How to find the intercept point(s) between the radial line (i.e. damping ratio) and the root locus?

I would like to automatically detect the intercept point(s) between the radial line which corresponds the damping ratio (i.e. the overshoot) and the root locus for a negative unity feedback. For example, the following script shows the intersect point

sys = zpk(-3,[-1+i -1-i],1);
rlocus(sys)
zeta = 0.95; % damping ratio
sgrid(zeta,0) % radial line

The result is

Sometimes, the radial line will intersect with more than one points. Is there any way to list all intercept points?

Answer 1

[KSSV]

You may use this function:

https://in.mathworks.com/matlabcentral/fileexchange/22441-curve-intersections?focused=5165138&tab=function