def greatCircle(self, bearing):
'''Compute the n-vector normal to great circle obtained by
heading on given compass bearing from this point as its
n-vector.
Direction of vector is such that initial bearing vector
b = c × p.
@arg bearing: Initial compass bearing (C{degrees}).
@return: N-vector representing great circle (L{Nvector}).
@raise Valuerror: Polar coincidence.
@example:
>>> n = LatLon(53.3206, -1.7297).toNvector()
>>> gc = n.greatCircle(96.0) # [-0.794, 0.129, 0.594]
'''
s, c = sincos2d(Bearing(bearing))
e = NorthPole.cross(self, raiser=_pole_) # easting
n = self.cross(e, raiser=_point_) # northing
e = e.times(c / e.length)
n = n.times(s / n.length)
return n.minus(e)
def destination(self, distance, bearing, radius=R_M, height=None):
'''Locate the destination from this point after having
travelled the given distance on the given bearing.
@param distance: Distance travelled (C{meter}, same units
as B{C{radius}}).
@param bearing: Bearing from this point (compass C{degrees360}).
@keyword radius: Mean earth radius (C{meter}).
@keyword height: Optional height at destination, overriding
the default height (C{meter}, same units as
B{C{radius}}).
@return: Destination point (L{LatLon}).
@raise Valuerror: Polar coincidence.
@example:
>>> p = LatLon(51.4778, -0.0015)
>>> q = p.destination(7794, 300.7)
>>> q.toStr() # 51.513546°N, 000.098345°W
@JSname: I{destinationPoint}.
'''
p = self.toNvector()
e = NorthPole.cross(p, raiser='pole').unit() # east vector at p
n = p.cross(e) # north vector at p
s, c = sincos2d(bearing)
q = n.times(c).plus(e.times(s)) # direction vector @ p
s, c = sincos2(float(distance) / float(radius)) # angular distance in radians
n = p.times(c).plus(q.times(s))
return n.toLatLon(height=height, LatLon=self.classof) # Nvector(n.x, n.y, n.z).toLatLon(...)
def destination(self, distance, bearing, radius=R_M, height=None):
'''Locate the destination from this point after having
travelled the given distance on the given bearing.
@arg distance: Distance travelled (C{meter}, same units
as B{C{radius}}).
@arg bearing: Bearing from this point (compass C{degrees360}).
@kwarg radius: Mean earth radius (C{meter}).
@kwarg height: Optional height at destination, overriding the
default height (C{meter}, same units as B{C{radius}}).
@return: Destination point (L{LatLon}).
@raise Valuerror: Polar coincidence ior invalid B{C{distance}},
B{C{bearing}}, B{C{radius}} or B{C{height}}.
@example:
>>> p = LatLon(51.4778, -0.0015)
>>> q = p.destination(7794, 300.7)
>>> q.toStr() # 51.513546°N, 000.098345°W
@JSname: I{destinationPoint}.
'''
a = _angular(distance, radius)
sa, ca, sb, cb = sincos2(a, Bearing_(bearing))
p = self.toNvector()
e = NorthPole.cross(p, raiser=_pole_).unit() # east vector at p
n = p.cross(e) # north vector at p
q = n.times(cb).plus(e.times(sb)) # direction vector @ p
n = p.times(ca).plus(q.times(sa))
return n.toLatLon(height=height, LatLon=self.classof) # Nvector(n.x, n.y, n.z).toLatLon(...)
def _gc(p, b):
n = p.toNvector()
de = NorthPole.cross(n, raiser='pole').unit() # east vector @ n
dn = n.cross(de) # north vector @ n
s, c = sincos2d(b)
dest = de.times(s)
dnct = dn.times(c)
d = dnct.plus(dest) # direction vector @ n
return n.cross(d) # great circle point + bearing
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