Yeah, the problem is with the main starship body, it has gotten messed up.
After deleting the generator curves, I can tell by looking at it that there are some duplicated surfaces in it, you can kind of see some edges look heavier than normal if you look closely, this is an indication that two edges are being drawn on top of each other which means multiple surfaces.
This is again another one of those things that will kind of semi-heal itself if you save it and reload it.
After doing that here, it is fixed up to a certain extent, and there are some duplicate surfaces that have been automatically separated out, dragging them around I can see this:
See that highlighted piece? That's a vertical plane that is embedded inside of the starship - it is what is causing problems and also responsible for the downward intersection edge that you saw.
This is what's called a "non-manifold" edge - one where more than two surfaces have become glued together along a common edge. Do you remember how that front piece got put together with the main body piece, was it through join? I think there may be a problem right now if you try to use Edit/Join on things that share a common surface (instead of just common open edges) - I think it may cause some problems along these lines.
If you can remember how that front piece was welded to the main body it could help track this down a bit more.
- Michael
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