# Coverage for pygeodesy/ellipsoidalNvector.py : 98%

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Ellipsoidal classes geodetic (lat-/longitude) L{LatLon}, geocentric (ECEF) L{Cartesian}, L{Ned} and L{Nvector} and functions L{meanOf}, L{sumOf} and L{toNed}. Pure Python implementation of n-vector-based geodetic (lat-/longitude) methods by I{(C) Chris Veness 2011-2016} published under the same MIT Licence**, see U{Vector-based geodesy <https://www.Movable-Type.co.UK/scripts/latlong-vectors.html>}. These classes and functions work with: (a) geodesic (polar) lat-/longitude points on the earth's surface and (b) 3-D vectors used as n-vectors representing points on the earth's surface or vectors normal to the plane of a great circle. See also Kenneth Gade U{'A Non-singular Horizontal Position Representation' <https://www.NavLab.net/Publications/A_Nonsingular_Horizontal_Position_Representation.pdf>}, The Journal of Navigation (2010), vol 63, nr 3, pp 395-417. ''' # make sure int/int division yields float quotient, see .basics from __future__ import division from pygeodesy.basics import _xinstanceof from pygeodesy.datums import _ellipsoidal_datum, _WGS84 from pygeodesy.ellipsoidalBase import CartesianEllipsoidalBase, \ LatLonEllipsoidalBase from pygeodesy.errors import _xkwds from pygeodesy.fmath import fdot from pygeodesy.interns import NN, _Nv00_, _COMMASPACE_ from pygeodesy.interns import _down_, _east_, _north_, _pole_ # PYCHOK used! from pygeodesy.lazily import _ALL_LAZY, _ALL_OTHER from pygeodesy.ltpTuples import Aer as _Aer, Ned as _Ned from pygeodesy.named import _NamedTuple, _xnamed from pygeodesy.nvectorBase import NorthPole, LatLonNvectorBase, \ NvectorBase, sumOf as _sumOf from pygeodesy.props import deprecated_class, deprecated_function, \ deprecated_method, Property_RO from pygeodesy.streprs import Fmt, fstr, _xzipairs from pygeodesy.units import Bearing, Distance, Height, Meter, Radius from pygeodesy.utily import sincos2d __all__ = _ALL_LAZY.ellipsoidalNvector __version__ = '21.04.24' class Cartesian(CartesianEllipsoidalBase): '''Extended to convert geocentric, L{Cartesian} points to L{Nvector} and n-vector-based, geodetic L{LatLon}. ''' @Property_RO def Ecef(self): '''Get the ECEF I{class} (L{EcefVeness}), I{lazily}. ''' from pygeodesy.ecef import EcefVeness return EcefVeness def toLatLon(self, **LatLon_and_kwds): # PYCHOK LatLon=LatLon, datum=None '''Convert this cartesian to an C{Nvector}-based geodetic point. @kwarg LatLon_and_kwds: Optional L{LatLon}, B{C{datum}} and other keyword arguments. Use C{B{LatLon}=...} to override this L{LatLon} class or specify C{B{LatLon}=None}. @return: The geodetic point (L{LatLon}) or if B{C{LatLon}} is set to 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}}. ''' kwds = _xkwds(LatLon_and_kwds, LatLon=LatLon, datum=self.datum) return CartesianEllipsoidalBase.toLatLon(self, **kwds) def toNvector(self, **Nvector_and_kwds): # PYCHOK Datums.WGS84 '''Convert this cartesian to L{Nvector} components, I{including height}. @kwarg Nvector_and_kwds: Optional L{Nvector}, B{C{datum}} and other keyword arguments. Use C{B{Nvector}=...