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, mainly intended I{for testing purposes}.
12Set env variable C{PYGEODESY_INTERSECTTOOL} to the (fully qualified) path of the C{IntersectTool} executable or use
13property L{Intersectool.IntersectTool}. For usage and some examples run C{"env PYGEODESY_INTERSECTTOOL=<IntersectTool-path>
14python3 -m pygeodesy.geodesici --help"}.
16Both L{Intersectool} and L{Intersector} provide methods C{All}, C{Closest}, C{Next} and C{Segment} and produce
17L{XDict} instances with 4 or more items. Adjacent methods C{All5}, C{Closest5}, C{Next5} and C{Segment} return
18or yield L{Intersectool5Tuple} or L{Intersector5Tuple}s with the lat-, longitude and azimuth of each intersection
19as an extended, geodesic C{Position}-like L{GDict} instance.
21For more details, see the C++ U{GeographicLib<https://GeographicLib.SourceForge.io/C++/doc/index.html>}
22documentation, I{Charles F.F. Karney}'s paper U{Geodesics intersections<https://arxiv.org/abs/2308.00495>}
23and I{S. Baselga Moreno & J.C. Martinez-Llario}'s U{Intersection and point-to-line solutions for geodesics
24on the ellipsoid<https://riunet.UPV.ES/bitstream/handle/10251/122902/Revised_Manuscript.pdf>}.
25'''
26# make sure int/int division yields float quotient
27from __future__ import division as _; del _ # noqa: E702 ;
29from pygeodesy.basics import _copy, _enumereverse, map1, \
30 _xinstanceof, _xor, typename
31from pygeodesy.constants import EPS, INF, INT0, PI, PI2, PI_4, \
32 _0_0, _0_5, _1_0, _1_5, _2_0, _3_0, \
33 _45_0, _64_0, _90_0, isfinite
34from pygeodesy.constants import _EPSjam # PYCHOK used!
35from pygeodesy.ellipsoids import _EWGS84, Fmt, unstr
36from pygeodesy.errors import GeodesicError, IntersectionError, _an, \
37 _xgeodesics, _xkwds, _xkwds_get, \
38 _xkwds_kwds, _xkwds_pop2
39# from pygeodesy.errors import exception_chaining # _MODS
40from pygeodesy.fmath import euclid, fdot
41from pygeodesy.fsums import Fsum, fsum1_, _ceil
42# from pygeodesy.internals import typename # from .basics
43from pygeodesy.interns import NN, _A_, _B_, _c_, _COMMASPACE_, _DMAIN_, \
44 _HASH_, _M_, _not_, _SPACE_, _too_
45from pygeodesy.karney import Caps, _diff182, GDict, _sincos2de, _Xables
46from pygeodesy.lazily import _ALL_DOCS, _ALL_LAZY, _ALL_MODS as _MODS
47from pygeodesy.named import ADict, _NamedBase, _NamedTuple, _Pass
48# from pygeodesy.namedTuples import _LL4Tuple # _MODS
49from pygeodesy.props import deprecated_method, Property, \
50 Property_RO, property_RO, property_ROver
51from pygeodesy.solveBase import _SolveCapsBase, pairs
52# from pygeodesy.streprs import pairs # from .solveBase
53# from pygeodesy.streprs import Fmt, unstr # from .ellipsoids
54from pygeodesy.units import Azimuth as Azi, Degrees, Int, _isDegrees, \
55 Lat, Lon, Meter, Meter_
56from pygeodesy.utily import atan2, sincos2, fabs, radians
58# from math import ceil as _ceil, fabs, radians # .fsums, .utily
60__all__ = _ALL_LAZY.geodesici
61__version__ = '26.02.04'
63_0t = 0, # int
64_1_1t = -1, +1
65_1_0_1t = -1, 0, +1
66_aAB_ = 'aAB'
67_c__ = '-c' # PYCHOK used!
68_cWGS84 = _EWGS84.a * PI2 # outer circumference
69_EPS3 = EPS * _3_0
70_EPSr5 = pow(EPS, 0.2) # PYCHOK used! 7.4e-4 or ~3"
71_i__ = '-i' # PYCHOK used!
72_latA_ = 'latA'
73_lonA_ = 'lonA'
74_n__ = '-n' # PYCHOK used!
75_o__ = '-o' # PYCHOK used!
76_R__ = '-R'
77_sAB_ = 'sAB'
78_sX0_ = 'sX0'
79_TRIPS = 128
82class XDict(ADict):
83 '''4+Item result from L{Intersectool} and L{Intersector} methods C{All},
84 C{Closest}, C{Next} and C{Segment} with the intersection offsets
85 C{sA}, C{sB} and C{sX0} in C{meter} and the coincidence indicator
86 C{c}, an C{int}, +1 for parallel, -1 for anti-parallel or 0 otherwise.
88 Offsets C{sA} and C{sB} are distances measured I{along} geodesic line
89 C{glA} respectively C{glB}, but C{sX0} is the I{L1-distance} between
90 the intersection and the I{origin} C{X0}.
92 If present, distance C{sAB} and angular distance C{aAB} represent the
93 separation between the intersection point on geodesic lines C{glA}
94 and C{glB} in C{meter} respectively C{degrees}, typically below
95 C{5e-9 meter} or C{5 nm} respectively C{5e-14 degrees} or C{1 n"}.
97 For segments, indicators C{kA} and C{kB} are C{0} if the segments
98 intersect or C{-1} or C{+1} if the intersection is I{before} the
99 start, respectively I{after} the end of the segment, similar to
100 L{Intersection3Tuple<Intersection3Tuple>}. Segment indicator C{k}
101 is I{Karney}'s C{segmode}, equal C{kA * 3 + kB}.
102 '''
103 _Delta = EPS # default margin, see C{Intersector._Delto}
105 def __add__(self, other):
106 X = _copy(self)
107 X += other
108 return X
110 def __eq__(self, other):
111 return not self.__ne__(other)
113 def __iadd__(self, other):
114 if isinstance(other, tuple): # and len(other) == 2:
115 a, b = other
116 else:
117 # _xinstanceof(XDict, other=other)
118 a = other.sA
119 b = other.sB
120 if other.c:
121 self.c = other.c
122 self.sA += a # PYCHOK sA
123 self.sB += b # PYCHOK sB
124 return self
126 def __le__(self, other):
127 # _xinstanceof(XDict, other=other)
128 return self == other or self < other
130 def __lt__(self, other):
131 # _xinstanceof(XDict, other=other)
132 return self.sA < other.sA or (self.sA == other.sA and # PYCHOK sA
133 self.sB < other.sB and # PYCHOK sB
134 self != other)
136 def __ne__(self, other):
137 # _xinstanceof(XDict, other=other)
138 return self is not other and self.L1(other) > self._Delta
140 def _corners(self, sA, sB, T2):
141 # yield all corners further than C{T2}
142 a, b = self.sA, self.sB # PYCHOK sA, sB
143 for x in (0, sA):
144 for y in (0, sB):
145 if _L1(x - a, y - b) >= T2:
146 yield XDict_(x, y)
148 def _fixCoincident(self, X, c0=0):
149 # return the mid-point if C{X} is anti-/parallel
150 c = c0 or X.c
151 if c:
152 s = (self.sA - X.sA + # PYCHOK sA
153 (self.sB - X.sB) * c) * _0_5 # PYCHOK sB
154 X = X + (s, s * c) # NOT +=
155 return X
157 def _fixSegment(self, sA, sB): # PYCHOK no cover
158 # modify this anti-/parallel C{XDict}
159 a, b, c = self.sA, self.sB, self.c # PYCHOK sA, sB, c
161 def _g(): # intersection in smallest gap
162 if c > 0: # distance to [A, B] is |(a - b) - (A - B)|
163 t = a - b # consider corners [0, sB] and [sA, 0]
164 t = fabs(t + sB) < fabs(t - sA)
165 s = a + b
166 else: # distance to [A, B] is |(a + b) - (A + B)|
167 t = a + b # consider corner [0, 0] and [sA, sB]
168 t = fabs(t) < fabs(t - (sA + sB))
169 s = sB + (a - b)
170 return (sB if t else sA) - s
172 ta = -a
173 tb = sA - a
174 tc = -c * b
175 td = -c * (b - sB)
177 ga = 0 <= (b + c * ta) <= sB
178 gb = 0 <= (b + c * tb) <= sB
179 gc = 0 <= (a + tc) <= sA
180 gd = 0 <= (a + td) <= sA
182 # test opposite rectangle sides first
183 s = ((ta + tb) if ga and gb else (
184 (tc + td) if gc and gd else (
185 (ta + tc) if ga and gc else (
186 (ta + td) if ga and gd else (
187 (tb + tc) if gb and gc else (
188 (tb + td) if gb and gd else _g())))))) * _0_5
189 self += s, s * c
191 @property_RO
192 def _is00(self):
193 return not (self.sA or self.sB) # PYCHOK sA, sB
195 def L1(self, other=None):
196 '''Return the C{L1} distance.
197 '''
198 a, b = self.sA, self.sB # PYCHOK sA, sB
199 if other is not None:
200 # _xinstanceof(XDict, other=other)
201 a -= other.sA
202 b -= other.sB
203 return _L1(a, b)
205 def _nD1(self, D1):
206 # yield the C{Closest} starts
207 D_ = 0, D1, -D1
208 for a, b in zip((0, 1, -1, 0, 0),
209 (0, 0, 0, 1, -1)):
210 yield self + (D_[a], D_[b])
212 def _nD2(self, D2):
213 # yield the C{Next} starts
214 D22 = D2 * _2_0
215 D_ = 0, D2, D22, -D22, -D2
216 for a, b in zip((-1, -1, 1, 1, -2, 0, 2, 0),
217 (-1, 1, -1, 1, 0, 2, 0, -2)):
218 yield self + (D_[a], D_[b])
220 def _nmD3(self, n, m, D3): # d3 / 2
221 # yield the C{All} starts
222 yield self
223 for i in range(n, m, 2):
224 for j in range(n, m, 2):
225 if i or j: # skip self
226 yield self + ((i + j) * D3,
227 (i - j) * D3)
229 def _outSide(self, sA, sB):
230 # is this C{Xdist} outside one or both segments?
