Coverage for pygeodesy/geodesici.py: 91%
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2# -*- coding: utf-8 -*-
4u'''Classes L{Intersectool} and L{Intersector} to find the intersections of two geodesic lines or line segments.
6Class 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>}.
9Class 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}.
12Set env variable C{PYGEODESY_INTERSECTTOOL} to the (fully qualified) path of the C{IntersectTool} executable. For usage
13and some examples run C{"env PYGEODESY_INTERSECTTOOL=<IntersectTool-path> python3 -m pygeodesy.geodesici --help"}.
15Both L{Intersectool} and L{Intersector} provide methods C{All}, C{Closest}, C{Next} and C{Segment} and produce
16L{XDict} instances with 4 or more items. Adjacent methods C{All5}, C{Closest5}, C{Next5} and C{Segment} return
17or yield L{Intersectool5Tuple} or L{Intersector5Tuple}s with the lat-, longitude and azimuth of each intersection
18as an extended, geodesic C{Position}-like L{GDict} instance.
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 _45_0, _64_0, _90_0, isfinite, \
33 _EPSjam # PYCHOK used!
34from pygeodesy.ellipsoids import _EWGS84, Fmt, unstr
35from pygeodesy.errors import GeodesicError, IntersectionError, _an, \
36 _xgeodesics, _xkwds_get, _xkwds_kwds, \
37 _xkwds_pop2
38# from pygeodesy.errors import exception_chaining # _MODS
39from pygeodesy.fmath import euclid, fdot
40from pygeodesy.fsums import Fsum, fsum1_, _ceil
41from pygeodesy.interns import NN, _A_, _B_, _c_, _COMMASPACE_, _HASH_, \
42 _M_, _not_, _SPACE_, _too_
43from pygeodesy.karney import Caps, _diff182, GDict, _sincos2de, _Xables
44from pygeodesy.lazily import _ALL_DOCS, _ALL_LAZY, _ALL_MODS as _MODS
45from pygeodesy.named import ADict, _NamedBase, _NamedTuple, _Pass
46# from pygeodesy.namedTuples import _LL4Tuple # _MODS
47from pygeodesy.props import deprecated_method, Property, \
48 Property_RO, property_RO, property_ROver
49from pygeodesy.solveBase import _SolveCapsBase, pairs
50# from pygeodesy.streprs import pairs # from .solveBase
51# from pygeodesy.streprs import Fmt, unstr # from .ellipsoids
52from pygeodesy.units import Azimuth as Azi, Degrees, Float, Int, \
53 _isDegrees, Lat, Lon, Meter, Meter_
54from pygeodesy.utily import atan2, sincos2, fabs, radians
56# from math import ceil as _ceil, fabs, radians # .fsums, .utily
58__all__ = _ALL_LAZY.geodesici
59__version__ = '24.12.22'
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
80class XDict(ADict):
81 '''4+Item result from L{Intersectool} and L{Intersector} methods
82 C{All}, C{Closest}, C{Next} and C{Segment} with the intersection
83 offsets C{sA}, C{sB} and C{sX0} in C{meter} and the coincidence
84 indicator C{c}, an C{int}, +1 for parallel, -1 for anti-parallel
85 or 0 otherwise.
87 Offsets C{sA} and C{sB} are distances measured I{along} geodesic
88 line C{glA} respectively C{glB}, but C{sX0} is the I{L1-distance}
89 between the intersection and the I{origin} C{X0}.
91 If present, distance C{sAB} and angular distance C{aAB} represent
92 the difference between the intersection point on geodesic lines
93 C{glA} and C{glB} in C{meter} respectively C{degrees}, typically
94 below C{5e-9 meter} or C{5 nm} and C{5e-14 degrees} or C{1 n"}.
96 For segments, indicators C{kA} and C{kB} are C{0} if the segments
97 intersect or C{-1} or C{+1} if the intersection is I{before} the
98 start, respectively I{after} the end of the segment, similar to
99 L{Intersection3Tuple<Intersection3Tuple>}. Segment indicator
100 C{k} is I{Karney}'s C{segmode}, equal C{kA * 3 + kB}.
101 '''
102 _Delta = EPS # default margin, see C{Intersector._Delto}
104 def __add__(self, other):
105 X = _copy(self)
106 X += other
107 return X
109 def __eq__(self, other):
110 return not self.__ne__(other)
112 def __iadd__(self, other):
113 if isinstance(other, tuple): # and len(other) == 2:
114 a, b = other
115 else:
116 # _xinstanceof(XDict, other=other)
117 a = other.sA
118 b = other.sB
119 if other.c:
120 self.c = other.c
121 self.sA += a # PYCHOK sA
122 self.sB += b # PYCHOK sB
123 return self
125 def __le__(self, other):
126 # _xinstanceof(XDict, other=other)
127 return self == other or self < other
129 def __lt__(self, other):
130 # _xinstanceof(XDict, other=other)
131 return (self.sA < other.sA or (self.sA == other.sA and # PYCHOK sA
132 self.sB < other.sB) and self != other) # PYCHOK sB
134 def __ne__(self, other):
135 # _xinstanceof(XDict, other=other)
136 return self is not other and self.L1(other) > self._Delta
138 def _corners(self, sA, sB, T2):
139 # yield all corners further than C{T2}
140 a, b = self.sA, self.sB # PYCHOK sA, sB
141 for x in (0, sA):
142 for y in (0, sB):
143 if _L1(x - a, y - b) >= T2:
144 yield XDict_(x, y)
146 def _fixCoincident(self, X, c0=0):
147 # return the mid-point if C{X} is anti-/parallel
148 c = c0 or X.c
149 if c:
150 s = (self.sA - X.sA + # PYCHOK sA
151 (self.sB - X.sB) * c) * _0_5 # PYCHOK sB
152 X = X + (s, s * c) # NOT +=
153 return X
155 def _fixSegment(self, sA, sB): # PYCHOK no cover
156 # modify this anti-/parallel C{XDict}
157 a, b, c = self.sA, self.sB, self.c # PYCHOK sA, sB, c
159 def _g(): # intersection in smallest gap
160 if c > 0: # distance to [A, B] is |(a - b) - (A - B)|
161 t = a - b # consider corners [0, sB] and [sA, 0]
162 t = fabs(t + sB) < fabs(t - sA)
163 s = a + b
164 else: # distance to [A, B] is |(a + b) - (A + B)|
165 t = a + b # consider corner [0, 0] and [sA, sB]
166 t = fabs(t) < fabs(t - (sA + sB))
167 s = sB + (a - b)
168 return (sB if t else sA) - s
170 ta = -a
171 tb = sA - a
172 tc = -c * b
173 td = -c * (b - sB)
175 ga = 0 <= (b + c * ta) <= sB
176 gb = 0 <= (b + c * tb) <= sB
177 gc = 0 <= (a + tc) <= sA
178 gd = 0 <= (a + td) <= sA
180 # test opposite rectangle sides first
181 s = ((ta + tb) if ga and gb else (
182 (tc + td) if gc and gd else (
183 (ta + tc) if ga and gc else (
184 (ta + td) if ga and gd else (
185 (tb + tc) if gb and gc else (
186 (tb + td) if gb and gd else _g())))))) * _0_5
187 self += s, s * c
189 @property_RO
190 def _is00(self):
191 return not (self.sA or self.sB) # PYCHOK sA, sB
193 def L1(self, other=None):
194 '''Return the C{L1} distance.
195 '''
196 a, b = self.sA, self.sB # PYCHOK sA, sB
197 if other is not None:
198 # _xinstanceof(XDict, other=other)
199 a -= other.sA
200 b -= other.sB
201 return _L1(a, b)
203 def _nD1(self, D1):
204 # yield the C{Closest} starts
205 D_ = 0, D1, -D1
206 for a, b in zip((0, 1, -1, 0, 0),
207 (0, 0, 0, 1, -1)):
208 yield self + (D_[a], D_[b])
210 def _nD2(self, D2):
211 # yield the C{Next} starts
212 D22 = D2 * _2_0
213 D_ = 0, D2, D22, -D22, -D2
214 for a, b in zip((-1, -1, 1, 1, -2, 0, 2, 0),
215 (-1, 1, -1, 1, 0, 2, 0, -2)):
216 yield self + (D_[a], D_[b])
218 def _nmD3(self, n, m, D3): # d3 / 2
219 # yield the C{All} starts
220 yield self
221 for i in range(n, m, 2):
222 for j in range(n, m, 2):
223 if i or j: # skip self
224 yield self + ((i + j) * D3,
225 (i - j) * D3)
227 def _outSide(self, sA, sB):
228 # is this C{Xdist} outside one or both segments?
229 a, b = self.sA, self.sB # PYCHOK sA, sB
230 kA = -1 if a < 0 else (+1 if a > sA else INT0)
231 kB = -1 if b < 0 else (+1 if b > sB else INT0)
232 self.set_(kA=kA, kB=kB, k=(kA * 3 + kB) or INT0)
233 return bool(kA or kB)
235 def _skip(self, S_, T1_Delta):
236 # remove starts from list C{S_} near this C{XDict}
237 for j, S in _enumereverse(S_):
238 if S.L1(self) < T1_Delta:
239 S_.pop(j)
242def XDict_(sA=_0_0, sB=_0_0, c=INT0, sX0=_0_0):
243 '''(INTERNAL) New L{XDict} from positionals.
244 '''
245 return XDict(sA=sA, sB=sB, c=c, sX0=sX0)
247_X000 = XDict_() # PYCHOK origin
248_XINF = XDict_(INF)
251class _IntersectBase(_NamedBase):
252 '''(INTERNAL) Base class for L{Intersectool} and L{Intersector}.
253 '''
254 # _g = None
256 def __init__(self, geodesic, **name):
257 _xinstanceof(*_EWGS84._Geodesics, geodesic=geodesic)
258 self._g = geodesic
259 if name:
260 self.name = name
262 @Property_RO
263 def a(self):
264 '''Get the I{equatorial} radius, semi-axis (C{meter}).
265 '''
266 return self.ellipsoid.a
268 equatoradius = a # = Requatorial
270 def All(self, glA, glB, **kwds): # PYCHOK no cover
271 '''(INTERNAL) I{Must be overloaded}.'''
272 self._notOverloaded(glA, glB, **kwds)
274 @Property_RO
275 def _cHalf(self): # normalizer, semi-circumference
276 return self.R * PI # ~20K Km WGS84
278 @Property_RO
279 def _cMax(self): # outer circumference
280 return max(self.a, self.ellipsoid.b, self.R) * PI2
282 @property_RO
283 def datum(self):
284 '''Get the geodesic's datum (C{Datum}).
