Burr

I like your thinking on this but I'm lost.

I've created a surface of 4 points by 4 points and started moving some of the points on the surface around. I've then trimmed the surface with another curve. All good so far. I've then selected all the edges of the trimmed surface and deleted them but all I get is the original surface back before trimming with no additional points.

Are you able to elaborate a bit more on your suggestion, it sounds interesting ?