

596

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

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

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

600 if k2:

601 A.set_(k2=X.kA)

602 B.set_(k2=X.kB)

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

604 sAB = _xkwds_get(X, sAB=s)

605 if a and s and s != sAB:

606 a *= sAB / s # adjust a

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

608 B._2X(glB, **_2X), sAB, a, X.c)

609

610 @Property

611 def IntersectTool(self):

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

613 executable (C{filename}).

614 '''

615 return self._Xable_path

616

617 @IntersectTool.setter # PYCHOK setter!

618 def IntersectTool(self, path):

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

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

621

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

623 C{IntersectTool} executable.

624 '''

625 self._setXable(path)

626

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

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

629 two (goedetic) points or a (goedetic) point and an (forward) azimuth.

630

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

632 '''

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

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

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

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

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

638 if name:

639 gl.name= name

640 return gl

641

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

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

644

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

646

647 @return: An L{XDict}.

648 '''

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

650 return X

651

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

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

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

655

656 def _smi4(**gl):

657 try:

658 n, gl = gl.popitem()

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

660 except Exception as x:

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

662 s = il.s13

663 m = s * _0_5

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

665

666 sA, mA, iA, A = _smi4(glA=glA)

667 sB, mB, iB, B = _smi4(glB=glB)

668 X = XDict_(mA, mB) # centers

669 _ = X._outSide(sA, sB)

670 if _C: # _Names_ABs

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

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

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

674 return X, A, iA, B, iB

675

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

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

678

679 @return: A L{Middle5Tuple}.

680 '''

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

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

683 return Middle5Tuple(self._illz2G(A, iA),

684 self._illz2G(B, iB), s, a, c)

685

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

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

688

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

690

691 @return: An L{XDict}.

692 '''

693 if eps1 or _C:

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

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

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

697 **_C) # _R=None

698

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

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

701

702 @return: An L{Intersectool5Tuple}.

703 '''

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

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

706

707 def _R_option(self, _R=None):

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

709 '''

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

711

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

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

714

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

716

717 @return: An L{XDict}.

718 '''

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

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

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

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

723 try:

724 ks = self.k2kAkB(int(X.k))

725 except Exception as x:

726 raise GeodesicError(glA=glA, glB=glB, X=str(X), cause=x)

727 return X.set_(**ks)

728

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

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

731

732 @return: An L{Intersectool5Tuple}.

733 '''

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

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

736

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

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

739

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

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

742 (0..9) and the C{sep}arator string to join. Trailing

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

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

745

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

747 '''

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

749 status=self.status,

750 IntersectTool=self.IntersectTool)

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

752

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

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

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

756 '''

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

758 # self._i_alt: 8,

759 # self._n_alt: 4,

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

761 cmd = self._cmdBasic

762 Names = self._Names_XDict # has _c_ always

763 if _k_sX0:

764 Names += _k_sX0,

765 if _C:

766 cmd += self._C_option

767 Names += self._Names_ABs

768 if _R:

769 cmd += self._R_option(**_R)

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

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

772

773

774 class Intersector(_IntersectBase):

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

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

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

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

779

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

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

782 '''

783

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

785 '''New L{Intersector}.

786

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

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

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

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

791

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

793 large or no initial convergence.

794

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

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

797 '''

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

799 E = self.ellipsoid

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

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

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

803 if self.f > 0:

804 t3 = self._obliqDist4()[0]

805 t4 = t1

806 else: # PYCHOK no cover

807 t1, t2, t3 = t2, t1, t5

808 t4, _, _ = self._polarB3()

809

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

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

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

813 self._T1 = t1 # min distance between intersects

814 self._T2 = t2 = t1 * _2_0

815# self._T5 = t5 # not used

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

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

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

819

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

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

822

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

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

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

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

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

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

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

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

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

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

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

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

835 distances C{sAB} and C{aSB}.

836

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

838

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

840 invalid, incompatible or ill-configured.

841

842 @raise IntersectionError: No convergence.

843 '''

844 self._xLines(glA, glB)

845 if X0 is None:

846 try: # determine X0

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

848 except GeodesicError: # no .Distance

849 X0 = _X000

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

851

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

853 xMaX0 = sMaX0 + D

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

855 d3 = xMaX0 / m

856 T2d3D = self._T2d3Delta(d3)

857

858 C_ = _List(D) # closest coincident

859 X_ = _List(D) # intersections found

860 c0 = 0

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

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

863 while S_:

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

865 if Q in X_:

866 continue

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

868 _X0fx = X0._fixCoincident

869 Q = _X0fx(Q) # Q = Q'

870 if c0 and Q in C_:

871 continue

872 C_.addend(Q)

873 # elimate all existing intersections

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

875 c0 = Q.c

876 for j, X in _enumereverse(X_):

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

878 X_.pop(j)

879

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

881 args = self._m12_M12_M21(glA, s0)

882 _cjD = self._conjDist

883 for s in (-_D, _D):

884 s += s0

885 sa = 0

886 while True:

887 i += 1

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

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

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

891 break

892

893 elif c0 and Q in C_: # Q.c == 0

894 continue

895 else:

896 a = len(X_)

897

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

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

900 X._skip(S_, T2d3D)

901

902 return X_.sorter(sMaX0, self._C, glA, glB, _C=_C) # generator

903

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

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

906

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

908 for each intersection found.

909

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

911 '''

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

913 yield self._In5T(glA, glB, X, X)

914

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

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

917 '''

918 X = _copy(S)

919 for _ in range(_TRIPS):

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

921 X += S

922 i += 1

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

924 return self._Delto(X), i

925

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

927

928 def _C(self, X, glA, glB, _C=False, _MM=False):

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

930 if _C:

931 A = self._Position(glA, X.sA)

932 B = self._Position(glB, X.sB)

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

934 X.set_(latA=A.lat2, lonA=A.lon2,

935 latB=B.lat2, lonB=B.lon2)

936 if _MM: # in .Middle5

937 X.set_(sMM=s, aMM=a)

938 else:

939 X.set_(sAB=s, aAB=a)

940 return X

941

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

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

944

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

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

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

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

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

950 and C{aSB} between the intersections.

