
2.2 Transformations 27
(x
0
, x
1
)
2(x
0
, x
1
)2(x
0
+ sx
1
,
x
1
)
(x
0
+ sx
1
,
x
1
)
Figure 2.7 Shearing of points (x
0
, x
1
) in the x
0
direction. As the x
1
value increases for points,
the amount of shearing in the x
0
direction increases.
Shearing
Shearing operations are applied less often than rotations, reflections, and scalings, but
I include them here anyway since they tend to be grouped into those transformations
of interest in computer graphics. To motivate the idea, consider a shearing in two
dimensions, as illustrated in Figure 2.7.
In two dimensions, the shearing in the x
0
direction has the matrix representation
S =
1 s
01
This maps the point (x
0
, x
1
) to (y
0
, y
1
)