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 Degrees, Float, Int, _isDegrees, \

53 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__ = '24.07.22'

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 Azi(Degrees):

81 '''(INTERNAL) Azimuth C{Unit}.

82 '''

83 pass

84

85

86 class XDict(ADict):

87 '''4+Item result from L{Intersectool} and L{Intersector} methods

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

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

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

91 or 0 otherwise.

92

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

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

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

96

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

98 the difference between the intersection point on geodesic lines

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

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

101

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

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

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

105 L{Intersection3Tuple<Intersection3Tuple>}. Segment indicator

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

107 '''

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

109

110 def __add__(self, other):

111 X = _copy(self)

112 X += other

113 return X

114

115 def __eq__(self, other):

116 return not self.__ne__(other)

117

118 def __iadd__(self, other):

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

120 a, b = other

121 else:

122 # _xinstanceof(XDict, other=other)

123 a = other.sA

124 b = other.sB

125 if other.c:

126 self.c = other.c

127 self.sA += a # PYCHOK sA

128 self.sB += b # PYCHOK sB

129 return self

130

131 def __le__(self, other):

132 # _xinstanceof(XDict, other=other)

133 return self == other or self < other

134

135 def __lt__(self, other):

136 # _xinstanceof(XDict, other=other)

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

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

139

140 def __ne__(self, other):

141 # _xinstanceof(XDict, other=other)

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

143

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

145 # yield all corners further than C{T2}

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

147 for x in (0, sA):

148 for y in (0, sB):

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

150 yield XDict_(x, y)

151

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

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

154 c = c0 or X.c

155 if c:

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

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

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

159 return X

160

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

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

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

164

165 def _g(): # intersection in smallest gap

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

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

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

169 s = a + b

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

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

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

173 s = sB + (a - b)

174 return (sB if t else sA) - s

175

176 ta = -a

177 tb = sA - a

178 tc = -c * b

179 td = -c * (b - sB)

180

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

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

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

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

185

186 # test opposite rectangle sides first

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

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

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

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

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

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

193 self += s, s * c

194

195 @property_RO

196 def _is00(self):

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

198

199 def L1(self, other=None):

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

201 '''

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

203 if other is not None:

204 # _xinstanceof(XDict, other=other)

205 a -= other.sA

206 b -= other.sB

207 return _L1(a, b)

208

209 def _nD1(self, D1):

210 # yield the C{Closest} starts

211 D_ = 0, D1, -D1

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

213 (0, 0, 0, 1, -1)):

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

215

216 def _nD2(self, D2):

217 # yield the C{Next} starts

218 D22 = D2 * _2_0

219 D_ = 0, D2, D22, -D22, -D2

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

221 (-1, 1, -1, 1, 0, 2, 0, -2)):

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

223

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

225 # yield the C{All} starts

226 yield self

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

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

229 if i or j: # skip self

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

231 (i - j) * D3)

232

233 def _outSide(self, sA, sB):

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

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

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

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

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

239 return bool(kA or kB)

240

241 def _skip(self, S_, T1_Delta):

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

243 for j, S in _enumereverse(S_):

244 if S.L1(self) < T1_Delta:

245 S_.pop(j)

246

247

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

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

250 '''

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

252

253_X000 = XDict_() # PYCHOK origin

254_XINF = XDict_(INF)

255

256

257 class _IntersectBase(_NamedBase):

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

259 '''

260 # _g = None

261

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

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

264 self._g = geodesic

265 if name:

266 self.name = name

267

268 @Property_RO

269 def a(self):

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

271 '''

272 return self.ellipsoid.a

273

274 equatoradius = a # = Requatorial

275

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

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

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

279

280 @Property_RO

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

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

283

284 @Property_RO

285 def _cMax(self): # outer circumference

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

287

288 @property_RO

289 def datum(self):

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

291 '''

292 return self.geodesic.datum

293

294 @Property_RO

295 def ellipsoid(self):

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

297 '''

298 return self.geodesic.datum.ellipsoid

299

300 @Property_RO

301 def f(self):

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

303 '''

304 return self.ellipsoid.f

305

306 flattening = f

307

308 @property_RO

309 def geodesic(self):

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

311 '''

312 return self._g

313

314 def _illz2G(self, G, il):

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

316 '''

317 try:

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

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

320 except AttributeError:

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

322 G.set_(**r)

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

324# if not hasattr(il, n):

325# setattr(il, n, v)

326 return G

327

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

329 **LatLon_and_kwds):

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

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

332

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

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

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

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

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

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

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

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

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

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

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

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

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

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

347

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

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

350

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

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

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

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

355

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

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

358

359 @raise IntersectionError: No convergence.

360 '''

361

362 def _args(s, e):

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

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

365

366 try:

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

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

369 except Exception as x:

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

371

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

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

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

375

376 _LL4T = _MODS.namedTuples._LL4Tuple

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

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

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

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

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

382 _xkwds_get(X, kB=0))

383

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

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

386 B.lat2, B.lon2)

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

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

389

390 def k2kAkB(self, k):

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

392

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

394

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

396

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

398 '''

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

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

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

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

403 raise GeodesicError(k=k)

404

405# def k2kAkB(self, k):

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

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

408# if kB > 1:

409# kA += 1

410# kB -= 3

411# return kA, kB

412

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

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

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

416

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

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

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

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

421 else:

422 t += Azi(azi1=azi1_lat2),

423 return t

424

425 @deprecated_method

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

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

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

429

430 @Property_RO

431 def R(self):

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

433 '''

434 return self.ellipsoid.R2

435

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

437 _g = _xkwds_get

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

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

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

441 if a: # degrees to meter, approx.

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

443 s = _g(sMaX0_C, _R=s)

444 if s < _EPS3:

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

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

447

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

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

450 if eps1 is not None:

451 a = glA.lat1 - glB.lat1

452 b = glA.lon1 - glB.lon1

453 if euclid(a, b) > eps1:

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

455 return _xkwds_kwds(eps_C, _C=False)

456

457

458 class Intersectool(_IntersectBase, _SolveCapsBase):

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

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

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

462

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

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

465

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

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

468 '''

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

470 _C_option = '-C',

471 _Error = GeodesicError

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

473 _linelimit = 1200 # line printer width X 10

474 _n_alt = _n__, # Next latA lonA aziA aziB

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

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

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

478 _Xable_name = 'IntersectTool'

479 _Xable_path = _getenv(_PYGEODESY_INTERSECTTOOL_, _PYGEODESY_INTERSECTTOOL_)

480

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

482 '''New L{IntersectTool}.

483

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

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

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

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

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

489 is in C{meter}, ignored otherwise.