} to override this L{Nvector} class or specify C{B{Nvector}=None}. @return: The C{n-vector} components (L{Nvector}) or if B{C{Nvector}} is set to C{None}, a L{Vector4Tuple}C{(x, y, z, h)} @raise TypeError: Invalid B{C{Nvector_and_kwds}}. @example: >>> from ellipsoidalNvector import LatLon >>> c = Cartesian(3980581, 97, 4966825) >>> n = c.toNvector() # (0.62282, 0.000002, 0.78237, +0.24) ''' kwds = _xkwds(Nvector_and_kwds, Nvector=Nvector, datum=self.datum) return CartesianEllipsoidalBase.toNvector(self, **kwds) class LatLon(LatLonNvectorBase, LatLonEllipsoidalBase): '''An n-vector-based, ellipsoidal L{LatLon} point. @example: >>> from ellipsoidalNvector import LatLon >>> p = LatLon(52.205, 0.119) # height=0, datum=Datums.WGS84 ''' _Nv = None # cached toNvector (L{Nvector}) def _update(self, updated, *attrs): # PYCHOK args '''(INTERNAL) Zap cached attributes if updated. ''' if updated: LatLonNvectorBase._update(self, updated, _Nv=self._Nv) # special case LatLonEllipsoidalBase._update(self, updated, *attrs) # def crossTrackDistanceTo(self, start, end, radius=R_M): # '''Return the (signed) distance from this point to the great # circle defined by a start point and an end point or bearing. # # @arg start: Start point of great circle path (L{LatLon}). # @arg end: End point of great circle path (L{LatLon}) or # initial bearing (compass C{degrees360}) at the # start point. # @kwarg radius: Mean earth radius (C{meter}). # # @return: Distance to great circle, negative if to left or # positive if to right of path (C{meter}, same units # as B{C{radius}}). # # @raise TypeError: If B{C{start}} or B{C{end}} point is not L{LatLon}. # # @example: # # >>> p = LatLon(53.2611, -0.7972) # # >>> s = LatLon(53.3206, -1.7297) # >>> b = 96.0 # >>> d = p.crossTrackDistanceTo(s, b) # -305.7 # # >>> e = LatLon(53.1887, 0.1334) # >>> d = p.crossTrackDistanceTo(s, e) # -307.5 # ''' # self.others(start=start) # # if isscalar(end): # gc from point and bearing # gc = start.greatCircle(end) # else: # gc by two points # gc = start.toNvector().cross(end.toNvector()) # # # (signed) angle between point and gc normal vector # v = self.toNvector() # a = gc.angleTo(v, vSign=v.cross(gc)) # a = (-PI_2 - a) if a < 0 else (PI_2 - a) # return a * float(radius) def deltaTo(self, other): '''Calculate the local delta from this to an other point. The delta is returned as a North-East-Down (NED) vector. Note, this is a linear delta, unrelated to a geodesic on the ellipsoid. The points need not be defined on the same datum. @arg other: The other point (L{LatLon}). @return: Delta of this point (L{Ned}). @raise TypeError: The B{C{other}} point is not L{LatLon}. @raise ValueError: If ellipsoids are incompatible. @example: >>> a = LatLon(49.66618, 3.45063) >>> b = LatLon(48.88667, 2.37472) >>> delta = a.deltaTo(b) # [N:-86126, E:-78900, D:1069] >>> d = delta.length # 116807.681 m >>> b = delta.bearing # 222.493° >>> e = delta.elevation # -0.5245° ''' self.ellipsoids(other) # throws TypeError and ValueError # get delta in cartesian frame dc = other.toCartesian().minus(self.toCartesian()) # rotate dc to get delta in n-vector reference # frame using the rotation matrix row vectors nv, ev, dv = self._rotation3 return Ned(dc.dot(nv), dc.dot(ev), dc.dot(dv), name=self.name) # def destination(self, distance, bearing, radius=R_M, height=None): # '''Return the destination point after traveling from this # point the given distance on the given initial bearing. # # @arg distance: Distance traveled (C{meter}, same units as # given earth B{C{radius}}). # @arg bearing: Initial bearing (compass C{degrees360}). # @kwarg radius: Mean earth radius (C{meter}). # @kwarg height: Optional height at destination point, # overriding default (C{meter}, same units # as B{C{radius}}). # # @return: Destination point (L{LatLon}). # # @example: # # >>> p = LatLon(51.4778, -0.0015) # >>> q = p.destination(7794, 300.7) # >>> q.toStr() # '51.5135°N, 