Coverage for pygeodesy/geodesicx/gxline.py: 96%
247 statements
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« prev ^ index » next coverage.py v7.2.2, created at 2023-11-12 13:23 -0500
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# - beta = latitude on auxiliary sphere
25# - omega = longitude on auxiliary sphere
26# - lambda = longitude
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 # from .karney
40from pygeodesy.constants import NAN, _EPSmin, _EPSqrt as _TOL, \
41 _0_0, _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, \
51 _sincos2d, _xinstanceof
52from pygeodesy.props import Property_RO, _update_all
53# from pygeodesy.streprs import pairs # _MODS
54from pygeodesy.utily import atan2d as _atan2d_reverse, sincos2
56from math import atan2, cos, degrees, fabs, floor, radians, sin
58__all__ = ()
59__version__ = '23.11.09'
61_glXs = [] # instances of C{[_]GeodesicLineExact} to be updated
62# underflow guard, we require _TINY * EPS > 0, _TINY + EPS == EPS
63_TINY = _EPSmin
64# assert (_TINY * EPS) > 0 and (_TINY + EPS) == EPS
67def _update_glXs(gX): # see GeodesicExact.C4order and -._ef_reset_k2
68 '''(INTERNAL) Zap cached/memoized C{Property[_RO]}s of
69 any L{GeodesicLineExact} instances tied to the given
70 L{GeodesicExact} instance B{C{gX}}.
71 '''
72 _xinstanceof(_MODS.geodesicx.GeodesicExact, gX=gX)
73 for glX in _glXs: # PYCHOK use weakref?
74 if glX._gX is gX:
75 _update_all(glX)
78class _GeodesicLineExact(_GeodesicBase):
79 '''(INTERNAL) Base class for L{GeodesicLineExact}.
80 '''
81 _a13 = _s13 = NAN
82 _azi1 = _0_0
83 _cchi1 = NAN
84 _dn1 = NAN
85 _gX = None # Exact only
86 _k2 = NAN
87 _lat1 = _lon1 = _0_0
88 _salp0 = _calp0 = NAN
89 _salp1 = _calp1 = NAN
90 _somg1 = _comg1 = NAN
91 _ssig1 = _csig1 = NAN
93 def __init__(self, gX, lat1, lon1, azi1, caps, _debug, *salp1_calp1, **name): # name=NN
94 '''(INTERNAL) New C{[_]GeodesicLineExact} instance.
95 '''
96 _xinstanceof(_MODS.geodesicx.GeodesicExact, gX=gX)
97 Cs = Caps
98 if _debug: # PYCHOK no cover
99 self._debug |= _debug & Cs._DEBUG_ALL
100 # _CapsBase.debug._update(self)
101 if salp1_calp1:
102 salp1, calp1 = salp1_calp1
103 else:
104 azi1 = _norm180(azi1)
105 # guard against salp0 underflow,
106 # also -0 is converted to +0
107 salp1, calp1 = _sincos2d(_around(azi1))
108 if name: # *args, name=NN): Python3
109 name = _xkwds_get(name, name=NN)
110 if name:
111 self.name = name
113 self._gX = gX # GeodesicExact only
114 self._lat1 = lat1 = _fix90(lat1)
115 self._lon1 = lon1
116 self._azi1 = azi1
117 self._salp1 = salp1
118 self._calp1 = calp1
119 # allow lat, azimuth and unrolling of lon
120 self._caps = caps | Cs._LINE
122 sbet1, cbet1 = gX._sinf1cos2d(_around(lat1))
123 self._dn1 = gX._dn(sbet1, cbet1)
124 # Evaluate alp0 from sin(alp1) * cos(bet1) = sin(alp0), with alp0
125 # in [0, pi/2 - |bet1|]. Alt: calp0 = hypot(sbet1, calp1 * cbet1),
126 # but the following is slightly better, consider the case salp1 = 0.
127 self._salp0, self._calp0 = _sin1cos2(salp1, calp1, sbet1, cbet1)
128 self._k2 = self._calp0**2 * gX.ep2
129 # Evaluate sig with tan(bet1) = tan(sig1) * cos(alp1).