285 '''
286 return self.geodesic.datum
288 @Property_RO
289 def ellipsoid(self):
290 '''Get the C{geodesic}'s ellipsoid (C{Ellipsoid}).
291 '''
292 return self.geodesic.datum.ellipsoid
294 @Property_RO
295 def f(self):
296 '''Get the I{flattening} (C{scalar}), C{0} for spherical, negative for prolate.
297 '''
298 return self.ellipsoid.f
300 flattening = f
302 @property_RO
303 def geodesic(self):
304 '''Get the C{geodesic} (C{Geodesic...}).
305 '''
306 return self._g
308 def _illz2G(self, G, il):
309 '''(INTERNAL) Set C{InverseLine} 1-/2-attrs into C{G}, a C{GDict}.
310 '''
311 try:
312 G.set_(lat1=il.lat1, lon1=il.lon1, azi1=il.azi1, a12=il.a13, # .Arc()
313 lat2=il.lat2, lon2=il.lon2, azi2=il.azi2, s12=il.s13) # .Distance()
314 except AttributeError:
315 r = il.Position(il.s13, outmask=Caps._STD_LINE) # isfinite(il.s13)
316 G.set_(**r)
317# for n, v in r.items():
318# if not hasattr(il, n):
319# setattr(il, n, v)
320 return G
322 def intersect7(self, start1, end1, start2, end2, X0=_X000, aMaX0=0, sMaX0=_cWGS84,
323 **LatLon_and_kwds):
324 '''Yield the intersection points of two lines, each defined by two (ellipsoidal)
325 points or by an (ellipsoidal) start point and an azimuth from North.
327 @arg start1: Start point of the first line (C{LatLon}).
328 @arg end1: End point of the first line (C{LatLon}) or the azimuth at the
329 B{C{start1}} point (compass C{degrees360}).
330 @arg start2: Start point of the second line (C{LatLon}).
331 @arg end2: End point of the second line (C{LatLon}) or the azimuth at the
332 B{C{start2}} point (compass C{degrees360}).
333 @kwarg X0: Optional I{origin} for I{L1-distances} (L{XDict}) or C{None} for
334 the L{Middle<Intersector.Middle>}, otherwise C{XDiff_(0, 0)}.
335 @kwarg aMaX0: Upper limit for the I{angular L1-distance}
336 (C{degrees}) or C{None} or C{0} for unlimited.
337 @kwarg sMaX0_C: Optional, upper limit C{B{sMaX0}=2*PI*R} for the
338 I{L1-distance} to B{C{X0}} (C{meter}).
339 @kwarg LatLon_and_kwds: Optional class C{B{LatLon}=None} to return intersection
340 points and optional, additional B{C{LatLon}} keyword arguments.
342 @note: The C{lat} and C{lon} attr of B{C{start1}}, B{C{end1}}, B{C{start2}} and
343 B{C{end2}} are used I{verbatim}, ignoring C{datum} or C{ellipsoid}.
345 @return: Yield an L{Intersect7Tuple}C{(A, B, sAB, aAB, c, kA, kB)} for every
346 intersection found, with C{A} and C{B} each a B{C{LatLon}} or if
347 C{B{LatLon} is None} or not specified, a L{LatLon4Tuple}C{(lat, lon,
348 height, datum)} with C{height 0} and this C{datum}.
350 @raise GeodesicError: Invalid B{C{start1}}, B{C{end1}}, B{C{start2}} or
351 B{C{end2}} or B{C{end1}} and B{C{end2}} differ in type.
353 @raise IntersectionError: No convergence.
354 '''
356 def _args(s, e):
357 t = (e,) if _isDegrees(e) else (e.lat, e.lon)
358 return (s.lat, s.lon) + t
360 try:
361 glA = self.Line(*_args(start1, end1))
362 glB = self.Line(*_args(start2, end2))
363 except Exception as x:
364 raise GeodesicError(start1=start1, end1=end1, start2=start2, end2=end2, cause=x)
366 LL, kwds = _xkwds_pop2(LatLon_and_kwds, LatLon=None)
367 d, kwds = _xkwds_pop2(kwds, datum=self.datum)
368 h, kwds = _xkwds_pop2(kwds, height=0)
370 _LL4T = _MODS.namedTuples._LL4Tuple
371 for X in self.All(glA, glB, X0=X0, aMaX0=aMaX0, sMaX0=sMaX0, _C=True):
372 A = B = _LL4T(X.latA, X.lonA, h, d, LL, kwds, iteration=X.iteration)
373 if X.sAB or X.latA != X.latB or X.lonA != X.lonB:
374 B = _LL4T(X.latB, X.lonB, h, d, LL, kwds, iteration=X.iteration)
375 yield Intersect7Tuple(A, B, X.sAB, X.aAB, X.c, _xkwds_get(X, kA=0),
376 _xkwds_get(X, kB=0))
378 def _Inversa12(self, A, B=None):
379 lls = (0, 0, A, 0) if B is None else (A.lat2, A.lon2,
380 B.lat2, B.lon2)
381 r = self._g.Inverse(*lls, outmask=Caps.DISTANCE)
382 return r.s12, r.a12 # .a12 always in r
384 def k2kAkB(self, k):
385 '''Unravel C{k} into C{kA} and C{kB}.
387 @arg k: Segment indicator C{kA * 3 + kB} (C{int}).
389 @return: An C{ADict(k=k, kA=kA, kB=kB)}.
391 @raise GeodesicError: Invalid B{C{k}}.
392 '''
393 for kA in range(-1, 2):
394 for kB in range(-1, 2):
395 if (kA * 3 + kB) == k:
396 return ADict(k=k, kA=kA, kB=kB)
397 raise GeodesicError(k=k)
399# def k2kAkB(self, k):
400# # unravel C{k} into C{kA} and C{kB}.
401# kA, kB = divmod(k, 3)
402# if kB > 1:
403# kA += 1
404# kB -= 3
405# return kA, kB
407 def Line(self, lat1, lon1, azi1_lat2, *lon2, **name): # PYCHOK no cover
408 '''(INTERNAL) I{Must be overloaded}.'''
409 self._notOverloaded(lat1, lon1, azi1_lat2, *lon2, **name)
411 def _ll3z4ll(self, lat1, lon1, azi1_lat2, *lon2):
412 t = Lat(lat1=lat1), Lon(lon1=lon1)
413 if lon2: # get azis for All, keep lat-/lons
414 t += Lat(lat2=azi1_lat2), Lon(lon2=lon2[0])
415 else:
416 t += Azi(azi1=azi1_lat2),
417 return t
419 @deprecated_method
420 def Next5s(self, glA, glB, X0=_X000, aMax=1801, sMax=0, **unused): # PYCHOK no cover
421 '''DEPRECATED on 2024.07.02, use method C{All5}.'''
422 return self.All5(glA, glB, X0=X0, aMaX0=aMax, sMaX0=sMax) # PYCHOK attr
424 @Property_RO
425 def R(self):
426 '''Get the I{authalic} earth radius (C{meter}).
427 '''
428 return self.ellipsoid.R2
430 def _sMaX0_C2(self, aMaX0=0, **sMaX0_C):
431 _g = _xkwds_get
432 s = _g(sMaX0_C, sMaX0=self._cMax)
433 s = _g(sMaX0_C, sMax=s) # for backward ...
434 a = _g(sMaX0_C, aMax=aMaX0) # ... compatibility
435 if a: # degrees to meter, approx.
436 s = min(s, self.R * radians(a)) # ellipsoid.degrees2m(a)
437 s = _g(sMaX0_C, _R=s)
438 if s < _EPS3:
439 s = _EPS3 # raise GeodesicError(sMaX0=s)
440 return s, _g(sMaX0_C, _C=False)
442 def _xNext(self, glA, glB, eps1, **eps_C): # PYCHOK no cover
443 eps1 = _xkwds_get(eps_C, eps=eps1) # eps for backward compatibility
444 if eps1 is not None:
445 a = glA.lat1 - glB.lat1
446 b = glA.lon1 - glB.lon1
447 if euclid(a, b) > eps1:
448 raise GeodesicError(lat_=a, lon_=b, eps1=eps1)
449 return _xkwds_kwds(eps_C, _C=False)
452class Intersectool(_IntersectBase, _SolveCapsBase):
453 '''Wrapper to invoke I{Karney}'s utility U{IntersectTool
454 <https://GeographicLib.SourceForge.io/C++/doc/IntersectTool.1.html>}
455 similar to class L{Intersector<geodesici.Intersector>}.
457 @note: Use property C{IntersectTool} or env variable C{PYGEODESY_INTERSECTTOOL}
458 to specify the (fully qualified) path to the C{IntersectTool} executable.
460 @note: This C{Intersectool} is intended I{for testing purposes only}, it invokes
461 the C{IntersectTool} executable for I{every} method call.
462 '''
463 _c_alt = _c__, # Closest latA lonA aziA latB lonB aziB
464 _C_option = '-C',
465 _Error = GeodesicError
466 _i_alt = _i__, # Segment latA1 lonA1 latA2 lonA2 latB1 lonB1 latB2 lonB2
467 _linelimit = 1200 # line printer width X 10
468 _n_alt = _n__, # Next latA lonA aziA aziB
469 _Names_ABs = _latA_, _lonA_, 'latB', 'lonB', _sAB_ # -C to stderr
470 _Names_XDict = 'sA', 'sB', _c_ # plus 'k' from -i or 'sX0' from -R
471 _o_alt = _o__, # Offset latA lonA aziA latB lonB aziB x0 y0
472 _Xable_name = _Xables.IntersectTool.__name__
473 _Xable_path = _Xables.IntersectTool()
475 def __init__(self, a_geodesic=None, f=None, **name):
476 '''New L{IntersectTool}.
478 @arg a_geodesic: Earth' equatorial axis (C{meter}) or a geodesic
479 (L{GeodesicExact<pygeodesy.geodesicx.GeodesicExact>},
480 wrapped L{Geodesic<pygeodesy.geodesicw.Geodesic>} or
481 L{GeodesicSolve<pygeodesy.geodsolve.GeodesicSolve>}).
482 @kwarg f: Earth' flattening (C{scalar}), required if B{C{a_geodesic}}
483 is in C{meter}, ignored otherwise.
