You didn’t internalize your base geometry nor posting your 3dm, so the file you posted has been useless for now…
Anyway, you can make intersection curves by using MMX or BBX depending on your type of base geometry.
And you could do curve thickening by using plugins like dendro.
In the attached def, I used subD as a base geometry by using the multipipe command in R7
Thickened 3DVorinoi_re.gh (27.7 KB)