
# -*- coding: utf-8 -*-

u'''Ellipsoidal, I{Vincenty}-based geodesy.

I{Thaddeus Vincenty}'s geodetic (lat-/longitude) L{LatLon}, geocentric
(ECEF) L{Cartesian} and L{VincentyError} classes and functions L{areaOf},
L{intersections2}, L{nearestOn} and L{perimeterOf}.

Pure Python implementation of geodesy tools for ellipsoidal earth models,
transcoded from JavaScript originals by I{(C) Chris Veness 2005-2016}
and published under the same MIT Licence**, see U{Vincenty geodesics
<https://www.Movable-Type.co.UK/scripts/LatLongVincenty.html>}.  More
at U{geographiclib<https://PyPI.org/project/geographiclib>} and
U{GeoPy<https://PyPI.org/project/geopy>}.

Calculate geodesic distance between two points using the U{Vincenty
<https://WikiPedia.org/wiki/Vincenty's_formulae>} formulae and one of
several ellipsoidal earth models.  The default model is WGS-84, the
most widely used globally-applicable model for the earth ellipsoid.

Other ellipsoids offering a better fit to the local geoid include Airy
(1830) in the UK, Clarke (1880) in Africa, International 1924 in much
of Europe, and GRS-67 in South America.  North America (NAD83) and
Australia (GDA) use GRS-80, which is equivalent to the WGS-84 model.

Great-circle distance uses a I{spherical} model of the earth with the
mean earth radius defined by the International Union of Geodesy and
Geophysics (IUGG) as M{(2 * a + b) / 3 = 6371008.7714150598} or about
6,371,009 meter (for WGS-84, resulting in an error of up to about 0.5%).

Here's an example usage of C{ellipsoidalVincenty}:

    >>> from pygeodesy.ellipsoidalVincenty import LatLon
    >>> Newport_RI = LatLon(41.49008, -71.312796)
    >>> Cleveland_OH = LatLon(41.499498, -81.695391)
    >>> Newport_RI.distanceTo(Cleveland_OH)
    866,455.4329158525  # meter

To change the ellipsoid model used by the Vincenty formulae use:

    >>> from pygeodesy import Datums
    >>> from pygeodesy.ellipsoidalVincenty import LatLon
    >>> p = LatLon(0, 0, datum=Datums.OSGB36)

or by converting to anothor datum:

    >>> p = p.toDatum(Datums.OSGB36)
'''
# make sure int/int division yields float quotient, see .basics
from __future__ import division as _; del _  # PYCHOK semicolon

from pygeodesy.constants import EPS, EPS0, _0_0, _1_0, _2_0, _3_0, _4_0, _6_0
from pygeodesy.ellipsoidalBase import CartesianEllipsoidalBase, intersecant2, \
                                     _nearestOn
from pygeodesy.ellipsoidalBaseDI import LatLonEllipsoidalBaseDI, \
                                       _intersection3, _intersections2, _TOL_M
from pygeodesy.errors import _and, _ValueError, _xkwds
from pygeodesy.fmath import Fpolynomial, hypot, hypot1
from pygeodesy.interns import _ambiguous_, _antipodal_, _COLONSPACE_, \
                              _to_, _SPACE_,  _limit_  # PYCHOK used!
from pygeodesy.lazily import _ALL_DOCS, _ALL_LAZY, _ALL_MODS as _MODS, _ALL_OTHER
from pygeodesy.namedTuples import Destination2Tuple, Destination3Tuple, \
                                  Distance3Tuple
from pygeodesy.points import Fmt, ispolar  # PYCHOK exported
from pygeodesy.props import deprecated_function, deprecated_method, \
                            Property_RO, property_doc_
# from pygeodesy.streprs import Fmt  # from .points
from pygeodesy.units import Number_, Scalar_
from pygeodesy.utily import atan2b, atan2d, sincos2, sincos2d, unroll180, wrap180

from math import atan2, cos, degrees, fabs, radians, tan

__all__ = _ALL_LAZY.ellipsoidalVincenty
__version__ = '23.10.08'

_antipodal_to_ = _SPACE_(_antipodal_, _to_)


class VincentyError(_ValueError):
    '''Error raised from I{Vincenty}'s C{direct} and C{inverse} methods
       for coincident points or lack of convergence.
    '''
    pass


class Cartesian(CartesianEllipsoidalBase):
    '''Extended to convert geocentric, L{Cartesian} points to
       Vincenty-based, ellipsoidal, geodetic L{LatLon}.
    '''
    @Property_RO
    def Ecef(self):
        '''Get the ECEF I{class} (L{EcefVeness}), I{lazily}.
        '''
        return _MODS.ecef.EcefVeness

    def toLatLon(self, **LatLon_and_kwds):  # PYCHOK LatLon=LatLon, datum=None
        '''Convert this cartesian point to a C{Vincenty}-based geodetic point.

