InterpolatedCartesianRepresentation¶

class interpolated_coordinates.InterpolatedCartesianRepresentation(representation: BaseRepresentation, *args: Any, **kwargs: Any)[source]¶

Bases: InterpolatedRepresentation

Attributes Summary

`affine`
`derivative_type`	The class used when taking a derivative.
`uninterpolated`	Return the underlying Representation.

Methods Summary

`__call__`([affine])	Evaluate interpolated representation.
`clear_derivatives`()	Return self, clearing cached derivatives.
`copy`(args, *kwargs)	Return an instance containing copies of the internal data.
`derivative`([n])	Construct a new spline representing the derivative of this spline.
`from_cartesian`(other)	Create a representation of this class from a Cartesian one.
`headless_tangent_vectors`()	Headless tangent vector at each point in affine.
`represent_as`(other_class[, differential_class])	Convert coordinates to another representation.
`tangent_vectors`()	Tangent vectors along the curve, from the origin.
`to_cartesian`()	Convert the representation to its Cartesian form.
`transform`(matrix)	Transform the cartesian coordinates using a 3x3 matrix.
`with_differentials`(differentials)	Realize Representation, with new differentials.
`without_differentials`()	Return a copy of the representation without attached differentials.

Attributes Documentation

affine¶

derivative_type¶: The class used when taking a derivative.

uninterpolated¶: Return the underlying Representation.

Methods Documentation

__call__(affine: Quantity | None = None) → BaseRepresentation¶

Evaluate interpolated representation.

Parameters:

affineQuantity array_like: The affine interpolation parameter. If None, returns representation points.

Returns:

BaseRepresenation: Representation of type self.data evaluated with affine

clear_derivatives() → IRoDType¶: Return self, clearing cached derivatives.

copy(*args: Any, **kwargs: Any) → IRoDType¶

Return an instance containing copies of the internal data.

Parameters are as for copy().

Returns:

interpolated_coordinates.InterpolatedBaseRepresentationOrDifferential: Same type as this instance.

derivative(n: int = 1) → InterpolatedDifferential¶

Construct a new spline representing the derivative of this spline.

Parameters:

nint, optional: Order of derivative to evaluate. Default: 1

from_cartesian(other: CartesianRepresentation | CartesianDifferential) → IRoDType¶

Create a representation of this class from a Cartesian one.

Parameters:

otherCartesianRepresentation or CartesianDifferential

The representation to turn into this class

Note: the affine parameter of this class is used. The representation must be the same length as the affine parameter.

Returns:

representationobject of this class: A new representation of this class’s type.

Raises:

ValueError: If other is not same length as the this instance’s affine parameter.

headless_tangent_vectors() → IRType¶

Headless tangent vector at each point in affine.

\(\vec{x} + \partial_{\affine} \vec{x}(\affine) \Delta\affine\)

represent_as(other_class: BaseRepresentation, differential_class: BaseDifferential | None = None) → InterpolatedRepresentation¶

Convert coordinates to another representation.

If the instance is of the requested class, it is returned unmodified. By default, conversion is done via Cartesian coordinates. Also note that orientation information at the origin is not preserved by conversions through Cartesian coordinates. See the docstring for represent_as() for an example.

Parameters:

other_classBaseRepresentation subclass: The type of representation to turn the coordinates into.
differential_classdict of BaseDifferential, optional: Classes in which the differentials should be represented. Can be a single class if only a single differential is attached, otherwise it should be a dict keyed by the same keys as the differentials.

tangent_vectors() → IRType¶

Tangent vectors along the curve, from the origin.

\(\vec{x} + \partial_{\affine} \vec{x}(\affine) \Delta\affine\)

to_cartesian() → IRoDType¶

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:

cartreprCartesianRepresentation or CartesianDifferential: The representation in Cartesian form. If starting from a Cart

transform(matrix: NDArray) → ICRType[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:

matrixndarray: A 3x3 transformation matrix, such as a rotation 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>

with_differentials(differentials: Sequence[BaseDifferential]) → IRType¶

Realize Representation, with new differentials.

Create a new representation with the same positions as this representation, but with these new differentials.

Differential keys that already exist in this object’s differential dict are overwritten.

Parameters:

differentialsSequence of BaseDifferential: The differentials for the new representation to have.

Returns:

newrepr: A copy of this representation, but with the differentials as its differentials.

without_differentials() → IRType¶

Return a copy of the representation without attached differentials.

Returns:

newrepr: A shallow copy of this representation, without any differentials. If no differentials were present, no copy is made.

Navigation

InterpolatedCartesianRepresentation¶