This is a mouthful to describe, so I hope the video is worth a thousand words: 
curvenear.3dm (77.6 KB)
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Is there a unit tolerance setting for ācurves on/near surfaceā, because when I open the very same file in Alias, I get a whole millimeter as the tolerance settingā¦ which I wonder if itās the source of my problemsā¦
But the unit dialog in Rhino has very few options:
Itās not, really; video clips are painful on their own, and require multiple viewing unless accompanied by a clear description of the problem to give the doctor some idea what to look for in the clip. Remember we come at this with zero context and you know exactly what youāre up to.
I do see that it does not look quite as Iād expect - I am comparing the edges as matched to the edge curves as pulledā¦ still pokingā¦
What I see is, the edge curve pulled to the surface goes to some location and and MatchSrf for position goes to a slightly, but larger than tolerance, location, with or without ārefineā. Pulling a point from the edge to the surface matches the curve pull. For now it looks like MatchSrf is getting it wrong.
RH-59325 MatchSrf - edge location
-Pascal
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Thank you for looking into this!
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I notice often problems with degree 2 surfaces in Rhino. If you change the degree to 3 it doesnāt happen
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Ah - good catch - Iāve seen this as well, and I did not think to check it - the target surface is rational.
-Pascal
Very funny results with āTangencyā and āPreserve isocurve directionā happen on your sample model. 
Looks like Rhino gets super confused in trying to figure out the desired direction.
I always wondered why Rhino does not use a common direction for the entire edge to be matched? (especially for the āMatch target isocurve directionā option) 
In many cases, different portions of the same edge go to totally different directions, which does not make any sense and basically destroys the intent of the modeler. The proper way would be for Rhino to use the direction that corresponds to the majority of the edge.
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