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

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 _90_0, isfinite

33 from pygeodesy.ellipsoids import _EWGS84, Fmt, unstr

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

35 _xgeodesics, _xkwds_get, _xkwds_kwds, \

36 _xkwds_pop2

37# from pygeodesy.errors import exception_chaining # _MODS

38 from pygeodesy.fmath import euclid, fdot

39 from pygeodesy.fsums import Fsum, fsum1_, _ceil

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

41 _HASH_, _M_, _not_, _SPACE_, _too_

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

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

44 _getenv, _PYGEODESY_INTERSECTTOOL_

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

46# from pygeodesy.namedTuples import _LL4Tuple # _MODS

47 from pygeodesy.props import deprecated_method, Property, \

48 Property_RO, property_RO, property_ROver

49 from pygeodesy.solveBase import _SolveCapsBase, pairs

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

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

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

53 _isDegrees, Lat, Lon, Meter, Meter_

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

55

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

57

58__all__ = _ALL_LAZY.geodesici

59__version__ = '24.07.25'

60

61_0t = 0, # int

62_1_1t = -1, +1

63_1_0_1t = -1, 0, +1

64_aAB_ = 'aAB'

65_c__ = '-c' # PYCHOK used!

66_cWGS84 = _EWGS84.a * PI2 # outer circumference

67_EPS3 = EPS * _3_0

68_EPSr5 = pow(EPS, 0.2) # PYCHOK used! 7.4e-4 or ~3"

69_i__ = '-i' # PYCHOK used!

70_latA_ = 'latA'

71_lonA_ = 'lonA'

72_n__ = '-n' # PYCHOK used!

73_o__ = '-o' # PYCHOK used!

74_R__ = '-R'

75_sAB_ = 'sAB'

76_sX0_ = 'sX0'

77_TRIPS = 128

78

79

80 class XDict(ADict):

81 '''4+Item result from L{Intersectool} and L{Intersector} methods

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

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

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

85 or 0 otherwise.

86

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

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

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

90

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

92 the difference between the intersection point on geodesic lines

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

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

95

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

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

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

99 L{Intersection3Tuple<Intersection3Tuple>}. Segment indicator

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

101 '''

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

103

104 def __add__(self, other):

105 X = _copy(self)

106 X += other

107 return X

108

109 def __eq__(self, other):

110 return not self.__ne__(other)

111

112 def __iadd__(self, other):

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

114 a, b = other

115 else:

116 # _xinstanceof(XDict, other=other)

117 a = other.sA

118 b = other.sB

119 if other.c:

120 self.c = other.c

121 self.sA += a # PYCHOK sA

122 self.sB += b # PYCHOK sB

123 return self

124

125 def __le__(self, other):

126 # _xinstanceof(XDict, other=other)

127 return self == other or self < other

128

129 def __lt__(self, other):

130 # _xinstanceof(XDict, other=other)

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

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

133

134 def __ne__(self, other):

135 # _xinstanceof(XDict, other=other)

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

137

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

139 # yield all corners further than C{T2}

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

141 for x in (0, sA):

142 for y in (0, sB):

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

144 yield XDict_(x, y)

145

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

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

148 c = c0 or X.c

149 if c:

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

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

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

153 return X

154

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

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

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

158

159 def _g(): # intersection in smallest gap

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

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

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

163 s = a + b

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

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

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

167 s = sB + (a - b)

168 return (sB if t else sA) - s

169

170 ta = -a

171 tb = sA - a

172 tc = -c * b

173 td = -c * (b - sB)

174

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

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

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

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

179

180 # test opposite rectangle sides first

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

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

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

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

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

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

187 self += s, s * c

188

189 @property_RO

190 def _is00(self):

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

192

193 def L1(self, other=None):

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

195 '''

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

197 if other is not None:

198 # _xinstanceof(XDict, other=other)

199 a -= other.sA

200 b -= other.sB

201 return _L1(a, b)

202

203 def _nD1(self, D1):

204 # yield the C{Closest} starts

205 D_ = 0, D1, -D1

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

207 (0, 0, 0, 1, -1)):

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

209

210 def _nD2(self, D2):

211 # yield the C{Next} starts

212 D22 = D2 * _2_0

213 D_ = 0, D2, D22, -D22, -D2

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

215 (-1, 1, -1, 1, 0, 2, 0, -2)):

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

217

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

219 # yield the C{All} starts

220 yield self

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

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

223 if i or j: # skip self

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

225 (i - j) * D3)

226

227 def _outSide(self, sA, sB):

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

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

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

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

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

233 return bool(kA or kB)

234

235 def _skip(self, S_, T1_Delta):

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

237 for j, S in _enumereverse(S_):

238 if S.L1(self) < T1_Delta:

239 S_.pop(j)

240

241

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

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

244 '''

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

246

247_X000 = XDict_() # PYCHOK origin

248_XINF = XDict_(INF)

249

250

251 class _IntersectBase(_NamedBase):

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

253 '''

254 # _g = None

255

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

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

258 self._g = geodesic

259 if name:

260 self.name = name

261

262 @Property_RO

263 def a(self):

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

265 '''

266 return self.ellipsoid.a

267

268 equatoradius = a # = Requatorial

269

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

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

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

273

274 @Property_RO

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

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

277

278 @Property_RO

279 def _cMax(self): # outer circumference

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

281

282 @property_RO

283 def datum(self):

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

285 '''

286 return self.geodesic.datum

287

288 @Property_RO

289 def ellipsoid(self):

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

291 '''

292 return self.geodesic.datum.ellipsoid

293

294 @Property_RO

295 def f(self):

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

297 '''

298 return self.ellipsoid.f

299

300 flattening = f

301

302 @property_RO

303 def geodesic(self):

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

305 '''

306 return self._g

307

308 def _illz2G(self, G, il):

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

310 '''

311 try:

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

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

314 except AttributeError:

315 r = il.Position(il.s13, outmask=Caps._STD_LINE) # isfinite(il.s13)

316 G.set_(**r)

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

318# if not hasattr(il, n):

319# setattr(il, n, v)

320 return G

321

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

323 **LatLon_and_kwds):

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

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

326

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

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

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

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

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

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

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

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

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

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

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

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

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

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

341

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

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

344

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

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

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

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

349

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

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

352

353 @raise IntersectionError: No convergence.