130 # sig = 0 is nearest northward crossing of equator.
131 # With bet1 = 0, alp1 = pi/2, we have sig1 = 0 (equatorial line).
132 # With bet1 = pi/2, alp1 = -pi, sig1 = pi/2
133 # With bet1 = -pi/2, alp1 = 0 , sig1 = -pi/2
134 # Evaluate omg1 with tan(omg1) = sin(alp0) * tan(sig1).
135 # With alp0 in (0, pi/2], quadrants for sig and omg coincide.
136 # No atan2(0,0) ambiguity at poles since cbet1 = +epsilon.
137 # With alp0 = 0, omg1 = 0 for alp1 = 0, omg1 = pi for alp1 = pi.
138 self._somg1 = sbet1 * self._salp0
139 self._comg1 = c = (cbet1 * calp1) if (sbet1 or calp1) else _1_0
140 # Without normalization we have schi1 = somg1.
141 self._cchi1 = gX.f1 * self._dn1 * c
142 self._ssig1, self._csig1 = _norm2(sbet1, c) # sig1 in (-pi, pi]
143 # _norm2(somg1, comg1) # no need to normalize!
144 # _norm2(schi1?, cchi1) # no need to normalize!
145 if not (caps & Cs.LINE_OFF):
146 _glXs.append(self)
147 # no need to pre-compute other attrs based on _Caps.X. All are
148 # Property_RO's, computed once and cached/memoized until reset
149 # when C4order is changed or Elliptic function reset is invoked.
151 def __del__(self): # XXX use weakref?
152 if _glXs: # may be empty or None
153 try: # PYCHOK no cover
154 _glXs.remove(self)
155 except (TypeError, ValueError):
156 pass
157 self._gX = None
158 # _update_all(self) # throws TypeError during Python 2 cleanup
160 def _update(self, updated, *attrs, **unused):
161 if updated:
162 _update_all(self, *attrs)
164 @Property_RO
165 def a1(self):
166 '''Get the I{equatorial arc} (C{degrees}), the arc length between
167 the northward equatorial crossing and the first point.
168 '''
169 return _atan2d(self._ssig1, self._csig1) # or NAN
171 equatorarc = a1
173 @Property_RO
174 def a13(self):
175 '''Get the arc length to reference point 3 (C{degrees}).
177 @see: Methods L{Arc} and L{SetArc}.
178 '''
179 return self._a13
181 def Arc(self):
182 '''Return the arc length to reference point 3 (C{degrees} or C{NAN}).
184 @see: Method L{SetArc} and property L{a13}.
185 '''
186 return self.a13
188 def ArcPosition(self, a12, outmask=Caps.STANDARD):
189 '''Find the position on the line given B{C{a12}}.
191 @arg a12: Spherical arc length from the first point to the
192 second point (C{degrees}).
193 @kwarg outmask: Bit-or'ed combination of L{Caps} values specifying
194 the quantities to be returned.
196 @return: A L{GDict} with up to 12 items C{lat1, lon1, azi1, lat2,
197 lon2, azi2, m12, a12, s12, M12, M21, S12} with C{lat1},
198 C{lon1}, C{azi1} and arc length C{a12} always included,
199 except when C{a12=NAN}.
201 @note: By default, C{B{outmask}=STANDARD}, meaning thc C{lat1},
202 C{lon1}, C{azi1}, C{lat2}, C{lon2}, C{azi2}, C{s12} and
203 C{a12} entries are returned, except when C{a12=NAN}.
204 '''
205 return self._GDictPosition(True, a12, outmask)
207 @Property_RO
208 def azi0(self):
209 '''Get the I{equatorial azimuth}, the azimuth of this geodesic line
210 as it crosses the equator in a northward direction (C{degrees90}).
211 '''
212 return _atan2d(*self.azi0_sincos2) # or NAN
214 equatorazimuth = azi0
216 @Property_RO
217 def azi0_sincos2(self):
218 '''Get the sine and cosine of the I{equatorial azimuth} (2-tuple C{(sin, cos)}).
219 '''
220 return self._salp0, self._calp0
222 @Property_RO
223 def azi1(self):
224 '''Get the azimuth at the first point (compass C{degrees}).
