Coverage for pygeodesy/rhumbBase.py: 93%
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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 method C{Intersection} to iteratively find the intersection
11of two rhumb lines and C{PlumbTo} to find the I{perpendicular} intersection of a rumb line and a
12geodesic or rhumb line from a given 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
26from pygeodesy.basics import _copysign, unsigned0, _xinstanceof
27from pygeodesy.constants import EPS, EPS0, EPS1, INT0, NAN, _over, \
28 _EPSqrt as _TOL, _0_0, _0_01, _1_0, _90_0
29# from pygeodesy.datums import Datum, _spherical_datum # from .formy
30# from pygeodesy.datums import _earth_datum, _WGS84 # from .karney
31from pygeodesy.errors import IntersectionError, itemsorted, RhumbError, \
32 _xdatum, _xkwds, _xkwds_pop, _Xorder
33# from pygeodesy.etm import ExactTransverseMercator # _MODS
34from pygeodesy.fmath import euclid, favg, sqrt_a, Fsum
35from pygeodesy.formy import opposing, Datum, _spherical_datum
36# from pygeodesy.fsums import Fsum # from .fmath
37from pygeodesy.interns import NN, _coincident_, _COMMASPACE_, _Dash, \
38 _dunder_nameof, _parallel_, _too_, _under
39from pygeodesy.karney import _atan2d, Caps, _CapsBase, _diff182, _fix90, \
40 _norm180, GDict, _earth_datum, _WGS84
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
48from pygeodesy.units import Float_, Lat, Lon, Meter, Radius_, Int # PYCHOK shared
49from pygeodesy.utily import acos1, _azireversed, _loneg, sincos2d, sincos2d_, \
50 _unrollon, _Wrap
51from pygeodesy.vector3d import _intersect3d3, Vector3d # in .Intersection below
53from math import cos, fabs
55__all__ = ()
56__version__ = '23.11.09'
58_anti_ = _Dash('anti')
59_rls = [] # instances of C{RbumbLine...} to be updated
60_TRIPS = 65 # .Intersection, .PlumbTo, 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 _datum = _WGS84
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 _earth_datum(self, a_earth, f=f, name=name)
103 if not exact:
104 self.exact = False
105 if name:
106 self.name = name
108 @Property_RO
109 def a(self):
110 '''Get the C{ellipsoid}'s equatorial radius, semi-axis (C{meter}).
111 '''
112 return self.ellipsoid.a
114 equatoradius = a
116 def ArcDirect(self, lat1, lon1, azi12, a12, outmask=Caps.LATITUDE_LONGITUDE):
117 '''Solve the I{direct rhumb} problem, optionally with area.
119 @arg lat1: Latitude of the first point (C{degrees90}).
120 @arg lon1: Longitude of the first point (C{degrees180}).
121 @arg azi12: Azimuth of the rhumb line (compass C{degrees}).
122 @arg a12: Angle along the rhumb line from the given to the
123 destination point (C{degrees}), can be negative.
125 @return: L{GDict} with 2 up to 8 items C{lat2, lon2, a12, S12,
126 lat1, lon1, azi12, s12} with the destination point's
127 latitude C{lat2} and longitude C{lon2} in C{degrees},
128 the rhumb angle C{a12} in C{degrees} and area C{S12}
129 under the rhumb line in C{meter} I{squared}.
131 @raise ImportError: Package C{numpy} not found or not installed,
132 only required for area C{S12} when C{B{exact}
133 is True} and L{RhumbAux}.
135 @note: If B{C{a12}} is large enough that the rhumb line crosses
136 a pole, the longitude of the second point is indeterminate
137 and C{NAN} is returned for C{lon2} and area C{S12}.
139 @note: If the given point is a pole, the cosine of its latitude is
140 taken to be C{sqrt(L{EPS})}. This position is extremely
141 close to the actual pole and allows the calculation to be
142 carried out in finite terms.
143 '''
144 s12 = a12 * self._mpd
145 return self._DirectRhumb(lat1, lon1, azi12, a12, s12, outmask)
147 @Property_RO
148 def b(self):
149 '''Get the C{ellipsoid}'s polar radius, semi-axis (C{meter}).
150 '''
151 return self.ellipsoid.b
153 polaradius = b
155 @property
156 def datum(self):
157 '''Get this rhumb's datum (L{Datum}).
158 '''
159 return self._datum
161 @datum.setter # PYCHOK setter!
162 def datum(self, datum):
163 '''Set this rhumb's datum (L{Datum}).
165 @raise RhumbError: If C{abs(B{f}} exceeds non-zero C{f_max} and C{exact=False}.
166 '''
167 _xinstanceof(Datum, datum=datum)
168 if self._datum != datum:
169 self._exactest(self.exact, datum.ellipsoid, self.f_max)
170 _update_all_rls(self)
171 self._datum = datum
173 def _Direct(self, ll1, azi12, s12, **outmask):
174 '''(INTERNAL) Short-cut version, see .latlonBase.rhumb....
175 '''
176 return self.Direct(ll1.lat, ll1.lon, azi12, s12, **outmask)
178 def Direct(self, lat1, lon1, azi12, s12, outmask=Caps.LATITUDE_LONGITUDE):
179 '''Solve the I{direct rhumb} problem, optionally with area.
181 @arg lat1: Latitude of the first point (C{degrees90}).
182 @arg lon1: Longitude of the first point (C{degrees180}).
183 @arg azi12: Azimuth of the rhumb line (compass C{degrees}).
184 @arg s12: Distance along the rhumb line from the given to
185 the destination point (C{meter}), can be negative.
187 @return: L{GDict} with 2 up to 8 items C{lat2, lon2, a12, S12,
188 lat1, lon1, azi12, s12} with the destination point's
189 latitude C{lat2} and longitude C{lon2} in C{degrees},
190 the rhumb angle C{a12} in C{degrees} and area C{S12}
191 under the rhumb line in C{meter} I{squared}.
193 @raise ImportError: Package C{numpy} not found or not installed,
194 only required for area C{S12} when C{B{exact}
195 is True} and L{RhumbAux}.
197 @note: If B{C{s12}} is large enough that the rhumb line crosses
198 a pole, the longitude of the second point is indeterminate
199 and C{NAN} is returned for C{lon2} and area C{S12}.
201 @note: If the given point is a pole, the cosine of its latitude is
202 taken to be C{sqrt(L{EPS})}. This position is extremely
203 close to the actual pole and allows the calculation to be
204 carried out in finite terms.