231 a, b = self.sA, self.sB # PYCHOK sA, sB
232 kA = -1 if a < 0 else (+1 if a > sA else INT0)
233 kB = -1 if b < 0 else (+1 if b > sB else INT0)
234 self.set_(kA=kA, kB=kB, k=(kA * 3 + kB) or INT0)
235 return bool(kA or kB)
237 def _skip(self, S_, T1_Delta):
238 # remove starts from list C{S_} near this C{XDict}
239 for j, S in _enumereverse(S_):
240 if S.L1(self) < T1_Delta:
241 S_.pop(j)
244def XDict_(sA=_0_0, sB=_0_0, c=INT0, sX0=_0_0):
245 '''(INTERNAL) New L{XDict} from positionals.
246 '''
247 return XDict(sA=sA, sB=sB, c=c, sX0=sX0)
249_X000 = XDict_() # PYCHOK origin
250_XINF = XDict_(INF)
253class _IntersectBase(_NamedBase):
254 '''(INTERNAL) Base class for L{Intersectool} and L{Intersector}.
255 '''
256 # _g = None
258 def __init__(self, geodesic, **name):
259 _xinstanceof(*_EWGS84._Geodesics, geodesic=geodesic)
260 self._g = geodesic
261 if name:
262 self.name = name
264 @Property_RO
265 def a(self):
266 '''Get the I{equatorial} radius, semi-axis (C{meter}).
267 '''
268 return self.ellipsoid.a
270 equatoradius = a # = Requatorial
272 def All(self, glA, glB, **kwds): # PYCHOK no cover
273 '''(INTERNAL) I{Must be overloaded}.'''
274 self._notOverloaded(glA, glB, **kwds)
276 @Property_RO
277 def _cHalf(self): # normalizer, semi-circumference
278 return self.R * PI # ~20K Km WGS84
280 @Property_RO
281 def _cMax(self): # outer circumference
282 return max(self.a, self.ellipsoid.b, self.R) * PI2
284 @property_RO
285 def datum(self):
286 '''Get the geodesic's datum (C{Datum}).
287 '''
288 return self.geodesic.datum
290 @Property_RO
291 def ellipsoid(self):
292 '''Get the C{geodesic}'s ellipsoid (C{Ellipsoid}).
293 '''
294 return self.geodesic.datum.ellipsoid
296 @Property_RO
297 def f(self):
298 '''Get the I{flattening} (C{scalar}), C{0} for spherical, negative for prolate.
299 '''
300 return self.ellipsoid.f
302 flattening = f
304 @property_RO
305 def geodesic(self):
306 '''Get the C{Geodesic} (C{GeodesicExact, GeodesicSolve, or ...}).
307 '''
308 return self._g
310 def _illz2G(self, G, il):
311 '''(INTERNAL) Set C{InverseLine} 1-/2-attrs into C{G}, a C{GDict}.
312 '''
313 try:
314 G.set_(lat1=il.lat1, lon1=il.lon1, azi1=il.azi1, a12=il.a13, # .Arc()
315 lat2=il.lat2, lon2=il.lon2, azi2=il.azi2, s12=il.s13) # .Distance()
316 except AttributeError:
317 r = il.Position(il.s13, outmask=Caps.STANDARD_LINE) # isfinite(il.s13)
318 G.set_(**r)
319# for n, v in r.items():
320# if not hasattr(il, n):
321# setattr(il, n, v)
322 return G
324 def intersect7(self, start1, end1, start2, end2, X0=_X000, aMaX0=0, sMaX0=_cWGS84,
325 **LatLon_and_kwds):
326 '''Yield the intersections of two geodesic lines, each defined by a start
327 and end point or by a start point and an azimuth (bearing from North).
329 @arg start1: Start point of the first line (C{LatLon}).
330 @arg end1: End point of the first line (C{LatLon}) or the azimuth at the
331 B{C{start1}} point (compass C{degrees360}).
332 @arg start2: Start point of the second line (C{LatLon}).
333 @arg end2: End point of the second line (C{LatLon}) or the azimuth at the
334 B{C{start2}} point (compass C{degrees360}).
335 @kwarg X0: Optional I{origin} for I{L1-distances} (L{XDict}) or C{None} for
336 the L{Middle<Intersector.Middle>}, otherwise C{XDiff_(0, 0)}.
337 @kwarg aMaX0: Upper limit for the I{angular L1-distance}
338 (C{degrees}) or C{None} or C{0} for unlimited.
339 @kwarg sMaX0_C: Optional, upper limit C{B{sMaX0}=2*PI*R} for the
340 I{L1-distance} to B{C{X0}} (C{meter}).
341 @kwarg LatLon_and_kwds: Optional class C{B{LatLon}=None} to return intersection
342 points and optional, additional B{C{LatLon}} keyword arguments.
344 @note: The C{lat} and C{lon} attr of B{C{start1}}, B{C{end1}}, B{C{start2}} and
345 B{C{end2}} are used I{verbatim}, ignoring C{datum} or C{ellipsoid}.
347 @return: Yield an L{Intersect7Tuple}C{(A, B, sAB, aAB, c, kA, kB)} for every
348 intersection found, with C{A} and C{B} each a B{C{LatLon}} or if
349 C{B{LatLon} is None} or not specified, a L{LatLon4Tuple}C{(lat, lon,
350 height, datum)} with C{height 0} and this C{datum}.
352 @raise GeodesicError: Invalid B{C{start1}}, B{C{end1}}, B{C{start2}} or
353 B{C{end2}} or B{C{end1}} and B{C{end2}} differ in type.
355 @raise IntersectionError: No convergence.
356 '''
358 def _args(s, e):
359 t = (e,) if _isDegrees(e) else (e.lat, e.lon)
360 return (s.lat, s.lon) + t
362 try:
363 glA = self.Line(*_args(start1, end1))
364 glB = self.Line(*_args(start2, end2))
365 except Exception as x:
366 raise GeodesicError(start1=start1, end1=end1, start2=start2, end2=end2, cause=x)
368 LL, kwds = _xkwds_pop2(LatLon_and_kwds, LatLon=None)
369 d, kwds = _xkwds_pop2(kwds, datum=self.datum)
370 h, kwds = _xkwds_pop2(kwds, height=0)
372 _LL4T = _MODS.namedTuples._LL4Tuple
373 for X in self.All(glA, glB, X0=X0, aMaX0=aMaX0, sMaX0=sMaX0, _C=True):
374 A = B = _LL4T(X.latA, X.lonA, h, d, LL, kwds, iteration=X.iteration)
375 if X.sAB or X.latA != X.latB or X.lonA != X.lonB:
376 B = _LL4T(X.latB, X.lonB, h, d, LL, kwds, iteration=X.iteration)
377 yield Intersect7Tuple(A, B, X.sAB, X.aAB, X.c, _xkwds_get(X, kA=0),
378 _xkwds_get(X, kB=0))
380 def _Inversa12(self, A, B=None):
381 lls = (0, 0, A, 0) if B is None else (A.lat2, A.lon2,
382 B.lat2, B.lon2)
383 r = self._g.Inverse(*lls, outmask=Caps.DISTANCE)
384 return r.s12, r.a12 # .a12 always in r
386 def k2kAkB(self, k):
387 '''Unravel C{k} into C{kA} and C{kB}.
389 @arg k: Segment indicator C{kA * 3 + kB} (C{int}).
391 @return: An C{ADict(k=k, kA=kA, kB=kB)}.
393 @raise GeodesicError: Invalid B{C{k}}.
394 '''
395 for kA in range(-1, 2):
396 for kB in range(-1, 2):
397 if (kA * 3 + kB) == k:
398 return ADict(k=k, kA=kA, kB=kB)
399 raise GeodesicError(k=k)
401# def k2kAkB(self, k):
402# # unravel C{k} into C{kA} and C{kB}.
403# kA, kB = divmod(k, 3)
404# if kB > 1:
405# kA += 1
406# kB -= 3
407# return kA, kB
409 def Line(self, lat1, lon1, azi1_lat2, *lon2, **name): # PYCHOK no cover
410 '''(INTERNAL) I{Must be overloaded}.'''
411 self._notOverloaded(lat1, lon1, azi1_lat2, *lon2, **name)
413 def _ll3z4ll(self, lat1, lon1, azi1_lat2, *lon2):
414 t = Lat(lat1=lat1), Lon(lon1=lon1)
415 if lon2: # get azis for All, keep lat-/lons
416 t += Lat(lat2=azi1_lat2), Lon(lon2=lon2[0])
417 else:
418 t += Azi(azi1=azi1_lat2),
419 return t
421 @deprecated_method
422 def Next5s(self, glA, glB, X0=_X000, aMax=1801, sMax=0, **unused): # PYCHOK no cover
423 '''DEPRECATED on 2024.07.02, use method C{All5}.'''
424 return self.All5(glA, glB, X0=X0, aMaX0=aMax, sMaX0=sMax) # PYCHOK attr
426 @Property_RO
427 def R(self):
428 '''Get the I{authalic} earth radius (C{meter}).
429 '''
430 return self.ellipsoid.R2
432 def _sMaX0_C2(self, aMaX0=0, **sMaX0_C):
433 _g = _xkwds_get
434 s = _g(sMaX0_C, sMaX0=self._cMax)
435 s = _g(sMaX0_C, sMax=s) # for backward ...
436 a = _g(sMaX0_C, aMax=aMaX0) # ... compatibility
437 if a: # degrees to meter, approx.
