Coverage for pygeodesy/geodesicx/gxline.py: 97%
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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, _EPSmin, _EPSqrt as _TOL, _0_0, \
41 _1_0, _180_0, _2__PI, _copysign_1_0
42from pygeodesy.errors import _xError, _xkwds_get
43from pygeodesy.fsums import fsumf_, fsum1f_
44from pygeodesy.geodesicx.gxbases import _cosSeries, _GeodesicBase, \
45 _sincos12, _sin1cos2
46# from pygeodesy.geodesicw import _Intersecant2 # _MODS
47from pygeodesy.interns import NN, _COMMASPACE_
48from pygeodesy.lazily import _ALL_DOCS, _ALL_MODS as _MODS
49from pygeodesy.karney import _around, _atan2d, Caps, GDict, _fix90, \
50 _K_2_0, _norm2, _norm180, _sincos2, _sincos2d
51from pygeodesy.props import Property_RO, _update_all
52# from pygeodesy.streprs import pairs # _MODS
53from pygeodesy.utily import atan2d as _atan2d_reverse, sincos2
55from math import atan2, cos, degrees, fabs, floor, radians, sin
57__all__ = ()
58__version__ = '24.02.21'
60_glXs = [] # instances of C{[_]GeodesicLineExact} to be updated
61# underflow guard, we require _TINY * EPS > 0, _TINY + EPS == EPS
62_TINY = _EPSmin
63# assert (_TINY * EPS) > 0 and (_TINY + EPS) == EPS
66def _update_glXs(gX): # see GeodesicExact.C4order and -._ef_reset_k2
67 '''(INTERNAL) Zap cached/memoized C{Property[_RO]}s of
68 any L{GeodesicLineExact} instances tied to the given
69 L{GeodesicExact} instance B{C{gX}}.
70 '''
71 _xGeodesicExact(gX=gX)
72 for glX in _glXs: # PYCHOK use weakref?
73 if glX._gX is gX:
74 _update_all(glX)
77def _xGeodesicExact(**gX):
78 '''(INTERNAL) Check a L{GeodesicExact} instance.
79 '''
80 _MODS.basics._xinstanceof(_MODS.geodesicx.GeodesicExact, **gX)
83class _GeodesicLineExact(_GeodesicBase):
84 '''(INTERNAL) Base class for L{GeodesicLineExact}.
85 '''
86 _a13 = _s13 = NAN
87# _azi1 = _0_0
88# _cchi1 = NAN
89# _dn1 = NAN
90 _gX = None # Exact only
91# _k2 = NAN
92# _lat1 = _lon1 = _0_0
93# _salp0 = _calp0 = NAN
94# _salp1 = _calp1 = NAN
95# _somg1 = _comg1 = NAN
96# _ssig1 = _csig1 = NAN
98 def __init__(self, gX, lat1, lon1, azi1, caps, _debug, *salp1_calp1, **name): # name=NN
99 '''(INTERNAL) New C{[_]GeodesicLineExact} instance.
100 '''
101 _xGeodesicExact(gX=gX)
102 Cs = Caps
103 if _debug: # PYCHOK no cover
104 self._debug |= _debug & Cs._DEBUG_ALL
105 # _CapsBase.debug._update(self)
106 if salp1_calp1:
107 salp1, calp1 = salp1_calp1
108 else:
109 azi1 = _norm180(azi1)
110 # guard against salp0 underflow,
111 # also -0 is converted to +0
112 salp1, calp1 = _sincos2d(_around(azi1))
113 if name: # *args, name=NN): Python3
114 name = _xkwds_get(name, name=NN)
115 if name:
116 self.name = name
118 self._gX = gX # GeodesicExact only
119 self._lat1 = lat1 = _fix90(lat1)
120 self._lon1 = lon1
121 self._azi1 = azi1
122 self._salp1 = salp1
123 self._calp1 = calp1
124 # allow lat, azimuth and unrolling of lon
125 self._caps = caps | Cs._LINE
127 sbet1, cbet1 = gX._sinf1cos2d(_around(lat1))
128 self._dn1 = gX._dn(sbet1, cbet1)
129 # Evaluate alp0 from sin(alp1) * cos(bet1) = sin(alp0), with alp0
130 # in [0, pi/2 - |bet1|]. Alt: calp0 = hypot(sbet1, calp1 * cbet1),
131 # but the following is slightly better, consider the case salp1 = 0.
