## Revision 5c1429d8764d087f7c84a83cfb2fed95153b8abe (click the page title to view the current version)

## Changes from 5c1429d8764d087f7c84a83cfb2fed95153b8abe to fb69306a414b992332659c04926f734f6c59e436

---
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 $\mathbb{R}^3$
2. If the object moves, the constituent points move
3. The points have to move so that they preserve the shape of the object