NURBS surface fitting for a closed region on mesh

Question

I'm developing a tool that allows users to select a closed boundary (a polygon) on the triangle mesh and then from this boundary, generate a NURBS surface fitting the original mesh surface.

My idea is as following:

1. Generate a list of NURBS curves from the closed boundary (polygon)
2. Combine such curves together using NURBS loft surface technique (Reference: The Nurbs book - Les A. Piegl, Wayne Tiller)

My problem arise at the first step, where I am trying to interpolate a list of NURBS curves, which require an input of sample points. To get such sample points, I am planing to generate a point grid on region inside the closed boundary, and then, for each row of this point grid, I will take sample points from this. But I don't know how to create a point grid on the mesh. Could you help me out?

This is just my idea, and if you know more about NURBS fitting for a region of mesh surface, please suggest me some material about it.

Thanks in advance.