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 _intersection3, _intersections2, \
56 LatLonEllipsoidalBaseDI, _TOL_M
57from pygeodesy.errors import _and, _ValueError, _xkwds
58from pygeodesy.fmath import Fpolynomial, hypot, hypot1
59from pygeodesy.interns import _ambiguous_, _antipodal_, _COLONSPACE_, _to_, _SPACE_
60from pygeodesy.lazily import _ALL_DOCS, _ALL_LAZY, _ALL_MODS as _MODS, _ALL_OTHER
61from pygeodesy.namedTuples import Destination2Tuple, Destination3Tuple, \
62 Distance3Tuple
63from pygeodesy.points import Fmt, ispolar # PYCHOK exported
64from pygeodesy.props import deprecated_function, deprecated_method, \
65 Property_RO, property_doc_
66# from pygeodesy.streprs import Fmt # from .points
67from pygeodesy.units import Number_, Scalar_
68from pygeodesy.utily import atan2b, atan2d, sincos2, sincos2d, unroll180, wrap180
70from math import atan2, cos, degrees, fabs, radians, tan
72__all__ = _ALL_LAZY.ellipsoidalVincenty
73__version__ = '23.03.20'
75_antipodal_to_ = _SPACE_(_antipodal_, _to_)
76_limit_ = 'limit' # PYCHOK used!
79class VincentyError(_ValueError):
80 '''Error raised from I{Vincenty}'s C{direct} and C{inverse} methods
81 for coincident points or lack of convergence.
82 '''
83 pass
86class Cartesian(CartesianEllipsoidalBase):
87 '''Extended to convert geocentric, L{Cartesian} points to
88 Vincenty-based, ellipsoidal, geodetic L{LatLon}.
89 '''
90 @Property_RO
91 def Ecef(self):
92 '''Get the ECEF I{class} (L{EcefVeness}), I{lazily}.
93 '''
94 return _MODS.ecef.EcefVeness
96 def toLatLon(self, **LatLon_and_kwds): # PYCHOK LatLon=LatLon, datum=None
97 '''Convert this cartesian point to a C{Vincenty}-based geodetic point.
99 @kwarg LatLon_and_kwds: Optional L{LatLon} and L{LatLon} keyword
100 arguments as C{datum}. Use C{B{LatLon}=...,
101 B{datum}=...} to override this L{LatLon}
102 class or specify C{B{LatLon}=None}.
104 @return: The geodetic point (L{LatLon}) or if B{C{LatLon}} is C{None},
105 an L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M, datum)}
106 with C{C} and C{M} if available.
108 @raise TypeError: Invalid B{C{LatLon_and_kwds}} argument.
109 '''
110 kwds = _xkwds(LatLon_and_kwds, LatLon=LatLon, datum=self.datum)
111 return CartesianEllipsoidalBase.toLatLon(self, **kwds)
114class LatLon(LatLonEllipsoidalBaseDI):
115 '''Using the formulae devised by U{I{Thaddeus Vincenty (1975)}
116 <https://WikiPedia.org/wiki/Vincenty's_formulae>} for an (oblate)
117 ellipsoidal model of the earth to compute the geodesic distance
118 and bearings between two given points or the destination point
119 given an start point and (initial) bearing.
121 Set the earth model to be used with the keyword argument
122 datum. The default is Datums.WGS84, which is the most globally
123 accurate. For other models, see the Datums in module datum.
125 Note: This implementation of I{Vincenty} methods may not converge
126 for some valid points, raising a L{VincentyError}. In that case,
127 a result may be obtained by increasing the tolerance C{epsilon}
128 and/or iteration C{limit}, see properties L{LatLon.epsilon} and
129 L{LatLon.iterations}.
130 '''
131 _epsilon = 1e-12 # radians, about 6 um
132# _iteration = None # iteration number from .named._NamedBase
133 _iterations = 201 # default max, 200 vs Veness' 1,000
135 @deprecated_method
136 def bearingTo(self, other, wrap=False): # PYCHOK no cover
137 '''DEPRECATED, use method L{initialBearingTo} or L{bearingTo2}.
138 '''
139 return self.initialBearingTo(other, wrap=wrap)
141 @Property_RO
142 def Ecef(self):
143 '''Get the ECEF I{class} (L{EcefVeness}), I{lazily}.
144 '''
145 return _MODS.ecef.EcefVeness
147 @property_doc_(''' the convergence epsilon (C{radians}).''')
148 def epsilon(self):
149 '''Get the convergence epsilon (C{radians}).
150 '''
151 return self._epsilon
153 @epsilon.setter # PYCHOK setter!
154 def epsilon(self, epsilon):
155 '''Set the convergence epsilon (C{radians}).
157 @raise TypeError: Non-scalar B{C{epsilon}}.
