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 2005-2024}
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
54# from pygeodesy.ecef import EcefVeness # _MODS
55from pygeodesy.ellipsoidalBase import CartesianEllipsoidalBase, _nearestOn
56from pygeodesy.ellipsoidalBaseDI import LatLonEllipsoidalBaseDI, \
57 _intersection3, _intersections2, \
58 _TOL_M, intersecant2
59# from pygeodesy.ellipsoidalExact import areaOf, perimeterOf # _MODS
60# from pygeodesy.ellipsoidalKarney import areaOf, perimeterOf # _MODS
61from pygeodesy.errors import _and, _ValueError, _xkwds
62from pygeodesy.fmath import Fpolynomial, hypot, hypot1
63from pygeodesy.interns import _ambiguous_, _antipodal_, _COLONSPACE_, \
64 _to_, _SPACE_, _limit_ # PYCHOK used!
65from pygeodesy.lazily import _ALL_DOCS, _ALL_LAZY, _ALL_MODS as _MODS
66from pygeodesy.namedTuples import Destination2Tuple, Destination3Tuple, \
67 Distance3Tuple
68from pygeodesy.points import Fmt, ispolar # PYCHOK exported
69from pygeodesy.props import deprecated_function, deprecated_method, \
70 property_doc_, property_RO
71# from pygeodesy.streprs import Fmt # from .points
72from pygeodesy.units import Number_, Scalar_
73from pygeodesy.utily import atan2, atan2b, atan2d, sincos2, sincos2d, \
74 unroll180, wrap180
76from math import cos, degrees, fabs, radians, tan as _tan
78__all__ = _ALL_LAZY.ellipsoidalVincenty
79__version__ = '25.04.21'
81_antipodal_to_ = _SPACE_(_antipodal_, _to_)
84class VincentyError(_ValueError):
85 '''Error raised by I{Vincenty}'s C{Direct} and C{Inverse} methods
86 for coincident points or lack of convergence.
87 '''
88 pass
91class Cartesian(CartesianEllipsoidalBase):
92 '''Extended to convert geocentric, L{Cartesian} points to
93 Vincenty-based, ellipsoidal, geodetic L{LatLon}.
94 '''
95 @property_RO
96 def Ecef(self):
97 '''Get the ECEF I{class} (L{EcefVeness}), I{once}.
98 '''
99 return _Ecef()
101 def toLatLon(self, **LatLon_and_kwds): # PYCHOK LatLon=LatLon, datum=None
102 '''Convert this cartesian point to a C{Vincenty}-based geodetic point.
104 @kwarg LatLon_and_kwds: Optional L{LatLon} and L{LatLon} keyword
105 arguments as C{datum}. Use C{B{LatLon}=...,
106 B{datum}=...} to override this L{LatLon}
107 class or specify C{B{LatLon}=None}.
109 @return: The geodetic point (L{LatLon}) or if C{B{LatLon} is None},
110 an L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M, datum)}
111 with C{C} and C{M} if available.
113 @raise TypeError: Invalid B{C{LatLon_and_kwds}} argument.
114 '''
115 kwds = _xkwds(LatLon_and_kwds, LatLon=LatLon, datum=self.datum)
116 return CartesianEllipsoidalBase.toLatLon(self, **kwds)
119class LatLon(LatLonEllipsoidalBaseDI):
120 '''New point on an (oblate) ellipsoidal earth model, using the formulae devised
121 by U{I{Thaddeus Vincenty}<https://WikiPedia.org/wiki/Vincenty's_formulae>}
122 (1975) to compute geodesic distances, bearings (azimuths), etc.
124 Set the earth model to be used with the keyword argument datum. The default
125 is C{Datums.WGS84}, which is the most globally accurate. For other models,
126 see the L{Datums<pygeodesy.datums>}.
128 @note: This implementation of I{Vincenty} methods may not converge for some
129 valid points, raising a L{VincentyError}. In that case, a result may
130 be obtained by increasing the tolerance C{epsilon} and/or iteration
131 C{limit}, see properties L{LatLon.epsilon} and L{LatLon.iterations}.
132 '''
133 _epsilon = 1e-12 # radians, about 6 um
134# _iteration = None # iteration number from .named._NamedBase
135 _iterations = 201 # 5, default max, 200 vs Veness' 1,000
137 @deprecated_method
138 def bearingTo(self, other, wrap=False): # PYCHOK no cover
139 '''DEPRECATED, use method L{initialBearingTo} or L{bearingTo2}.