205 '''
206 a12 = _over(s12, self._mpd)
207 return self._DirectRhumb(lat1, lon1, azi12, a12, s12, outmask)
209 def Direct8(self, lat1, lon1, azi12, s12, outmask=Caps.LATITUDE_LONGITUDE_AREA):
210 '''Like method L{Rhumb.Direct} but returning a L{Rhumb8Tuple} with area C{S12}.
211 '''
212 return self.Direct(lat1, lon1, azi12, s12, outmask=outmask).toRhumb8Tuple()
214 def _DirectLine(self, ll1, azi12, **caps_name):
215 '''(INTERNAL) Short-cut version, see .latlonBase.
216 '''
217 return self.DirectLine(ll1.lat, ll1.lon, azi12, **caps_name)
219 def DirectLine(self, lat1, lon1, azi12, **caps_name):
220 '''Define a C{RhumbLine} in terms of the I{direct} rhumb
221 problem to compute several points on a single rhumb line.
223 @arg lat1: Latitude of the first point (C{degrees90}).
224 @arg lon1: Longitude of the first point (C{degrees180}).
225 @arg azi12: Azimuth of the rhumb line (compass C{degrees}).
226 @kwarg caps_name: Optional keyword arguments C{B{name}=NN} and
227 C{B{caps}=Caps.STANDARD}, a bit-or'ed combination of
228 L{Caps} values specifying the required capabilities.
229 Include C{Caps.LINE_OFF} if updates to the B{C{rhumb}}
230 should I{not} be reflected in this rhumb line.
232 @return: A C{RhumbLine...} instance and invoke its method
233 C{.Position} to compute each point.
235 @note: Updates to this rhumb are reflected in the returned
236 rhumb line, unless C{B{caps} |= Caps.LINE_OFF}.
237 '''
238 return self._RhumbLine(self, lat1, lon1, azi12, **caps_name)
240 Line = DirectLine # synonyms
242 def _DirectRhumb(self, lat1, lon1, azi12, a12, s12, outmask):
243 '''(INTERNAL) See methods C{.ArcDirect} and C{.Direct}.
244 '''
245 rl = self._RhumbLine(self, lat1, lon1, azi12, caps=Caps.LINE_OFF,
246 name=self.name)
247 return rl._Position(a12, s12, outmask | self._debug) # lat2, lon2, S12
249 @Property
250 def ellipsoid(self):
251 '''Get this rhumb's ellipsoid (L{Ellipsoid}).
252 '''
253 return self.datum.ellipsoid
255 @ellipsoid.setter # PYCHOK setter!
256 def ellipsoid(self, a_earth_f):
257 '''Set this rhumb's ellipsoid (L{Ellipsoid}, L{Ellipsoid2}, L{Datum} or
258 L{a_f2Tuple}) or (equatorial) radius and flattening (2-tuple C{(a, f)}).
260 @raise RhumbError: If C{abs(B{f}} exceeds non-zero C{f_max} and C{exact=False}.
261 '''
262 self.datum = _spherical_datum(a_earth_f, Error=RhumbError)
264 @Property
265 def exact(self):
266 '''Get the I{exact} option (C{bool}).
267 '''
268 return self._exact
270 @exact.setter # PYCHOK setter!
271 def exact(self, exact):
272 '''Set the I{exact} option (C{bool}). If C{True}, use I{exact} rhumb
273 expressions, otherwise a series expansion (accurate for oblate or
274 prolate ellipsoids with C{abs(flattening)} below C{f_max}.
276 @raise RhumbError: If C{B{exact}=False} and C{abs(flattening})
277 exceeds non-zero C{f_max}.
279 @see: Option U{B{-s}<https://GeographicLib.SourceForge.io/C++/doc/RhumbSolve.1.html>}
280 and U{ACCURACY<https://GeographicLib.SourceForge.io/C++/doc/RhumbSolve.1.html#ACCURACY>}.
281 '''
282 x = bool(exact)
283 if self._exact != x:
284 self._exactest(x, self.ellipsoid, self.f_max)
285 _update_all_rls(self)
286 self._exact = x
288 def _exactest(self, exact, ellipsoid, f_max):
289 # Helper for property setters C{ellipsoid}, C{exact} and C{f_max}
290 if fabs(ellipsoid.f) > f_max > 0 and not exact:
291 raise RhumbError(exact=exact, f=ellipsoid.f, f_max=f_max)
293 @Property_RO
294 def f(self):
295 '''Get the C{ellipsoid}'s flattening (C{float}).
296 '''
297 return self.ellipsoid.f
299 flattening = f
301 @property
302 def f_max(self):
303 '''Get the I{max.} flattening (C{float}).
304 '''
305 return self._f_max
307 @f_max.setter # PYCHOK setter!
308 def f_max(self, f_max): # PYCHOK no cover
309 '''Set the I{max.} flattening, not to exceed (C{float}).
311 @raise RhumbError: If C{exact=False} and C{abs(flattening})
312 exceeds non-zero C{f_max}.
313 '''
314 f = Float_(f_max=f_max, low=_0_0, high=EPS1)
315 if self._f_max != f:
316 self._exactest(self.exact, self.ellipsoid, f)
317 self._f_max = f
319 def _Inverse(self, ll1, ll2, wrap, **outmask):
320 '''(INTERNAL) Short-cut version, see .latlonBase.rhumb....
321 '''
322 if wrap:
323 ll2 = _unrollon(ll1, _Wrap.point(ll2))
324 return self.Inverse(ll1.lat, ll1.lon, ll2.lat, ll2.lon, **outmask)
326 def Inverse(self, lat1, lon1, lat2, lon2, outmask=Caps.AZIMUTH_DISTANCE):
327 '''Solve the I{inverse rhumb} problem.
329 @arg lat1: Latitude of the first point (C{degrees90}).
330 @arg lon1: Longitude of the first point (C{degrees180}).
331 @arg lat2: Latitude of the second point (C{degrees90}).
332 @arg lon2: Longitude of the second point (C{degrees180}).
334 @return: L{GDict} with 4 to 9 items C{lat1, lon1, lat2, lon2,
335 azi12, azi21, s12, a12, S12}, the rhumb line's azimuth
336 C{azi12} and I{reverse} azimuth C{azi21}, both in
337 compass C{degrees} between C{-180} and C{+180}, the
338 rhumb distance C{s12} and rhumb angle C{a12} between
339 both points in C{meter} respectively C{degrees} and
340 the area C{S12} under the rhumb line in C{meter}
341 I{squared}.
343 @raise ImportError: Package C{numpy} not found or not installed,
344 only required for L{RhumbAux} area C{S12}
345 when C{B{exact} is True}.
347 @note: The shortest rhumb line is found. If the end points are
348 on opposite meridians, there are two shortest rhumb lines
349 and the East-going one is chosen.
