Extracting data on a surface

I have a CFD solution on an unstructured grid and I want to extract the data on one of the bounding surfaces. I did the following steps.
ExtractSurface > Clip in X normal > Clip in Y normal > Clip at an Z, so that I should have got the bottom surface which is curved.
But I ended up with this

How can I resolve this issue?
Thank you.

How do you define this surface mathematically ?

The surface is given by z = quadratic function of x, for x in (0,x0)

Can you use FindData to extract the corresponding Cells then ?

Can I use Find Data to extract all points on the surface? The surface can have millions of solution points.
I should have made it more clear. The surface can be considered as three segments: z=z1 for x<0; z=f(x^2) in (0,x0); z=z2 for x>x0.
I tried the SliceAlongPolyLine filter as well. But that did not get me what I wanted.

Yes it should

Could you please elaborate on how this can be done? I’d appreciate it.
Also, I am curious why the steps followed my did not work.

This how to do it with pvpython.

QuerySelect(QueryString='your mathematical expression here', FieldType='POINT', InsideOut=0)