Creating a bridge between cardinal B[formula omitted]-spline fundamental functions for interpolation and subdivision

Abstract

This paper presents innovative contributions to the fields of cardinal spline interpolation and subdivision. In particular, it unifies cardinal Br-spline fundamental functions for interpolation that are made of r=ML+1 (L∈N∪{0}) distinct pieces between each pair of interpolation nodes and are featured by the properties of C2M−2 smoothness, approximation order 2M and support width 2M(r+1)r, with the basic limit functions of a special class of non-stationary subdivision schemes of arity M.After introducing a general result, we focus our attention on the subclass of fourth-order accurate, C2 smooth Br-splines with maximum width of the compact support 6. The binary subdivision scheme yielding these fundamental functions outperforms the existing interpolatory schemes and seems to be the most adequate starting point to obtain compactly supported fundamental (spline) functions for local interpolation over quadrilateral and triangular meshes.