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# -*- coding: utf-8 -*- 

 

u'''(INTERNAL) Ellipsoidal direct/inverse geodesy base class 

C{LatLonEllipsoidalBaseDI} and functions. 

''' 

# make sure int/int division yields float quotient, see .basics 

from __future__ import division 

 

from pygeodesy.basics import issubclassof 

from pygeodesy.ellipsoidalBase import LatLonEllipsoidalBase, Property_RO 

from pygeodesy.errors import _AssertionError, IntersectionError, _IsnotError, \ 

_ValueError, _xellipsoidal, _xError, _xkwds_not 

from pygeodesy.fmath import favg, fmean_, fsum_ 

from pygeodesy.formy import _radical2 

from pygeodesy.interns import _ellipsoidal_ # PYCHOK used! 

from pygeodesy.interns import EPS, PI, _datum_, _epoch_, _exceed_PI_radians_, \ 

_height_, _no_, _near_concentric_, _reframe_, \ 

_too_, _0_0 

from pygeodesy.lazily import _ALL_DOCS 

from pygeodesy.namedTuples import Bearing2Tuple, Destination2Tuple, \ 

Intersection3Tuple, _LL4Tuple 

# from pygeodesy.props import Property_RO # from .ellipsoidalBase 

from pygeodesy.streprs import Fmt 

from pygeodesy.units import Height, Radius_, Scalar, _1mm as _TOL_M 

from pygeodesy.utily import m2degrees, unroll180, wrap90, wrap180, wrap360 

 

__all__ = () 

__version__ = '21.06.28' 

 

_TRIPS = 17 # _intersect3, _intersects2, _nearestOn interations, 6 is sufficient 

 

 

class LatLonEllipsoidalBaseDI(LatLonEllipsoidalBase): 

'''(INTERNAL) Base class for C{ellipsoidal*.LatLon} classes 

with I{overloaded} C{Direct} and C{Inverse} methods. 

''' 

 

def bearingTo2(self, other, wrap=False): 

'''Compute the initial and final bearing (forward and reverse 

azimuth) from this to an other point, using this C{Inverse} 

method. See methods L{initialBearingTo} and L{finalBearingTo} 

for more details. 

 

@arg other: The other point (C{LatLon}). 

@kwarg wrap: Wrap and unroll longitudes (C{bool}). 

 

@return: A L{Bearing2Tuple}C{(initial, final)}. 

 

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

 

@raise ValueError: If this and the B{C{other}} point's L{Datum} 

ellipsoids are not compatible. 

''' 

r = self._Inverse(other, wrap) 

return Bearing2Tuple(r.initial, r.final, name=self.name) 

 

def destination(self, distance, bearing, height=None): 

'''Compute the destination point after having travelled for 

the given distance from this point along a geodesic given 

by an initial bearing, using this C{Direct} method. See 

method L{destination2} for more details. 

 

@arg distance: Distance (C{meter}). 

@arg bearing: Initial bearing in (compass C{degrees360}). 

@kwarg height: Optional height, overriding the default 

height (C{meter}, same units as C{distance}). 

 

@return: The destination point (C{LatLon}). 

''' 

return self._Direct(distance, bearing, self.classof, height).destination 

 

def destination2(self, distance, bearing, height=None): 

'''Compute the destination point and the final bearing (reverse 

azimuth) after having travelled for the given distance from 

this point along a geodesic given by an initial bearing, 

using this C{Direct} method. 

 

The distance must be in the same units as this point's datum 

axes, conventionally C{meter}. The distance is measured on 

the surface of the ellipsoid, ignoring this point's height. 

 

The initial and final bearing (forward and reverse azimuth) 

are in compass C{degrees360}. 

 

The destination point's height and datum are set to this 

point's height and datum, unless the former is overridden. 

 

@arg distance: Distance (C{meter}). 

@arg bearing: Initial bearing (compass C{degrees360}). 

@kwarg height: Optional height, overriding the default 

height (C{meter}, same units as C{distance}). 

 

@return: A L{Destination2Tuple}C{(destination, final)}. 

''' 

r = self._Direct(distance, bearing, self.classof, height) 

return self._xnamed(r) 

 

def _Direct(self, distance, bearing, LL, height): # overloaded by I{Vincenty} 

'''(INTERNAL) I{Karney}'s C{Direct} method. 

 

@return: A L{Destination2Tuple}C{(destination, final)} or 

a L{Destination3Tuple}C{(lat, lon, final)} if 

B{C{LL}} is C{None}. 