132 self._salp0, self._calp0 = _sin1cos2(salp1, calp1, sbet1, cbet1)
133 self._k2 = self._calp0**2 * gX.ep2
134 # Evaluate sig with tan(bet1) = tan(sig1) * cos(alp1).
135 # sig = 0 is nearest northward crossing of equator.
136 # With bet1 = 0, alp1 = pi/2, we have sig1 = 0 (equatorial line).
137 # With bet1 = pi/2, alp1 = -pi, sig1 = pi/2
138 # With bet1 = -pi/2, alp1 = 0 , sig1 = -pi/2
139 # Evaluate omg1 with tan(omg1) = sin(alp0) * tan(sig1).
140 # With alp0 in (0, pi/2], quadrants for sig and omg coincide.
141 # No atan2(0,0) ambiguity at poles since cbet1 = +epsilon.
142 # With alp0 = 0, omg1 = 0 for alp1 = 0, omg1 = pi for alp1 = pi.
143 self._somg1 = sbet1 * self._salp0
144 self._comg1 = c = (cbet1 * calp1) if (sbet1 or calp1) else _1_0
145 # Without normalization we have schi1 = somg1.
146 self._cchi1 = gX.f1 * self._dn1 * c
147 self._ssig1, self._csig1 = _norm2(sbet1, c) # sig1 in (-pi, pi]
148 # _norm2(somg1, comg1) # no need to normalize!
149 # _norm2(schi1?, cchi1) # no need to normalize!
150 if not (caps & Cs.LINE_OFF):
151 _glXs.append(self)
152 # no need to pre-compute other attrs based on _Caps.X. All are
153 # Property_RO's, computed once and cached/memoized until reset
154 # when C4order is changed or Elliptic function reset is invoked.
156 def __del__(self): # XXX use weakref?
157 if _glXs: # may be empty or None
158 try: # PYCHOK no cover
159 _glXs.remove(self)
160 except (TypeError, ValueError):
161 pass
162 self._gX = None
163 # _update_all(self) # throws TypeError during Python 2 cleanup
165 def _update(self, updated, *attrs, **unused):
166 if updated:
167 _update_all(self, *attrs)
169 @Property_RO
170 def a1(self):
171 '''Get the I{equatorial arc} (C{degrees}), the arc length between
172 the northward equatorial crossing and the first point.
173 '''
174 return _atan2d(self._ssig1, self._csig1) # or NAN
176 equatorarc = a1
178 @Property_RO
179 def a13(self):
180 '''Get the arc length to reference point 3 (C{degrees}).
182 @see: Methods L{Arc} and L{SetArc}.
183 '''
184 return self._a13
186 def Arc(self):
187 '''Return the arc length to reference point 3 (C{degrees} or C{NAN}).
189 @see: Method L{SetArc} and property L{a13}.
190 '''
191 return self.a13
193 def ArcPosition(self, a12, outmask=Caps.STANDARD):
194 '''Find the position on the line given B{C{a12}}.
196 @arg a12: Spherical arc length from the first point to the
197 second point (C{degrees}).
198 @kwarg outmask: Bit-or'ed combination of L{Caps} values specifying
199 the quantities to be returned.
201 @return: A L{GDict} with up to 12 items C{lat1, lon1, azi1, lat2,
202 lon2, azi2, m12, a12, s12, M12, M21, S12} with C{lat1},
203 C{lon1}, C{azi1} and arc length C{a12} always included,
204 except when C{a12=NAN}.
206 @note: By default, C{B{outmask}=STANDARD}, meaning thc C{lat1},
207 C{lon1}, C{azi1}, C{lat2}, C{lon2}, C{azi2}, C{s12} and
208 C{a12} entries are returned, except when C{a12=NAN}.
209 '''
210 return self._GDictPosition(True, a12, outmask)
212 @Property_RO
213 def azi0(self):
214 '''Get the I{equatorial azimuth}, the azimuth of this geodesic line
215 as it crosses the equator in a northward direction (C{degrees90}).
