Graphics Reference
In-Depth Information
Y
t
I
X
Fig. 7.4.
2D homogeneous coordinates can be visualized as a plane in 3D space,
generally where
t
= 1, for convenience.
which solves the above problem of adding a constant.
Let's now go on to see how homogeneous coordinates are used in practice.
7.3.1 2D Translation
The algebraic and matrix notation for 2D translation is
x
=
x
+
t
x
y
=
y
+
t
y
(7.21)
or, using matrices,
⎡
⎤
⎡
⎤
⎡
⎤
x
y
1
10
t
x
01
t
y
00 1
x
y
1
⎣
⎦
=
⎣
⎦
·
⎣
⎦
(7.22)
7.3.2 2D Scaling
The algebraic and matrix notation for 2D scaling is
x
=
s
x
x
y
=
s
y
y
(7.23)
or, using matrices,
⎡
⎤
⎡
⎤
⎡
⎤
x
y
1
s
x
00
0
s
y
0
001
x
y
1
⎣
⎦
=
⎣
⎦
.
⎣
⎦
(7.24)
