Coverage for pygeodesy/geodesicw.py: 90%
210 statements
« prev ^ index » next coverage.py v7.2.2, created at 2024-03-08 13:06 -0500
« prev ^ index » next coverage.py v7.2.2, created at 2024-03-08 13:06 -0500
2# -*- coding: utf-8 -*-
4u'''Wrapper around Python classes C{geodesic.Geodesic} and C{geodesicline.GeodesicLine} from
5I{Karney}'s Python package U{geographiclib<https://PyPI.org/project/geographiclib>}, provided
6that package is installed.
8The I{wrapped} class methods return a L{GDict} instance offering access to the C{dict} items
9either by C{key} or by C{attribute} name.
11With env variable C{PYGEODESY_GEOGRAPHICLIB} left undefined or set to C{"2"}, this module,
12L{pygeodesy.geodesicx} and L{pygeodesy.karney} will use U{GeographicLib 2.0
13<https://GeographicLib.SourceForge.io/C++/doc/>} transcoding, otherwise C{1.52} or older.
14'''
16from pygeodesy.basics import _copysign, _xinstanceof
17from pygeodesy.constants import EPS, NAN, _EPSqrt as _TOL, _0_5
18from pygeodesy.datums import _earth_datum, _WGS84, _EWGS84
19# from pygeodesy.dms import F_D # from .latlonBase
20# from pygeodesy.ellipsoids import _EWGS84 # from .datums
21from pygeodesy.errors import IntersectionError, GeodesicError
22from pygeodesy.fsums import Fsum, Fmt, unstr
23from pygeodesy.interns import NN, _DOT_, _dunder_nameof, _SPACE_, \
24 _to_, _too_,_under
25from pygeodesy.karney import _atan2d, Caps, Direct9Tuple, GDict, \
26 _kWrapped, Inverse10Tuple
27from pygeodesy.latlonBase import LatLonBase as _LLB, F_D, Radius_
28from pygeodesy.lazily import _ALL_LAZY, _ALL_MODS as _MODS
29from pygeodesy.named import callername, classname
30from pygeodesy.namedTuples import Destination3Tuple, Distance3Tuple
31from pygeodesy.props import Property, Property_RO, property_RO
32# from pygeodesy.streprs import Fmt, unstr # from .fsums
33# from pygeodesy.units import Radius_ # from .latlonBase
34from pygeodesy.utily import _unrollon, _Wrap, wrap360, fabs # PYCHOK used!
36from contextlib import contextmanager
37# from math import fabs # from .utily
39__all__ = _ALL_LAZY.geodesicw
40__version__ = '24.02.21'
42_plumb_ = 'plumb'
43_TRIPS = 65
46class _gWrapped(_kWrapped):
47 ''''(INTERNAL) Wrapper for some of I{Karney}'s U{geographiclib
48 <https://PyPI.org/project/geographiclib>} classes.
49 '''
51 @Property_RO # MCCABE 24
52 def Geodesic(self):
53 '''Get the I{wrapped} C{geodesic.Geodesic} class from I{Karney}'s Python
54 U{geographiclib<https://GitHub.com/geographiclib/geographiclib-python>},
55 provided the latter is installed.
56 '''
57 _Geodesic = self.geographiclib.Geodesic
58 # assert Caps._STD == _Geodesic.STANDARD
60 class Geodesic(_Geodesic):
61 '''I{Wrapper} for I{Karney}'s Python U{geodesic.Geodesic
62 <https://PyPI.org/project/geographiclib>} class.
63 '''
64 _datum = _WGS84
65 _debug = 0 # like .geodesicx.bases._GeodesicBase
66 LINE_OFF = 0 # in .azimuthal._GnomonicBase and .css.CassiniSoldner
68 def __init__(self, a_ellipsoid=_EWGS84, f=None, name=NN): # PYCHOK signature
69 '''New I{wrapped} C{geodesic.Geodesic} instance.