951

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

953

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

955 invalid, incompatible or ill-configured.

956

957 @raise IntersectionError: No convergence.

958 '''

959 self._xLines(glA, glB)

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

961 while S_:

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

963 X = X0._fixCoincident(X)

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

965 d0 = X.L1(X0)

966 if d0 < self._T1:

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

968 break

969 if d0 < d or Q is X0:

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

971 X._skip(S_, self._T2D1Delta)

972

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

974

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

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

977

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

979 or C{None} if none found.

980

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

982 '''

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

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

985

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

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

988 # if semi:

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

990 # else:

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

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

993 for _ in range(_TRIPS):

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

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

996 m23 = m13 * M12

997 M32 = M31 * M12

998 if m12: # PYCHOK no cover

999 m23 -= m12 * M13

1000 if m13:

1001 M32 += (_1 - M13 * M31) * m12 / m13

1002 if semi:

1003 M23 = M13 * M21

1004 # when m12 -> eps, (1 - M12 * M21) -> eps^2, I suppose.

1005 if m12 and m13:

1006 M23 += (_1 - M12 * M21) * m13 / m12

1007 d = m23 * M23 / (_1 - M23 * M32)

1008 else:

1009 d = -m23 / M32

1010 s, d = _S2(d)

1011 if _abs(d) <= self._Tol:

1012 break

1013 return s

1014

1015 _gl3 = None

1016

1017 @Property

1018 def _conjDist3s(self):

1019 gl, self._gl3, _D = self._gl3, None, self._cHalf

1020 return tuple(self._conjDist(gl, s) for s in (-_D, 0, _D))

1021

1022 @_conjDist3s.setter # PYCHOK setter!

1023 def _conjDist3(self, gl):

1024 # _XLines(gl, gl)

1025 self._gl3 = gl

1026

1027 def _conjDist3Tt_(self, c, X0=_X000):

1028 for s in self._conjDist3s:

1029 T = XDict_(s, s * c, c)

1030 yield self._Delto(T), T.L1(X0)

1031

1032 def _conjDist5(self, azi):

1033 gl = self._Line(azi1=azi)

1034 s = self._conjDist(gl, self._cHalf)

1035 X, _ = self._Basic2(gl, gl, XDict_(s * _0_5, -s * _1_5))

1036 return s, (X.L1() - s * _2_0), azi, X.sA, X.sB

1037

1038 @Property_RO

1039 def Delta(self):

1040 '''Get the equality and tiling margin (C{meter}).

1041 '''

1042 return self._cHalf * _EPSr5 # ~15 Km WGS84

1043

1044 def _Delto(self, X):

1045 # copy Delta into X, overriding X's default

1046 X._Delta = self.Delta # NOT X.set_(self.Delta)

1047 return X

1048

1049 @Property_RO

1050 def _EPS3R(self):

1051 return _EPS3 * self.R

1052

1053 @Property_RO

1054 def _faPI_4(self):

1055 return (self.f + _2_0) * self.a * PI_4

1056

1057 @Property_RO

1058 def _GeodesicLines(self):

1059 '''(INTERNAL) Get the C{Geodesic...Line} class(es).

1060 '''

1061 return type(self._Line()),

1062

1063 def _In5T(self, glA, glB, S, X, k2=False, **_2X):

1064 # Return an intersection as C{Intersector5Tuple}.

1065 A = self._Position(glA, S.sA)

1066 B = self._Position(glB, S.sB)

1067 if k2:

1068 A.set_(k2=X.kA)

1069 B.set_(k2=X.kB)

1070 s, a = self._Inversa12(A, B)

1071 return Intersector5Tuple(A._2X(glA, **_2X),

1072 B._2X(glB, **_2X), s, a, X.c, iteration=X.iteration)

1073

1074 def _Inverse(self, A, B): # caps=Caps.STANDARD

1075 return self._g.Inverse(A.lat2, A.lon2, B.lat2, B.lon2)

1076

1077 def Line(self, lat1, lon1, azi1_lat2, *lon2, **name):

1078 '''Return a geodesic line from this C{Intersector}'s geodesic, specified by

1079 two (goedetic) points or a (goedetic) point and an (initial) azimuth.

1080

1081 @arg lat1: Latitude of the first point (C{degrees}).

1082 @arg lon1: Longitude of the first point (C{degrees}).

1083 @arg azi1_lat2: Azimuth at the first point (compass C{degrees}) if no

1084 B{C{lon2}} argument is given, otherwise the latitude of

1085 the second point (C{degrees}).

1086 @arg lon2: If given, the longitude of the second point (C{degrees}).

1087 @kwarg name: Optional C{B{name}=NN} (C{str}).

1088

1089 @return: A line (from L{geodesic<Intersector.geodesic>}C{.Line} or

1090 C{.InverseLine} method) with C{LINE_CAPS}.

1091 '''

1092 args = self._ll3z4ll(lat1, lon1, azi1_lat2, *lon2)

1093 gl = self._g.InverseLine(*args, caps=Caps.LINE_CAPS) if lon2 else \

1094 self._g.Line( *args, caps=Caps.LINE_CAPS)

1095 if name:

1096 gl.name= name

1097 return gl

1098

1099 def _Line(self, lat1=0, lon1=0, azi1=0):

1100 return self._g.Line(lat1, lon1, azi1, caps=Caps.LINE_CAPS)

1101

1102 def Middle(self, glA, glB, raiser=True, **_C):

1103 '''Get the mid-points on two geodesic line segments.

