Coverage for pygeodesy/geodesicw.py: 89%
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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, _xkwds_pop2
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__ = '24.04.07'
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
67 _name = NN
69 def __init__(self, a_ellipsoid=_EWGS84, f=None, name=NN): # PYCHOK signature
70 '''New I{wrapped} C{geodesic.Geodesic} instance.
72 @arg a_ellipsoid: The equatorial radius I{a} (C{meter}, conventionally),
73 an ellipsoid (L{Ellipsoid}) or a datum (L{Datum}).
74 @arg f: The ellipsoid's flattening (C{scalar}), ignored if B{C{a_ellipsoid})
75 is not C{meter}.
76 @kwarg name: Optional name (C{str}).
77 '''
78 _earth_datum(self, a_ellipsoid, f=f, name=name) # raiser=NN
79 with _wargs(self, *self.ellipsoid.a_f, name=name) as args:
80 _Geodesic.__init__(self, *args)
81 if name:
82 self._name = str(name)
84 def ArcDirect(self, lat1, lon1, azi1, a12, outmask=Caps._STD):
85 '''Return the C{_Geodesic.ArcDirect} result as L{GDict}.
86 '''
87 with _wargs(self, lat1, lon1, azi1, a12, outmask) as args:
88 d = _Geodesic.ArcDirect(self, *args)
89 return GDict(d)
91 def ArcDirectLine(self, lat1, lon1, azi1, a12, caps=Caps._STD_LINE, **name):
92 '''Return the C{_Geodesic.ArcDirectLine} as I{wrapped} C{GeodesicLine}.
93 '''
94 return self._GenDirectLine(lat1, lon1, azi1, True, a12, caps, **name)
96 Area = _Geodesic.Polygon # like GeodesicExact.Area
98 @property_RO
99 def datum(self):
100 '''Get this geodesic's datum (C{Datum}).
101 '''
102 return self._datum
104 @Property
105 def debug(self):
106 '''Get the C{debug} option (C{bool}).
107 '''
108 return bool(self._debug)
110 @debug.setter # PYCHOK setter!
111 def debug(self, debug):
112 '''Set the C{debug} option (C{bool}) to include more
113 details in L{GDict} results.
114 '''
115 self._debug = Caps._DEBUG_ALL if debug else 0
117 def Direct(self, lat1, lon1, azi1, s12=0, outmask=Caps._STD):
118 '''Return the C{_Geodesic.Direct} result as L{GDict}.
119 '''
120 with _wargs(self, lat1, lon1, azi1, s12, outmask) as args:
121 d = _Geodesic.Direct(self, *args)
122 return GDict(d)
124 def Direct3(self, lat1, lon1, azi1, s12): # PYCHOK outmask
125 '''Return the destination lat, lon and reverse azimuth
126 in C{degrees} as L{Destination3Tuple}.
127 '''
128 d = self.Direct(lat1, lon1, azi1, s12, outmask=Caps._DIRECT3)
129 return Destination3Tuple(d.lat2, d.lon2, d.azi2)
131 def _DirectLine(self, ll1, azi12, s12=0, **caps_name):
132 '''(INTERNAL) Short-cut version.
133 '''
134 return self.DirectLine(ll1.lat, ll1.lon, azi12, s12, **caps_name)
136 def DirectLine(self, lat1, lon1, azi1, s12, caps=Caps._STD_LINE, **name):
137 '''Return the C{_Geodesic.DirectLine} as I{wrapped} C{GeodesicLine}.
138 '''
139 return self._GenDirectLine(lat1, lon1, azi1, False, s12, caps, **name)
141 @Property_RO
142 def ellipsoid(self):
143 '''Get this geodesic's ellipsoid (C{Ellipsoid}).
144 '''
145 return self.datum.ellipsoid
147 @property_RO
148 def f1(self): # in .css.CassiniSoldner.reset
149 '''Get the geodesic's ellipsoid's I{1 - flattening} (C{float}).
150 '''
151 return getattr(self, _under(Geodesic.f1.name), self.ellipsoid.f1)
153 def _GDictDirect(self, lat, lon, azi, arcmode, s12_a12, outmask=Caps._STD):
154 '''(INTERNAL) Get C{_Geodesic._GenDirect} result as C{GDict}.