351 @note: If either point is a pole, the cosine of its latitude is
352 taken to be C{sqrt(L{EPS})}. This position is extremely
353 close to the actual pole and allows the calculation to be
354 carried out in finite terms.
355 '''
356 r = GDict(lat1=lat1, lon1=lon1, lat2=lat2, lon2=lon2, name=self.name)
357 Cs = Caps
358 if (outmask & Cs.AZIMUTH_DISTANCE_AREA):
359 lon12, _ = _diff182(lon1, lon2, K_2_0=True)
360 y, x, s1, s2 = self._Inverse4(lon12, r, outmask)
361 if (outmask & Cs.AZIMUTH):
362 z = _atan2d(y, x)
363 r.set_(azi12=z, azi21=_azireversed(z))
364 if (outmask & Cs.AREA):
365 S12 = self._S12d(s1, s2, lon12)
366 r.set_(S12=unsigned0(S12)) # like .gx
367 return r
369 def _Inverse4(self, lon12, r, outmask): # PYCHOK no cover
370 '''(INTERNAL) I{Must be overloaded}.'''
371 _MODS.named.notOverloaded(self, lon12, r, Caps.toStr(outmask))
373 def Inverse8(self, lat1, lon1, azi12, s12, outmask=Caps.AZIMUTH_DISTANCE_AREA):
374 '''Like method L{Rhumb.Inverse} but returning a L{Rhumb8Tuple} with area C{S12}.
375 '''
376 return self.Inverse(lat1, lon1, azi12, s12, outmask=outmask).toRhumb8Tuple()
378 def _InverseLine(self, ll1, ll2, wrap, **caps_name):
379 '''(INTERNAL) Short-cut version, see .latlonBase.
380 '''
381 if wrap:
382 ll2 = _unrollon(ll1, _Wrap.point(ll2))
383 return self.InverseLine(ll1.lat, ll1.lon, ll2.lat, ll2.lon, **caps_name)
385 def InverseLine(self, lat1, lon1, lat2, lon2, **caps_name):
386 '''Define a C{RhumbLine} in terms of the I{inverse} rhumb problem.
388 @arg lat1: Latitude of the first point (C{degrees90}).
389 @arg lon1: Longitude of the first point (C{degrees180}).
390 @arg lat2: Latitude of the second point (C{degrees90}).
391 @arg lon2: Longitude of the second point (C{degrees180}).
392 @kwarg caps_name: Optional keyword arguments C{B{name}=NN} and
393 C{B{caps}=Caps.STANDARD}, a bit-or'ed combination of
394 L{Caps} values specifying the required capabilities.
395 Include C{Caps.LINE_OFF} if updates to the B{C{rhumb}}
396 should I{not} be reflected in this rhumb line.
398 @return: A C{RhumbLine...} instance and invoke its method
399 C{ArcPosition} or C{Position} to compute points.
401 @note: Updates to this rhumb are reflected in the returned
402 rhumb line, unless C{B{caps} |= Caps.LINE_OFF}.
403 '''
404 r = self.Inverse(lat1, lon1, lat2, lon2, outmask=Caps.AZIMUTH)
405 return self._RhumbLine(self, lat1, lon1, r.azi12, **caps_name)
407 @Property_RO
408 def _mpd(self): # PYCHOK no cover
409 '''(INTERNAL) I{Must be overloaded}.'''
410 _MODS.named.notOverloaded(self)
412 @property_RO
413 def RAorder(self):
414 '''Get the I{Rhumb Area} order, C{None} always.
415 '''
416 return None
418 @property_RO
419 def _RhumbLine(self): # PYCHOK no cover
420 '''(INTERNAL) I{Must be overloaded}.'''
421 _MODS.named.notOverloaded(self, underOK=True)
423 def _S12d(self, s1, s2, lon): # PYCHOK no cover
424 '''(INTERNAL) I{Must be overloaded}.'''
425 _MODS.named.notOverloaded(self, s1, s2, lon)
427 @Property
428 def TMorder(self):
429 '''Get the I{Transverse Mercator} order (C{int}, 4, 5, 6, 7 or 8).
430 '''
431 return self._mTM
433 @TMorder.setter # PYCHOK setter!
434 def TMorder(self, order):
435 '''Set the I{Transverse Mercator} order (C{int}, 4, 5, 6, 7 or 8).
437 @note: Setting C{TMorder} turns property C{exact} off, but only
438 for L{Rhumb} instances.
439 '''
440 m = _Xorder(_MODS.ktm._AlpCoeffs, RhumbError, TMorder=order)
441 if self._mTM != m:
442 _update_all_rls(self)
443 self._mTM = m
444 if self.exact and isinstance(self, _MODS.rhumbx.Rhumb):
445 self.exact = False
447 def toStr(self, prec=6, sep=_COMMASPACE_, **unused): # PYCHOK signature
448 '''Return this C{Rhumb} as string.
450 @kwarg prec: The C{float} precision, number of decimal digits (0..9).
451 Trailing zero decimals are stripped for B{C{prec}} values
452 of 1 and above, but kept for negative B{C{prec}} values.
453 @kwarg sep: Separator to join (C{str}).
455 @return: Tuple items (C{str}).
456 '''
457 d = dict(ellipsoid=self.ellipsoid, RAorder=self.RAorder,
458 exact=self.exact, TMorder=self.TMorder)
459 return sep.join(pairs(itemsorted(d, asorted=False), prec=prec))
462class RhumbLineBase(_CapsBase):
463 '''(INTERNAL) Base class for C{rhumbaux.RhumbLineAux} and C{rhumbx.RhumbLine}.
464 '''
465 _azi12 = _0_0
466 _calp = _1_0
467# _caps = 0
468# _debug = 0
469# _lat1 = _0_0
470# _lon1 = _0_0
471# _lon12 = _0_0
472 _Rhumb = RhumbBase # compatible C{Rhumb} class
473 _rhumb = None # C{Rhumb} instance
474 _salp = _0_0
475 _talp = _0_0
477 def __init__(self, rhumb, lat1, lon1, azi12, caps=Caps.STANDARD, name=NN):
478 '''New C{RhumbLine}.
479 '''
480 _xinstanceof(self._Rhumb, rhumb=rhumb)
482 self._lat1 = _Lat(lat1=_fix90(lat1))
483 self._lon1 = _Lon(lon1= lon1)
484 self._lon12 = _norm180(self._lon1)
485 if azi12: # non-zero, non-None
486 self.azi12 = _norm180(azi12)
488 n = name or rhumb.name
489 if n:
490 self.name=n
492 self._caps = caps
493 self._debug |= (caps | rhumb._debug) & Caps._DEBUG_DIRECT_LINE
494 if (caps & Caps.LINE_OFF): # copy to avoid updates
495 self._rhumb = rhumb.copy(deep=False, name=_under(rhumb.name))
496 else:
497 self._rhumb = rhumb
498 _rls.append(self)
500 def __del__(self): # XXX use weakref?
