[quote=“jim, post:7, topic:28161”]

You are lucky to get any curve at all in a situation like this since there is no one-to-one correspondence between the sequence of points on the line and the sequence of points on the pulled curve. There are places on the line that are perpendicular to more than one place on the surface.

[/quote] I disagree, there is a one-to-one correspondence between the points on the line and the locus of closest points on the surface, with the exception of one point on the line which has two closest points on the surface. That point corresponds to the interior ends of the two resulting curve segments.

[quote=“jim, post:7, topic:28161”]

However if all you are interested in is a smooth curve, then all you have to do is run RemoveMultiKnot and you will have a smooth curve that is very close to the same shape.

[/quote] Thanks for the reminder about RemoveMultiKnot. I don’t think I’ve used it before. It appears to resolve the problem.