Can I use Mathematica to create visualized rotation of a shape? Specifically, I'm trying to draw a rectangle $R$ with vertices where $r>0$ and $\theta\in(0,\pi/4$):
$$ \\ R= \begin{pmatrix} re^{i\theta} \\ -re^{-i\theta} \\ -re^{i\theta} \\ re^{-i\theta} \end{pmatrix}$$
Then rotating it by $2\theta$ to create a 2nd rectangle $R'$ where:
$$R'= e^{i2\theta}*R = e^{i2\theta}\begin{pmatrix} re^{i\theta} \\ -re^{-i\theta} \\ -re^{i\theta} \\ re^{-i\theta} \end{pmatrix} = \begin{pmatrix} re^{i3\theta} \\ -re^{i\theta} \\ -re^{i3\theta} \\ re^{i\theta} \end{pmatrix}$$
Ideally the final graphic would start with $R$, then show a "shadow" of $R$ rotating to the position of $R'$. At the end, the graphic would show both $R$ and $R'$.
Graphics
to draw your shapes parametrically and then useAnimate
orManipulate
to animate them. $\endgroup$ – L.Yu May 23 '19 at 22:38