Coverage for pygeodesy/ellipsoidalVincenty.py: 99%
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2# -*- coding: utf-8 -*-
4u'''Ellipsoidal, I{Vincenty}-based geodesy.
6I{Thaddeus Vincenty}'s geodetic (lat-/longitude) L{LatLon}, geocentric
7(ECEF) L{Cartesian} and L{VincentyError} classes and functions L{areaOf},
8L{intersections2}, L{nearestOn} and L{perimeterOf}.
10Pure Python implementation of geodesy tools for ellipsoidal earth models,
11transcoded from JavaScript originals by I{(C) Chris Veness 2005-2016}
12and published under the same MIT Licence**, see U{Vincenty geodesics
13<https://www.Movable-Type.co.UK/scripts/LatLongVincenty.html>}. More
14at U{geographiclib<https://PyPI.org/project/geographiclib>} and
15U{GeoPy<https://PyPI.org/project/geopy>}.
17Calculate geodesic distance between two points using the U{Vincenty
18<https://WikiPedia.org/wiki/Vincenty's_formulae>} formulae and one of
19several ellipsoidal earth models. The default model is WGS-84, the
20most widely used globally-applicable model for the earth ellipsoid.
22Other ellipsoids offering a better fit to the local geoid include Airy
23(1830) in the UK, Clarke (1880) in Africa, International 1924 in much
24of Europe, and GRS-67 in South America. North America (NAD83) and
25Australia (GDA) use GRS-80, which is equivalent to the WGS-84 model.
27Great-circle distance uses a I{spherical} model of the earth with the
28mean earth radius defined by the International Union of Geodesy and
29Geophysics (IUGG) as M{(2 * a + b) / 3 = 6371008.7714150598} or about
306,371,009 meter (for WGS-84, resulting in an error of up to about 0.5%).
32Here's an example usage of C{ellipsoidalVincenty}:
34 >>> from pygeodesy.ellipsoidalVincenty import LatLon
35 >>> Newport_RI = LatLon(41.49008, -71.312796)
36 >>> Cleveland_OH = LatLon(41.499498, -81.695391)
37 >>> Newport_RI.distanceTo(Cleveland_OH)
38 866,455.4329158525 # meter
40To change the ellipsoid model used by the Vincenty formulae use:
42 >>> from pygeodesy import Datums
43 >>> from pygeodesy.ellipsoidalVincenty import LatLon
44 >>> p = LatLon(0, 0, datum=Datums.OSGB36)
46or by converting to anothor datum:
48 >>> p = p.toDatum(Datums.OSGB36)
49'''
50# make sure int/int division yields float quotient, see .basics
51from __future__ import division as _; del _ # PYCHOK semicolon
53from pygeodesy.constants import EPS, EPS0, _0_0, _1_0, _2_0, _3_0, _4_0, _6_0
54from pygeodesy.ellipsoidalBase import CartesianEllipsoidalBase, _nearestOn
55from pygeodesy.ellipsoidalBaseDI import LatLonEllipsoidalBaseDI, \
56 _intersection3, _intersections2, \
57 _TOL_M, intersecant2
58from pygeodesy.errors import _and, _ValueError, _xkwds
59from pygeodesy.fmath import Fpolynomial, hypot, hypot1
60from pygeodesy.interns import _ambiguous_, _antipodal_, _COLONSPACE_, \
61 _to_, _SPACE_, _limit_ # PYCHOK used!
62from pygeodesy.lazily import _ALL_DOCS, _ALL_LAZY, _ALL_MODS as _MODS, _ALL_OTHER
63from pygeodesy.namedTuples import Destination2Tuple, Destination3Tuple, \
64 Distance3Tuple
65from pygeodesy.points import Fmt, ispolar # PYCHOK exported
66from pygeodesy.props import deprecated_function, deprecated_method, \
67 property_doc_, property_RO
68# from pygeodesy.streprs import Fmt # from .points
69from pygeodesy.units import Number_, Scalar_
70from pygeodesy.utily import atan2b, atan2d, sincos2, sincos2d, unroll180, wrap180
72from math import atan2, cos, degrees, fabs, radians, tan
74__all__ = _ALL_LAZY.ellipsoidalVincenty
75__version__ = '24.06.11'
77_antipodal_to_ = _SPACE_(_antipodal_, _to_)
80class VincentyError(_ValueError):
81 '''Error raised by I{Vincenty}'s C{Direct} and C{Inverse} methods
82 for coincident points or lack of convergence.
