Pascal, the report for the latest service release (Rhino 7, version 7.5.21068) mentions that the bug “OffsetCrvOnSrf: ThroughPoint failed in some cases (RH-62817)” have been fixed. However, I just updated my Rhino 7 and tried exactly the same 3dm file that I uploaded in post #4 in this topic 24 days ago and the latest Rhino 7.5 still fails to create an offset curve on surface.