---
title: Change of Basis
categories: 3D lecture
---

# Motion examples

1.  Translation
    $$\vec{x}' = \vec{x}+\vec{t}$$
1.  Rotation
    $$\vec{x}' = \vec{x}\cdot R$$
    - But note that $R$ is not an arbitrary matrix.
    - We'll return to the restrictions
 
# Definition: Rigid Body Motion

1.  3D Object is a set of points in $\mathbb{R}^3$