''' 

g = self.geodesic 

r = g.Direct3(self.lat, self.lon, bearing, distance) 

if LL: 

r = self._Direct2Tuple(LL, height, r) 

return r 

 

def _Direct2Tuple(self, LL, height, r): 

'''(INTERNAL) Helper for C{._Direct} result L{Destination2Tuple}. 

''' 

h = self.height if height is None else height 

d = LL(wrap90(r.lat), wrap180(r.lon), height=h, datum=self.datum, name=self.name, 

**_xkwds_not(None, epoch=self.epoch, reframe=self.reframe)) 

return Destination2Tuple(d, wrap360(r.final)) 

 

def distanceTo(self, other, wrap=False, **unused): # ignore radius=R_M 

'''Compute the distance between this and an other point 

along a geodesic, using this C{Inverse} method. See method 

L{distanceTo3} for more details. 

 

@arg other: The other point (C{LatLon}). 

@kwarg wrap: Wrap and unroll longitudes (C{bool}). 

 

@return: Distance (C{meter}). 

 

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

 

@raise ValueError: If this and the B{C{other}} point's L{Datum} 

ellipsoids are not compatible. 

''' 

return self._Inverse(other, wrap, azis=False).distance 

 

def distanceTo3(self, other, wrap=False): 

'''Compute the distance, the initial and final bearing along 

a geodesic between this and an other point, using this 

C{Inverse} method. 

 

The distance is in the same units as this point's datum axes, 

conventionally meter. The distance is measured on the surface 

of the ellipsoid, ignoring this point's height. 

 

The initial and final bearing (forward and reverse azimuth) 

are in compass C{degrees360} from North. 

 

@arg other: Destination point (C{LatLon}). 

@kwarg wrap: Wrap and unroll longitudes (C{bool}). 

 

@return: A L{Distance3Tuple}C{(distance, initial, final)}. 

 

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

 

@raise ValueError: If this and the B{C{other}} point's L{Datum} 

ellipsoids are not compatible. 

''' 

return self._xnamed(self._Inverse(other, wrap)) 

 

def finalBearingOn(self, distance, bearing): 

'''Compute the final bearing (reverse azimuth) after having 

travelled for the given distance along a geodesic given by 

an initial bearing from this point, using this C{Direct} 

method. See method L{destination2} for more details. 

 

@arg distance: Distance (C{meter}). 

@arg bearing: Initial bearing (compass C{degrees360}). 

 

@return: Final bearing (compass C{degrees360}). 

''' 

return self._Direct(distance, bearing, None, None).final 

 

def finalBearingTo(self, other, wrap=False): 

'''Compute the final bearing (reverse azimuth) after having 

travelled along a geodesic from this point to an other 

point, using this C{Inverse} method. See method 

L{distanceTo3} for more details. 

 

@arg other: The other point (C{LatLon}). 

@kwarg wrap: Wrap and unroll longitudes (C{bool}). 

 

@return: Final bearing (compass C{degrees360}). 

 

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

 

@raise ValueError: If this and the B{C{other}} point's L{Datum} 

ellipsoids are not compatible. 

''' 

return self._Inverse(other, wrap).final 

 

@Property_RO 

def geodesic(self): # overloaded by I{Karney}'s, N/A for I{Vincenty} 

'''N/A, invalid (C{None} I{always}). 

''' 

return None # PYCHOK no cover 

 

def initialBearingTo(self, other, wrap=False): 

'''Compute the initial bearing (forward azimuth) to travel 

along a geodesic from this point to an other point, 

using this C{Inverse} method. See method L{distanceTo3} 

for more details. 

 

@arg other: The other point (C{LatLon}). 

@kwarg wrap: Wrap and unroll longitudes (C{bool}). 

 

@return: Initial bearing (compass C{degrees360}). 

 

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

 

@raise ValueError: If this and the B{C{other}} point's L{Datum} 

ellipsoids are not compatible. 

''' 

return self._Inverse(other, wrap).initial 

 

def intermediateTo(self, other, fraction, height=None, wrap=False): 

'''Return the point at given fraction along the geodesic between 

this and an other point, using this C{Direct} and C{Inverse} 

methods. 

 

@arg other: The other point (C{LatLon}). 

@arg fraction: Fraction between both points ranging from 

0, meaning this to 1, the other point (C{float}). 

@kwarg height: Optional height, overriding the fractional 

height (C{meter}). 

@kwarg wrap: Wrap and unroll longitudes (C{bool}). 

 

@return: Intermediate point (C{LatLon}). 

 

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

 

@raise UnitError: Invalid B{C{fraction}} or B{C{height}}. 

 

@raise ValueError: If this and the B{C{other}} point's L{Datum} 

ellipsoids are not compatible. 

