CoordSystems

CoordSystems is a Python package to help working with different coordinate reference systems at the same time. The intention is to support annotated types for Cartesian, Polar and Spherical coordinates.

Installation

Just install it with pip:

pip install coordsystems

Usage

The Coordinate types carries out the conversion when needed. For example, when summing a Cartesian and a Spherical, the Spherical will be first converted to Cartesian, and then summed up.

from coordsystems import Cartesian, Spherical

c = Cartesian([1, 2, 3]) # x = 1, y = 2, z = 3
s = Spherical([1, 0, 0]) # r = 1, θ = 0, φ = 0
Cartesian(s) # Cartesian([0, 0, 1])
c + s # Cartesian([1, 2, 4])
c.x # 1
s.phi # 0

Cartesian system

In a Cartesian System (here assuming 3D), each coordinate is written as a multiple of a unit basis vector ($\vec i$, $\vec j$ and $\vec k$). Those unit vectors are in the direction usually known as $x$ (for $\vec i$), $y$ (for $\vec j$) and $z$ (for $\vec k$).

To mark a point as a Cartesian point, just use the Cartesian constructor, passing a list or numpy.ndarray with each coordinate, or another Coordinate object.

In a Cartesian system, the vector sum is just the element-wise sum. So $(1,2,3) + (1,0,0) = (2,2,3)$.

Spherical system

In a Spherical System (necessarily 3D), each point is described also by three coordinates (because they are the same $\mathbb{R}^3$ space), but now with $r$ (radius), $\theta$ (polar angle) and $\phi$ (azimuthal angle).

Different from Cartesian systems, here the vector sum isn't trivial. For example, $(2, \frac{\pi}{2}, \pi) + (\frac{1}{2}, \frac{\pi}{6}, 0) = (1.7321, \frac{\pi}{3}, \pi)$. Actually, it's easier to convert them to Cartesian, perform the sum, and convert it back again. Luckily, a Spherical object do it for you:

>>> import numpy as np
>>> from coordsystems import Spherical
>>> Spherical([2, np.pi/2, np.pi]) + Spherical([1, np.pi/6, 0])
Spherical([1.7320508075688772, 1.0471975511965976, 3.141592653589793])

Accessing coordinates

In a p = Cartesian(...), you can access directly each coordinate (p.x, p.y, p.z) or use indexing (p[0] == p['x'] == p.x).

In a q = Spherical(...), you can also access each coordinate independently (q.r, q.theta and q.phi). Indexing notation isn't implemented yet.

In any case, the implemented operations takes care of the system and try to do any operation in a Cartesian base, converting stuff when appropriate.

TODO

We still need to implement many things in this package before it gets ready for production.

• Number * Coordinate multiplication
• Spherical indexing access
• Option to choose the symbol for polar and azimuthal angles (if θ = polar and φ = azimuthal or the opposite).
• Cartesian custom basis (allow not only the canonical basis).