Coverage for pygeodesy/geodesici.py: 90%
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2# -*- coding: utf-8 -*-
4u'''Classes L{Intersectool} and L{Intersector}, a pure Python version of I{Karney}'s C++ class
5U{Intersect<https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1Intersect.html>}
6to find the intersections of two geodesic lines or line segments.
8L{Intersectool} and L{Intersector} methods C{All}, C{Closest}, C{Next} and C{Segment} produce
10L{XDict} instances with 4 or more items. Adjacent methods C{All5}, C{Closest5}, C{Next5} and
11C{Segment} return or yield L{Intersectool5Tuple} or L{Intersector5Tuple}s with the lat-, longitude
12azimuth of each intersection as an extended or C{Position}-like L{GDict}.
14Class L{Intersectool} is a wrapper to invoke I{Karney}'s U{IntersectTool
15<https://GeographicLib.SourceForge.io/C++/doc/IntersectTool.1.html>} utility like class L{Intersector},
16but intended I{for testing purposes only}.
18Set env variable C{PYGEODESY_INTERSECTTOOL} to the (fully qualified) path of the C{IntersectTool} executable.
20For more details, see the C++ U{GeographicLib<https://GeographicLib.SourceForge.io/C++/doc/index.html>}
21documentation, I{Charles F.F. Karney}'s paper U{Geodesics intersections<https://arxiv.org/abs/2308.00495>}
22and I{S. Baselga Moreno & J.C. Martinez-Llario}'s U{Intersection and point-to-line solutions for geodesics
23on the ellipsoid<https://riunet.UPV.ES/bitstream/handle/10251/122902/Revised_Manuscript.pdf>}.
24'''
25# make sure int/int division yields float quotient
26from __future__ import division as _; del _ # PYCHOK semicolon
28from pygeodesy.basics import _copy, _enumereverse, map1, \
29 _xinstanceof, _xor
30from pygeodesy.constants import EPS, INF, INT0, PI, PI2, PI_4, \
31 _0_0, _0_5, _1_0, _1_5, _2_0, _3_0, \
32 _90_0, isfinite
33from pygeodesy.ellipsoids import _EWGS84, Fmt, unstr
34from pygeodesy.errors import GeodesicError, IntersectionError, _an, \
35 _xgeodesics, _xkwds_get, _xkwds_kwds
36# from pygeodesy.errors import exception_chaining # _MODS
37from pygeodesy.fmath import euclid, fdot
38from pygeodesy.fsums import Fsum, fsum1_, _ceil
39from pygeodesy.interns import NN, _A_, _B_, _c_, _COMMASPACE_, \
40 _HASH_, _M_, _not_, _SPACE_, _too_
41from pygeodesy.interns import _m_ # PYCHOK used!
42from pygeodesy.karney import Caps, _diff182, GDict, _sincos2de
43from pygeodesy.lazily import _ALL_LAZY, _ALL_MODS as _MODS, \
44 _getenv, _PYGEODESY_INTERSECTTOOL_
45from pygeodesy.named import ADict, _NamedBase, _NamedTuple, _Pass
46from pygeodesy.props import deprecated_method, Property, \
47 Property_RO, property_RO
48from pygeodesy.solveBase import _SolveCapsBase, pairs
49# from pygeodesy.streprs import pairs # from .solveBase
50# from pygeodesy.streprs import Fmt, unstr # from .ellipsoids
51from pygeodesy.units import Degrees, Float, Int, Lat, Lon, \
52 Meter, Meter_
53from pygeodesy.utily import sincos2, atan2, fabs, radians
55# from math import atan2, ceil as _ceil, fabs, radians # .fsums, .utily
57__all__ = _ALL_LAZY.geodesici
58__version__ = '24.07.09'
60_0t = 0, # int
61_1_1t = -1, +1
62_1_0_1t = -1, 0, +1
63_c__ = '-c' # PYCHOK used!
64_C__ = '-C' # PYCHOK used!
65_EPS3 = EPS * _3_0
66_EPSr5 = pow(EPS, 0.2) # PYCHOK used! 7.4e-4 or ~3"
67_i__ = '-i' # PYCHOK used!
68_latA_ = 'latA'
69_lonA_ = 'lonA'
70_n__ = '-n' # PYCHOK used!
71_o__ = '-o' # PYCHOK used!
72_R__ = '-R'
73_sAB_ = 'sAB'
74_sX0_ = 'sX0'
75_TRIPS = 128
78class Azi(Degrees):
79 '''(INTERNAL) Azimuth C{Unit}.
80 '''
81 pass
84class XDict(ADict):
85 '''4+Item result from L{Intersectool} and L{Intersector} methods
86 C{All}, C{Closest}, C{Next} and C{Segment} with the intersection
87 offsets C{sA}, C{sB} and C{sX0} in C{meter} and the coincidence
88 indicator C{c}, an C{int}, +1 for parallel, -1 for anti-parallel
89 or 0 otherwise.
91 Offsets C{sA} and C{sB} are distances measured I{along} geodesic
92 line C{glA} respectively C{glB}, but C{sX0} is the I{L1-distance}
93 between the intersection and the I{origin} C{X0}.
95 Segment indicators C{kA} and C{kB} are C{0} if the segments
96 intersect or C{-1} or C{+1} if the intersection is I{before}
97 the start, respectively I{after} the end of the segment, like
98 L{Intersection3Tuple<Intersection3Tuple>}. Segment indicator
99 C{k} is I{Karney}'s C{segmode}, equal C{kA * 3 + kB}.
100 '''
101 _Delta = EPS # default margin, see C{Intersector._Delto}
103 def __add__(self, other):
104 X = _copy(self)
105 X += other
106 return X
108 def __eq__(self, other):
109 return not self.__ne__(other)
111 def __iadd__(self, other):
112 if isinstance(other, tuple): # and len(other) == 2:
113 a, b = other
114 else:
115 # _xinstanceof(XDict, other=other)
116 a = other.sA
117 b = other.sB
118 if other.c:
119 self.c = other.c
120 self.sA += a # PYCHOK sA
121 self.sB += b # PYCHOK sB
122 return self
124 def __le__(self, other):
125 # _xinstanceof(XDict, other=other)
126 return self == other or self < other
128 def __lt__(self, other):
129 # _xinstanceof(XDict, other=other)
130 return (self.sA < other.sA or (self.sA == other.sA and # PYCHOK sA
131 self.sB < other.sB) and self != other) # PYCHOK sB
133 def __ne__(self, other):
134 # _xinstanceof(XDict, other=other)
135 return self is not other and self.L1(other) > self._Delta
137 def _corners(self, sA, sB, T2):
138 # yield all corners further than C{T2}
139 a, b = self.sA, self.sB # PYCHOK sA, sB
140 for x in (0, sA):
141 for y in (0, sB):
142 if _L1(x - a, y - b) >= T2:
143 yield XDict_(x, y)
145 def _fixCoincident(self, X, c0=0):
146 # return the mid-point if C{X} is anti-/parallel
147 c = c0 or X.c
148 if c:
149 s = (self.sA - X.sA + # PYCHOK sA
150 (self.sB - X.sB) * c) * _0_5 # PYCHOK sB
151 X = X + (s, s * c) # NOT +=
152 return X
154 def _fixSegment(self, sA, sB): # PYCHOK no cover
155 # modify this anti-/parallel C{XDict}
156 a, b, c = self.sA, self.sB, self.c # PYCHOK sA, sB, c
158 def _g(): # intersection in smallest gap
159 if c > 0: # distance to [A, B] is |(a - b) - (A - B)|
160 t = a - b # consider corners [0, sB] and [sA, 0]
161 t = fabs(t + sB) < fabs(t - sA)
162 s = a + b
163 else: # distance to [A, B] is |(a + b) - (A + B)|
164 t = a + b # consider corner [0, 0] and [sA, sB]
165 t = fabs(t) < fabs(t - (sA + sB))
166 s = sB + (a - b)
167 return (sB if t else sA) - s
169 ta = -a
170 tb = sA - a
171 tc = -c * b
172 td = -c * (b - sB)
174 ga = 0 <= (b + c * ta) <= sB
175 gb = 0 <= (b + c * tb) <= sB
176 gc = 0 <= (a + tc) <= sA
177 gd = 0 <= (a + td) <= sA
179 # test opposite rectangle sides first
180 s = ((ta + tb) if ga and gb else (
181 (tc + td) if gc and gd else (
182 (ta + tc) if ga and gc else (
183 (ta + td) if ga and gd else (
184 (tb + tc) if gb and gc else (
185 (tb + td) if gb and gd else _g())))))) * _0_5
186 self += s, s * c
188 @property_RO
189 def _is00(self):
190 return not (self.sA or self.sB) # PYCHOK sA, sB
192 def L1(self, other=None):
193 '''Return the C{L1} distance.
194 '''
195 a, b = self.sA, self.sB # PYCHOK sA, sB
196 if other is not None:
197 # _xinstanceof(XDict, other=other)
198 a -= other.sA
199 b -= other.sB
200 return _L1(a, b)
202 def _nD1(self, D1):
203 # yield the C{Closest} starts
204 D_ = 0, D1, -D1
205 for a, b in zip((0, 1, -1, 0, 0),
206 (0, 0, 0, 1, -1)):
207 yield self + (D_[a], D_[b])
209 def _nD2(self, D2):
210 # yield the C{Next} starts
211 D22 = D2 * _2_0
212 D_ = 0, D2, D22, -D22, -D2
213 for a, b in zip((-1, -1, 1, 1, -2, 0, 2, 0),
214 (-1, 1, -1, 1, 0, 2, 0, -2)):
215 yield self + (D_[a], D_[b])
217 def _nmD3(self, n, m, D3): # d3 / 2
218 # yield the C{All} starts
219 yield self
220 for i in range(n, m, 2):
221 for j in range(n, m, 2):
222 if i or j: # skip self
223 yield self + ((i + j) * D3,
224 (i - j) * D3)
226 def _outSide(self, sA, sB):
227 # is this C{Xdist} outside one or both segments?
