Using and Designing Coordinate Representations¶
As described in the Overview of astropy.coordinates concepts, the actual coordinate
data in astropy.coordinates
frames is represented via
“Representation classes”. These can be used to store 3-d coordinates in
various representations, such as cartesian, spherical polar, cylindrical, and
so on. The built-in representation classes are:
CartesianRepresentation
: cartesian coordinatesx
,y
, andz
SphericalRepresentation
: spherical polar coordinates represented by a longitude (lon
), a latitude (lat
), and a distance (distance
). The latitude is a value ranging from -90 to 90 degrees.UnitSphericalRepresentation
: spherical polar coordinates on a unit sphere, represented by a longitude (lon
) and latitude (lat
)PhysicsSphericalRepresentation
: spherical polar coordinates, represented by an inclination (theta
) and azimuthal angle (phi
), and radiusr
. The inclination goes from 0 to 180 degrees, and is related to the latitude in theSphericalRepresentation
bytheta = 90 deg - lat
.CylindricalRepresentation
: cylindrical polar coordinates, represented by a cylindrical radius (rho
), azimuthal angle (phi
), and height (z
).
Note
For information about using and changing the representation of
SkyCoord
objects, see the
Representations section.
Instantiating and converting¶
Representation classes should be instantiated with Quantity
objects:
>>> from astropy import units as u
>>> from astropy.coordinates.representation import CartesianRepresentation
>>> car = CartesianRepresentation(3 * u.kpc, 5 * u.kpc, 4 * u.kpc)
>>> car
<CartesianRepresentation (x, y, z) in kpc
(3.0, 5.0, 4.0)>
Representations can be converted to other representations using the
represent_as
method:
>>> from astropy.coordinates.representation import SphericalRepresentation, CylindricalRepresentation
>>> sph = car.represent_as(SphericalRepresentation)
>>> sph
<SphericalRepresentation (lon, lat, distance) in (rad, rad, kpc)
(1.03037682652, 0.601264216679, 7.07106781187)>
>>> cyl = car.represent_as(CylindricalRepresentation)
>>> cyl
<CylindricalRepresentation (rho, phi, z) in (kpc, rad, kpc)
(5.83095189485, 1.03037682652, 4.0)>
All representations can be converted to each other without loss of
information, with the exception of
UnitSphericalRepresentation
. This class
is used to store the longitude and latitude of points but does not contain
any distance to the points, and assumes that they are located on a unit and
dimensionless sphere:
>>> from astropy.coordinates.representation import UnitSphericalRepresentation
>>> sph_unit = car.represent_as(UnitSphericalRepresentation)
>>> sph_unit
<UnitSphericalRepresentation (lon, lat) in rad
(1.03037682652, 0.601264216679)>
Converting back to cartesian, the absolute scaling information has been removed, and the points are still located on a unit sphere:
>>> sph_unit = car.represent_as(UnitSphericalRepresentation)
>>> sph_unit.represent_as(CartesianRepresentation)
<CartesianRepresentation (x, y, z) [dimensionless]
(0.424264068712, 0.707106781187, 0.565685424949)>
Array values¶
Array Quantity
objects can also be passed to
representations:
>>> import numpy as np
>>> x = np.random.random(100)
>>> y = np.random.random(100)
>>> z = np.random.random(100)
>>> car_array = CartesianRepresentation(x * u.m, y * u.m, z * u.m)
>>> car_array
<CartesianRepresentation (x, y, z) in m
[(0.7093..., 0.7788..., 0.3842...),
(0.8434..., 0.4543..., 0.9579...),
...
(0.0179..., 0.8587..., 0.4916...),
(0.0207..., 0.3355..., 0.2799...)]>
Creating your own representations¶
To create your own representation class, your class must inherit from the
BaseRepresentation
class. In addition the following must be defined:
__init__
method:Has a signature like
__init__(self, comp1, comp2, comp3, copy=True)
for inputting the representation component values.from_cartesian
class method:Takes a
CartesianRepresentation
object and returns an instance of your class.to_cartesian
method:Returns a
CartesianRepresentation
object.components
property:Returns a tuple of the names of the coordinate components (such as
x
,lon
, and so on).attr_classes
class attribute (OrderedDict
):Defines the initializer class for each component.In most cases this class should be derived from
Quantity
. In particular these class initializers must take the value as the first argument and accept aunit
keyword which takes aUnit
initializer orNone
to indicate no unit. Also not that the keys of this dictionary are treated as the names of the components for this representation, with the default ordered given in the order they appear as keys.recommended_units
dictionary (optional):Maps component names to the recommended unit to convert the values of that component to. Can be
None
(or missing) to indicate there is no preferred unit. If this dictionary is not defined, no conversion of components to particular units will occur.
In pseudo-code, this means that your class will look like:
class MyRepresentation(BaseRepresentation):
attr_classes = OrderedDict([('comp1', ComponentClass1),
('comp2', ComponentClass2),
('comp3', ComponentClass3)])
# recommended_units is optional
recommended_units = {'comp1': u.unit1, 'comp2': u.unit2, 'comp3': u.unit3}
def __init__(self, ...):
...
@classmethod
def from_cartesian(self, cartesian):
...
return MyRepresentation(...)
def to_cartesian(self):
...
return CartesianRepresentation(...)
@property
def components(self):
return 'comp1', 'comp2', 'comp3'
Once you do this, you will then automatically be able to call
represent_as
to convert other representations to/from your representation
class. Your representation will also be available for use in SkyCoord
and all frame classes.
A representation class may also have a _unit_representation
attribute
(although it is not required). This attribute points to the appropriate
“unit” representation (i.e., a representation that is dimensionless). This is
probably only meaningful for subclasses of
SphericalRepresentation
, where it is assumed that it
will be a subclass of UnitSphericalRepresentation
.