# Coverage for pygeodesy/ellipsoidalNvector.py : 94%

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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. @newfield example: Example, Examples ''' from pygeodesy.datum import Datum, Datums from pygeodesy.ecef import EcefVeness from pygeodesy.ellipsoidalBase import CartesianEllipsoidalBase, \ LatLonEllipsoidalBase from pygeodesy.fmath import fdot, fStr, hypot_ from pygeodesy.lazily import _ALL_LAZY, _2kwds from pygeodesy.named import LatLon3Tuple, _Named, Ned3Tuple, _xnamed from pygeodesy.nvectorBase import NorthPole, LatLonNvectorBase, \ NvectorBase, sumOf as _sumOf from pygeodesy.utily import degrees90, degrees360, property_RO, _TypeError from math import asin, atan2, cos, radians, sin # all public contants, classes and functions __all__ = _ALL_LAZY.ellipsoidalNvector + ( 'Cartesian', 'LatLon', 'Ned', 'Nvector', # classes 'meanOf', 'sumOf', 'toNed') # functions __version__ = '20.02.28' class Cartesian(CartesianEllipsoidalBase): '''Extended to convert geocentric, L{Cartesian} points to L{Nvector} and n-vector-based, geodetic L{LatLon}. ''' def toLatLon(self, **kwds): # PYCHOK LatLon=LatLon, datum=None '''Convert this cartesian point to an C{Nvector}-based geodetic point. @keyword kwds: Optional, additional B{C{LatLon}} keyword arguments, ignored if C{B{LatLon}=None}. Specify C{LatLon=...} to override this L{LatLon} class or set C{B{LatLon}=None}. @return: The B{C{LatLon}} point (L{LatLon}) or when C{B{LatLon}=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}} or B{C{kwds}}. ''' kwds = _2kwds(kwds, LatLon=LatLon, datum=self.datum) return CartesianEllipsoidalBase.toLatLon(self, **kwds) def toNvector(self, **kwds): # PYCHOK Datums.WGS84 '''Convert this cartesian to L{Nvector} components, I{including height}. @keyword kwds: Optional, additional B{C{Nvector}} keyword arguments, ignored if C{B{Nvector}=None}. Specify C{Nvector=...} to override this L{Nvector} class or set C{B{Nvector}=None}. @return: The B{C{Nvector}} components (L{Nvector}) or a L{Vector4Tuple}C{(x, y, z, h)} if C{B{Nvector}=None}. @raise TypeError: Invalid B{C{Nvector}} or B{C{kwds}}. @example: >>> from ellipsoidalNvector import LatLon >>> c = Cartesian(3980581, 97, 4966825) >>> n = c.toNvector() # (0.62282, 0.000002, 0.78237, +0.24) ''' kwds = _2kwds(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 ''' _Ecef = EcefVeness #: (INTERNAL) Preferred C{Ecef...} class, backward compatible. _Nv = None #: (INTERNAL) Cached toNvector (L{Nvector}). # _v3d = None #: (INTERNAL) Cached toVector3d (L{Vector3d}). _r3 = None #: (INTERNAL) Cached _rotation3 (3-Tuple L{Nvector}). def _rotation3(self): '''(INTERNAL) Build the rotation matrix from n-vector coordinate frame axes. ''' if self._r3 is None: nv = self.toNvector() # local (n-vector) coordinate frame d = nv.negate() # down (opposite to n-vector) e = NorthPole.cross(nv, raiser='pole').unit() # east (pointing perpendicular to the plane) n = e.cross(d) # north (by right hand rule) self._r3 = n, e, d # matrix rows return self._r3 def _update(self, updated, *attrs): '''(INTERNAL) Zap cached attributes if updated. ''' if updated: if self._Nv: self._Nv._fromll = None self._Nv = None LatLonNvectorBase._update(self, updated, '_r3', *attrs) 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. # # @param start: Start point of great circle path (L{LatLon}). # @param end: End point of great circle path (L{LatLon}) or # initial bearing (compass C{degrees360}) at # the start point. # @keyword 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, name='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)) # if a < 0: # a = -PI_2 - a # else: # a = PI_2 - a # return a * float(radius) def deltaTo(self, other): '''Calculate the NED 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. @param 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 n, e, d = self._rotation3() # 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 return Ned(dc.dot(n), dc.dot(e), dc.dot(d), 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. # # @param distance: Distance traveled (C{meter}, same units as # given earth B{C{radius}}). # @param bearing: Initial bearing (compass