Euclidean Transformation

Euclidean transformation is a vector transformation operation that is used to track moving objects

$${\text{X}}_{3\times 1}^{\prime }={\text{R}}_{3\times 3}{\text{X}}_{3\times 1}+{\text{t}}_{3\times 1}$$

$\text{R}$ is the rotation matrix and $\text{t}$ is the translation matrix

Concatenation Euclidean transformations is highly messed up. Use Homogeneous Coordinates to make it easier

$$\left[\begin{array}{c}{\text{x}}^{\prime }\\ 1\end{array}\right]=\text{E}\left[\begin{array}{c}\text{x}\\ 1\end{array}\right]$$ $$\text{E}=\left[\begin{array}{cc}\text{R}& \text{t}\\ {\text{0}}^T& \text{1}\end{array}\right]$$