Basically you have three ways.
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Use the combination of vtkimplictfunction.
you can clip the vertical one out using vtkcylinder as input for vtkclippolydata. -
In higher version of vtk, you can use booleanfilter, but it is slow.
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And at least, you can covert polydata to imagedata and do anything you want.
By the way, could you tell me what is your background and rendering setting? It looks pretty good.