Coverage for pygeodesy/geodesicx/gxline.py: 92%
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2# -*- coding: utf-8 -*-
4u'''A pure Python version of I{Karney}'s C++ class U{GeodesicLineExact
5<https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1GeodesicLineExact.html>}.
7Class L{GeodesicLineExact} follows the naming, methods and return
8values from class C{GeodesicLine} from I{Karney}'s Python U{geographiclib
9<https://GeographicLib.SourceForge.io/1.52/python/index.html>}.
11Copyright (C) U{Charles Karney<mailto:Karney@Alum.MIT.edu>} (2008-2023)
12and licensed under the MIT/X11 License. For more information, see the
13U{GeographicLib<https://GeographicLib.SourceForge.io>} documentation.
14'''
15# make sure int/int division yields float quotient
16from __future__ import division as _; del _ # PYCHOK semicolon
18# A copy of comments from Karney's C{GeodesicLineExact.cpp}:
19#
20# This is a reformulation of the geodesic problem. The
21# notation is as follows:
22# - at a general point (no suffix or 1 or 2 as suffix)
23# - phi = latitude
24# - lambda = longitude
25# - beta = latitude on auxiliary sphere
26# - omega = longitude on auxiliary sphere
27# - alpha = azimuth of great circle
28# - sigma = arc length along great circle
29# - s = distance
30# - tau = scaled distance (= sigma at multiples of PI/2)
31# - at northwards equator crossing
32# - beta = phi = 0
33# - omega = lambda = 0
34# - alpha = alpha0
35# - sigma = s = 0
36# - a 12 suffix means a difference, e.g., s12 = s2 - s1.
37# - s and c prefixes mean sin and cos
39# from pygeodesy.basics import _xinstanceof # _MODS
40from pygeodesy.constants import NAN, _EPSqrt as _TOL, _0_0, _1_0, \
41 _180_0, _2__PI, _copysign_1_0, isfinite
42from pygeodesy.errors import _xError, _xkwds_pop2
43from pygeodesy.fsums import fsumf_, fsum1f_
44from pygeodesy.geodesicx.gxbases import _cosSeries, _GeodesicBase, \
45 _sincos12, _sin1cos2, \
46 _sinf1cos2d, _TINY
47# from pygeodesy.geodesicw import _Intersecant2 # _MODS
48from pygeodesy.lazily import _ALL_DOCS, _ALL_MODS as _MODS
49from pygeodesy.karney import _around, _atan2d, Caps, GDict, _fix90, \
50 _K_2_0, _llz2gl, _norm2, _norm180, \
51 _sincos2, _sincos2d
52from pygeodesy.props import Property_RO, property_ROver, _update_all
53from pygeodesy.utily import atan2, atan2d as _atan2d_reverse, sincos2
55from math import cos, degrees, fabs, floor, radians, sin
57__all__ = ()
58__version__ = '24.11.24'
60_glXs = [] # instances of C{[_]GeodesicLineExact} to be updated
63def _update_glXs(gX): # see GeodesicExact.C4order and -._ef_reset_k2
64 '''(INTERNAL) Zap cached/memoized C{Property[_RO]}s of
65 any L{GeodesicLineExact} instances tied to the given
66 L{GeodesicExact} instance B{C{gX}}.
67 '''
68 _xGeodesicExact(gX=gX)
69 for glX in _glXs: # PYCHOK use weakref?
70 if glX._gX is gX:
71 _update_all(glX)
74def _xGeodesicExact(**gX):
75 '''(INTERNAL) Check a L{GeodesicExact} instance.
76 '''
77 _MODS.basics._xinstanceof(_MODS.geodesicx.GeodesicExact, **gX)
80class _GeodesicLineExact(_GeodesicBase):
81 '''(INTERNAL) Base class for L{GeodesicLineExact}.