501 if _rls: # may be empty or None
502 try: # PYCHOK no cover
503 _rls.remove(self)
504 except (TypeError, ValueError):
505 pass
506 self._rhumb = None
507 # _update_all(self) # throws TypeError during Python 2 cleanup
509 def ArcPosition(self, a12, outmask=Caps.LATITUDE_LONGITUDE):
510 '''Compute a point at a given angular distance on this rhumb line.
512 @arg a12: The angle along this rhumb line from its origin to the
513 point (C{degrees}), can be negative.
514 @kwarg outmask: Bit-or'ed combination of L{Caps} values specifying
515 the quantities to be returned.
517 @return: L{GDict} with 4 to 8 items C{azi12, a12, s12, S12, lat2,
518 lon2, lat1, lon1} with latitude C{lat2} and longitude
519 C{lon2} of the point in C{degrees}, the rhumb distance
520 C{s12} in C{meter} from the start point of and the area
521 C{S12} under this rhumb line in C{meter} I{squared}.
523 @raise ImportError: Package C{numpy} not found or not installed,
524 only required for L{RhumbLineAux} area C{S12}
525 when C{B{exact} is True}.
527 @note: If B{C{a12}} is large enough that the rhumb line crosses a
528 pole, the longitude of the second point is indeterminate and
529 C{NAN} is returned for C{lon2} and area C{S12}.
531 If the first point is a pole, the cosine of its latitude is
532 taken to be C{sqrt(L{EPS})}. This position is extremely
533 close to the actual pole and allows the calculation to be
534 carried out in finite terms.
535 '''
536 return self._Position(a12, self.degrees2m(a12), outmask)
538 @Property
539 def azi12(self):
540 '''Get this rhumb line's I{azimuth} (compass C{degrees}).
541 '''
542 return self._azi12
544 @azi12.setter # PYCHOK setter!
545 def azi12(self, azi12):
546 '''Set this rhumb line's I{azimuth} (compass C{degrees}).
547 '''
548 z = _norm180(azi12)
549 if self._azi12 != z:
550 if self._rhumb:
551 _update_all(self)
552 self._azi12 = z
553 self._salp, self._calp = t = sincos2d(z) # no NEG0
554 self._talp = _over(*t)
556 @property_RO
557 def azi12_sincos2(self): # PYCHOK no cover
558 '''Get the sine and cosine of this rhumb line's I{azimuth} (2-tuple C{(sin, cos)}).
559 '''
560 return self._scalp, self._calp
562 @property_RO
563 def datum(self):
564 '''Get this rhumb line's datum (L{Datum}).
565 '''
566 return self.rhumb.datum
568 def degrees2m(self, angle):
569 '''Convert an angular distance along this rhumb line to C{meter}.
571 @arg angle: Angular distance (C{degrees}).
573 @return: Distance (C{meter}).
574 '''
575 return float(angle) * self.rhumb._mpd
577 @deprecated_method
578 def distance2(self, lat, lon): # PYCHOK no cover
579 '''DEPRECATED on 23.09.23, use method L{RhumbLineAux.Inverse} or L{RhumbLine.Inverse}.
581 @return: A L{Distance2Tuple}C{(distance, initial)} with the C{distance}
582 in C{meter} and C{initial} bearing (azimuth) in C{degrees}.
583 '''
584 r = self.Inverse(lat, lon)
585 return Distance2Tuple(r.s12, r.azi12)
587 @property_RO
588 def ellipsoid(self):
589 '''Get this rhumb line's ellipsoid (L{Ellipsoid}).
590 '''
591 return self.rhumb.ellipsoid
593 @property_RO
594 def exact(self):
595 '''Get this rhumb line's I{exact} option (C{bool}).
596 '''
597 return self.rhumb.exact
599 def Intersecant2(self, lat0, lon0, radius, napier=True, **tol_eps):
600 '''Compute the intersection(s) of this rhumb line and a circle.
602 @arg lat0: Latitude of the circle center (C{degrees}).
603 @arg lon0: Longitude of the circle center (C{degrees}).
604 @arg radius: Radius of the circle (C{meter}, conventionally).
605 @kwarg napier: If C{True}, apply I{Napier}'s spherical triangle
606 instead of planar trigonometry (C{bool}).
607 @kwarg tol_eps: Optional keyword arguments, see method
608 method L{Intersection} for further details.
610 @return: 2-Tuple C{(P, Q)} with both intersections (representing
611 a rhumb chord), each a L{GDict} from method L{Intersection}
612 extended to 18 items by C{lat3, lon3, azi03, a03, s03}
613 with azimuth C{azi03} of, distance C{a03} in C{degrees}
614 and C{s03} in C{meter} along the rhumb line from the circle
615 C{lat0, lon0} to the chord center C{lat3, lon3}. If this
616 rhumb line is tangential to the circle, both points
617 are the same L{GDict} instance with distances C{s02} and
618 C{s03} near-equal to the B{C{radius}}.
620 @raise IntersectionError: The circle and this rhumb line
621 do not intersect.
623 @raise UnitError: Invalid B{C{radius}}.
624 '''
625 r = Radius_(radius)
626 p = q = self.PlumbTo(lat0, lon0, exact=None, **tol_eps)
627 a = q.s02
628 t = dict(lat3=q.lat2, lon3=q.lon2, azi03=q.azi02, a03=q.a02, s03=a)
629 if a < r:
630 t.update(iteration=q.iteration, lat0=q.lat1, lon0=q.lon1, # or lat0, lon0
631 name=_dunder_nameof(self.Intersecant2, self.name))
632 if fabs(a) < EPS0: # coincident centers
633 d, h = _0_0, r
634 else:
635 d = q.s12
636 if napier: # Napier rule (R1) cos(b) = cos(c) / cos(a)
637 # <https://WikiPedia.org/wiki/Spherical_trigonometry>
638 m = self.rhumb._mpr
639 h = (acos1(cos(r / m) / cos(a / m)) * m) if m else _0_0
640 else:
641 h = _copysign(sqrt_a(r, a), a)
642 p = q = self.Position(d + h).set_(**t)
643 if h:
644 q = self.Position(d - h).set_(**t)
645 elif a > r:
646 t = _too_(Fmt.distant(a))
647 raise IntersectionError(self, lat0, lon0, radius,
648 txt=t, **tol_eps)
649 else: # tangential
650 q.set_(**t) # == p.set(_**t)
651 return p, q
653 def intersection2(self, other, **tol_eps): # PYCHOK no cover
654 '''DEPRECATED on 23.10.10, use method L{Intersection}.'''
