Coverage for pygeodesy/rhumbBase.py: 96%
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2# -*- coding: utf-8 -*-
4u'''Base classes C{RhumbBase} and C{RhumbLineBase}, pure Python version of I{Karney}'s C++
5classes U{Rhumb<https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1Rhumb.html>}
6and U{RhumbLine<https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1RhumbLine.html>}
7from I{GeographicLib versions 2.0} and I{2.2} and I{Karney}'s C++ example U{Rhumb intersect
8<https://SourceForge.net/p/geographiclib/discussion/1026620/thread/2ddc295e/>}.
10Class L{RhumbLine} has been enhanced with methods C{intersection2} and C{nearestOn4} to iteratively
11find the intersection of two rhumb lines, respectively the nearest point on a rumb line along a
12geodesic or perpendicular 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>} (2014-2023) and licensed under the MIT/X11
21License. For more information, see the U{GeographicLib<https://GeographicLib.SourceForge.io>} documentation.
22'''
23# make sure int/int division yields float quotient
24from __future__ import division as _; del _ # PYCHOK semicolon
26# from pygeodesy.basics import _xinstanceof # from .karney
27from pygeodesy.constants import EPS, EPS1, INT0, _EPSqrt as _TOL, \
28 _0_0, _0_01, _1_0, _90_0
29# from pygeodesy.datums import _spherical_datum # from .formy
30# from pygeodesy.ellipsoids import _EWGS84 # from .karney
31from pygeodesy.errors import IntersectionError, itemsorted, RhumbError, \
32 _xdatum, _xkwds, _Xorder
33# from pygeodesy.etm import ExactTransverseMercator # _MODS
34from pygeodesy.fmath import euclid, favg, fabs, Fsum
35from pygeodesy.formy import opposing, _spherical_datum
36# from pygeodesy.fsums import Fsum # from .fmath
37from pygeodesy.interns import NN, _coincident_, _COMMASPACE_, _intersection_, \
38 _no_, _parallel_, _under
39from pygeodesy.karney import Caps, _CapsBase, _diff182, _fix90, _norm180, \
40 _EWGS84, _xinstanceof
41# from pygeodesy.ktm import KTransverseMercator, _AlpCoeffs # _MODS
42from pygeodesy.lazily import _ALL_DOCS, _ALL_MODS as _MODS
43# from pygeodesy.named import notOverloaded # _MODS
44from pygeodesy.namedTuples import Distance2Tuple, LatLon2Tuple, NearestOn4Tuple
45from pygeodesy.props import Property, Property_RO, property_RO, _update_all
46from pygeodesy.streprs import Fmt, pairs, unstr
47from pygeodesy.units import Float_, Lat, Lon, Meter, Int # PYCHOK shared
48from pygeodesy.utily import _loneg, sincos2d, sincos2d_, _unrollon, _Wrap, \
49 sincos2_ # PYCHOK shared
50from pygeodesy.vector3d import _intersect3d3, Vector3d # in .intersection2 below
52# from math import fabs # from .fmath
54__all__ = ()
55__version__ = '23.09.15'
57_rls = [] # instances of C{RbumbLine...} to be updated
58_TRIPS = 65 # .intersection2, .nearestOn4, 19+
61class _Lat(Lat):
62 '''(INTERNAL) Latitude B{C{lat}}.
63 '''
64 def __init__(self, *lat, **Error_name):
65 kwds = _xkwds(Error_name, clip=0, Error=RhumbError)
66 Lat.__new__(_Lat, *lat, **kwds)
69class _Lon(Lon):
70 '''(INTERNAL) Longitude B{C{lon}}.
71 '''
72 def __init__(self, *lon, **Error_name):
73 kwds = _xkwds(Error_name, clip=0, Error=RhumbError)
74 Lon.__new__(_Lon, *lon, **kwds)
77def _update_all_rls(r):
78 '''(INTERNAL) Zap cached/memoized C{Property[_RO]}s
79 of any C{RhumbLine} instances tied to the given
80 C{Rhumb} instance B{C{r}}.
81 '''
82 # _xinstanceof(_MODS.rhumbaux.RhumbAux, _MODS.rhumbx.Rhumb, r=r)
83 _update_all(r)
84 for rl in _rls: # PYCHOK use weakref?