228 a, b = self.sA, self.sB # PYCHOK sA, sB
229 kA = -1 if a < 0 else (+1 if a > sA else INT0)
230 kB = -1 if b < 0 else (+1 if b > sB else INT0)
231 self.set_(kA=kA, kB=kB, k=(kA * 3 + kB) or INT0)
232 return bool(kA or kB)
234 def _skip(self, S_, T1_Delta):
235 # remove starts from list C{S_} near this C{XDict}
236 for j, S in _enumereverse(S_):
237 if S.L1(self) < T1_Delta:
238 S_.pop(j)
241def XDict_(sA=_0_0, sB=_0_0, c=INT0, sX0=_0_0):
242 '''(INTERNAL) New L{XDict} from positionals.
243 '''
244 return XDict(sA=sA, sB=sB, c=c, sX0=sX0)
246_X000 = XDict_() # PYCHOK origin
247_XINF = XDict_(INF)
250class _IntersectBase(_NamedBase):
251 '''(INTERNAL) Base class for L{Intersectool} and L{Intersector}.
252 '''
253 # _g = None
255 def __init__(self, geodesic, **name):
256 _xinstanceof(*_EWGS84._Geodesics, geodesic=geodesic)
257 self._g = geodesic
258 if name:
259 self.name = name
261 @Property_RO
262 def a(self):
263 '''Get the I{equatorial} radius, semi-axis (C{meter}).
264 '''
265 return self.ellipsoid.a
267 equatoradius = a # = Requatorial
269 @Property_RO
270 def _cHalf(self): # normalizer, semi-circumference
271 return self.R * PI # ~20K Km WGS84
273 @Property_RO
274 def _cMax(self): # outer circumference
275 return max(self.a, self.ellipsoid.b, self.R) * PI2
277 @property_RO
278 def datum(self):
279 '''Get the geodesic's datum (C{Datum}).
280 '''
281 return self.geodesic.datum
283 @Property_RO
284 def ellipsoid(self):
285 '''Get the C{geodesic}'s ellipsoid (C{Ellipsoid}).
286 '''
287 return self.geodesic.datum.ellipsoid
289 @Property_RO
290 def f(self):
291 '''Get the I{flattening} (C{scalar}), C{0} for spherical, negative for prolate.
292 '''
293 return self.ellipsoid.f
295 flattening = f
297 @property_RO
298 def geodesic(self):
299 '''Get the C{geodesic} (C{Geodesic...}).
300 '''
301 return self._g
303 def _Inversa12(self, A, B=None):
304 lls = (0, 0, A, 0) if B is None else (A.lat2, A.lon2,
305 B.lat2, B.lon2)
306 r = self._g.Inverse(*lls, outmask=Caps.DISTANCE)
307 return r.s12, r.a12 # .a12 always in r
309 def _ll3z4ll(self, lat1, lon1, azi1_lat2, *lon2):
310 t = Lat(lat1=lat1), Lon(lon1=lon1)
311 if lon2: # get azis for All, keep lat-/lons
312 t += Lat(lat2=azi1_lat2), Lon(lon2=lon2[0])
313 else:
314 t += Azi(azi1=azi1_lat2),
315 return t
317 @deprecated_method
318 def Next5s(self, glA, glB, X0=_X000, aMax=1801, sMax=0, **unused):
319 '''DEPRECATED on 2024.07.02, use method L{All5}.'''
320 return self.All5(glA, glB, X0=X0, aMaX0=aMax, sMaX0=sMax) # PYCHOK attr
322 @Property_RO
323 def R(self):
324 '''Get the I{authalic} earth radius (C{meter}).
325 '''
326 return self.ellipsoid.R2
328 def _sMaX0_C2(self, aMaX0, **sMaX0_C):
329 _g = _xkwds_get
330 s = _g(sMaX0_C, sMaX0=self._cMax)
331 s = _g(sMaX0_C, sMax=s) # for backward ...
332 a = _g(sMaX0_C, aMax=aMaX0) # ... compatibility
333 if a: # degrees to meter, approx.
334 s = max(s, self.R * radians(a)) # ellipsoid.degrees2m(a)
335 s = _g(sMaX0_C, _R=s)
336 if s < _EPS3:
337 s = _EPS3 # raise GeodesicError(sMaX0=s)
338 return s, _xkwds_kwds(sMaX0_C, _C=False)
340 def _xNext(self, glA, glB, eps1, **eps_C): # PYCHOK no cover
341 eps1 = _xkwds_get(eps_C, eps=eps1) # eps for backward compatibility
342 if eps1 is not None:
343 a = glA.lat1 - glB.lat1
344 b = glA.lon1 - glB.lon1
345 if euclid(a, b) > eps1:
346 raise GeodesicError(lat=a, lon=b, eps1=eps1)
347 return _xkwds_kwds(eps_C, _C=False)
350class Intersectool(_IntersectBase, _SolveCapsBase):
351 '''Wrapper to invoke I{Karney}'s utility U{IntersectTool
352 <https://GeographicLib.SourceForge.io/C++/doc/IntersectTool.1.html>}
353 similar to class L{Intersector<geodesici.Intersector>}.
355 @note: Use property C{IntersectTool} or env variable C{PYGEODESY_INTERSECTTOOL}
356 to specify the (fully qualified) path to the C{IntersectTool} executable.
358 @note: This C{Intersectool} is intended I{for testing purposes only}, it invokes
359 the C{IntersectTool} executable for I{every} method call.
360 '''
361 _Error = GeodesicError
362 _linelimit = 1200 # line printer width X 10
363 _Names_ABs = _latA_, _lonA_, 'latB', 'lonB', _sAB_ # -C to stderr
364 _Names_XDict = 'sA', 'sB', _c_ # plus 'k' from -i or 'sX0' from -R
365 _Xable_name = 'IntersectTool'
366 _Xable_path = _getenv(_PYGEODESY_INTERSECTTOOL_, _PYGEODESY_INTERSECTTOOL_)
368 def __init__(self, a_geodesic=None, f=None, **name):
369 '''New L{IntersectTool}.
371 @arg a_geodesic: Earth' equatorial axis (C{meter}) or a geodesic
372 (L{GeodesicExact<pygeodesy.geodesicx.GeodesicExact>},
373 wrapped L{Geodesic<pygeodesy.geodesicw.Geodesic>} or
374 L{GeodesicSolve<pygeodesy.geodsolve.GeodesicSolve>}).
375 @kwarg f: Earth' flattening (C{scalar}), required if B{C{a_geodesic}}
376 is in C{meter}, ignored otherwise.
377 @kwarg name: Optional C{B{name}=NN} (C{str}).
379 @raise GeodesicError: The eccentricity of the B{C{geodesic}}'s ellipsoid is too
380 large or no initial convergence.
382 @see: The B{Note} at I{Karney}'s C++ U{Intersect<https://GeographicLib.sourceforge.io/
383 C++/doc/classGeographicLib_1_1Intersect.html#ae41f54c9a44836f6c8f140f6994930cf>}.
384 '''
385 g = self._GeodesicExact() if a_geodesic is None else (a_geodesic if f is None else
386 self._GeodesicExact(a_geodesic, f))
387 _IntersectBase.__init__(self, g, **name)
389 def All(self, glA, glB, X0=_X000, eps1=_0_0, aMaX0=0, **sMaX0_C):
390 '''Yield all intersection of two geodesic lines up to a limit.
392 @kwarg eps1: Optional margin for the L{euclid<pygeodesy.euclid>}ean distance
393 (C{degrees}) between the C{(lat1, lon1)} points of both lines for
394 using the L{IntersectTool<Intersectool.IntersectTool>}'s C{"-n"}
395 option, unless C{B{eps1}=None}.
397 @return: An L{XDict} for each intersection.
398 '''
399 def _xz2(**gl):
400 try:
401 n, gl = gl.popitem() # _xkwds_item2(gl)
402 try:
403 return self._c_alt, (gl.azi1,)
404 except (AttributeError, KeyError):
405 return self._i_alt, (gl.lat2, gl.lon2)
406 except Exception as x:
407 raise GeodesicError(n, gl, cause=x)
409 _t, a = _xz2(glA=glA)
410 _x, b = _xz2(glB=glB)
411 if _x is not _t:
412 raise GeodesicError(glA=glA, glB=glB)
414 A = glA.lat1, glA.lon1
415 B = glB.lat1, glB.lon1
416 if _x is self._c_alt:
417 if X0 is _X000 or X0._is00:
418 if eps1 is not None and \
419 euclid(glA.lat1 - glB.lat1,
420 glA.lon1 - glB.lon1) <= eps1:
421 _x, B = self._n_alt, ()
422 else: # non-zero offset
423 _x = self._o_alt
424 b += X0.sA, X0.sB
426 sMaX0, _C = self._sMaX0_C2(aMaX0, **sMaX0_C)
427 for X in self._XDictInvoke(_x, _sX0_, (A + a + B + b),
428 _R=sMaX0, **_C):
429 yield X.set_(c=int(X.c))
431 def All5(self, glA, glB, X0=_X000, **aMaX0_sMaX0):
432 '''Yield all intersection of two geodesic lines up to a limit.
434 @return: An L{Intersectool5Tuple} for each intersection.
435 '''
436 for X in self.All(glA, glB, X0=X0, _C=True, **aMaX0_sMaX0):
437 yield self._In5T(glA, glB, X, X)
439 @Property_RO
440 def _C_option(self):
441 return (_C__,)
443 @Property_RO
444 def _cmdBasic(self):
445 '''(INTERNAL) Get the basic C{IntersectTool} cmd (C{tuple}).
446 '''
447 return (self.IntersectTool,) + (self._e_option +
448 self._E_option +
449 self._p_option)
451 @Property_RO
452 def _c_alt(self):
453 '''(INTERNAL) Get the C{Closest} format (C{tuple}).
454 '''
455 return _c__, # latA lonA aziA latB lonB aziB
457 def Closest(self, glA, glB, X0=_X000, _C=False):
458 '''Find the closest intersection of two geodesic lines.
460 @kwarg _C: Use C{B{_C}=True} to include the C{"-C"} results (C{bool}).
462 @return: An L{XDict}.
463 '''
464 args = glA.lat1, glA.lon1, glA.azi1, \
465 glB.lat1, glB.lon1, glB.azi1
466 if X0 is _X000 or X0._is000:
467 _x = self._c_alt
468 else:
469 _x = self._o_alt
470 args += X0.sA, X0.sB
471 return self._XDictInvoke(_x, NN, args, _C=_C) # _R=None)
473 def Closest5(self, glA, glB, **unused):
474 '''Find the closest intersection of two geodesic lines.
