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 _90_0, isfinite
33from pygeodesy.ellipsoids import _EWGS84, Fmt, unstr
34from pygeodesy.errors import GeodesicError, IntersectionError, _an, \
35 _xgeodesics, _xkwds_get, _xkwds_kwds, \
36 _xkwds_pop2
37# from pygeodesy.errors import exception_chaining # _MODS
38from pygeodesy.fmath import euclid, fdot
39from pygeodesy.fsums import Fsum, fsum1_, _ceil
40from pygeodesy.interns import NN, _A_, _B_, _c_, _COMMASPACE_, \
41 _HASH_, _M_, _not_, _SPACE_, _too_
42from pygeodesy.karney import Caps, _diff182, GDict, _sincos2de
43from pygeodesy.lazily import _ALL_DOCS, _ALL_LAZY, _ALL_MODS as _MODS, \
44 _getenv, _PYGEODESY_INTERSECTTOOL_
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 Degrees, Float, Int, _isDegrees, \
53 Lat, Lon, Meter, Meter_
54from pygeodesy.utily import sincos2, atan2, fabs, radians
56# from math import atan2, ceil as _ceil, fabs, radians # .fsums, .utily
58__all__ = _ALL_LAZY.geodesici
59__version__ = '24.07.22'
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 Azi(Degrees):
81 '''(INTERNAL) Azimuth C{Unit}.
82 '''
83 pass
86class XDict(ADict):
87 '''4+Item result from L{Intersectool} and L{Intersector} methods
88 C{All}, C{Closest}, C{Next} and C{Segment} with the intersection
89 offsets C{sA}, C{sB} and C{sX0} in C{meter} and the coincidence
90 indicator C{c}, an C{int}, +1 for parallel, -1 for anti-parallel
91 or 0 otherwise.
93 Offsets C{sA} and C{sB} are distances measured I{along} geodesic
94 line C{glA} respectively C{glB}, but C{sX0} is the I{L1-distance}
95 between the intersection and the I{origin} C{X0}.
97 If present, distance C{sAB} and angular distance C{aAB} represent
98 the difference between the intersection point on geodesic lines
99 C{glA} and C{glB} in C{meter} respectively C{degrees}, typically
100 below C{5e-9 meter} or C{5 nm} and C{5e-14 degrees} or C{1 n"}.
102 For segments, indicators C{kA} and C{kB} are C{0} if the segments
103 intersect or C{-1} or C{+1} if the intersection is I{before} the
104 start, respectively I{after} the end of the segment, similar to
105 L{Intersection3Tuple<Intersection3Tuple>}. Segment indicator
106 C{k} is I{Karney}'s C{segmode}, equal C{kA * 3 + kB}.
107 '''
108 _Delta = EPS # default margin, see C{Intersector._Delto}
110 def __add__(self, other):
111 X = _copy(self)
112 X += other
113 return X
115 def __eq__(self, other):
116 return not self.__ne__(other)
118 def __iadd__(self, other):
119 if isinstance(other, tuple): # and len(other) == 2:
120 a, b = other
121 else:
122 # _xinstanceof(XDict, other=other)
123 a = other.sA
124 b = other.sB
125 if other.c:
126 self.c = other.c
127 self.sA += a # PYCHOK sA
128 self.sB += b # PYCHOK sB
129 return self
131 def __le__(self, other):
132 # _xinstanceof(XDict, other=other)
133 return self == other or self < other
135 def __lt__(self, other):
136 # _xinstanceof(XDict, other=other)
137 return (self.sA < other.sA or (self.sA == other.sA and # PYCHOK sA
138 self.sB < other.sB) and self != other) # PYCHOK sB
140 def __ne__(self, other):
141 # _xinstanceof(XDict, other=other)
142 return self is not other and self.L1(other) > self._Delta
144 def _corners(self, sA, sB, T2):
145 # yield all corners further than C{T2}
146 a, b = self.sA, self.sB # PYCHOK sA, sB
147 for x in (0, sA):
148 for y in (0, sB):
149 if _L1(x - a, y - b) >= T2:
150 yield XDict_(x, y)
152 def _fixCoincident(self, X, c0=0):
153 # return the mid-point if C{X} is anti-/parallel
154 c = c0 or X.c
155 if c:
156 s = (self.sA - X.sA + # PYCHOK sA
157 (self.sB - X.sB) * c) * _0_5 # PYCHOK sB
158 X = X + (s, s * c) # NOT +=
159 return X
161 def _fixSegment(self, sA, sB): # PYCHOK no cover
162 # modify this anti-/parallel C{XDict}
163 a, b, c = self.sA, self.sB, self.c # PYCHOK sA, sB, c
165 def _g(): # intersection in smallest gap
166 if c > 0: # distance to [A, B] is |(a - b) - (A - B)|
167 t = a - b # consider corners [0, sB] and [sA, 0]
168 t = fabs(t + sB) < fabs(t - sA)
169 s = a + b
170 else: # distance to [A, B] is |(a + b) - (A + B)|
171 t = a + b # consider corner [0, 0] and [sA, sB]
172 t = fabs(t) < fabs(t - (sA + sB))
173 s = sB + (a - b)
174 return (sB if t else sA) - s
176 ta = -a
177 tb = sA - a
178 tc = -c * b
179 td = -c * (b - sB)
181 ga = 0 <= (b + c * ta) <= sB
182 gb = 0 <= (b + c * tb) <= sB
183 gc = 0 <= (a + tc) <= sA
184 gd = 0 <= (a + td) <= sA
186 # test opposite rectangle sides first
187 s = ((ta + tb) if ga and gb else (
188 (tc + td) if gc and gd else (
189 (ta + tc) if ga and gc else (
190 (ta + td) if ga and gd else (
191 (tb + tc) if gb and gc else (
192 (tb + td) if gb and gd else _g())))))) * _0_5
193 self += s, s * c
195 @property_RO
196 def _is00(self):
197 return not (self.sA or self.sB) # PYCHOK sA, sB
199 def L1(self, other=None):
200 '''Return the C{L1} distance.
201 '''
202 a, b = self.sA, self.sB # PYCHOK sA, sB
203 if other is not None:
204 # _xinstanceof(XDict, other=other)
205 a -= other.sA
206 b -= other.sB
207 return _L1(a, b)
209 def _nD1(self, D1):
210 # yield the C{Closest} starts
211 D_ = 0, D1, -D1
212 for a, b in zip((0, 1, -1, 0, 0),
213 (0, 0, 0, 1, -1)):
214 yield self + (D_[a], D_[b])
216 def _nD2(self, D2):
217 # yield the C{Next} starts
218 D22 = D2 * _2_0
219 D_ = 0, D2, D22, -D22, -D2
220 for a, b in zip((-1, -1, 1, 1, -2, 0, 2, 0),
221 (-1, 1, -1, 1, 0, 2, 0, -2)):
222 yield self + (D_[a], D_[b])
224 def _nmD3(self, n, m, D3): # d3 / 2
225 # yield the C{All} starts
226 yield self
227 for i in range(n, m, 2):
228 for j in range(n, m, 2):
229 if i or j: # skip self
230 yield self + ((i + j) * D3,
231 (i - j) * D3)
233 def _outSide(self, sA, sB):
234 # is this C{Xdist} outside one or both segments?
235 a, b = self.sA, self.sB # PYCHOK sA, sB
236 kA = -1 if a < 0 else (+1 if a > sA else INT0)
237 kB = -1 if b < 0 else (+1 if b > sB else INT0)
238 self.set_(kA=kA, kB=kB, k=(kA * 3 + kB) or INT0)
239 return bool(kA or kB)
241 def _skip(self, S_, T1_Delta):
242 # remove starts from list C{S_} near this C{XDict}
243 for j, S in _enumereverse(S_):
244 if S.L1(self) < T1_Delta:
245 S_.pop(j)
248def XDict_(sA=_0_0, sB=_0_0, c=INT0, sX0=_0_0):
249 '''(INTERNAL) New L{XDict} from positionals.
250 '''
251 return XDict(sA=sA, sB=sB, c=c, sX0=sX0)
253_X000 = XDict_() # PYCHOK origin
254_XINF = XDict_(INF)
257class _IntersectBase(_NamedBase):
258 '''(INTERNAL) Base class for L{Intersectool} and L{Intersector}.
259 '''
260 # _g = None
262 def __init__(self, geodesic, **name):
263 _xinstanceof(*_EWGS84._Geodesics, geodesic=geodesic)
264 self._g = geodesic
265 if name:
266 self.name = name
268 @Property_RO
269 def a(self):
270 '''Get the I{equatorial} radius, semi-axis (C{meter}).
271 '''
272 return self.ellipsoid.a
274 equatoradius = a # = Requatorial
276 def All(self, glA, glB, **kwds): # PYCHOK no cover
277 '''(INTERNAL) I{Must be overloaded}.'''
278 self._notOverloaded(glA, glB, **kwds)
280 @Property_RO
281 def _cHalf(self): # normalizer, semi-circumference
282 return self.R * PI # ~20K Km WGS84
284 @Property_RO
285 def _cMax(self): # outer circumference
286 return max(self.a, self.ellipsoid.b, self.R) * PI2
288 @property_RO
289 def datum(self):
290 '''Get the geodesic's datum (C{Datum}).
291 '''
292 return self.geodesic.datum
294 @Property_RO
295 def ellipsoid(self):
296 '''Get the C{geodesic}'s ellipsoid (C{Ellipsoid}).
297 '''
298 return self.geodesic.datum.ellipsoid
300 @Property_RO
301 def f(self):
302 '''Get the I{flattening} (C{scalar}), C{0} for spherical, negative for prolate.
303 '''
304 return self.ellipsoid.f
306 flattening = f
308 @property_RO
309 def geodesic(self):
310 '''Get the C{geodesic} (C{Geodesic...}).
311 '''
312 return self._g
314 def _illz2G(self, G, il):
315 '''(INTERNAL) Set C{InverseLine} 1-/2-attrs into C{G}, a C{GDict}.
316 '''
317 try:
318 G.set_(lat1=il.lat1, lon1=il.lon1, azi1=il.azi1, a12=il.a13, # .Arc()
319 lat2=il.lat2, lon2=il.lon2, azi2=il.azi2, s12=il.s13) # .Distance()
320 except AttributeError:
321 r = il.Position(il.s13, outmask=Caps._STD_LINE) # isfinite(il.s13)
322 G.set_(**r)
323# for n, v in r.items():
324# if not hasattr(il, n):
325# setattr(il, n, v)
326 return G
328 def intersect7(self, start1, end1, start2, end2, X0=_X000, aMaX0=0, sMaX0=_cWGS84,
329 **LatLon_and_kwds):
330 '''Yield the intersection points of two lines, each defined by two (ellipsoidal)
331 points or by an (ellipsoidal) start point and an azimuth from North.