225 '''
226 return self._azi1
228 @Property_RO
229 def azi1_sincos2(self):
230 '''Get the sine and cosine of the first point's azimuth (2-tuple C{(sin, cos)}).
231 '''
232 return self._salp1, self._calp1
234 @Property_RO
235 def _B41(self):
236 '''(INTERNAL) Cached/memoized.
237 '''
238 return _cosSeries(self._C4a, self._ssig1, self._csig1)
240 @Property_RO
241 def _C4a(self):
242 '''(INTERNAL) Cached/memoized.
243 '''
244 return self.geodesic._C4f_k2(self._k2)
246 @Property_RO
247 def _caps_DISTANCE_IN(self):
248 '''(INTERNAL) Get C{Caps.DISTANCE_IN} and C{_OUT}.
249 '''
250 return self.caps & (Caps.DISTANCE_IN & Caps._OUT_MASK)
252 @Property_RO
253 def _D0k2(self):
254 '''(INTERNAL) Cached/memoized.
255 '''
256 return self._eF.cD * _2__PI * self._k2
258 @Property_RO
259 def _D1(self):
260 '''(INTERNAL) Cached/memoized.
261 '''
262 return self._eF.deltaD(self._ssig1, self._csig1, self._dn1)
264 def Distance(self):
265 '''Return the distance to reference point 3 (C{meter} or C{NAN}).
267 @see: Method L{SetDistance} and property L{s13}.
268 '''
269 return self.s13
271 @Property_RO
272 def _E0b(self):
273 '''(INTERNAL) Cached/memoized.
274 '''
275 return self._eF.cE * _2__PI * self.geodesic.b
277 @Property_RO
278 def _E1(self):
279 '''(INTERNAL) Cached/memoized.
280 '''
281 return self._eF.deltaE(self._ssig1, self._csig1, self._dn1)
283 @Property_RO
284 def _eF(self):
285 '''(INTERNAL) Cached/memoized C{Elliptic} function.
286 '''
287 # see .gx.GeodesicExact._ef_reset_k2
288 return _MODS.elliptic.Elliptic(k2=-self._k2, alpha2=-self.geodesic.ep2)
290 def _GDictPosition(self, arcmode, s12_a12, outmask=Caps.STANDARD): # MCCABE 17
291 '''(INTERNAL) Generate a new position along the geodesic.
293 @return: A L{GDict} with up to 12 items C{lat1, lon1, azi1, lat2,
294 lon2, azi2, m12, a12, s12, M12, M21, S12} with C{lat1},
295 C{lon1}, C{azi1} and arc length C{a12} always included,
296 except when C{a12=NAN}.
297 '''
299 r = GDict(a12=NAN, s12=NAN) # note both a12 and s12, always
300 if not (arcmode or self._caps_DISTANCE_IN): # PYCHOK no cover
301 return r # Uninitialized or impossible distance requested
303 Cs = Caps
304 if self._debug: # PYCHOK no cover
305 outmask |= self._debug & Cs._DEBUG_DIRECT_LINE
306 outmask &= self._caps & Cs._OUT_MASK
308 eF = self._eF
309 gX = self.geodesic # ._gX
311 if arcmode:
312 # s12_a12 is spherical arc length
313 E2 = _0_0
314 sig12 = radians(s12_a12)
315 if _K_2_0:
316 ssig12, csig12 = sincos2(sig12) # utily, no NEG0
317 else: # PYCHOK no cover
318 a = fabs(s12_a12) # 0 <= fabs(_remainder(s12_a12, _180_0)) <= 90
319 a -= floor(a / _180_0) * _180_0 # 0 <= 0 < 180
320 ssig12 = _0_0 if a == 0 else sin(sig12)
321 csig12 = _0_0 if a == 90 else cos(sig12)
322 else: # s12_a12 is distance
323 t = s12_a12 / self._E0b
324 s, c = _sincos2(t) # tau12
325 # tau2 = tau1 + tau12