1104

1105 @arg glA: A geodesic line (L{Line<Intersector.Line>}, 4-C{args}).

1106 @arg glB: An other geodesic line (L{Line<Intersector.Line>}, 4-C{args}).

1107 @kwarg raiser: If C{True}, check that B{C{glA}} and B{C{glB}} are a

1108 4-C{args} L{Line<Intersector.Line>} or C{InverseLine}

1109 (C{bool}).

1110 @kwarg _C: If C{True}, include the lat-/longitudes C{latA}, C{lonA},

1111 C{latB}, C{lonB} of the mid-points and half-lengths C{sA}

1112 and C{sB} in C{meter} of the respective line segments.

1113

1114 @return: The mid-point and half-length of each segment (L{XDict}),

1115 B{C{_C}} above.

1116

1117 @raise GeodesicError: Geodesic line B{C{glA}} or B{C{glB}} invalid,

1118 incompatible, ill-configured or not a 4-C{args

1119 Line} or other C{InverseLine}.

1120 '''

1121 M, _, _ = self._middle3(glA, glB, raiser)

1122 return self._C(M, glA, glB, **_C) if _C else M

1123

1124 def _middle3(self, glA, glB, raiser): # in .All, .Segment

1125 # return segment length C{sA} and C{sB} and the

1126 # center C{X0} of rectangle [sA, sB]

1127 self._xLines(glA, glB, s13=raiser) # need .Arc, .Distance

1128 sA = glA.Distance()

1129 sB = glB.Distance()

1130 X = XDict_(sA * _0_5, sB * _0_5)

1131 # _ = X._outSide(sA, sB)

1132 return self._Delto(X), sA, sB

1133

1134 def Middle5(self, glA, glB, raiser=True):

1135 '''Get the mid-points of two geodesic line segments and distances.

1136

1137 @return: A L{Middle5Tuple}C{(A, B, sMM, aMM, c)}.

1138

1139 @see: Method L{Middle} for further details.

1140 '''

1141 M, _, _ = self._middle3(glA, glB, raiser)

1142 M = self._C(M, glA, glB, _C=True, _MM=True)

1143 A, B, s, a, c = self._In5T(glA, glB, M, M, _2X=_M_)

1144 return Middle5Tuple(self._illz2G(A, glA),

1145 self._illz2G(B, glB), s, a, c)

1146

1147 def _m12_M12_M21(self, gl, s):

1148 P = gl.Position(s, outmask=Caps._REDUCEDLENGTH_GEODESICSCALE)

1149 return P.m12, P.M12, P.M21

1150

1151 def Next(self, glA, glB, eps1=None, **_C): # PYCHOK no cover

1152 '''Yield the next intersection of two I{intersecting} geodesic lines.

1153

1154 @arg glA: A geodesic line (L{Line<Intersector.Line>}).

1155 @arg glB: An other geodesic line (L{Line<Intersector.Line>}).

1156 @kwarg eps1: Optional margin for the L{euclid<pygeodesy.euclid>}ean

1157 distance (C{degrees}) between the C{(lat1, lon1)} points

1158 of both lines or C{None} for unchecked.

1159 @kwarg _C: If C{True}, include the lat-/longitudes C{latA}, C{lonA},

1160 C{latB}, C{lonB} of and distances C{sAB} and C{aSB}

1161 between the intersections.

1162

1163 @return: The intersection (L{XDict}) or C{None} if none found.

1164

1165 @raise GeodesicError: Geodesic line B{C{glA}} or B{C{glB}} invalid,

1166 incompatible, ill-configured or C{(lat1, lon1)}

1167 not B{C{eps1}}-equal.

1168

1169 @raise IntersectionError: No convergence.

1170

1171 @note: Offset C{X0} is implicit, zeros.

1172 '''

1173 self._xLines(glA, glB)

1174 if eps1 or _C: # eps

1175 _C = self._xNext(glA, glB, eps1, **_C)

1176

1177 X0, self._conjDist3s = _X000, glA # reset Property

1178 Q, d, S_, i = _XINF, INF, list(X0._nD2(self._D2)), 0

1179 while S_:

1180 X, i = self._Basic2(glA, glB, S_.pop(0), i)

1181 X = X0._fixCoincident(X)

1182 t = X.L1(X0) # == X.L1()

1183 c, z = X.c, (t <= self.Delta) # X == X0

1184 if z:

1185 if not c:

1186 continue

1187 Tt_ = self._conjDist3Tt_(c, X0)

1188 else:

1189 Tt_ = (X, t),

1190

1191 for T, t in Tt_:

1192 if t < d or Q is _XINF:

1193 Q, d, q = T, t, i

1194 i += 1

1195

1196 for s in ((_1_1t if z else _1_0_1t)

1197 if c else _0t):

1198 T = X

1199 if s and c:

1200 s *= self._D2

1201 T = X + (s, s * c) # NOT +=

1202 T._skip(S_, self._T2D2Delta)

1203

1204 return None if Q is _XINF else self._C(Q, glA, glB, **_C).set_(sX0=d, iteration=q)

1205

1206 def Next5(self, glA, glB, **eps1): # PYCHOK no cover

1207 '''Yield the next intersection of two I{intersecting} geodesic lines.

1208

1209 @return: An L{Intersector5Tuple}C{(A, B, sAB, aAB, c)} or C{None}

1210 if none found.

1211

1212 @see: Method L{Next} for further details.

