Versor
In mathematics, a versor is a quaternion of norm one (a unit quaternion). Each versor has the form
q
=
exp
(
a
r
)
=
cos
a
+
r
sin
a
,
r
2
=
−
1
,
a
∈
[
0
,
π
]
,
{\displaystyle q=\exp(a\mathbf {r} )=\cos a+\mathbf {r} \sin a,\quad \mathbf {r} ^{2}=-1,\quad a\in [0,\pi ],}
where the r2 = −1 condition means that r is a unit-length vector quaternion (or that the first component of r is zero, and the last three components of r are a unit vector in 3 dimensions). The corresponding 3-dimensional rotation has the angle 2a about the axis r in axis–angle representation. In case a = π/2 (a right angle), then
q
=
r
{\displaystyle q=\mathbf {r} }
, and the resulting unit vector is termed a right versor.
The collection of versors with quaternion multiplication forms a group, and the set of versors is a 3-sphere in the 4-dimensional quaternion algebra.
Similar Artists