140 '''
141 return self.initialBearingTo(other, wrap=wrap)
143 @property_RO
144 def Ecef(self):
145 '''Get the ECEF I{class} (L{EcefVeness}), I{once}.
146 '''
147 return _Ecef()
149 @property_doc_(''' the convergence epsilon (C{radians}).''')
150 def epsilon(self):
151 '''Get the convergence epsilon (C{radians}).
152 '''
153 return self._epsilon
155 @epsilon.setter # PYCHOK setter!
156 def epsilon(self, epsilon):
157 '''Set the convergence epsilon (C{radians}).
159 @raise TypeError: Non-scalar B{C{epsilon}}.
161 @raise ValueError: Out of bounds B{C{epsilon}}.
162 '''
163 self._epsilon = Scalar_(epsilon=epsilon)
165 @property_doc_(''' the iteration limit (C{int}).''')
166 def iterations(self):
167 '''Get the iteration limit (C{int}).
168 '''
169 return self._iterations - 1
171 @iterations.setter # PYCHOK setter!
172 def iterations(self, limit):
173 '''Set the iteration limit (C{int}).
175 @raise TypeError: Non-scalar B{C{limit}}.
177 @raise ValueError: Out-of-bounds B{C{limit}}.
178 '''
179 self._iterations = Number_(limit, name=_limit_, low=4, high=1000) + 1
181 def toCartesian(self, **Cartesian_datum_kwds): # PYCHOK Cartesian=Cartesian, datum=None
182 '''Convert this point to C{Vincenty}-based cartesian (ECEF) coordinates.
184 @kwarg Cartesian_datum_kwds: Optional L{Cartesian}, B{C{datum}} and other
185 keyword arguments, ignored if C{B{Cartesian}=None}. Use
186 C{B{Cartesian}=...} to override this L{Cartesian} class
187 or specify C{B{Cartesian}=None}.
189 @return: The cartesian point (L{Cartesian}) or if C{B{Cartesian} is None},
190 an L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M, datum)} with
191 C{C} and C{M} if available.
193 @raise TypeError: Invalid B{C{Cartesian}}, B{C{datum}} or other B{C{Cartesian_datum_kwds}}.
194 '''
195 kwds = _xkwds(Cartesian_datum_kwds, Cartesian=Cartesian,
196 datum=self.datum)
197 return LatLonEllipsoidalBaseDI.toCartesian(self, **kwds)
199 def _Direct(self, distance, bearing, llr, height):
200 '''(INTERNAL) Direct Vincenty method.
202 @raise TypeError: The B{C{other}} point is not L{LatLon}.
204 @raise ValueError: If this and the B{C{other}} point's L{Datum} ellipsoids are
205 not compatible.
207 @raise VincentyError: Vincenty fails to converge for the current limits, see
208 L{epsilon<LatLon.epsilon>} and L{iterations<LatLon.iterations>}.
209 '''
210 E = self.ellipsoid()
211 f = E.f
213 sb, cb = sincos2d(bearing)
214 s1, c1, t1 = _sincostan3r(self.phi, f)
216 eps = self.epsilon
217 s12 = atan2(t1, cb) * _2_0
218 sa, ca2 = _sincos22(c1 * sb)
219 A, B = _AB2(ca2 * E.e22) # e22 == (a / b)**2 - 1
220 s = d = distance / (A * E.b)
221 for i in range(1, self._iterations): # 1-origin
222 ss, cs = sincos2(s)
223 c2sm, e = cos(s12 + s), s
224 s = _Ds(B, cs, ss, c2sm, d)
225 e = fabs(s - e)
226 if e < eps:
227 self._iteration = i
228 break
229 else:
230 t = self._no_convergence(e)
231 raise VincentyError(t, txt=repr(self)) # self.toRepr()
233 t = s1 * ss - c1 * cs * cb
234 # final bearing (reverse azimuth +/- 180)
235 d = atan2b(sa, -t)
236 if llr:
237 b = cb * ss
238 a = atan2d(s1 * cs + c1 * b, hypot(sa, t) * E.b_a)
239 b = atan2d(sb * ss, -s1 * b + c1 * cs) + self.lon \
240 - degrees(_Dl(f, ca2, sa, s, cs, ss, c2sm))
241 t = Destination3Tuple(a, wrap180(b), d)
242 r = self._Direct2Tuple(self.classof, height, t)
243 else:
244 r = Destination2Tuple(None, d, name=self.name)
245 r._iteration = i
246 return r
248 def _Inverse(self, other, wrap, azis=True): # PYCHOK signature
249 '''(INTERNAL) Inverse Vincenty method.
