QUATERNIONS

These were used to govern 3-D mathematics before vectors were invented.

In a nutshell, Quaternions are four-dimensional numbers in the same sense that Complex Numbers are two-dimensional numbers.

a + bi + cj + dk

i^2 = j^2 = k^2 = -1.

ij = k

ijj = kj

-i = kj

-ki = kkj

-ki = -j

ki = j

kii = ji

ji = -k

jji = -jk

-i = -jk

i = jk

Multiplication is associative but not commutative ab is not necessarily equal to ba.

In OpenGl, quaternions can be used to manipulate the axes in a more sophisticated manner.  Used correctly, they can rotate around fixed axes, not relative axes from previous rotations.