Projection/Intersection of a body imported from a step file onto a sketch produces gaps
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I have a very round-shaped/curvy solid body imported from a step file. From what I know, it was originally designed in SolidWorks. I try to make a silhouette in an intersecting sketch by projecting that body onto it. Since the body is solid, I'd expect it to yield a nicely closed profile. However, in all directions I put this sketch in I get a projection where the lines/arcs/splines at many places almost, but not quite touch, which only can be seen by zooming in very deeply (which is for some reason EXTREMELY SLOW!!). The fact that the points are not blackened is also a clue. So, I cannot easily fix this by adding line sections or tangent arcs to join the open line endings. Sometimes, lines are even missing completely, leaving a large gap in the projection. Producing intersections often yields similar problems.
Is this a known issue? Can I work around this somehow? Is there e.g. some simple way to connect open endings of projected lines and curves, so that zooming is not necessary?