 

@see: Methods L{distanceTo3} and L{destination}. 

''' 

t = self.distanceTo3(other, wrap=wrap) 

f = Scalar(fraction=fraction) 

h = self._havg(other, f=f) if height is None else Height(height) 

return self.destination(t.distance * f, t.initial, height=h) 

 

def _Inverse(self, other, wrap, **unused): # azis=False, overloaded by I{Vincenty} 

'''(INTERNAL) I{Karney}'s C{Inverse} method. 

 

@return: A L{Distance3Tuple}C{(distance, initial, final)}. 

 

@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. 

''' 

_ = self.ellipsoids(other) 

g = self.geodesic 

_, lon = unroll180(self.lon, other.lon, wrap=wrap) 

return g.Inverse3(self.lat, self.lon, other.lat, lon) 

 

 

def _Equidistant00(equidistant, p1): 

'''(INTERNAL) Get an C{Equidistant*(0, 0, ...)} instance. 

''' 

from pygeodesy.azimuthal import _Equidistants 

 

if equidistant is None or not callable(equidistant): 

equidistant = p1.Equidistant 

elif not issubclassof(equidistant, *_Equidistants): # PYCHOK no cover 

t = tuple(_.__name__ for _ in _Equidistants) 

raise _IsnotError(*t, equidistant=equidistant) 

return equidistant(0, 0, p1.datum) 

 

 

def _intersect3(s1, end1, s2, end2, height=None, wrap=True, # MCCABE? 

equidistant=None, tol=_TOL_M, LatLon=None, **LatLon_kwds): 

'''(INTERNAL) Intersect two (ellipsoidal) path, see L{_intersection} 

above, separated to allow callers to embellish any exceptions. 

''' 

from pygeodesy.sphericalTrigonometry import _intersect as _si, LatLon as _LLS 

from pygeodesy.vector3d import _intersect3d3 as _vi3 

 

# E = s1.ellipsoids(s2) 

# assert E == s1.ellispoids(e1) == s1.ellipsoids(e2) 

 

e1 = s1.others(end1=end1) 

e2 = s1.others(end2=end2) 

 

if wrap: # unroll180 == .karney._unroll2 

e1 = _unrollon(s1, e1) 

e2 = _unrollon(s2, e2) 

 

# get the azimuthal equidistant projection 

A = _Equidistant00(equidistant, s1) 

e = max(tol, EPS) 

 

# gu-/estimate initial intersection, spherically ... 

t = _si(_LLS(s1.lat, s1.lon, height=s1.height), 

_LLS(e1.lat, e1.lon, height=e1.height), 

_LLS(s2.lat, s2.lon, height=s2.height), 

_LLS(e2.lat, e2.lon, height=e2.height), 

height=height, wrap=False, LatLon=_LLS) # unrolled already 

h, n = t.height, t.name 

 

# ... and iterate as Karney describes, @see: 

# LatLonEllipsoidalBase.LatLon.intersections2 

c = None # force first d == c to False 

for i in range(1, _TRIPS): 

A.reset(t.lat, t.lon) # gu-/estimate as origin 

# convert start and end points to projection 

# space and compute an intersection there 

v, o1, o2 = _vi3(A.forward(s1.lat, s1.lon), 

A.forward(e1.lat, e1.lon), 

A.forward(s2.lat, s2.lon), 

A.forward(e2.lat, e2.lon), 

eps=e, useZ=False) 

# convert intersection back to geodetic 

t, d = A._reverse2(v.x, v.y) 

# break if below tolerance or if unchanged 

if d < e or d == c: 

t._iteration = i 

break 

c = d 

else: 

raise IntersectionError(_no_(Fmt.convergence(e))) 

 

r = _LL4Tuple(t.lat, t.lon, h, t.datum, LatLon, LatLon_kwds, inst=s1, name=n) 

r._iteration = t._iteration # _NamedTuple._iteration 

return Intersection3Tuple(r, o1, o2) 

 

 

def _intersection3(start1, end1, start2, end2, height=None, wrap=True, 

equidistant=None, tol=_TOL_M, LatLon=None, **LatLon_kwds): 

'''(INTERNAL) Iteratively compute the intersection point of two paths, 

each defined by an (ellipsoidal) start and end point. 