71 @arg a_ellipsoid: An ellipsoid (L{Ellipsoid}) or datum (L{Datum})
72 or the equatorial radius I{a} of the ellipsoid (C{meter}).
73 @arg f: The flattening of the ellipsoid (C{scalar}), ignored if
74 B{C{a_ellipsoid}) is not specified as C{scalar}.
75 @kwarg name: Optional ellipsoid name (C{str}), ignored like B{C{f}}.
76 '''
77 _earth_datum(self, a_ellipsoid, f=f, name=name) # raiser=NN
78 with _wargs(self, *self.ellipsoid.a_f, name=name) as args:
79 _Geodesic.__init__(self, *args)
81 def ArcDirect(self, lat1, lon1, azi1, a12, outmask=Caps._STD):
82 '''Return the C{_Geodesic.ArcDirect} result as L{GDict}.
83 '''
84 with _wargs(self, lat1, lon1, azi1, a12, outmask) as args:
85 d = _Geodesic.ArcDirect(self, *args)
86 return GDict(d)
88 def ArcDirectLine(self, lat1, lon1, azi1, a12, caps=Caps._STD_LINE):
89 '''Return the C{_Geodesic.ArcDirectLine} as I{wrapped} C{GeodesicLine}.
90 '''
91 return self._GenDirectLine(lat1, lon1, azi1, True, a12, caps)
93 Area = _Geodesic.Polygon # like GeodesicExact.Area
95 @property_RO
96 def datum(self):
97 '''Get this geodesic's datum (C{Datum}).
98 '''
99 return self._datum
101 @Property
102 def debug(self):
103 '''Get the C{debug} option (C{bool}).
104 '''
105 return bool(self._debug)
107 @debug.setter # PYCHOK setter!
108 def debug(self, debug):
109 '''Set the C{debug} option (C{bool}) to include more
110 details in L{GDict} results.
111 '''
112 self._debug = Caps._DEBUG_ALL if debug else 0
114 def Direct(self, lat1, lon1, azi1, s12=0, outmask=Caps._STD):
115 '''Return the C{_Geodesic.Direct} result as L{GDict}.
116 '''
117 with _wargs(self, lat1, lon1, azi1, s12, outmask) as args:
118 d = _Geodesic.Direct(self, *args)
119 return GDict(d)
121 def Direct3(self, lat1, lon1, azi1, s12): # PYCHOK outmask
122 '''Return the destination lat, lon and reverse azimuth
123 in C{degrees} as L{Destination3Tuple}.
124 '''
125 d = self.Direct(lat1, lon1, azi1, s12, outmask=Caps._DIRECT3)
126 return Destination3Tuple(d.lat2, d.lon2, d.azi2)
128 def _DirectLine(self, ll1, azi12, s12=0, **caps_name):
129 '''(INTERNAL) Short-cut version.
130 '''
131 return self.DirectLine(ll1.lat, ll1.lon, azi12, s12, **caps_name)
133 def DirectLine(self, lat1, lon1, azi1, s12, caps=Caps._STD_LINE):
134 '''Return the C{_Geodesic.DirectLine} as I{wrapped} C{GeodesicLine}.
135 '''
136 return self._GenDirectLine(lat1, lon1, azi1, False, s12, caps)
138 @Property_RO
139 def ellipsoid(self):
140 '''Get this geodesic's ellipsoid (C{Ellipsoid}).
141 '''
142 return self.datum.ellipsoid
144 @property_RO
145 def f1(self): # in .css.CassiniSoldner.reset
146 '''Get the geodesic's ellipsoid's I{1 - flattening} (C{float}).
147 '''
148 return getattr(self, _under(Geodesic.f1.name), self.ellipsoid.f1)
150 def _GDictDirect(self, lat, lon, azi, arcmode, s12_a12, outmask=Caps._STD):
151 '''(INTERNAL) Get C{_Geodesic._GenDirect} result as C{GDict}.
