vtkParametricSpline not smooth

I am using vtkParametricSpline and vtkParametricFunctionSource to draw a curve, but the line is not smooth.

import vtk

points = vtk.vtkPoints()
points.InsertNextPoint(0.0, 0.0, 0.0)
points.InsertNextPoint(1.0, 1.0, 0.0)
points.InsertNextPoint(2.0, 0.0, 0.0)
points.InsertNextPoint(3.0, -1.0, 0.0)
points.InsertNextPoint(4.0, 0.0, 0.0)

spline = vtk.vtkParametricSpline()
spline.SetPoints(points)  
spline.SetClosed(False)   

spline_source = vtk.vtkParametricFunctionSource()
spline_source.SetParametricFunction(spline)
spline_source.SetUResolution(100)  
spline_source.Update()

mapper = vtk.vtkPolyDataMapper()
mapper.SetInputConnection(spline_source.GetOutputPort())

actor = vtk.vtkActor()
actor.SetMapper(mapper)
actor.GetProperty().SetColor(1.0, 0.0, 0.0)  
actor.GetProperty().SetLineWidth(30)          

renderer = vtk.vtkRenderer()
render_window = vtk.vtkRenderWindow()
render_window.AddRenderer(renderer)

interactor = vtk.vtkRenderWindowInteractor()
interactor.SetRenderWindow(render_window)

renderer.AddActor(actor)
renderer.SetBackground(1.0, 1.0, 1.0)  

renderer.ResetCamera()
render_window.Render()
interactor.Start()

I have set the resolution using SetUResolution, but why are there still some noticeable gaps in the curve?