83 '''
84 pass
87class Cartesian(CartesianEllipsoidalBase):
88 '''Extended to convert geocentric, L{Cartesian} points to
89 Vincenty-based, ellipsoidal, geodetic L{LatLon}.
90 '''
91 @property_RO
92 def Ecef(self):
93 '''Get the ECEF I{class} (L{EcefVeness}), I{once}.
94 '''
95 return _Ecef()
97 def toLatLon(self, **LatLon_and_kwds): # PYCHOK LatLon=LatLon, datum=None
98 '''Convert this cartesian point to a C{Vincenty}-based geodetic point.
100 @kwarg LatLon_and_kwds: Optional L{LatLon} and L{LatLon} keyword
101 arguments as C{datum}. Use C{B{LatLon}=...,
102 B{datum}=...} to override this L{LatLon}
103 class or specify C{B{LatLon}=None}.
105 @return: The geodetic point (L{LatLon}) or if C{B{LatLon} is None},
106 an L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M, datum)}
107 with C{C} and C{M} if available.
109 @raise TypeError: Invalid B{C{LatLon_and_kwds}} argument.
110 '''
111 kwds = _xkwds(LatLon_and_kwds, LatLon=LatLon, datum=self.datum)
112 return CartesianEllipsoidalBase.toLatLon(self, **kwds)
115class LatLon(LatLonEllipsoidalBaseDI):
116 '''New point on an (oblate) ellipsoidal earth model, using the formulae devised
117 by U{I{Thaddeus Vincenty}<https://WikiPedia.org/wiki/Vincenty's_formulae>}
118 (1975) to compute geodesic distances, bearings (azimuths), etc.
120 Set the earth model to be used with the keyword argument datum. The default
121 is C{Datums.WGS84}, which is the most globally accurate. For other models,
122 see the L{Datums<pygeodesy.datums>}.
124 @note: This implementation of I{Vincenty} methods may not converge for some
125 valid points, raising a L{VincentyError}. In that case, a result may
126 be obtained by increasing the tolerance C{epsilon} and/or iteration
127 C{limit}, see properties L{LatLon.epsilon} and L{LatLon.iterations}.
128 '''
129 _epsilon = 1e-12 # radians, about 6 um
130# _iteration = None # iteration number from .named._NamedBase
131 _iterations = 201 # 5, default max, 200 vs Veness' 1,000
133 @deprecated_method
134 def bearingTo(self, other, wrap=False): # PYCHOK no cover
135 '''DEPRECATED, use method L{initialBearingTo} or L{bearingTo2}.
136 '''
137 return self.initialBearingTo(other, wrap=wrap)
139 @property_RO
140 def Ecef(self):
141 '''Get the ECEF I{class} (L{EcefVeness}), I{once}.
142 '''
143 return _Ecef()
145 @property_doc_(''' the convergence epsilon (C{radians}).''')
146 def epsilon(self):
147 '''Get the convergence epsilon (C{radians}).
148 '''
149 return self._epsilon
151 @epsilon.setter # PYCHOK setter!
152 def epsilon(self, epsilon):
153 '''Set the convergence epsilon (C{radians}).
155 @raise TypeError: Non-scalar B{C{epsilon}}.
157 @raise ValueError: Out of bounds B{C{epsilon}}.
158 '''
159 self._epsilon = Scalar_(epsilon=epsilon)
161 @property_doc_(''' the iteration limit (C{int}).''')
162 def iterations(self):
163 '''Get the iteration limit (C{int}).
