Consider two such polygons $P_1(x_{1},y_{1},r_1)$ and $P_2(x_{2},y_{2},r_2)$, where $(x_{1}, y_{1})$ and $(x_{2}, y_{2})$ are the coordinates of the center to $P_1$ and $P_2$, respectively, and $r_1$ and $r_2$ is the radius of $P_1$ and $P_2$. The vertices of the polygons are given by $$ P_{1\ell} = \left[\begin{matrix}x_{1}\\y_{1}\end{matrix}\right] + r_1\left[\begin{matrix}\cos\theta\\\sin\theta\end{matrix}\right] \qquad\text{and}\qquad P_{2\ell} = \left[\begin{matrix}x_{2}\\y_{2}\end{matrix}\right] + r_2\left[\begin{matrix}\cos\theta\\\sin\theta\end{matrix}\right], $$
where $\theta = 2\pi\ell/L$ for $\ell = 1, \ldots, L$ and $L \geq 3$. I have a particular case where $x_{1} = y_{1}$ and $x_{2} = y_{2}$. I'd like to calculate the distance between these polygon from Haudorff's distance. In this particular case is it possible to simplify the distance without go through for all points?
P.S.: I'm no mathematician, sorry for notation.