655 p = self.Intersection(other, **tol_eps)
656 r = LatLon2Tuple(p.lat2, p.lon2, name=self.intersection2.__name__)
657 r._iteration = p.iteration
658 return r
660 def Intersection(self, other, tol=_TOL, **eps):
661 '''I{Iteratively} find the intersection of this and an other rhumb line.
663 @arg other: The other rhumb line (C{RhumbLine}).
664 @kwarg tol: Tolerance for longitudinal convergence and parallel
665 error (C{degrees}).
666 @kwarg eps: Tolerance for L{pygeodesy.intersection3d3} (C{EPS}).
668 @return: The intersection point, a L{Position}-like L{GDict} with
669 13 items C{lat1, lon1, azi12, a12, s12, lat2, lon2, lat0,
670 lon0, azi02, a02, s02, at} with the rhumb angle C{a02}
671 and rhumb distance C{s02} between the start point C{lat0,
672 lon0} of the B{C{other}} rhumb line and the intersection
673 C{lat2, lon2}, the azimuth C{azi02} of the B{C{other}}
674 rhumb line and the angle C{at} between both rhumb lines.
675 See method L{Position} for further details.
677 @raise IntersectionError: No convergence for this B{C{tol}} or
678 no intersection for an other reason.
680 @see: Methods C{distance2} and C{PlumbTo} and function
681 L{pygeodesy.intersection3d3}.
683 @note: Each iteration involves a round trip to this rhumb line's
684 L{ExactTransverseMercator} or L{KTransverseMercator}
685 projection and function L{pygeodesy.intersection3d3} in
686 that domain.
687 '''
688 _xinstanceof(RhumbLineBase, other=other)
689 _xdatum(self.rhumb, other.rhumb, Error=RhumbError)
690 try:
691 if self.others(other) is self:
692 raise ValueError(_coincident_)
693 # make invariants and globals locals
694 _s_3d, s_az = self._xTM3d, self.azi12
695 _o_3d, o_az = other._xTM3d, other.azi12
696 p = opposing(s_az, o_az, margin=tol)
697 if p is not None: # == t in (True, False)
698 raise ValueError(_anti_(_parallel_) if p else _parallel_)
699 _diff = euclid # approximate length
700 _i3d3 = _intersect3d3 # NOT .vector3d.intersection3d3
701 _LL2T = LatLon2Tuple
702 _xTMr = self.xTM.reverse # ellipsoidal or spherical
703 # use halfway point as initial estimate
704 p = _LL2T(favg(self.lat1, other.lat1),
705 favg(self.lon1, other.lon1))
706 for i in range(1, _TRIPS):
707 v = _i3d3(_s_3d(p), s_az, # point + bearing
708 _o_3d(p), o_az, useZ=False, **eps)[0]
709 t = _xTMr(v.x, v.y, lon0=p.lon) # PYCHOK Reverse4Tuple
710 d = _diff(t.lon - p.lon, t.lat) # PYCHOK t.lat + p.lat - p.lat
711 p = _LL2T(t.lat + p.lat, t.lon) # PYCHOK t.lon + p.lon = lon0
712 if d < tol: # 19 trips
713 break
714 else:
715 raise ValueError(Fmt.no_convergence(d))
717 n = _dunder_nameof(self.Intersection, self.name)
718 r = self.Inverse( p.lat, p.lon, outmask=Caps.DISTANCE)
719 t = other.Inverse(p.lat, p.lon, outmask=Caps.DISTANCE)
720 P = GDict(lat1=self.lat1, lat2=p.lat, lat0=other.lat1,
721 lon1=self.lon1, lon2=p.lon, lon0=other.lon1,
722 azi12= self.azi12, a12=r.a12, s12=r.s12,
723 azi02=other.azi12, a02=t.a12, s02=t.s12,
724 at=other.azi12 - self.azi12, name=n)
725 P._iteration = i # .set_(iteration=i, ...) only
726 except Exception as x:
727 raise IntersectionError(self, other, tol=tol,
728 eps=eps, cause=x)
729 return P
731 def Inverse(self, lat2, lon2, wrap=False, **outmask):
732 '''Return the rhumb angle, distance, azimuth, I{reverse} azimuth, etc. of
733 a rhumb line between the given point and this rhumb line's start point.
735 @arg lat2: Latitude of the point (C{degrees}).
736 @arg lon2: Longitude of the points (C{degrees}).
737 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll B{C{lat2}}
738 and B{C{lon2}} (C{bool}).
740 @return: L{GDict} with 8 items C{a12, s12, azi12, azi21, lat1, lon1,
741 lat2, lon2}, the rhumb angle C{a12} and rhumb distance C{s12}
742 between both points in C{degrees} respectively C{meter}, the
743 rhumb line's azimuth C{azi12} and I{reverse} azimuth C{azi21}
744 both in compass C{degrees} between C{-180} and C{+180}.
745 '''
746 if wrap:
747 _, lat2, lon2 = _Wrap.latlon3(self.lon1, _fix90(lat2), lon2, wrap)
748 r = self.rhumb.Inverse(self.lat1, self.lon1, lat2, lon2, **outmask)
749 return r
751 @Property_RO
752 def isLoxodrome(self):
753 '''Is this rhumb line a meridional (C{None}), a parallel
754 (C{False}) or a C{True} loxodrome?
756 @see: I{Osborne's} U{2.5 Rumb lines and loxodromes
757 <https://Zenodo.org/record/35392>}, page 37.
758 '''
759 return bool(self._salp) if self._calp else None
761 @Property_RO
762 def lat1(self):
763 '''Get this rhumb line's latitude (C{degrees90}).
764 '''
765 return self._lat1
767 @Property_RO
768 def lon1(self):
769 '''Get this rhumb line's longitude (C{degrees180}).
770 '''
771 return self._lon1
773 @Property_RO
774 def latlon1(self):
775 '''Get this rhumb line's lat- and longitude (L{LatLon2Tuple}C{(lat, lon)}).
776 '''
777 return LatLon2Tuple(self.lat1, self.lon1)
779 def m2degrees(self, distance):
780 '''Convert a distance along this rhumb line to an angular distance.
782 @arg distance: Distance (C{meter}).
784 @return: Angular distance (C{degrees}).
785 '''
786 return _over(float(distance), self.rhumb._mpd)
788 @property_RO
789 def _mu1(self): # PYCHOK no cover
790 '''(INTERNAL) I{Must be overloaded}.'''
