def toNvector(self, h=None, Nvector=None, **kwds):
'''Convert this point to C{n-vector} (normal to the earth's
surface) components, I{including height}.
@keyword h: Optional height, overriding this point's
height (C{meter}).
@keyword Nvector: Optional (sub-)class to return the
C{n-vector} components (C{Nvector})
or C{None}.
@keyword kwds: Optional, additional B{C{Nvector}} keyword
arguments, ignored if C{B{Nvector}=None}.
@return: A B{C{Nvector}} or an L{Vector4Tuple}C{(x, y, z, h)}
if C{B{Nvector}=None}.
@raise TypeError: Invalid B{C{Nvector}} or B{C{kwds}}.
'''
if kwds or h not in (None, self.height):
r = Vector3Tuple(*self.toVector3d().to3xyz())
r = r._4Tuple(self.height if h is None else h)
if Nvector is not None:
r = Nvector(r.x, r.y, r.z, h=r.h, ll=self, **kwds)
else: # self.height, no kwds
r = self._v4t
if r is None:
r = Vector3Tuple(*self.toVector3d().to3xyz())
self._v4t = r = r._4Tuple(self.height)
if Nvector is not None:
r = Nvector(r.x, r.y, r.z, h=r.h, ll=self)
return self._xnamed(r)
def parse3d(str3d, sep=_COMMA_, name=NN, Vector=Vector3d, **Vector_kwds):
'''Parse an C{"x, y, z"} string.
@arg str3d: X, y and z values (C{str}).
@kwarg sep: Optional separator (C{str}).
@kwarg name: Optional instance name (C{str}).
@kwarg Vector: Optional class (L{Vector3d}).
@kwarg Vector_kwds: Optional B{C{Vector}} keyword arguments,
ignored if B{C{Vector=None}}.
@return: New B{C{Vector}} or if B{C{Vector}} is C{None},
a L{Vector3Tuple}C{(x, y, z)}.
@raise VectorError: Invalid B{C{str3d}}.
'''
try:
v = [float(v.strip()) for v in str3d.split(sep)]
if len(v) != 3:
raise ValueError
except (TypeError, ValueError) as x:
raise VectorError(str3d=str3d, txt=str(x))
r = Vector3Tuple(*v) if Vector is None else \
Vector(*v, **Vector_kwds)
return _xnamed(r, name, force=True)
def to3xyz(self): # overloads LatLonBase.to3xyz # PYCHOK no cover
'''DEPRECATED, use method C{toEcef}.
@return: A L{Vector3Tuple}C{(x, y, z)}.
'''
if self._3xyz is None:
r = self.toEcef()
self._3xyz = Vector3Tuple(r.x, r.y, r.z)
return self._xrenamed(self._3xyz)
def to3xyz(self): # PYCHOK no cover
'''DEPRECATED, use method C{toEcef}.
@return: A L{Vector3Tuple}C{(x, y, z)}.
@note: Overloads C{LatLonBase.to3xyz}
'''
r = self.toEcef()
return self._xnamed(Vector3Tuple(r.x, r.y, r.z))
def toVector(self, Vector=None):
'''Return the geocentric C{(x, y, z)} coordinates as vector.
@keyword Vector: Optional vector (sub-)class to return
C{(x, y, z)} or C{None}.
@return: A C{Vector}C{(x, y, z)} instance or if B{C{Vector}}
is C{None} a L{Vector3Tuple}C{(x, y, z)}.
'''
r = Vector3Tuple(self.x, self.y, self.z) if Vector is None else \
Vector(self.x, self.y, self.z) # PYCHOK x, y, z
return self._xnamed(r)
def to3xyz(self):
'''Convert this (geodetic) point to (n-)vector (normal
to the earth's surface) x/y/z components, ignoring
the height.
@return: A L{Vector3Tuple}C{(x, y, z)} in C{units},
NOT 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)
r = Vector3Tuple(ca * cb, ca * sb, sa)
return self._xnamed(r)
def philam2n_xyz(phi, lam):
'''Convert lat-, longitude to C{n-vector} (normal to the
earth's surface) X, Y and Z components.