438 s = min(s, self.R * radians(a)) # ellipsoid.degrees2m(a)
439 s = _g(sMaX0_C, _R=s)
440 if s < _EPS3:
441 s = _EPS3 # raise GeodesicError(sMaX0=s)
442 return s, _g(sMaX0_C, _C=False)
444 def _xNext(self, glA, glB, eps1, **eps_C): # PYCHOK no cover
445 eps1 = _xkwds_get(eps_C, eps=eps1) # eps for backward compatibility
446 if eps1 is not None:
447 a = glA.lat1 - glB.lat1
448 b = glA.lon1 - glB.lon1
449 if euclid(a, b) > eps1:
450 raise GeodesicError(lat_=a, lon_=b, eps1=eps1)
451 return _xkwds_kwds(eps_C, _C=False)
454class Intersectool(_IntersectBase, _SolveCapsBase):
455 '''Wrapper to invoke I{Karney}'s utility U{IntersectTool
456 <https://GeographicLib.SourceForge.io/C++/doc/IntersectTool.1.html>}
457 similar to class L{Intersector<geodesici.Intersector>}.
459 @note: Use property C{IntersectTool} or env variable C{PYGEODESY_INTERSECTTOOL}
460 to specify the (fully qualified) path to the C{IntersectTool} executable.
462 @note: This C{Intersectool} is intended I{for testing purposes only}, it invokes
463 the C{IntersectTool} executable for I{every} method call.
464 '''
465 _c_alt = _c__, # Closest latA lonA aziA latB lonB aziB
466 _C_option = '-C',
467 _Error = GeodesicError
468 _i_alt = _i__, # Segment latA1 lonA1 latA2 lonA2 latB1 lonB1 latB2 lonB2
469 _linelimit = 1200 # line printer width X 10
470 _n_alt = _n__, # Next latA lonA aziA aziB
471 _Names_ABs = _latA_, _lonA_, 'latB', 'lonB', _sAB_ # -C to stderr
472 _Names_XDict = 'sA', 'sB', _c_ # plus 'k' from -i or 'sX0' from -R
473 _o_alt = _o__, # Offset latA lonA aziA latB lonB aziB x0 y0
474 _Xable_name = _Xables.IntersectTool.__name__ # typename
475 _Xable_path = _Xables.IntersectTool()
477 def __init__(self, a_geodesic=None, f=None, **name):
478 '''New L{IntersectTool}.
480 @arg a_geodesic: Earth' equatorial axis (C{meter}) or a C{Geodesic}
481 (L{GeodesicExact<pygeodesy.geodesicx.GeodesicExact>},
482 wrapped L{Geodesic<pygeodesy.geodesicw.Geodesic>} or
483 L{GeodesicSolve<pygeodesy.geodsolve.GeodesicSolve>}).
484 @kwarg f: Earth' flattening (C{scalar}), required if B{C{a_geodesic}}
485 is in C{meter}, ignored otherwise.
486 @kwarg name: Optional C{B{name}=NN} (C{str}).
488 @raise GeodesicError: The eccentricity of the B{C{geodesic}}'s ellipsoid is too
489 large or no initial convergence.
491 @see: The B{Note} at I{Karney}'s C++ U{Intersect<https://GeographicLib.SourceForge.io/
492 C++/doc/classGeographicLib_1_1Intersect.html#ae41f54c9a44836f6c8f140f6994930cf>}.
493 '''
494 g = self._GeodesicExact() if a_geodesic is None else (a_geodesic if f is None else
495 self._GeodesicExact(a_geodesic, f))
496 _IntersectBase.__init__(self, g, **name)
498 def All(self, glA, glB, X0=_X000, eps1=_0_0, aMaX0=0, **sMaX0_C): # PYCHOK signature
499 '''Yield all intersections of two geodesic lines up to a limit.
501 @kwarg eps1: Optional margin for the L{euclid<pygeodesy.euclid>}ean distance
502 (C{degrees}) between the C{(lat1, lon1)} points of both lines for
503 using the L{IntersectTool<Intersectool.IntersectTool>}'s C{"-n"}
504 option, unless C{B{eps1}=None}.
506 @return: An L{XDict} for each intersection.
507 '''
508 for X, _ in self._All2(glA, glB, X0, eps1, aMaX0=aMaX0, **sMaX0_C):
509 yield X
511 def _All2(self, glA, glB, X0, eps1, **aMaX0_sMaX0_C): # MCCABE 13
512 '''(INTERNAL) Helper for methods C{.All} and C{.All5}.
513 '''
514 def _xz2(**gl):
515 try:
516 n, gl = gl.popitem() # _xkwds_item2(gl)
517 try:
518 return self._c_alt, (gl.azi1,)
519 except (AttributeError, KeyError):
520 return self._i_alt, (gl.lat2, gl.lon2)
521 except Exception as x:
522 raise GeodesicError(n, gl, cause=x)
524 _t, a = _xz2(glA=glA)
525 _x, b = _xz2(glB=glB)
526 if _x is not _t:
527 raise GeodesicError(glA=glA, glB=glB)
529 A = glA.lat1, glA.lon1
530 B = glB.lat1, glB.lon1
531 if _x is self._c_alt:
532 if X0 is _X000 or X0._is00:
533 if eps1 is not None and \
534 euclid(glA.lat1 - glB.lat1,
535 glA.lon1 - glB.lon1) <= eps1:
536 _x, B = self._n_alt, ()
537 else: # non-zero offset
538 _x = self._o_alt
539 b += X0.sA, X0.sB
541 sMaX0, _C = self._sMaX0_C2(**aMaX0_sMaX0_C)
542 for X in self._XDictInvoke(_x, _sX0_, (A + a + B + b),
543 _C=_C, _R=sMaX0):
544 if _C:
545 T = self._In5T(glA, glB, X, X)
546 if _aAB_ not in X:
547 X.set_(sAB=T.sAB, aAB=T.aAB)
548 else:
549 T = None
550 yield X.set_(c=int(X.c)), T
552 def All5(self, glA, glB, X0=_X000, **aMaX0_sMaX0):
553 '''Yield all intersections of two geodesic lines up to a limit.
555 @return: An L{Intersectool5Tuple} for each intersection.
556 '''
557 for _, T in self._All2(glA, glB, X0, _0_0, _C=True, **aMaX0_sMaX0):
558 yield T
560 @Property_RO
561 def _cmdBasic(self):
562 '''(INTERNAL) Get the basic C{IntersectTool} cmd (C{tuple}).
563 '''
564 return (self.IntersectTool,) + (self._e_option +
565 self._E_option +
566 self._p_option)
568 def Closest(self, glA, glB, X0=_X000, _C=False):
569 '''Find the closest intersection of two geodesic lines.
571 @kwarg _C: Use C{B{_C}=True} to include the C{"-C"} results (C{bool}).
573 @return: An L{XDict}.
574 '''
575 args = glA.lat1, glA.lon1, glA.azi1, \
576 glB.lat1, glB.lon1, glB.azi1
577 if X0 is _X000 or X0._is000:
578 _x = self._c_alt
579 else:
580 _x = self._o_alt
581 args += X0.sA, X0.sB
582 return self._XDictInvoke(_x, NN, args, _C=_C) # _R=None)
584 def Closest5(self, glA, glB, **unused):
585 '''Find the closest intersection of two geodesic lines.
587 @return: An L{Intersectool5Tuple}.
588 '''
589 X = self.Closest(glA, glB, _C=True)
590 return self._In5T(glA, glB, X, X)
592 @property_ROver
593 def _GeodesicExact(self):
594 '''Get the I{class} L{GeodesicExact}, I{once}.
595 '''
596 return _MODS.geodesicx.GeodesicExact # overwrite property_ROver
598 def _In5T(self, glA, glB, S, X, k2=False, **_2X):
599 A = GDict(glA).set_(lat2=X.latA, lon2=X.lonA, s12=S.sA)
600 B = GDict(glB).set_(lat2=X.latB, lon2=X.lonB, s12=S.sB)
601 if k2:
602 A.set_(k2=X.kA)
603 B.set_(k2=X.kB)
604 s, a = self._Inversa12(A, B)
605 sAB = _xkwds_get(X, sAB=s)
606 if a and s and s != sAB:
607 a *= sAB / s # adjust a
608 return Intersectool5Tuple(A._2X(glA, **_2X),
609 B._2X(glB, **_2X), sAB, a, X.c)
611 @Property
612 def IntersectTool(self):
613 '''Get the U{IntersectTool<https://GeographicLib.SourceForge.io/C++/doc/IntersectTool.1.html>}
614 executable (C{filename}).
615 '''
616 return self._Xable_path
618 @IntersectTool.setter # PYCHOK setter!
619 def IntersectTool(self, path):
620 '''Set the U{IntersectTool<https://GeographicLib.SourceForge.io/C++/doc/IntersectTool.1.html>}
621 executable (C{filename}), the (fully qualified) path to the C{IntersectTool} executable.
623 @raise GeodesicError: Invalid B{C{path}}, B{C{path}} doesn't exist or isn't the
624 C{IntersectTool} executable.
625 '''
626 self._setXable(path)
628 def Line(self, lat1, lon1, azi1_lat2, *lon2, **name):
629 '''Return a geodesic line from this C{Intersector}'s geodesic, specified
630 by two points or a point and an azimuth (bearing from North).
632 @return: A 3- or 6-item, named L{GDict}.
633 '''
634 args = self._ll3z4ll(lat1, lon1, azi1_lat2, *lon2)
635 gl = GDict((u.name, u) for u in args)
636# if lon2: # get azis for All, use lat-/lons as given
637# r = self._g.Inverse(outmask=Caps.AZIMUTH, *args)
638# gl.set_(azi1=Azi(azi1=r.azi1), azi2=Azi(azi2=r.azi2))
639 if name:
640 gl.name= name
641 return gl
643 def Middle(self, glA, glB, **_C):
644 '''Get the mid-points on two geodesic line segments.
646 @kwarg _C: Use C{B{_C}=True} to include the C{"-C"} results (C{bool}).
648 @return: An L{XDict}.