159 @raise ValueError: Out of bounds B{C{epsilon}}.
160 '''
161 self._epsilon = Scalar_(epsilon=epsilon)
163 @property_doc_(''' the iteration limit (C{int}).''')
164 def iterations(self):
165 '''Get the iteration limit (C{int}).
166 '''
167 return self._iterations - 1
169 @iterations.setter # PYCHOK setter!
170 def iterations(self, limit):
171 '''Set the iteration limit (C{int}).
173 @raise TypeError: Non-scalar B{C{limit}}.
175 @raise ValueError: Out-of-bounds B{C{limit}}.
176 '''
177 self._iterations = Number_(limit, name=_limit_, low=4, high=1000) + 1
179 def toCartesian(self, **Cartesian_datum_kwds): # PYCHOK Cartesian=Cartesian, datum=None
180 '''Convert this point to C{Vincenty}-based cartesian (ECEF)
181 coordinates.
183 @kwarg Cartesian_datum_kwds: Optional L{Cartesian}, B{C{datum}} and other
184 keyword arguments, ignored if C{B{Cartesian}=None}. Use
185 C{B{Cartesian}=...} to override this L{Cartesian} class
186 or specify C{B{Cartesian}=None}.
188 @return: The cartesian point (L{Cartesian}) or if B{C{Cartesian}}
189 is C{None}, an L{Ecef9Tuple}C{(x, y, z, lat, lon, height,
190 C, M, datum)} with C{C} and C{M} if available.
192 @raise TypeError: Invalid B{C{Cartesian}}, B{C{datum}} or other
193 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}
205 ellipsoids are not compatible.
207 @raise VincentyError: Vincenty fails to converge for the current
208 L{LatLon.epsilon} and L{LatLon.iterations}
209 limits.
210 '''
211 E = self.ellipsoid()
212 f = E.f
214 sb, cb = sincos2d(bearing)
215 s1, c1, t1 = _sincostan3(self.phi, f)
217 eps = self.epsilon
218 s12 = atan2(t1, cb) * _2_0
219 sa, ca2 = _sincos22(c1 * sb)
220 A, B = _AB2(ca2 * E.e22) # e22 == (a / b)**2 - 1
221 s = d = distance / (A * E.b)
222 for i in range(1, self._iterations): # 1-origin
223 ss, cs = sincos2(s)
224 c2sm, e = cos(s12 + s), s
225 s = _Ds(B, cs, ss, c2sm, d)
226 e = fabs(s - e)
227 if e < eps:
228 self._iteration = i
229 break
230 else:
231 t = self._no_convergence(e)
232 raise VincentyError(t, txt=repr(self)) # self.toRepr()
234 t = s1 * ss - c1 * cs * cb
235 # final bearing (reverse azimuth +/- 180)
236 d = atan2b(sa, -t)
237 if llr:
238 b = cb * ss
239 a = atan2d(s1 * cs + c1 * b, hypot(sa, t) * E.b_a)
240 b = atan2d(sb * ss, -s1 * b + c1 * cs) + self.lon \
241 - degrees(_Dl(f, ca2, sa, s, cs, ss, c2sm))
242 t = Destination3Tuple(a, wrap180(b), d)
243 r = self._Direct2Tuple(self.classof, height, t)
244 else:
245 r = Destination2Tuple(None, d, name=self.name)
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, _ = _sincostan3( self.phi, f)
265 s2, c2, _ = _sincostan3(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)
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
322 return Distance3Tuple(d, f, r, name=self.name)
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 _sincos22(sa):
376 # 2-Tuple C{(sin(a), cos(a)**2)}
377 ca2 = _1_0 - sa**2
378 return sa, (_0_0 if ca2 < EPS0 else ca2) # XXX EPS?
381def _sincostan3(a, f):
382 # I{Reduced} C{(sin(B{a}), cos(B{a}), tan(B{a}))}
383 if a: # see L{sincostan3}
384 t = (_1_0 - f) * tan(a)
385 if t:
386 c = _1_0 / hypot1(t)
387 s = t * c
388 return s, c, t
389 return _0_0, _1_0, _0_0
392@deprecated_function
393def areaOf(points, **datum_wrap):
394 '''DEPRECATED, use function L{ellipsoidalExact.areaOf} or L{ellipsoidalKarney.areaOf}.
395 '''
396 try:
397 return _MODS.ellipsoidalKarney.areaOf(points, **datum_wrap)
398 except ImportError:
399 return _MODS.ellipsoidalExact.areaOf(points, **datum_wrap)
402def intersection3(start1, end1, start2, end2, height=None, wrap=True,
403 equidistant=None, tol=_TOL_M, LatLon=LatLon, **LatLon_kwds):
404 '''Iteratively compute the intersection point of two paths, each defined
405 by two (ellipsoidal) points or by an (ellipsoidal) start point and an
406 initial bearing from North.