155 '''
156 with _wargs(self, lat, lon, azi, arcmode, s12_a12, outmask) as args:
157 t = _Geodesic._GenDirect(self, *args)
158 return Direct9Tuple(t).toGDict() # *t
160 def _GDictInverse(self, lat1, lon1, lat2, lon2, outmask=Caps._STD):
161 '''(INTERNAL) Get C{_Geodesic._GenInverse} result as L{Inverse10Tuple}.
162 '''
163 with _wargs(self, lat1, lon1, lat2, lon2, outmask) as args:
164 t = _Geodesic._GenInverse(self, *args)
165 return Inverse10Tuple(t).toGDict(lon1=lon1, lon2=lon2) # *t
167 def _GenDirectLine(self, lat1, lon1, azi1, arcmode, s12_a12, *caps, **name):
168 '''(INTERNAL) Invoked by C{_Geodesic.DirectLine} and C{-.ArcDirectLine},
169 returning the result as a I{wrapped} C{GeodesicLine}.
170 '''
171 with _wargs(self, lat1, lon1, azi1, arcmode, s12_a12, *caps, **name) as args:
172 t = _Geodesic._GenDirectLine(self, *args)
173 return self._Line13(t, **name)
175 def _Inverse(self, ll1, ll2, wrap, **outmask):
176 '''(INTERNAL) Short-cut version, see .ellipsoidalBaseDI.intersecant2.
177 '''
178 if wrap:
179 ll2 = _unrollon(ll1, _Wrap.point(ll2))
180 return self.Inverse(ll1.lat, ll1.lon, ll2.lat, ll2.lon, **outmask)
182 def Inverse(self, lat1, lon1, lat2, lon2, outmask=Caps._STD):
183 '''Return the C{_Geodesic.Inverse} result as L{GDict}.
184 '''
185 with _wargs(self, lat1, lon1, lat2, lon2, outmask) as args:
186 d = _Geodesic.Inverse(self, *args)
187 return GDict(d)
189 def Inverse1(self, lat1, lon1, lat2, lon2, wrap=False):
190 '''Return the non-negative, I{angular} distance in C{degrees}.
192 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll
193 B{C{lat2}} and BC{lon2}} (C{bool}).
194 '''
195 # see .FrechetKarney.distance, .HausdorffKarney._distance
196 # and .HeightIDWkarney._distances
197 if wrap:
198 _, lat2, lon2 = _Wrap.latlon3(lat1, lat2, lon2, True) # _Geodesic.LONG_UNROLL
199 r = self.Inverse(lat1, lon1, lat2, lon2)
200 # XXX _Geodesic.DISTANCE needed for 'a12'?
201 return fabs(r.a12)
203 def Inverse3(self, lat1, lon1, lat2, lon2): # PYCHOK outmask
204 '''Return the distance in C{meter} and the forward and reverse
205 azimuths in C{degrees} as L{Distance3Tuple}.
206 '''
207 r = self.Inverse(lat1, lon1, lat2, lon2, outmask=Caps._INVERSE3)
208 return Distance3Tuple(r.s12, wrap360(r.azi1), wrap360(r.azi2))
210 def _InverseLine(self, ll1, ll2, wrap, **caps_name):
211 '''(INTERNAL) Short-cut version.
212 '''
213 if wrap:
214 ll2 = _unrollon(ll1, _Wrap.point(ll2))
215 return self.InverseLine(ll1.lat, ll1.lon, ll2.lat, ll2.lon, **caps_name)
217 def InverseLine(self, lat1, lon1, lat2, lon2, caps=Caps._STD_LINE, **name):
218 '''Return the C{_Geodesic.InverseLine} as I{wrapped} C{GeodesicLine}.
219 '''
220 with _wargs(self, lat1, lon1, lat2, lon2, caps, **name) as args:
221 t = _Geodesic.InverseLine(self, *args)
222 return self._Line13(t, **name)
224 def Line(self, lat1, lon1, azi1, caps=Caps._STD_LINE, **name):
225 '''Set up a I{wrapped} C{GeodesicLine} to compute several points
226 along a single, I{wrapped} (this) geodesic.