82 '''
83 _a13 = _s13 = NAN
84# _azi1 = _0_0
85# _cchi1 = NAN
86# _dn1 = NAN
87 _gX = None # Exact only
88# _k2 = NAN
89# _lat1 = _lon1 = _0_0
90# _salp0 = _calp0 = NAN
91# _salp1 = _calp1 = NAN
92# _somg1 = _comg1 = NAN
93# _ssig1 = _csig1 = NAN
95 def __init__(self, gX, lat1, lon1, azi1, caps, **name_):
96 '''(INTERNAL) New C{[_]GeodesicLineExact} instance.
97 '''
98# _xGeodesicExact(gX=gX)
99 if azi1 is None: # see GeodesicExact.InverseLine
100 (salp1, calp1), name_ = _xkwds_pop2(name_, _s_calp1=(_0_0, _1_0))
101 azi1 = _atan2d(salp1, calp1)
102 else: # guard against salp0 underflow, convert -0 to +0
103 azi1 = _norm180(azi1)
104 salp1, calp1 = _sincos2d(_around(azi1))
105 if name_:
106 self.name = name_
108 self._gX = gX # GeodesicExact only
109 self._lat1 = lat1 = _fix90(lat1)
110 self._lon1 = lon1
111 self._azi1 = azi1
112 self._salp1 = salp1
113 self._calp1 = calp1
114 # allow lat, azimuth and unrolling of lon
115 self._caps = caps | Caps._AZIMUTH_LATITUDE_LONG_UNROLL
117 sbet1, cbet1 = _sinf1cos2d(_around(lat1), gX.f1)
118 self._dn1 = gX._dn(sbet1, cbet1)
119 # Evaluate alp0 from sin(alp1) * cos(bet1) = sin(alp0), with alp0
120 # in [0, pi/2 - |bet1|]. Alt: calp0 = hypot(sbet1, calp1 * cbet1),
121 # but the following is slightly better, consider the case salp1 = 0.
122 self._salp0, self._calp0 = _sin1cos2(salp1, calp1, sbet1, cbet1)
123 self._k2 = self._calp0**2 * gX.ep2
124 # Evaluate sig with tan(bet1) = tan(sig1) * cos(alp1).
125 # sig = 0 is nearest northward crossing of equator.
126 # With bet1 = 0, alp1 = pi/2, we have sig1 = 0 (equatorial line).
127 # With bet1 = pi/2, alp1 = -pi, sig1 = pi/2
128 # With bet1 = -pi/2, alp1 = 0 , sig1 = -pi/2
129 # Evaluate omg1 with tan(omg1) = sin(alp0) * tan(sig1).
130 # With alp0 in (0, pi/2], quadrants for sig and omg coincide.
131 # No atan2(0,0) ambiguity at poles since cbet1 = +epsilon.
132 # With alp0 = 0, omg1 = 0 for alp1 = 0, omg1 = pi for alp1 = pi.
133 self._somg1 = sbet1 * self._salp0
134 self._comg1 = c = (cbet1 * calp1) if (sbet1 or calp1) else _1_0
135 # Without normalization we have schi1 = somg1.
136 self._cchi1 = gX.f1 * self._dn1 * c
137 self._ssig1, self._csig1 = _norm2(sbet1, c) # sig1 in (-pi, pi]
138 # _norm2(somg1, comg1) # no need to normalize!
139 # _norm2(schi1?, cchi1) # no need to normalize!
140 if not (caps & Caps.LINE_OFF):
141 _glXs.append(self)
142 # no need to pre-compute other attrs for (caps & Caps.X). All are
143 # Property_RO's, computed once and cached/memoized until reset when
144 # arc, distance, C4order is changed or Elliptic function is reset.
146 def __del__(self): # XXX use weakref?
147 if _glXs: # may be empty or None
148 try: # PYCHOK no cover
149 _glXs.remove(self)
150 except (TypeError, ValueError):
151 pass
152 self._gX = None
153 # _update_all(self) # throws TypeError during Python 2 cleanup
155 def _update(self, updated, *attrs, **unused):
156 if updated:
157 _update_all(self, *attrs)
159 @Property_RO
160 def a1(self):
161 '''Get the I{equatorial arc} (C{degrees}), the arc length between
162 the northward equatorial crossing and the first point.
