VTKCutter leaves gaps, does not return the every point it intersects

I have an STL file, I’m working on it a while to collect xyz data through the line drawn on its surface(red line).
Screenshot from 2022-07-21 05-34-04

I wrote a function using VTKCutter and believed that the class was collecting each point its implicit function(plane in this case) intersects. But it turns out, it leaves many points not included and I checked there are many more using polydata.GetPoints() with little manipulation. Problems like that had been encountered for sure(for example in here) but though searched a lot, I could not find the solution that uses solely vtkCutter(I know I can use other methods like vtkBox and clipping but this way I prefer). I believe it is simple tolerance problem but in class’ reference page there is no method I can adjust with it. I appreciate any help. Thank you.

def set_cutter(self):
       global OutLinePts
       plane = vtkPlane()
       polydata = copydeep(self.actorMain)
       cutter = vtkCutter()#cutter class extract the data that intersects with the given function

       cutterMapper = vtkPolyDataMapper()
       actor_cutter = vtkActor()

*The red line is the actor of vtkCutter with function plane.