Graphics Reference
In-Depth Information
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
+
a
21
)
x
=
1
4
y
(a
23
+
=
z
a
32
)
1
4
y
(a
13
−
s
=
a
31
)
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
).
11.10 Summary
Quaternion algebra offers a simple and efficient way for computing rotations, but
can also be evaluated in matrix form. We have also shown that it is possible to move
between both forms of notation. It is left to the reader to code up some of these ideas
and explore issues of accuracy and efficiency.
11.10.1 Summary of Quaternion Transforms
Given
+
ˆ
q
=
s
v
=
cos
(θ/
2
)
+
sin
(θ/
2
)(x
i
+
y
j
+
z
k
)
p
=
0
+
u
.
