Coverage for pygeodesy/rhumbBase.py: 95%
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2# -*- coding: utf-8 -*-
4u'''Base classes C{RhumbBase} and C{RhumbLineBase}, pure Python version of I{Karney}'s C++
5classes U{Rhumb<https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1Rhumb.html>}
6and U{RhumbLine<https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1RhumbLine.html>}
7from I{GeographicLib versions 2.0} and I{2.2} and I{Karney}'s C++ example U{Rhumb intersect
8<https://SourceForge.net/p/geographiclib/discussion/1026620/thread/2ddc295e/>}.
10Class L{RhumbLine} has been enhanced with methods C{Intersection} and C{NearestOn} to iteratively
11find the intersection of two rhumb lines, respectively the nearest point on a rumb line along a
12geodesic or perpendicular rhumb line from an other point.
14For more details, see the C++ U{GeographicLib<https://GeographicLib.SourceForge.io/C++/doc/index.html>}
15documentation, especially the U{Class List<https://GeographicLib.SourceForge.io/C++/doc/annotated.html>},
16the background information on U{Rhumb lines<https://GeographicLib.SourceForge.io/C++/doc/rhumb.html>},
17the utily U{RhumbSolve<https://GeographicLib.SourceForge.io/C++/doc/RhumbSolve.1.html>} and U{Online
18rhumb line calculations<https://GeographicLib.SourceForge.io/cgi-bin/RhumbSolve>}.
20Copyright (C) U{Charles Karney<mailto:Karney@Alum.MIT.edu>} (2014-2023) and licensed under the MIT/X11
21License. For more information, see the U{GeographicLib<https://GeographicLib.SourceForge.io>} documentation.
22'''
23# make sure int/int division yields float quotient
24from __future__ import division as _; del _ # PYCHOK semicolon
26# from pygeodesy.basics import unsigned0, _xinstanceof # from .karney
27from pygeodesy.constants import EPS, EPS1, INT0, _EPSqrt as _TOL, NAN, \
28 _0_0, _0_01, _1_0, _90_0, _over
29# from pygeodesy.datums import _spherical_datum # from .formy
30# from pygeodesy.ellipsoids import _EWGS84 # from .karney
31from pygeodesy.errors import IntersectionError, itemsorted, RhumbError, \
32 _xdatum, _xkwds, _Xorder
33# from pygeodesy.etm import ExactTransverseMercator # _MODS
34from pygeodesy.fmath import euclid, favg, sqrt_a, fabs, Fsum
35from pygeodesy.formy import opposing, _spherical_datum
36# from pygeodesy.fsums import Fsum # from .fmath
37from pygeodesy.interns import NN, _coincident_, _COMMASPACE_, _Dash, \
38 _no_, _parallel_, _too_, _under
39from pygeodesy.karney import _atan2d, Caps, _CapsBase, _diff182, _fix90, \
40 GDict, _norm180, _EWGS84, unsigned0, _xinstanceof
41# from pygeodesy.ktm import KTransverseMercator, _AlpCoeffs # _MODS
42from pygeodesy.lazily import _ALL_DOCS, _ALL_MODS as _MODS
43# from pygeodesy.named import notOverloaded # _MODS
44from pygeodesy.namedTuples import Distance2Tuple, LatLon2Tuple
45from pygeodesy.props import deprecated_method, Property, Property_RO, \
46 property_RO, _update_all
47from pygeodesy.streprs import Fmt, pairs, unstr
48from pygeodesy.units import Float_, Lat, Lon, Meter, Radius_, Int # PYCHOK shared
49from pygeodesy.utily import atan2d, _azireversed, _loneg, sincos2d, \
50 sincos2d_, _unrollon, _Wrap, sincos2_ # PYCHOK shared
51from pygeodesy.vector3d import _intersect3d3, Vector3d # in .Intersection below
53# from math import fabs # from .fmath
55__all__ = ()
56__version__ = '23.10.10'
58_anti_ = _Dash('anti')
59_rls = [] # instances of C{RbumbLine...} to be updated
60_TRIPS = 65 # .Intersection, .NearestOn, 19+
63class _Lat(Lat):
64 '''(INTERNAL) Latitude B{C{lat}}.
65 '''
66 def __init__(self, *lat, **Error_name):
67 kwds = _xkwds(Error_name, clip=0, Error=RhumbError)
68 Lat.__new__(_Lat, *lat, **kwds)
71class _Lon(Lon):
72 '''(INTERNAL) Longitude B{C{lon}}.
73 '''
74 def __init__(self, *lon, **Error_name):
75 kwds = _xkwds(Error_name, clip=0, Error=RhumbError)
76 Lon.__new__(_Lon, *lon, **kwds)
79def _update_all_rls(r):
80 '''(INTERNAL) Zap cached/memoized C{Property[_RO]}s
81 of any C{RhumbLine} instances tied to the given
82 C{Rhumb} instance B{C{r}}.
83 '''
84 # _xinstanceof(_MODS.rhumbaux.RhumbAux, _MODS.rhumbx.Rhumb, r=r)
85 _update_all(r)
86 for rl in _rls: # PYCHOK use weakref?
87 if rl._rhumb is r:
88 _update_all(rl)
91class RhumbBase(_CapsBase):
92 '''(INTERNAL) Base class for C{rhumbaux.RhumbAux} and C{rhumbx.Rhumb}.
93 '''
94 _E = _EWGS84
95 _exact = True
96 _f_max = _0_01
97 _mTM = 6 # see .TMorder
99 def __init__(self, a_earth, f, exact, name):
100 '''New C{rhumbaux.RhumbAux} or C{rhumbx.Rhum}.
101 '''
102 if f is not None:
103 self.ellipsoid = a_earth, f
104 elif a_earth not in (_EWGS84, None):
105 self.ellipsoid = a_earth
106 if not exact:
107 self.exact = False
108 if name:
109 self.name = name
111 @Property_RO
112 def a(self):
113 '''Get the C{ellipsoid}'s equatorial radius, semi-axis (C{meter}).
114 '''
115 return self.ellipsoid.a
117 equatoradius = a
119 def ArcDirect(self, lat1, lon1, azi12, a12, outmask=Caps.LATITUDE_LONGITUDE):
120 '''Solve the I{direct rhumb} problem, optionally with area.
122 @arg lat1: Latitude of the first point (C{degrees90}).
123 @arg lon1: Longitude of the first point (C{degrees180}).
124 @arg azi12: Azimuth of the rhumb line (compass C{degrees}).
125 @arg a12: Angle along the rhumb line from the given to the
126 destination point (C{degrees}), can be negative.