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

491

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

493 large or no initial convergence.

494

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

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

497 '''

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

499 self._GeodesicExact(a_geodesic, f))

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

501

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

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

504

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

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

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

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

509

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

511 '''

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

513 yield X

514

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

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

517 '''

518 def _xz2(**gl):

519 try:

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

521 try:

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

523 except (AttributeError, KeyError):

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

525 except Exception as x:

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

527

528 _t, a = _xz2(glA=glA)

529 _x, b = _xz2(glB=glB)

530 if _x is not _t:

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

532

533 A = glA.lat1, glA.lon1

534 B = glB.lat1, glB.lon1

535 if _x is self._c_alt:

536 if X0 is _X000 or X0._is00:

537 if eps1 is not None and \

538 euclid(glA.lat1 - glB.lat1,

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

540 _x, B = self._n_alt, ()

541 else: # non-zero offset

542 _x = self._o_alt

543 b += X0.sA, X0.sB

544

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

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

547 _C=_C, _R=sMaX0):

548 if _C:

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

550 if _aAB_ not in X:

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

552 else:

553 T = None

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

555

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

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

558

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

560 '''

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

562 yield T

563

564 @Property_RO

565 def _cmdBasic(self):

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

567 '''

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

569 self._E_option +

570 self._p_option)

571

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

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

574

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

576

577 @return: An L{XDict}.

578 '''

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

580 glB.lat1, glB.lon1, glB.azi1

581 if X0 is _X000 or X0._is000:

582 _x = self._c_alt

583 else:

584 _x = self._o_alt

585 args += X0.sA, X0.sB

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

587

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

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

590

591 @return: An L{Intersectool5Tuple}.

592 '''

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

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

595

596 @property_ROver

597 def _GeodesicExact(self):

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

599 '''

600 return _MODS.geodesicx.GeodesicExact # overwrite propertyROver

601

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

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

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

605 if k2:

606 A.set_(k2=X.kA)

607 B.set_(k2=X.kB)

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

609 sAB = _xkwds_get(X, sAB=s)

610 if a and s and s != sAB:

611 a *= sAB / s # adjust a

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

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

614

615 @Property

616 def IntersectTool(self):

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

618 executable (C{filename}).

619 '''

620 return self._Xable_path

621

622 @IntersectTool.setter # PYCHOK setter!

623 def IntersectTool(self, path):

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

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

626

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

628 C{IntersectTool} executable.

629 '''

630 self._setXable(path)

631

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

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

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

635

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

637 '''

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

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

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

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

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

643 if name:

644 gl.name= name

645 return gl

646

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

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

649

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

651

652 @return: An L{XDict}.

653 '''

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

655 return X

656

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

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

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

660

661 def _smi4(**gl):

662 try:

663 n, gl = gl.popitem()

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

665 except Exception as x:

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

667 s = il.s13

668 m = s * _0_5

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

670

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

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

673 X = XDict_(mA, mB) # centers

674 _ = X._outSide(sA, sB)

675 if _C: # _Names_ABs

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

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

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

679 return X, A, iA, B, iB

680

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

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

683

684 @return: A L{Middle5Tuple}.

685 '''

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

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

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

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

690

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

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

693

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

695

696 @return: An L{XDict}.

697 '''

698 if eps1 or _C:

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

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

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

702 **_C) # _R=None

703

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

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

706

707 @return: An L{Intersectool5Tuple}.

708 '''

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

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

711

712 def _R_option(self, _R=None):

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

714 '''

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

716

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

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

719

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

721

722 @return: An L{XDict}.

723 '''

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

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

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

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

728 try:

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

730 except Exception as x:

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

732 return X.set_(**ks)

733

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

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

736

737 @return: An L{Intersectool5Tuple}.

738 '''

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

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

741

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

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

744

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

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

747 (0..9) and the C{sep}arator string to join. Trailing

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

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

750

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

752 '''

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

754 status=self.status,

755 IntersectTool=self.IntersectTool)

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

757

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

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

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

761 '''

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

763 # self._i_alt: 8,

764 # self._n_alt: 4,

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

766 cmd = self._cmdBasic

767 Names = self._Names_XDict # has _c_ always

768 if _k_sX0:

769 Names += _k_sX0,

770 if _C:

771 cmd += self._C_option

772 Names += self._Names_ABs

773 if _R:

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

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

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

777

778

779 class Intersector(_IntersectBase):

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

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

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

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

784

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

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

787 '''

788

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

790 '''New L{Intersector}.

791

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

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

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

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

796

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

798 large or no initial convergence.

799

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

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

802 '''

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

804 E = self.ellipsoid

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

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

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

808 if self.f > 0:

809 t3 = self._obliqDist4()[0]

810 t4 = t1

811 else: # PYCHOK no cover

812 t1, t2, t3 = t2, t1, t5

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

814

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

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

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

818 self._T1 = t1 # min distance between intersects

819 self._T2 = t2 = t1 * _2_0

820# self._T5 = t5 # not used

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

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

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

824

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

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

827

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

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

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

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

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

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

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

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

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

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

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

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

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

841

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

843

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

845 invalid, incompatible or ill-configured.

846

847 @raise IntersectionError: No convergence.

848 '''

849 self._xLines(glA, glB)

850 if X0 is None:

851 try: # determine X0

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

853 except GeodesicError: # no .Distance

854 X0 = _X000

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

856

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

858 xMaX0 = sMaX0 + D

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

860 d3 = xMaX0 / m

861 T2d3D = self._T2d3Delta(d3)

862

863 C_ = _List(D) # closest coincident

864 X_ = _List(D) # intersections found

865 c0 = 0

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

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

868 while S_:

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

870 if Q in X_:

871 continue

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

873 _X0fx = X0._fixCoincident

874 Q = _X0fx(Q) # Q = Q'

875 if c0 and Q in C_:

876 continue

877 C_.addend(Q)

878 # elimate all existing intersections

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

880 c0 = Q.c

881 for j, X in _enumereverse(X_):

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

883 X_.pop(j)

884

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

886 args = self._m12_M12_M21(glA, s0)

887 _cjD = self._conjDist

888 for s in (-_D, _D):

889 s += s0

890 sa = 0

891 while True:

892 i += 1

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

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

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

896 break

897

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

899 continue

900 else:

901 a = len(X_)

902

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

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

905 X._skip(S_, T2d3D)

906

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

908

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

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

911

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

913 for each intersection found.

