Graphics Reference
In-Depth Information
projection from the point
P
¢ onto the x-axis. The matrices for these maps with respect
to homogeneous coordinates are:
10 0
00
1
2
00 1
Ê
ˆ
100
010
421
100
010
421
Ê
ˆ
Ê
ˆ
Á
Á
˜
˜
Á
Á
˜
˜
-
1
Á
Á
˜
˜
T
´
T
´
S
´
Ë
¯
Ë
¯
--
Ë
¯
1
2
1
2
1
2
1
2
Ê
ˆ
Ê
ˆ
-
0
0
Á
Á
Á
Á
˜
˜
˜
˜
Á
Á
Á
Á
˜
˜
˜
˜
1
2
0
1
2
0
-
1
1
2
1
2
0
R
´
R
´
0
-
0
Ë
¯
Ë
¯
1
0
1
Multiplying these matrices together gives that
3
2
1
2
1
2
Ê
ˆ
---
Á
Á
Á
Á
˜
˜
˜
˜
C ´
5
2
5
3
2
1
1
2
2
.
Ë
¯
In other words, C is defined by the equations
3
2
5
2
1
2
3
2
-+ +
xy
5
-+ +
xy
1
x
¢=
,
y
¢=
.
1
2
1
2
1
2
1
2
-+ +
xy
2
-+ +
xy
2
Since
3
2
1
2
1
2
Ê
ˆ
---
Á
Á
Á
Á
˜
˜
˜
˜
15
2
9
2
3
2
=
Ê
Ë
ˆ
¯
,
(
)
5
2
5
3
2
1
1
2
2
541
Ë
¯
and
15
2
9
2
3
2
È
Í
˘
˙
=
[
]
,,
531
,,,
it follows that C(5,4) = (5,3). We could also have deduced this by substituting 5 for x
and 3 for y in the equations above.