333 @arg start1: Start point of the first line (C{LatLon}).
334 @arg end1: End point of the first line (C{LatLon}) or the azimuth at the
335 B{C{start1}} point (compass C{degrees360}).
336 @arg start2: Start point of the second line (C{LatLon}).
337 @arg end2: End point of the second line (C{LatLon}) or the azimuth at the
338 B{C{start2}} point (compass C{degrees360}).
339 @kwarg X0: Optional I{origin} for I{L1-distances} (L{XDict}) or C{None} for
340 the L{Middle<Intersector.Middle>}, otherwise C{XDiff_(0, 0)}.
341 @kwarg aMaX0: Upper limit for the I{angular L1-distance}
342 (C{degrees}) or C{None} or C{0} for unlimited.
343 @kwarg sMaX0_C: Optional, upper limit C{B{sMaX0}=2*PI*R} for the
344 I{L1-distance} to B{C{X0}} (C{meter}).
345 @kwarg LatLon_and_kwds: Optional class C{B{LatLon}=None} to return intersection
346 points and optional, additional B{C{LatLon}} keyword arguments.
348 @note: The C{lat} and C{lon} attr of B{C{start1}}, B{C{end1}}, B{C{start2}} and
349 B{C{end2}} are used I{verbatim}, ignoring C{datum} or C{ellipsoid}.
351 @return: Yield an L{Intersect7Tuple}C{(A, B, sAB, aAB, c, kA, kB)} for every
352 intersection found, with C{A} and C{B} each a B{C{LatLon}} or if
353 C{B{LatLon} is None} or not specified, a L{LatLon4Tuple}C{(lat, lon,
354 height, datum)} with C{height 0} and this C{datum}.
356 @raise GeodesicError: Invalid B{C{start1}}, B{C{end1}}, B{C{start2}} or
357 B{C{end2}} or B{C{end1}} and B{C{end2}} differ in type.
359 @raise IntersectionError: No convergence.
360 '''
362 def _args(s, e):
363 t = (e,) if _isDegrees(e) else (e.lat, e.lon)
364 return (s.lat, s.lon) + t
366 try:
367 glA = self.Line(*_args(start1, end1))
368 glB = self.Line(*_args(start2, end2))
369 except Exception as x:
370 raise GeodesicError(start1=start1, end1=end1, start2=start2, end2=end2, cause=x)
372 LL, kwds = _xkwds_pop2(LatLon_and_kwds, LatLon=None)
373 d, kwds = _xkwds_pop2(kwds, datum=self.datum)
374 h, kwds = _xkwds_pop2(kwds, height=0)
376 _LL4T = _MODS.namedTuples._LL4Tuple
377 for X in self.All(glA, glB, X0=X0, aMaX0=aMaX0, sMaX0=sMaX0, _C=True):
378 A = B = _LL4T(X.latA, X.lonA, h, d, LL, kwds, iteration=X.iteration)
379 if X.sAB or X.latA != X.latB or X.lonA != X.lonB:
380 B = _LL4T(X.latB, X.lonB, h, d, LL, kwds, iteration=X.iteration)
381 yield Intersect7Tuple(A, B, X.sAB, X.aAB, X.c, _xkwds_get(X, kA=0),
382 _xkwds_get(X, kB=0))
384 def _Inversa12(self, A, B=None):
385 lls = (0, 0, A, 0) if B is None else (A.lat2, A.lon2,
386 B.lat2, B.lon2)
387 r = self._g.Inverse(*lls, outmask=Caps.DISTANCE)
388 return r.s12, r.a12 # .a12 always in r
390 def k2kAkB(self, k):
391 '''Unravel C{k} into C{kA} and C{kB}.
393 @arg k: Segment indicator C{kA * 3 + kB} (C{int}).
395 @return: An C{ADict(k=k, kA=kA, kB=kB)}.
397 @raise GeodesicError: Invalid B{C{k}}.
398 '''
399 for kA in range(-1, 2):
400 for kB in range(-1, 2):
401 if (kA * 3 + kB) == k:
402 return ADict(k=k, kA=kA, kB=kB)
403 raise GeodesicError(k=k)
405# def k2kAkB(self, k):
406# # unravel C{k} into C{kA} and C{kB}.
407# kA, kB = divmod(k, 3)
408# if kB > 1:
409# kA += 1
410# kB -= 3
411# return kA, kB
413 def Line(self, lat1, lon1, azi1_lat2, *lon2, **name): # PYCHOK no cover
414 '''(INTERNAL) I{Must be overloaded}.'''
415 self._notOverloaded(lat1, lon1, azi1_lat2, *lon2, **name)
417 def _ll3z4ll(self, lat1, lon1, azi1_lat2, *lon2):
418 t = Lat(lat1=lat1), Lon(lon1=lon1)
419 if lon2: # get azis for All, keep lat-/lons
420 t += Lat(lat2=azi1_lat2), Lon(lon2=lon2[0])
421 else:
422 t += Azi(azi1=azi1_lat2),
423 return t
425 @deprecated_method
426 def Next5s(self, glA, glB, X0=_X000, aMax=1801, sMax=0, **unused): # PYCHOK no cover
427 '''DEPRECATED on 2024.07.02, use method C{All5}.'''
428 return self.All5(glA, glB, X0=X0, aMaX0=aMax, sMaX0=sMax) # PYCHOK attr
430 @Property_RO
431 def R(self):
432 '''Get the I{authalic} earth radius (C{meter}).
433 '''
434 return self.ellipsoid.R2
436 def _sMaX0_C2(self, aMaX0=0, **sMaX0_C):
437 _g = _xkwds_get
438 s = _g(sMaX0_C, sMaX0=self._cMax)
439 s = _g(sMaX0_C, sMax=s) # for backward ...
440 a = _g(sMaX0_C, aMax=aMaX0) # ... compatibility
441 if a: # degrees to meter, approx.
442 s = min(s, self.R * radians(a)) # ellipsoid.degrees2m(a)
443 s = _g(sMaX0_C, _R=s)
444 if s < _EPS3:
445 s = _EPS3 # raise GeodesicError(sMaX0=s)
446 return s, _g(sMaX0_C, _C=False)
448 def _xNext(self, glA, glB, eps1, **eps_C): # PYCHOK no cover
449 eps1 = _xkwds_get(eps_C, eps=eps1) # eps for backward compatibility
450 if eps1 is not None:
451 a = glA.lat1 - glB.lat1
452 b = glA.lon1 - glB.lon1
453 if euclid(a, b) > eps1:
454 raise GeodesicError(lat_=a, lon_=b, eps1=eps1)
455 return _xkwds_kwds(eps_C, _C=False)
458class Intersectool(_IntersectBase, _SolveCapsBase):
459 '''Wrapper to invoke I{Karney}'s utility U{IntersectTool
460 <https://GeographicLib.SourceForge.io/C++/doc/IntersectTool.1.html>}
461 similar to class L{Intersector<geodesici.Intersector>}.
463 @note: Use property C{IntersectTool} or env variable C{PYGEODESY_INTERSECTTOOL}
464 to specify the (fully qualified) path to the C{IntersectTool} executable.
466 @note: This C{Intersectool} is intended I{for testing purposes only}, it invokes
467 the C{IntersectTool} executable for I{every} method call.
468 '''
469 _c_alt = _c__, # Closest latA lonA aziA latB lonB aziB
470 _C_option = '-C',
471 _Error = GeodesicError
472 _i_alt = _i__, # Segment latA1 lonA1 latA2 lonA2 latB1 lonB1 latB2 lonB2
473 _linelimit = 1200 # line printer width X 10
474 _n_alt = _n__, # Next latA lonA aziA aziB
475 _Names_ABs = _latA_, _lonA_, 'latB', 'lonB', _sAB_ # -C to stderr
476 _Names_XDict = 'sA', 'sB', _c_ # plus 'k' from -i or 'sX0' from -R
477 _o_alt = _o__, # Offset latA lonA aziA latB lonB aziB x0 y0
478 _Xable_name = 'IntersectTool'
479 _Xable_path = _getenv(_PYGEODESY_INTERSECTTOOL_, _PYGEODESY_INTERSECTTOOL_)
481 def __init__(self, a_geodesic=None, f=None, **name):
482 '''New L{IntersectTool}.
484 @arg a_geodesic: Earth' equatorial axis (C{meter}) or a geodesic
485 (L{GeodesicExact<pygeodesy.geodesicx.GeodesicExact>},
486 wrapped L{Geodesic<pygeodesy.geodesicw.Geodesic>} or
487 L{GeodesicSolve<pygeodesy.geodsolve.GeodesicSolve>}).
488 @kwarg f: Earth' flattening (C{scalar}), required if B{C{a_geodesic}}
489 is in C{meter}, ignored otherwise.
490 @kwarg name: Optional C{B{name}=NN} (C{str}).
492 @raise GeodesicError: The eccentricity of the B{C{geodesic}}'s ellipsoid is too
493 large or no initial convergence.
495 @see: The B{Note} at I{Karney}'s C++ U{Intersect<https://GeographicLib.sourceforge.io/
496 C++/doc/classGeographicLib_1_1Intersect.html#ae41f54c9a44836f6c8f140f6994930cf>}.
497 '''
498 g = self._GeodesicExact() if a_geodesic is None else (a_geodesic if f is None else
499 self._GeodesicExact(a_geodesic, f))
500 _IntersectBase.__init__(self, g, **name)
502 def All(self, glA, glB, X0=_X000, eps1=_0_0, aMaX0=0, **sMaX0_C): # PYCHOK signature
503 '''Yield all intersection of two geodesic lines up to a limit.
505 @kwarg eps1: Optional margin for the L{euclid<pygeodesy.euclid>}ean distance
506 (C{degrees}) between the C{(lat1, lon1)} points of both lines for
507 using the L{IntersectTool<Intersectool.IntersectTool>}'s C{"-n"}
508 option, unless C{B{eps1}=None}.
510 @return: An L{XDict} for each intersection.
511 '''
512 for X, _ in self._All2(glA, glB, X0, eps1, aMaX0=aMaX0, **sMaX0_C):
513 yield X
515 def _All2(self, glA, glB, X0, eps1, **aMaX0_sMaX0_C): # MCCABE 13
516 '''(INTERNAL) Helper for methods C{.All} and C{.All5}.
