def length(self):
'''Get the length (norm, magnitude) of this vector (C{float}).
@see: Properties C{length2} and C{euclid}.
'''
if self._length is None:
self._length = hypot_(self.x, self.y, self.z)
return self._length
def toCartesian(self,
h=None,
Cartesian=None,
datum=None,
**Cartesian_kwds):
'''Convert this n-vector to C{Nvector}-based cartesian (ECEF)
coordinates.
@kwarg h: Optional height, overriding this n-vector's height (C{meter}).
@kwarg Cartesian: Optional class to return the (ECEF)
coordinates (L{Cartesian}).
@kwarg datum: Optional, spherical datum (C{Datum}).
@kwarg Cartesian_kwds: Optional, additional B{C{Cartesian}}
keyword arguments, ignored if
B{C{Cartesian=None}}.
@return: The cartesian (ECEF) coordinates (B{C{Cartesian}}) or
if B{C{Cartesian}} 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 TypeError: Invalid B{C{Cartesian}}.
@raise ValueError: Invalid B{C{h}}.
@example:
>>> v = Nvector(0.5, 0.5, 0.7071)
>>> c = v.toCartesian() # [3194434, 3194434, 4487327]
>>> p = c.toLatLon() # 45.0°N, 45.0°E
'''
x, y, z = self.x, self.y, self.z
h = self.h if h is None else Height(h=h)
d = datum or self.datum
E = d.ellipsoid
# Kenneth Gade eqn (22)
n = E.b / hypot_(x * E.a_b, y * E.a_b, z)
r = h + n * E.a_b**2
c = self.Ecef(d).reverse(x * r, y * r, z * (n + h), M=True)
if Cartesian is not None: # class or .classof
c = Cartesian(c, **Cartesian_kwds)
return self._xnamed(c)
def toCartesian(self, Cartesian=Cartesian):
'''Convert this n-vector to a cartesian point.
@keyword Cartesian: Optional, cartesion (sub-)class to
return the point (L{Cartesian}).
@return: Cartesian equivalent to this n-vector
(B{C{Cartesian}}).
@example:
>>> v = Nvector(0.5, 0.5, 0.7071)
>>> c = v.toCartesian() # [3194434, 3194434, 4487327]
>>> p = c.toLatLon() # 45.0°N, 45.0°E
'''
E = self.datum.ellipsoid
x, y, z, h = self.to4xyzh()
# Kenneth Gade eqn (22)
n = E.b / hypot_(x * E.a_b, y * E.a_b, z)
r = h + n * E.a_b**2
c = Cartesian(x * r, y * r, z * (n + h))
return self._xnamed(c)
def toCartesian(self, h=None, Cartesian=None, datum=None, **kwds):
'''Convert this n-vector to C{Nvector}-based cartesian (ECEF)
coordinates.
@keyword height: Optional height, overriding this n-vector's
height (C{meter}).
@keyword Cartesian: Optional (sub-)class to return the
(ECEF)coordinates (L{Cartesian}).
@keyword datum: Optional, spherical datum (C{Datum}).
@keyword kwds: Optional, additional C{name=value} pairs
for B{C{Cartesian}} instance, provided
B{C{Cartesian}} is not C{None}.
@return: Cartesian (ECEF) coordinates (B{C{Cartesian}}).
@raise TypeError: Invalid B{C{Cartesian}}.
@example:
>>> v = Nvector(0.5, 0.5, 0.7071)
>>> c = v.toCartesian() # [3194434, 3194434, 4487327]
>>> p = c.toLatLon() # 45.0°N, 45.0°E
'''
x, y, z = self.x, self.y, self.z
if h is None:
h = self.h
d = datum or self.datum
E = d.ellipsoid
# Kenneth Gade eqn (22)
n = E.b / hypot_(x * E.a_b, y * E.a_b, z)
r = h + n * E.a_b**2
c = self.Ecef(d).reverse(x * r, y * r, z * (n + h), M=True)
if Cartesian is not None: # class or .classof
c = Cartesian(c, **kwds)
return self._xnamed(c)
def hypot3(x, y, z):
'''DEPRECATED, use function L{hypot_}.
'''
from pygeodesy.fmath import hypot_
return hypot_(x, y, z)
def length(self):
'''Get the length (norm, magnitude) of this vector (C{float}).
'''
if self._length is None:
self._length = hypot_(self.x, self.y, self.z)
return self._length
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
def toNvector(self,
Nvector=None,
datum=None,
**Nvector_kwds): # PYCHOK Datums.WGS84
'''Convert this cartesian to C{n-vector} components.
@kwarg Nvector: Optional class to return the C{n-vector}
components (C{Nvector}) or C{None}.
@kwarg datum: Optional datum (L{Datum}, L{Ellipsoid}, L{Ellipsoid2}
or L{a_f2Tuple}) overriding this cartesian's datum.
@kwarg Nvector_kwds: Optional, additional B{C{Nvector}} keyword
arguments, ignored if B{C{Nvector=None}}.
@return: The C{unit, n-vector} components (B{C{Nvector}}) or a
L{Vector4Tuple}C{(x, y, z, h)} if B{C{Nvector}} is C{None}.
@raise TypeError: Invalid B{C{datum}}.
@raise ValueError: The B{C{Cartesian}} at origin.
@example:
>>> c = Cartesian(3980581, 97, 4966825)
>>> n = c.toNvector() # (x=0.622818, y=0.00002, z=0.782367, h=0.242887)
'''
d = _ellipsoidal_datum(datum or self.datum, name=self.name)
r = self._v4t
if r is None or d != self.datum:
# <https://www.Movable-Type.co.UK/scripts/geodesy/docs/
# latlon-nvector-ellipsoidal.js.html#line309>
E = d.ellipsoid
x, y, z = self.xyz
# Kenneth Gade eqn 23
p = hypot2(x, y) * E.a2_
q = (z**2 * E.e12) * E.a2_
r = fsum_(p, q, -E.e4) / 6
s = (p * q * E.e4) / (4 * r**3)
t = cbrt(fsum_(1, s, sqrt(s * (2 + s))))
u = r * fsum_(_1_0, t, _1_0 / t)
v = sqrt(u**2 + E.e4 * q)
w = E.e2 * fsum_(u, v, -q) / (2 * v)
k = sqrt(fsum_(u, v, w**2)) - w
if abs(k) < EPS:
raise _ValueError(origin=self)
e = k / (k + E.e2)
# d = e * hypot(x, y)
# tmp = 1 / hypot(d, z) == 1 / hypot(e * hypot(x, y), z)
t = hypot_(e * x, e * y, z) # == 1 / tmp
if t < EPS:
raise _ValueError(origin=self)
h = fsum_(k, E.e2, -_1_0) / k * t
s = e / t # == e * tmp
r = Vector4Tuple(x * s, y * s, z / t, h)
self._v4t = r if d == self.datum else None
if Nvector is not None:
r = Nvector(r.x, r.y, r.z, h=r.h, datum=d, **Nvector_kwds)
return self._xnamed(r)
