algorithmic modeling for Rhino
For the first case create a closed nurbs curve using as control points the quad "sets" (per division). That said there's no guarantee (general case when dividing nurbs surfaces) that the quads are co-planar (planarity between 4 points is the condition where the diagonals have a min distance "less" than the document's tolerance - "zero" so to speak [but "zero" and zero are very different animals, he he]).
For the other do the same using the 6 neighbor points. If this is a mesh (and in most cases of that type is) use Sandbox for finding the required connectivity info (i.e. an integer tree where the branch index is the given point index and items are indices pointing to the neighbor "surrounding"/neighbor points). Alternatively (still using an other Sandbox connectivity tree) you can find points on the lines from the given point to the neighbors (and then do the nurbs). This gives you a rather "finer" control.
For instance - case: mesh: (using C# and not Sandbox BUT IS ENTIRELY doable with native components and Sandbox as well).
Of course you can exclude boundary points etc etc (capability not included).
Play with the slider in the red group.
Thank you! your script helped me.
But it is beyond my understanding.
Well ... let's hope that some good Samaritan could provide a solution using native components (as I said: is doable).
Well ... anything is doable (at least related with what I think that you are after).
Speaking for my involvement ... the only unfortunate thingy is that I'm used on that C# approach (Note: it's a matter of personal preference, nothing more nothing less) - thus any related solution it could be difficult for you (or useless) to manage if you are not familiar with the language.
BTW: the only thing that's NOT doable with native components is a capability to manage collections of solutions on-the-fly (say: variants) - but this is another animal anyway.
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