2012/09/26 by Jörg Peters, Peters, Jorg
Engineering · #41A15 #65D07 #Advanced Numerical Analysis Techniques #Advanced machining processes and optimization #Computer Vision and Pattern Recognition (cs.CV) #Drilling and Well Engineering #FOS: Computer and information sciences #FOS: Mathematics #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.1209.5826
openalex publication_date 2012/09/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Splines can be constructed by convolving the indicator function of the Voronoi cell of a lattice. This paper presents simple criteria that imply that only a small subset of such spline families can be refined: essentially the well-known box splines and tensor-product splines. Among the many non-refinable constructions are hex-splines and their generalization to non-Cartesian lattices. An example shows how non-refinable splines can exhibit increased approximation error upon refinement of the lattice.