1213 '''

1214 X = self.Next(glA, glB, **eps1)

1215 return X if X is None else self._In5T(glA, glB, X, X)

1216

1217 def _obliqDist4(self):

1218 zx = _45_0

1219 if self.f:

1220 _abs, _cjD5 = fabs, self._conjDist5

1221

1222 _, ds0, z0, _, _ = _cjD5(zx + _1_0)

1223 s1, ds1, z1, sAx, sBx = _cjD5(zx - _1_0)

1224 sx, dsx, zx = s1, _abs(ds1), z1

1225 # find ds(azi) = 0 by secant method

1226 for _ in range(16):

1227 if ds1 == ds0:

1228 break

1229 z = (z0 * ds1 - z1 * ds0) / (ds1 - ds0)

1230 _, ds0, z0 = s1, ds1, z1

1231 s1, ds1, z1, a, b = _cjD5(z)

1232 if _abs(ds1) < dsx:

1233 sx, dsx, zx, sAx, sBx = s1, _abs(ds1), z, a, b

1234 if not dsx:

1235 break

1236 else:

1237 sx, sAx, sBx = self._cHalf, _0_5, -_1_5

1238 return sx, zx, sAx, sBx

1239

1240 def _polarB3(self, lats=False): # PYCHOK no cover

1241 latx = _64_0

1242 lat = _90_0 - latx

1243 if self.f:

1244 _d, _pD2 = fdot, self._polarDist2

1245

1246 s0, lat0 = _pD2(latx - _1_0)

1247 s1, lat1 = _pD2(latx + _1_0)

1248 s2, lat2 = \

1249 sx, latx = _pD2(latx)

1250 prolate = self.f < 0

1251 # solve for ds(lat) / dlat = 0 with a quadratic fit

1252 for _ in range(_TRIPS):

1253 t = (lat1 - lat0), (lat0 - lat2), (lat2 - lat1)

1254 d = _d(t, s2, s1, s0) * _2_0

1255 if not d: # or isnan(d)

1256 break

1257 lat = _d(t, (lat1 + lat0) * s2,

1258 (lat0 + lat2) * s1,

1259 (lat2 + lat1) * s0) / d

1260 s0, lat0 = s1, lat1

1261 s1, lat1 = s2, lat2

1262 s2, lat2 = _pD2(lat)

1263 if (s2 < sx) if prolate else (s2 > sx):

1264 sx, latx = s2, lat2

1265 if lats:

1266 _, lat = _pD2(latx, lat2=True)

1267 sx += sx

1268 else:

1269 sx = self._cHalf

1270 return sx, latx, lat

1271

1272 def _polarDist2(self, lat1, lat2=False):

1273 gl = self._Line(lat1=lat1)

1274 s = self._conjDist(gl, self._faPI_4, semi=True)

1275 if lat2:

1276 lat1 = gl.Position(s, outmask=Caps.LATITUDE).lat2

1277 return s, lat1

1278

1279 def _Position(self, gl, s):

1280 return gl.Position(s, outmask=Caps.STANDARD_LINE)

1281

1282 def Segment(self, glA, glB, proven=None, raiser=True, **_C):

1283 '''Find the intersection between two geodesic line segments.

1284

1285 @kwarg proven: Conjecture is that whenever two geodesic line

1286 segments intersect, the intersection is the

1287 one closest to the mid-points of segments.

1288 If so, use C{B{proven}=True}, otherwise find

1289 intersections on the segments and specify

1290 C{B{proven}=None} to return the first or

1291 C{B{proven}=False} the closest (C{bool}).

1292 @kwarg raiser: If C{True}, check that B{C{glA}} and B{C{glB}}

1293 are a 4-C{args} L{Line<Intersector.Line>} or

1294 C{InverseLine} (C{bool}).

1295 @kwarg _C: If C{True}, include the lat-/longitudes C{latA},

1296 C{lonA}, C{latB}, C{lonB} of and distances C{sAB}

1297 and C{aSB} between the intersections.

1298

1299 @return: The intersection of the segments (L{XDict}) with

1300 indicators C{kA}, C{kB} and C{k} set or if no

1301 intersection is found, C{None}.

1302

1303 @raise GeodesicError: Geodesic line B{C{glA}} or B{C{glB}}

1304 invalid, incompatible, ill-configured or

1305 not an C{InverseLine} or 4-C{args Line}.

1306

1307 @raise IntersectionError: No convergence.

1308

1309 @see: Method L{Middle<Intersector.Middle>} for further details.

1310 '''

1311 X0, sA, sB = self._middle3(glA, glB, raiser)

1312 Q = self.Closest(glA, glB, X0) # to X0

1313 if Q is not None:

1314 if Q.c: # anti-/parallel

1315 Q._fixSegment(sA, sB)

1316 # are rectangle [sA, sB] corners further from X0 than Q?

1317 d0 = X0.L1(Q)

1318 if Q._outSide(sA, sB) and d0 <= X0.L1() and not proven:

1319 i = Q.iteration

1320 for T in Q._corners(sA, sB, self._T2):

1321 X, i = self._Basic2(glA, glB, T, i)

1322 X = T._fixCoincident(X)

1323 if not X._outSide(sA, sB):

1324 d = X0.L1(X)

1325 if d < d0 or proven is None:

1326 Q, d0 = X, d

1327 if proven is None:

1328 break

1329 Q.set_(iteration=i)

1330

1331 Q = self._C(Q, glA, glB, **_C).set_(sX0=d0)

1332 return Q

1333

1334 def Segment5(self, glA, glB, **proven_raiser):

1335 '''Find the intersection between two geodesic line segments.

1336

1337 @return: An L{Intersector5Tuple}C{(A, B, sAB, aAB, c)}

1338 or C{None} if none found.

1339

1340 @see: Method L{Segment} for further details.

1341 '''

1342 X = self.Segment(glA, glB, **proven_raiser)

1343 return X if X is None else self._In5T(glA, glB, X, X, k2=True)

1344

1345 def _Spherical(self, glA, glB, S):

1346 '''(INTERNAL) Get solution based from a spherical triangle.

1347 '''

1348 # threshold for coincident geodesics/intersections ~4.3 nm WGS84.