326 E2 = -eF.deltaEinv(*_sincos12(-s, c, *self._stau1_ctau1))
327 sig12 = fsum1f_(self._E1, -E2, t) # == t - (E2 - E1)
328 ssig12, csig12 = _sincos2(sig12)
330 salp0, calp0 = self._salp0, self._calp0
331 ssig1, csig1 = self._ssig1, self._csig1
333 # sig2 = sig1 + sig12
334 ssig2, csig2 = _sincos12(-ssig12, csig12, ssig1, csig1)
335 dn2 = eF.fDelta(ssig2, csig2)
336 # sin(bet2) = cos(alp0) * sin(sig2) and
337 # cbet2 = hypot(salp0, calp0 * csig2). Alt:
338 # cbet2 = hypot(csig2, salp0 * ssig2)
339 sbet2, cbet2 = _sin1cos2(calp0, salp0, csig2, ssig2)
340 if cbet2 == 0: # salp0 = 0, csig2 = 0, break degeneracy
341 cbet2 = csig2 = _TINY
342 # tan(alp0) = cos(sig2) * tan(alp2)
343 salp2 = salp0
344 calp2 = calp0 * csig2 # no need to normalize
346 if (outmask & Cs.DISTANCE):
347 if arcmode: # or f_0_01
348 E2 = eF.deltaE(ssig2, csig2, dn2)
349 # AB1 = _E0 * (E2 - _E1)
350 # s12 = _b * (_E0 * sig12 + AB1)
351 # = _b * _E0 * (sig12 + (E2 - _E1))
352 # = _b * _E0 * (E2 - _E1 + sig12)
353 s12 = self._E0b * fsum1f_(E2, -self._E1, sig12)
354 else:
355 s12 = s12_a12
356 r.set_(s12=s12)
358 if (outmask & Cs._DEBUG_DIRECT_LINE): # PYCHOK no cover
359 r.set_(sig12=sig12, dn2=dn2, b=gX.b, e2=gX.e2, f1=gX.f1,
360 E0b=self._E0b, E1=self._E1, E2=E2, eFk2=eF.k2, eFa2=eF.alpha2)
362 if (outmask & Cs.LONGITUDE):
363 schi1 = self._somg1
364 cchi1 = self._cchi1
365 schi2 = ssig2 * salp0
366 cchi2 = gX.f1 * dn2 * csig2 # schi2 = somg2 without normalization
367 lam12 = salp0 * self._H0e2_f1 * fsum1f_(eF.deltaH(ssig2, csig2, dn2),
368 -self._H1, sig12)
369 if (outmask & Cs.LONG_UNROLL):
370 _a, t = atan2, _copysign_1_0(salp0) # east-going?
371 tchi1 = t * schi1
372 tchi2 = t * schi2
373 chi12 = t * fsum1f_(_a(ssig1, csig1), -_a(ssig2, csig2),
374 _a(tchi2, cchi2), -_a(tchi1, cchi1), sig12)
375 lon2 = self.lon1 + degrees(chi12 - lam12)
376 else:
377 chi12 = atan2(*_sincos12(schi1, cchi1, schi2, cchi2))
378 lon2 = _norm180(self._lon1_norm180 + _norm180(degrees(chi12 - lam12)))
379 r.set_(lon2=lon2)
380 if (outmask & Cs._DEBUG_DIRECT_LINE): # PYCHOK no cover
381 r.set_(ssig2=ssig2, chi12=chi12, H0e2_f1=self._H0e2_f1,
382 csig2=csig2, lam12=lam12, H1=self._H1)
384 if (outmask & Cs.LATITUDE):
385 r.set_(lat2=_atan2d(sbet2, gX.f1 * cbet2))
387 if (outmask & Cs.AZIMUTH):
388 r.set_(azi2=_atan2d_reverse(salp2, calp2, reverse=outmask & Cs.REVERSE2))
390 if (outmask & Cs._REDUCEDLENGTH_GEODESICSCALE):
391 dn1 = self._dn1
392 J12 = self._D0k2 * fsumf_(eF.deltaD(ssig2, csig2, dn2), -self._D1, sig12)
393 if (outmask & Cs._DEBUG_DIRECT_LINE): # PYCHOK no cover
394 r.set_(ssig1=ssig1, dn1=dn1, D0k2=self._D0k2,
395 csig1=csig1, J12=J12, D1=self._D1)
396 if (outmask & Cs.REDUCEDLENGTH):
397 # Add parens around (csig1 * ssig2) and (ssig1 * csig2) to
398 # ensure accurate cancellation in the case of coincident points.