85 if rl._rhumb is r:
86 _update_all(rl)
89class RhumbBase(_CapsBase):
90 '''(INTERNAL) Base class for C{rhumbaux.RhumbAux} and C{rhumbx.Rhumb}.
91 '''
92 _E = _EWGS84
93 _exact = True
94 _f_max = _0_01
95 _mTM = 6 # see .TMorder
97 def __init__(self, a_earth, f, exact, name):
98 '''New C{rhumbaux.RhumbAux} or C{rhumbx.Rhum}.
99 '''
100 if f is not None:
101 self.ellipsoid = a_earth, f
102 elif a_earth not in (_EWGS84, None):
103 self.ellipsoid = a_earth
104 if not exact:
105 self.exact = False
106 if name:
107 self.name = name
109 @Property_RO
110 def a(self):
111 '''Get the C{ellipsoid}'s equatorial radius, semi-axis (C{meter}).
112 '''
113 return self.ellipsoid.a
115 equatoradius = a
117 @Property_RO
118 def b(self):
119 '''Get the C{ellipsoid}'s polar radius, semi-axis (C{meter}).
120 '''
121 return self.ellipsoid.b
123 polaradius = b
125 def _Direct(self, ll1, azi12, s12, **outmask):
126 '''(INTERNAL) Short-cut version, see .latlonBase.
127 '''
128 return self.Direct(ll1.lat, ll1.lon, azi12, s12, **outmask)
130 def Direct(self, lat1, lon1, azi12, s12, outmask=0): # PYCHOK no cover
131 '''I{Must be overloaded}, see function C{notOverloaded}.
132 '''
133 _MODS.named.notOverloaded(self, lat1, lon1, azi12, s12, outmask=outmask)
135 def Direct8(self, lat1, lon1, azi12, s12, outmask=Caps.LATITUDE_LONGITUDE_AREA):
136 '''Like method L{Rhumb.Direct} but returning a L{Rhumb8Tuple} with area C{S12}.
137 '''
138 return self.Direct(lat1, lon1, azi12, s12, outmask=outmask).toRhumb8Tuple()
140 def _DirectLine(self, ll1, azi12, **caps_name):
141 '''(INTERNAL) Short-cut version, see .latlonBase.
142 '''
143 return self.DirectLine(ll1.lat, ll1.lon, azi12, **caps_name)
145 def DirectLine(self, lat1, lon1, azi12, **caps_name):
146 '''Define a C{RhumbLine} in terms of the I{direct} rhumb
147 problem to compute several points on a single rhumb line.
149 @arg lat1: Latitude of the first point (C{degrees90}).
150 @arg lon1: Longitude of the first point (C{degrees180}).
151 @arg azi12: Azimuth of the rhumb line (compass C{degrees}).
152 @kwarg caps_name: Optional keyword arguments C{B{name}=NN} and
153 C{B{caps}=Caps.STANDARD}, a bit-or'ed combination of
154 L{Caps} values specifying the required capabilities.
155 Include C{Caps.LINE_OFF} if updates to the B{C{rhumb}}
156 should I{not} be reflected in this rhumb line.
158 @return: A C{RhumbLine...} instance and invoke its method
159 C{.Position} to compute each point.
161 @note: Updates to this rhumb are reflected in the returned
162 rhumb line, unless C{B{caps} |= Caps.LINE_OFF}.
163 '''
164 return self._RhumbLine(self, lat1=lat1, lon1=lon1, azi12=azi12,
165 **caps_name)
167 Line = DirectLine # synonyms
169 @Property
170 def ellipsoid(self):
171 '''Get this rhumb's ellipsoid (L{Ellipsoid}).
172 '''
173 return self._E
175 @ellipsoid.setter # PYCHOK setter!
176 def ellipsoid(self, a_earth_f):
177 '''Set this rhumb's ellipsoid (L{Ellipsoid}, L{Ellipsoid2}, L{Datum} or
178 L{a_f2Tuple}) or (equatorial) radius and flattening (2-tuple C{(a, f)}).
180 @raise RhumbError: If C{abs(B{f}} exceeds non-zero C{f_max} and C{exact=False}.