163 '''
164 return _atan2d(self._ssig1, self._csig1) # or NAN
166 equatorarc = a1
168 @Property_RO
169 def a13(self):
170 '''Get the arc length to reference point 3 (C{degrees}).
172 @see: Methods L{Arc} and L{SetArc}.
173 '''
174 return self._a13
176 def Arc(self):
177 '''Return the arc length to reference point 3 (C{degrees} or C{NAN}).
179 @see: Method L{SetArc} and property L{a13}.
180 '''
181 return self.a13
183 def ArcPosition(self, a12, outmask=Caps.STANDARD):
184 '''Find the position on the line given B{C{a12}}.
186 @arg a12: Spherical arc length from the first point to the
187 second point (C{degrees}).
188 @kwarg outmask: Bit-or'ed combination of L{Caps} values specifying
189 the quantities to be returned.
191 @return: A L{GDict} with up to 12 items C{lat1, lon1, azi1, lat2,
192 lon2, azi2, m12, a12, s12, M12, M21, S12} with C{lat1},
193 C{lon1}, C{azi1} and arc length C{a12} always included,
194 except when C{a12=NAN}.
196 @note: By default, C{B{outmask}=STANDARD}, meaning thc C{lat1},
197 C{lon1}, C{azi1}, C{lat2}, C{lon2}, C{azi2}, C{s12} and
198 C{a12} entries are returned, except when C{a12=NAN}.
199 '''
200 return self._GDictPosition(True, a12, outmask)
202 @Property_RO
203 def azi0(self):
204 '''Get the I{equatorial azimuth}, the azimuth of this geodesic line
205 as it crosses the equator in a northward direction (C{degrees90}).
206 '''
207 return _atan2d(*self.azi0_sincos2) # or NAN
209 equatorazimuth = azi0
211 @Property_RO
212 def azi0_sincos2(self):
213 '''Get the sine and cosine of the I{equatorial azimuth} (2-tuple C{(sin, cos)}).
214 '''
215 return self._salp0, self._calp0
217 @Property_RO
218 def azi1(self):
219 '''Get the azimuth at the first point (compass C{degrees}).
220 '''
221 return self._azi1
223 @Property_RO
224 def azi1_sincos2(self):
225 '''Get the sine and cosine of the first point's azimuth (2-tuple C{(sin, cos)}).
226 '''
227 return self._salp1, self._calp1
229 @Property_RO
230 def _B41(self):
231 '''(INTERNAL) Cached/memoized.
232 '''
233 return _cosSeries(self._C4a, self._ssig1, self._csig1)
235 @Property_RO
236 def _C4a(self):
237 '''(INTERNAL) Cached/memoized.
238 '''
239 return self.geodesic._C4f_k2(self._k2)
241 @Property_RO
242 def _caps_DISTANCE_IN(self):
243 '''(INTERNAL) Get C{Caps.DISTANCE_IN} and C{_OUT}.
244 '''
245 return self.caps & (Caps.DISTANCE_IN & Caps._OUT_MASK)
247 @Property_RO
248 def _D0k2(self):
249 '''(INTERNAL) Cached/memoized.
250 '''
251 return self._eF.cD * _2__PI * self._k2
253 @Property_RO
254 def _D1(self):
255 '''(INTERNAL) Cached/memoized.
256 '''
257 return self._eF.deltaD(self._ssig1, self._csig1, self._dn1)
259 def Distance(self):
260 '''Return the distance to reference point 3 (C{meter} or C{NAN}).
262 @see: Method L{SetDistance} and property L{s13}.
263 '''
264 return self.s13
266 @Property_RO
267 def _E0b(self):
268 '''(INTERNAL) Cached/memoized.
