Yep you right, there is a very little difference for the triangle!
And if you have more than 3 vertex the method of conics seems out the subject! :)

Hello,

maybe it is possible to split or trim a backround face by the structure. Then select the edges of each patch (maybe script?) and join them. After that you can reconstruct the edgeloop by controlpoints (reconstruct script). The facepatch schould have a centerpoint which can be selected for scaling. Sorry, but I don't have moi at the Moment, to test it. So it's only an idea.

Kind regards
Karsten