1349 A = self._Position(glA, S.sA)

1350 B = self._Position(glB, S.sB)

1351 D = self._Inverse(A, B)

1352

1353 a, da = _diff182(A.azi2, D.azi1) # interior angle at A

1354 b, db = _diff182(B.azi2, D.azi2) # exterior angle at B

1355 c, dc = _diff182(a, b)

1356 if fsum1_(dc, db, -da, c) < 0: # inverted triangle

1357 a, da = -a, -da

1358 b, db = -b, -db

1359 sa, ca = _sincos2de(a, da)

1360 sb, cb = _sincos2de(b, db)

1361

1362 e, z, _abs = _EPS3, D.s12, fabs

1363 if _abs(z) <= self._EPS3R: # XXX z <= ...

1364 sA = sB = 0 # at intersection

1365 c = 1 if _abs(sa - sb) <= e and _abs(ca - cb) <= e else (

1366 -1 if _abs(sa + sb) <= e and _abs(ca + cb) <= e else 0)

1367 elif _abs(sa) <= e and _abs(sb) <= e: # coincident

1368 sA = ca * z * _0_5 # choose mid-point

1369 sB = -cb * z * _0_5

1370 c = 1 if (ca * cb) > 0 else -1

1371 # alt1: sA = ca * z; sB = 0

1372 # alt2: sB = -cb * z; sA = 0

1373 else: # general case

1374 sz, cz = sincos2(z / self.R)

1375 # [SKIP: Divide args by |sz| to avoid possible underflow

1376 # in {sa, sb} * sz; this is probably not necessary].

1377 # Definitely need to treat sz < 0 (z > PI*R) correctly in

1378 # order to avoid some convergence failures in _Basic2.

1379 sA = atan2(sb * sz, sb * ca * cz - sa * cb) * self.R

1380 sB = atan2(sa * sz, -sa * cb * cz + sb * ca) * self.R

1381 c = 0

1382 return XDict_(sA, sB, c) # no ._Delto

1383

1384 @Property_RO

1385 def _T2D1Delta(self):

1386 return self._T2d3Delta(self._D1)

1387

1388 @Property_RO

1389 def _T2D2Delta(self):

1390 return self._T2d3Delta(self._D2)

1391

1392 def _T2d3Delta(self, d3):

1393 return self._T2 - d3 - self.Delta

1394

1395 @Property_RO

1396 def _Tol(self): # convergence tolerance

1397 return self._cHalf * _EPSjam

1398

1399 def toStr(self, **prec_sep_name): # PYCHOK signature

1400 '''Return this C{Intersector} as string.

1401

1402 @see: L{Ellipsoid.toStr<pygeodesy.ellipsoids.Ellipsoid.toStr>}

1403 for further details.

1404

1405 @return: C{Intersector} (C{str}).

1406 '''

1407 return self._instr(props=(Intersector.geodesic,), **prec_sep_name)

1408

1409 def _xLines(self, glA, glB, s13=False):

1410 # check two geodesic lines vs this geodesic

1411 C, gls = Caps.LINE_CAPS, dict(glA=glA, glB=glB)

1412 _xinstanceof(*self._GeodesicLines, **gls)

1413 for n, gl in gls.items():

1414 try:

1415 _xgeodesics(gl.geodesic, self.geodesic)

1416 if s13 and not isfinite(gl.s13): # or not gl.caps & Caps.DISTANCE_IN

1417 t = _an(typename(gl.geodesic.InverseLine))

1418 raise TypeError(_not_(t))

1419 c = gl.caps & C

1420 if c != C: # not gl.caps_(C)

1421 c, C, x = map1(bin, c, C, _xor(c, C))

1422 t = _SPACE_(typename(_xor), repr(x))[1:]

1423 raise GeodesicError(caps=c, LINE_CAPS=C, txt=t)

1424 except Exception as x:

1425 raise GeodesicError(n, gl, cause=x)

1426

1427

1428 class Intersect7Tuple(_NamedTuple):

1429 '''7-Tuple C{(A, B, sAB, aAB, c, kA, kB)} with C{A} and C{B} each

1430 a C{LatLon} or L{LatLon4Tuple}C{(lat, lon, height, datum)} of

1431 the intersection on each geodesic line, the distance C{sAB} in

1432 in C{meter} and angular distance C{aAB} in C{degrees} between

1433 C{A} and C{B}, coincidence indicator C{c} and segment indicators

1434 C{kA} and C{kB} all C{int}, see L{XDict} and method U{intersect7

1435 <_IntersectBase.intersect7>}.

1436 '''

1437 _Names_ = (_A_, _B_, _sAB_, _aAB_, _c_, 'kA', 'kB')

1438 _Units_ = (_Pass, _Pass, Meter, Degrees, Int, Int, Int)

1439

1440

1441 class Intersectool5Tuple(_NamedTuple):

1442 '''5-Tuple C{(A, B, sAB, aAB, c)} with C{A} and C{B} the C{Position}

1443 of the intersection on each geodesic line, the distance C{sAB}

1444 between C{A} and C{B} in C{meter}, the angular distance C{aAB} in

1445 C{degrees} and coincidence indicator C{c} (C{int}), see L{XDict}.

1446

1447 @note: C{A} and C{B} are each a C{GDict} with C{lat1}, C{lon1} and

1448 C{azi1} or C{lat2}, C{lon2} from the geodesic line C{glA}

1449 respectively C{glB} and the intersection location in C{latX},

1450 C{lonX}, distance C{s1X} in C{meter} and angular distance

1451 C{a1M} in C{degrees} and the segment indicator C{kX}. See

1452 L{XDict} for more details.

1453 '''

1454 _Names_ = Intersect7Tuple._Names_[:5]

1455 _Units_ = Intersect7Tuple._Units_[:5]

1456

1457

1458 class Intersector5Tuple(Intersectool5Tuple):

1459 '''5-Tuple C{(A, B, sAB, aAB, c)} with C{A} and C{B} the C{Position}

1460 of the intersection on each geodesic line, the distance C{sAB}

1461 between C{A} and C{B} in C{meter}, angular distance C{aAB} in

1462 C{degrees} and coincidence indicator C{c} (C{int}), see L{XDict}.

1463

1464 @note: C{A} and C{B} are each a C{GeodesicLine...Position} for

1465 C{outmask=Caps.STANDARD} with the intersection location in

1466 C{latX}, C{lonX}, azimuth in C{aziX}, distance C{s1X} in

1467 C{meter} and angular distance C{a1X} in C{degrees} and the

1468 segment indicator C{kX}. See L{XDict} for more details.