181 '''
182 E = _spherical_datum(a_earth_f, Error=RhumbError).ellipsoid
183 if self._E != E:
184 self._exactest(self.exact, E, self.f_max)
185 _update_all_rls(self)
186 self._E = E
188 @Property
189 def exact(self):
190 '''Get the I{exact} option (C{bool}).
191 '''
192 return self._exact
194 @exact.setter # PYCHOK setter!
195 def exact(self, exact):
196 '''Set the I{exact} option (C{bool}). If C{True}, use I{exact} rhumb
197 expressions, otherwise a series expansion (accurate for oblate or
198 prolate ellipsoids with C{abs(flattening)} below C{f_max}.
200 @raise RhumbError: If C{B{exact}=False} and C{abs(flattening})
201 exceeds non-zero C{f_max}.
203 @see: Option U{B{-s}<https://GeographicLib.SourceForge.io/C++/doc/RhumbSolve.1.html>}
204 and U{ACCURACY<https://GeographicLib.SourceForge.io/C++/doc/RhumbSolve.1.html#ACCURACY>}.
205 '''
206 x = bool(exact)
207 if self._exact != x:
208 self._exactest(x, self.ellipsoid, self.f_max)
209 _update_all_rls(self)
210 self._exact = x
212 def _exactest(self, exact, ellipsoid, f_max):
213 # Helper for property setters C{ellipsoid}, C{exact} and C{f_max}
214 if fabs(ellipsoid.f) > f_max > 0 and not exact:
215 raise RhumbError(exact=exact, f=ellipsoid.f, f_max=f_max)
217 @Property_RO
218 def f(self):
219 '''Get the C{ellipsoid}'s flattening (C{float}).
220 '''
221 return self.ellipsoid.f
223 flattening = f
225 @property
226 def f_max(self):
227 '''Get the I{max.} flattening (C{float}).
228 '''
229 return self._f_max
231 @f_max.setter # PYCHOK setter!
232 def f_max(self, f_max): # PYCHOK no cover
233 '''Set the I{max.} flattening, not to exceed (C{float}).
235 @raise RhumbError: If C{exact=False} and C{abs(flattening})
236 exceeds non-zero C{f_max}.
237 '''
238 f = Float_(f_max=f_max, low=_0_0, high=EPS1)
239 if self._f_max != f:
240 self._exactest(self.exact, self.ellipsoid, f)
241 self._f_max = f
243 def _Inverse(self, ll1, ll2, wrap, **outmask):
244 '''(INTERNAL) Short-cut version, see .latlonBase.
245 '''
246 if wrap:
247 ll2 = _unrollon(ll1, _Wrap.point(ll2))
248 return self.Inverse(ll1.lat, ll1.lon, ll2.lat, ll2.lon, **outmask)
250 def Inverse(self, lat1, lon1, lat2, lon2, outmask=0): # PYCHOK no cover
251 '''I{Must be overloaded}, see function C{notOverloaded}.
252 '''
253 _MODS.named.notOverloaded(self, lat1, lon1, lat2, lon2, outmask=outmask)
255 def Inverse8(self, lat1, lon1, azi12, s12, outmask=Caps.AZIMUTH_DISTANCE_AREA):
256 '''Like method L{Rhumb.Inverse} but returning a L{Rhumb8Tuple} with area C{S12}.
257 '''
258 return self.Inverse(lat1, lon1, azi12, s12, outmask=outmask).toRhumb8Tuple()
260 def _InverseLine(self, ll1, ll2, wrap, **caps_name):
261 '''(INTERNAL) Short-cut version, see .latlonBase.
262 '''
263 if wrap:
264 ll2 = _unrollon(ll1, _Wrap.point(ll2))
265 return self.InverseLine(ll1.lat, ll1.lon, ll2.lat, ll2.lon, **caps_name)
267 def InverseLine(self, lat1, lon1, lat2, lon2, **caps_name):
268 '''Define a C{RhumbLine} in terms of the I{inverse} rhumb problem.
270 @arg lat1: Latitude of the first point (C{degrees90}).
271 @arg lon1: Longitude of the first point (C{degrees180}).
272 @arg lat2: Latitude of the second point (C{degrees90}).
273 @arg lon2: Longitude of the second point (C{degrees180}).