@arg phi: Latitude (C{radians}).
@arg lam: Longitude (C{radians}).
@return: A L{Vector3Tuple}C{(x, y, z)}.
@see: Function L{latlon2n_xyz}.
@note: These are C{n-vector} x, y and z components,
I{NOT} geocentric ECEF x, y and z coordinates!
'''
# Kenneth Gade eqn 3, but using right-handed
# vector x -> 0°E,0°N, y -> 90°E,0°N, z -> 90°N
sa, ca, sb, cb = sincos2(phi, lam)
return Vector3Tuple(ca * cb, ca * sb, sa)
def sumOf(vectors, Vector=Vector3d, **kwds):
'''Compute the vectorial sum of several vectors.
@param vectors: Vectors to be added (L{Vector3d}[]).
@keyword Vector: Optional class for the vectorial sum (L{Vector3d}).
@keyword 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{vectors}}.
'''
n, vectors = len2(vectors)
if n < 1:
raise VectorError('no vectors: %r' & (n, ))
r = Vector3Tuple(fsum(v.x for v in vectors), fsum(v.y for v in vectors),
fsum(v.z for v in vectors))
if Vector is not None:
r = Vector(r.x, r.y, r.z, **kwds) # PYCHOK x, y, z
return r
def sumOf(vectors, Vector=Vector3d, **Vector_kwds):
'''Compute the vectorial sum of several vectors.
@arg vectors: Vectors to be added (L{Vector3d}[]).
@kwarg Vector: Optional class for the vectorial sum (L{Vector3d}).
@kwarg Vector_kwds: Optional B{C{Vector}} keyword arguments,
ignored if B{C{Vector=None}}.
@return: Vectorial sum (B{C{Vector}}).
@raise VectorError: No B{C{vectors}}.
'''
n, vectors = len2(vectors)
if n < 1:
raise VectorError(vectors=n, txt=_Missing)
r = Vector3Tuple(fsum(v.x for v in vectors), fsum(v.y for v in vectors),
fsum(v.z for v in vectors))
if Vector is not None:
r = Vector(r.x, r.y, r.z, **Vector_kwds) # PYCHOK x, y, z
return r
def toVector(self, Vector=None, **kwds):
'''Convert this point to C{n-vector} (normal to the earth's
surface) components, I{ignoring height}.
@keyword Vector: Optional (sub-)class to return the
C{n-vector} components (L{Vector3d})
or C{None}.
@keyword kwds: Optional, additional B{C{Vector}} keyword
arguments, ignored if C{B{Vector}=None}.
@return: A B{C{Vector}} or if C{B{Vector}=None}, an
L{Vector3Tuple}C{(x, y, z)}.
@raise TypeError: Invalid B{C{Vector}} or B{C{kwds}}.
'''
# 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)
r = Vector3Tuple(ca * cb, ca * sb, sa)
if Vector is not None:
r = Vector(r.x, r.y, r.z, **kwds) # PYCHOK Vector3Tuple
return self._xnamed(r)
def transform(self, x, y, z, inverse=False):
'''Transform a (geocentric) Cartesian point, forward or inverse.
@arg x: X coordinate (C{meter}).
@arg y: Y coordinate (C{meter}).
@arg z: Z coordinate (C{meter}).
@kwarg inverse: Optional direction, forward or inverse (C{bool}).
@return: A L{Vector3Tuple}C{(x, y, z)}, transformed.
'''
if inverse:
_xyz = -1, -x, -y, -z
_s1 = self.s1 - 2 # == -(1 - s * 1e-6)) == -(1 - (s1 - 1))
else:
_xyz = 1, x, y, z
_s1 = self.s1
# x', y', z' = (.tx + x * .s1 - y * .rz + z * .ry,
# .ty + x * .rz + y * .s1 - z * .rx,
# .tz - x * .ry + y * .rx + z * .s1)
r = Vector3Tuple(fdot(_xyz, self.tx, _s1, -self.rz, self.ry),
fdot(_xyz, self.ty, self.rz, _s1, -self.rx),
fdot(_xyz, self.tz, -self.ry, self.rx, _s1))
return self._xnamed(r)
def to3xyz(self): # overloads _LatLonHeightBase.to3xyz
'''Convert this (ellipsoidal) geodetic C{LatLon} point to
(geocentric) cartesian x/y/z components.