128 @return: L{GDict} with 2 up to 8 items C{lat2, lon2, a12, S12,
129 lat1, lon1, azi12, s12} with the destination point's
130 latitude C{lat2} and longitude C{lon2} in C{degrees},
131 the rhumb angle C{a12} in C{degrees} and area C{S12}
132 under the rhumb line in C{meter} I{squared}.
134 @raise ImportError: Package C{numpy} not found or not installed,
135 only required for area C{S12} when C{B{exact}
136 is True} and L{RhumbAux}.
138 @note: If B{C{a12}} is large enough that the rhumb line crosses
139 a pole, the longitude of the second point is indeterminate
140 and C{NAN} is returned for C{lon2} and area C{S12}.
142 @note: If the given point is a pole, the cosine of its latitude is
143 taken to be C{sqrt(L{EPS})}. This position is extremely
144 close to the actual pole and allows the calculation to be
145 carried out in finite terms.
146 '''
147 s12 = a12 * self._mpd
148 return self._DirectRhumb(lat1, lon1, azi12, a12, s12, outmask)
150 @Property_RO
151 def b(self):
152 '''Get the C{ellipsoid}'s polar radius, semi-axis (C{meter}).
153 '''
154 return self.ellipsoid.b
156 polaradius = b
158 def _Direct(self, ll1, azi12, s12, **outmask):
159 '''(INTERNAL) Short-cut version, see .latlonBase.
160 '''
161 return self.Direct(ll1.lat, ll1.lon, azi12, s12, **outmask)
163 def Direct(self, lat1, lon1, azi12, s12, outmask=Caps.LATITUDE_LONGITUDE):
164 '''Solve the I{direct rhumb} problem, optionally with area.
166 @arg lat1: Latitude of the first point (C{degrees90}).
167 @arg lon1: Longitude of the first point (C{degrees180}).
168 @arg azi12: Azimuth of the rhumb line (compass C{degrees}).
169 @arg s12: Distance along the rhumb line from the given to
170 the destination point (C{meter}), can be negative.
172 @return: L{GDict} with 2 up to 8 items C{lat2, lon2, a12, S12,
173 lat1, lon1, azi12, s12} with the destination point's
174 latitude C{lat2} and longitude C{lon2} in C{degrees},
175 the rhumb angle C{a12} in C{degrees} and area C{S12}
176 under the rhumb line in C{meter} I{squared}.
178 @raise ImportError: Package C{numpy} not found or not installed,
179 only required for area C{S12} when C{B{exact}
180 is True} and L{RhumbAux}.
182 @note: If B{C{s12}} is large enough that the rhumb line crosses
183 a pole, the longitude of the second point is indeterminate
184 and C{NAN} is returned for C{lon2} and area C{S12}.
186 @note: If the given point is a pole, the cosine of its latitude is
187 taken to be C{sqrt(L{EPS})}. This position is extremely
188 close to the actual pole and allows the calculation to be
189 carried out in finite terms.
190 '''
191 a12 = _over(s12, self._mpd)
192 return self._DirectRhumb(lat1, lon1, azi12, a12, s12, outmask)
194 def Direct8(self, lat1, lon1, azi12, s12, outmask=Caps.LATITUDE_LONGITUDE_AREA):
195 '''Like method L{Rhumb.Direct} but returning a L{Rhumb8Tuple} with area C{S12}.
196 '''
197 return self.Direct(lat1, lon1, azi12, s12, outmask=outmask).toRhumb8Tuple()
199 def _DirectLine(self, ll1, azi12, **caps_name):
200 '''(INTERNAL) Short-cut version, see .latlonBase.
201 '''
202 return self.DirectLine(ll1.lat, ll1.lon, azi12, **caps_name)
204 def DirectLine(self, lat1, lon1, azi12, **caps_name):
205 '''Define a C{RhumbLine} in terms of the I{direct} rhumb
206 problem to compute several points on a single rhumb line.
208 @arg lat1: Latitude of the first point (C{degrees90}).
209 @arg lon1: Longitude of the first point (C{degrees180}).
210 @arg azi12: Azimuth of the rhumb line (compass C{degrees}).
211 @kwarg caps_name: Optional keyword arguments C{B{name}=NN} and
212 C{B{caps}=Caps.STANDARD}, a bit-or'ed combination of
213 L{Caps} values specifying the required capabilities.
214 Include C{Caps.LINE_OFF} if updates to the B{C{rhumb}}
215 should I{not} be reflected in this rhumb line.
217 @return: A C{RhumbLine...} instance and invoke its method
218 C{.Position} to compute each point.
220 @note: Updates to this rhumb are reflected in the returned
221 rhumb line, unless C{B{caps} |= Caps.LINE_OFF}.
222 '''
223 return self._RhumbLine(self, lat1, lon1, azi12, **caps_name)
225 Line = DirectLine # synonyms
227 def _DirectRhumb(self, lat1, lon1, azi12, a12, s12, outmask):
228 '''(INTERNAL) See methods C{.ArcDirect} and C{.Direct}.
229 '''
230 rl = self._RhumbLine(self, lat1, lon1, azi12, caps=Caps.LINE_OFF,
231 name=self.name)
232 return rl._Position(a12, s12, outmask | self._debug) # lat2, lon2, S12
234 @Property
235 def ellipsoid(self):
236 '''Get this rhumb's ellipsoid (L{Ellipsoid}).
237 '''
238 return self._E
240 @ellipsoid.setter # PYCHOK setter!
241 def ellipsoid(self, a_earth_f):
242 '''Set this rhumb's ellipsoid (L{Ellipsoid}, L{Ellipsoid2}, L{Datum} or
243 L{a_f2Tuple}) or (equatorial) radius and flattening (2-tuple C{(a, f)}).
245 @raise RhumbError: If C{abs(B{f}} exceeds non-zero C{f_max} and C{exact=False}.
246 '''
247 E = _spherical_datum(a_earth_f, Error=RhumbError).ellipsoid
248 if self._E != E:
249 self._exactest(self.exact, E, self.f_max)
250 _update_all_rls(self)
251 self._E = E
253 @Property
254 def exact(self):
255 '''Get the I{exact} option (C{bool}).
256 '''
257 return self._exact
259 @exact.setter # PYCHOK setter!
260 def exact(self, exact):
261 '''Set the I{exact} option (C{bool}). If C{True}, use I{exact} rhumb
262 expressions, otherwise a series expansion (accurate for oblate or
263 prolate ellipsoids with C{abs(flattening)} below C{f_max}.
265 @raise RhumbError: If C{B{exact}=False} and C{abs(flattening})
266 exceeds non-zero C{f_max}.
