SphericalCoordinateSystem

class pisces.geometry.coordinates.coordinate_systems.SphericalCoordinateSystem(**parameters)

Spherical coordinate system in three dimensions.

Coordinates

• \(r\): Radial distance from the origin.

• \(\theta\): Polar angle (radians) from the positive z-axis.

• \(\phi\): Azimuthal angle (radians) from the positive x-axis.

Conversion to Cartesian

\[\begin{split}x = r \sin\theta \cos\phi \\ y = r \sin\theta \sin\phi \\ z = r \cos\theta\end{split}\]

Conversion from Cartesian

\[\begin{split}r = \sqrt{x^2 + y^2 + z^2} \\ \theta = \arccos\left(\frac{z}{r}\right) \\ \phi = \arctan2(y, x)\end{split}\]

Notes

This system is used for problems with spherical symmetry. All angles are expressed in radians.

Methods

__init__(**parameters)	Initialize the coordinate system with validated parameters.
convert_coords_from(other, *coordinates)	Convert coordinates from another coordinate system into this system.
convert_coords_to(other, *coordinates)	Convert coordinates from this system into another coordinate system.
convert_from_cartesian(x, y, z)	Convert coordinates from Cartesian to this system.
convert_to_cartesian(r, theta, phi)	Convert coordinates from this system to Cartesian.
copy()	Return a shallow copy of the coordinate system.
default_parameters()	Return a copy of the default parameters for this coordinate system.
from_dict(data)	Deserialize a coordinate system from a dictionary.
from_json_string(json_string)	Deserialize a coordinate system from a JSON string.
to_dict()	Return a dictionary representation of the coordinate system, including its class name and parameters.
to_json_string()	Serialize the coordinate system to a JSON string.

Attributes

axes	Return the names of the axes in this coordinate system.
ndim	Return the number of dimensions of this coordinate system.
parameters	Return a copy of the coordinate system's parameters.