517 '''
518 def _xz2(**gl):
519 try:
520 n, gl = gl.popitem() # _xkwds_item2(gl)
521 try:
522 return self._c_alt, (gl.azi1,)
523 except (AttributeError, KeyError):
524 return self._i_alt, (gl.lat2, gl.lon2)
525 except Exception as x:
526 raise GeodesicError(n, gl, cause=x)
528 _t, a = _xz2(glA=glA)
529 _x, b = _xz2(glB=glB)
530 if _x is not _t:
531 raise GeodesicError(glA=glA, glB=glB)
533 A = glA.lat1, glA.lon1
534 B = glB.lat1, glB.lon1
535 if _x is self._c_alt:
536 if X0 is _X000 or X0._is00:
537 if eps1 is not None and \
538 euclid(glA.lat1 - glB.lat1,
539 glA.lon1 - glB.lon1) <= eps1:
540 _x, B = self._n_alt, ()
541 else: # non-zero offset
542 _x = self._o_alt
543 b += X0.sA, X0.sB
545 sMaX0, _C = self._sMaX0_C2(**aMaX0_sMaX0_C)
546 for X in self._XDictInvoke(_x, _sX0_, (A + a + B + b),
547 _C=_C, _R=sMaX0):
548 if _C:
549 T = self._In5T(glA, glB, X, X)
550 if _aAB_ not in X:
551 X.set_(sAB=T.sAB, aAB=T.aAB)
552 else:
553 T = None
554 yield X.set_(c=int(X.c)), T
556 def All5(self, glA, glB, X0=_X000, **aMaX0_sMaX0):
557 '''Yield all intersection of two geodesic lines up to a limit.
559 @return: An L{Intersectool5Tuple} for each intersection.
560 '''
561 for _, T in self._All2(glA, glB, X0, _0_0, _C=True, **aMaX0_sMaX0):
562 yield T
564 @Property_RO
565 def _cmdBasic(self):
566 '''(INTERNAL) Get the basic C{IntersectTool} cmd (C{tuple}).
567 '''
568 return (self.IntersectTool,) + (self._e_option +
569 self._E_option +
570 self._p_option)
572 def Closest(self, glA, glB, X0=_X000, _C=False):
573 '''Find the closest intersection of two geodesic lines.
575 @kwarg _C: Use C{B{_C}=True} to include the C{"-C"} results (C{bool}).
577 @return: An L{XDict}.
578 '''
579 args = glA.lat1, glA.lon1, glA.azi1, \
580 glB.lat1, glB.lon1, glB.azi1
581 if X0 is _X000 or X0._is000:
582 _x = self._c_alt
583 else:
584 _x = self._o_alt
585 args += X0.sA, X0.sB
586 return self._XDictInvoke(_x, NN, args, _C=_C) # _R=None)
588 def Closest5(self, glA, glB, **unused):
589 '''Find the closest intersection of two geodesic lines.
591 @return: An L{Intersectool5Tuple}.
592 '''
593 X = self.Closest(glA, glB, _C=True)
594 return self._In5T(glA, glB, X, X)
596 @property_ROver
597 def _GeodesicExact(self):
598 '''Get the I{class} L{GeodesicExact}, I{once}.
599 '''
600 return _MODS.geodesicx.GeodesicExact # overwrite propertyROver
602 def _In5T(self, glA, glB, S, X, k2=False, **_2X):
603 A = GDict(glA).set_(lat2=X.latA, lon2=X.lonA, s12=S.sA)
604 B = GDict(glB).set_(lat2=X.latB, lon2=X.lonB, s12=S.sB)
605 if k2:
606 A.set_(k2=X.kA)
607 B.set_(k2=X.kB)
608 s, a = self._Inversa12(A, B)
609 sAB = _xkwds_get(X, sAB=s)
610 if a and s and s != sAB:
611 a *= sAB / s # adjust a
612 return Intersectool5Tuple(A._2X(glA, **_2X),
613 B._2X(glB, **_2X), sAB, a, X.c)
615 @Property
616 def IntersectTool(self):
617 '''Get the U{IntersectTool<https://GeographicLib.SourceForge.io/C++/doc/IntersectTool.1.html>}
618 executable (C{filename}).
619 '''
620 return self._Xable_path
622 @IntersectTool.setter # PYCHOK setter!
623 def IntersectTool(self, path):
624 '''Set the U{IntersectTool<https://GeographicLib.SourceForge.io/C++/doc/IntersectTool.1.html>}
625 executable (C{filename}), the (fully qualified) path to the C{IntersectTool} executable.
627 @raise GeodesicError: Invalid B{C{path}}, B{C{path}} doesn't exist or isn't the
628 C{IntersectTool} executable.
629 '''
630 self._setXable(path)
632 def Line(self, lat1, lon1, azi1_lat2, *lon2, **name):
633 '''Return a geodesic line from this C{Intersector}'s geodesic, specified by
634 two (goedetic) points or a (goedetic) point and an (forward) azimuth.
636 @return: A 3- or 6-item, named L{GDict}.
637 '''
638 args = self._ll3z4ll(lat1, lon1, azi1_lat2, *lon2)
639 gl = GDict((u.name, u) for u in args)
640# if lon2: # get azis for All, use lat-/lons as given
641# r = self._g.Inverse(outmask=Caps.AZIMUTH, *args)
642# gl.set_(azi1=Azi(azi1=r.azi1), azi2=Azi(azi2=r.azi2))
643 if name:
644 gl.name= name
645 return gl
647 def Middle(self, glA, glB, **_C):
648 '''Get the mid-points on two geodesic line segments.
650 @kwarg _C: Use C{B{_C}=True} to include the C{"-C"} results (C{bool}).
652 @return: An L{XDict}.
653 '''
654 X, _, _, _, _ = self._middle5(glA, glB, **_C)
655 return X
657 def _middle5(self, glA, glB, _C=False, **unused):
658 # return intersections C{A} and C{B} and the
659 # center C{X0} of rectangle [sA, sB]
661 def _smi4(**gl):
662 try:
663 n, gl = gl.popitem()
664 il = self._g.InverseLine(gl.lat1, gl.lon1, gl.lat2, gl.lon2)
665 except Exception as x:
666 raise GeodesicError(n, gl, cause=x)
667 s = il.s13
668 m = s * _0_5
669 return s, m, il, (il.Position(m, outmask=Caps._STD_LINE) if _C else None)
671 sA, mA, iA, A = _smi4(glA=glA)
672 sB, mB, iB, B = _smi4(glB=glB)
673 X = XDict_(mA, mB) # centers
674 _ = X._outSide(sA, sB)
675 if _C: # _Names_ABs
676 s, a = self._Inversa12(A, B)
677 X.set_(latA=A.lat2, lonA=A.lon2, aMM=a, # assert sA == A.s12
678 latB=B.lat2, lonB=B.lon2, sMM=s) # assert sB == B.s12
679 return X, A, iA, B, iB
681 def Middle5(self, glA, glB, **unused):
682 '''Get the mid-points on two geodesic line segments and their distance.
684 @return: A L{Middle5Tuple}.
685 '''
686 X, A, iA, B, iB = self._middle5(glA, glB, _C=True)
687 A, B, s, a, c = self._In5T(A, B, X, X, _2X=_M_)
688 return Middle5Tuple(self._illz2G(A, iA),
689 self._illz2G(B, iB), s, a, c)
691 def Next(self, glA, glB, eps1=None, **_C): # PYCHOK no cover
692 '''Find the next intersection of two I{intersecting} geodesic lines.
694 @kwarg _C: Use C{B{_C}=True} to include the option C{"-C"} results (C{bool}).
696 @return: An L{XDict}.
697 '''
698 if eps1 or _C:
699 _C = self._xNext(glA, glB, eps1, **_C)
700 return self._XDictInvoke(self._n_alt, NN,
701 (glA.lat1, glA.lon1, glA.azi1, glB.azi1),
702 **_C) # _R=None
704 def Next5(self, glA, glB, **eps1): # PYCHOK no cover
705 '''Find the next intersection of two I{intersecting} geodesic lines.
707 @return: An L{Intersectool5Tuple}.
708 '''
709 X = self.Next(glA, glB, _C=True, **eps1)
710 return self._In5T(glA, glB, X, X)
712 def _R_option(self, _R=None):
713 '''(INTERNAL) Get the C{-R maxdist} option.
714 '''
715 return () if _R is None else (_R__, str(_R)) # -R maxdist
717 def Segment(self, glA, glB, **_C_unused):
718 '''Find the intersection between two geodesic line segments.
720 @kwarg _C: Use C{B{_C}=True} to include the option C{"-C"} results (C{bool}).
722 @return: An L{XDict}.
723 '''
724 X = self._XDictInvoke(self._i_alt, 'k',
725 (glA.lat1, glA.lon1, glA.lat2, glA.lon2,
726 glB.lat1, glB.lon1, glB.lat2, glB.lon2),
727 _C=_xkwds_get(_C_unused, _C=False)) # _R=None
728 try:
729 ks = self.k2kAkB(int(X.k))
730 except Exception as x:
731 raise GeodesicError(glA=glA, glB=glB, X=str(X), cause=x)
732 return X.set_(**ks)
734 def Segment5(self, glA, glB, **unused):
735 '''Find the next intersection of two I{intersecting} geodesic lines.
737 @return: An L{Intersectool5Tuple}.
738 '''
739 X = self.Segment(glA, glB, _C=True)
740 return self._In5T(glA, glB, X, X, k2=True)
742 def toStr(self, prec=6, sep=_COMMASPACE_, **unused): # PYCHOK signature
743 '''Return this C{Intersectool} as string.
745 @kwarg prec_sep: Keyword argumens C{B{prec}=6} and C{B{sep}=", "}
746 for the C{float} C{prec}ision, number of decimal digits
747 (0..9) and the C{sep}arator string to join. Trailing
748 zero decimals are stripped for B{C{prec}} values of 1
749 and above, but kept for negative B{C{prec}} values.
751 @return: Intersectool items (C{str}).
752 '''
753 d = dict(geodesic=self.geodesic, invokation=self.invokation,
754 status=self.status,
755 IntersectTool=self.IntersectTool)
756 return sep.join(pairs(d, prec=prec))
758 def _XDictInvoke(self, alt, _k_sX0, args, _C=False, **_R):
759 '''(INTERNAL) Invoke C{IntersectTool}, return results as C{XDict} or
760 a C{generator} if keyword argument C{B{_R}=sMaX0} is specified.