268 @see: Option U{B{-s}<https://GeographicLib.SourceForge.io/C++/doc/RhumbSolve.1.html>}
269 and U{ACCURACY<https://GeographicLib.SourceForge.io/C++/doc/RhumbSolve.1.html#ACCURACY>}.
270 '''
271 x = bool(exact)
272 if self._exact != x:
273 self._exactest(x, self.ellipsoid, self.f_max)
274 _update_all_rls(self)
275 self._exact = x
277 def _exactest(self, exact, ellipsoid, f_max):
278 # Helper for property setters C{ellipsoid}, C{exact} and C{f_max}
279 if fabs(ellipsoid.f) > f_max > 0 and not exact:
280 raise RhumbError(exact=exact, f=ellipsoid.f, f_max=f_max)
282 @Property_RO
283 def f(self):
284 '''Get the C{ellipsoid}'s flattening (C{float}).
285 '''
286 return self.ellipsoid.f
288 flattening = f
290 @property
291 def f_max(self):
292 '''Get the I{max.} flattening (C{float}).
293 '''
294 return self._f_max
296 @f_max.setter # PYCHOK setter!
297 def f_max(self, f_max): # PYCHOK no cover
298 '''Set the I{max.} flattening, not to exceed (C{float}).
300 @raise RhumbError: If C{exact=False} and C{abs(flattening})
301 exceeds non-zero C{f_max}.
302 '''
303 f = Float_(f_max=f_max, low=_0_0, high=EPS1)
304 if self._f_max != f:
305 self._exactest(self.exact, self.ellipsoid, f)
306 self._f_max = f
308 def _Inverse(self, ll1, ll2, wrap, **outmask):
309 '''(INTERNAL) Short-cut version, see .latlonBase.
310 '''
311 if wrap:
312 ll2 = _unrollon(ll1, _Wrap.point(ll2))
313 return self.Inverse(ll1.lat, ll1.lon, ll2.lat, ll2.lon, **outmask)
315 def Inverse(self, lat1, lon1, lat2, lon2, outmask=Caps.AZIMUTH_DISTANCE):
316 '''Solve the I{inverse rhumb} problem.
318 @arg lat1: Latitude of the first point (C{degrees90}).
319 @arg lon1: Longitude of the first point (C{degrees180}).
320 @arg lat2: Latitude of the second point (C{degrees90}).
321 @arg lon2: Longitude of the second point (C{degrees180}).
323 @return: L{GDict} with 4 to 9 items C{lat1, lon1, lat2, lon2,
324 azi12, azi21, s12, a12, S12}, the rhumb line's azimuth
325 C{azi12} and I{reverse} azimuth C{azi21}, both in
326 compass C{degrees} between C{-180} and C{+180}, the
327 rhumb distance C{s12} and rhumb angle C{a12} between
328 both points in C{meter} respectively C{degrees} and
329 the area C{S12} under the rhumb line in C{meter}
330 I{squared}.
332 @raise ImportError: Package C{numpy} not found or not installed,
333 only required for L{RhumbAux} area C{S12}
334 when C{B{exact} is True}.
336 @note: The shortest rhumb line is found. If the end points are
337 on opposite meridians, there are two shortest rhumb lines
338 and the East-going one is chosen.
340 @note: If either point is a pole, the cosine of its latitude is
341 taken to be C{sqrt(L{EPS})}. This position is extremely
342 close to the actual pole and allows the calculation to be
343 carried out in finite terms.
344 '''
345 r = GDict(lat1=lat1, lon1=lon1, lat2=lat2, lon2=lon2, name=self.name)
346 Cs = Caps
347 if (outmask & Cs.AZIMUTH_DISTANCE_AREA):
348 lon12, _ = _diff182(lon1, lon2, K_2_0=True)
349 y, x, s1, s2 = self._Inverse4(lon12, r, outmask)
350 if (outmask & Cs.AZIMUTH):
351 z = _atan2d(y, x)
352 r.set_(azi12=z, azi21=_azireversed(z))
353 if (outmask & Cs.AREA):
354 S12 = self._S12d(s1, s2, lon12)
355 r.set_(S12=unsigned0(S12)) # like .gx
356 return r
358 def _Inverse4(self, lon12, r, outmask): # PYCHOK no cover
359 '''(INTERNAL) I{Must be overloaded}.'''
360 _MODS.named.notOverloaded(self, lon12, r, Caps.toStr(outmask))
362 def Inverse8(self, lat1, lon1, azi12, s12, outmask=Caps.AZIMUTH_DISTANCE_AREA):
363 '''Like method L{Rhumb.Inverse} but returning a L{Rhumb8Tuple} with area C{S12}.
364 '''
365 return self.Inverse(lat1, lon1, azi12, s12, outmask=outmask).toRhumb8Tuple()
367 def _InverseLine(self, ll1, ll2, wrap, **caps_name):
368 '''(INTERNAL) Short-cut version, see .latlonBase.
369 '''
370 if wrap:
371 ll2 = _unrollon(ll1, _Wrap.point(ll2))
372 return self.InverseLine(ll1.lat, ll1.lon, ll2.lat, ll2.lon, **caps_name)
374 def InverseLine(self, lat1, lon1, lat2, lon2, **caps_name):
375 '''Define a C{RhumbLine} in terms of the I{inverse} rhumb problem.
377 @arg lat1: Latitude of the first point (C{degrees90}).
378 @arg lon1: Longitude of the first point (C{degrees180}).
379 @arg lat2: Latitude of the second point (C{degrees90}).
380 @arg lon2: Longitude of the second point (C{degrees180}).
381 @kwarg caps_name: Optional keyword arguments C{B{name}=NN} and
382 C{B{caps}=Caps.STANDARD}, a bit-or'ed combination of
383 L{Caps} values specifying the required capabilities.
384 Include C{Caps.LINE_OFF} if updates to the B{C{rhumb}}
385 should I{not} be reflected in this rhumb line.
387 @return: A C{RhumbLine...} instance and invoke its method
388 C{ArcPosition} or C{Position} to compute points.
390 @note: Updates to this rhumb are reflected in the returned
391 rhumb line, unless C{B{caps} |= Caps.LINE_OFF}.
392 '''
393 r = self.Inverse(lat1, lon1, lat2, lon2, outmask=Caps.AZIMUTH)
394 return self._RhumbLine(self, lat1, lon1, r.azi12, **caps_name)
396 @Property_RO
397 def _mpd(self): # PYCHOK no cover
398 '''(INTERNAL) I{Must be overloaded}.'''