476 @return: An L{Intersectool5Tuple}.
477 '''
478 X = self.Closest(glA, glB, _C=True)
479 return self._In5T(glA, glB, X, X)
481 @property_RO
482 def _GeodesicExact(self):
483 '''Get the I{class} L{GeodesicExact}, I{once}.
484 '''
485 Intersectool._GeodesicExact = G = _MODS.geodesicx.GeodesicExact # overwrite property_RO
486 return G
488 @Property_RO
489 def _i_alt(self):
490 '''(INTERNAL) Get the C{Segment} format (C{tuple}).
491 '''
492 return _i__, # latA1 lonA1 latA2 lonA2 latB1 lonB1 latB2 lonB2
494 def _In5T(self, glA, glB, S, X, k2=False, **_2X):
495 A = GDict(glA).set_(lat2=X.latA, lon2=X.lonA, s12=S.sA)
496 B = GDict(glB).set_(lat2=X.latB, lon2=X.lonB, s12=S.sB)
497 if k2:
498 A.set_(k2=X.kA)
499 B.set_(k2=X.kB)
500 s, a = self._Inversa12(A, B)
501 sAB = _xkwds_get(X, sAB=s)
502 if a and s and s != sAB:
503 a *= sAB / s # adjust a
504 return Intersectool5Tuple(A._2X(glA, **_2X),
505 B._2X(glB, **_2X), sAB, a, X.c)
507 @Property
508 def IntersectTool(self):
509 '''Get the U{IntersectTool<https://GeographicLib.SourceForge.io/C++/doc/IntersectTool.1.html>}
510 executable (C{filename}).
511 '''
512 return self._Xable_path
514 @IntersectTool.setter # PYCHOK setter!
515 def IntersectTool(self, path):
516 '''Set the U{IntersectTool<https://GeographicLib.SourceForge.io/C++/doc/IntersectTool.1.html>}
517 executable (C{filename}), the (fully qualified) path to the C{IntersectTool} executable.
519 @raise GeodesicError: Invalid B{C{path}}, B{C{path}} doesn't exist or isn't the
520 C{IntersectTool} executable.
521 '''
522 self._setXable(path)
524 def Line(self, lat1, lon1, azi1_lat2, *lon2, **name):
525 '''Return a geodesic line from this C{Intersector}'s geodesic, specified by
526 two (goedetic) points or a (goedetic) point and an (initial) azimuth.
528 @return: A 3- or 6-item, named L{GDict}.
529 '''
530 args = self._ll3z4ll(lat1, lon1, azi1_lat2, *lon2)
531 gl = GDict((u.name, u) for u in args)
532# if lon2: # get azis for All, use lat-/lons as given
533# r = self._g.Inverse(outmask=Caps.AZIMUTH, *args)
534# gl.set_(azi1=Azi(azi1=r.azi1), azi2=Azi(azi2=r.azi2))
535 if name:
536 gl.name= name
537 return gl
539 def Middle(self, glA, glB, **_C):
540 '''Get the mid-points on two geodesic line segments.
542 @kwarg _C: Use C{B{_C}=True} to include the C{"-C"} results (C{bool}).
544 @return: An L{XDict}.
545 '''
546 X, _, _, _, _ = self._middle5(glA, glB, **_C)
547 return X
549 def _middle5(self, glA, glB, _C=False, **unused):
550 # return intersections C{A} and C{B} and the
551 # center C{X0} of rectangle [sA, sB]
553 def _smi4(**gl):
554 try:
555 n, gl = gl.popitem()
556 il = self._g.InverseLine(gl.lat1, gl.lon1, gl.lat2, gl.lon2)
557 except Exception as x:
558 raise GeodesicError(n, gl, cause=x)
559 s = il.s13
560 m = s * _0_5
561 return s, m, il, (il.Position(m, outmask=Caps._STD_LINE) if _C else None)
563 sA, mA, iA, A = _smi4(glA=glA)
564 sB, mB, iB, B = _smi4(glB=glB)
565 X = XDict_(mA, mB) # center
566 _ = X._outSide(sA, sB)
567 if _C: # _Names_ABs
568 s, a = self._Inversa12(A, B)
569 X.set_(latA=A.lat2, lonA=A.lon2, aMM=a, # assert sA == A.s12
570 latB=B.lat2, lonB=B.lon2, sMM=s) # assert sB == B.s12
571 return X, A, iA, B, iB
573 def Middle5(self, glA, glB, **unused):
574 '''Get the mid-points on two geodesic line segments and their distance.
576 @return: A L{Middle5Tuple}.
577 '''
578 X, A, iA, B, iB = self._middle5(glA, glB, _C=True)
579 A, B, s, a, c = self._In5T(A, B, X, X, _2X=_M_)
580 return Middle5Tuple(_llz2G(A, glA, iA), _llz2G(B, glB, iB), s, a, c)
582 @Property_RO
583 def _n_alt(self):
584 '''(INTERNAL) Get the C{Next} format (C{tuple}).
585 '''
586 return _n__, # latA lonA aziA aziB
588 def Next(self, glA, glB, eps1=None, **_C): # PYCHOK no cover
589 '''Find the next intersection of two I{intersecting} geodesic lines.
591 @kwarg _C: Use C{B{_C}=True} to include the option C{"-C"} results (C{bool}).
593 @return: An L{XDict}.
594 '''
595 if eps1 or _C:
596 _C = self._xNext(glA, glB, eps1, **_C)
597 return self._XDictInvoke(self._n_alt, NN,
598 (glA.lat1, glA.lon1, glA.azi1, glB.azi1),
599 **_C) # _R=None
601 def Next5(self, glA, glB, **eps1): # PYCHOK no cover
602 '''Find the next intersection of two I{intersecting} geodesic lines.
604 @return: An L{Intersectool5Tuple}.
605 '''
606 X = self.Next(glA, glB, _C=True, **eps1)
607 return self._In5T(glA, glB, X, X)
609 @Property_RO
610 def _o_alt(self):
611 '''(INTERNAL) Get the C{Offset} format (C{tuple}).
612 '''
613 return _o__, # latA lonA aziA latB lonB aziB x0 y0
615 def _R_option(self, _R=None):
616 '''(INTERNAL) Get the C{-R maxdist} option.
617 '''
618 return () if _R is None else (_R__, str(_R)) # -R maxdist
620 def Segment(self, glA, glB, **_C_unused):
621 '''Find the intersection between two geodesic line segments.
623 @kwarg _C: Use C{B{_C}=True} to include the option C{"-C"} results (C{bool}).
625 @return: An L{XDict}.
626 '''
627 X = self._XDictInvoke(self._i_alt, 'k',
628 (glA.lat1, glA.lon1, glA.lat2, glA.lon2,
629 glB.lat1, glB.lon1, glB.lat2, glB.lon2),
630 _C=_xkwds_get(_C_unused, _C=False)) # _R=None
631 k = int(X.k)
632 for kA in range(-1, 2):
633 for kB in range(-1, 2):
634 if (kA * 3 + kB) == k:
635 return X.set_(k=k, kA=kA, kB=kB)
636 raise GeodesicError(k=k, glA=glA, glB=glB, txt=repr(X))
638 def Segment5(self, glA, glB, **unused):
639 '''Find the next intersection of two I{intersecting} geodesic lines.
641 @return: An L{Intersectool5Tuple}.
642 '''
643 X = self.Segment(glA, glB, _C=True)
644 return self._In5T(glA, glB, X, X, k2=True)
646 def toStr(self, prec=6, sep=_COMMASPACE_, **unused): # PYCHOK signature
647 '''Return this C{Intersectool} as string.
649 @kwarg prec_sep: Keyword argumens C{B{prec}=6} and C{B{sep}=", "}
650 for the C{float} C{prec}ision, number of decimal digits
651 (0..9) and the C{sep}arator string to join. Trailing
652 zero decimals are stripped for B{C{prec}} values of 1
653 and above, but kept for negative B{C{prec}} values.
655 @return: Intersectool items (C{str}).
656 '''
657 d = dict(geodesic=self.geodesic, invokation=self.invokation,
658 status=self.status,
659 IntersectTool=self.IntersectTool)
660 return sep.join(pairs(d, prec=prec))
662 def _XDictInvoke(self, alt, _k_sX0, args, _C=False, **_R):
663 '''(INTERNAL) Invoke C{IntersectTool}, return results as C{XDict} or
664 a C{generator} if keyword argument C{B{_R}=sMaX0} is specified.
665 '''
666 # assert len(args) == {self._c_alt: 6,
667 # self._i_alt: 8,
668 # self._n_alt: 4,
669 # self._o_alt: 8}.get(alt, len(args))
670 cmd = self._cmdBasic
671 Names = self._Names_XDict # has _c_ always
672 if _k_sX0:
673 Names += _k_sX0,
674 if _C:
675 cmd += self._C_option
676 Names += self._Names_ABs
677 if _R:
678 cmd += self._R_option(**_R)
679 X, _R = self._DictInvoke2(cmd + alt, Names, XDict, args, **_R)
680 return X if _R else X.set_(c=int(X.c)) # generator or XDict
683class Intersector(_IntersectBase):
684 '''Finder of intersections between two goedesic lines, each an instance
685 of L{GeodesicLineExact<pygeodesy.geodesicx.GeodesicLineExact>},
686 wrapped L{GeodesicLine<pygeodesy.geodesicw.GeodesicLine>} or
687 L{GeodesicLineSolve<pygeodesy.geodsolve.GeodesicLineSolve>}.
689 @see: I{Karney}'s C++ class U{Intersect<https://GeographicLib.sourceforge.io/
690 C++/doc/classGeographicLib_1_1Intersect.html#details>} for more details.
691 '''
692 # _D1 = 0
693 # _D2 = 0
694 # _T1 = 0
695 # _T5 = 0
697 def __init__(self, geodesic, **name):
698 '''New L{Intersector}.
700 @arg geodesic: The geodesic (L{GeodesicExact<pygeodesy.geodesicx.GeodesicExact>},
701 wrapped L{Geodesic<pygeodesy.geodesicw.Geodesic>} or
702 L{GeodesicSolve<pygeodesy.geodsolve.GeodesicSolve>}).
703 @kwarg name: Optional C{B{name}=NN} (C{str}).