761 '''
762 # assert len(args) == {self._c_alt: 6,
763 # self._i_alt: 8,
764 # self._n_alt: 4,
765 # self._o_alt: 8}.get(alt, len(args))
766 cmd = self._cmdBasic
767 Names = self._Names_XDict # has _c_ always
768 if _k_sX0:
769 Names += _k_sX0,
770 if _C:
771 cmd += self._C_option
772 Names += self._Names_ABs
773 if _R:
774 cmd += self._R_option(**_R)
775 X, _R = self._DictInvoke2(cmd + alt, args, Names, XDict, **_R)
776 return X if _R else X.set_(c=int(X.c)) # generator or XDict
779class Intersector(_IntersectBase):
780 '''Finder of intersections between two goedesic lines, each an instance
781 of L{GeodesicLineExact<pygeodesy.geodesicx.GeodesicLineExact>},
782 wrapped L{GeodesicLine<pygeodesy.geodesicw.GeodesicLine>} or
783 L{GeodesicLineSolve<pygeodesy.geodsolve.GeodesicLineSolve>}.
785 @see: I{Karney}'s C++ class U{Intersect<https://GeographicLib.sourceforge.io/
786 C++/doc/classGeographicLib_1_1Intersect.html#details>} for more details.
787 '''
789 def __init__(self, geodesic, **name):
790 '''New L{Intersector}.
792 @arg geodesic: The geodesic (L{GeodesicExact<pygeodesy.geodesicx.GeodesicExact>},
793 wrapped L{Geodesic<pygeodesy.geodesicw.Geodesic>} or
794 L{GeodesicSolve<pygeodesy.geodsolve.GeodesicSolve>}).
795 @kwarg name: Optional C{B{name}=NN} (C{str}).
797 @raise GeodesicError: The eccentricity of the B{C{geodesic}}'s ellipsoid is too
798 large or no initial convergence.
800 @see: The B{Note} at I{Karney}'s C++ U{Intersect<https://GeographicLib.sourceforge.io/
801 C++/doc/classGeographicLib_1_1Intersect.html#ae41f54c9a44836f6c8f140f6994930cf>}.
802 '''
803 _IntersectBase.__init__(self, geodesic, **name)
804 E = self.ellipsoid
805 t1 = E.b * PI # min distance between intersects
806 t2 = self._polarDist2(_90_0)[0] * _2_0 # furthest, closest intersect
807 t5 = self._Inversa12( _90_0)[0] * _2_0 # longest, shortest geodesic
808 if self.f > 0:
809 t3 = self._obliqDist4()[0]
810 t4 = t1
811 else: # PYCHOK no cover
812 t1, t2, t3 = t2, t1, t5
813 t4, _, _ = self._polarB3()
815 self._D1 = d1 = t2 * _0_5 # ~E.L tile spacing for Closest
816 self._D2 = d2 = t3 / _1_5 # tile spacing for Next
817 self._D3 = d3 = t4 - self.Delta # tile spacing for All
818 self._T1 = t1 # min distance between intersects
819 self._T2 = t2 = t1 * _2_0
820# self._T5 = t5 # not used
821 if not (d1 < d3 and d2 < d3 and d2 < t2):
822 t = Fmt.PARENSPACED(_too_('eccentric'), E.e)
823 raise GeodesicError(ellipsoid=E.toStr(terse=2), txt=t)
825 def All(self, glA, glB, X0=None, aMaX0=0, **sMaX0_C): # MCCABE 13
826 '''Yield all intersection of two geodesic lines up to a limit.
828 @arg glA: A geodesic line (L{Line<Intersector.Line>}).
829 @arg glB: An other geodesic line (L{Line<Intersector.Line>}).
830 @kwarg X0: Optional I{origin} for I{L1-distances} (L{XDict}) or
831 C{None} for the L{Middle<Intersector.Middle>} of both
832 lines if both are a 4-C{args} L{Line<Intersector.Line>}
833 or C{InverseLine}, otherwise C{XDiff_(0, 0)}.
834 @kwarg aMaX0: Upper limit for the I{angular L1-distance}
835 (C{degrees}) or C{None} or C{0} for unlimited.
836 @kwarg sMaX0_C: Optional, upper limit C{B{sMaX0}=2*PI*R} for the
837 I{L1-distance} to B{C{X0}} (C{meter}) and option
838 C{B{_C}=False} to include the intersection lat-/
839 longitudes C{latA}, C{lonA}, C{latB}, C{lonB} and
840 distances C{sAB} and C{aSB}.
842 @return: Yield an L{XDict} for each intersection found.
844 @raise GeodesicError: Geodesic line B{C{glA}} or B{C{glB}}
845 invalid, incompatible or ill-configured.
847 @raise IntersectionError: No convergence.
848 '''
849 self._xLines(glA, glB)
850 if X0 is None:
851 try: # determine X0
852 X0, _, _ = self._middle3(glA, glB, True)
853 except GeodesicError: # no .Distance
854 X0 = _X000
855 sMaX0, _C = self._sMaX0_C2(aMaX0, **sMaX0_C)
857 D, _D = self.Delta, self._cHalf # C++ _d
858 xMaX0 = sMaX0 + D
859 m = int(_ceil(xMaX0 / self._D3)) # m x m tiles
860 d3 = xMaX0 / m
861 T2d3D = self._T2d3Delta(d3)
863 C_ = _List(D) # closest coincident
864 X_ = _List(D) # intersections found
865 c0 = 0
866 S_ = list(X0._nmD3(1 - m, m, d3 * _0_5))
867 # assert len(S_) == m * m + (m - 1) % 2
868 while S_:
869 Q, i = self._Basic2(glA, glB, S_.pop(0))
870 if Q in X_:
871 continue
872 if Q.c: # coincident intersection # PYCHOK no cover
873 _X0fx = X0._fixCoincident
874 Q = _X0fx(Q) # Q = Q'
875 if c0 and Q in C_:
876 continue
877 C_.addend(Q)
878 # elimate all existing intersections
879 # on this line (which didn't set c0)
880 c0 = Q.c
881 for j, X in _enumereverse(X_):
882 if _X0fx(X, c0).L1(Q) <= D: # X' == Q
883 X_.pop(j)
885 a, s0 = len(X_), Q.sA
886 args = self._m12_M12_M21(glA, s0)
887 _cjD = self._conjDist
888 for s in (-_D, _D):
889 s += s0
890 sa = 0
891 while True:
892 i += 1
893 sa = _cjD(glA, s + sa, *args) - s0
894 X = Q + (sa, sa * c0)
895 if X_.addend(X, X0.L1(X), i) > xMaX0:
896 break
898 elif c0 and Q in C_: # Q.c == 0
899 continue
900 else:
901 a = len(X_)
903 X_.addend(Q, X0.L1(Q), i + 1)
904 for X in X_[a:]: # addended Xs
905 X._skip(S_, T2d3D)
907 return X_.sorter(sMaX0, self._C, glA, glB, _C=_C) # generator
909 def All5(self, glA, glB, X0=_X000, **aMaX0_sMaX0_C):
910 '''Yield all intersection of two geodesic lines up to a limit.
912 @return: Yield an L{Intersector5Tuple}C{(A, B, sAB, aAB, c)}
913 for each intersection found.
915 @see: Methods L{All} for further details.
916 '''
917 for X in self.All(glA, glB, X0=X0, **aMaX0_sMaX0_C):
918 yield self._In5T(glA, glB, X, X)
920 def _Basic2(self, glA, glB, S, i=0):
921 '''(INTERNAL) Get a basic solution.
922 '''
923 X = _copy(S)
924 for _ in range(_TRIPS):
925 S = self._Spherical(glA, glB, X)
926 X += S
927 i += 1
928 if X.c or S.L1() <= self._Tol: # or isnan
929 return self._Delto(X), i
931 raise IntersectionError(Fmt.no_convergence(S.L1(), self._Tol))
933 def _C(self, X, glA, glB, _C=False, _MM=False):
934 # add the C{_C} items to C{X}, if requested.
935 if _C:
936 A = self._Position(glA, X.sA)
937 B = self._Position(glB, X.sB)
938 s, a = self._Inversa12(A, B)
939 X.set_(latA=A.lat2, lonA=A.lon2,
940 latB=B.lat2, lonB=B.lon2)
941 if _MM: # in .Middle5
942 X.set_(sMM=s, aMM=a)
943 else:
944 X.set_(sAB=s, aAB=a)
945 return X
947 def Closest(self, glA, glB, X0=_X000, **_C):
948 '''Find the closest intersection of two geodesic lines.
950 @arg glA: A geodesic line (L{Line<Intersector.Line>}).
951 @arg glB: An other geodesic line (L{Line<Intersector.Line>}).
952 @kwarg X0: Optional I{origin} for I{L1-closeness} (L{XDict}).
953 @kwarg _C: If C{True}, include the lat-/longitudes C{latA},
954 C{lonA}, C{latB}, C{lonB} oon and distances C{sAB}
955 and C{aSB} between the intersections.
957 @return: The intersection (L{XDict}) or C{None} if none found.
959 @raise GeodesicError: Geodesic line B{C{glA}} or B{C{glB}}
960 invalid, incompatible or ill-configured.
962 @raise IntersectionError: No convergence.
963 '''
964 self._xLines(glA, glB)
965 Q, d, S_, i = X0, INF, list(X0._nD1(self._D1)), 0
966 while S_:
967 X, i = self._Basic2(glA, glB, S_.pop(0), i)
968 X = X0._fixCoincident(X)
969 if X.L1(Q) > self.Delta: # X != Q
970 d0 = X.L1(X0)
971 if d0 < self._T1:
972 Q, d, q = X, d0, i
973 break
974 if d0 < d or Q is X0:
975 Q, d, q = X, d0, i
976 X._skip(S_, self._T2D1Delta)
978 return None if Q is X0 else self._C(Q, glA, glB, **_C).set_(sX0=d, iteration=q)
980 def Closest5(self, glA, glB, X0=_X000):
981 '''Find the closest intersection of two geodesic lines.
983 @return: An L{Intersector5Tuple}C{(A, B, sAB, aAB, c)}
984 or C{None} if none found.
986 @see: Method L{Closest} for further details.
987 '''
988 X = self.Closest(glA, glB, X0=X0)
989 return X if X is None else self._In5T(glA, glB, X, X)
991 def _conjDist(self, gl, s, m12=0, M12=1, M21=1, semi=False):
992 # Find semi-/conjugate point relative to s0 which is close to s1.
