Rotation in Three Dimensions - 3D Math Primer for Graphics and Game Development - page 293

(c) 0.364 −0.106 0.848 −0.372

(d) 0.383 0.924 0.000 0.000

(e) 1.000 0.000 0.000 0.000

(f) −0.364 0.106 −0.848 0.372

(g) 0.354 −0.146 −0.853 −0.354

(h) 0.726 0.061 −0.348 0.590

(i) −0.383 −0.924 0.000 0.000

5. Match each of the following axis-angle orientations with the corresponding
orientation from Figure 8.13. (Hint: this can be quite di cult to visualize.
Try converting the axis and angle to quaternion and then using the results
of your previous results. Then see if you can visualize it.)

(a) 98.4 o , [−0.863,−0.357,−0.357]
(b) 0 o , [0.707,−0.707, 0.000]
(c) 87.0 o , [0.089,−0.506, 0.857]
(d) 137 o , [−0.114, 0.910, 0.399]
(e) 135 o , [1.000, 0.000, 0.000]
(f) 261.6 o , [0.863, 0.357, 0.357]
(g) 139 o , [−0.156,−0.912,−0.378]
(h) 7200 o , [0.000,−1.000, 0.000]
(i) −135 o , [−1.000, 0.000, 0.000]

6. Derive the quaternion multiplication formula, by interpreting quaternions
as 4D complex numbers and applying the rules from Equation (8.10).

7. Compute a quaternion that performs twice the rotation of the quaternion

0.965 0.149 −0.149 0.149 .

8. Consider the quaternions:

a = 0.233 0.060 −0.257 −0.935

b = −0.752 0.286 0.374 0.459

(a) Compute the dot product ab.

(b) Compute the quaternion product ab.

(c) Compute the difference from a to b.