
# -*- 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 accurate and 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 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} meter or approx. 6371009
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

You can change the ellipsoid model used by the Vincenty formulae
as follows:

    >>> 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.basics import isnear0  # from .ellipsoidalBaseDI
# from pygeodesy.datums import _WGS84  # from .ellipsoidalBase
from pygeodesy.ellipsoidalBase import CartesianEllipsoidalBase, _nearestOn, \
                                     _WGS84
from pygeodesy.ellipsoidalBaseDI import fsum_, isnear0, LatLonEllipsoidalBaseDI, \
                                       _TOL_M, _intersection3, _intersections2
from pygeodesy.errors import _ValueError, _xkwds
from pygeodesy.fmath import fpolynomial, hypot, hypot1
# from pygeodesy.fsums import fsum_  # from .ellipsoidalBaseDI
from pygeodesy.interns import EPS, NN, _ambiguous_, _antipodal_, \
                             _convergence_, _no_, _SPACE_, _to_, \
                             _0_0, _1_0, _2_0, _3_0, _4_0, _6_0, _16_0
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 ispolar  # PYCHOK exported
from pygeodesy.props import deprecated_function, deprecated_method, \
                            Property_RO, property_doc_
from pygeodesy.units import Number_, Scalar_
from pygeodesy.utily import atan2b, atan2d, sincos2, unroll180

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

__all__ = _ALL_LAZY.ellipsoidalVincenty
__version__ = '22.01.17'

_antipodal__ = _antipodal_ + _SPACE_
_limit_      = 'limit'  # PYCHOK used!


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
    _iterations = 100    # max 100 vs Veness' 500

    @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.

           @arg epsilon: New 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

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

           @arg limit: New 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=500)

    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} is None}.  Use
                                        C{B{Cartesian}=...} to override this
                                        L{Cartesian} class or specify
                                        C{B{Cartesian} is 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}
                                 limit.
        '''
        E = self.ellipsoid()

        c1, s1, t1 = _r3(self.lat, E.f)

        i = radians(bearing)  # initial bearing (forward azimuth)
        si, ci = sincos2(i)
        s12 = atan2(t1, ci) * _2_0

        sa = c1 * si
        c2a = _1_0 - sa**2
        if c2a < EPS:
            c2a = _0_0
            A, B = _1_0, _0_0
        else:  # e22 == (a / b)**2 - 1
            A, B = _p2(c2a * E.e22)

        s = d = distance / (E.b * A)
        for self._iteration in range(1, self._iterations + 1):
            ss, cs = sincos2(s)
            c2sm = cos(s12 + s)
            s_, s = s, d + _ds(B, cs, ss, c2sm)
            if abs(s - s_) < self._epsilon:
                break
        else:
            raise VincentyError(_no_(_convergence_), txt=repr(self))  # self.toRepr()

        t = s1 * ss - c1 * cs * ci
        # final bearing (reverse azimuth +/- 180)
        r = atan2b(sa, -t)

        if llr:
            a = atan2d(s1 * cs + c1 * ss * ci, E.b_a * hypot(sa, t))
            b = atan2d(ss * si, c1 * cs - s1 * ss * ci)
            d = degrees(_dl(E.f, c2a, sa, s, cs, ss, c2sm))
            t = Destination3Tuple(a, fsum_(b, self.lon, -d), r)
            r = self._Direct2Tuple(self.classof, height, t)
        else:
            r = Destination2Tuple(None, r, name=self.name)
        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}
                                 limit and/or if this and the B{C{other}}
                                 point are coincident or near-antipodal.
        '''
        E = self.ellipsoids(other)

        c1, s1, _ = _r3(self.lat, E.f)
        c2, s2, _ = _r3(other.lat, E.f)

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

        dl, _ = unroll180(self.lon, other.lon, wrap=wrap)
        ll = dl = radians(dl)
        for self._iteration in range(1, self._iterations + 1):
            ll_ = ll
            sll, cll = sincos2(ll)

            ss = hypot(c2 * sll, c1s2 - s1c2 * cll)
            if ss < EPS:  # coincident or antipodal, ...
                if self.isantipodeTo(other, eps=self._epsilon):
                    t = '%r %s%s %r' % (self, _antipodal__, _to_, other)
                    raise VincentyError(_ambiguous_, txt=t)
                # return zeros like Karney, but unlike Veness
                return Distance3Tuple(_0_0, 0, 0)

            cs = s1s2 + c1c2 * cll
            s = atan2(ss, cs)