914

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

916 '''

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

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

919

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

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

922 '''

923 X = _copy(S)

924 for _ in range(_TRIPS):

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

926 X += S

927 i += 1

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

929 return self._Delto(X), i

930

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

932

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

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

935 if _C:

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

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

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

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

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

941 if _MM: # in .Middle5

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

943 else:

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

945 return X

946

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

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

949

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

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

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

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

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

955 and C{aSB} between the intersections.

956

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

958

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

960 invalid, incompatible or ill-configured.

961

962 @raise IntersectionError: No convergence.

963 '''

964 self._xLines(glA, glB)

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

966 while S_:

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

968 X = X0._fixCoincident(X)

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

970 d0 = X.L1(X0)

971 if d0 < self._T1:

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

973 break

974 if d0 < d or Q is X0:

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

976 X._skip(S_, self._T2D1Delta)

977

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

979

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

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

982

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

984 or C{None} if none found.

985

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

987 '''

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

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

990

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

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

993 # if semi:

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

995 # else:

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

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

998 for _ in range(_TRIPS):

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

1000 # see "Algorithms for geodesics", eqs. 31, 32, 33.

1001 m23 = m13 * M12

1002 M32 = M31 * M12

1003 if m12: # PYCHOK no cover

1004 m23 -= m12 * M13

1005 if m13:

1006 M32 += (_1 - M13 * M31) * m12 / m13

1007 if semi:

1008 M23 = M13 * M21

1009 # when m12 -> eps, (1 - M12 * M21) -> eps^2, I suppose.

1010 if m12 and m13:

1011 M23 += (_1 - M12 * M21) * m13 / m12

1012 d = m23 * M23 / (_1 - M23 * M32)

1013 else:

1014 d = -m23 / M32

1015 s, d = _S2(d)

1016 if _abs(d) <= self._Tol:

1017 break

1018 return s

1019

1020 _gl3 = None

1021

1022 @Property

1023 def _conjDist3s(self):

1024 gl, self._gl3, _D = self._gl3, None, self._cHalf

1025 return tuple(self._conjDist(gl, s) for s in (-_D, 0, _D))

1026

1027 @_conjDist3s.setter # PYCHOK setter!

1028 def _conjDist3(self, gl):

1029 # _XLines(gl, gl)

1030 self._gl3 = gl

1031

1032 def _conjDist3Tt_(self, c, X0=_X000):

1033 for s in self._conjDist3s:

1034 T = XDict_(s, s * c, c)

1035 yield self._Delto(T), T.L1(X0)

1036

1037 def _conjDist5(self, azi):

1038 gl = self._Line(azi1=azi)

1039 s = self._conjDist(gl, self._cHalf)

1040 X, _ = self._Basic2(gl, gl, XDict_(s * _0_5, -s * _1_5))

1041 return s, (X.L1() - s * _2_0), azi, X.sA, X.sB

1042

1043 @Property_RO

1044 def Delta(self):

1045 '''Get the equality and tiling margin (C{meter}).

1046 '''

1047 return self._cHalf * _EPSr5 # ~15 Km WGS84

1048

1049 def _Delto(self, X):

1050 # copy Delta into X, overriding X's default

1051 X._Delta = self.Delta # NOT X.set_(self.Delta)

1052 return X

1053

1054 @Property_RO

1055 def _EPS3R(self):

1056 return _EPS3 * self.R

1057

1058 @Property_RO

1059 def _faPI_4(self):

1060 return (self.f + _2_0) * self.a * PI_4

1061

1062 @Property_RO

1063 def _GeodesicLines(self):

1064 '''(INTERNAL) Get the C{Geodesic...Line} class(es).

1065 '''

1066 return type(self._Line()),

1067

1068 def _In5T(self, glA, glB, S, X, k2=False, **_2X):

1069 # Return an intersection as C{Intersector5Tuple}.

1070 A = self._Position(glA, S.sA)

1071 B = self._Position(glB, S.sB)

1072 if k2:

1073 A.set_(k2=X.kA)

1074 B.set_(k2=X.kB)

1075 s, a = self._Inversa12(A, B)

1076 return Intersector5Tuple(A._2X(glA, **_2X),

1077 B._2X(glB, **_2X), s, a, X.c, iteration=X.iteration)

1078

1079 def _Inverse(self, A, B): # caps=Caps.STANDARD

1080 return self._g.Inverse(A.lat2, A.lon2, B.lat2, B.lon2)

1081

1082 def Line(self, lat1, lon1, azi1_lat2, *lon2, **name):

1083 '''Return a geodesic line from this C{Intersector}'s geodesic, specified by

1084 two (goedetic) points or a (goedetic) point and an (initial) azimuth.

1085

1086 @arg lat1: Latitude of the first point (C{degrees}).

1087 @arg lon1: Longitude of the first point (C{degrees}).

1088 @arg azi1_lat2: Azimuth at the first point (compass C{degrees}) if no

1089 B{C{lon2}} argument is given, otherwise the latitude of

1090 the second point (C{degrees}).

1091 @arg lon2: If given, the longitude of the second point (C{degrees}).

1092 @kwarg name: Optional C{B{name}=NN} (C{str}).

1093

1094 @return: A line (from L{geodesic<Intersector.geodesic>}C{.Line} or

1095 C{.InverseLine} method) with C{LINE_CAPS}.

1096 '''

1097 args = self._ll3z4ll(lat1, lon1, azi1_lat2, *lon2)

1098 gl = self._g.InverseLine(*args, caps=Caps.LINE_CAPS) if lon2 else \

1099 self._g.Line( *args, caps=Caps.LINE_CAPS)

1100 if name:

1101 gl.name= name

1102 return gl

1103

1104 def _Line(self, lat1=0, lon1=0, azi1=0):

1105 return self._g.Line(lat1, lon1, azi1, caps=Caps.LINE_CAPS)

1106

1107 def Middle(self, glA, glB, raiser=True, **_C):

1108 '''Get the mid-points on two geodesic line segments.

1109

1110 @arg glA: A geodesic line (L{Line<Intersector.Line>}, 4-C{args}).

1111 @arg glB: An other geodesic line (L{Line<Intersector.Line>}, 4-C{args}).

1112 @kwarg raiser: If C{True}, check that B{C{glA}} and B{C{glB}} are a

1113 4-C{args} L{Line<Intersector.Line>} or C{InverseLine}

1114 (C{bool}).

1115 @kwarg _C: If C{True}, include the lat-/longitudes C{latA}, C{lonA},

1116 C{latB}, C{lonB} of the mid-points and half-lengths C{sA}

1117 and C{sB} in C{meter} of the respective line segments.