705 @raise GeodesicError: The eccentricity of the B{C{geodesic}}'s ellipsoid is too
706 large or no initial convergence.
708 @see: The B{Note} at I{Karney}'s C++ U{Intersect<https://GeographicLib.sourceforge.io/
709 C++/doc/classGeographicLib_1_1Intersect.html#ae41f54c9a44836f6c8f140f6994930cf>}.
710 '''
711 _IntersectBase.__init__(self, geodesic, **name)
712 E = self.ellipsoid
713 t1 = E.b * PI # min distance between intersects
714 t2 = self._polarDist2(_90_0)[0] * _2_0 # furthest, closest intersect
715 t5 = self._Inversa12( _90_0)[0] * _2_0 # longest, shortest geodesic
716 if self.f > 0:
717 t3 = self._obliqDist4()[0]
718 t4 = t1
719 else: # PYCHOK no cover
720 t1, t2, t3 = t2, t1, t5
721 t4, _, _ = self._polarB3()
723 self._D1 = d1 = t2 * _0_5 # ~E.L tile spacing for Closest
724 self._D2 = d2 = t3 / _1_5 # tile spacing for Next
725 self._D3 = d3 = t4 - self.Delta # tile spacing for All
726 self._T1 = t1 # min distance between intersects
727 self._T2 = t2 = t1 * _2_0
728# self._T5 = t5 # not used
729 if not (d1 < d3 and d2 < d3 and d2 < t2):
730 t = Fmt.PARENSPACED(_too_('eccentric'), E.e)
731 raise GeodesicError(ellipsoid=E.toStr(terse=2), txt=t)
733 def All(self, glA, glB, X0=None, aMaX0=0, **sMaX0_C): # MCCABE 13
734 '''Yield all intersection of two geodesic lines up to a limit.
736 @arg glA: A geodesic line (L{Line<Intersector.Line>}).
737 @arg glB: An other geodesic line (L{Line<Intersector.Line>}).
738 @kwarg X0: Optional I{origin} for I{L1-distances} (L{XDict}) or
739 C{None} for the L{Middle<Intersector.Middle>} of both
740 lines if both are a 4-C{args} L{Line<Intersector.Line>}
741 or C{InverseLine}, otherwise C{XDiff_(0, 0)}.
742 @kwarg aMaX0: Upper limit for the I{angular L1-distance}
743 (C{degrees}) or C{None} or C{0} for unlimited.
744 @kwarg sMaX0_C: Optional, upper limit C{B{sMaX0}=2*PI*R} for the
745 I{L1-distance} to B{C{X0}} (C{meter}) and option
746 C{B{_C}=False} to include the intersection lat-/
747 longitudes C{latA}, C{lonA}, C{latB}, C{lonB} and
748 distances C{sAB} and C{aSB}.
750 @return: Yield an L{XDict} for each intersection found.
752 @raise GeodesicError: Geodesic line B{C{glA}} or B{C{glB}}
753 invalid, incompatible or ill-configured.
755 @raise IntersectionError: No convergence.
756 '''
757 self._xLines(glA, glB)
758 if X0 is None:
759 try: # determine X0
760 X0, _, _ = self._middle3(glA, glB, True)
761 except GeodesicError: # no .Distance
762 X0 = _X000
763 sMaX0, _C = self._sMaX0_C2(aMaX0, **sMaX0_C)
765 D, _D = self.Delta, self._cHalf # C++ _d
766 xMaX0 = sMaX0 + D
767 m = int(_ceil(xMaX0 / self._D3)) # m x m tiles
768 d3 = xMaX0 / m
769 T2d3D = self._T2d3Delta(d3)
771 C_ = _List(D) # closest coincident
772 X_ = _List(D) # intersections found
773 c0 = 0
774 S_ = list(X0._nmD3(1 - m, m, d3 * _0_5))
775 # assert len(S_) == m * m + (m - 1) % 2
776 while S_:
777 Q, i = self._Basic2(glA, glB, S_.pop(0))
778 if Q in X_:
779 continue
780 if Q.c: # coincident intersection # PYCHOK no cover
781 _X0fx = X0._fixCoincident
782 Q = _X0fx(Q) # Q = Q'
783 if c0 and Q in C_:
784 continue
785 C_.addend(Q)
786 # elimate all existing intersections
787 # on this line (which didn't set c0)
788 c0 = Q.c
789 for j, X in _enumereverse(X_):
790 if _X0fx(X, c0).L1(Q) <= D: # X' == Q
791 X_.pop(j)
793 a, s0 = len(X_), Q.sA
794 args = self._m12_M12_M21(glA, s0)
795 _cjD = self._conjDist
796 for s in (-_D, _D):
797 s += s0
798 sa = 0
799 while True:
800 i += 1
801 sa = _cjD(glA, s + sa, *args) - s0
802 X = Q + (sa, sa * c0)
803 if X_.addend(X, X0.L1(X), i) > xMaX0:
804 break
806 elif c0 and Q in C_: # Q.c == 0
807 continue
808 else:
809 a = len(X_)
811 X_.addend(Q, X0.L1(Q), i + 1)
812 for X in X_[a:]: # addended Xs
813 X._skip(S_, T2d3D)
815 return X_.sorter(sMaX0, self._C, glA, glB, **_C) # generator
817 def All5(self, glA, glB, X0=_X000, **aMaX0_sMaX0_C):
818 '''Yield all intersection of two geodesic lines up to a limit.
820 @return: Yield an L{Intersector5Tuple}C{(A, B, sAB, aAB, c)}
821 for each intersection found.
823 @see: Methods L{All} for further details.
824 '''
825 for X in self.All(glA, glB, X0=X0, **aMaX0_sMaX0_C):
826 yield self._In5T(glA, glB, X, X)
828 def _Basic2(self, glA, glB, S, i=0):
829 '''(INTERNAL) Get a basic solution.
830 '''
831 X = _copy(S)
832 for _ in range(_TRIPS):
833 S = self._Spherical(glA, glB, X)
834 X += S
835 i += 1
836 if X.c or S.L1() <= self._Tol: # or isnan
837 return self._Delto(X), i
839 raise IntersectionError(Fmt.no_convergence(S.L1(), self._Tol))
841 def _C(self, X, glA, glB, _C=False, _AB=True):
842 # add the C{_C} items to C{X}, if requested.
843 if _C:
844 A = self._Position(glA, X.sA)
845 B = self._Position(glB, X.sB)
846 s, a = self._Inversa12(A, B)
847 X.set_(latA=A.lat2, lonA=A.lon2,
848 latB=B.lat2, lonB=B.lon2)
849 if _AB:
850 X.set_(sAB=s, aAB=a)
851 else:
852 X.set_(sMM=s, aMM=a)
853 return X
855 def Closest(self, glA, glB, X0=_X000, **_C):
856 '''Find the closest intersection of two geodesic lines.
858 @arg glA: A geodesic line (L{Line<Intersector.Line>}).
859 @arg glB: An other geodesic line (L{Line<Intersector.Line>}).
860 @kwarg X0: Optional I{origin} for I{L1-closeness} (L{XDict}).
861 @kwarg _C: If C{True}, include the lat-/longitudes C{latA},
862 C{lonA}, C{latB}, C{lonB} oon and distances C{sAB}
863 and C{aSB} between the intersections.
865 @return: The intersection (L{XDict}) or C{None} if none found.
867 @raise GeodesicError: Geodesic line B{C{glA}} or B{C{glB}}
868 invalid, incompatible or ill-configured.
870 @raise IntersectionError: No convergence.
871 '''
872 self._xLines(glA, glB)
873 Q, d, S_, i = X0, INF, list(X0._nD1(self._D1)), 0
874 while S_:
875 X, i = self._Basic2(glA, glB, S_.pop(0), i)
876 X = X0._fixCoincident(X)
877 if X.L1(Q) > self.Delta: # X != Q
878 d0 = X.L1(X0)
879 if d0 < self._T1:
880 Q, d, q = X, d0, i
881 break
882 if d0 < d or Q is X0:
883 Q, d, q = X, d0, i
884 X._skip(S_, self._T2D1Delta)
886 return None if Q is X0 else self._C(Q, glA, glB, **_C).set_(sX0=d, iteration=q)
888 def Closest5(self, glA, glB, X0=_X000):
889 '''Find the closest intersection of two geodesic lines.
891 @return: An L{Intersector5Tuple}C{(A, B, sAB, aAB, c)}
892 or C{None} if none found.
894 @see: Method L{Closest} for further details.
895 '''
896 X = self.Closest(glA, glB, X0=X0)
897 return X if X is None else self._In5T(glA, glB, X, X)
899 def _conjDist(self, gl, s, m12=0, M12=1, M21=1, semi=False):
900 # Find semi-/conjugate point relative to s0 which is close to s1.
901 # if semi:
902 # solve for M23 = 0 using dM23 / ds3 = - (1 - M23 * M32) / m23
903 # else:
904 # solve for m23 = 0 using dm23 / ds3 = M32
905 _S2, _abs, _1 = Fsum(s).fsum2_, fabs, _1_0
906 for _ in range(_TRIPS):
907 m13, M13, M31 = self._m12_M12_M21(gl, s)
908 # see "Algorithms for geodesics", eqs. 31, 32, 33.
909 m23 = m13 * M12
910 M32 = M31 * M12
911 if m12: # PYCHOK no cover
912 m23 -= m12 * M13
913 if m13:
914 M32 += (_1 - M13 * M31) * m12 / m13
915 if semi:
916 M23 = M13 * M21
917 # when m12 -> eps, (1 - M12 * M21) -> eps^2, I suppose.
918 if m12 and m13:
919 M23 += (_1 - M12 * M21) * m13 / m12
920 d = m23 * M23 / (_1 - M23 * M32)
921 else:
922 d = -m23 / M32
923 s, d = _S2(d)
924 if _abs(d) <= self._Tol:
925 break
926 return s
928 _gl3 = None
930 @Property
931 def _conjDist3s(self):
932 gl, self._gl3, _D = self._gl3, None, self._cHalf
933 return tuple(self._conjDist(gl, s) for s in (-_D, 0, _D))
935 @_conjDist3s.setter # PYCHOK setter!
