Game Development Reference
In-Depth Information
2
4
3
5
0.061
0.814
0.578
(c)
−0.900
0.296
−0.322
−0.433 −0.500
0.750
2
4
−0.713 −0.450 −0.538
3
5
0.091
0.702
−0.706
(d)
0.696
−0.552 −0.460
2
4
1.000
3
5
0.000
0.000
(e)
0.000
1.000
0.000
0.000
0.000
1.000
2
4
−0.707
3
5
0.000
0.707
(f)
0.500
0.707
0.500
−0.500
0.707 −0.500
2. Match each of the following Euler angle triples with the corresponding
orientation from
Figure 8.13,
and determine whether the orientation is in
the canonical set of Euler angles. If not, say why not.
(a) h = 180
o
, p = 45
o
, b = 180
o
(b) h = −135
o
, p = −45
o
, b = 0
o
(c) h = 0
o
, p = −90
o
, b = −45
o
(d) h = 123
o
, p = 33.5
o
, b = −32.7
o
(e) h = 0
o
, p = 0
o
, b = 0
o
(f) h = 0
o
, p = 135
o
, b = 0
o
(g) h = −45
o
, p = −90
o
, b = 0
o
(h) h = 180
o
, p = −180
o
, b = 180
o
(i) h = −30
o
, p = 30
o
, b = 70
o
3. (a) Construct a quaternion to rotate 30
o
about the x-axis.
(b) What is the magnitude of this quaternion?
(c) What is its conjugate?
(d) Assume the quaternion is used to rotate points from object space to
upright space of some object. What is the orientation, in Euler angles,
of this object?
4. Match each of the following quaternions with the corresponding orientation
from Figure 8.13. These quaternions transform vectors from object space
to upright space. (We told you that quaternions are harder for humans to
use! Try converting these to matrix or Euler angle form and take advantage
of your previous work.)
(a)
−1.000
0.000
0.000
0.000
(b)
0.653
−0.653 −0.271 −0.271
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