354 '''

355

356 def _args(s, e):

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

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

359

360 try:

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

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

363 except Exception as x:

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

365

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

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

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

369

370 _LL4T = _MODS.namedTuples._LL4Tuple

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

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

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

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

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

376 _xkwds_get(X, kB=0))

377

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

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

380 B.lat2, B.lon2)

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

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

383

384 def k2kAkB(self, k):

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

386

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

388

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

390

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

392 '''

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

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

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

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

397 raise GeodesicError(k=k)

398

399# def k2kAkB(self, k):

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

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

402# if kB > 1:

403# kA += 1

404# kB -= 3

405# return kA, kB

406

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

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

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

410

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

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

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

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

415 else:

416 t += Azi(azi1=azi1_lat2),

417 return t

418

419 @deprecated_method

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

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

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

423

424 @Property_RO

425 def R(self):

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

427 '''

428 return self.ellipsoid.R2

429

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

431 _g = _xkwds_get

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

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

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

435 if a: # degrees to meter, approx.

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

437 s = _g(sMaX0_C, _R=s)

438 if s < _EPS3:

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

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

441

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

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

444 if eps1 is not None:

445 a = glA.lat1 - glB.lat1

446 b = glA.lon1 - glB.lon1

447 if euclid(a, b) > eps1:

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

449 return _xkwds_kwds(eps_C, _C=False)

450

451

452 class Intersectool(_IntersectBase, _SolveCapsBase):

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

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

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

456

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

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

459

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

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

462 '''

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

464 _C_option = '-C',

465 _Error = GeodesicError

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

467 _linelimit = 1200 # line printer width X 10

468 _n_alt = _n__, # Next latA lonA aziA aziB

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

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

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

472 _Xable_name = 'IntersectTool'

473 _Xable_path = _getenv(_PYGEODESY_INTERSECTTOOL_, _PYGEODESY_INTERSECTTOOL_)

474

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

476 '''New L{IntersectTool}.

477

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

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

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

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

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

483 is in C{meter}, ignored otherwise.

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

485

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

487 large or no initial convergence.

488

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

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

491 '''

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

493 self._GeodesicExact(a_geodesic, f))

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

495

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

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

498

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

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

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

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

503

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

505 '''

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

507 yield X

508

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

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

511 '''

512 def _xz2(**gl):

513 try:

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

515 try:

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

517 except (AttributeError, KeyError):

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

519 except Exception as x:

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

521

522 _t, a = _xz2(glA=glA)

523 _x, b = _xz2(glB=glB)

524 if _x is not _t:

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

526

527 A = glA.lat1, glA.lon1

528 B = glB.lat1, glB.lon1

529 if _x is self._c_alt:

530 if X0 is _X000 or X0._is00:

531 if eps1 is not None and \

532 euclid(glA.lat1 - glB.lat1,

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

534 _x, B = self._n_alt, ()

535 else: # non-zero offset

536 _x = self._o_alt

537 b += X0.sA, X0.sB

538

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

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

541 _C=_C, _R=sMaX0):

542 if _C:

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

544 if _aAB_ not in X:

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

546 else:

547 T = None

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

549

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

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

552

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

554 '''

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

556 yield T

557

558 @Property_RO

559 def _cmdBasic(self):

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

561 '''

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

563 self._E_option +

564 self._p_option)

565

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

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

568

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

570

571 @return: An L{XDict}.

572 '''

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

574 glB.lat1, glB.lon1, glB.azi1

575 if X0 is _X000 or X0._is000:

576 _x = self._c_alt

577 else:

578 _x = self._o_alt

579 args += X0.sA, X0.sB

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

581

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

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

584

585 @return: An L{Intersectool5Tuple}.

586 '''

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

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

589

590 @property_ROver

591 def _GeodesicExact(self):

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

593 '''

594 return _MODS.geodesicx.GeodesicExact # overwrite property_ROver

595

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

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

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

599 if k2:

600 A.set_(k2=X.kA)

601 B.set_(k2=X.kB)

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

603 sAB = _xkwds_get(X, sAB=s)

604 if a and s and s != sAB:

605 a *= sAB / s # adjust a

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

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

608

609 @Property

610 def IntersectTool(self):

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

612 executable (C{filename}).

613 '''

614 return self._Xable_path

615

616 @IntersectTool.setter # PYCHOK setter!

617 def IntersectTool(self, path):

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

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

620

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

622 C{IntersectTool} executable.

623 '''

624 self._setXable(path)

625

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

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

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

629

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

631 '''

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

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

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

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

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

637 if name:

638 gl.name= name

639 return gl

640

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

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

643

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

645

646 @return: An L{XDict}.

647 '''

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

649 return X

650

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

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

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

654

655 def _smi4(**gl):

656 try:

657 n, gl = gl.popitem()

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

659 except Exception as x:

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

661 s = il.s13

662 m = s * _0_5

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

664

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

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

667 X = XDict_(mA, mB) # centers

668 _ = X._outSide(sA, sB)

669 if _C: # _Names_ABs

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

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

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

673 return X, A, iA, B, iB

674

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

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

677

678 @return: A L{Middle5Tuple}.

679 '''

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

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

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

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

684

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

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

687

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

689

690 @return: An L{XDict}.

691 '''

692 if eps1 or _C:

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

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

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

696 **_C) # _R=None

697

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

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

700

701 @return: An L{Intersectool5Tuple}.

702 '''

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

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

705

706 def _R_option(self, _R=None):

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

708 '''

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

710

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

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

713

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

715

716 @return: An L{XDict}.

717 '''

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

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

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

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

722 try:

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

724 except Exception as x:

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

726 return X.set_(**ks)

727

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

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

730

731 @return: An L{Intersectool5Tuple}.

732 '''

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

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

735

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

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

738

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

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

741 (0..9) and the C{sep}arator string to join. Trailing

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

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

744

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

746 '''

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

748 status=self.status,

749 IntersectTool=self.IntersectTool)

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

751

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

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

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

755 '''

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

757 # self._i_alt: 8,

758 # self._n_alt: 4,

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

760 cmd = self._cmdBasic

761 Names = self._Names_XDict # has _c_ always

762 if _k_sX0:

763 Names += _k_sX0,

764 if _C:

765 cmd += self._C_option

766 Names += self._Names_ABs

767 if _R:

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

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

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

771

772

773 class Intersector(_IntersectBase):

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

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

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

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

778

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

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

781 '''

782

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

784 '''New L{Intersector}.

785

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

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

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

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

790

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

792 large or no initial convergence.

793

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

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

796 '''

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

798 E = self.ellipsoid

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

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

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

802 if self.f > 0:

803 t3 = self._obliqDist4()[0]

804 t4 = t1

805 else: # PYCHOK no cover

806 t1, t2, t3 = t2, t1, t5

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

808

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

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

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

812 self._T1 = t1 # min distance between intersects

813 self._T2 = t2 = t1 * _2_0

814# self._T5 = t5 # not used

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

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

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

818

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

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

821

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

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

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

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

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

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

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

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

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

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

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

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

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

835

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

837

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

839 invalid, incompatible or ill-configured.