251 @raise TypeError: The B{C{other}} point is not L{LatLon}.
253 @raise ValueError: If this and the B{C{other}} point's L{Datum}
254 ellipsoids are not compatible.
256 @raise VincentyError: Vincenty fails to converge for the current
257 L{LatLon.epsilon} and L{LatLon.iterations}
258 limits and/or if this and the B{C{other}}
259 point are coincident or near-antipodal.
260 '''
261 E = self.ellipsoids(other)
262 f = E.f
264 s1, c1, _ = _sincostan3r( self.phi, f)
265 s2, c2, _ = _sincostan3r(other.phi, f)
267 c1c2, s1c2 = c1 * c2, s1 * c2
268 c1s2, s1s2 = c1 * s2, s1 * s2
270 eps = self.epsilon
271 d, _ = unroll180(self.lon, other.lon, wrap=wrap)
272 dl = ll = radians(d)
273 for i in range(1, self._iterations): # 1-origin
274 sll, cll = sincos2(ll)
276 ss = hypot(c2 * sll, c1s2 - s1c2 * cll)
277 if ss < EPS: # coincident or antipodal, ...
278 if self.isantipodeTo(other, eps=eps):
279 t = self._is_to(other, True)
280 raise VincentyError(_ambiguous_, txt=t)
281 self._iteration = i
282 # return zeros like Karney, unlike Veness
283 return Distance3Tuple(_0_0, 0, 0, iteration=i)
285 cs = s1s2 + c1c2 * cll
286 s, e = atan2(ss, cs), ll
287 sa, ca2 = _sincos22(c1c2 * sll / ss)
288 if ca2:
289 c2sm = cs - _2_0 * s1s2 / ca2
290 ll = _Dl(f, ca2, sa, s, cs, ss, c2sm, dl)
291 else: # equatorial line
292 ll = dl + f * sa * s
293 e = fabs(ll - e)
294 if e < eps:
295 self._iteration = i
296 break
297# elif abs(ll) > PI and self.isantipodeTo(other, eps=eps):
298# # omitted and applied *after* failure to converge below,
299# # see footnote under Inverse <https://WikiPedia.org/wiki/
300# # Vincenty's_formulae> and <https://GitHub.com/chrisveness/
301# # geodesy/blob/master/latlon-ellipsoidal-vincenty.js>
302# raise VincentyError(_ambiguous_, self._is_to(other, True))
303 else:
304 t = self._is_to(other, self.isantipodeTo(other, eps=eps))
305 raise VincentyError(self._no_convergence(e), txt=t)
307 if ca2: # e22 == (a / b)**2 - 1
308 A, B = _AB2(ca2 * E.e22)
309 s = -A * _Ds(B, cs, ss, c2sm, -s)
311 b = E.b
312# if self.height or other.height:
313# b += self._havg(other)
314 d = b * s
316 if azis: # forward and reverse azimuth
317 s, c = sincos2(ll)
318 f = atan2b(c2 * s, c1s2 - s1c2 * c)
319 r = atan2b(c1 * s, -s1c2 + c1s2 * c)
320 else:
321 f = r = _0_0 # NAN
322 return Distance3Tuple(d, f, r, name=self.name, iteration=i)
324 def _is_to(self, other, anti):
325 '''(INTERNAL) Return I{'<self> [antipodal] to <other>'} text (C{str}).
326 '''
327 t = _antipodal_to_ if anti else _to_
328 return _SPACE_(repr(self), t, repr(other))
330 def _no_convergence(self, e):
331 '''(INTERNAL) Return I{'no convergence (..): ...'} text (C{str}).
