Surface Manipulation by square relation

Hello,

I am new to this forum and to grasshopper and have been trying to create my own surface manipulation script. Essentially, I am looking to create a function similar to cage edit but with more control. Specifically, by using a square relation of the distance (from point along surface being moved to all other points along that surface) and the distance (that those points are moved in relation to the distance the first point is moved. Essentially, creating a parabolic curve along that surface in all directions from the point moved.


I know this may not sound very clear so I created a conceptual pdf to illustrate what I am trying to achieve and it is attached to this post.

I am assuming a flat 2d surface as the original surface to be manipulated and am considering starting the script by mapping grid points along the surface, then trying to relate those points to each other in every possible combination possible so that all of them are linked to all other points. The biggest problem I see here is handling the lists of points along the surface in an organized order that will be based on the relationship of the distance of all points along that surface to all other points along that surface, so that I can then use that relationship to control the distance points are moved in relation to the the distance of the first move.

I have been told that this may be better approached through rhino scripting and  although I would be interested in going in that route I would like to first tackle it in GH.

Thanks to anyone who may be of help!

Andrew