936 def _conjDist3(self, gl):
937 # _XLines(gl, gl)
938 self._gl3 = gl
940 def _conjDist3Tt_(self, c, X0=_X000):
941 for s in self._conjDist3s:
942 T = XDict_(s, s * c, c)
943 yield self._Delto(T), T.L1(X0)
945 def _conjDist5(self, azi):
946 gl = self._Line(azi1=azi)
947 s = self._conjDist(gl, self._cHalf)
948 X, _ = self._Basic2(gl, gl, XDict_(s * _0_5, -s * _1_5))
949 return s, (X.L1() - s * _2_0), azi, X.sA, X.sB
951 @Property_RO
952 def Delta(self):
953 '''Get the equality and tiling margin (C{meter}).
954 '''
955 return self._cHalf * _EPSr5 # ~15 Km WGS84
957 def _Delto(self, X):
958 # copy Delta into X, overriding X's default
959 X._Delta = self.Delta # NOT X.set_(self.Delta)
960 return X
962 @Property_RO
963 def _EPS3R(self):
964 return _EPS3 * self.R
966 @Property_RO
967 def _faPI_4(self):
968 return (self.f + _2_0) * self.a * PI_4
970 @Property_RO
971 def _GeodesicLines(self):
972 '''(INTERNAL) Get the C{Geodesic...Line} class(es).
973 '''
974 return type(self._Line()),
976 def _In5T(self, glA, glB, S, X, k2=False, **_2X):
977 # Return an intersection as C{Intersector5Tuple}.
978 A = self._Position(glA, S.sA)
979 B = self._Position(glB, S.sB)
980 if k2:
981 A.set_(k2=X.kA)
982 B.set_(k2=X.kB)
983 s, a = self._Inversa12(A, B)
984 return Intersector5Tuple(A._2X(glA, **_2X),
985 B._2X(glB, **_2X), s, a, X.c, iteration=X.iteration)
987 def _Inverse(self, A, B): # caps=Caps.STANDARD
988 return self._g.Inverse(A.lat2, A.lon2, B.lat2, B.lon2)
990 def Line(self, lat1, lon1, azi1_lat2, *lon2, **name):
991 '''Return a geodesic line from this C{Intersector}'s geodesic, specified by
992 two (goedetic) points or a (goedetic) point and an (initial) azimuth.
994 @arg lat1: Latitude of the first point (C{degrees}).
995 @arg lon1: Longitude of the first point (C{degrees}).
996 @arg azi1_lat2: Azimuth at the first point (compass C{degrees}) if no
997 B{C{lon2}} argument is given, otherwise the latitude of
998 the second point (C{degrees}).
999 @arg lon2: If given, the longitude of the second point (C{degrees}).
1000 @kwarg name: Optional C{B{name}=NN} (C{str}).
1002 @return: A line (from L{geodesic<Intersector.geodesic>}C{.Line} or
1003 C{.InverseLine} method) with C{LINE_CAPS}.
1004 '''
1005 args = self._ll3z4ll(lat1, lon1, azi1_lat2, *lon2)
1006 gl = self._g.InverseLine(*args, caps=Caps.LINE_CAPS) if lon2 else \
1007 self._g.Line( *args, caps=Caps.LINE_CAPS)
1008 if name:
1009 gl.name= name
1010 return gl
1012 def _Line(self, lat1=0, lon1=0, azi1=0):
1013 return self._g.Line(lat1, lon1, azi1, caps=Caps.LINE_CAPS)
1015 def Middle(self, glA, glB, raiser=True, **_C):
1016 '''Get the mid-points on two geodesic line segments.
1018 @arg glA: A geodesic line (L{Line<Intersector.Line>}, 4-C{args}).
1019 @arg glB: An other geodesic line (L{Line<Intersector.Line>}, 4-C{args}).
1020 @kwarg raiser: If C{True}, check that B{C{glA}} and B{C{glB}} are a
1021 4-C{args} L{Line<Intersector.Line>} or C{InverseLine}
1022 (C{bool}).
1023 @kwarg _C: If C{True}, include the lat-/longitudes C{latA}, C{lonA},
1024 C{latB}, C{lonB} of the mid-points and half-lengths C{sA}
1025 and C{sB} in C{meter} of the respective line segments.
1027 @return: The mid-point and half-length of each segment (L{XDict}),
1028 B{C{_C}} above.
1030 @raise GeodesicError: Geodesic line B{C{glA}} or B{C{glB}} invalid,
1031 incompatible, ill-configured or not a 4-C{args
1032 Line} or other C{InverseLine}.
1033 '''
1034 M, _, _ = self._middle3(glA, glB, raiser)
1035 # _ = X._outSide(sA, sB)
1036 return self._C(M, glA, glB, _AB=False, **_C) if _C else M
1038 def _middle3(self, glA, glB, raiser): # in .All
1039 # return segment length C{sA} and C{sB} and the
1040 # center C{X0} of rectangle [sA, sB]
1041 self._xLines(glA, glB, s13=raiser) # need .Distance
1042 sA = glA.Distance()
1043 sB = glB.Distance()
1044 X = XDict_(sA * _0_5, sB * _0_5) # center
1045 return self._Delto(X), sA, sB
1047 def Middle5(self, glA, glB, **raiser):
1048 '''Get the mid-points of two geodesic line segments and distances.
1050 @return: A L{Middle5Tuple}C{(A, B, sMM, aMM, c)}.
1052 @see: Method L{Middle} for further details.
1053 '''
1054 M = self.Middle(glA, glB, _C=True, **raiser)
1055 A, B, s, a, c = self._In5T(glA, glB, M, M, _2X=_M_)
1056 return Middle5Tuple(_llz2G(A, glA, glA), _llz2G(B, glB, glB), s, a, c)
1058 def _m12_M12_M21(self, gl, s):
1059 P = gl.Position(s, outmask=Caps._REDUCEDLENGTH_GEODESICSCALE)
1060 return P.m12, P.M12, P.M21
1062 def Next(self, glA, glB, eps1=None, **_C): # PYCHOK no cover
1063 '''Yield the next intersection of two I{intersecting} geodesic lines.
1065 @arg glA: A geodesic line (L{Line<Intersector.Line>}).
1066 @arg glB: An other geodesic line (L{Line<Intersector.Line>}).
1067 @kwarg eps1: Optional margin for the L{euclid<pygeodesy.euclid>}ean
1068 distance (C{degrees}) between the C{(lat1, lon1)} points
1069 of both lines or C{None} for unchecked.
1070 @kwarg _C: If C{True}, include the lat-/longitudes C{latA}, C{lonA},
1071 C{latB}, C{lonB} of and distances C{sAB} and C{aSB}
1072 between the intersections.
1074 @return: The intersection (L{XDict}) or C{None} if none found.
1076 @raise GeodesicError: Geodesic line B{C{glA}} or B{C{glB}} invalid,
1077 incompatible, ill-configured or C{(lat1, lon1)}
1078 not B{C{eps1}}-equal.
1080 @raise IntersectionError: No convergence.
1082 @note: Offset C{X0} is implicit, zeros.
1083 '''
1084 self._xLines(glA, glB)
1085 if eps1 or _C: # eps
1086 _C = self._xNext(glA, glB, eps1, **_C)
1088 X0, self._conjDist3s = _X000, glA # reset Property
1089 Q, d, S_, i = _XINF, INF, list(X0._nD2(self._D2)), 0
1090 while S_:
1091 X, i = self._Basic2(glA, glB, S_.pop(0), i)
1092 X = X0._fixCoincident(X)
1093 t = X.L1(X0) # == X.L1()
1094 c, z = X.c, (t <= self.Delta) # X == X0
1095 if z:
1096 if not c:
1097 continue
1098 Tt_ = self._conjDist3Tt_(c, X0)
1099 else:
1100 Tt_ = (X, t),
1102 for T, t in Tt_:
1103 if t < d or Q is _XINF:
1104 Q, d, q = T, t, i
1105 i += 1
1107 for s in ((_1_1t if z else _1_0_1t)
1108 if c else _0t):
1109 T = X
1110 if s and c:
1111 s *= self._D2
1112 T = X + (s, s * c) # NOT +=
1113 T._skip(S_, self._T2D2Delta)
1115 return None if Q is _XINF else self._C(Q, glA, glB, **_C).set_(sX0=d, iteration=q)
1117 def Next5(self, glA, glB, **eps1): # PYCHOK no cover
1118 '''Yield the next intersection of two I{intersecting} geodesic lines.
1120 @return: An L{Intersector5Tuple}C{(A, B, sAB, aAB, c)} or C{None}
1121 if none found.
1123 @see: Method L{Next} for further details.
