Now when we remove detail by removing wavelets, the geometry part is easy. We interpolate the extra model vertices to the wavelet we are going to remove, and then subtract the wavelet's vertex values from the model.
However, if our intension was to simplify the model so that rendering would be faster, we have gained nothing: we still have as many line segments to draw as before. We may be able to combine some of the line segments, but only if the vertex separating them is not needed by any of the remaining wavelets.
Now the problem that we deal with is exactly this: we want to make the model simpler, not just to make it look simpler. But how do we know when it is safe to remove a vertex from the model?