152 '''
153 with _wargs(self, lat, lon, azi, arcmode, s12_a12, outmask) as args:
154 t = _Geodesic._GenDirect(self, *args)
155 return Direct9Tuple(t).toGDict() # *t
157 def _GDictInverse(self, lat1, lon1, lat2, lon2, outmask=Caps._STD):
158 '''(INTERNAL) Get C{_Geodesic._GenInverse} result as L{Inverse10Tuple}.
159 '''
160 with _wargs(self, lat1, lon1, lat2, lon2, outmask) as args:
161 t = _Geodesic._GenInverse(self, *args)
162 return Inverse10Tuple(t).toGDict(lon1=lon1, lon2=lon2) # *t
164 def _GenDirectLine(self, lat1, lon1, azi1, arcmode, s12_a12, *caps):
165 '''(INTERNAL) Invoked by C{_Geodesic.DirectLine} and C{-.ArcDirectLine},
166 returning the result as a I{wrapped} C{GeodesicLine}.
167 '''
168 with _wargs(self, lat1, lon1, azi1, arcmode, s12_a12, *caps) as args:
169 t = _Geodesic._GenDirectLine(self, *args)
170 return self._Line13(t)
172 def _Inverse(self, ll1, ll2, wrap, **outmask):
173 '''(INTERNAL) Short-cut version, see .ellipsoidalBaseDI.intersecant2.
174 '''
175 if wrap:
176 ll2 = _unrollon(ll1, _Wrap.point(ll2))
177 return self.Inverse(ll1.lat, ll1.lon, ll2.lat, ll2.lon, **outmask)
179 def Inverse(self, lat1, lon1, lat2, lon2, outmask=Caps._STD):
180 '''Return the C{_Geodesic.Inverse} result as L{GDict}.
181 '''
182 with _wargs(self, lat1, lon1, lat2, lon2, outmask) as args:
183 d = _Geodesic.Inverse(self, *args)
184 return GDict(d)
186 def Inverse1(self, lat1, lon1, lat2, lon2, wrap=False):
187 '''Return the non-negative, I{angular} distance in C{degrees}.
189 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll
190 B{C{lat2}} and BC{lon2}} (C{bool}).
191 '''
192 # see .FrechetKarney.distance, .HausdorffKarney._distance
193 # and .HeightIDWkarney._distances
194 if wrap:
195 _, lat2, lon2 = _Wrap.latlon3(lat1, lat2, lon2, True) # _Geodesic.LONG_UNROLL
196 r = self.Inverse(lat1, lon1, lat2, lon2)
197 # XXX _Geodesic.DISTANCE needed for 'a12'?
198 return fabs(r.a12)
200 def Inverse3(self, lat1, lon1, lat2, lon2): # PYCHOK outmask
201 '''Return the distance in C{meter} and the forward and reverse
202 azimuths in C{degrees} as L{Distance3Tuple}.
203 '''
204 r = self.Inverse(lat1, lon1, lat2, lon2, outmask=Caps._INVERSE3)
205 return Distance3Tuple(r.s12, wrap360(r.azi1), wrap360(r.azi2))
207 def _InverseLine(self, ll1, ll2, wrap, **caps_name):
208 '''(INTERNAL) Short-cut version.
209 '''
210 if wrap:
211 ll2 = _unrollon(ll1, _Wrap.point(ll2))
212 return self.InverseLine(ll1.lat, ll1.lon, ll2.lat, ll2.lon, **caps_name)
214 def InverseLine(self, lat1, lon1, lat2, lon2, caps=Caps._STD_LINE):
215 '''Return the C{_Geodesic.InverseLine} as I{wrapped} C{GeodesicLine}.
216 '''
217 with _wargs(self, lat1, lon1, lat2, lon2, caps) as args:
218 t = _Geodesic.InverseLine(self, *args)
219 return self._Line13(t)
221 def Line(self, lat1, lon1, azi1, caps=Caps._STD_LINE):
222 '''Set up a I{wrapped} C{GeodesicLine} to compute several points
223 along a single, I{wrapped} (this) geodesic.