332 '''
333 t = (Fmt.PARENSPACED(*t) for t in ((LatLon.epsilon.name, self.epsilon),
334 (LatLon.iterations.name, self.iterations)))
335 return _COLONSPACE_(Fmt.no_convergence(e), _and(*t))
338def _AB2(u2): # WGS84 e22 = 0.00673949674227643
339 # 2-Tuple C{(A, B)} polynomials
340 if u2:
341 A = Fpolynomial(u2, 16384, 4096, -768, 320, -175).fover(16384)
342 B = Fpolynomial(u2, 0, 256, -128, 74, -47).fover( 1024)
343 return A, B
344 return _1_0, _0_0
347def _c2sm2(c2sm):
348 # C{2 * c2sm**2 - 1}
349 return c2sm**2 * _2_0 - _1_0
352def _Dl(f, ca2, sa, s, cs, ss, c2sm, dl=_0_0):
353 # C{Dl}
354 if f and sa:
355 C = f * ca2 / _4_0
356 C *= f - C * _3_0 + _1_0
357 if C and ss:
358 s += C * ss * (c2sm +
359 C * cs * _c2sm2(c2sm))
360 dl += (_1_0 - C) * f * sa * s
361 return dl
364def _Ds(B, cs, ss, c2sm, d):
365 # C{Ds - d}
366 if B and ss:
367 c2sm2 = _c2sm2(c2sm)
368 ss2 = (ss**2 * _4_0 - _3_0) * (c2sm2 * _2_0 - _1_0)
369 B *= ss * (c2sm + B / _4_0 * (c2sm2 * cs -
370 B / _6_0 * c2sm * ss2))
371 d += B
372 return d
375def _Ecef():
376 # get the Ecef class and overwrite property_RO
377 Cartesian.Ecef = LatLon.Ecef = E = _MODS.ecef.EcefVeness
378 return E
381def _sincos22(sa):
382 # 2-Tuple C{(sin(a), cos(a)**2)}
383 ca2 = _1_0 - sa**2
384 return sa, (_0_0 if ca2 < EPS0 else ca2) # XXX EPS?
387def _sincostan3r(a, f):
388 # I{Reduced} 3-tuple C{(sin(B{a}), cos(B{a}), tan(B{a}))}
389 if a: # see L{sincostan3}
390 t = (_1_0 - f) * _tan(a)
391 if t:
392 c = _1_0 / hypot1(t)
393 s = c * t
394 return s, c, t
395 return _0_0, _1_0, _0_0
398@deprecated_function
399def areaOf(points, **datum_wrap):
400 '''DEPRECATED, use function L{ellipsoidalExact.areaOf} or L{ellipsoidalKarney.areaOf}.
401 '''
402 try:
403 return _MODS.ellipsoidalKarney.areaOf(points, **datum_wrap)
404 except ImportError:
405 return _MODS.ellipsoidalExact.areaOf(points, **datum_wrap)
408def intersection3(start1, end1, start2, end2, height=None, wrap=False, # was=True
409 equidistant=None, tol=_TOL_M, LatLon=LatLon, **LatLon_kwds):
410 '''I{Iteratively} compute the intersection point of two lines, each defined
411 by two (ellipsoidal) points or by an (ellipsoidal) start point and an
412 (initial) bearing from North.
414 @arg start1: Start point of the first line (L{LatLon}).
415 @arg end1: End point of the first line (L{LatLon}) or the initial bearing
416 at the first point (compass C{degrees360}).
417 @arg start2: Start point of the second line (L{LatLon}).
418 @arg end2: End point of the second line (L{LatLon}) or the initial bearing
419 at the second point (compass C{degrees360}).
420 @kwarg height: Optional height at the intersection (C{meter}, conventionally)
421 or C{None} for the mean height.
422 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the B{C{start2}}
423 and B{C{end*}} points (C{bool}).
424 @kwarg equidistant: An azimuthal equidistant projection (I{class} or function
425 L{pygeodesy.equidistant}) or C{None} for the preferred
426 C{B{start1}.Equidistant}.
427 @kwarg tol: Tolerance for convergence and for skew line distance and length
428 (C{meter}, conventionally).
429 @kwarg LatLon: Optional class to return the intersection points (L{LatLon})
430 or C{None}.