227 '''
228 return _wrapped.GeodesicLine(self, lat1, lon1, azi1, caps=caps, **name)
230 def _Line13(self, t, **name):
231 '''(INTERNAL) Wrap C{_GeodesicLine}, add distance and arc length
232 to reference point 3.
233 '''
234 gl = _wrapped.GeodesicLine(self, t.lat1, t.lon1, t.azi1, caps=t.caps,
235 salp1=t.salp1, calp1=t.calp1, **name)
236 gl.a13, gl.s13 = t.a13, t.s13
237 return gl
239 @property_RO
240 def name(self):
241 '''Get the name (C{str}).
242 '''
243 return self._name
245# Polygon = _Geodesic.Polygon
247 # Geodesic.ArcDirect.__doc__ = _Geodesic.ArcDirect.__doc__
248 # Geodesic.Direct.__doc__ = _Geodesic.Direct.__doc__
249 # Geodesic.Inverse.__doc__ = _Geodesic.Inverse.__doc__
250 # Geodesic.InverseLine.__doc__ = _Geodesic.InverseLinr.__doc__
251 # Geodesic.Line.__doc__ = _Geodesic.Line.__doc__
252 return Geodesic
254 @Property_RO # MCCABE 16
255 def GeodesicLine(self):
256 '''Get the I{wrapped} C{geodesicline.GeodesicLine} class from I{Karney}'s
257 Python U{geographiclib<https://GitHub.com/geographiclib/geographiclib-python>},
258 provided the latter is installed.
259 '''
260 _GeodesicLine = self.geographiclib.GeodesicLine
262 class GeodesicLine(_GeodesicLine):
263 '''I{Wrapper} for I{Karney}'s Python U{geodesicline.GeodesicLine
264 <https://PyPI.org/project/geographiclib>} class.
265 '''
266 _geodesic = None
267 _name = NN
269 def __init__(self, geodesic, lat1, lon1, azi1, **caps_name_): # salp1=NAN, calp1=NAN, name=NN
270 '''New I{wrapped} C{geodesicline.GeodesicLine} instance.
272 @arg geodesic: A I{wrapped} C{Geodesic} instance.
273 @arg lat1: Latitude of the first points (C{degrees}).
274 @arg lon1: Longitude of the first points (C{degrees}).
275 @arg azi1: Azimuth at the first points (compass C{degrees360}).
276 @kwarg caps_name_: Optional keyword arguments C{B{caps}=Caps.STANDARD},
277 a bit-or'ed combination of L{Caps} values specifying the
278 capabilities the C{GeodesicLine} instance should possess,
279 an optional C{B{name}=NN} plus C{salp1=NAN} and C{calp1=NAN}
280 for I{INTERNAL} use.
281 '''
282 _xinstanceof(_wrapped.Geodesic, geodesic=geodesic)
283 with _wargs(self, geodesic, lat1, lon1, azi1, **caps_name_) as args:
284 name, caps_ = _xkwds_pop2(caps_name_, name=geodesic.name)
285 _GeodesicLine.__init__(self, *args, **caps_)
286 if name:
287 self._name = str(name)
288 self._geodesic = geodesic
290 @Property_RO
291 def a1(self):
292 '''Get the I{equatorial arc} (C{degrees}), the arc length between
293 the northward equatorial crossing and point C{(lat1, lon1)}.
295 @see: U{EquatorialArc<https://GeographicLib.SourceForge.io/
296 C++/doc/classGeographicLib_1_1GeodesicLine.html>}
297 '''
298 try:
299 return _atan2d(self._ssig1, self._csig1)
300 except AttributeError:
301 return NAN # see .geodesicx.gxline._GeodesicLineExact
303 equatorarc = a1
305 def Arc(self):
306 '''Return the angular distance to point 3 (C{degrees} or C{NAN}).
307 '''
308 return self.a13
310 def ArcPosition(self, a12, outmask=Caps._STD):
311 '''Return the position at C{B{a12} degrees} on this line.