224 '''
225 return _wrapped.GeodesicLine(self, lat1, lon1, azi1, caps=caps)
227 def _Line13(self, t):
228 '''(INTERNAL) Wrap C{_GeodesicLine}, add distance and arc length
229 to reference point 3.
230 '''
231 gl = _wrapped.GeodesicLine(self, t.lat1, t.lon1, t.azi1, caps=t.caps,
232 salp1=t.salp1, calp1=t.calp1)
233 gl.a13, gl.s13 = t.a13, t.s13
234 return gl
236# Polygon = _Geodesic.Polygon
238 # Geodesic.ArcDirect.__doc__ = _Geodesic.ArcDirect.__doc__
239 # Geodesic.Direct.__doc__ = _Geodesic.Direct.__doc__
240 # Geodesic.Inverse.__doc__ = _Geodesic.Inverse.__doc__
241 # Geodesic.InverseLine.__doc__ = _Geodesic.InverseLinr.__doc__
242 # Geodesic.Line.__doc__ = _Geodesic.Line.__doc__
243 return Geodesic
245 @Property_RO # MCCABE 16
246 def GeodesicLine(self):
247 '''Get the I{wrapped} C{geodesicline.GeodesicLine} class from I{Karney}'s
248 Python U{geographiclib<https://GitHub.com/geographiclib/geographiclib-python>},
249 provided the latter is installed.
250 '''
251 _GeodesicLine = self.geographiclib.GeodesicLine
253 class GeodesicLine(_GeodesicLine):
254 '''I{Wrapper} for I{Karney}'s Python U{geodesicline.GeodesicLine
255 <https://PyPI.org/project/geographiclib>} class.
256 '''
257 _geodesic = None
259 def __init__(self, geodesic, lat1, lon1, azi1, **caps_): # salp1=NAN, calp1=NAN
260 '''New I{wrapped} C{geodesicline.GeodesicLine} instance.
262 @arg geodesic: A I{wrapped} C{Geodesic} instance.
263 @arg lat1: Latitude of the first points (C{degrees}).
264 @arg lon1: Longitude of the first points (C{degrees}).
265 @arg azi1: Azimuth at the first points (compass C{degrees360}).
266 @kwarg caps_: Optional, bit-or'ed combination of L{Caps} values
267 specifying the capabilities the C{GeodesicLine}
268 instance should possess (plus optional keyword
269 arguments C{salp1=NAN} and C{calp1=NAN}).
270 '''
271 _xinstanceof(_wrapped.Geodesic, geodesic=geodesic)
272 with _wargs(self, geodesic, lat1, lon1, azi1, **caps_) as args:
273 _GeodesicLine.__init__(self, *args, **caps_)
274 self._geodesic = geodesic
276 @Property_RO
277 def a1(self):
278 '''Get the I{equatorial arc} (C{degrees}), the arc length between
279 the northward equatorial crossing and point C{(lat1, lon1)}.
281 @see: U{EquatorialArc<https://GeographicLib.SourceForge.io/
282 C++/doc/classGeographicLib_1_1GeodesicLine.html>}
283 '''
284 try:
285 return _atan2d(self._ssig1, self._csig1)
286 except AttributeError:
287 return NAN # see .geodesicx.gxline._GeodesicLineExact
289 equatorarc = a1
291 def Arc(self):
292 '''Return the angular distance to point 3 (C{degrees} or C{NAN}).
293 '''
294 return self.a13
296 def ArcPosition(self, a12, outmask=Caps._STD):
297 '''Return the position at C{B{a12} degrees} on this line.
299 @arg a12: Angular distance from this line's first point
300 (C{degrees}).
302 @see: Method L{Position} for further details.
303 '''
304 with _wargs(self, a12, outmask) as args:
305 d = _GeodesicLine.ArcPosition(self, *args)
306 return GDict(d)
308 @Property_RO
309 def azi0(self): # see .css.CassiniSoldner.forward4
310 '''Get the I{equatorial azimuth} (C{degrees}), the azimuth of the
311 geodesic line as it crosses the equator in a northward direction.