269 '''
270 return self._eF.cE * _2__PI * self.geodesic.b
272 @Property_RO
273 def _E1(self):
274 '''(INTERNAL) Cached/memoized.
275 '''
276 return self._eF.deltaE(self._ssig1, self._csig1, self._dn1)
278 @Property_RO
279 def _eF(self):
280 '''(INTERNAL) Cached/memoized C{Elliptic} function.
281 '''
282 # see .gx.GeodesicExact._ef_reset_k2
283 return _MODS.elliptic.Elliptic(k2=-self._k2, alpha2=-self.geodesic.ep2)
285 def _GDictPosition(self, arcmode, s12_a12, outmask=Caps.STANDARD): # MCCABE 17
286 '''(INTERNAL) Generate a new position along the geodesic.
288 @return: A L{GDict} with up to 12 items C{lat1, lon1, azi1, lat2,
289 lon2, azi2, m12, a12, s12, M12, M21, S12} with C{lat1},
290 C{lon1}, C{azi1} and arc length C{a12} always included,
291 except when C{a12=NAN}.
292 '''
293 Cs = Caps
294 if outmask:
295 outmask &= self._caps & Cs._OUT_MASK
296 eF = self._eF
297 gX = self.geodesic # ._gX
298 r = GDict(a12=NAN, s12=NAN) # both a12 and s12, always
300 if not isfinite(s12_a12):
301 # E2 = sig12 = ssig12 = csig12 = NAN
302 return r._toNAN(outmask)
303 elif arcmode: # s12_a12 is (spherical) arc length
304 r.set_(a12=s12_a12)
305 sig12 = radians(s12_a12)
306 if _K_2_0:
307 ssig12, csig12 = sincos2(sig12) # utily, no NEG0
308 else: # PYCHOK no cover
309 a = fabs(s12_a12) # 0 <= fabs(_remainder(s12_a12, _180_0)) <= 90
310 a -= floor(a / _180_0) * _180_0 # 0 <= 0 < 180
311 ssig12 = _0_0 if a == 0 else sin(sig12)
312 csig12 = _0_0 if a == 90 else cos(sig12)
313 E2 = _0_0
314 elif self._caps_DISTANCE_IN: # s12_a12 is distance
315 t = s12_a12 / self._E0b
316 s, c = _sincos2(t) # tau12
317 # tau2 = tau1 + tau12
318 E2 = -eF.deltaEinv(*_sincos12(-s, c, *self._stau1_ctau1))
319 sig12 = fsum1f_(self._E1, -E2, t) # == t - (E2 - E1)
320 ssig12, csig12 = _sincos2(sig12)
321 r.set_(a12=degrees(sig12))
322 else: # uninitialized or impossible distance requested
323 return r
325 # sig2 = sig1 + sig12
326 ssig1, csig1 = self._ssig1, self._csig1
327 ssig2, csig2 = t = _sincos12(-ssig12, csig12, ssig1, csig1)
328 dn2 = eF.fDelta(*t)
330 if (outmask & Cs.DISTANCE):
331 outmask ^= Cs.DISTANCE
332 if arcmode: # or f_0_01
333 E2 = eF.deltaE(ssig2, csig2, dn2)
334 # AB1 = _E0 * (E2 - _E1)
335 # s12 = _b * (_E0 * sig12 + AB1)
336 # = _b * _E0 * (sig12 + (E2 - _E1))
337 # = _b * _E0 * (E2 - _E1 + sig12)
338 s12 = self._E0b * fsum1f_(E2, -self._E1, sig12)