''' 

s1 = _xellipsoidal(start1=start1) 

s2 = s1.others(start2=start2) 

 

try: 

return _intersect3(s1, end1, s2, end2, height=height, wrap=wrap, 

equidistant=equidistant, tol=tol, 

LatLon=LatLon, **LatLon_kwds) 

except (TypeError, ValueError) as x: 

raise _xError(x, start1=start1, end1=end1, start2=start2, end2=end2) 

 

 

def _intersections2(center1, radius1, center2, radius2, height=None, wrap=True, 

equidistant=None, tol=_TOL_M, LatLon=None, **LatLon_kwds): 

'''(INTERNAL) Iteratively compute the intersection points of two circles, 

each defined by an (ellipsoidal) center point and a radius. 

''' 

c1 = _xellipsoidal(center1=center1) 

c2 = c1.others(center2=center2) 

 

try: 

return _intersects2(c1, radius1, c2, radius2, height=height, wrap=wrap, 

equidistant=equidistant, tol=tol, 

LatLon=LatLon, **LatLon_kwds) 

except (TypeError, ValueError) as x: 

raise _xError(x, center1=center1, radius1=radius1, 

center2=center2, radius2=radius2) 

 

 

def _intersects2(c1, radius1, c2, radius2, height=None, wrap=True, # MCCABE 15 

equidistant=None, tol=_TOL_M, LatLon=None, **LatLon_kwds): 

'''(INTERNAL) Intersect two (ellipsoidal) circles, see L{_intersections2} 

above, separated to allow callers to embellish any exceptions. 

''' 

from pygeodesy.sphericalTrigonometry import _intersects2 as _si2, LatLon as _LLS 

from pygeodesy.vector3d import _intersects2 as _vi2 

 

def _latlon4(t, h, n, c): 

r = _LL4Tuple(t.lat, t.lon, h, t.datum, LatLon, LatLon_kwds, inst=c, name=n) 

r._iteration = t.iteration # ._iteration for tests 

return r 

 

r1 = Radius_(radius1=radius1) 

r2 = Radius_(radius2=radius2) 

 

E = c1.ellipsoids(c2) 

# get the azimuthal equidistant projection 

A = _Equidistant00(equidistant, c1) 

 

if r1 < r2: 

c1, c2 = c2, c1 

r1, r2 = r2, r1 

 

if r1 > (min(E.b, E.a) * PI): 

raise _ValueError(_exceed_PI_radians_) 

 

if wrap: # unroll180 == .karney._unroll2 

c2 = _unrollon(c1, c2) 

 

# distance between centers and radii are 

# measured along the ellipsoid's surface 

m = c1.distanceTo(c2, wrap=False) # meter 

if m < max(r1 - r2, EPS): 

raise IntersectionError(_near_concentric_) 

if fsum_(r1, r2, -m) < 0: 

raise IntersectionError(_too_(Fmt.distant(m))) 

 

f = _radical2(m, r1, r2).ratio # "radical fraction" 

r = E.rocMean(favg(c1.lat, c2.lat, f=f)) 

e = max(m2degrees(tol, radius=r), EPS) 

 

# gu-/estimate initial intersections, spherically ... 

t1, t2 = _si2(_LLS(c1.lat, c1.lon, height=c1.height), r1, 

_LLS(c2.lat, c2.lon, height=c2.height), r2, 

radius=r, height=height, wrap=False, too_d=m) # unrolled already 

h, n = t1.height, t1.name 

 

# ... and iterate as Karney describes, @see: 

# LatLonEllipsoidalBase.LatLon.intersections2 

ts, ta = [], None 

for t in ((t1,) if t1 is t2 else (t1, t2)): 

c = None # force first d == c to False 

for i in range(1, _TRIPS): 

A.reset(t.lat, t.lon) # gu-/estimate as origin 

# convert centers to projection space 

t1 = A.forward(c1.lat, c1.lon) 

t2 = A.forward(c2.lat, c2.lon) 

# compute intersections in projection space 

v1, v2 = _vi2(t1, r1, # XXX * t1.scale?, 

t2, r2, # XXX * t2.scale?, 

sphere=False, too_d=m) 

# convert intersections back to geodetic 

t1, d1 = A._reverse2(v1.x, v1.y) 

if v1 is v2: # abutting 

t, d = t1, d1 # PYCHOK no cover 

else: 

t2, d2 = A._reverse2(v2.x, v2.y) 

# consider only the closer intersection 

t, d = (t1, d1) if d1 < d2 else (t2, d2) 

# break if below tolerance or if unchanged 

if d < e or d == c: 

t._iteration = i # _NamedTuple._iteration 

ts.append(t) 

if v1 is v2: # abutting 

ta = t # PYCHOK no coves 

break 

c = d 

else: 

raise IntersectionError(_no_(Fmt.convergence(tol))) 

