Non-uniform Interpolatory Subdivision Based on Local Interpolants of Minimal Degree

This paper presents new univariate linear non-uniform interpolatory subdivision constructions that yield high smoothness, C and C, and are based on least-degree spline interpolants. This approach is motivated by evidence, partly presented here, that constructions based on high-degree local interpolants fail to yield satisfactory shape, especially for sparse, non-uniform samples. While this improves on earlier schemes, a broad consideration of alternatives yields two technically simpler constructions that result in comparable shape and smoothness: careful pre-processing of sparse, non-uniform samples and interlaced fitting with splines of increasing smoothness. We briefly compare these solutions to recent non-linear interpolatory subdivision schemes.