649 '''
650 return self._middle5(glA, glB, **_C)[0]
652 def _middle5(self, glA, glB, _C=False, **unused):
653 # return intersections C{A} and C{B} and the
654 # center C{X0} of rectangle [sA, sB]
656 def _smi4(**gl):
657 try:
658 n, gl = gl.popitem()
659 il = self._g.InverseLine(gl.lat1, gl.lon1, gl.lat2, gl.lon2)
660 except Exception as x:
661 raise GeodesicError(n, gl, cause=x)
662 s = il.s13
663 m = s * _0_5
664 return s, m, il, (il.Position(m, outmask=Caps.STANDARD_LINE) if _C else None)
666 sA, mA, iA, A = _smi4(glA=glA)
667 sB, mB, iB, B = _smi4(glB=glB)
668 X = XDict_(mA, mB) # centers
669 _ = X._outSide(sA, sB)
670 if _C: # _Names_ABs
671 s, a = self._Inversa12(A, B)
672 X.set_(latA=A.lat2, lonA=A.lon2, aMM=a, # assert sA == A.s12
673 latB=B.lat2, lonB=B.lon2, sMM=s) # assert sB == B.s12
674 return X, A, iA, B, iB
676 def Middle5(self, glA, glB, **unused):
677 '''Get the mid-points on two geodesic line segments and their distance.
679 @return: A L{Middle5Tuple}.
680 '''
681 X, A, iA, B, iB = self._middle5(glA, glB, _C=True)
682 A, B, s, a, c = self._In5T(A, B, X, X, _2X=_M_)
683 return Middle5Tuple(self._illz2G(A, iA),
684 self._illz2G(B, iB), s, a, c)
686 def Next(self, glA, glB, eps1=None, **_C): # PYCHOK no cover
687 '''Find the next intersection of two I{intersecting} geodesic lines.
689 @kwarg _C: Use C{B{_C}=True} to include the option C{"-C"} results (C{bool}).
691 @return: An L{XDict}.
692 '''
693 if eps1 or _C:
694 _C = self._xNext(glA, glB, eps1, **_C)
695 return self._XDictInvoke(self._n_alt, NN,
696 (glA.lat1, glA.lon1, glA.azi1, glB.azi1),
697 **_C) # _R=None
699 def Next5(self, glA, glB, **eps1): # PYCHOK no cover
700 '''Find the next intersection of two I{intersecting} geodesic lines.
702 @return: An L{Intersectool5Tuple}.
703 '''
704 X = self.Next(glA, glB, _C=True, **eps1)
705 return self._In5T(glA, glB, X, X)
707 def _R_option(self, _R=None):
708 '''(INTERNAL) Get the C{-R maxdist} option.
709 '''
710 return () if _R is None else (_R__, str(_R)) # -R maxdist
712 def Segment(self, glA, glB, **_C_unused):
713 '''Find the intersection between two geodesic line segments.
715 @kwarg _C: Use C{B{_C}=True} to include the option C{"-C"} results (C{bool}).
717 @return: An L{XDict}.
718 '''
719 X = self._XDictInvoke(self._i_alt, 'k', (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 of
775 L{GeodesicLineExact<pygeodesy.geodesicx.GeodesicLineExact>}, wrapped
776 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{GeodesicLineSolve<pygeodesy.geodsolve.GeodesicLineSolve>}).
789 @kwarg name: Optional C{B{name}=NN} (C{str}).
791 @raise GeodesicError: The B{C{geodesic}}'s ellipsoid is too eccentric or no initial convergence.
793 @see: The B{Note} at I{Karney}'s C++ U{Intersect<https://GeographicLib.SourceForge.io/
794 C++/doc/classGeographicLib_1_1Intersect.html#ae41f54c9a44836f6c8f140f6994930cf>}.
795 '''
796 _IntersectBase.__init__(self, geodesic, **name)
797 E = self.ellipsoid
798 t1 = E.b * PI # min distance between intersects
799 t2 = self._polarDist2(_90_0)[0] * _2_0 # furthest distance to closest intersect
800 if self.f > 0:
801 t3 = self._obliqDist4()[0] # half furthest min distance to next intersect
802 t4 = t1 # capture radius for spherical
803 else: # PYCHOK no cover
804 t1, t2 = t2, t1
805 t3 = self._Inversa12( _90_0)[0] * _2_0 # longest, shortest geodesic
806 t4 = self._polarB3()[0]
808 self._D1 = d1 = t2 * _0_5 # ~E.L tile spacing for Closest
809 self._D2 = d2 = t3 / _1_5 # tile spacing for Next
810 self._D3 = d3 = t4 - self.Delta # tile spacing for All
811 self._T1 = t1 # min distance between intersects
812 self._T2 = t2 = t1 * _2_0
813 if not (d1 < d3 and d2 < d3 and d2 < t2):
814 t = Fmt.PARENSPACED(_too_('eccentric'), E.e)
815 raise GeodesicError(ellipsoid=E.toStr(terse=2), txt=t)
817 def All(self, glA, glB, X0=None, aMaX0=0, **sMaX0_C): # MCCABE 15
818 '''Yield all intersections of two geodesic lines up to a limit.
820 @arg glA: A geodesic line (L{Line<Intersector.Line>}).
821 @arg glB: An other geodesic line (L{Line<Intersector.Line>}).
822 @kwarg X0: Optional I{origin} for I{L1-distances} (L{XDict}) or
823 C{None} for the L{Middle<Intersector.Middle>} of both
824 lines if both are a 4-C{args} L{Line<Intersector.Line>}
825 or C{InverseLine}, otherwise C{XDiff_(0, 0)}.
826 @kwarg aMaX0: Upper limit for the I{angular L1-distance}
827 (C{degrees}) or C{None} or C{0} for unlimited.
828 @kwarg sMaX0_C: Optional, upper limit C{B{sMaX0}=2*PI*R} for the
829 I{L1-distance} to B{C{X0}} (C{meter}) and option
830 C{B{_C}=False} to include the intersection lat-/
831 longitudes C{latA}, C{lonA}, C{latB}, C{lonB} and
832 distances C{sAB} and C{aSB}.
834 @return: Yield an L{XDict} for each intersection found.
836 @raise GeodesicError: Geodesic line B{C{glA}} or B{C{glB}}
837 invalid, incompatible or ill-configured.
839 @raise IntersectionError: No convergence.
840 '''
841 self._xLines(glA, glB)
842 if X0 is None:
843 try: # determine X0
844 X0, _, _ = self._middle3(glA, glB, True)
845 except GeodesicError: # no .Distance
846 X0 = _X000
847 sMaX0, _C = self._sMaX0_C2(aMaX0, **sMaX0_C)
849 D, _D = self.Delta, self._cHalf # C++ _d
850 xMaX0 = sMaX0 + D
851 m = int(_ceil(xMaX0 / self._D3)) # m x m tiles
852 d3 = xMaX0 / m
853 T2d3D = self._T2d3Delta(d3)
855 C_ = _List(D) # closest coincident
856 X_ = _List(D) # intersections found
857 c0 = 0
858 S_ = list(X0._nmD3(1 - m, m, d3 * _0_5))
859 # assert len(S_) == m * m + (m - 1) % 2
860 while S_:
861 Q, i = self._Basic2(glA, glB, S_.pop(0))
862 if Q in X_:
863 continue
864 if Q.c: # coincident intersection # PYCHOK no cover
865 _X0fx = X0._fixCoincident
866 Q = _X0fx(Q) # Q = Q'
867 if c0 and Q in C_:
868 continue
869 C_.addend(Q)
870 # elimate all existing intersections
871 # on this line (which didn't set c0)
872 c0 = Q.c
873 for j, X in _enumereverse(X_):
874 if _X0fx(X, c0).L1(Q) <= D: # X' == Q
875 X_.pop(j)
877 a, s0 = len(X_), Q.sA
878 args = self._m12_M12_M21(glA, s0)
879 _cjD = self._conjDist
880 for s in (-_D, _D):
881 s += s0
882 sa = 0
883 while True:
884 i += 1
885 sa = _cjD(glA, s + sa, *args) - s0
886 X = Q + (sa, sa * c0)
887 if X_.addend(X, X0.L1(X), i) > xMaX0:
888 break
890 elif c0 and Q in C_: # Q.c == 0
891 continue
892 else:
893 a = len(X_)
895 X_.addend(Q, X0.L1(Q), i + 1)
896 for X in X_[a:]: # addended Xs
897 X._skip(S_, T2d3D)
899 return X_.sorter(sMaX0, self._C, glA, glB, _C=_C) # generator
901 def All5(self, glA, glB, X0=_X000, **aMaX0_sMaX0_C):
902 '''Yield all intersection of two geodesic lines up to a limit.
904 @return: Yield an L{Intersector5Tuple}C{(A, B, sAB, aAB, c)}
905 for each intersection found.
907 @see: Methods L{All} for further details.
908 '''
909 for X in self.All(glA, glB, X0=X0, **aMaX0_sMaX0_C):
910 yield self._In5T(glA, glB, X, X)
912 def _Basic2(self, glA, glB, S, i=0):
913 '''(INTERNAL) Get a basic solution.
914 '''
915 X = _copy(S)
916 for _ in range(_TRIPS):
917 S = self._Spherical(glA, glB, X)
918 X += S
919 i += 1
920 if X.c or not (S.L1() > self._Tol): # or isnan
921 return self._Delto(X), i
923 raise IntersectionError(Fmt.no_convergence(S.L1(), self._Tol))
925 def _C(self, X, glA, glB, _C=False, _MM=False):
926 # add the C{_C} items to C{X}, if requested.
927 if _C:
928 A = self._Position(glA, X.sA)
929 B = self._Position(glB, X.sB)
930 s, a = self._Inversa12(A, B)
931 X.set_(latA=A.lat2, lonA=A.lon2,
932 latB=B.lat2, lonB=B.lon2)
933 if _MM: # in .Middle5
934 X.set_(sMM=s, aMM=a)
935 else:
936 X.set_(sAB=s, aAB=a)
937 return X
939 def Closest(self, glA, glB, X0=_X000, **_C):
940 '''Find the closest intersection of two geodesic lines.
942 @arg glA: A geodesic line (L{Line<Intersector.Line>}).
943 @arg glB: An other geodesic line (L{Line<Intersector.Line>}).
944 @kwarg X0: Optional I{origin} for I{L1-closeness} (L{XDict}).
945 @kwarg _C: If C{True}, include the lat-/longitudes C{latA},
946 C{lonA}, C{latB}, C{lonB} and distances C{sAB}
947 and C{aSB} between the intersections.