399 _MODS.named.notOverloaded(self)
401 @property_RO
402 def _RhumbLine(self): # PYCHOK no cover
403 '''(INTERNAL) I{Must be overloaded}.'''
404 _MODS.named.notOverloaded(self, underOK=True)
406 def _S12d(self, s1, s2, lon): # PYCHOK no cover
407 '''(INTERNAL) I{Must be overloaded}.'''
408 _MODS.named.notOverloaded(self, s1, s2, lon)
410 @Property
411 def TMorder(self):
412 '''Get the I{Transverse Mercator} order (C{int}, 4, 5, 6, 7 or 8).
413 '''
414 return self._mTM
416 @TMorder.setter # PYCHOK setter!
417 def TMorder(self, order):
418 '''Set the I{Transverse Mercator} order (C{int}, 4, 5, 6, 7 or 8).
420 @note: Setting C{TMorder} turns property C{exact} off, but only
421 for L{Rhumb} instances.
422 '''
423 m = _Xorder(_MODS.ktm._AlpCoeffs, RhumbError, TMorder=order)
424 if self._mTM != m:
425 _update_all_rls(self)
426 self._mTM = m
427 if self.exact and isinstance(self, _MODS.rhumbx.Rhumb):
428 self.exact = False
430 def toStr(self, prec=6, sep=_COMMASPACE_, **unused): # PYCHOK no cover
431 '''I{Must be overloaded}.'''
432 _MODS.named.notOverloaded(self, prec=prec, sep=sep)
435class RhumbLineBase(_CapsBase):
436 '''(INTERNAL) Base class for C{rhumbaux.RhumbLineAux} and C{rhumbx.RhumbLine}.
437 '''
438 _azi12 = _0_0
439 _calp = _1_0
440# _caps = 0
441# _debug = 0
442# _lat1 = _0_0
443# _lon1 = _0_0
444# _lon12 = _0_0
445 _Rhumb = RhumbBase # compatible C{Rhumb} class
446 _rhumb = None # C{Rhumb} instance
447 _salp = _0_0
448 _talp = _0_0
450 def __init__(self, rhumb, lat1, lon1, azi12, caps=Caps.STANDARD, name=NN):
451 '''New C{RhumbLine}.
452 '''
453 _xinstanceof(self._Rhumb, rhumb=rhumb)
455 self._lat1 = _Lat(lat1=_fix90(lat1))
456 self._lon1 = _Lon(lon1= lon1)
457 self._lon12 = _norm180(self._lon1)
458 if azi12: # non-zero, non-None
459 self.azi12 = _norm180(azi12)
461 n = name or rhumb.name
462 if n:
463 self.name=n
465 self._caps = caps
466 self._debug |= (caps | rhumb._debug) & Caps._DEBUG_DIRECT_LINE
467 if (caps & Caps.LINE_OFF): # copy to avoid updates
468 self._rhumb = rhumb.copy(deep=False, name=_under(rhumb.name))
469 else:
470 self._rhumb = rhumb
471 _rls.append(self)
473 def __del__(self): # XXX use weakref?
474 if _rls: # may be empty or None
475 try: # PYCHOK no cover
476 _rls.remove(self)
477 except (TypeError, ValueError):
478 pass
479 self._rhumb = None
480 # _update_all(self) # throws TypeError during Python 2 cleanup
482 def ArcPosition(self, a12, outmask=Caps.LATITUDE_LONGITUDE):
483 '''Compute a point at a given angular distance on this rhumb line.
485 @arg a12: The angle along this rhumb line from its origin to the
486 point (C{degrees}), can be negative.
487 @kwarg outmask: Bit-or'ed combination of L{Caps} values specifying
488 the quantities to be returned.
490 @return: L{GDict} with 4 to 8 items C{azi12, a12, s12, S12, lat2,
491 lon2, lat1, lon1} with latitude C{lat2} and longitude
492 C{lon2} of the point in C{degrees}, the rhumb distance
493 C{s12} in C{meter} from the start point of and the area
494 C{S12} under this rhumb line in C{meter} I{squared}.
496 @raise ImportError: Package C{numpy} not found or not installed,
497 only required for L{RhumbLineAux} area C{S12}
498 when C{B{exact} is True}.
500 @note: If B{C{a12}} is large enough that the rhumb line crosses a
501 pole, the longitude of the second point is indeterminate and
502 C{NAN} is returned for C{lon2} and area C{S12}.
504 If the first point is a pole, the cosine of its latitude is
505 taken to be C{sqrt(L{EPS})}. This position is extremely
506 close to the actual pole and allows the calculation to be
507 carried out in finite terms.
508 '''
509 return self._Position(a12, self.degrees2m(a12), outmask)
511 @Property
512 def azi12(self):
513 '''Get this rhumb line's I{azimuth} (compass C{degrees}).
514 '''
515 return self._azi12
517 @azi12.setter # PYCHOK setter!
518 def azi12(self, azi12):
519 '''Set this rhumb line's I{azimuth} (compass C{degrees}).
520 '''
521 z = _norm180(azi12)
522 if self._azi12 != z:
523 if self._rhumb:
524 _update_all(self)
525 self._azi12 = z
526 self._salp, self._calp = t = sincos2d(z) # no NEG0
527 self._talp = _over(*t)
529 @property_RO
530 def azi12_sincos2(self): # PYCHOK no cover
531 '''Get the sine and cosine of this rhumb line's I{azimuth} (2-tuple C{(sin, cos)}).
532 '''
533 return self._scalp, self._calp
535 def degrees2m(self, angle):
536 '''Convert an angular distance along this rhumb line to C{meter}.
538 @arg angle: Angular distance (C{degrees}).
540 @return: Distance (C{meter}).
541 '''
542 return float(angle) * self.rhumb._mpd
544 @deprecated_method
545 def distance2(self, lat, lon): # PYCHOK no cover
546 '''DEPRECATED on 23.09.23, use method L{RhumbLineAux.Inverse} or L{RhumbLine.Inverse}.
548 @return: A L{Distance2Tuple}C{(distance, initial)} with the C{distance}
549 in C{meter} and C{initial} bearing (azimuth) in C{degrees}.
550 '''
551 r = self.Inverse(lat, lon)
552 return Distance2Tuple(r.s12, r.azi12)
554 @property_RO
555 def ellipsoid(self):
556 '''Get this rhumb line's ellipsoid (L{Ellipsoid}).
557 '''
558 return self.rhumb.ellipsoid
560 @property_RO
561 def exact(self):
562 '''Get this rhumb line's I{exact} option (C{bool}).
