Quaternion Transforms in Space - Rotation Transforms for Computer Graphics - page 180

2 1

1

x =± + a 11 − a 22 − a 33

1
4 x (a 12 +

y = a 21 )

1
4 x (a 13 +

z = a 31 )

1
4 x (a 32 −

s = a 23 )

2 1

1

y =± − a 11 + a 22 − a 33

1
4 y (a 12 +

x = a 21 )

1
4 y (a 23 +

=

z a 32 )

1
4 y (a 13 − a 31 )

s =

2 1

1

z =± − a 11 − a 22 + a 33

1
4 z (a 13 +

x = a 31 )

1
4 z (a 23 +

y = a 32 )

1
4 z (a 21 −

s = a 12 ).