216 '''
217 return _atan2d(*self.azi0_sincos2) # or NAN
219 equatorazimuth = azi0
221 @Property_RO
222 def azi0_sincos2(self):
223 '''Get the sine and cosine of the I{equatorial azimuth} (2-tuple C{(sin, cos)}).
224 '''
225 return self._salp0, self._calp0
227 @Property_RO
228 def azi1(self):
229 '''Get the azimuth at the first point (compass C{degrees}).
230 '''
231 return self._azi1
233 @Property_RO
234 def azi1_sincos2(self):
235 '''Get the sine and cosine of the first point's azimuth (2-tuple C{(sin, cos)}).
236 '''
237 return self._salp1, self._calp1
239 @Property_RO
240 def _B41(self):
241 '''(INTERNAL) Cached/memoized.
242 '''
243 return _cosSeries(self._C4a, self._ssig1, self._csig1)
245 @Property_RO
246 def _C4a(self):
247 '''(INTERNAL) Cached/memoized.
248 '''
249 return self.geodesic._C4f_k2(self._k2)
251 @Property_RO
252 def _caps_DISTANCE_IN(self):
253 '''(INTERNAL) Get C{Caps.DISTANCE_IN} and C{_OUT}.
254 '''
255 return self.caps & (Caps.DISTANCE_IN & Caps._OUT_MASK)
257 @Property_RO
258 def _D0k2(self):
259 '''(INTERNAL) Cached/memoized.
260 '''
261 return self._eF.cD * _2__PI * self._k2
263 @Property_RO
264 def _D1(self):
265 '''(INTERNAL) Cached/memoized.
266 '''
267 return self._eF.deltaD(self._ssig1, self._csig1, self._dn1)
269 def Distance(self):
270 '''Return the distance to reference point 3 (C{meter} or C{NAN}).
272 @see: Method L{SetDistance} and property L{s13}.
273 '''
274 return self.s13
276 @Property_RO
277 def _E0b(self):
278 '''(INTERNAL) Cached/memoized.
279 '''
280 return self._eF.cE * _2__PI * self.geodesic.b
282 @Property_RO
283 def _E1(self):
284 '''(INTERNAL) Cached/memoized.
285 '''
286 return self._eF.deltaE(self._ssig1, self._csig1, self._dn1)
288 @Property_RO
289 def _eF(self):
290 '''(INTERNAL) Cached/memoized C{Elliptic} function.
291 '''
292 # see .gx.GeodesicExact._ef_reset_k2
293 return _MODS.elliptic.Elliptic(k2=-self._k2, alpha2=-self.geodesic.ep2)
295 def _GDictPosition(self, arcmode, s12_a12, outmask=Caps.STANDARD): # MCCABE 17
296 '''(INTERNAL) Generate a new position along the geodesic.
298 @return: A L{GDict} with up to 12 items C{lat1, lon1, azi1, lat2,
299 lon2, azi2, m12, a12, s12, M12, M21, S12} with C{lat1},
300 C{lon1}, C{azi1} and arc length C{a12} always included,
301 except when C{a12=NAN}.
