I need to remove the portion of the orange ring which is outside of the green ring in the attached file. Nothing seems to work. Intersection finds only a small portion of the intersection between them. The rings are bodies of revolution, and both are copies of the same original.
The original ring was created using Revolve, and the profile curve was a closed polycurve with sharp corners. The result was a single surface with creases. It appears that BooleanSplit, Split, Trim, Intersect, etc. do not work properly with two creased surfaces.
I used DivideAlongCreases to convert the creased surfaces with rings to polysurfaces.
Everything appears to work properly with the polysurfaces.