CartesianRepresentation¶
- class astropy.coordinates.CartesianRepresentation(x, y=None, z=None, unit=None, xyz_axis=None, differentials=None, copy=True)[source]¶
Bases:
BaseRepresentation
Representation of points in 3D cartesian coordinates.
- Parameters:
- x, y, z
Quantity
orarray
The x, y, and z coordinates of the point(s). If
x
,y
, andz
have different shapes, they should be broadcastable. If not quantity,unit
should be set. If onlyx
is given, it is assumed that it contains an array with the 3 coordinates stored alongxyz_axis
.- unitastropy:unit-like
If given, the coordinates will be converted to this unit (or taken to be in this unit if not given.
- xyz_axis
int
, optional The axis along which the coordinates are stored when a single array is provided rather than distinct
x
,y
, andz
(default: 0).- differentials
dict
,CartesianDifferential
, optional Any differential classes that should be associated with this representation. The input must either be a single
CartesianDifferential
instance, or a dictionary ofCartesianDifferential
s 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.- copybool, optional
If
True
(default), arrays will be copied. IfFalse
, arrays will be references, though possibly broadcast to ensure matching shapes.
- x, y, z
Attributes Summary
The 'x' component of the points(s).
Return a vector array of the x, y, and z coordinates.
The 'y' component of the points(s).
The 'z' component of the points(s).
Methods Summary
cross
(other)Cross product of two representations.
dot
(other)Dot product of two representations.
from_cartesian
(other)Create a representation of this class from a supplied Cartesian one.
get_xyz
([xyz_axis])Return a vector array of the x, y, and z coordinates.
mean
(*args, **kwargs)Vector mean.
norm
()Vector norm.
Scale factors for each component's direction.
sum
(*args, **kwargs)Vector sum.
Convert the representation to its Cartesian form.
transform
(matrix)Transform the cartesian coordinates using a 3x3 matrix.
Cartesian unit vectors in the direction of each component.
Attributes Documentation
- attr_classes = {'x': <class 'astropy.units.quantity.Quantity'>, 'y': <class 'astropy.units.quantity.Quantity'>, 'z': <class 'astropy.units.quantity.Quantity'>}¶
- x¶
The ‘x’ component of the points(s).
- xyz¶
Return a vector array of the x, y, and z coordinates.
- y¶
The ‘y’ component of the points(s).
- z¶
The ‘z’ component of the points(s).
Methods Documentation
- cross(other)[source]¶
Cross product of two representations.
- Parameters:
- other
BaseRepresentation
subclass instance If not already cartesian, it is converted.
- other
- Returns:
- cross_product
CartesianRepresentation
With vectors perpendicular to both
self
andother
.
- cross_product
- dot(other)[source]¶
Dot product of two representations.
Note that any associated differentials will be dropped during this operation.
- Parameters:
- other
BaseRepresentation
subclass instance If not already cartesian, it is converted.
- other
- Returns:
- dot_product
Quantity
The sum of the product of the x, y, and z components of
self
andother
.
- dot_product
- classmethod from_cartesian(other)[source]¶
Create a representation of this class from a supplied Cartesian one.
- Parameters:
- other
CartesianRepresentation
The representation to turn into this class
- other
- Returns:
- representation
BaseRepresentation
subclass instance A new representation of this class’s type.
- representation
- mean(*args, **kwargs)[source]¶
Vector mean.
Returns a new CartesianRepresentation instance with the means of the x, y, and z components.
Refer to
mean
for full documentation of the arguments, noting thataxis
is the entry in theshape
of the representation, and that theout
argument cannot be used.
- norm()[source]¶
Vector norm.
The norm is the standard Frobenius norm, i.e., the square root of the sum of the squares of all components with non-angular units.
Note that any associated differentials will be dropped during this operation.
- Returns:
- norm
astropy.units.Quantity
Vector norm, with the same shape as the representation.
- norm
- scale_factors()[source]¶
Scale factors for each component’s direction.
Given unit vectors \(\hat{e}_c\) and scale factors \(f_c\), a change in one component of \(\delta c\) corresponds to a change in representation of \(\delta c \times f_c \times \hat{e}_c\).
- sum(*args, **kwargs)[source]¶
Vector sum.
Returns a new CartesianRepresentation instance with the sums of the x, y, and z components.
Refer to
sum
for full documentation of the arguments, noting thataxis
is the entry in theshape
of the representation, and that theout
argument cannot be used.
- to_cartesian()[source]¶
Convert the representation to its Cartesian form.
Note that any differentials get dropped. Also note that orientation information at the origin is not preserved by conversions through Cartesian coordinates. For example, transforming an angular position defined at distance=0 through cartesian coordinates and back will lose the original angular coordinates:
>>> import astropy.units as u >>> import astropy.coordinates as coord >>> rep = coord.SphericalRepresentation( ... lon=15*u.deg, ... lat=-11*u.deg, ... distance=0*u.pc) >>> rep.to_cartesian().represent_as(coord.SphericalRepresentation) <SphericalRepresentation (lon, lat, distance) in (rad, rad, pc) (0., 0., 0.)>
- Returns:
- cartrepr
CartesianRepresentation
The representation in Cartesian form.
- cartrepr
- transform(matrix)[source]¶
Transform the cartesian coordinates using a 3x3 matrix.
This returns a new representation and does not modify the original one. Any differentials attached to this representation will also be transformed.
- Parameters:
- matrix
ndarray
A 3x3 transformation matrix, such as a rotation matrix.
- matrix
Examples
We can start off by creating a cartesian representation object:
>>> from astropy import units as u >>> from astropy.coordinates import CartesianRepresentation >>> rep = CartesianRepresentation([1, 2] * u.pc, ... [2, 3] * u.pc, ... [3, 4] * u.pc)
We now create a rotation matrix around the z axis:
>>> from astropy.coordinates.matrix_utilities import rotation_matrix >>> rotation = rotation_matrix(30 * u.deg, axis='z')
Finally, we can apply this transformation:
>>> rep_new = rep.transform(rotation) >>> rep_new.xyz <Quantity [[ 1.8660254 , 3.23205081], [ 1.23205081, 1.59807621], [ 3. , 4. ]] pc>
- unit_vectors()[source]¶
Cartesian unit vectors in the direction of each component.
Given unit vectors \(\hat{e}_c\) and scale factors \(f_c\), a change in one component of \(\delta c\) corresponds to a change in representation of \(\delta c \times f_c \times \hat{e}_c\).
- Returns:
- unit_vectors
dict
ofCartesianRepresentation
The keys are the component names.
- unit_vectors