1124 '''
1125 X = self.Next(glA, glB, **eps1)
1126 return X if X is None else self._In5T(glA, glB, X, X)
1128 def _obliqDist4(self):
1129 zx = 45.0
1130 if self.f:
1131 _abs, _cjD5 = fabs, self._conjDist5
1133 _, ds0, z0, _, _ = _cjD5(zx + _1_0)
1134 s1, ds1, z1, sAx, sBx = _cjD5(zx - _1_0)
1135 sx, dsx, zx = s1, _abs(ds1), z1
1136 # find ds(azi) = 0 by secant method
1137 for _ in range(16):
1138 if ds1 == ds0:
1139 break
1140 z = (z0 * ds1 - z1 * ds0) / (ds1 - ds0)
1141 _, ds0, z0 = s1, ds1, z1
1142 s1, ds1, z1, a, b = _cjD5(z)
1143 if _abs(ds1) < dsx:
1144 sx, dsx, zx, sAx, sBx = s1, _abs(ds1), z, a, b
1145 if not dsx:
1146 break
1147 else:
1148 sx, sAx, sBx = self._cHalf, _0_5, -_1_5
1149 return sx, zx, sAx, sBx
1151 def _polarB3(self, lats=False): # PYCHOK no cover
1152 latx = 64.0
1153 lat = _90_0 - latx
1154 if self.f:
1155 _d, _pD2 = fdot, self._polarDist2
1157 s0, lat0 = _pD2(latx - _1_0)
1158 s1, lat1 = _pD2(latx + _1_0)
1159 s2, lat2 = \
1160 sx, latx = _pD2(latx)
1161 prolate = self.f < 0
1162 # solve for ds(lat) / dlat = 0 with a quadratic fit
1163 for _ in range(_TRIPS):
1164 t = (lat1 - lat0), (lat0 - lat2), (lat2 - lat1)
1165 d = _d(t, s2, s1, s0) * _2_0
1166 if not d: # or isnan(d)
1167 break
1168 lat = _d(t, (lat1 + lat0) * s2,
1169 (lat0 + lat2) * s1,
1170 (lat2 + lat1) * s0) / d
1171 s0, lat0 = s1, lat1
1172 s1, lat1 = s2, lat2
1173 s2, lat2 = _pD2(lat)
1174 if (s2 < sx) if prolate else (s2 > sx):
1175 sx, latx = s2, lat2
1176 if lats:
1177 _, lat = _pD2(latx, lat2=True)
1178 sx += sx
1179 else:
1180 sx = self._cHalf
1181 return sx, latx, lat
1183 def _polarDist2(self, lat1, lat2=False):
1184 gl = self._Line(lat1=lat1)
1185 s = self._conjDist(gl, self._faPI_4, semi=True)
1186 if lat2:
1187 lat1 = gl.Position(s, outmask=Caps.LATITUDE).lat2
1188 return s, lat1
1190 def _Position(self, gl, s):
1191 return gl.Position(s, outmask=Caps._STD_LINE)
1193 def Segment(self, glA, glB, proven=None, raiser=True, **_C):
1194 '''Find the intersection between two geodesic line segments.
1196 @kwarg proven: Conjecture is that whenever two geodesic line
1197 segments intersect, the intersection is the
1198 one closest to the mid-points of segments.
1199 If so, use C{B{proven}=True}, otherwise find
1200 intersections on the segments and specify
1201 C{B{proven}=None} to return the first or
1202 C{B{proven}=False} the closest (C{bool}).
1203 @kwarg raiser: If C{True}, check that B{C{glA}} and B{C{glB}}
1204 are an 4-C{args} L{Line<Intersector.Line>} or
1205 C{InverseLine} (C{bool}).
1206 @kwarg _C: If C{True}, include the lat-/longitudes C{latA},
1207 C{lonA}, C{latB}, C{lonB} of and distances C{sAB}
1208 and C{aSB} between the intersections.
1210 @return: The intersection of the segments (L{XDict}) with
1211 indicators C{kA}, C{kB} and C{k} set or if no
1212 intersection is found, C{None}.
1214 @raise GeodesicError: Geodesic line B{C{glA}} or B{C{glB}}
1215 invalid, incompatible, ill-configured or
1216 not an C{InverseLine} or 4-C{args Line}.
1218 @raise IntersectionError: No convergence.
1220 @see: Method L{Middle<Intersector.Middle>} for further details.
1221 '''
1222 X0, sA, sB = self._middle3(glA, glB, raiser)
1223 Q = self.Closest(glA, glB, X0) # to X0
1224 if Q is not None:
1225 if Q.c: # anti-/parallel
1226 Q._fixSegment(sA, sB)
1227 # are rectangle [sA, sB] corners further from X0 than Q?
1228 d0 = X0.L1(Q)
1229 if Q._outSide(sA, sB) and d0 <= X0.L1() and not proven:
1230 i = Q.iteration
1231 for T in X0._corners(sA, sB, self._T2):
1232 X, i = self._Basic2(glA, glB, T, i)
1233 X = T._fixCoincident(X)
1234 if not X._outSide(sA, sB):
1235 d = X0.L1(X)
1236 if d < d0 or proven is None:
1237 Q, d0 = X, d
1238 if proven is None:
1239 break
1240 Q.set_(iteration=i)
1242 Q = self._C(Q, glA, glB, **_C).set_(sX0=d0)
1243 return Q
1245 def Segment5(self, glA, glB, **proven_raiser):
1246 '''Find the intersection between two geodesic line segments.
1248 @return: An L{Intersector5Tuple}C{(A, B, sAB, aAB, c)}
1249 or C{None} if none found.
1251 @see: Method L{Segment} for further details.
1252 '''
1253 X = self.Segment(glA, glB, **proven_raiser)
1254 return X if X is None else self._In5T(glA, glB, X, X, k2=True)
1256 def _Spherical(self, glA, glB, S):
1257 '''(INTERNAL) Get solution based from a spherical triangle.
1258 '''
1259 # threshold for coincident geodesics/intersections ~4.3 nm WGS84.
1260 A = self._Position(glA, S.sA)
1261 B = self._Position(glB, S.sB)
1262 D = self._Inverse(A, B)
1264 a, da = _diff182(A.azi2, D.azi1) # interior angle at A
1265 b, db = _diff182(B.azi2, D.azi2) # exterior angle at B
1266 c, dc = _diff182(a, b)
1267 if fsum1_(dc, db, -da, c) < 0: # inverted triangle
1268 a, da = -a, -da
1269 b, db = -b, -db
1270 sa, ca = _sincos2de(a, da)
1271 sb, cb = _sincos2de(b, db)
1273 e, z, _abs = _EPS3, D.s12, fabs
1274 if _abs(z) <= self._EPS3R: # XXX z <= ...
1275 sA = sB = 0 # at intersection
1276 c = 1 if _abs(sa - sb) <= e and _abs(ca - cb) <= e else (
1277 -1 if _abs(sa + sb) <= e and _abs(ca + cb) <= e else 0)
1278 elif _abs(sa) <= e and _abs(sb) <= e: # coincident
1279 sA = ca * z * _0_5 # choose mid-point
1280 sB = -cb * z * _0_5
1281 c = 1 if (ca * cb) > 0 else -1
1282 # alt1: sA = ca * z; sB = 0
1283 # alt2: sB = -cb * z; sA = 0
1284 else: # general case
1285 sz, cz = sincos2(z / self.R)
1286 # [SKIP: Divide args by |sz| to avoid possible underflow
1287 # in {sa, sb} * sz; this is probably not necessary].
1288 # Definitely need to treat sz < 0 (z > PI*R) correctly in
1289 # order to avoid some convergence failures in _Basic2.
1290 sA = atan2(sb * sz, sb * ca * cz - sa * cb) * self.R
1291 sB = atan2(sa * sz, -sa * cb * cz + sb * ca) * self.R
1292 c = 0
1293 return XDict_(sA, sB, c) # no ._Delto
1295 @Property_RO
1296 def _T2D1Delta(self):
1297 return self._T2d3Delta(self._D1)
1299 @Property_RO
1300 def _T2D2Delta(self):
1301 return self._T2d3Delta(self._D2)
1303 def _T2d3Delta(self, d3):
1304 return self._T2 - d3 - self.Delta
1306 @Property_RO
1307 def _Tol(self): # convergence tolerance
1308 return self._cHalf * pow(EPS, 0.75) # _0_75
1310 def toStr(self, **prec_sep_name): # PYCHOK signature
1311 '''Return this C{Intersector} as string.
1313 @see: L{Ellipsoid.toStr<pygeodesy.ellipsoids.Ellipsoid.toStr>}
1314 for further details.
1316 @return: C{Intersector} (C{str}).
1317 '''
1318 return self._instr(props=(Intersector.geodesic,), **prec_sep_name)
1320 def _xLines(self, glA, glB, s13=False):
1321 # check two geodesic lines vs this geodesic
1322 C, gls = Caps.LINE_CAPS, dict(glA=glA, glB=glB)
1323 _xinstanceof(*self._GeodesicLines, **gls)
1324 for n, gl in gls.items():
1325 try:
1326 _xgeodesics(gl.geodesic, self.geodesic)
1327 if s13 and not isfinite(gl.s13): # or not gl.caps & Caps.DISTANCE_IN
1328 t = gl.geodesic.InverseLine.__name__
1329 raise TypeError(_not_(_an(t)))
1330 c = gl.caps & C
1331 if c != C: # not gl.caps_(C)
1332 c, C, x = map1(bin, c, C, _xor(c, C))
1333 x = _SPACE_(_xor.__name__, repr(x))[1:]
1334 raise GeodesicError(caps=c, LINE_CAPS=C, txt=x)
1335 except Exception as x:
1336 raise GeodesicError(n, gl, cause=x)
1339class Intersectool5Tuple(_NamedTuple):
1340 '''5-Tuple C{(A, B, sAB, aAB, c)} with C{A} and C{B} the C{Position}
1341 of the intersection on each geodesic line, the distance C{sAB}
1342 between C{A} and C{B} in C{meter}, the angular distance C{aAB} in
1343 C{degrees} and coincidence indicator C{c} (C{int}), see L{XDict}.
1345 @note: C{A} and C{B} are each a C{GDict} with C{lat1}, C{lon1} and
1346 C{azi1} or C{lat2}, C{lon2} from the geodesic line C{glA}
1347 respectively C{glB} and the intersection location in C{latX},
1348 C{lonX}, distance C{s1X} in C{meter} and angular distance
1349 C{a1M} in C{degrees} and the segment indicator C{kX}. See
1350 L{XDict} for more details.
1351 '''
1352 _Names_ = (_A_, _B_, _sAB_, 'aAB', _c_)
1353 _Units_ = (_Pass, _Pass, Meter, Degrees, Int)
1356class Intersector5Tuple(Intersectool5Tuple):
1357 '''5-Tuple C{(A, B, sAB, aAB, c)} with C{A} and C{B} the C{Position}
1358 of the intersection on each geodesic line, the distance C{sAB}
1359 between C{A} and C{B} in C{meter}, angular distance C{aAB} in
1360 C{degrees} and coincidence indicator C{c} (C{int}), see L{XDict}.
1362 @note: C{A} and C{B} are each a C{GeodesicLine...Position} for
1363 C{outmask=Caps.STANDARD} with the intersection location in
1364 C{latX}, C{lonX}, azimuth in C{aziX}, distance C{s1X} in
1365 C{meter} and angular distance C{a1X} in C{degrees} and the
1366 segment indicator C{kX}. See L{XDict} for more details.