484 @kwarg name: Optional C{B{name}=NN} (C{str}).
486 @raise GeodesicError: The eccentricity of the B{C{geodesic}}'s ellipsoid is too
487 large or no initial convergence.
489 @see: The B{Note} at I{Karney}'s C++ U{Intersect<https://GeographicLib.sourceforge.io/
490 C++/doc/classGeographicLib_1_1Intersect.html#ae41f54c9a44836f6c8f140f6994930cf>}.
491 '''
492 g = self._GeodesicExact() if a_geodesic is None else (a_geodesic if f is None else
493 self._GeodesicExact(a_geodesic, f))
494 _IntersectBase.__init__(self, g, **name)
496 def All(self, glA, glB, X0=_X000, eps1=_0_0, aMaX0=0, **sMaX0_C): # PYCHOK signature
497 '''Yield all intersection of two geodesic lines up to a limit.
499 @kwarg eps1: Optional margin for the L{euclid<pygeodesy.euclid>}ean distance
500 (C{degrees}) between the C{(lat1, lon1)} points of both lines for
501 using the L{IntersectTool<Intersectool.IntersectTool>}'s C{"-n"}
502 option, unless C{B{eps1}=None}.
504 @return: An L{XDict} for each intersection.
505 '''
506 for X, _ in self._All2(glA, glB, X0, eps1, aMaX0=aMaX0, **sMaX0_C):
507 yield X
509 def _All2(self, glA, glB, X0, eps1, **aMaX0_sMaX0_C): # MCCABE 13
510 '''(INTERNAL) Helper for methods C{.All} and C{.All5}.
511 '''
512 def _xz2(**gl):
513 try:
514 n, gl = gl.popitem() # _xkwds_item2(gl)
515 try:
516 return self._c_alt, (gl.azi1,)
517 except (AttributeError, KeyError):
518 return self._i_alt, (gl.lat2, gl.lon2)
519 except Exception as x:
520 raise GeodesicError(n, gl, cause=x)
522 _t, a = _xz2(glA=glA)
523 _x, b = _xz2(glB=glB)
524 if _x is not _t:
525 raise GeodesicError(glA=glA, glB=glB)
527 A = glA.lat1, glA.lon1
528 B = glB.lat1, glB.lon1
529 if _x is self._c_alt:
530 if X0 is _X000 or X0._is00:
531 if eps1 is not None and \
532 euclid(glA.lat1 - glB.lat1,
533 glA.lon1 - glB.lon1) <= eps1:
534 _x, B = self._n_alt, ()
535 else: # non-zero offset
536 _x = self._o_alt
537 b += X0.sA, X0.sB
539 sMaX0, _C = self._sMaX0_C2(**aMaX0_sMaX0_C)
540 for X in self._XDictInvoke(_x, _sX0_, (A + a + B + b),
541 _C=_C, _R=sMaX0):
542 if _C:
543 T = self._In5T(glA, glB, X, X)
544 if _aAB_ not in X:
545 X.set_(sAB=T.sAB, aAB=T.aAB)
546 else:
547 T = None
548 yield X.set_(c=int(X.c)), T
550 def All5(self, glA, glB, X0=_X000, **aMaX0_sMaX0):
551 '''Yield all intersection of two geodesic lines up to a limit.
553 @return: An L{Intersectool5Tuple} for each intersection.
554 '''
555 for _, T in self._All2(glA, glB, X0, _0_0, _C=True, **aMaX0_sMaX0):
556 yield T
558 @Property_RO
559 def _cmdBasic(self):
560 '''(INTERNAL) Get the basic C{IntersectTool} cmd (C{tuple}).
561 '''
562 return (self.IntersectTool,) + (self._e_option +
563 self._E_option +
564 self._p_option)
566 def Closest(self, glA, glB, X0=_X000, _C=False):
567 '''Find the closest intersection of two geodesic lines.
569 @kwarg _C: Use C{B{_C}=True} to include the C{"-C"} results (C{bool}).
571 @return: An L{XDict}.
572 '''
573 args = glA.lat1, glA.lon1, glA.azi1, \
574 glB.lat1, glB.lon1, glB.azi1
575 if X0 is _X000 or X0._is000:
576 _x = self._c_alt
577 else:
578 _x = self._o_alt
579 args += X0.sA, X0.sB
580 return self._XDictInvoke(_x, NN, args, _C=_C) # _R=None)
582 def Closest5(self, glA, glB, **unused):
583 '''Find the closest intersection of two geodesic lines.
585 @return: An L{Intersectool5Tuple}.
586 '''
587 X = self.Closest(glA, glB, _C=True)
588 return self._In5T(glA, glB, X, X)
590 @property_ROver
591 def _GeodesicExact(self):
592 '''Get the I{class} L{GeodesicExact}, I{once}.
593 '''
594 return _MODS.geodesicx.GeodesicExact # overwrite property_ROver
596 def _In5T(self, glA, glB, S, X, k2=False, **_2X):
597 A = GDict(glA).set_(lat2=X.latA, lon2=X.lonA, s12=S.sA)
598 B = GDict(glB).set_(lat2=X.latB, lon2=X.lonB, s12=S.sB)
599 if k2:
600 A.set_(k2=X.kA)
601 B.set_(k2=X.kB)
602 s, a = self._Inversa12(A, B)
603 sAB = _xkwds_get(X, sAB=s)
604 if a and s and s != sAB:
605 a *= sAB / s # adjust a
606 return Intersectool5Tuple(A._2X(glA, **_2X),
607 B._2X(glB, **_2X), sAB, a, X.c)
609 @Property
610 def IntersectTool(self):
611 '''Get the U{IntersectTool<https://GeographicLib.SourceForge.io/C++/doc/IntersectTool.1.html>}
612 executable (C{filename}).
613 '''
614 return self._Xable_path
616 @IntersectTool.setter # PYCHOK setter!
617 def IntersectTool(self, path):
618 '''Set the U{IntersectTool<https://GeographicLib.SourceForge.io/C++/doc/IntersectTool.1.html>}
619 executable (C{filename}), the (fully qualified) path to the C{IntersectTool} executable.
621 @raise GeodesicError: Invalid B{C{path}}, B{C{path}} doesn't exist or isn't the
622 C{IntersectTool} executable.
623 '''
624 self._setXable(path)
626 def Line(self, lat1, lon1, azi1_lat2, *lon2, **name):
627 '''Return a geodesic line from this C{Intersector}'s geodesic, specified by
628 two (goedetic) points or a (goedetic) point and an (forward) azimuth.
630 @return: A 3- or 6-item, named L{GDict}.
631 '''
632 args = self._ll3z4ll(lat1, lon1, azi1_lat2, *lon2)
633 gl = GDict((u.name, u) for u in args)
634# if lon2: # get azis for All, use lat-/lons as given
635# r = self._g.Inverse(outmask=Caps.AZIMUTH, *args)
636# gl.set_(azi1=Azi(azi1=r.azi1), azi2=Azi(azi2=r.azi2))
637 if name:
638 gl.name= name
639 return gl
641 def Middle(self, glA, glB, **_C):
642 '''Get the mid-points on two geodesic line segments.
644 @kwarg _C: Use C{B{_C}=True} to include the C{"-C"} results (C{bool}).
646 @return: An L{XDict}.
647 '''
648 X, _, _, _, _ = self._middle5(glA, glB, **_C)
649 return X
651 def _middle5(self, glA, glB, _C=False, **unused):
652 # return intersections C{A} and C{B} and the
653 # center C{X0} of rectangle [sA, sB]
655 def _smi4(**gl):
656 try:
657 n, gl = gl.popitem()
658 il = self._g.InverseLine(gl.lat1, gl.lon1, gl.lat2, gl.lon2)
659 except Exception as x:
660 raise GeodesicError(n, gl, cause=x)
661 s = il.s13
662 m = s * _0_5
663 return s, m, il, (il.Position(m, outmask=Caps._STD_LINE) if _C else None)
665 sA, mA, iA, A = _smi4(glA=glA)
666 sB, mB, iB, B = _smi4(glB=glB)
667 X = XDict_(mA, mB) # centers
668 _ = X._outSide(sA, sB)
669 if _C: # _Names_ABs
670 s, a = self._Inversa12(A, B)
671 X.set_(latA=A.lat2, lonA=A.lon2, aMM=a, # assert sA == A.s12
672 latB=B.lat2, lonB=B.lon2, sMM=s) # assert sB == B.s12
673 return X, A, iA, B, iB
675 def Middle5(self, glA, glB, **unused):
676 '''Get the mid-points on two geodesic line segments and their distance.
678 @return: A L{Middle5Tuple}.
679 '''
680 X, A, iA, B, iB = self._middle5(glA, glB, _C=True)
681 A, B, s, a, c = self._In5T(A, B, X, X, _2X=_M_)
682 return Middle5Tuple(self._illz2G(A, iA),
683 self._illz2G(B, iB), s, a, c)
685 def Next(self, glA, glB, eps1=None, **_C): # PYCHOK no cover
686 '''Find the next intersection of two I{intersecting} geodesic lines.
688 @kwarg _C: Use C{B{_C}=True} to include the option C{"-C"} results (C{bool}).
690 @return: An L{XDict}.
691 '''
692 if eps1 or _C:
693 _C = self._xNext(glA, glB, eps1, **_C)
694 return self._XDictInvoke(self._n_alt, NN,
695 (glA.lat1, glA.lon1, glA.azi1, glB.azi1),
696 **_C) # _R=None
698 def Next5(self, glA, glB, **eps1): # PYCHOK no cover
699 '''Find the next intersection of two I{intersecting} geodesic lines.
701 @return: An L{Intersectool5Tuple}.
702 '''
703 X = self.Next(glA, glB, _C=True, **eps1)
704 return self._In5T(glA, glB, X, X)
706 def _R_option(self, _R=None):
707 '''(INTERNAL) Get the C{-R maxdist} option.
708 '''
709 return () if _R is None else (_R__, str(_R)) # -R maxdist
711 def Segment(self, glA, glB, **_C_unused):
712 '''Find the intersection between two geodesic line segments.
714 @kwarg _C: Use C{B{_C}=True} to include the option C{"-C"} results (C{bool}).
716 @return: An L{XDict}.
