Fast and exact evaluation of box splines via the PP-form

2016/06/28 by Joshua Horacsek, Horacsek, Joshua, Usman Alim +1 · 1 citation
Engineering · #Advanced Measurement and Metrology Techniques #Advanced Numerical Analysis Techniques #Advanced machining processes and optimization #FOS: Mathematics #Functional Analysis (math.FA) #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.1606.08910

openalex publication_date 2016/06/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For the class of non-degenerate box splines, we prove that these box splines are piecewise polynomial. This is not a new result, it is in fact a well known and useful property of box splines. However, our proof is constructive, and the main result of this work is a corollary that follows from this proof, namely one that gives an explicit construction scheme for the polynomial pieces in the interior regions of any non-degenerate box spline.

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