C{degrees360}). # @keyword radius: Mean earth radius (C{meter}). # @keyword 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 = float(distance) / float(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. @param delta: Delta from this to the other point in the local tangent plane (LTP) of this point (L{Ned}). @return: Destination point (L{Cartesian}). @raise TypeError: If {delta} is not L{Ned}. @example: >>> a = LatLon(49.66618, 3.45063) >>> delta = toNed(116807.681, 222.493, -0.5245) # [N:-86126, E:-78900, D:1069] >>> b = a.destinationNed(delta) # 48.88667°N, 002.37472°E @JSname: I{destinationPoint}. ''' _TypeError(Ned, delta=delta) n, e, d = self._rotation3() # convert NED delta to standard Vector3d in coordinate frame of n-vector dn = delta.toVector3d().to3xyz() # rotate dn to get delta in cartesian (ECEF) coordinate # reference frame using the rotation matrix column vectors dc = Cartesian(fdot(dn, n.x, e.x, d.x), fdot(dn, n.y, e.y, d.y), fdot(dn, n.z, e.z, d.z)) # apply (cartesian) delta to this Cartesian to # obtain destination point as cartesian v = self.toCartesian().plus(dc) # the plus() gives a plain vector return v.toLatLon(datum=self.datum, LatLon=self.classof) # Cartesian(v.x, v.y, v.z).toLatLon(...) def distanceTo(self, other, radius=None): '''Approximate the distance from this to an other point. @param other: The other point (L{LatLon}). @keyword radius: Mean earth radius (C{meter}). @return: Distance (C{meter}, same units as B{C{radius}}). @raise TypeError: The B{C{other}} point is not L{LatLon}. @example: >>> p = LatLon(52.205, 0.119) >>> q = LatLon(48.857, 2.351); >>> d = p.distanceTo(q) # 404300 ''' self.others(other) v1 = self.toVector3d() v2 = other.toVector3d() r = self.datum.ellipsoid.R1 if radius is None else radius return v1.angleTo(v2) * float(r) def equals(self, other, eps=None): '''DEPRECATED, use method C{isequalTo}. ''' return self.isequalTo(other, eps=eps) # PYCHOK no cover def isequalTo(self, other, eps=None): '''Compare this point with an other point. @param other: The other point (L{LatLon}). @keyword 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}. @see: Use method L{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. # # @param 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)' # ''' # b, a = self.to2ab() # c = radians(bearing) # # ca, sa = cos(a), sin(a) # cb, sb = cos(b), sin(b) # cc, sc = cos(c), sin(c) # # return self._xnamed(Nvector(sa * cc - ca * sb * sc, # -ca * cc - sa * sb * sc, # cb * sc) # def initialBearingTo(self, other): # '''Return the initial bearing (forward azimuth) from this # to an other point. # # @param 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. @param other: The other point (L{LatLon}). @param fraction: Fraction between both points ranging from 0 = this point to 1 = other point (C{float}). @keyword 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(...) def toCartesian(self, **kwds): # PYCHOK Cartesian=Cartesian, datum=None '''Convert this point to an C{Nvector}-based geodetic point. @keyword kwds: Optional, additional B{C{LatLon}} keyword arguments, ignored if C{B{LatLon}=None}. Specify C{LatLon=...} to override this L{LatLon} class or set C{B{LatLon}=None}. @return: The B{C{LatLon}} point (L{LatLon}) or when C{B{LatLon}=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}} or B{C{kwds}}. ''' kwds = _2kwds(kwds, Cartesian=Cartesian, datum=self.datum) return LatLonEllipsoidalBase.toCartesian(self, **kwds) def toNvector(self, **kwds): # PYCHOK signature '''Convert this point to L{Nvector} components, I{including height}. @keyword kwds: Optional, additional B{C{Nvector}} keyword arguments, ignored if C{B{Nvector}=None}. Specify C{Nvector=...