How can I determine the radius (of curvature) at a point on a surface in a direction I specify?

More specifically, I want to know the radius of curvature of a surface at a point on an edge, in the direction perpendicular to this edge.

The principal curvatures have no relation to the direction of the (trimmed or not) edge in many cases. So this I cannot use. I had the idea to add a perp frame to the edge at the specified point and then intersect this with the surface and measure the curve radius at that point. This works in most cases, but when the point is at a corner point of the surface it can happen no curve intersection is found.