791 _MODS.named.notOverloaded(self, underOK=True)
793 def _mu2lat(self, mu2): # PYCHOK no cover
794 '''(INTERNAL) I{Must be overloaded}.'''
795 _MODS.named.notOverloaded(self, mu2, underOK=True)
797 @deprecated_method
798 def nearestOn4(self, lat0, lon0, **exact_eps_est_tol):
799 '''DEPRECATED on 23.10.10, use method L{PlumbTo}.'''
800 P = self.PlumbTo(lat0, lon0, **exact_eps_est_tol)
801 r = _MODS.deprecated.NearestOn4Tuple(P.lat2, P.lon2, P.s12, P.azi02,
802 name=self.nearestOn4.__name__)
803 r._iteration = P.iteration
804 return r
806 @deprecated_method
807 def NearestOn(self, lat0, lon0, **exact_eps_est_tol):
808 '''DEPRECATED on 23.10.30, use method L{PlumbTo}.'''
809 return self.PlumbTo(lat0, lon0, **exact_eps_est_tol)
811 def PlumbTo(self, lat0, lon0, exact=None, eps=EPS, est=None, tol=_TOL):
812 '''Compute the I{perpendicular} intersection of this rumb line with a geodesic
813 from the given point, in part transcoded from I{Karney}'s C++ U{rhumb-intercept
814 <https://SourceForge.net/p/geographiclib/discussion/1026620/thread/2ddc295e/>}.
816 @arg lat0: Latitude of the point (C{degrees}).
817 @arg lon0: Longitude of the point (C{degrees}).
818 @kwarg exact: If C{None}, use a rhumb line perpendicular to this rhumb
819 line, otherwise use an I{exact} C{Geodesic...} from the
820 given point perpendicular to this rhumb line (C{bool} or
821 C{Geodesic...}), see method L{Ellipsoid.geodesic_}.
822 @kwarg eps: Optional tolerance for L{pygeodesy.intersection3d3} (C{EPS}),
823 used only if C{B{exact} is None}.
824 @kwarg est: Optional, initial estimate for the distance C{s12} of the
825 intersection I{along} this rhumb line (C{meter}), used only
826 if C{B{exact} is not None}.
827 @kwarg tol: Longitudinal convergence tolerance (C{degrees}) or distance
828 tolerance (C(meter)) when C{B{exact} is None}, respectively
829 C{not None}.
831 @return: The intersection point on this rhumb line, a L{GDict} from method
832 L{Intersection} if B{C{exact}=None}. If B{C{exact}} is not C{None},
833 a L{Position}-like L{GDict} of 13 items C{azi12, a12, s12, lat2,
834 lat1, lat0, lon2, lon1, lon0, azi0, a02, s02, at} with distance
835 C{a02} in C{degrees} and C{s02} in C{meter} between the given point
836 C{lat0, lon0} and the intersection C{lat2, lon2}, geodesic azimuth
837 C{azi0} at the given point and the (perpendicular) angle C{at}
838 between the geodesic and this rhumb line at the intersection. The
839 I{geodesic} azimuth at the intersection is C{(at + azi12)}. See
840 method L{Position} for further details.
842 @raise ImportError: I{Karney}'s U{geographiclib
843 <https://PyPI.org/project/geographiclib>}
844 package not found or not installed.
846 @raise IntersectionError: No convergence for this B{C{eps}} or no
847 intersection for some other reason.
849 @see: Methods C{distance2}, C{Intersecant2} and C{Intersection}
850 and function L{pygeodesy.intersection3d3}.
851 '''
852 Cs = Caps
853 if exact is None:
854 z = _norm180(self.azi12 + _90_0) # perpendicular azimuth
855 rl = RhumbLineBase(self.rhumb, lat0, lon0, z, caps=Cs.LINE_OFF)
856 P = self.Intersection(rl, tol=tol, eps=eps)
858 else: # C{rhumb-intercept}
859 E = self.ellipsoid
860 _gI = E.geodesic_(exact=exact).Inverse
861 gm = Cs.STANDARD | Cs._REDUCEDLENGTH_GEODESICSCALE # ^ Cs.DISTANCE_IN
862 if est is None: # get an estimate from the "perpendicular" geodesic
863 r = _gI(self.lat1, self.lon1, lat0, lon0, outmask=Cs.AZIMUTH_DISTANCE)
864 d, _ = _diff182(r.azi2, self.azi12, K_2_0=True)
865 _, s12 = sincos2d(d)
866 s12 *= r.s12 # signed
867 else:
868 s12 = Meter(est=est)
869 try:
870 tol = Float_(tol=tol, low=EPS, high=None)
871 # def _over(p, q): # see @note at method C{.Position}
872 # return (p / (q or _copysign(tol, q))) if isfinite(q) else NAN
874 _ErT = E.rocPrimeVertical # aka rocTransverse
875 _S12 = Fsum(s12).fsum2_
876 for i in range(1, _TRIPS): # suffix 1 == C++ 2, 2 == C++ 3
877 P = self.Position(s12) # outmask = Cs.LATITUDE_LONGITUDE
878 r = _gI(lat0, lon0, P.lat2, P.lon2, outmask=gm)
879 d, _ = _diff182(self.azi12, r.azi2, K_2_0=True)
880 s, c, s2, c2 = sincos2d_(d, r.lat2)
881 c2 *= _ErT(r.lat2)
882 s *= _over(s2 * self._salp, c2) - _over(s * r.M21, r.m12)
883 s12, t = _S12(c / s) # XXX _over?
884 if fabs(t) < tol: # or fabs(c) < EPS
885 break
886 P.set_(azi0=r.azi1, a02=r.a12, s02=r.s12, # azi2=r.azi2,
887 lat0=lat0, lon0=lon0, iteration=i, at=r.azi2 - self.azi12,
888 name=_dunder_nameof(self.PlumbTo, self.name))
889 except Exception as x: # Fsum(NAN) Value-, ZeroDivisionError
890 raise IntersectionError(lat0, lon0, tol=tol, exact=exact,
891 eps=eps, est=est, iteration=i, cause=x)
893 return P
895 def Position(self, s12, outmask=Caps.LATITUDE_LONGITUDE):
896 '''Compute a point at a given distance on this rhumb line.
898 @arg s12: The distance along this rhumb line from its origin to
899 the point (C{meters}), can be negative.
900 @kwarg outmask: Bit-or'ed combination of L{Caps} values specifying
901 the quantities to be returned.