399 r.set_(m12=gX.b * fsum1f_(dn2 * (csig1 * ssig2),
400 -dn1 * (ssig1 * csig2),
401 -J12 * (csig1 * csig2)))
402 if (outmask & Cs.GEODESICSCALE):
403 t = self._k2 * (ssig2 - ssig1) * (ssig2 + ssig1) / (dn2 + dn1)
404 r.set_(M12=csig12 + ssig1 * (t * ssig2 - csig2 * J12) / dn1,
405 M21=csig12 - ssig2 * (t * ssig1 - csig1 * J12) / dn2)
407 if (outmask & Cs.AREA):
408 A4 = salp0 * calp0
409 if A4:
410 # tan(alp) = tan(alp0) * sec(sig)
411 # tan(alp2-alp1) = (tan(alp2) - tan(alp1)) / (tan(alp2) * tan(alp1) + 1)
412 # = calp0 * salp0 * (csig1 - csig2) / (salp0^2 + calp0^2 * csig1 * csig2)
413 # If csig12 > 0, write
414 # csig1 - csig2 = ssig12 * (csig1 * ssig12 / (1 + csig12) + ssig1)
415 # else
416 # csig1 - csig2 = csig1 * (1 - csig12) + ssig12 * ssig1
417 # No need to normalize
418 salp12 = (((ssig12 * csig1 / (_1_0 + csig12) + ssig1) * ssig12) if csig12 > 0 else
419 (csig1 * (_1_0 - csig12) + ssig1 * ssig12)) * A4
420 calp12 = salp0**2 + calp0**2 * csig1 * csig2
421 A4 *= gX._e2a2
422 B41 = self._B41
423 B42 = _cosSeries(self._C4a, ssig2, csig2)
424 S12 = (B42 - B41) * A4
425 else:
426 S12 = A4 = B41 = B42 = _0_0
427 # alp12 = alp2 - alp1, used in atan2 so no need to normalize
428 salp12, calp12 = _sincos12(self._salp1, self._calp1, salp2, calp2)
429 # We used to include some patch up code that purported to deal
430 # with nearly meridional geodesics properly. However, this turned
431 # out to be wrong once salp1 = -0 was allowed (via InverseLine).
432 # In fact, the calculation of {s,c}alp12 was already correct
433 # (following the IEEE rules for handling signed zeros). So,
434 # the patch up code was unnecessary (as well as dangerous).
435 if (outmask & Cs._DEBUG_DIRECT_LINE): # PYCHOK no cover
436 r.set_(salp12=salp12, salp0=salp0, B41=B41, A4=A4,
437 calp12=calp12, calp0=calp0, B42=B42, c2=gX.c2)
438 S12 += gX.c2 * atan2(salp12, calp12)
439 r.set_(S12=S12)
441 r.set_(a12=s12_a12 if arcmode else degrees(sig12),
442 lat1=self.lat1, # == _fix90(lat1)
443 lon1=self.lon1 if (outmask & Cs.LONG_UNROLL) else self._lon1_norm180,
444 azi1=_norm180(self.azi1))
445 return r
447 def _GenPosition(self, arcmode, s12_a12, outmask):
448 '''(INTERNAL) Generate a new position along the geodesic.
450 @return: L{Direct9Tuple}C{(a12, lat2, lon2, azi2,
451 s12, m12, M12, M21, S12)}.
452 '''
453 r = self._GDictPosition(arcmode, s12_a12, outmask)
454 return r.toDirect9Tuple()
456 def _GenSet(self, arcmode, s13_a13):
457 '''(INTERNAL) Aka C++ C{GenSetDistance}.
458 '''
459 if arcmode:
460 self.SetArc(s13_a13)
461 else:
462 self.SetDistance(s13_a13)
463 return self # for gx.GeodesicExact.InverseLine and -._GenDirectLine
465 @Property_RO
466 def geodesic(self):
467 '''Get the I{exact} geodesic (L{GeodesicExact}).