313 @arg a12: Angular distance from this line's first point
314 (C{degrees}).
316 @see: Method L{Position} for further details.
317 '''
318 with _wargs(self, a12, outmask) as args:
319 d = _GeodesicLine.ArcPosition(self, *args)
320 return GDict(d)
322 @Property_RO
323 def azi0(self): # see .css.CassiniSoldner.forward4
324 '''Get the I{equatorial azimuth} (C{degrees}), the azimuth of the
325 geodesic line as it crosses the equator in a northward direction.
327 @see: U{EquatorialAzimuth<https://GeographicLib.SourceForge.io/
328 C++/doc/classGeographicLib_1_1GeodesicLine.html>}
329 '''
330 try:
331 return _atan2d(self._salp0, self._calp0)
332 except AttributeError:
333 return NAN # see .geodesicx.gxline._GeodesicLineExact
335 equatorazimuth = azi0
337 def Distance(self):
338 '''Return the distance to reference point 3 (C{meter} or C{NAN}).
339 '''
340 return self.s13
342 @property_RO
343 def geodesic(self):
344 '''Get the I{wrapped} geodesic (L{Geodesic}).
345 '''
346 return self._geodesic
348 def Intersecant2(self, lat0, lon0, radius, tol=_TOL):
349 '''Compute the intersection(s) of this geodesic line and a circle.
351 @arg lat0: Latitude of the circle center (C{degrees}).
352 @arg lon0: Longitude of the circle center (C{degrees}).
353 @arg radius: Radius of the circle (C{meter}, conventionally).
354 @kwarg tol: Convergence tolerance (C{scalar}).
356 @return: 2-Tuple C{(P, Q)} with both intersections (representing a
357 geodesic chord), each a L{GDict} from method L{Position}
358 extended to 14 items by C{lon0, lat0, azi0, a02, s02, at}
359 with the circle center C{lat0}, C{lon0}, azimuth C{azi0} at,
360 distance C{a02} in C{degrees} and C{s02} in C{meter} along
361 the geodesic from the circle center to the intersection
362 C{lat2}, C{lon2} and the angle C{at} between the geodesic
363 and this line at the intersection. The I{geodesic} azimuth
364 at the intersection is C{(at + azi2)}. If this line is
365 tangential to the circle, both intersections are the same
366 L{GDict} instance.
368 @raise IntersectionError: The circle and this geodesic line do not
369 intersect.
371 @raise UnitError: Invalid B{C{radius}}.
372 '''
373 return _Intersecant2(self, lat0, lon0, radius, tol=tol)
375 def PlumbTo(self, lat0, lon0, est=None, tol=_TOL):
376 '''Compute the I{perpendicular} intersection of this geodesic line
377 with a geodesic from the given point.
379 @arg lat0: Latitude of the point (C{degrees}).
380 @arg lon0: Longitude of the point (C{degrees}).
381 @kwarg est: Optional, initial estimate for the distance C{s12} of
382 the intersection I{along} this geodesic line (C{meter}).
383 @kwarg tol: Convergence tolerance (C(meter)).
385 @return: The intersection point on this geodesic line, a L{GDict}
386 from method L{Position} extended to 14 items C{lat1, lon1,
387 azi1, lat2, lon2, azi2, a12, s12, lat0, lon0, azi0, a02,
388 s02, at} with C{a02} and C{s02} the distance in C{degrees}
389 and C{meter} from the given point C{lat0, lon0} to the
390 intersection C{lat2, lon2}, azimuth C{azi0} at the given
391 point and the (perpendicular) angle C{at} between the
392 geodesic and this line at the intersection point. The
393 geodesic azimuth at the intersection is C{(at + azi2)}.
394 See method L{Position} for further details.
396 @see: Methods C{Intersecant2}, C{Intersection} and C{Position}.
397 '''
398 return _PlumbTo(self, lat0, lon0, est=est, tol=tol)
400 def Position(self, s12, outmask=Caps._STD):
401 '''Return the position at distance C{B{s12} meter} on this line.
403 @arg s12: Distance from this line's first point (C{meter}).
404 @kwarg outmask: Bit-or'ed combination of L{Caps} values specifying
405 the quantities to be returned.
