# Licensed under a 3-clause BSD style license - see LICENSE.rst
"""Cylindrical representations and differentials."""
import operator
import numpy as np
import astropy.units as u
from astropy.coordinates.angles import Angle
from astropy.utils.compat import COPY_IF_NEEDED
from .base import BaseDifferential, BaseRepresentation
from .cartesian import CartesianRepresentation
from .spherical import PhysicsSphericalRepresentation, _spherical_op_funcs
[docs]
class CylindricalRepresentation(BaseRepresentation):
"""
Representation of points in 3D cylindrical coordinates.
Parameters
----------
rho : `~astropy.units.Quantity`
The distance from the z axis to the point(s).
phi : `~astropy.units.Quantity` or str
The azimuth of the point(s), in angular units, which will be wrapped
to an angle between 0 and 360 degrees. This can also be instances of
`~astropy.coordinates.Angle`,
z : `~astropy.units.Quantity`
The z coordinate(s) of the point(s)
differentials : dict, `~astropy.coordinates.CylindricalDifferential`, optional
Any differential classes that should be associated with this
representation. The input must either be a single
`~astropy.coordinates.CylindricalDifferential` instance, or a dictionary of of differential
instances with keys set to a string representation of the SI unit with
which the differential (derivative) is taken. For example, for a
velocity differential on a positional representation, the key would be
``'s'`` for seconds, indicating that the derivative is a time
derivative.
copy : bool, optional
If `True` (default), arrays will be copied. If `False`, arrays will
be references, though possibly broadcast to ensure matching shapes.
"""
attr_classes = {"rho": u.Quantity, "phi": Angle, "z": u.Quantity}
def __init__(self, rho, phi=None, z=None, differentials=None, copy=True):
super().__init__(rho, phi, z, copy=copy, differentials=differentials)
if not self._rho.unit.is_equivalent(self._z.unit):
raise u.UnitsError("rho and z should have matching physical types")
@property
def rho(self):
"""
The distance of the point(s) from the z-axis.
"""
return self._rho
@property
def phi(self):
"""
The azimuth of the point(s).
"""
return self._phi
@property
def z(self):
"""
The height of the point(s).
"""
return self._z
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def unit_vectors(self):
sinphi, cosphi = np.sin(self.phi), np.cos(self.phi)
l = np.broadcast_to(1.0, self.shape)
return {
"rho": CartesianRepresentation(cosphi, sinphi, 0, copy=COPY_IF_NEEDED),
"phi": CartesianRepresentation(-sinphi, cosphi, 0, copy=COPY_IF_NEEDED),
"z": CartesianRepresentation(0, 0, l, unit=u.one, copy=COPY_IF_NEEDED),
}
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def scale_factors(self):
rho = self.rho / u.radian
l = np.broadcast_to(1.0 * u.one, self.shape, subok=True)
return {"rho": l, "phi": rho, "z": l}
[docs]
@classmethod
def from_cartesian(cls, cart):
"""
Converts 3D rectangular cartesian coordinates to cylindrical polar
coordinates.
"""
rho = np.hypot(cart.x, cart.y)
phi = np.arctan2(cart.y, cart.x)
z = cart.z
return cls(rho=rho, phi=phi, z=z, copy=False)
[docs]
def to_cartesian(self):
"""
Converts cylindrical polar coordinates to 3D rectangular cartesian
coordinates.
"""
x = self.rho * np.cos(self.phi)
y = self.rho * np.sin(self.phi)
z = self.z
return CartesianRepresentation(x=x, y=y, z=z, copy=False)
def _scale_operation(self, op, *args):
if any(
differential.base_representation is not self.__class__
for differential in self.differentials.values()
):
return super()._scale_operation(op, *args)
phi_op, _, rho_op = _spherical_op_funcs(op, *args)
z_op = lambda x: op(x, *args)
result = self.__class__(
rho_op(self.rho), phi_op(self.phi), z_op(self.z), copy=COPY_IF_NEEDED
)
for key, differential in self.differentials.items():
new_comps = (
op(getattr(differential, comp))
for op, comp in zip(
(rho_op, operator.pos, z_op), differential.components
)
)
result.differentials[key] = differential.__class__(*new_comps, copy=False)
return result
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def represent_as(self, other_class, differential_class=None):
if isinstance(other_class, type):
if issubclass(other_class, PhysicsSphericalRepresentation):
diffs = self._re_represent_differentials(
other_class, differential_class
)
r = np.hypot(self.rho, self.z)
return other_class(
r=r,
theta=np.arccos(self.z / r),
phi=self.phi,
differentials=diffs,
)
return super().represent_as(other_class, differential_class)
[docs]
class CylindricalDifferential(BaseDifferential):
"""Differential(s) of points in cylindrical coordinates.
Parameters
----------
d_rho : `~astropy.units.Quantity` ['speed']
The differential cylindrical radius.
d_phi : `~astropy.units.Quantity` ['angular speed']
The differential azimuth.
d_z : `~astropy.units.Quantity` ['speed']
The differential height.
copy : bool, optional
If `True` (default), arrays will be copied. If `False`, arrays will
be references, though possibly broadcast to ensure matching shapes.
"""
base_representation = CylindricalRepresentation
def __init__(self, d_rho, d_phi=None, d_z=None, copy=True):
super().__init__(d_rho, d_phi, d_z, copy=copy)
if not self._d_rho.unit.is_equivalent(self._d_z.unit):
raise u.UnitsError("d_rho and d_z should have equivalent units.")