274 @kwarg caps_name: Optional keyword arguments C{B{name}=NN} and
275 C{B{caps}=Caps.STANDARD}, a bit-or'ed combination of
276 L{Caps} values specifying the required capabilities.
277 Include C{Caps.LINE_OFF} if updates to the B{C{rhumb}}
278 should I{not} be reflected in this rhumb line.
280 @return: A C{RhumbLine...} instance and invoke its method
281 C{.Position} to compute each point.
283 @note: Updates to this rhumb are reflected in the returned
284 rhumb line, unless C{B{caps} |= Caps.LINE_OFF}.
285 '''
286 r = self.Inverse(lat1, lon1, lat2, lon2, outmask=Caps.AZIMUTH)
287 return self._RhumbLine(self, lat1=lat1, lon1=lon1, azi12=r.azi12,
288 **caps_name)
290 @Property_RO
291 def _RhumbLine(self): # PYCHOK no cover
292 '''I{Must be overloaded}, see function C{notOverloaded}.
293 '''
294 _MODS.named.notOverloaded(self)
296 def _TMorder(self, order):
297 '''(INTERNAL) Set the I{Transverse Mercator} order (C{int}).
299 @note: Setting C{TMorder} turns property C{exact} off.
300 '''
301 x = self.exact
302 n = _Xorder(_MODS.ktm._AlpCoeffs, RhumbError, TMorder=order)
303 if self._mTM != n:
304 _update_all_rls(self)
305 self._mTM = n
306 x = False
307 return x
309 def toStr(self, prec=6, sep=_COMMASPACE_, **unused): # PYCHOK no cover
310 '''I{Must be overloaded}, see function C{notOverloaded}.
311 '''
312 _MODS.named.notOverloaded(self, prec=prec, sep=sep)
315class RhumbLineBase(RhumbBase):
316 '''(INTERNAL) Class C{RhumbLine}
317 '''
318 _azi12 = _0_0
319# _caps = 0
320# _debug = 0
321# _lat1 = _0_0
322# _lon1 = _0_0
323# _lon12 = _0_0
324 _salp = _0_0
325 _calp = _1_0
326 _Rhumb = RhumbBase # compatible C{Rhumb} class
327 _rhumb = None # C{Rhumb} instance
329 def __init__(self, rhumb, lat1, lon1, azi12, caps=Caps.STANDARD, name=NN):
330 '''New C{RhumbLine}.
331 '''
332 _xinstanceof(self._Rhumb, rhumb=rhumb)
334 self._lat1 = _Lat(lat1=_fix90(lat1))
335 self._lon1 = _Lon(lon1= lon1)
336 self._lon12 = _norm180(self._lon1)
337 if azi12: # non-zero, non-None
338 self.azi12 = _norm180(azi12)
340 n = name or rhumb.name
341 if n:
342 self.name=n
344 self._caps = caps
345 self._debug |= (caps | rhumb._debug) & Caps._DEBUG_DIRECT_LINE
346 if (caps & Caps.LINE_OFF): # copy to avoid updates
347 self._rhumb = rhumb.copy(deep=False, name=_under(rhumb.name))
348 else:
349 self._rhumb = rhumb
350 _rls.append(self)
352 def __del__(self): # XXX use weakref?
353 if _rls: # may be empty or None
354 try: # PYCHOK no cover
355 _rls.remove(self)
356 except (TypeError, ValueError):
357 pass
358 self._rhumb = None
359 # _update_all(self) # throws TypeError during Python 2 cleanup
361 @Property
362 def azi12(self):
363 '''Get this rhumb line's I{azimuth} (compass C{degrees}).
364 '''
365 return self._azi12
367 @azi12.setter # PYCHOK setter!
368 def azi12(self, azi12):
369 '''Set this rhumb line's I{azimuth} (compass C{degrees}).
370 '''
371 z = _norm180(azi12)
372 if self._azi12 != z:
373 if self._rhumb:
374 _update_all(self)
375 self._azi12 = z
376 self._salp, self._calp = sincos2d(z) # no NEG0
378 @property_RO
379 def azi12_sincos2(self): # PYCHOK no cover
380 '''Get the sine and cosine of this rhumb line's I{azimuth} (2-tuple C{(sin, cos)}).
381 '''
382 return self._scalp, self._calp
384 def distance2(self, lat, lon):
385 '''Return the distance from and (initial) bearing at the given
386 point to this rhumb line's start point.
