More accurate alternative to rlocfind to analyze root locus in control systems engineering

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To find the gain at the point where the root locus intersects a line of constant damping ratio, the rlocfind function can be used, but the user has to manually select a point and Matlab finds the closest point on the root locus to the selection. Is there a way to find the exact point of intersection without having to make the selection manually?
h = tf([2 5 1],[1 2 3]);
rlocus(h) % Root locus
z = 0.707; sgrid(z,0)
k = rlocfind(h)

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