339 else:
340 s12 = s12_a12
341 r.set_(s12=s12)
343 if not outmask: # all done, see ._GenSet
344 return r
346 if self._debug: # PYCHOK no cover
347 outmask |= self._debug & Cs._DEBUG_DIRECT_LINE
349 if (outmask & Cs._DEBUG_DIRECT_LINE): # PYCHOK no cover
350 r.set_(sig12=sig12, dn2=dn2, b=gX.b, e2=gX.e2, f1=gX.f1,
351 E0b=self._E0b, E1=self._E1, E2=E2, eFk2=eF.k2, eFa2=eF.alpha2)
353 # sin(bet2) = cos(alp0) * sin(sig2) and
354 # cbet2 = hypot(salp0, calp0 * csig2). Alt:
355 # cbet2 = hypot(csig2, salp0 * ssig2)
356 salp0, calp0 = self._salp0, self._calp0
357 sbet2, cbet2 = _sin1cos2(calp0, salp0, csig2, ssig2)
358 if cbet2 == 0: # salp0 = 0, csig2 = 0, break degeneracy
359 cbet2 = csig2 = _TINY
360 # tan(alp0) = cos(sig2) * tan(alp2)
361 salp2 = salp0
362 calp2 = calp0 * csig2 # no need to normalize
364 if (outmask & Cs.AZIMUTH):
365 r.set_(azi2=_atan2d_reverse(salp2, calp2,
366 reverse=outmask & Cs.REVERSE2))
368 if (outmask & Cs.LATITUDE):
369 r.set_(lat2=_atan2d(sbet2, gX.f1 * cbet2))
371 if (outmask & Cs.LONGITUDE):
372 schi1 = self._somg1
373 cchi1 = self._cchi1
374 schi2 = ssig2 * salp0
375 cchi2 = gX.f1 * dn2 * csig2 # schi2 = somg2 without normalization
376 lam12 = salp0 * self._H0e2_f1 * fsum1f_(eF.deltaH(ssig2, csig2, dn2),
377 -self._H1, sig12)
378 if (outmask & Cs.LONG_UNROLL):
379 t = _copysign_1_0(salp0) # east-going?
380 tchi1 = t * schi1
381 tchi2 = t * schi2
382 chi12 = t * fsum1f_(atan2(ssig1, csig1), -atan2(ssig2, csig2),
383 atan2(tchi2, cchi2), -atan2(tchi1, cchi1), sig12)
384 lon2 = self.lon1 + degrees(chi12 - lam12)
385 else:
386 chi12 = atan2(*_sincos12(schi1, cchi1, schi2, cchi2))
387 lon2 = _norm180(self._lon1_norm180 + _norm180(degrees(chi12 - lam12)))
388 r.set_(lon2=lon2)
389 if (outmask & Cs._DEBUG_DIRECT_LINE): # PYCHOK no cover
390 r.set_(ssig2=ssig2, chi12=chi12, H0e2_f1=self._H0e2_f1,
391 csig2=csig2, lam12=lam12, H1=self._H1)
393 if (outmask & Cs._REDUCEDLENGTH_GEODESICSCALE):
394 dn1 = self._dn1
395 J12 = self._D0k2 * fsumf_(eF.deltaD(ssig2, csig2, dn2), -self._D1, sig12)
396 if (outmask & Cs._DEBUG_DIRECT_LINE): # PYCHOK no cover
397 r.set_(ssig1=ssig1, dn1=dn1, D0k2=self._D0k2,
398 csig1=csig1, J12=J12, D1=self._D1)
399 if (outmask & Cs.REDUCEDLENGTH):
400 # Add parens around (csig1 * ssig2) and (ssig1 * csig2) to
401 # ensure accurate cancellation in the case of coincident points.