717 '''
718 X = self._XDictInvoke(self._i_alt, 'k',
719 (glA.lat1, glA.lon1, glA.lat2, glA.lon2,
720 glB.lat1, glB.lon1, glB.lat2, glB.lon2),
721 _C=_xkwds_get(_C_unused, _C=False)) # _R=None
722 try:
723 ks = self.k2kAkB(int(X.k))
724 except Exception as x:
725 raise GeodesicError(glA=glA, glB=glB, X=str(X), cause=x)
726 return X.set_(**ks)
728 def Segment5(self, glA, glB, **unused):
729 '''Find the next intersection of two I{intersecting} geodesic lines.
731 @return: An L{Intersectool5Tuple}.
732 '''
733 X = self.Segment(glA, glB, _C=True)
734 return self._In5T(glA, glB, X, X, k2=True)
736 def toStr(self, prec=6, sep=_COMMASPACE_, **unused): # PYCHOK signature
737 '''Return this C{Intersectool} as string.
739 @kwarg prec_sep: Keyword argumens C{B{prec}=6} and C{B{sep}=", "}
740 for the C{float} C{prec}ision, number of decimal digits
741 (0..9) and the C{sep}arator string to join. Trailing
742 zero decimals are stripped for B{C{prec}} values of 1
743 and above, but kept for negative B{C{prec}} values.
745 @return: Intersectool items (C{str}).
746 '''
747 d = dict(geodesic=self.geodesic, invokation=self.invokation,
748 status=self.status,
749 IntersectTool=self.IntersectTool)
750 return sep.join(pairs(d, prec=prec))
752 def _XDictInvoke(self, alt, _k_sX0, args, _C=False, **_R):
753 '''(INTERNAL) Invoke C{IntersectTool}, return results as C{XDict} or
754 a C{generator} if keyword argument C{B{_R}=sMaX0} is specified.
755 '''
756 # assert len(args) == {self._c_alt: 6,
757 # self._i_alt: 8,
758 # self._n_alt: 4,
759 # self._o_alt: 8}.get(alt, len(args))
760 cmd = self._cmdBasic
761 Names = self._Names_XDict # has _c_ always
762 if _k_sX0:
763 Names += _k_sX0,
764 if _C:
765 cmd += self._C_option
766 Names += self._Names_ABs
767 if _R:
768 cmd += self._R_option(**_R)
769 X, _R = self._DictInvoke2(cmd + alt, args, Names, XDict, **_R)
770 return X if _R else X.set_(c=int(X.c)) # generator or XDict
773class Intersector(_IntersectBase):
774 '''Finder of intersections between two goedesic lines, each an instance
775 of L{GeodesicLineExact<pygeodesy.geodesicx.GeodesicLineExact>},
776 wrapped L{GeodesicLine<pygeodesy.geodesicw.GeodesicLine>} or
777 L{GeodesicLineSolve<pygeodesy.geodsolve.GeodesicLineSolve>}.
779 @see: I{Karney}'s C++ class U{Intersect<https://GeographicLib.sourceforge.io/
780 C++/doc/classGeographicLib_1_1Intersect.html#details>} for more details.
781 '''
783 def __init__(self, geodesic, **name):
784 '''New L{Intersector}.
786 @arg geodesic: The geodesic (L{GeodesicExact<pygeodesy.geodesicx.GeodesicExact>},
787 wrapped L{Geodesic<pygeodesy.geodesicw.Geodesic>} or
788 L{GeodesicSolve<pygeodesy.geodsolve.GeodesicSolve>}).
789 @kwarg name: Optional C{B{name}=NN} (C{str}).
791 @raise GeodesicError: The eccentricity of the B{C{geodesic}}'s ellipsoid is too
792 large or no initial convergence.
794 @see: The B{Note} at I{Karney}'s C++ U{Intersect<https://GeographicLib.sourceforge.io/
795 C++/doc/classGeographicLib_1_1Intersect.html#ae41f54c9a44836f6c8f140f6994930cf>}.
796 '''
797 _IntersectBase.__init__(self, geodesic, **name)
798 E = self.ellipsoid
799 t1 = E.b * PI # min distance between intersects
800 t2 = self._polarDist2(_90_0)[0] * _2_0 # furthest, closest intersect
801 t5 = self._Inversa12( _90_0)[0] * _2_0 # longest, shortest geodesic
802 if self.f > 0:
803 t3 = self._obliqDist4()[0]
804 t4 = t1
805 else: # PYCHOK no cover
806 t1, t2, t3 = t2, t1, t5
807 t4, _, _ = self._polarB3()
809 self._D1 = d1 = t2 * _0_5 # ~E.L tile spacing for Closest
810 self._D2 = d2 = t3 / _1_5 # tile spacing for Next
811 self._D3 = d3 = t4 - self.Delta # tile spacing for All
812 self._T1 = t1 # min distance between intersects
813 self._T2 = t2 = t1 * _2_0
814# self._T5 = t5 # not used
815 if not (d1 < d3 and d2 < d3 and d2 < t2):
816 t = Fmt.PARENSPACED(_too_('eccentric'), E.e)
817 raise GeodesicError(ellipsoid=E.toStr(terse=2), txt=t)
819 def All(self, glA, glB, X0=None, aMaX0=0, **sMaX0_C): # MCCABE 13
820 '''Yield all intersection of two geodesic lines up to a limit.
822 @arg glA: A geodesic line (L{Line<Intersector.Line>}).
823 @arg glB: An other geodesic line (L{Line<Intersector.Line>}).
824 @kwarg X0: Optional I{origin} for I{L1-distances} (L{XDict}) or
825 C{None} for the L{Middle<Intersector.Middle>} of both
826 lines if both are a 4-C{args} L{Line<Intersector.Line>}
827 or C{InverseLine}, otherwise C{XDiff_(0, 0)}.
828 @kwarg aMaX0: Upper limit for the I{angular L1-distance}
829 (C{degrees}) or C{None} or C{0} for unlimited.
830 @kwarg sMaX0_C: Optional, upper limit C{B{sMaX0}=2*PI*R} for the
831 I{L1-distance} to B{C{X0}} (C{meter}) and option
832 C{B{_C}=False} to include the intersection lat-/
833 longitudes C{latA}, C{lonA}, C{latB}, C{lonB} and
834 distances C{sAB} and C{aSB}.
836 @return: Yield an L{XDict} for each intersection found.
838 @raise GeodesicError: Geodesic line B{C{glA}} or B{C{glB}}
839 invalid, incompatible or ill-configured.
841 @raise IntersectionError: No convergence.
842 '''
843 self._xLines(glA, glB)
844 if X0 is None:
845 try: # determine X0
846 X0, _, _ = self._middle3(glA, glB, True)
847 except GeodesicError: # no .Distance
848 X0 = _X000
849 sMaX0, _C = self._sMaX0_C2(aMaX0, **sMaX0_C)
851 D, _D = self.Delta, self._cHalf # C++ _d
852 xMaX0 = sMaX0 + D
853 m = int(_ceil(xMaX0 / self._D3)) # m x m tiles
854 d3 = xMaX0 / m
855 T2d3D = self._T2d3Delta(d3)
857 C_ = _List(D) # closest coincident
858 X_ = _List(D) # intersections found
859 c0 = 0
860 S_ = list(X0._nmD3(1 - m, m, d3 * _0_5))
861 # assert len(S_) == m * m + (m - 1) % 2
862 while S_:
863 Q, i = self._Basic2(glA, glB, S_.pop(0))
864 if Q in X_:
865 continue
866 if Q.c: # coincident intersection # PYCHOK no cover
867 _X0fx = X0._fixCoincident
868 Q = _X0fx(Q) # Q = Q'
869 if c0 and Q in C_:
870 continue
871 C_.addend(Q)
872 # elimate all existing intersections
873 # on this line (which didn't set c0)
874 c0 = Q.c
875 for j, X in _enumereverse(X_):
876 if _X0fx(X, c0).L1(Q) <= D: # X' == Q
877 X_.pop(j)
879 a, s0 = len(X_), Q.sA
880 args = self._m12_M12_M21(glA, s0)
881 _cjD = self._conjDist
882 for s in (-_D, _D):
883 s += s0
884 sa = 0
885 while True:
886 i += 1
887 sa = _cjD(glA, s + sa, *args) - s0
888 X = Q + (sa, sa * c0)
889 if X_.addend(X, X0.L1(X), i) > xMaX0:
890 break
892 elif c0 and Q in C_: # Q.c == 0
893 continue
894 else:
895 a = len(X_)
897 X_.addend(Q, X0.L1(Q), i + 1)
898 for X in X_[a:]: # addended Xs
899 X._skip(S_, T2d3D)
901 return X_.sorter(sMaX0, self._C, glA, glB, _C=_C) # generator
903 def All5(self, glA, glB, X0=_X000, **aMaX0_sMaX0_C):
904 '''Yield all intersection of two geodesic lines up to a limit.
906 @return: Yield an L{Intersector5Tuple}C{(A, B, sAB, aAB, c)}
907 for each intersection found.
909 @see: Methods L{All} for further details.
910 '''
911 for X in self.All(glA, glB, X0=X0, **aMaX0_sMaX0_C):
912 yield self._In5T(glA, glB, X, X)
914 def _Basic2(self, glA, glB, S, i=0):
915 '''(INTERNAL) Get a basic solution.
916 '''
917 X = _copy(S)
918 for _ in range(_TRIPS):
919 S = self._Spherical(glA, glB, X)
920 X += S
921 i += 1
922 if X.c or S.L1() <= self._Tol: # or isnan
923 return self._Delto(X), i
925 raise IntersectionError(Fmt.no_convergence(S.L1(), self._Tol))
927 def _C(self, X, glA, glB, _C=False, _MM=False):
928 # add the C{_C} items to C{X}, if requested.
929 if _C:
930 A = self._Position(glA, X.sA)
931 B = self._Position(glB, X.sB)
932 s, a = self._Inversa12(A, B)
933 X.set_(latA=A.lat2, lonA=A.lon2,
934 latB=B.lat2, lonB=B.lon2)
935 if _MM: # in .Middle5
936 X.set_(sMM=s, aMM=a)
937 else:
938 X.set_(sAB=s, aAB=a)
939 return X
941 def Closest(self, glA, glB, X0=_X000, **_C):
942 '''Find the closest intersection of two geodesic lines.
944 @arg glA: A geodesic line (L{Line<Intersector.Line>}).
945 @arg glB: An other geodesic line (L{Line<Intersector.Line>}).
946 @kwarg X0: Optional I{origin} for I{L1-closeness} (L{XDict}).
947 @kwarg _C: If C{True}, include the lat-/longitudes C{latA},
948 C{lonA}, C{latB}, C{lonB} oon and distances C{sAB}
949 and C{aSB} between the intersections.
