I’m afraid point line interpolator is not related to what you want to do. What you want to do should be doable with the Subdivide filter however it works only on triangles.
You can actually use Subdivivde on the input dataset but it is a very inneficient way to get the correct result:
Alternatively, you could use ResampleWithDataSet if you can generate the correct line yourself.
Probably that makes sense.
Anyway, a short follow-up on this. When I applied slice filter, the exact radius is 2.5, but I had to supply something like 2.50001 to have paraview find the line. Can we pass a tolerance for floating-point comparison?