[−][src]Module micromath::quaternion
Quaternions are a number system that extends the complex numbers which can be used for efficiently computing spatial rotations.
The quaternion
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Quaternions 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 |