Quaternions

Class and mathematical functions for quaternion numbers.

Installation

Python

This is a Python 3 module. If you don't have Python installed, get the latest version here.

The Quaternions module

Install with pip:

pip install quaternions-for-python

If you want to build from source, you can clone the repository with the following terminal command:

git clone https://github.com/zachartrand/Quaternions.git

How to use

Using the quaternions module

The quaternions module is designed to be imported to use quaternion numbers just like complex numbers in Python. The rest of this file assumes you import the class like this:

>>> from quaternions import Quaternion

To create a quaternion, simply type

>>> Quaternion(a, b, c, d)

where a, b, c, and d correspond to a quaternion of the form a + bi + cj + dk. For example, creating the quaternion 1 - 2i - 3j + 4k looks like this in the Python interpreter:

>>> q1 = Quaternion(1, -2, -3, 4)
>>> q1
Quaternion(1.0, -2.0, -3.0, 4.0)
>>> print(q1)
(1 - 2i - 3j + 4k)

Quaternions have mathematical functionality built in. Adding or multipling two quaternions together uses the same syntax as ints and floats:

>>> q1, q2 = Quaternion(1, -2, -3, 4), Quaternion(1, 4, -3, -2)
>>> print(q1)
(1 - 2i - 3j + 4k)
>>> print(q2)
(1 + 4i - 3j - 2k)
>>> print(q1 + q2)
(2 + 2i - 6j + 2k)
>>> print(q1 - q2)
(-6i + 0j + 6k)
>>> print(q2 - q1)
(6i + 0j - 6k)
>>> print(q1 * q2)
(8 + 20i + 6j + 20k)
>>> print(q2 * q1)
(8 - 16i - 18j - 16k)
>>> print(q1/q2)
(-0.19999999999999996 - 0.8i - 0.4j - 0.4k)
>>> print(1/q2 * q1)
(-0.19999999999999996 + 0.4i + 0.4j + 0.8k)
>>> print(q2/q1)
(-0.19999999999999996 + 0.8i + 0.4j + 0.4k)

Check the documentation for other useful methods of the Quaternion class.

Using the qmath module

The qmath module contains some functions that are compatible with quaternions, similarly to how the cmath module works. These include the exponential function, the natural logarithm, and the pow function. It also includes a function, rotate3d, that takes an iterable of coordinates and rotates them a given angle around a given axis (the z-axis by default). Here is an example rotating the point (1, 0, 0) around the z-axis:

>>> from quaternions import qmath
>>>
>>> p = (1, 0, 0)
>>>
>>> p = qmath.rotate3d(p, 90); print(p)
(0.0, 1.0, 0.0)
>>> p = qmath.rotate3d(p, 90); print(p)
(-1.0, 0.0, 0.0)
>>> p = qmath.rotate3d(p, 90); print(p)
(0.0, -1.0, 0.0)
>>> p = qmath.rotate3d(p, 90); print(p)
(1.0, 0.0, 0.0)