Extract maximum "i" surface from vtkStructuredGrid?

I have a vtkStructuredGrid, read in from a CFD datafile.
I’d like to be able to extract the surface where i is maximum, that is to say the surface where the first index is maximum, over all of the other two indices.

Is there a way to do that? (The surface is like a tube of toothpaste that has been twisted up - I can’t just dot the surface normal with (1, 0, 0) for instance).

I just found vtkStructuredGridGeometryFilter, which looks like it might work for me.