How do I get one set of path points to follow another set of path points?

Hello,

Setup:

1. I have an "S" shaped set of x,y coordinates with a straight line in the middle. The distribution of the coordinates is uneven across the path as the top, line, and bottom part of the S shape are different sizes.
2. I have a set of points created by an exponential equation.

What I'm trying to do: Get the exponential points to follow the the S-shaped path while maintaining their distance from the outside, centerline, or inside.

Relevant Example:

Think of the shape of a trumpet if described in numbers. The exponetial equation gives the tube and flare of the horn. The path tells it where the bends are along the path.

I've dug in may directions but am wondering if there is some magic that can allow me to place a point anywhere along that path such that I can get a measurement of the exponential line offset from that point on the S. Or, conversely, to put a size from the exponential equation in and it will tell me how far along the S-path I have gone.

I haven't been able to figure out so much as to how to have a curve "fold back on itself" in libreoffice calc - but figure that the math has to be available even if the charts are unable to describe this for me.

In editing programs, this might be a "point on path" option that takes the whole line starting at 0 and ending at 1. I'd like to know how to find out or calculate what is going on at any point 0.XXX along this path for the distances given by the exponential equation.

Thanks for your help!

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