000.0983°W' ? # ''' # r = _angular(distance, radius) # angular distance in radians # # great circle by starting from this point on given bearing # gc = self.greatCircle(bearing) # # v1 = self.toNvector() # x = v1.times(cos(r)) # component of v2 parallel to v1 # y = gc.cross(v1).times(sin(r)) # component of v2 perpendicular to v1 # # v2 = x.plus(y).unit() # return v2.toLatLon(height=self.height if height is C{None} else height) def destinationNed(self, delta): '''Calculate the destination point using the supplied NED delta from this point. @arg delta: Delta from this to the other point in the local tangent plane (LTP) of this point (L{Ned}). @return: Destination point (L{LatLon}). @raise TypeError: If B{C{delta}} is not L{Ned}. @example: >>> a = LatLon(49.66618, 3.45063) >>> delta = Ned(-86126, -78900, 1069) # from Aer(222.493, -0.5245, 116807.681) >>> b = a.destinationNed(delta) # 48.886669°N, 002.374721°E or 48°53′12.01″N, 002°22′29.0″E +0.20m @JSname: I{destinationPoint}. ''' _xinstanceof(Ned, delta=delta) nv, ev, dv = self._rotation3 # convert NED delta to standard coordinate frame of n-vector dn = delta.ned # rotate dn to get delta in cartesian (ECEF) coordinate # reference frame using the rotation matrix column vectors dc = Cartesian(fdot(dn, nv.x, ev.x, dv.x), fdot(dn, nv.y, ev.y, dv.y), fdot(dn, nv.z, ev.z, dv.z)) # apply (cartesian) delta to this Cartesian to obtain destination as cartesian v = self.toCartesian().plus(dc) return v.toLatLon(datum=self.datum, LatLon=self.classof) # Cartesian(v.x, v.y, v.z).toLatLon(...) def distanceTo(self, other, radius=None, wrap=False): '''Approximate the distance from this to an other point. @arg other: The other point (L{LatLon}). @kwarg radius: Mean earth radius (C{meter}). @kwarg wrap: Wrap/unroll the angular distance (C{bool}). @return: Distance (C{meter}, same units as B{C{radius}}). @raise TypeError: The B{C{other}} point is not L{LatLon}. @raise ValueError: Invalid B{C{radius}}. @example: >>> p = LatLon(52.205, 0.119) >>> q = LatLon(48.857, 2.351); >>> d = p.distanceTo(q) # 404300 ''' self.others(other) a = self._N_vector.angleTo(other._N_vector, wrap=wrap) r = self.datum.ellipsoid.R1 if radius is None else Radius(radius) return abs(a) * r @Property_RO def Ecef(self): '''Get the ECEF I{class} (L{EcefVeness}), I{lazily}. ''' from pygeodesy.ecef import EcefVeness return EcefVeness @deprecated_method def equals(self, other, eps=None): # PYCHOK no cover '''DEPRECATED, use method L{isequalTo}. ''' return self.isequalTo(other, eps=eps) def isequalTo(self, other, eps=None): '''Compare this point with an other point. @arg other: The other point (L{LatLon}). @kwarg eps: Optional margin (C{float}). @return: C{True} if points are identical, including datum, I{ignoring height}, C{False} otherwise. @raise TypeError: The B{C{other}} point is not L{LatLon}. @raise ValueError: Invalid B{C{eps}}. @see: Method C{isequalTo3} to include I{height}. @example: >>> p = LatLon(52.205, 0.119) >>> q = LatLon(52.205, 0.119) >>> e = p.isequalTo(q) # True ''' return LatLonEllipsoidalBase.isequalTo(self, other, eps=eps) \ if self.datum == other.datum else False # def greatCircle(self, bearing): # '''Return the great circle heading on the given bearing # from this point. # # Direction of vector is such that initial bearing vector # b = c × p, where p is representing this point. # # @arg bearing: Bearing from this point (compass C{degrees360}). # # @return: N-vector representing great circle (L{Nvector}). # # @example: # # >>> p = LatLon(53.3206, -1.7297) # >>> g = p.greatCircle(96.0) # >>> g.toStr() # '(-0.794, 0.129, 0.594)' # ''' # a, b, _ = self.philamheight # t = radians(bearing) # # sa, ca, sb, cb, st, ct = sincos2(a, b, t) # return self._xnamed(Nvector(sb * ct - sa * cb * st, # -cb * ct - sa * sb * st, # ca * st) # def initialBearingTo(self, other): # '''Return the initial bearing (forward azimuth) from this # to an other point. # # @arg other: The other point (L{LatLon}). # # @return: Initial bearing (compass C{degrees360}). # # @raise TypeError: The B{C{other}} point is not L{LatLon}. # # @example: # # >>> p1 = LatLon(52.205, 0.119) # >>> p2 = LatLon(48.857, 2.351) # >>> b = p1.bearingTo(p2) # 156.2 # # @JSname: I{bearingTo}. # ''' # self.others(other) # # v1 = self.toNvector() # v2 = other.toNvector() # # gc1 = v1.cross(v2) # gc through v1 & v2 # gc2 = v1.cross(_NP3) # gc through v1 & North pole # # # bearing is (signed) angle between gc1 & gc2 # return degrees360(gc1.angleTo(gc2, vSign=v1)) def intermediateTo(self, other, fraction, height=None): '''Return the point at given fraction between this and an other point. @arg other: The other point (L{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}). @return: Intermediate point (L{LatLon}). @raise TypeError: The B{C{other}} point is not L{LatLon}. @example: >>> p = LatLon(52.205, 0.119) >>> q = LatLon(48.857, 2.351) >>> p = p.intermediateTo(q, 0.25) # 51.3721°N, 000.7073°E @JSname: I{intermediatePointTo}. ''' self.others(other) i = other.toNvector().times(fraction).plus( self.toNvector().times(1 - fraction)) if height is None: h = self._havg(other, f=fraction) else: h = height return i.toLatLon(height=h, LatLon=self.classof) # Nvector(i.x, i.y, i.z).toLatLon(...) @Property_RO def _rotation3(self): '''(INTERNAL) Get the rotation matrix from n-vector coordinate frame axes. ''' nv = self.toNvector() # local (n-vector) coordinate frame dv = nv.negate() # down, opposite to n-vector ev = NorthPole.cross(nv, raiser=_pole_).unit() # east, pointing perpendicular to the plane nv = ev.cross(dv) # north, by right hand rule return nv, ev, dv # matrix rows def toCartesian(self, **Cartesian_and_kwds): # PYCHOK Cartesian=Cartesian, datum=None '''Convert this point to an C{Nvector}-based geodetic point. @kwarg Cartesian_and_kwds: Optional L{Cartesian}, B{C{datum}} and other keyword arguments. Use C{B{Cartesian}=...} to override this L{Cartesian} class or specify C{B{Cartesian}=None}. @return: The geodetic point (L{Cartesian}) or if B{C{Cartesian}} is set to 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}} or other B{C{Cartesian_and_kwds}}. ''' kwds = _xkwds(Cartesian_and_kwds, Cartesian=Cartesian, datum=self.datum) return LatLonEllipsoidalBase.toCartesian(self, **kwds) def toNvector(self, **Nvector_and_kwds): # PYCHOK signature '''Convert this point to L{Nvector} components, I{including height}. @kwarg Nvector_and_kwds: Optional L{Nvector}, B{C{datum}} and other keyword arguments. Use C{B{Nvector}=...} to override this L{Nvector} class or specify C{B{Nvector}=None}. @return: The C{n-vector} components (L{Nvector}) or if B{C{Nvector}} is set to C{None}, a L{Vector4Tuple}C{(x, y, z, h)}. @raise TypeError: Invalid B{C{Nvector}} or other B{C{Nvector_and_kwds}}. @example: >>> p = LatLon(45, 45) >>> n = p.toNvector() >>> n.toStr() # [0.50, 0.50, 0.70710] ''' kwds = _xkwds(Nvector_and_kwds, Nvector=Nvector, datum=self.datum) return LatLonNvectorBase.toNvector(self, **kwds) class Ned(_Ned): '''DEPRECATED, use L{pygeodesy.Ned}.''' def __init__(self, north, east, down, name=NN): deprecated_class(self.