1367 '''
1368 _Names_ = Intersectool5Tuple._Names_
1371class Middle5Tuple(Intersectool5Tuple):
1372 '''5-Tuple C{(A, B, sMM, aMM, c)} with C{A} and C{B} the I{line segments}
1373 including the mid-point location in C{latM}, C{lonM}, distance C{s1M}
1374 in C{meter} and angular distance C{a1M} in C{degrees}, the distance
1375 between both mid-points C{sMM} in C{meter} and angular distance C{aMM}
1376 in C{degrees} and coincidence indicator C{c} (C{int}). See L{XDict}
1377 for more details.
1378 '''
1379 _Names_ = (_A_, _B_, 'sMM', 'aMM', _c_)
1382class _List(list):
1384 _Delta = 0 # equality margin
1386 def __init__(self, Delta):
1387 self._Delta = Delta
1388# list.__init__(self)
1390 def __contains__(self, other):
1391 # handle C{if X in this: ...}
1392 a, b = other.sA, other.sB
1393 D, _D1 = self._Delta, _L1
1394 for X in self:
1395 if _D1(X.sA - a, X.sB - b) <= D:
1396 return True
1397 return False
1399 def addend(self, X, *d0_i):
1400 # append an item, updated
1401 if d0_i:
1402 d0, i = d0_i
1403 X.set_(sX0=d0, iteration=i)
1404 self.append(X)
1405 return X.sX0
1407 def sorter(self, sMaX0, dot_C, glA, glB, **_C):
1408 # trim and sort the X items
1410 def _key(X):
1411 return X.sX0 # rank of X
1413 t = (X for X in self if X.sX0 <= sMaX0)
1414 for X in sorted(t, key=_key):
1415 yield dot_C(X, glA, glB, **_C) if _C else X
1418def _L1(a, b):
1419 '''(INTERNAL) Return the I{L1} distance.
1420 '''
1421 return fabs(a) + fabs(b)
1424def _llz2G(G, gl, il):
1425 '''(INTERNAL) Set C{InverseLine} attrs in C{G}, a C{GDict}.
1426 '''
1427 return G.set_(lat1=gl.lat1, lon1=gl.lon1, azi1=il.azi1, a12=il.a13, # .Arc()
1428 lat2=gl.lat2, lon2=gl.lon2, azi2=il.azi2, s12=il.s13) # .Distance()
1431if __name__ == '__main__': # MCCABE 14
1433 from pygeodesy import printf
1435 def _main(args):
1437 from pygeodesy import GeodesicExact
1438 from pygeodesy.internals import _plural, _usage
1439 from pygeodesy.interns import _COLONSPACE_, _DASH_, _DOT_, \
1440 _EQUAL_, _i_, _n_, _version_, _X_
1441 import re
1443 class XY0(Float):
1444 pass
1446 def _opts(_h): # for _usage()
1447 ll4 = ' latA1 lonA1'
1448 ll4 += ll4.replace('1', '2')
1449 ll4 += ll4.replace(_A_, _B_)
1450 llz = _SPACE_(NN, _latA_, _lonA_, 'aziA')
1451 llz2 = llz + llz.replace(_A_, _B_)
1452 return dict(opts='-Verbose|V--version|v--help|h--Tool|T--Check|C-R meter-',
1453 alts=((_c_ + llz2),
1454 (_i_ + ll4),
1455 (_m_ + ll4),
1456 (_M_ + ll4),
1457 (_n_ + llz + ' aziB'),
1458 ('o' + llz2 + ' x0 y0')),
1459 help=_h if isinstance(_h, str) else NN)
1461 def _starts(opt, arg, n=0):
1462 return opt.startswith(arg) and len(arg.lstrip(_DASH_)) > n
1464 _isopt = re.compile('^[-]+[a-z]*$', flags=re.IGNORECASE).match
1466 I = Intersector(GeodesicExact()) # PYCHOK I
1467 M = m = _R = None
1468 _T = _V = _h = _C = False
1470 while args and _isopt(args[0]):
1471 arg = args.pop(0)
1472 if arg == _C__ or _starts('--Check', arg):
1473 _C = True
1474 elif arg == _c__:
1475 M, m = I.Closest, 6 # latA lonA aziA latB lonB aziB
1476 elif arg == '-h' or _starts('--help', arg):
1477 _h = args[0] if args and _isopt(args[0]) else True
1478 elif arg == _i__:
1479 M, m = I.Segment, 8 # latA1 lonA1 latA2 lonA2 latB1 lonB1 latB2 lonB2
1480 elif arg == '-m':
1481 M, m = I.Middle, 8 # latA1 lonA1 latA2 lonA2 latB1 lonB1 latB2 lonB2
1482 _R = None
1483 elif arg == '-M':
1484 M, m = I.Middle5, 8 # latA1 lonA1 latA2 lonA2 latB1 lonB1 latB2 lonB2
1485 _R = _C = None
1486 elif arg == _n__:
1487 M, m = I.Next, 4 # latA lonA aziA aziB
1488 elif arg == _o__:
1489 M, m = I.Closest, 8 # latA lonA aziA latB lonB aziB x0 y0
1490 elif arg == _R__ and args:
1491 _R = args.pop(0)
1492 elif arg == '-T' or _starts('--Tool', arg):
1493 I = Intersectool() # PYCHOK I
1494 if _V:
1495 I.verbose = True
1496 if I.IntersectTool in (_PYGEODESY_INTERSECTTOOL_, None): # not set
1497 I.IntersectTool = '/opt/local/bin/IntersectTool' # '/opt/local/Cellar/geographiclib/2.3/bin/IntersectTool' # HomeBrew
1498 M, _T = None, True
1499 elif arg == '-V' or _starts('--Verbose', arg):
1500 _V = True
1501 if _T:
1502 I.verbose = True
1503 elif arg == '-v' or _starts('--version', arg):
1504 printf(_COLONSPACE_(*((_version_, I.version) if _T else
1505 (__version__, repr(I)))))
1506 else:
1507 raise ValueError('invalid option %r' % (arg,))
1509 if _h or M is None:
1510 printf(_usage(__file__, **_opts(_h)), nl=1)
1511# exit(0)
1512 else:
1513 n = len(args)
1514 if n < m:
1515 n = _plural('only %s arg' % (n,), n) if n else 'no args'
1516 raise ValueError('%s, need %s' % (n, m))
1517 args[:] = args[:m]
1519 kwds = dict(_C=True) if _C else {}
1520 if M == I.Next: # -n
1521 # get latA lonA aziA latA lonA aziB
1522 args[3:] = args[:2] + args[3:4]
1523 elif M == I.Closest and m > 6: # -o
1524 y0 = Meter(y0=args.pop())
1525 x0 = Meter(x0=args.pop())
1526 kwds.update(X0=XDict_(x0, y0))
1527 if _R:
1528 m = Meter_(_R, name=_R__, low=0)
1529 kwds.update(sMaX0=m)
1530 M = I.All
1532 n = len(args) // 2
1533 glA = I.Line(*args[:n])
1534 glB = I.Line(*args[n:])
1536 m = _DOT_(I.__class__.__name__, M.__name__)
1537 if _V:
1538 X = _SPACE_(_X_, _EQUAL_, m)
1539 printf(unstr(X, glA, glB, **kwds))
1541 X = M(glA, glB, **kwds)
1542 if X is None or isinstance(X, (XDict, tuple)):
1543 printf(_COLONSPACE_(m, repr(X)))
1544 else:
1545 for i, X in enumerate(X):
1546 printf(_COLONSPACE_(Fmt.INDEX(m, i), repr(X)))
1548 from sys import argv, stderr
1549 try:
1550 if len(argv) == 2 and argv[1] == _HASH_:
1551 from pygeodesy.internals import _usage_argv
1553 s = _SPACE_(*_usage_argv(__file__))
1554 for t in ('-h', '-h -n',
1555 '-c 0 0 45 40 10 135',
1556 '-C -c 0 0 45 40 10 135',
1557 '-T -R 2.6e7 -c 0 0 45 40 10 135',
1558 '-c 50 -4 -147.7 0 0 90',
1559 '-C -c 50 -4 -147.7 0 0 90',
1560 '# % echo 0 0 10 10 50 -4 50S 4W | IntersectTool -i -p 0 -C',
1561 '# -631414 5988887 0 -3',
1562 '# -4.05187 -4.00000 -4.05187 -4.00000 0',
1563 '-C -m 0 0 10 10 50 -4 50S 4W',
1564 '-M 0 0 10 10 50 -4 50S 4W',
1565 '-i 0 0 10 10 50 -4 50S 4W',
1566 '-T -i 0 0 10 10 50 -4 50S 4W',
1567 '-C -i 0 0 10 10 50 -4 50S 4W',
1568 '-T -C -i 0 0 10 10 50 -4 50S 4W',
1569 '-V -T -i 0 0 10 10 50 -4 -50 -4',
1570 '-C -R 4e7 -c 50 -4 -147.7 0 0 90',
1571 '-T -C -R 4e7 -c 50 -4 -147.7 0 0 90',
1572 '-R 4e7 -i 0 0 10 10 50 -4 -50 -4',
1573 '-T -R 4e7 -i 0 0 10 10 50 -4 -50 -4'):
1574 if t.startswith(_HASH_):
1575 printf(t, nl=int(t[2] == '%'))
1576 else:
1577 printf(_SPACE_(_HASH_, s, t), nl=1)
1578 argv[1:] = t = t.split()
1579 _main(t)
1580 else:
1581 _main(argv[1:])
1583 except Exception as x:
1584 x = _SPACE_(x, NN, _HASH_, *argv)
1585 printf(x, file=stderr, nl=1)
1586 if '-V' in x or _MODS.errors.exception_chaining():
1587 raise
1588 exit(1)
1590# % env PYGEODESY_INTERSECTTOOL=... python3 -m pygeodesy.geodesici -h
1591#
1592# usage: python3 -m ....pygeodesy.geodesici [--Verbose | -V] [--version | -v] [--help | -h] [--Tool | -T] [--Check | -C] [-R meter]
1593# [-c latA lonA aziA latB lonB aziB |
1594# -i latA1 lonA1 latA2 lonA2 latB1 lonB1 latB2 lonB2 |
1595# -m latA1 lonA1 latA2 lonA2 latB1 lonB1 latB2 lonB2 |
1596# -M latA1 lonA1 latA2 lonA2 latB1 lonB1 latB2 lonB2 |
1597# -n latA lonA aziA aziB |
1598# -o latA lonA aziA latB lonB aziB x0 y0]
1600# % python3 -m ....pygeodesy.geodesici -h -n
1601#
1602# usage: python3 -m ....pygeodesy.geodesici -n latA lonA aziA aziB
