Constructing a Poncelet $\infty$-gon

Move the slider and the pink points.

Starting from six given points, we here construct a chain of points and lines that locally behaves like an $(n_4)$-configuration. Move the slider to change the length of the construction.

You can move the initial points as well (the pink ones). Since the construction is numerically very sensitive the movement of your mouse will only be transfered with a tiny fraction to the position of the points.