388 @arg lat: Latitude of the point (C{degrees}).
389 @arg lon: Longitude of the points (C{degrees}).
391 @return: A L{Distance2Tuple}C{(distance, initial)} with the C{distance}
392 in C{meter} and C{initial} bearing in C{degrees}.
394 @see: Methods C{intersection2} and C{nearestOn4} of L{RhumbLineAux} and
395 L{RhumbLine}.
396 '''
397 r = self.rhumb.Inverse(self.lat1, self.lon1, lat, lon)
398# outmask=Caps.AZIMUTH_DISTANCE)
399 return Distance2Tuple(r.s12, r.azi12)
401 @property_RO
402 def ellipsoid(self):
403 '''Get this rhumb line's ellipsoid (L{Ellipsoid}).
404 '''
405 return self.rhumb.ellipsoid
407 @property_RO
408 def exact(self):
409 '''Get this rhumb line's I{exact} option (C{bool}).
410 '''
411 return self.rhumb.exact
413 def intersection2(self, other, tol=_TOL, **eps):
414 '''I{Iteratively} find the intersection of this and an other rhumb line.
416 @arg other: The other rhumb line (C{RhumbLine}).
417 @kwarg tol: Tolerance for longitudinal convergence and parallel
418 error (C{degrees}).
419 @kwarg eps: Tolerance for L{pygeodesy.intersection3d3} (C{EPS}).
421 @return: A L{LatLon2Tuple}{(lat, lon)} with the C{lat}- and
422 C{lon}gitude of the intersection point.
424 @raise IntersectionError: No convergence for this B{C{tol}} or
425 no intersection for an other reason.
427 @see: Methods C{distance2} and C{nearestOn4} and function
428 L{pygeodesy.intersection3d3}.
430 @note: Each iteration involves a round trip to this rhumb line's
431 L{ExactTransverseMercator} or L{KTransverseMercator}
432 projection and invoking function L{pygeodesy.intersection3d3}
433 in that domain.
434 '''
435 _xinstanceof(RhumbLineBase, other=other)
436 _xdatum(self.rhumb, other.rhumb, Error=RhumbError)
437 try:
438 if other is self:
439 raise ValueError(_coincident_)
440 # make invariants and globals locals
441 _s_3d, s_az = self._xTM3d, self.azi12
442 _o_3d, o_az = other._xTM3d, other.azi12
443 t = opposing(s_az, o_az, margin=tol)
444 if t is not None: # == t in (True, False)
445 raise ValueError(_parallel_)
446 _diff = euclid # approximate length
447 _i3d3 = _intersect3d3 # NOT .vector3d.intersection3d3
448 _LL2T = LatLon2Tuple
449 _xTMr = self.xTM.reverse # ellipsoidal or spherical
450 # use halfway point as initial estimate
451 p = _LL2T(favg(self.lat1, other.lat1),
452 favg(self.lon1, other.lon1))
453 for i in range(1, _TRIPS):
454 v = _i3d3(_s_3d(p), s_az, # point + bearing
455 _o_3d(p), o_az, useZ=False, **eps)[0]
456 t = _xTMr(v.x, v.y, lon0=p.lon) # PYCHOK Reverse4Tuple
457 d = _diff(t.lon - p.lon, t.lat) # PYCHOK t.lat + p.lat - p.lat
458 p = _LL2T(t.lat + p.lat, t.lon) # PYCHOK t.lon + p.lon = lon0
459 if d < tol: # 19 trips
460 return _LL2T(p.lat, p.lon, iteration=i, # PYCHOK p...
461 name=self.intersection2.__name__)
462 except Exception as x:
463 raise IntersectionError(_no_(_intersection_), cause=x)
464 t = unstr(self.intersection2, tol=tol, **eps)
465 raise IntersectionError(Fmt.no_convergence(d), txt=t)
467 @Property_RO
468 def isLoxodrome(self):
469 '''Is this rhumb line a loxodrome (C{True} if non-meridional and
470 non-parallel, C{False} if parallel or C{None} if meridional)?
472 @see: I{Osborne's} U{2.5 Rumb lines and loxodromes
473 <https://Zenodo.org/record/35392>}, page 37.
