Catenary surfaces with the boundary matched

Hello everyone, I am doning a groups of catenary surfaces, i wonder how to modified the data to match the boundary of each surface。

catenary (18.0 KB)

Use midpoint for second point input for Arc 3Pt.

catenary (11.7 KB)

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Really appreciate your solution, if the second point (B point) is not the middle one, are there some ways to match the lines? Cause I find if I use the Point on curve, the points are in the reverse direction.