431 @kwarg LatLon_kwds: Optional, additional B{C{LatLon}} keyword arguments,
432 ignored if C{B{LatLon} is None}.
434 @return: An L{Intersection3Tuple}C{(point, outside1, outside2)} with C{point}
435 a B{C{LatLon}} or if C{B{LatLon} is None}, a L{LatLon4Tuple}C{(lat,
436 lon, height, datum)}.
438 @raise IntersectionError: Skew, colinear, parallel or otherwise
439 non-intersecting lines or no convergence
440 for the given B{C{tol}}.
442 @raise TypeError: Invalid or non-ellipsoidal B{C{start1}}, B{C{end1}},
443 B{C{start2}} or B{C{end2}} or invalid B{C{equidistant}}.
445 @note: For each line specified with an initial bearing, a pseudo-end point
446 is computed as the C{destination} along that bearing at about 1.5
447 times the distance from the start point to an initial gu-/estimate
448 of the intersection point (and between 1/8 and 3/8 of the authalic
449 earth perimeter).
451 @see: U{The B{ellipsoidal} case<https://GIS.StackExchange.com/questions/48937/
452 calculating-intersection-of-two-circles>} and U{Karney's paper
453 <https://ArXiv.org/pdf/1102.1215.pdf>}, pp 20-21, section B{14. MARITIME
454 BOUNDARIES} for more details about the iteration algorithm.
455 '''
456 return _intersection3(start1, end1, start2, end2, height=height, wrap=wrap,
457 equidistant=equidistant, tol=tol, LatLon=LatLon, **LatLon_kwds)
460def intersections2(center1, radius1, center2, radius2, height=None, wrap=False, # was=True
461 equidistant=None, tol=_TOL_M, LatLon=LatLon, **LatLon_kwds):
462 '''I{Iteratively} compute the intersection points of two circles, each defined
463 by an (ellipsoidal) center point and a radius.
465 @arg center1: Center of the first circle (L{LatLon}).
466 @arg radius1: Radius of the first circle (C{meter}, conventionally).
467 @arg center2: Center of the second circle (L{LatLon}).
468 @arg radius2: Radius of the second circle (C{meter}, same units as
469 B{C{radius1}}).
470 @kwarg height: Optional height for the intersection points (C{meter},
471 conventionally) or C{None} for the I{"radical height"}
472 at the I{radical line} between both centers.
473 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll B{C{center2}}
474 (C{bool}).
475 @kwarg equidistant: An azimuthal equidistant projection (I{class} or
476 function L{pygeodesy.equidistant}) or C{None} for
477 the preferred C{B{center1}.Equidistant}.
478 @kwarg tol: Convergence tolerance (C{meter}, same units as B{C{radius1}}
479 and B{C{radius2}}).
480 @kwarg LatLon: Optional class to return the intersection points (L{LatLon})
481 or C{None}.
482 @kwarg LatLon_kwds: Optional, additional B{C{LatLon}} keyword arguments,
483 ignored if C{B{LatLon} is None}.
485 @return: 2-Tuple of the intersection points, each a B{C{LatLon}} instance
486 or L{LatLon4Tuple}C{(lat, lon, height, datum)} if C{B{LatLon} is
487 None}. For abutting circles, both points are the same instance,
488 aka the I{radical center}.
490 @raise IntersectionError: Concentric, antipodal, invalid or non-intersecting
491 circles or no convergence for the B{C{tol}}.
493 @raise TypeError: Invalid or non-ellipsoidal B{C{center1}} or B{C{center2}}
494 or invalid B{C{equidistant}}.
496 @raise UnitError: Invalid B{C{radius1}}, B{C{radius2}} or B{C{height}}.
498 @see: U{The B{ellipsoidal} case<https://GIS.StackExchange.com/questions/48937/
499 calculating-intersection-of-two-circles>}, U{Karney's paper
500 <https://ArXiv.org/pdf/1102.1215.pdf>}, pp 20-21, section B{14. MARITIME BOUNDARIES},
501 U{circle-circle<https://MathWorld.Wolfram.com/Circle-CircleIntersection.html>} and
502 U{sphere-sphere<https://MathWorld.Wolfram.com/Sphere-SphereIntersection.html>}
503 intersections.
