def to4xyzh(self, h=None):
'''Return this n-vector's components as 4-tuple.
@keyword h: Optional height, overriding this n-vector's
height (C{meter}).
@return: A L{Vector4Tuple}C{(x, y, z, h)}.
'''
r = Vector4Tuple(self.x, self.y, self.z, self.h if h is None else h)
return self._xnamed(r)
def toNvector(self,
Nvector=None,
datum=None,
**kwds): # PYCHOK Datums.WGS84
'''Convert this cartesian to C{n-vector} components.
@keyword Nvector: Optional (sub-)class to return the
C{n-vector} components (C{Nvector})
or C{None}.
@keyword datum: Optional datum (L{Datum}) overriding this
cartesian's datum.
@keyword kwds: Optional, additional B{C{Nvector}} keyword
arguments, ignored if C{B{Nvector}=None}.
@return: Unit vector B{C{Nvector}} or a L{Vector4Tuple}C{(x,
y, z, h)} if B{C{Nvector}=None}.
@raise ValueError: The B{C{Cartesian}} at origin.
'''
d = datum or self.datum
r = self._v4t
if r is None or self.datum != d:
E = d.ellipsoid
x, y, z = self.to3xyz()
# 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, t, 1 / 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('%s: %r' % ('origin', self))
e = k / (k + E.e2)
t = hypot(e * hypot(x, y), z)
if t < EPS:
raise ValueError('%s: %r' % ('origin', self))
h = fsum_(k, E.e2, -1) / k * t
s = e / t
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, **kwds)
return self._xnamed(r)
def to4xyzh(self, h=None):
'''Convert this (geodetic) point to n-vector (normal
to the earth's surface) x/y/z components and height.
@keyword h: Optional height, overriding this point's
height (C{meter}).
@return: A L{Vector4Tuple}C{(x, y, z, h)}, all in
(C{meter}).
'''
# Kenneth Gade eqn (3), but using right-handed
# vector x -> 0°E,0°N, y -> 90°E,0°N, z -> 90°N
# a, b = self.to2ab()
# sa, ca, sb, cb = sincos2(a, b)
# x, y, z = ca * cb, ca * sb, sa
# XXX don't use self.to3xyz() + ....
x, y, z = LatLonHeightBase.to3xyz(self)
r = Vector4Tuple(x, y, z, self.height if h is None else h)
return self._xnamed(r)
def to4xyzh(self, h=None): # PYCHOK no cover
'''DEPRECATED, use property C{xyzh} or C{xyz.to4Tuple}C{(}B{C{h}}C{)}.
'''
return self.xyzh if h in (None, self.h) else \
self._xnamed(Vector4Tuple(self.x, self.y, self.z, h))
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}) 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 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 = datum or self.datum
_xinstanceof(Datum, datum=d)
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, t, 1 / 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) / 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)