840

841 @raise IntersectionError: No convergence.

842 '''

843 self._xLines(glA, glB)

844 if X0 is None:

845 try: # determine X0

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

847 except GeodesicError: # no .Distance

848 X0 = _X000

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

850

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

852 xMaX0 = sMaX0 + D

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

854 d3 = xMaX0 / m

855 T2d3D = self._T2d3Delta(d3)

856

857 C_ = _List(D) # closest coincident

858 X_ = _List(D) # intersections found

859 c0 = 0

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

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

862 while S_:

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

864 if Q in X_:

865 continue

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

867 _X0fx = X0._fixCoincident

868 Q = _X0fx(Q) # Q = Q'

869 if c0 and Q in C_:

870 continue

871 C_.addend(Q)

872 # elimate all existing intersections

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

874 c0 = Q.c

875 for j, X in _enumereverse(X_):

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

877 X_.pop(j)

878

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

880 args = self._m12_M12_M21(glA, s0)

881 _cjD = self._conjDist

882 for s in (-_D, _D):

883 s += s0

884 sa = 0

885 while True:

886 i += 1

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

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

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

890 break

891

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

893 continue

894 else:

895 a = len(X_)

896

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

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

899 X._skip(S_, T2d3D)

900

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

902

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

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

905

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

907 for each intersection found.

908

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

910 '''

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

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

913

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

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

916 '''

917 X = _copy(S)

918 for _ in range(_TRIPS):

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

920 X += S

921 i += 1

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

923 return self._Delto(X), i

924

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

926

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

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

929 if _C:

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

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

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

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

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

935 if _MM: # in .Middle5

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

937 else:

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

939 return X

940

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

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

943

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

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

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

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

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

949 and C{aSB} between the intersections.

950

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

952

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

954 invalid, incompatible or ill-configured.

955

956 @raise IntersectionError: No convergence.

957 '''

958 self._xLines(glA, glB)

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

960 while S_:

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

962 X = X0._fixCoincident(X)

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

964 d0 = X.L1(X0)

965 if d0 < self._T1:

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

967 break

968 if d0 < d or Q is X0:

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

970 X._skip(S_, self._T2D1Delta)

971

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

973

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

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

976

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

978 or C{None} if none found.

979

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

981 '''

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

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

984

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

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

987 # if semi:

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

989 # else:

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

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

992 for _ in range(_TRIPS):

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

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

995 m23 = m13 * M12

996 M32 = M31 * M12

997 if m12: # PYCHOK no cover

998 m23 -= m12 * M13

999 if m13:

1000 M32 += (_1 - M13 * M31) * m12 / m13

1001 if semi:

1002 M23 = M13 * M21

1003 # when m12 -> eps, (1 - M12 * M21) -> eps^2, I suppose.

1004 if m12 and m13:

1005 M23 += (_1 - M12 * M21) * m13 / m12

1006 d = m23 * M23 / (_1 - M23 * M32)

1007 else:

1008 d = -m23 / M32

1009 s, d = _S2(d)

1010 if _abs(d) <= self._Tol:

1011 break

1012 return s

1013

1014 _gl3 = None

1015

1016 @Property

1017 def _conjDist3s(self):

1018 gl, self._gl3, _D = self._gl3, None, self._cHalf

1019 return tuple(self._conjDist(gl, s) for s in (-_D, 0, _D))

1020

1021 @_conjDist3s.setter # PYCHOK setter!

1022 def _conjDist3(self, gl):

1023 # _XLines(gl, gl)

1024 self._gl3 = gl

1025

1026 def _conjDist3Tt_(self, c, X0=_X000):

1027 for s in self._conjDist3s:

1028 T = XDict_(s, s * c, c)

1029 yield self._Delto(T), T.L1(X0)

1030

1031 def _conjDist5(self, azi):

1032 gl = self._Line(azi1=azi)

1033 s = self._conjDist(gl, self._cHalf)

1034 X, _ = self._Basic2(gl, gl, XDict_(s * _0_5, -s * _1_5))

1035 return s, (X.L1() - s * _2_0), azi, X.sA, X.sB

1036

1037 @Property_RO

1038 def Delta(self):

1039 '''Get the equality and tiling margin (C{meter}).

1040 '''

1041 return self._cHalf * _EPSr5 # ~15 Km WGS84

1042

1043 def _Delto(self, X):

1044 # copy Delta into X, overriding X's default

1045 X._Delta = self.Delta # NOT X.set_(self.Delta)

1046 return X

1047

1048 @Property_RO

1049 def _EPS3R(self):

1050 return _EPS3 * self.R

1051

1052 @Property_RO

1053 def _faPI_4(self):

1054 return (self.f + _2_0) * self.a * PI_4

1055

1056 @Property_RO

1057 def _GeodesicLines(self):

1058 '''(INTERNAL) Get the C{Geodesic...Line} class(es).

1059 '''

1060 return type(self._Line()),

1061

1062 def _In5T(self, glA, glB, S, X, k2=False, **_2X):

1063 # Return an intersection as C{Intersector5Tuple}.

1064 A = self._Position(glA, S.sA)

1065 B = self._Position(glB, S.sB)

1066 if k2:

1067 A.set_(k2=X.kA)

1068 B.set_(k2=X.kB)

1069 s, a = self._Inversa12(A, B)

1070 return Intersector5Tuple(A._2X(glA, **_2X),

1071 B._2X(glB, **_2X), s, a, X.c, iteration=X.iteration)

1072

1073 def _Inverse(self, A, B): # caps=Caps.STANDARD

1074 return self._g.Inverse(A.lat2, A.lon2, B.lat2, B.lon2)

1075

1076 def Line(self, lat1, lon1, azi1_lat2, *lon2, **name):

1077 '''Return a geodesic line from this C{Intersector}'s geodesic, specified by

1078 two (goedetic) points or a (goedetic) point and an (initial) azimuth.

1079

1080 @arg lat1: Latitude of the first point (C{degrees}).

1081 @arg lon1: Longitude of the first point (C{degrees}).

1082 @arg azi1_lat2: Azimuth at the first point (compass C{degrees}) if no

1083 B{C{lon2}} argument is given, otherwise the latitude of

1084 the second point (C{degrees}).

1085 @arg lon2: If given, the longitude of the second point (C{degrees}).

1086 @kwarg name: Optional C{B{name}=NN} (C{str}).

