_Match for curvature with the merge option is great for creating a single smooth curve from two. Unless one curve is straight: the match works but the merge resolutely fails. Best you can do is join.

At a) we have a curve and a line matched for curvature but incapable of merging.
At b) the degree of the line has been upped to 3 but still no cigar.
At c) the line has been distorted and now merge works. Shame about the shape.

Hmm, yes it seems a little buggy here. First, I thought - what if I make the curvature match myself first - by aligning the second and third control points along the tangent of the line - then try it. Match with merge did not work. I used the following settings, choosing the blue curve first, then the red line:

I then used ChangeDegree to change your blue curves to degree 5 - because I always heard that one should avoid even degree curves (except for 2) - and presto ! the merge succeeded - but only on the pre-matched set of curves.

Thanks for investigating. Takeaway from that is you changed the degree of the curve, but kept the line the same, and that goes part way to a solution. I’ll have to try rebuilding all the curves to degree 5 then running match once to align and then again to merge.

Hi Dennis - merged curves cannot be exploded. There is no ‘kink’ or potential kink (fully multiple knot) at what were the end points of the input curves.

For the first curve provided in the original post, the degree-4 curve is linear at its end but is about 0.35° G1-discontinuous with the line. If either curve is rotated to be over 1° G1-discontinuous, the _Match with Merge will work. It seems that when Continuity is set to Curvature, the original curves are already considered G2-continuous, but a merge does not occur.

Changing the model’s angle tolerance to 0.1° doesn’t affect the result; the 1° tolerance may be hard-coded.

A workaround is to first _Match with Continuity set to Tangency, then again with it set to Curvature.

Hi Steve- Yeah - this seems wrong to me, off hand - they still ought to be merged - looks like maybe the command just bails as soon as the curves are determined to be g2.