How do I create a knot lines based mesh of any NURBS geometry in Rhino?

I want to take any geometry and then create a mesh (not the usual mesh of triangles or quads, etc. as they are not smooth) on the original geometry by using the knot lines. As an example, see how a NURBS surface File:NURBSsurfaces.jpg - Derivative has lines for constant parametric values along the two dimensions creating a ‘mesh’ on the original surface.
Additionally, what would also be exciting is to be able to refine this mesh. Also, would this refinement be local or global in nature?
Thank you!

Hello - like this:

?

-Pascal

Hi, thank you! Yes, the subdivided surface on the right is what a the surface might look like if you are creating a mesh based on the knot lines. It looks very smooth as compared to the polygon based mesh on the left. Also, would it be possible to export the mesh information like its elements and topology (connectivity of elements) based on the original control points and knot vectors that would have been used to define the original NURBS surface.

I am not sure I understand - you can get more polygons than I show , in the mesh, but it will never be smooth.

-Pascal

Hi Pascal, how did you convert the NURBS surface to mesh you have shown on the right side image.

Hello- the object on the right is an untrimmed surface. The object on the left is a very coarse mesh created from the surface. I was simply trying to show you that the mesh will follow the UV flow of the isocurves.

-Pascal

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To create a mesh with vertices at the intersection of the knot lines of a NURBS surface:

Copy Inplace the surface if it needs to remain.
ChangeDegree both the U degree and the V degree to 1.
ExtractControlPolygon from the degree 1 surface.
Result is a mesh with the vertices at the intersection of the knots of the original mesh.

KnotsMeshDC.3dm (1.6 MB)

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