949 @return: The intersection (L{XDict}) or C{None} if none found.
951 @raise GeodesicError: Geodesic line B{C{glA}} or B{C{glB}}
952 invalid, incompatible or ill-configured.
954 @raise IntersectionError: No convergence.
955 '''
956 self._xLines(glA, glB)
957 Q, d, S_, i = X0, INF, list(X0._nD1(self._D1)), 0
958 while S_:
959 X, i = self._Basic2(glA, glB, S_.pop(0), i)
960 X = X0._fixCoincident(X)
961 if X.L1(Q) > self.Delta: # X != Q
962 d0 = X.L1(X0)
963 if d0 < self._T1:
964 Q, d, q = X, d0, i
965 break
966 if d0 < d or Q is X0:
967 Q, d, q = X, d0, i
968 X._skip(S_, self._T2D1Delta)
970 return None if Q is X0 else self._C(Q, glA, glB, **_C).set_(sX0=d, iteration=q)
972 def Closest5(self, glA, glB, X0=_X000):
973 '''Find the closest intersection of two geodesic lines.
975 @return: An L{Intersector5Tuple}C{(A, B, sAB, aAB, c)}
976 or C{None} if none found.
978 @see: Method L{Closest} for further details.
979 '''
980 X = self.Closest(glA, glB, X0=X0)
981 return X if X is None else self._In5T(glA, glB, X, X)
983 def _conjDist(self, gl, s, m12=0, M12=1, M21=1, semi=False):
984 # Find semi-/conjugate point relative to s0 which is close to s1.
985 # if semi:
986 # solve for M23 = 0 using dM23 / ds3 = - (1 - M23 * M32) / m23
987 # else:
988 # solve for m23 = 0 using dm23 / ds3 = M32
989 _S2, _abs, _1 = Fsum(s).fsum2_, fabs, _1_0
990 for _ in range(_TRIPS): # 2..3
991 m13, M13, M31 = self._m12_M12_M21(gl, s)
992 # see "Algorithms for geodesics", eqs. 31, 32, 33.
993 m23 = m13 * M12
994 M32 = M31 * M12
995 if m12: # PYCHOK no cover
996 m23 -= m12 * M13
997 if m12 and m13:
998 M32 += (_1 - M13 * M31) * m12 / m13
999 if semi:
1000 M23 = M13 * M21
1001 # when m12 -> eps, (1 - M12 * M21) -> eps^2, I suppose.
1002 if m12 and m13:
1003 M23 += (_1 - M12 * M21) * m13 / m12
1004 d = m23 * M23 / (_1 - M23 * M32)
1005 else:
1006 d = -m23 / M32
1007 s, d = _S2(d)
1008 if _abs(d) <= self._Tol:
1009 break
1010 return s
1012 _gl3 = None
1014 @Property
1015 def _conjDist3s(self):
1016 gl, self._gl3, _D = self._gl3, None, self._cHalf
1017 return tuple(self._conjDist(gl, s) for s in (-_D, 0, _D))
1019 @_conjDist3s.setter # PYCHOK setter!
1020 def _conjDist3(self, gl):
1021 # _XLines(gl, gl)
1022 self._gl3 = gl
1024 def _conjDist3Tt_(self, c, X0=_X000):
1025 for s in self._conjDist3s:
1026 T = XDict_(s, s * c, c)
1027 yield self._Delto(T), T.L1(X0)
1029 def _conjDist5(self, azi):
1030 gl = self._Line(azi1=azi)
1031 s = self._conjDist(gl, self._cHalf)
1032 X, _ = self._Basic2(gl, gl, XDict_(s * _0_5, -s * _1_5))
1033 return s, (X.L1() - s * _2_0), azi, X.sA, X.sB
1035 @Property_RO
1036 def Delta(self):
1037 '''Get the equality and tiling margin (C{meter}).
1038 '''
1039 return self._cHalf * _EPSr5 # ~15 Km WGS84
1041 def _Delto(self, X):
1042 # copy Delta into X, overriding X's default
1043 X._Delta = self.Delta # NOT X.set_(self.Delta)
1044 return X
1046 @Property_RO
1047 def _EPS3R(self):
1048 return _EPS3 * self.R
1050 @Property_RO
1051 def _faPI_4(self):
1052 return (self.f + _2_0) * self.a * PI_4
1054 @Property_RO
1055 def _GeodesicLine(self):
1056 '''(INTERNAL) Get the C{GeodesicLine} class (C{GeodesicLineExact, GeodesicLineSolve or ...}).
1057 '''
1058 return type(self._Line()), # as *args tuple
1060 def _In5T(self, glA, glB, S, X, k2=False, **_2X):
1061 # Return an intersection as C{Intersector5Tuple}.
1062 A = self._Position(glA, S.sA)
1063 B = self._Position(glB, S.sB)
1064 if k2:
1065 A.set_(k2=X.kA)
1066 B.set_(k2=X.kB)
1067 s, a = self._Inversa12(A, B)
1068 return Intersector5Tuple(A._2X(glA, **_2X),
1069 B._2X(glB, **_2X), s, a, X.c, iteration=X.iteration)
1071 def _Inverse(self, A, B): # caps=Caps.STANDARD
1072 return self._g.Inverse(A.lat2, A.lon2, B.lat2, B.lon2)
1074 def Line(self, lat1, lon1, azi1_lat2, *lon2, **name):
1075 '''Return a geodesic line from this C{Intersector}'s geodesic, specified by
1076 two points or a point and an azimuth (bearing from North).
1078 @arg lat1: Latitude of the first point (C{degrees}).
1079 @arg lon1: Longitude of the first point (C{degrees}).
1080 @arg azi1_lat2: Azimuth at the first point (compass C{degrees}) if no
1081 B{C{lon2}} argument is given, otherwise the latitude of
1082 the second point (C{degrees}).
1083 @arg lon2: If given, the longitude of the second point (C{degrees}).
1084 @kwarg name: Optional C{B{name}=NN} (C{str}).
1086 @return: A line (from L{geodesic<Intersector.geodesic>}C{.Line} or
1087 C{.InverseLine} method) with C{LINE_CAPS}.
1088 '''
1089 args = self._ll3z4ll(lat1, lon1, azi1_lat2, *lon2)
1090 kwds = _xkwds(name, caps=Caps.LINE_CAPS)
1091 return self._g.InverseLine(*args, **kwds) if lon2 else \
1092 self._g.Line( *args, **kwds)
1094 def _Line(self, lat1=0, lon1=0, azi1=0):
1095 return self._g.Line(lat1, lon1, azi1, caps=Caps.LINE_CAPS)
1097 def Middle(self, glA, glB, raiser=True, **_C):
1098 '''Get the mid-points on two geodesic line segments.
1100 @arg glA: A geodesic line (L{Line<Intersector.Line>}, 4-C{args}).
1101 @arg glB: An other geodesic line (L{Line<Intersector.Line>}, 4-C{args}).
1102 @kwarg raiser: If C{True}, check that B{C{glA}} and B{C{glB}} are a
1103 4-C{args} L{Line<Intersector.Line>} or C{InverseLine}
1104 (C{bool}).
1105 @kwarg _C: If C{True}, include the lat-/longitudes C{latA}, C{lonA},
1106 C{latB}, C{lonB} of the mid-points and half-lengths C{sA}
1107 and C{sB} in C{meter} of the respective line segments.
1109 @return: The mid-point and half-length of each segment (L{XDict}),
1110 B{C{_C}} above.
1112 @raise GeodesicError: Geodesic line B{C{glA}} or B{C{glB}} invalid,
1113 incompatible, ill-configured or not a 4-C{args
1114 Line} or other C{InverseLine}.
1115 '''
1116 M, _, _ = self._middle3(glA, glB, raiser)
1117 return self._C(M, glA, glB, **_C) if _C else M
1119 def _middle3(self, glA, glB, raiser): # in .All, .Segment
1120 # return segment length C{sA} and C{sB} and the
1121 # center C{X0} of rectangle [sA, sB]
1122 self._xLines(glA, glB, s13=raiser) # need .Arc, .Distance
1123 sA = glA.Distance()
1124 sB = glB.Distance()
1125 X = XDict_(sA * _0_5, sB * _0_5)
1126 # _ = X._outSide(sA, sB)
1127 return self._Delto(X), sA, sB
1129 def Middle5(self, glA, glB, raiser=True):
1130 '''Get the mid-points of two geodesic line segments and distances.
1132 @return: A L{Middle5Tuple}C{(A, B, sMM, aMM, c)}.
1134 @see: Method L{Middle} for further details.
1135 '''
1136 M, _, _ = self._middle3(glA, glB, raiser)
1137 M = self._C(M, glA, glB, _C=True, _MM=True)
1138 A, B, s, a, c = self._In5T(glA, glB, M, M, _2X=_M_)
1139 return Middle5Tuple(self._illz2G(A, glA),
1140 self._illz2G(B, glB), s, a, c)
1142 def _m12_M12_M21(self, gl, s):
1143 P = gl.Position(s, outmask=Caps._REDUCEDLENGTH_GEODESICSCALE)
1144 return P.m12, P.M12, P.M21
1146 def Next(self, glA, glB, eps1=None, **_C): # PYCHOK no cover
1147 '''Yield the next intersection of two I{intersecting} geodesic lines.
1149 @arg glA: A geodesic line (L{Line<Intersector.Line>}).
1150 @arg glB: An other geodesic line (L{Line<Intersector.Line>}).
1151 @kwarg eps1: Optional margin for the L{euclid<pygeodesy.euclid>}ean
1152 distance (C{degrees}) between the C{(lat1, lon1)} points
1153 of both lines or C{None} for unchecked.
1154 @kwarg _C: If C{True}, include the lat-/longitudes C{latA}, C{lonA},
1155 C{latB}, C{lonB} of and distances C{sAB} and C{aSB}
1156 between the intersections.
1158 @return: The intersection (L{XDict}) or C{None} if none found.
1160 @raise GeodesicError: Geodesic line B{C{glA}} or B{C{glB}} invalid,
1161 incompatible, ill-configured or C{(lat1, lon1)}
1162 not B{C{eps1}}-equal.
