Another way.

I also thought there was no need to act on all the faces. Here is a complex model. Skirt made with TIG's extrude-edges-by-vector-to-object EEbyVTO. Only problem I have trouble getting all the edges to go all the way to the face (I wonder if there's a lack of technique on my part). So I then pull the face up and intersect with model. (This method seems to choke on an even more complex model, but it might work.)

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