Page 295 -

The matrices corresponding to these transformations, in 2-D, are
respectively:

s  0
S =  x  (9.8)
x
 0 1 

1 0 
S =   (9.9)
y 0 s
 y 

In-Class Exercises

Pb. 9.12 Find the transformation matrix for simultaneously compressing
the x-coordinate by a factor of 2, while expanding the y-coordinate by a fac-
tor of 2. Apply this transformation to the trapezoid of Example 9.1 and plot
the result.

Pb. 9.13 Find the inverse matrices for S and S .
x
y

9.1.5 Translation
r
A translation is defined by a vector T = (, ), and the transformation of the
t t
x y
coordinates is given simply by:
+
x ′ = x t
x
(9.10)
+
y ′ = y t
y
or, written in matrix form as:

t
x ′   x  
x
  =   +   (9.11)
t
′ y
y
     
y
The effect of translation over the matrix G is described by the relation:
G = G T ones+ * ( ,1 n + )1 (9.12)
T
where n is the number of points being translated.

© 2001 by CRC Press LLC