1604# % python3 -m ....pygeodesy.geodesici -c 0 0 45 40 10 135
1605# Intersector.Closest: XDict(c=0, sA=3862290.547855, sB=2339969.547699, sX0=6202260.095554)
1607# % python3 -m ....pygeodesy.geodesici -C -c 0 0 45 40 10 135
1608# Intersector.Closest: XDict(aAB=0.0, c=0, latA=23.875306, latB=23.875306, lonA=26.094096, lonB=26.094096, sA=3862290.547855, sAB=0.0, sB=2339969.547699, sX0=6202260.095554)
1610# % env PYGEODESY_INTERSECTTOOL=...python3 -m ....pygeodesy.geodesici -T -R 2.6e7 -c 0 0 45 40 10 135
1611# Intersectool.All[0]: XDict(c=0, sA=3862290.547855, sB=2339969.547699, sX0=6202260.095554)
1613# % python3 -m ....pygeodesy.geodesici -c 50 -4 -147.7 0 0 90
1614# Intersector.Closest: XDict(c=0, sA=6058048.653081, sB=-3311252.995823, sX0=9369301.648903)
1616# % python3 -m ....pygeodesy.geodesici -C -c 50 -4 -147.7 0 0 90
1617# Intersector.Closest: XDict(aAB=0.0, c=0, latA=0.0, latB=-0.0, lonA=-29.745492, lonB=-29.745492, sA=6058048.653081, sAB=0.0, sB=-3311252.995823, sX0=9369301.648903)
1619# % echo 0 0 10 10 50 -4 50S 4W | IntersectTool -i -p 0 -C
1620# -631414 5988887 0 -3
1621# -4.05187 -4.00000 -4.05187 -4.00000 0
1623# % python3 -m ....pygeodesy.geodesici -C -m 0 0 10 10 50 -4 50S 4W
1624# Intersector.Middle: XDict(aMM=10.262308, c=0, latA=5.019509, latB=0.036282, lonA=4.961883, lonB=-4.0, sA=782554.549609, sB=5536835.161499, sMM=1138574.546746, sX0=0.0)
1626# % python3 -m ....pygeodesy.geodesici -M 0 0 10 10 50 -4 50S 4W
1627# Intersector.Middle5: Middle5Tuple(A=GDict(a12=14.106434, a1M=7.053396, azi1=44.75191, azi2=45.629037, aziM=44.969535, lat1=0.0, lat2=10.0, latM=5.019509, lon1=0.0, lon2=10.0, lonM=4.961883, s12=1565109.099218, s1M=782554.549609), B=GDict(a12=99.810444, a1M=49.869061, azi1=180.0, azi2=180.0, aziM=180.0, lat1=50.0, lat2=-50.0, latM=0.036282, lon1=-4.0, lon2=-4.0, lonM=-4.0, s12=11073670.322999, s1M=5536835.161499), sMM=1138574.546746, aMM=10.262308, c=0)
1629# % python3 -m ....pygeodesy.geodesici -i 0 0 10 10 50 -4 50S 4W
1630# Intersector.Segment: XDict(c=0, k=-3, kA=-1, kB=0, sA=-631414.26877, sB=5988887.278435, sX0=1866020.935315)
1632# % env PYGEODESY_INTERSECTTOOL=... python3 -m ....pygeodesy.geodesici -T -i 0 0 10 10 50 -4 50S 4W
1633# Intersectool.Segment: XDict(c=0, k=-3, kA=-1, kB=0, sA=-631414.26877, sB=5988887.278435)
1635# % python3 -m ....pygeodesy.geodesici -C -i 0 0 10 10 50 -4 50S 4W
1636# Intersector.Segment: XDict(aAB=0.0, c=0, k=-3, kA=-1, kB=0, latA=-4.051871, latB=-4.051871, lonA=-4.0, lonB=-4.0, sA=-631414.26877, sAB=0.0, sB=5988887.278435, sX0=1866020.935315)
1638# % env PYGEODESY_INTERSECTTOOL=... python3 -m ....pygeodesy.geodesici -T -C -i 0 0 10 10 50 -4 50S 4W
1639# Intersectool.Segment: XDict(c=0, k=-3, kA=-1, kB=0, latA=-4.051871, latB=-4.051871, lonA=-4.0, lonB=-4.0, sA=-631414.26877, sAB=0.0, sB=5988887.278435)
1641# % env PYGEODESY_INTERSECTTOOL=... python3 -m ....pygeodesy.geodesici -V -T -i 0 0 10 10 50 -4 -50 -4
1642# Intersectool@1: /opt/local/bin/IntersectTool --version (invoke)
1643# Intersectool@1: '/opt/local/bin/IntersectTool: GeographicLib version 2.3' (0)
1644# Intersectool@1: /opt/local/bin/IntersectTool: GeographicLib version 2.3 (0)
1645# X = Intersectool.Segment(GDict(lat1=0.0, lat2=10.0, lon1=0.0, lon2=10.0), GDict(lat1=50.0, lat2=-50.0, lon1=-4.0, lon2=-4.0))
1646# Intersectool@2: /opt/local/bin/IntersectTool -E -p 10 -i \ 0.0 0.0 10.0 10.0 50.0 -4.0 -50.0 -4.0 (Segment)
1647# Intersectool@2: '-631414.2687702414 5988887.2784352796 0 -3' (0)
1648# Intersectool@2: sA=-631414.2687702414, sB=5988887.2784352796, c=0, k=-3 (0)
1649# Intersectool.Segment: XDict(c=0, k=-3, kA=-1, kB=0, sA=-631414.26877, sB=5988887.278435)
1651# % python3 -m ....pygeodesy.geodesici -C -R 4e7 -c 50 -4 -147.7 0 0 90
1652# Intersector.All[0]: XDict(aAB=0.0, c=0, latA=0.0, latB=-0.0, lonA=-29.745492, lonB=-29.745492, sA=6058048.653081, sAB=0.0, sB=-3311252.995823, sX0=9369301.648903)
1653# Intersector.All[1]: XDict(aAB=0.0, c=0, latA=0.0, latB=0.0, lonA=150.046964, lonB=150.046964, sA=-13941907.021445, sAB=0.0, sB=16703151.659744, sX0=30645058.681189)
1654# Intersector.All[2]: XDict(aAB=0.0, c=0, latA=-0.0, latB=-0.0, lonA=-30.16058, lonB=-30.16058, sA=-33941862.69597, sAB=0.0, sB=-3357460.370268, sX0=37299323.066238)
1655# Intersector.All[3]: XDict(aAB=0.0, c=0, latA=-0.0, latB=0.0, lonA=150.046964, lonB=150.046964, sA=-13941907.021445, sAB=0.0, sB=-23371865.025835, sX0=37313772.047279)
1657# % env PYGEODESY_INTERSECTTOOL=... python3 -m ....pygeodesy.geodesici -T -C -R 4e7 -c 50 -4 -147.7 0 0 90
1658# Intersectool.All[0]: XDict(c=0, latA=-0.0, latB=-0.0, lonA=-29.745492, lonB=-29.745492, sA=6058048.653081, sAB=0.0, sB=-3311252.995823, sX0=9369301.648903)
1659# Intersectool.All[1]: XDict(c=0, latA=0.0, latB=0.0, lonA=150.046964, lonB=150.046964, sA=-13941907.021445, sAB=0.0, sB=16703151.659744, sX0=30645058.681189)
1660# Intersectool.All[2]: XDict(c=0, latA=-0.0, latB=-0.0, lonA=-30.16058, lonB=-30.16058, sA=-33941862.69597, sAB=0.0, sB=-3357460.370268, sX0=37299323.066238)
1661# Intersectool.All[3]: XDict(c=0, latA=-0.0, latB=0.0, lonA=150.046964, lonB=150.046964, sA=-13941907.021445, sAB=0.0, sB=-23371865.025835, sX0=37313772.047279)
1663# % python3 -m ....pygeodesy.geodesici -R 4e7 -i 0 0 10 10 50 -4 -50 -4
1664# Intersector.All[0]: XDict(c=0, sA=-631414.26877, sB=5988887.278435, sX0=1866020.935315)
1665# Intersector.All[1]: XDict(c=0, sA=19422725.117572, sB=-14062417.105648, sX0=38239422.83511)
1666# Intersector.All[2]: XDict(c=0, sA=19422725.117572, sB=25945445.811603, sX0=39048781.218067)
1667# Intersector.All[3]: XDict(c=0, sA=39476927.464575, sB=5894074.699478, sX0=39051612.452944)
1669# % env PYGEODESY_INTERSECTTOOL=... python3 -m ....pygeodesy.geodesici -T -R 4e7 -i 0 0 10 10 50 -4 -50 -4
1670# Intersectool.All[0]: XDict(c=0, sA=-631414.26877, sB=5988887.278435, sX0=1862009.05513)
1671# Intersectool.All[1]: XDict(c=0, sA=19422725.117572, sB=-14062417.105648, sX0=38243434.715295)
1672# Intersectool.All[2]: XDict(c=0, sA=19422725.117572, sB=25945445.811603, sX0=39044769.337882)
1673# Intersectool.All[3]: XDict(c=0, sA=39476927.464575, sB=5894074.699478, sX0=39047600.57276)
1676# **) MIT License
1677#
1678# Copyright (C) 2024-2024 -- mrJean1 at Gmail -- All Rights Reserved.
1679#
1680# Permission is hereby granted, free of charge, to any person obtaining a
1681# copy of this software and associated documentation files (the "Software"),
1682# to deal in the Software without restriction, including without limitation
1683# the rights to use, copy, modify, merge, publish, distribute, sublicense,
1684# and/or sell copies of the Software, and to permit persons to whom the
1685# Software is furnished to do so, subject to the following conditions:
1686#
1687# The above copyright notice and this permission notice shall be included
1688# in all copies or substantial portions of the Software.
1689#
1690# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
1691# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
1692# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
1693# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR
1694# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
1695# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
1696# OTHER DEALINGS IN THE SOFTWARE.