Is it possible to get function from bunch of points?

Question

I have some points which I know the position in 3D. and that points made in sequence. for example,

. (x1,y1,z1)

                                 (x5,y5,z5)
                                     .         
                                              .(x6,y6,z6)
     . (x2,y2,z2)           .(x4,y4,z4)

                 .
              (x3,y3,z3)

and from this bunch of points, is it possible to get function like y(x) = bla bla~ if it possible, how to I get it?

I tried to do that using interpolation, but I can't.

Alright, I have these bunch of points and If I plot it in 3d, it looks like these. I also only make interpolation between two each markers.

And, I want to make a function to calculate parametric curves. but I have no Idea.