993 # if semi:
994 # solve for M23 = 0 using dM23 / ds3 = - (1 - M23 * M32) / m23
995 # else:
996 # solve for m23 = 0 using dm23 / ds3 = M32
997 _S2, _abs, _1 = Fsum(s).fsum2_, fabs, _1_0
998 for _ in range(_TRIPS):
999 m13, M13, M31 = self._m12_M12_M21(gl, s)
1000 # see "Algorithms for geodesics", eqs. 31, 32, 33.
1001 m23 = m13 * M12
1002 M32 = M31 * M12
1003 if m12: # PYCHOK no cover
1004 m23 -= m12 * M13
1005 if m13:
1006 M32 += (_1 - M13 * M31) * m12 / m13
1007 if semi:
1008 M23 = M13 * M21
1009 # when m12 -> eps, (1 - M12 * M21) -> eps^2, I suppose.
1010 if m12 and m13:
1011 M23 += (_1 - M12 * M21) * m13 / m12
1012 d = m23 * M23 / (_1 - M23 * M32)
1013 else:
1014 d = -m23 / M32
1015 s, d = _S2(d)
1016 if _abs(d) <= self._Tol:
1017 break
1018 return s
1020 _gl3 = None
1022 @Property
1023 def _conjDist3s(self):
1024 gl, self._gl3, _D = self._gl3, None, self._cHalf
1025 return tuple(self._conjDist(gl, s) for s in (-_D, 0, _D))
1027 @_conjDist3s.setter # PYCHOK setter!
1028 def _conjDist3(self, gl):
1029 # _XLines(gl, gl)
1030 self._gl3 = gl
1032 def _conjDist3Tt_(self, c, X0=_X000):
1033 for s in self._conjDist3s:
1034 T = XDict_(s, s * c, c)
1035 yield self._Delto(T), T.L1(X0)
1037 def _conjDist5(self, azi):
1038 gl = self._Line(azi1=azi)
1039 s = self._conjDist(gl, self._cHalf)
1040 X, _ = self._Basic2(gl, gl, XDict_(s * _0_5, -s * _1_5))
1041 return s, (X.L1() - s * _2_0), azi, X.sA, X.sB
1043 @Property_RO
1044 def Delta(self):
1045 '''Get the equality and tiling margin (C{meter}).
1046 '''
1047 return self._cHalf * _EPSr5 # ~15 Km WGS84
1049 def _Delto(self, X):
1050 # copy Delta into X, overriding X's default
1051 X._Delta = self.Delta # NOT X.set_(self.Delta)
1052 return X
1054 @Property_RO
1055 def _EPS3R(self):
1056 return _EPS3 * self.R
1058 @Property_RO
1059 def _faPI_4(self):
1060 return (self.f + _2_0) * self.a * PI_4
1062 @Property_RO
1063 def _GeodesicLines(self):
1064 '''(INTERNAL) Get the C{Geodesic...Line} class(es).
1065 '''
1066 return type(self._Line()),
1068 def _In5T(self, glA, glB, S, X, k2=False, **_2X):
1069 # Return an intersection as C{Intersector5Tuple}.
1070 A = self._Position(glA, S.sA)
1071 B = self._Position(glB, S.sB)
1072 if k2:
1073 A.set_(k2=X.kA)
1074 B.set_(k2=X.kB)
1075 s, a = self._Inversa12(A, B)
1076 return Intersector5Tuple(A._2X(glA, **_2X),
1077 B._2X(glB, **_2X), s, a, X.c, iteration=X.iteration)
1079 def _Inverse(self, A, B): # caps=Caps.STANDARD
1080 return self._g.Inverse(A.lat2, A.lon2, B.lat2, B.lon2)
1082 def Line(self, lat1, lon1, azi1_lat2, *lon2, **name):
1083 '''Return a geodesic line from this C{Intersector}'s geodesic, specified by
1084 two (goedetic) points or a (goedetic) point and an (initial) azimuth.
1086 @arg lat1: Latitude of the first point (C{degrees}).
1087 @arg lon1: Longitude of the first point (C{degrees}).
1088 @arg azi1_lat2: Azimuth at the first point (compass C{degrees}) if no
1089 B{C{lon2}} argument is given, otherwise the latitude of
1090 the second point (C{degrees}).
1091 @arg lon2: If given, the longitude of the second point (C{degrees}).
1092 @kwarg name: Optional C{B{name}=NN} (C{str}).
1094 @return: A line (from L{geodesic<Intersector.geodesic>}C{.Line} or
1095 C{.InverseLine} method) with C{LINE_CAPS}.
1096 '''
1097 args = self._ll3z4ll(lat1, lon1, azi1_lat2, *lon2)
1098 gl = self._g.InverseLine(*args, caps=Caps.LINE_CAPS) if lon2 else \
1099 self._g.Line( *args, caps=Caps.LINE_CAPS)
1100 if name:
1101 gl.name= name
1102 return gl
1104 def _Line(self, lat1=0, lon1=0, azi1=0):
1105 return self._g.Line(lat1, lon1, azi1, caps=Caps.LINE_CAPS)
1107 def Middle(self, glA, glB, raiser=True, **_C):
1108 '''Get the mid-points on two geodesic line segments.
1110 @arg glA: A geodesic line (L{Line<Intersector.Line>}, 4-C{args}).
1111 @arg glB: An other geodesic line (L{Line<Intersector.Line>}, 4-C{args}).
1112 @kwarg raiser: If C{True}, check that B{C{glA}} and B{C{glB}} are a
1113 4-C{args} L{Line<Intersector.Line>} or C{InverseLine}
1114 (C{bool}).
1115 @kwarg _C: If C{True}, include the lat-/longitudes C{latA}, C{lonA},
1116 C{latB}, C{lonB} of the mid-points and half-lengths C{sA}
1117 and C{sB} in C{meter} of the respective line segments.
1119 @return: The mid-point and half-length of each segment (L{XDict}),
1120 B{C{_C}} above.
1122 @raise GeodesicError: Geodesic line B{C{glA}} or B{C{glB}} invalid,
1123 incompatible, ill-configured or not a 4-C{args
1124 Line} or other C{InverseLine}.
1125 '''
1126 M, _, _ = self._middle3(glA, glB, raiser)
1127 return self._C(M, glA, glB, **_C) if _C else M
1129 def _middle3(self, glA, glB, raiser): # in .All, .Segment
1130 # return segment length C{sA} and C{sB} and the
1131 # center C{X0} of rectangle [sA, sB]
1132 self._xLines(glA, glB, s13=raiser) # need .Arc, .Distance
1133 sA = glA.Distance()
1134 sB = glB.Distance()
1135 X = XDict_(sA * _0_5, sB * _0_5)
1136 # _ = X._outSide(sA, sB)
1137 return self._Delto(X), sA, sB
1139 def Middle5(self, glA, glB, raiser=True):
1140 '''Get the mid-points of two geodesic line segments and distances.
1142 @return: A L{Middle5Tuple}C{(A, B, sMM, aMM, c)}.
1144 @see: Method L{Middle} for further details.
1145 '''
1146 M, _, _ = self._middle3(glA, glB, raiser)
1147 M = self._C(M, glA, glB, _C=True, _MM=True)
1148 A, B, s, a, c = self._In5T(glA, glB, M, M, _2X=_M_)
1149 return Middle5Tuple(self._illz2G(A, glA),
1150 self._illz2G(B, glB), s, a, c)
1152 def _m12_M12_M21(self, gl, s):
1153 P = gl.Position(s, outmask=Caps._REDUCEDLENGTH_GEODESICSCALE)
1154 return P.m12, P.M12, P.M21
1156 def Next(self, glA, glB, eps1=None, **_C): # PYCHOK no cover
1157 '''Yield the next intersection of two I{intersecting} geodesic lines.
1159 @arg glA: A geodesic line (L{Line<Intersector.Line>}).
1160 @arg glB: An other geodesic line (L{Line<Intersector.Line>}).
1161 @kwarg eps1: Optional margin for the L{euclid<pygeodesy.euclid>}ean
1162 distance (C{degrees}) between the C{(lat1, lon1)} points
1163 of both lines or C{None} for unchecked.
1164 @kwarg _C: If C{True}, include the lat-/longitudes C{latA}, C{lonA},
1165 C{latB}, C{lonB} of and distances C{sAB} and C{aSB}
1166 between the intersections.
1168 @return: The intersection (L{XDict}) or C{None} if none found.
1170 @raise GeodesicError: Geodesic line B{C{glA}} or B{C{glB}} invalid,
1171 incompatible, ill-configured or C{(lat1, lon1)}
1172 not B{C{eps1}}-equal.
1174 @raise IntersectionError: No convergence.
1176 @note: Offset C{X0} is implicit, zeros.
1177 '''
1178 self._xLines(glA, glB)
1179 if eps1 or _C: # eps
1180 _C = self._xNext(glA, glB, eps1, **_C)
1182 X0, self._conjDist3s = _X000, glA # reset Property
1183 Q, d, S_, i = _XINF, INF, list(X0._nD2(self._D2)), 0
1184 while S_:
1185 X, i = self._Basic2(glA, glB, S_.pop(0), i)
1186 X = X0._fixCoincident(X)
1187 t = X.L1(X0) # == X.L1()
1188 c, z = X.c, (t <= self.Delta) # X == X0
1189 if z:
1190 if not c:
1191 continue
1192 Tt_ = self._conjDist3Tt_(c, X0)
1193 else:
1194 Tt_ = (X, t),
1196 for T, t in Tt_:
1197 if t < d or Q is _XINF:
1198 Q, d, q = T, t, i
1199 i += 1
1201 for s in ((_1_1t if z else _1_0_1t)
1202 if c else _0t):
1203 T = X
1204 if s and c:
1205 s *= self._D2
1206 T = X + (s, s * c) # NOT +=
1207 T._skip(S_, self._T2D2Delta)
1209 return None if Q is _XINF else self._C(Q, glA, glB, **_C).set_(sX0=d, iteration=q)
1211 def Next5(self, glA, glB, **eps1): # PYCHOK no cover
1212 '''Yield the next intersection of two I{intersecting} geodesic lines.
1214 @return: An L{Intersector5Tuple}C{(A, B, sAB, aAB, c)} or C{None}
1215 if none found.
1217 @see: Method L{Next} for further details.