563 '''
564 return self.rhumb.exact
566 def Intersecant2(self, lat0, lon0, radius, **tol_eps):
567 '''Compute the intersection(s) of this rhumb line and a circle.
569 @arg lat0: Latitude of the circle center (C{degrees}).
570 @arg lon0: Longitude of the circle center (C{degrees}).
571 @arg radius: Radius of the circle (C{meter}, conventionally).
572 @kwarg tol_eps: Optional keyword arguments, see method
573 method L{Intersection} for further details.
575 @return: 2-Tuple C{(P, Q)} with the 2 intersections
576 (representing a chord), each a L{GDict} from method
577 L{Intersection} extended to 14 items with C{azi03,
578 a03, s03, lat3, lon3} for the chord center C{lat3,
579 lon3} and the angle C{a03}, distance C{s03}, azimuth
580 C{azi03} and start point C{lat0, lon0} of the rhumb
581 line perpendicular to this rhumb line. If this
582 rhumb line is tangential to the circle, both points
583 are the same L{GDict} instance with rhumb distances
584 C{s02} and C{s03} near-equal to the B{C{radius}}.
586 @raise IntersectionError: The circle and this rhumb line
587 do not intersect.
589 @raise UnitError: Invalid B{C{radius}}.
590 '''
591 r = Radius_(radius)
592 p = q = self.NearestOn(lat0, lon0, exact=None, **tol_eps)
593 d = q.s02
594 t = dict(azi03=q.azi02, a03=q.a02, s03=d, lat3=q.lat2, lon3=q.lon2)
595 if d < r:
596 a = sqrt_a(r, d)
597 s = q.s12
598 i = q.iteration
599 n = self.name or self.Intersecant2.__name__
600 t.update(lat0=q.lat1, lon0=q.lon1) # or lat0, lon0
601 p = self.Position(s + a).set_(name=n, **t)
602 q = self.Position(s - a).set_(name=n, **t)
603 p._iteration = q._iteration = i
604 elif d > r:
605 t = unstr(self.Intersecant2, lat0, lon0, radius=radius, **tol_eps)
606 raise IntersectionError(_no_(t), txt=_too_(Fmt.distant(d)))
607 else: # tangential
608 q.set_(**t) # == p.set(_**t)
609 return p, q
611 def intersection2(self, other, **tol_eps): # PYCHOK no cover
612 '''DEPRECATED on 23.10.10, use method L{Intersection}.'''
613 p = self.Intersection(other, **tol_eps)
614 r = LatLon2Tuple(p.lat2, p.lon2, name=self.intersection2.__name__)
615 r._iteration = p.iteration
616 return r
618 def Intersection(self, other, tol=_TOL, **eps):
619 '''I{Iteratively} find the intersection of this and an other rhumb line.
621 @arg other: The other rhumb line (C{RhumbLine}) or C{None} for a
622 rhumb line perpendicular to this one.
623 @kwarg tol: Tolerance for longitudinal convergence and parallel
624 error (C{degrees}).
625 @kwarg eps: Tolerance for L{pygeodesy.intersection3d3} (C{EPS}).
627 @return: The intersection point, a L{Position}-like L{GDict} with
628 12 items C{azi12, a12, s12, lat2, lat1, lat0, lon1, lon2,
629 lon0, azi02, a02, s02} with C{a02} and C{s02} the rhumb
630 angle and rhumb distance between the intersection C{lat2,
631 lon2} point and the start point C{lat0, lon0} on the
632 B{C{other}} rhumb line and the latter's azimuth C{azi02}.
633 See method L{Position} for further details.
635 @raise IntersectionError: No convergence for this B{C{tol}} or
636 no intersection for an other reason.
638 @see: Methods C{distance2} and C{NearestOn} and function
639 L{pygeodesy.intersection3d3}.
641 @note: Each iteration involves a round trip to this rhumb line's
642 L{ExactTransverseMercator} or L{KTransverseMercator}
643 projection and function L{pygeodesy.intersection3d3} in
644 that domain.
645 '''
646 _xinstanceof(RhumbLineBase, other=other)
647 _xdatum(self.rhumb, other.rhumb, Error=RhumbError)
648 try:
649 if self.others(other) is self:
650 raise ValueError(_coincident_)
651 # make invariants and globals locals
652 _s_3d, s_az = self._xTM3d, self.azi12
653 _o_3d, o_az = other._xTM3d, other.azi12
654 p = opposing(s_az, o_az, margin=tol)
655 if p is not None: # == t in (True, False)
656 raise ValueError(_anti_(_parallel_) if p else _parallel_)
657 _diff = euclid # approximate length
658 _i3d3 = _intersect3d3 # NOT .vector3d.intersection3d3
659 _LL2T = LatLon2Tuple
660 _xTMr = self.xTM.reverse # ellipsoidal or spherical
661 # use halfway point as initial estimate
662 p = _LL2T(favg(self.lat1, other.lat1),
663 favg(self.lon1, other.lon1))
664 for i in range(1, _TRIPS):
665 v = _i3d3(_s_3d(p), s_az, # point + bearing
666 _o_3d(p), o_az, useZ=False, **eps)[0]
667 t = _xTMr(v.x, v.y, lon0=p.lon) # PYCHOK Reverse4Tuple
668 d = _diff(t.lon - p.lon, t.lat) # PYCHOK t.lat + p.lat - p.lat
669 p = _LL2T(t.lat + p.lat, t.lon) # PYCHOK t.lon + p.lon = lon0
670 if d < tol: # 19 trips
671 lat, lon = p.lat, p.lon # PYCHOK p...
672 t = other.Inverse(lat, lon, outmask=Caps.DISTANCE)
673 r = self.Inverse( lat, lon, outmask=Caps.DISTANCE)
674 p = GDict(azi12=self.azi12, a12=r.a12, s12=r.s12,
675 lat2=lat, lat1=self.lat1, lat0=other.lat1,
676 lon2=lon, lon1=self.lon1, lon0=other.lon1,
677 azi02=other.azi12, a02=t.a12, s02=t.s12,
678 name=self.name or self.Intersection.__name__)
679 p._iteration = i
680 return p
681 else:
682 raise ValueError(Fmt.no_convergence(d))
684 except Exception as x:
685 t = unstr(self.Intersection, other, tol=tol, eps=eps)
686 raise IntersectionError(_no_(t), cause=x)
688 def Inverse(self, lat2, lon2, wrap=False, **outmask):
689 '''Return the rhumb angle, distance, azimuth, I{reverse} azimuth, etc. of
690 a rhumb line between the given point and this rhumb line's start point.
692 @arg lat2: Latitude of the point (C{degrees}).
