Graphics Reference
In-Depth Information
and the position vector to be rotated is
120
which makes
cos 90
=
s
=
0
√
2
2
sin 90
√
2
=−
x
=−
√
2
2
sin 90
√
2
=
y
=
z
=
0
⎡
⎤
⎡
⎤
⎡
⎤
0
−
10
1
2
0
−
2
⎣
⎦
⎣
⎦
=
⎣
⎦
qv
q
¯
=
−
100
00
−
1
0
(7.25)
−
1
which is the same result.
To summarize:
a position vector
v
=
x
v
i
+
y
v
j
+
z
v
k
is rotated about an axis
q
=
x
i
+
y
j
+
z
k
either using
cos
2
q
0
v
cos
2
q
sin
sin
qv
¯
q
=
2
+
+
2
−
or
⎡
⎤
⎡
⎤
2y
2
z
2
1
−
+
2xy
−
sz
2xz
+
sy
x
v
y
v
z
v
⎣
⎦
⎣
⎦
2x
2
z
2
qv
q
¯
=
2xy
+
sz
1
−
+
2yz
−
sx
2x
2
y
2
2xz
−
sy
2yz
+
sx
1
−
+
where
cos
2
s
=
x y, and z incorporate sin
2
and the axis components.