} to override this L{Nvector} class or set C{B{Nvector}=None}. @return: The B{C{Nvector}} components (L{Nvector}) or a L{Vector4Tuple}C{(x, y, z, h)} if C{B{Nvector}=None}. @raise TypeError: Invalid B{C{Nvector}} or B{C{kwds}}. @example: >>> p = LatLon(45, 45) >>> n = p.toNvector() >>> n.toStr() # [0.50, 0.50, 0.70710] ''' kwds = _2kwds(kwds, Nvector=Nvector, datum=self.datum) return LatLonNvectorBase.toNvector(self, **kwds) # def toVector3d(self): # '''Convert this point to a L{Vector3d} normal to the # earth's surface. # # @return: Vector representing this point (L{Vector3d}). # # @example: # # >>> p = LatLon(45, 45) # >>> v = p.toVector3d() # >>> v.toStr() # '(0.50, 0.50, 0.707)' # ''' # if self._v3d is None: # x, y, z, _ = self.toNvector() # self._v3d = Vector3d(x, y, z) # return self._v3d class Ned(_Named): '''North-Eeast-Down (NED), also known as Local Tangent Plane (LTP), is a vector in the local coordinate frame of a body. ''' _bearing = None #: (INTERNAL) Cache bearing (compass C{degrees360}). _down = None #: (INTERNAL) Down component (C{meter}). _east = None #: (INTERNAL) East component (C{meter}). _elevation = None #: (INTERNAL) Cache elevation (C{degrees}). _length = None #: (INTERNAL) Cache length (C{float}). _north = None #: (INTERNAL) North component (C{meter}). def __init__(self, north, east, down, name=''): '''New North-East-Down vector. @param north: North component (C{meter}). @param east: East component (C{meter}). @param down: Down component, normal to the surface of the ellipsoid (C{meter}). @keyword name: Optional name (C{str}). @example: >>> from ellipsiodalNvector import Ned >>> delta = Ned(110569, 111297, 1936) >>> delta.toStr(prec=0) # [N:110569, E:111297, D:1936] ''' self._north = north or 0 self._east = east or 0 self._down = down or 0 if name: self.name = name def __str__(self): return self.toStr() @property_RO def bearing(self): '''Get the bearing of this NED vector (compass C{degrees360}). ''' if self._bearing is None: self._bearing = degrees360(atan2(self.east, self.north)) return self._bearing @property_RO def down(self): '''Gets the Down component of this NED vector (C{meter}). ''' return self._down @property_RO def east(self): '''Gets the East component of this NED vector (C{meter}). ''' return self._east @property_RO def elevation(self): '''Get the elevation, tilt of this NED vector in degrees from horizontal, i.e. tangent to ellipsoid surface (C{degrees90}). ''' if self._elevation is None: self._elevation = -degrees90(asin(self.down / self.length)) return self._elevation @property_RO def length(self): '''Gets the length of this NED vector (C{meter}). ''' if self._length is None: self._length = hypot_(self.north, self.east, self.down) return self._length @property_RO def north(self): '''Gets the North component of this NED vector (C{meter}). ''' return self._north def to3ned(self): '''Return this NED vector as north/east/down components. @return: An L{Ned3Tuple}C{(north, east, down)}. ''' r = Ned3Tuple(self.north, self.east, self.down) return self._xnamed(r) def toStr(self, prec=3, fmt='[%s]', sep=', '): # PYCHOK expected '''Return a string representation of this NED vector. @keyword prec: Optional number of decimals, unstripped (C{int}). @keyword fmt: Optional enclosing backets format (C{str}). @keyword sep: Optional separator between NEDs (C{str}). @return: This Ned as "[N:f, E:f, D:f]" (C{str}). ''' t3 = fStr(self.to3ned(), prec=prec, sep=' ').split() return fmt % (sep.join('%s:%s' % t for t in zip('NED', t3)),) def toStr2(self, prec=None, fmt='[%s]', sep=', '): # PYCHOK expected '''Return a string representation of this NED vector as length, bearing and elevation. @keyword prec: Optional number of decimals, unstripped (C{int}). @keyword fmt: Optional enclosing backets format (C{str}). @keyword 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 t3 = (fStr(self.length, prec=3 if prec is None else prec), toDMS(self.bearing, form=F_D, prec=prec, ddd=0), toDMS(self.elevation, form=F_D, prec=prec, ddd=0)) return fmt % (sep.join('%s:%s' % t for t in zip('LBE', t3)),) def toVector3d(self): '''Return this NED vector as a 3-d vector. @return: The vector(north, east, down) (L{Vector3d}). ''' from pygeodesy.vector3d import Vector3d return Vector3d(*self.to3ned(), name=self.name) _Nvll = LatLon(0, 0) #: (INTERNAL) 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 = Datums.WGS84 #: (INTERNAL) Default datum (L{Datum}). _Ecef = EcefVeness #: (INTERNAL) Preferred C{Ecef...