@return: A L{Vector3Tuple}C{(x, y, z)}.
'''
if self._3xyz is None:
a, b = self.to2ab()
sa, ca, sb, cb = sincos2(a, b)
E = self.ellipsoid()
# radius of curvature in prime vertical
t = E.e2s2(sa) # r, _ = E.roc2_(sa, 1)
if t < EPS:
r = 0
elif t > EPS1:
r = E.a
else:
r = E.a / sqrt(t)
h = self.height
t = (h + r) * ca
self._3xyz = Vector3Tuple(t * cb, t * sb, (h + r * E.e12) * sa)
return self._xrenamed(self._3xyz)
def to3xyz(self):
'''Return this vector as a 3-tuple.
@return: A L{Vector3Tuple}C{(x, y, z)}.
'''
return self._xnamed(Vector3Tuple(self.x, self.y, self.z))
def testCartesian(self, module, Sph=False, Nv=True): # MCCABE 45
self.subtitle(module, 'Cartesian')
Cartesian = module.Cartesian
LatLon = module.LatLon
Nvector = module.Nvector if Nv else Vector4Tuple
datum = Datums.Sphere if Sph else Datums.WGS84
datum2 = None if Sph else Datums.WGS72
# <https://www.Movable-Type.co.UK/scripts/geodesy/docs/
# latlon-nvector-ellipsoidal.js.html#line309>
c = Cartesian(3980581, 97, 4966825, datum=datum)
self.test('Cartesian0', c.toStr(prec=0), '[3980581, 97, 4966825]')
self.test('Cartesian4', c.toStr(prec=4),
'[3980581.0, 97.0, 4966825.0]')
self.test('isEllipsoidal', c.isEllipsoidal, not Sph)
self.test('isSpherical', c.isSpherical, Sph)
self.testCopy(c)
n = c.toNvector() # (x=0.622818, y=0.00002, z=0.782367, h=0.242887)
t = n.classname # Nvector.__name__
if Nv:
self.test(
t, repr(n), 'Nvector(0.62538, 0.00002, 0.78032, -5918.38)'
if Sph else 'Nvector(0.62282, 0.00002, 0.78237, +0.24)')
self.test(
t + '3', n.toStr(prec=3), '(0.625, 0.0, 0.78, -5918.38)'
if Sph else '(0.623, 0.0, 0.782, +0.24)')
self.test(
t + '6', n.toStr(prec=6),
'(0.625377, 0.000015, 0.780323, -5918.38)' if Sph else
'(0.622818, 0.000015, 0.782367, +0.24)') # PYCHOK attribute
else:
self.test(
t,
repr(n),
'(x=0.6253769790183048, y=1.5239375097448227e-05, z=0.7803227754472505, h=-5918.3802583276365)'
if Sph else
'(x=0.6228177647454303, y=1.517701139112776e-05, z=0.782366941841975, h=0.24288680875513333)',
known=True)
for ll in (
(50.0379, 8.5622), # FRA
(51.47, 0.4543), # LHR
# <https://www.EdWilliams.org/avform.htm#XTE>
(degrees(0.709186), -degrees(1.287762)), # JFK
(33. + 57. / 60, -(118. + 24. / 60)), # LAX
# <https://GeographicLib.SourceForge.io/html/python/examples.html>
(-41.32, 174.81), # WNZ, Wellington, NZ
(40.96, 5.50), # SAL, Salamanca, Spain
(40.1, 116.6), # BJS, Beijing Airport
(37.6, -122.4)): # SFO
if datum2:
t = c.convertDatum(datum2).convertDatum(datum)
self.test('convertDatum', t, c) # PYCHOK attribute
p = LatLon(*ll)
q = p.toCartesian().toLatLon()
t = str(q)
self.test('LatLon', t, p,
known=t.endswith('m')) # PYCHOK attribute
# c = Cartesian(3980581, 97, 4966825, datum=datum)
t = c.copy()
self.test('copy', t.isequalTo(c), True)
self.test('__eq__', t == c, True)
self.test('__ne__', t != c, False)
if hasattr(Cartesian, 'convertRefFrame'):