1164 @raise IntersectionError: No convergence.
1166 @note: Offset C{X0} is implicit, zeros.
1167 '''
1168 self._xLines(glA, glB)
1169 if eps1 or _C: # eps
1170 _C = self._xNext(glA, glB, eps1, **_C)
1172 X0, self._conjDist3s = _X000, glA # reset Property
1173 Q, d, S_, i = _XINF, INF, list(X0._nD2(self._D2)), 0
1174 while S_:
1175 X, i = self._Basic2(glA, glB, S_.pop(0), i)
1176 X = X0._fixCoincident(X)
1177 t = X.L1(X0) # == X.L1()
1178 c, z = X.c, (t <= self.Delta) # X == X0
1179 if z:
1180 if not c:
1181 continue
1182 Tt_ = self._conjDist3Tt_(c, X0)
1183 else:
1184 Tt_ = (X, t),
1186 for T, t in Tt_:
1187 if t < d or Q is _XINF:
1188 Q, d, q = T, t, i
1189 i += 1
1191 for s in ((_1_1t if z else _1_0_1t)
1192 if c else _0t):
1193 T = X
1194 if s and c:
1195 s *= self._D2
1196 T = X + (s, s * c) # NOT +=
1197 T._skip(S_, self._T2D2Delta)
1199 return None if Q is _XINF else self._C(Q, glA, glB, **_C).set_(sX0=d, iteration=q)
1201 def Next5(self, glA, glB, **eps1): # PYCHOK no cover
1202 '''Yield the next intersection of two I{intersecting} geodesic lines.
1204 @return: An L{Intersector5Tuple}C{(A, B, sAB, aAB, c)} or C{None}
1205 if none found.
1207 @see: Method L{Next} for further details.
1208 '''
1209 X = self.Next(glA, glB, **eps1)
1210 return X if X is None else self._In5T(glA, glB, X, X)
1212 def _obliqDist4(self):
1213 zx = _45_0
1214 if self.f:
1215 _abs, _cjD5 = fabs, self._conjDist5
1217 _, ds0, z0, _, _ = _cjD5(zx + _1_0)
1218 s1, ds1, z1, sAx, sBx = _cjD5(zx - _1_0)
1219 sx, dsx, zx = s1, _abs(ds1), z1
1220 # find ds(azi) = 0 by secant method
1221 for _ in range(16):
1222 if ds1 == ds0:
1223 break
1224 z = (z0 * ds1 - z1 * ds0) / (ds1 - ds0)
1225 _, ds0, z0 = s1, ds1, z1
1226 s1, ds1, z1, a, b = _cjD5(z)
1227 if _abs(ds1) < dsx:
1228 sx, dsx, zx, sAx, sBx = s1, _abs(ds1), z, a, b
1229 if not dsx:
1230 break
1231 else:
1232 sx, sAx, sBx = self._cHalf, _0_5, -_1_5
1233 return sx, zx, sAx, sBx
1235 def _polarB3(self, lats=False): # PYCHOK no cover
1236 latx = _64_0
1237 lat = _90_0 - latx
1238 if self.f:
1239 _d, _pD2 = fdot, self._polarDist2
1241 s0, lat0 = _pD2(latx - _1_0)
1242 s1, lat1 = _pD2(latx + _1_0)
1243 s2, lat2 = \
1244 sx, latx = _pD2(latx)
1245 # solve for ds(lat) / dlat = 0 with a quadratic fit
1246 for _ in range(8): # 1..2
1247 t = (lat1 - lat0), (lat0 - lat2), (lat2 - lat1)
1248 d = _d(t, s2, s1, s0) * _2_0
1249 if not (d > 0 or d < 0): # d == 0 or isnan(d)
1250 break
1251 lat = _d(t, (lat1 + lat0) * s2,
1252 (lat0 + lat2) * s1,
1253 (lat2 + lat1) * s0) / d
1254 s0, lat0 = s1, lat1
1255 s1, lat1 = s2, lat2
1256 s2, lat2 = _pD2(lat)
1257 if (s2 < sx) if self.f < 0 else (s2 > sx):
1258 sx, latx = s2, lat2
1259 if lats:
1260 _, lat = _pD2(latx, lat2=True)
1261 sx += sx
1262 else:
1263 sx = self._cHalf
1264 return sx, latx, lat
1266 def _polarDist2(self, lat1, lat2=False):
1267 gl = self._Line(lat1=lat1)
1268 s = self._conjDist(gl, self._faPI_4, semi=True)
1269 if lat2:
1270 lat1 = gl.Position(s, outmask=Caps.LATITUDE).lat2
1271 return s, lat1
1273 def _Position(self, gl, s):
1274 return gl.Position(s, outmask=Caps.STANDARD_LINE)
1276 def Segment(self, glA, glB, proven=None, raiser=True, **_C):
1277 '''Find the intersection between two geodesic line segments.
1279 @kwarg proven: Conjecture is that whenever two geodesic line
1280 segments intersect, the intersection is the
1281 one closest to the mid-points of segments.
1282 If so, use C{B{proven}=True}, otherwise find
1283 intersections on the segments and specify
1284 C{B{proven}=None} to return the first or
1285 C{B{proven}=False} the closest (C{bool}).
1286 @kwarg raiser: If C{True}, check that B{C{glA}} and B{C{glB}}
1287 are a 4-C{args} L{Line<Intersector.Line>} or
1288 C{InverseLine} (C{bool}).
1289 @kwarg _C: If C{True}, include the lat-/longitudes C{latA},
1290 C{lonA}, C{latB}, C{lonB} of and distances C{sAB}
1291 and C{aSB} between the intersections.
1293 @return: The intersection of the segments (L{XDict}) with
1294 indicators C{kA}, C{kB} and C{k} set or if no
1295 intersection is found, C{None}.
1297 @raise GeodesicError: Geodesic line B{C{glA}} or B{C{glB}}
1298 invalid, incompatible, ill-configured or
1299 not an C{InverseLine} or 4-C{args Line}.
1301 @raise IntersectionError: No convergence.
1303 @see: Method L{Middle<Intersector.Middle>} for further details.
1304 '''
1305 X0, sA, sB = self._middle3(glA, glB, raiser)
1306 Q = self.Closest(glA, glB, X0) # to X0
1307 if Q is not None:
1308 if Q.c: # anti-/parallel
1309 Q._fixSegment(sA, sB)
1310 # are rectangle [sA, sB] corners further from X0 than Q?
1311 d0 = X0.L1(Q)
1312 if Q._outSide(sA, sB) and d0 <= X0.L1() and not proven:
1313 i = Q.iteration
1314 for T in Q._corners(sA, sB, self._T2):
1315 X, i = self._Basic2(glA, glB, T, i)
1316 X = T._fixCoincident(X)
1317 if not X._outSide(sA, sB):
1318 d = X0.L1(X)
1319 if d < d0 or proven is None:
1320 Q, d0 = X, d
1321 if proven is None:
1322 break
1323 Q.set_(iteration=i)
1325 Q = self._C(Q, glA, glB, **_C).set_(sX0=d0)
1326 return Q
1328 def Segment5(self, glA, glB, **proven_raiser):
1329 '''Find the intersection between two geodesic line segments.
1331 @return: An L{Intersector5Tuple}C{(A, B, sAB, aAB, c)}
1332 or C{None} if none found.
1334 @see: Method L{Segment} for further details.
1335 '''
1336 X = self.Segment(glA, glB, **proven_raiser)
1337 return X if X is None else self._In5T(glA, glB, X, X, k2=True)
1339 def _Spherical(self, glA, glB, S):
1340 '''(INTERNAL) Get solution based from a spherical triangle.
1341 '''
1342 # threshold for coincident geodesics/intersections ~4.3 nm WGS84.
1343 A = self._Position(glA, S.sA)
1344 B = self._Position(glB, S.sB)
1345 D = self._Inverse(A, B)
1347 a, da = _diff182(A.azi2, D.azi1) # interior angle at A
1348 b, db = _diff182(B.azi2, D.azi2) # exterior angle at B
1349 c, dc = _diff182(a, b)
1350 if fsum1_(dc, db, -da, c) < 0: # inverted triangle
1351 a, da = -a, -da
1352 b, db = -b, -db
1353 sa, ca = _sincos2de(a, da)
1354 sb, cb = _sincos2de(b, db)
1356 e, z, _abs = _EPS3, D.s12, fabs
1357 if _abs(z) <= self._EPS3R: # XXX z <= ...
1358 sA = sB = 0 # at intersection
1359 c = 1 if _abs(sa - sb) <= e and _abs(ca - cb) <= e else (
1360 -1 if _abs(sa + sb) <= e and _abs(ca + cb) <= e else 0)
1361 elif _abs(sa) <= e and _abs(sb) <= e: # coincident
1362 sA = ca * z * _0_5 # choose mid-point
1363 sB = -cb * z * _0_5
1364 c = 1 if (ca * cb) > 0 else -1
1365 # alt1: sA = ca * z; sB = 0
1366 # alt2: sB = -cb * z; sA = 0
1367 else: # general case
1368 sz, cz = sincos2(z / self.R)
1369 # [SKIP: Divide args by |sz| to avoid possible underflow
1370 # in {sa, sb} * sz; this is probably not necessary].
1371 # Definitely need to treat sz < 0 (z > PI*R) correctly in
1372 # order to avoid some convergence failures in _Basic2.
1373 sA = atan2(sb * sz, sb * ca * cz - sa * cb) * self.R
1374 sB = atan2(sa * sz, -sa * cb * cz + sb * ca) * self.R
1375 c = 0
1376 return XDict_(sA, sB, c) # no ._Delto
1378 @Property_RO
1379 def _T2D1Delta(self):
1380 return self._T2d3Delta(self._D1)
1382 @Property_RO
1383 def _T2D2Delta(self):
1384 return self._T2d3Delta(self._D2)
1386 def _T2d3Delta(self, d3):
1387 return self._T2 - d3 - self.Delta
1389 @Property_RO
1390 def _Tol(self): # convergence tolerance
1391 return self._cHalf * _EPSjam
1393 def toStr(self, **prec_sep_name): # PYCHOK signature
1394 '''Return this C{Intersector} as string.
