Coverage for pygeodesy/rhumb/bases.py: 94%
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2# -*- coding: utf-8 -*-
4u'''(INTERNAL) base classes C{RhumbBase} and C{RhumbLineBase}, pure Python version of I{Karney}'s
5C++ classes 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{RhumbLineBase} has been enhanced with methods C{Intersecant2}, C{Intersection} and C{PlumbTo}
11to iteratively find the intersection of a rhumb line and a circle or an other rhumb line, respectively
12a perpendicular geodesic or other rhumb line.
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>} (2014-2024) 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 _ # noqa: E702 ;
26from pygeodesy.basics import _copysign, itemsorted, unsigned0, _xinstanceof
27from pygeodesy.constants import EPS, EPS0, EPS1, INT0, NAN, _over, \
28 _EPSqrt as _TOL, _0_0, _0_01, _1_0, _90_0
29from pygeodesy.datums import Datum, _earth_datum, _spherical_datum, _WGS84
30from pygeodesy.errors import IntersectionError, RhumbError, _xdatum, \
31 _xkwds, _xkwds_pop2, _Xorder
32# from pygeodesy.etm import ExactTransverseMercator # _MODS
33from pygeodesy.fmath import euclid, favg, sqrt_a, Fsum
34# from pygeodesy.formy import opposing # _MODS
35# from pygeodesy.fsums import Fsum # from .fmath
36from pygeodesy.internals import typename, _under
37from pygeodesy.interns import NN, _coincident_, _COMMASPACE_, _Dash, \
38 _DMAIN_, _parallel_, _too_
39from pygeodesy.karney import _atan2d, Caps, _CapsBase, _diff182, _fix90, \
40 _norm180, GDict
41# from pygeodesy.ktm import KTransverseMercator, _AlpCoeffs # _MODS
42from pygeodesy.lazily import _ALL_DOCS, _ALL_MODS as _MODS
43from pygeodesy.namedTuples import Distance2Tuple, LatLon2Tuple
44from pygeodesy.props import deprecated_method, Property, Property_RO, \
45 property_RO, _update_all
46from pygeodesy.streprs import Fmt, pairs
47from pygeodesy.units import Float_, Lat, Lon, Meter, Radius_
48from pygeodesy.utily import acos1, _azireversed, _loneg, sincos2d, sincos2d_, \
49 _unrollon, _Wrap
50from pygeodesy.vector3d import _intersect3d3, Vector3d # in .Intersection below
52from math import cos, fabs
54__all__ = ()
55__version__ = '25.05.12'
57_anti_ = _Dash('anti')
58_rls = [] # instances of C{RbumbLine...} to be updated
59_TRIPS = 129 # .Intersection, .PlumbTo, 19+
62class _Lat(Lat):
63 '''(INTERNAL) Latitude B{C{lat}}.
64 '''
65 def __init__(self, *lat, **Error_name):
66 kwds = _xkwds(Error_name, clip=0, Error=RhumbError)
67 Lat.__new__(_Lat, *lat, **kwds)
70class _Lon(Lon):
71 '''(INTERNAL) Longitude B{C{lon}}.
72 '''
73 def __init__(self, *lon, **Error_name):
74 kwds = _xkwds(Error_name, clip=0, Error=RhumbError)
75 Lon.__new__(_Lon, *lon, **kwds)
78def _update_all_rls(r):
79 '''(INTERNAL) Zap cached/memoized C{Property[_RO]}s
80 of any C{RhumbLine} instances tied to the given
81 C{Rhumb} instance B{C{r}}.
82 '''
83 # _xinstanceof(_MODS.rhumb.aux_.RhumbAux, _MODS.rhumb.ekx.Rhumb, r=r)
84 _update_all(r)
85 for rl in _rls: # PYCHOK use weakref?
86 if rl._rhumb is r:
87 _update_all(rl)
90class RhumbBase(_CapsBase):
91 '''(INTERNAL) Base class for C{rhumb.aux_.RhumbAux} and C{rhumb.ekx.Rhumb}.
92 '''
93 _datum = _WGS84
94 _exact = True
95 _f_max = _0_01
96 _mTM = 6 # see .TMorder
98 def __init__(self, a_earth, f, exact, TMorder_name):
99 '''New C{RhumbAux} or C{Rhumb}.
100 '''
101 if TMorder_name:
102 M = self._mTM
103 m, name = _xkwds_pop2(TMorder_name, TMorder=M)
104 if m != M:
105 self.TMorder = m
106 else:
107 name = {}
108 _earth_datum(self, a_earth, f=f, **name)
109 if not exact:
110 self.exact = False
111 if name:
112 self.name = name
114 @Property_RO
115 def a(self):
116 '''Get the C{ellipsoid}'s equatorial radius, semi-axis (C{meter}).
117 '''
118 return self.ellipsoid.a
120 equatoradius = a
122 def ArcDirect(self, lat1, lon1, azi12, a12, outmask=Caps.LATITUDE_LONGITUDE):
123 '''Solve the I{direct rhumb} problem, optionally with area.
125 @arg lat1: Latitude of the first point (C{degrees90}).
126 @arg lon1: Longitude of the first point (C{degrees180}).
127 @arg azi12: Azimuth of the rhumb line (compass C{degrees}).
128 @arg a12: Angle along the rhumb line from the given to the
129 destination point (C{degrees}), can be negative.
131 @return: L{GDict} with 2 up to 8 items C{lat2, lon2, a12, S12,
132 lat1, lon1, azi12, s12} with the destination point's
133 latitude C{lat2} and longitude C{lon2} in C{degrees},
134 the rhumb angle C{a12} in C{degrees} and area C{S12}
135 under the rhumb line in C{meter} I{squared}.
137 @raise ImportError: Package C{numpy} not found or not installed,
138 only required for area C{S12} when C{B{exact}
139 is True} and L{RhumbAux}.
141 @note: If B{C{a12}} is large enough that the rhumb line crosses
142 a pole, the longitude of the second point is indeterminate
143 and C{NAN} is returned for C{lon2} and area C{S12}.
145 @note: If the given point is a pole, the cosine of its latitude is
146 taken to be C{sqrt(L{EPS})}. This position is extremely
147 close to the actual pole and allows the calculation to be
148 carried out in finite terms.
149 '''
150 s12 = a12 * self._mpd
151 return self._DirectRhumb(lat1, lon1, azi12, a12, s12, outmask)
153 @Property_RO
154 def b(self):
155 '''Get the C{ellipsoid}'s polar radius, semi-axis (C{meter}).
156 '''
157 return self.ellipsoid.b
159 polaradius = b
161 @property
162 def datum(self):
163 '''Get this rhumb's datum (L{Datum}).
164 '''
165 return self._datum
167 @datum.setter # PYCHOK setter!
168 def datum(self, datum):
169 '''Set this rhumb's datum (L{Datum}).
171 @raise RhumbError: If C{abs(B{f}} exceeds non-zero C{f_max} and C{exact=False}.
