squaternion 2025.3.2

Some simple functions for quaternion math

Simple Quaternions (squaternion)

Generally I don't need all of the capabilities (or complexity) of quaternion math libraries. Basically I just need a way to convert between Euler and Quaternion representations and have a nice way to print them out.

This has basically no imports outside of standard python 3.x libraries. It should be easier to get on embedded python systems without having to build numpy. Also, this tries to be fast by using a frozen dataclass available in python3.

Install

pip install squaternion

Usage

from squaternion import Quaternion

# if you know the values you want Quaternion(w, x, y, z), note this is a
# attr frozen class so it is immutable once created
q = Quaternion(1,0,0,0)

# multiplication for scalar (int, double) and with another quaternion
q = Quaternion(1,2,3,4)
q*q => Quaternion(w=-28, x=4, y=6, z=8)
3*q => Quaternion(w=3, x=6, y=9, z=12)
q*3.0 => Quaternion(w=3.0, x=6.0, y=9.0, z=12.0)

# Addition and subtraction
q = Quaternion(1,2,3,4)
q+q => Quaternion(w=2, x=4, y=6, z=8)

# numpy can do some things, but it will change the tuple to an array, so you might
# need to transform it back to a quaternion
q = Quaternion(1,2,3,4)
np.dot(q,q) => 30
np.sqrt(np.dot(q,q)) => 5.477225575051661
q/np.sqrt(np.dot(q,q)) => array([0.18257419, 0.36514837, 0.54772256, 0.73029674])
Quaternion(*(q/np.sqrt(np.dot(q,q)))) => Quaternion(w=0.18257418583505536, x=0.3651483716701107, y=0.5477225575051661, z=0.7302967433402214)

# however you typically don't think in 4 dimensions, so create from
# euler angles from_eluer(roll, pitch, yaw), default is radians, but set
# degrees true if giving degrees
q = Quaternion.from_euler(0, -90, 100, degrees=True)

# can get the euler angles back out in degrees (set to True)
e = q.to_euler(degrees=True)
d = q.to_dict()
t = q.to_tuple()
r = q.to_rot() # returns a rotation matrix as tuple
r = np.array( q.to_rot() ) # rotation matrix as numpy array

# iterate through values
for i in q:
    print(f"{i}")

# indexing like a namedtuple
z = q[3]
z = q[-1]
v = q[-3:]
w = q[0]

# class properties
v = q.vector     # returns a tuple (x,y,z)
s = q.scalar     # returns a double (w)
n = q.normalize  # returns unit quaternion
m = q.magnitude  # returns the magnitude of the quaternion
a = q.angle      # returns angle of rotation in radians
a = q.axis       # returns axis of rotation

# useful attr functions
q == q    # compare will return True
q != q    # will return False

w = q.w
x = q.x
y = q.y
z = q.z

print(q)  # pretty print => Quaternion(w,x,y,z)
print(f"{q:.4f}") # print only 4 decimal places

Alternatives

This is a basic library that converts between Euler angles and Quaternions. There are other libraries that do so much more listed below ... but I don't need all of that.

• scipy.spatial.transform.Rotation: has everything you could want, with lots of imports
• tinyquaternion: appears to be more functional but needs numpy
• quaternions: another good lightweight quaternion package
• pyrr: seems good, integrated with numpy

References

• Wikipedia Convert Between Quaternions and Euler Angles
• Wikipedia Euler Angle Definitions
• Wikipedia Gimbal Lock

MIT License

Copyright (c) 2014 Kevin Walchko

Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:

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