1118

1119 @return: The mid-point and half-length of each segment (L{XDict}),

1120 B{C{_C}} above.

1121

1122 @raise GeodesicError: Geodesic line B{C{glA}} or B{C{glB}} invalid,

1123 incompatible, ill-configured or not a 4-C{args

1124 Line} or other C{InverseLine}.

1125 '''

1126 M, _, _ = self._middle3(glA, glB, raiser)

1127 return self._C(M, glA, glB, **_C) if _C else M

1128

1129 def _middle3(self, glA, glB, raiser): # in .All, .Segment

1130 # return segment length C{sA} and C{sB} and the

1131 # center C{X0} of rectangle [sA, sB]

1132 self._xLines(glA, glB, s13=raiser) # need .Arc, .Distance

1133 sA = glA.Distance()

1134 sB = glB.Distance()

1135 X = XDict_(sA * _0_5, sB * _0_5)

1136 # _ = X._outSide(sA, sB)

1137 return self._Delto(X), sA, sB

1138

1139 def Middle5(self, glA, glB, raiser=True):

1140 '''Get the mid-points of two geodesic line segments and distances.

1141

1142 @return: A L{Middle5Tuple}C{(A, B, sMM, aMM, c)}.

1143

1144 @see: Method L{Middle} for further details.

1145 '''

1146 M, _, _ = self._middle3(glA, glB, raiser)

1147 M = self._C(M, glA, glB, _C=True, _MM=True)

1148 A, B, s, a, c = self._In5T(glA, glB, M, M, _2X=_M_)

1149 return Middle5Tuple(self._illz2G(A, glA),

1150 self._illz2G(B, glB), s, a, c)

1151

1152 def _m12_M12_M21(self, gl, s):

1153 P = gl.Position(s, outmask=Caps._REDUCEDLENGTH_GEODESICSCALE)

1154 return P.m12, P.M12, P.M21

1155

1156 def Next(self, glA, glB, eps1=None, **_C): # PYCHOK no cover

1157 '''Yield the next intersection of two I{intersecting} geodesic lines.

1158

1159 @arg glA: A geodesic line (L{Line<Intersector.Line>}).

1160 @arg glB: An other geodesic line (L{Line<Intersector.Line>}).

1161 @kwarg eps1: Optional margin for the L{euclid<pygeodesy.euclid>}ean

1162 distance (C{degrees}) between the C{(lat1, lon1)} points

1163 of both lines or C{None} for unchecked.

1164 @kwarg _C: If C{True}, include the lat-/longitudes C{latA}, C{lonA},

1165 C{latB}, C{lonB} of and distances C{sAB} and C{aSB}

1166 between the intersections.

1167

1168 @return: The intersection (L{XDict}) or C{None} if none found.

1169

1170 @raise GeodesicError: Geodesic line B{C{glA}} or B{C{glB}} invalid,

1171 incompatible, ill-configured or C{(lat1, lon1)}

1172 not B{C{eps1}}-equal.

1173

1174 @raise IntersectionError: No convergence.

1175

1176 @note: Offset C{X0} is implicit, zeros.

1177 '''

1178 self._xLines(glA, glB)

1179 if eps1 or _C: # eps

1180 _C = self._xNext(glA, glB, eps1, **_C)

1181

1182 X0, self._conjDist3s = _X000, glA # reset Property

1183 Q, d, S_, i = _XINF, INF, list(X0._nD2(self._D2)), 0

1184 while S_:

1185 X, i = self._Basic2(glA, glB, S_.pop(0), i)

1186 X = X0._fixCoincident(X)

1187 t = X.L1(X0) # == X.L1()

1188 c, z = X.c, (t <= self.Delta) # X == X0

1189 if z:

1190 if not c:

1191 continue

1192 Tt_ = self._conjDist3Tt_(c, X0)

1193 else:

1194 Tt_ = (X, t),

1195

1196 for T, t in Tt_:

1197 if t < d or Q is _XINF:

1198 Q, d, q = T, t, i

1199 i += 1

1200

1201 for s in ((_1_1t if z else _1_0_1t)

1202 if c else _0t):

1203 T = X

1204 if s and c:

1205 s *= self._D2

1206 T = X + (s, s * c) # NOT +=

1207 T._skip(S_, self._T2D2Delta)

1208

1209 return None if Q is _XINF else self._C(Q, glA, glB, **_C).set_(sX0=d, iteration=q)

1210

1211 def Next5(self, glA, glB, **eps1): # PYCHOK no cover

1212 '''Yield the next intersection of two I{intersecting} geodesic lines.

1213

1214 @return: An L{Intersector5Tuple}C{(A, B, sAB, aAB, c)} or C{None}

1215 if none found.

1216

1217 @see: Method L{Next} for further details.

1218 '''

1219 X = self.Next(glA, glB, **eps1)

1220 return X if X is None else self._In5T(glA, glB, X, X)

1221

1222 def _obliqDist4(self):

1223 zx = 45.0

1224 if self.f:

1225 _abs, _cjD5 = fabs, self._conjDist5

1226

1227 _, ds0, z0, _, _ = _cjD5(zx + _1_0)

1228 s1, ds1, z1, sAx, sBx = _cjD5(zx - _1_0)

1229 sx, dsx, zx = s1, _abs(ds1), z1

1230 # find ds(azi) = 0 by secant method

1231 for _ in range(16):

1232 if ds1 == ds0:

1233 break

1234 z = (z0 * ds1 - z1 * ds0) / (ds1 - ds0)

1235 _, ds0, z0 = s1, ds1, z1

1236 s1, ds1, z1, a, b = _cjD5(z)

1237 if _abs(ds1) < dsx:

1238 sx, dsx, zx, sAx, sBx = s1, _abs(ds1), z, a, b

1239 if not dsx:

1240 break

1241 else:

1242 sx, sAx, sBx = self._cHalf, _0_5, -_1_5

1243 return sx, zx, sAx, sBx

1244

1245 def _polarB3(self, lats=False): # PYCHOK no cover

1246 latx = 64.0

1247 lat = _90_0 - latx

1248 if self.f:

1249 _d, _pD2 = fdot, self._polarDist2

1250

1251 s0, lat0 = _pD2(latx - _1_0)

1252 s1, lat1 = _pD2(latx + _1_0)

1253 s2, lat2 = \

1254 sx, latx = _pD2(latx)

1255 prolate = self.f < 0

1256 # solve for ds(lat) / dlat = 0 with a quadratic fit

1257 for _ in range(_TRIPS):

1258 t = (lat1 - lat0), (lat0 - lat2), (lat2 - lat1)

1259 d = _d(t, s2, s1, s0) * _2_0

1260 if not d: # or isnan(d)

