 # Extract point3D from a surface

Hi all,
I have 2 polyline curves, and then I used Loft function to create a surface from those two.
I can easily use subdivide curve (u,v) to get a set of points from the surface.
However, my situation is I need to know how Rhino came up with those points? What is the mathematical equations behind them? Can anybody please point me to the right direction?
Thank you.
Tien

I do not believe that the details of the algorithms or used in Rhino have been published. However some of the basic equations are described in Essential Mathematics for Computational Design https://developer.rhino3d.com/guides/general/essential-mathematics/ With sufficient knowledge of NURBS modeling it is possible to figure out how some of the Rhino commands work.

Loft between two curves creates a ruled surface which is a surface made up of straight lines connecting corresponding points on the two curves. The straight ruling lines are v isocurves (lines of constant v). Point on the surface will be a linear interpolation of the points on the curves at the ends of the ruling lines. What is not obvious is how Rhino selects the corresponding points on the two curves. One way to determine that would be to make an assumption and then test the assumption.

Thank you. I think you have pointed me to the right direction. Searching NURBS surface on Google has given me tons of materials.