# Coverage for pygeodesy/ellipsoidalBaseDI.py : 97%

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''' # 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, _concentric_, _datum_, _epoch_, \ _exceed_PI_radians_, _height_, _no_, _near_, \ _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__ = '21.09.02' _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.vector2d 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. # # Permission is hereby granted, free of charge, to any person obtaining a # copy of this software and associated documentation files (the "Software"), # to deal in the Software without restriction, including without limitation # the rights to use, copy, modify, merge, publish, distribute, sublicense, # and/or sell copies of the Software, and to permit persons to whom the # Software is furnished to do so, subject to the following conditions: # # The above copyright notice and this permission notice shall be included # in all copies or substantial portions of the Software. # # THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS # OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, # FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL # THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR # OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, # ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR # OTHER DEALINGS IN THE SOFTWARE.