1087

1088 @return: A line (from L{geodesic<Intersector.geodesic>}C{.Line} or

1089 C{.InverseLine} method) with C{LINE_CAPS}.

1090 '''

1091 args = self._ll3z4ll(lat1, lon1, azi1_lat2, *lon2)

1092 gl = self._g.InverseLine(*args, caps=Caps.LINE_CAPS) if lon2 else \

1093 self._g.Line( *args, caps=Caps.LINE_CAPS)

1094 if name:

1095 gl.name= name

1096 return gl

1097

1098 def _Line(self, lat1=0, lon1=0, azi1=0):

1099 return self._g.Line(lat1, lon1, azi1, caps=Caps.LINE_CAPS)

1100

1101 def Middle(self, glA, glB, raiser=True, **_C):

1102 '''Get the mid-points on two geodesic line segments.

1103

1104 @arg glA: A geodesic line (L{Line<Intersector.Line>}, 4-C{args}).

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

1106 @kwarg raiser: If C{True}, check that B{C{glA}} and B{C{glB}} are a

1107 4-C{args} L{Line<Intersector.Line>} or C{InverseLine}

1108 (C{bool}).

1109 @kwarg _C: If C{True}, include the lat-/longitudes C{latA}, C{lonA},

1110 C{latB}, C{lonB} of the mid-points and half-lengths C{sA}

1111 and C{sB} in C{meter} of the respective line segments.

1112

1113 @return: The mid-point and half-length of each segment (L{XDict}),

1114 B{C{_C}} above.

1115

1116 @raise GeodesicError: Geodesic line B{C{glA}} or B{C{glB}} invalid,

1117 incompatible, ill-configured or not a 4-C{args

1118 Line} or other C{InverseLine}.

1119 '''

1120 M, _, _ = self._middle3(glA, glB, raiser)

1121 return self._C(M, glA, glB, **_C) if _C else M

1122

1123 def _middle3(self, glA, glB, raiser): # in .All, .Segment

1124 # return segment length C{sA} and C{sB} and the

1125 # center C{X0} of rectangle [sA, sB]

1126 self._xLines(glA, glB, s13=raiser) # need .Arc, .Distance

1127 sA = glA.Distance()

1128 sB = glB.Distance()

1129 X = XDict_(sA * _0_5, sB * _0_5)

1130 # _ = X._outSide(sA, sB)

1131 return self._Delto(X), sA, sB

1132

1133 def Middle5(self, glA, glB, raiser=True):

1134 '''Get the mid-points of two geodesic line segments and distances.

1135

1136 @return: A L{Middle5Tuple}C{(A, B, sMM, aMM, c)}.

1137

1138 @see: Method L{Middle} for further details.

1139 '''

1140 M, _, _ = self._middle3(glA, glB, raiser)

1141 M = self._C(M, glA, glB, _C=True, _MM=True)

1142 A, B, s, a, c = self._In5T(glA, glB, M, M, _2X=_M_)

1143 return Middle5Tuple(self._illz2G(A, glA),

1144 self._illz2G(B, glB), s, a, c)

1145

1146 def _m12_M12_M21(self, gl, s):

1147 P = gl.Position(s, outmask=Caps._REDUCEDLENGTH_GEODESICSCALE)

1148 return P.m12, P.M12, P.M21

1149

1150 def Next(self, glA, glB, eps1=None, **_C): # PYCHOK no cover

1151 '''Yield the next intersection of two I{intersecting} geodesic lines.

1152

1153 @arg glA: A geodesic line (L{Line<Intersector.Line>}).

1154 @arg glB: An other geodesic line (L{Line<Intersector.Line>}).

1155 @kwarg eps1: Optional margin for the L{euclid<pygeodesy.euclid>}ean

1156 distance (C{degrees}) between the C{(lat1, lon1)} points

1157 of both lines or C{None} for unchecked.

1158 @kwarg _C: If C{True}, include the lat-/longitudes C{latA}, C{lonA},

1159 C{latB}, C{lonB} of and distances C{sAB} and C{aSB}

1160 between the intersections.

1161

1162 @return: The intersection (L{XDict}) or C{None} if none found.

1163

1164 @raise GeodesicError: Geodesic line B{C{glA}} or B{C{glB}} invalid,

1165 incompatible, ill-configured or C{(lat1, lon1)}

1166 not B{C{eps1}}-equal.

1167

1168 @raise IntersectionError: No convergence.

1169

1170 @note: Offset C{X0} is implicit, zeros.

1171 '''

1172 self._xLines(glA, glB)

1173 if eps1 or _C: # eps

1174 _C = self._xNext(glA, glB, eps1, **_C)

1175

1176 X0, self._conjDist3s = _X000, glA # reset Property

1177 Q, d, S_, i = _XINF, INF, list(X0._nD2(self._D2)), 0

1178 while S_:

1179 X, i = self._Basic2(glA, glB, S_.pop(0), i)

1180 X = X0._fixCoincident(X)

1181 t = X.L1(X0) # == X.L1()

1182 c, z = X.c, (t <= self.Delta) # X == X0

1183 if z:

1184 if not c:

1185 continue

1186 Tt_ = self._conjDist3Tt_(c, X0)

1187 else:

1188 Tt_ = (X, t),

1189

1190 for T, t in Tt_:

1191 if t < d or Q is _XINF:

1192 Q, d, q = T, t, i

1193 i += 1

1194

1195 for s in ((_1_1t if z else _1_0_1t)

1196 if c else _0t):

1197 T = X

1198 if s and c:

1199 s *= self._D2

1200 T = X + (s, s * c) # NOT +=

1201 T._skip(S_, self._T2D2Delta)

1202

1203 return None if Q is _XINF else self._C(Q, glA, glB, **_C).set_(sX0=d, iteration=q)

1204

1205 def Next5(self, glA, glB, **eps1): # PYCHOK no cover

1206 '''Yield the next intersection of two I{intersecting} geodesic lines.

1207

1208 @return: An L{Intersector5Tuple}C{(A, B, sAB, aAB, c)} or C{None}

1209 if none found.

1210

1211 @see: Method L{Next} for further details.