408 @arg start1: Start point of the first path (L{LatLon}).
409 @arg end1: End point of the first path (L{LatLon}) or the initial bearing
410 at the first point (compass C{degrees360}).
411 @arg start2: Start point of the second path (L{LatLon}).
412 @arg end2: End point of the second path (L{LatLon}) or the initial bearing
413 at the second point (compass C{degrees360}).
414 @kwarg height: Optional height at the intersection (C{meter}, conventionally)
415 or C{None} for the mean height.
416 @kwarg wrap: Wrap and unroll longitudes (C{bool}).
417 @kwarg equidistant: An azimuthal equidistant projection (I{class} or function
418 L{pygeodesy.equidistant}) or C{None} for the preferred
419 C{B{start1}.Equidistant}.
420 @kwarg tol: Tolerance for convergence and for skew line distance and length
421 (C{meter}, conventionally).
422 @kwarg LatLon: Optional class to return the intersection points (L{LatLon})
423 or C{None}.
424 @kwarg LatLon_kwds: Optional, additional B{C{LatLon}} keyword arguments,
425 ignored if C{B{LatLon} is None}.
427 @return: An L{Intersection3Tuple}C{(point, outside1, outside2)} with C{point}
428 a B{C{LatLon}} or if C{B{LatLon} is None}, a L{LatLon4Tuple}C{(lat,
429 lon, height, datum)}.
431 @raise IntersectionError: Skew, colinear, parallel or otherwise
432 non-intersecting paths or no convergence
433 for the given B{C{tol}}.
435 @raise TypeError: Invalid or non-ellipsoidal B{C{start1}}, B{C{end1}},
436 B{C{start2}} or B{C{end2}} or invalid B{C{equidistant}}.
438 @note: For each path specified with an initial bearing, a pseudo-end point
439 is computed as the C{destination} along that bearing at about 1.5
440 times the distance from the start point to an initial gu-/estimate
441 of the intersection point (and between 1/8 and 3/8 of the authalic
442 earth perimeter).
444 @see: U{The B{ellipsoidal} case<https://GIS.StackExchange.com/questions/48937/
445 calculating-intersection-of-two-circles>} and U{Karney's paper
446 <https://ArXiv.org/pdf/1102.1215.pdf>}, pp 20-21, section B{14. MARITIME
447 BOUNDARIES} for more details about the iteration algorithm.
448 '''
449 return _intersection3(start1, end1, start2, end2, height=height, wrap=wrap,
450 equidistant=equidistant, tol=tol, LatLon=LatLon, **LatLon_kwds)
453def intersections2(center1, radius1, center2, radius2, height=None, wrap=True,
454 equidistant=None, tol=_TOL_M, LatLon=LatLon, **LatLon_kwds):
455 '''Iteratively compute the intersection points of two circles, each defined
456 by an (ellipsoidal) center point and a radius.
458 @arg center1: Center of the first circle (L{LatLon}).
459 @arg radius1: Radius of the first circle (C{meter}, conventionally).
460 @arg center2: Center of the second circle (L{LatLon}).
461 @arg radius2: Radius of the second circle (C{meter}, same units as
462 B{C{radius1}}).
463 @kwarg height: Optional height for the intersection points (C{meter},
464 conventionally) or C{None} for the I{"radical height"}
465 at the I{radical line} between both centers.
466 @kwarg wrap: Wrap and unroll longitudes (C{bool}).
467 @kwarg equidistant: An azimuthal equidistant projection (I{class} or
468 function L{pygeodesy.equidistant}) or C{None} for
469 the preferred C{B{center1}.Equidistant}.
470 @kwarg tol: Convergence tolerance (C{meter}, same units as B{C{radius1}}
471 and B{C{radius2}}).
472 @kwarg LatLon: Optional class to return the intersection points (L{LatLon})
473 or C{None}.
474 @kwarg LatLon_kwds: Optional, additional B{C{LatLon}} keyword arguments,
475 ignored if C{B{LatLon} is None}.
477 @return: 2-Tuple of the intersection points, each a B{C{LatLon}} instance
478 or L{LatLon4Tuple}C{(lat, lon, height, datum)} if C{B{LatLon} is
479 None}. For abutting circles, both points are the same instance,
480 aka the I{radical center}.
482 @raise IntersectionError: Concentric, antipodal, invalid or non-intersecting
483 circles or no convergence for the B{C{tol}}.
485 @raise TypeError: Invalid or non-ellipsoidal B{C{center1}} or B{C{center2}}
486 or invalid B{C{equidistant}}.
488 @raise UnitError: Invalid B{C{radius1}}, B{C{radius2}} or B{C{height}}.