302 '''
304 r = GDict(a12=NAN, s12=NAN) # note both a12 and s12, always
305 if not (arcmode or self._caps_DISTANCE_IN): # PYCHOK no cover
306 return r # Uninitialized or impossible distance requested
308 Cs = Caps
309 if self._debug: # PYCHOK no cover
310 outmask |= self._debug & Cs._DEBUG_DIRECT_LINE
311 outmask &= self._caps & Cs._OUT_MASK
313 eF = self._eF
314 gX = self.geodesic # ._gX
316 if arcmode:
317 # s12_a12 is spherical arc length
318 E2 = _0_0
319 sig12 = radians(s12_a12)
320 if _K_2_0:
321 ssig12, csig12 = sincos2(sig12) # utily, no NEG0
322 else: # PYCHOK no cover
323 a = fabs(s12_a12) # 0 <= fabs(_remainder(s12_a12, _180_0)) <= 90
324 a -= floor(a / _180_0) * _180_0 # 0 <= 0 < 180
325 ssig12 = _0_0 if a == 0 else sin(sig12)
326 csig12 = _0_0 if a == 90 else cos(sig12)
327 else: # s12_a12 is distance
328 t = s12_a12 / self._E0b
329 s, c = _sincos2(t) # tau12
330 # tau2 = tau1 + tau12
331 E2 = -eF.deltaEinv(*_sincos12(-s, c, *self._stau1_ctau1))
332 sig12 = fsum1f_(self._E1, -E2, t) # == t - (E2 - E1)
333 ssig12, csig12 = _sincos2(sig12)
335 salp0, calp0 = self._salp0, self._calp0
336 ssig1, csig1 = self._ssig1, self._csig1
338 # sig2 = sig1 + sig12
339 ssig2, csig2 = _sincos12(-ssig12, csig12, ssig1, csig1)
340 dn2 = eF.fDelta(ssig2, csig2)
341 # sin(bet2) = cos(alp0) * sin(sig2) and
342 # cbet2 = hypot(salp0, calp0 * csig2). Alt:
343 # cbet2 = hypot(csig2, salp0 * ssig2)
344 sbet2, cbet2 = _sin1cos2(calp0, salp0, csig2, ssig2)
345 if cbet2 == 0: # salp0 = 0, csig2 = 0, break degeneracy
346 cbet2 = csig2 = _TINY
347 # tan(alp0) = cos(sig2) * tan(alp2)
348 salp2 = salp0
349 calp2 = calp0 * csig2 # no need to normalize
351 if (outmask & Cs.DISTANCE):
352 if arcmode: # or f_0_01
353 E2 = eF.deltaE(ssig2, csig2, dn2)
354 # AB1 = _E0 * (E2 - _E1)
355 # s12 = _b * (_E0 * sig12 + AB1)
356 # = _b * _E0 * (sig12 + (E2 - _E1))
357 # = _b * _E0 * (E2 - _E1 + sig12)
358 s12 = self._E0b * fsum1f_(E2, -self._E1, sig12)
359 else:
360 s12 = s12_a12
361 r.set_(s12=s12)
363 if (outmask & Cs._DEBUG_DIRECT_LINE): # PYCHOK no cover
364 r.set_(sig12=sig12, dn2=dn2, b=gX.b, e2=gX.e2, f1=gX.f1,
365 E0b=self._E0b, E1=self._E1, E2=E2, eFk2=eF.k2, eFa2=eF.alpha2)
367 if (outmask & Cs.LONGITUDE):
368 schi1 = self._somg1
369 cchi1 = self._cchi1
370 schi2 = ssig2 * salp0
371 cchi2 = gX.f1 * dn2 * csig2 # schi2 = somg2 without normalization
372 lam12 = salp0 * self._H0e2_f1 * fsum1f_(eF.deltaH(ssig2, csig2, dn2),
373 -self._H1, sig12)
374 if (outmask & Cs.LONG_UNROLL):
375 _a, t = atan2, _copysign_1_0(salp0) # east-going?
376 tchi1 = t * schi1
377 tchi2 = t * schi2
378 chi12 = t * fsum1f_(_a(ssig1, csig1), -_a(ssig2, csig2),
379 _a(tchi2, cchi2), -_a(tchi1, cchi1), sig12)
380 lon2 = self.lon1 + degrees(chi12 - lam12)
381 else:
382 chi12 = atan2(*_sincos12(schi1, cchi1, schi2, cchi2))
383 lon2 = _norm180(self._lon1_norm180 + _norm180(degrees(chi12 - lam12)))
384 r.set_(lon2=lon2)
385 if (outmask & Cs._DEBUG_DIRECT_LINE): # PYCHOK no cover
386 r.set_(ssig2=ssig2, chi12=chi12, H0e2_f1=self._H0e2_f1,
387 csig2=csig2, lam12=lam12, H1=self._H1)
389 if (outmask & Cs.LATITUDE):
390 r.set_(lat2=_atan2d(sbet2, gX.f1 * cbet2))
392 if (outmask & Cs.AZIMUTH):
393 r.set_(azi2=_atan2d_reverse(salp2, calp2, reverse=outmask & Cs.REVERSE2))
395 if (outmask & Cs._REDUCEDLENGTH_GEODESICSCALE):
396 dn1 = self._dn1
397 J12 = self._D0k2 * fsumf_(eF.deltaD(ssig2, csig2, dn2), -self._D1, sig12)
398 if (outmask & Cs._DEBUG_DIRECT_LINE): # PYCHOK no cover
399 r.set_(ssig1=ssig1, dn1=dn1, D0k2=self._D0k2,
400 csig1=csig1, J12=J12, D1=self._D1)
401 if (outmask & Cs.REDUCEDLENGTH):
402 # Add parens around (csig1 * ssig2) and (ssig1 * csig2) to
403 # ensure accurate cancellation in the case of coincident points.