1212 '''

1213 X = self.Next(glA, glB, **eps1)

1214 return X if X is None else self._In5T(glA, glB, X, X)

1215

1216 def _obliqDist4(self):

1217 zx = 45.0

1218 if self.f:

1219 _abs, _cjD5 = fabs, self._conjDist5

1220

1221 _, ds0, z0, _, _ = _cjD5(zx + _1_0)

1222 s1, ds1, z1, sAx, sBx = _cjD5(zx - _1_0)

1223 sx, dsx, zx = s1, _abs(ds1), z1

1224 # find ds(azi) = 0 by secant method

1225 for _ in range(16):

1226 if ds1 == ds0:

1227 break

1228 z = (z0 * ds1 - z1 * ds0) / (ds1 - ds0)

1229 _, ds0, z0 = s1, ds1, z1

1230 s1, ds1, z1, a, b = _cjD5(z)

1231 if _abs(ds1) < dsx:

1232 sx, dsx, zx, sAx, sBx = s1, _abs(ds1), z, a, b

1233 if not dsx:

1234 break

1235 else:

1236 sx, sAx, sBx = self._cHalf, _0_5, -_1_5

1237 return sx, zx, sAx, sBx

1238

1239 def _polarB3(self, lats=False): # PYCHOK no cover

1240 latx = 64.0

1241 lat = _90_0 - latx

1242 if self.f:

1243 _d, _pD2 = fdot, self._polarDist2

1244

1245 s0, lat0 = _pD2(latx - _1_0)

1246 s1, lat1 = _pD2(latx + _1_0)

1247 s2, lat2 = \

1248 sx, latx = _pD2(latx)

1249 prolate = self.f < 0

1250 # solve for ds(lat) / dlat = 0 with a quadratic fit

1251 for _ in range(_TRIPS):

1252 t = (lat1 - lat0), (lat0 - lat2), (lat2 - lat1)

1253 d = _d(t, s2, s1, s0) * _2_0

1254 if not d: # or isnan(d)

1255 break

1256 lat = _d(t, (lat1 + lat0) * s2,

1257 (lat0 + lat2) * s1,

1258 (lat2 + lat1) * s0) / d

1259 s0, lat0 = s1, lat1

1260 s1, lat1 = s2, lat2

1261 s2, lat2 = _pD2(lat)

1262 if (s2 < sx) if prolate else (s2 > sx):

1263 sx, latx = s2, lat2

1264 if lats:

1265 _, lat = _pD2(latx, lat2=True)

1266 sx += sx

1267 else:

1268 sx = self._cHalf

1269 return sx, latx, lat

1270

1271 def _polarDist2(self, lat1, lat2=False):

1272 gl = self._Line(lat1=lat1)

1273 s = self._conjDist(gl, self._faPI_4, semi=True)

1274 if lat2:

1275 lat1 = gl.Position(s, outmask=Caps.LATITUDE).lat2

1276 return s, lat1

1277

1278 def _Position(self, gl, s):

1279 return gl.Position(s, outmask=Caps._STD_LINE)

1280

1281 def Segment(self, glA, glB, proven=None, raiser=True, **_C):

1282 '''Find the intersection between two geodesic line segments.

1283

1284 @kwarg proven: Conjecture is that whenever two geodesic line

1285 segments intersect, the intersection is the

1286 one closest to the mid-points of segments.

1287 If so, use C{B{proven}=True}, otherwise find

1288 intersections on the segments and specify

1289 C{B{proven}=None} to return the first or

1290 C{B{proven}=False} the closest (C{bool}).

1291 @kwarg raiser: If C{True}, check that B{C{glA}} and B{C{glB}}

1292 are a 4-C{args} L{Line<Intersector.Line>} or

1293 C{InverseLine} (C{bool}).

1294 @kwarg _C: If C{True}, include the lat-/longitudes C{latA},

1295 C{lonA}, C{latB}, C{lonB} of and distances C{sAB}

1296 and C{aSB} between the intersections.

1297

1298 @return: The intersection of the segments (L{XDict}) with

1299 indicators C{kA}, C{kB} and C{k} set or if no

1300 intersection is found, C{None}.

1301

1302 @raise GeodesicError: Geodesic line B{C{glA}} or B{C{glB}}

1303 invalid, incompatible, ill-configured or

1304 not an C{InverseLine} or 4-C{args Line}.

1305

1306 @raise IntersectionError: No convergence.

1307

1308 @see: Method L{Middle<Intersector.Middle>} for further details.

1309 '''

1310 X0, sA, sB = self._middle3(glA, glB, raiser)

1311 Q = self.Closest(glA, glB, X0) # to X0

1312 if Q is not None:

1313 if Q.c: # anti-/parallel

1314 Q._fixSegment(sA, sB)

1315 # are rectangle [sA, sB] corners further from X0 than Q?

1316 d0 = X0.L1(Q)

1317 if Q._outSide(sA, sB) and d0 <= X0.L1() and not proven:

1318 i = Q.iteration

1319 for T in Q._corners(sA, sB, self._T2):

1320 X, i = self._Basic2(glA, glB, T, i)

1321 X = T._fixCoincident(X)

1322 if not X._outSide(sA, sB):

1323 d = X0.L1(X)

1324 if d < d0 or proven is None:

1325 Q, d0 = X, d

1326 if proven is None:

1327 break

1328 Q.set_(iteration=i)

1329

1330 Q = self._C(Q, glA, glB, **_C).set_(sX0=d0)

1331 return Q

1332

1333 def Segment5(self, glA, glB, **proven_raiser):

1334 '''Find the intersection between two geodesic line segments.

1335

1336 @return: An L{Intersector5Tuple}C{(A, B, sAB, aAB, c)}

1337 or C{None} if none found.

1338

1339 @see: Method L{Segment} for further details.

1340 '''

1341 X = self.Segment(glA, glB, **proven_raiser)

1342 return X if X is None else self._In5T(glA, glB, X, X, k2=True)

1343

1344 def _Spherical(self, glA, glB, S):

1345 '''(INTERNAL) Get solution based from a spherical triangle.

1346 '''

1347 # threshold for coincident geodesics/intersections ~4.3 nm WGS84.

1348 A = self._Position(glA, S.sA)

1349 B = self._Position(glB, S.sB)

1350 D = self._Inverse(A, B)

1351

1352 a, da = _diff182(A.azi2, D.azi1) # interior angle at A

1353 b, db = _diff182(B.azi2, D.azi2) # exterior angle at B

1354 c, dc = _diff182(a, b)

1355 if fsum1_(dc, db, -da, c) < 0: # inverted triangle

1356 a, da = -a, -da

1357 b, db = -b, -db

1358 sa, ca = _sincos2de(a, da)

1359 sb, cb = _sincos2de(b, db)

1360

1361 e, z, _abs = _EPS3, D.s12, fabs

1362 if _abs(z) <= self._EPS3R: # XXX z <= ...

1363 sA = sB = 0 # at intersection

1364 c = 1 if _abs(sa - sb) <= e and _abs(ca - cb) <= e else (

1365 -1 if _abs(sa + sb) <= e and _abs(ca + cb) <= e else 0)

1366 elif _abs(sa) <= e and _abs(sb) <= e: # coincident

1367 sA = ca * z * _0_5 # choose mid-point

1368 sB = -cb * z * _0_5

1369 c = 1 if (ca * cb) > 0 else -1

1370 # alt1: sA = ca * z; sB = 0

1371 # alt2: sB = -cb * z; sA = 0

1372 else: # general case

1373 sz, cz = sincos2(z / self.R)

1374 # [SKIP: Divide args by |sz| to avoid possible underflow

1375 # in {sa, sb} * sz; this is probably not necessary].