402 r.set_(m12=gX.b * fsum1f_(dn2 * (csig1 * ssig2),
403 -dn1 * (ssig1 * csig2),
404 -J12 * (csig1 * csig2)))
405 if (outmask & Cs.GEODESICSCALE):
406 t = self._k2 * (ssig2 - ssig1) * (ssig2 + ssig1) / (dn2 + dn1)
407 r.set_(M12=csig12 + ssig1 * (t * ssig2 - csig2 * J12) / dn1,
408 M21=csig12 - ssig2 * (t * ssig1 - csig1 * J12) / dn2)
410 if (outmask & Cs.AREA):
411 A4 = salp0 * calp0
412 if A4:
413 # tan(alp) = tan(alp0) * sec(sig)
414 # tan(alp2-alp1) = (tan(alp2) - tan(alp1)) / (tan(alp2) * tan(alp1) + 1)
415 # = calp0 * salp0 * (csig1 - csig2) / (salp0^2 + calp0^2 * csig1 * csig2)
416 # If csig12 > 0, write
417 # csig1 - csig2 = ssig12 * (csig1 * ssig12 / (1 + csig12) + ssig1)
418 # else
419 # csig1 - csig2 = csig1 * (1 - csig12) + ssig12 * ssig1
420 # No need to normalize
421 salp12 = (((ssig12 * csig1 / (_1_0 + csig12) + ssig1) * ssig12) if csig12 > 0 else
422 (csig1 * (_1_0 - csig12) + ssig1 * ssig12)) * A4
423 calp12 = salp0**2 + calp0**2 * csig1 * csig2
424 A4 *= gX._e2a2
425 B41 = self._B41
426 B42 = _cosSeries(self._C4a, ssig2, csig2)
427 S12 = (B42 - B41) * A4
428 else:
429 S12 = A4 = B41 = B42 = _0_0
430 # alp12 = alp2 - alp1, used in atan2 so no need to normalize
431 salp12, calp12 = _sincos12(self._salp1, self._calp1, salp2, calp2)
432 # We used to include some patch up code that purported to deal
433 # with nearly meridional geodesics properly. However, this turned
434 # out to be wrong once salp1 = -0 was allowed (via InverseLine).
435 # In fact, the calculation of {s,c}alp12 was already correct
436 # (following the IEEE rules for handling signed zeros). So,
437 # the patch up code was unnecessary (as well as dangerous).
438 if (outmask & Cs._DEBUG_DIRECT_LINE): # PYCHOK no cover
439 r.set_(salp12=salp12, salp0=salp0, B41=B41, A4=A4,
440 calp12=calp12, calp0=calp0, B42=B42, c2=gX.c2)
441 S12 += gX.c2 * atan2(salp12, calp12)
442 r.set_(S12=S12)
444 r.set_(azi1=_norm180(self.azi1),
445 lat1=self.lat1, # == _fix90(lat1)
446 lon1=self.lon1 if (outmask & Cs.LONG_UNROLL) else self._lon1_norm180)
447 return r
449 def _GenPosition(self, arcmode, s12_a12, outmask):
450 '''(INTERNAL) Generate a new position along the geodesic.
452 @return: L{Direct9Tuple}C{(a12, lat2, lon2, azi2,
453 s12, m12, M12, M21, S12)}.
454 '''
455 r = self._GDictPosition(arcmode, s12_a12, outmask)
456 return r.toDirect9Tuple()
458 def _GenSet(self, debug, s12=None, a12=None, **llz2):
459 '''(INTERNAL) Aka C++ C{GenSetDistance}.
460 '''
461 Cs = Caps
462 if debug: # PYCHOK no cover
463 self._debug |= debug & Cs._DEBUG_ALL
464 # _CapsBase.debug._update(self)
465 if s12 is None:
466 if a12 is None: # see GeodesicExact.Line
467 return self
468 s12 = self._GDictPosition(True, a12, outmask=Cs.DISTANCE).s12 if a12 else _0_0
469 elif a12 is None:
470 a12 = self._GDictPosition(False, s12, 0).a12 if s12 else _0_0
471 self._s13 = s12
472 self._a13 = a12
473 self._caps |= Cs.DISTANCE | Cs.DISTANCE_IN
474 # _update_all(self) # new, from GeodesicExact.*Line
475 return _llz2gl(self, **llz2)
477 @Property_RO
478 def geodesic(self):
479 '''Get the I{exact} geodesic (L{GeodesicExact}).
