Create trigonometric curves on 3D surface

I want to be able to create offset trigonometric curves on a 3d brep to use as toolpath geometry for milling on center line with a ball endmill

here's the approach I've taken.

I have created a trigonometric curve like the example in the GH primer and then I offset it in Y which looks like this:

I then use a random component to offset the curves in X which looks something like this:

Then I trim the curves to fit inside the blank I want to cut

 I can then run a ball endmill on center along the lines and get a cool pattern.

What I want to do now is figure out how to get the trigonometric curves on to a 3D brep so that I can apply this machining technique to a non planar surfaces.

As it stands now, the amplitude of the curves fluctuate in Z along a center line that is constant with Z0.0.  

I want to make it so the center lines of the curves follow the 3D surface instead of remaining on Z0.0. I want to do this while still being able to randomly stagger the curves in X.

Any ideas on how I could create a definition that could do this?