1376 # Definitely need to treat sz < 0 (z > PI*R) correctly in

1377 # order to avoid some convergence failures in _Basic2.

1378 sA = atan2(sb * sz, sb * ca * cz - sa * cb) * self.R

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

1380 c = 0

1381 return XDict_(sA, sB, c) # no ._Delto

1382

1383 @Property_RO

1384 def _T2D1Delta(self):

1385 return self._T2d3Delta(self._D1)

1386

1387 @Property_RO

1388 def _T2D2Delta(self):

1389 return self._T2d3Delta(self._D2)

1390

1391 def _T2d3Delta(self, d3):

1392 return self._T2 - d3 - self.Delta

1393

1394 @Property_RO

1395 def _Tol(self): # convergence tolerance

1396 return self._cHalf * pow(EPS, 0.75) # _0_75

1397

1398 def toStr(self, **prec_sep_name): # PYCHOK signature

1399 '''Return this C{Intersector} as string.

1400

1401 @see: L{Ellipsoid.toStr<pygeodesy.ellipsoids.Ellipsoid.toStr>}

1402 for further details.

1403

1404 @return: C{Intersector} (C{str}).

1405 '''

1406 return self._instr(props=(Intersector.geodesic,), **prec_sep_name)

1407

1408 def _xLines(self, glA, glB, s13=False):

1409 # check two geodesic lines vs this geodesic

1410 C, gls = Caps.LINE_CAPS, dict(glA=glA, glB=glB)

1411 _xinstanceof(*self._GeodesicLines, **gls)

1412 for n, gl in gls.items():

1413 try:

1414 _xgeodesics(gl.geodesic, self.geodesic)

1415 if s13 and not isfinite(gl.s13): # or not gl.caps & Caps.DISTANCE_IN

1416 t = gl.geodesic.InverseLine.__name__

1417 raise TypeError(_not_(_an(t)))

1418 c = gl.caps & C

1419 if c != C: # not gl.caps_(C)

1420 c, C, x = map1(bin, c, C, _xor(c, C))

1421 x = _SPACE_(_xor.__name__, repr(x))[1:]

1422 raise GeodesicError(caps=c, LINE_CAPS=C, txt=x)

1423 except Exception as x:

1424 raise GeodesicError(n, gl, cause=x)

1425

1426

1427 class Intersect7Tuple(_NamedTuple):

1428 '''7-Tuple C{(A, B, sAB, aAB, c, kA, kB)} with C{A} and C{B} each

1429 a C{LatLon} or L{LatLon4Tuple}C{(lat, lon, height, datum)} of

1430 the intersection on each geodesic line, the distance C{sAB} in

1431 in C{meter} and angular distance C{aAB} in C{degrees} between

1432 C{A} and C{B}, coincidence indicator C{c} and segment indicators

1433 C{kA} and C{kB} all C{int}, see L{XDict} and method U{intersect7

1434 <_IntersectBase.intersect7>}.

1435 '''

1436 _Names_ = (_A_, _B_, _sAB_, _aAB_, _c_, 'kA', 'kB')

1437 _Units_ = (_Pass, _Pass, Meter, Degrees, Int, Int, Int)

1438

1439

1440 class Intersectool5Tuple(_NamedTuple):

1441 '''5-Tuple C{(A, B, sAB, aAB, c)} with C{A} and C{B} the C{Position}

1442 of the intersection on each geodesic line, the distance C{sAB}

1443 between C{A} and C{B} in C{meter}, the angular distance C{aAB} in

1444 C{degrees} and coincidence indicator C{c} (C{int}), see L{XDict}.

1445

1446 @note: C{A} and C{B} are each a C{GDict} with C{lat1}, C{lon1} and

1447 C{azi1} or C{lat2}, C{lon2} from the geodesic line C{glA}

1448 respectively C{glB} and the intersection location in C{latX},

1449 C{lonX}, distance C{s1X} in C{meter} and angular distance

1450 C{a1M} in C{degrees} and the segment indicator C{kX}. See

1451 L{XDict} for more details.

1452 '''

1453 _Names_ = Intersect7Tuple._Names_[:5]

1454 _Units_ = Intersect7Tuple._Units_[:5]

1455

1456

1457 class Intersector5Tuple(Intersectool5Tuple):

1458 '''5-Tuple C{(A, B, sAB, aAB, c)} with C{A} and C{B} the C{Position}

1459 of the intersection on each geodesic line, the distance C{sAB}

1460 between C{A} and C{B} in C{meter}, angular distance C{aAB} in

1461 C{degrees} and coincidence indicator C{c} (C{int}), see L{XDict}.

1462

1463 @note: C{A} and C{B} are each a C{GeodesicLine...Position} for

1464 C{outmask=Caps.STANDARD} with the intersection location in

1465 C{latX}, C{lonX}, azimuth in C{aziX}, distance C{s1X} in

1466 C{meter} and angular distance C{a1X} in C{degrees} and the

1467 segment indicator C{kX}. See L{XDict} for more details.

1468 '''

1469 _Names_ = Intersectool5Tuple._Names_

1470

1471

1472 class Middle5Tuple(Intersectool5Tuple):

1473 '''5-Tuple C{(A, B, sMM, aMM, c)} with C{A} and C{B} the I{line segments}

1474 including the mid-point location in C{latM}, C{lonM}, distance C{s1M}

1475 in C{meter} and angular distance C{a1M} in C{degrees}, the distance

1476 between both mid-points C{sMM} in C{meter} and angular distance C{aMM}

1477 in C{degrees} and coincidence indicator C{c} (C{int}). See L{XDict}

1478 for more details.

1479 '''

1480 _Names_ = (_A_, _B_, 'sMM', 'aMM', _c_)

1481

1482

1483 class _List(list):

1484

1485 _Delta = 0 # equality margin

1486

1487 def __init__(self, Delta):

1488 self._Delta = Delta

1489# list.__init__(self)

1490

1491 def __contains__(self, other):

1492 # handle C{if X in this: ...}

1493 a, b = other.sA, other.sB

1494 D, _D1 = self._Delta, _L1

1495 for X in self:

1496 if _D1(X.sA - a, X.sB - b) <= D:

1497 return True

1498 return False

1499

1500 def addend(self, X, *d0_i):

1501 # append an item, updated

1502 if d0_i:

1503 d0, i = d0_i

1504 X.set_(sX0=d0, iteration=i)

1505 self.append(X)

1506 return X.sX0

1507

1508 def sorter(self, sMaX0, dot_C, glA, glB, **_C):

1509 # trim and sort the X items

1510

1511 def _key(X):

1512 return X.sX0 # rank of X

1513

1514 t = (X for X in self if X.sX0 <= sMaX0)

1515 for X in sorted(t, key=_key):

1516 yield dot_C(X, glA, glB, **_C) if _C else X

1517

1518

1519 def _L1(a, b):

1520 '''(INTERNAL) Return the I{L1} distance.