           @kwarg LatLon_and_kwds: Optional L{LatLon} and L{LatLon} keyword
                                   arguments as C{datum}.  Use C{B{LatLon}=...,
                                   B{datum}=...} to override this L{LatLon}
                                   class or specify C{B{LatLon}=None}.

           @return: The geodetic point (L{LatLon}) or if B{C{LatLon}} is C{None},
                    an L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M, datum)}
                    with C{C} and C{M} if available.

           @raise TypeError: Invalid B{C{LatLon_and_kwds}} argument.
        '''
        kwds = _xkwds(LatLon_and_kwds, LatLon=LatLon, datum=self.datum)
        return CartesianEllipsoidalBase.toLatLon(self, **kwds)


class LatLon(LatLonEllipsoidalBaseDI):
    '''Using the formulae devised by U{I{Thaddeus Vincenty (1975)}
       <https://WikiPedia.org/wiki/Vincenty's_formulae>} for an (oblate)
       ellipsoidal model of the earth to compute the geodesic distance
       and bearings between two given points or the destination point
       given an start point and (initial) bearing.

       Set the earth model to be used with the keyword argument
       datum.  The default is Datums.WGS84, which is the most globally
       accurate.  For other models, see the Datums in module datum.

       Note: This implementation of I{Vincenty} methods may not converge
       for some valid points, raising a L{VincentyError}.  In that case,
       a result may be obtained by increasing the tolerance C{epsilon}
       and/or iteration C{limit}, see properties L{LatLon.epsilon} and
       L{LatLon.iterations}.
    '''
    _epsilon    = 1e-12  # radians, about 6 um
#   _iteration  = None   # iteration number from .named._NamedBase
    _iterations = 201    # 5, default max, 200 vs Veness' 1,000

    @deprecated_method
    def bearingTo(self, other, wrap=False):  # PYCHOK no cover
        '''DEPRECATED, use method L{initialBearingTo} or L{bearingTo2}.
        '''
        return self.initialBearingTo(other, wrap=wrap)

    @Property_RO
    def Ecef(self):
        '''Get the ECEF I{class} (L{EcefVeness}), I{lazily}.
        '''
        return _MODS.ecef.EcefVeness

    @property_doc_(''' the convergence epsilon (C{radians}).''')
    def epsilon(self):
        '''Get the convergence epsilon (C{radians}).
        '''
        return self._epsilon

    @epsilon.setter  # PYCHOK setter!
    def epsilon(self, epsilon):
        '''Set the convergence epsilon (C{radians}).

           @raise TypeError: Non-scalar B{C{epsilon}}.

           @raise ValueError: Out of bounds B{C{epsilon}}.
        '''
        self._epsilon = Scalar_(epsilon=epsilon)

    @property_doc_(''' the iteration limit (C{int}).''')
    def iterations(self):
        '''Get the iteration limit (C{int}).
        '''
        return self._iterations - 1

    @iterations.setter  # PYCHOK setter!
    def iterations(self, limit):
        '''Set the iteration limit (C{int}).

           @raise TypeError: Non-scalar B{C{limit}}.

           @raise ValueError: Out-of-bounds B{C{limit}}.
        '''
        self._iterations = Number_(limit, name=_limit_, low=4, high=1000) + 1

    def toCartesian(self, **Cartesian_datum_kwds):  # PYCHOK Cartesian=Cartesian, datum=None
        '''Convert this point to C{Vincenty}-based cartesian (ECEF)
           coordinates.

           @kwarg Cartesian_datum_kwds: Optional L{Cartesian}, B{C{datum}} and other
                            keyword arguments, ignored if C{B{Cartesian}=None}.  Use
                            C{B{Cartesian}=...} to override this L{Cartesian} class
                            or specify C{B{Cartesian}=None}.

           @return: The cartesian point (L{Cartesian}) or if B{C{Cartesian}}
                    is C{None}, an L{Ecef9Tuple}C{(x, y, z, lat, lon, height,
                    C, M, datum)} with C{C} and C{M} if available.