172 '''
173 _xinstanceof(Datum, datum=datum)
174 if self._datum != datum:
175 self._exactest(self.exact, datum.ellipsoid, self.f_max)
176 _update_all_rls(self)
177 self._datum = datum
179 def _Direct(self, ll1, azi12, s12, **outmask):
180 '''(INTERNAL) Short-cut version, see .latlonBase.rhumb....
181 '''
182 return self.Direct(ll1.lat, ll1.lon, azi12, s12, **outmask)
184 def Direct(self, lat1, lon1, azi12, s12, outmask=Caps.LATITUDE_LONGITUDE):
185 '''Solve the I{direct rhumb} problem, optionally with area.
187 @arg lat1: Latitude of the first point (C{degrees90}).
188 @arg lon1: Longitude of the first point (C{degrees180}).
189 @arg azi12: Azimuth of the rhumb line (compass C{degrees}).
190 @arg s12: Distance along the rhumb line from the given to
191 the destination point (C{meter}), can be negative.
193 @return: L{GDict} with 2 up to 8 items C{lat2, lon2, a12, S12,
194 lat1, lon1, azi12, s12} with the destination point's
195 latitude C{lat2} and longitude C{lon2} in C{degrees},
196 the rhumb angle C{a12} in C{degrees} and area C{S12}
197 under the rhumb line in C{meter} I{squared}.
199 @raise ImportError: Package C{numpy} not found or not installed,
200 only required for area C{S12} when C{B{exact}
201 is True} and L{RhumbAux}.
203 @note: If B{C{s12}} is large enough that the rhumb line crosses
204 a pole, the longitude of the second point is indeterminate
205 and C{NAN} is returned for C{lon2} and area C{S12}.
207 @note: If the given point is a pole, the cosine of its latitude is
208 taken to be C{sqrt(L{EPS})}. This position is extremely
209 close to the actual pole and allows the calculation to be
210 carried out in finite terms.
211 '''
212 a12 = _over(s12, self._mpd)
213 return self._DirectRhumb(lat1, lon1, azi12, a12, s12, outmask)
215 def Direct8(self, lat1, lon1, azi12, s12, outmask=Caps.LATITUDE_LONGITUDE_AREA):
216 '''Like method L{Rhumb.Direct} but returning a L{Rhumb8Tuple} with area C{S12}.
217 '''
218 return self.Direct(lat1, lon1, azi12, s12, outmask=outmask).toRhumb8Tuple()
220 def _DirectLine(self, ll1, azi12, **caps_name):
221 '''(INTERNAL) Short-cut version, see .latlonBase.
222 '''
223 return self.DirectLine(ll1.lat, ll1.lon, azi12, **caps_name)
225 def DirectLine(self, lat1, lon1, azi12, **caps_name):
226 '''Define a C{RhumbLine} in terms of the I{direct} rhumb
227 problem to compute several points on a single rhumb line.
229 @arg lat1: Latitude of the first point (C{degrees90}).
230 @arg lon1: Longitude of the first point (C{degrees180}).
231 @arg azi12: Azimuth of the rhumb line (compass C{degrees}).
232 @kwarg caps_name: Optional keyword arguments C{B{name}=NN} and
233 C{B{caps}=Caps.STANDARD}, a bit-or'ed combination of
234 L{Caps<pygeodesy.karney.Caps>} values specifying the
235 required capabilities. Include C{Caps.LINE_OFF} if
236 updates to the B{C{rhumb}} should I{not be reflected}
237 in this rhumb line.
239 @return: A C{RhumbLine...} instance and invoke its method
240 C{.Position} to compute each point.
242 @note: Updates to this rhumb are reflected in the returned
243 rhumb line, unless C{B{caps} |= Caps.LINE_OFF}.
244 '''
245 return self._RhumbLine(self, lat1, lon1, azi12, **caps_name)
247 Line = DirectLine # synonyms
249 def _DirectRhumb(self, lat1, lon1, azi12, a12, s12, outmask):
250 '''(INTERNAL) See methods C{.ArcDirect} and C{.Direct}.
251 '''
252 rl = self._RhumbLine(self, lat1, lon1, azi12, caps=Caps.LINE_OFF,
253 name=self.name)
254 return rl._Position(a12, s12, outmask | self._debug) # lat2, lon2, S12
256 @Property
257 def ellipsoid(self):
258 '''Get this rhumb's ellipsoid (L{Ellipsoid}).
259 '''
260 return self.datum.ellipsoid
262 @ellipsoid.setter # PYCHOK setter!
263 def ellipsoid(self, a_earth_f):
264 '''Set this rhumb's ellipsoid (L{Ellipsoid}, L{Ellipsoid2}, L{Datum} or
265 L{a_f2Tuple}) or (equatorial) radius and flattening (2-tuple C{(a, f)}).
267 @raise RhumbError: If C{abs(B{f}} exceeds non-zero C{f_max} and C{exact=False}.
268 '''
269 self.datum = _spherical_datum(a_earth_f, Error=RhumbError)
271 @Property
272 def exact(self):
273 '''Get the I{exact} option (C{bool}).
274 '''
275 return self._exact
277 @exact.setter # PYCHOK setter!
278 def exact(self, exact):
279 '''Set the I{exact} option (C{bool}). If C{True}, use I{exact} rhumb
280 expressions, otherwise a series expansion (accurate for oblate or
281 prolate ellipsoids with C{abs(flattening)} below C{f_max}.
283 @raise RhumbError: If C{B{exact}=False} and C{abs(flattening})
284 exceeds non-zero C{f_max}.
286 @see: Option U{B{-s}<https://GeographicLib.SourceForge.io/C++/doc/RhumbSolve.1.html>}
287 and U{ACCURACY<https://GeographicLib.SourceForge.io/C++/doc/RhumbSolve.1.html#ACCURACY>}.
288 '''
289 x = bool(exact)
290 if self._exact != x:
291 self._exactest(x, self.ellipsoid, self.f_max)
292 _update_all_rls(self)
293 self._exact = x
295 def _exactest(self, exact, ellipsoid, f_max):
296 # Helper for property setters C{ellipsoid}, C{exact} and C{f_max}
297 if fabs(ellipsoid.f) > f_max > 0 and not exact:
298 raise RhumbError(exact=exact, f=ellipsoid.f, f_max=f_max)
300 @Property_RO
301 def f(self):
302 '''Get the C{ellipsoid}'s flattening (C{float}).
303 '''
304 return self.ellipsoid.f
306 flattening = f
308 @property
309 def f_max(self):
310 '''Get the I{max.} flattening (C{float}).
311 '''
312 return self._f_max
314 @f_max.setter # PYCHOK setter!
315 def f_max(self, f_max): # PYCHOK no cover
316 '''Set the I{max.} flattening, not to exceed (C{float}).
318 @raise RhumbError: If C{exact=False} and C{abs(flattening})
319 exceeds non-zero C{f_max}.