903 @return: L{GDict} with 4 to 8 items C{azi12, a12, s12, S12, lat2,
904 lat1, lon2, lon1} with latitude C{lat2} and longitude
905 C{lon2} of the point in C{degrees}, the rhumb angle C{a12}
906 in C{degrees} from the start point of and the area C{S12}
907 under this rhumb line in C{meter} I{squared}.
909 @raise ImportError: Package C{numpy} not found or not installed,
910 only required for L{RhumbLineAux} area C{S12}
911 when C{B{exact} is True}.
913 @note: If B{C{s12}} is large enough that the rhumb line crosses a
914 pole, the longitude of the second point is indeterminate and
915 C{NAN} is returned for C{lon2} and area C{S12}.
917 If the first point is a pole, the cosine of its latitude is
918 taken to be C{sqrt(L{EPS})}. This position is extremely
919 close to the actual pole and allows the calculation to be
920 carried out in finite terms.
921 '''
922 return self._Position(self.m2degrees(s12), s12, outmask)
924 def _Position(self, a12, s12, outmask):
925 '''(INTERNAL) C{Arc-/Position} helper.
926 '''
927 r = GDict(azi12=self.azi12, a12=a12, s12=s12, name=self.name)
928 Cs = Caps
929 if (outmask & Cs.LATITUDE_LONGITUDE_AREA):
930 if a12 or s12:
931 mu12 = self._calp * a12
932 mu2 = self._mu1 + mu12
933 if fabs(mu2) > 90: # past pole
934 mu2 = _norm180(mu2) # reduce to [-180, 180)
935 if fabs(mu2) > 90: # point on anti-meridian
936 mu2 = _norm180(_loneg(mu2))
937 lat2 = self._mu2lat(mu2)
938 lon2 = S12 = NAN
939 else:
940 lat2, lon2, S1, S2 = self._Position4(a12, mu2, s12, mu12)
941 if (outmask & Cs.AREA):
942 S12 = self.rhumb._S12d(S1, S2, lon2)
943 S12 = unsigned0(S12) # like .gx
944# else:
945# S12 = None # unused
946 if (outmask & Cs.LONGITUDE):
947 if (outmask & Cs.LONG_UNROLL):
948 lon2 += self.lon1
949 else:
950 lon2 = _norm180(self._lon12 + lon2)
951 else: # coincident
952 lat2, lon2 = self.latlon1
953 S12 = _0_0
955 if (outmask & Cs.AREA):
956 r.set_(S12=S12)
957 if (outmask & Cs.LATITUDE):
958 r.set_(lat2=lat2, lat1=self.lat1)
959 if (outmask & Cs.LONGITUDE):
960 r.set_(lon2=lon2, lon1=self.lon1)
961 return r
963 def _Position4(self, a12, mu2, s12, mu12): # PYCHOK no cover
964 '''(INTERNAL) I{Must be overloaded}.'''
965 _MODS.named.notOverloaded(self, a12, s12, mu2, mu12)
967 @Property_RO
968 def rhumb(self):
969 '''Get this rhumb line's rhumb (L{RhumbAux} or L{Rhumb}).
970 '''
971 return self._rhumb
973 def toStr(self, prec=6, sep=_COMMASPACE_, **unused): # PYCHOK signature
974 '''Return this C{RhumbLine} as string.
976 @kwarg prec: The C{float} precision, number of decimal digits (0..9).
977 Trailing zero decimals are stripped for B{C{prec}} values
978 of 1 and above, but kept for negative B{C{prec}} values.
979 @kwarg sep: Separator to join (C{str}).
981 @return: C{RhumbLine} (C{str}).
982 '''
983 d = dict(rhumb=self.rhumb, lat1=self.lat1, lon1=self.lon1,
984 azi12=self.azi12, exact=self.exact,
985 TMorder=self.TMorder, xTM=self.xTM)
986 return sep.join(pairs(itemsorted(d, asorted=False), prec=prec))
988 @property_RO
989 def TMorder(self):
990 '''Get this rhumb line's I{Transverse Mercator} order (C{int}, 4, 5, 6, 7 or 8).
991 '''
992 return self.rhumb.TMorder
994 @Property_RO
995 def xTM(self):
996 '''Get this rhumb line's I{Transverse Mercator} projection (L{ExactTransverseMercator}
997 if I{exact} and I{ellipsoidal}, otherwise L{KTransverseMercator} for C{TMorder}).
998 '''
999 E = self.ellipsoid
1000 # ExactTransverseMercator doesn't handle spherical earth models
1001 return _MODS.etm.ExactTransverseMercator(E) if self.exact and E.isEllipsoidal else \
1002 _MODS.ktm.KTransverseMercator(E, TMorder=self.TMorder)
1004 def _xTM3d(self, latlon0, z=INT0, V3d=Vector3d):
1005 '''(INTERNAL) C{xTM.forward} this C{latlon1} to C{V3d} with B{C{latlon0}}
1006 as current intersection estimate and central meridian.
1007 '''
1008 t = self.xTM.forward(self.lat1 - latlon0.lat, self.lon1, lon0=latlon0.lon)
1009 return V3d(t.easting, t.northing, z)
1012class _PseudoRhumbLine(RhumbLineBase):
1013 '''(INTERNAL) Pseudo-rhumb line for a geodesic (line), see C{geodesicw._PlumbTo}.
