Finding normal curvature from principal curvatures?

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Anna Case
Anna Case 2020-6-10
I have two principal curvatures defined as:
k1 = H + sqrt(H.^2 - K);
k2 = H - sqrt(H.^2 - K);
and I would like to define the normal curvature as:
kn = k1.*cos(the).^2 + k2.*sin(the).^2;
However, I'm having some trouble finding the (theta). What I understand is that this will be the angle in the tangent plane measured CCW from the direction of minimum curvature. My principal curvatures are saved as an [x,y] matrix of values -- how do I find the direction of minimum curvature and relate this back to the tangent plane?

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