474 '''
475 return bool(self._salp) if self._calp else None
477 @Property_RO
478 def lat1(self):
479 '''Get this rhumb line's latitude (C{degrees90}).
480 '''
481 return self._lat1
483 @Property_RO
484 def lon1(self):
485 '''Get this rhumb line's longitude (C{degrees180}).
486 '''
487 return self._lon1
489 @Property_RO
490 def latlon1(self):
491 '''Get this rhumb line's lat- and longitude (L{LatLon2Tuple}C{(lat, lon)}).
492 '''
493 return LatLon2Tuple(self.lat1, self.lon1)
495 def _mu22(self, mu12, mu1):
496 mu2 = mu12 + mu1
497 x90 = fabs(mu2) > 90
498 if x90: # reduce to [-180, 180)
499 mu2 = _norm180(mu2)
500 if fabs(mu2) > 90: # point on anti-meridian
501 mu2 = _norm180(_loneg(mu2))
502 return mu2, x90
504 def nearestOn4(self, lat, lon, tol=_TOL, exact=None, eps=EPS, est=None):
505 '''I{Iteratively} locate the point on this rhumb line nearest to the
506 given point, in part transcoded from I{Karney}'s C++ U{rhumb-intercept
507 <https://SourceForge.net/p/geographiclib/discussion/1026620/thread/2ddc295e/>}.
509 @arg lat: Latitude of the point (C{degrees}).
510 @arg lon: Longitude of the point (C{degrees}).
511 @kwarg tol: Longitudinal convergence tolerance (C{degrees}) or the
512 distance tolerance (C(meter)) when C{B{exact} is None},
513 respectively C{not None}.
514 @kwarg exact: If C{None}, use a rhumb line perpendicular to this rhumb
515 line, otherwise use an I{exact} C{Geodesic...} from the
516 given point perpendicular to this rhumb line (C{bool} or
517 C{Geodesic...}), see method L{Ellipsoid.geodesic_}.
518 @kwarg eps: Optional tolerance for L{pygeodesy.intersection3d3}
519 (C{EPS}), used only if C{B{exact} is None}.
520 @kwarg est: Optional, initial estimate for the distance C{s13} of
521 the intersection I{along} this rhumb line (C{meter}),
522 used only if C{B{exact} is not None}.
524 @return: A L{NearestOn4Tuple}C{(lat, lon, distance, normal)} with
525 the C{lat}- and C{lon}gitude of the nearest point on and
526 the C{distance} in C{meter} to this rhumb line and the
527 C{normal} azimuth at the intersection.
529 @raise ImportError: I{Karney}'s U{geographiclib
530 <https://PyPI.org/project/geographiclib>}
531 package not found or not installed.
533 @raise IntersectionError: No convergence for this B{C{eps}} or
534 no intersection for an other reason.
536 @see: Methods C{distance2} and C{intersection2} and function
537 L{pygeodesy.intersection3d3}.
538 '''
539 if exact is None:
540 z = _norm180(self.azi12 + _90_0) # perpendicular azimuth
541 rl = RhumbLineBase(self.rhumb, lat, lon, z, caps=Caps.LINE_OFF)
542 p = self.intersection2(rl, tol=tol, eps=eps)
543 t = rl.distance2(p.lat, p.lon)
544 r = NearestOn4Tuple(p.lat, p.lon, t.distance, z,
545 iteration=p.iteration)
546 else: # C{rhumb-intercept}
547 azi = self.azi12
548 szi = self._salp
549 E = self.ellipsoid
550 gX = E.geodesic_(exact=exact)
551 Cs = Caps
552 gm = Cs.AZIMUTH | Cs.LATITUDE_LONGITUDE | Cs.REDUCEDLENGTH | Cs.GEODESICSCALE
553 if est is None: # get an estimate from the perpendicular
554 r = gX.Inverse(self.lat1, self.lon1, lat, lon, outmask=Cs.AZIMUTH_DISTANCE)
555 d, _ = _diff182(r.azi2, azi, K_2_0=True)
556 _, c = sincos2d(d)
557 s12 = c * r.s12 # signed
558 else:
559 s12 = Meter(est=est)
560 try:
561 tol = Float_(tol=tol, low=EPS, high=None)
562 # def _over(p, q): # see @note at RhumbLine[Aux].Position
563 # return (p / (q or _copysign(tol, q))) if isfinite(q) else NAN
565 _s12 = Fsum(s12).fsum2_
566 for i in range(1, _TRIPS): # suffix 1 == C++ 2, 2 == C++ 3
567 p = self.Position(s12) # outmask=Cs.LATITUDE_LONGITUDE
568 r = gX.Inverse(lat, lon, p.lat2, p.lon2, outmask=gm)
569 d, _ = _diff182(azi, r.azi2, K_2_0=True)
570 s, c, s2, c2 = sincos2d_(d, r.lat2)
571 c2 *= E.rocPrimeVertical(r.lat2) # aka rocTransverse
572 s *= (s2 * szi / c2) - (s * r.M21 / r.m12) # XXX _over?