164 '''
165 return self._iterations - 1
167 @iterations.setter # PYCHOK setter!
168 def iterations(self, limit):
169 '''Set the iteration limit (C{int}).
171 @raise TypeError: Non-scalar B{C{limit}}.
173 @raise ValueError: Out-of-bounds B{C{limit}}.
174 '''
175 self._iterations = Number_(limit, name=_limit_, low=4, high=1000) + 1
177 def toCartesian(self, **Cartesian_datum_kwds): # PYCHOK Cartesian=Cartesian, datum=None
178 '''Convert this point to C{Vincenty}-based cartesian (ECEF) coordinates.
180 @kwarg Cartesian_datum_kwds: Optional L{Cartesian}, B{C{datum}} and other
181 keyword arguments, ignored if C{B{Cartesian}=None}. Use
182 C{B{Cartesian}=...} to override this L{Cartesian} class
183 or specify C{B{Cartesian}=None}.
185 @return: The cartesian point (L{Cartesian}) or if C{B{Cartesian} is None},
186 an L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M, datum)} with
187 C{C} and C{M} if available.
189 @raise TypeError: Invalid B{C{Cartesian}}, B{C{datum}} or other B{C{Cartesian_datum_kwds}}.
190 '''
191 kwds = _xkwds(Cartesian_datum_kwds, Cartesian=Cartesian,
192 datum=self.datum)
193 return LatLonEllipsoidalBaseDI.toCartesian(self, **kwds)
195 def _Direct(self, distance, bearing, llr, height):
196 '''(INTERNAL) Direct Vincenty method.
198 @raise TypeError: The B{C{other}} point is not L{LatLon}.
200 @raise ValueError: If this and the B{C{other}} point's L{Datum} ellipsoids are
201 not compatible.
203 @raise VincentyError: Vincenty fails to converge for the current limits, see
204 L{epsilon<LatLon.epsilon>} and L{iterations<LatLon.iterations>}.
205 '''
206 E = self.ellipsoid()
207 f = E.f
209 sb, cb = sincos2d(bearing)
210 s1, c1, t1 = _sincostan3r(self.phi, f)
212 eps = self.epsilon
213 s12 = atan2(t1, cb) * _2_0
214 sa, ca2 = _sincos22(c1 * sb)
215 A, B = _AB2(ca2 * E.e22) # e22 == (a / b)**2 - 1
216 s = d = distance / (A * E.b)
217 for i in range(1, self._iterations): # 1-origin
218 ss, cs = sincos2(s)
219 c2sm, e = cos(s12 + s), s
220 s = _Ds(B, cs, ss, c2sm, d)
221 e = fabs(s - e)
222 if e < eps:
223 self._iteration = i
224 break
225 else:
226 t = self._no_convergence(e)
227 raise VincentyError(t, txt=repr(self)) # self.toRepr()
229 t = s1 * ss - c1 * cs * cb
230 # final bearing (reverse azimuth +/- 180)
231 d = atan2b(sa, -t)
232 if llr:
233 b = cb * ss
234 a = atan2d(s1 * cs + c1 * b, hypot(sa, t) * E.b_a)
235 b = atan2d(sb * ss, -s1 * b + c1 * cs) + self.lon \
236 - degrees(_Dl(f, ca2, sa, s, cs, ss, c2sm))
237 t = Destination3Tuple(a, wrap180(b), d)
238 r = self._Direct2Tuple(self.classof, height, t)
239 else:
240 r = Destination2Tuple(None, d, name=self.name)
241 r._iteration = i
242 return r
244 def _Inverse(self, other, wrap, azis=True): # PYCHOK signature
245 '''(INTERNAL) Inverse Vincenty method.
247 @raise TypeError: The B{C{other}} point is not L{LatLon}.
249 @raise ValueError: If this and the B{C{other}} point's L{Datum}
250 ellipsoids are not compatible.
252 @raise VincentyError: Vincenty fails to converge for the current
253 L{LatLon.epsilon} and L{LatLon.iterations}
254 limits and/or if this and the B{C{other}}
255 point are coincident or near-antipodal.