1218 '''
1219 X = self.Next(glA, glB, **eps1)
1220 return X if X is None else self._In5T(glA, glB, X, X)
1222 def _obliqDist4(self):
1223 zx = 45.0
1224 if self.f:
1225 _abs, _cjD5 = fabs, self._conjDist5
1227 _, ds0, z0, _, _ = _cjD5(zx + _1_0)
1228 s1, ds1, z1, sAx, sBx = _cjD5(zx - _1_0)
1229 sx, dsx, zx = s1, _abs(ds1), z1
1230 # find ds(azi) = 0 by secant method
1231 for _ in range(16):
1232 if ds1 == ds0:
1233 break
1234 z = (z0 * ds1 - z1 * ds0) / (ds1 - ds0)
1235 _, ds0, z0 = s1, ds1, z1
1236 s1, ds1, z1, a, b = _cjD5(z)
1237 if _abs(ds1) < dsx:
1238 sx, dsx, zx, sAx, sBx = s1, _abs(ds1), z, a, b
1239 if not dsx:
1240 break
1241 else:
1242 sx, sAx, sBx = self._cHalf, _0_5, -_1_5
1243 return sx, zx, sAx, sBx
1245 def _polarB3(self, lats=False): # PYCHOK no cover
1246 latx = 64.0
1247 lat = _90_0 - latx
1248 if self.f:
1249 _d, _pD2 = fdot, self._polarDist2
1251 s0, lat0 = _pD2(latx - _1_0)
1252 s1, lat1 = _pD2(latx + _1_0)
1253 s2, lat2 = \
1254 sx, latx = _pD2(latx)
1255 prolate = self.f < 0
1256 # solve for ds(lat) / dlat = 0 with a quadratic fit
1257 for _ in range(_TRIPS):
1258 t = (lat1 - lat0), (lat0 - lat2), (lat2 - lat1)
1259 d = _d(t, s2, s1, s0) * _2_0
1260 if not d: # or isnan(d)
1261 break
1262 lat = _d(t, (lat1 + lat0) * s2,
1263 (lat0 + lat2) * s1,
1264 (lat2 + lat1) * s0) / d
1265 s0, lat0 = s1, lat1
1266 s1, lat1 = s2, lat2
1267 s2, lat2 = _pD2(lat)
1268 if (s2 < sx) if prolate else (s2 > sx):
1269 sx, latx = s2, lat2
1270 if lats:
1271 _, lat = _pD2(latx, lat2=True)
1272 sx += sx
1273 else:
1274 sx = self._cHalf
1275 return sx, latx, lat
1277 def _polarDist2(self, lat1, lat2=False):
1278 gl = self._Line(lat1=lat1)
1279 s = self._conjDist(gl, self._faPI_4, semi=True)
1280 if lat2:
1281 lat1 = gl.Position(s, outmask=Caps.LATITUDE).lat2
1282 return s, lat1
1284 def _Position(self, gl, s):
1285 return gl.Position(s, outmask=Caps._STD_LINE)
1287 def Segment(self, glA, glB, proven=None, raiser=True, **_C):
1288 '''Find the intersection between two geodesic line segments.
1290 @kwarg proven: Conjecture is that whenever two geodesic line
1291 segments intersect, the intersection is the
1292 one closest to the mid-points of segments.
1293 If so, use C{B{proven}=True}, otherwise find
1294 intersections on the segments and specify
1295 C{B{proven}=None} to return the first or
1296 C{B{proven}=False} the closest (C{bool}).
1297 @kwarg raiser: If C{True}, check that B{C{glA}} and B{C{glB}}
1298 are a 4-C{args} L{Line<Intersector.Line>} or
1299 C{InverseLine} (C{bool}).
1300 @kwarg _C: If C{True}, include the lat-/longitudes C{latA},
1301 C{lonA}, C{latB}, C{lonB} of and distances C{sAB}
1302 and C{aSB} between the intersections.
1304 @return: The intersection of the segments (L{XDict}) with
1305 indicators C{kA}, C{kB} and C{k} set or if no
1306 intersection is found, C{None}.
1308 @raise GeodesicError: Geodesic line B{C{glA}} or B{C{glB}}
1309 invalid, incompatible, ill-configured or
1310 not an C{InverseLine} or 4-C{args Line}.
1312 @raise IntersectionError: No convergence.
1314 @see: Method L{Middle<Intersector.Middle>} for further details.
1315 '''
1316 X0, sA, sB = self._middle3(glA, glB, raiser)
1317 Q = self.Closest(glA, glB, X0) # to X0
1318 if Q is not None:
1319 if Q.c: # anti-/parallel
1320 Q._fixSegment(sA, sB)
1321 # are rectangle [sA, sB] corners further from X0 than Q?
1322 d0 = X0.L1(Q)
1323 if Q._outSide(sA, sB) and d0 <= X0.L1() and not proven:
1324 i = Q.iteration
1325 for T in Q._corners(sA, sB, self._T2):
1326 X, i = self._Basic2(glA, glB, T, i)
1327 X = T._fixCoincident(X)
1328 if not X._outSide(sA, sB):
1329 d = X0.L1(X)
1330 if d < d0 or proven is None:
1331 Q, d0 = X, d
1332 if proven is None:
1333 break
1334 Q.set_(iteration=i)
1336 Q = self._C(Q, glA, glB, **_C).set_(sX0=d0)
1337 return Q
1339 def Segment5(self, glA, glB, **proven_raiser):
1340 '''Find the intersection between two geodesic line segments.
1342 @return: An L{Intersector5Tuple}C{(A, B, sAB, aAB, c)}
1343 or C{None} if none found.
1345 @see: Method L{Segment} for further details.
1346 '''
1347 X = self.Segment(glA, glB, **proven_raiser)
1348 return X if X is None else self._In5T(glA, glB, X, X, k2=True)
1350 def _Spherical(self, glA, glB, S):
1351 '''(INTERNAL) Get solution based from a spherical triangle.
1352 '''
1353 # threshold for coincident geodesics/intersections ~4.3 nm WGS84.
1354 A = self._Position(glA, S.sA)
1355 B = self._Position(glB, S.sB)
1356 D = self._Inverse(A, B)
1358 a, da = _diff182(A.azi2, D.azi1) # interior angle at A
1359 b, db = _diff182(B.azi2, D.azi2) # exterior angle at B
1360 c, dc = _diff182(a, b)
1361 if fsum1_(dc, db, -da, c) < 0: # inverted triangle
1362 a, da = -a, -da
1363 b, db = -b, -db
1364 sa, ca = _sincos2de(a, da)
1365 sb, cb = _sincos2de(b, db)
1367 e, z, _abs = _EPS3, D.s12, fabs
1368 if _abs(z) <= self._EPS3R: # XXX z <= ...
1369 sA = sB = 0 # at intersection
1370 c = 1 if _abs(sa - sb) <= e and _abs(ca - cb) <= e else (
1371 -1 if _abs(sa + sb) <= e and _abs(ca + cb) <= e else 0)
1372 elif _abs(sa) <= e and _abs(sb) <= e: # coincident
1373 sA = ca * z * _0_5 # choose mid-point
1374 sB = -cb * z * _0_5
1375 c = 1 if (ca * cb) > 0 else -1
1376 # alt1: sA = ca * z; sB = 0
1377 # alt2: sB = -cb * z; sA = 0
1378 else: # general case
1379 sz, cz = sincos2(z / self.R)
1380 # [SKIP: Divide args by |sz| to avoid possible underflow
1381 # in {sa, sb} * sz; this is probably not necessary].
1382 # Definitely need to treat sz < 0 (z > PI*R) correctly in
1383 # order to avoid some convergence failures in _Basic2.
1384 sA = atan2(sb * sz, sb * ca * cz - sa * cb) * self.R
1385 sB = atan2(sa * sz, -sa * cb * cz + sb * ca) * self.R
1386 c = 0
1387 return XDict_(sA, sB, c) # no ._Delto
1389 @Property_RO
1390 def _T2D1Delta(self):
1391 return self._T2d3Delta(self._D1)
1393 @Property_RO
1394 def _T2D2Delta(self):
1395 return self._T2d3Delta(self._D2)
1397 def _T2d3Delta(self, d3):
1398 return self._T2 - d3 - self.Delta
1400 @Property_RO
1401 def _Tol(self): # convergence tolerance
1402 return self._cHalf * pow(EPS, 0.75) # _0_75
1404 def toStr(self, **prec_sep_name): # PYCHOK signature
1405 '''Return this C{Intersector} as string.
1407 @see: L{Ellipsoid.toStr<pygeodesy.ellipsoids.Ellipsoid.toStr>}
1408 for further details.
1410 @return: C{Intersector} (C{str}).
1411 '''
1412 return self._instr(props=(Intersector.geodesic,), **prec_sep_name)
1414 def _xLines(self, glA, glB, s13=False):
1415 # check two geodesic lines vs this geodesic
1416 C, gls = Caps.LINE_CAPS, dict(glA=glA, glB=glB)
1417 _xinstanceof(*self._GeodesicLines, **gls)
1418 for n, gl in gls.items():
1419 try:
1420 _xgeodesics(gl.geodesic, self.geodesic)
1421 if s13 and not isfinite(gl.s13): # or not gl.caps & Caps.DISTANCE_IN
1422 t = gl.geodesic.InverseLine.__name__
1423 raise TypeError(_not_(_an(t)))
1424 c = gl.caps & C
1425 if c != C: # not gl.caps_(C)
1426 c, C, x = map1(bin, c, C, _xor(c, C))
1427 x = _SPACE_(_xor.__name__, repr(x))[1:]
1428 raise GeodesicError(caps=c, LINE_CAPS=C, txt=x)
1429 except Exception as x:
1430 raise GeodesicError(n, gl, cause=x)
1433class Intersect7Tuple(_NamedTuple):
1434 '''7-Tuple C{(A, B, sAB, aAB, c, kA, kB)} with C{A} and C{B} each
1435 a C{LatLon} or L{LatLon4Tuple}C{(lat, lon, height, datum)} of
1436 the intersection on each geodesic line, the distance C{sAB} in
1437 in C{meter} and angular distance C{aAB} in C{degrees} between
1438 C{A} and C{B}, coincidence indicator C{c} and segment indicators
1439 C{kA} and C{kB} all C{int}, see L{XDict} and method U{intersect7
1440 <_IntersectBase.intersect7>}.
