Module micromath::quaternion

Quaternions are a number system that extends the complex numbers which can be used for efficiently computing spatial rotations.

They are computed as the quotient of two directed lines in a three-dimensional space, or equivalently as the quotient of two vectors.

For given real numbers a, b, c, and d, they take the form:

a + bi + cj + dk

where i, j, and k are the fundamental quaternion units:

i² = j² = k² = i*j*k = -1

Quaternion multiplication is noncommutative:

x	1	i	j	k
1	1	i	j	k
i	i	-1	k	-j
j	j	-k	-1	i
k	k	j	-i	-1

Structs

Quaternion

Quaternion