 

if ta: # abutting circles 

pass # PYCHOK no cover 

elif len(ts) == 2: 

return (_latlon4(ts[0], h, n, c1), 

_latlon4(ts[1], h, n, c2)) 

elif len(ts) == 1: # PYCHOK no cover 

ta = ts[0] # assume abutting 

else: # PYCHOK no cover 

raise _AssertionError(ts=ts) 

r = _latlon4(ta, h, n, c1) 

return r, r 

 

 

def _nearestOn(point, point1, point2, within=True, height=None, wrap=True, 

equidistant=None, tol=_TOL_M, LatLon=None, **LatLon_kwds): 

'''(INTERNAL) Get closest point, imported by .ellipsoidalExact, 

-GeodSolve, -Karney and -Vincenty to embellish exceptions. 

''' 

try: 

p = _xellipsoidal(point=point) 

return _nearestOne(p, point1, point2, within=within, height=height, wrap=wrap, 

equidistant=equidistant, tol=tol, LatLon=LatLon, **LatLon_kwds) 

except (TypeError, ValueError) as x: 

raise _xError(x, point=point, point1=point1, point2=point2) 

 

 

def _nearestOne(p, point1, point2, within=True, height=None, wrap=True, 

equidistant=None, tol=_TOL_M, LatLon=None, **LatLon_kwds): 

'''(INTERNAL) Get closest point, like L{_intersects2} above, 

separated to allow callers to embellish any exceptions. 

''' 

from pygeodesy.sphericalNvector import LatLon as _LLS 

from pygeodesy.vector3d import _nearestOn as _vnOn, Vector3d 

 

def _v(t, h): 

return Vector3d(t.x, t.y, h) 

 

p1 = p.others(point1=point1) 

p2 = p.others(point2=point2) 

 

_ = p.ellipsoids(p1) 

E = p.ellipsoids(p2) 

 

if wrap: 

p1 = _unrollon(p, p1) 

p2 = _unrollon(p, p2) 

p2 = _unrollon(p1, p2) 

 

r = E.rocMean(fmean_(p.lat, p1.lat, p2.lat)) 

e = max(m2degrees(tol, radius=r), EPS) 

 

# get the azimuthal equidistant projection 

A = _Equidistant00(equidistant, p) 

 

# gu-/estimate initial nearestOn, spherically ... wrap=False, only! 

t = _LLS(p.lat, p.lon, height=p.height).nearestOn( 

_LLS(p1.lat, p1.lon, height=p1.height), 

_LLS(p2.lat, p2.lon, height=p2.height), within=within, height=height) 

n = t.name 

if height is False: # PYCHOK no cover 

h = t.height # use heights as Z 

h1 = p1.height 

h2 = p2.height 

else: 

h = h1 = h2 = _0_0 

 

# ... and iterate as Karney describes, @see: 

# LatLonEllipsoidalBase.LatLon.intersections2 

c = None # force first d == c to False 

# closest to origin, .z to interpolate height 

p = Vector3d(0, 0, h) 

for i in range(1, _TRIPS): 

A.reset(t.lat, t.lon) # gu-/estimate as origin 

# convert points to projection space 

# and compute the nearest one there 

v = _vnOn(p, _v(A.forward(p1.lat, p1.lon), h1), 

_v(A.forward(p2.lat, p2.lon), h2), 

within=within) 

# convert nearest one back to geodetic 

t, d = A._reverse2(v.x, v.y) 

# break if below tolerance or if unchanged 

if d < e or d == c: 

t._iteration = i # _NamedTuple._iteration 

if height is False: 

h = v.z # nearest interpolated 

break 

c = d 

else: 

raise _ValueError(_no_(Fmt.convergence(tol))) 

 

r = _LL4Tuple(t.lat, t.lon, h, t.datum, LatLon, LatLon_kwds, inst=p, name=n) 

r._iteration = t.iteration # ._iteration for tests 

return r 

 

 

def _unrollon(p1, p2): # unroll180 == .karney._unroll2 

# wrap, unroll and replace longitude if different 

_, lon = unroll180(p1.lon, p2.lon, wrap=True) 

if abs(lon - p2.lon) > EPS: 

p2 = p2.classof(p2.lat, lon, **_xkwds_not(None, 

height=getattr(p2, _height_, None), 

datum=getattr(p2, _datum_, None), 

epoch=getattr(p2, _epoch_, None), 

reframe=getattr(p2, _reframe_, None))) 

return p2 

 

 

__all__ += _ALL_DOCS(LatLonEllipsoidalBaseDI) 

 

# **) MIT License 

# 

# Copyright (C) 2016-2021 -- mrJean1 at Gmail -- All Rights Reserved. 

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