1396 @see: L{Ellipsoid.toStr<pygeodesy.ellipsoids.Ellipsoid.toStr>}
1397 for further details.
1399 @return: C{Intersector} (C{str}).
1400 '''
1401 return self._instr(props=(Intersector.geodesic,), **prec_sep_name)
1403 def _xLines(self, glA, glB, s13=False):
1404 # check two geodesic lines vs this geodesic
1405 gls, C = dict(glA=glA, glB=glB), Caps.LINE_CAPS
1406 _xinstanceof(*self._GeodesicLine, **gls)
1407 for n, gl in gls.items():
1408 try:
1409 _xgeodesics(gl.geodesic, self.geodesic)
1410 if s13 and not isfinite(gl.s13): # or not gl.caps & Caps.DISTANCE_IN
1411 t = _an(typename(gl.geodesic.InverseLine))
1412 raise TypeError(_not_(t))
1413 c = gl.caps & C
1414 if c != C: # not gl.caps_(C)
1415 c, C, x = map1(bin, c, C, _xor(c, C))
1416 t = _SPACE_(typename(_xor), repr(x))[1:]
1417 raise GeodesicError(caps=c, LINE_CAPS=C, txt=t)
1418 except Exception as x:
1419 raise GeodesicError(n, gl, cause=x)
1422class Intersect7Tuple(_NamedTuple):
1423 '''7-Tuple C{(A, B, sAB, aAB, c, kA, kB)} with C{A} and C{B} each
1424 a C{LatLon} or L{LatLon4Tuple}C{(lat, lon, height, datum)} of
1425 the intersection on each geodesic line, the distance C{sAB} in
1426 in C{meter} and angular distance C{aAB} in C{degrees} between
1427 C{A} and C{B}, coincidence indicator C{c} and segment indicators
1428 C{kA} and C{kB} all C{int}, see L{XDict} and method U{intersect7
1429 <_IntersectBase.intersect7>}.
1430 '''
1431 _Names_ = (_A_, _B_, _sAB_, _aAB_, _c_, 'kA', 'kB')
1432 _Units_ = (_Pass, _Pass, Meter, Degrees, Int, Int, Int)
1435class Intersectool5Tuple(_NamedTuple):
1436 '''5-Tuple C{(A, B, sAB, aAB, c)} with C{A} and C{B} the C{Position}
1437 of the intersection on each geodesic line, the distance C{sAB}
1438 between C{A} and C{B} in C{meter}, the angular distance C{aAB} in
1439 C{degrees} and coincidence indicator C{c} (C{int}), see L{XDict}.
1441 @note: C{A} and C{B} are each a C{GDict} with C{lat1}, C{lon1} and
1442 C{azi1} or C{lat2}, C{lon2} from the geodesic line C{glA}
1443 respectively C{glB} and the intersection location in C{latX},
1444 C{lonX}, distance C{s1X} in C{meter} and angular distance
1445 C{a1X} in C{degrees} and the segment indicator C{kX}. See
1446 L{XDict} for more details.
1447 '''
1448 _Names_ = Intersect7Tuple._Names_[:5]
1449 _Units_ = Intersect7Tuple._Units_[:5]
1452class Intersector5Tuple(Intersectool5Tuple):
1453 '''5-Tuple C{(A, B, sAB, aAB, c)} with C{A} and C{B} the C{Position}
1454 of the intersection on each geodesic line, the distance C{sAB}
1455 between C{A} and C{B} in C{meter}, angular distance C{aAB} in
1456 C{degrees} and coincidence indicator C{c} (C{int}), see L{XDict}.
1458 @note: C{A} and C{B} are each a C{GeodesicLine...Position} for
1459 C{outmask=Caps.STANDARD} with the intersection location in
1460 C{latX}, C{lonX}, azimuth in C{aziX}, distance C{s1X} in
1461 C{meter} and angular distance C{a1X} in C{degrees} and the
1462 segment indicator C{kX}. See L{XDict} for more details.
1463 '''
1464 _Names_ = Intersectool5Tuple._Names_
1465# _Units_ = Intersectool5Tuple._Units_
1468class Middle5Tuple(Intersectool5Tuple):
1469 '''5-Tuple C{(A, B, sMM, aMM, c)} with C{A} and C{B} the I{line segments}
1470 including the mid-point location in C{latM}, C{lonM}, distance C{s1M}
1471 in C{meter} and angular distance C{a1M} in C{degrees}, the distance
1472 between both mid-points C{sMM} in C{meter} and angular distance C{aMM}
1473 in C{degrees} and coincidence indicator C{c} (C{int}). See L{XDict}
1474 for more details.
1475 '''
1476 _Names_ = (_A_, _B_, 'sMM', 'aMM', _c_)
1477# _Units_ = Intersectool5Tuple._Units_
1480class _List(list):
1482 _Delta = 0 # equality margin
1484 def __init__(self, Delta):
1485 self._Delta = Delta
1486# list.__init__(self)
1488 def __contains__(self, other):
1489 # handle C{if X in this: ...}
1490 a, b = other.sA, other.sB
1491 D, _D1 = self._Delta, _L1
1492 for X in self:
1493 if _D1(X.sA - a, X.sB - b) <= D:
1494 return True
1495 return False
1497 def addend(self, X, *d0_i):
1498 # append an item, updated
1499 if d0_i:
1500 d0, i = d0_i
1501 X.set_(sX0=d0, iteration=i)
1502 self.append(X)
1503 return X.sX0
1505 def sorter(self, sMaX0, dot_C, glA, glB, **_C):
1506 # trim and sort the X items
1508 def _key(X):
1509 return X.sX0 # rank of X
1511 t = (X for X in self if X.sX0 <= sMaX0)
1512 for X in sorted(t, key=_key):
1513 yield dot_C(X, glA, glB, **_C) if _C else X
1516def _L1(a, b):
1517 '''(INTERNAL) Return the I{L1} distance.
1518 '''
1519 return fabs(a) + fabs(b)
1522__all__ += _ALL_DOCS(_IntersectBase)
1524if __name__ == _DMAIN_: # MCCABE 36
1526 from pygeodesy import printf
1527 __help_ = '--help'
1529 def _main(args):
1531 from pygeodesy import Float, GeodesicExact
1532 from pygeodesy.internals import _plural, _usage
1533 from pygeodesy.interns import _COLONSPACE_, _DOT_, _EQUAL_, \
1534 _i_, _m_, _n_, _version_, _X_
1535 import re
1537 class XY0(Float):
1538 pass
1540 def _opts(_h): # for _usage()
1541 ll4 = ' latA1 lonA1'
1542 ll4 += ll4.replace('1', '2')
1543 ll4 += ll4.replace(_A_, _B_)
1544 llz = _SPACE_(NN, _latA_, _lonA_, 'aziA')
1545 llz2 = llz + llz.replace(_A_, _B_)
1546 return dict(opts='-Verbose|V--version|v--help|h--Tool|T--Check|C-R <meter>-',
1547 alts=((_c_ + llz2),
1548 (_i_ + ll4),
1549 (_m_ + ll4),
1550 (_n_ + llz + ' aziB'),
1551 ('o' + llz2 + ' x0 y0')),
1552 help=_h if isinstance(_h, str) else NN)
1554 def _starts(Opt, arg):
1555 return arg == Opt[1:3] or (len(arg) > 2 and Opt.startswith(arg))
1557 _isopt = re.compile('^[-]+[a-z]*$', flags=re.IGNORECASE).match
1559 I = Intersector(GeodesicExact()) # noqa: E741 I is eye
1560 M = m = _R = None
1561 _T = _V = _h = _C = False
1563 while args and _isopt(args[0]):
1564 arg = args.pop(0)
1565 if arg == _c__:
1566 M, m = I.Closest, 6 # latA lonA aziA latB lonB aziB
1567 elif _starts('--Check', arg):
1568 _C = True
1569 elif _starts(__help_, arg):
1570 _h = args[0] if args and _isopt(args[0]) else True
1571 elif arg == _i__:
1572 M, m = I.Segment, 8 # latA1 lonA1 latA2 lonA2 latB1 lonB1 latB2 lonB2
1573 elif arg == '-m':
1574 M, m = I.Middle, 8 # latA1 lonA1 latA2 lonA2 latB1 lonB1 latB2 lonB2
1575 _R = None # zap -R
1576 elif arg == _n__:
1577 M, m = I.Next, 4 # latA lonA aziA aziB
1578 elif arg == _o__:
1579 M, m = I.Closest, 8 # latA lonA aziA latB lonB aziB x0 y0
1580 elif arg == _R__ and args:
1581 _R = args.pop(0)
1582 elif _starts('--Tool', arg):
1583 I = Intersectool() # noqa: E741 I is eye
1584 if _V:
1585 I.verbose = True
1586 if not _Xables.X_OK(I.IntersectTool):
1587 I.IntersectTool = _Xables.IntersectTool(_Xables.bin_)
1588 elif _V:
1589 _ = I.version
1590 M, _T = None, True
1591 elif _starts('--Verbose', arg):
1592 _V = True
1593 if _T:
1594 I.verbose = True
1595 elif _starts('--version', arg):
1596 printf(_COLONSPACE_(*((_version_, I.version) if _T else
1597 (__version__, repr(I)))))
1598 else:
1599 raise ValueError('invalid option %r' % (arg,))
1601 if _h or M is None:
1602 printf(_usage(__file__, **_opts(_h)), nl=1)
1603 else:
1604 n = len(args)
1605 if n < m:
1606 n = _plural('only %s arg' % (n,), n) if n else 'no args'
1607 raise ValueError('%s, need %s' % (n, m))
1608 args[:] = args[:m]
1610 kwds = dict(_C=True) if _C else {}
1611 if M == I.Next: # -n
1612 # get latA lonA aziA latA lonA aziB
1613 args[3:] = args[:2] + args[3:4]
1614 elif M == I.Closest and m > 6: # -o
1615 y0 = Meter(y0=args.pop())
1616 x0 = Meter(x0=args.pop())
1617 kwds.update(X0=XDict_(x0, y0))
1618 if _R:
1619 m = Meter_(_R, name=_R__, low=0)
1620 kwds.update(sMaX0=m)
1621 M = I.All
1623 n = len(args) // 2
1624 glA = I.Line(*args[:n])
1625 glB = I.Line(*args[n:])
1627 m = _DOT_(*map1(typename, type(I), M))
1628 if _V:
1629 X = _SPACE_(_X_, _EQUAL_, m)
1630 printf(unstr(X, glA, glB, **kwds))
1632 X = M(glA, glB, **kwds)
1633 if X is None or isinstance(X, (XDict, tuple)):
1634 printf(_COLONSPACE_(m, repr(X)))
1635 else:
1636 for i, X in enumerate(X):
1637 printf(_COLONSPACE_(Fmt.INDEX(m, i), repr(X)))
1639 def _examples():
1641 from pygeodesy.internals import _usage_argv
1643 s = _SPACE_(*_usage_argv(__file__))
1644 for t in ('-h', '-h -n',
1645 '-c 0 0 45 40 10 135',
1646 '-C -c 0 0 45 40 10 135',
1647 '-T -R 2.6e7 -c 0 0 45 40 10 135',
1648 '-c 50 -4 -147.7 0 0 90',
1649 '-C -c 50 -4 -147.7 0 0 90',
1650 '# % echo 0 0 10 10 50 -4 50S 4W | IntersectTool -i -p 0 -C',
1651 '# -631414 5988887 0 -3',
1652 '# -4.05187 -4.00000 -4.05187 -4.00000 0',
1653 '-m 0 0 10 10 50 -4 50S 4W',
1654 '-C -m 0 0 10 10 50 -4 50S 4W',
1655 '-i 0 0 10 10 50 -4 50S 4W',
1656 '-T -i 0 0 10 10 50 -4 50S 4W',
1657 '-C -i 0 0 10 10 50 -4 50S 4W',
1658 '-T -C -i 0 0 10 10 50 -4 50S 4W',
1659 '-V -T -i 0 0 10 10 50 -4 -50 -4',
1660 '-C -R 4e7 -c 50 -4 -147.7 0 0 90',
1661 '-T -C -R 4e7 -c 50 -4 -147.7 0 0 90',
1662 '-R 4e7 -i 0 0 10 10 50 -4 -50 -4',
1663 '-T -R 4e7 -i 0 0 10 10 50 -4 -50 -4'):
1664 if t.startswith(_HASH_):
1665 printf(t, nl=int(t[2] == '%'))
1666 else:
1667 printf(_SPACE_(_HASH_, s, t), nl=1)
1668 argv[1:] = t = t.split()
1669 _main(t)
1671 from sys import argv, stderr
1672 try:
1673 if len(argv) == 2 and argv[1] == __help_:
1674 _examples()
1675 else:
1676 _main(argv[1:])
1678 except Exception as x:
1679 x = _SPACE_(x, NN, _HASH_, *argv)
1680 printf(x, file=stderr, nl=1)
1681 if '-V' in x or _MODS.errors.exception_chaining():
1682 raise
1683 exit(1)
1686# % env PYGEODESY_INTERSECTTOOL=<path-to-IntersectTool> python3 -m pygeodesy.geodesici --help
1688# % python3 -m pygeodesy.geodesici -h
1689#
1690# usage: python3 -m ....pygeodesy.geodesici [--Verbose | -V] [--version | -v] [--help | -h] [--Tool | -T] [--Check | -C] [-R meter]
1691# [-c latA lonA aziA latB lonB aziB |
1692# -i latA1 lonA1 latA2 lonA2 latB1 lonB1 latB2 lonB2 |
1693# -m latA1 lonA1 latA2 lonA2 latB1 lonB1 latB2 lonB2 |
1694# -n latA lonA aziA aziB |
1695# -o latA lonA aziA latB lonB aziB x0 y0]
1697# % python3 -m ....pygeodesy.geodesici -h -n
1698#
1699# usage: python3 -m ....pygeodesy.geodesici -n latA lonA aziA aziB
1701# % python3 -m ....pygeodesy.geodesici -c 0 0 45 40 10 135
1702# Intersector.Closest: XDict(c=0, sA=3862290.547855, sB=2339969.547699, sX0=6202260.095554)
1704# % python3 -m ....pygeodesy.geodesici -C -c 0 0 45 40 10 135
1705# 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)
1707# % env PYGEODESY_INTERSECTTOOL=...python3 -m ....pygeodesy.geodesici -T -R 2.6e7 -c 0 0 45 40 10 135
1708# Intersectool.All[0]: XDict(c=0, sA=3862290.547855, sB=2339969.547699, sX0=6202260.095554)
1710# % python3 -m ....pygeodesy.geodesici -c 50 -4 -147.7 0 0 90
1711# Intersector.Closest: XDict(c=0, sA=6058048.653081, sB=-3311252.995823, sX0=9369301.648903)
1713# % python3 -m ....pygeodesy.geodesici -C -c 50 -4 -147.7 0 0 90
1714# 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)
1716# % echo 0 0 10 10 50 -4 50S 4W | IntersectTool -i -p 0 -C
1717# -631414 5988887 0 -3
1718# -4.05187 -4.00000 -4.05187 -4.00000 0
1720# % python3 -m ....pygeodesy.geodesici -m 0 0 10 10 50 -4 50S 4W
1721# Intersector.Middle: XDict(c=0, sA=782554.549609, sB=5536835.161499, sX0=0.0)
1723# % python3 -m ....pygeodesy.geodesici -C -m 0 0 10 10 50 -4 50S 4W
1724# 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)
1726# % python3 -m ....pygeodesy.geodesici -i 0 0 10 10 50 -4 50S 4W
1727# Intersector.Segment: XDict(c=0, k=-3, kA=-1, kB=0, sA=-631414.26877, sB=5988887.278435, sX0=1866020.935315)
1729# % env PYGEODESY_INTERSECTTOOL=... python3 -m ....pygeodesy.geodesici -T -i 0 0 10 10 50 -4 50S 4W
1730# Intersectool.Segment: XDict(c=0, k=-3, kA=-1, kB=0, sA=-631414.26877, sB=5988887.278435)
1732# % python3 -m ....pygeodesy.geodesici -C -i 0 0 10 10 50 -4 50S 4W
1733# 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)
1735# % env PYGEODESY_INTERSECTTOOL=... python3 -m ....pygeodesy.geodesici -T -C -i 0 0 10 10 50 -4 50S 4W
1736# 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)
1738# % env PYGEODESY_INTERSECTTOOL=... python3 -m ....pygeodesy.geodesici -V -T -i 0 0 10 10 50 -4 -50 -4
1739# Intersectool@1: /opt/local/bin/IntersectTool --version (invoke)
1740# Intersectool@1: '/opt/local/bin/IntersectTool: GeographicLib version 2.3' (0)
1741# Intersectool@1: /opt/local/bin/IntersectTool: GeographicLib version 2.3 (0)
1742# 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))
1743# 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)
1744# Intersectool@2: '-631414.2687702414 5988887.2784352796 0 -3' (0)
1745# Intersectool@2: sA=-631414.2687702414, sB=5988887.2784352796, c=0, k=-3 (0)
1746# Intersectool.Segment: XDict(c=0, k=-3, kA=-1, kB=0, sA=-631414.26877, sB=5988887.278435)
1748# % python3 -m ....pygeodesy.geodesici -C -R 4e7 -c 50 -4 -147.7 0 0 90
1749# 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)
1750# 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)
1751# 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)
1752# 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)
1754# % env PYGEODESY_INTERSECTTOOL=... python3 -m ....pygeodesy.geodesici -T -C -R 4e7 -c 50 -4 -147.7 0 0 90
1755# 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)
1756# 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)
1757# 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)
1758# 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)
1760# % python3 -m ....pygeodesy.geodesici -R 4e7 -i 0 0 10 10 50 -4 -50 -4
1761# Intersector.All[0]: XDict(c=0, sA=-631414.26877, sB=5988887.278435, sX0=1866020.935315)
1762# Intersector.All[1]: XDict(c=0, sA=19422725.117572, sB=-14062417.105648, sX0=38239422.83511)
1763# Intersector.All[2]: XDict(c=0, sA=19422725.117572, sB=25945445.811603, sX0=39048781.218067)
1764# Intersector.All[3]: XDict(c=0, sA=39476927.464575, sB=5894074.699478, sX0=39051612.452944)
1766# % env PYGEODESY_INTERSECTTOOL=... python3 -m ....pygeodesy.geodesici -T -R 4e7 -i 0 0 10 10 50 -4 -50 -4
1767# Intersectool.All[0]: XDict(c=0, sA=-631414.26877, sB=5988887.278435, sX0=1862009.05513)
1768# Intersectool.All[1]: XDict(c=0, sA=19422725.117572, sB=-14062417.105648, sX0=38243434.715295)
1769# Intersectool.All[2]: XDict(c=0, sA=19422725.117572, sB=25945445.811603, sX0=39044769.337882)
1770# Intersectool.All[3]: XDict(c=0, sA=39476927.464575, sB=5894074.699478, sX0=39047600.57276)
1773# **) MIT License
1774#
1775# Copyright (C) 2024-2026 -- mrJean1 at Gmail -- All Rights Reserved.
1776#
1777# Permission is hereby granted, free of charge, to any person obtaining a
1778# copy of this software and associated documentation files (the "Software"),
1779# to deal in the Software without restriction, including without limitation
1780# the rights to use, copy, modify, merge, publish, distribute, sublicense,
1781# and/or sell copies of the Software, and to permit persons to whom the
1782# Software is furnished to do so, subject to the following conditions:
1783#
1784# The above copyright notice and this permission notice shall be included
1785# in all copies or substantial portions of the Software.
1786#
1787# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
1788# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
1789# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
1790# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR
1791# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
1792# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
1793# OTHER DEALINGS IN THE SOFTWARE.