951 @return: The intersection (L{XDict}) or C{None} if none found.
953 @raise GeodesicError: Geodesic line B{C{glA}} or B{C{glB}}
954 invalid, incompatible or ill-configured.
956 @raise IntersectionError: No convergence.
957 '''
958 self._xLines(glA, glB)
959 Q, d, S_, i = X0, INF, list(X0._nD1(self._D1)), 0
960 while S_:
961 X, i = self._Basic2(glA, glB, S_.pop(0), i)
962 X = X0._fixCoincident(X)
963 if X.L1(Q) > self.Delta: # X != Q
964 d0 = X.L1(X0)
965 if d0 < self._T1:
966 Q, d, q = X, d0, i
967 break
968 if d0 < d or Q is X0:
969 Q, d, q = X, d0, i
970 X._skip(S_, self._T2D1Delta)
972 return None if Q is X0 else self._C(Q, glA, glB, **_C).set_(sX0=d, iteration=q)
974 def Closest5(self, glA, glB, X0=_X000):
975 '''Find the closest intersection of two geodesic lines.
977 @return: An L{Intersector5Tuple}C{(A, B, sAB, aAB, c)}
978 or C{None} if none found.
980 @see: Method L{Closest} for further details.
981 '''
982 X = self.Closest(glA, glB, X0=X0)
983 return X if X is None else self._In5T(glA, glB, X, X)
985 def _conjDist(self, gl, s, m12=0, M12=1, M21=1, semi=False):
986 # Find semi-/conjugate point relative to s0 which is close to s1.
987 # if semi:
988 # solve for M23 = 0 using dM23 / ds3 = - (1 - M23 * M32) / m23
989 # else:
990 # solve for m23 = 0 using dm23 / ds3 = M32
991 _S2, _abs, _1 = Fsum(s).fsum2_, fabs, _1_0
992 for _ in range(_TRIPS):
993 m13, M13, M31 = self._m12_M12_M21(gl, s)
994 # see "Algorithms for geodesics", eqs. 31, 32, 33.
995 m23 = m13 * M12
996 M32 = M31 * M12
997 if m12: # PYCHOK no cover
998 m23 -= m12 * M13
999 if m13:
1000 M32 += (_1 - M13 * M31) * m12 / m13
1001 if semi:
1002 M23 = M13 * M21
1003 # when m12 -> eps, (1 - M12 * M21) -> eps^2, I suppose.
1004 if m12 and m13:
1005 M23 += (_1 - M12 * M21) * m13 / m12
1006 d = m23 * M23 / (_1 - M23 * M32)
1007 else:
1008 d = -m23 / M32
1009 s, d = _S2(d)
1010 if _abs(d) <= self._Tol:
1011 break
1012 return s
1014 _gl3 = None
1016 @Property
1017 def _conjDist3s(self):
1018 gl, self._gl3, _D = self._gl3, None, self._cHalf
1019 return tuple(self._conjDist(gl, s) for s in (-_D, 0, _D))
1021 @_conjDist3s.setter # PYCHOK setter!
1022 def _conjDist3(self, gl):
1023 # _XLines(gl, gl)
1024 self._gl3 = gl
1026 def _conjDist3Tt_(self, c, X0=_X000):
1027 for s in self._conjDist3s:
1028 T = XDict_(s, s * c, c)
1029 yield self._Delto(T), T.L1(X0)
1031 def _conjDist5(self, azi):
1032 gl = self._Line(azi1=azi)
1033 s = self._conjDist(gl, self._cHalf)
1034 X, _ = self._Basic2(gl, gl, XDict_(s * _0_5, -s * _1_5))
1035 return s, (X.L1() - s * _2_0), azi, X.sA, X.sB
1037 @Property_RO
1038 def Delta(self):
1039 '''Get the equality and tiling margin (C{meter}).
1040 '''
1041 return self._cHalf * _EPSr5 # ~15 Km WGS84
1043 def _Delto(self, X):
1044 # copy Delta into X, overriding X's default
1045 X._Delta = self.Delta # NOT X.set_(self.Delta)
1046 return X
1048 @Property_RO
1049 def _EPS3R(self):
1050 return _EPS3 * self.R
1052 @Property_RO
1053 def _faPI_4(self):
1054 return (self.f + _2_0) * self.a * PI_4
1056 @Property_RO
1057 def _GeodesicLines(self):
1058 '''(INTERNAL) Get the C{Geodesic...Line} class(es).
1059 '''
1060 return type(self._Line()),
1062 def _In5T(self, glA, glB, S, X, k2=False, **_2X):
1063 # Return an intersection as C{Intersector5Tuple}.
1064 A = self._Position(glA, S.sA)
1065 B = self._Position(glB, S.sB)
1066 if k2:
1067 A.set_(k2=X.kA)
1068 B.set_(k2=X.kB)
1069 s, a = self._Inversa12(A, B)
1070 return Intersector5Tuple(A._2X(glA, **_2X),
1071 B._2X(glB, **_2X), s, a, X.c, iteration=X.iteration)
1073 def _Inverse(self, A, B): # caps=Caps.STANDARD
1074 return self._g.Inverse(A.lat2, A.lon2, B.lat2, B.lon2)
1076 def Line(self, lat1, lon1, azi1_lat2, *lon2, **name):
1077 '''Return a geodesic line from this C{Intersector}'s geodesic, specified by
1078 two (goedetic) points or a (goedetic) point and an (initial) azimuth.
1080 @arg lat1: Latitude of the first point (C{degrees}).
1081 @arg lon1: Longitude of the first point (C{degrees}).
1082 @arg azi1_lat2: Azimuth at the first point (compass C{degrees}) if no
1083 B{C{lon2}} argument is given, otherwise the latitude of
1084 the second point (C{degrees}).
1085 @arg lon2: If given, the longitude of the second point (C{degrees}).
1086 @kwarg name: Optional C{B{name}=NN} (C{str}).
1088 @return: A line (from L{geodesic<Intersector.geodesic>}C{.Line} or
1089 C{.InverseLine} method) with C{LINE_CAPS}.
1090 '''
1091 args = self._ll3z4ll(lat1, lon1, azi1_lat2, *lon2)
1092 gl = self._g.InverseLine(*args, caps=Caps.LINE_CAPS) if lon2 else \
1093 self._g.Line( *args, caps=Caps.LINE_CAPS)
1094 if name:
1095 gl.name= name
1096 return gl
1098 def _Line(self, lat1=0, lon1=0, azi1=0):
1099 return self._g.Line(lat1, lon1, azi1, caps=Caps.LINE_CAPS)
1101 def Middle(self, glA, glB, raiser=True, **_C):
1102 '''Get the mid-points on two geodesic line segments.
1104 @arg glA: A geodesic line (L{Line<Intersector.Line>}, 4-C{args}).
1105 @arg glB: An other geodesic line (L{Line<Intersector.Line>}, 4-C{args}).
1106 @kwarg raiser: If C{True}, check that B{C{glA}} and B{C{glB}} are a
1107 4-C{args} L{Line<Intersector.Line>} or C{InverseLine}
1108 (C{bool}).
1109 @kwarg _C: If C{True}, include the lat-/longitudes C{latA}, C{lonA},
1110 C{latB}, C{lonB} of the mid-points and half-lengths C{sA}
1111 and C{sB} in C{meter} of the respective line segments.
1113 @return: The mid-point and half-length of each segment (L{XDict}),
1114 B{C{_C}} above.
1116 @raise GeodesicError: Geodesic line B{C{glA}} or B{C{glB}} invalid,
1117 incompatible, ill-configured or not a 4-C{args
1118 Line} or other C{InverseLine}.
1119 '''
1120 M, _, _ = self._middle3(glA, glB, raiser)
1121 return self._C(M, glA, glB, **_C) if _C else M
1123 def _middle3(self, glA, glB, raiser): # in .All, .Segment
1124 # return segment length C{sA} and C{sB} and the
1125 # center C{X0} of rectangle [sA, sB]
1126 self._xLines(glA, glB, s13=raiser) # need .Arc, .Distance
1127 sA = glA.Distance()
1128 sB = glB.Distance()
1129 X = XDict_(sA * _0_5, sB * _0_5)
1130 # _ = X._outSide(sA, sB)
1131 return self._Delto(X), sA, sB
1133 def Middle5(self, glA, glB, raiser=True):
1134 '''Get the mid-points of two geodesic line segments and distances.
1136 @return: A L{Middle5Tuple}C{(A, B, sMM, aMM, c)}.
1138 @see: Method L{Middle} for further details.
1139 '''
1140 M, _, _ = self._middle3(glA, glB, raiser)
1141 M = self._C(M, glA, glB, _C=True, _MM=True)
1142 A, B, s, a, c = self._In5T(glA, glB, M, M, _2X=_M_)
1143 return Middle5Tuple(self._illz2G(A, glA),
1144 self._illz2G(B, glB), s, a, c)
1146 def _m12_M12_M21(self, gl, s):
1147 P = gl.Position(s, outmask=Caps._REDUCEDLENGTH_GEODESICSCALE)
1148 return P.m12, P.M12, P.M21
1150 def Next(self, glA, glB, eps1=None, **_C): # PYCHOK no cover
1151 '''Yield the next intersection of two I{intersecting} geodesic lines.
1153 @arg glA: A geodesic line (L{Line<Intersector.Line>}).
1154 @arg glB: An other geodesic line (L{Line<Intersector.Line>}).
1155 @kwarg eps1: Optional margin for the L{euclid<pygeodesy.euclid>}ean
1156 distance (C{degrees}) between the C{(lat1, lon1)} points
1157 of both lines or C{None} for unchecked.
1158 @kwarg _C: If C{True}, include the lat-/longitudes C{latA}, C{lonA},
1159 C{latB}, C{lonB} of and distances C{sAB} and C{aSB}
1160 between the intersections.
1162 @return: The intersection (L{XDict}) or C{None} if none found.
1164 @raise GeodesicError: Geodesic line B{C{glA}} or B{C{glB}} invalid,
1165 incompatible, ill-configured or C{(lat1, lon1)}
1166 not B{C{eps1}}-equal.
1168 @raise IntersectionError: No convergence.
1170 @note: Offset C{X0} is implicit, zeros.