573 s12, t = _s12(c / s) # XXX _over?
574 if fabs(t) < tol: # or fabs(c) < EPS
575 break
576 r = NearestOn4Tuple(r.lat2, r.lon2, s12, r.azi2,
577 iteration=i)
578 except Exception as x: # Fsum(NAN) Value-, ZeroDivisionError
579 raise IntersectionError(_no_(_intersection_), cause=x)
580 return r
582 def Position(self, s12, outmask=0): # PYCHOK no cover
583 '''I{Must be overloaded}, see function C{notOverloaded}.
584 '''
585 _MODS.named.notOverloaded(self, s12, outmask=outmask)
587 @Property_RO
588 def rhumb(self):
589 '''Get this rhumb line's rhumb (L{RhumbAux} or L{Rhumb}).
590 '''
591 return self._rhumb
593 def toStr(self, prec=6, sep=_COMMASPACE_, **unused): # PYCHOK signature
594 '''Return this C{RhumbLine} as string.
596 @kwarg prec: The C{float} precision, number of decimal digits (0..9).
597 Trailing zero decimals are stripped for B{C{prec}} values
598 of 1 and above, but kept for negative B{C{prec}} values.
599 @kwarg sep: Separator to join (C{str}).
601 @return: C{RhumbLine} (C{str}).
602 '''
603 d = dict(rhumb=self.rhumb, lat1=self.lat1, lon1=self.lon1,
604 azi12=self.azi12, exact=self.exact,
605 TMorder=self.TMorder, xTM=self.xTM)
606 return sep.join(pairs(itemsorted(d, asorted=False), prec=prec))
608 @property_RO
609 def TMorder(self):
610 '''Get this rhumb line's I{Transverse Mercator} order (C{int}, 4, 5, 6, 7 or 8).
611 '''
612 return self.rhumb.TMorder
614 @Property_RO
615 def xTM(self):
616 '''Get this rhumb line's I{Transverse Mercator} projection (L{ExactTransverseMercator}
617 if I{exact} and I{ellipsoidal}, otherwise L{KTransverseMercator} for C{TMorder}).
618 '''
619 E = self.ellipsoid
620 # ExactTransverseMercator doesn't handle spherical earth models
621 return _MODS.etm.ExactTransverseMercator(E) if self.exact and E.isEllipsoidal else \
622 _MODS.ktm.KTransverseMercator(E, TMorder=self.TMorder)
624 def _xTM3d(self, latlon0, z=INT0, V3d=Vector3d):
625 '''(INTERNAL) C{xTM.forward} this C{latlon1} to C{V3d} with B{C{latlon0}}
626 as current intersection estimate and central meridian.