256 '''
257 E = self.ellipsoids(other)
258 f = E.f
260 s1, c1, _ = _sincostan3r( self.phi, f)
261 s2, c2, _ = _sincostan3r(other.phi, f)
263 c1c2, s1c2 = c1 * c2, s1 * c2
264 c1s2, s1s2 = c1 * s2, s1 * s2
266 eps = self.epsilon
267 d, _ = unroll180(self.lon, other.lon, wrap=wrap)
268 dl = ll = radians(d)
269 for i in range(1, self._iterations): # 1-origin
270 sll, cll = sincos2(ll)
272 ss = hypot(c2 * sll, c1s2 - s1c2 * cll)
273 if ss < EPS: # coincident or antipodal, ...
274 if self.isantipodeTo(other, eps=eps):
275 t = self._is_to(other, True)
276 raise VincentyError(_ambiguous_, txt=t)
277 self._iteration = i
278 # return zeros like Karney, unlike Veness
279 return Distance3Tuple(_0_0, 0, 0, iteration=i)
281 cs = s1s2 + c1c2 * cll
282 s, e = atan2(ss, cs), ll
283 sa, ca2 = _sincos22(c1c2 * sll / ss)
284 if ca2:
285 c2sm = cs - _2_0 * s1s2 / ca2
286 ll = _Dl(f, ca2, sa, s, cs, ss, c2sm, dl)
287 else: # equatorial line
288 ll = dl + f * sa * s
289 e = fabs(ll - e)
290 if e < eps:
291 self._iteration = i
292 break
293# elif abs(ll) > PI and self.isantipodeTo(other, eps=eps):
294# # omitted and applied *after* failure to converge below,
295# # see footnote under Inverse <https://WikiPedia.org/wiki/
296# # Vincenty's_formulae> and <https://GitHub.com/chrisveness/
297# # geodesy/blob/master/latlon-ellipsoidal-vincenty.js>
298# raise VincentyError(_ambiguous_, self._is_to(other, True))
299 else:
300 t = self._is_to(other, self.isantipodeTo(other, eps=eps))
301 raise VincentyError(self._no_convergence(e), txt=t)
303 if ca2: # e22 == (a / b)**2 - 1
304 A, B = _AB2(ca2 * E.e22)
305 s = -A * _Ds(B, cs, ss, c2sm, -s)
307 b = E.b
308# if self.height or other.height:
309# b += self._havg(other)
310 d = b * s
312 if azis: # forward and reverse azimuth
313 s, c = sincos2(ll)
314 f = atan2b(c2 * s, c1s2 - s1c2 * c)
315 r = atan2b(c1 * s, -s1c2 + c1s2 * c)
316 else:
317 f = r = _0_0 # NAN
318 return Distance3Tuple(d, f, r, name=self.name, iteration=i)
320 def _is_to(self, other, anti):
321 '''(INTERNAL) Return I{'<self> [antipodal] to <other>'} text (C{str}).
322 '''
323 t = _antipodal_to_ if anti else _to_
324 return _SPACE_(repr(self), t, repr(other))
326 def _no_convergence(self, e):
327 '''(INTERNAL) Return I{'no convergence (..): ...'} text (C{str}).