320 '''
321 f = Float_(f_max=f_max, low=_0_0, high=EPS1)
322 if self._f_max != f:
323 self._exactest(self.exact, self.ellipsoid, f)
324 self._f_max = f
326 def _Inverse(self, ll1, ll2, wrap, **outmask):
327 '''(INTERNAL) Short-cut version, see .latlonBase.rhumb....
328 '''
329 if wrap:
330 ll2 = _unrollon(ll1, _Wrap.point(ll2))
331 return self.Inverse(ll1.lat, ll1.lon, ll2.lat, ll2.lon, **outmask)
333 def Inverse(self, lat1, lon1, lat2, lon2, outmask=Caps.AZIMUTH_DISTANCE):
334 '''Solve the I{inverse rhumb} problem.
336 @arg lat1: Latitude of the first point (C{degrees90}).
337 @arg lon1: Longitude of the first point (C{degrees180}).
338 @arg lat2: Latitude of the second point (C{degrees90}).
339 @arg lon2: Longitude of the second point (C{degrees180}).
341 @return: L{GDict} with 4 to 9 items C{lat1, lon1, lat2, lon2,
342 azi12, azi21, s12, a12, S12}, the rhumb line's azimuth
343 C{azi12} and I{reverse} azimuth C{azi21}, both in
344 compass C{degrees} between C{-180} and C{+180}, the
345 rhumb distance C{s12} and rhumb angle C{a12} between
346 both points in C{meter} respectively C{degrees} and
347 the area C{S12} under the rhumb line in C{meter}
348 I{squared}.
350 @raise ImportError: Package C{numpy} not found or not installed,
351 only required for L{RhumbAux} area C{S12}
352 when C{B{exact} is True}.
354 @note: The shortest rhumb line is found. If the end points are
355 on opposite meridians, there are two shortest rhumb lines
356 and the East-going one is chosen.
358 @note: If either point is a pole, the cosine of its latitude is
359 taken to be C{sqrt(L{EPS})}. This position is extremely
360 close to the actual pole and allows the calculation to be
361 carried out in finite terms.
362 '''
363 r = GDict(lat1=lat1, lon1=lon1, lat2=lat2, lon2=lon2, name=self.name)
364 Cs = Caps
365 if (outmask & Cs.AZIMUTH_DISTANCE_AREA):
366 lon12, _ = _diff182(lon1, lon2, K_2_0=True)
367 y, x, s1, s2 = self._Inverse4(lon12, r, outmask)
368 if (outmask & Cs.AZIMUTH):
369 z = _atan2d(y, x)
370 r.set_(azi12=z, azi21=_azireversed(z))
371 if (outmask & Cs.AREA):
372 S12 = self._S12d(s1, s2, lon12)
373 r.set_(S12=unsigned0(S12)) # like .gx
374 return r
376 def _Inverse4(self, lon12, r, outmask): # PYCHOK no cover
377 '''(INTERNAL) I{Must be overloaded}.'''
378 self._notOverloaded(lon12, r, Caps.toStr(outmask)) # underOK=True
380 def Inverse8(self, lat1, lon1, azi12, s12, outmask=Caps.AZIMUTH_DISTANCE_AREA):
381 '''Like method L{Rhumb.Inverse} but returning a L{Rhumb8Tuple} with area C{S12}.
382 '''
383 return self.Inverse(lat1, lon1, azi12, s12, outmask=outmask).toRhumb8Tuple()
385 def _InverseLine(self, ll1, ll2, wrap, **caps_name):
386 '''(INTERNAL) Short-cut version, see .latlonBase.
387 '''
388 if wrap:
389 ll2 = _unrollon(ll1, _Wrap.point(ll2))
390 return self.InverseLine(ll1.lat, ll1.lon, ll2.lat, ll2.lon, **caps_name)
392 def InverseLine(self, lat1, lon1, lat2, lon2, **caps_name):
393 '''Define a C{RhumbLine} in terms of the I{inverse} rhumb problem.
395 @arg lat1: Latitude of the first point (C{degrees90}).
396 @arg lon1: Longitude of the first point (C{degrees180}).
397 @arg lat2: Latitude of the second point (C{degrees90}).
398 @arg lon2: Longitude of the second point (C{degrees180}).
399 @kwarg caps_name: Optional keyword arguments C{B{name}=NN} and
400 C{B{caps}=Caps.STANDARD}, a bit-or'ed combination of
401 L{Caps<pygeodesy.karney.Caps>} values specifying the
402 required capabilities. Include C{Caps.LINE_OFF} if
403 updates to the B{C{rhumb}} should I{not be reflected}
404 in this rhumb line.
406 @return: A C{RhumbLine...} instance and invoke its method
407 C{ArcPosition} or C{Position} to compute points.
409 @note: Updates to this rhumb are reflected in the returned
410 rhumb line, unless C{B{caps} |= Caps.LINE_OFF}.
411 '''
412 r = self.Inverse(lat1, lon1, lat2, lon2, outmask=Caps.AZIMUTH)
413 return self._RhumbLine(self, lat1, lon1, r.azi12, **caps_name)
415 @Property_RO
416 def _mpd(self): # PYCHOK no cover
417 '''(INTERNAL) I{Must be overloaded}.'''
418 _MODS.named.notOverloaded(self)
420 @property_RO
421 def RAorder(self):
422 '''Get the I{Rhumb Area} order, C{None} always.
423 '''
424 return None
426 @property_RO
427 def _RhumbLine(self): # PYCHOK no cover
428 '''(INTERNAL) I{Must be overloaded}.'''
429 self._notOverloaded(underOK=True)
431 def _S12d(self, s1, s2, lon): # PYCHOK no cover
432 '''(INTERNAL) I{Must be overloaded}.'''
433 self._notOverloaded(s1, s2, lon) # underOK=True
435 @Property
436 def TMorder(self):
437 '''Get the L{KTransverseMercator} order (C{int}, 4, 5, 6, 7 or 8).
438 '''
439 return self._mTM
441 @TMorder.setter # PYCHOK setter!
442 def TMorder(self, order):
443 '''Set the L{KTransverseMercator} order (C{int}, 4, 5, 6, 7 or 8).
445 @note: Setting C{TMorder} turns property C{exact} off, but only
446 for L{Rhumb} instances.
447 '''
448 m = _Xorder(_MODS.ktm._AlpCoeffs, RhumbError, TMorder=order)
449 if self._mTM != m:
450 _update_all_rls(self)
451 self._mTM = m
452 if self.exact and isinstance(self, _MODS.rhumb.ekx.Rhumb):
453 self.exact = False
455 def toStr(self, prec=6, sep=_COMMASPACE_, **unused): # PYCHOK signature
456 '''Return this C{Rhumb} as string.
458 @kwarg prec: The C{float} precision, number of decimal digits (0..9).
459 Trailing zero decimals are stripped for B{C{prec}} values
460 of 1 and above, but kept for negative B{C{prec}} values.
461 @kwarg sep: Separator to join (C{str}).
463 @return: Tuple items (C{str}).