480 '''
481 _xGeodesicExact(geodesic=self._gX)
482 return self._gX
484 def Intersecant2(self, lat0, lon0, radius, tol=_TOL):
485 '''Compute the intersection(s) of this geodesic line and a circle.
487 @arg lat0: Latitude of the circle center (C{degrees}).
488 @arg lon0: Longitude of the circle center (C{degrees}).
489 @arg radius: Radius of the circle (C{meter}, conventionally).
490 @kwarg tol: Convergence tolerance (C{scalar}).
492 @return: 2-Tuple C{(P, Q)} with both intersections (representing
493 a geodesic chord), each a L{GDict} from method L{Position}
494 extended to 14 items by C{lon0, lat0, azi0, a02, s02, at}
495 with the circle center C{lat0}, C{lon0}, azimuth C{azi0}
496 at, distance C{a02} in C{degrees} and C{s02} in C{meter}
497 along the geodesic from the circle center to the intersection
498 C{lat2}, C{lon2} and the angle C{at} between the geodesic
499 and this line at the intersection. The geodesic azimuth
500 at the intersection is C{(at + azi2)}. If this geodesic
501 line is tangential to the circle, both points are the same
502 L{GDict} instance.
504 @raise IntersectionError: The circle and this geodesic line do not
505 intersect, no I{perpencular} geodetic
506 intersection or no convergence.
508 @raise UnitError: Invalid B{C{radius}}.
509 '''
510 try:
511 return _MODS.geodesicw._Intersecant2(self, lat0, lon0, radius, tol=tol)
512 except (TypeError, ValueError) as x:
513 raise _xError(x, lat0, lon0, radius, tol=_TOL)
515 @Property_RO
516 def _H0e2_f1(self):
517 '''(INTERNAL) Cached/memoized.
518 '''
519 return self._eF.cH * _2__PI * self.geodesic._e2_f1
521 @Property_RO
522 def _H1(self):
523 '''(INTERNAL) Cached/memoized.
524 '''
525 return self._eF.deltaH(self._ssig1, self._csig1, self._dn1)
527 @Property_RO
528 def lat1(self):
529 '''Get the latitude of the first point (C{degrees}).
530 '''
531 return self._lat1
533 @Property_RO
534 def lon1(self):
535 '''Get the longitude of the first point (C{degrees}).
536 '''
537 return self._lon1
539 @Property_RO
540 def _lon1_norm180(self):
541 '''(INTERNAL) Cached/memoized.
542 '''
543 return _norm180(self._lon1)
545 def PlumbTo(self, lat0, lon0, est=None, tol=_TOL):
546 '''Compute the I{perpendicular} intersection of this geodesic line
547 and a geodesic from the given point.
549 @arg lat0: Latitude of the point (C{degrees}).
550 @arg lon0: Longitude of the point (C{degrees}).
551 @kwarg est: Optional, initial estimate for the distance C{s12} of
552 the intersection I{along} this geodesic line (C{meter}).
553 @kwarg tol: Convergence tolerance (C(meter)).
555 @return: The intersection point on this geodesic line, a L{GDict}
556 from method L{Position} extended to 14 items C{lat1, lon1,
557 azi1, lat2, lon2, azi2, a12, s12, lat0, lon0, azi0, a02,
558 s02, at} with distance C{a02} in C{degrees} and C{s02} in
559 C{meter} between the given C{lat0, lon0} point and the
560 intersection C{lat2, lon2}, azimuth C{azi0} at the given
561 point and C{at} the (perpendicular) angle between the
562 geodesic and this line at the intersection. The geodesic
563 azimuth at the intersection is C{(at + azi2)}. See method
564 L{Position} for further details.
566 @see: Methods C{Intersecant2}, C{Intersection} and C{Position}.
567 '''
568 return _MODS.geodesicw._PlumbTo(self, lat0, lon0, est=est, tol=tol)
570 def Position(self, s12, outmask=Caps.STANDARD):
571 '''Find the position on the line given B{C{s12}}.
