Skip to main content
Python Software Foundation 20th Year Anniversary Fundraiser  Donate today!

This is a library for dealing with quaternions in Python in a unified way.

Project description

Quaternions library
===================

[![Coverage Status](https://coveralls.io/repos/github/satellogic/quaternions/badge.svg)](https://coveralls.io/github/satellogic/quaternions)
[![Build Status](https://travis-ci.org/satellogic/quaternions.svg?branch=add_travis_ci)](https://travis-ci.org/satellogic/quaternions)

This is a library for dealing with quaternions in python in a unified way.

To install it:

```bash
$ pip install satellogic_quaternions
```

Examples of code:

```python
In [1]: from quaternions import Quaternion

In [2]: q1 = Quaternion(1, 2, 3, 4)

In [3]: q2 = Quaternion(2, 3, 5, 8)

In [4]: q1 + q2
Out[4]: Quaternion(3, 5, 8, 12)

In [5]: q1 * q2
Out[5]: Quaternion(-51, 3, 15, 15)

In [6]: q1 / q2
Out[6]: Quaternion(0.53921568627450989, 0.049019607843137247, -0.029411764705882353, 0.0098039215686274439)

In [7]: print(q1)
(1+2i+3j+4k)
```

~~Most of~~ all the quaternions we use are unitary (not like the example above)

```python
In [8]: q1.is_unitary()
Out[8]: False

In [9]: q1 / q1.norm()
Out[9]: Quaternion(0.18257418583505536, 0.36514837167011072, 0.54772255750516607, 0.73029674334022143)

In [10]: q1 /= q1.norm()

In [11]: q1.is_unitary()
Out[11]: True
```

Usually, quaternions are used for rotating vectors. This is done with `numpy`:
```python
In [12]: q1.matrix
Out[12]:
array([[-0.66666667, 0.66666667, 0.33333333],
[ 0.13333333, -0.33333333, 0.93333333],
[ 0.73333333, 0.66666667, 0.13333333]])

In [14]: q1.matrix.dot([2, 3, -4])
Out[14]: array([-0.66666667, -4.46666667, 2.93333333])

In [16]: q1.matrix.dot([1, 0, 0])
Out[16]: array([-0.66666667, 0.13333333, 0.73333333])
```

A unitary quaternion matrix is unitary. The inverse is the transpose and it is also the
matrix of the inverse quaternion. And the inverse quaternion of a unitary quaternion is
the conjugate:

```python
In [17]: q1.conjugate()
Out[17]: Quaternion(0.18257418583505536, -0.36514837167011072, -0.54772255750516607, -0.73029674334022143)

In [18]: q1
Out[18]: Quaternion(0.18257418583505536, 0.36514837167011072, 0.54772255750516607, 0.73029674334022143)

In [19]: q1 * q1.conjugate()
Out[19]: Quaternion(0.99999999999999978, 0.0, 0.0, 0.0)

In [20]: q1.conjugate().matrix
Out[20]:
array([[-0.66666667, 0.13333333, 0.73333333],
[ 0.66666667, -0.33333333, 0.66666667],
[ 0.33333333, 0.93333333, 0.13333333]])
```

License
=======

quaternions is Satellogic SA Copyright 2017. All our code is GPLv3 licensed.


Project details


Download files

Download the file for your platform. If you're not sure which to choose, learn more about installing packages.

Files for satellogic-quaternions, version 0.1.5
Filename, size File type Python version Upload date Hashes
Filename, size satellogic_quaternions-0.1.5-py3-none-any.whl (11.3 kB) File type Wheel Python version py3 Upload date Hashes View
Filename, size satellogic_quaternions-0.1.5.tar.gz (9.1 kB) File type Source Python version None Upload date Hashes View

Supported by

AWS AWS Cloud computing Datadog Datadog Monitoring DigiCert DigiCert EV certificate Facebook / Instagram Facebook / Instagram PSF Sponsor Fastly Fastly CDN Google Google Object Storage and Download Analytics Microsoft Microsoft PSF Sponsor Pingdom Pingdom Monitoring Salesforce Salesforce PSF Sponsor Sentry Sentry Error logging StatusPage StatusPage Status page