404 r.set_(m12=gX.b * fsum1f_(dn2 * (csig1 * ssig2),
405 -dn1 * (ssig1 * csig2),
406 -J12 * (csig1 * csig2)))
407 if (outmask & Cs.GEODESICSCALE):
408 t = self._k2 * (ssig2 - ssig1) * (ssig2 + ssig1) / (dn2 + dn1)
409 r.set_(M12=csig12 + ssig1 * (t * ssig2 - csig2 * J12) / dn1,
410 M21=csig12 - ssig2 * (t * ssig1 - csig1 * J12) / dn2)
412 if (outmask & Cs.AREA):
413 A4 = salp0 * calp0
414 if A4:
415 # tan(alp) = tan(alp0) * sec(sig)
416 # tan(alp2-alp1) = (tan(alp2) - tan(alp1)) / (tan(alp2) * tan(alp1) + 1)
417 # = calp0 * salp0 * (csig1 - csig2) / (salp0^2 + calp0^2 * csig1 * csig2)
418 # If csig12 > 0, write
419 # csig1 - csig2 = ssig12 * (csig1 * ssig12 / (1 + csig12) + ssig1)
420 # else
421 # csig1 - csig2 = csig1 * (1 - csig12) + ssig12 * ssig1
422 # No need to normalize
423 salp12 = (((ssig12 * csig1 / (_1_0 + csig12) + ssig1) * ssig12) if csig12 > 0 else
424 (csig1 * (_1_0 - csig12) + ssig1 * ssig12)) * A4
425 calp12 = salp0**2 + calp0**2 * csig1 * csig2
426 A4 *= gX._e2a2
427 B41 = self._B41
428 B42 = _cosSeries(self._C4a, ssig2, csig2)
429 S12 = (B42 - B41) * A4
430 else:
431 S12 = A4 = B41 = B42 = _0_0
432 # alp12 = alp2 - alp1, used in atan2 so no need to normalize
433 salp12, calp12 = _sincos12(self._salp1, self._calp1, salp2, calp2)
434 # We used to include some patch up code that purported to deal
435 # with nearly meridional geodesics properly. However, this turned
436 # out to be wrong once salp1 = -0 was allowed (via InverseLine).
437 # In fact, the calculation of {s,c}alp12 was already correct
438 # (following the IEEE rules for handling signed zeros). So,
439 # the patch up code was unnecessary (as well as dangerous).
440 if (outmask & Cs._DEBUG_DIRECT_LINE): # PYCHOK no cover
441 r.set_(salp12=salp12, salp0=salp0, B41=B41, A4=A4,
442 calp12=calp12, calp0=calp0, B42=B42, c2=gX.c2)
443 S12 += gX.c2 * atan2(salp12, calp12)
444 r.set_(S12=S12)
446 r.set_(a12=s12_a12 if arcmode else degrees(sig12),
447 lat1=self.lat1, # == _fix90(lat1)
448 lon1=self.lon1 if (outmask & Cs.LONG_UNROLL) else self._lon1_norm180,
449 azi1=_norm180(self.azi1))
450 return r
452 def _GenPosition(self, arcmode, s12_a12, outmask):
453 '''(INTERNAL) Generate a new position along the geodesic.
455 @return: L{Direct9Tuple}C{(a12, lat2, lon2, azi2,
456 s12, m12, M12, M21, S12)}.
457 '''
458 r = self._GDictPosition(arcmode, s12_a12, outmask)
459 return r.toDirect9Tuple()
461 def _GenSet(self, arcmode, s13_a13):
462 '''(INTERNAL) Aka C++ C{GenSetDistance}.