1521 '''

1522 return fabs(a) + fabs(b)

1523

1524

1525__all__ += _ALL_DOCS(_IntersectBase)

1526

1527 if __name__ == '__main__': # MCCABE 14

1528

1529 from pygeodesy import printf

1530 __help_ = '--help'

1531

1532 def _main(args):

1533

1534 from pygeodesy import GeodesicExact

1535 from pygeodesy.internals import _plural, _usage

1536 from pygeodesy.interns import _COLONSPACE_, _DOT_, _EQUAL_, \

1537 _i_, _m_, _n_, _version_, _X_

1538 import re

1539

1540 class XY0(Float):

1541 pass

1542

1543 def _opts(_h): # for _usage()

1544 ll4 = ' latA1 lonA1'

1545 ll4 += ll4.replace('1', '2')

1546 ll4 += ll4.replace(_A_, _B_)

1547 llz = _SPACE_(NN, _latA_, _lonA_, 'aziA')

1548 llz2 = llz + llz.replace(_A_, _B_)

1549 return dict(opts='-Verbose|V--version|v--help|h--Tool|T--Check|C-R meter-',

1550 alts=((_c_ + llz2),

1551 (_i_ + ll4),

1552 (_m_ + ll4),

1553 (_n_ + llz + ' aziB'),

1554 ('o' + llz2 + ' x0 y0')),

1555 help=_h if isinstance(_h, str) else NN)

1556

1557 def _starts(Opt, arg):

1558 return arg == Opt[1:3] or (len(arg) > 2 and Opt.startswith(arg))

1559

1560 _isopt = re.compile('^[-]+[a-z]*$', flags=re.IGNORECASE).match

1561

1562 I = Intersector(GeodesicExact()) # PYCHOK I

1563 M = m = _R = None

1564 _T = _V = _h = _C = False

1565

1566 while args and _isopt(args[0]):

1567 arg = args.pop(0)

1568 if arg == _c__:

1569 M, m = I.Closest, 6 # latA lonA aziA latB lonB aziB

1570 elif _starts('--Check', arg):

1571 _C = True

1572 elif _starts(__help_, arg):

1573 _h = args[0] if args and _isopt(args[0]) else True

1574 elif arg == _i__:

1575 M, m = I.Segment, 8 # latA1 lonA1 latA2 lonA2 latB1 lonB1 latB2 lonB2

1576 elif arg == '-m':

1577 M, m = I.Middle, 8 # latA1 lonA1 latA2 lonA2 latB1 lonB1 latB2 lonB2

1578 _R = None # zap -R

1579 elif arg == _n__:

1580 M, m = I.Next, 4 # latA lonA aziA aziB

1581 elif arg == _o__:

1582 M, m = I.Closest, 8 # latA lonA aziA latB lonB aziB x0 y0

1583 elif arg == _R__ and args:

1584 _R = args.pop(0)

1585 elif _starts('--Tool', arg):

1586 I = Intersectool() # PYCHOK I

1587 if _V:

1588 I.verbose = True

1589 if I.IntersectTool in (_PYGEODESY_INTERSECTTOOL_, None): # not set

1590 I.IntersectTool = '/opt/local/bin/IntersectTool' # '/opt/local/Cellar/geographiclib/2.3/bin/IntersectTool' # HomeBrew

1591 elif _V:

1592 _ = I.version

1593 M, _T = None, True

1594 elif _starts('--Verbose', arg):

1595 _V = True

1596 if _T:

1597 I.verbose = True

1598 elif _starts('--version', arg):

1599 printf(_COLONSPACE_(*((_version_, I.version) if _T else

1600 (__version__, repr(I)))))

1601 else:

1602 raise ValueError('invalid option %r' % (arg,))

1603

1604 if _h or M is None:

1605 printf(_usage(__file__, **_opts(_h)), nl=1)

1606 else:

1607 n = len(args)

1608 if n < m:

1609 n = _plural('only %s arg' % (n,), n) if n else 'no args'

1610 raise ValueError('%s, need %s' % (n, m))

1611 args[:] = args[:m]

1612

1613 kwds = dict(_C=True) if _C else {}

1614 if M == I.Next: # -n

1615 # get latA lonA aziA latA lonA aziB

1616 args[3:] = args[:2] + args[3:4]

1617 elif M == I.Closest and m > 6: # -o

1618 y0 = Meter(y0=args.pop())

1619 x0 = Meter(x0=args.pop())

1620 kwds.update(X0=XDict_(x0, y0))

1621 if _R:

1622 m = Meter_(_R, name=_R__, low=0)

1623 kwds.update(sMaX0=m)

1624 M = I.All

1625

1626 n = len(args) // 2

1627 glA = I.Line(*args[:n])

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

1629

1630 m = _DOT_(I.__class__.__name__, M.__name__)

1631 if _V:

1632 X = _SPACE_(_X_, _EQUAL_, m)

1633 printf(unstr(X, glA, glB, **kwds))

1634

1635 X = M(glA, glB, **kwds)

1636 if X is None or isinstance(X, (XDict, tuple)):

1637 printf(_COLONSPACE_(m, repr(X)))

1638 else:

1639 for i, X in enumerate(X):

1640 printf(_COLONSPACE_(Fmt.INDEX(m, i), repr(X)))

1641

1642 from sys import argv, stderr

1643 try:

1644 if len(argv) == 2 and argv[1] == __help_:

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 else:

1675 _main(argv[1:])

1676

1677 except Exception as x:

1678 x = _SPACE_(x, NN, _HASH_, *argv)

1679 printf(x, file=stderr, nl=1)

1680 if '-V' in x or _MODS.errors.exception_chaining():

1681 raise

1682 exit(1)

1683

1684# % env PYGEODESY_INTERSECTTOOL=... python3 -m pygeodesy.geodesici --help

1685

1686# % python3 -m pygeodesy.geodesici -h

1687#

1688# usage: python3 -m ....pygeodesy.geodesici [--Verbose | -V] [--version | -v] [--help | -h] [--Tool | -T] [--Check | -C] [-R meter]