1171 '''
1172 self._xLines(glA, glB)
1173 if eps1 or _C: # eps
1174 _C = self._xNext(glA, glB, eps1, **_C)
1176 X0, self._conjDist3s = _X000, glA # reset Property
1177 Q, d, S_, i = _XINF, INF, list(X0._nD2(self._D2)), 0
1178 while S_:
1179 X, i = self._Basic2(glA, glB, S_.pop(0), i)
1180 X = X0._fixCoincident(X)
1181 t = X.L1(X0) # == X.L1()
1182 c, z = X.c, (t <= self.Delta) # X == X0
1183 if z:
1184 if not c:
1185 continue
1186 Tt_ = self._conjDist3Tt_(c, X0)
1187 else:
1188 Tt_ = (X, t),
1190 for T, t in Tt_:
1191 if t < d or Q is _XINF:
1192 Q, d, q = T, t, i
1193 i += 1
1195 for s in ((_1_1t if z else _1_0_1t)
1196 if c else _0t):
1197 T = X
1198 if s and c:
1199 s *= self._D2
1200 T = X + (s, s * c) # NOT +=
1201 T._skip(S_, self._T2D2Delta)
1203 return None if Q is _XINF else self._C(Q, glA, glB, **_C).set_(sX0=d, iteration=q)
1205 def Next5(self, glA, glB, **eps1): # PYCHOK no cover
1206 '''Yield the next intersection of two I{intersecting} geodesic lines.
1208 @return: An L{Intersector5Tuple}C{(A, B, sAB, aAB, c)} or C{None}
1209 if none found.
1211 @see: Method L{Next} for further details.
1212 '''
1213 X = self.Next(glA, glB, **eps1)
1214 return X if X is None else self._In5T(glA, glB, X, X)
1216 def _obliqDist4(self):
1217 zx = _45_0
1218 if self.f:
1219 _abs, _cjD5 = fabs, self._conjDist5
1221 _, ds0, z0, _, _ = _cjD5(zx + _1_0)
1222 s1, ds1, z1, sAx, sBx = _cjD5(zx - _1_0)
1223 sx, dsx, zx = s1, _abs(ds1), z1
1224 # find ds(azi) = 0 by secant method
1225 for _ in range(16):
1226 if ds1 == ds0:
1227 break
1228 z = (z0 * ds1 - z1 * ds0) / (ds1 - ds0)
1229 _, ds0, z0 = s1, ds1, z1
1230 s1, ds1, z1, a, b = _cjD5(z)
1231 if _abs(ds1) < dsx:
1232 sx, dsx, zx, sAx, sBx = s1, _abs(ds1), z, a, b
1233 if not dsx:
1234 break
1235 else:
1236 sx, sAx, sBx = self._cHalf, _0_5, -_1_5
1237 return sx, zx, sAx, sBx
1239 def _polarB3(self, lats=False): # PYCHOK no cover
1240 latx = _64_0
1241 lat = _90_0 - latx
1242 if self.f:
1243 _d, _pD2 = fdot, self._polarDist2
1245 s0, lat0 = _pD2(latx - _1_0)
1246 s1, lat1 = _pD2(latx + _1_0)
1247 s2, lat2 = \
1248 sx, latx = _pD2(latx)
1249 prolate = self.f < 0
1250 # solve for ds(lat) / dlat = 0 with a quadratic fit
1251 for _ in range(_TRIPS):
1252 t = (lat1 - lat0), (lat0 - lat2), (lat2 - lat1)
1253 d = _d(t, s2, s1, s0) * _2_0
1254 if not d: # or isnan(d)
1255 break
1256 lat = _d(t, (lat1 + lat0) * s2,
1257 (lat0 + lat2) * s1,
1258 (lat2 + lat1) * s0) / d
1259 s0, lat0 = s1, lat1
1260 s1, lat1 = s2, lat2
1261 s2, lat2 = _pD2(lat)
1262 if (s2 < sx) if prolate else (s2 > sx):
1263 sx, latx = s2, lat2
1264 if lats:
1265 _, lat = _pD2(latx, lat2=True)
1266 sx += sx
1267 else:
1268 sx = self._cHalf
1269 return sx, latx, lat
1271 def _polarDist2(self, lat1, lat2=False):
1272 gl = self._Line(lat1=lat1)
1273 s = self._conjDist(gl, self._faPI_4, semi=True)
1274 if lat2:
1275 lat1 = gl.Position(s, outmask=Caps.LATITUDE).lat2
1276 return s, lat1
1278 def _Position(self, gl, s):
1279 return gl.Position(s, outmask=Caps._STD_LINE)
1281 def Segment(self, glA, glB, proven=None, raiser=True, **_C):
1282 '''Find the intersection between two geodesic line segments.
1284 @kwarg proven: Conjecture is that whenever two geodesic line
1285 segments intersect, the intersection is the
1286 one closest to the mid-points of segments.
1287 If so, use C{B{proven}=True}, otherwise find
1288 intersections on the segments and specify
1289 C{B{proven}=None} to return the first or
1290 C{B{proven}=False} the closest (C{bool}).
1291 @kwarg raiser: If C{True}, check that B{C{glA}} and B{C{glB}}
1292 are a 4-C{args} L{Line<Intersector.Line>} or
1293 C{InverseLine} (C{bool}).
1294 @kwarg _C: If C{True}, include the lat-/longitudes C{latA},
1295 C{lonA}, C{latB}, C{lonB} of and distances C{sAB}
1296 and C{aSB} between the intersections.
1298 @return: The intersection of the segments (L{XDict}) with
1299 indicators C{kA}, C{kB} and C{k} set or if no
1300 intersection is found, C{None}.
1302 @raise GeodesicError: Geodesic line B{C{glA}} or B{C{glB}}
1303 invalid, incompatible, ill-configured or
1304 not an C{InverseLine} or 4-C{args Line}.
1306 @raise IntersectionError: No convergence.
1308 @see: Method L{Middle<Intersector.Middle>} for further details.
1309 '''
1310 X0, sA, sB = self._middle3(glA, glB, raiser)
1311 Q = self.Closest(glA, glB, X0) # to X0
1312 if Q is not None:
1313 if Q.c: # anti-/parallel
1314 Q._fixSegment(sA, sB)
1315 # are rectangle [sA, sB] corners further from X0 than Q?
1316 d0 = X0.L1(Q)
1317 if Q._outSide(sA, sB) and d0 <= X0.L1() and not proven:
1318 i = Q.iteration
1319 for T in Q._corners(sA, sB, self._T2):
1320 X, i = self._Basic2(glA, glB, T, i)
1321 X = T._fixCoincident(X)
1322 if not X._outSide(sA, sB):
1323 d = X0.L1(X)
1324 if d < d0 or proven is None:
1325 Q, d0 = X, d
1326 if proven is None:
1327 break
1328 Q.set_(iteration=i)
1330 Q = self._C(Q, glA, glB, **_C).set_(sX0=d0)
1331 return Q
1333 def Segment5(self, glA, glB, **proven_raiser):
1334 '''Find the intersection between two geodesic line segments.
1336 @return: An L{Intersector5Tuple}C{(A, B, sAB, aAB, c)}
1337 or C{None} if none found.
1339 @see: Method L{Segment} for further details.
1340 '''
1341 X = self.Segment(glA, glB, **proven_raiser)
1342 return X if X is None else self._In5T(glA, glB, X, X, k2=True)
1344 def _Spherical(self, glA, glB, S):
1345 '''(INTERNAL) Get solution based from a spherical triangle.
1346 '''
1347 # threshold for coincident geodesics/intersections ~4.3 nm WGS84.
1348 A = self._Position(glA, S.sA)
1349 B = self._Position(glB, S.sB)
1350 D = self._Inverse(A, B)
1352 a, da = _diff182(A.azi2, D.azi1) # interior angle at A
1353 b, db = _diff182(B.azi2, D.azi2) # exterior angle at B
1354 c, dc = _diff182(a, b)
1355 if fsum1_(dc, db, -da, c) < 0: # inverted triangle
1356 a, da = -a, -da
1357 b, db = -b, -db
1358 sa, ca = _sincos2de(a, da)
1359 sb, cb = _sincos2de(b, db)
1361 e, z, _abs = _EPS3, D.s12, fabs
1362 if _abs(z) <= self._EPS3R: # XXX z <= ...
1363 sA = sB = 0 # at intersection
1364 c = 1 if _abs(sa - sb) <= e and _abs(ca - cb) <= e else (
1365 -1 if _abs(sa + sb) <= e and _abs(ca + cb) <= e else 0)
1366 elif _abs(sa) <= e and _abs(sb) <= e: # coincident
1367 sA = ca * z * _0_5 # choose mid-point
1368 sB = -cb * z * _0_5
1369 c = 1 if (ca * cb) > 0 else -1
1370 # alt1: sA = ca * z; sB = 0
1371 # alt2: sB = -cb * z; sA = 0
1372 else: # general case
1373 sz, cz = sincos2(z / self.R)
1374 # [SKIP: Divide args by |sz| to avoid possible underflow
1375 # in {sa, sb} * sz; this is probably not necessary].
1376 # Definitely need to treat sz < 0 (z > PI*R) correctly in
1377 # order to avoid some convergence failures in _Basic2.
1378 sA = atan2(sb * sz, sb * ca * cz - sa * cb) * self.R
1379 sB = atan2(sa * sz, -sa * cb * cz + sb * ca) * self.R
1380 c = 0
1381 return XDict_(sA, sB, c) # no ._Delto
1383 @Property_RO
1384 def _T2D1Delta(self):
1385 return self._T2d3Delta(self._D1)
1387 @Property_RO
1388 def _T2D2Delta(self):
1389 return self._T2d3Delta(self._D2)
1391 def _T2d3Delta(self, d3):
1392 return self._T2 - d3 - self.Delta
1394 @Property_RO
1395 def _Tol(self): # convergence tolerance
1396 return self._cHalf * _EPSjam
1398 def toStr(self, **prec_sep_name): # PYCHOK signature
1399 '''Return this C{Intersector} as string.
1401 @see: L{Ellipsoid.toStr<pygeodesy.ellipsoids.Ellipsoid.toStr>}
1402 for further details.
1404 @return: C{Intersector} (C{str}).