468 '''
469 _xinstanceof(_MODS.geodesicx.GeodesicExact, geodesic=self._gX)
470 return self._gX
472 def Intersecant2(self, lat0, lon0, radius, tol=_TOL):
473 '''Compute the intersection(s) of this geodesic line and a circle.
475 @arg lat0: Latitude of the circle center (C{degrees}).
476 @arg lon0: Longitude of the circle center (C{degrees}).
477 @arg radius: Radius of the circle (C{meter}, conventionally).
478 @kwarg tol: Convergence tolerance (C{scalar}).
480 @return: 2-Tuple C{(P, Q)} with both intersections (representing
481 a geodesic chord), each a L{GDict} from method L{Position}
482 extended to 14 items by C{lon0, lat0, azi0, a02, s02, at}
483 with the circle center C{lat0}, C{lon0}, azimuth C{azi0}
484 at, distance C{a02} in C{degrees} and C{s02} in C{meter}
485 along the geodesic from the circle center to the intersection
486 C{lat2}, C{lon2} and the angle C{at} between the geodesic
487 and this line at the intersection. The geodesic azimuth
488 at the intersection is C{(at + azi2)}. If this geodesic
489 line is tangential to the circle, both points are the same
490 L{GDict} instance.
492 @raise IntersectionError: The circle and this geodesic line do not
493 intersect, no I{perpencular} geodetic
494 intersection or no convergence.
496 @raise UnitError: Invalid B{C{radius}}.
497 '''
498 try:
499 return _MODS.geodesicw._Intersecant2(self, lat0, lon0, radius, tol=tol)
500 except (TypeError, ValueError) as x:
501 raise _xError(x, lat0, lon0, radius, tol=_TOL)
503 @Property_RO
504 def _H0e2_f1(self):
505 '''(INTERNAL) Cached/memoized.
506 '''
507 return self._eF.cH * _2__PI * self.geodesic._e2_f1
509 @Property_RO
510 def _H1(self):
511 '''(INTERNAL) Cached/memoized.
512 '''
513 return self._eF.deltaH(self._ssig1, self._csig1, self._dn1)
515 @Property_RO
516 def lat1(self):
517 '''Get the latitude of the first point (C{degrees}).
518 '''
519 return self._lat1
521 @Property_RO
522 def lon1(self):
523 '''Get the longitude of the first point (C{degrees}).
524 '''
525 return self._lon1
527 @Property_RO
528 def _lon1_norm180(self):
529 '''(INTERNAL) Cached/memoized.
530 '''
531 return _norm180(self._lon1)
533 def PlumbTo(self, lat0, lon0, est=None, tol=_TOL):
534 '''Compute the I{perpendicular} intersection of this geodesic line
535 and a geodesic from the given point.
537 @arg lat0: Latitude of the point (C{degrees}).
538 @arg lon0: Longitude of the point (C{degrees}).
539 @kwarg est: Optional, initial estimate for the distance C{s12} of
540 the intersection I{along} this geodesic line (C{meter}).
541 @kwarg tol: Convergence tolerance (C(meter)).
543 @return: The intersection point on this geodesic line, a L{GDict}
544 from method L{Position} extended to 14 items C{lat1, lon1,
545 azi1, lat2, lon2, azi2, a12, s12, lat0, lon0, azi0, a02,
546 s02, at} with distance C{a02} in C{degrees} and C{s02} in
547 C{meter} between the given C{lat0, lon0} point and the
548 intersection C{lat2, lon2}, azimuth C{azi0} at the given
549 point and C{at} the (perpendicular) angle between the
550 geodesic and this line at the intersection. The geodesic
551 azimuth at the intersection is C{(at + azi2)}. See method
552 L{Position} for further details.
554 @see: Methods C{Intersecant2}, C{Intersection} and C{Position}.
555 '''
556 return _MODS.geodesicw._PlumbTo(self, lat0, lon0, est=est, tol=tol)
558 def Position(self, s12, outmask=Caps.STANDARD):
559 '''Find the position on the line given B{C{s12}}.
561 @arg s12: Distance from this this line's first point (C{meter}).