1469 '''

1470 _Names_ = Intersectool5Tuple._Names_

1471

1472

1473 class Middle5Tuple(Intersectool5Tuple):

1474 '''5-Tuple C{(A, B, sMM, aMM, c)} with C{A} and C{B} the I{line segments}

1475 including the mid-point location in C{latM}, C{lonM}, distance C{s1M}

1476 in C{meter} and angular distance C{a1M} in C{degrees}, the distance

1477 between both mid-points C{sMM} in C{meter} and angular distance C{aMM}

1478 in C{degrees} and coincidence indicator C{c} (C{int}). See L{XDict}

1479 for more details.

1480 '''

1481 _Names_ = (_A_, _B_, 'sMM', 'aMM', _c_)

1482

1483

1484 class _List(list):

1485

1486 _Delta = 0 # equality margin

1487

1488 def __init__(self, Delta):

1489 self._Delta = Delta

1490# list.__init__(self)

1491

1492 def __contains__(self, other):

1493 # handle C{if X in this: ...}

1494 a, b = other.sA, other.sB

1495 D, _D1 = self._Delta, _L1

1496 for X in self:

1497 if _D1(X.sA - a, X.sB - b) <= D:

1498 return True

1499 return False

1500

1501 def addend(self, X, *d0_i):

1502 # append an item, updated

1503 if d0_i:

1504 d0, i = d0_i

1505 X.set_(sX0=d0, iteration=i)

1506 self.append(X)

1507 return X.sX0

1508

1509 def sorter(self, sMaX0, dot_C, glA, glB, **_C):

1510 # trim and sort the X items

1511

1512 def _key(X):

1513 return X.sX0 # rank of X

1514

1515 t = (X for X in self if X.sX0 <= sMaX0)

1516 for X in sorted(t, key=_key):

1517 yield dot_C(X, glA, glB, **_C) if _C else X

1518

1519

1520 def _L1(a, b):

1521 '''(INTERNAL) Return the I{L1} distance.

1522 '''

1523 return fabs(a) + fabs(b)

1524

1525

1526__all__ += _ALL_DOCS(_IntersectBase)

1527

1528 if __name__ == _DMAIN_: # MCCABE 14

1529

1530 from pygeodesy import printf

1531 __help_ = '--help'

1532

1533 def _main(args):

1534

1535 from pygeodesy import GeodesicExact

1536 from pygeodesy.internals import _plural, _usage

1537 from pygeodesy.interns import _COLONSPACE_, _DOT_, _EQUAL_, \

1538 _i_, _m_, _n_, _version_, _X_

1539 import re

1540

1541 class XY0(Float):

1542 pass

1543

1544 def _opts(_h): # for _usage()

1545 ll4 = ' latA1 lonA1'

1546 ll4 += ll4.replace('1', '2')

1547 ll4 += ll4.replace(_A_, _B_)

1548 llz = _SPACE_(NN, _latA_, _lonA_, 'aziA')

1549 llz2 = llz + llz.replace(_A_, _B_)

1550 return dict(opts='-Verbose|V--version|v--help|h--Tool|T--Check|C-R <meter>-',

1551 alts=((_c_ + llz2),

1552 (_i_ + ll4),

1553 (_m_ + ll4),

1554 (_n_ + llz + ' aziB'),

1555 ('o' + llz2 + ' x0 y0')),

1556 help=_h if isinstance(_h, str) else NN)

1557

1558 def _starts(Opt, arg):

1559 return arg == Opt[1:3] or (len(arg) > 2 and Opt.startswith(arg))

1560

1561 _isopt = re.compile('^[-]+[a-z]*$', flags=re.IGNORECASE).match

1562

1563 I = Intersector(GeodesicExact()) # PYCHOK I

1564 M = m = _R = None

1565 _T = _V = _h = _C = False

1566

1567 while args and _isopt(args[0]):

1568 arg = args.pop(0)

1569 if arg == _c__:

1570 M, m = I.Closest, 6 # latA lonA aziA latB lonB aziB

1571 elif _starts('--Check', arg):

1572 _C = True

1573 elif _starts(__help_, arg):

1574 _h = args[0] if args and _isopt(args[0]) else True

1575 elif arg == _i__:

1576 M, m = I.Segment, 8 # latA1 lonA1 latA2 lonA2 latB1 lonB1 latB2 lonB2

1577 elif arg == '-m':

1578 M, m = I.Middle, 8 # latA1 lonA1 latA2 lonA2 latB1 lonB1 latB2 lonB2

1579 _R = None # zap -R

1580 elif arg == _n__:

1581 M, m = I.Next, 4 # latA lonA aziA aziB

1582 elif arg == _o__:

1583 M, m = I.Closest, 8 # latA lonA aziA latB lonB aziB x0 y0

1584 elif arg == _R__ and args:

1585 _R = args.pop(0)

1586 elif _starts('--Tool', arg):

1587 I = Intersectool() # PYCHOK I

1588 if _V:

1589 I.verbose = True

1590 if not _Xables.X_OK(I.IntersectTool):

1591 I.IntersectTool = _Xables.IntersectTool(_Xables.bin_)

1592 elif _V:

