Class and mathematical functions for quaternion numbers.

Related tags

Miscellaneouspythonquaternionmathematical-functionsobject-oriented-programmingquaternion-numbers
Overview

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)
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Releases(1.1.3)

  • 1.1.3(Jul 23, 2022)

    Quaternions v1.1.3 Release

    Install

    You can install the module with pip:

    pip install quaternions-for-python

    If you have a previous version installed, upgrade to the latest version:

    pip install --upgrade quaternions-for-python
    Source code(tar.gz)
    Source code(zip)

  • v1.1.1(May 5, 2022)

    Quaternions v1.1.1 Release

    Install

    You can install the module with pip:

    pip install quaternions-for-python

    If you have a previous version installed, upgrade to the latest version:

    pip install --upgrade quaternions-for-python

    What's new

    • A Read the Docs site for Quaternions is now live! Read through the documentation here: https://quaternions-for-python.readthedocs.io/
    • Added comments to source code to explain functions and algorithms.
    • Rewrote some code to be more efficient/readable.
    • Reformatted/fixed typos in docstrings.
    • Miscellaneous changes.
    Source code(tar.gz)
    Source code(zip)

  • v1.1.0(Aug 20, 2021)

    Quaternions v1.1.0 Release

    What's new

    • qmath.rotate_Euler function that allows yaw, pitch, and roll rotations.
    • qmath has cross_product and dot_product functions which use quaternions on the backend to calculate vector products.
    • Quaternion class has properties angle_in_radians and angle_in_degrees.

    Bug fixes

    • Fixed bug in the qmath.log function where a variable was called without assignment.
    • Removed NotImplemented from magic methods where they were used inappropriately.

    Docstring changes

    Docstrings are being changed for Sphinx compatibilty. A ReadTheDocs page coming soon!

    Source code(tar.gz)
    Source code(zip)

  • v1.0.0(Aug 15, 2021)

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