573 @arg s12: Distance from this this line's first point (C{meter}).
574 @kwarg outmask: Bit-or'ed combination of L{Caps} values specifying
575 the quantities to be returned.
577 @return: A L{GDict} with up to 12 items C{lat1, lon1, azi1, lat2,
578 lon2, azi2, m12, a12, s12, M12, M21, S12} with C{lat1},
579 C{lon1}, C{azi1} and arc length C{a12} always included,
580 except when C{a12=NAN}.
582 @note: By default, C{B{outmask}=STANDARD}, meaning thc C{lat1},
583 C{lon1}, C{azi1}, C{lat2}, C{lon2}, C{azi2}, C{s12} and
584 C{a12} entries are returned, except when C{a12=NAN}.
586 @note: This L{GeodesicLineExact} instance must have been
587 constructed with capability C{Caps.DISTANCE_IN} set.
588 '''
589 return self._GDictPosition(False, s12, outmask)
591 @Property_RO
592 def s13(self):
593 '''Get the distance to reference point 3 (C{meter} or C{NAN}).
595 @see: Methods L{Distance} and L{SetDistance}.
596 '''
597 return self._s13
599 def SetArc(self, a13):
600 '''Set reference point 3 in terms relative to the first point.
602 @arg a13: Spherical arc length from the first to the reference
603 point (C{degrees}).
605 @return: The distance C{s13} (C{meter}) between the first and
606 the reference point or C{NAN}.
607 '''
608 if self._a13 != a13:
609 self._GenSet(0, a12=a13)
610 _update_all(self)
611 return self._s13
613 def SetDistance(self, s13):
614 '''Set reference point 3 in terms relative to the first point.
616 @arg s13: Distance from the first to the reference point (C{meter}).
618 @return: The arc length C{a13} (C{degrees}) between the first
619 and the reference point or C{NAN}.
620 '''
621 if self._s13 != s13:
622 self._GenSet(0, s12=s13)
623 _update_all(self)
624 return self._a13
626 @Property_RO
627 def _stau1_ctau1(self):
628 '''(INTERNAL) Cached/memoized.
629 '''
630 s, c = _sincos2(self._E1)
631 # tau1 = sig1 + B11
632 return _sincos12(-s, c, self._ssig1, self._csig1)
633 # unnecessary because Einv inverts E
634 # return -self._eF.deltaEinv(stau1, ctau1)
636 @property_ROver
637 def _toProps7(self):
638 '''(INTERNAL) 7-Tuple of C{toStr} properties.
639 '''
640 C = _GeodesicLineExact
641 return C.lat1, C.lon1, C.azi1, C.a13, C.s13, C.caps, C.geodesic
643 def toStr(self, **prec_sep_name): # PYCHOK signature
644 '''Return this C{GeodesicLineExact} as string.
646 @see: L{Ellipsoid.toStr<pygeodesy.ellipsoids.Ellipsoid.toStr>}
647 for further details.
649 @return: C{GeodesicLineExact} (C{str}).
650 '''
651 return self._instr(props=self._toProps7, **prec_sep_name)
654__all__ += _ALL_DOCS(_GeodesicLineExact)
656# **) MIT License
657#
658# Copyright (C) 2016-2025 -- mrJean1 at Gmail -- All Rights Reserved.
659#
660# Permission is hereby granted, free of charge, to any person obtaining a
661# copy of this software and associated documentation files (the "Software"),
662# to deal in the Software without restriction, including without limitation
663# the rights to use, copy, modify, merge, publish, distribute, sublicense,
664# and/or sell copies of the Software, and to permit persons to whom the
665# Software is furnished to do so, subject to the following conditions:
666#
667# The above copyright notice and this permission notice shall be included
668# in all copies or substantial portions of the Software.
669#
670# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
671# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
672# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
673# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR
674# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
675# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
676# OTHER DEALINGS IN THE SOFTWARE.