CG Homework 5, due Thu 2016-10-06 9am

  1. (2 pts) What is the quaternion for the rotation by 90 degrees about the axis (5,4,3), followed by the rotation by 180 degrees about the axis (0,0,1)?
  2. (2 pts) What is that rotation's axis and angle?
  3. (2 pts) (Reread My note on 3D Interpolation, which I discussed in lecture 11.) You wish to interpolate a smooth, constant speed, path on a sphere from \(\left(\frac{1}{\sqrt{2}},0,\frac{1}{\sqrt{2}}\right)\) to \(\left( \frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}} \right)\). Give the 1/3 and 2/3 points of that path.
  4. (14 pts) Do question 3.2 on page 132 of the textbook.

(Total: 20 points.)