464 '''
465 d = dict(ellipsoid=self.ellipsoid, RAorder=self.RAorder,
466 exact=self.exact, TMorder=self.TMorder)
467 return sep.join(pairs(itemsorted(d, asorted=False), prec=prec))
470class RhumbLineBase(_CapsBase):
471 '''(INTERNAL) Base class for C{rhumb.aux_.RhumbLineAux} and C{rhumb.ekx.RhumbLine}.
472 '''
473 _azi12 = _0_0
474 _calp = _1_0
475# _caps = \
476# _debug = 0
477# _lat1 = \
478# _lon1 = \
479# _lon12 = _0_0
480 _Rhumb = RhumbBase # compatible C{Rhumb} class
481 _rhumb = None # C{Rhumb} instance
482 _salp = \
483 _talp = _0_0
485 def __init__(self, rhumb, lat1, lon1, azi12, caps=Caps.STANDARD, name=NN):
486 '''New C{RhumbLine} or C{RhumbLineAux}.
487 '''
488 _xinstanceof(self._Rhumb, rhumb=rhumb)
490 self._lat1 = _Lat(lat1=_fix90(lat1))
491 self._lon1 = _Lon(lon1= lon1)
492 self._lon12 = _norm180(self._lon1)
493 if azi12: # non-zero, non-None
494 self.azi12 = _norm180(azi12)
496 n = name or rhumb.name
497 if n:
498 self.name=n
500 self._caps = caps
501 self._debug |= (caps | rhumb._debug) & Caps._DEBUG_DIRECT_LINE
502 if (caps & Caps.LINE_OFF): # copy to avoid updates
503 self._rhumb = rhumb.copy(deep=False, name=_under(rhumb.name))
504 else:
505 self._rhumb = rhumb
506 _rls.append(self)
508 def __del__(self): # XXX use weakref?
509 if _rls: # may be empty or None
510 try: # PYCHOK no cover
511 _rls.remove(self)
512 except (TypeError, ValueError):
513 pass
514 self._rhumb = None
515 # _update_all(self) # throws TypeError during Python 2 cleanup
517 def ArcPosition(self, a12, outmask=Caps.LATITUDE_LONGITUDE):
518 '''Compute a point at a given angular distance on this rhumb line.
520 @arg a12: The angle along this rhumb line from its origin to the
521 point (C{degrees}), can be negative.
522 @kwarg outmask: Bit-or'ed combination of L{Caps<pygeodesy.karney.Caps>}
523 values specifying the quantities to be returned.
525 @return: L{GDict} with 4 to 8 items C{azi12, a12, s12, S12, lat2,
526 lon2, lat1, lon1} with latitude C{lat2} and longitude
527 C{lon2} of the point in C{degrees}, the rhumb distance
528 C{s12} in C{meter} from the start point of and the area
529 C{S12} under this rhumb line in C{meter} I{squared}.
531 @raise ImportError: Package C{numpy} not found or not installed,
532 only required for L{RhumbLineAux} area C{S12}
533 when C{B{exact} is True}.
535 @note: If B{C{a12}} is large enough that the rhumb line crosses a
536 pole, the longitude of the second point is indeterminate and
537 C{NAN} is returned for C{lon2} and area C{S12}.
539 If the first point is a pole, the cosine of its latitude is
540 taken to be C{sqrt(L{EPS})}. This position is extremely
541 close to the actual pole and allows the calculation to be
542 carried out in finite terms.
543 '''
544 return self._Position(a12, self.degrees2m(a12), outmask)
546 @Property
547 def azi12(self):
548 '''Get this rhumb line's I{azimuth} (compass C{degrees}).
549 '''
550 return self._azi12
552 @azi12.setter # PYCHOK setter!
553 def azi12(self, azi12):
554 '''Set this rhumb line's I{azimuth} (compass C{degrees}).
555 '''
556 z = _norm180(azi12)
557 if self._azi12 != z:
558 if self._rhumb:
559 _update_all(self)
560 self._azi12 = z
561 self._salp, self._calp = t = sincos2d(z) # no NEG0
562 self._talp = _over(*t)
564 @property_RO
565 def azi12_sincos2(self): # PYCHOK no cover
566 '''Get the sine and cosine of this rhumb line's I{azimuth} (2-tuple C{(sin, cos)}).
567 '''
568 return self._scalp, self._calp
570 @property_RO
571 def datum(self):
572 '''Get this rhumb line's datum (L{Datum}).
573 '''
574 return self.rhumb.datum
576 def degrees2m(self, angle):
577 '''Convert an angular distance along this rhumb line to C{meter}.
579 @arg angle: Angular distance (C{degrees}).
581 @return: Distance (C{meter}).
582 '''
583 return float(angle) * self.rhumb._mpd
585 @deprecated_method
586 def distance2(self, lat, lon): # PYCHOK no cover
587 '''DEPRECATED on 23.09.23, use method L{RhumbLineAux.Inverse} or L{RhumbLine.Inverse}.
589 @return: A L{Distance2Tuple}C{(distance, initial)} with the C{distance}
590 in C{meter} and C{initial} bearing (azimuth) in C{degrees}.
591 '''
592 r = self.Inverse(lat, lon)
593 return Distance2Tuple(r.s12, r.azi12)
595 @property_RO
596 def ellipsoid(self):
597 '''Get this rhumb line's ellipsoid (L{Ellipsoid}).
598 '''
599 return self.rhumb.ellipsoid
601 @property_RO
602 def exact(self):
603 '''Get this rhumb line's I{exact} option (C{bool}).
604 '''
605 return self.rhumb.exact
607 def Intersecant2(self, lat0, lon0, radius, napier=True, **tol_eps):
608 '''Compute the intersection(s) of this rhumb line and a circle.
610 @arg lat0: Latitude of the circle center (C{degrees}).
611 @arg lon0: Longitude of the circle center (C{degrees}).
612 @arg radius: Radius of the circle (C{meter}, conventionally).
613 @kwarg napier: If C{True}, apply I{Napier}'s spherical triangle
614 instead of planar trigonometry (C{bool}).
615 @kwarg tol_eps: Optional keyword arguments, see method
616 method L{Intersection} for further details.
618 @return: 2-Tuple C{(P, Q)} with both intersections (representing
619 a rhumb chord), each a L{GDict} from method L{Intersection}
620 extended to 18 items by C{lat3, lon3, azi03, a03, s03}
621 with azimuth C{azi03} of, distance C{a03} in C{degrees}
622 and C{s03} in C{meter} along the rhumb line from the circle
623 C{lat0, lon0} to the chord center C{lat3, lon3}. If this
624 rhumb line is tangential to the circle, both points
625 are the same L{GDict} instance with distances C{s02} and
626 C{s03} near-equal to the B{C{radius}}.
628 @raise IntersectionError: The circle and this rhumb line
629 do not intersect.
631 @raise UnitError: Invalid B{C{radius}}.