           @raise TypeError: Invalid B{C{Cartesian}}, B{C{datum}} or other
                             B{C{Cartesian_datum_kwds}}.
        '''
        kwds = _xkwds(Cartesian_datum_kwds, Cartesian=Cartesian,
                                                datum=self.datum)
        return LatLonEllipsoidalBaseDI.toCartesian(self, **kwds)

    def _Direct(self, distance, bearing, llr, height):
        '''(INTERNAL) Direct Vincenty method.

           @raise TypeError: The B{C{other}} point is not L{LatLon}.

           @raise ValueError: If this and the B{C{other}} point's L{Datum}
                              ellipsoids are not compatible.

           @raise VincentyError: Vincenty fails to converge for the current
                                 L{LatLon.epsilon} and L{LatLon.iterations}
                                 limits.
        '''
        E = self.ellipsoid()
        f = E.f

        sb, cb     =  sincos2d(bearing)
        s1, c1, t1 = _sincostan3r(self.phi, f)

        eps     =  self.epsilon
        s12     =  atan2(t1, cb) * _2_0
        sa, ca2 = _sincos22(c1 * sb)
        A,  B   = _AB2(ca2 * E.e22)  # e22 == (a / b)**2 - 1
        s = d   =  distance / (A * E.b)
        for i in range(1, self._iterations):  # 1-origin
            ss, cs  = sincos2(s)
            c2sm, e = cos(s12 + s), s
            s = _Ds(B, cs, ss, c2sm, d)
            e =  fabs(s - e)
            if e < eps:
                self._iteration = i
                break
        else:
            t = self._no_convergence(e)
            raise VincentyError(t, txt=repr(self))  # self.toRepr()

        t = s1 * ss - c1 * cs * cb
        # final bearing (reverse azimuth +/- 180)
        d = atan2b(sa, -t)
        if llr:
            b = cb * ss
            a = atan2d(s1 * cs + c1 * b, hypot(sa, t) * E.b_a)
            b = atan2d(sb * ss, -s1 * b + c1 * cs) + self.lon \
              - degrees(_Dl(f, ca2, sa, s, cs, ss, c2sm))
            t = Destination3Tuple(a, wrap180(b), d)
            r = self._Direct2Tuple(self.classof, height, t)
        else:
            r = Destination2Tuple(None, d, name=self.name)
        r._iteration = i
        return r

    def _Inverse(self, other, wrap, azis=True):  # PYCHOK signature
        '''(INTERNAL) Inverse Vincenty method.

           @raise TypeError: The B{C{other}} point is not L{LatLon}.

           @raise ValueError: If this and the B{C{other}} point's L{Datum}
                              ellipsoids are not compatible.

           @raise VincentyError: Vincenty fails to converge for the current
                                 L{LatLon.epsilon} and L{LatLon.iterations}
                                 limits and/or if this and the B{C{other}}
                                 point are coincident or near-antipodal.
        '''
        E = self.ellipsoids(other)
        f = E.f

        s1, c1, _ = _sincostan3r( self.phi, f)
        s2, c2, _ = _sincostan3r(other.phi, f)

        c1c2, s1c2 = c1 * c2, s1 * c2
        c1s2, s1s2 = c1 * s2, s1 * s2

        eps  = self.epsilon
        d, _ = unroll180(self.lon, other.lon, wrap=wrap)
        dl   = ll = radians(d)
        for i in range(1, self._iterations):  # 1-origin
            sll, cll = sincos2(ll)

            ss = hypot(c2 * sll, c1s2 - s1c2 * cll)
            if ss < EPS:  # coincident or antipodal, ...
                if self.isantipodeTo(other, eps=eps):
                    t = self._is_to(other, True)
                    raise VincentyError(_ambiguous_, txt=t)
                self._iteration = i
                # return zeros like Karney, unlike Veness
                return Distance3Tuple(_0_0, 0, 0, iteration=i)