328 '''
329 t = (Fmt.PARENSPACED(*t) for t in ((LatLon.epsilon.name, self.epsilon),
330 (LatLon.iterations.name, self.iterations)))
331 return _COLONSPACE_(Fmt.no_convergence(e), _and(*t))
334def _AB2(u2): # WGS84 e22 = 0.00673949674227643
335 # 2-Tuple C{(A, B)} polynomials
336 if u2:
337 A = Fpolynomial(u2, 16384, 4096, -768, 320, -175).fover(16384)
338 B = Fpolynomial(u2, 0, 256, -128, 74, -47).fover( 1024)
339 return A, B
340 return _1_0, _0_0
343def _c2sm2(c2sm):
344 # C{2 * c2sm**2 - 1}
345 return c2sm**2 * _2_0 - _1_0
348def _Dl(f, ca2, sa, s, cs, ss, c2sm, dl=_0_0):
349 # C{Dl}
350 if f and sa:
351 C = f * ca2 / _4_0
352 C *= f - C * _3_0 + _1_0
353 if C and ss:
354 s += C * ss * (c2sm +
355 C * cs * _c2sm2(c2sm))
356 dl += (_1_0 - C) * f * sa * s
357 return dl
360def _Ds(B, cs, ss, c2sm, d):
361 # C{Ds - d}
362 if B and ss:
363 c2sm2 = _c2sm2(c2sm)
364 ss2 = (ss**2 * _4_0 - _3_0) * (c2sm2 * _2_0 - _1_0)
365 B *= ss * (c2sm + B / _4_0 * (c2sm2 * cs -
366 B / _6_0 * c2sm * ss2))
367 d += B
368 return d
371def _Ecef():
372 # get the Ecef class and overwrite property_RO
373 Cartesian.Ecef = LatLon.Ecef = E = _MODS.ecef.EcefVeness
374 return E
377def _sincos22(sa):
378 # 2-Tuple C{(sin(a), cos(a)**2)}
379 ca2 = _1_0 - sa**2
380 return sa, (_0_0 if ca2 < EPS0 else ca2) # XXX EPS?
383def _sincostan3r(a, f):
384 # I{Reduced} 3-tuple C{(sin(B{a}), cos(B{a}), tan(B{a}))}
385 if a: # see L{sincostan3}
386 t = (_1_0 - f) * tan(a)
387 if t:
388 c = _1_0 / hypot1(t)
389 s = c * t
390 return s, c, t
391 return _0_0, _1_0, _0_0
394@deprecated_function
395def areaOf(points, **datum_wrap):
396 '''DEPRECATED, use function L{ellipsoidalExact.areaOf} or L{ellipsoidalKarney.areaOf}.
397 '''
398 try:
399 return _MODS.ellipsoidalKarney.areaOf(points, **datum_wrap)
400 except ImportError:
401 return _MODS.ellipsoidalExact.areaOf(points, **datum_wrap)
404def intersection3(start1, end1, start2, end2, height=None, wrap=False, # was=True
405 equidistant=None, tol=_TOL_M, LatLon=LatLon, **LatLon_kwds):
406 '''I{Iteratively} compute the intersection point of two lines, each defined
407 by two (ellipsoidal) points or by an (ellipsoidal) start point and an
408 (initial) bearing from North.
410 @arg start1: Start point of the first line (L{LatLon}).
411 @arg end1: End point of the first line (L{LatLon}) or the initial bearing
412 at the first point (compass C{degrees360}).
413 @arg start2: Start point of the second line (L{LatLon}).
414 @arg end2: End point of the second line (L{LatLon}) or the initial bearing
415 at the second point (compass C{degrees360}).
416 @kwarg height: Optional height at the intersection (C{meter}, conventionally)
417 or C{None} for the mean height.
418 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the B{C{start2}}
419 and B{C{end*}} points (C{bool}).
420 @kwarg equidistant: An azimuthal equidistant projection (I{class} or function
421 L{pygeodesy.equidistant}) or C{None} for the preferred
422 C{B{start1}.Equidistant}.
423 @kwarg tol: Tolerance for convergence and for skew line distance and length
424 (C{meter}, conventionally).
425 @kwarg LatLon: Optional class to return the intersection points (L{LatLon})
426 or C{None}.
427 @kwarg LatLon_kwds: Optional, additional B{C{LatLon}} keyword arguments,
428 ignored if C{B{LatLon} is None}.
430 @return: An L{Intersection3Tuple}C{(point, outside1, outside2)} with C{point}
431 a B{C{LatLon}} or if C{B{LatLon} is None}, a L{LatLon4Tuple}C{(lat,
432 lon, height, datum)}.
434 @raise IntersectionError: Skew, colinear, parallel or otherwise
435 non-intersecting lines or no convergence
436 for the given B{C{tol}}.