1593 _ = I.version

1594 M, _T = None, True

1595 elif _starts('--Verbose', arg):

1596 _V = True

1597 if _T:

1598 I.verbose = True

1599 elif _starts('--version', arg):

1600 printf(_COLONSPACE_(*((_version_, I.version) if _T else

1601 (__version__, repr(I)))))

1602 else:

1603 raise ValueError('invalid option %r' % (arg,))

1604

1605 if _h or M is None:

1606 printf(_usage(__file__, **_opts(_h)), nl=1)

1607 else:

1608 n = len(args)

1609 if n < m:

1610 n = _plural('only %s arg' % (n,), n) if n else 'no args'

1611 raise ValueError('%s, need %s' % (n, m))

1612 args[:] = args[:m]

1613

1614 kwds = dict(_C=True) if _C else {}

1615 if M == I.Next: # -n

1616 # get latA lonA aziA latA lonA aziB

1617 args[3:] = args[:2] + args[3:4]

1618 elif M == I.Closest and m > 6: # -o

1619 y0 = Meter(y0=args.pop())

1620 x0 = Meter(x0=args.pop())

1621 kwds.update(X0=XDict_(x0, y0))

1622 if _R:

1623 m = Meter_(_R, name=_R__, low=0)

1624 kwds.update(sMaX0=m)

1625 M = I.All

1626

1627 n = len(args) // 2

1628 glA = I.Line(*args[:n])

1629 glB = I.Line(*args[n:])

1630

1631 m = _DOT_(*map1(typename, type(I), M))

1632 if _V:

1633 X = _SPACE_(_X_, _EQUAL_, m)

1634 printf(unstr(X, glA, glB, **kwds))

1635

1636 X = M(glA, glB, **kwds)

1637 if X is None or isinstance(X, (XDict, tuple)):

1638 printf(_COLONSPACE_(m, repr(X)))

1639 else:

1640 for i, X in enumerate(X):

1641 printf(_COLONSPACE_(Fmt.INDEX(m, i), repr(X)))

1642

1643 def _examples():

1644

1645 from pygeodesy.internals import _usage_argv

1646

1647 s = _SPACE_(*_usage_argv(__file__))

1648 for t in ('-h', '-h -n',

1649 '-c 0 0 45 40 10 135',

1650 '-C -c 0 0 45 40 10 135',

1651 '-T -R 2.6e7 -c 0 0 45 40 10 135',

1652 '-c 50 -4 -147.7 0 0 90',

1653 '-C -c 50 -4 -147.7 0 0 90',

1654 '# % echo 0 0 10 10 50 -4 50S 4W | IntersectTool -i -p 0 -C',

1655 '# -631414 5988887 0 -3',

1656 '# -4.05187 -4.00000 -4.05187 -4.00000 0',

1657 '-m 0 0 10 10 50 -4 50S 4W',

1658 '-C -m 0 0 10 10 50 -4 50S 4W',

1659 '-i 0 0 10 10 50 -4 50S 4W',

1660 '-T -i 0 0 10 10 50 -4 50S 4W',

1661 '-C -i 0 0 10 10 50 -4 50S 4W',

1662 '-T -C -i 0 0 10 10 50 -4 50S 4W',

1663 '-V -T -i 0 0 10 10 50 -4 -50 -4',

1664 '-C -R 4e7 -c 50 -4 -147.7 0 0 90',

1665 '-T -C -R 4e7 -c 50 -4 -147.7 0 0 90',

1666 '-R 4e7 -i 0 0 10 10 50 -4 -50 -4',

1667 '-T -R 4e7 -i 0 0 10 10 50 -4 -50 -4'):

1668 if t.startswith(_HASH_):

1669 printf(t, nl=int(t[2] == '%'))

1670 else:

1671 printf(_SPACE_(_HASH_, s, t), nl=1)

1672 argv[1:] = t = t.split()

1673 _main(t)

1674

1675 from sys import argv, stderr

1676 try:

1677 if len(argv) == 2 and argv[1] == __help_:

1678 _examples()

1679 else:

1680 _main(argv[1:])

1681

1682 except Exception as x:

1683 x = _SPACE_(x, NN, _HASH_, *argv)

1684 printf(x, file=stderr, nl=1)

1685 if '-V' in x or _MODS.errors.exception_chaining():

1686 raise

1687 exit(1)

1688

1689# % env PYGEODESY_INTERSECTTOOL=... python3 -m pygeodesy.geodesici --help

1690

1691# % python3 -m pygeodesy.geodesici -h

1692#

1693# usage: python3 -m ....pygeodesy.geodesici [--Verbose | -V] [--version | -v] [--help | -h] [--Tool | -T] [--Check | -C] [-R meter]

1694# [-c latA lonA aziA latB lonB aziB |

1695# -i latA1 lonA1 latA2 lonA2 latB1 lonB1 latB2 lonB2 |

1696# -m latA1 lonA1 latA2 lonA2 latB1 lonB1 latB2 lonB2 |

1697# -n latA lonA aziA aziB |

1698# -o latA lonA aziA latB lonB aziB x0 y0]

1699

1700# % python3 -m ....pygeodesy.geodesici -h -n

1701#

1702# usage: python3 -m ....pygeodesy.geodesici -n latA lonA aziA aziB

1703

1704# % python3 -m ....pygeodesy.geodesici -c 0 0 45 40 10 135

1705# Intersector.Closest: XDict(c=0, sA=3862290.547855, sB=2339969.547699, sX0=6202260.095554)

1706

1707# % python3 -m ....pygeodesy.geodesici -C -c 0 0 45 40 10 135

1708# 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)

1709

1710# % env PYGEODESY_INTERSECTTOOL=...python3 -m ....pygeodesy.geodesici -T -R 2.6e7 -c 0 0 45 40 10 135