            cs   = s1s2 + c1c2 * cll
            s, e = atan2(ss, cs), ll
            sa, ca2 = _sincos22(c1c2 * sll / ss)
            if ca2:
                c2sm =  cs - _2_0 * s1s2 / ca2
                ll   = _Dl(f, ca2, sa, s, cs, ss, c2sm, dl)
            else:  # equatorial line
                ll   =  dl + f * sa * s
            e = fabs(ll - e)
            if e < eps:
                self._iteration = i
                break
#           elif abs(ll) > PI and self.isantipodeTo(other, eps=eps):
#               # omitted and applied *after* failure to converge below,
#               # see footnote under Inverse <https://WikiPedia.org/wiki/
#               # Vincenty's_formulae> and <https://GitHub.com/chrisveness/
#               # geodesy/blob/master/latlon-ellipsoidal-vincenty.js>
#               raise VincentyError(_ambiguous_, self._is_to(other, True))
        else:
            t = self._is_to(other, self.isantipodeTo(other, eps=eps))
            raise VincentyError(self._no_convergence(e), txt=t)

        if ca2:  # e22 == (a / b)**2 - 1
            A,   B = _AB2(ca2 * E.e22)
            s = -A * _Ds(B, cs, ss, c2sm, -s)

        b = E.b
#       if self.height or other.height:
#           b += self._havg(other)
        d = b * s

        if azis:  # forward and reverse azimuth
            s, c = sincos2(ll)
            f = atan2b(c2 * s,  c1s2 - s1c2 * c)
            r = atan2b(c1 * s, -s1c2 + c1s2 * c)
        else:
            f = r = _0_0
        return Distance3Tuple(d, f, r, name=self.name, iteration=i)

    def _is_to(self, other, anti):
        '''(INTERNAL) Return I{'<self> [antipodal] to <other>'} text (C{str}).
        '''
        t = _antipodal_to_ if anti else _to_
        return _SPACE_(repr(self), t, repr(other))

    def _no_convergence(self, e):
        '''(INTERNAL) Return I{'no convergence (..): ...'} text (C{str}).
        '''
        t = (Fmt.PARENSPACED(*t) for t in ((LatLon.epsilon.name,    self.epsilon),
                                           (LatLon.iterations.name, self.iterations)))
        return _COLONSPACE_(Fmt.no_convergence(e), _and(*t))


def _AB2(u2):  # WGS84 e22 = 0.00673949674227643
    # 2-Tuple C{(A, B)} polynomials
    if u2:
        A = Fpolynomial(u2, 16384, 4096, -768, 320, -175).fover(16384)
        B = Fpolynomial(u2,     0,  256, -128,  74,  -47).fover( 1024)
        return A, B
    return _1_0, _0_0


def _c2sm2(c2sm):
    # C{2 * c2sm**2 - 1}
    return c2sm**2 * _2_0 - _1_0


def _Dl(f, ca2, sa, s, cs, ss, c2sm, dl=_0_0):
    # C{Dl}
    if f and sa:
        C  = f * ca2 / _4_0
        C *= f - C * _3_0 + _1_0
        if C and ss:
            s += C * ss * (c2sm +
                 C * cs * _c2sm2(c2sm))
        dl += (_1_0 - C) * f * sa * s
    return dl


def _Ds(B, cs, ss, c2sm, d):
    # C{Ds - d}
    if B and ss:
        c2sm2 = _c2sm2(c2sm)
        ss2 = (ss**2 * _4_0 - _3_0) * (c2sm2 * _2_0 - _1_0)
        B  *= ss * (c2sm + B / _4_0 * (c2sm2 * cs -
                           B / _6_0 *  c2sm  * ss2))
        d  += B
    return d


def _sincos22(sa):
    # 2-Tuple C{(sin(a), cos(a)**2)}
    ca2 = _1_0 - sa**2
    return sa, (_0_0 if ca2 < EPS0 else ca2)  # XXX EPS?


def _sincostan3r(a, f):
    # I{Reduced} C{(sin(B{a}), cos(B{a}), tan(B{a}))}
    if a:  # see L{sincostan3}
        t = (_1_0 - f) * tan(a)
        if t:
            c = _1_0 / hypot1(t)
            s =  t * c
            return s, c, t
    return _0_0, _1_0, _0_0


@deprecated_function
def areaOf(points, **datum_wrap):
    '''DEPRECATED, use function L{ellipsoidalExact.areaOf} or L{ellipsoidalKarney.areaOf}.
    '''
    try:
        return _MODS.ellipsoidalKarney.areaOf(points, **datum_wrap)
    except ImportError:
        return _MODS.ellipsoidalExact.areaOf(points, **datum_wrap)


def intersection3(start1, end1, start2, end2, height=None, wrap=False,  # was=True
                  equidistant=None, tol=_TOL_M, LatLon=LatLon, **LatLon_kwds):
    '''I{Iteratively} compute the intersection point of two lines, each defined
       by two (ellipsoidal) points or by an (ellipsoidal) start point and an
       (initial) bearing from North.