490 @see: U{The B{ellipsoidal} case<https://GIS.StackExchange.com/questions/48937/
491 calculating-intersection-of-two-circles>}, U{Karney's paper
492 <https://ArXiv.org/pdf/1102.1215.pdf>}, pp 20-21, section B{14. MARITIME BOUNDARIES},
493 U{circle-circle<https://MathWorld.Wolfram.com/Circle-CircleIntersection.html>} and
494 U{sphere-sphere<https://MathWorld.Wolfram.com/Sphere-SphereIntersection.html>}
495 intersections.
496 '''
497 return _intersections2(center1, radius1, center2, radius2, height=height, wrap=wrap,
498 equidistant=equidistant, tol=tol, LatLon=LatLon, **LatLon_kwds)
501def nearestOn(point, point1, point2, within=True, height=None, wrap=False,
502 equidistant=None, tol=_TOL_M, LatLon=LatLon, **LatLon_kwds):
503 '''Iteratively locate the closest point on the geodesic between
504 two other (ellipsoidal) points.
506 @arg point: Reference point (C{LatLon}).
507 @arg point1: Start point of the geodesic (C{LatLon}).
508 @arg point2: End point of the geodesic (C{LatLon}).
509 @kwarg within: If C{True} return the closest point I{between}
510 B{C{point1}} and B{C{point2}}, otherwise the
511 closest point elsewhere on the geodesic (C{bool}).
512 @kwarg height: Optional height for the closest point (C{meter},
513 conventionally) or C{None} or C{False} for the
514 interpolated height. If C{False}, the closest
515 takes the heights of the points into account.
516 @kwarg wrap: Wrap and unroll longitudes (C{bool}).
517 @kwarg equidistant: An azimuthal equidistant projection (I{class}
518 or function L{pygeodesy.equidistant}) or C{None}
519 for the preferred C{B{point}.Equidistant}.
520 @kwarg tol: Convergence tolerance (C{meter}).
521 @kwarg LatLon: Optional class to return the closest point
522 (L{LatLon}) or C{None}.
523 @kwarg LatLon_kwds: Optional, additional B{C{LatLon}} keyword
524 arguments, ignored if C{B{LatLon} is None}.
526 @return: Closest point, a B{C{LatLon}} instance or if C{B{LatLon}
527 is None}, a L{LatLon4Tuple}C{(lat, lon, height, datum)}.
529 @raise ImportError: Package U{geographiclib
530 <https://PyPI.org/project/geographiclib>}
531 not installed or not found, but only if
532 C{B{equidistant}=}L{EquidistantKarney}.
534 @raise TypeError: Invalid or non-ellipsoidal B{C{point}}, B{C{point1}}
535 or B{C{point2}} or invalid B{C{equidistant}}.
537 @raise ValueError: No convergence for the B{C{tol}}.
539 @see: U{The B{ellipsoidal} case<https://GIS.StackExchange.com/questions/48937/
540 calculating-intersection-of-two-circles>} and U{Karney's paper
541 <https://ArXiv.org/pdf/1102.1215.pdf>}, pp 20-21, section B{14. MARITIME
542 BOUNDARIES} for more details about the iteration algorithm.
543 '''
544 return _nearestOn(point, point1, point2, within=within, height=height, wrap=wrap,
545 equidistant=equidistant, tol=tol, LatLon=LatLon, **LatLon_kwds)
548@deprecated_function
549def perimeterOf(points, **closed_datum_wrap):
550 '''DEPRECATED, use function L{ellipsoidalExact.perimeterOf} or L{ellipsoidalKarney.perimeterOf}.
551 '''
552 try:
553 return _MODS.ellipsoidalKarney.perimeterOf(points, **closed_datum_wrap)
554 except ImportError:
555 return _MODS.ellipsoidalExact.perimeterOf(points, **closed_datum_wrap)
558__all__ += _ALL_OTHER(Cartesian, LatLon,
559 intersection3, intersections2, ispolar, # from .points
560 nearestOn) + _ALL_DOCS(areaOf, perimeterOf) # deprecated
562# **) MIT License
563#
564# Copyright (C) 2016-2023 -- mrJean1 at Gmail -- All Rights Reserved.
565#
566# Permission is hereby granted, free of charge, to any person obtaining a
567# copy of this software and associated documentation files (the "Software"),
568# to deal in the Software without restriction, including without limitation
569# the rights to use, copy, modify, merge, publish, distribute, sublicense,
570# and/or sell copies of the Software, and to permit persons to whom the
571# Software is furnished to do so, subject to the following conditions:
572#
573# The above copyright notice and this permission notice shall be included
574# in all copies or substantial portions of the Software.
575#
576# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
577# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
578# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
579# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR
580# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
581# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
582# OTHER DEALINGS IN THE SOFTWARE.