438 @raise TypeError: Invalid or non-ellipsoidal B{C{start1}}, B{C{end1}},
439 B{C{start2}} or B{C{end2}} or invalid B{C{equidistant}}.
441 @note: For each line specified with an initial bearing, a pseudo-end point
442 is computed as the C{destination} along that bearing at about 1.5
443 times the distance from the start point to an initial gu-/estimate
444 of the intersection point (and between 1/8 and 3/8 of the authalic
445 earth perimeter).
447 @see: U{The B{ellipsoidal} case<https://GIS.StackExchange.com/questions/48937/
448 calculating-intersection-of-two-circles>} and U{Karney's paper
449 <https://ArXiv.org/pdf/1102.1215.pdf>}, pp 20-21, section B{14. MARITIME
450 BOUNDARIES} for more details about the iteration algorithm.
451 '''
452 return _intersection3(start1, end1, start2, end2, height=height, wrap=wrap,
453 equidistant=equidistant, tol=tol, LatLon=LatLon, **LatLon_kwds)
456def intersections2(center1, radius1, center2, radius2, height=None, wrap=False, # was=True
457 equidistant=None, tol=_TOL_M, LatLon=LatLon, **LatLon_kwds):
458 '''I{Iteratively} compute the intersection points of two circles, each defined
459 by an (ellipsoidal) center point and a radius.
461 @arg center1: Center of the first circle (L{LatLon}).
462 @arg radius1: Radius of the first circle (C{meter}, conventionally).
463 @arg center2: Center of the second circle (L{LatLon}).
464 @arg radius2: Radius of the second circle (C{meter}, same units as
465 B{C{radius1}}).
466 @kwarg height: Optional height for the intersection points (C{meter},
467 conventionally) or C{None} for the I{"radical height"}
468 at the I{radical line} between both centers.
469 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll B{C{center2}}
470 (C{bool}).
471 @kwarg equidistant: An azimuthal equidistant projection (I{class} or
472 function L{pygeodesy.equidistant}) or C{None} for
473 the preferred C{B{center1}.Equidistant}.
474 @kwarg tol: Convergence tolerance (C{meter}, same units as B{C{radius1}}
475 and B{C{radius2}}).
476 @kwarg LatLon: Optional class to return the intersection points (L{LatLon})
477 or C{None}.
478 @kwarg LatLon_kwds: Optional, additional B{C{LatLon}} keyword arguments,
479 ignored if C{B{LatLon} is None}.
481 @return: 2-Tuple of the intersection points, each a B{C{LatLon}} instance
482 or L{LatLon4Tuple}C{(lat, lon, height, datum)} if C{B{LatLon} is
483 None}. For abutting circles, both points are the same instance,
484 aka the I{radical center}.
486 @raise IntersectionError: Concentric, antipodal, invalid or non-intersecting
487 circles or no convergence for the B{C{tol}}.
489 @raise TypeError: Invalid or non-ellipsoidal B{C{center1}} or B{C{center2}}
490 or invalid B{C{equidistant}}.
492 @raise UnitError: Invalid B{C{radius1}}, B{C{radius2}} or B{C{height}}.
494 @see: U{The B{ellipsoidal} case<https://GIS.StackExchange.com/questions/48937/
495 calculating-intersection-of-two-circles>}, U{Karney's paper
496 <https://ArXiv.org/pdf/1102.1215.pdf>}, pp 20-21, section B{14. MARITIME BOUNDARIES},
497 U{circle-circle<https://MathWorld.Wolfram.com/Circle-CircleIntersection.html>} and
498 U{sphere-sphere<https://MathWorld.Wolfram.com/Sphere-SphereIntersection.html>}
499 intersections.
500 '''
501 return _intersections2(center1, radius1, center2, radius2, height=height, wrap=wrap,
502 equidistant=equidistant, tol=tol, LatLon=LatLon, **LatLon_kwds)
505def nearestOn(point, point1, point2, within=True, height=None, wrap=False,
506 equidistant=None, tol=_TOL_M, LatLon=LatLon, **LatLon_kwds):
507 '''I{Iteratively} locate the closest point on the geodesic between
508 two other (ellipsoidal) points.
