Releasing time exclusive Limit Surface Sampling chapter from Pragmatic VEX: Volume 1 course.
To generate interpolating surfaces for other subdivision schemes we need a method of determining the position and the normal at a set of points on the limit surface. Because the surface is the result of repeated application of a subdivision step, we can analyze the behavior of a small neighborhood of points as they converge to the limit surface in order to determine the surface properties at the point of convergence.