693 @arg lon2: Longitude of the points (C{degrees}).
694 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll B{C{lat2}}
695 and B{C{lon2}} (C{bool}).
697 @return: L{GDict} with 8 items C{a12, s12, azi12, azi21, lat1, lon1,
698 lat2, lon2}, the rhumb angle C{a12} and rhumb distance C{s12}
699 between both points in C{degrees} respectively C{meter}, the
700 rhumb line's azimuth C{azi12} and I{reverse} azimuth C{azi21}
701 both in compass C{degrees} between C{-180} and C{+180}.
702 '''
703 if wrap:
704 _, lat2, lon2 = _Wrap.latlon3(self.lon1, _fix90(lat2), lon2, wrap)
705 r = self.rhumb.Inverse(self.lat1, self.lon1, lat2, lon2, **outmask)
706 return r
708 @Property_RO
709 def isLoxodrome(self):
710 '''Is this rhumb line a meridional (C{None}), a parallel
711 (C{False}) or a C{True} loxodrome?
713 @see: I{Osborne's} U{2.5 Rumb lines and loxodromes
714 <https://Zenodo.org/record/35392>}, page 37.
715 '''
716 return bool(self._salp) if self._calp else None
718 @Property_RO
719 def lat1(self):
720 '''Get this rhumb line's latitude (C{degrees90}).
721 '''
722 return self._lat1
724 @Property_RO
725 def lon1(self):
726 '''Get this rhumb line's longitude (C{degrees180}).
727 '''
728 return self._lon1
730 @Property_RO
731 def latlon1(self):
732 '''Get this rhumb line's lat- and longitude (L{LatLon2Tuple}C{(lat, lon)}).
733 '''
734 return LatLon2Tuple(self.lat1, self.lon1)
736 def m2degrees(self, distance):
737 '''Convert a distance along this rhumb line to an angular distance.
739 @arg distance: Distance (C{meter}).
741 @return: Angular distance (C{degrees}).
742 '''
743 return _over(float(distance), self.rhumb._mpd)
745 @property_RO
746 def _mu1(self): # PYCHOK no cover
747 '''(INTERNAL) I{Must be overloaded}.'''
748 _MODS.named.notOverloaded(self, underOK=True)
750 def _mu2lat(self, mu2): # PYCHOK no cover
751 '''(INTERNAL) I{Must be overloaded}.'''
752 _MODS.named.notOverloaded(self, mu2, underOK=True)
754 @deprecated_method
755 def nearestOn4(self, lat, lon, **exact_eps_est_tol):
756 '''DEPRECATED on 23.10.10, use method L{NearestOn}.'''
757 p = self.NearestOn(lat, lon, **exact_eps_est_tol)
758 r = _MODS.deprecated.NearestOn4Tuple(p.lat2, p.lon2, p.s12, p.azi02,
759 name=self.nearestOn4.__name__)
760 r._iteration = p.iteration
761 return r
763 def NearestOn(self, lat0, lon0, exact=None, eps=EPS, est=None, tol=_TOL):
764 '''I{Iteratively} locate the point on this rhumb line nearest to the
765 given point, in part transcoded from I{Karney}'s C++ U{rhumb-intercept
766 <https://SourceForge.net/p/geographiclib/discussion/1026620/thread/2ddc295e/>}.
768 @arg lat0: Latitude of the point (C{degrees}).
769 @arg lon0: Longitude of the point (C{degrees}).
770 @kwarg exact: If C{None}, use a rhumb line perpendicular to this rhumb
771 line, otherwise use an I{exact} C{Geodesic...} from the
772 given point perpendicular to this rhumb line (C{bool} or
773 C{Geodesic...}), see method L{Ellipsoid.geodesic_}.
774 @kwarg eps: Optional tolerance for L{pygeodesy.intersection3d3}
775 (C{EPS}), used only if C{B{exact} is None}.
776 @kwarg est: Optional, initial estimate for the distance C{s13} of
777 the intersection I{along} this rhumb line (C{meter}),
778 used only if C{B{exact} is not None}.
779 @kwarg tol: Longitudinal convergence tolerance (C{degrees}) or the
780 distance tolerance (C(meter)) when C{B{exact} is None},
781 respectively C{not None}.
783 @return: The nearest point on this rhumb line, a L{GDict} from method
784 L{Intersection} if B{C{exact}=None}. If B{C{exact}} is not
785 C{None}, a L{GDict} of 13 items C{azi12, a12, s12, lat2, lat1,
786 lon2, lon1, a02, s02, azi0, azi2, lat0, lon0} with C{a02} and
787 C{s02} the angle respectively distance from the given C{lat0,
788 lon0} to the nearest C{lat2, lon2} point along the specified
789 C{geodetic} and C{azi0} and C{azi2} the (forward) azimuth at
790 the given respectively the nearest point. The latter is always
791 perpendicular to this rhumb line's azimuth. See method
792 L{Position} for further details.
794 @raise ImportError: I{Karney}'s U{geographiclib
795 <https://PyPI.org/project/geographiclib>}
796 package not found or not installed.
798 @raise IntersectionError: No convergence for this B{C{eps}} or
799 no intersection for an other reason.
801 @note: The (forward) azimuth C{azi2} at the nearest point is
802 always perpendicular to this rhumb line's azimuth.
804 @see: Methods C{distance2}, C{Intersecant2} and C{Intersection}
805 and function L{pygeodesy.intersection3d3}.
806 '''
807 Cs = Caps
808 if exact is None:
809 z = _norm180(self.azi12 + _90_0) # perpendicular azimuth
810 rl = RhumbLineBase(self.rhumb, lat0, lon0, z, caps=Cs.LINE_OFF)
811 p = self.Intersection(rl, tol=tol, eps=eps)
813 else: # C{rhumb-intercept}
814 azi = self.azi12
815 szi = self._salp
816 E = self.ellipsoid
817 _gI = E.geodesic_(exact=exact).Inverse
818 gm = Cs.STANDARD | Cs._REDUCEDLENGTH_GEODESICSCALE # ^ Cs.DISTANCE_IN
819 if est is None: # get an estimate from the "perpendicular" geodesic
820 r = _gI(self.lat1, self.lon1, lat0, lon0, outmask=Cs.AZIMUTH_DISTANCE)
821 d, _ = _diff182(r.azi2, azi, K_2_0=True)
822 _, s12 = sincos2d(d)
823 s12 *= r.s12 # signed
824 else:
825 s12 = Meter(est=est)
826 try:
827 tol = Float_(tol=tol, low=EPS, high=None)
828 # def _over(p, q): # see @note at RhumbLine[Aux].Position
829 # return (p / (q or _copysign(tol, q))) if isfinite(q) else NAN
831 _ErT = E.rocPrimeVertical # aka rocTransverse
832 _S12 = Fsum(s12).fsum2_
833 for i in range(1, _TRIPS): # suffix 1 == C++ 2, 2 == C++ 3
834 p = self.Position(s12) # outmask = Cs.LATITUDE_LONGITUDE
835 r = _gI(lat0, lon0, p.lat2, p.lon2, outmask=gm)
836 d, _ = _diff182(azi, r.azi2, K_2_0=True)
837 s, c, s2, c2 = sincos2d_(d, r.lat2)
838 c2 *= _ErT(r.lat2)
839 s *= _over(s2 * szi, c2) - _over(s * r.M21, r.m12)
840 s12, t = _S12(c / s) # XXX _over?