__class__) _Ned.__init__(self, north, east, down, name=name) @deprecated_method # PYCHOK expected def toRepr(self, prec=None, fmt=Fmt.SQUARE, sep=_COMMASPACE_, **unused): '''DEPRECATED, use L{ltpTuples.Aer}. Return a string representation of this NED vector as length, bearing and elevation. @kwarg prec: Optional number of decimals, unstripped (C{int}). @kwarg fmt: Optional enclosing backets format (C{str}). @kwarg sep: Optional separator between NEDs (C{str}). @return: This Ned as "[L:f, B:degrees360, E:degrees90]" (C{str}). ''' from pygeodesy.dms import F_D, toDMS t = (fstr(self.slantrange, prec=3 if prec is None else prec), toDMS(self.azimuth, form=F_D, prec=prec, ddd=0), toDMS(self.elevation, form=F_D, prec=prec, ddd=0)) return _xzipairs('LBE', t, sep=sep, fmt=fmt) class Ned3Tuple(_NamedTuple): # @see: .ltpTuples '''3-Tuple C{(north, east, down)}. DEPRECATED, use L{pygeodesy.Ned4Tuple}. ''' _Names_ = (_north_, _east_, _down_) _Units_ = ( Meter, Meter, Meter) def __new__(cls, north, east, down, name=NN): deprecated_class(cls) return _NamedTuple.__new__(cls, north, east, down, name=name) _Nvll = LatLon(0, 0, name=_Nv00_) # reference instance (L{LatLon}) class Nvector(NvectorBase): '''An n-vector is a position representation using a (unit) vector normal to the earth ellipsoid. Unlike lat-/longitude points, n-vectors have no singularities or discontinuities. For many applications, n-vectors are more convenient to work with than other position representations like lat-/longitude, earth-centred earth-fixed (ECEF) vectors, UTM coordinates, etc. Note commonality with L{sphericalNvector.Nvector}. ''' _datum = _WGS84 # default datum (L{Datum}) def __init__(self, x, y, z, h=0, datum=None, ll=None, name=NN): '''New n-vector normal to the earth's surface. @arg x: X component (C{meter}). @arg y: Y component (C{meter}). @arg z: Z component (C{meter}). @kwarg h: Optional height above model surface (C{meter}). @kwarg datum: Optional datum this n-vector is defined in (L{Datum}, L{Ellipsoid}, L{Ellipsoid2} or L{a_f2Tuple}). @kwarg ll: Optional, original latlon (C{LatLon}). @kwarg name: Optional name (C{str}). @raise TypeError: If B{C{datum}} is not a L{Datum}. @example: >>> from ellipsoidalNvector import Nvector >>> v = Nvector(0.5, 0.5, 0.7071, 1) >>> v.toLatLon() # 45.0°N, 045.0°E, +1.00m ''' NvectorBase.__init__(self, x, y, z, h=h, ll=ll, name=name) if datum not in (None, self._datum): self._datum = _ellipsoidal_datum(datum, name=name) @Property_RO def datum(self): '''Get this n-vector's datum (L{Datum}). ''' return self._datum def toCartesian(self, **Cartesian_and_kwds): # PYCHOK Cartesian=Cartesian '''Convert this n-vector to C{Nvector}-based cartesian (ECEF) coordinates. @kwarg Cartesian_and_kwds: Optional L{Cartesian}, B{C{h}}, B{C{datum}} and other keyword arguments. 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 set to 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_and_kwds}}. @example: >>> v = Nvector(0.5, 0.5, 0.7071) >>> c = v.toCartesian() # [3194434, 3194434, 4487327] >>> p = c.toLatLon() # 45.0°N, 45.0°E ''' kwds = _xkwds(Cartesian_and_kwds, h=self.h, Cartesian=Cartesian, datum=self.datum) return NvectorBase.toCartesian(self, **kwds) # class or .classof def toLatLon(self, **LatLon_and_kwds): # PYCHOK height=None, LatLon=LatLon '''Convert this n-vector to an C{Nvector}-based geodetic point. @kwarg LatLon_and_kwds: Optional L{LatLon}, B{C{height}}, B{C{datum}} and other keyword arguments. Use C{B{LatLon}=...