1261 break

1262 lat = _d(t, (lat1 + lat0) * s2,

1263 (lat0 + lat2) * s1,

1264 (lat2 + lat1) * s0) / d

1265 s0, lat0 = s1, lat1

1266 s1, lat1 = s2, lat2

1267 s2, lat2 = _pD2(lat)

1268 if (s2 < sx) if prolate else (s2 > sx):

1269 sx, latx = s2, lat2

1270 if lats:

1271 _, lat = _pD2(latx, lat2=True)

1272 sx += sx

1273 else:

1274 sx = self._cHalf

1275 return sx, latx, lat

1276

1277 def _polarDist2(self, lat1, lat2=False):

1278 gl = self._Line(lat1=lat1)

1279 s = self._conjDist(gl, self._faPI_4, semi=True)

1280 if lat2:

1281 lat1 = gl.Position(s, outmask=Caps.LATITUDE).lat2

1282 return s, lat1

1283

1284 def _Position(self, gl, s):

1285 return gl.Position(s, outmask=Caps._STD_LINE)

1286

1287 def Segment(self, glA, glB, proven=None, raiser=True, **_C):

1288 '''Find the intersection between two geodesic line segments.

1289

1290 @kwarg proven: Conjecture is that whenever two geodesic line

1291 segments intersect, the intersection is the

1292 one closest to the mid-points of segments.

1293 If so, use C{B{proven}=True}, otherwise find

1294 intersections on the segments and specify

1295 C{B{proven}=None} to return the first or

1296 C{B{proven}=False} the closest (C{bool}).

1297 @kwarg raiser: If C{True}, check that B{C{glA}} and B{C{glB}}

1298 are a 4-C{args} L{Line<Intersector.Line>} or

1299 C{InverseLine} (C{bool}).

1300 @kwarg _C: If C{True}, include the lat-/longitudes C{latA},

1301 C{lonA}, C{latB}, C{lonB} of and distances C{sAB}

1302 and C{aSB} between the intersections.

1303

1304 @return: The intersection of the segments (L{XDict}) with

1305 indicators C{kA}, C{kB} and C{k} set or if no

1306 intersection is found, C{None}.

1307

1308 @raise GeodesicError: Geodesic line B{C{glA}} or B{C{glB}}

1309 invalid, incompatible, ill-configured or

1310 not an C{InverseLine} or 4-C{args Line}.

1311

1312 @raise IntersectionError: No convergence.

1313

1314 @see: Method L{Middle<Intersector.Middle>} for further details.

1315 '''

1316 X0, sA, sB = self._middle3(glA, glB, raiser)

1317 Q = self.Closest(glA, glB, X0) # to X0

1318 if Q is not None:

1319 if Q.c: # anti-/parallel

1320 Q._fixSegment(sA, sB)

1321 # are rectangle [sA, sB] corners further from X0 than Q?

1322 d0 = X0.L1(Q)

1323 if Q._outSide(sA, sB) and d0 <= X0.L1() and not proven:

1324 i = Q.iteration

1325 for T in Q._corners(sA, sB, self._T2):

1326 X, i = self._Basic2(glA, glB, T, i)

1327 X = T._fixCoincident(X)

1328 if not X._outSide(sA, sB):

1329 d = X0.L1(X)

1330 if d < d0 or proven is None:

1331 Q, d0 = X, d

1332 if proven is None:

1333 break

1334 Q.set_(iteration=i)

1335

1336 Q = self._C(Q, glA, glB, **_C).set_(sX0=d0)

1337 return Q

1338

1339 def Segment5(self, glA, glB, **proven_raiser):

1340 '''Find the intersection between two geodesic line segments.

1341

1342 @return: An L{Intersector5Tuple}C{(A, B, sAB, aAB, c)}

1343 or C{None} if none found.

1344

1345 @see: Method L{Segment} for further details.

1346 '''

1347 X = self.Segment(glA, glB, **proven_raiser)

1348 return X if X is None else self._In5T(glA, glB, X, X, k2=True)

1349

1350 def _Spherical(self, glA, glB, S):

1351 '''(INTERNAL) Get solution based from a spherical triangle.

1352 '''

1353 # threshold for coincident geodesics/intersections ~4.3 nm WGS84.

1354 A = self._Position(glA, S.sA)

1355 B = self._Position(glB, S.sB)

1356 D = self._Inverse(A, B)

1357

1358 a, da = _diff182(A.azi2, D.azi1) # interior angle at A

1359 b, db = _diff182(B.azi2, D.azi2) # exterior angle at B

1360 c, dc = _diff182(a, b)

1361 if fsum1_(dc, db, -da, c) < 0: # inverted triangle

1362 a, da = -a, -da

1363 b, db = -b, -db

1364 sa, ca = _sincos2de(a, da)

1365 sb, cb = _sincos2de(b, db)

1366

1367 e, z, _abs = _EPS3, D.s12, fabs

1368 if _abs(z) <= self._EPS3R: # XXX z <= ...

1369 sA = sB = 0 # at intersection

1370 c = 1 if _abs(sa - sb) <= e and _abs(ca - cb) <= e else (

1371 -1 if _abs(sa + sb) <= e and _abs(ca + cb) <= e else 0)

1372 elif _abs(sa) <= e and _abs(sb) <= e: # coincident

1373 sA = ca * z * _0_5 # choose mid-point

1374 sB = -cb * z * _0_5

1375 c = 1 if (ca * cb) > 0 else -1

1376 # alt1: sA = ca * z; sB = 0

1377 # alt2: sB = -cb * z; sA = 0

1378 else: # general case

1379 sz, cz = sincos2(z / self.R)

1380 # [SKIP: Divide args by |sz| to avoid possible underflow

1381 # in {sa, sb} * sz; this is probably not necessary].

1382 # Definitely need to treat sz < 0 (z > PI*R) correctly in

1383 # order to avoid some convergence failures in _Basic2.

1384 sA = atan2(sb * sz, sb * ca * cz - sa * cb) * self.R

1385 sB = atan2(sa * sz, -sa * cb * cz + sb * ca) * self.R

1386 c = 0

1387 return XDict_(sA, sB, c) # no ._Delto

1388

1389 @Property_RO

1390 def _T2D1Delta(self):

1391 return self._T2d3Delta(self._D1)

1392

1393 @Property_RO

1394 def _T2D2Delta(self):

1395 return self._T2d3Delta(self._D2)

1396

1397 def _T2d3Delta(self, d3):

1398 return self._T2 - d3 - self.Delta

1399

1400 @Property_RO

1401 def _Tol(self): # convergence tolerance

1402 return self._cHalf * pow(EPS, 0.75) # _0_75

1403

1404 def toStr(self, **prec_sep_name): # PYCHOK signature

1405 '''Return this C{Intersector} as string.

