the small scale structure without loosing the information on the global spatial distribution. To properly compare the results, we adopted the same kernel size for all the populations of both clusters.

We calculated six iso-density contours for each population and used the least square method to fit each contour with an ellipse as in @radim1998. The directions of the resulting minor and major axes are plotted in each panel. The resulting ellipticity, $e$, is plotted as a function of the semi-major axis, $a$ in Figure \[fig:ell\].

We confirm that $\omega\,$Centauri has an elliptical shape [e.g. @harris1996].

The ellipticity of Fe-poor and Fe-rich stars slightly increases from e$\sim$0.05 to 0.07 and from e$\sim$0.06 to 0.08, respectively, when moving from $a \sim 3\,\rm arcmin$ to $15\,\rm arcmin$. As a consequence, the ellipticity difference is $\Delta e \sim 0.015$ with statistical significance of $\sim$70%.

The major axis of the best-fit ellipses are coincident within one-sigma in both populations.

In the case of M22, both Fe-poor and Fe-rich stars have similar ellipticities ($e \simeq 0.1$) over the entire analyzed field of view and their major axis have similar directions.\
Finally, as expected for oblate rotators, we find that the rotation axis [from @sollima2019 solid 