quaternions

This repository contains auxiliary functions for quaternion based motion tracking written entirely in base python.

Basics

The main object Quaternion can be imported directly using:

from quaternions.Quaternion import Quaternion

my_quaternion = Quaternion(q_0, q_1, q_2, q_3)

However, some auxiliary functions and the Matrix class won't be available. So it is recommended to import the library in the following way:

import quaternions.Quaternion as qtn

my_quaternion = qtn.Quaternion(q_0, q_1, q_2, q_3)

my_matrix = qtn.Matrix([[1, 2], [3, 4]])

Rotations

From and To Tait-Bryan Angles

A rotation quaternion can be created from the Tait-Bryan angles using:

from math import radians

yaw = radians(90)
pitch = radians(45)
roll = radians(30)

rot_quaternion = qtn.tb2quaternion(yaw, pitch, roll)

And a vector quaternion can be rotated by:

new_quaternion = my_quaternion.rotate(rot_quaternion)

Or transform the rotation quaternion back to Tait-Bryan angles:

yaw, pitch, roll = rot_quaternion.tb

It must be noted that the coordinate axis used is the standard coordinate axis (x - forward, y - left, z - up) and rotation order is Z (yaw) -> Y (pitch) -> X (roll).

From and To Angle-Axis notation

Rotation quaternions can also be created using the angle-axis notation:

angle = radians(90)
axis = (1, 1, 1)
rot_quaternion = qtn.aa2quaternion(angle, axis)

And back:

angle, axis = rot_quaternion.aa

The resulting quaternion will aply a rotation of angle radians around the 3D axis vector.

Notes

Remember that all vector quaternions should have real component (q_0) equal to 0.

Remember that all rotation quaternions must be normalized. This can be done using the in-place operation normalize:

rot_quaternion.normalize()

Matrix and Quaternion usage is designed to be as similar as numpy array usage as possible, however 2D indexing has not been implemented yet.