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title: More Mathematics for 3D Modelling
categories: session
geometry: margin=2cm
fontsize: 12pt
---
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.
+ [3D Motion]() (additional notes)
## Quaternions
**Reading** Appendix 2.A. May want to drop this.
# Exercises
1. Complete the exercises from last week.
1. Exercise 2.7.
1. Exercise 2.10.
1. Exercise 2.11.
To calculate eigenvalues and -vectors in Python, you can
use `numpy.linalg.eig`.
3. 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?
2. Ma 2004:40 Exercise 2.14. Hint: start by drawing
2. Ma 2004:40 Exercise 2.13
