This will be the last session on 3D Modelling, designed to tie up loose ends. It contents will therefore depend on the challenges encountered in the three first sessions.

• Velocity

Tentative Topics

• 3D Motion (additional notes)

Quaternions

Reading Appendix 2.A. May want to drop this.

Exercises

1. Complete the exercises from last week.

2. Given a rotational matrix \[ \begin{bmatrix} \cos(\pi/6) & -\sin(\pi/6) & 0 \\ \sin(\pi/6) & \cos(\pi/6) & 0 \\ 0 & 0 & 1 \end{bmatrix} \] and a translation \(\vec{v}=[1,0,2]\).

   What are the homogenous matrices describing each of the following operations:
   • rotate by \(R\) and then translate by \(\vec{v}\)
   • translate by \(\vec{v}\) and then rotate by \(R\)
3. Suppose you have rotated by \(R\) and then translated by \(\vec{v}\) as given in the previous exercise. What is the homogeneous matrix to undo this operation?
4. Ma 2004:40 Exercise 2.14. Hint: start by drawing

5. Ma 2004:40 Exercise 2.13