Rotations and quaternions
How do we represent rotation matrices?
2.
Unit quaternions [Shoemake SIGGRAPH’85]
q
= (
n
sin
θ
/2, cos
θ
/2) = (
w
,
s
)
quaternion multiplication (division is easy)
q
0
q
1
= (
s
1
w
0
+
s
0
w
1
,
s
0
s
1
-
w
0
·
w
1
)