627 '''
628 t = self.xTM.forward(self.lat1 - latlon0.lat, self.lon1, lon0=latlon0.lon)
629 return V3d(t.easting, t.northing, z)
632__all__ += _ALL_DOCS(RhumbBase, RhumbLineBase)
635if __name__ == '__main__':
637 from pygeodesy import printf, Rhumb as R, RhumbAux as A
639 A = A(_EWGS84).Line(30, 0, 45)
640 R = R(_EWGS84).Line(30, 0, 45)
642 for i in range(1, 10):
643 s = .5e6 + 1e6 / i
644 a = A.Position(s).lon2
645 r = R.Position(s).lon2
646 e = (fabs(a - r) / a) if a else 0
647 printf('Position.lon2 %.14f vs %.14f, diff %g', r, a, e)
649 for exact in (None, False, True, None):
650 for est in (None, 1e6):
651 a = A.nearestOn4(60, 0, exact=exact, est=est)
652 r = R.nearestOn4(60, 0, exact=exact, est=est)
653 printf('%s, iteration=%s, exact=%s, est=%s\n%s, iteration=%s',
654 a.toRepr(), a.iteration, exact, est,
655 r.toRepr(), r.iteration, nl=1)
657# % python3 -m pygeodesy.rhumbBase
659# Position.lon2 11.61455846901637 vs 11.61455846901637, diff 3.05885e-16
660# Position.lon2 7.58982302826842 vs 7.58982302826842, diff 2.34045e-16
661# Position.lon2 6.28526067416369 vs 6.28526067416369, diff 1.41311e-16
662# Position.lon2 5.63938995325146 vs 5.63938995325146, diff 1.57495e-16
663# Position.lon2 5.25385527435707 vs 5.25385527435707, diff 3.38105e-16
664# Position.lon2 4.99764604290380 vs 4.99764604290380, diff 8.88597e-16
665# Position.lon2 4.81503363740473 vs 4.81503363740473, diff 1.84459e-16
666# Position.lon2 4.67828821748836 vs 4.67828821748835, diff 5.69553e-16
667# Position.lon2 4.57205667906283 vs 4.57205667906283, diff 1.94262e-16
669# NearestOn4Tuple(lat=45.0, lon=15.830286, distance=1977981.142985, normal=135.0), iteration=9, exact=None, est=None
670# NearestOn4Tuple(lat=45.0, lon=15.830286, distance=1977981.142985, normal=135.0), iteration=9
672# NearestOn4Tuple(lat=45.0, lon=15.830286, distance=1977981.142985, normal=135.0), iteration=9, exact=None, est=1000000.0
673# NearestOn4Tuple(lat=45.0, lon=15.830286, distance=1977981.142985, normal=135.0), iteration=9
675# NearestOn4Tuple(lat=49.634582, lon=25.767876, distance=3083112.636236, normal=135.0), iteration=5, exact=False, est=None
676# NearestOn4Tuple(lat=49.634582, lon=25.767876, distance=3083112.636236, normal=135.0), iteration=5
678# NearestOn4Tuple(lat=49.634582, lon=25.767876, distance=3083112.636236, normal=135.0), iteration=7, exact=False, est=1000000.0
679# NearestOn4Tuple(lat=49.634582, lon=25.767876, distance=3083112.636236, normal=135.0), iteration=7
681# NearestOn4Tuple(lat=49.634582, lon=25.767876, distance=3083112.636236, normal=135.0), iteration=5, exact=True, est=None
682# NearestOn4Tuple(lat=49.634582, lon=25.767876, distance=3083112.636236, normal=135.0), iteration=5
684# NearestOn4Tuple(lat=49.634582, lon=25.767876, distance=3083112.636236, normal=135.0), iteration=7, exact=True, est=1000000.0
685# NearestOn4Tuple(lat=49.634582, lon=25.767876, distance=3083112.636236, normal=135.0), iteration=7
687# NearestOn4Tuple(lat=45.0, lon=15.830286, distance=1977981.142985, normal=135.0), iteration=9, exact=None, est=None
688# NearestOn4Tuple(lat=45.0, lon=15.830286, distance=1977981.142985, normal=135.0), iteration=9
690# NearestOn4Tuple(lat=45.0, lon=15.830286, distance=1977981.142985, normal=135.0), iteration=9, exact=None, est=1000000.0
691# NearestOn4Tuple(lat=45.0, lon=15.830286, distance=1977981.142985, normal=135.0), iteration=9
693# **) MIT License
694#
695# Copyright (C) 2022-2023 -- mrJean1 at Gmail -- All Rights Reserved.
696#
697# Permission is hereby granted, free of charge, to any person obtaining a
698# copy of this software and associated documentation files (the "Software"),
699# to deal in the Software without restriction, including without limitation
700# the rights to use, copy, modify, merge, publish, distribute, sublicense,
701# and/or sell copies of the Software, and to permit persons to whom the
702# Software is furnished to do so, subject to the following conditions:
703#
704# The above copyright notice and this permission notice shall be included
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707# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
708# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
709# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
710# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR
711# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
712# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
713# OTHER DEALINGS IN THE SOFTWARE.