313 @see: U{EquatorialAzimuth<https://GeographicLib.SourceForge.io/
314 C++/doc/classGeographicLib_1_1GeodesicLine.html>}
315 '''
316 try:
317 return _atan2d(self._salp0, self._calp0)
318 except AttributeError:
319 return NAN # see .geodesicx.gxline._GeodesicLineExact
321 equatorazimuth = azi0
323 def Distance(self):
324 '''Return the distance to reference point 3 (C{meter} or C{NAN}).
325 '''
326 return self.s13
328 @property_RO
329 def geodesic(self):
330 '''Get the I{wrapped} geodesic (L{Geodesic}).
331 '''
332 return self._geodesic
334 def Intersecant2(self, lat0, lon0, radius, tol=_TOL):
335 '''Compute the intersection(s) of this geodesic line and a circle.
337 @arg lat0: Latitude of the circle center (C{degrees}).
338 @arg lon0: Longitude of the circle center (C{degrees}).
339 @arg radius: Radius of the circle (C{meter}, conventionally).
340 @kwarg tol: Convergence tolerance (C{scalar}).
342 @return: 2-Tuple C{(P, Q)} with both intersections (representing a
343 geodesic chord), each a L{GDict} from method L{Position}
344 extended to 14 items by C{lon0, lat0, azi0, a02, s02, at}
345 with the circle center C{lat0}, C{lon0}, azimuth C{azi0} at,
346 distance C{a02} in C{degrees} and C{s02} in C{meter} along
347 the geodesic from the circle center to the intersection
348 C{lat2}, C{lon2} and the angle C{at} between the geodesic
349 and this line at the intersection. The I{geodesic} azimuth
350 at the intersection is C{(at + azi2)}. If this line is
351 tangential to the circle, both intersections are the same
352 L{GDict} instance.
354 @raise IntersectionError: The circle and this geodesic line do not
355 intersect.
357 @raise UnitError: Invalid B{C{radius}}.
358 '''
359 return _Intersecant2(self, lat0, lon0, radius, tol=tol)
361 def PlumbTo(self, lat0, lon0, est=None, tol=_TOL):
362 '''Compute the I{perpendicular} intersection of this geodesic line
363 with a geodesic from the given point.
365 @arg lat0: Latitude of the point (C{degrees}).
366 @arg lon0: Longitude of the point (C{degrees}).
367 @kwarg est: Optional, initial estimate for the distance C{s12} of
368 the intersection I{along} this geodesic line (C{meter}).
369 @kwarg tol: Convergence tolerance (C(meter)).
371 @return: The intersection point on this geodesic line, a L{GDict}
372 from method L{Position} extended to 14 items C{lat1, lon1,
373 azi1, lat2, lon2, azi2, a12, s12, lat0, lon0, azi0, a02,
374 s02, at} with C{a02} and C{s02} the distance in C{degrees}
375 and C{meter} from the given point C{lat0, lon0} to the
376 intersection C{lat2, lon2}, azimuth C{azi0} at the given
377 point and the (perpendicular) angle C{at} between the
378 geodesic and this line at the intersection point. The
379 geodesic azimuth at the intersection is C{(at + azi2)}.
380 See method L{Position} for further details.
382 @see: Methods C{Intersecant2}, C{Intersection} and C{Position}.
383 '''
384 return _PlumbTo(self, lat0, lon0, est=est, tol=tol)
386 def Position(self, s12, outmask=Caps._STD):
387 '''Return the position at distance C{B{s12} meter} on this line.
389 @arg s12: Distance from this line's first point (C{meter}).
390 @kwarg outmask: Bit-or'ed combination of L{Caps} values specifying
391 the quantities to be returned.
393 @return: A L{GDict} with up to 12 items C{lat1, lon1, azi1, lat2,
394 lon2, azi2, m12, a12, s12, M12, M21, S12} with C{lat1},
395 C{lon1}, C{azi1} and arc length C{a12} always included,
396 except when C{a12=NAN}.
