Graphics Programs Reference
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x =L
x =M
y =N
(a)
(b)
Figure 1.15: Glide Reflection.
1.2.8 Improper Rotations
A rotation followed by a reflection about one of the coordinate axes is called an improper
rotation . The transformation matrices for the two possible improper rotations in two
dimensions (Figure 1.16) are
cos θ
10
0
= cos θ
,
sin θ
sin θ
sin θ
cos θ
1
sin θ
cos θ
cos θ
=
,
sin θ
10
01
cos θ
sin θ
sin θ
cos θ
sin θ
cos θ
and the transformation rules therefore are
x = x cos θ + y sin θ,
y = x sin θ
y cos θ,
x =
y =
x cos θ
y sin θ,
x sin θ + y cos θ.
Notice that the determinant of an improper rotation matrix equals
1, like that of a
pure reflection.
(a)
(b)
Figure 1.16: Improper Rotations.
 
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