504 '''
505 return _intersections2(center1, radius1, center2, radius2, height=height, wrap=wrap,
506 equidistant=equidistant, tol=tol, LatLon=LatLon, **LatLon_kwds)
509def nearestOn(point, point1, point2, within=True, height=None, wrap=False,
510 equidistant=None, tol=_TOL_M, LatLon=LatLon, **LatLon_kwds):
511 '''I{Iteratively} locate the closest point on the geodesic between
512 two other (ellipsoidal) points.
514 @arg point: Reference point (C{LatLon}).
515 @arg point1: Start point of the geodesic (C{LatLon}).
516 @arg point2: End point of the geodesic (C{LatLon}).
517 @kwarg within: If C{True}, return the closest point I{between}
518 B{C{point1}} and B{C{point2}}, otherwise the
519 closest point elsewhere on the geodesic (C{bool}).
520 @kwarg height: Optional height for the closest point (C{meter},
521 conventionally) or C{None} or C{False} for the
522 interpolated height. If C{False}, the closest
523 takes the heights of the points into account.
524 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll both
525 B{C{point1}} and B{C{point2}} (C{bool}).
526 @kwarg equidistant: An azimuthal equidistant projection (I{class}
527 or function L{pygeodesy.equidistant}) or C{None}
528 for the preferred C{B{point}.Equidistant}.
529 @kwarg tol: Convergence tolerance (C{meter}).
530 @kwarg LatLon: Optional class to return the closest point
531 (L{LatLon}) or C{None}.
532 @kwarg LatLon_kwds: Optional, additional B{C{LatLon}} keyword
533 arguments, ignored if C{B{LatLon} is None}.
535 @return: Closest point, a B{C{LatLon}} instance or if C{B{LatLon}
536 is None}, a L{LatLon4Tuple}C{(lat, lon, height, datum)}.
538 @raise ImportError: Package U{geographiclib
539 <https://PyPI.org/project/geographiclib>}
540 not installed or not found, but only if
541 C{B{equidistant}=}L{EquidistantKarney}.
543 @raise TypeError: Invalid or non-ellipsoidal B{C{point}}, B{C{point1}}
544 or B{C{point2}} or invalid B{C{equidistant}}.
546 @raise ValueError: No convergence for the B{C{tol}}.
548 @see: U{The B{ellipsoidal} case<https://GIS.StackExchange.com/questions/48937/
549 calculating-intersection-of-two-circles>} and U{Karney's paper
550 <https://ArXiv.org/pdf/1102.1215.pdf>}, pp 20-21, section B{14. MARITIME
551 BOUNDARIES} for more details about the iteration algorithm.
552 '''
553 return _nearestOn(point, point1, point2, within=within, height=height, wrap=wrap,
554 equidistant=equidistant, tol=tol, LatLon=LatLon, **LatLon_kwds)
557@deprecated_function
558def perimeterOf(points, **closed_datum_wrap):
559 '''DEPRECATED, use function L{ellipsoidalExact.perimeterOf} or L{ellipsoidalKarney.perimeterOf}.
560 '''
561 try:
562 return _MODS.ellipsoidalKarney.perimeterOf(points, **closed_datum_wrap)
563 except ImportError:
564 return _MODS.ellipsoidalExact.perimeterOf(points, **closed_datum_wrap)
567__all__ += _ALL_DOCS(Cartesian, LatLon, intersecant2, # from .ellipsoidalBaseDI
568 intersection3, intersections2, ispolar, # from .points
569 nearestOn,
570 areaOf, perimeterOf) # DEPRECATED
572# **) MIT License
573#
574# Copyright (C) 2016-2025 -- mrJean1 at Gmail -- All Rights Reserved.
575#
576# Permission is hereby granted, free of charge, to any person obtaining a
577# copy of this software and associated documentation files (the "Software"),
578# to deal in the Software without restriction, including without limitation
579# the rights to use, copy, modify, merge, publish, distribute, sublicense,
580# and/or sell copies of the Software, and to permit persons to whom the
581# Software is furnished to do so, subject to the following conditions:
582#
583# The above copyright notice and this permission notice shall be included
584# in all copies or substantial portions of the Software.
585#
586# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
587# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
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589# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR
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