407 @return: A L{GDict} with up to 12 items C{lat1, lon1, azi1, lat2,
408 lon2, azi2, m12, a12, s12, M12, M21, S12} with C{lat1},
409 C{lon1}, C{azi1} and arc length C{a12} always included,
410 except when C{a12=NAN}.
411 '''
412 with _wargs(self, s12, outmask) as args:
413 d = _GeodesicLine.Position(self, *args)
414 return GDict(d)
416 # GeodesicLine.ArcPosition.__doc__ = _GeodesicLine.ArcPosition.__doc__
417 # GeodesicLine.Position.__doc__ = _GeodesicLine.Position.__doc__
418 return GeodesicLine
420 @Property_RO
421 def Geodesic_WGS84(self):
422 '''Get the I{wrapped} C{Geodesic(WGS84)} singleton, provided the
423 U{geographiclib<https://PyPI.org/project/geographiclib>} package
424 is installed, otherwise an C{ImportError}.
425 '''
426 return _EWGS84.geodesic
428_wrapped = _gWrapped() # PYCHOK singleton, .ellipsoids, .test/base.py
431def Geodesic(a_ellipsoid, f=None, name=NN):
432 '''Return a I{wrapped} C{geodesic.Geodesic} instance from I{Karney}'s
433 Python U{geographiclib<https://PyPI.org/project/geographiclib>},
434 provide the latter is installed, otherwise an C{ImportError}.
436 @arg a_ellipsoid: An ellipsoid (L{Ellipsoid}) or datum (L{Datum})
437 or the equatorial radius I{a} of the ellipsoid (C{meter}).
438 @arg f: The flattening of the ellipsoid (C{scalar}), ignored if
439 B{C{a_ellipsoid}}) is not specified as C{meter}.
440 @kwarg name: Optional ellipsoid name (C{str}), ignored like B{C{f}}.
441 '''
442 return _wrapped.Geodesic(a_ellipsoid, f=f, name=name)
445def GeodesicLine(geodesic, lat1, lon1, azi1, caps=Caps._STD_LINE):
446 '''Return a I{wrapped} C{geodesicline.GeodesicLine} instance from I{Karney}'s
447 Python U{geographiclib<https://PyPI.org/project/geographiclib>}, provided
448 the latter is installed, otherwise an C{ImportError}.
450 @arg geodesic: A I{wrapped} L{Geodesic} instance.
451 @arg lat1: Latitude of the first points (C{degrees}).
452 @arg lon1: Longitude of the first points (C{degrees}).
453 @arg azi1: Azimuth at the first points (compass C{degrees360}).
454 @kwarg caps: Optional, bit-or'ed combination of L{Caps} values
455 specifying the capabilities the C{GeodesicLine}
456 instance should possess, i.e., which quantities can
457 be returned by calls to C{GeodesicLine.Position}
458 and C{GeodesicLine.ArcPosition}.
459 '''
460 return _wrapped.GeodesicLine(geodesic, lat1, lon1, azi1, caps=caps)
463def Geodesic_WGS84():
464 '''Get the I{wrapped} L{Geodesic}C{(WGS84)} singleton, provided
465 U{geographiclib<https://PyPI.org/project/geographiclib>} is
466 installed, otherwise an C{ImportError}.
467 '''
468 return _wrapped.Geodesic_WGS84
471class _wargs(object): # see also .formy._idllmn6, .latlonBase._toCartesian3, .vector2d._numpy
472 '''(INTERNAL) C{geographiclib} caller and exception mapper.
473 '''
474 @contextmanager # <https://www.Python.org/dev/peps/pep-0343/> Examples
475 def __call__(self, inst, *args, **kwds):
476 '''(INTERNAL) Yield C{tuple(B{args})} with any errors raised
477 as L{GeodesicError} embellished with all B{C{kwds}}.