562 @kwarg outmask: Bit-or'ed combination of L{Caps} values specifying
563 the quantities to be returned.
565 @return: A L{GDict} with up to 12 items C{lat1, lon1, azi1, lat2,
566 lon2, azi2, m12, a12, s12, M12, M21, S12} with C{lat1},
567 C{lon1}, C{azi1} and arc length C{a12} always included,
568 except when C{a12=NAN}.
570 @note: By default, C{B{outmask}=STANDARD}, meaning thc C{lat1},
571 C{lon1}, C{azi1}, C{lat2}, C{lon2}, C{azi2}, C{s12} and
572 C{a12} entries are returned, except when C{a12=NAN}.
574 @note: This L{GeodesicLineExact} instance must have been
575 constructed with capability C{Caps.DISTANCE_IN} set.
576 '''
577 return self._GDictPosition(False, s12, outmask)
579 @Property_RO
580 def s13(self):
581 '''Get the distance to reference point 3 (C{meter} or C{NAN}).
583 @see: Methods L{Distance} and L{SetDistance}.
584 '''
585 return self._s13
587 def SetArc(self, a13):
588 '''Set reference point 3 in terms relative to the first point.
590 @arg a13: Spherical arc length from the first to the reference
591 point (C{degrees}).
593 @return: The distance C{s13} (C{meter}) between the first and
594 the reference point or C{NAN}.
595 '''
596 if self._a13 != a13:
597 self._a13 = a13
598 self._s13 = self._GDictPosition(True, a13, Caps.DISTANCE).s12 # if a13 else _0_0
599 _update_all(self)
600 return self._s13
602 def SetDistance(self, s13):
603 '''Set reference point 3 in terms relative to the first point.
605 @arg s13: Distance from the first to the reference point (C{meter}).
607 @return: The arc length C{a13} (C{degrees}) between the first
608 and the reference point or C{NAN}.
609 '''
610 if self._s13 != s13:
611 self._s13 = s13
612 self._a13 = self._GDictPosition(False, s13, 0).a12 if s13 else _0_0
613 _update_all(self)
614 return self._a13 # NAN for GeodesicLineExact without Cap.DISTANCE_IN
616 @Property_RO
617 def _stau1_ctau1(self):
618 '''(INTERNAL) Cached/memoized.
619 '''
620 s, c = _sincos2(self._E1)
621 # tau1 = sig1 + B11
622 return _sincos12(-s, c, self._ssig1, self._csig1)
623 # unnecessary because Einv inverts E
624 # return -self._eF.deltaEinv(stau1, ctau1)
626 def toStr(self, prec=6, sep=_COMMASPACE_, **unused): # PYCHOK signature
627 '''Return this C{GeodesicLineExact} as string.
629 @kwarg prec: The C{float} precision, number of decimal digits (0..9).
630 Trailing zero decimals are stripped for B{C{prec}} values
631 of 1 and above, but kept for negative B{C{prec}} values.
632 @kwarg sep: Separator to join (C{str}).
634 @return: C{GeodesicLineExact} (C{str}).
635 '''
636 d = dict(geodesic=self.geodesic,
637 lat1=self.lat1, lon1=self.lon1, azi1=self.azi1,
638 a13=self.a13, s13=self.s13)
639 return sep.join(_MODS.streprs.pairs(d, prec=prec))
642__all__ += _ALL_DOCS(_GeodesicLineExact)
644# **) MIT License
645#
646# Copyright (C) 2016-2023 -- mrJean1 at Gmail -- All Rights Reserved.
647#
648# Permission is hereby granted, free of charge, to any person obtaining a
649# copy of this software and associated documentation files (the "Software"),
650# to deal in the Software without restriction, including without limitation
651# the rights to use, copy, modify, merge, publish, distribute, sublicense,
652# and/or sell copies of the Software, and to permit persons to whom the
653# Software is furnished to do so, subject to the following conditions:
654#
655# The above copyright notice and this permission notice shall be included
656# in all copies or substantial portions of the Software.
657#
658# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
659# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
660# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
661# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR
662# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
663# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
664# OTHER DEALINGS IN THE SOFTWARE.