       @arg start1: Start point of the first line (L{LatLon}).
       @arg end1: End point of the first line (L{LatLon}) or the initial bearing
                  at the first point (compass C{degrees360}).
       @arg start2: Start point of the second line (L{LatLon}).
       @arg end2: End point of the second line (L{LatLon}) or the initial bearing
                  at the second point (compass C{degrees360}).
       @kwarg height: Optional height at the intersection (C{meter}, conventionally)
                      or C{None} for the mean height.
       @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the B{C{start2}}
                    and B{C{end*}} points (C{bool}).
       @kwarg equidistant: An azimuthal equidistant projection (I{class} or function
                           L{pygeodesy.equidistant}) or C{None} for the preferred
                           C{B{start1}.Equidistant}.
       @kwarg tol: Tolerance for convergence and for skew line distance and length
                   (C{meter}, conventionally).
       @kwarg LatLon: Optional class to return the intersection points (L{LatLon})
                      or C{None}.
       @kwarg LatLon_kwds: Optional, additional B{C{LatLon}} keyword arguments,
                           ignored if C{B{LatLon} is None}.

       @return: An L{Intersection3Tuple}C{(point, outside1, outside2)} with C{point}
                a B{C{LatLon}} or if C{B{LatLon} is None}, a L{LatLon4Tuple}C{(lat,
                lon, height, datum)}.

       @raise IntersectionError: Skew, colinear, parallel or otherwise
                                 non-intersecting lines or no convergence
                                 for the given B{C{tol}}.

       @raise TypeError: Invalid or non-ellipsoidal B{C{start1}}, B{C{end1}},
                         B{C{start2}} or B{C{end2}} or invalid B{C{equidistant}}.

       @note: For each line specified with an initial bearing, a pseudo-end point
              is computed as the C{destination} along that bearing at about 1.5
              times the distance from the start point to an initial gu-/estimate
              of the intersection point (and between 1/8 and 3/8 of the authalic
              earth perimeter).

       @see: U{The B{ellipsoidal} case<https://GIS.StackExchange.com/questions/48937/
             calculating-intersection-of-two-circles>} and U{Karney's paper
             <https://ArXiv.org/pdf/1102.1215.pdf>}, pp 20-21, section B{14. MARITIME
             BOUNDARIES} for more details about the iteration algorithm.
    '''
    return _intersection3(start1, end1, start2, end2, height=height, wrap=wrap,
                          equidistant=equidistant, tol=tol, LatLon=LatLon, **LatLon_kwds)


def intersections2(center1, radius1, center2, radius2, height=None, wrap=False,  # was=True
                   equidistant=None, tol=_TOL_M, LatLon=LatLon, **LatLon_kwds):
    '''I{Iteratively} compute the intersection points of two circles, each defined
       by an (ellipsoidal) center point and a radius.

       @arg center1: Center of the first circle (L{LatLon}).
       @arg radius1: Radius of the first circle (C{meter}, conventionally).
       @arg center2: Center of the second circle (L{LatLon}).
       @arg radius2: Radius of the second circle (C{meter}, same units as
                     B{C{radius1}}).
       @kwarg height: Optional height for the intersection points (C{meter},
                      conventionally) or C{None} for the I{"radical height"}
                      at the I{radical line} between both centers.
       @kwarg wrap: If C{True}, wrap or I{normalize} and unroll B{C{center2}}
                    (C{bool}).
       @kwarg equidistant: An azimuthal equidistant projection (I{class} or
                           function L{pygeodesy.equidistant}) or C{None} for
                           the preferred C{B{center1}.Equidistant}.
       @kwarg tol: Convergence tolerance (C{meter}, same units as B{C{radius1}}
                   and B{C{radius2}}).
       @kwarg LatLon: Optional class to return the intersection points (L{LatLon})
                      or C{None}.
       @kwarg LatLon_kwds: Optional, additional B{C{LatLon}} keyword arguments,
                           ignored if C{B{LatLon} is None}.

       @return: 2-Tuple of the intersection points, each a B{C{LatLon}} instance
                or L{LatLon4Tuple}C{(lat, lon, height, datum)} if C{B{LatLon} is
                None}.  For abutting circles, both points are the same instance,
                aka the I{radical center}.