478 '''
479 try:
480 yield args
481 except Exception as x:
482 n = _DOT_(classname(inst), callername(up=2, underOK=True))
483 raise GeodesicError(unstr(n, *args, **kwds), cause=x)
485_wargs = _wargs() # PYCHOK singleton
488def _Intersecant2(gl, lat0, lon0, radius, tol=_TOL, form=F_D): # MCCABE in LatLonEllipsoidalBaseDI.intersecant2, .geodesicx.gxline.Intersecant2
489 # (INTERNAL) Return the intersections of a circle at C{lat0, lon0}
490 # and a geodesic line as a 2-Tuple C{(P, Q)}, each a C{GDict}.
491 r = Radius_(radius)
492 n = _dunder_nameof(_Intersecant2)[1:]
493 _P = gl.Position
494 _I = gl.geodesic.Inverse
495 _a = fabs
497 def _R3(s):
498 # radius, intersection, etc. at distance C{s}
499 P = _P(s)
500 d = _I(lat0, lon0, P.lat2, P.lon2)
501 return _a(d.s12), P, d
503 def _bisect2(s, c, Rc, r, tol, _R3):
504 _s = Fsum(c).fsumf_
505 for i in range(_TRIPS):
506 b = _s(s)
507 Rb, P, d = _R3(b)
508 if Rb > r:
509 break
510 else: # b >>> s and c >>> s
511 raise ValueError(Fmt.no_convergence(b, s))
512 __2 = _0_5 # Rb > r > Rc
513 for i in range(_TRIPS): # 47-48
514 s = (b + c) * __2
515 R, P, d = _R3(s)
516 if Rb > R > r:
517 b, Rb = s, R
518 elif Rc < R < r:
519 c, Rc = s, R
520 t = _a(b - c)
521 if t < tol: # or _a(R - r) < tol:
522 break
523 else: # t = min(t, _a(R - r))
524 raise ValueError(Fmt.no_convergence(t, tol))
525 i += C.iteration # combine iterations
526 P.set_(lat0=lat0, lon0=lon0, azi0=d.azi1, iteration=i,
527 a02=d.a12, s02=d.s12, at=d.azi2 - P.azi2, name=n)
528 return P, s
530 # get the perpendicular intersection of 2 geodesics,
531 # one the plumb, pseudo-rhumb line to the other
532 C = _PlumbTo(gl, lat0, lon0, tol=tol)
533 try:
534 a = _a(C.s02) # distance between centers
535 if a < r:
536 c = C.s12 # distance along pseudo-rhumb line
537 h = _copysign(r, c) # past half chord length
538 P, p = _bisect2( h, c, a, r, tol, _R3)
539 Q, q = _bisect2(-h, c, a, r, tol, _R3)
540 if _a(p - q) < max(EPS, tol):
541 Q = P
542 elif a > r:
543 raise ValueError(_too_(Fmt.distant(a)))
544 else: # tangential
545 P = Q = C
546 except Exception as x:
547 t = _LLB(C.lat2, C.lon2).toStr(form=form)
548 t = _SPACE_(x, _plumb_, _to_, Fmt.PAREN(t))
549 raise IntersectionError(t, txt=None, cause=x)
551 return P, Q
554def _PlumbTo(gl, lat0, lon0, est=None, tol=_TOL):
555 # (INTERNAL) Return the I{perpendicular} intersection of
556 # a geodesic from C{(lat0, lon0)} and a geodesic (line).
557 pl = _MODS.rhumb.bases._PseudoRhumbLine(gl)
558 return pl.PlumbTo(lat0, lon0, exact=gl.geodesic,
559 est=est, tol=tol)
561# **) MIT License
562#
563# Copyright (C) 2016-2024 -- mrJean1 at Gmail -- All Rights Reserved.
564#
565# Permission is hereby granted, free of charge, to any person obtaining a
566# copy of this software and associated documentation files (the "Software"),
567# to deal in the Software without restriction, including without limitation
568# the rights to use, copy, modify, merge, publish, distribute, sublicense,
569# and/or sell copies of the Software, and to permit persons to whom the
570# Software is furnished to do so, subject to the following conditions:
571#
572# The above copyright notice and this permission notice shall be included
573# in all copies or substantial portions of the Software.
574#
575# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
576# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
577# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
578# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR
579# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
580# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
581# OTHER DEALINGS IN THE SOFTWARE.