632 '''
633 r = Radius_(radius)
634 p = q = self.PlumbTo(lat0, lon0, exact=None, **tol_eps)
635 a = q.s02
636 t = dict(lat3=q.lat2, lon3=q.lon2, azi03=q.azi02, a03=q.a02, s03=a)
637 if a < r:
638 t.update(iteration=q.iteration, lat0=q.lat1, lon0=q.lon1, # or lat0, lon0
639 name=typename(self.Intersecant2, self.name))
640 if fabs(a) < EPS0: # coincident centers
641 d, h = _0_0, r
642 else:
643 d = q.s12
644 if napier: # Napier rule (R1) cos(b) = cos(c) / cos(a)
645 # <https://WikiPedia.org/wiki/Spherical_trigonometry>
646 m = self.rhumb._mpr
647 h = (acos1(cos(r / m) / cos(a / m)) * m) if m else _0_0
648 else:
649 h = _copysign(sqrt_a(r, a), a)
650 p = q = self.Position(d + h).set_(**t)
651 if h:
652 q = self.Position(d - h).set_(**t)
653 elif a > r:
654 t = _too_(Fmt.distant(a))
655 raise IntersectionError(self, lat0, lon0, radius,
656 txt=t, **tol_eps)
657 else: # tangential
658 q.set_(**t) # == p.set(_**t)
659 return p, q
661 @deprecated_method
662 def intersection2(self, other, **tol_eps): # PYCHOK no cover
663 '''DEPRECATED on 23.10.10, use method L{Intersection}.'''
664 p = self.Intersection(other, **tol_eps)
665 r = LatLon2Tuple(p.lat2, p.lon2, name=typename(self.intersection2))
666 r._iteration = p.iteration
667 return r
669 def Intersection(self, other, tol=_TOL, **eps):
670 '''I{Iteratively} find the intersection of this and an other rhumb line.
672 @arg other: The other rhumb line (C{RhumbLine}).
673 @kwarg tol: Tolerance for longitudinal convergence and parallel
674 error (C{degrees}).
675 @kwarg eps: Tolerance for L{pygeodesy.intersection3d3} (C{EPS}).
677 @return: The intersection point, a L{Position}-like L{GDict} with
678 13 items C{lat1, lon1, azi12, a12, s12, lat2, lon2, lat0,
679 lon0, azi02, a02, s02, at} with the rhumb angle C{a02}
680 and rhumb distance C{s02} between the start point C{lat0,
681 lon0} of the B{C{other}} rhumb line and the intersection
682 C{lat2, lon2}, the azimuth C{azi02} of the B{C{other}}
683 rhumb line and the angle C{at} between both rhumb lines.
684 See method L{Position} for further details.
686 @raise IntersectionError: No convergence for this B{C{tol}} or
687 no intersection for an other reason.
689 @see: Methods C{distance2} and C{PlumbTo} and function
690 L{pygeodesy.intersection3d3}.
692 @note: Each iteration involves a round trip to this rhumb line's
693 L{ExactTransverseMercator} or L{KTransverseMercator}
694 projection and function L{pygeodesy.intersection3d3} in
695 that domain.
696 '''
697 _xinstanceof(RhumbLineBase, other=other)
698 _xdatum(self.rhumb, other.rhumb, Error=RhumbError)
699 try:
700 if self.others(other) is self:
701 raise ValueError(_coincident_)
702 # make invariants and globals locals
703 _s_3d, s_az = self._xTM3d, self.azi12
704 _o_3d, o_az = other._xTM3d, other.azi12
705 p = _MODS.formy.opposing(s_az, o_az, margin=tol)
706 if p is not None: # == isbool(p)
707 raise ValueError(_anti_(_parallel_) if p else _parallel_)
708 _diff = euclid # approximate length
709 _i3d3 = _intersect3d3 # NOT .vector3d.intersection3d3
710 _LL2T = LatLon2Tuple
711 _xTMr = self.xTM.reverse # ellipsoidal or spherical
712 # use halfway point as initial estimate
713 p = _LL2T(favg(self.lat1, other.lat1),
714 favg(self.lon1, other.lon1))
715 for i in range(1, _TRIPS):
716 v = _i3d3(_s_3d(p), s_az, # point + bearing
717 _o_3d(p), o_az, useZ=False, **eps)[0]
718 t = _xTMr(v.x, v.y, lon0=p.lon) # PYCHOK Reverse4Tuple
719 d = _diff(t.lon - p.lon, t.lat) # PYCHOK t.lat + p.lat - p.lat
720 p = _LL2T(t.lat + p.lat, t.lon) # PYCHOK t.lon + p.lon = lon0
721 if d < tol: # 19+ trips
722 break
723 else:
724 raise ValueError(Fmt.no_convergence(d, tol))
726 P = GDict(lat1=self.lat1, lat2=p.lat, lat0=other.lat1,
727 lon1=self.lon1, lon2=p.lon, lon0=other.lon1,
728 name=typename(self.Intersection, self.name))
729 r = self.Inverse(p.lat, p.lon, outmask=Caps.DISTANCE)
730 t = other.Inverse(p.lat, p.lon, outmask=Caps.DISTANCE)
731 P.set_(azi12= self.azi12, a12=r.a12, s12=r.s12,
732 azi02=other.azi12, a02=t.a12, s02=t.s12,
733 at=other.azi12 - self.azi12, iteration=i)
734 except Exception as x:
735 raise IntersectionError(self, other, tol=tol,
736 eps=eps, cause=x)
737 return P
739 def Inverse(self, lat2, lon2, wrap=False, **outmask):
740 '''Return the rhumb angle, distance, azimuth, I{reverse} azimuth, etc. of
741 a rhumb line between the given point and this rhumb line's start point.
743 @arg lat2: Latitude of the point (C{degrees}).
744 @arg lon2: Longitude of the points (C{degrees}).
745 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll B{C{lat2}}
746 and B{C{lon2}} (C{bool}).
748 @return: L{GDict} with 8 items C{a12, s12, azi12, azi21, lat1, lon1,
749 lat2, lon2}, the rhumb angle C{a12} and rhumb distance C{s12}
750 between both points in C{degrees} respectively C{meter}, the
751 rhumb line's azimuth C{azi12} and I{reverse} azimuth C{azi21}
752 both in compass C{degrees} between C{-180} and C{+180}.
753 '''
754 if wrap:
755 _, lat2, lon2 = _Wrap.latlon3(self.lon1, _fix90(lat2), lon2, wrap)
756 r = self.rhumb.Inverse(self.lat1, self.lon1, lat2, lon2, **outmask)
757 return r
759 @Property_RO
760 def isLoxodrome(self):
761 '''Is this rhumb line a meridional (C{None}), a parallel
762 (C{False}) or a C{True} loxodrome?
764 @see: I{Osborne's} U{2.5 Rumb lines and loxodromes
765 <https://Zenodo.org/record/35392>}, page 37.
766 '''
767 return bool(self._salp) if self._calp else None
769 @Property_RO
770 def lat1(self):
771 '''Get this rhumb line's latitude (C{degrees90}).
