Lane-Riesenfeld construction

For higher degree B-splines, degree n say, we can determine the new control points by taking means of consecutive control points for degree n — 1. This is called the Lane-Riesenfeld construction. 

We can go further, by inventing a degree=—1 construction which doubles the coordinates of all the control points and intersperses them with new points with zero coordinates. The degree=0 construction is then recovered by applying the Lane-Riesenfeld construction. 

---