Isocurves vs control points grids

Hey all!
Can someone help me understand how surfaces are defined in Rhino? If I make surface with a 10 divisions I end up with what is seen in the image: meaning I have the control points grid (which is irregular, having the extremities denser) and the isocurves grid (which is regular).
If I check the density of the UV domain of this surface is uniform (isometric), however, if I generate a surface from a regular grid of points (se the green surface that is generated based on an uniform grid of control points) that will act as control points for the newly created surface), then I would get aberrations in the domain towards the edges (it becomes less dense and not isometric, as the isocurves indicate). The conclusion is that I need those control points to be at a closer distance towards the edges but I don’t know how to determine that.

Thank you for your time!

Rhino uses NURBS surfaces which are fundamentally different from meshes. I’m guessing you are not familar with NURBS surfaces. Some fundamentals of NURBS surfaces include the control point generaly do not lie on the surface. (Recgtangular planar surfaces are an exception.) Also the control points do not directly relate to parameter values.

Is there a particular reason you are trying to create a surface by inputing control points? If you want the surface to fit through a grid of points in Rhino you can use SrfPtGrid. I don’t know what the equivalent is in Grasshopper.

It sounds like you are asking where to place that first row of control points to produce a uniform knot structure.

If the spacing for knots is X then the distance for the first row of points next to an edge will be X/3.
I’m assuming you are trying to maintain knot uniformity relative to some plane.
Lets say the knot spacing is uniform in the XY plane. That would mean the CV’s X and Y positions would remain constant and would only vary in the Z direction.