Game Development Reference
In-Depth Information
F IGURE 9.4
The car is rotated.
The matrix form of orientation looks like this:
cos θ
sin θ
Θ
=
sin θ
cos θ
where θ is the orientation angle, as before. This matrix is usually called the “rotation
matrix”: it can be used to rotate a location. We can work out the new position of the
headlamp by multiplying the relative position of the headlamp by the rotation matrix
cos θ
q b
sin θ
q =
sin θ
cos θ
where q b is the relative location of the headlamp. In our case, where θ
=
3 π/ 8, we get
0 . 38
1 . 5
0 . 57
1 . 27
1 . 10
0 . 92
+
0 . 69
q =
=
=
0 . 92
0 . 38
0 . 75
1 . 39
0 . 29
whereallvaluesaregiventotwodecimalplaces.
After applying the orientation in this way we can then apply the change in position
as before. The total process looks like this:
q
=
Θ q b +
p
[9.2]
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