463 '''
464 if arcmode:
465 self.SetArc(s13_a13)
466 else:
467 self.SetDistance(s13_a13)
468 return self # for gx.GeodesicExact.InverseLine and -._GenDirectLine
470 @Property_RO
471 def geodesic(self):
472 '''Get the I{exact} geodesic (L{GeodesicExact}).
473 '''
474 _xGeodesicExact(geodesic=self._gX)
475 return self._gX
477 def Intersecant2(self, lat0, lon0, radius, tol=_TOL):
478 '''Compute the intersection(s) of this geodesic line and a circle.
480 @arg lat0: Latitude of the circle center (C{degrees}).
481 @arg lon0: Longitude of the circle center (C{degrees}).
482 @arg radius: Radius of the circle (C{meter}, conventionally).
483 @kwarg tol: Convergence tolerance (C{scalar}).
485 @return: 2-Tuple C{(P, Q)} with both intersections (representing
486 a geodesic chord), each a L{GDict} from method L{Position}
487 extended to 14 items by C{lon0, lat0, azi0, a02, s02, at}
488 with the circle center C{lat0}, C{lon0}, azimuth C{azi0}
489 at, distance C{a02} in C{degrees} and C{s02} in C{meter}
490 along the geodesic from the circle center to the intersection
491 C{lat2}, C{lon2} and the angle C{at} between the geodesic
492 and this line at the intersection. The geodesic azimuth
493 at the intersection is C{(at + azi2)}. If this geodesic
494 line is tangential to the circle, both points are the same
495 L{GDict} instance.
497 @raise IntersectionError: The circle and this geodesic line do not
498 intersect, no I{perpencular} geodetic
499 intersection or no convergence.
501 @raise UnitError: Invalid B{C{radius}}.
502 '''
503 try:
504 return _MODS.geodesicw._Intersecant2(self, lat0, lon0, radius, tol=tol)
505 except (TypeError, ValueError) as x:
506 raise _xError(x, lat0, lon0, radius, tol=_TOL)
508 @Property_RO
509 def _H0e2_f1(self):
510 '''(INTERNAL) Cached/memoized.
511 '''
512 return self._eF.cH * _2__PI * self.geodesic._e2_f1
514 @Property_RO
515 def _H1(self):
516 '''(INTERNAL) Cached/memoized.
517 '''
518 return self._eF.deltaH(self._ssig1, self._csig1, self._dn1)
520 @Property_RO
521 def lat1(self):
522 '''Get the latitude of the first point (C{degrees}).
523 '''
524 return self._lat1
526 @Property_RO
527 def lon1(self):
528 '''Get the longitude of the first point (C{degrees}).
529 '''
530 return self._lon1
532 @Property_RO
533 def _lon1_norm180(self):
534 '''(INTERNAL) Cached/memoized.
535 '''
536 return _norm180(self._lon1)
538 def PlumbTo(self, lat0, lon0, est=None, tol=_TOL):
539 '''Compute the I{perpendicular} intersection of this geodesic line
540 and a geodesic from the given point.
542 @arg lat0: Latitude of the point (C{degrees}).
543 @arg lon0: Longitude of the point (C{degrees}).
544 @kwarg est: Optional, initial estimate for the distance C{s12} of
545 the intersection I{along} this geodesic line (C{meter}).
546 @kwarg tol: Convergence tolerance (C(meter)).
548 @return: The intersection point on this geodesic line, a L{GDict}
549 from method L{Position} extended to 14 items C{lat1, lon1,
550 azi1, lat2, lon2, azi2, a12, s12, lat0, lon0, azi0, a02,
551 s02, at} with distance C{a02} in C{degrees} and C{s02} in
552 C{meter} between the given C{lat0, lon0} point and the
553 intersection C{lat2, lon2}, azimuth C{azi0} at the given
554 point and C{at} the (perpendicular) angle between the
555 geodesic and this line at the intersection. The geodesic
556 azimuth at the intersection is C{(at + azi2)}. See method
557 L{Position} for further details.
559 @see: Methods C{Intersecant2}, C{Intersection} and C{Position}.
560 '''
561 return _MODS.geodesicw._PlumbTo(self, lat0, lon0, est=est, tol=tol)
563 def Position(self, s12, outmask=Caps.STANDARD):
564 '''Find the position on the line given B{C{s12}}.
