Game Development Reference
In-Depth Information
5. This matrix is a standard a
ne transform matrix with a right-most column of [0, 0, 0, 1]
T
,
as discussed in Section 6.4.3. Thus, it can be decomposed into a linear portion and a
translation portion:
2
4
−0.1495 −0.1986 −0.9685
3
5
0
−0.8256
0.5640
0.0117
0
M =
−0.5439 −0.8015
0.2484
0
1.7928
−5.3116
8.0151
1
2
4
3
5
2
4
1
3
5
−0.1495 −0.1986 −0.9685
0
0
0
0
−0.8256
0.5640
0.0117
0
0
1
0
0
=
.
−0.5439 −0.8015
0.2484
0
0
0
1
0
0
0
0
1
1.7928 −5.3116
8.0151
1
Now taking the inverse is easy, especially when we realize that the linear portion is the
same matrix as the previous exercise. The only real work is to multiply the translation
row by the inverse of the linear portion:
0
@
2
4
3
5
2
4
1
3
5
1
A
−1
−0.1495 −0.1986 −0.9685
0
0
0
0
−0.8256
0.5640
0.0117
0
0
1
0
0
M
−1
=
−0.5439 −0.8015
0.2484
0
0
0
1
0
0
0
0
1
1.7928 −5.3116
8.0151
1
2
4
1
3
5
2
4
−0.1495 −0.1986 −0.9685
3
5
−1
−1
0
0
0
0
0
1
0
0
−0.8256
0.5640
0.0117
0
=
0
0
1
0
−0.5439 −0.8015
0.2484
0
1.7928 −5.3116
8.0151
1
0
0
0
1
2
4
1
3
5
2
4
3
5
0
0
0
−0.1495 −0.8256 −0.5439
0
0
1
0
0
−0.1986
0.5640
−0.8015
0
=
0
0
1
0
−0.9685
0.0117
0.2484
0
−1.7928
5.3116 −8.0151
1
0
0
0
1
2
4
−0.1495 −0.8256 −0.5439
3
5
0
−0.1986
0.5640
−0.8015
0
=
.
−0.9685
0.0117
0.2484
0
6.976
4.382
−5.273
1
2
4
1
3
5
0
0
0
0
1
0
0
6. T([4, 2, 3]) =
0
0
1
0
4
2
3
1
7. First, calculate the rotation matrix:
2
4
1
3
5
2
4
1.000
3
5
0
0
0
0.000
0.000
0.000
cos(20
o
)
sin(20
o
)
0
0
0.000
0.940
0.342
0.000
R
x
(20
o
) =
=
.
0 −sin(20
o
)
cos(20
o
)
0
0.000 −0.342
0.940
0.000
0
0
0
1
0.000
0.000
0.000
1.000
Search WWH ::
Custom Search