pass # PYCHOK attribute
for B in (False, True): # check return types
t = c.__class__
self.test('Cartesian', t, t)
# self.testReturnType(c.Ecef, Ecef, c.Ecef.__name__)
self.testReturnType(c.latlon, LatLon2Tuple, 'latlon')
self.testReturnType(c.latlonheight, LatLon3Tuple, 'latlonheight')
self.testReturnType(c.latlonheightdatum, LatLon4Tuple,
'latlonheightdatum')
self.testReturnType(c.isequalTo(c), bool, 'isequalTo')
self.testReturnType(c.philam, PhiLam2Tuple, 'philam')
self.testReturnType(c.philamheight, PhiLam3Tuple, 'philamheight')
self.testReturnType(c.philamheightdatum, PhiLam4Tuple,
'philamheightdatum')
self.testReturnType(c.to3llh(), LatLon4Tuple, 'to3llh')
self.testReturnType(c.toEcef(), Ecef9Tuple, 'toEcef')
self.testReturnType(c.toLatLon(), Ecef9Tuple if B else LatLon,
'toLatLon')
self.testReturnType(c.toNvector(), Vector4Tuple if B else Nvector,
'toNvector')
self.testReturnType(c.xyz, Vector3Tuple, 'xyz')
c = CartesianBase(c) # PYCHOK attribute
if hasattr(Cartesian, 'intersections2'):
# <https://GIS.StackExchange.com/questions/48937/calculating-intersection-of-two-circles>
c = Cartesian(-0.00323306, -0.7915, 0.61116)
self.test('intersections2', c.toLatLon(height=0),
'37.673442°N, 090.234036°W')
d = Cartesian(-0.0134464, -0.807775, 0.589337)
self.test('intersections2', d.toLatLon(height=0),
'36.109987°N, 090.95367°W')
x, y = c.intersections2(0.0312705, d, 0.0421788,
radius=None) # radii in radians
self.test('intersections2', x.toStr(prec=6),
'[-0.032779, -0.784769, 0.61892]'
) # -0.0327606, -0.784759, 0.618935
self.test('intersections2', x.toLatLon(height=0),
'38.237342°N, 092.391779°W') # 38.23838°N, 092.390487°W
if y is not x:
self.test('intersections2', y.toStr(prec=6),
'[0.025768, -0.798347, 0.601646]'
) # 0.0257661, -0.798332, 0.601666
self.test(
'intersections2', y.toLatLon(height=0),
'36.987868°N, 088.151309°W') # 36.98931°N, 088.151425°W
try:
from pygeodesy.vector3d import intersections2
u = Vector3Tuple(-0.00323306, -0.7915, 0.61116)
v = Vector3Tuple(-0.0134464, -0.807775, 0.589337)
c, r = intersections2(u, 0.0312705, v, 0.0421788, sphere=True)
self.test('intersections2', c.toStr(prec=6),
'(-0.0035, -0.791926, 0.610589)')
self.test('intersections2',
r.toStr(prec=6),
'0.031261',
known=True) # XXX G and g formats may add 1 decimal
v1, v2 = intersections2(u, 0.0312705, v, 0.0421788, sphere=False)
self.test('intersections2', v1.toStr(prec=6),
'(-0.021973, -0.766467, 0)')
if v2 is not v1:
self.test('intersections2', v2.toStr(prec=6),
'(0.027459, -0.797488, 0)')
except ImportError:
pass
def xyz(self):
'''Get the X, Y and Z components (L{Vector3Tuple}C{(x, y, z)}).
'''
if self._xyz is None:
self._xyz = Vector3Tuple(self.x, self.y, self.z)
return self._xnamed(self._xyz)
def xyz(self):
'''Get the geocentric C{(x, y, z)} coordinates (L{Vector3Tuple}C{(x, y, z)}).
'''
return self._xnamed(Vector3Tuple(self.x, self.y, self.z))