1405 '''
1406 return self._instr(props=(Intersector.geodesic,), **prec_sep_name)
1408 def _xLines(self, glA, glB, s13=False):
1409 # check two geodesic lines vs this geodesic
1410 C, gls = Caps.LINE_CAPS, dict(glA=glA, glB=glB)
1411 _xinstanceof(*self._GeodesicLines, **gls)
1412 for n, gl in gls.items():
1413 try:
1414 _xgeodesics(gl.geodesic, self.geodesic)
1415 if s13 and not isfinite(gl.s13): # or not gl.caps & Caps.DISTANCE_IN
1416 t = gl.geodesic.InverseLine.__name__
1417 raise TypeError(_not_(_an(t)))
1418 c = gl.caps & C
1419 if c != C: # not gl.caps_(C)
1420 c, C, x = map1(bin, c, C, _xor(c, C))
1421 x = _SPACE_(_xor.__name__, repr(x))[1:]
1422 raise GeodesicError(caps=c, LINE_CAPS=C, txt=x)
1423 except Exception as x:
1424 raise GeodesicError(n, gl, cause=x)
1427class Intersect7Tuple(_NamedTuple):
1428 '''7-Tuple C{(A, B, sAB, aAB, c, kA, kB)} with C{A} and C{B} each
1429 a C{LatLon} or L{LatLon4Tuple}C{(lat, lon, height, datum)} of
1430 the intersection on each geodesic line, the distance C{sAB} in
1431 in C{meter} and angular distance C{aAB} in C{degrees} between
1432 C{A} and C{B}, coincidence indicator C{c} and segment indicators
1433 C{kA} and C{kB} all C{int}, see L{XDict} and method U{intersect7
1434 <_IntersectBase.intersect7>}.
1435 '''
1436 _Names_ = (_A_, _B_, _sAB_, _aAB_, _c_, 'kA', 'kB')
1437 _Units_ = (_Pass, _Pass, Meter, Degrees, Int, Int, Int)
1440class Intersectool5Tuple(_NamedTuple):
1441 '''5-Tuple C{(A, B, sAB, aAB, c)} with C{A} and C{B} the C{Position}
1442 of the intersection on each geodesic line, the distance C{sAB}
1443 between C{A} and C{B} in C{meter}, the angular distance C{aAB} in
1444 C{degrees} and coincidence indicator C{c} (C{int}), see L{XDict}.
1446 @note: C{A} and C{B} are each a C{GDict} with C{lat1}, C{lon1} and
1447 C{azi1} or C{lat2}, C{lon2} from the geodesic line C{glA}
1448 respectively C{glB} and the intersection location in C{latX},
1449 C{lonX}, distance C{s1X} in C{meter} and angular distance
1450 C{a1M} in C{degrees} and the segment indicator C{kX}. See
1451 L{XDict} for more details.
1452 '''
1453 _Names_ = Intersect7Tuple._Names_[:5]
1454 _Units_ = Intersect7Tuple._Units_[:5]
1457class Intersector5Tuple(Intersectool5Tuple):
1458 '''5-Tuple C{(A, B, sAB, aAB, c)} with C{A} and C{B} the C{Position}
1459 of the intersection on each geodesic line, the distance C{sAB}
1460 between C{A} and C{B} in C{meter}, angular distance C{aAB} in
1461 C{degrees} and coincidence indicator C{c} (C{int}), see L{XDict}.
1463 @note: C{A} and C{B} are each a C{GeodesicLine...Position} for
1464 C{outmask=Caps.STANDARD} with the intersection location in
1465 C{latX}, C{lonX}, azimuth in C{aziX}, distance C{s1X} in
1466 C{meter} and angular distance C{a1X} in C{degrees} and the
1467 segment indicator C{kX}. See L{XDict} for more details.
1468 '''
1469 _Names_ = Intersectool5Tuple._Names_
1472class Middle5Tuple(Intersectool5Tuple):
1473 '''5-Tuple C{(A, B, sMM, aMM, c)} with C{A} and C{B} the I{line segments}
1474 including the mid-point location in C{latM}, C{lonM}, distance C{s1M}
1475 in C{meter} and angular distance C{a1M} in C{degrees}, the distance
1476 between both mid-points C{sMM} in C{meter} and angular distance C{aMM}
1477 in C{degrees} and coincidence indicator C{c} (C{int}). See L{XDict}
1478 for more details.
1479 '''
1480 _Names_ = (_A_, _B_, 'sMM', 'aMM', _c_)
1483class _List(list):
1485 _Delta = 0 # equality margin
1487 def __init__(self, Delta):
1488 self._Delta = Delta
1489# list.__init__(self)
1491 def __contains__(self, other):
1492 # handle C{if X in this: ...}
1493 a, b = other.sA, other.sB
1494 D, _D1 = self._Delta, _L1
1495 for X in self:
1496 if _D1(X.sA - a, X.sB - b) <= D:
1497 return True
1498 return False
1500 def addend(self, X, *d0_i):
1501 # append an item, updated
1502 if d0_i:
1503 d0, i = d0_i
1504 X.set_(sX0=d0, iteration=i)
1505 self.append(X)
1506 return X.sX0
1508 def sorter(self, sMaX0, dot_C, glA, glB, **_C):
1509 # trim and sort the X items
1511 def _key(X):
1512 return X.sX0 # rank of X
1514 t = (X for X in self if X.sX0 <= sMaX0)
1515 for X in sorted(t, key=_key):
1516 yield dot_C(X, glA, glB, **_C) if _C else X
1519def _L1(a, b):
1520 '''(INTERNAL) Return the I{L1} distance.
1521 '''
1522 return fabs(a) + fabs(b)
1525__all__ += _ALL_DOCS(_IntersectBase)
1527if __name__ == '__main__': # MCCABE 14
1529 from pygeodesy import printf
1530 __help_ = '--help'
1532 def _main(args):
1534 from pygeodesy import GeodesicExact
1535 from pygeodesy.internals import _plural, _usage
1536 from pygeodesy.interns import _COLONSPACE_, _DOT_, _EQUAL_, \
1537 _i_, _m_, _n_, _version_, _X_
1538 import re
1540 class XY0(Float):
1541 pass
1543 def _opts(_h): # for _usage()
1544 ll4 = ' latA1 lonA1'
1545 ll4 += ll4.replace('1', '2')
1546 ll4 += ll4.replace(_A_, _B_)
1547 llz = _SPACE_(NN, _latA_, _lonA_, 'aziA')
1548 llz2 = llz + llz.replace(_A_, _B_)
1549 return dict(opts='-Verbose|V--version|v--help|h--Tool|T--Check|C-R <meter>-',
1550 alts=((_c_ + llz2),
1551 (_i_ + ll4),
1552 (_m_ + ll4),
1553 (_n_ + llz + ' aziB'),
1554 ('o' + llz2 + ' x0 y0')),
1555 help=_h if isinstance(_h, str) else NN)
1557 def _starts(Opt, arg):
1558 return arg == Opt[1:3] or (len(arg) > 2 and Opt.startswith(arg))
1560 _isopt = re.compile('^[-]+[a-z]*$', flags=re.IGNORECASE).match
1562 I = Intersector(GeodesicExact()) # PYCHOK I
1563 M = m = _R = None
1564 _T = _V = _h = _C = False
1566 while args and _isopt(args[0]):
1567 arg = args.pop(0)
1568 if arg == _c__:
1569 M, m = I.Closest, 6 # latA lonA aziA latB lonB aziB
1570 elif _starts('--Check', arg):
1571 _C = True
1572 elif _starts(__help_, arg):
1573 _h = args[0] if args and _isopt(args[0]) else True
1574 elif arg == _i__:
1575 M, m = I.Segment, 8 # latA1 lonA1 latA2 lonA2 latB1 lonB1 latB2 lonB2
1576 elif arg == '-m':
1577 M, m = I.Middle, 8 # latA1 lonA1 latA2 lonA2 latB1 lonB1 latB2 lonB2
1578 _R = None # zap -R
1579 elif arg == _n__:
1580 M, m = I.Next, 4 # latA lonA aziA aziB
1581 elif arg == _o__:
1582 M, m = I.Closest, 8 # latA lonA aziA latB lonB aziB x0 y0
1583 elif arg == _R__ and args:
1584 _R = args.pop(0)
1585 elif _starts('--Tool', arg):
1586 I = Intersectool() # PYCHOK I
1587 if _V:
1588 I.verbose = True
1589 if not _Xables.X_OK(I.IntersectTool):
1590 I.IntersectTool = _Xables.IntersectTool(_Xables.bin_)
1591 elif _V:
1592 _ = I.version
1593 M, _T = None, True
1594 elif _starts('--Verbose', arg):
1595 _V = True
1596 if _T:
1597 I.verbose = True
1598 elif _starts('--version', arg):
1599 printf(_COLONSPACE_(*((_version_, I.version) if _T else
1600 (__version__, repr(I)))))
1601 else:
1602 raise ValueError('invalid option %r' % (arg,))
1604 if _h or M is None:
1605 printf(_usage(__file__, **_opts(_h)), nl=1)
1606 else:
1607 n = len(args)
1608 if n < m:
1609 n = _plural('only %s arg' % (n,), n) if n else 'no args'
1610 raise ValueError('%s, need %s' % (n, m))
1611 args[:] = args[:m]
1613 kwds = dict(_C=True) if _C else {}
1614 if M == I.Next: # -n
1615 # get latA lonA aziA latA lonA aziB
1616 args[3:] = args[:2] + args[3:4]
1617 elif M == I.Closest and m > 6: # -o
1618 y0 = Meter(y0=args.pop())
1619 x0 = Meter(x0=args.pop())
1620 kwds.update(X0=XDict_(x0, y0))
1621 if _R:
1622 m = Meter_(_R, name=_R__, low=0)
1623 kwds.update(sMaX0=m)
1624 M = I.All
1626 n = len(args) // 2
1627 glA = I.Line(*args[:n])
1628 glB = I.Line(*args[n:])
1630 m = _DOT_(I.__class__.__name__, M.__name__)
1631 if _V:
1632 X = _SPACE_(_X_, _EQUAL_, m)
1633 printf(unstr(X, glA, glB, **kwds))
1635 X = M(glA, glB, **kwds)
1636 if X is None or isinstance(X, (XDict, tuple)):
1637 printf(_COLONSPACE_(m, repr(X)))
1638 else:
1639 for i, X in enumerate(X):
1640 printf(_COLONSPACE_(Fmt.INDEX(m, i), repr(X)))
1642 def _examples():
1644 from pygeodesy.internals import _usage_argv
1646 s = _SPACE_(*_usage_argv(__file__))
1647 for t in ('-h', '-h -n',
1648 '-c 0 0 45 40 10 135',
1649 '-C -c 0 0 45 40 10 135',
