Links points along an axis

Hi all,

First of all, sorry for my bad english, I hope i will be understandable. This is my first question here, I always found some help within this forum.

Here's my problem: I've got  a surface  with random points on them. What I am trying to do is to make line between points in the direction of the lenght of this shell. Ultimately, I would like to have smooth curve "running" along the surface . Does anyone has any idea how to do that? Thank you so much.