            sa = c1c2 * sll / ss
            c2a = _1_0 - sa**2
            if isnear0(c2a):
                c2a = _0_0  # equatorial line
                ll = dl + E.f * sa * s
            else:
                c2sm = cs - 2 * s1s2 / c2a
                ll = dl + _dl(E.f, c2a, sa, s, cs, ss, c2sm)

            if abs(ll - ll_) < self._epsilon:
                break
#           # omitted and applied only after failure to converge below, see footnote
#           # under Inverse at <https://WikiPedia.org/wiki/Vincenty's_formulae>
#           # <https://GitHub.com/ChrisVeness/geodesy/blob/master/latlon-vincenty.js>
#           elif abs(ll) > PI and self.isantipodeTo(other, eps=self._epsilon):
#              raise VincentyError('%s, %r %sto %r' % ('ambiguous', self,
#                                  _antipodal__, other))
        else:
            t = _antipodal__ if self.isantipodeTo(other, eps=self._epsilon) else NN
            t = '%r %s%s %r' % (self, t, _to_, other)
            raise VincentyError(_no_(_convergence_), txt=t)

        if c2a:  # e22 == (a / b)**2 - 1
            A, B = _p2(c2a * E.e22)
            s = A * (s - _ds(B, cs, ss, c2sm))

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

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


def _c2sm2(c2sm):
    '''(INTERNAL) 2 * c2sm**2 - 1.
    '''
    return _2_0 * c2sm**2 - _1_0


def _dl(f, c2a, sa, s, cs, ss, c2sm):
    '''(INTERNAL) Dl.
    '''
    C = f / _16_0 * c2a * (_4_0 + f * (_4_0 - _3_0 * c2a))
    return (_1_0 - C) * f * sa * (s + C * ss * (c2sm +
                                      C * cs * _c2sm2(c2sm)))


def _ds(B, cs, ss, c2sm):
    '''(INTERNAL) Ds.
    '''
    if B:
        c2sm2 = _c2sm2(c2sm)
        ss2 = (_4_0 * ss**2 - _3_0) * (_2_0 * c2sm2 - _1_0)
        B *= ss * (c2sm + B / _4_0 * (c2sm2 * cs -
                          B / _6_0 *  c2sm  * ss2))
    return B


def _p2(u2):  # e'2 WGS84 = 0.00673949674227643
    '''(INTERNAL) Compute A, B polynomials.
    '''
    A = fpolynomial(u2, 16384, 4096, -768, 320, -175) / 16384
    B = fpolynomial(u2,     0,  256, -128,  74,  -47) / 1024
    return A, B


def _r3(a, f):
    '''(INTERNAL) Reduced cos, sin, tan.
    '''
    t = (_1_0 - f) * tan(radians(a))
    c =  _1_0 / hypot1(t)
    s =  t * c
    return c, s, t


@deprecated_function
def areaOf(points, datum=_WGS84, wrap=True):  # PYCHOK no cover
    '''DEPRECATED, use function L{ellipsoidalExact.areaOf} or L{ellipsoidalKarney.areaOf}.
    '''
    return _MODS.ellipsoidalKarney.areaOf(points, datum=datum, wrap=wrap)


def intersection3(start1, end1, start2, end2, height=None, wrap=True,
                  equidistant=None, tol=_TOL_M, LatLon=LatLon, **LatLon_kwds):
    '''Interatively compute the intersection point of two paths, each defined
       by two (ellipsoidal) points or by an (ellipsoidal) start point and a
       bearing from North.

       @arg start1: Start point of the first path (L{LatLon}).
       @arg end1: End point of the first path (L{LatLon}) or the initial bearing
                  at the first point (compass C{degrees360}).
       @arg start2: Start point of the second path (L{LatLon}).
       @arg end2: End point of the second path (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: Wrap and unroll longitudes (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 paths 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 path 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=True,
                   equidistant=None, tol=_TOL_M, LatLon=LatLon, **LatLon_kwds):
    '''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: Wrap and unroll longitudes (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):
    '''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: Wrap and unroll longitudes (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=False, datum=_WGS84, wrap=True):  # PYCHOK no cover
    '''DEPRECATED, use function L{ellipsoidalExact.perimeterOf} or L{ellipsoidalKarney.perimeterOf}.
    '''
    return _MODS.ellipsoidalKarney.perimeterOf(points, closed=closed, datum=datum, wrap=wrap)


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

# **) MIT License
#
# Copyright (C) 2016-2022 -- mrJean1 at Gmail -- All Rights Reserved.
#
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