1441 '''
1442 _Names_ = (_A_, _B_, _sAB_, _aAB_, _c_, 'kA', 'kB')
1443 _Units_ = (_Pass, _Pass, Meter, Degrees, Int, Int, Int)
1446class Intersectool5Tuple(_NamedTuple):
1447 '''5-Tuple C{(A, B, sAB, aAB, c)} with C{A} and C{B} the C{Position}
1448 of the intersection on each geodesic line, the distance C{sAB}
1449 between C{A} and C{B} in C{meter}, the angular distance C{aAB} in
1450 C{degrees} and coincidence indicator C{c} (C{int}), see L{XDict}.
1452 @note: C{A} and C{B} are each a C{GDict} with C{lat1}, C{lon1} and
1453 C{azi1} or C{lat2}, C{lon2} from the geodesic line C{glA}
1454 respectively C{glB} and the intersection location in C{latX},
1455 C{lonX}, distance C{s1X} in C{meter} and angular distance
1456 C{a1M} in C{degrees} and the segment indicator C{kX}. See
1457 L{XDict} for more details.
1458 '''
1459 _Names_ = Intersect7Tuple._Names_[:5]
1460 _Units_ = Intersect7Tuple._Units_[:5]
1463class Intersector5Tuple(Intersectool5Tuple):
1464 '''5-Tuple C{(A, B, sAB, aAB, c)} with C{A} and C{B} the C{Position}
1465 of the intersection on each geodesic line, the distance C{sAB}
1466 between C{A} and C{B} in C{meter}, angular distance C{aAB} in
1467 C{degrees} and coincidence indicator C{c} (C{int}), see L{XDict}.
1469 @note: C{A} and C{B} are each a C{GeodesicLine...Position} for
1470 C{outmask=Caps.STANDARD} with the intersection location in
1471 C{latX}, C{lonX}, azimuth in C{aziX}, distance C{s1X} in
1472 C{meter} and angular distance C{a1X} in C{degrees} and the
1473 segment indicator C{kX}. See L{XDict} for more details.
1474 '''
1475 _Names_ = Intersectool5Tuple._Names_
1478class Middle5Tuple(Intersectool5Tuple):
1479 '''5-Tuple C{(A, B, sMM, aMM, c)} with C{A} and C{B} the I{line segments}
1480 including the mid-point location in C{latM}, C{lonM}, distance C{s1M}
1481 in C{meter} and angular distance C{a1M} in C{degrees}, the distance
1482 between both mid-points C{sMM} in C{meter} and angular distance C{aMM}
1483 in C{degrees} and coincidence indicator C{c} (C{int}). See L{XDict}
1484 for more details.
1485 '''
1486 _Names_ = (_A_, _B_, 'sMM', 'aMM', _c_)
1489class _List(list):
1491 _Delta = 0 # equality margin
1493 def __init__(self, Delta):
1494 self._Delta = Delta
1495# list.__init__(self)
1497 def __contains__(self, other):
1498 # handle C{if X in this: ...}
1499 a, b = other.sA, other.sB
1500 D, _D1 = self._Delta, _L1
1501 for X in self:
1502 if _D1(X.sA - a, X.sB - b) <= D:
1503 return True
1504 return False
1506 def addend(self, X, *d0_i):
1507 # append an item, updated
1508 if d0_i:
1509 d0, i = d0_i
1510 X.set_(sX0=d0, iteration=i)
1511 self.append(X)
1512 return X.sX0
1514 def sorter(self, sMaX0, dot_C, glA, glB, **_C):
1515 # trim and sort the X items
1517 def _key(X):
1518 return X.sX0 # rank of X
1520 t = (X for X in self if X.sX0 <= sMaX0)
1521 for X in sorted(t, key=_key):
1522 yield dot_C(X, glA, glB, **_C) if _C else X
1525def _L1(a, b):
1526 '''(INTERNAL) Return the I{L1} distance.
1527 '''
1528 return fabs(a) + fabs(b)
1531__all__ += _ALL_DOCS(_IntersectBase)
1533if __name__ == '__main__': # MCCABE 14
1535 from pygeodesy import printf
1536 __help_ = '--help'
1538 def _main(args):
1540 from pygeodesy import GeodesicExact
1541 from pygeodesy.internals import _plural, _usage
1542 from pygeodesy.interns import _COLONSPACE_, _DOT_, _EQUAL_, \
1543 _i_, _m_, _n_, _version_, _X_
1544 import re
1546 class XY0(Float):
1547 pass
1549 def _opts(_h): # for _usage()
1550 ll4 = ' latA1 lonA1'
1551 ll4 += ll4.replace('1', '2')
1552 ll4 += ll4.replace(_A_, _B_)
1553 llz = _SPACE_(NN, _latA_, _lonA_, 'aziA')
1554 llz2 = llz + llz.replace(_A_, _B_)
1555 return dict(opts='-Verbose|V--version|v--help|h--Tool|T--Check|C-R meter-',
1556 alts=((_c_ + llz2),
1557 (_i_ + ll4),
1558 (_m_ + ll4),
1559 (_n_ + llz + ' aziB'),
1560 ('o' + llz2 + ' x0 y0')),
1561 help=_h if isinstance(_h, str) else NN)
1563 def _starts(Opt, arg):
1564 return arg == Opt[1:3] or (len(arg) > 2 and Opt.startswith(arg))
1566 _isopt = re.compile('^[-]+[a-z]*$', flags=re.IGNORECASE).match
1568 I = Intersector(GeodesicExact()) # PYCHOK I
1569 M = m = _R = None
1570 _T = _V = _h = _C = False
1572 while args and _isopt(args[0]):
1573 arg = args.pop(0)
1574 if arg == _c__:
1575 M, m = I.Closest, 6 # latA lonA aziA latB lonB aziB
1576 elif _starts('--Check', arg):
1577 _C = True
1578 elif _starts(__help_, arg):
1579 _h = args[0] if args and _isopt(args[0]) else True
1580 elif arg == _i__:
1581 M, m = I.Segment, 8 # latA1 lonA1 latA2 lonA2 latB1 lonB1 latB2 lonB2
1582 elif arg == '-m':
1583 M, m = I.Middle, 8 # latA1 lonA1 latA2 lonA2 latB1 lonB1 latB2 lonB2
1584 _R = None # zap -R
1585 elif arg == _n__:
1586 M, m = I.Next, 4 # latA lonA aziA aziB
1587 elif arg == _o__:
1588 M, m = I.Closest, 8 # latA lonA aziA latB lonB aziB x0 y0
1589 elif arg == _R__ and args:
1590 _R = args.pop(0)
1591 elif _starts('--Tool', arg):
1592 I = Intersectool() # PYCHOK I
1593 if _V:
1594 I.verbose = True
1595 if I.IntersectTool in (_PYGEODESY_INTERSECTTOOL_, None): # not set
1596 I.IntersectTool = '/opt/local/bin/IntersectTool' # '/opt/local/Cellar/geographiclib/2.3/bin/IntersectTool' # HomeBrew
1597 elif _V:
1598 _ = I.version
1599 M, _T = None, True
1600 elif _starts('--Verbose', arg):
1601 _V = True
1602 if _T:
1603 I.verbose = True
1604 elif _starts('--version', arg):
1605 printf(_COLONSPACE_(*((_version_, I.version) if _T else
1606 (__version__, repr(I)))))
1607 else:
1608 raise ValueError('invalid option %r' % (arg,))
1610 if _h or M is None:
1611 printf(_usage(__file__, **_opts(_h)), nl=1)
1612 else:
1613 n = len(args)
1614 if n < m:
1615 n = _plural('only %s arg' % (n,), n) if n else 'no args'
1616 raise ValueError('%s, need %s' % (n, m))
1617 args[:] = args[:m]
1619 kwds = dict(_C=True) if _C else {}
1620 if M == I.Next: # -n
1621 # get latA lonA aziA latA lonA aziB
1622 args[3:] = args[:2] + args[3:4]
1623 elif M == I.Closest and m > 6: # -o
1624 y0 = Meter(y0=args.pop())
1625 x0 = Meter(x0=args.pop())
1626 kwds.update(X0=XDict_(x0, y0))
1627 if _R:
1628 m = Meter_(_R, name=_R__, low=0)
1629 kwds.update(sMaX0=m)
1630 M = I.All
1632 n = len(args) // 2
1633 glA = I.Line(*args[:n])
1634 glB = I.Line(*args[n:])
1636 m = _DOT_(I.__class__.__name__, M.__name__)
1637 if _V:
1638 X = _SPACE_(_X_, _EQUAL_, m)
1639 printf(unstr(X, glA, glB, **kwds))
1641 X = M(glA, glB, **kwds)
1642 if X is None or isinstance(X, (XDict, tuple)):
1643 printf(_COLONSPACE_(m, repr(X)))
1644 else:
1645 for i, X in enumerate(X):
1646 printf(_COLONSPACE_(Fmt.INDEX(m, i), repr(X)))
1648 from sys import argv, stderr
1649 try:
1650 if len(argv) == 2 and argv[1] == __help_:
1651 from pygeodesy.internals import _usage_argv
1653 s = _SPACE_(*_usage_argv(__file__))
1654 for t in ('-h', '-h -n',
1655 '-c 0 0 45 40 10 135',
1656 '-C -c 0 0 45 40 10 135',
1657 '-T -R 2.6e7 -c 0 0 45 40 10 135',
1658 '-c 50 -4 -147.7 0 0 90',
1659 '-C -c 50 -4 -147.7 0 0 90',
1660 '# % echo 0 0 10 10 50 -4 50S 4W | IntersectTool -i -p 0 -C',
1661 '# -631414 5988887 0 -3',
1662 '# -4.05187 -4.00000 -4.05187 -4.00000 0',
1663 '-m 0 0 10 10 50 -4 50S 4W',
1664 '-C -m 0 0 10 10 50 -4 50S 4W',
1665 '-i 0 0 10 10 50 -4 50S 4W',
1666 '-T -i 0 0 10 10 50 -4 50S 4W',
1667 '-C -i 0 0 10 10 50 -4 50S 4W',
1668 '-T -C -i 0 0 10 10 50 -4 50S 4W',
1669 '-V -T -i 0 0 10 10 50 -4 -50 -4',
1670 '-C -R 4e7 -c 50 -4 -147.7 0 0 90',
1671 '-T -C -R 4e7 -c 50 -4 -147.7 0 0 90',
1672 '-R 4e7 -i 0 0 10 10 50 -4 -50 -4',
1673 '-T -R 4e7 -i 0 0 10 10 50 -4 -50 -4'):
1674 if t.startswith(_HASH_):
1675 printf(t, nl=int(t[2] == '%'))
1676 else:
1677 printf(_SPACE_(_HASH_, s, t), nl=1)
1678 argv[1:] = t = t.split()
1679 _main(t)
1680 else:
1681 _main(argv[1:])