1406

1407 @see: L{Ellipsoid.toStr<pygeodesy.ellipsoids.Ellipsoid.toStr>}

1408 for further details.

1409

1410 @return: C{Intersector} (C{str}).

1411 '''

1412 return self._instr(props=(Intersector.geodesic,), **prec_sep_name)

1413

1414 def _xLines(self, glA, glB, s13=False):

1415 # check two geodesic lines vs this geodesic

1416 C, gls = Caps.LINE_CAPS, dict(glA=glA, glB=glB)

1417 _xinstanceof(*self._GeodesicLines, **gls)

1418 for n, gl in gls.items():

1419 try:

1420 _xgeodesics(gl.geodesic, self.geodesic)

1421 if s13 and not isfinite(gl.s13): # or not gl.caps & Caps.DISTANCE_IN

1422 t = gl.geodesic.InverseLine.__name__

1423 raise TypeError(_not_(_an(t)))

1424 c = gl.caps & C

1425 if c != C: # not gl.caps_(C)

1426 c, C, x = map1(bin, c, C, _xor(c, C))

1427 x = _SPACE_(_xor.__name__, repr(x))[1:]

1428 raise GeodesicError(caps=c, LINE_CAPS=C, txt=x)

1429 except Exception as x:

1430 raise GeodesicError(n, gl, cause=x)

1431

1432

1433 class Intersect7Tuple(_NamedTuple):

1434 '''7-Tuple C{(A, B, sAB, aAB, c, kA, kB)} with C{A} and C{B} each

1435 a C{LatLon} or L{LatLon4Tuple}C{(lat, lon, height, datum)} of

1436 the intersection on each geodesic line, the distance C{sAB} in

1437 in C{meter} and angular distance C{aAB} in C{degrees} between

1438 C{A} and C{B}, coincidence indicator C{c} and segment indicators

1439 C{kA} and C{kB} all C{int}, see L{XDict} and method U{intersect7

1440 <_IntersectBase.intersect7>}.

1441 '''

1442 _Names_ = (_A_, _B_, _sAB_, _aAB_, _c_, 'kA', 'kB')

1443 _Units_ = (_Pass, _Pass, Meter, Degrees, Int, Int, Int)

1444

1445

1446 class Intersectool5Tuple(_NamedTuple):

1447 '''5-Tuple C{(A, B, sAB, aAB, c)} with C{A} and C{B} the C{Position}

1448 of the intersection on each geodesic line, the distance C{sAB}

1449 between C{A} and C{B} in C{meter}, the angular distance C{aAB} in

1450 C{degrees} and coincidence indicator C{c} (C{int}), see L{XDict}.

1451

1452 @note: C{A} and C{B} are each a C{GDict} with C{lat1}, C{lon1} and

1453 C{azi1} or C{lat2}, C{lon2} from the geodesic line C{glA}

1454 respectively C{glB} and the intersection location in C{latX},

1455 C{lonX}, distance C{s1X} in C{meter} and angular distance

1456 C{a1M} in C{degrees} and the segment indicator C{kX}. See

1457 L{XDict} for more details.

1458 '''

1459 _Names_ = Intersect7Tuple._Names_[:5]

1460 _Units_ = Intersect7Tuple._Units_[:5]

1461

1462

1463 class Intersector5Tuple(Intersectool5Tuple):

1464 '''5-Tuple C{(A, B, sAB, aAB, c)} with C{A} and C{B} the C{Position}

1465 of the intersection on each geodesic line, the distance C{sAB}

1466 between C{A} and C{B} in C{meter}, angular distance C{aAB} in

1467 C{degrees} and coincidence indicator C{c} (C{int}), see L{XDict}.

1468

1469 @note: C{A} and C{B} are each a C{GeodesicLine...Position} for

1470 C{outmask=Caps.STANDARD} with the intersection location in

1471 C{latX}, C{lonX}, azimuth in C{aziX}, distance C{s1X} in

1472 C{meter} and angular distance C{a1X} in C{degrees} and the

1473 segment indicator C{kX}. See L{XDict} for more details.

1474 '''

1475 _Names_ = Intersectool5Tuple._Names_

1476

1477

1478 class Middle5Tuple(Intersectool5Tuple):

1479 '''5-Tuple C{(A, B, sMM, aMM, c)} with C{A} and C{B} the I{line segments}

1480 including the mid-point location in C{latM}, C{lonM}, distance C{s1M}

1481 in C{meter} and angular distance C{a1M} in C{degrees}, the distance

1482 between both mid-points C{sMM} in C{meter} and angular distance C{aMM}

1483 in C{degrees} and coincidence indicator C{c} (C{int}). See L{XDict}

1484 for more details.

1485 '''

1486 _Names_ = (_A_, _B_, 'sMM', 'aMM', _c_)

1487

1488

1489 class _List(list):

1490

1491 _Delta = 0 # equality margin

1492

1493 def __init__(self, Delta):

1494 self._Delta = Delta

1495# list.__init__(self)

1496

1497 def __contains__(self, other):

1498 # handle C{if X in this: ...}

1499 a, b = other.sA, other.sB

1500 D, _D1 = self._Delta, _L1

1501 for X in self:

1502 if _D1(X.sA - a, X.sB - b) <= D:

1503 return True

1504 return False

1505

1506 def addend(self, X, *d0_i):

1507 # append an item, updated

1508 if d0_i:

1509 d0, i = d0_i

1510 X.set_(sX0=d0, iteration=i)

1511 self.append(X)

1512 return X.sX0

1513

1514 def sorter(self, sMaX0, dot_C, glA, glB, **_C):

1515 # trim and sort the X items

1516

1517 def _key(X):

1518 return X.sX0 # rank of X

1519

1520 t = (X for X in self if X.sX0 <= sMaX0)

1521 for X in sorted(t, key=_key):

1522 yield dot_C(X, glA, glB, **_C) if _C else X

1523

1524

1525 def _L1(a, b):

1526 '''(INTERNAL) Return the I{L1} distance.