566 @arg s12: Distance from this this line's first point (C{meter}).
567 @kwarg outmask: Bit-or'ed combination of L{Caps} values specifying
568 the quantities to be returned.
570 @return: A L{GDict} with up to 12 items C{lat1, lon1, azi1, lat2,
571 lon2, azi2, m12, a12, s12, M12, M21, S12} with C{lat1},
572 C{lon1}, C{azi1} and arc length C{a12} always included,
573 except when C{a12=NAN}.
575 @note: By default, C{B{outmask}=STANDARD}, meaning thc C{lat1},
576 C{lon1}, C{azi1}, C{lat2}, C{lon2}, C{azi2}, C{s12} and
577 C{a12} entries are returned, except when C{a12=NAN}.
579 @note: This L{GeodesicLineExact} instance must have been
580 constructed with capability C{Caps.DISTANCE_IN} set.
581 '''
582 return self._GDictPosition(False, s12, outmask)
584 @Property_RO
585 def s13(self):
586 '''Get the distance to reference point 3 (C{meter} or C{NAN}).
588 @see: Methods L{Distance} and L{SetDistance}.
589 '''
590 return self._s13
592 def SetArc(self, a13):
593 '''Set reference point 3 in terms relative to the first point.
595 @arg a13: Spherical arc length from the first to the reference
596 point (C{degrees}).
598 @return: The distance C{s13} (C{meter}) between the first and
599 the reference point or C{NAN}.
600 '''
601 if self._a13 != a13:
602 self._a13 = a13
603 self._s13 = self._GDictPosition(True, a13, Caps.DISTANCE).s12 # if a13 else _0_0
604 _update_all(self)
605 return self._s13
607 def SetDistance(self, s13):
608 '''Set reference point 3 in terms relative to the first point.
610 @arg s13: Distance from the first to the reference point (C{meter}).
612 @return: The arc length C{a13} (C{degrees}) between the first
613 and the reference point or C{NAN}.
614 '''
615 if self._s13 != s13:
616 self._s13 = s13
617 self._a13 = self._GDictPosition(False, s13, 0).a12 if s13 else _0_0
618 _update_all(self)
619 return self._a13 # NAN for GeodesicLineExact without Cap.DISTANCE_IN
621 @Property_RO
622 def _stau1_ctau1(self):
623 '''(INTERNAL) Cached/memoized.
624 '''
625 s, c = _sincos2(self._E1)
626 # tau1 = sig1 + B11
627 return _sincos12(-s, c, self._ssig1, self._csig1)
628 # unnecessary because Einv inverts E
629 # return -self._eF.deltaEinv(stau1, ctau1)
631 def toStr(self, prec=6, sep=_COMMASPACE_, **unused): # PYCHOK signature
632 '''Return this C{GeodesicLineExact} as string.
634 @kwarg prec: The C{float} precision, number of decimal digits (0..9).
635 Trailing zero decimals are stripped for B{C{prec}} values
636 of 1 and above, but kept for negative B{C{prec}} values.
637 @kwarg sep: Separator to join (C{str}).
639 @return: C{GeodesicLineExact} (C{str}).
640 '''
641 d = dict(geodesic=self.geodesic,
642 lat1=self.lat1, lon1=self.lon1, azi1=self.azi1,
643 a13=self.a13, s13=self.s13)
644 return sep.join(_MODS.streprs.pairs(d, prec=prec))
647__all__ += _ALL_DOCS(_GeodesicLineExact)
649# **) MIT License
650#
651# Copyright (C) 2016-2024 -- mrJean1 at Gmail -- All Rights Reserved.
652#
653# Permission is hereby granted, free of charge, to any person obtaining a
654# copy of this software and associated documentation files (the "Software"),
655# to deal in the Software without restriction, including without limitation
656# the rights to use, copy, modify, merge, publish, distribute, sublicense,
657# and/or sell copies of the Software, and to permit persons to whom the
658# Software is furnished to do so, subject to the following conditions:
659#
660# The above copyright notice and this permission notice shall be included
661# in all copies or substantial portions of the Software.
662#
663# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
664# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
665# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
666# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR
667# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
668# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
669# OTHER DEALINGS IN THE SOFTWARE.