Generate the shape of a vase from fragments of scanned 3D pottery

I’m a beginner with Grasshopper. I’m working on a project to generate the shape of a vase from fragments of scanned 3D pottery. In the initial stages, I was able to generate a “Bounding Box” from the fragments and obtain curves that make up the surfaces of the fragments by dividing them equally. However, I’m struggling with connecting these curves, similar to Rhino’s “BlendCrv,” and creating cross-section curves, to ultimately use “loft” and create the shape of the vase.
Please, can you provide some guidance?

vessel from (157.6 KB)

In case you wanted to connect the curves and loft, I would not suggest doing that. The curves you created can be connected but they will never have the right definition and the resulting loft won’t be a nice surface / polysurface.

Similar curves can be created with the contour component in less steps but the result is just as bad.

In case you have access to Rhino 7, you can use QuadRemesh. The mesh output consist of quad faces which can be turned into surfaces and the result can be a closed polysurface.

Overall what is the reason to rebuild the object and does the result have to be a polysurface?

vessel from (172.9 KB)

Thank you for your answer!
Sorry it was not in proper English.

I am trying to create a vase shape from the curved surface of a 3D scanned piece of a vessel as shown in the attached photo.
I was able to get this far yesterday by trial and error, but I can see that it is not a proper patch.

I would love to be corrected.

vessel from (158.0 KB)

What does the intact piece look like, and where does this fragment locate in that whole?

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I don’t understand what you’re trying to achieve. A sketch would help.