1650 '-T -R 2.6e7 -c 0 0 45 40 10 135',
1651 '-c 50 -4 -147.7 0 0 90',
1652 '-C -c 50 -4 -147.7 0 0 90',
1653 '# % echo 0 0 10 10 50 -4 50S 4W | IntersectTool -i -p 0 -C',
1654 '# -631414 5988887 0 -3',
1655 '# -4.05187 -4.00000 -4.05187 -4.00000 0',
1656 '-m 0 0 10 10 50 -4 50S 4W',
1657 '-C -m 0 0 10 10 50 -4 50S 4W',
1658 '-i 0 0 10 10 50 -4 50S 4W',
1659 '-T -i 0 0 10 10 50 -4 50S 4W',
1660 '-C -i 0 0 10 10 50 -4 50S 4W',
1661 '-T -C -i 0 0 10 10 50 -4 50S 4W',
1662 '-V -T -i 0 0 10 10 50 -4 -50 -4',
1663 '-C -R 4e7 -c 50 -4 -147.7 0 0 90',
1664 '-T -C -R 4e7 -c 50 -4 -147.7 0 0 90',
1665 '-R 4e7 -i 0 0 10 10 50 -4 -50 -4',
1666 '-T -R 4e7 -i 0 0 10 10 50 -4 -50 -4'):
1667 if t.startswith(_HASH_):
1668 printf(t, nl=int(t[2] == '%'))
1669 else:
1670 printf(_SPACE_(_HASH_, s, t), nl=1)
1671 argv[1:] = t = t.split()
1672 _main(t)
1674 from sys import argv, stderr
1675 try:
1676 if len(argv) == 2 and argv[1] == __help_:
1677 _examples()
1678 else:
1679 _main(argv[1:])
1681 except Exception as x:
1682 x = _SPACE_(x, NN, _HASH_, *argv)
1683 printf(x, file=stderr, nl=1)
1684 if '-V' in x or _MODS.errors.exception_chaining():
1685 raise
1686 exit(1)
1688# % env PYGEODESY_INTERSECTTOOL=... python3 -m pygeodesy.geodesici --help
1690# % python3 -m pygeodesy.geodesici -h
1691#
1692# usage: python3 -m ....pygeodesy.geodesici [--Verbose | -V] [--version | -v] [--help | -h] [--Tool | -T] [--Check | -C] [-R meter]
1693# [-c latA lonA aziA latB lonB aziB |
1694# -i latA1 lonA1 latA2 lonA2 latB1 lonB1 latB2 lonB2 |
1695# -m latA1 lonA1 latA2 lonA2 latB1 lonB1 latB2 lonB2 |
1696# -n latA lonA aziA aziB |
1697# -o latA lonA aziA latB lonB aziB x0 y0]
1699# % python3 -m ....pygeodesy.geodesici -h -n
1700#
1701# usage: python3 -m ....pygeodesy.geodesici -n latA lonA aziA aziB
1703# % python3 -m ....pygeodesy.geodesici -c 0 0 45 40 10 135
1704# Intersector.Closest: XDict(c=0, sA=3862290.547855, sB=2339969.547699, sX0=6202260.095554)
1706# % python3 -m ....pygeodesy.geodesici -C -c 0 0 45 40 10 135
1707# Intersector.Closest: XDict(aAB=0.0, c=0, latA=23.875306, latB=23.875306, lonA=26.094096, lonB=26.094096, sA=3862290.547855, sAB=0.0, sB=2339969.547699, sX0=6202260.095554)
1709# % env PYGEODESY_INTERSECTTOOL=...python3 -m ....pygeodesy.geodesici -T -R 2.6e7 -c 0 0 45 40 10 135
1710# Intersectool.All[0]: XDict(c=0, sA=3862290.547855, sB=2339969.547699, sX0=6202260.095554)
1712# % python3 -m ....pygeodesy.geodesici -c 50 -4 -147.7 0 0 90
1713# Intersector.Closest: XDict(c=0, sA=6058048.653081, sB=-3311252.995823, sX0=9369301.648903)
1715# % python3 -m ....pygeodesy.geodesici -C -c 50 -4 -147.7 0 0 90
1716# Intersector.Closest: XDict(aAB=0.0, c=0, latA=0.0, latB=-0.0, lonA=-29.745492, lonB=-29.745492, sA=6058048.653081, sAB=0.0, sB=-3311252.995823, sX0=9369301.648903)
1718# % echo 0 0 10 10 50 -4 50S 4W | IntersectTool -i -p 0 -C
1719# -631414 5988887 0 -3
1720# -4.05187 -4.00000 -4.05187 -4.00000 0
1722# % python3 -m ....pygeodesy.geodesici -m 0 0 10 10 50 -4 50S 4W
1723# Intersector.Middle: XDict(c=0, sA=782554.549609, sB=5536835.161499, sX0=0.0)
1725# % python3 -m ....pygeodesy.geodesici -C -m 0 0 10 10 50 -4 50S 4W
1726# Intersector.Middle: XDict(aAB=10.262308, c=0, latA=5.019509, latB=0.036282, lonA=4.961883, lonB=-4.0, sA=782554.549609, sAB=1138574.546746, sB=5536835.161499, sX0=0.0)
1728# % python3 -m ....pygeodesy.geodesici -i 0 0 10 10 50 -4 50S 4W
1729# Intersector.Segment: XDict(c=0, k=-3, kA=-1, kB=0, sA=-631414.26877, sB=5988887.278435, sX0=1866020.935315)
1731# % env PYGEODESY_INTERSECTTOOL=... python3 -m ....pygeodesy.geodesici -T -i 0 0 10 10 50 -4 50S 4W
1732# Intersectool.Segment: XDict(c=0, k=-3, kA=-1, kB=0, sA=-631414.26877, sB=5988887.278435)
1734# % python3 -m ....pygeodesy.geodesici -C -i 0 0 10 10 50 -4 50S 4W
1735# Intersector.Segment: XDict(aAB=0.0, c=0, k=-3, kA=-1, kB=0, latA=-4.051871, latB=-4.051871, lonA=-4.0, lonB=-4.0, sA=-631414.26877, sAB=0.0, sB=5988887.278435, sX0=1866020.935315)
1737# % env PYGEODESY_INTERSECTTOOL=... python3 -m ....pygeodesy.geodesici -T -C -i 0 0 10 10 50 -4 50S 4W
1738# Intersectool.Segment: XDict(c=0, k=-3, kA=-1, kB=0, latA=-4.051871, latB=-4.051871, lonA=-4.0, lonB=-4.0, sA=-631414.26877, sAB=0.0, sB=5988887.278435)
1740# % env PYGEODESY_INTERSECTTOOL=... python3 -m ....pygeodesy.geodesici -V -T -i 0 0 10 10 50 -4 -50 -4
1741# Intersectool@1: /opt/local/bin/IntersectTool --version (invoke)
1742# Intersectool@1: '/opt/local/bin/IntersectTool: GeographicLib version 2.3' (0)
1743# Intersectool@1: /opt/local/bin/IntersectTool: GeographicLib version 2.3 (0)
1744# 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))
1745# 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)
1746# Intersectool@2: '-631414.2687702414 5988887.2784352796 0 -3' (0)
1747# Intersectool@2: sA=-631414.2687702414, sB=5988887.2784352796, c=0, k=-3 (0)
1748# Intersectool.Segment: XDict(c=0, k=-3, kA=-1, kB=0, sA=-631414.26877, sB=5988887.278435)
1750# % python3 -m ....pygeodesy.geodesici -C -R 4e7 -c 50 -4 -147.7 0 0 90
1751# 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)
1752# 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)
1753# 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)
1754# Intersector.All[3]: XDict(aAB=0.0, c=0, latA=-0.0, latB=0.0, lonA=150.046964, lonB=150.046964, sA=-13941907.021445, sAB=0.0, sB=-23371865.025835, sX0=37313772.047279)
1756# % env PYGEODESY_INTERSECTTOOL=... python3 -m ....pygeodesy.geodesici -T -C -R 4e7 -c 50 -4 -147.7 0 0 90
1757# 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)
1758# 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)
1759# 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)
1760# Intersectool.All[3]: XDict(c=0, latA=-0.0, latB=0.0, lonA=150.046964, lonB=150.046964, sA=-13941907.021445, sAB=0.0, sB=-23371865.025835, sX0=37313772.047279)
1762# % python3 -m ....pygeodesy.geodesici -R 4e7 -i 0 0 10 10 50 -4 -50 -4
1763# Intersector.All[0]: XDict(c=0, sA=-631414.26877, sB=5988887.278435, sX0=1866020.935315)
1764# Intersector.All[1]: XDict(c=0, sA=19422725.117572, sB=-14062417.105648, sX0=38239422.83511)
1765# Intersector.All[2]: XDict(c=0, sA=19422725.117572, sB=25945445.811603, sX0=39048781.218067)
1766# Intersector.All[3]: XDict(c=0, sA=39476927.464575, sB=5894074.699478, sX0=39051612.452944)
1768# % env PYGEODESY_INTERSECTTOOL=... python3 -m ....pygeodesy.geodesici -T -R 4e7 -i 0 0 10 10 50 -4 -50 -4
1769# Intersectool.All[0]: XDict(c=0, sA=-631414.26877, sB=5988887.278435, sX0=1862009.05513)
1770# Intersectool.All[1]: XDict(c=0, sA=19422725.117572, sB=-14062417.105648, sX0=38243434.715295)
1771# Intersectool.All[2]: XDict(c=0, sA=19422725.117572, sB=25945445.811603, sX0=39044769.337882)
1772# Intersectool.All[3]: XDict(c=0, sA=39476927.464575, sB=5894074.699478, sX0=39047600.57276)
1775# **) MIT License
1776#
1777# Copyright (C) 2024-2025 -- mrJean1 at Gmail -- All Rights Reserved.
1778#
1779# Permission is hereby granted, free of charge, to any person obtaining a
1780# copy of this software and associated documentation files (the "Software"),
1781# to deal in the Software without restriction, including without limitation
1782# the rights to use, copy, modify, merge, publish, distribute, sublicense,
1783# and/or sell copies of the Software, and to permit persons to whom the
1784# Software is furnished to do so, subject to the following conditions:
1785#
1786# The above copyright notice and this permission notice shall be included
1787# in all copies or substantial portions of the Software.
1788#
1789# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
1790# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
1791# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
1792# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR
1793# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
1794# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
1795# OTHER DEALINGS IN THE SOFTWARE.