1527 '''

1528 return fabs(a) + fabs(b)

1529

1530

1531__all__ += _ALL_DOCS(_IntersectBase)

1532

1533 if __name__ == '__main__': # MCCABE 14

1534

1535 from pygeodesy import printf

1536 __help_ = '--help'

1537

1538 def _main(args):

1539

1540 from pygeodesy import GeodesicExact

1541 from pygeodesy.internals import _plural, _usage

1542 from pygeodesy.interns import _COLONSPACE_, _DOT_, _EQUAL_, \

1543 _i_, _m_, _n_, _version_, _X_

1544 import re

1545

1546 class XY0(Float):

1547 pass

1548

1549 def _opts(_h): # for _usage()

1550 ll4 = ' latA1 lonA1'

1551 ll4 += ll4.replace('1', '2')

1552 ll4 += ll4.replace(_A_, _B_)

1553 llz = _SPACE_(NN, _latA_, _lonA_, 'aziA')

1554 llz2 = llz + llz.replace(_A_, _B_)

1555 return dict(opts='-Verbose|V--version|v--help|h--Tool|T--Check|C-R meter-',

1556 alts=((_c_ + llz2),

1557 (_i_ + ll4),

1558 (_m_ + ll4),

1559 (_n_ + llz + ' aziB'),

1560 ('o' + llz2 + ' x0 y0')),

1561 help=_h if isinstance(_h, str) else NN)

1562

1563 def _starts(Opt, arg):

1564 return arg == Opt[1:3] or (len(arg) > 2 and Opt.startswith(arg))

1565

1566 _isopt = re.compile('^[-]+[a-z]*$', flags=re.IGNORECASE).match

1567

1568 I = Intersector(GeodesicExact()) # PYCHOK I

1569 M = m = _R = None

1570 _T = _V = _h = _C = False

1571

1572 while args and _isopt(args[0]):

1573 arg = args.pop(0)

1574 if arg == _c__:

1575 M, m = I.Closest, 6 # latA lonA aziA latB lonB aziB

1576 elif _starts('--Check', arg):

1577 _C = True

1578 elif _starts(__help_, arg):

1579 _h = args[0] if args and _isopt(args[0]) else True

1580 elif arg == _i__:

1581 M, m = I.Segment, 8 # latA1 lonA1 latA2 lonA2 latB1 lonB1 latB2 lonB2

1582 elif arg == '-m':

1583 M, m = I.Middle, 8 # latA1 lonA1 latA2 lonA2 latB1 lonB1 latB2 lonB2

1584 _R = None # zap -R

1585 elif arg == _n__:

1586 M, m = I.Next, 4 # latA lonA aziA aziB

1587 elif arg == _o__:

1588 M, m = I.Closest, 8 # latA lonA aziA latB lonB aziB x0 y0

1589 elif arg == _R__ and args:

1590 _R = args.pop(0)

1591 elif _starts('--Tool', arg):

1592 I = Intersectool() # PYCHOK I

1593 if _V:

1594 I.verbose = True

1595 if I.IntersectTool in (_PYGEODESY_INTERSECTTOOL_, None): # not set

1596 I.IntersectTool = '/opt/local/bin/IntersectTool' # '/opt/local/Cellar/geographiclib/2.3/bin/IntersectTool' # HomeBrew

1597 elif _V:

1598 _ = I.version

1599 M, _T = None, True

1600 elif _starts('--Verbose', arg):

1601 _V = True

1602 if _T:

1603 I.verbose = True

1604 elif _starts('--version', arg):

1605 printf(_COLONSPACE_(*((_version_, I.version) if _T else

1606 (__version__, repr(I)))))

1607 else:

1608 raise ValueError('invalid option %r' % (arg,))

1609

1610 if _h or M is None:

1611 printf(_usage(__file__, **_opts(_h)), nl=1)

1612 else:

1613 n = len(args)

1614 if n < m:

1615 n = _plural('only %s arg' % (n,), n) if n else 'no args'

1616 raise ValueError('%s, need %s' % (n, m))

1617 args[:] = args[:m]

1618

1619 kwds = dict(_C=True) if _C else {}

1620 if M == I.Next: # -n

1621 # get latA lonA aziA latA lonA aziB

1622 args[3:] = args[:2] + args[3:4]

1623 elif M == I.Closest and m > 6: # -o

1624 y0 = Meter(y0=args.pop())

1625 x0 = Meter(x0=args.pop())

1626 kwds.update(X0=XDict_(x0, y0))

1627 if _R:

1628 m = Meter_(_R, name=_R__, low=0)

1629 kwds.update(sMaX0=m)

1630 M = I.All

1631

1632 n = len(args) // 2

1633 glA = I.Line(*args[:n])

1634 glB = I.Line(*args[n:])

1635

1636 m = _DOT_(I.__class__.__name__, M.__name__)

1637 if _V:

1638 X = _SPACE_(_X_, _EQUAL_, m)

1639 printf(unstr(X, glA, glB, **kwds))

1640

1641 X = M(glA, glB, **kwds)

1642 if X is None or isinstance(X, (XDict, tuple)):

1643 printf(_COLONSPACE_(m, repr(X)))

1644 else:

1645 for i, X in enumerate(X):

1646 printf(_COLONSPACE_(Fmt.INDEX(m, i), repr(X)))

1647

1648 from sys import argv, stderr

1649 try:

1650 if len(argv) == 2 and argv[1] == __help_:

1651 from pygeodesy.internals import _usage_argv

1652

1653 s = _SPACE_(*_usage_argv(__file__))

1654 for t in ('-h', '-h -n',

1655 '-c 0 0 45 40 10 135',

1656 '-C -c 0 0 45 40 10 135',

1657 '-T -R 2.6e7 -c 0 0 45 40 10 135',

1658 '-c 50 -4 -147.7 0 0 90',

1659 '-C -c 50 -4 -147.7 0 0 90',

1660 '# % echo 0 0 10 10 50 -4 50S 4W | IntersectTool -i -p 0 -C',

1661 '# -631414 5988887 0 -3',

1662 '# -4.05187 -4.00000 -4.05187 -4.00000 0',

1663 '-m 0 0 10 10 50 -4 50S 4W',

1664 '-C -m 0 0 10 10 50 -4 50S 4W',

1665 '-i 0 0 10 10 50 -4 50S 4W',

1666 '-T -i 0 0 10 10 50 -4 50S 4W',

1667 '-C -i 0 0 10 10 50 -4 50S 4W',

1668 '-T -C -i 0 0 10 10 50 -4 50S 4W',

1669 '-V -T -i 0 0 10 10 50 -4 -50 -4',

1670 '-C -R 4e7 -c 50 -4 -147.7 0 0 90',

1671 '-T -C -R 4e7 -c 50 -4 -147.7 0 0 90',

1672 '-R 4e7 -i 0 0 10 10 50 -4 -50 -4',

1673 '-T -R 4e7 -i 0 0 10 10 50 -4 -50 -4'):

1674 if t.startswith(_HASH_):

1675 printf(t, nl=int(t[2] == '%'))

1676 else:

1677 printf(_SPACE_(_HASH_, s, t), nl=1)