397 '''
398 with _wargs(self, s12, outmask) as args:
399 d = _GeodesicLine.Position(self, *args)
400 return GDict(d)
402 # GeodesicLine.ArcPosition.__doc__ = _GeodesicLine.ArcPosition.__doc__
403 # GeodesicLine.Position.__doc__ = _GeodesicLine.Position.__doc__
404 return GeodesicLine
406 @Property_RO
407 def Geodesic_WGS84(self):
408 '''Get the I{wrapped} C{Geodesic(WGS84)} singleton, provided the
409 U{geographiclib<https://PyPI.org/project/geographiclib>} package
410 is installed, otherwise an C{ImportError}.
411 '''
412 return _EWGS84.geodesic
414_wrapped = _gWrapped() # PYCHOK singleton, .ellipsoids, .test/base.py
417def Geodesic(a_ellipsoid, f=None, name=NN):
418 '''Return a I{wrapped} C{geodesic.Geodesic} instance from I{Karney}'s
419 Python U{geographiclib<https://PyPI.org/project/geographiclib>},
420 provide the latter is installed, otherwise an C{ImportError}.
422 @arg a_ellipsoid: An ellipsoid (L{Ellipsoid}) or datum (L{Datum})
423 or the equatorial radius I{a} of the ellipsoid (C{meter}).
424 @arg f: The flattening of the ellipsoid (C{scalar}), ignored if
425 B{C{a_ellipsoid}}) is not specified as C{meter}.
426 @kwarg name: Optional ellipsoid name (C{str}), ignored like B{C{f}}.
427 '''
428 return _wrapped.Geodesic(a_ellipsoid, f=f, name=name)
431def GeodesicLine(geodesic, lat1, lon1, azi1, caps=Caps._STD_LINE):
432 '''Return a I{wrapped} C{geodesicline.GeodesicLine} instance from I{Karney}'s
433 Python U{geographiclib<https://PyPI.org/project/geographiclib>}, provided
434 the latter is installed, otherwise an C{ImportError}.
436 @arg geodesic: A I{wrapped} L{Geodesic} instance.
437 @arg lat1: Latitude of the first points (C{degrees}).
438 @arg lon1: Longitude of the first points (C{degrees}).
439 @arg azi1: Azimuth at the first points (compass C{degrees360}).
440 @kwarg caps: Optional, bit-or'ed combination of L{Caps} values
441 specifying the capabilities the C{GeodesicLine}
442 instance should possess, i.e., which quantities can
443 be returned by calls to C{GeodesicLine.Position}
444 and C{GeodesicLine.ArcPosition}.
445 '''
446 return _wrapped.GeodesicLine(geodesic, lat1, lon1, azi1, caps=caps)
449def Geodesic_WGS84():
450 '''Get the I{wrapped} L{Geodesic}C{(WGS84)} singleton, provided
451 U{geographiclib<https://PyPI.org/project/geographiclib>} is
452 installed, otherwise an C{ImportError}.
453 '''
454 return _wrapped.Geodesic_WGS84
457class _wargs(object): # see also .formy._idllmn6, .latlonBase._toCartesian3, .vector2d._numpy
458 '''(INTERNAL) C{geographiclib} caller and exception mapper.
459 '''
460 @contextmanager # <https://www.Python.org/dev/peps/pep-0343/> Examples
461 def __call__(self, inst, *args, **kwds):
462 '''(INTERNAL) Yield C{tuple(B{args})} with any errors raised
463 as L{GeodesicError} embellished with all B{C{kwds}}.
464 '''
465 try:
466 yield args
467 except (AttributeError, TypeError, ValueError) as x:
468 n = _DOT_(classname(inst), callername(up=3, underOK=True))
469 raise GeodesicError(unstr(n, *args, **kwds), cause=x)
471_wargs = _wargs() # PYCHOK singleton
474def _Intersecant2(gl, lat0, lon0, radius, tol=_TOL, form=F_D): # MCCABE in LatLonEllipsoidalBaseDI.intersecant2, .geodesicx.gxline.Intersecant2
475 # (INTERNAL) Return the intersections of a circle at C{lat0, lon0}
476 # and a geodesic line as a 2-Tuple C{(P, Q)}, each a C{GDict}.