510 @arg point: Reference point (C{LatLon}).
511 @arg point1: Start point of the geodesic (C{LatLon}).
512 @arg point2: End point of the geodesic (C{LatLon}).
513 @kwarg within: If C{True} return the closest point I{between}
514 B{C{point1}} and B{C{point2}}, otherwise the
515 closest point elsewhere on the geodesic (C{bool}).
516 @kwarg height: Optional height for the closest point (C{meter},
517 conventionally) or C{None} or C{False} for the
518 interpolated height. If C{False}, the closest
519 takes the heights of the points into account.
520 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll both
521 B{C{point1}} and B{C{point2}} (C{bool}).
522 @kwarg equidistant: An azimuthal equidistant projection (I{class}
523 or function L{pygeodesy.equidistant}) or C{None}
524 for the preferred C{B{point}.Equidistant}.
525 @kwarg tol: Convergence tolerance (C{meter}).
526 @kwarg LatLon: Optional class to return the closest point
527 (L{LatLon}) or C{None}.
528 @kwarg LatLon_kwds: Optional, additional B{C{LatLon}} keyword
529 arguments, ignored if C{B{LatLon} is None}.
531 @return: Closest point, a B{C{LatLon}} instance or if C{B{LatLon}
532 is None}, a L{LatLon4Tuple}C{(lat, lon, height, datum)}.
534 @raise ImportError: Package U{geographiclib
535 <https://PyPI.org/project/geographiclib>}
536 not installed or not found, but only if
537 C{B{equidistant}=}L{EquidistantKarney}.
539 @raise TypeError: Invalid or non-ellipsoidal B{C{point}}, B{C{point1}}
540 or B{C{point2}} or invalid B{C{equidistant}}.
542 @raise ValueError: No convergence for the B{C{tol}}.
544 @see: U{The B{ellipsoidal} case<https://GIS.StackExchange.com/questions/48937/
545 calculating-intersection-of-two-circles>} and U{Karney's paper
546 <https://ArXiv.org/pdf/1102.1215.pdf>}, pp 20-21, section B{14. MARITIME
547 BOUNDARIES} for more details about the iteration algorithm.
548 '''
549 return _nearestOn(point, point1, point2, within=within, height=height, wrap=wrap,
550 equidistant=equidistant, tol=tol, LatLon=LatLon, **LatLon_kwds)
553@deprecated_function
554def perimeterOf(points, **closed_datum_wrap):
555 '''DEPRECATED, use function L{ellipsoidalExact.perimeterOf} or L{ellipsoidalKarney.perimeterOf}.
556 '''
557 try:
558 return _MODS.ellipsoidalKarney.perimeterOf(points, **closed_datum_wrap)
559 except ImportError:
560 return _MODS.ellipsoidalExact.perimeterOf(points, **closed_datum_wrap)
563__all__ += _ALL_OTHER(Cartesian, LatLon, intersecant2, # from .ellipsoidalBaseDI
564 intersection3, intersections2, ispolar, # from .points
565 nearestOn) + _ALL_DOCS(areaOf, perimeterOf) # deprecated
567# **) MIT License
568#
569# Copyright (C) 2016-2024 -- mrJean1 at Gmail -- All Rights Reserved.
570#
571# Permission is hereby granted, free of charge, to any person obtaining a
572# copy of this software and associated documentation files (the "Software"),
573# to deal in the Software without restriction, including without limitation
574# the rights to use, copy, modify, merge, publish, distribute, sublicense,
575# and/or sell copies of the Software, and to permit persons to whom the
576# Software is furnished to do so, subject to the following conditions:
577#
578# The above copyright notice and this permission notice shall be included
579# in all copies or substantial portions of the Software.
580#
581# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
582# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
583# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
584# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR
585# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
586# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
587# OTHER DEALINGS IN THE SOFTWARE.