} to override this L{LatLon} class or specify C{B{LatLon}=None}. @return: The geodetic point (L{LatLon}) or if B{C{LatLon}} is set to 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}}. @example: >>> v = Nvector(0.5, 0.5, 0.7071) >>> p = v.toLatLon() # 45.0°N, 45.0°E ''' kwds = _xkwds(LatLon_and_kwds, height=self.h, datum=self.datum, LatLon=LatLon) return NvectorBase.toLatLon(self, **kwds) # class or .classof def unit(self, ll=None): '''Normalize this vector to unit length. @kwarg ll: Optional, original latlon (C{LatLon}). @return: Normalised vector (L{Nvector}). ''' u = NvectorBase.unit(self, ll=ll) if u.datum != self.datum: u._overwrite(datum=self.datum) return u def meanOf(points, datum=_WGS84, height=None, LatLon=LatLon, **LatLon_kwds): '''Compute the geographic mean of several points. @arg points: Points to be averaged (L{LatLon}[]). @kwarg datum: Optional datum to use (L{Datum}). @kwarg height: Optional height at mean point, overriding the mean height (C{meter}). @kwarg LatLon: Optional class to return the mean point (L{LatLon}) or C{None}. @kwarg LatLon_kwds: Optional, additional B{C{LatLon}} keyword arguments, ignored if C{B{LatLon}=None}. @return: Geographic mean point and mean height (B{C{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 ValueError: Insufficient number of B{C{points}}. ''' Ps = _Nvll.PointsIter(points) # geographic mean m = sumOf(p._N_vector for p in Ps.iterate(closed=False)) kwds = _xkwds(LatLon_kwds, height=height, datum=datum, LatLon=LatLon, name=meanOf.__name__) return m.toLatLon(**kwds) def sumOf(nvectors, Vector=Nvector, h=None, **Vector_kwds): '''Return the vectorial sum of two or more n-vectors. @arg nvectors: Vectors to be added (L{Nvector}[]). @kwarg Vector: Optional class for the vectorial sum (L{Nvector}). @kwarg h: Optional height, overriding the mean height (C{meter}). @kwarg Vector_kwds: Optional, additional B{C{Vector}} keyword arguments, ignored if C{B{Vector}=None}. @return: Vectorial sum (B{C{Vector}}). @raise VectorError: No B{C{nvectors}}. ''' return _sumOf(nvectors, Vector=Vector, h=h, **Vector_kwds) @deprecated_function def toNed(distance, bearing, elevation, Ned=Ned, name=NN): '''DEPRECATED, use L{pygeodesy.Aer}C{(bearing, elevation, distance).xyzLocal.toNed(B{Ned}, name=B{name})} or L{XyzLocal}C{(pygeodesy.Aer(bearing, elevation, distance)).toNed(B{Ned}, name=B{name})}. Create an NED vector from distance, bearing and elevation (in local coordinate system). @arg distance: NED vector length (C{meter}). @arg bearing: NED vector bearing (compass C{degrees360}). @arg elevation: NED vector elevation from local coordinate frame horizontal (C{degrees}). @kwarg Ned: Optional class to return the NED (C{Ned}) or C{None}. @kwarg name: Optional name (C{str}). @return: An NED vector equivalent to this B{C{distance}}, B{C{bearing}} and B{C{elevation}} (DEPRECATED L{Ned}) or a DEPRECATED L{Ned3Tuple}C{(north, east, down)} if C{B{Ned}=None}. @raise ValueError: Invalid B{C{distance}}, B{C{bearing}} or B{C{elevation}}. @JSname: I{fromDistanceBearingElevation}. ''' if True: # use new Aer class n, e, d, _ = _Aer(bearing, elevation, distance).xyz4 else: # DEPRECATED d = Distance(distance) sb, cb, se, ce = sincos2d(Bearing(bearing), Height(elevation=elevation)) n = cb * d * ce e = sb * d * ce d *= se r = Ned3Tuple(n, e, -d) if Ned is None else \ Ned(n, e, -d) return _xnamed(r, name) __all__ += _ALL_OTHER(Cartesian, LatLon, Ned, Nvector, # classes meanOf, sumOf, toNed) # **) 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.