1678 argv[1:] = t = t.split()

1679 _main(t)

1680 else:

1681 _main(argv[1:])

1682

1683 except Exception as x:

1684 x = _SPACE_(x, NN, _HASH_, *argv)

1685 printf(x, file=stderr, nl=1)

1686 if '-V' in x or _MODS.errors.exception_chaining():

1687 raise

1688 exit(1)

1689

1690# % env PYGEODESY_INTERSECTTOOL=... python3 -m pygeodesy.geodesici --help

1691

1692# % python3 -m pygeodesy.geodesici -h

1693#

1694# usage: python3 -m ....pygeodesy.geodesici [--Verbose | -V] [--version | -v] [--help | -h] [--Tool | -T] [--Check | -C] [-R meter]

1695# [-c latA lonA aziA latB lonB aziB |

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

1697# -m latA1 lonA1 latA2 lonA2 latB1 lonB1 latB2 lonB2 |

1698# -n latA lonA aziA aziB |

1699# -o latA lonA aziA latB lonB aziB x0 y0]

1700

1701# % python3 -m ....pygeodesy.geodesici -h -n

1702#

1703# usage: python3 -m ....pygeodesy.geodesici -n latA lonA aziA aziB

1704

1705# % python3 -m ....pygeodesy.geodesici -c 0 0 45 40 10 135

1706# Intersector.Closest: XDict(c=0, sA=3862290.547855, sB=2339969.547699, sX0=6202260.095554)

1707

1708# % python3 -m ....pygeodesy.geodesici -C -c 0 0 45 40 10 135

1709# 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)

1710

1711# % env PYGEODESY_INTERSECTTOOL=...python3 -m ....pygeodesy.geodesici -T -R 2.6e7 -c 0 0 45 40 10 135

1712# Intersectool.All[0]: XDict(c=0, sA=3862290.547855, sB=2339969.547699, sX0=6202260.095554)

1713

1714# % python3 -m ....pygeodesy.geodesici -c 50 -4 -147.7 0 0 90

1715# Intersector.Closest: XDict(c=0, sA=6058048.653081, sB=-3311252.995823, sX0=9369301.648903)

1716

1717# % python3 -m ....pygeodesy.geodesici -C -c 50 -4 -147.7 0 0 90

1718# 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)

1719

1720# % echo 0 0 10 10 50 -4 50S 4W | IntersectTool -i -p 0 -C

1721# -631414 5988887 0 -3

1722# -4.05187 -4.00000 -4.05187 -4.00000 0

1723

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

1725# Intersector.Middle: XDict(c=0, sA=782554.549609, sB=5536835.161499, sX0=0.0)

1726

1727# % python3 -m ....pygeodesy.geodesici -C -m 0 0 10 10 50 -4 50S 4W

1728# 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)

1729

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

1731# Intersector.Segment: XDict(c=0, k=-3, kA=-1, kB=0, sA=-631414.26877, sB=5988887.278435, sX0=1866020.935315)

1732

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

1734# Intersectool.Segment: XDict(c=0, k=-3, kA=-1, kB=0, sA=-631414.26877, sB=5988887.278435)

1735

1736# % python3 -m ....pygeodesy.geodesici -C -i 0 0 10 10 50 -4 50S 4W

1737# 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)

1738

1739# % env PYGEODESY_INTERSECTTOOL=... python3 -m ....pygeodesy.geodesici -T -C -i 0 0 10 10 50 -4 50S 4W

1740# 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)

1741

1742# % env PYGEODESY_INTERSECTTOOL=... python3 -m ....pygeodesy.geodesici -V -T -i 0 0 10 10 50 -4 -50 -4

1743# Intersectool@1: /opt/local/bin/IntersectTool --version (invoke)

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

1745# Intersectool@1: /opt/local/bin/IntersectTool: GeographicLib version 2.3 (0)

1746# 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))

1747# 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)

1748# Intersectool@2: '-631414.2687702414 5988887.2784352796 0 -3' (0)

1749# Intersectool@2: sA=-631414.2687702414, sB=5988887.2784352796, c=0, k=-3 (0)

1750# Intersectool.Segment: XDict(c=0, k=-3, kA=-1, kB=0, sA=-631414.26877, sB=5988887.278435)

1751

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

1753# 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)

1754# 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)

1755# 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)

1756# 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)

1757

1758# % env PYGEODESY_INTERSECTTOOL=... python3 -m ....pygeodesy.geodesici -T -C -R 4e7 -c 50 -4 -147.7 0 0 90

1759# 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)

1760# 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)

1761# 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)

1762# 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)

1763

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

1765# Intersector.All[0]: XDict(c=0, sA=-631414.26877, sB=5988887.278435, sX0=1866020.935315)

1766# Intersector.All[1]: XDict(c=0, sA=19422725.117572, sB=-14062417.105648, sX0=38239422.83511)

1767# Intersector.All[2]: XDict(c=0, sA=19422725.117572, sB=25945445.811603, sX0=39048781.218067)

1768# Intersector.All[3]: XDict(c=0, sA=39476927.464575, sB=5894074.699478, sX0=39051612.452944)

1769

1770# % env PYGEODESY_INTERSECTTOOL=... python3 -m ....pygeodesy.geodesici -T -R 4e7 -i 0 0 10 10 50 -4 -50 -4

1771# Intersectool.All[0]: XDict(c=0, sA=-631414.26877, sB=5988887.278435, sX0=1862009.05513)

1772# Intersectool.All[1]: XDict(c=0, sA=19422725.117572, sB=-14062417.105648, sX0=38243434.715295)

1773# Intersectool.All[2]: XDict(c=0, sA=19422725.117572, sB=25945445.811603, sX0=39044769.337882)

1774# Intersectool.All[3]: XDict(c=0, sA=39476927.464575, sB=5894074.699478, sX0=39047600.57276)

1775

1776

1777# **) MIT License

1778#

1779# Copyright (C) 2024-2024 -- mrJean1 at Gmail -- All Rights Reserved.

1780#

1781# Permission is hereby granted, free of charge, to any person obtaining a

1782# copy of this software and associated documentation files (the "Software"),

1783# to deal in the Software without restriction, including without limitation

1784# the rights to use, copy, modify, merge, publish, distribute, sublicense,

1785# and/or sell copies of the Software, and to permit persons to whom the

1786# Software is furnished to do so, subject to the following conditions:

1787#

1788# The above copyright notice and this permission notice shall be included

1789# in all copies or substantial portions of the Software.

1790#

1791# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS

1792# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,

1793# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL

1794# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR

1795# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,

1796# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR

1797# OTHER DEALINGS IN THE SOFTWARE.