1683 except Exception as x:
1684 x = _SPACE_(x, NN, _HASH_, *argv)
1685 printf(x, file=stderr, nl=1)
1686 if '-V' in x or _MODS.errors.exception_chaining():
1687 raise
1688 exit(1)
1690# % env PYGEODESY_INTERSECTTOOL=... python3 -m pygeodesy.geodesici --help
1692# % python3 -m pygeodesy.geodesici -h
1693#
1694# usage: python3 -m ....pygeodesy.geodesici [--Verbose | -V] [--version | -v] [--help | -h] [--Tool | -T] [--Check | -C] [-R meter]
1695# [-c latA lonA aziA latB lonB aziB |
1696# -i latA1 lonA1 latA2 lonA2 latB1 lonB1 latB2 lonB2 |
1697# -m latA1 lonA1 latA2 lonA2 latB1 lonB1 latB2 lonB2 |
1698# -n latA lonA aziA aziB |
1699# -o latA lonA aziA latB lonB aziB x0 y0]
1701# % python3 -m ....pygeodesy.geodesici -h -n
1702#
1703# usage: python3 -m ....pygeodesy.geodesici -n latA lonA aziA aziB
1705# % python3 -m ....pygeodesy.geodesici -c 0 0 45 40 10 135
1706# Intersector.Closest: XDict(c=0, sA=3862290.547855, sB=2339969.547699, sX0=6202260.095554)
1708# % python3 -m ....pygeodesy.geodesici -C -c 0 0 45 40 10 135
1709# Intersector.Closest: XDict(aAB=0.0, c=0, latA=23.875306, latB=23.875306, lonA=26.094096, lonB=26.094096, sA=3862290.547855, sAB=0.0, sB=2339969.547699, sX0=6202260.095554)
1711# % env PYGEODESY_INTERSECTTOOL=...python3 -m ....pygeodesy.geodesici -T -R 2.6e7 -c 0 0 45 40 10 135
1712# Intersectool.All[0]: XDict(c=0, sA=3862290.547855, sB=2339969.547699, sX0=6202260.095554)
1714# % python3 -m ....pygeodesy.geodesici -c 50 -4 -147.7 0 0 90
1715# Intersector.Closest: XDict(c=0, sA=6058048.653081, sB=-3311252.995823, sX0=9369301.648903)
1717# % python3 -m ....pygeodesy.geodesici -C -c 50 -4 -147.7 0 0 90
1718# Intersector.Closest: XDict(aAB=0.0, c=0, latA=0.0, latB=-0.0, lonA=-29.745492, lonB=-29.745492, sA=6058048.653081, sAB=0.0, sB=-3311252.995823, sX0=9369301.648903)
1720# % echo 0 0 10 10 50 -4 50S 4W | IntersectTool -i -p 0 -C
1721# -631414 5988887 0 -3
1722# -4.05187 -4.00000 -4.05187 -4.00000 0
1724# % python3 -m ....pygeodesy.geodesici -m 0 0 10 10 50 -4 50S 4W
1725# Intersector.Middle: XDict(c=0, sA=782554.549609, sB=5536835.161499, sX0=0.0)
1727# % python3 -m ....pygeodesy.geodesici -C -m 0 0 10 10 50 -4 50S 4W
1728# Intersector.Middle: XDict(aAB=10.262308, c=0, latA=5.019509, latB=0.036282, lonA=4.961883, lonB=-4.0, sA=782554.549609, sAB=1138574.546746, sB=5536835.161499, sX0=0.0)
1730# % python3 -m ....pygeodesy.geodesici -i 0 0 10 10 50 -4 50S 4W
1731# Intersector.Segment: XDict(c=0, k=-3, kA=-1, kB=0, sA=-631414.26877, sB=5988887.278435, sX0=1866020.935315)
1733# % env PYGEODESY_INTERSECTTOOL=... python3 -m ....pygeodesy.geodesici -T -i 0 0 10 10 50 -4 50S 4W
1734# Intersectool.Segment: XDict(c=0, k=-3, kA=-1, kB=0, sA=-631414.26877, sB=5988887.278435)
1736# % python3 -m ....pygeodesy.geodesici -C -i 0 0 10 10 50 -4 50S 4W
1737# Intersector.Segment: XDict(aAB=0.0, c=0, k=-3, kA=-1, kB=0, latA=-4.051871, latB=-4.051871, lonA=-4.0, lonB=-4.0, sA=-631414.26877, sAB=0.0, sB=5988887.278435, sX0=1866020.935315)
1739# % env PYGEODESY_INTERSECTTOOL=... python3 -m ....pygeodesy.geodesici -T -C -i 0 0 10 10 50 -4 50S 4W
1740# Intersectool.Segment: XDict(c=0, k=-3, kA=-1, kB=0, latA=-4.051871, latB=-4.051871, lonA=-4.0, lonB=-4.0, sA=-631414.26877, sAB=0.0, sB=5988887.278435)
1742# % env PYGEODESY_INTERSECTTOOL=... python3 -m ....pygeodesy.geodesici -V -T -i 0 0 10 10 50 -4 -50 -4
1743# Intersectool@1: /opt/local/bin/IntersectTool --version (invoke)
1744# Intersectool@1: '/opt/local/bin/IntersectTool: GeographicLib version 2.3' (0)
1745# Intersectool@1: /opt/local/bin/IntersectTool: GeographicLib version 2.3 (0)
1746# X = Intersectool.Segment(GDict(lat1=0.0, lat2=10.0, lon1=0.0, lon2=10.0), GDict(lat1=50.0, lat2=-50.0, lon1=-4.0, lon2=-4.0))
1747# Intersectool@2: /opt/local/bin/IntersectTool -E -p 10 -i \ 0.0 0.0 10.0 10.0 50.0 -4.0 -50.0 -4.0 (Segment)
1748# Intersectool@2: '-631414.2687702414 5988887.2784352796 0 -3' (0)
1749# Intersectool@2: sA=-631414.2687702414, sB=5988887.2784352796, c=0, k=-3 (0)
1750# Intersectool.Segment: XDict(c=0, k=-3, kA=-1, kB=0, sA=-631414.26877, sB=5988887.278435)
1752# % python3 -m ....pygeodesy.geodesici -C -R 4e7 -c 50 -4 -147.7 0 0 90
1753# Intersector.All[0]: XDict(aAB=0.0, c=0, latA=0.0, latB=-0.0, lonA=-29.745492, lonB=-29.745492, sA=6058048.653081, sAB=0.0, sB=-3311252.995823, sX0=9369301.648903)
1754# Intersector.All[1]: XDict(aAB=0.0, c=0, latA=0.0, latB=0.0, lonA=150.046964, lonB=150.046964, sA=-13941907.021445, sAB=0.0, sB=16703151.659744, sX0=30645058.681189)
1755# Intersector.All[2]: XDict(aAB=0.0, c=0, latA=-0.0, latB=-0.0, lonA=-30.16058, lonB=-30.16058, sA=-33941862.69597, sAB=0.0, sB=-3357460.370268, sX0=37299323.066238)
1756# Intersector.All[3]: XDict(aAB=0.0, c=0, latA=-0.0, latB=0.0, lonA=150.046964, lonB=150.046964, sA=-13941907.021445, sAB=0.0, sB=-23371865.025835, sX0=37313772.047279)
1758# % env PYGEODESY_INTERSECTTOOL=... python3 -m ....pygeodesy.geodesici -T -C -R 4e7 -c 50 -4 -147.7 0 0 90
1759# Intersectool.All[0]: XDict(c=0, latA=-0.0, latB=-0.0, lonA=-29.745492, lonB=-29.745492, sA=6058048.653081, sAB=0.0, sB=-3311252.995823, sX0=9369301.648903)
1760# Intersectool.All[1]: XDict(c=0, latA=0.0, latB=0.0, lonA=150.046964, lonB=150.046964, sA=-13941907.021445, sAB=0.0, sB=16703151.659744, sX0=30645058.681189)
1761# Intersectool.All[2]: XDict(c=0, latA=-0.0, latB=-0.0, lonA=-30.16058, lonB=-30.16058, sA=-33941862.69597, sAB=0.0, sB=-3357460.370268, sX0=37299323.066238)
1762# Intersectool.All[3]: XDict(c=0, latA=-0.0, latB=0.0, lonA=150.046964, lonB=150.046964, sA=-13941907.021445, sAB=0.0, sB=-23371865.025835, sX0=37313772.047279)
1764# % python3 -m ....pygeodesy.geodesici -R 4e7 -i 0 0 10 10 50 -4 -50 -4
1765# Intersector.All[0]: XDict(c=0, sA=-631414.26877, sB=5988887.278435, sX0=1866020.935315)
1766# Intersector.All[1]: XDict(c=0, sA=19422725.117572, sB=-14062417.105648, sX0=38239422.83511)
1767# Intersector.All[2]: XDict(c=0, sA=19422725.117572, sB=25945445.811603, sX0=39048781.218067)
1768# Intersector.All[3]: XDict(c=0, sA=39476927.464575, sB=5894074.699478, sX0=39051612.452944)
1770# % env PYGEODESY_INTERSECTTOOL=... python3 -m ....pygeodesy.geodesici -T -R 4e7 -i 0 0 10 10 50 -4 -50 -4
1771# Intersectool.All[0]: XDict(c=0, sA=-631414.26877, sB=5988887.278435, sX0=1862009.05513)
1772# Intersectool.All[1]: XDict(c=0, sA=19422725.117572, sB=-14062417.105648, sX0=38243434.715295)
1773# Intersectool.All[2]: XDict(c=0, sA=19422725.117572, sB=25945445.811603, sX0=39044769.337882)
1774# Intersectool.All[3]: XDict(c=0, sA=39476927.464575, sB=5894074.699478, sX0=39047600.57276)
1777# **) MIT License
1778#
1779# Copyright (C) 2024-2024 -- mrJean1 at Gmail -- All Rights Reserved.
1780#
1781# Permission is hereby granted, free of charge, to any person obtaining a
1782# copy of this software and associated documentation files (the "Software"),
1783# to deal in the Software without restriction, including without limitation
1784# the rights to use, copy, modify, merge, publish, distribute, sublicense,
1785# and/or sell copies of the Software, and to permit persons to whom the
1786# Software is furnished to do so, subject to the following conditions:
1787#
1788# The above copyright notice and this permission notice shall be included
1789# in all copies or substantial portions of the Software.
1790#
1791# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
1792# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
1793# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
1794# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR
1795# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
1796# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
1797# OTHER DEALINGS IN THE SOFTWARE.