       @raise IntersectionError: Concentric, antipodal, invalid or non-intersecting
                                 circles or no convergence for the B{C{tol}}.

       @raise TypeError: Invalid or non-ellipsoidal B{C{center1}} or B{C{center2}}
                         or invalid B{C{equidistant}}.

       @raise UnitError: Invalid B{C{radius1}}, B{C{radius2}} or B{C{height}}.

       @see: U{The B{ellipsoidal} case<https://GIS.StackExchange.com/questions/48937/
             calculating-intersection-of-two-circles>}, U{Karney's paper
             <https://ArXiv.org/pdf/1102.1215.pdf>}, pp 20-21, section B{14. MARITIME BOUNDARIES},
             U{circle-circle<https://MathWorld.Wolfram.com/Circle-CircleIntersection.html>} and
             U{sphere-sphere<https://MathWorld.Wolfram.com/Sphere-SphereIntersection.html>}
             intersections.
    '''
    return _intersections2(center1, radius1, center2, radius2, height=height, wrap=wrap,
                           equidistant=equidistant, tol=tol, LatLon=LatLon, **LatLon_kwds)


def nearestOn(point, point1, point2, within=True, height=None, wrap=False,
              equidistant=None, tol=_TOL_M, LatLon=LatLon, **LatLon_kwds):
    '''I{Iteratively} locate the closest point on the geodesic between
       two other (ellipsoidal) points.

       @arg point: Reference point (C{LatLon}).
       @arg point1: Start point of the geodesic (C{LatLon}).
       @arg point2: End point of the geodesic (C{LatLon}).
       @kwarg within: If C{True} return the closest point I{between}
                      B{C{point1}} and B{C{point2}}, otherwise the
                      closest point elsewhere on the geodesic (C{bool}).
       @kwarg height: Optional height for the closest point (C{meter},
                      conventionally) or C{None} or C{False} for the
                      interpolated height.  If C{False}, the closest
                      takes the heights of the points into account.
       @kwarg wrap: If C{True}, wrap or I{normalize} and unroll both
                    B{C{point1}} and B{C{point2}} (C{bool}).
       @kwarg equidistant: An azimuthal equidistant projection (I{class}
                           or function L{pygeodesy.equidistant}) or C{None}
                           for the preferred C{B{point}.Equidistant}.
       @kwarg tol: Convergence tolerance (C{meter}).
       @kwarg LatLon: Optional class to return the closest point
                      (L{LatLon}) or C{None}.
       @kwarg LatLon_kwds: Optional, additional B{C{LatLon}} keyword
                           arguments, ignored if C{B{LatLon} is None}.

       @return: Closest point, a B{C{LatLon}} instance or if C{B{LatLon}
                is None}, a L{LatLon4Tuple}C{(lat, lon, height, datum)}.

       @raise ImportError: Package U{geographiclib
                           <https://PyPI.org/project/geographiclib>}
                           not installed or not found, but only if
                           C{B{equidistant}=}L{EquidistantKarney}.

       @raise TypeError: Invalid or non-ellipsoidal B{C{point}}, B{C{point1}}
                         or B{C{point2}} or invalid B{C{equidistant}}.

       @raise ValueError: No convergence for the B{C{tol}}.

       @see: U{The B{ellipsoidal} case<https://GIS.StackExchange.com/questions/48937/
             calculating-intersection-of-two-circles>} and U{Karney's paper
             <https://ArXiv.org/pdf/1102.1215.pdf>}, pp 20-21, section B{14. MARITIME
             BOUNDARIES} for more details about the iteration algorithm.
    '''
    return _nearestOn(point, point1, point2, within=within, height=height, wrap=wrap,
                      equidistant=equidistant, tol=tol, LatLon=LatLon, **LatLon_kwds)


@deprecated_function
def perimeterOf(points, **closed_datum_wrap):
    '''DEPRECATED, use function L{ellipsoidalExact.perimeterOf} or L{ellipsoidalKarney.perimeterOf}.
    '''
    try:
        return _MODS.ellipsoidalKarney.perimeterOf(points, **closed_datum_wrap)
    except ImportError:
        return _MODS.ellipsoidalExact.perimeterOf(points, **closed_datum_wrap)


__all__ += _ALL_OTHER(Cartesian, LatLon, intersecant2,  # from .ellipsoidalBase
                      intersection3, intersections2, ispolar,  # from .points
                      nearestOn) + _ALL_DOCS(areaOf, perimeterOf)  # deprecated

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