477 r = Radius_(radius)
478 n = _dunder_nameof(_Intersecant2)[1:]
479 _P = gl.Position
480 _I = gl.geodesic.Inverse
481 _a = fabs
483 def _R3(s):
484 # radius, intersection, etc. at distance C{s}
485 P = _P(s)
486 d = _I(lat0, lon0, P.lat2, P.lon2)
487 return _a(d.s12), P, d
489 def _bisect2(s, c, Rc, r, tol):
490 _s = Fsum(c).fsumf_
491 for i in range(_TRIPS):
492 b = _s(s)
493 Rb, P, d = _R3(b)
494 if Rb > r:
495 break
496 else: # b >>> s and c >>> s
497 raise ValueError(Fmt.no_convergence(b, s))
498 __2 = _0_5 # Rb > r > Rc
499 for i in range(_TRIPS): # 47-48
500 s = (b + c) * __2
501 R, P, d = _R3(s)
502 if Rb > R > r:
503 b, Rb = s, R
504 elif Rc < R < r:
505 c, Rc = s, R
506 t = _a(b - c)
507 if t < tol: # or _a(R - r) < tol:
508 break
509 else: # t = min(t, _a(R - r))
510 raise ValueError(Fmt.no_convergence(t, tol))
511 i += C.iteration # combine iterations
512 P.set_(lat0=lat0, lon0=lon0, azi0=d.azi1, iteration=i,
513 a02=d.a12, s02=d.s12, at=d.azi2 - P.azi2, name=n)
514 return P, s
516 # get the perpendicular intersection of 2 geodesics,
517 # one the plumb, pseudo-rhumb line to the other
518 C = _PlumbTo(gl, lat0, lon0, tol=tol)
519 try:
520 a = _a(C.s02) # distance between centers
521 if a < r:
522 c = C.s12 # distance along pseudo-rhumb line
523 h = _copysign(r, c) # past half chord length
524 P, p = _bisect2( h, c, a, r, tol)
525 Q, q = _bisect2(-h, c, a, r, tol)
526 if _a(p - q) < max(EPS, tol):
527 Q = P
528 elif a > r:
529 raise ValueError(_too_(Fmt.distant(a)))
530 else: # tangential
531 P = Q = C
532 except Exception as x:
533 t = _LLB(C.lat2, C.lon2).toStr(form=form)
534 t = _SPACE_(x, _plumb_, _to_, Fmt.PAREN(t))
535 raise IntersectionError(t, txt=None, cause=x)
537 return P, Q
540def _PlumbTo(gl, lat0, lon0, est=None, tol=_TOL):
541 # (INTERNAL) Return the I{perpendicular} intersection of
542 # a geodesic from C{(lat0, lon0)} and a geodesic (line).
543 pl = _MODS.rhumb.bases._PseudoRhumbLine(gl)
544 return pl.PlumbTo(lat0, lon0, exact=gl.geodesic,
545 est=est, tol=tol)
547# **) MIT License
548#
549# Copyright (C) 2016-2024 -- mrJean1 at Gmail -- All Rights Reserved.
550#
551# Permission is hereby granted, free of charge, to any person obtaining a
552# copy of this software and associated documentation files (the "Software"),
553# to deal in the Software without restriction, including without limitation
554# the rights to use, copy, modify, merge, publish, distribute, sublicense,
555# and/or sell copies of the Software, and to permit persons to whom the
556# Software is furnished to do so, subject to the following conditions:
557#
558# The above copyright notice and this permission notice shall be included
559# in all copies or substantial portions of the Software.
560#
561# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
562# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
563# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
564# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR
565# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
566# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
567# OTHER DEALINGS IN THE SOFTWARE.