UV Surface to UV Mesh

Good afternoon,
I created a grid of points where there is a line for each point (starting point). The length of these lines is proportional to the distance to an attractor point. With the lines’ end point I created a surface (as Daniel Christev does here: https://www.youtube.com/watch?v=Vyst-H_muuI). I’d like to triangulate this surface in a way that the lines’ end poins are the vertices of such triangles. In order to do that, I’m trying to make a mesh so that I can divide it in triangles. My problem is, however, that whenever I tried to make a mesh out of this surface (Mesh Surface UV) I get this result:

where in green you can see the points I’d like to be the UV coordinates of the mesh as opposed to the division I get. I don’t exactly know what to do, since I can’t seem to find the right component or the right way to deal with it. Any ideas?