841 if fabs(t) < tol: # or fabs(c) < EPS
842 break
843 p.set_(azi0=r.azi1, azi2=r.azi2, a02=r.a12, s02=r.s12,
844 lat0=lat0, lon0=lon0, name=self.name or
845 self.NearestOn.__name__)
846 p._iteration = i
847 except Exception as x: # Fsum(NAN) Value-, ZeroDivisionError
848 t = unstr(self.NearestOn, lat0, lon0, tol=tol, exact=exact,
849 iteration=i, eps=eps, est=est)
850 raise IntersectionError(_no_(t), cause=x)
852 return p
854 def Position(self, s12, outmask=Caps.LATITUDE_LONGITUDE):
855 '''Compute a point at a given distance on this rhumb line.
857 @arg s12: The distance along this rhumb line from its origin to
858 the point (C{meters}), can be negative.
859 @kwarg outmask: Bit-or'ed combination of L{Caps} values specifying
860 the quantities to be returned.
862 @return: L{GDict} with 4 to 8 items C{azi12, a12, s12, S12, lat2,
863 lat1. lon2, lon1} with latitude C{lat2} and longitude
864 C{lon2} of the point in C{degrees}, the rhumb angle C{a12}
865 in C{degrees} from the start point of and the area C{S12}
866 under this rhumb line in C{meter} I{squared}.
868 @raise ImportError: Package C{numpy} not found or not installed,
869 only required for L{RhumbLineAux} area C{S12}
870 when C{B{exact} is True}.
872 @note: If B{C{s12}} is large enough that the rhumb line crosses a
873 pole, the longitude of the second point is indeterminate and
874 C{NAN} is returned for C{lon2} and area C{S12}.
876 If the first point is a pole, the cosine of its latitude is
877 taken to be C{sqrt(L{EPS})}. This position is extremely
878 close to the actual pole and allows the calculation to be
879 carried out in finite terms.
880 '''
881 return self._Position(self.m2degrees(s12), s12, outmask)
883 def _Position(self, a12, s12, outmask):
884 '''(INTERNAL) C{Arc-/Position} helper.
885 '''
886 r = GDict(azi12=self.azi12, a12=a12, s12=s12, name=self.name)
887 Cs = Caps
888 if (outmask & Cs.LATITUDE_LONGITUDE_AREA):
889 if a12 or s12:
890 mu12 = self._calp * a12
891 mu2 = self._mu1 + mu12
892 if fabs(mu2) > 90: # past pole
893 mu2 = _norm180(mu2) # reduce to [-180, 180)
894 if fabs(mu2) > 90: # point on anti-meridian
895 mu2 = _norm180(_loneg(mu2))
896 lat2 = self._mu2lat(mu2)
897 lon2 = S12 = NAN
898 else:
899 lat2, lon2, S1, S2 = self._Position4(a12, mu2, s12, mu12)
900 if (outmask & Cs.AREA):
901 S12 = self.rhumb._S12d(S1, S2, lon2)
902 S12 = unsigned0(S12) # like .gx
903# else:
904# S12 = None # unused
905 if (outmask & Cs.LONGITUDE):
906 if (outmask & Cs.LONG_UNROLL):
907 lon2 += self.lon1
908 else:
909 lon2 = _norm180(self._lon12 + lon2)
910 else: # coincident
911 lat2, lon2 = self.latlon1
912 S12 = _0_0
914 if (outmask & Cs.AREA):
915 r.set_(S12=S12)
916 if (outmask & Cs.LATITUDE):
917 r.set_(lat2=lat2, lat1=self.lat1)
918 if (outmask & Cs.LONGITUDE):
919 r.set_(lon2=lon2, lon1=self.lon1)
920 return r
922 def _Position4(self, a12, mu2, s12, mu12): # PYCHOK no cover
923 '''(INTERNAL) I{Must be overloaded}.'''
924 _MODS.named.notOverloaded(self, a12, s12, mu2, mu12)
926 @Property_RO
927 def rhumb(self):
928 '''Get this rhumb line's rhumb (L{RhumbAux} or L{Rhumb}).
929 '''
930 return self._rhumb
932 def toStr(self, prec=6, sep=_COMMASPACE_, **unused): # PYCHOK signature
933 '''Return this C{RhumbLine} as string.
935 @kwarg prec: The C{float} precision, number of decimal digits (0..9).
936 Trailing zero decimals are stripped for B{C{prec}} values
937 of 1 and above, but kept for negative B{C{prec}} values.
938 @kwarg sep: Separator to join (C{str}).
940 @return: C{RhumbLine} (C{str}).
941 '''
942 d = dict(rhumb=self.rhumb, lat1=self.lat1, lon1=self.lon1,
943 azi12=self.azi12, exact=self.exact,
944 TMorder=self.TMorder, xTM=self.xTM)
945 return sep.join(pairs(itemsorted(d, asorted=False), prec=prec))
947 @property_RO
948 def TMorder(self):
949 '''Get this rhumb line's I{Transverse Mercator} order (C{int}, 4, 5, 6, 7 or 8).
950 '''
951 return self.rhumb.TMorder
953 @Property_RO
954 def xTM(self):
955 '''Get this rhumb line's I{Transverse Mercator} projection (L{ExactTransverseMercator}
956 if I{exact} and I{ellipsoidal}, otherwise L{KTransverseMercator} for C{TMorder}).
957 '''
958 E = self.ellipsoid
959 # ExactTransverseMercator doesn't handle spherical earth models
960 return _MODS.etm.ExactTransverseMercator(E) if self.exact and E.isEllipsoidal else \
961 _MODS.ktm.KTransverseMercator(E, TMorder=self.TMorder)
963 def _xTM3d(self, latlon0, z=INT0, V3d=Vector3d):
964 '''(INTERNAL) C{xTM.forward} this C{latlon1} to C{V3d} with B{C{latlon0}}
965 as current intersection estimate and central meridian.