1689# [-c latA lonA aziA latB lonB aziB |

1690# -i latA1 lonA1 latA2 lonA2 latB1 lonB1 latB2 lonB2 |

1691# -m latA1 lonA1 latA2 lonA2 latB1 lonB1 latB2 lonB2 |

1692# -n latA lonA aziA aziB |

1693# -o latA lonA aziA latB lonB aziB x0 y0]

1694

1695# % python3 -m ....pygeodesy.geodesici -h -n

1696#

1697# usage: python3 -m ....pygeodesy.geodesici -n latA lonA aziA aziB

1698

1699# % python3 -m ....pygeodesy.geodesici -c 0 0 45 40 10 135

1700# Intersector.Closest: XDict(c=0, sA=3862290.547855, sB=2339969.547699, sX0=6202260.095554)

1701

1702# % python3 -m ....pygeodesy.geodesici -C -c 0 0 45 40 10 135

1703# 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)

1704

1705# % env PYGEODESY_INTERSECTTOOL=...python3 -m ....pygeodesy.geodesici -T -R 2.6e7 -c 0 0 45 40 10 135

1706# Intersectool.All[0]: XDict(c=0, sA=3862290.547855, sB=2339969.547699, sX0=6202260.095554)

1707

1708# % python3 -m ....pygeodesy.geodesici -c 50 -4 -147.7 0 0 90

1709# Intersector.Closest: XDict(c=0, sA=6058048.653081, sB=-3311252.995823, sX0=9369301.648903)

1710

1711# % python3 -m ....pygeodesy.geodesici -C -c 50 -4 -147.7 0 0 90

1712# 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)

1713

1714# % echo 0 0 10 10 50 -4 50S 4W | IntersectTool -i -p 0 -C

1715# -631414 5988887 0 -3

1716# -4.05187 -4.00000 -4.05187 -4.00000 0

1717

1718# % python3 -m ....pygeodesy.geodesici -m 0 0 10 10 50 -4 50S 4W

1719# Intersector.Middle: XDict(c=0, sA=782554.549609, sB=5536835.161499, sX0=0.0)

1720

1721# % python3 -m ....pygeodesy.geodesici -C -m 0 0 10 10 50 -4 50S 4W

1722# 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)

1723

1724# % python3 -m ....pygeodesy.geodesici -i 0 0 10 10 50 -4 50S 4W

1725# Intersector.Segment: XDict(c=0, k=-3, kA=-1, kB=0, sA=-631414.26877, sB=5988887.278435, sX0=1866020.935315)

1726

1727# % env PYGEODESY_INTERSECTTOOL=... python3 -m ....pygeodesy.geodesici -T -i 0 0 10 10 50 -4 50S 4W

1728# Intersectool.Segment: XDict(c=0, k=-3, kA=-1, kB=0, sA=-631414.26877, sB=5988887.278435)

1729

1730# % python3 -m ....pygeodesy.geodesici -C -i 0 0 10 10 50 -4 50S 4W

1731# 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)

1732

1733# % env PYGEODESY_INTERSECTTOOL=... python3 -m ....pygeodesy.geodesici -T -C -i 0 0 10 10 50 -4 50S 4W

1734# 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)

1735

1736# % env PYGEODESY_INTERSECTTOOL=... python3 -m ....pygeodesy.geodesici -V -T -i 0 0 10 10 50 -4 -50 -4

1737# Intersectool@1: /opt/local/bin/IntersectTool --version (invoke)

1738# Intersectool@1: '/opt/local/bin/IntersectTool: GeographicLib version 2.3' (0)

1739# Intersectool@1: /opt/local/bin/IntersectTool: GeographicLib version 2.3 (0)

1740# 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))

1741# 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)

1742# Intersectool@2: '-631414.2687702414 5988887.2784352796 0 -3' (0)

1743# Intersectool@2: sA=-631414.2687702414, sB=5988887.2784352796, c=0, k=-3 (0)

1744# Intersectool.Segment: XDict(c=0, k=-3, kA=-1, kB=0, sA=-631414.26877, sB=5988887.278435)

1745

1746# % python3 -m ....pygeodesy.geodesici -C -R 4e7 -c 50 -4 -147.7 0 0 90

1747# 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)

1748# 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)

1749# 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)

1750# 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)

1751

1752# % env PYGEODESY_INTERSECTTOOL=... python3 -m ....pygeodesy.geodesici -T -C -R 4e7 -c 50 -4 -147.7 0 0 90

1753# 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)

1754# 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)

1755# 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)

1756# 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)

1757

1758# % python3 -m ....pygeodesy.geodesici -R 4e7 -i 0 0 10 10 50 -4 -50 -4

1759# Intersector.All[0]: XDict(c=0, sA=-631414.26877, sB=5988887.278435, sX0=1866020.935315)

1760# Intersector.All[1]: XDict(c=0, sA=19422725.117572, sB=-14062417.105648, sX0=38239422.83511)

1761# Intersector.All[2]: XDict(c=0, sA=19422725.117572, sB=25945445.811603, sX0=39048781.218067)

1762# Intersector.All[3]: XDict(c=0, sA=39476927.464575, sB=5894074.699478, sX0=39051612.452944)

1763

1764# % env PYGEODESY_INTERSECTTOOL=... python3 -m ....pygeodesy.geodesici -T -R 4e7 -i 0 0 10 10 50 -4 -50 -4

1765# Intersectool.All[0]: XDict(c=0, sA=-631414.26877, sB=5988887.278435, sX0=1862009.05513)

1766# Intersectool.All[1]: XDict(c=0, sA=19422725.117572, sB=-14062417.105648, sX0=38243434.715295)

1767# Intersectool.All[2]: XDict(c=0, sA=19422725.117572, sB=25945445.811603, sX0=39044769.337882)

1768# Intersectool.All[3]: XDict(c=0, sA=39476927.464575, sB=5894074.699478, sX0=39047600.57276)

1769

1770

1771# **) MIT License

1772#

1773# Copyright (C) 2024-2024 -- mrJean1 at Gmail -- All Rights Reserved.

1774#

1775# Permission is hereby granted, free of charge, to any person obtaining a

1776# copy of this software and associated documentation files (the "Software"),

1777# to deal in the Software without restriction, including without limitation

1778# the rights to use, copy, modify, merge, publish, distribute, sublicense,

1779# and/or sell copies of the Software, and to permit persons to whom the

1780# Software is furnished to do so, subject to the following conditions:

1781#

1782# The above copyright notice and this permission notice shall be included

1783# in all copies or substantial portions of the Software.

1784#

1785# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS

1786# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,

1787# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL

1788# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR

1789# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,

1790# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR

1791# OTHER DEALINGS IN THE SOFTWARE.