1014 '''
1015 def __init__(self, gl, name=NN):
1016 R = RhumbBase(gl.geodesic.ellipsoid, None, True, name)
1017 RhumbLineBase.__init__(self, R, gl.lat1, gl.lon1, 0, caps=Caps.LINE_OFF)
1018 self._azi1 = self.azi12 = gl.azi1
1019 self._gl = gl
1020 self._gD = gl.geodesic.Direct
1022 def PlumbTo(self, lat0, lon0, **exact_eps_est_tol): # PYCHOK signature
1023 P = RhumbLineBase.PlumbTo(self, lat0, lon0, **exact_eps_est_tol)
1024 P.set_(azi1=self._gl.azi1, azi2=_xkwds_pop(P, azi12=None))
1025 return P # geodesic L{Position}
1027 def Position(self, s12, **unused): # PYCHOK signature
1028 r = self._gD(self.lat1, self.lon1, self._azi1, s12)
1029 self._azi1 = r.azi1
1030 self.azi12 = z = r.azi2
1031 self._salp, _ = sincos2d(z)
1032 return r.set_(azi12=z)
1035__all__ += _ALL_DOCS(RhumbBase, RhumbLineBase)
1037if __name__ == '__main__':
1039 from pygeodesy import printf, Rhumb as R, RhumbAux as A
1040 from pygeodesy.ellipsoids import _EWGS84
1042 A = A(_EWGS84).Line(30, 0, 45)
1043 R = R(_EWGS84).Line(30, 0, 45)
1045 for i in range(1, 10):
1046 s = .5e6 + 1e6 / i
1047 a = A.Position(s).lon2
1048 r = R.Position(s).lon2
1049 e = (fabs(a - r) / a) if a else 0
1050 printf('# Position.lon2 %.14f vs %.14f, diff %g', r, a, e)
1052 for exact in (None, False, True):
1053 for est in (None, 1e6):
1054 a = A.PlumbTo(60, 0, exact=exact, est=est)
1055 r = R.PlumbTo(60, 0, exact=exact, est=est)
1056 printf('# %s, iteration=%s, exact=%s, est=%s\n# %s, iteration=%s',
1057 a.toRepr(), a.iteration, exact, est,
1058 r.toRepr(), r.iteration, nl=1)
1060# % python3 -m pygeodesy.rhumbBase
1062# Position.lon2 11.61455846901637 vs 11.61455846901637, diff 3.05885e-16
1063# Position.lon2 7.58982302826842 vs 7.58982302826842, diff 2.34045e-16
1064# Position.lon2 6.28526067416369 vs 6.28526067416369, diff 2.82623e-16
1065# Position.lon2 5.63938995325146 vs 5.63938995325146, diff 1.57495e-16
1066# Position.lon2 5.25385527435707 vs 5.25385527435707, diff 0
1067# Position.lon2 4.99764604290380 vs 4.99764604290380, diff 8.88597e-16
1068# Position.lon2 4.81503363740473 vs 4.81503363740473, diff 1.84459e-16
1069# Position.lon2 4.67828821748836 vs 4.67828821748835, diff 5.69553e-16
1070# Position.lon2 4.57205667906283 vs 4.57205667906283, diff 5.82787e-16
1072# Intersection(a02=17.798332, a12=19.521356, at=90.0, azi02=135.0, azi12=45.0, lat0=60.0, lat1=30.0, lat2=45.0, lon0=0.0, lon1=0.0, lon2=15.830286, name='Intersection', s02=1977981.142985, s12=2169465.957531), iteration=9, exact=None, est=None
1073# Intersection(a02=17.798332, a12=19.521356, at=90.0, azi02=135.0, azi12=45.0, lat0=60.0, lat1=30.0, lat2=45.0, lon0=0.0, lon1=0.0, lon2=15.830286, name='Intersection', s02=1977981.142985, s12=2169465.957531), iteration=9
1075# Intersection(a02=17.798332, a12=19.521356, at=90.0, azi02=135.0, azi12=45.0, lat0=60.0, lat1=30.0, lat2=45.0, lon0=0.0, lon1=0.0, lon2=15.830286, name='Intersection', s02=1977981.142985, s12=2169465.957531), iteration=9, exact=None, est=1000000.0
1076# Intersection(a02=17.798332, a12=19.521356, at=90.0, azi02=135.0, azi12=45.0, lat0=60.0, lat1=30.0, lat2=45.0, lon0=0.0, lon1=0.0, lon2=15.830286, name='Intersection', s02=1977981.142985, s12=2169465.957531), iteration=9
1078# PlumbTo(a02=17.967658, a12=27.74256, at=90.0, azi0=113.73626, azi12=45.0, lat0=60, lat1=30.0, lat2=49.634582, lon0=0, lon1=0.0, lon2=25.767876, name='PlumbTo', s02=1997960.116871, s12=3083112.636236), iteration=5, exact=False, est=None
1079# PlumbTo(a02=17.967658, a12=27.74256, at=90.0, azi0=113.73626, azi12=45.0, lat0=60, lat1=30.0, lat2=49.634582, lon0=0, lon1=0.0, lon2=25.767876, name='PlumbTo', s02=1997960.116871, s12=3083112.636236), iteration=5
1081# PlumbTo(a02=17.967658, a12=27.74256, at=90.0, azi0=113.73626, azi12=45.0, lat0=60, lat1=30.0, lat2=49.634582, lon0=0, lon1=0.0, lon2=25.767876, name='PlumbTo', s02=1997960.116871, s12=3083112.636236), iteration=7, exact=False, est=1000000.0
1082# PlumbTo(a02=17.967658, a12=27.74256, at=90.0, azi0=113.73626, azi12=45.0, lat0=60, lat1=30.0, lat2=49.634582, lon0=0, lon1=0.0, lon2=25.767876, name='PlumbTo', s02=1997960.116871, s12=3083112.636236), iteration=7
1084# PlumbTo(a02=17.967658, a12=27.74256, at=90.0, azi0=113.73626, azi12=45.0, lat0=60, lat1=30.0, lat2=49.634582, lon0=0, lon1=0.0, lon2=25.767876, name='PlumbTo', s02=1997960.116871, s12=3083112.636236), iteration=5, exact=True, est=None
1085# PlumbTo(a02=17.967658, a12=27.74256, at=90.0, azi0=113.73626, azi12=45.0, lat0=60, lat1=30.0, lat2=49.634582, lon0=0, lon1=0.0, lon2=25.767876, name='PlumbTo', s02=1997960.116871, s12=3083112.636236), iteration=5
1087# PlumbTo(a02=17.967658, a12=27.74256, at=90.0, azi0=113.73626, azi12=45.0, lat0=60, lat1=30.0, lat2=49.634582, lon0=0, lon1=0.0, lon2=25.767876, name='PlumbTo', s02=1997960.116871, s12=3083112.636236), iteration=7, exact=True, est=1000000.0
1088# PlumbTo(a02=17.967658, a12=27.74256, at=90.0, azi0=113.73626, azi12=45.0, lat0=60, lat1=30.0, lat2=49.634582, lon0=0, lon1=0.0, lon2=25.767876, name='PlumbTo', s02=1997960.116871, s12=3083112.636236), iteration=7
1090# **) MIT License
1091#
1092# Copyright (C) 2022-2023 -- mrJean1 at Gmail -- All Rights Reserved.
1093#
1094# Permission is hereby granted, free of charge, to any person obtaining a
1095# copy of this software and associated documentation files (the "Software"),
1096# to deal in the Software without restriction, including without limitation
1097# the rights to use, copy, modify, merge, publish, distribute, sublicense,
1098# and/or sell copies of the Software, and to permit persons to whom the
1099# Software is furnished to do so, subject to the following conditions:
1100#
1101# The above copyright notice and this permission notice shall be included
1102# in all copies or substantial portions of the Software.
1103#
1104# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
1105# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
1106# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
1107# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR
1108# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
1109# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
1110# OTHER DEALINGS IN THE SOFTWARE.