Game Development Reference
In-Depth Information
Now concatenate this with the translation matrix from the previous exercise. We know
this will simply copy the rotation portion into the upper 3×3, and the translation into the
bottom row.
2
4
1.000
3
5
2
4
1.000
3
5
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.940
0.342
0.000
0.000
1.000
0.000
0.000
R
x
(20
o
) T([4, 2, 3]) =
0.000 −0.342
0.940
0.000
0.000
0.000
1.000
0.000
0.000
0.000
0.000
1.000
4.000
2.000
3.000
1.000
2
4
1.000
3
5
0.000
0.000
0.000
0.000
0.940
0.342
0.000
=
0.000 −0.342
0.940
0.000
4.000
2.000
3.000
1.000
8. This time we concatenate the matrices in the opposite order, and the translation portion
gets rotated.
2
4
1.000
3
5
2
4
1.000
3
5
0.000
0.000
0.000
0.000
0.000
0.000
0.000
1.000
0.000
0.000
0.000
0.940
0.342
0.000
T([4, 2, 3]) R
x
(20
o
) =
0.000
0.000
1.000
0.000
0.000 −0.342
0.940
0.000
4.000
2.000
3.000
1.000
0.000
0.000
0.000
1.000
2
4
1.000
3
5
0.000
0.000
0.000
0.000
0.940
0.342
0.000
=
0.000 −0.342
0.940
0.000
4.000
0.853
3.503
1.000
2
4
1
3
5
0
0
1/5
0
1
0
0
9.
0
0
1
0
0
0
0
0
2
4
1
3
5
0
0
1/5
5
0
1
0
0
105
5
−81
7
89
21
10.
105 −243
89
1
=
105 −243
89
⇒
0
0
1
0
0
0
0
0
B.7
Chapter 7
(Page 214.)
In some places in this section, we use the notation (x, y)
c
to indicate Cartesian coordinates, and
(r, θ)
p
to indicate polar coordinates. If plain (a, b) coordinates are used, then the context will
make it clear whether the coordinates are Cartesian or polar.
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