I have a hollow object (a torus but I have the same issue with any open channel object) of some nominal thickness that I’d like to intersect a surface (in my case a curved one) so that the object opening is retained across the surface.

In the picture I’ve created what I’m going for with a hollow torus and a flat planar surface. I think I’ve tried all permutations of Union, Intersect, and Subtract but perhaps I’m missing something. Ideas? Links to similar forum topics?

Thanks!