966 '''
967 t = self.xTM.forward(self.lat1 - latlon0.lat, self.lon1, lon0=latlon0.lon)
968 return V3d(t.easting, t.northing, z)
971__all__ += _ALL_DOCS(RhumbBase, RhumbLineBase)
973if __name__ == '__main__':
975 from pygeodesy import printf, Rhumb as R, RhumbAux as A
977 A = A(_EWGS84).Line(30, 0, 45)
978 R = R(_EWGS84).Line(30, 0, 45)
980 for i in range(1, 10):
981 s = .5e6 + 1e6 / i
982 a = A.Position(s).lon2
983 r = R.Position(s).lon2
984 e = (fabs(a - r) / a) if a else 0
985 printf('# Position.lon2 %.14f vs %.14f, diff %g', r, a, e)
987 for exact in (None, False, True):
988 for est in (None, 1e6):
989 a = A.NearestOn(60, 0, exact=exact, est=est)
990 r = R.NearestOn(60, 0, exact=exact, est=est)
991 printf('# %s, iteration=%s, exact=%s, est=%s\n# %s, iteration=%s',
992 a.toRepr(), a.iteration, exact, est,
993 r.toRepr(), r.iteration, nl=1)
995# % python3 -m pygeodesy.rhumbBase
997# Position.lon2 11.61455846901637 vs 11.61455846901637, diff 6.11769e-16
998# Position.lon2 7.58982302826842 vs 7.58982302826842, diff 1.17022e-16
999# Position.lon2 6.28526067416369 vs 6.28526067416369, diff 2.82623e-16
1000# Position.lon2 5.63938995325146 vs 5.63938995325146, diff 4.72486e-16
1001# Position.lon2 5.25385527435707 vs 5.25385527435707, diff 1.69053e-16
1002# Position.lon2 4.99764604290380 vs 4.99764604290380, diff 3.55439e-16
1003# Position.lon2 4.81503363740473 vs 4.81503363740473, diff 1.84459e-16
1004# Position.lon2 4.67828821748836 vs 4.67828821748835, diff 5.69553e-16
1005# Position.lon2 4.57205667906283 vs 4.57205667906283, diff 1.94262e-16
1007# Intersection(a02=17.798332, a12=19.521356, azi02=135.0, azi12=45.0, lat1=30.0, lat2=45.0, lon1=0.0, lon2=15.830286, name='Intersection', s02=1977981.142985, s12=2169465.957531), iteration=9, exact=None, est=None
1008# Intersection(a02=17.798332, a12=19.521356, azi02=135.0, azi12=45.0, lat1=30.0, lat2=45.0, lon1=0.0, lon2=15.830286, name='Intersection', s02=1977981.142985, s12=2169465.957531), iteration=9
1010# Intersection(a02=17.798332, a12=19.521356, azi02=135.0, azi12=45.0, lat1=30.0, lat2=45.0, lon1=0.0, lon2=15.830286, name='Intersection', s02=1977981.142985, s12=2169465.957531), iteration=9, exact=None, est=1000000.0
1011# Intersection(a02=17.798332, a12=19.521356, azi02=135.0, azi12=45.0, lat1=30.0, lat2=45.0, lon1=0.0, lon2=15.830286, name='Intersection', s02=1977981.142985, s12=2169465.957531), iteration=9
1013# NearestOn(a02=17.978107, a12=27.74256, azi0=113.73626, azi12=45.0, azi2=135.0, lat1=30.0, lat2=49.634582, lon1=0.0, lon2=25.767876, name='NearestOn', s02=1997960.116871, s12=3083112.636236), iteration=5, exact=False, est=None
1014# NearestOn(a02=17.978107, a12=27.74256, azi0=113.73626, azi12=45.0, azi2=135.0, lat1=30.0, lat2=49.634582, lon1=0.0, lon2=25.767876, name='NearestOn', s02=1997960.116871, s12=3083112.636236), iteration=5
1016# NearestOn(a02=17.978107, a12=27.74256, azi0=113.73626, azi12=45.0, azi2=135.0, lat1=30.0, lat2=49.634582, lon1=0.0, lon2=25.767876, name='NearestOn', s02=1997960.116871, s12=3083112.636236), iteration=7, exact=False, est=1000000.0
1017# NearestOn(a02=17.978107, a12=27.74256, azi0=113.73626, azi12=45.0, azi2=135.0, lat1=30.0, lat2=49.634582, lon1=0.0, lon2=25.767876, name='NearestOn', s02=1997960.116871, s12=3083112.636236), iteration=7
1019# NearestOn(a02=17.978107, a12=27.74256, azi0=113.73626, azi12=45.0, azi2=135.0, lat1=30.0, lat2=49.634582, lon1=0.0, lon2=25.767876, name='NearestOn', s02=1997960.116871, s12=3083112.636236), iteration=5, exact=True, est=None
1020# NearestOn(a02=17.978107, a12=27.74256, azi0=113.73626, azi12=45.0, azi2=135.0, lat1=30.0, lat2=49.634582, lon1=0.0, lon2=25.767876, name='NearestOn', s02=1997960.116871, s12=3083112.636236), iteration=5
1022# NearestOn(a02=17.978107, a12=27.74256, azi0=113.73626, azi12=45.0, azi2=135.0, lat1=30.0, lat2=49.634582, lon1=0.0, lon2=25.767876, name='NearestOn', s02=1997960.116871, s12=3083112.636236), iteration=7, exact=True, est=1000000.0
1023# NearestOn(a02=17.978107, a12=27.74256, azi0=113.73626, azi12=45.0, azi2=135.0, lat1=30.0, lat2=49.634582, lon1=0.0, lon2=25.767876, name='NearestOn', s02=1997960.116871, s12=3083112.636236), iteration=7
1025# **) MIT License
1026#
1027# Copyright (C) 2022-2023 -- mrJean1 at Gmail -- All Rights Reserved.
1028#
1029# Permission is hereby granted, free of charge, to any person obtaining a
1030# copy of this software and associated documentation files (the "Software"),
1031# to deal in the Software without restriction, including without limitation
1032# the rights to use, copy, modify, merge, publish, distribute, sublicense,
1033# and/or sell copies of the Software, and to permit persons to whom the
1034# Software is furnished to do so, subject to the following conditions:
1035#
1036# The above copyright notice and this permission notice shall be included
1037# in all copies or substantial portions of the Software.
1038#
1039# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
1040# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
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1042# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR
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