Using Quaternion with Python ~ numpy-quaternion ~

Introduction

Quaternion and numpy-quaternion seem to be the top two libraries in the world that handle quaternions in Python, but probably because the person who made the reference page for pyquaternion was the first in Japan, the quaternion calculation in Python is overflowing in the streets. It's just pyquaternion (is there only?).

However, numpy-quaternion seems to have a lower calculation cost. Reference: https://www.theoj.org/joss-papers/joss.00787/10.21105.joss.00787.pdf

Also, comparing the number of stars on github, there are more numpy-quaternions (as of December 13, 2019, numpy-quaternion is 276 and pyquaternion is 138).

I feel that the affinity with numpy is also better than pyquaternion because of the ease of handling batch conversion. Would you like to use it?

github repository: https://github.com/moble/quaternion Documentation: https://quaternion.readthedocs.io/en/latest/ PyPI: https://pypi.org/project/numpy-quaternion/

Installation

pip install numpy-quaternion

You can easily enter with.

Also,

import quaternion

You can import the library with.

Quaternion notation

quat = (w, x, y, z) = \left(\underbrace{\cos\frac{\theta}{2}}_{Real part},\ \underbrace{\lambda_x\sin\frac{\theta}{2},\ \lambda_y\sin\frac{\theta}{2},\ \lambda_z\sin\frac{\theta}{2}}_{Imaginary number(vector)Department}\right)

How to use

Less than,

import numpy as np
import quaternion

will do.

Make a quaternion

quat = np.quaternion(w, x, y, z)

Quaternion is added to the attribute of numpy. For example

print(np.quaternion(1,0,0,0))
# -> quaternion(1, 0, 0, 0)

type(np.quaternion(1,0,0,0))
# -> quaternion.quaternion

It becomes.

Quaternion synthesis

q1 = np.quaternion(1, 2, 3, 4)
q2 = np.quaternion(4, 5, 6, 7)
print(q1*q2)
# -> quaternion(-52, 10, 24, 20)

Multiplication is defined. For the time being, other four arithmetic operations are also defined, but do you sometimes use sums ... It is not defined in Eigen of C ++.

methods of np.quaternion

Only a part will be taken up. It does not cover things related to spherical functions or linear interpolation. Reference: https://quaternion.readthedocs.io/en/latest/_autosummary/quaternion.html

Member variables

Member function

quaternion method

The point is that the methods in this area are not one-dimensional, but can also be used for multidimensional arrays. If the size of the last dimension requires a quaternion, it should be 4, if it is 3D, it should be 3D, and if it is 3x3, the last 2D should be 3x3.

Official documentation

https://quaternion.readthedocs.io/en/latest/index.html

By the way, the author of this library seems to have a big Euler angle. Stop if you see someone using it! Say that and walk away from the spot and mess with your mom! Is written

Finally

Where is the demand for quaternions in Python? Unity is C #, and I'm talking about using Unity's functions in the first place, and Python is too slow for robots, which is out of the question ...