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)
2 Jun 14, 2022
3 Nov 28, 2021
1 Jul 7, 2021
1 Jan 7, 2022
25 Sep 4, 2022
60 Apr 1, 2022
8 Dec 14, 2022
1 Jan 31, 2022
16 Nov 17, 2022
27 Dec 08, 2022
3 Mar 13, 2022
7 Dec 06, 2022
4 Dec 12, 2022
5.8k Jan 03, 2023
2 Oct 23, 2021
79 Dec 14, 2022
2 Jan 10, 2022
100 Jan 01, 2023
2 Sep 08, 2022
1 Nov 17, 2021
8 May 01, 2022
633 Dec 23, 2022
3 Feb 15, 2022
3 Jan 03, 2022
407 Nov 17, 2022
1 Dec 17, 2021
0 Sep 06, 2022