Quaternions.jl

A Julia module with quaternion, octonion and dual-quaternion functionality

Quaternions are best known for their suitability as representations of 3D rotational orientation. They can also be viewed as an extension of complex numbers.

Implemented functions are:

+-*/^
real  
imag  (a vector)  
conj  
abs  
abs2  
exp  
log  
normalize  
normalizea  (return normalized quaternion and absolute value as a pair)  
angleaxis  (taken as an orientation, return the angle and axis (3 vector) as a tuple)  
angle  
axis  
exp  
log  
sin  
cos  
sqrt  
linpol  (interpolate between 2 normalized quaternions)  

Dual quaternions are an extension, combining quaternions with dual numbers. On top of just orientation, they can represent all rigid transformations.

There are two conjugation concepts here

conj  (quaternion conjugation)  
dconj (dual conjugation)

further implemented here:

Q0  (the 'real' quaternion)  
Qe  ( the 'dual' part)  
+-*/^  
abs  
abs2  
normalize  
normalizea  
angleaxis  
angle  
axis  
exp  
log  
sqrt  

Octonions form the logical next step on the Complex-Quaternion path. They play a role, for instance, in the mathematical foundation of String theory.

+-*/^
real  
imag  (a vector)  
conj  
abs  
abs2  
exp  
log  
normalize  
normalizea  (return normalized octonion and absolute value as a tuple)  
exp  
log  
sqrt