772 '''
773 return self._lat1
775 @Property_RO
776 def lon1(self):
777 '''Get this rhumb line's longitude (C{degrees180}).
778 '''
779 return self._lon1
781 @Property_RO
782 def latlon1(self):
783 '''Get this rhumb line's lat- and longitude (L{LatLon2Tuple}C{(lat, lon)}).
784 '''
785 return LatLon2Tuple(self.lat1, self.lon1)
787 def m2degrees(self, distance):
788 '''Convert a distance along this rhumb line to an angular distance.
790 @arg distance: Distance (C{meter}).
792 @return: Angular distance (C{degrees}).
793 '''
794 return _over(float(distance), self.rhumb._mpd)
796 @property_RO
797 def _mu1(self): # PYCHOK no cover
798 '''(INTERNAL) I{Must be overloaded}.'''
799 self._notOverloaded(underOK=True)
801 def _mu2lat(self, mu2): # PYCHOK no cover
802 '''(INTERNAL) I{Must be overloaded}.'''
803 self._notOverloaded(mu2) # underOK=True
805 @deprecated_method
806 def nearestOn4(self, lat0, lon0, **exact_eps_est_tol): # PYCHOK no cover
807 '''DEPRECATED on 23.10.10, use method L{PlumbTo}.'''
808 P = self.PlumbTo(lat0, lon0, **exact_eps_est_tol)
809 r = _MODS.deprecated.classes.NearestOn4Tuple(P.lat2, P.lon2, P.s12, P.azi02,
810 name=typename(self.nearestOn4))
811 r._iteration = P.iteration
812 return r
814 @deprecated_method
815 def NearestOn(self, lat0, lon0, **exact_eps_est_tol): # PYCHOK no cover
816 '''DEPRECATED on 23.10.30, use method L{PlumbTo}.'''
817 return self.PlumbTo(lat0, lon0, **exact_eps_est_tol)
819 def PlumbTo(self, lat0, lon0, exact=None, eps=EPS, est=None, tol=_TOL):
820 '''Compute the I{perpendicular} intersection of this rhumb line with a geodesic
821 from the given point (transcoded from I{Karney}'s C++ U{rhumb-intercept
822 <https://SourceForge.net/p/geographiclib/discussion/1026620/thread/2ddc295e/>}).
824 @arg lat0: Latitude of the point on the geodesic (C{degrees}).
825 @arg lon0: Longitude of the point on the geodesic (C{degrees}).
826 @kwarg exact: If C{None}, use a rhumb line perpendicular to this rhumb line,
827 otherwise use an I{exact} C{Geodesic...} from the given point
828 perpendicular to this rhumb line (C{bool} or C{Geodesic...}),
829 see method L{geodesic_<pygeodesy.Ellipsoid.geodesic_>}.
830 @kwarg eps: Optional tolerance (C{EPS}), used only if C{B{exact} is None},
831 see function L{intersection3d3<pygeodesy.intersection3d3>}.
832 @kwarg est: Optionally, an initial estimate for the distance C{s12} of the
833 intersection I{along} this rhumb line (C{meter}), used only if
834 C{B{exact} is not None}.
835 @kwarg tol: Longitudinal convergence tolerance (C{degrees}) or distance
836 tolerance (C(meter)) when C{B{exact} is None}, respectively
837 C{not None}.
839 @return: The intersection point on this rhumb line, a L{GDict} from method
840 L{Intersection} if B{C{exact}=None}. If C{B{exact} is not None},
841 a L{Position}-like L{GDict} of 13 items C{azi12, a12, s12, lat2,
842 lat1, lat0, lon2, lon1, lon0, azi0, a02, s02, at} with distance
843 C{a02} in C{degrees} and C{s02} in C{meter} between the given point
844 C{lat0, lon0} and the intersection C{lat2, lon2}, geodesic azimuth
845 C{azi0} at the given point and the (perpendicular) angle C{at}
846 between the geodesic and this rhumb line at the intersection. The
847 I{geodesic} azimuth at the intersection is C{(at + azi12)}. See
848 method L{Position} for further details.
850 @raise ImportError: I{Karney}'s U{geographiclib
851 <https://PyPI.org/project/geographiclib>}
852 package not found or not installed.
854 @raise IntersectionError: No convergence for this B{C{eps}} or B{C{tol}} or
855 no intersection for some other reason.
857 @see: Methods C{distance2}, C{Intersecant2} and C{Intersection} and function
858 L{intersection3d3<pygeodesy.intersection3d3>}.
859 '''
860 Cs, tol = Caps, Float_(tol=tol, low=EPS, high=None)
862# def _over(p, q): # see @note at method C{.Position}
863# if p:
864# p = (p / (q or _copysign(tol, q))) if isfinite(q) else NAN
865# return p
867 if exact is None:
868 z = _norm180(self.azi12 + _90_0) # perpendicular azimuth
869 rl = RhumbLineBase(self.rhumb, lat0, lon0, z, caps=Cs.LINE_OFF)
870 P = self.Intersection(rl, tol=tol, eps=eps)
872 else: # C{rhumb-intercept}
873 E = self.ellipsoid
874 _gI = E.geodesic_(exact=exact).Inverse
875 gm = Cs.STANDARD | Cs._REDUCEDLENGTH_GEODESICSCALE # ^ Cs.DISTANCE_IN
876 if est is None: # get an estimate from the "perpendicular" geodesic
877 r = _gI(self.lat1, self.lon1, lat0, lon0, outmask=Cs.AZIMUTH_DISTANCE)
878 d, _ = _diff182(r.azi2, self.azi12, K_2_0=True)
879 _, s12 = sincos2d(d)
880 s12 *= r.s12 # signed
881 else:
882 s12 = Meter(est=est)
883 try:
884 _abs = fabs
885 _d2 = _diff182
886 _ErT = E.rocPrimeVertical # aka rocTransverse
887 _ovr = _over
888 _S12 = Fsum(s12).fsum2f_
889 _scd = sincos2d_
890 for i in range(1, _TRIPS): # 9+, suffix 1 == C++ 2, 2 == C++ 3
891 P = self.Position(s12) # outmask=Cs.LATITUDE_LONGITUDE
892 r = _gI(lat0, lon0, P.lat2, P.lon2, outmask=gm)
893 d, _ = _d2(self.azi12, r.azi2, K_2_0=True)
894 s, c, s2, c2 = _scd(d, r.lat2)
895 c2 *= _ErT(r.lat2)
896 s *= _ovr(s2 * self._salp, c2) - _ovr(s * r.M21, r.m12)
897 s12, t = _S12(c / s) # XXX _ovr?