} class, backward compatible. def __init__(self, x, y, z, h=0, datum=None, ll=None, name=''): '''New n-vector normal to the earth's surface. @param x: X component (C{meter}). @param y: Y component (C{meter}). @param z: Z component (C{meter}). @keyword h: Optional height above model surface (C{meter}). @keyword datum: Optional datum this n-vector is defined within (L{Datum}). @keyword ll: Optional, original latlon (C{LatLon}). @keyword 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: _TypeError(Datum, datum=datum) self._datum = datum @property_RO def datum(self): '''Get this n-vector's datum (L{Datum}). ''' return self._datum def toCartesian(self, **kwds): # PYCHOK Cartesian=Cartesian '''Convert this n-vector to C{Nvector}-based cartesian (ECEF) coordinates. @keyword kwds: Optional, additional B{C{Cartesian}} keyword arguments, ignored if C{B{Cartesian}=None}. Specify C{Cartesian=...} to override this L{Cartesian} class or set C{B{Cartesian}=None}. @return: The B{C{Cartesian}} point (L{Cartesian}) or if C{B{Cartesian}=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 B{C{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 = _2kwds(kwds, h=self.h, Cartesian=Cartesian, datum=self.datum) return NvectorBase.toCartesian(self, **kwds) # class or .classof def toLatLon(self, **kwds): # PYCHOK height=None, LatLon=LatLon '''Convert this n-vector to an C{Nvector}-based geodetic point. @keyword kwds: Optional, additional B{C{LatLon}} keyword arguments, ignored if C{B{LatLon}=None}. Specify C{LatLon=...} to override this L{LatLon} class or set C{B{LatLon}=None}. @return: The B{C{LatLon}} point (L{LatLon}) or a L{LatLon3Tuple}C{(lat, lon, height)} if C{B{LatLon}=None}. @raise TypeError: Invalid B{C{LatLon}} or B{C{kwds}}. @example: >>> v = Nvector(0.5, 0.5, 0.7071) >>> p = v.toLatLon() # 45.0°N, 45.0°E ''' kwds = _2kwds(kwds, height=self.h, LatLon=LatLon, datum=self.datum) return NvectorBase.toLatLon(self, **kwds) # class or .classof def unit(self, ll=None): '''Normalize this vector to unit length. @keyword ll: Optional, original latlon (C{LatLon}). @return: Normalised vector (L{Nvector}). ''' if self._united is None: u = NvectorBase.unit(self, ll=ll) if u.datum != self.datum: u._datum = self.datum # self._united = u._united = u return self._united def meanOf(points, datum=Datums.WGS84, height=None, LatLon=LatLon): '''Compute the geographic mean of several points. @param points: Points to be averaged (L{LatLon}[]). @keyword datum: Optional datum to use (L{Datum}). @keyword height: Optional height at mean point, overriding the mean height (C{meter}). @keyword LatLon: Optional (sub-)class to return the mean point (L{LatLon}) or C{None}. @return: Geographic mean point and mean height (B{C{LatLon}}) or a L{LatLon3Tuple}C{(lat, lon, height)} if B{C{LatLon}} is C{None}. @raise ValueError: Insufficient number of B{C{points}}. ''' _, points = _Nvll.points2(points, closed=False) # geographic mean m = sumOf(p.toNvector() for p in points) a, b, h = m.to3llh() if height is not None: h = height r = LatLon3Tuple(a, b, h) if LatLon is None else \ LatLon(a, b, height=h, datum=datum) return _xnamed(r, meanOf.__name__) def sumOf(nvectors, Vector=Nvector, h=None, **kwds): '''Return the vectorial sum of two or more n-vectors. @param nvectors: Vectors to be added (L{Nvector}[]). @keyword Vector: Optional class for the vectorial sum (L{Nvector}). @keyword h: Optional height, overriding the mean height (C{meter}). @keyword kwds: Optional, additional B{C{Vector}} keyword arguments. @return: Vectorial sum (B{C{Vector}}). @raise VectorError: No B{C{nvectors}}. ''' return _sumOf(nvectors, Vector=Vector, h=h, **kwds) def toNed(distance, bearing, elevation, name=''): '''Create an NED vector from distance, bearing and elevation (in local coordinate system). @param distance: NED vector length (C{meter}). @param bearing: NED vector bearing (compass C{degrees360}). @param elevation: NED vector elevation from local coordinate frame horizontal (C{degrees}). @keyword name: Optional name (C{str}). @return: NED vector equivalent to this B{C{distance}}, B{C{bearing}} and B{C{elevation}} (L{Ned}). @JSname: I{fromDistanceBearingElevation}. ''' b, e = radians(bearing), radians(elevation) d = float(distance) dce = d * cos(e) return Ned(cos(b) * dce, sin(b) * dce, -sin(e) * d, name=name) # **) MIT License # # Copyright (C) 2016-2020 -- 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.