# Homework 6, due Wed Oct 9, 2013 (RPI, ECSE-4750)

Hand in your solution on RPILMS. Each team should submit their solution under only 1 student's name. The other student's submission should just name the lead student. (This makes it easier for us to avoid grading it twice.) For programming exercises, hand in code and screen dumps. We won't run your code, but will use the screendumps to judge how it worked.

1. (2 pts) What is the quaternion for a rotation by 90 degrees about the axis (2,3,4)?
2. (2) Apply it to the point (1,0,0).
3. (2) What is the quaternion for a rotation by 180 degrees about the axis (0,1,0)?
4. (2) What is the quaternion for the rotation by 90 degrees about the axis (2,3,4), followed by the rotation by 180 degrees about the axis (0,1,0)?
5. (2) What is that rotation's axis and angle?
6. (4) You wish to interpolate a smooth, constant speed, path on a sphere from {$\left(\frac{1}{\sqrt{2}},\frac{1}{\sqrt{2}},0\right)$} to {$\left( \frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}} \right)$}. Give the midpoint of that path.
7. (16) Do exercise 4.59 on page 160. Hand in the code and a video with audio commentary showing you using your program to demonstrate the in-betweening.

(Total: 30 points.)