898 if _abs(t) < tol: # or _abs(c) < EPS
899 break
900 P.set_(azi0=r.azi1, a02=r.a12, s02=r.s12, # azi2=r.azi2,
901 lat0=lat0, lon0=lon0, iteration=i, at=r.azi2 - self.azi12,
902 name=typename(self.PlumbTo, self.name))
903 except Exception as x: # Fsum(NAN) Value-, ZeroDivisionError
904 raise IntersectionError(lat0=lat0, lon0=lon0, tol=tol, exact=exact,
905 eps=eps, est=est, iteration=i, cause=x)
907 return P
909 def Position(self, s12, outmask=Caps.LATITUDE_LONGITUDE):
910 '''Compute a point at a given distance on this rhumb line.
912 @arg s12: The distance along this rhumb line from its origin to the point
913 (C{meters}), can be negative.
914 @kwarg outmask: Bit-or'ed combination of L{Caps<pygeodesy.karney.Caps>}
915 values specifying the quantities to be returned.
917 @return: L{GDict} with 4 to 8 items C{azi12, a12, s12, S12, lat2, lat1,
918 lon2, lon1} with latitude C{lat2} and longitude C{lon2} of the
919 point in C{degrees}, the rhumb angle C{a12} in C{degrees} from
920 the start point of and the area C{S12} under this rhumb line
921 in C{meter} I{squared}.
923 @raise ImportError: Package C{numpy} not found or not installed, required
924 only for L{RhumbLineAux} area C{S12} when C{B{exact}
925 is True}.
927 @note: If B{C{s12}} is large enough that the rhumb line crosses a pole, the
928 longitude of the second point is indeterminate and C{NAN} is returned
929 for C{lon2} and area C{S12}.
931 If the first point is a pole, the cosine of its latitude is taken to
932 be C{sqrt(L{EPS})}. This position is extremely close to the actual
933 pole and allows the calculation to be carried out in finite terms.
934 '''
935 return self._Position(self.m2degrees(s12), s12, outmask)
937 def _Position(self, a12, s12, outmask):
938 '''(INTERNAL) C{Arc-/Position} helper.
939 '''
940 r = GDict(azi12=self.azi12, a12=a12, s12=s12, name=self.name)
941 Cs = Caps
942 if (outmask & Cs.LATITUDE_LONGITUDE_AREA):
943 if a12 or s12:
944 mu12 = self._calp * a12
945 mu2 = self._mu1 + mu12
946 if fabs(mu2) > 90: # past pole
947 mu2 = _norm180(mu2) # reduce to [-180, 180)
948 if fabs(mu2) > 90: # point on anti-meridian
949 mu2 = _norm180(_loneg(mu2))
950 lat2 = self._mu2lat(mu2)
951 lon2 = S12 = NAN
952 else:
953 lat2, lon2, S1, S2 = self._Position4(a12, mu2, s12, mu12)
954 if (outmask & Cs.AREA):
955 S12 = self.rhumb._S12d(S1, S2, lon2)
956 S12 = unsigned0(S12) # like .gx
957# else:
958# S12 = None # unused
959 if (outmask & Cs.LONGITUDE):
960 if (outmask & Cs.LONG_UNROLL):
961 lon2 += self.lon1
962 else:
963 lon2 = _norm180(self._lon12 + lon2)
964 else: # coincident
965 lat2, lon2 = self.latlon1
966 S12 = _0_0
968 if (outmask & Cs.AREA):
969 r.set_(S12=S12)
970 if (outmask & Cs.LATITUDE):
971 r.set_(lat2=lat2, lat1=self.lat1)
972 if (outmask & Cs.LONGITUDE):
973 r.set_(lon2=lon2, lon1=self.lon1)
974 return r
976 def _Position4(self, a12, mu2, s12, mu12): # PYCHOK no cover
977 '''(INTERNAL) I{Must be overloaded}.'''
978 self._notOverloaded(a12, s12, mu2, mu12) # underOK=True
980 @Property_RO
981 def rhumb(self):
982 '''Get this rhumb line's rhumb (L{RhumbAux} or L{Rhumb}).
983 '''
984 return self._rhumb
986 def toStr(self, prec=6, sep=_COMMASPACE_, **unused): # PYCHOK signature
987 '''Return this C{RhumbLine} as string.
989 @kwarg prec: The C{float} precision, number of decimal digits (0..9).
990 Trailing zero decimals are stripped for B{C{prec}} values
991 of 1 and above, but kept for negative B{C{prec}} values.
992 @kwarg sep: Separator to join (C{str}).
994 @return: C{RhumbLine} (C{str}).
995 '''
996 d = dict(rhumb=self.rhumb, lat1=self.lat1, lon1=self.lon1,
997 azi12=self.azi12, exact=self.exact,
998 TMorder=self.TMorder, xTM=self.xTM)
999 return sep.join(pairs(itemsorted(d, asorted=False), prec=prec))
1001 @property_RO
1002 def TMorder(self):
1003 '''Get this rhumb line's I{Transverse Mercator} order (C{int}, 4, 5, 6, 7 or 8).
1004 '''
1005 return self.rhumb.TMorder
1007 @Property_RO
1008 def xTM(self):
1009 '''Get this rhumb line's I{Transverse Mercator} projection (L{ExactTransverseMercator}
1010 if I{exact} and I{ellipsoidal}, otherwise L{KTransverseMercator} for C{TMorder}).
1011 '''
1012 E = self.ellipsoid
1013 # ExactTransverseMercator doesn't handle spherical earth models
1014 return _MODS.etm.ExactTransverseMercator(E) if self.exact and E.isEllipsoidal else \
1015 _MODS.ktm.KTransverseMercator(E, TMorder=self.TMorder)
1017 def _xTM3d(self, latlon0, z=INT0, V3d=Vector3d):
1018 '''(INTERNAL) C{xTM.forward} this C{latlon1} to C{V3d} with B{C{latlon0}}
1019 as current intersection estimate and central meridian.
1020 '''
1021 t = self.xTM.forward(self.lat1 - latlon0.lat, self.lon1, lon0=latlon0.lon)
1022 return V3d(t.easting, t.northing, z)
1025class _PseudoRhumbLine(RhumbLineBase):
1026 '''(INTERNAL) Pseudo-rhumb line for a geodesic (line), see C{geodesicw._PlumbTo}.
