Today, I test a set of points using the built-ins BSplineSurface[] and BSplineFunction[], respectively.

(*about nets and knots, please see the addendum's link*)
Graphics3D[BSplineSurface[nets, SplineKnots -> knots]] // AbsoluteTiming

h = BSplineFunction[nets, SplineKnots -> knots]
ParametricPlot3D[h[x, y], {x, 0, 1}, {y, 0, 1}] // AbsoluteTiming

Show[{ParametricPlot3D[h[x, y], {x, 0, 1}, {y, 0, 1}], 
      Graphics3D[{Opacity[0.5], 
                  BSplineSurface[nets, SplineKnots -> knots]}]}, 
     Boxed -> False, Axes -> False]

Obviously, the surface generated by BSplineSurface[] is very smooth, especially at the corner. In addtion, it is also much faster than the latter. However, for the combination of ParametricPlot3D[] and BSplineFunction[], which cannot generate a smooth surface when without the help of option PlotPoints -> 100(That's means, it will take more time to compute!).

So I have the following question:

• What strategy does they use to sample the 3D points?

Addendum

The nets and knots vector that in the V direction could be downloaded from here and here, respectively. (Thanks for happy fish's help:))

Moreover, the knots vector that in the U direction is:

U = {0.,0.,0.,0.,0.502247,1.,1.,1.,1.};
knots = {U, V};