1711# Intersectool.All[0]: XDict(c=0, sA=3862290.547855, sB=2339969.547699, sX0=6202260.095554)

1712

1713# % python3 -m ....pygeodesy.geodesici -c 50 -4 -147.7 0 0 90

1714# Intersector.Closest: XDict(c=0, sA=6058048.653081, sB=-3311252.995823, sX0=9369301.648903)

1715

1716# % python3 -m ....pygeodesy.geodesici -C -c 50 -4 -147.7 0 0 90

1717# 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)

1718

1719# % echo 0 0 10 10 50 -4 50S 4W | IntersectTool -i -p 0 -C

1720# -631414 5988887 0 -3

1721# -4.05187 -4.00000 -4.05187 -4.00000 0

1722

1723# % python3 -m ....pygeodesy.geodesici -m 0 0 10 10 50 -4 50S 4W

1724# Intersector.Middle: XDict(c=0, sA=782554.549609, sB=5536835.161499, sX0=0.0)

1725

1726# % python3 -m ....pygeodesy.geodesici -C -m 0 0 10 10 50 -4 50S 4W

1727# Intersector.Middle: XDict(aAB=10.262308, c=0, latA=5.019509, latB=0.036282, lonA=4.961883, lonB=-4.0, sA=782554.549609, sAB=1138574.546746, sB=5536835.161499, sX0=0.0)

1728

1729# % python3 -m ....pygeodesy.geodesici -i 0 0 10 10 50 -4 50S 4W

1730# Intersector.Segment: XDict(c=0, k=-3, kA=-1, kB=0, sA=-631414.26877, sB=5988887.278435, sX0=1866020.935315)

1731

1732# % env PYGEODESY_INTERSECTTOOL=... python3 -m ....pygeodesy.geodesici -T -i 0 0 10 10 50 -4 50S 4W

1733# Intersectool.Segment: XDict(c=0, k=-3, kA=-1, kB=0, sA=-631414.26877, sB=5988887.278435)

1734

1735# % python3 -m ....pygeodesy.geodesici -C -i 0 0 10 10 50 -4 50S 4W

1736# 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)

1737

1738# % env PYGEODESY_INTERSECTTOOL=... python3 -m ....pygeodesy.geodesici -T -C -i 0 0 10 10 50 -4 50S 4W

1739# 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)

1740

1741# % env PYGEODESY_INTERSECTTOOL=... python3 -m ....pygeodesy.geodesici -V -T -i 0 0 10 10 50 -4 -50 -4

1742# Intersectool@1: /opt/local/bin/IntersectTool --version (invoke)

1743# Intersectool@1: '/opt/local/bin/IntersectTool: GeographicLib version 2.3' (0)

1744# Intersectool@1: /opt/local/bin/IntersectTool: GeographicLib version 2.3 (0)

1745# 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))

1746# 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)

1747# Intersectool@2: '-631414.2687702414 5988887.2784352796 0 -3' (0)

1748# Intersectool@2: sA=-631414.2687702414, sB=5988887.2784352796, c=0, k=-3 (0)

1749# Intersectool.Segment: XDict(c=0, k=-3, kA=-1, kB=0, sA=-631414.26877, sB=5988887.278435)

1750

1751# % python3 -m ....pygeodesy.geodesici -C -R 4e7 -c 50 -4 -147.7 0 0 90

1752# 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)

1753# 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)

1754# 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)

1755# 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)

1756

1757# % env PYGEODESY_INTERSECTTOOL=... python3 -m ....pygeodesy.geodesici -T -C -R 4e7 -c 50 -4 -147.7 0 0 90

1758# 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)

1759# 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)

1760# 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)

1761# 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)

1762

1763# % python3 -m ....pygeodesy.geodesici -R 4e7 -i 0 0 10 10 50 -4 -50 -4

1764# Intersector.All[0]: XDict(c=0, sA=-631414.26877, sB=5988887.278435, sX0=1866020.935315)

1765# Intersector.All[1]: XDict(c=0, sA=19422725.117572, sB=-14062417.105648, sX0=38239422.83511)

1766# Intersector.All[2]: XDict(c=0, sA=19422725.117572, sB=25945445.811603, sX0=39048781.218067)

1767# Intersector.All[3]: XDict(c=0, sA=39476927.464575, sB=5894074.699478, sX0=39051612.452944)

1768

1769# % env PYGEODESY_INTERSECTTOOL=... python3 -m ....pygeodesy.geodesici -T -R 4e7 -i 0 0 10 10 50 -4 -50 -4

1770# Intersectool.All[0]: XDict(c=0, sA=-631414.26877, sB=5988887.278435, sX0=1862009.05513)

1771# Intersectool.All[1]: XDict(c=0, sA=19422725.117572, sB=-14062417.105648, sX0=38243434.715295)

1772# Intersectool.All[2]: XDict(c=0, sA=19422725.117572, sB=25945445.811603, sX0=39044769.337882)

1773# Intersectool.All[3]: XDict(c=0, sA=39476927.464575, sB=5894074.699478, sX0=39047600.57276)

1774

1775

1776# **) MIT License

1777#

1778# Copyright (C) 2024-2025 -- mrJean1 at Gmail -- All Rights Reserved.

1779#

1780# Permission is hereby granted, free of charge, to any person obtaining a

1781# copy of this software and associated documentation files (the "Software"),

1782# to deal in the Software without restriction, including without limitation

1783# the rights to use, copy, modify, merge, publish, distribute, sublicense,

1784# and/or sell copies of the Software, and to permit persons to whom the

1785# Software is furnished to do so, subject to the following conditions:

1786#

1787# The above copyright notice and this permission notice shall be included

1788# in all copies or substantial portions of the Software.

1789#

1790# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS

1791# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,

1792# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL

1793# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR

1794# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,

1795# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR

1796# OTHER DEALINGS IN THE SOFTWARE.