1027 '''
1028 def __init__(self, gl, name=NN):
1029 R = RhumbBase(gl.geodesic.ellipsoid, None, True, name)
1030 RhumbLineBase.__init__(self, R, gl.lat1, gl.lon1, 0, caps=Caps.LINE_OFF)
1031 self._azi1 = self.azi12 = gl.azi1
1032 self._gl = gl
1033 self._gD = gl.geodesic.Direct
1035 def PlumbTo(self, lat0, lon0, **exact_eps_est_tol): # PYCHOK signature
1036 P = RhumbLineBase.PlumbTo(self, lat0, lon0, **exact_eps_est_tol)
1037 z, P = _xkwds_pop2(P, azi12=None)
1038 P.set_(azi1=self._gl.azi1, azi2=z)
1039 return P # geodesic L{Position}
1041 def Position(self, s12, **unused): # PYCHOK signature
1042 r = self._gD(self.lat1, self.lon1, self._azi1, s12)
1043 self._azi1 = r.azi1
1044 self.azi12 = z = r.azi2
1045 self._salp, _ = sincos2d(z)
1046 return r.set_(azi12=z)
1049__all__ += _ALL_DOCS(RhumbBase, RhumbLineBase)
1051if __name__ == _DMAIN_:
1053 from pygeodesy import printf, Rhumb as Rh, RhumbAux as Ah
1054 from pygeodesy.basics import _zip
1055 from pygeodesy.ellipsoids import _EWGS84
1057 Al = Ah(_EWGS84).Line(30, 0, 45)
1058 Rl = Rh(_EWGS84).Line(30, 0, 45)
1060 for i in range(1, 10):
1061 s = .5e6 + 1e6 / i
1062 a = Al.Position(s).lon2
1063 r = Rl.Position(s).lon2
1064 e = (fabs(a - r) / a) if a else 0
1065 printf('# Position.lon2 %.14f vs %.14f, diff %g', r, a, e)
1067 for exact in (None, False, True):
1068 for est in (None, 1e6):
1069 a = Al.PlumbTo(60, 0, exact=exact, est=est)
1070 r = Rl.PlumbTo(60, 0, exact=exact, est=est)
1071 printf('# %s, iteration=%s, exact=%s, est=%s\n# %s, iteration=%s',
1072 a.toRepr(), a.iteration, exact, est,
1073 r.toRepr(), r.iteration, nl=1)
1075 NE_=(71.688899882813, 0.2555198244234, 44095641862956.11)
1076 LHR=(77.7683897102557, 5771083.38332803, 37395209100030.39)
1077 NRT=(-92.38888798169965, 12782581.067684170, -63760642939072.50)
1079 def _ref(fmt, r3, x3):
1080 e3 = []
1081 for r, x in _zip(r3, x3): # strict=True
1082 e = fabs(r - x) / fabs(x)
1083 e3.append('%.g' % (e,))
1084 printf((fmt % r3) + ', rel errors: ' + ', '.join(e3))
1086 for R in (Ah, Rh): # <https://GeographicLib.SourceForge.io/cgi-bin/RhumbSolve -p 9> version 2.2
1087 rh = R(exact=True) # WGS84 default
1088 printf('# %r', rh, nl=1)
1089 r = rh.Direct8(40.6, -73.8, 51, 5.5e6) # from JFK about NE
1090 _ref('# JFK NE lat2=%.12f, lon2=%.12f, S12=%.1f', (r.lat2, r.lon2, r.S12), NE_)
1091 r = rh.Inverse8(40.6, -73.8, 51.6, -0.5) # JFK to LHR
1092 _ref('# JFK-LHR azi12=%.12f, s12=%.3f S12=%.1f', (r.azi12, r.s12, r.S12), LHR)
1093 r = rh.Inverse8(40.6, -73.8, 35.8, 140.3) # JFK to Tokyo Narita
1094 _ref('# JFK-NRT azi12=%.12f, s12=%.3f S12=%.1f', (r.azi12, r.s12, r.S12), NRT)
1096# % python3.10 -m pygeodesy3.rhumb.Bases
1098# Position.lon2 11.61455846901637 vs 11.61455846901637, diff 3.05885e-16
1099# Position.lon2 7.58982302826842 vs 7.58982302826842, diff 2.34045e-16
1100# Position.lon2 6.28526067416369 vs 6.28526067416369, diff 2.82623e-16
1101# Position.lon2 5.63938995325146 vs 5.63938995325146, diff 1.57495e-16
1102# Position.lon2 5.25385527435707 vs 5.25385527435707, diff 0
1103# Position.lon2 4.99764604290380 vs 4.99764604290380, diff 8.88597e-16
1104# Position.lon2 4.81503363740473 vs 4.81503363740473, diff 1.84459e-16
1105# Position.lon2 4.67828821748836 vs 4.67828821748835, diff 5.69553e-16
1106# Position.lon2 4.57205667906283 vs 4.57205667906283, diff 5.82787e-16
1108# 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
1109# 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
1111# 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
1112# 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
1114# 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
1115# 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
1117# 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
1118# 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
1120# 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
1121# 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
1123# 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
1124# 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
1126# RhumbAux(RAorder=None, TMorder=6, ellipsoid=Ellipsoid(name='WGS84', a=6378137, b=6356752.31424518, f_=298.25722356, f=0.00335281, f2=0.00336409, n=0.00167922, e=0.08181919, e2=0.00669438, e21=0.99330562, e22=0.0067395, e32=0.00335843, A=6367449.14582341, L=10001965.72931272, R1=6371008.77141506, R2=6371007.18091847, R3=6371000.79000916, Rbiaxial=6367453.63451633, Rtriaxial=6372797.5559594), exact=True)
1127# JFK NE lat2=71.688899882813, lon2=0.255519824423, S12=44095641862956.1, rel errors: 4e-16, 2e-13, 4e-16
1128# JFK-LHR azi12=77.768389710256, s12=5771083.383 S12=37395209100030.4, rel errors: 5e-16, 3e-16, 8e-16
1129# JFK-NRT azi12=-92.388887981700, s12=12782581.068 S12=-63760642939072.5, rel errors: 0, 1e-16, 7e-16
1131# Rhumb(RAorder=6, TMorder=6, ellipsoid=Ellipsoid(name='WGS84', a=6378137, b=6356752.31424518, f_=298.25722356, f=0.00335281, f2=0.00336409, n=0.00167922, e=0.08181919, e2=0.00669438, e21=0.99330562, e22=0.0067395, e32=0.00335843, A=6367449.14582341, L=10001965.72931272, R1=6371008.77141506, R2=6371007.18091847, R3=6371000.79000916, Rbiaxial=6367453.63451633, Rtriaxial=6372797.5559594), exact=True)
1132# JFK NE lat2=71.688899882813, lon2=0.255519824423, S12=44095641862956.1, rel errors: 2e-16, 1e-13, 5e-16
1133# JFK-LHR azi12=77.768389710256, s12=5771083.383 S12=37395209100030.4, rel errors: 4e-16, 3e-16, 6e-16
1134# JFK-NRT azi12=-92.388887981700, s12=12782581.068 S12=-63760642939072.5, rel errors: 0, 1e-16, 1e-16
1136# **) MIT License
1137#
1138# Copyright (C) 2022-2025 -- mrJean1 at Gmail -- All Rights Reserved.
1139#
1140# Permission is hereby granted, free of charge, to any person obtaining a
1141# copy of this software and associated documentation files (the "Software"),
1142# to deal in the Software without restriction, including without limitation
1143# the rights to use, copy, modify, merge, publish, distribute, sublicense,
1144# and/or sell copies of the Software, and to permit persons to whom the
1145# Software is furnished to do so, subject to the following conditions:
1146#
1147# The above copyright notice and this permission notice shall be included
1148# in all copies or substantial portions of the Software.
1149#
1150# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
1151# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
1152# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
1153# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR
1154# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
1155# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
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