22 Chapter 2 The Graphics System
Similar rotation mat rices may be constructed for rotations about the other coor-
dinate axes. The matrix representing a rotation in the xz-plane is
R =
⎡
⎣
cos θ 0 sin θ
01 0
− sin θ 0cosθ
⎤
⎦
= I + (sin θ)S +(1 − cos θ)S
2
(2.20)
where
S =
⎡
⎣
001
010
−100
⎤
⎦
Figure 2.4 (b) is a 3D view of a positive-angle rotation about the y-axis, which
is a counterclockwise rotation in the xz-plane as shown. The mat rix representing a
rotation in the yz-plane is
R =
⎡
⎣
10 0
0cosθ − sin θ
0 sin θ cos θ
⎤
⎦
= I + (sin θ)S +(1 − cos θ)S
2
(2.21)
where
S =
⎡
⎣
10 0
00−1
01 0
⎤
⎦
Figure 2.4 (c) is a 3D view of a positive-angle rotation about the x-axis, which is
a counterclockwise rotation in the yz-plane as shown.
In general, the matrix representing a rotation about