I hope I am able to formulate this question properly as I am not extremely versed in differential geometry. I have an arbitrary 3d smooth surface, S, defined by discrete points and their respective normal, N. I also have an arbitrary vector, V, pointing at that surface. I need the min and max principal curvatures,κmin and κmax, at a point, P, from the curves, L, formed by the intersection of the arbitrary surface and a plane, Q, which V lies on and rotates about V. So let θ be the angle between N and V, γ be the angle of rotation of Q about V in the clockwise direction. Please refer to the picture below to get a better illustration of the problem. Is there a generic formula for such a problem out there. I haven't ran across anything as of yet.